THIS BOOK \S A PART OF THE LIBRARY OF = An Introduction to Biophysics An Introduction to Biophysics By OTTO STUHLMAN, JR. Ph.D. PROFESSOR OF PHYSICS UNIVERSITY OF NORTH CAROLINA New York • JOHN WILEY & SONS, Inc London • CHAPMAN & HALL, Limited Copyright, 1943, by OTTO STUHLMAN, Jr. All Rights Reserved This book or any part thereof must not be reproduced in any form without the written permission of the publisher. PRINTED IN THE UNITED STATES OF AMERICA PREFACE As a result of the increased demands for physics by students whose primary interests lie in the biological sciences, this book has been written with the hope that it may lead to a fuller appreciation and understanding of the applications of physics to biological problems. I trust that it will prove suitable as a textbook for mature students who have had a year's work in college mathematics followed by one year's study of the fundamental principles of physics and chemistry. In lieu of a more appropriate name, it is proposed to designate all those biological observations which are explainable in terms of physical principles as biophysical phenomena. Which topics are representative of an ideal cross section of the available biophysical material is at present a debatable question. In order to avoid the imputation of superficiality in dealing with this cross section, only such subjects are discussed as are representative of the major subdivisions of physics. In the general field of radiation no better example can be found of the cooperative effect of the biological and physical sciences than the problem of radiation therapy. Here, as in much of the biophysical research, the tools have been supplied by the physicist so that the medical scientist can use them to point the way in which the physicist should work to make the tools progressively more effective. This cooperative progress in the field of radiation is portrayed in the chapters on the biophysically active x-rays and applied radioactivity. The influence of physics on physiological optics and acoustics is pre- sented in the chapters discussing the biophysical characteristics of the eye and auditory biophysics. In the field of physical optics, where its applications merge with the medical sciences, the emission and adsorption of biophysically active light are discussed because of the general desire for information dealing with the effect of ultraviolet radiation on life processes. The possibility of revealing the nature of the living cell membrane is at present being pushed with great success through the study of the physical properties of molecular-film structures. The chapter discussing structure and properties of surfaces and membranes is introduced to illustrate how the modern molecular concept of matter is influencing the developments in this biophysical field of investigation. Vl PREFACE To what extent the field of bioelectrical measurements has been en- riched since the celebrated investigations of du Bois-Raymond, with the aid of vacuum-tube amplification technique coupled to the modern cathode-ray oscillograph, is discussed as the biophysical problem of nerve conduction. The final chapter discusses the technical limitations of the optical microscope and points to the electron microscope, with its enormous resolving power, as the instrument which awaits the cooperative interests of experts in the biological sciences as the tool to investigate the struc- ture of organic matter. The publishers have generously cooperated by subscribing to the pedagogic axiom that one good illustration equals 1000 printed words. The General Electric X-Ray Corporation, the Victoreen Instrument Company, Bausch and Lomb Optical Company, National Carbon Com- pany, Weston Electrical Instrument Corporation, Kipp and Zonen, Fisher Scientific Company, American Standards Association, Central Scientific Company, Allen B. DuMont Laboratories, Eastman Kodak Company, Electro-Medical Laboratory, Inc., and the R. C. A. Research Laboratories have all been generous in supplying many original photo- graphic illustrations, for which I express my appreciation. It is a pleasure to thank Dr. S. J. M. Allen for furnishing the new data on x-ray absorption coefficients; Mr. J. L. Weatherwax for the use of his water phantom data; Mrs. E. H. Quimby, of the Memorial Hospital, New York, for clinical data on radiation therapy; Dr. D. B. Lindsley for the original electroencephalograms; and Dr. V. K. Zworykin for the photographs of the electron microscopes. I am indebted for many excellent suggestions made by my colleagues in the Medical School. For criticisms of various chapters I am indebted to Professors H. A. Blair, H. D. Crockford, J. F. Dashiell, R. B. Lyddane, A. E. Ruark, and P. E. Shearin. O. S. Chapel Hill, N. C. January, 1943 CONTENTS CHAPTER PAGE I. BlOPHYSICALLY ACTIVE X-RAYS 1 II. Applied Radioactivity 55 III. Biophysical Characteristics of the Eye 100 IV. Emission and Absorption of Biophysically Active Light 133 V. The Structure and Properties of Surfaces and Membranes . . . 170 VI. The Biophysical Problem of Nerve Conduction 211 VII. Auditory Biophysics 253 VIII. The Compound Microscope; The Electron Microscope 311 appendices 1. Physical Constants 353 2. Problems 355 Name Index 361 Subject Index 367 /^ 37987 VII Chapter I BIOPHYSICALLY ACTIVE X-RAYS It was at the University of Wurzburg, Bavaria, in November, 1895, that Wilhelm C. Rontgen* discovered x-rays. While experimenting and presumably repeating some of Lenard's contemporary experiments on cathode rays in extreme vacuum he is supposed to have observed that a sheet of paper covered with barium platinocyanide placed near a Hittorf tube (according to Zehnder [1933] )f or near a Lenard tube (according to Stark [1935]) became fluorescent although the tube had been enclosed in an opaque cardboard cover. In accordance with Rontgen's will, all papers and letters bearing dates 1895 to 1900 were destroyed so that no written record of the de- tails of his first experiments is available. His first publication, "Ona New Kind of Ray," which appeared in 1895, contained a description of the three chief properties of the new ray, i.e., its effect on a photographic plate, its ability to produce fluores- cence in many substances, and its ability to make the air through which it had passed electrically conductive. He discovered that substances varied in opacity and that flesh was more transparent than bone. He further recognized that x-rays which originated from a tube that pos- sessed a comparatively low air pressure were more easily absorbed by substances than x-rays orginating from a tube exhausted to a very high vacuum. He called the latter " hard " and the former " soft " x-rays; i.e., it was harder to pass a current through the tubes when they were very highly evacuated. Gas Tubes The general method of producing roentgen rays is always the same, namely: accelerating electrons to a high velocity in an electrostatic field and then suddenly stopping them by collision with a solid body, the so-called target. The electrons are liberated by the positive-ion bombardment from the surface of a concave aluminum cathode immersed * His signature is written Rontgen; its modern version is Roentgen. t Brackets enclosing dates [1933] refer to a citation in the bibliography at the end of each chapter. 1 2 BIOPHYSICALLY ACTIVE X-RAYS in a low-pressure gas. They travel in straight lines until they collide with the target, from the surface of which the roentgen rays are emitted. The thin platinum targets of the early gas tubes were rapidly replaced by thin disks of platinum, backed by massive pieces of copper. The copper support served as a good heat conductor, since it was early recog- nized that most of the energy of the cathode rays after the rays collided with the target appeared as heat. For a metal to be suitable as material for a practical x-ray target, in medical diagnostic work, it was found that it must possess the following properties: (1) a high melting point, (2) a low vapor pressure, (3) a high thermal conductivity, (4) a high atomic number. Tungsten fulfills all these requirements and hence replaced platinum in most of the later gas tubes. Coolidge High-Vacuum Tube No radical changes took place in the construction and method of generating x-rays until the introduction, in 1913, of the Coolidge x-ray tube with a hot tungsten-filament cathode. By 1909 O. W. Richardson and his students at Princeton had shown under what conditions electrons may be expected to be emitted by high- temperature metal filaments in vacuo. This work terminated in Richardson's thermionic law, which was subsequently slightly modified in its theoretical derivation through the use of the Fermi-Dirac law of distribution of energies in the electrons in the metal, giving / = AT 2 e- b/T where I is the saturation current in amperes per square centimeter of the emitting filament surface; A, a universal constant, is the same for all emitting metals; T is the absolute temperature of the filament; and b = e0/3OO/c, in which k is Boltzmann's constant. e$/300 is called the work function of the metal emitting the thermoelectrons, and its magni- tude is expressed in electron volts. The work function is not the total potential barrier at the surface through which the inner electrons of the metal must pass, but the difference between this energy and the inner energy of the electrons. The value of A for tungsten is 60.2 amp/cm 2 / degree 2 , and its work function is equal to 4.52 volts. The electron emission from a metal surface, heated in vacuo, increases exponentially with the temperature of the metal, so that a small change in temperature will result in a very large increase in electron emission. If a metal electrode is placed opposite such an emitting surface and a difference of potential is applied, so as to accelerate the free electrons toward the plate, it is found that when the temperature of the filament COOLIDGE HIGH-VACUUM TUBE 3 is increased the electron current does not increase as rapidly as the increase in number of thermoelectrons. The electron current moving from filament to plate is said to be limited by " space charge." Repulsion by the thermoelectrons surrounding the filament prevents all the emitted electrons from moving towards the collecting plate. The electron current has a maximum or saturation value expressed by the relation deduced by Langmuir, _ V2 [7 v 3/2 where e and m are the charge and the mass of the electron, x the distance between the electrodes, and V their difference of potential. It is essen- tial to have the electrodes quite close together in order to have electron currents of appreciable magnitudes flow between the electrodes. A close approximation for tungsten is i = 2.33 X 10 -6 v 3/2 /x 2 amperes per square centimeter of thermoelectron-emitting surface. Scale ~l — r- — 1 12 3 inches Hot-filament cathode^v V-Tungsten target Fig. 1-1. A universal Coolidge tube which may be used up to 200,000 volts with an 8-ma current between target and hot-cathode filament. Solid tungsten target. Coolidge [1913] designed an x-ray tube using the thermoelectron current from a hot filament in a high vacuum to replace the cathode-ray stream for bombarding the target in order to generate the x-rays. Using a heated tungsten filament as his source of electrons, and a disk of tungsten, backed by copper for heat conduction, as a target, Coolidge found that it was possible to obtain a very stable discharge which permitted more accurate reproducible results, that the tube could be made smaller, that a greater flexibility could be obtained since current through the tube and the voltage across the tube could be varied independently, and that the tube had a comparatively long life. The commercial form of Coolidge tubes varies in size and shape de- pending on operating conditions. Figures 1-1, 2, and 3 show some available commercial forms. Figure 1-1 is an air-cooled type that will carry 8 ma between hot filament and its solid tungsten target when excited at a difference of potential of 200,000 volts. This design of Coolidge tube is used primarily for therapeutic work. Figure 1-2 shows an x-ray tube having a copper-backed tungsten target with an air-cooled 4 BIOPHYSICALLY ACTIVE X-RAYS radiator. It can be designed to operate over a wide range of energy ratings; filament current range 3.5 to 5.0 amp, tube current from 25 to 150 ma, and potentials from 30 to 100 kv. Fig. 1-2. A fluoroscopic and radiographic x-ray tube. It will operate at 30 ma for long exposures and will take 100 ma at 85 kv for i 1 ^ second. Air-cooled radiator, Pyrex glass bulb. In an x-ray tube of the stationary-anode type, the electron stream is directed against a fixed area on the target which is known as the focal spot. The rating of a tube is limited by the ability of the target to dissipate the heat generated by the colliding electrons. In practice, the magnitude of the voltage, electron current, and time must be such that the bombarding area is not brought too close to the melting point. WP t*' s • jtftfc ___ __mb ^titttfMt •fC 1 *'^^ \j aJ^ttmm Fig. 1-3. A rotating-anode Coolidge (RT 1-2) tube in which a large disk of tungsten replaces the conventional massive copper anode with tungsten button insert. The disk rotates during exposure. Anode speed 3000 rpm. Effective focus 1 mm 200 ma, 73 kv peak, exposure i^ sec. A stationary anode with effective focus 3.8 mm uses 200 ma, 82 kv peak, exposure 2*s second. (By courtesy of the General Electric X-Ray Corporation.) If it were possible to move the hot metal target out of, and a cool metal target into, the electron path, the time of operation of the tube could be extended. This is what is done in the General Electric Company's rotating-anode tube, Fig. 1-3. The target in this tube is a disk of tung- sten fastened to the end of a short shaft of the rotor of an induction motor, mounted in ball bearings. Outside the glass wall of the tube surrounding the circumference of the rotor is the stator of the motor. A 60-cycle current energizes the motor and rotates the target at about 3000 rpm. During excitation the target rotates so that relatively cool GENERATION OF X-RAYS 5 metal is brought continuously before the electron stream. This form of target allows an exceedingly small effective focus, 1 mm or 2 mm square, to be used in a tube operating at high electrical energy. Generation of X-Rays X-rays are produced by the sudden stoppage or deceleration of high- speed electrons. In this process the very high kinetic energy of the moving electrons is converted into radiant energy of very short wave- length, while some of the energy due to the deceleration is converted into heat. In modern practice, the generation of x-rays takes place in an evacu- ated tube having two electrodes, one emitting electrons and the other acting as a target upon which the electrons are projected by a high difference of potential placed between the electron emitter and the target. The electron emitter, in a commercial form of x-ray tube, is a spirally or helically wound filament of tungsten wire, which is heated to any desired temperature by means of a variable current from a 6-volt step- down transformer usually connected to a commercial 110-volt alter- nating-current source. Its operating temperature may be regulated by a current control, which in turn controls the number of electrons emitted. If the positive accelerating potential of the target is comparatively small, the current flowing from filament to target will be less than that calculable from Richardson's equation. This reduction is due to the repulsion of these negative electrons in the region between filament and target on the electrons coming out of the hot-wire filament. An electron cloud is formed in the space between target and filament with its greatest electron density just in front of the filament. This electron cloud is the space charge. If the voltage of the target is very great, the electron current passing between filament and target will be appreciably greater than that given by Richardson's equation. This increase is due to the large potential gradient at the surface of the filament which pulls electrons out of the filament and adds them to the normal emission. This so-called field emission may become greater than the thermionic emission calculable from the Richardson equation. The highly accelerated electron stream is guided by a properly de- signed electrical field to fall on a small area of the target. The interposed target suddenly decelerates these electrons. Some lose their kinetic energy by a head-on collision with an atom of the target so that at a single encounter they give up all their kinetic energy. Under these 6 BIOPHYSICALLY ACTIVE X-RAYS circumstances the kinetic energy of the electron is converted into a single quantum of radiant energy of short wavelength. Some of the high-speed electrons do not have such favorable encounters. They may pass close to the nuclei of the atoms of the target and may be de- flected. At each such deceleration some kinetic energy is converted into radiant energy, but of longer wavelength. The closer the electron approaches the nucleus, the greater is its loss in velocity and energy and the greater are the energy and frequency of the radiant energy or released photon. The great majority of the electrons undergo no such collisions but dissipate their energy in penetrating the target. This energy manifests itself as thermal motions of the atoms. Thus much of the kinetic energy of the electron stream appears as heat. The shortest wavelength of the radiant energy emitted by the target is quantitatively obtainable from the relation proposed by Einstein in 1905 on theoretical grounds and verified experimentally by Duane and Hunt [1915], namely, that the kinetic energy „ eV he E = = hv = — 300 X where E is the kinetic energy of the colliding electron of electrostatic charge e (4.8025 X 10 -10 esu), V the difference in potential between filament and target in volts, 300 the conversion factor which makes possible the use of volts for V instead of absolute units, h is Planck's radiation constant (6.624 X 10 -27 erg second), v the frequency of the emitted photon or x-radiation of wavelength X. The velocity of light c enters the relation because c = v\. Upon substituting these values in the above equation, it is found that XV = 12,395 where X is expressed in angstrom units (1 A = 10 8 cm) and V in volts. For instance, it may be desirable to know the shortest x-ray wave- length emitted by the target when an electron, arriving under a difference of potential of 100 kv, between filament and target, is decelerated so that all its energy is converted into one quantum of x-radiation. Under these circumstances XV = X X 100,000 = 12,395 X = 0.12 A = 0.12 X 10 _8 cm o When compared with the wavelength of visible light (5500 A), the x-radiation has a wavelength about 50,000 times smaller. X-RAY SPECTRAL DISTRIBUTION 7 Of the total energy incident on the target, less than 1 per cent is con- verted into x-radiation even under a driving potential of 100,000 volts. The remainder, or 99 per cent, of the incident energy of the impinging electrons can raise the temperature of the target even to its melting point. This rise in temperature necessitates a rapid cooling of the target by circulating oil or by radiating fins. Thus, regarded as a machine for producing x-rays, a Coolidge x-ray tube has a very low TABLE 1-1 Hardness of Radiation (As used in this book.) X in A kv Very hard 0.05 247 Hard 0.10 123 Medium hard 0.15 82 Soft 0.25 49 Medium soft 0.50 25 Very soft " Grenz rays " 2.0 6.1 efficiency, but the radiant energy emitted has a remarkably high pene- trating power because of its high frequency (v) or short wavelength (X). Soft and Hard X-Rays Soft x-radiations and hard x-radiations correspond to long and short wavelengths, respectively. The soft rays are produced by compara- tively low electron-accelerating potentials and the hard by high poten- tials. Soft x-rays are readily absorbed; those not so readily absorbed by the same substance are qualitatively designated as hard x-rays. These differences are only descriptive and have no quantitative signifi- cance. For all practical purposes the radiations emitted by a tungsten- target x-ray tube in terms of a scale of hardness may be roughly classified as shown in Table 1-1. X-Ray Spectral Distribution Corresponding with a given applied voltage, a definite distribution of intensity at different wavelengths is found, depending on the material of the target. Since in medical or biophysical work ordinarily tungsten 8 BIOPHYSICALLY ACTIVE X-RAYS and occasionally molybdenum targets are used, the discussion will be limited to the emissions from these two metals. 0.4 Wavelength in A /5 2 0,«1«2 K series Tungsten j_ 123.5 41.2 30.9 24.7 Comparable kv-peak voltage (V p ) 20.6 _L L series at — *• 1.0 to 1.7 A 17.6 Fig. 1-4. These curves show the general radiations from a tungsten target. The value of the maximum at the peak of each curve moves to longer wavelengths as the exciting kilovoltage is reduced. The glass bulb if 1 mm thick transmits about 25 per cent of the 1-A wavelength emitted. The attached characteristic line spec- trum of the K series shows relative positions of these emissions with respect to the general radiation curves. (Curves after C. T. Ulrey [1918].) Figure 1-4 shows the intensity of emission of the x-radiations at different wavelengths from a tungsten target bombarded by electrons which had been accelerated by various voltages across a Coolidge tube. X-RAY SPECTRAL DISTRIBUTION 9 At these low kilovoltages a continuous spectrum, as indicated by the smooth curves, is observed outside the glass-jacketed vacuum tube. Compare these data with those represented in Fig. 1-5, and note partic- ularly the sharp peaks which appear in the 110-kv spectrum emitted by a tungsten target. The continuous spectrum or " general radiation " begins sud- denly at the minimum wave- length Xq obtainable from 100 90 80 \ V P = 12,395 , is the maximum po- across the tube. If a where V tential rectified alternating potential is used to excite the roentgen tube, then V p is the peak volt- age. From X the intensity rises rapidly to a maximum (X max ), from which it gradually declines. In the roentgenographic re- gion generally used for diagnos- tic work or superficial therapy, namely, 100 to 50 kv (0.12 to 0.25 A), the maximum intensity of the general radiation, to a good approximation, is found at 70 .2 60 '^50 TO a 40 30 20 10 1 KcXya 2 110-kv tungsten spectrum No filter 0.28 mm tungsten filter 0.1 0.2 0.3 o 0.4 Wavelengths in A 0.5 *max l.GXo Fig. 1-5. These curves show the general x-ray spectrum of tungsten with super- imposed characteristic K series. Note that the 0.28-mm tungsten filter does not change the distribution of the wavelengths. Com- pare these with the curves of Fig. 1-14, where filters other than tungsten were used. (By courtesy of A. W. Hull.) These curves are typical examples of the distribution in intensity of a continuous spectrum emitted by a tungsten target excited by the indicated differences of potential. Note particularly that these are general radiation curves with the bright-line spectra of tungsten missing. They show that the continuous spectrum possesses a rapid intensity increase on the short-wavelength side of the curve and that its maximum intensity shifts to longer wavelengths as the exciting voltage is de- creased, and also that the total x-radiant energy, as indicated by the area under each curve, rapidly increases with the increase in exciting potential. This area, when expressed in terms of intensity, is for all practical purposes proportional to the square of. the exciting potential. 10 BIOPHYSICALLY ACTIVE X-RAYS The overall intensity may also be increased by an increase in the electron current flowing from filament to target. The latter increase may also be obtained by raising the temperature of the filament. Since the impinging electrons must be decelerated through collision with the atoms of the target, one may conclude that, the greater the density of the atoms in the target, the more frequently will these colli- sions occur. Broadly speaking, the density increases with the atomic number; hence an increase in the atomic number of the target material should parallel an increase in emitted x-ray intensity. It has been shown by Nicholas [1930] that the total amount of con- tinuous spectral energy emitted per second I = constant V 3/2 zi where V is the potential across the tube, z the atomic number of the element used as a target, and i the current passing from filament to target in the form of the stream of bombarding electrons. This relation is limited to values of V extending from 40 to 150 kv. Characteristic X-Ray Emission Spectra The peaks superimposed on the general radiation curves shown in Fig. 1-5 compose the X-line spectrum. They make their appearance at certain exciting potentials characteristic of the element out of which the target is constructed. The K series of tungsten makes its first appearance at the characteristic exciting potential of 69.3 kv. Below this voltage it never appears, but at this voltage and above it these radiations are always present. Table 1-2 shows the most prominent of the tungsten and molybdenum spectral emissions in angstrom units, classified into their appropriate series with an indication of their relative intensities. The spectrum of tungsten, plotted at the bottom of the intensity-wavelength curves of Fig. 1-4, shows the relative wavelength positions of these characteristic emissions with respect to the general radiation. This so-called i£-series radiation of tungsten is caused by a disturbance in the configuration of the innermost K ring of electrons. Suppose that one of the electrons about to collide with a tungsten atom possessed sufficient energy to penetrate to the innermost group of K electrons and succeeded in removing one of them by a collision process. To re-estab- lish the undisturbed normal state an electron from the nearest outer group or L configuration will replace the missing electron. This L configuration, having lost an electron, will have a replacement drop in from the M configuration, etc., until all other electron adjustments have taken place. CHARACTERISTIC X-RAY EMISSION SPECTRA 11 Each adjustment necessitates radiation of an x-ray quantum or bundle of energy designated as a " photon " because of the interatomic energy exchange which is involved. The radiations originating as the result of an adjustment of the electrons from the L to the K configuration are called the characteristic K series (Table 1-2), i.e., characteristic TABLE 1-2 Prominent X-Ray Emission Lines Wavelengths in 10 -8 cm (A) Element Tungsten Molybdenum Atomic Number 74 42 Relative Intensity K series \ X 50 100 35 16 »2 0, 02 0.2135 0.2089 0.1844 0.1794 0.7119 0.7076 0.6308 0.6193 L series 11.5 100 1.4845 1.4735 5.400 5.394 M series «i 6.973 Excitation Potentials in Kilovolts of the K series 69.3 20.0 L series 12.1 2.87 M series 2.81 of the tungsten atom. The radiations emitted as the adjustment pro- gresses from the M to the L configuration are called the L series. Be- cause of their long wavelength (X = 6.9 A), these radiations never appear outside of a tungsten-target Coolidge tube owing to the opacity of the glass for these " extremely soft " x-rays. When the radiations from a tungsten target are examined with the aid of an x-ray spectrometer, sharp peaks are found on the emission curve. These are resolved into four principal homogeneous emissions, the Ka 2 , Kai, K&x, and K& 2 , of which the Kai emission is the most intense (Table 1-2). 12 BIOPHYSICALLY ACTIVE X-RAYS The X-Ray Spectrometer An ionization spectrometer of the Bragg type may be used to obtain curves similar to those shown in Figs. 1-4 and 1-5. The x-ray beam emitted by the target of the Coolidge tube T (Fig. 1-6) is collimated by the narrow slits s. It strikes the surface of a three- dimensional crystal grating G, is deviated, and enters the ionization Fig. 1-6. A diagrammatic representation of a Bragg x-ray spectrometer using an ionization chamber to measure the intensity of the x-radiations. chamber C. The gas in the ionization chamber is ionized by the ab- sorbed x-radiation, and this ionization current, which is proportional to the intensity of the deviated beam, is recorded by the electrometer E. The ionization chamber and the crystal may be rotated about the center of the calibrated spectrometer circle. The wavelength of the x-radiation entering the ionization chamber is then obtained from the relation nX = 2d sin 6 where n is the spectral order, X the wavelength, 20 the angle between direct and deviated beams obtained from the spectrometer scale, and d the distance between the reflecting planes of the crystal. If we exam- ine the first-order spectrum for which n = 1, the wavelength may be obtained if the crystal constant d is known. Suppose that we use a rock salt (NaCl) crystal as the three-dimen- sional grating. This salt crystallizes in a cubic form, the Na and CI ions occupying alternate positions at the corners of elementary cubes in the cubic lattice characteristic of this crystal. The arrangements of the lattice are similar to the scheme shown in Fig. 1-7, which repre- sents a horizontal plane of a three-dimensional array of diffraction centers with the Na and CI ions located at the bright and dark points. THE X-RAY SPECTROMETER 13 When the x-ray beam reaches the crystal it encounters an array of ions (points) symbolized by the open and closed circles. A portion of the incident wave train is reflected from some ion P in the face of the crystal; another portion penetrates deeper and is reflected by an o • J CI O 4 ^\ s> ; i • ! O _ _ j < 2d > O ( • ) (o) Na Fig. 1-7. This shows, in a schematic way, the location of the Na and CI ions in a sodium chloride crystal and the reflection by the crystal of a monochromatic beam of x-rays incident at glancing angle 9. ion at a distance d below P. This latter train travels a longer distance abc, which must be an integral multiple of the wavelength of the x-ray so that on emerging and entering the ionization chamber it reinforces the upper wave train. The geometry of the diagram shows that this path difference is equal to 2d sin 8. For the wave trains to reinforce each other 7i\ = 2d sin where n is a whole number and is called the spectral " order." This relation is known as Bragg's law. The value of d may be obtained as follows. There are two ions per molecule, and, as each ion is confined to a volume equal to d 3 , a molecule of NaCl occupies a volume equal to 2d 3 . Since one mole of a substance contains 6.06 X 10 23 molecules, the number of molecules per cubic centimeter is p X 6.06 X 10 23 /M, where p is the density and M is the molecular weight. Hence 3 M 2 X p X 6.06 X 10 23 14 BIOPHYSICALLY ACTIVE X-RAYS The value of p for a rock salt crystal is 2.165, and its molecular weight is 58.46. Hence the value of the " lattice constant " of NaCl is d = 2.814 X 1(T 8 cm Using this value of d in the Bragg equation when a crystal of rock salt serves as a grating, one may compute the wavelengths for any glancing angle 6 observed on the spectrometer table. If at the same time the ionization current due to the absorption of the x-rays in the ionization chamber is observed, one has a measure of the intensity of the x-rays possessing that particular wavelength. The plot of these values gives the curves shown in Figs. 1-4 and 1-5. Obviously this is a tedious method, and for therapeutic and other practical uses such de- tailed information is not necessary. A simplified method of obtaining practically the same information will be outlined after the study of the law of x-ray absorption involved in the procedure. Absorption The medical radiologist cannot neglect the phenomena associated with absorption of x-radiation in both diagnostic and therapeutic branches if quantitative reproducible results are to be obtained. In therapeutic work where filters are constantly used to absorb the longer- wavelength radiations, which, for large doses, are dangerous to the patient, a knowledge of the processes involved in absorption is indis- pensable. When a beam of x-radiation is incident upon any medium, several effects may occur, all of which result in the reduction of its energy. These effects are : 1. The photoelectric effect. Loss by absorption with the resulting emission of electrons. 2. Scattering of the primary radiation and Compton scattering, collectively classified as secondary radiation. Unfortunately, the re- moval of energy from the incident beam is not a true additive property of absorption and scattering, but to a good approximation we may write Energy loss = Loss due to absorption + Loss due to scattering If the energy loss of an x-ray beam passing through matter followed a true absorption law and were dependent only on the thickness of the absorbing layer, then for a given wavelength the energy would be de- creased in each succeeding centimeter of absorbing layer by the same fractional amount. For instance, if the incident beam were composed of hard x-rays and the absorption in the first centimeter were 20 per ABSORPTION 15 cent of an incident 100 units of energy, 80 units would pass through this first centimeter. These 80 units would then be incident on the second centimeter of the absorbing medium, and this second centimeter would absorb 20 per cent of the 80 units incident on it and transmit 64 units; the next centimeter would absorb 20 per cent of the 64 units and trans- mit 51.2 units of energy; and successive centimeter layers would trans- mit 41, 32.8, 27.2 units, etc. The energy loss of an x-ray beam passing through matter is, however, also dependent on the wavelength. Long wavelengths (soft x-rays) are absorbed much more readily than short waves (hard x-rays). It has been found experimentally that for restricted wavelength regions the absorption varies as the cube of the wavelength. Therefore, if the wavelength of the incident radiation on tissue is composed of a beam of soft x-rays, it is found that the first centimeter of tissue absorbs 63 per cent of the incident energy, while successive layers would transmit 37, 13.7, 5.1, 1.9, and 0.7 per cent. To appreciate the difference in opacity in changing from hard to soft x-rays, compare this last value with the effect of the shorter wavelengths where the fifth layer transmitted 32.8 per cent. The energy loss is also dependent on the kind of material used as an absorber. The loss is proportionally larger for a greater density of the absorbing substance. This implies that absorption is an additive atomic property and depends only upon the number and kind of atoms compos- ing a molecule. The absorption varies as the fourth power of the atomic number, for a given wavelength. It has been found empirically that the absorption may be represented approximately, over restricted regions of wavelengths, by what is gen- erally known as Owen's law, namely, that the absorption coefficient per atom (fx a ) in the path of the x-ray beam is given by Ha = CX 3 z 4 in which C is an experimental constant and z the atomic number. When X is limited to the restricted radiation of wavelengths less than the K characteristic wavelengths of the absorbing atom, as for instance in the o use of filters of Al and Cu for X between 0.50 and 0.71 A, then the experi- mental constants C A i and C Cu are 0.0217 and 0.0221, respectively. Using Owen's absorption law, let us compare the relative opacity of bone and fleshy tissues exposed to the same beam of monochromatic x-rays. Fleshy tissues are composed chiefly of H and O. Their absorp- tion is comparable to water. The molecular absorption of H 2 is proportional to 2 X l 4 + 8 4 = 4098 16 BIOPHYSICALLY ACTIVE X-RAYS The absorption of bone, composed chiefly of Ca3(P0 4 ) 2 , is proportional to 3 X 20 4 + 2 X 15 4 + 8 X 8 4 = 614,000 so that the relative absorption Bone = 152 Water i.e., bone is 152 times more opaque than water. If a lead bullet is embedded in the bone, then its absorption is propor- tional to the fourth power of the atomic number of lead, i.e., 82 4 . Lead is therefore about 74 times more opaque than bone. Barium sulphate, BaSC>4, which is most commonly used as an ali- mentary contrast agent, has an absorption proportional to 56 4 + 16 4 + 4 X 8 4 It is very opaque because of the high atomic number of Ba. Two or more adjacent substances transmitting different proportions of the incident energy show intensity contrasts which are very large for long wavelengths and small for shorter ones. Thus when soft x-rays are used, for radiographic work, they will produce a greater contrast between adjacent substances than x-rays of shorter wavelengths. This contrast effectiveness is illustrated in the use of gases such as sterile oxygen to give radiographic relief effects. In the well-known pneumoperitoneum method, sterile oxygen is injected into the peri- nephritic fatty tissues, and, in consequence of the small absorption of oxygen, the more absorptive kidney is thrown into relief. The same method has been used to inflate the Fallopian tubes. Carbon dioxide has also been employed for this purpose. Quantitative Statement of the Absorption Laws The simple absorption law discussed on the preceding pages is a logarithmic depreciation law of the form where I is the incident intensity, / is the intensity of the x-radiation transmitted by a unit thickness, e is the base of the Napierian logarithms (e = 2.72), and m is a constant for a given medium of thickness d and is called the coefficient of absorption. Its numerical value, in any given medium, depends upon: (a) the nature of the medium, (6) the wavelength of the incident radiation. For logarithms to the base 10 MASS ABSORPTION COEFFICIENTS 17 this absorption law may be written 2.303 , n = -—- (log 7 - log I) cm a The absorption coefficient p, or " Unear absorption," is the fractional decrease in intensity of a beam of unit cross section per unit (linear) path length through the absorbing medium. The " Unear absorption coefficient " of a given beam of x-radiation is much greater in water than in steam; hence, its value depends on the nature of the medium. To get a more fundamental constant, an absorption coefficient that is characteristic of the absorbing substance is required; hence a mass absorption coefficient* is used defined by ix m = fx/p, where p is the density of the material. The absorption law in terms of the mass absorption coefficient takes the form I = V~ (M/p) " pd = I e~' lmpd Experiments have shown that the mass absorption coefficient of a substance for x-radiation is independent of its physical state. Thus the mass absorption coefficient of water is the same whether the water is in the form of liquid or of gas. The independence of the mass absorption coefficient of the physical and chemical states of an element sharply distinguishes x-radiation from light. For instance, carbon in the form of diamond is optically trans- parent, whereas in the form of graphite it is opaque. The mass absorption coefficient of both forms for x-radiation, however, is the same. Mass Absorption Coefficients Increase with Increase in Wave- length Figure 1-8 shows how the mass absorption coefficient of copper or aluminum, common forms of therapeutic filter material, very rapidly increases with an increase in wavelength. Table 1-3 gives tabulated values of the mass absorption coefficients of aluminum and copper in detail. Note the change in the values of fx m for copper between 1.389 and 1.293 X 10~ 8 cm. In x-ray technique an understanding of the comparative opacity of common filter elements like aluminum, copper, and lead is essential for the interpretation of the quality of radiation transmitted by these filters. Attention should be called to the enormous difference in opacity of copper and aluminum for the longer wavelengths. * Mass absorption coefficient is the fraction of a beam 1 cm 2 cross section absorbed per gram of substance traversed. 18 co l ^TF^/C^LLF ACTIVE X-RAY s CN O CN © -* CO CN CO B co © . « o d i-H 1-H d d >H <3i d CO © s Oh o CN o I— 1 LO LO LO CN 1-H CO 1-H Xf © CO o © d d Si' "3 © © u 6 o o CN o •"» lO 00 os »o co © CO © O g o o o os co K 1-H LO IH lO •e* 00 CO Q i-H CO "0 co CO o i-H .« H ff d © PQ K o CO o i-H CN CM CN LO O 3 00 © © T-H PQ CN LO co fe § © CN CN s * co co LO OS d © O rzj • rH 1— ( co co " ,< CO CO tH © 5 a CO CN OS CO »o LO OS CN d CN © a. i-H OS o tH lO © r^ II CN © CN © CN 6 LO LO o a. t> CN CO © © to i-H t- t> Eh ■* © fe CO CO © H CO J> 00 T-H 1-H OS CO CO © © i-H OS © E to © H o CO t^ O LO -HJ t~ i-H i-H O OS OS CN 1-H T-H © © fc o M Fh o o 00 o CO CO © CN lO Pn co CO CO 1-H 1-H o © © DO 00 CO O PQ ^ 1-H O co 3 1-H 0.14 tx m = 510 X 3 + 0.75 Richtmyer [1921] Absorption Formulas for Organic Materials* Applicable to Wavelength Region o A Formulas Absorbing Material 0.05 to 0.5 0.05 to 0.5 0.05 to 0.5 0.05 to 0.5 tx m = 2.5 X 3 + 0.18 ii m = 11X 3 + 0.18 tx m = 1.6X 3 + 0.18 tx m = 2.2X 3 + 0.18 Blood Bones Fat Muscle 0.2 to 0.5 y. m = 2.5 X 3 + 0.18 Hydrogen * Compare blood with hydrogen. After Mayneord [1929], attributed to Kiistner. It will be noticed that 1 mm of aluminum allows 36 per cent of the incident energy to be transmitted at 80 kv, 2 mm allows 23 per cent, and 3 mm only 16 per cent to be transmitted. Evidently 3 mm does not transmit one third as much as 1 mm. Neither does the transmission increase linearly with the applied voltage. The absorption governing these phenomena can, however, be represented by the empirical equa- tions shown in Table 1-4, where ju OT is the mass absorption coefficient for the wavelength region designated and p is the filter density (pai = 2.70 grams/cc and p Cu = 8.94 grams/cc). Scattering Coefficients Next the contribution made to the energy loss of the x-ray beam passing through a filter, by scattering, must be considered. Here, as for absorption, an analogous mass scattering coefficient (. •°30 c o 'in E25 (A ^^"^2 mm ^-— •"^ CO = 20 u %^^^ \^**"^ ha 0> „ — "d mm °"15 — 1^ iiii 60 70 80 90 100 Kilovolts across x-ray tube 110 120 Fig. 1-9. The per cent transmission of aluminum niters at increased kilovoltage using a constant source of potential. The tube wall was 1.3 mm cerium glass. (After L. S. Taylor, Natl. Bur. Standards.) TABLE 1-5 X = 0.7A X = 0.1 A Element Mass Absorption Coefficient Mm Mass Scattering Coefficient Cm Mass Absorption Coefficient Mass Scattering Coefficient C Al Cu Ag Pb 0.605 5.22 51.0 Very large Very large 0.18 0.20 0.29 0.48 0.82 0.142 0.156 0.325 1.05 3.50 0.14 0.14 0.18 0.35 0.67 By courtesy of C. W. Hewlett [1921]. For all practical purposes the various influences contributing to the scattering of the energy for any given metal are separable into: 1. The influence of thickness on scattering. 2. The influence of density of the filter on scattering. 3. The wavelength of the incident energy. 4. The departure of the incident beam from a parallel column. The scattering of x-radiation in passing through matter is dependent on the thickness of the filter in such a way that each succeeding centi- meter of filter thickness converts the same fractional amount of the inci- 22 BIOPHYSICALLY ACTIVE X-RAYS dent energy into scattered radiation. If the wavelength is large as compared to the diameters of the atoms composing the absorbing filter, the atomic scattering is independent of the incident wavelength and we may call this an example of true scattering. Under these circum- stances the scattered radiation has the same wavelength as the incident radiation, and each atom acts as a source for emitting scattered rays in all directions. Some of the energy is scattered forward, and back- ward, as well as sideways. The scattered x-radiation may penetrate and be absorbed by the filter in a manner similar to the incident energy. Its intensity is additive to the unabsorbed primary x-radiation at every point in the absorbing substance so that the total intensity at any point in the absorber is increased by the scattering process. The scattering occurs within the medium; the smaller the density of the absorbing medium, the greater is the possibility that the scattered ray emerges. The scattered radiation which escapes from an absorbing medium of great density is less than that escaping from a less dense medium. It has been found that the intensity of a beam of hard rays is reduced by scattering more than by mass absorption. Very soft rays are reduced in intensity more because of mass absorption than because of the scatter- ing effect. Table 1-5 shows the relative importance of the mass absorption coeffi- cient and the mass scattering coefficients for various wavelengths and filters. As the wavelengths of the x-radiation decrease, for any given filter, scattering becomes more and more the predominating factor in the absorption of the energy, for the scattering coefficients become increasingly great in comparison to the mass absorption coefficients. For absorbing material containing elements of small atomic number the scattering for any given wavelength is predominantly more effective. On comparing the loss due to scattering with the loss due to absorption, it is found that for light elements and soft rays (0.7 A) the absorption loss is roughly three times as great as the scattering loss. For hard rays (0.1 A) the loss is about equally distributed between the two effects. For the heavy elements the loss due to scattering is nearly neg- ligible for soft rays, but it is about 20 per cent or less for the hard rays. Finally, the scattering is smaller in proportion to the absorption, the greater the density of the absorbing medium. This loss explains why tissue, owing to the low density and small mass of its constituent atoms, produces so much scattered radiation when subjected to x-ray examination. SCATTERED X-RADIATION 23 Scattered X-Radiations as Modified by the Compton Effect The preceding section discussed the properties of the scattered x-radia- tions which possessed the same wavelength as the incident energy. Coexisting with this phenomenon are found scattered x-radiations having longer wavelengths than the incident energy. In 1922, A. H. Compton first demonstrated experimentally that a modification of the wavelength took place as the result of the scattering of the incident x-ray energy by the electrons in the material. He found, for instance, that, when very soft x-radiation having a wavelength o equal to 0.7078 A was allowed to penetrate a cube of carbon, the scat- tered radiation emitted by the cube at right angles to the incident beam was composed of two groups of wavelengths. The first was a true, or o regularly scattered wave with unmodified wavelength (X = 0.7078 A); in addition, he found a modified scattered wavelength equal to 0.7320 A, the increase in wavelength amounting to 0.0242 A. Therapeutically speaking, the Compton scattered energy is softer than the incident and regularly scattered energy. If the wavelength o of the primary beam is exactly 1.0 A (very soft radiation), the wave- length of the x-rays emitted at right angles to the incident beam will increase by 0.0242 A, so that its wavelength becomes 1.0242 A. This increase in wavelength of about 2 per cent is not very important. If, o however, a primary beam whose wavelength is 0.1 A is examined (hard o radiation), the increase in wavelength is also 0.0242 A, so that the modi- o fied scattered wavelength is 0.1242 A. This increase is nearly 25 per cent, and if any considerable proportion of the modified x-radiation is present, the properties of this scattered beam will be very different from those of an unmodified beam. Such changes in wavelength imply great changes in the mass absorption coefficient. If, in addition, the intensity of the modified portion of the beam is greater than the intensity of the unmodified wavelength of the beam then a serious error arises by not taking the Compton scattering into consideration in biological absorbing material. Table 1-6 shows to what dimensions the error may rise when elements of small atomic number are used as absorbing material. In deep therapy where radiations comparable to gamma rays are used, the softening of the scattered beam by the tissues is even more pronounced. A. H. Compton has shown that it is possible to calculate the increase in wavelength (AX) as a function of the angle of scattering 0: that is, the angle at which an observer measures the scattered radiation with respect to the direction of the incident ray, from the simple relation h ,, AX = — (1 — cos Incident photon r Original position of electron at rest Modified x-radiation increased in wavelength > a;=axis Recoiling electron Fig. 1-10. A diagrammatic representation of the Compton effect. Note the increase in wavelength (X + AX) of the x-ray photon scattered by the stationary free electron e, and the resulting direction and velocity of the electron after the en- counter. Through the explanation of this extraordinary change in wavelength A. H. Compton proved the existence of a collision phenomenon in which an incident quantum of x-radiation or photon of energy content hv collides with a free electron in the absorbing material. The photon acts as if it were a perfectly elastic entity colliding with a perfectly elastic electron. The incident photon may be pictured as colliding elastically with a stationary electron, and giving it a glancing blow. In this process it communicates energy and momentum to the deflected electron and in turn loses an amount equal to that passed on to the electron, but in such a way as not to violate the laws of conservation of energy and momentum. This collision is represented pictorially in Fig. 1-10. Here the incident x-ray photon, of energy content E = hv, is shown colliding with an electron at rest of mass m . The incident energy E is divided between the modified photon bouncing off at angle with energy E^ and the electron recoiling at angle d with energy E g . The law of conservation of energy demands that E =E ~ u e or that hv = hvi + m c' W 1 - 8 2 J SCATTERED X-RADIATION 25 Here m = ?n /(l — B 2 ) 112 is the relativistic mass of the electron of energy content mc 2 , and mq is identified as its rest mass. 3 = v/c, where v is the recoil velocity of the electron and c the velocity of light. These equations involve relativity calculations because of the high velocity of recoil of the electron, necessitating the use of an effective mass (m) which is greater than the rest mass (m ). The next step is to consider the application of the law of conservation of momentum as applied to the collision. This law leads to two equa- tions, one for the momentum along the x axis, or the x component, here chosen in the direction of the incident x-ray photon, and one at right angles to it, the y component. hv hvi . J . — = — cos -\- mv cos d (x component) c c = — sin — mv sin 6 (y component) c The x-ray photon E of energy content hv, considered as a colliding entity, is moving with the velocity of light c. It has a relativistic mass of hv/c 2 . Its linear momentum is hv/c. From these relations the increase in wavelength (AX) can be computed, recalling that c = v\, and is found to be ft , AX = (1 — cos 0) m Q c Evaluating h, rriQ, and c, we find that AX = 0.0242 (1 - cos 0) where X is expressed in 10 -8 cm, i.e., angstrom units (A). For values of 4> equal to 90° AX = 0.0242 A For values of equal to 0° AX = This result shows that the increase in wavelength is independent of the original or incident wavelength and that the modified scattered radia- tion depends for its increase in wavelength upon the direction in which it is scattered. For back scattering, where = 180°, the increase in o wavelength AX amounts to 0.04848 A. The conclusion is that the softest scattered radiation appears in the direction = 180°, and that this modified scattered radiation hardens as approaches zero, at which point its wavelength increase is zero. 26 BIOPHYSICALLY ACTIVE X-RAYS Therapeutically, the back scattering is therefore a decidedly important phenomenon, especially for very hard x-rays, because of the increase in wavelength and its accompanying greater absorption in this direction. TABLE 1-6 Ratio of Intensities of Modified to Unmodified X-Radiation in the Compton Effect Source, Ag K line (0.56 A) Observations made at 120° with incident beam Scattering Element Atomic Number Intensity Ratios Li 3 oo C 6 5.48 Al 13 2.61 Si 14 2.33 K 19 1.72 Ca 20 1.71 Ni 28 0.40 Cu 29 0.21 For additional data see Y. H. Woo [1926]. Courtesy Physical Review. The Compton modified scattering varies with the atomic number of the filter or absorber element. Thus for elements of smaller atomic number than lithium all the incident energy is modified and scattered as softer radiation, whereas for lead practically none of it is modified. Table 1-6 due to Y. H. Woo [1926] gives some idea of the importance of the ratio of the intensities of the modified to the unmodified x-radia- tion, especially when tissue and absorbing material of low atomic number are radiated. The Translucence oe Human Tissue The above discussion on the transmission of x-radiation by matter permits a rather unusual conclusion about matter of low atomic weight: that it is translucent and not transparent to x-radiations. If the human eye were sensitive to x-rays, human tissue, which is composed wholly of elements of low atomic number, would be seen as a bright vaporlike substance if irradiated with x-radiations. An x-ray photograph (radio- graph) of an internal organ of the human body is similar to a photograph of a building taken in a fog: the parts of the building nearer the camera would appear more clearly in the photograph, and the distant parts less clearly or not at all; while the larger outlines would be visible with MEASUREMENT OF QUALITY OF X-RADIATION 27 structural details rather indistinct. The photograph lacks contrast and detail. In a similar way the lack of contrast and detail in a radiograph is attributable to the scattering of the x-radiation into the geometrical shadow of the object. Measurement of Quality of X-Radiation by Absorption The radiation emitted by an x-ray tube is heterogeneous. It consists of a continuous spectrum overlaid with a line spectrum characteristic of the metal target, provided that the potential across the tube is suffi- ciently high to excite the characteristic radiation of the target. The " quality " of the radiation, especially with regard to its therapeutic applications, depends both upon the wavelength content of the spectrum and upon the distribution of the energy over its whole range of wave- lengths as measured on the outside of the glass housing of the x-ray tube. The direct determination of this spectral composition is beset with considerable experimental difficulties, as we have seen. Accordingly, an indirect way of obtaining the same results has recently been developed by W. S. Taylor and his associates at the Bureau of Standards, by using a so-called filtration method. The specification of x-radiation quality, with the aid of an absorption curve, has been recommended by the x-ray standardization committee [1934] of the Radiological Society of North America. The committee reported: " For most 'practical purposes the quality of x-radiation may be satisfactorily specified in terms of the copper or aluminum absorption curve combined with a statement of the initial filtration. In lieu of an absorption curve, the equivalent constant potential applied to the tube terminals to yield the same curve may be stated as a single numerical magnitude. Up to 100 kv (constant) aluminum absorption curves and above 100 kv (constant) copper absorption curves shall be used to establish the equivalent potential. " In order to obtain the complete absorption curve, filters in the form of successively thicker sheets of a metal are placed in the diaphragmed beam of an x-ray tube driven at constant potential and predetermined constant milliamperage. The transmitted intensities are obtained by means of an ionization chamber (spectral distribution of energy assumed constant) placed below the absorber. Typical results as obtained by Taylor and Singer [1930] are shown in Figs. I— 11 and 12, for copper and aluminum filters of increasing thick- ness for radiations from a tube with tungsten target excited at various potentials. If the absorption of filters were of the simple exponential type (/ = I e~ fix ), then plotting log per cent transmission as a function of 28 BIOPHYSICALLY ACTIVE X-RAYS filter thickness a straight line of slope ju is obtained. The curves in Figs. I— 11 and 12 show that the complete absorption curves do degen- erate into straight lines, but only at high voltages and large values of filter thickness. Hence, absorption for thick filters and high potentials can, to a close approximation, be represented by an equivalent composite absorption constant (c), such that / = I§e~ cx for comparatively large values of x. For copper this result is attained at 150 kv with a 2-mm filter and for aluminum at 110 kv with a 10-mm filter. 100 80 CO §E 60 3£ w »40 0> a. 20 t\ \\ "Complete" absorption curve \\ of general x-radiation in copper - \\ N \ ^ - \ x \ v "- \ \ "v - I N ^ \ S " \ ^ *"*-^ 150 kv \ X ""-^lOOkv ~~ — — _^^ - " \l00kv — ^- 2.0 1.0- U o 1 2 Copper filter thickness in mm Fig. 1-11. After Taylor and Singer [1930]. The outstanding features of these absorption curves may be inter- preted quite readily. The steeper the slope, the softer and more absorb- able is the radiation. The slope in the more heavily filtered portion decreases symmetrically with the increase in tube voltage. Mono- chromatic x-radiation gives a straight-line absorption curve. The degree to which the absorption curve approximates a straight line is a measure of the homogeneity of the radiation. The similarity in the variation of absorption by different materials makes it possible to derive simple relationships between x-ray absorption characteristics of different materials. It is possible to compare the x-radiation output of two x-ray machines by means of the absorption curves obtained from each at various voltages. Effective Wavelength of a Heterogeneous X-Ray Beam The effective wavelength emitted by the target was defined by Duane [1928] as " the wavelength of monochromatic radiation that would produce the same effects (the readings of the instrument employed to detect it) that the actual (heterogeneous) radiation produces." In order to obtain the quality of an unknown beam of heterogeneous WAVELENGTH OF A HETEROGENEOUS X-RAY BEAM 2.0 29 5 10 Aluminum filter thickness in mm Fig. 1-12. Decrease of the per cent transmission with increased filter thickness. From their shape, the solid curves seem to indicate an exponential absorption. Had they followed an exponential law of absorption the broken curves would have been straight lines. Note that at large filter thicknesses the broken curves become linear. (After Taylor and Singer.) radiation it is possible to make use of absorption measurements. These measurements determine the comparable wavelength of a homogeneous radiation which would be reduced in intensity by a given filter in the same degree as the heterogeneous radiation. The heterogeneous radia- tion is then designated as having an effective wavelength equal to that of its corresponding homogeneous radiation. This does not imply, however, that the effective wavelength equivalent can produce the same biological results as its comparable heterogeneous beam. Illustrations of the method for determining the effective wavelength with its composite absorption coefficient are found in Fig. 1-13, where with increasing thickness of the copper filter the logarithm of the trans- mitted energy is plotted against thickness of filter material. Suppose that one were interested in obtaining a beam of radiation 30 BIOPHYSICALLY ACTIVE X-RAYS which possessed an effective wavelength of 0.2 A. The table of mass absorption coefficients shows that copper possesses a mass absorption coefficient 1.6 for this wavelength. The broken line in Fig. 1-13 is drawn with slope 1.6. This represents the relation log e (I/Io) = —ex, in Which c = 1.6, or log 10 (//J ) = -cz/2.3026. 0.5 1.0 1.5 2.0 Copper filter thickness in mm 2.5 Fig. 1-13. Taylor's method of evaluating the effective wavelength of a hetero- geneous beam of x-radiation. A line drawn parallel to this broken line contacts the 152-kv curve at 0.4 mm and the 106-kv curve at 0.9 mm. The conclusion is that, when an x-ray tube is excited at 152 kv and a 0.4-mm copper filter is placed in the beam, the radiation passing through the copper filter has an effective wavelength of 0.2 A. A similar effective wavelength may also be produced by a 0.6-mm copper filter introduced into a 130-kv beam or by a 0.9-mm copper filter in a 106-kv beam, if all other factors remain constant. The converse question may arise: what effective wavelength is trans- mitted by a 1.0-mm copper filter? Let us assume the radiation whose quality is to be determined as that produced by 120 kv. A tangent is drawn to the curve at the 1.0-mm thickness. The slope of the tangent WAVELENGTH OF A HETEROGENEOUS X-RAY BEAM 31 at this point is 1.13. This is the composite absorption coefficient. Referring to Table 1-3 one may observe that the effective wavelength comparable to this mass absorption coefficient of copper is 0.173 A. Upon drawing a tangent to the same curve at the 2.0-mm thickness mark it is found that the slope at this point corresponds to a composite absorption coefficient of 0.81 comparable with an effective wavelength of 0.15 A. Note that, as the thickness of the filter increases, the slope decreases, and hence the effective transmitted wavelength decreases; i.e., successive filters harden the transmitted rays. 10 6- Tungsten target 40 kv unfiltered 0.3 0.4 0.5 0.6 0.7 Wavelength in A 1.0 Fig. 1-14. A diagrammatic representation of the general radiation emitted from a tungsten target with and without a filter. Note the general hardening of the emission without change in Xn but a pronounced change in X max and loss in intensity of the filtered beam. Compare this with the 30-kv unfiltered beam having about the same area and longer effective wavelength. (After A. W. Hull.) This general hardening of filtered x-rays was originally observed by Hull. His spectral distribution curves are shown in Fig. 1-14. Thus if a copper or aluminum filter is placed in the path of the x-radiation the intensity of the filtered radiation is much decreased but the decrease is proportionally greater in the longer-wavelength region owing to the relatively greater absorption of these wavelengths. As a result the effective value of the wavelength is decreased. This is due to the fact that X max is transferred to shorter wavelengths without changing the value of X . For comparison a 30-kv unfiltered emission curve is shown having about the same intensity as the 40-kv filtered radiation, but note that its effective wavelength is much longer. 32 BIOPHYSICALLY ACTIVE X-RAYS Half- Value Layer The quality of a heterogeneous x-ray beam can be described by the thickness of a filter which will reduce the intensity of the beam to one half its initial value. The absorption curves shown in Figs. I— 11 and 1-12 indicate that, the shorter the effective wavelength of the x-radia- tion, the thicker the half-value layer of the filtering material must be. Inasmuch as the composite absorption coefficient varies with thickness of the added filter, there is no simple direct quantitative relation con- necting effective wavelength with half-value layer. The intensity of a heterogeneous beam of x-radiation, if evaluated by the half-value layer or effective wavelength method, shows that the latter has the advantage, in that it presents a clearer physical picture of the radiation quality. Action of X-Radiation on Living Tissues Almost immediately after the discovery of x-rays was announced it was suggested that, by virtue of their penetrating power, they might be used therapeutically to influence deep-seated pathological processes. In order to evaluate their physiological effectiveness it is essential to know the relative penetration, absorption, and resulting ionization of the x-radiation, for the energy must be absorbed to be effective. The energy penetrating the tissue may be completely absorbed and excite secondary phenomena. It is to these secondary phenomena that the action of the primary radiation is attributed. The pioneer workers in radiography and roentgen therapy developed cancer of the fingers after exposure to the soft x-rays emitted by the then prevalent gas x-ray tubes. Repeated exposure of the hands to soft radiation results first in keratosis (horny excrescences) that are usually multiple. At first dry and scaly, the surface epithelium in time becomes superficially eroded and the lesions become moist. This con- dition is an important danger signal indicating activity of the process. The next progressive stage is the development of carcinomata (rarely sarcomata). It is therefore important to appreciate the danger of small, repeated exposures to soft x-radiation. As in inorganic material, the relative amount of the x-radiation ab- sorbed by tissue in its superficial layers is also determined by its wave- length. Since the absorption is very great for long wavelengths, the superficial layers of tissues irradiated by the entering energy are affected to a greater extent than the deeper-lying tissue. As pointed out in previous sections, the control of physical factors governing the quality and quantity of x-radiation with which a patient is radiated is repro- ACTION OF X-RADIATION ON LIVING TISSUES 33 ducible, but biological units of dosage contain factors still largely un- known. Biological units of dosage of x-radiation have been expressed in terms of an erythema of the skin. An erythema may be defined as a reddening of the skin within a week or ten days, followed by tanning within about a month's time. In human beings the amount of radiation necessary to produce just a mild erythema of the skin seems to depend upon the amount of pig- mentation present and the thickness of the skin. An intensity which may produce a mild erythema on the inside of the thigh or forearm of a thin-skinned blond may cause no visible change in the skin of a dark brunette. The palms, soles, and the back of the neck can tolerate much more radiation than the dorsal surface of the forearm. It is difficult to distinguish the effects due to the changes in the epi- thelial cells of the skin from the secondary changes brought about by injury to the subcutaneous capillary bed. The basal cells of the skin, or Malpighian* layer, seem to be the most sensitive, and they show vacuoles, pycnosis, and lack of staining power after large doses of radia- tion. It has been noted (Packard [1926]) that a sufficient dose of x-radiation may bring the process of growth and repair of the matrix cells of the hair to a standstill with the result that the hair is loosened and falls out. The single greatest secondary factor in skin changes following radia- tion exposure is the modification of cell nutrition by the capillaries. It is the engorgement of the capillaries of the area radiated that is identified with the erythema noted at various periods after exposure. ^ With properly filtered hard rays, the radiation through very small portals (holes in lead plates) does not produce an erythema, probably because there is no participation of adjacent tissues in the general reac- tion of the capillaries of the skin, so that an increase in blood circulation could not be identified visibly. Bone and cartilage are resistant to x-radiation. It is common thera- peutic knowledge that cartilage may be damaged by very intensive irradiation, especially in the region of the neck if larynx and trachea are subjected to intensive crossfire radiation. Experiments on young rats have shown that, when the jaws are subjected to large doses (Leist [1927]), the odontoblasts, which are especially sensitive, are destroyed; smaller doses produce only pulp injury. The precursors of the circulating blood cells in bone marrow are very sensitive to irradiation. * The deeper portion of the epidermis, consisting of cells whose protoplasm has not yet changed into horny material. 34 BIOPHYSICALLY ACTIVE X-RAYS The coagulating power of the blood (Lindhardt [1924]) is not affected except in therapeutic cases irradiated for castration or hyperthyroidism, where it is found to fluctuate in amount. The most sensitive cells in the testis, according to Feroux and Regaud [1927], are the basal cells or spermatogonads. The adult sperms are apparently insensitive, since they show no change after irradiation. S. L. Warren [1928], in a review of the physiological effects of roentgen rays upon normal body tissues, lists the tissues in a descending scale of sensitivity, beginning with a moderate sensitivity, in the following rough order: thymus, stomach, colon, and bladder epithelium; salivary epi- thelium; probably kidney epithelium; hair papillae; blood-vessel endothelium; fibroblasts; and young connective-tissue cells including collagenous fibrils. Next in order of decreasing sensitivity are: the mucosa of the mouth, esophagus, rectum, and vagina; the lung paren- chyma; pleura; skin epithelium; and the structures of the eye. Next come the smooth, striated, and cardiac musculatures; cartilage; bone, including osteoblasts; teeth; normoblasts; Sertoli's cells; and stroma cells of testes and ovary. The most resistant cells may be listed in the following order: adult thyroid, adult pituitary, brain and nerve cells, nerve trunks and endings, tendons and joint capsules, adult sperm cells, and red blood cells. Latent Period In a review of the literature on the latent period Regaud [1925] points out that sensitive cells of the epidermis are the generating cells of the basal layers, and that the changes in the skin occur as these cells are elevated toward the cornified surface. The period of latency is a meas- ure of the time which is necessary for the cells from the basal layer to reach the cornified stage in their progress to the surface. The same is true of the testes, where the sensitive cells are the spermatogonads. Until time has passed to allow successive generations of cells to reach maturity, the injury is not apparent. This is the latent period for the spermatozoa. The thymus cells are very sensitive to radiation and have a very short latent period. This latent period conforms to the interval of time extending from the death of these very sensitive cells, in this case the lymphocytes, to the disintegration and absorption of the cell bodies. An important biological effect of x-rays and 7-rays is the increase produced by them in the rate of mutation of genes. All types of muta- tion occur, but none have been observed which may specifically be attributed to x-ray absorption. The interpretation seems to center around the concept that "one direct hit" (Crowther [1924]) suffices LATENT PERIOD 35 for the initiation of mutations. The hit may be supposed to take place in some sensitive region in the chromosome. In the case of Escherichia coli (B. coli) the volume essential to life as estimated from the area in which the hit took place was less than 6 per cent of the bacterium itself (Wyckoff [1930]). This volume is about 0.75 m 3 - It was concluded from this work that the absorption of a single x-ray photon was sufficient to kill an organism, although on the average only about one in twenty of the absorbed photons was effective. The biophysical effects of x-rays are due to energy actually absorbed by the tissues. This energy absorption, as previously indicated, does not take place directly, but through secondary processes, i.e., through the production within the tissues of high-velocity electrons and some of lower velocity due to Compton scattering. These electrons give up their energy in producing ionization along their paths (Table 1-8). At this point the study must be taken over by the biochemist, who should explain why, as a result of sufficient ionization thus produced, living tissue of all kinds disintegrates. From the experimental evidence available, one may conclude that absorbed photons in the form of x-rays and 7-rays for equal ionization doses produce equal effects. Genetic changes occur in direct proportion to the dose of radiation and are independent of its wavelength. The biological effects of radiation are intimately related to ionization phenomena produced in a specific region of the living organism. The same number of ions may, however, be produced in the same region and during the same time interval by ionizing radiations of very different frequencies. In general, the biological effect is probably the same in kind but not in degree. The receptor in which this ionization takes place is fundamentally the living cell. A cell, whether it lives as an isolated entity or as a part of an organism, is enclosed in a membrane which permits the passage into the cell of substances necessary to maintain its normal life and excludes others. The adjustment of the semi-permeability of the cell's mem- brane is so delicate that it can differentiate between two such very similar elements as sodium and potassium. The living cell is equipped to maintain the physical and chemical characteristics of its cytoplasm in a very constant state. The nucleus, located inside the cell and acting as the controlling center of the cell, is well protected by its environment. The x-ray energy passing through the cell wall, contents, and nucleus, if absorbed, will start a train of well-developed changes. The changes that occur depend on many factors, but primarily on the magnitude of the dose of radiation. The nucleus contains a certain definite number of threadlike structures 36 BIOPHYSICALLY ACTIVE X-RAYS known as chromosomes, which carry the hereditary factors in the form of physicochemical units called genes. The remarkable effect following the absorption of the radiant energy is an alteration of the genetic nature of the cell (Goodspeed and Uber [1939]), which results from the ioniza- tion accompanying the passage of high-speed electrons through the nucleus and chromosomes. The effect of the ionizing radiations is to increase markedly the frequency of mutations, so that geneticists need not wait for the very rare probability of spontaneous genetic changes in order to study the problems of heredity and variations. For purposes of study those changes which cause differences in the physical appear- ance of Drosophila have been found most convenient. For a further discussion of these very fundamental problems see Chapter II, " The Biological Roentgen," and Chapter IV, " Effect of Ultraviolet Radiation on Bacteria." X-Ray Protection The protective materials commonly used in radiology are: (1) sheet lead; (2) lead-impregnated glass and rubber; (3) concrete. The absorptive values of sheet lead for various thicknesses and various wavelengths of radiation are given by Mutscheller [1925] and reproduced in Table 1-7. These results show that absolute protection is impossible even with 8 mm of lead. Under practical conditions faced by an x-ray operator, a protection comparable to 8 mm of lead is seldom attainable. Mutscheller has, however, found that an operator can safely subject himself to a " toler- ance dose " of 1/100 of an erythema dose in 30 days' exposure. On the basis of this definition we can assume that during radiographic o work with an effective wavelength equal to 0.17 A, with 50 exposures per day, each of 5 seconds at 20 milliamperes current, the operator standing 10 feet from the tube would receive about 1 erythema dose in 1 month. To reduce this to 1/100 of an erythema dose, lead protection of 1.2 mm is needed. If fluoroscopic work is undertaken during 2 hours per day, using 4 ma, about 6 erythema doses would be received in the same time and distance. Under these working conditions 1.8 mm of lead as a protection is necessary. During radiotherapy work, where 4 ma for 10 hours a day may be used, 28.5 erythema doses per month under similar conditions are re- ceived and from 5 to 6 mm of lead are needed for protection. Protective gloves or gauntlets and aprons are constructed of rubber impregnated with 55 per # cent lead oxide. They are comparatively heavy but ensure protection. Lead-rubber aprons can be obtained in different weights. The usual 7-lb apron is made of -j^in. leaded rubber MEASUREMENT OF LEAD EQUIVALENT 37 TABLE 1-7 Percentage op Energy Transmitted through Various Thicknesses op Lead Tungsten target excited at kilovolt peak indicated mm 124 113 103 95.4 88.9 82.7 77.8 73 70 65 62 kv Pb peak 1.0 23.9 19.8 15.7 11.9 8.61 6.00 3.94 2.44 1.45 0.794 0.410 1.2 17.9 14.3 10.8 7.74 5.27 3.42 2.06 1.16 0.62 0.302 0.137 1.4 13.5 10.3 7.48 5.05 3.23 1.95 1.08 0.55 0.27 0.115 0.046 1.6 10.1 7.47 5.17 3.30 1.98 1.11 0.566 0.26 0.114 0.044 0.015 1.8 7.60 5.40 3.57 2.15 1.21 0.63 0.297 0.13 0.049 0.017 0.005 2.0 5.71 3.90 2.46 1.41 0.74 0.36 0.155 0.059 0.021 0.006 2.6 2.42 1.48 0.81 0.39 0.17 0.07 0.02 3.0 1.364 0.77 0.39 0.17 0.064 0.02 3.6 0.578 0.29 0.13 0.05 0.015 4.0 0.326 0.15 0.06 0.02 4.6 0.138 0.058 0.02 5.0 0.078 0.030 0.01 6.0 0.019 0.006 0.001 7.0 0.004 0.001 8.0 0.001 weighing about 1.5 lb per sq ft, and is equivalent to 0.5 mm of lead. They should be frequently tested for holes and cracks. Lead glass is merely a glass into which lead salts have been introduced. A thickness of 15 to 20 mm has an opacity equivalent of about 2.5 mm of lead. Some of the commercial lead glasses are ^ in. thick and have a protective value equal to ^ their thickness in sheet lead. The glass must be entirely free from air holes and other flaws. For proper protec- tion 2.0 mm lead^equivalent is recommended. Measurement of Lead Equivalent The " lead equivalent " of a given thickness of absorbing material to be used as a protective layer is the ratio of the thickness of lead to the thickness of the material which absorbs a given x-ray beam to the same extent. The protective lead equivalent of gloves, aprons, and other guards is very simple to determine in practice. It can be obtained by means of a lead foil echelon under the actual working conditions to which the operator is subjected. An echelon or step wedge is constructed of layers of plane parallel lead foils so arranged that the edges, each overlapping its neighbor, resemble a flight of stairs. Such a series of equally spaced steps may be built up of 25 layers, each with a thickness of 0.2 mm. The echelon and sample protective material are then placed on a paper-covered photographic 38 BIOPHYSICALLY ACTIVE X-RAYS film of suitable size so that sample and echelon are in contact along their long sides. The whole is exposed to the particular radiation against which the operator wishes to protect himself. The developed photographic image then shows the relative trans- parency of lead and protective material. The photographic density of the image of this protective material is matched against the image of one of the steps of the echelon. A sufficiently accurate estimate of matched density can be obtained by direct observation. The lead layer having the same photographic blackening as the unknown material is chosen as representing its lead equivalent. Concrete as a protective material was investigated by Singer, Taylor, and Charlton [1938], who found that the thickness of a concrete barrier which will provide adequate protection at 400 kv is about 26.5 cm, and the required thickness at 200 kv is 22 cm. The radiation due to scattering is often so widespread that the whole room is filled with it, since it is emitted from floors, walls, table, attached metal parts, and patient. This emission may be a source of great danger in specific x-ray installations and apparatus. The best practice for protection during radiographic and radiotherapeutic technique is un- questionably to enclose the operator and controls in a booth protected by lead or barium plaster. This protection cannot be obtained in fluoroscopic work, and it is here that the most danger arises. A simple test shows the possible extent to which the operator is exposed to x-radia- tion. With patient placed upon an x-ray couch and with undercouch tube box, a fluorescent screen between patient and operator at right angles to the couch top will be found to be brightly illuminated if scatter- ing danger exists. It is very probable that under these circumstances the usual lead equivalent of the operator's apron is insufficient protec- tion. For proper protection 1.5 mm lead equivalent is recommended. It has been suggested that, since the region of the operator so radiated is that of the hypochondrium, it is very probable that the overfrequent occurrence of duodenal ulcer in radiologists may be attributed to the direct effect of radiation upon the mucosa of the duodenum, resulting at first in a generalized inflammation and later in definite ulceration. The United States Department of Commerce, National Bureau of Standards, issues a handbook HB 20, " Protection from X-Rays," price 10 cents, containing the recommendations of a committee representing the International Safety Committee and National Bureau of Standards. Ionization of a Gas by X-Radiation Since, in therapeutic work, speed and comparative ease of operation are essential, ionization measurements are being used as the most direct IONIZATION OF A GAS BY X-RADIATION 39 method of determining the intensity of an x-ray beam under practical conditions. In order to evaluate the intensity of the x-radiation in terms of the ionization produced in a gas, it is necessary to have some understanding of this process. Thus, when a beam of x-rays traverses matter, three things are observed : a certain fraction of the incident energy is trans- mitted; a second fraction of the energy is absorbed with the resulting emission of photoelectrons; a third fraction is scattered in all directions and then absorbed and additional photoelectrons are emitted. The volume ionized by these photoelectrons is much larger than that pene- trated by the primary rays. The total number of ions which the photo- electrons in turn produce in the gas is far greater than their own number. X-ray absorption by the gas is to a great extent, therefore, an indirect process. It is the absorbed portion that is responsible for ionization. Let us first examine an ideal condition: A very large volume of gas, oxygen for example, is contained in a metal vessel, at 760 mm pressure and 0° C. A monochromatic beam of x-radiation of frequency v in passing through the gas will lose part of its energy through absorption. The energy extracted from the beam manifests itself by the appearance of a large number of atoms, ions, and electrons mixed with the gas mole- cules. The electrons are photoelectrons which are emitted by an atom when it absorbs a photon of energy hv. Their kinetic energy of emission is proportional to the frequency of the absorbed photon and is \rrw 2 = hv. Using x-radiation of 1.0- A wavelength, we can calculate the velocity of emission to be of the order of 6.5 X 10 9 cm/sec. When these high-speed photoelectrons traverse the gas they may collide with neighboring molecules and atoms and ionize them, each electron making many collisions. At each collision additional ions are produced, until after frequent collisions the energy is so reduced that the power of ioniz- ation is lost. This is the fundamental energy exchange process involved in ionization of a gas, and it is essentially an indirect process because of the emission of photoelectrons when x-radiation is the instigator of the process. This ionization process is even more complicated when hard x-rays are used. Under these circumstances a quantum of energy hv may collide with an electron, resulting in Compton scattering accompanied by the usual recoil electrons. These recoiling electrons may possess enough kinetic energy to ionize a molecule or atom with which they collide before their available ionization energy is dissipated. X-radia- tion excited at 200 kv or more may produce ionization of greater abun- dance by means of these recoil electrons than through the liberated photo- electrons. A third effect, though a practically negligible one, is the 40 BIOPHYSICALLY ACTIVE X-RAYS possibility of exciting the gas to emit its characteristic radiation through electron collisions. The characteristic radiation emitted under these circumstances, however, is of such long wavelength that it is reabsorbed before traveling very far. Let us next introduce electrodes, in the form of two parallel metal plates, into the gas. Then connect these electrodes to the terminals of a battery having a difference of potential of several hundred volts, and insert a very sensitive ammeter in the circuit. If the beam of x-radia- tion is now passed through that volume of gas lying between the two plates, the ionized condition of the gas manifests itself by a current flowing through the ammeter. Such an ionization current is very small and for best results must be measured by a sensitive electrostatic instru- ment in the form of an electrometer. Potential in volts applied to plates Fig. 1-15. A typical saturation curve obtained by means of an ionization chamber. The extended curve becomes asymptotic to the potential axis. This asymp- totic value is the saturation value I a attained when the applied potential is V a . The variation of the current with successively greater potentials applied to the electrodes is shown in Fig. 1-15. It will be noted that, although the intensity of the x-ray beam is kept constant, the ionization current increases with the voltage applied to the plates, but reaches a flat maximum, where it remains despite further increase in plate voltage. This maximum value to which the current rises is called its " saturation ,; value 7 S . This saturation value of current is attained when all the ions are removed from the gas as fast as they are formed as a result of absorp- tion of energy from the x-ray beam. The removal of all the electrons and ions from the gas is accomplished by applying a minimum voltage V s across the ionization chamber. The minimum voltage is called the saturation voltage, and the resulting ionization current is said to have reached its saturation value. IONIZATION OF A GAS BY X-RADIATION 41 It has been found that several factors such as distance between the plates, their shape, their size, and their enclosure influence the potential at which the saturation current value is attained. For a specific design of apparatus, however, the potential at which saturation takes place depends only on the degree of ionization, which in turn depends on the intensity of the x-radiation. As a practical guide for determining the distance between the electrode plates one must possess some information about the distance high-speed photoelectrons may travel in a gas. TABLE 1-8 Range op High-Speed Electrons Air, p = 1012.9 millibars, t = 0° C kv 10 50 100 500 1000 Range in air, cm Range in water, cm 0.2 5.2 2.3X10" 4 21 1 . 3 X 10~ 2 160 360 0.42 After Kulenkampff [1926]. Kulenkampff 's [1926] experiments have shown that the energy of ionization is nearly independent of the wavelength of the absorbed x-radiation in the region 0.56 to 2.0 A and is equal to 35 volts per ion pair. The range of the electron in its passage through the gas before its ionization ability has been exhausted is shown in Table 1-8. These data also show that, when the energy of a photon of wavelength 0.12 A (100-kv) is absorbed, the emitted electron has a velocity of 16.45 X 10 9 cm/sec and ceases to ionize after having attained a range of 21 cm. These data were taken into consideration in designing the " standard parallel-plate ionization chamber " when the international unit of x-ray quantity, the roentgen (r), was established. A source of error encountered in ionization measurements is attribut- able to the x-radiation striking the walls of the chamber. The radiation falling on the metal produces an emission both of high-speed photo- electrons and of x-radiations characteristic of the metal. These effects, if not eliminated, are measured as part of the ionization recorded by the current-measuring instrument. In order that the ionization current recorded shall be a true measure of the intensity of the x-radiation, three conditions must be fulfilled by an ionization measurement : 1. No radiation must strike the walls of the ionization chamber. 2. Sufficient volume of a gas must be interposed into the path of 42 BIOPHYSICALLY ACTIVE X-RAYS the beam of x-radiation so that all high-speed electrons may have suffi- cient range in which to dissipate their energy. 3. A saturation current value must be utilized to measure the ioniza- tion. International Unit of X-Ray Quantity. The Roentgen In the report of the Committee on the Standardization of X-ray Measurements as published in Radiology, Vol. 22, p. 289, 1934, a defini- tion for a unit effective intensity for biological purpose is set up called the roentgen (" r " unit). It has been accepted in the United States and defined as follows: " The roentgen is the quantity of x-radiation which, when the secondary electrons are fully utilized and the effects of all scattered radiation avoided, produces in 1 cc of atmospheric air at 0° C and 76 cm mercury pressure such a degree of conductivity that 1 esu of charge is measured wider saturation conditions."* What is wanted in roentgen therapy work or in biological reactions to x-radiation is not the energy content of an x-ray beam but rather the amount that will be utilized in the tissue. For example, suppose that one considers the biological effectiveness of two beams of different wave- lengths. The beam having the greater biological effect is not the one with the greater energy content but the one that will lose the greater amount of energy in 1 cc of tissue. If the total energy content were available, to decide which beam was biologically more effective, it would be necessary to know the distributions of energy in each beam for each wavelength and the coefficients of absorption and scattering for each wavelength. Ionization measurements, however, include all these factors, since an electrometer, introduced into the electrical circuit, indicates a current proportional to the energy absorbed. Parallel-Plate Standard Ionization Chamber The Bureau of Standards has constructed a standard ionization cham- ber under the direction of L. S. Taylor [1930]. Figure 1-16 shows the assembled chamber diagrammatically. In the standard chamber the plate spacing P1P2 must be sufficiently great so that if any photoelec- trons strike them their contribution to the ionization is negligibly small. It was found that, for a parallel-plate ionization chamber with a 200-kv * The Fifth International Congress of Radiology held in Chicago [1937] provi- sionally adopted the following definition: " The roentgen shall be the quantity of X- or gamma-radiation such that the associated corpuscular emission per 0.001293 gram of air produces, in air, ions carrying 1 esu of quantity of electricity of either sign." This definition rules out any possible ionization by scattered x-rays, a matter left uncertain in the original definition. PARALLEL-PLATE STANDARD IONIZATION CHAMBER 43 beam passing centrally between the plates, a spacing of 12 cm was satis- factory. Since a guard ring GG surrounds the collector plate P 2 , and since a perfectly parallel electric field across the whole width of the collector electrode P\P 2 was desirable, the widths of the guard plates were made from one and one half to two times the plate spacing. Thus for a plate spacing of 12 cm the guards must be about 20 cm wide. The standard chamber is rather large and unwieldy. In order to reduce the guard-ring dimensions to 5 cm a guard wire system was added. X-radi Ground 1 12 cm T37cm hole To electrometer Ground Fig. 1-16. Diagrammatic section to scale of the National Bureau of Standards guarded-field ionization chamber. For use with 50- to 200-kv x-radiation. Guard wires a, b, c, etc., used to aid in creating a parallel field between electrodes P1P2G. Pi aluminum collector electrode, shielded by guard ring G. The electric field between the plates is rendered parallel by placing ten small aluminum guard wires (a, b, c, • • •) across the ends of the chamber parallel to the electrodes about 1.1 cm apart, except for the center pair which are spaced about 1.6 cm apart. The electrode system is completely surrounded by a lead box. The diaphragm system used with this design is held in place by a lead-lined brass tube which fastens in front of the ionization chamber. The limiting diaphragm has a diameter of 0.8 cm; the inner end is diaphragmed to 1.2 cm. At the back of the chamber the beam passes out through a 3-cm hole covered with a thin sheet of celluloid to eliminate air drafts. X-radiation, in passing through the diaphragms and then between the plates P1P2, produces ions in this space. They are drawn to the plates along the paths of the lines of force. The effective volume of air ionized is that of a cylinder of cross section equal to the area A and length equal to the effective length of the collector electode P 2 . The electric field must also be of sufficient magnitude, as provided by the battery B, so that all the ions are removed before any are lost by recom- 44 BIOPHYSICALLY ACTIVE X-RAYS bination. For this purpose a field strength of about 150 volts/cm is sufficient. Since the degree of ionization is determined by the mass absorption coefficient of x-radiation by the gas, corrections must be made for the temperature and pressure of the air in the chamber, for by definition the air must represent conditions at 0° C and 1012.9 millibars (760 mm) pressure. Under these circumstances, if I is the current, measured by the elec- trometer, in electrostatic units, L the effective length of the collector electrode P2, A the area of the limiting diaphragm in square centimeters, T the absolute temperature, and p the pressure in millimeters of mer- cury, then the intensity of the x-ray beam as measured in roentgens per second is _r_ _7_ T 760 sec ~ L X A ' 273 ' p Thus, if the area A and the length L are each unity, so that we are considering 1 cc of air at T = 273° K, and if p = 760 mm, then r/sec = I. If now 7 is 1 esu of current (1/30,000 microampere), then, since Q = It, r has the dimensions of quantity. The unit of quantity of radiation defined this way is a unit of dosage. In order to get a clearer conception of the magnitude of 1 roentgen, we may choose a technical x-ray tube with glass walls, driven at 100-kv constant potential and 5-ma current. At a distance of 2 meters, using no filter, this tube emits in 1 second about 0.1 r, and at 180 kv its intensity is about 0.2 r/sec. 1 r is equal to 1 esu X 1 second Small Ionization Chambers For therapeutic or biological purposes it is, of course, impracticable to handle such a large instrument as the one discussed above, because it lacks mobility. A portable instrument has been developed with a small ionization chamber, an electrostatic current-measuring device with calibrated scale, and an electrostatic charger for supplying the potential for the saturation current measurements, all housed as a self-contained unit. The ionization chamber may be cylindrical, with the ion collector in the form of a coaxial rod of graphite. The outer shell of the ionization chamber is usually some very thin material comparable to an " air wall," as for instance Bakelite, whose effective atomic number closely approxi- mates that of air.* This outer shell, with its internally conducting layer * Effective atomic number of air is 7.69. VICTOREEN CONDENSER-METER 45 of graphite, is earthed to the apparatus, and the central graphite elec- trode of the " thimble chamber " is connected to a potential recording device usually in the form of an electroscope or string electrometer. Fig. 1-17. The Victoreen condenser r-meter. A portable instrument for measur- ing roentgens per minute. Its detachable chamber tube facilitates measurement directly on the patient and simplifies phantom measurements. (By courtesy of the Victoreen Instrument Company, Cleveland, Ohio.) Figure 1-17 shows one form of r-meter with a thimble chamber of the condenser type, with its string electrometer calibrated in roentgen units. It is a practical dosage instrument having a range from zero to 25 r. Victoreen Condenser-Meter In this type of instrument, shown in detail in Fig. 1-18, the chamber at C is made of any substance having a effective low atomic number (Bakelite). The thin chamber wall with its internally conducting deposit of graphite, Fig. 1-19, constitutes one electrode of the ionization chamber which is grounded to the case. The internal rod electrode C of graphite is connected by a well-shielded conductor to the string elec- trometer F. The string of the electrometer F, its connection, and the graphite electrode are charged by means of a rotating amber wheel A. The position of the deflected (charged) string is viewed through the low-power microscope T. The image of the string is seen in the plane 46 BIOPHYSICALLY ACTIVE X-RAYS of the calibrated transparent scale situated below the eyepiece. This scale is calibrated to read 0-25 r in half r units. It is illuminated from below by the small lamp L connected to a small dry cell. The whole Fig. 1-18. Detailed construction of the Victoreen condenser r-meter. Small thimble ionization chamber attached at C. String electrometer F is charged by frictional electricity from wheel A. Huygens' eyepiece with transparent scale cali- brated in roentgens inserted above T. Lamp L illuminates F and calibrated scale through low-power objective 0. Thimble ionization chamber U — 2.5 cm- Amber Amber ^Graphite Thin Bakelite Fig. 1-19. Removable thimble ionization chamber of the Victoreen condenser r-meter. weighs 10 pounds. Most of the weight is attributable to the lead- shielded construction. After the string electrometer has been charged, to read zero on the r scale, the charged chamber tube (condenser), Fig. 1-19, can be removed and placed in the path of the x-ray beam whose intensity one wishes to measure. The x-ray tube is then activated for 1 minute. The cham- IONIZATION MEASUREMENTS IN A WATER PHANTOM 47 ber tube is then reinserted into its socket. This connects the partly discharged graphite electrode to the electrometer, and the string drops to a point on the r scale indicating directly the roentgens per minute emitted by the tube at the point in space previously occupied by the chamber tube. The ionization produced in the small thimble chamber by the x-radia- tion neutralizes the charge given to the insulated graphite rod, and it is this decrease in charge that is recorded by the electrometer, which has been previously calibrated in r units by means of a standard ionization chamber. Usually the capacitance of these instruments is small. The loss in charge due to the ionization is Q = CV. The capacitance is constant, but the potential of the graphite rod has dropped from V 2 , its charged potential, to P 1} its partially discharged potential state, during the 1-minute exposure to the x-radiation. Since Q = It = C I = 7 (V 2 - Pi) = I t t it follows that the roentgens per minute are proportional only to the change in potential. In order that the above thimble chamber may effectively simulate the standard open-air chamber, it is necessary to construct the walls of this chamber from material of low atomic number so that the so-called " wall effect " of this chamber is equivalent to a comparable mass of air. The x-radiation incident on this chamber wall and internal collector electrode produces, owing to absorption, secondary x-rays and photo- electrons. These contribute to the ionization within the chamber in a manner different from that in the standard open-air chamber. The ionization contributed by these sources depends upon the atomic number of the materials of which wall and electrode are constructed. The walls of the chamber, therefore, must be made out of a material whose effective ionization is that of the free air. Accordingly horn, celluloid, or Bake- lite is used in the construction of these small ionization chambers. Ionization Measurements in a Water Phantom Small ionization chambers such as have been described above are especially well adapted for intensity measurements within a " water phantom." A water phantom consists merely of a water container, constructed to simulate human tissue. A small water-tight ionization chamber may be used to measure the effective penetration of an x-ray beam. According to Kulenkampff [1926], the relative absorption of average 48 BIOPHYSICALLY ACTIVE X-RAYS Narrow beam / X , Surface of water human tissue to water is about 800/830, which is sufficiently near to unity so that, for all purposes, water may be substituted as an absorbing medium for tissue in measurements of intensity at varying situations and distances from an x-ray tube. In order to avoid errors arising from the effects contributed by the walls and bottom of the water container, the phantom is preferably constructed of a material having a scattering power approximating that of water (Quimby [1939]), such as sheets of wax or " presswood." The procedure in determining depth dosage is then as follows. Ionization measurements are made at various depths below the sur- face of the water to determine the variation of intensity with depth. The intensity at a point beneath the surface will also depend upon the horizontal and vertical coordi- nates of the point, since we are dealing with a volume effect*. This intensity will depend on the hard- ness of the radiation, the distance of the x-ray tube above the surface of the water, and the size of the portal of entry. The size of the portal is determined by a lead dia- phragm placed at the surface of the water. The distribution of the intensity with depth for a narrow cone of x-rays is shown in Fig. 1-20. The radiation observed at the points outside the geometric beam, indicated by the dotted lines, is due to scattered radiation produced by the material lying in the path of the primary beam, while the radia- tion intensity inside the geometrical beam is due to unabsorbed radiation reaching that depth plus that due to scattering. Weatherwax [1934] has shown with the aid of water phantoms that when large ports of entry are used 30 to 35 per cent of the intensity just below the surface is due to scattered radiation, coming from the deeper layers of water, while 50 to 60 per cent of the radiation reaching 10-cm depth is made up of scattered radiation. These results show the impossibility of predicting predetermined intensities in irradiated tissue on the basis of absorption alone. 2 4 Distance across beam in cm Fig. 1-20. A narrow beam of x-rays is directed perpendicularly to the water surface. These so-called "Isodose" curves were obtained from a water phan- tom using a thimble chamber ionization meter. (By courtesy of J. L. Weather- wax [1934]). FLUOROSCOPE 49 Fluokoscope A fluoroscope is an instrument used for the roentgenoscopic examina- tion of a patient. Certain minerals have the property of absorbing x-radiation and re-emitting radiant energy of longer wavelengths which may be of sufficient length to be classed as ordinary light. This property we designate as photoluminescence or fluorescence. Stokes established the fact that the wavelength of the emitted energy was always greater than that of the exciting energy. It was through the luminescence of a platinum salt that Rontgen in 1895 discovered x-rays. When light is used as the exciting source of luminescence, the luminous radiations originate in the superficial molec- ular layers and then only on that side of the material turned towards the source of the radiation. If x-radiation, however, is the source of the excitation, fluorescent radiations from all sides of the material may be obtained. The effect may be represented to be a resonance phenomenon between the frequency of vibration of the exciting absorbed radiant energy and the frequency of the electrons revolving about the radiated atoms. .That fluorescence is associated with the property of the periph- eral electrons is supported by the changes in fluorescence due to tem- perature variations and by the presence or absence of fluorescence in chemical combinations of the same elements. BaCl 2 and BaPtCN 4 are fluorescent; BaC0 3 , Ba 2 C0 3 , and Ba 2 FeCN 6 are non-fluorescent. The platinocyanides in general exhibit varying degrees of fluorescence, especially the above-mentioned barium and calcium salts, but the mag- nesium salt is non-fluorescent. TABLE 1-9 Compound Fluorescent Band Wavelength Range A Maximum of Emission Band o at A CaWCV BaPtCN 4 t K 2 PtCN 4 CaPtCN 4 4800-3750 5090-4420 4900-4120 5090-4550 4330 4800 4500 4800 Compounds Colors of Fluorescence CaW04, calcium tungstate (white salt) CdWO*4, cadmium tungstate Zn 2 Si04, zinc silicate (willemite) Cadmium zinc sulfide (silver-activated) Light blue Light blue Green Yellow-green * Used in radiographic intensifying screens. t Used in visual intensifying screens. 50 BIOPHYSICALLY ACTIVE X-RAYS The color of the fluorescence is greatly dependent upon the wavelength of the x-radiation. If too short a wavelength is used, practically no fluorescence occurs. 6600 4000 Violet l 5000 j j 6000 Blue Green Yellow 7000 A Fig. 1-21. These curves show the relative spectral distribution of the emissions from a commercial form of fluoroscopic screen with its maximum in the region of o most sensitive cone vision. Wavelength 5560 A; color yellow-green. The calcium tungstate screen with its blue emission is used for photographic roentgenological examination of body structures. Note the position of its emission spectrum in relation to the curve for sensitivity of high-speed x-ray photographic film. Each type of luminescent compound emits a definite spectral range of fluorescent radiation with one or more spectral bands possessing maxima of rather definite wavelengths. The more common forms of salts that are used in the construction of fluoroscope screens are shown in Table 1-9. The relative position of the fluorescent bands emitted by a commercial fluoroscopic and roentgenographic screen and their relative visibility as compared with the photographic spectral sensitivity of a high-speed x-ray film are shown in Fig. 1-21. From these curves it becomes appar- ent that a fluorescent screen with an emission maximum in the yellow green is eminently well adapted for radioscopic work, and that calcium tungstate with its blue fluorescence is best adapted for photographic work. Application of Fluorescent Screens to Radiology If the luminescent material is applied in a thin layer to a cardboard screen support, and if the mounted compounds emit visible radiations when excited by x-rays, we have a technical radioscopic screen. These APPLICATION OF FLUORESCENT SCREENS 51 screens are used in visual fluoroscopic examinations of body structure. If the mounted compounds emit radiations predominantly in the blue, photographically sensitive wavelength region, then these mounts are designated as intensifying screens and are used for roentgenographic work. In the construction of a screen the compound is carefully sifted for uniformity of fragments. Marcotte (British patent 184,485; 1921) claims that the fluorescence varies with crystal size, first rising to a maximum and then decreasing. He also maintains that the color of the fluorescent light from the tungstates of calcium and cadmium undergoes a parallel variation with crystal size, changing from yellow-green, blue- green, to blue-white, and that ungraded crystals in consequence give a luminosity of mixed color. The proper grade of crystals is mixed with a binder of cellulose, ace- tone, or amyl or methyl acetate (20 per cent); the resulting mass is heated to 45° C and then poured into molds and rolled to a thickness of 0.02 in. These screens are claimed to be inert to soap and alkali. In the trade they are referred to as " washable screens." For radioscopic work the screens must satisfy the following require- ments : 1. Brilliancy. A yellow-green with maximum intensity at 5560 A is recommended. 2. Clearness of definition. Coarse crystals produce great brilliancy but poor definition. Small crystals give less brilliancy and better defini- tion. 3. Contrast. This depends on the use of a fluorescent material of heavy atomic weight, such as BaPtCN 4 , in which the fluorescent atom is the platinum atom and not the barium atom, since absorption takes place in the region of the K and L platinum spectral lines. With the presence of this heavy atom, variations of absorption and fluorescence can be obtained as the hardness of the exciting radiation varies. Addi- tional contrast may be obtained if greenish fluorescent emission screens are used and if the general illumination in the x-ray room is strong red light such as supplied by a bright photographic ruby light bulb. 4. Absence of after-glow. Successive exposures to the exciting x-radiation must be spaced for sufficient time to elapse so that the accom- panying phosphorescence, if present, has had time to decay below the threshold of absolute visibility of the eye. The after-glow phosphores- cence can be controlled by dilution of the sensitive material with insen- sitive crystals, but unfortunately at the expense of its original brilliancy. 5. Protection. The fluoroscopic screen is mounted in a frame cov- ered with a lead glass plate -j^- in. or more in thickness, to protect the 52 BIOPHYSICALLY ACTIVE X-RAYS operator from x-radiations. A fine-focus x-ray tube driven at 88 to 105 kv peak and 3 to 5 ma is usually recommended to give sharp images. Intensifying Screens The blue fluorescing screens are used for roentgenographic work. The x-ray film is pressed in close contact between the active faces of two such screens. X-ray photographic films are coated on both sides (duplitized), thus permitting the photographically active blue fluores- cent emissions from the activated surface of each screen to irradiate the film. Calcium tungstate is nearly universally used in the production of intensifying screens because its region of maximum fluorescence is be- o tween 3570 and 5100 A. As seen in Fig. 1-21 this emission band lies within the spectral photographic-sensitivity region of the x-ray film. The older forms of intensifying screens were merely sheets of card- board coated with the fluorescent material. In the present type of intensifying screens the calcium tungstate is introduced into the cellu- loid binding material itself. This type of screen is washable and flexi- ble, and it can be closely pressed to the photographic material so as to reduce distortion of the photographic image. In the manufacture of intensifying screens the following factors are kept in mind for high-quality work. 1. Speed refers to the relative amount of x-radiation required to produce a developable photographic image when films are used with or without screens. If a given product, distance X milliampere X kilo- volt-peak X time, produces a desired photographic density with no screens, and the same density can be obtained with the aid of screens in one fifth the time, using the same x-ray intensity, then the screens are said to have a speed factor of 5 to 1 at that intensity. A cassette con- taining a good double screen should possess a speed factor from 5 or 6 to 1. The major factor used in controlling the speed of screens is the size of the calcium tungstate crystals. Ordinarily, the larger the crystals (other factors being constant), the faster the screens. The screen speed also varies with the x-ray tube's peak voltage excitation, i.e., effective wavelength; in general, the higher the kilovolt-peak, the faster are the screens. 2. Grain is usually caused by the use of too large crystals of calcium tungstate or the presence of impurities. Screens of very high speed must of necessity be grainy, owing to the large crystals used. A com- promise is always made by the manufacturer in the size of the crystals in order that maximum speed may be obtained with minimum of grain. Too much grain will materially mar the diagnostic value of a film in BIBLIOGRAPHY 53 radiographs of the chest, sinus, mastoid, or small-body localization, or in industrial work where castings and welded seams are examined for blow holes or faults. 3. Lag due to phosphorescence of the crystals after the x-radiation exposure has ceased is caused by impurities in the calcium tungstate. A cassette fitted with a screen possessing lag should be unloaded immedi- ately after an exposure and not reloaded with photographic film until the phosphorescence has entirely disappeared. A screen may be tested for lag as follows : Lay a small piece of lead, a bunch of keys, or some metal object on a cassette containing the screens under examination, but with no film between the screens. Subject the empty cassette with super- imposed opaque metal objects to a moderately long exposure. Take the cassette to the photographic dark room and place a film in the cas- sette. Close the screens over the film and allow it to stand for ten minutes. Develop the film in the normal manner. If any appreciable lag is present, an image of the opaque metal object will be visible on the film. BIBLIOGRAPHY 1913 Coolidge, W. D., Phys. Rev., 2, 409. 1915 Duane, W., and F. L. Hunt, Phys. Rev., 6, 166. 1916 Hull, A. W., Gen. Elec. Rev., 19, 603. 1918 Ulrey, C. T., Phys. Rev., 11, 401. 1921 Hewlett, C. W., Phys. Rev., 17, 284. 1921 Richtmyer, F. K, Phys. Rev., 18, 13. 1922 Duane, W., and K. C. Mazumder, Proc. Natl. Acad. Sci., 8, 45. 1924 Crowther, J. A., Proc. Roy. Soc, B96, 207. 1924 Lindhardt, S. V., Strahlentherapie, 16, 754. 1925 Mutscheller, A., Am. J. Roentgenol., 13, 65. 1925 Regaud, C, Paris Med., 1, 113. 1926 Kulenkampff, H., Ann. Physik, 79, 97. 1926 Packard, C, J. Cancer Research, 10, 319. 1926 Woo, Y. H., Phys. Rev., 28, 426. 1927 Feroux, R., and C. Regaud, Compt. rend., 97, 330. 1927 Leist, M., Strahlentherapie, 24, 268. 1928 Duane, W., Am. J. Roentgenol, 20, 241. 1928 Warren, S. L., Physiol. Rev., 8, 92. 1929 Mayneord, W. V., The Physics of X-Ray Therapy, J. and A. Churchill, London. 1930 Nicholas, W. W., J. Research Natl. Bur. Standards, 5, 843. 1930 Taylor, L. S., J. Research Natl. Bur. Standards, 5, 517. 1930 Taylor, L. S., and G. Singer, /. Research Natl. Bur. Standards, 5, 507. 1930 Wyckoff, R. W. G., /. Exptl. Med., 52, 435. 1933 Zehnder, L., Helv. Phijs. Acta, 6, 608. 1934 Radiological Society of North America, " Report of Committee on Standardization of X-Ray Measurements," Radiology, 22, 289. 54 BIOPHY SIC ALLY ACTIVE X-RAYS 1934 Weatherwax, J. L., Physics of Radiology, Paul B. Hoeber, New York, N.Y. 1935 Stark, J., Physik. Z., 36, 280. 1937 Fifth International Congress of Radiology, Radiology, 29, 634. 1938 Singer, G., L. S. Taylor, and A. L. Charlton, J. Research Natl. Bur. Standards, 21, 783. 1939 Goodspeed, T. H., and F. M. Uber, Bot. Rev., 5, 1. 1939 Quimby, E. H., The Physical Basis of Radiation Therapy, A Syllabus of Lec- tures, Memorial Hospital, New York, New York. 1941 Failla, G., " Biological Effects of Ionizing Radiations," a review, /. Applied Phys., 12, 279. Chapter II APPLIED RADIOACTIVITY At the meeting of the Academy of Science in Paris, on the twenty- fourth of February, 1896, Henri Becquerel read his epoch-making paper in which he announced that compounds of uranium emitted radiations that were able to affect a photographic plate through an envelope opaque to light. Rontgen had just previously announced (1895) that x-rays appeared to originate from those parts of his discharge tubes which fluoresced intensely. Becquerel at this time was investigating the cause of phos- phorescent emissions. He apparently reasoned that a direct connection must exist between the cause of phosphorescence and the x-rays pro- ducing the fluorescence in Rontgen's vacuum tubes, since both fogged a photographic plate enclosed in a light-tight envelope. It was, however, the accidental fogging of a photographic plate by means of a sample of uranium mineral not previously activated to fluorescence by sunlight that led him to the conclusion that fluorescence had nothing to do with the fogging of a covered photographic plate. His conclusion was that some active radiation was emitted spontaneously from the uranium mineral. He coined the word " radioactive " to designate this type of active radiation. After Becquerel 's discovery, numerous substances were examined for similar properties, and as a result the radioactive properties of the uranium-radium, actinium, and thorium families of elements were established. Mme. Curie, for instance, succeeded in isolating minute quantities of two highly radioactive substances from uranium minerals, to which she gave the names polonium and radium. Rutherford, by 1899, through a series of brilliant investigations, conclusively showed that the radiations continuously emitted by uran- ium could be separated into two types. He called the first "alpha rays." These were easily absorbed b}^ a few thin sheets of paper and produced intense ionization in the air through which they passed. The second, a more penetrating type, he called " beta rays." These beta rays have speeds ranging from three to ten times the speed of alpha rays and are able to penetrate several centimeters of air or even 1 mm of aluminum. 55 56 APPLIED RADIOACTIVITY Subsequently Villard (1900) discovered that a third and very pene- trating type of radiation was also associated with beta-ray emissions from uranium minerals, and these were designated by the third letter in the alphabet, namely, " gamma rays." By 1913 Rutherford and Soddy had coordinated the various radio- active processes and proposed an acceptable theory of spontaneous disintegration of their " nuclear atom model " to account for the radio- activity of the atom. They suggested that the nuclear disintegration was explosive and was accompanied by the ejection of an alpha particle or if the explosion resulted in the ejection of a beta particle then the disintegration was accompanied by the emission of a gamma ray. The ejected alpha particle was shown to be a particle of matter comparable to a helium atom which had lost its two planetary electrons, i.e., a helium nucleus. The beta particles were found to be high-speed nega- tive electrons, and the accompanying gamma-ray emission was dis- covered to have the properties of x-radiation of exceptionally short wavelength. As the result of the explosive emission of an alpha particle, any atom drops in the scale of atomic numbers by two units and there is a loss in atomic weight equal to the atomic weight of a helium nucleus. Since the helium nucleus is equal to four mass units, its loss will reduce the mass of the parent atom by four units. This residue is a new, but less massive, atom having physical and chemical properties different from its parent atom. Disintegration of Radium Radioactive changes are accompanied by the emission of alpha or beta particles. They are never emitted simultaneously. All radium salts actively emit alpha and beta particles with the accompanying gamma radiations. Usually gamma radiations accompany beta-particle ejec- tions. Sometimes weak gamma radiations also accompany alpha- particle emissions. The radium atom is an unstable complex structure. Its atomic weight is 226, and its atomic number is 88. Its compact unstable mas- sive nucleus can be represented pictorially as surrounded by 88 planetary electrons. We can imagine this nucleus undergoing a sudden explosive readjustment with the emission of an alpha particle of characteristic speed. The residue is the radon atom of atomic weight 222. It is a radioactive inert gas sometimes called radium emanation. This and the subsequent transformations are shown schematically in Fig. II— 1; all but the last atoms contain radioactive nuclei. A radio- DISINTEGRATION OF RADIUM 57 active nucleus is one which spontaneously changes itself into another nucleus of another element by emitting a charged particle. Radon gas is a short-lived residue which rapidly disintegrates with the liberation of alpha particles and changes into a solid, radium A. In turn, this element breaks up into radium B in an analogous way. These and subsequent decomposition products are found adhering to the walls of a vessel which originally contained radon gas and which make these surfaces radioactive. 88 Atomic number c trnnc Very strong -ybtrong 7 Includes groups 214 & 210 214 214 \ 0.04%\ a. 214 \ y \ y ""* ^7 Polonium 84 Weak /3 -/RaD V/*-/ RaEV/?{ RaF 210 210 n Stable lead RaG isotope ^ J 4 206 Natural alpha particle = 2 He .Charge +2, mass units 4. Fig. II— 1. Radium and its family of products. Radium B, however, undergoes a different type of change, one accom- panied by the emission of a gamma radiation and of a high-speed beta particle. Since the gamma ray is a short-wave x-radiation, its emission results in no appreciable loss in mass. The beta particle is a high-speed negative electron. The ejection of such an electron is accompanied by an inappreciable loss in atomic mass; the new element, radium C, is therefore considered as having the same atomic mass as its parent atom radium B. Biophysically speaking, this and the next group of radioactive nuclear 58 APPLIED RADIOACTIVITY changes are the most important links in this chain of reactions. We depend upon the characteristic gamma radiations at this stage of the degenerating process to furnish the necessary effective, deeply pene- trating radiations used in gamma-radiation therapy. The schematic disintegration diagram indicates that radium C may undergo disintegration in either of two ways. By the emission of an alpha particle it degenerates to RaC", or by the emission of a beta parti- cle and a gamma ray it changes to radium C. As the alpha-ray process of degeneration occurs in only 0.04 per cent of the atoms present, for all practical purposes this transformation product is negligible. The other 99.96 per cent of the radium C atoms participating undergo a high-speed beta-particle ejection with its accompanying gamma radiation. The resulting product is radium C, of atomic weight 214. Radium C in turn degenerates with the emission of an alpha particle to radium D. By successive steps radium D degenerates into radium G, a stable isotope of lead of atomic weight 206, which is the end of the uranium-radium chain. Decay Constant In the process of disintegration of a radioactive element, we are in reality observing only the statistical nature of the disintegration of a large group of atoms, in which, on the average, the number of atoms that are disintegrating each second is a constant fraction of those present at any given moment. For instance, if we isolate 10,000 atoms which possess the property of disintegration at the rate of 2 per cent per second, then during the first second we would lose 200 atoms, leaving 9800. During the second second we would lose 2 per cent of 9800 or 196, leaving 9604. In the next second we again lose 2 per cent of these, etc. We are here dealing with the exponential law of depreciation. Thus, if we let N be the number of atoms which survive after a time t, and No the number originally present at time zero, then the above exponential law of depreciation of number is expressed thus : .— xt N = N e where X is the constant indicating the rate of disintegration of the atoms. The radioactive decay constant X is defined as that proportion of active matter which undergoes change each second. The larger the value of this constant, the greater will be the activity of disintegration. The magnitude of the decay constant of each of the therapeutically valuable radioactive atoms is shown in Table II— 1. DECAY CONSTANT 59 TABLE II-l Substance Decay Constant X per sec Half-Value Period or Half-Life Amount in Milli- grams in Equilib- rium with 1 Gram of Radium Ra 1.38 X 10 -11 1600 yr 1.0000 Radon 2.097 X 10~ 6 3.825 days 0.00625 RaA 3.79 X 10~ 3 3.05 min 0.0000034 RaB 4.31 X 10~ 4 26.8 min 0.000030 RaC 5.86 x ltr 4 19.7 min 0.000022 RaC 10 6 10 -6 sec Negligible RaC" 8.75 X 10~ 3 1 . 32 min 0.0000015 RaD 1.0 X io~ 9 22 yr RaE 1.61 X 10~ 6 5 . days 0.0081 RaF 5.73 X 10" 8 140 days 0.22 (polonium) RaG Stable The decay constant (X) for radium is 1.38 X 10 _u per sec. This means that, in a group of 10 11 atoms, 1.38 on the average disintegrate per second. One gram of radium contains 6.07 X 10 23 /226, or 26.8 X 10 20 atoms. Then 26.8 X 10 20 X 1.38 X KT 11 or 3.7 X 10 10 atoms in each gram of radium disintegrate per second. The decay constant for radon is 2.097 X 10 -6 per sec, which means that approximately 2 atoms in every million disintegrate per second. In 1 gram of radon gas, 570,000 X 10 10 atoms disintegrate per second, a rate which indicates that radon is more than 150,000 times as active as an equal mass of radium. Suppose that we have 1000 relative units of radon and 1 hour later we wish to use this material; how many units will still be available? The following formula can be used to calculate N, the number of units available after 1 hour for which t = 3600 sec. N = N e- Xt N = 1000e _2097xl0_ x3600 loge (l55>. log in )- \1000/ -75.06 X 10 -4 75.06 X 10" 4 2.3026 = -32.5 X 10 ,-4 N = 993 60 APPLIED RADIOACTIVITY Half-Life The number of seconds required for the radioactivity of a substance to fall to half its original value is called its half-life or half-value period. This value of t may be obtained by setting N 2 Then log e 2 = X* or logio 2 Xt 2.3026 To illustrate what is meant by half-life of a radioactive substance one may use that therapeutically valuable radioactive gas radon. It disintegrates in a typical way by the emission of an alpha particle. Its decay constant is 2.097 X 10 -6 per sec. Figure II-2 shows graphically 100 90 80 t>0 .= 70 C § 60 ■2 50 = 40 o o 2 30 20 10 S, N =ioo ' ) I I I ' - \ Radon decay '- _o_Ny Half-value period or half-life 2 K i 1 _L. . ^SfJWerage life 1 1 1- I I 4 ' >>,, ^ I I 3.825 | 5.52 [2x3.825 I i + i I 1 6 8 Time in days 10 12 14 Fig. II-2. The percentage of radon remaining after any time recorded in days. A'o is taken as an arbitrary activity of 100 units. how radon disintegrates in the course of 14 days. Note that half of the original number N remains after 3.825 days, and one-fourth after 7.65 days. It is simpler to calculate the number of days it takes for the original amount to reduce to half-value, by using the above decay RADIOACTIVE EQUILIBRIUM 61 law. For X substitute the value 2.097 X 10 -6 , and solve for t. . 2.097 X 10~ 6 * login 2 = 6 2.3026 t = 3.825 days The quantity 1/X is that average time in seconds in which the number of original atoms is reduced to 1/e ( = 0.36788) of their original count. This is called the average lije of a radioactive substance, even though some of its atoms may exist for only a short time and others for a long time. The average life of radon is 1/X = 1/(2.097 X 10~ 6 ) sec = 476,871 sec = 5.52 days. Radioactive Equilibrium The following example illustrates what is meant by an equilibrium state. Suppose that you are given a closed vessel containing many millions of microorganisms. At the close of each day you are asked to investigate the number of deaths and the number of births. Suppose that at the end of 30 days you find that the birth rate equals the death rate. You have found that an equilibrium state has been established if from then on the death rate equals the birth rate. Similarly the population content of 1 gram of freshly prepared radium sulphate is about 26.8 X 10 20 molecules. In the first day (about one- millionth of these) 3.2 X 10 15 of the radium atoms will disintegrate to form the atoms of the radon gas. As soon as some radon atoms are formed, however, some of them will disintegrate, so that by the end of 3.825 days half of them have disintegrated. In this process about 16 per cent of the radon atoms disintegrate per day. Hence at the end of the first day 16 per cent of 3.2 X 10 15 atoms have disintegrated, leaving 2.7 X 10 15 radon atoms. By the end of the second day 3.2 X 10 15 4- 2.7 X 10 15 , or 5.9 X 10 15 , are present, of which 0.9 X 10 15 disinte- grate, leaving 5 X 10 15 atoms. By the end of the third day there are 8.2 X 10 15 atoms, of which 1.3 X 10 15 disintegrate. At the end of about 30 days nearly as many radon atoms are disintegrating as are supplied by the disintegrating radium atoms. Radioactive equilibrium has then been established between radium and radon. The maximum amount of radon that can accumulate from a given quantity of radium under these circumstances is called its equilibrium amount. Table II— 1 shows the various amounts of the radioactive substances in equilibrium with 1 mg of radium. Figure II— 3 shows the increase in number of radon atoms, despite their decomposition in the presence of the more slowly decomposing 62 APPLIED RADIOACTIVITY radium, during the course of 35 days. Note particularly how the growth of radon conforms to an exponential rise in time, and that for all practi- cal purposes it attains its maximum value in about 30 days. A mathematical analysis of radon equilibrating in the presence of radium leads to the following general law N = N max (1 - e~^ ) where iV max = (Xi/X 2 )iVo- Here N is the number of radium atoms originally present, Xi the decay constant of radium, and X 2 the decay constant of radon. Since the radium atom has a very long life compared to the radon atom (X 2 > Xi ) and no radon is present initially, the above expression describes the results accurately. 15 20 Time in days Fig. II-3. The net increase in number of radon atoms in the presence of radium. Despite the rapid decay, radon is formed at the same rate as it disintegrates at about the thirtieth day. After this ./Vmax maintains its constant value. Radon, when used for therapeutic purposes, is pumped off the radium and sealed in small capsules. Initially such a capsule contains only radon gas. Radon progressively disintegrates, and the successive products of decay are RaA, RaB, RaC, etc. The state of equilibrium between radon and its products is reached in about 4 hours. The rate of decay of radon cannot be neglected in calculating the equilibrium of the end products despite its rapid decay. The relative number of these atoms is therefore different when in equilibrium with radon than when in equilibrium with radium. This type of equilibrium is referred to as " transient." In transient equilibrium the products RaA, RaB, NATURE OF THE RADIATIONS 63 and RaC (in the presence of radon) are about 0.05 per cent, 0.5 per cent, and 1.0 per cent greater, respectively, than those corresponding with the equilibrium mixture values of radium shown in Table II— 1. -L I ^.-.bt-.Y-radiation '•::',;c:'::^ Nature of the Radiations A sample of radium salt, after radioactive equilibrium has been at- tained, will emit alpha rays, beta rays, and gamma radiation. The alpha rays are rather massive particles carrying a positive charge of electricity ; the beta rays are negative electrons with rather large velocities of ejec- tion. To demonstrate these properties put a small sample of radium salt in the bottom of a cylindrical hole in a lead block and then place the block so that the vertically emitted rays pass at right angles through an intense magnetic field furnished by a powerful electromagnet, as shown in Fig. II-4. The magnetic lines of force are represented as entering into and per- pendicular to the plane of the paper. It is found that the beta particles are deflected to the right and the alpha particles to the left. The beta particles are observed to move on the arc of a circle while they are in the magnetic field. Their deflection to the right proves them to be negatively charged. The alpha parti- cles are observed to undergo a similar deflection to the left; hence they are posi- tively charged. The rela- tive curvature of the paths depends on their relative values of e/m and velocity, such that Hev = mv 2 /R. Here H is the intensity of the magnetic field, and R the radius of curvature of the circular paths. The vertically emitted group of rays, called gamma radiations, suffer no deflection. This lack of deflection shows that they carry no net charge. They have been identified as radiant energy comparable to very short-wave x-rays. Fig. II-4. Depicting the deflection of alpha and beta rays in a uniform magnetic field, set per- pendicularly to the paper and directed downward. Gamma rays not deflectable. 64 APPLIED RADIOACTIVITY Alpha Rays Alpha particles are ejected as if they were high-velocity projectiles originating in the nucleus. They are doubly charged positive frag- ments of matter and have a structure like that of the helium nucleus. On the average they have a velocity equal to about one-twentieth the velocity of light. They are able to penetrate about 6.97 cm of air at standard atmospheric pressure before dissipating their energy. A single particle during its passage through air produces as many as 150,000 ions by collision. TABLE II-2 Ranges in Solid Elements as Compared with Water and Mica Alpha particles of RaC. Units of range are 10~ 4 cm. Element Al Ag Ni Au Pt Water Range 40.6 19.2 18.4 14.0 12.8 60.0 Mica 36 TABLE II-3 Beta-Ray Absorption Coefficients (m) in Aluminum Elements RaB RaC + RaC" RaD M cm -1 890 80 13 50 5500 Velocity, 10 10 cm/sec 1 . 08-2 .47 1 . 14-2 .96 . 96-1 . 20 RaE 45.5 2.05-2.84 Velocity of light is 3 X 10 10 cm/sec. The number of alpha particles emitted from 1 gram of pure radium per second is 3.7 X 10 10 . When radium is in radioactive equilibrium with its products, the same number of particles is also emitted per second by each of its important alpha rayers, viz., Rn, RaA, RaC', and RaF. Consequently, the number of alpha particles from 1 gram of radium in radioactive equilibrium is 5 X 3.7 X 10 10 , or 18.5 X 10 10 . We are now in a position to appreciate the terrific bombardment that the walls of a glass ampule are subjected to when they enclose as little as a milligram of radium salt. The ranges in some metals used as alpha-ray filters are listed in Table II-2. These data show what thickness of metallic capsules can be used for radium containers which will completely absorb the alpha particles. The range in mica is about 0.036 mm. Since mica and glass may be considered comparable it can be appreciated why a glass radium needle with 0.04-mm wall thickness is sufficient to absorb all the alpha particles. An aluminum filter 0.04 mm thick is sufficient protection against the physiological effects of alpha particles when open radium applicators are used in dermatology. BETA-RAY DISTRIBUTION OF ENERGY 65 Beta Rays The beta rays from the disintegration products of radium consist of streams of negative electrons possessing a wide range of velocities, the swiftest having a velocity nearly equal to that of light. RaC is out- standing in this respect, as seen in Table II— 3. One naturally is curious about the origin of such very high-speed electrons. It has been determined experimentally that, on the average, for every pair of disintegrating RaB and RaC atoms, 2.3 electrons are emitted, about 1.25 coming from RaB and 1.05 from RaC. These electrons may be either nuclear electrons or planetary electrons. The accompanying gamma rays have their origin in the nucleus. The number of electrons in excess of the one coming from the nucleus are planetary electrons, emitted as the result of the absorption of the gamma rays as they pass through the planetary electrons, and are referred to as photoelectrons. RaE emits only extremely weak gamma radiation. No photoelectrons are mixed in with the disintegration electrons which come from the nucleus. Emeleus [1924] actually found that, in the disintegration of each RaE atom, only one electron was emitted. RaD emits statistically about 1.5 electrons at each atomic disinte- gration. It was found that two of every three electrons are slow dis- integration electrons, and the third is emitted with high speed because of the internal conversion of the gamma radiation into electron emis- sions. Beta-Ray Distribution of Energy The distribution of energy among the emitted beta rays is determined by their electron spectra, obtained by means of their relative deflections by a magnetic field. As shown in Fig. II— 5, the strong magnetic field bends the negative electrons into arcs of circles. Their radii of curva- ture are proportional to their momentum (mv) of emission. Chadwick as early as 1914 showed that the magnetic field acted as a lens to focus all those electrons leaving the source with the same velocity. Advan- tage is taken of this fact in the design of a device for measuring the velocity distribution of a source of beta-ray electrons. The source, in the form of some radioactive material deposited on a fine wire, is fixed at S, Fig. II-5, perpendicular to the plane of the diagram. A wide slit is placed at A. Beyond, in the same plane with the slit is placed a photographic plate. The whole is contained in a light-tight evacuated box and placed between the poles of an electromagnet, with its field perpendicular to the plane of the paper. The magnetic field intensity 66 APPLIED RADIOACTIVITY H is varied by the current exciting the pole pieces of the electromagnet. The result is that electrons of the same velocity, though shot up at different angles, will describe circles of radius R, and converge to a line focus on the photographic plate. Groups of low-velocity electrons iffiN Vacuum pump ' ' l> I j /' y rays | I ( 1 .',' ll" >l" I II //, ^Z-Z^. /3rays ^\ Photographic plate •::::,\\ TJ Fig. II-5. A form of beta-ray spectrograph. This shows how the magnetic field, perpendicular to the plane of the paper, acts as a lens to focus the electrons. First used by Chadwick in 1914. converge nearer to the source than the high-velocity groups. For low- speed electrons the relative curvature of path is determined by Hev = m v 2 /R. For the very high-speed electrons the relativity mass of the electron must be used, so that HR = ?)IqC v/c e Vl - v 2 /& where ra is the rest mass of the electron of charge e and velocity v, and c is the velocity of light. The photographic images of the radiative source are lines lying parallel to the linear source of the beta rays. The line images due to the higher-velocity electrons are found farther from the slit. If radon had been used as the beta-ray source, the developed photographic plate would have shown a composite effect, a general background darkening with superimposed sharp linear images. A photometric analysis of such a plate is shown diagrammatically in Fig. II-6. The line images appear as humps on the curve. These are homogeneous velocity groups of emission. This curve indicates that theirs is a relatively small effect as compared to the numbers producing the continuous electron spec- trum. The latter produce the general background darkening of the photographic plate and are represented by the area under the broken curve. BETA-RAY DISTRIBUTION OF ENERGY 67 01 # 1000 2000 3000 4000 Values of Hr ~ velocity 5000 Fig. II-6. This is the beta-ray spectrum of radium B originally obtained by R. W. Gurney [1925]. It shows the velocity distribution of the beta rays from a radon source. The humps are homogeneous velocity groups superimposed on the general electron emission limited by the broken curve. The number of electrons composing the humps are small compared with those in the continuous spectrum, so that one practically always deals with a decidedly non-homogeneous distribution of velocities. TABLE II-4 Prominent Homogeneous Beta-Ray Velocity Groups Relative Intensity Energy in Kilovolts 17 11 80 91 100 16 7.6 2.4 4.7 50 20 10 Radium B Radium C Radium D 37.25 49.83 152.9 206.7 263.8 337.9 519.9 1037 1334 30.9 43.3 46.1 The relative intensity of these radiations is very small as compared with the general total back- ground radiation. Composite results of Ellis and Skinner, Proc. Roy. Soc, A 105, 60, 1924; Ellis and Astor, ibid., 119, 645, 192S; Ellis and Wooster, ibid., 114, 276, 1927; Ellis and Astor, ibid., 129, 180, 1930. 68 APPLIED RADIOACTIVITY The beta-ray electron spectrum, therefore, may be divided into two parts: (1) the disintegration electrons forming the continuous velocity spectrum, and (2) the photoelectrons, the characteristic line spectral images composing the homogeneous velocity groups. Figure 1 1-7 shows the relative intensities of the continuous beta-ray spectral velocity distributions emitted by RaB, RaC, and RaE without the superimposed photoelectric emissions. They all possess different but definite upper limits of velocity. These upper limits can also be J2 (D I \RaB ' jS-ray spectra / / \\ RaE r 1 1 \ l >*. l i I 2- 8 10 12 Energy^) Volts 14 16 18x10 Fig. II-7. These are the beta-ray spectra of RaB, RaE, and RaC with homo- geneous velocity groups omitted. RaB and RaC are from data by Gurney [1925], and RaE is reduced to the same scale from data by Madgwick [1927]. shown to exist by absorption methods. If aluminum is used as the absorber of the beta rays from RaE, it is found that a layer of aluminum 1.7 mm thick must be used to absorb the electrons having the highest velocity. The highest velocity electron emitted by RaC are stopped by 5 mm of aluminum. Radium B (Table 1 1-4) shows prominent photoelectric emission groups in the neighborhood of 263 kv; the very simple electron spectrum of RaD possesses a moderately prominent emission of electrons at 31 kv. For therapeutic use these homogeneous velocity groups are not sepa- rated from the continuous velocity distribution groups, but they must be kept in mind when beta-ray filters are used. Absorption of Beta Rays A thin-walled glass tube of radium salt or radon gas will emit beta rays and gamma radiations due to the decay products. The beta-ray ABSORPTION OF BETA RAYS 69 emission, as shown above, is not a homogeneous velocity group. If the electronic emission were, for simplicity's sake, confined to a narrow cylindrical pencil and were allowed to impinge normally on a metal filter, the electrons would be subject to so much scattering in their pas- sage through the metal that some of them would be found to be re- emitted on the incident side of the filter. Even under these simplified conditions it would be found that an original parallel beam had become diffused very rapidly. TABLE II-5 Relative Amounts of Radiation Transmitted by Various Metal Filters Thickness Amount of Radiation Relative to Amount Composition of Radiation Metal mm through . 5 mm Pt % Beta % Gamma Considered 100 Brass 0.5 160 33 67 1.0 111 8 92 2.0 100 100 3.0 95 100 4.0 92 100 Silver 0.5 128 17 83 1.0 103 100 2.0 94 100 3.0 90 100 Lead 0.5 118 12 88 1.0 97 100 2.0 88 100 3.0 83 100 Gold or 0.2 135 22 78 platinum 0.3 111 9 91 0.5 100 100 1.0 88 100 1.5 82 100 2.0 78 100 3.0 73 100 By Courtesy of E. H. Quimby, Memorial Hospital, New York. The absorption laws governing the loss of electrons, possessing random velocities, as they pass through matter are very complicated. For all practical therapeutic purposes the electrons which pass through a filter- ing metal can be considered as suffering an exponential reduction in number. 70 APPLIED RADIOACTIVITY When a flat radium salt " applicator " possessing a cover impervious to alpha rays is applied to the skin under clinical conditions, it is of importance to know the filter thickness that must be used to remove all the low-velocity beta particles in order to control the therapeutic effects. It has been found that 1 mm of aluminum reduces a 100 per cent electron intensity to 1.3 per cent, indicating that probably only the high-velocity electrons from RaB and RaC are coming through. The data of Table II-5 obtained by E. H. Quimby [1939] show that for all practical purposes a 2-mm brass, 1.0-mm silver, 1.0-mm lead, 0.5-mm gold, or 0.5-mm platinum filter will remove all the beta rays emitted by a radium source. Energy of Gamma Radiations Radium will attain its radioactive equilibrium with its products in about one month. Under these conditions it will emit about 88.8 per cent of the radioactive energy as alpha rays, 4.5 per cent as beta rays, and 6.7 per cent as gamma radiation. The short-wavelength gamma radiation is primarily due to the disintegration of RaB and RaC. Of these two, the gamma radiations from RaB are much more easily ab- sorbed than those from RaC. The gamma radiations from RaD are also comparatively soft, and moderate filtering removes them completely. TABLE II-6 Gamma Rays from RaB — > RaC. Most Intense Radiations Energy in Kilovolts Relative Intensity Wavelengths 10 8 cm 53.8 243 297 ," ■ 354 53 0.22 25 0.050 30 0.041 40 0.035 Gamma Rays from RaC -* RaC, RaC -> RaC", RaC -> RaD, and RaC" — RaD 612 941 1130 1426 30 0.020 7 0.013 13 0.0109 16 0.0086 Composite results from Ellis and Aston, Proc. Roy. Soc, A 129, 180, 1930. • Gamma radiations are comparable to x-rays but of shorter wavelength. Table II-6 shows some of their wavelengths and their equivalent ener- gies in electron volts. They range from 50 to 1400 kv. An x-ray tube ABSORPTION OF GAMMA RADIATION BY MATTER 71 driven at 1.5 million volts difference of potential will emit wavelengths approaching the shortest wavelengths of the gamma radiations emitted by RaC. Absorption of Gamma Radiation by Matter The reduction in intensity of gamma radiations by an absorbing sub- stance takes place, like the reduction of intensity of x-rays, in two dis- tinct ways : by true absorption and by scattering. In true absorption the energy of the gamma beam is completely absorbed by an atomic structure, and the result is emission of planetar}^ electrons (photoelectric emission). The scattering loss takes place as if the gamma radiation were composed of photons or bundles of energy. Photons colliding with electrons in the filter material communicate energy to the electrons, so that the electrons are set in motion. The penetrating photon is deflected by the electron from its path (see Comp- ton effect) after collision, and hence scattered. The scattered photon in this act, having lost some of its energy by the collision, moves off with less energy content. The number of photons emitted by radioactive material used in radiotherapy that suffer no energy loss in this scattering process is inappreciable. When gamma radiation of very short wavelength (hard gamma rays) passes through low-atomic-weight filters composed of aluminum, water, or tissue, the reduction in intensity of the beam is almost entirely due to scattering. This explains the comparative loss in different kinds of tissue as shown in Table II— 7. As the atomic number of the absorber increases, the loss due to the photoelectric process becomes more pro- nounced. TABLE II-7 Absorption of Gamma Rays by Various Kinds of Beef Tissue Type of Tissue Per Cent of Gamma Rays Absorbed in First Centimeter Solid bone 13.0 Porous bone 7.5 Liver 7.4 Spleen 7.3 Muscle 6.9 Brain 6.6 Fat 6.5 Lung 4.5 By Courtesy of G. Failla [1921]. 72 APPLIED RADIOACTIVITY TABLE II-8 Absorption by Lead of Gamma Rays from Radium C Ionization Thickness of Lead Arbitrary I 0.3 100 1.0* 61.6 2.0 33.1 3.0 19.9 4.0 11.7 5.0 7.07 6.0 4.26 7.0 2.57 8.0 1.62 9.0 1.00 10.0 0.63 15.0 0.07 20.0 0.01 * A 1 . 0-cm lead filter removes all beta raya TABLE II-9 Coefficients of Absorption Gamma radiation Value of m after having traversed an 8-mm lead fore-filter Filter 0-2.5 mm 2.5-5.0 mm 5-10 mm 10-15 mm Platinum 1.17 .... .... Lead 0.64 0.56 0.48 0.44 Zinc 0.28 0.27 0.25 0.27 Aluminum 0.11 0.11 0.11 0.11 Glass 0.087 0.087 0.087 0.087 Water 0.34 0.34 0.34 0.34 For gamma as well as x-rays the photoelectric absorption in high- atomic-number elements is approximately proportional to the fourth power of the atomic number of the filter and to the cube of the wave- length of the incident radiation. The total absorption coefficient n is therefore made up of two parts, the coefficient of photoelectric absorp- tion t, plus the coefficient of diffusion or scattering 4 contains 702 mg Ra element Definition of Curie One curie is defined as the amount of radon in equilibrium with 1 gram of radium. The amount in equilibrium with 1 mg is 1 millicurie (1 mc). The number of atoms in 1 curie is 1.71 X 10 16 . The volume of radon in equilibrium with 1 gram of radium is 0.65 cu mm (6.5 X 10 -6 gram). TABLE 11-13 Transient Activity of Radon Initial increase in beta- and gamma-ray activity in a radon preparation, due to accumulation of RaA, RaB, and RaC Time Transient Activity Hours Minutes Maximum equals 100 10 3.9 20 11.9 30 21.8 40 32.1 50 42.0 1 51.1 1 30 72.3 2 85.2 2 30 92.3 3 97.0 3 30 About 100 RADON EXTRACTION PLANTS 77 One gram of radium will produce 166 mc of radon daily. This amount will reduce by radioactive disintegration to 138.5 mc by the end of the first day and will disintegrate to 115.5 mc by the end of the second day. In the meantime, more radon will have been generated and will decom- pose in the same way, so that by the end of a month there will be avail- able 995 mc in equilibrium with 1 gram of radium. For all practical purposes this amount is taken as 1000 mc, although 60 days are required for radium to come into complete equilibrium with all its disintegrative products. A sample of the gas removed from the radium salt and concentrated into a capillary tube by pressure may have a " strength " as great as 100 mc. Owing to its disintegration, it will fall to a strength of 83.4 mc at the end of 1 day, to 69.6 mc at the end of 2 days, until at the end of 30 days its strength is only 0.45 mc. For its detailed change in strength refer to Table 11-14. Radon Extraction Plants Radon extraction and purification plants of a semi-automatic design were introduced in America by the late Professor William Duane of Harvard, and subsequently modified by Failla of the Memorial Hospital, New York City. p~H|,|-..,h J Switch I — Lead shield Battery-rheostat Copper gauze cylinder Heated chromel or tungsten wire Gold capillary tube Fig. II-8. A semi-diagrammatic representation of a radon-extraction plant. A typical installation may use 1 or more grams of radium bromide dissolved in dilute hydrochloric acid. It is usually divided into two portions of about 100 cc each and stored in 200-cc long-necked flasks. The flasks are joined at the top in such a way (Fig. II-8) that the accu- mulated gases can be led off through a continuous train of glass tubing 78 APPLIED RADIOACTIVITY through the top of a fireproof lead-lined safe to the purification appara- tus. The safe may be 32 by 18 by 16 in., with 5-in. walls. The whole purification plant is first well exhausted by a quick-action vacuum pump. Then the radon gas accumulates over the solutions and spreads into the lead-covered glass chamber S. The mercury trap T\ must be lowered so as to allow the gas to fill the chambers A, B, C, D. When T\ is raised the gas in A is pushed into the purification chambers B, C, D. Here the accumulated and compressed gases are passed over caustic potash to remove carbon dioxide. The chamber C contains a heated tungsten filament surrounded by a well-oxidized copper gauze. When the gases pass through this chamber the oxygen and hydrogen combine to form water vapor, which is removed by the phosphorus pentoxide tube D. This purification process takes about one-half hour. The purified gas is then allowed to expand into trap T 2 , from where it is compressed into the capillary tubes. One gram of radium in solution produces about 15 cc of mixed gas per day. It is well known that the alpha rays rapidly decompose water. As a result the gas contains about 1 part radon to 2500 parts of hydrogen and oxygen. The hydrogen and oxygen must be removed in order to provide a sufficiently active radon supply to be compressed into the capillary tubes. Formerly, when the capillary tubes were made of glass, the wall thick- ness was 0.5 mm, and the tubes were placed in hollow silver needles for radiation therapy. The present practice is to compress the radon into gold capillary tubing without glass lining. The gold tubes, cut into 4- or 5-mm sections, are the " seeds " used in radium therapy. Their external diameter is about 0.75 mm with wall thickness 0.3 mm. Plati- num seeds from 5 to 6 mm long are also employed; their radioactive strength varies from 1 to 5 mc. These seeds are standardized three and a half hours after they have been sealed off at the radon plant. In this time the decomposition products RaA, RaB, and RaC have reached their " transient " equilib- rium (Table 11-13) with the radon, after which the activity decays with the decay period characteristic of radon. The activity of the seeds follows the usual decay law (see Table 11-14), decreasing in activ- ity 22.08 per cent by the end of the first day and dropping to half strength in 3.825 days. A common hospital practice is to have 20 to 50 seeds available and to calibrate them daily when not in use. Radon Seed Implants If the seed is introduced into an incision in tissue, when its calibrated strength is 1 mc, then Table 11-14 can be consulted to determine its RADON SEED IMPLANTS 79 strength after any subsequent time, and the column labeled millicurie- hours (mc-hr) indicates the percentage of the radiation used up to the time of removal of the seed. If the seed is 4 days old, it will possess a potential activity of 48.42 per cent of its original maximum strength of 1 mc. In this time interval it has emitted 68.60 mc-hr. If this seed is used during the next 6 days on a second patient, its activity will reduce to 16.32 per cent of its initial value, and during these 6 days it has de- livered 42.8 mc-hr to the second patient. TABLE 11-14 Decay of Radon The number of millicuries (mc) available after any lapse of time if the original strength at time zero is 1 mc Time Day Hours Per Cent Remaining Mc-hr Used 100 . 00 0.00 1 99.25 1.00 2 98.50 1.99 3 97.76 2.98 4 97.02 3.96 5 96.29 4.94 10 92.72 9.62 15 89.29 14.25 20 85.98 18.64 83.42 22.08 5 80.32 26.18 10 77.35 30.15 15 74.48 33.98 20 71.72 37.60 2 69.59 40.45 2 10 64.52 47.12 2 20 59.82 53.42 3 58.05 55.80 4 48.42 68.60 5 40.43 79.30 6 33.70 88.40 7 28.11 95.78 8 23.45 102.1 9 19.56 107.0 10 16.32 111.4 15 6.59 124.4 20 2.66 129.4 25 1.1 131.8 30 0.4 132.7 Complete 0.0 133.3 80 APPLIED RADIOACTIVITY The quantity or intensity of the radiation delivered by a seed is ex- pressed in either of two ways. The fraction of the original activity used is stated in terms of the percentage of millicuries remaining in the seed, or the amount of radon disintegrating during tissue exposure is given as millicurie-hours delivered. Recently, the second notation is being used in America to denote the quantity of radiation delivered interstitially. 360 11 1 1 II 1 340 - - 320 - - 300 - - 280 - - 260 - - 240 - - 220 - Per cent intensity o> oo o o o o - 140 - - 120 - - 100 - 80 - - 60 - 40 - - 20 - l 1 1 1 I 1 - 0.5a 1.0a 1.5a 2.0a 2.5a Distance from center of seed 3.0a 3. Fig. II-9. Percentage intensity of radiation reaching different distances, from a buried gold seed. (By courtesy of E. Quimby [1928].) Intensity of Radiation in the Vicinity of Radon Seed Implants Since the radiations from radon must pass through the 0.3-mm gold envelope of the seed, the emitted energy will be composed primarily of gamma radiations, and the curve of Fig. II-9 reproduced from RADIUM SALTS AS A SOURCE OF GAMMA RADIATION 81 Quimby's [1928] data shows how the intensity decreased with distance from such a seed buried in tissue. Some of Quimby's illustrations serve to show how the empirical data represented by this curve can be used. Suppose that a preliminary experiment shows that a seed of 4 mc will bleach butter to a radius of 3.5 mm. How many millicuries will bleach butter to a radius of 5 mm? A distance from the center of the seed marked la on the curve is the radius of a full bleaching dose, here called 100 per cent intensity. Then la = 3.5 mm, or 5 mm = 1.43a. The curve shows that, at the distance 1.43a, bleaching of 46 per cent is produced. Thus x millicuries are necessary to produce 100 per cent bleaching when 4 mc produces 46 per cent bleaching. Hence z/4 = 100/46, or Z =8.7 mc. It has been found that 110 mc-hr produces an erythema at 10 mm. What is the erythema dose at a distance of 6 mm? Here la = 10 mm; 6 mm = 0.6a. The curve shows that 300 per cent intensity is equal to 0.6a. Hence z/110 = 100/300, or x = 36.6 mc-hr. It has been found that a seed of 5 mc produced necrosis in a rabbit muscle at a distance of 3. 1 mm. How far will a tube of 8 mc be effective? Ans. 3.85 mm. Radium Salts as a Source of Gamma Radiation Radium sulphate may also be used as a source of biologically effective gamma radiation. It was commercially available before 1911 at £20 to £25 per milligram. In 1911 it was quoted at £18. In America it could be obtained for $120 per milligram in 1913 and for about $100 in 1914. With the discovery of the Canadian deposits, the price sank to $70 in 1933. Recently it could be obtained at $20 per milligram. Fig. 11-10. Diagram of a typical radium needle. L, overall length of needle 36.5 mm; R, length of radium chamber 25 mm; E, length of eye 5 mm; P, length of point 6.5 mm. For interstitial radiation the salt is placed in a capillary needle-shaped tube containing from 1 to 25 mg of radium element. The radium tube is then placed as a core in the hollow cylindrical needle, 1 to 6 cm long, made of platinum or Monel metal. The construction of a typical needle is shown in Fig. 11-10. The hollow metal cylindrical tube contains the cell filled with the radium 82 APPLIED RADIOACTIVITY sulphate. The total thickness of the radium container and the wall of the needle is about 0.5 mm. If platinum is used, this is a sufficient thickness to absorb all beta rays. The internal cylindrical opening has a diameter of 0.6 mm. The diameter of the needle is 1.6 mm. The total overall length of the needle is 36.5 mm. If the radium chamber is to be longer than 25 mm it is good practice to use two or more radium tubes. Usually these contain 1 or 2 mg of radium each. In dermatology, fiat " applicators " are often used. They are in the form of very shallow round or square boxes. The radium salt is either placed under silver covers about 0.05 mm thick, to allow for considerable beta-ray transmission, or mixed with a varnish-like base and packed into the shallow opening, to give a uniform thickness of radiating ma- terial. Applicators vary in radium content from 2.5 to 10.0 mg of radium element per square centimeter. The intensity of the gamma radiation with increase in distance of either of the above sources does not follow the inverse-square law, since neither of them is a point source of radiation. Available data, however, indicate that the relative intensity varies with size, shape, and changes in distance from the skin. The emission characteristics are reliable, for the quality of the radiation is always the same under identical physical conditions. In practice, it has been found that gold radon seeds may be considered point sources. When these seeds are used for interstitial irradiation the amount of radiation passing through a unit area at any tissue depth is modified by absorption and scattering in the tissue. Actually, accord- ing to Quimby [1939], for the distances involved in practice, the absorp- tion and the scattering approximately compensate each other, so that the intensity of radiation within the tissues is about the same for a given source as its intensity at the same distance in air. Tissue Reaction to Gamma Radiations If a given amount of radiation is administered slowly, either by con- tinuous irradiation of low intensity or in fractions with rest periods of some hours or days between exposures, it is less effective in producing tissue changes than if it is delivered continuously at high intensity. Normal living tissue can tolerate a larger dose if the destructive radiation is administered slowly or administered in fractions with time intervals, and this tolerance is attributable to the recovery or life process of the type of cell radiated. Living tissue possesses dynamic recuperative properties which are not possessed by non-living material. It appears to resist the action of destructive agents. If the destructive radiation RADIUM DOSAGE 83 is applied slowly, it is to be expected that recuperation will be more effective than when the same amount is applied over a shorter period of time. If the destructive radiation is applied to normal cells and diseased cells alike, and the recuperative process of the normal cell is faster than that of the abnormal cell, then the division of a proposed dose into small doses with sufficient time intervals to allow the normal cells to recuperate completely will make it possible to produce regression of the abnormal cells without marked permanent damage to the normal structure. The data available seem to point to the conclusion that normal tissue recuperates faster from exposure to soft x-rays than to hard x-rays and that tissue recuperates definitely with less rapidity from the destructive effects of gamma rays. Radium Dosage It is highly desirable to have a common unit of dosage in radium and roentgen therapy. Recent attempts to do this have been made by Gray [1936], Mayneord and Roberts [1936], and Failla and Marinelli [1937]. To construct a standard gamma-ray ionization chamber somewhat after the specifications laid down by the definition for the roentgen has led to complications. Secondary electrons, due to gamma-ray absorp- tion, have very long paths in air, a fact which makes it necessary to use a large chamber. If the chamber is made large enough for the electron paths other difficulties are introduced that have not been completely solved. An indirect method of measuring gamma-ray intensities using small thimble-type ionization chambers, though unsatisfactory, appears to avoid some of the difficulties. The procedure is usually as follows: The small chamber is calibrated in terms of the standard air chamber in roentgens. It is then exposed to gamma radiation, and the calibrated roentgen scale is compared with the ionization produced by the gamma radiation in milligram-hours. The results thus obtained vary more than 13 per cent among seven independent investigations. Failla and Marinelli [1937] who reviewed these results concluded that the ionization dose and the roentgen dose do not bear the same relation to each other when the quality of the radiation varies over any considerable range. Further complications result from the fact that the ionization dose and the roentgen dose do not bear the same relation to each other even in the gamma-ray region, since the roentgen applies to a beam of radiation in which the scattered energy does not contribute to the ionization of 84 APPLIED RADIOACTIVITY the air of the standard chamber. The roentgen cannot be used as a unit of tissue dose where scattering is a predominant phenomenon. Since tissue dose is what the radiologist desires for his work, Failla sug- gested the following definition: " The roentgen is the quantity of any- ionizing radiation capable of producing 1.615 X 10 12 ion pairs per gram of air at a given point in a given medium under the conditions in which the radiation is to be utilized."* The unit thus defined can be used for measurements of radiation in air or tissues. It has been suggested that, as a temporary expedient, the gamma-ray quantity of 1 mg-hr measured at a distance of 1 cm from a point source of radium filtered through 0.5 mm platinum be adopted as equivalent to 8.3 " effective " roentgens. The Biological Roentgen Living organisms have been used as dosage indicators of both x-rays and gamma rays. The reaction most often used is the effect of the radiation upon the rate of cell growth and repair. Since the absorbed radiation can slow down the rate of cell division, a sufficient dose can stop cell division. This results in the death of the organism. A large variety of biological material has been used to test the lethal action of radiant energy, among them bacteria, yeasts, and spores of many kinds; algae and a great variety of seeds; protozoa; the eggs of salamanders, insects, and frogs. In order to get quantitatively reproducible results, large colonies of small organisms must be used so that the results may be handled statistically. If small enough, the entire organism can be considered as having been irradiated uniformly, and if the organism is properly suspended scattered radiation can be disregarded. The technique involved in evaluating the gamma radiation in terms of the roentgen is illustrated by some typical results obtained with Drosophila eggs. The lethal effects of 120-kv x-rays filtered with 0.25 mm Cu plus 1 mm Al will be compared with gamma rays from radon filtered with 0.5 mm Pt and 4 mm Bakelite. The criterion of the effect produced is the proportion of eggs, in a standard sample colony, which survive and hatch as larvae. A typical survival curve, as obtained by Packard [1936], is reproduced in Fig. 11-11. This shows the effect of various doses, of the above-specified * For the provisional definition of the roentgen for gamma radiation see Chapter I. THE BIOLOGICAL ROENTGEN 85 x-radiation measured in roentgens, in terms of the percentage of eggs which survived and were subsequently hatched. The form of the graph is that of a typical biophysical sigmoid-shaped response curve with its approximate constant slope at the point of inflec- tion. In this restricted region the percentage of eggs surviving per dose administered was nearly constant. The response to the radiation appar- ently differed greatly among similar individuals. Some were killed by small doses yet others remained alive even after exposure to large doses. These and other results also indicated that damage caused by ionizing 100 v • 90 • • Has 80 v: • • ■55 70 • > *^ff • '> = 60 — • \ • 10 • <•* ■*-> • £50 &!. U ka 0) *si Q-40 " • • • 30 20 - • 4 • • 10 I 1 i 1 i I ! • • 1 • t • 1 50 100 150 200 250 300 350 400 Dose in roentgens 450 Fig. II— 1 1 . A typical survival curve of Drosophila eggs after eggs have been sub- jected to the lethal effect of 120-kv x-rays. Fifty per cent of the eggs survive when exposed to 190 roentgens. (By courtesy of C. Packard.) radiations was probably traceable to chemical changes in the cell or in its surface structure which manifested themselves by changes in osmotic pressure, because expanded cells were frequently observed after irradiation both of tissue and of microorganisms. The experiments were then repeated with gamma-ray doses measured in millicurie-hours. Such an experiment is difficult because the eggs must be exposed at very short distances from the source and the intensity must be uniform over the field occupied by the eggs. Exner and Packard [1935] used highly compressed radon gas in a sufficiently small tube, with platinum walls 0.5 mm thick, so that it could be considered a point source. This was placed at the center of a spherical shell of Bakelite 4 mm thick. The eggs were placed on the outer surface of the shell, so 86 APPLIED RADIOACTIVITY that all eggs were 1 cm from the radiating source. The eggs were ex- posed to gamma radiations filtered by 0.5 mm of Pt and 4 mm of Bake- lite. They were tested for survival after exposures varying from 1 to 55 mc-hr. The results are shown in Fig. 11-12. 10 20 30 40 50 100 1 1 1 1 1 mc-hr ^v« • 90 • • • — 80 1 • — _70 • • ^X-ra) curve - CTJ • > • £60 _ • „. 3 CO •\^ •• . s "§50 • ■5? «_ U **\ ^40 • 30 20 — 10 — 1 I 1 i Roentgens i 50 100 150 200 250 Fig. 11-12. Survival of Drosophila eggs after exposure to gamma rays in millicurie- hours. The x-ray survival curve is shown superimposed on the gamma-ray survival data. Fifty per cent of the eggs survive when exposed to a dose of 38 mc-hr. (By courtesy of C. Packard.) If the x-ray survival data are superimposed on the gamma-ray data, it is found that a single curve fits the two sets of data equally well. Figure 11-12 shows how well the x-ray survival curve fits the gamma- ray data. These composite data show that 50 per cent of the eggs survive an exposure of 38 mc-hr and also 190 roentgens. These two doses are therefore biologically equivalent, if Drosophila eggs are acceptable as a standard test substance and if the response is independent of the wave- length of the radiant energy. The millicurie-hour is therefore equal to 5 " biological " roentgens (1 mc-hr = 5 br). Other recent attempts to measure x-rays and gamma rays in the same biological unit were made by Braun [1930]. Using Ascaris eggs, he obtained 1 mc-hr = 5.3 br. Henshaw and Francis [1936], using Droso- phila eggs, obtained 1 mc-hr == 5.4 br. ARTIFICIAL TRANSMUTATION 87 Artificial Transmutation The complex nucleus of radium contains 88 protons; therefore, its atomic number is 88. In addition, this nucleus contains 138 neutrons, making a total of 226 entities of atomic weight 226. The neutrons are supposed to play the role of a binding cement which holds the nucleus together in spite of the very strong electrostatic repulsive forces which the positive protons exert upon one another. Radium, like many of the natural radioactive types of atomic number greater than 80, does not possess a completely stable nuclear configura- tion. It can, however, become more stable by splitting off a nuclear fragment in the form of an alpha particle. Since radioactivity is a quality of the nucleus, it varies from one isotope to another of any element. This nuclear quality of a radioactive atom is the same whether the atom is part of a solid, a liquid, or a gas. It is the same whether the radioactive element is isolated or part of a chemical compound. Elements of small atomic number like Li, B, and N have stable nuclei. If, for instance, nitrogen is bombarded with sufficiently high-speed atomic projectiles, it might be possible to dislodge a nuclear proton fragment. The resulting " artificial " nucleus with its complement of planetary electrons would be a " transmuted " element. A transmu- tation may also be brought about by changing the number of neutrons, or by a combination of neutrons and protons in the nucleus. Thus, transmutation is not always a destruction of the nucleus, but frequently a synthesis in which neutrons or protons are added to an original nucleus. As early as 1919 Rutherford succeeded in producing the artificial transmutation of an element, although the isotopic elements thus pro- duced were not radioactive. In his first experiments he subjected nitrogen to an intensive bombardment of alpha particles from RaC' to see if he could disintegrate the nucleus of the nitrogen atom. He was successful in breaking down the nucleus, and the products of disintegra- tion were an isotopic atom of oxygen and a nuclear proton. The proton was ejected with a large amount of kinetic energy. This classic experiment is shown pictorially in Fig. 11-13. At the time of Rutherford's experiment the constitution of the nucleus was thought to be only protons and negative electrons. They were supposed to be closely and tightly bound together. Disruption of the nucleus was thought to be accomplished by the shooting of a high-speed pro- jectile in the form of an alpha particle at the very small nuclear target. The high-speed alpha particle colliding with the nucleus of the nitrogen 88 APPLIED RADIOACTIVITY atom occasionally succeeded in penetrating this nucleus. When it did this, a proton was ejected with high kinetic energy. For the purpose of this discussion an atomic nucleus is sufficiently specified by giving its atomic number, which is numerically equal to the positive charge of the nucleus, in integral multiples of the proton charge, and the mass number in multiples of the proton mass. Actu- ally, the atomic nuclei do not have masses that are exact multiples 2 He 4 + 7 N 14 > 8 U + ,11'+ Energy , • "\ Collides with (o o> • ' H ' , Nuclear proton Atomic projectile Alpha particle 2 Protons 2 Neutrons Target nucleus Nitrogen atom 7 Protons 7 Neutrons Isotope-oxygen atom \ n' 7 \ 8*J \ 8 Protons y "9 Neutrons Fig. 11-13. Rutherford's classic experiment. Nitrogen bombarded with alpha particles from RaC. of the mass of the proton, but the correction factor is not involved here. In the notation used in describing these disintegration phenomena, the upper right-hand corner of the symbol of the element is reserved for the isotopic mass (sO 17 ) and the lower left-hand corner for the atomic number. Since the discovery of the neutron by Chadwick in 1932, the accepted conclusion is that the alpha particle is made up of two neutrons and two protons bound tightly together as in the nucleus of the helium atom. The alpha-particle projectile is designated as 2He 4 . This mass, with its equivalent of 4 proton masses (neglect mass of nuclear electrons), joins the 14 protons of the nitrogen nucleus, which then loses 1 nuclear mass unit. This mass unit appears as an ejected high-velocity hydrogen nucleus iH 1 . The decomposition product has gained 3 mass units and forms a nucleus of 17 mass units. This is identified as O 17 , an atom of oxygen whose nucleus is 1 mass unit greater than normal oxygen (O 16 ). Hence it is an oxygen isotope. After this first definite example of the artificial transmutation of an element, many other transmutations were accomplished. By 1932 the Curie-Joliots had discovered that charged and uncharged particles were ARTIFICIAL TRANSMUTATION 89 emitted when boron was bombarded with alpha particles. The charged particles were electronic in nature but carried a positive charge. These positive charged electrons had just previously been discovered by Ander- son at the California Institute of Technology and named positrons by him. The uncharged particles were shown to have protonic mass. These neutral particles of protonic mass had been identified only a few months before by Chadwick in England, who gave them the name neutrons. The unusual part about the emissions discovered by the Curie-Joliots was the continued positron emission even after the bombardment by alpha particles had ceased. Thus the first artificial radioactivity had been produced as a property of a disintegration product. The reaction equation for this experiment is shown in Fig. 11-14. The alpha particle joins the boron nucleus, with the emission of a neu- tron. An unstable nitrogen nucleus results, which in turn explodes a lle+ b B X0 > 7 N 13 + Neutron then 7 N' 3 > 6 C' 3 + +1 e°+ Energy Neutron Alpha particle ^ Resu|t Boron stable nucleus ^^ y +i e Positron (positive electron) [ N 13 r \ Unstable (radioactive) Stable nucleus nucleus Fig. 11-14. The Curie-Joliot experiment. with the emission of a positron (+ie°) and the formation of a new stable nucleus carbon, C 13 . The success of the Curie-Joliot experiment raised a question of funda- mental importance. If the boron atom can be converted by alpha- particle bombardment into a new radioactive element, what would prevent other atoms from becoming radioactive if bombarded with any form of high-speed atomic projectile? The alpha particles, emitted by RaC', used in the above experiments possess kinetic energy of 1.23 X 10 -5 erg, corresponding with the energy acquired by an electron in passing between two points in a vacuum differing in potential by 7.66 million volts. It is obviously impracticable to impart to a charged particle, by a single high-voltage operation, energy comparable to that possessed by an alpha particle emitted by natural radioactive elements. It is practicable, however, for a voltage 90 APPLIED RADIOACTIVITY 1/nth as great to operate n successive times on a charged particle in the form of an ion and impart to it a prescribed amount of energy. An ingenious solution to this problem was proposed by E. O. Lawrence, in 1930, in the form of a magnetic resonance accelerator, or cyclotron. This instrument can produce extremely high-speed ions of various sorts by means of relatively small differences of potential applied a large number of consecutive times. The Cyclotron . The instrument finally adopted by Lawrence and Livingston [1934], and their co-workers, consists of a large, shallow, cylindrical metal vacuum chamber (Fig. 11-15) in which are inserted two insulated semi- um chamber 60 in. iameter Deflection plate pressu Fig. 11-15. Cyclotron. General view of a 60-in. D-shaped accelerating chamber which is placed between the magnetic pole pieces of the cyclotron. Direction of magnetic field perpendicular to paper. With the support of the Rockefeller Foundation a " Giant Cyclotron " is under construction at the University of California. It will contain 4900 tons of steel and copper, will have a 30-ft. vacuum chamber, and is expected to produce a beam of ions of more than 200 million electron volts. circular, flat, hollow D-shaped brass electrodes. The vacuum chamber can, for example, be 60 in. in diameter and about 18 in. high. The two electrodes, or " dees," are made of spun copper, and insulated from each other. They clear the vacuum-chamber walls by about 2 in. The vacuum chamber with its flat circular steel ends is supported between the pole pieces of a powerful electromagnet. These pole pieces are also 60 in. in diameter. The magnetic field acts in a direction normal to the radial plane of the dees, i.e., perpendicular to the plane of the paper in Fig. 11-15. THE CYCLOTRON 91 Dees D\ and D 2 are connected through an inductance in the manner shown, so that they form a capacitance in an oscillatory circuit. If a high-frequency potential is applied to the dees so that an alternating voltage (± 50,000 volts) is operative between them while the electrical center of the dee circuit is always at zero potential, an accelerating force is developed by the electric field across the diametral gap between the dees. Within the hollow dees, however, there exists a nearly field-free region. An insulator is inserted through the port at S to carry the connections to the hot tungsten spiral filament situated at the center of the vacuum chamber. This filament is kept at about 1000 volts negative with respect to the earth potential. The vacuum chamber may be filled with hydrogen, deuterium, or helium at low pressure. Positive ions are produced at the center of the vacuum chamber by collisions of the thermoelectrons with the gas molecules. A positive ion in the gap between the two dees will be accelerated by the intense electric field across this gap. In Fig. 11-15 is shown such an ion accelerated across the gap from A to B, after which it will pass into the field-free interior of D\. Under the influence of the per- pendicular magnetic field the ion will trace out a semicircular path BC within the dee and arrive at C. If the time which the ion has spent within Di is equal to half of the periodic time of oscillation of the high- frequency driving circuit, then, when the ion emerges into the gap be- tween the dees at C, the electric high-frequency field will be reversed and the ion will be given a second acceleration from C to E. It then enters the field-free region inside of D 2 with a greater velocity than it had when it passed through D x . Having a greater entrance velocity at E, it will describe a half-circle of greater radius and arrive at F to receive a further acceleration. As the speed increases, the ion describes larger and larger semicircles until it reaches the periphery of the chamber at(?. The magnetic intensity H will deflect the ion to describe a semicircle of radius R such that mv 2 /R = Hev, where v is the velocity of the ion of net charge e and mass m. After a large number of accelerations the energy of the ion is \mv 2 = eV, so that H 2 R 2 e 2m If e is expressed in electrostatic units and V in volts V = H 2 R 2 - (16.7 X 10- 20 ) volt m 92 APPLIED RADIOACTIVITY and if H and R are equal to 10,000 oersteds* and 10 cm, respectively, and the value of e/m for protons is used, it will be observed that the protons found traveling in a semicircle of 10-cm radius are those which possess energy equal to that produced by an electric field between two points in a vacuum of nearly half a million volts. These very high-speed ions emerge at G, where the edge of the dee is cut away. Here they are deflected by the oil-cooled copper deflection plate G, which is maintained at a steady potential of 50,000 volts nega- tive relative to the vacuum chamber, at earth potential. The ions are deflected into the target chamber T, where they can either be used for the bombardment of a substance mounted as a target or be passed through a thin metal window out of the vacuum chamber into the air. Artificial Radioactivity The cyclotron is therefore a source which can supply controlled charged-particle projectiles of enormous energy content. With these projectiles it becomes possible to penetrate the nuclear barrier of many atoms so that in their union they may enter into a reaction with each other, and convert them into artificially radioactive bodies. Among the artificially radioactive processes, beta-ray radioactivity is most common. This consists of the emission either of negative elec- trons or of positrons. A second type of spontaneous transmutation is electron capture, in which the atomic nucleus combines with and destroys one of its atomic electrons. Finally, there is the so-called isomeric transition, which involves only a shift in the configuration of the neutrons and protons in the nucleus without any change in their numbers. The experimental results obtained with the aid of high-speed deuteron projectiles show that radioactive nuclei were formed in which neutrons or alpha particles were emitted. In many cases it was found that the neutron of the deutron was captured and the proton emitted with high speed. This general type, the neutron-capture reaction, is illustrated by the radiosodium and radiophosphorus reactions. Radiosodium may be obtained by bombarding sodium chloride by a beam of high-speed deuterous from a cyclotron. The sodium atom captures the high-speed deuteron, as illustrated in Fig. 11-16, with the emission of a proton, and forms an unstable isotope nucleus, Na 24 . This radiosodium disintegration product has a half-life of 14.8 hours (Van * Unit field intensity. The oersted (formerly called the gauss) is that field which exerts a force of 1 dyne on unit magnetic pole. ARTIFICIAL RADIOACTIVITY 93 Voorhis [1936]). It ejects a high-speed (1.4-Mev) beta particle from its nucleus. This ejection is followed by the emission of a very hard gamma ray, and the end product is a stable magnesium nucleus. The ,H 2 +„Na 23 - »uNa +,H + Energy High-speed deuteron Heavy hydrogen nucleus Stable nucleus Proton { Na 24 } Unstable isotope radiosodium .24 Beta particle ,0 1.4 million electron-volts 3 Mev u Na' > 12 Mg"+? 7-ray emission 24 i -x Fig. 11-16. Radiosodium produced by deuteron bombardment. A possible sub- stitute for radium. Its gamma ray is more energetic than any emitted by radium. beta particle and gamma radiation possess energy of 1.4 and 3 million electron volts respectively. The latter artificially induced radioactive emission is more penetrating than any of the natural radium radiations. Radiophosphorus preparations may be obtained by bombarding red ,H 2 + 15 P 31 - -> 15 P 32 +,H , + Energy High-speed deuteron (0 2 Mev Red phosphorus N stable nucleus v . Beta particle 1.69 Mev ( p 32 ; Unstable isotope radiophosphorus Stable sulphur unexcited No 7 observed ^32 ^, fi S 32 +T Fig. 11-17. Radiophosphorus produced by bombarding red phosphorus with high-speed deuterium ions, from a cyclotron. phosphorus with high-speed deuterium ions, obtained by means of the cyclotron. The reaction is shown in Fig. 11-17. This reaction involves a beta decay emission without the accompanying gamma radiation. The resulting radiophosphorus (i 5 P 32 ) has a half -life of 14.30 days (Cacciapuoti [1938]). 94 APPLIED RADIOACTIVITY Radioactive Tracers Certain chemical compounds, when administered orally or intrave- nously, tend to concentrate themselves in certain organs of the body. It has recently become possible to make such chemical compounds radioactive, so that these specific regions where the radioactive chemical compound has concentrated may be irradiated without producing a large systemic effect or any skin injuries. If the radioactivity has a comparatively short half-life and the decomposition products of the artificially radioactive material are not toxic, no harm will result from its presence in the body, even if it is not promptly eliminated. If certain foodstuffs, such as, for instance, those containing calcium and phosphorus, are made temporarily radioactive, then they can be used as tracers by measuring the relative radioactivity of the tissue in which deposits have taken place. Such radioactive indicators or tracers have helped in the solution of certain therapeutic and physiological problems. When radiophosphorus is used as a tracer, a small amount of acti- vated sodium phosphate is added to ordinary sodium phosphate solution. The path and deposition of sodium phosphate are traced and located by the 1.7-million-volt electronic emissions. Estimates of deposition are carried out by observing the decay, at a given time, by means of a Geiger-M tiller counter tube and by comparing the results directly with the decay of a similar standard at the same time. This method avoids corrections for the rate of decay due to lapse of time. Thus, if it is desired to determine the radioactive phosphorus content of the bone of an animal to which an activated phosphate solution has been administered, and hence to determine any exchange in the phosphate of the bone, a known weight of bone ash from the animal is placed under the counter tube and the intensity of electron emission is determined. The source of phosphatides in egg yolks, the diffusion of phosphate ions into blood corpuscles, the mechanism of enzymatic phosphoryla- tions as in alcoholic fermentation, and numerous other problems have also been investigated with active phosphorus as an indicator. The use of radioactive sodium phosphate has been of great help in a study of the formation of goat milk. Samples of blood and milk, taken at intervals after the administration of labeled phosphate, were examined for the activity of the phosphate in the blood and the various phosphate compounds of milk. It was found that after three or four hours the inorganic phosphate of the milk was replaced by the active phosphate of the plasma. It was estimated that the time of formation of casein in the gland cells was about 1 hour. The fact that a few hours after the addition of the labeled phosphate the milk phosphatides were only RADIOACTIVE TRACERS 95 slightly active as compared with the inorganic phosphate indicated that the latter cannot be produced from the former. This experiment contradicts the view that the fats and inorganic phosphates are produced by the breaking up in the milk gland of the phosphatides of the blood. If iron is used as a target in the cyclotron and bombarded with high- speed deuterons (Livingood and Seaborg [1938]), about 1 atom in every 10 12 may be successfully transmuted into radioactive iron (half-life 47 ± 3 days) just as radioactive phosphorus was transformed. This mixture of stable and negative electron-emitting radioactive iron atoms ( 2 6Fe 59 ) can then be converted chemically to ferrous sulphate. If this ferrous sulphate, containing radioactive iron, is fed to anemic dogs, it will be absorbed and the new red blood cells which are formed will con- tain hemoglobin made with radioactive iron. Since the radioactive and normal atoms of iron are chemically inseparable, they will retain a constant proportionality to one another. The radioactive atom can thus act as a tracer to locate and follow the progressive use of iron atoms in normal and in anemic animals, as was demonstrated by Hahn, Ross, Bale, and Whipple [1940] and also by Miller and Hahn [1940]. New hemoglobin containing radioactive iron was found by them to be detect- able in the blood within about 4 hours. The iron was entirely used up in 4 to 7 days. In this way the breakdown of red blood cells and hemo- globin can be studied quantitatively. A radioactivated isotope of iodine 53I 126 emitting beta and gamma rays has, according to Tape and Cork [1938], been produced having a half-life of 13.0 ± 0.3 days. Experiments by Herz and Roberts [1941], and Hertz, Roberts, Means, and Evans [1940], have indicated that radioactive iodine is selectively taken up by the thyroid gland from the blood stream within a few minutes after administration. The thyroid gland plays fundamental roles in the regulation of growth' and of body heat. Its hormonal secretions are rich in iodine, and the metabolism of this element, which appears to be of basic importance in the proper functioning of the thyroid, is being studied with the aid of radioactive iodine. In human beings with toxic goiter, the thyroid gland has been found to take up practically all the administered iodine if the dose is 1 mg or less. Basic studies are in progress on the rate and mechanism of the conversion of the absorbed iodine into various chemical components of the hor- monal secretions of the thyroid gland (Hamilton [1941]). The upward and lateral movement of salts containing potassium, sodium, phosphorus, and bromine has been studied in growing and transpiring willow and geranium plants. Stout and Hoagland [1939] have shown that the path of rapid upward movement of salt is in the 96 APPLIED RADIOACTIVITY wood of the plant rather than in the bark. They also found a moder- ately rapid radial transfer from the wood to the bark. The considerable interest in the metabolism of calcium has been stimulated because radiocalcium (half-life 180 days) has become avail- able for studying this metabolic problem in bone, which is composed largely of calcium in the form of tricalcium phosphate. Radioactive tracers provide a unique method for investigating a normal animal or plant under equilibrium conditions. Many problems in physiology and biochemistry are being re-examined with the aid of radioactive tracers. The new results will probably provide valid evi- dence for discarding many alternative or conflicting interpretations of old observations. Radium Injuries and Radium Poisoning The earliest recorded radium injury was acquired by Becquerel, who, in carrying a tube of radium salt in his vest pocket for several hours, discovered several weeks later that he had developed a " radium burn," an inflammation in that part of the skin located underneath the pocket in which he had carried the radium salt. Curie then repeated the experi- ment on his own person and conclusively proved that the radiation was capable of effecting an inflammatory reaction in normal skin. Besnier was probably the first to suggest the use of radium as a therapeutic agent because of his familiarity with the results of roentgentherapy. Injury from radium may take place when a radioactive substance enters the blood stream by ingestion or injection. Modes of entrance of radium into the human body include breathing of radioactive gas, drinking of radium water nostrums, and intravenous and other injec- tions of radium salts. Technicians, chemists, and miners handling radioactive materials are often injured by the radiations . and can be poisoned by taking the material by mouth. As is generally true in any heavy-element poisoning, some radium salts are deposited in the bony tissues. A small fraction of the total amount of radium taken into the body becomes relatively fixed in the bones, the fixation being considerably higher after intravenous injection than after ingestion of radium. Retention is diminished by acidosis while on low-calcium diet, as this tends to increase the rate of elimination of calcium and heavy elements from the body. If radium is taken by mouth or by injection, a fraction of it remains permanently in the body. According to the individual, from 2 to 35 per cent of the radium received by mouth remains in the system more than 5 days after ingestion, and 55 to 65 per cent received by intravenous injection remains more than 5 days. By the tenth day after taking RADIUM INJURIES AND RADIUM POISONING 97 radium, the rate of elimination is below 1 per cent of the quantity remain- ing in the system. Several years later the daily rate of elimination is down to 0.002 to 0.005 per cent per day. At this low rate it would require 45 years to eliminate half the radium in the system. About 90 per cent of the eliminated radium is excreted in the feces, and the remaining 10 per cent in the urine. No radium is eliminated through the skin. Since radium decays into radon with the emission of an alpha particle, the radon thus formed can be exhaled in the breath. The fraction of the radon expired varies between extreme limits of 2 and 40 per cent of the total amount of radon produced in the body by the decay of radium. Depending on the resistance of the individual's system from 2 to 10 micrograms of radium, when " fixed " in the system, may be a fatal dose. The radioactive self-photographs of the bones of deceased victims show a lack of uniformity of distribution of deposited radium. In some individuals two or three small areas have been found to be intensely radioactive, the remainder of the bone displaying only a moderate amount of fairly evenly distributed radiation. This lack of uniformity in the deposition of the radium shows that an analysis of a fragment of bone chosen at random will not be representative of the nature of the deposit. Radium acts principally to destroy the blood-producing centers and to weaken the bones. Necrosis of the jaw, osteogenic sarcoma, and regenerative anemia are among the most common symptoms of radium poisoning. An ingenious method has been developed by Evans and Aub [1937] for measuring the gamma radiation from RaC in the patient's body and for determining the absolute amount of RaC from these observations. It involves the use of a very sensitive form of Geiger-Miiller counter responding to gamma radiations. In a victim of chronic radium poisoning, the radium is deposited non- uniformly throughout the bones, the highest concentration being in the vertebrae. The emitted gamma radiation is reduced by absorption and scattering of the tissue. The emerging radiation does not lend itself to computation of the RaC content of the patient, so that cali- bration observations are resorted to in order to evaluate the radiation. The effect of non-uniform distribution of radium and of internal absorption and scattering by the patient's body can be completely corrected by making a series of gamma-ray observations in which the patient is placed in definite geometrical relations with respect to the gamma-radiation detector. 98 APPLIED RADIOACTIVITY The patient lies on a light frame support with his body bent in an arc which has an outside radius of curvature of 1 meter. The gamma- radiation detector is placed at the center of curvature of the arc. Three observations are then made: first, with the ventral aspect of the body away from the counter; second, with the dorsal aspect away from the counter; and, third, with this position retained the total absorption of the body is directly measured by placing small radium standards behind the patient. From proper mathematical combinations of these measurements the absolute amount of RaC in the body can be computed directly. Safety of Personnel Handling Radioactive Materials Those persons engaged in handling radioactive preparations must take precautions for their own safety or they will suffer in health. The chief disabilities which may result are : (a) Damage to the skin which causes warty growths and ulceration, and which may lead to more serious conditions. (6) Damage to the reproductive organs. (c) Damage to the blood-forming organs which leads to forms of anemia. Damage to the skin is usually due to overexposure to beta rays and is more likely to occur during radon plant manipulations than when solid radium salts enclosed in metal tubes are handled. The fundamental rule for safety is that no radioactive preparation should be handled with bare fingers. Radium Standards One of the international radium standards is deposited in Paris; it consists of 22.23 mg of anhydrous RaCl 2 . The second one, at the Vienna Radium Institute, consists of 30.75 mg. Both were prepared in 1934 by Honigschmid and are composed of pure RaCl 2 free from every trace of barium. The United States Bureau of Standards possesses a secondary standard equal to 15.44 mg of radium element as of 1913. In a recent number of the Physical Review (1940), it is reported that a series of radioactive standards is being prepared for deposit at the National Bureau of Standards in Washington, D. C, to be used as working standards and to be made available to investigators. The standards under preparation are : 1. Radium standards; 100-cc solutions sealed in 200-cc Pyrex flasks containing 10 — 9 and 10 — n gram of radium to be used as emanation standards either directly or by subsolution. BIBLIOGRAPHY 99 2. Thorium standards: sealed ampules containing sublimed ThCl 4 . 3. One hundred-grams standard rock samples. For internal radioactive therapy it is proposed to make calibrated standard beta-ray sources available. BIBLIOGRAPHY 1921 Failla, G., Am. J. Roentgenol., 8, 215. 1924 Ellis, C. D., and H. W. B. Skinner, Proc. Roy. Soc. London, A105, 185. 1924 Emeleus, K. G., Proc. Cambridge Phil. Soc, 22, 400. 1925 Gurnet, R. W., Proc. Roy. Soc. London, A109, 540. 1927 Madgwick, M. G., Proc. Cambridge Phil. Soc, 23, 982. 1928 Quimby, E. H., Radiology, 14, 1. 1930 Braun, R., Strahlentherapie, 38, 11. 1934 Lawrence, E. O., and M. S. Livingston, Phys. Rev., 45, 608. 1935 Exner, F. M., and C. Packard, Radiology, 25, 391. 1936 Gray, L. H., Proc Roy. Soc London, A156, 578; A159, 263 (1937). 1936 Henshaw, P. S., and D. S. Francis, Radiology, 27, 569. 1936 Mayneord, W. V., and J. E. Roberts, British J. Radiol., 10, 365. 1936 Packard, C, Radiology, 27, 191. 1936 Van Voorhis, S. N, Phys. Rev., 49, 889. 1937 Evans, R. D., and J. C. Aub, Am. Assoc. Advancement Sci. Occasional Pub., No. 4, p. 227. 1937 Failla, G., and L. D. Marinelli, Am. J. Roentgenol., 38, 312. 1938 Cacciapuoti, B. N., N. Cimento, 15, 213. 1938 Livingood, J. J., and G. T. Seaborg, Phys. Rev., 54, 51. 1938 Tape, G. F., and J. M. Cork, Phys. Rev., 53, 676. 1939 Quimby, E. H., The Physical Basis of Radiation Therapy, Syllabus of Lectures, Memorial Hospital, New York, N. Y. 1939 Stout, P. R., and D. R. Hoagland, Am. J. Bot., 26, 320. 1940 Hahn, P. F., J. F. Ross, W. F. Bale, and G. H. Whipple, J. Exptl. Med., 71 731: 1940 Hertz, S., A. Roberts, J. H. Means, and R. D. Evans, Am. J. Physiol., 128, 565. 1940 Livingood, J. J., and G. T. Seaborg, " A Table of Induced Radioactivities," Rev. Modern Phys., 12, 30. 1940 Mann, W. B., " The Cyclotron," Chemical Publishing Co., New York, N. Y. 1940 Miller, L. L., and P. F. Hahn, J. Biol. Chem., 134, 585. 1941 Hamilton, J. G., J. Applied Phys., 12, 440. 1941 Hertz, S., and A. Roberts, Endocrinology, 29, 82. Chapter III BIOPHYSICAL CHARACTERISTICS OF THE EYE t The preceding chapters have discussed the biophysical properties of very high-frequency radiant energy, in the form of x-rays and gamma rays, but man does not possess the necessary sense organs with which to identify such radiations. Comparatively lower frequencies lying in the spectral wavelength band extending from 4000 to 7000 A, however, can be identified by a unique receptor mechanism, the eye, which is sensitive to changes in frequency and energy of this visible radiation. The expression " we see " means that we experience a sensation which begins as a photochemical reaction in the retina, provided that the intensity of the radiant energy is adequate and its frequency lies within the limits set by the transmission properties of the ocular media, photosensitivity of the retina, and propagation characteristics of nerve. A process such as vision in man represents a complicated series of events. As a form of consciousness and its directive function in behavior, vision must be studied by the methods of psychology. As an activity depending on the anatomical structure of the human eye and its nervous mechanism, vision is a physiological problem. So far as the processes involved rest on the physical responses of the ocular media to radiant energy, they relate to phenomena pertaining to the physical sciences. Merging the last two groups of facts into a single group of interre- lated biophysical phenomena permits a better organized approach to the problem of vision. ' Optical System of the Eye The optical system of the eye consists of those structures which together focus an image of an external object on the retina; they are the cornea, the aqueous humor, the crystalline lens, and the vitreous humor. The media are more or less inhomogeneous, and no satisfac- tory system of spherical refracting surfaces has been adapted that will replace them exactly. Of the many schematic models suggested, Gull- strand's (Table III— 1) seems to possess the most acceptable qualities. Figure III— 1 shows such an eye at rest, with its principal focal plane coinciding with the retina and with the refracting surfaces formed so that parallel rays are brought to a focus on the retina. 100 STRUCTURE OF THE EYEBALL 101 Structure of the Eyeball The human eyeball is an irregular sphere which for simplicity is reduced to an idealized schematic form having an equivalent anterior- posterior diameter of 24.15 mm, with transverse diameter 24.13 mm R=7.7 F = -15.707 Temporal side ! \ Center of rotation i2 = -12 HH t i ON\N' VisuaUxis 3^to 5X. AM ' ' /C~ ;\ 9°uDward \\ 3.6 \ / 7.2 Fovea centralis F= 24.387 mm AH= 1.348 mm AH=1.602 Optical axis \B= 24.00 w=1.336 Thickness >\ \ / 0.5 ^=1.336' «=1.376 Scale 5 mm i_j i i_i i Lens mean n'=1.413 Nasal side Fig. Ill— 1. Gullstrand's schematic eye. Unaccommodated and simplified. Length, A to retina 24.00 mm. All distances on optical axis measured from anterior pole A to B in millimeters. and vertical dimension 23.48 mm. In males the dimensions are from 0.5 to 0.6 mm greater than in females. Its mass is about 7 grams, and its volume about 6.5 cc; the average specific gravity is therefore 1.08. Five sixths of its external surface is formed by a firm white membrane called the sclera. Its anterior convex protrusion, the cornea, is transpar- ent and has an area equal to one sixth of the surface area. This corneal area has a horizontal diameter of 12.0 mm and a vertical diameter of 11.0 mm. Abnormal dimensions may arise as indicated in Fig. III-2. Attached to the eyeball behind and slightly to the nasal side is the optic nerve, the function of which is to convey to the brain the nerve impulses initiated in the retina by the light transmitted by the optical system. Cornea The protruding anterior transparent convex structure, called the cornea, is taken in the ideal schematic eye as 0.5 mm in thickness, and with an average index of refraction of 1.376. The anterior surface of the cornea has a radius of curvature of 7.7 mm. That large departures from this average value may exist is illustrated by the accompanying photographic reproductions, Fig. III-2. The posterior surface of the cornea has a radius of 6.8 mm. The simplified schematic cornea has been taken as having a radius of curvature of 7.8 mm, as shown in Table III— 1. 102 BIOPHYSICAL CHARACTERISTICS OF THE EYE TABLE III-l Gullstrand's Simplified Eye Unaccommodated Maximum Accommodation Index of refraction of Cornea 1.376 1.376 Aqueous humor 1.336 1.336 Vitreous humor 1.336 1.336 Lens 1.413 1.424 Radii of curvature of Equivalent cornea 7.8 mm 7.8 mm Anterior surface of lens 10.0 5.33 Posterior surface of lens -6.0 -5.33 Optical center of lens (0) 5.85 mm 5.2 mm Refracting power of eye +58.64 diopters +70.57 diopters Locations on optical axis of Anterior vertex of cornea (A) 0.0 mm 0.0 mm Posterior surface of cornea 0.5 0.5 Anterior pole of lens 3.6 3.2 Posterior pole of lens 7.2 7.2 Fovea centralis 24.01 24.01 Center of rotation 13-14 13-14 Complete optical system of eye First principal point 1 . 348 mm 1.772 mm Second principal point 1.602 2.086 First (anterior) focal point -15.707 -12.397 Second (posterior) focal point +24.387 +21.016 Anterior focal length +17.055 +14.169 Posterior focal length -22.785 -18.930 Posterior pole (B) 24.00 24.00 Near point -102.3 Drugs pass through the cornea by diffusion quite readily; thus atro- pine placed in the conjunctival sac formed by the lids rapidly reaches the interior of the eye. Aqueous Humor A clear transparent fluid fills the cavity lying between the cornea and the anterior surface of the crystalline lens. It is formed principally by the ciliary bodies. In chemical composition this fluid consists chiefly of water, traces of albumin, globulin, and a reducing sugar. An analysis of the intraocular fluids of the horse as obtained by Duke-Elder [1927] is shown in Table III-2. The intraocular pressure of this fluid varies AQUEOUS HUMOR 103 (a) (&) (ft) Fig. III-2. (a) Normal cornea, (b) Conical cornea (keratoconus). Corneal reflections photographed with a keratoscope. (cO Normal. (c 2 ) and (c 3 ) irregular astigmatism. (Photographs by courtesy of A. Marfaing, Institute of Ophthalmology, New York City.) TABLE III-2 Intraocular Fluids of the Horse Quantities in grams per 100 cc Aqueous Vitreous Serum Water 99.69 99.68 93.32 Solids 1.08 1.10 9.53 =a By Courtesy of W. S. Duke-Elder [1927]. between 25 and 30 mm of mercury. Pressure equilibrium is maintained by drainage through the canal of Schlemm (Fig. Ill— 3, S), and through the crypts in the anterior surface of the iris, or between the suspen- sory ligaments of the lens into the vitreous humor. Its index of refrac- tion, which may be obtained by means of an Abbe refractometer, is 1.336. If the temperature of the unclothed head and hence the aqueous humor is taken as 35° C, and since water at this temperature has an index of 1.3316, one can appreciate the contribution made by the salts 104 BIOPHYSICAL CHARACTERISTICS OF THE EYE in solution, for a 1.1068 per cent salt solution at 25° C has an index of refraction 1.3344. The axial thickness of the anterior chamber con- taining the aqueous humor is about 3.6 mm. Temporal Tendon w-rectus oculi lateralis Posterior surface of iris pigment layer Sclera Chorioidea Stratum pigmenti retinae m-rectus oculi medialis Nasal Fig. Ill— 3. Schematic horizontal meridional section of eyeball. Crystalline Lens The contents of the eyeball are partitioned by the iris into two parts. In front of the iris lies the anterior chamber whose outer boundary is the cornea. Behind the iris is the firm, convex crystalline lens. This lens is a transparent biconvex plastic mass enclosed in an elastic membrane, called the capsule (Fig. III-4). The elastic property of this capsular membrane accounts for the change in shape of the lens. This is shown by the fact that, when the capsule is pierced, the semi- solid lens substance is forced out as a blister; and, if the capsule is removed, the lens does not return to its original shape. The capsule varies in thickness. It is very thin at the posterior sur- face near its vertex, but thicker at its anterior pole. It increases in thickness toward the periphery of the lens. The result is that the inter- CRYSTALLINE LENS 105 A nal pressure of the lens causes the central section of the capsule to assume a different curvature from its peripheral section. Histologically the lens is composed of a number of radially arranged fibers each of which is a modified epithelial cell. These fibers are ar- ranged in concentric layers, the more peripheral being soft and nucleated, and of low refractive index, and the fibrous layers between have an intermediate structure and index of refraction. Gullst rand's schematic eye simulates the above complex structure by substituting for it a crystalline lens having an outer symmetric double convex cover over a core lens of greater index symmetrically placed with respect to the surrounding outer part. This sim- plified equivalent lens has a refractive index 1.413. It has the same size, shape, and focal length as the complex crystal- line lens of the human eye. The anterior pole of the human lens lies 3.6 mm behind the vertex of the cornea, and the posterior pole 7.2 mm behind it. Its anterior radius of curvature is 10.0 mm, and its posterior radius is —6.0 mm. When the lens is accommodated for near vision, its anterior pole A (Fig. Ill— 1) moves forward to within 3.2 mm of the cornea pole; its posterior lens sur- face retains its unaccommodated (focused for parallel light) position. The radii of curvature change so that its anterior radius of curvature at maxi- mum accommodation is reduced to 5.33 mm and its posterior radius to — 5.33 mm. This large posterior change is not universally accepted as representing the complex variations accompanying the rather in- volved change in position of the suspensory ligaments. When opacities form in the lens (cataract), this structure is removed by a surgical operation. It is then found that a lens of about 10 diop- ters* must be worn by the patient in order that he may see distinctly, and a 4-diopter spherical lens must be added when a glass for reading is prescribed. The optical center 0, of Gullstrand's simplified lens (Fig. Ill— 1), lies 5.85 mm from the vertex of the cornea and 5.2 mm from this vertex when the eye is accommodated for near vision. The first and second * In dealing with spectacle lenses, it is usual to take the unit of length as 1 meter. The reciprocal of the focal length measured in meters is its power in diopters. Fig. III-4. Scale representa- tion of crystalline lens showing changes in thickness of capsule. A, anterior pole. P, posterior pole. (By courtesy of E. F. Fincham [1926].) 106 BIOPHYSICAL CHARACTERISTICS OF THE EYE nodal points (iV, N') lie at 7.08 and 7.33 mm, respectively; hence they are nearly coincident with the posterior pole of the lens. Mechanism of Accommodation According to the Helmholtzian theory, the ciliary muscles (Fig. Ill— 5) adjust the lens for near vision by removing the tension from the periph- eral suspensory ligaments S. L. from which the lens is suspended, and thus allow the lens capsule to expand as the result of its internal hydro- static pressure. Lens Fig. Ill— 5. A diagrammatic representation of the mechanical interactions of ciliary muscle L, suspensory ligaments S.L., and lens. If L contracts, the choroid is stretched, b and c move down, removing tension from S.L., the suspensory ligaments of the lens. The vector diagram is supposed to show how the external forces act on the lense. S, canal of Schlemm; s.p., sphincter pupillae, circular muscle of the iris; c.f., circular fibers of the ciliary muscle; L, longitudinal fibers of the ciliary muscle; c, ciliary processes; O, ora serrata, end of retina. This change in shape of the lens is brought about indirectly through the contraction of the ciliary muscle. The ciliary muscle consists of two separate sets of unstriated muscle fibers : the more superficial set of longitudinal fibers L, and the deeper set of bundles of circular fibers c.j. The former originate at the sclerocorneal junction near S and are attached to the anterior part of the choroid coat behind the ciliary proc- esses below b. When these muscles contract they draw the choroid MECHANISM OF ACCOMMODATION 107 forward. A fundamental objection to Helmholtz's theory, as pointed out by Stilling [1912], is that the choroid cannot move forward when the longitudinal fibers contract. In Fig. Ill— 5, the ciliary muscle, suspensory ligaments, and lens are shown diagrammatically and a solution is given, on the assumption that the tissue at b is elastic. The longitudinal muscle L is shown slop- ing at an angle of 45 degrees; the circular fibers (c./.) lie directly below them. Let F c represent the force of contraction developed by the longitudinal muscles in a coordinate system whose Y axis represents the direction of a radius of the lens passing through the circular fibers above it and perpendicular to the optical axis of the lens. This force may be resolved into two components at right angles to each other, F a acting along the optical axis of the lens, and F r acting along a radius of the lens in a direction pointing from the periphery at right angles to the optical axis. If the radial ciliary muscles contract, lying as they do in the base of the ciliary processes, this contraction causes the apices of the processes to come together and form a smaller circle. In such a circular con- striction the forces must again act radially to decrease the circumference of the circle; this latter force is F r > in the diagram. It will be noted that both F r and F T , act in the same direction, tending to slacken the tension on the suspensory ligaments. The horizontal component of the force F a which is directed forward tends to slacken the tension in those suspensory ligaments which originate at b and which are attached to the anterior face of the lens. This force does not change the tension on those suspensory ligaments running from the anterior surface of the ciliary process to the posterior side of the lens. These keep the posterior face of the lens under constant tension and do not allow the hydrostatic pressure in the lens to change the radius of curvature of that face. The decreased tension over the anterior surface of the lens allows the lens to bulge in the anterior direction, but not with a uniform change in curvature. The distribution of the suspensory ligaments and the changed thickness of the capsule tend to prevent a uniform change in curvature. Helmholtz's theory assumes that in a condition of rest the suspensory ligaments which run from the ciliary processes to the capsule of the lens exert a tension upon the capsule which keeps the lens flattened, particu- larly along its anterior surface, since the ligaments are attached more numerously and more tangentially to this side. The above analysis attributes this greater flattening of the anterior surface of the lens to the increased tension applied to the capsule, to produce the far accom- modation, or vision for parallel light, in the normal eye. 108 BIOPHYSICAL CHARACTERISTICS OF THE EYE Amplitude of Accommodation Objects at a great distance are seen distinctly, as far as their definition permits, without accommodation. This condition is called the eye at rest. Practically all objects beyond a distance of 20 to 30 ft (6 to 10 meters) focus on the retina without muscular effort; hence, this distance is usually referred to as the far point. The near point is that point on the axis which is seen distinctly when the crystalline lens has its greatest refracting power. In youth this may be as little as 10 cm. The ampli- tude of accommodation is defined as the distance of the near point from the far point. TABLE III-3 Loss op Accommodation with Advancing Years Age in years 10 15 20 25 30 35 40 45 50 55 60 65 70 Power (F) of ac- commodation in diopters 14.0 12.6 11.2 9.9 8.5 7.1 5.7 3.7 1.9 1.2 1.0 1.0 1.0 From A. Duane's curves [1912]. The faculty of accommodation is greatest in early life, and diminishes rapidly with advancing years. In this process the near point gradually recedes, but the far point remains practically stationary until the age of 50 years. At 10 years the amplitude or range is from infinity to 7 cm when the maximum accommodation is used. At 20 and 40 years this near point lies at 10 and 22.2 cm, respectively, from the principal point. When the near point has retreated to a distance beyond 25 cm, so that it is no longer possible to read or write conveniently without spectacles, the condition of presbyopia, or old-age vision, has begun to set in. After this it becomes necessary to add a convex lens to the eye so that one may see distinctly at the usual working distance. The decreasing power of accommodation as age increases is expressed conveniently in the number of diopters which may be added to the refractive power* of the eye. Table III— 3 shows the results obtained by A. Duane [1912], from a comparative study of 1050 cases, for the mean power of accom- modation for different ages. The near point is measured from the anterior focus of the eye, i.e., from a point 15.2 mm in front of the cornea. The gradual reduction in the power of accommodation is attributed to the gradual decrease in elasticity of the lens. * Reciprocal of the focal length. Units diopters. mis 109 Viteeous Humor The soft jelly] ike mass which fills the entire cavity of the eye behind the crystalline lens is called the vitreous humor. About 99 per cent of its composition is water. Its index of refraction, readily obtainable with an Abbe refracto meter, is 1.336. It is a transparent, rather del- icate form of very loose gelatinous connective tissue whose scanty fibers are recognized only with the greatest difficulty. Occasionally a few large cells have been found in it, and small rounded cells somewhat resembling leucocytes are also observed in very limited numbers. These various cells may cast shadows upon the retina within the visual field. Such shadows possess a sort of " flitting " motion when the eyes are moved while looking at a bright light. Frequently one may observe them while looking through a microscope. In advanced age, crystals may form in the vitreous humor, which are observed to settle to the bottom of the eye when the eye is held still. Iris The eye possesses a diaphragm known as the iris. On looking into an eye, one sees the pupil, which is the image of the iris formed by the interposed cornea and the aqueous humor. From a geometrical optics point of view the iris plays the part of an adjustable stop, through whose aperture the amount of light admitted to the retina is controlled. The aperture of this stop is controlled by two bands of muscular tissue; the sphincter muscle and the radial muscle. The sphincter muscle forms a circular band under the inner rim of the iris, and its contraction causes the opening in the iris to decrease in size. The con- traction of the radial muscle, stretching from the rim to the outer cir- cumference of the iris, causes the opening to increase in size. Most optical instruments containing lens systems are provided with some means of blocking out such portions of a bundle of rays as are undesirable for one reason or another. This blocking is usually accom- plished by interposing in the path of the rays a plane opaque screen set at right angles to the axis, which contains a circular aperture with its center on the axis. The iris is such a perforated screen; it serves as an interior stop or aperture-stop, since it lies within the system. It is placed so as to decrease spherical aberration and thus " sharpen the focus " of the eye and also to control the brightness of the retinal image, which also depends on the size of the stop. If a rather powerful biconvex reading glass is used as a simple micro- scope, to examine a sheet of cross-section paper, it will be seen that the central portions of the image and the corners are not focused with equal 110 BIOPHYSICAL CHARACTERISTICS OF THE EYE sharpness, and that the lines also seem curved. This imperfect focusing results from the fact that this lens reproduces straight lines of a flat object as curved lines concave toward the lens. A diaphragm placed behind such a lens, leaving only the central area of the lens in use, will block out the peripheral field and allow only the axial rays to pass through the stop to form the image. These conditions are illustrated Fig. III-6. in Fig. Ill— 6, which shows the refracted path of the rays that pass through different zones of the lens. The outer zones are focused at c; the more axial zones are focused further out at b. The aberration is measured by the distance cb. A stop placed behind the lens as in Fig. III-6 reduces the aberration and sharpens the focus. Contraction of the pupil causes a reduction in intensity of the light and limits the beam of light to the central zones of the lens. The accompanying reduction in axial spherical aberration improves the definition of the image. Spherical Aberration of the Eye Since the cornea and the lens are nearly spherical surfaces, it might be expected that spherical aberration must be present. The crystalline lens, however, has a structure essentially different from that found in optical instruments. Owing to the graduated changes of index of refraction, rays passing through the central zone of the lens are refracted to a greater extent than the more peripheral rays, so that the rays marked b in Fig. Ill— 6 are more nearly superimposed on the rays c. In addition the more peripheral parts of the lens are flattened ; therefore, the lens deviates the rays less than those passing through this area of a spherical lens. Chromatic Aberration of the Eye In discussing the simple geometrical formation of images by lenses, it is always assumed that light is monochromatic. As a matter of CHROMATIC ABERRATION OF THE EYE 111 fact, when white light is used one must take into consideration not only the deviations but also dispersion. The convex lens in Fig. Ill— 7 shows how a parallel beam of white light, incident on its left face, is deviated and dispersed. It will be noticed that the violet light is more deviated than the red light; hence the lens has a shorter focal length for violet than for red light. Thus, if a screen is placed at A, we shall get a central white spot surrounded by a violet ring of color surrounded by green and yellow rings with an outside Fig. Ill— 7. Chromatic aberration or chromatic difference of focus of a simple biconvex lens. border of red; if the screen is placed at B, one may observe a white spot surrounded by a red ring of color surrounded by yellow and green rings with an outside border of violet. This difference of focus for rays of different wavelengths is called chromatic difference of focus; it is due to the fact that the index of refraction of the lens increases with a decrease in wavelength. If for the sake of simplicity a simplified eye is adopted consisting of one refracting surface enclosing a single medium composed of water, and giving the single refracting surface a radius of 5.13 mm, the differ- ent focal lengths of this eye for red and blue light can be calculated. The indices of refraction of water for red (6536 A) and blue (4308 A) light are 1.331 and 1.342, respectively. The focal lengths of the simpli- fied eye are therefore 20.57 and 20.14 mm. If the eye were unaccom- modated so that the retina lies at the focus of the yellow rays, approx- imately halfway between these foci, the focus of the blue ray would be about 0.22 mm behind the retina. Experiments have shown that, when such a series of foci are formed by the eye, the rays of greatest intensity form the most sharply focused image. For maximum brightness, the o narrow yellow-green part of the spectrum near 5560 A is used. For low o intensities the focus shifts to the blue-green near 5040 A. The colors having longer and shorter wavelengths form blurred disks of light of relatively low intensity on top of the sharply focused image. With an increase in the diameter of the pupil, the periphery of the lens is exposed 112 BIOPHYSICAL CHARACTERISTICS OF THE EYE so that the chromatic aberration increases ; on the other hand, the diffrac- tion decreases. The two changes, however, practically compensate each other, leaving the definition of the image unchanged, but the depth of focus decreases. Astigmatism In an ideal eye the refractive surfaces are sections of true spheres, and, all the meridians being of equal curvature, the refraction along these different meridians is equal. Such an eye with a small pupil will refract a cone of monochromatic light, issuing from a luminous point, to a focal point on the retina and will exclude the disturbing contributions of spherical aberration. If one or all of the refractive surfaces, how- ever, have unequal curvatures along different meridians, then the rays Rays due to greater curvature • ^ — o I I 1 Primary a • line focus t Secondary linp fnrnQ Closest approach to a point image line focus Fig. III-8. An astigmatic lens, showing the shape of the astigmatic ray bundles. from a luminous monochromatic point source cannot be brought to a single focal point, since the rays along the meridian of greater curvature will be brought to a focus first and begin to diverge before the rays along the lesser curvature are focused. Such a condition is called astigmatism (not a point). The effect can be illustrated by the diagram of Fig. Ill— 8, which represents the refraction of the rays from a luminous point by a cornea whose curvature along the vertical meridian is greater than the curvature along the horizontal meridian. The lower line of figures represents the section of the cone of light, or the images obtained at different distances. The images vary from a horizontal line to a vertical line, but at no place can a point be obtained at which rays along all meridians are focused. At B the rays along the vertical meridian are in focus; at A the rays along the horizontal meridian are brought to a focus. Ordinary astigmatism is usually attributed to a defect in the curva- ture of the cornea. The condition illustrated by Fig. Ill— 8 can be cor- BRIGHTNESS OF LUMINOUS RADIATION 113 rected by means of a convex cylindrical lens (+ cylinder), so chosen as to increase the refraction along the meridian in which the cornea has the least curvature; conversely, the refraction along the meridian of great- est curvature can be diminished by means of a concave cylindrical lens (— cylinder). A simple experiment illustrating astigmatism can be performed by closing the eyelids over a normal eye until only a narrow slit remains, so that the watery fluid bathing the eye forms a concave cylindrical lens which alters the curvature along the vertical meridian. The question is, why is the fluid lens concave? Which meridian is out of focus? Brightness of Luminous Radiation The amount of radiant energy necessary to produce a fixed luminous sensation of brightness varies enormously with the wavelength of the radiation. By brightness is meant the luminous flux per unit of emissive area viewed on a plane set perpendicular to the line of sight. It is measured in lumens per square centimeter — a unit called the lambert. Thus, when a diffusing surface reflects all the light incident upon it, its brightness in lamberts is equal to its illumination in lumens per square centimeter. The total visible energy emitted by a source per second is called the total luminous flux. The unit of flux, the lumen, is that flux emitted in unit solid angle by a point source having a luminous intensity of 1 international candle. A uniform point source of 1 candle intensity thus emits 4x lumens. One millilambert equals 0.929 lumen per square foot, or the brightness that would be produced by 0.929 foot-candle on a diffusing surface of 100 per cent reflection factor. Since most of the diffusing surfaces are ordinary " white " surfaces of 80 per cent reflection factor, 1 foot- candle produces a brightness on a white surface of 0.86 millilambert. Daylight brightness at sunrise and sunset is usually less than 100 millilamberts. The average brightness of an ordinary blue sky is about 500 millilamberts, but a moderate haze increases the brightness of the sky to 1500 millilamberts. The eye operates normally under intensities comparable to the bright- ness of white paper in full sunlight (10 lamberts) as an upper limit, and to a threshold of vision of 7 X 10~ 7 millilambert as a lower limit, or in a range of 20 billion to 1 — a greater range of sensitivity than most physi- cal instruments. It was found, however, that, when the brightness of a field of constant area varied by a factor of 10 billion, the retinal sensibility varied by a 114 BIOPHYSICAL CHARACTERISTICS OF THE EYE factor of only 10 million. Can this discrepancy be accounted for by a variation in the size of the pupil? The total range in pupillary diameter is from 2 to 8 mm, or a range in area from 1 to 16, the pupil adjusting itself so as to maintain constant light energy on the retina. Appar- ently, this is not a sufficient variation to account for the discrepancy. A time element, however, is also involved when the retina is exposed to the radiant energy. The time of the exposure, especially at threshold vision, modifies the expected results. The time element of the retinal exposure can be obtained from some data collected by Reeves [1918], which show that at low intensities the product of time and threshold brightness, measured in millilamberts, is only approximately constant. His data were obtained by using a carefully calibrated focal plane shutter for determining the time of exposure, when a 3 cm square test spot was placed at a distance of 35 cm. This result indicates that, the lower the intensity, the longer must the image remain on the retina to produce a sensation of brightness, and that a high intensity lingering for a short period of time does not produce the same brightness effect as a low intensity lingering for a long period of time. Hence the product of threshold by time should be constant if the energy density on the retina is to remain constant. The retina acts as if the radiant energy were integrated in some way to pro- duce the threshold effect. Therefore brightness increases in proportion as either the intensity or the time intervals are increased, and equal brightness near the threshold is obtained if the product time-intensity remains constant. That is, as duration is increased, intensity must be decreased in order that the response remain at threshold value. This relation ceases to be effective if the time of stimulation is longer than a critical duration of about 0.1 sec, as Reeves' data show in the sudden change in values of threshold X time for values of time greater than 0.160 sec. This fact is of importance in flashlight signaling. The blinker should remain open for at least 0.1 sec in order to make the greatest possible retinal impression. Energy Threshold If the energy entering the pupil is E ergs per second, it should be proportional to the square of the radius (r) of the pupil, inversely pro- portional to the square of the distance (D) of the test spot from the observer, and directly proportional to the area (A) of the test spot measured in square centimeters, to B its brightness in lamberts, and to RESPONSE OF THE PUPIL WITH CHANGES IN BRIGHTNESS 115 M the least mechanical equivalent of light; hence Br 2 AM E = & If M is taken as 151 X 10 -5 watt per lumen,* it can be shown that, for a stimulus possessing an area of 2 sq mm viewed at a distance of 35 cm and possessing a brightness of 0.000362 millilambert, the energy entering the eye is as low as 143 X 10 -10 erg per sec. The smallest num- ber of photons per second to which the retina will respond can now be calculated. Let us suppose that the test spot is emitting monochromatic light of wavelength 5560 X 10 -8 cm, corresponding with the region of maxi- mum retinal sensitivity. We can then calculate the energy content of 1 photon of this radiant energy incident on the retina. It is E = hv = hc/\, where h is Planck's constant, of magnitude 6.62 X 10~ 27 erg sec; c is the velocity of light and equal to 3 X 10 10 cm per sec; and X is the indicated wavelength. Hence E = 0.036 X 10 -10 erg. If the above threshold power value is accepted as 143 X 10 -10 erg per sec, then 4000 photons per second of this green radiation is used. If the exposure to produce an experienced sensation occurs in 0.002 sec, it follows that the retina responds to as few as 8 photons — an extraor- dinary and remarkable sensitivity. Hevesy and Paneth [1938] find that for a practiced eye about 30 photons of the above wavelength suffice for the unaided visual perception of an alpha-particle scintillation Barnes and Czerny [1932] find light flashes of 40 to 90 photons as the minimum sensitivity of the dark-adapted eye. A solution of visual purple extracted from the retinas of frogs by Dartnall et al. [1938] showed that the number of chromophoric group- ings in visual purple destroyed in relation to the number of photons absorbed is nearly equal to unity. Response of the Pupil with Changes in Brightness It has been found that the pupil has a different diameter for each brightness level. This adjustment is due to the fact that the pupil is automatically regulated so as to maintain constant light energy on the retina. In this connection the evidence supplied by Reeves [1920] from his study of the response of the pupil to changing intensities of light is significant. The diameter of the pupil at any given brightness was determined by means of a flashlight and motion-picture camera. The apparent diameters viewed through the cornea and aqueous humor * H. T. Wensel, J. Research Natl. Bur. Standards, 22, 375, 1939. 116 BIOPHYSICAL CHARACTERISTICS OF THE EYE TABLE III-4 Pupillary Diameter Changes with Changes in Brightness Brightness units B in millilamberts Pupillary diameters D in millimeters (average of 6 subjects) B 0.00015 0.01 1.0 10 55 100 D 8.0 7.6 7.0 5.0 4.0 3.1 2.8 Area/7r 16.0 14.4 12.3 6.25 4.00 2.40 1.96 LogB -4.17 -2.0 1.0 1.74 2.00 Log B X Area 4.00 4.18 3.92 By Courtesy of P. Reeves [1918], and the Eastman Kodak Company. were photographed and the dimensions were increased 7 per cent so as to obtain the actual dimensions. Under these circumstances the pupil- lary diameters shown in Table III— 4 were obtained. However, we can draw only an approximate conclusion from these results, namely, that the logarithm of the brightness times the pupillary area is nearly con- stant for brightness greater than 10.0 millilamberts. Reeves' work also shows that the response of the pupil under conditions of artificial light- ing is such that at 2000 millilamberts the diameter of the pupil is as small as 2 mm. This contraction of the pupil is comparable to that produced when a 100-watt lamp in a 5-in. diameter globe of good diffus- ing glass is held near the eye. Spectral Sensitivity of the Eye The quantitative study of the response of the retina to light of various wavelengths originated with R. A. Konig as early as 1893. His data ef visibility at low intensities are used in Fig. Ill— 9. The curve of visi- bility at high intensities, as adopted by the Illuminating Engineering Society to represent the composite results of Ives, Kingsbury, Nutting, Coblentz, Emerson, Hyde, Cody, and Forsythe, are also shown for comparison. The visibility at low intensities was determined by a threshold method, which consists in determining the least amount of energy that is just perceptible at each wavelength. The visibility at high intensities is determined by means of a direct measurement of the relative brightness of equal amounts of energy throughout the spectrum. From these curves it will be observed that the sensitivity of the eye shifts towards the blue end of the spectrum at low levels of illumination. This shift is attributed to a transition from cone to rod vision. Hence, if a red and blue field are matched at a high brightness level and then compared TRANSMISSION CHARACTERISTICS 117 at a low level as in moonlight, the red field appears darker and the blue lighter. This shift to rod vision accounts for the blue appearance of objects as seen by moonlight. (Full moon 0.02 ft-canclle.) 700 « 600 S.500 I 400 300 ■2 200 <100 Kb'nig's data Rod vision Low level illumination Cone vision Daylight vision normal observer 4000 i 5000 1 +6000 Violet Blue Green Yellow o Wavelengths in A Red 7000 Fig. Ill— 9. The visibility curves of the human eye or the brightness distribution of the visible spectrum. Rod vision attains its maximum visibility at 5040 A; cone vision, at 5560 A. The absolute visibility at maximum is 667 lumens per watt. The curves also show that the amount of radiant energy necessary to produce a desired sensation of brightness varies enormously with the wavelength. It is least in the yellow-green region at 5560 A, but for o low-level illumination this maximum brightness shifts to 5040 A. If a low-intensity spectrum is viewed and decreased in brightness, a point will be reached at which its violet and yellow ends disappear first, and Q the blue-green sensation due to 5040 A disappears last. In colorimetric methods of analysis as applied to clinical work, refer- ence will again be made to this phenomenon in determining the choice and relative accuracy of colorimetric comparison methods. Transmission Characteristics of the Ocular Media for Ultra- violet Radiations Extensive experiments on animal eyes have shown that ultraviolet radiation of high intensity and long exposure does not injure the retina since the optical media involved are opaque to these short wavelengths, but that this radiation will produce very painful conjunctivitis. o The cornea is opaque to all wavelengths below 2950 A, although some evidence exists that the cornea of the rabbit is transparent to shorter wavelengths. The cornea can transmit light of wavelength as small as 3000 A. 118 BIOPHYSICAL CHARACTERISTICS OF THE EYE o The crystalline lens is opaque to wavelengths below 3200 A, although young lenses have shown transmissions from 3150 to 3300 A. With increased age there is some absorption in the spectral region extending o from 4000 to 4200 A. The lens absorbs powerfully the ultraviolet radiations lying between 3000 and 3800 A roughly; it also fluoresces when this group of rays strikes it. The absorbed radiation is re-emitted as scattered light of longer wavelengths, and is therefore useless for image formation. This scattered light confuses the vision and should be externally absorbed, before entering the cornea, by means of a sheet of Crookes A glass. The vitreous humor, since it is composed chiefly of water with a slight addition of salts, is comparable to a layer of water 1.46 cm thick, and o like water it is transparent to short violet light around 2300 A. It has, o however, an absorption band reaching from 2500 to 2800 A. But o 2800 A is not transmitted by the cornea or by the lens; hence, the mini- o mum wavelength reaching the retina must be 3500 A, or longer. The combined tissues of the " normal eye " probably do not transmit o violet light below 4000 A, a good practical dividing line between the visual spectrum and the ultraviolet. In the development of artificial sunlight illuminants, Luckiesh [1930] has shown that, when the outer membrane of eyes was exposed to moderate intensities of illumination, even though wavelengths as short o as 2800 A were present in abundance, no conjunctivitis was developed. For instance, reading 3 hours from a book illuminated to an intensity of 300 ft-candles caused no inflammation of the conjunctiva. Intense direct ultraviolet radiations, however, will produce conjunctivitis. o Therefore it seems that 3100 A is a safe lower wavelength limit for inclu- sion in artificial sunlight, as used for general lighting. A 1-mm soda glass screen is ample protection against the inflammatory radiations emitted by lighting devices. Infra-Red Transmission o The near-infra-red region extends from about 7000 to 14,000 A. On a clear day with the sun at zenith and normal atmospheric pressure an intensity of 8540 ft-candles can be recorded. Of this intensity 44 per cent lies between 4000 and 7600 A and 36 per cent in the short-wave infra- red region. (See chapter on absorption.) The most efficient artificial producers of this radiation are high-temperature solids, as, for instance, the metal filaments in incandescent high-wattage tungsten-filament lamps. Visible radiation will penetrate great depths of water, but the trans- o mission factor of water falls off rapidly from 7600 A towards the longer INFRA-RED TRANSMISSION 119 wavelengths, as seen in Fig. 111-10. Since the optical system of the eye may be reduced, according to Luckiesh [1921], to an equivalent layer of water 2.28 cm thick, it is possible to predict the transmission of the optical system by analyzing the infra-red transmission curve of water of this thickness. The justification for this water equivalent lies in the fact that the cornea is composed of about 90 per cent water. The cortex of the lens is about 92 per cent water, falling to 84 per cent in the center. It will be noted in Fig. III-10 that the per cent transmission o of water falls off rapidly, reaching a very low value for 10,000 A and dropping to opacity at 14,000 A. -100 80 -60 40 20 -Visibl 2.28 cm Near infra-red- 0.06 cm water I \ I \ A _L 1^ / V _L 4,000 8,000 12,000 16,000 Wavelengths in A 20,000 24,000 Fig. Ill— 10. The spectral transmission of water in the near infra-red. Retina o o is sensitive to about 8350 A. Radiant energy, however, is transmitted up to 12,000 A. Retina does not respond to region between 8000 and 12,000 A despite the high trans- missivity of the medium. Values of the transmission of water at various thicknesses were obtained from Aschkinass, Ann. Physik, 55, 401 (1895). Values for 2.28 cm reproduced through the courtesy of M. Luckiesh [1921]. The visible limit at the red end of the spectrum under the most o favorable conditions has been found to be near 8350 A; under ordinary circumstances it is difficult to go beyond 8000 A, although some ex- o o perimenters place this limit at 7600 A. At 10,000 A the media of the eye are about 40 per cent transparent; although the transparency rises to 65 per cent at about 11,000 A, it rapidly drops to opacity near 12,000 o o A. Thus those rays having wavelengths greater than 8000 A do not excite a response in the retinal structure. The question is often raised as to the efficiency of protection by eye- glasses in the near infra-red. The spectral transmission of glass decreases quite rapidly beyond 30,000 A, but glasses are fairly transparent in the 120 BIOPHYSICAL CHARACTERISTICS OF THE EYE near infra-red. Even colored glasses have fairly high transmission factors in this region. The clear glasses, including quartz, are almost o perfectly transparent to 28,000 A and quite effectively transmit energy as far as 40,000 A. Special glasses of the cobalt blue type, however, have marked absorption bands between 5000 and 7000 A. A 2.5 per cent solution of crystallized cupric chloride is most effective in absorbing the long infra-red wavelength region. A layer of this fluid o 2 cm thick absorbs nearly all the radiation beyond 8000 A and still transmits rather freely in the visible region. Very high-temperature furnaces, and the products from such furnaces, immediately after withdrawal as in rolling mills or in glass-blowing establishments, subject the workmen to intense radiations. Goggles must be worn by the operators to protect the eyes against these radia- tions. For some operations such as welding, especially arc welding on iron, where the emission is not only rich in infra-red but exceptionally high in ultra-violet radiation, protective goggles must have a high absorption in the visible in addition to a well-nigh complete absorption in both the infra-red and ultraviolet region. For such purposes, special weld- ing glasses are available to meet the specifications drafted by the Federal Government in 1930 and published as " Federal Master Specifications. " The windows in aviator goggles, which are light green in color, are now being made which possess transmission properties very similar to the daylight visibility curve of the normal eye (Fig. Ill— 9) . If the windows in these goggles are 2 mm thick they have a total transmission of approximately 50 per cent in the visible. Cataracts or Lenticular Opacities The prevalence of lenticular opacities in the eye of tinplate mill men has been studied by Healy. In all, about 350 men were examined. The men entered the mill at about 18 years of age and developed an opacity about 15 years later. In this group 40 per cent of the men over 35 years of age had lenticular opacities (see Fig. Ill— 11) apparently caused by the manipulation of the red-hot tinplate at distances which vary from 2 to 5 ft from the eyes. A similar affliction, called " bottle- maker's cataract," is attributed by most ophthalmologists to infra-red absorption. In connection with these studies may be mentioned the experiments of Burge [1924], who investigated the cataracts produced in the eyes of fish living in water containing small quantities of calcium chloride or sodium silicate. His conclusions, briefly stated, were that, when excessive salts exist in the humor and the nutritive sources of the LENTICULAR OPACITIES 121 lens, the liability to cataractous conditions is increased. The trade cataracts mentioned above are usually attributed to the overheating of the eye as a whole with consequent disturbed nutrition of the lens. Fig. Ill— 11. Correction of a corneal opacity by a transplant from an enucleated eye. (a) Corneal opacity before operation, (b) Transplant 4 mm square taken from an enucleated eye of a stillborn child. Photographs by courtesy of A. Marfaing. For details on keratoplasty see R. Castroviejo, Am. J. Ophthalmol., 17, 932 (1934); for bibliography, see Arch. Ophthalmol., 22, 144 (1939). The near-infra-red rays, though freely transmitted by the cornea, are in large part absorbed by the iris. This excessive local absorption may in turn produce an abnormal stimulus to the processes controlling the secretion of the humor and thus may cause nutritional'disturbances in the lens. Retina The retina (pars optica retinae) may be said to be formed by the radial expansion of the fibers of the optic nerve which enter the eye at the inner side of its posterior pole, pierce the sclera and choroid, and spread out over the inner surface of the eyeball. The retina is considered to extend forward from the entrance of the optic nerve (optic disk) as far as the posterior margin of the ciliary body, where it apparently ends abruptly with an indented border, the ora serrata. During life the retina is perfectly transparent, despite its complex cell structure, with the exception of its pigment layer. It presents on its inner surface a slightly elevated yellow spot, the macula lutea, which is located at the posterior pole of the visual axis. The fovea centralis, a slight depression in the center of the yellow spot, is the result of an apparent thinning of the retinal layers at this point. The retina, if considered in detail, is made up of ten layers (Fig. 122 BIOPHYSICAL CHARACTERISTICS OF THE EYE III— 12). The radiant energy passes through them in the following order to reach the photoreceptor layer of rods and cones bounded on the external side by the pigment epithelium lying adjacent to the choroid: (1) the internal limiting membrane, (2) the optic nerve fiber layer, (3) the ganglion cell layer, (4) the inner plexiform layer, (5) the inner nuclear (bipolar cells) layer, (6) the external plexiform layer, , ... (7) the outer nuclear layer, (8) the external io [p,'(*)..° . | limiting membrane, (9) the photoreceptor layer, and (10) the pigment layer. The first six layers are grouped as contained in the cerebral portion and the last four in the neu- roephithelial portion of the structure. From a biophysical point of view the chief interest centers on the visual cells (9) and pigmented epithelium (10) as the basic ele- ments concerned with the interception of the radiant energy and the use of the absorbed energy to excite the nerve impulses that are propagated along the nerve fibers. 8- fr \ Retinal Receptor Mechanism The rod and cone visual cells are radially packed in a shell lying between the external limiting membrane and the pigmentary epithelium (10). Their photosensitive seg- ments are turned radially outward with Fig. 111-12. Grouping of the neurons in the human retina into functional systems. The incident light passes through the following layers: 1. Internal limiting membrane next to the vitreous humor. 2. Layer of optic never fibers. 3. Layer of ganglion cells which receive the nerve impulses from the bipolar cells above them. 4. Inner plexiform layer. 5. Inner nuclear or bipolar cell layer. 6. External plexiform layer. 7. Outer nuclear layer. 8. External limiting membrane. 9. Photoreceptor layer. Cones and rods mixed. Cones resemble flasks with narrow necks. They are about one-sixth shorter than the slender, nearly cylindrical rods. Rods about 2 microns thick and 60 microns long. The nerve impulses are sup- posed to originate in them as a result of the absorption of the incident radiant energy. 10. Pigment layer. Single pigmented cell, vertical section, hexagonally packed. Color, dark brown. RETINAL RECEPTOR MECHANISM 123 their outer segments pointing to the pigment cell layer. Protruding beyond the external limiting membrane (8) is a rod or filament-like structure divided into three segments : inner segment, fiber apparatus, and outer segment. If the structure is a cone, it is also divided into three sections: inner segment, lentiform bod} r , and outer segment. The rod and cone elements are regarded as specialized neuroepithelial cells and not as nerve cells. It has been suggested that the rods and cones are not distinct elements because various characteristics of the one are found in the other. Since in man the cones in the fovea resemble the rods at the periphery of the retina, it might be concluded that the cones have become specialized in one direction and the rods in the opposite direction, having a common relatively neutral ancestor. The distribution of rods and cones is not uniform throughout the retina. At the entrance of the optic nerve (optic disk), rods and cones are absent; hence light incident upon this area (blind spot) gives no visual sensation. The fovea centralis contains no rods. In the macula lutea, and in a widening circle around the fovea, rods and cones are present in approximately equal proportions. Towards the periphery the cones decrease in number until at the very margin only rods remain. The mosaic of rods and cones is very regular. Near the macula the cones are separated from each other by a single circle of rods; a short distance from the macula each cone is surrounded by series of three rows of rods, then four, and this pattern of increasing number of rods continues even close to the ora serrata, where only rods are found. The macula lutea is about 0.6 mm in diameter, and in this minute area a real image must be projected to produce distinct vision. The inference is that the cone structure is identified with perception of detail. The threshold for stimulation in this region is rather high and it is not appreciably increased by dark adaptation. The cones, there- fore, are not particularly adapted to perception of low intensities of illumination. This fact can be verified experimentally by looking at a night sky; the stars located at the border of the visual field appear much brighter than those lying at the center. In the most peripheral zones of the retina, where only rods are present, the threshold for vision is much less and can be decreased still more by dark adaptation; hence, the inference is that the rods respond best in dim illumination, and it has been found that they are particularly capable of detecting movements of retinal images of low intensity. Color perception, being associated with the cones, is most highly developed at the fovea. Here the inner layers of the retina become very much thinned, until near the center the transparent nerve tissues are represented merely by scattered cells of the inner nuclear and ganglion 124 BIOPHYSICAL CHARACTERISTICS OF THE EYE cell layers. The inner segments of the cones in the fovea are closely packed into a hexagonal pattern. This close-packed small elliptical depression, whose horizontal and vertical diameters are about 0.3 and 0.2 mm respectively, is also the seat of most distinct vision. The cones -0.10 mm Adjacent to the choroid Fig. Ill— 13. Visual cone and rod cells of man. Cone cells: a, from the ora ser- rata ; b, from fundus outside of macula lutea (yellow spot) ; c, from the margin of the macula lutea; d, from fovea centralis. Rod cell e contains visual purple. in this depression are very much longer, as illustrated by d in Fig. Ill— 13. They have the appearance of elongated rods. The number of cones in the fovea is about 4000. The number rods in the human retina totals about 130 million, the cones 7 million. Visual Acuity Acuity of vision is the ability to perceive the interspace between two very close objects. It is defined as the reciprocal of the just resolvable visual angle measured in minutes of arc. For the purpose of measure- ment a test object, in the form of an equally spaced ruled grating, a pair of parallel bars, or an incomplete circle or C-shaped figure, is employed. Experiments show that the interspace between two parallel bars must be increased as their distance from the eye is increased, and that VISUAL ACUITY 125 the angle at the eye, subtended by the interspace, must be greater than a certain minimum value. This angle is very close to 1 minute of arc, although values as low as 30 seconds have been obtained for persons of exceptionally good vision. Taking the posterior nodal point of the lens as 16.7 mm from the retina, 1 minute of arc corresponds with a distance of 0.0048 mm between the images at the retina. The diameter of the outer segment of a cone in the fovea is 0.002 mm, and its inner segment, which is a close-packed hexagonal mosaic, has a diameter of 0.003 mm; it follows that two points on an image can straddle a single cone and still be 0.0048 mm apart. Two point images can, therefore, be resolved by the mosaic of the fovea if one unilluminated cone lies between them. E. Hering in 1900 advanced the following interpretation in support of the mosaic-pattern- structure theory. Figure III— 14 shows a scale drawing of the retinal mosaic on which an image with a broken line of separation between light and dark portions is indicated. It is as- sumed that a change in stimulation of a single cone or column of cones is necessary to perceive the displacement of a retinal image. In image a the upper half of the cells in column c is stim- ulated, but in the lower section no cell of this column is stimulated. Hence a break in the edge of the image should be perceived. In b the image is shown slightly displaced to the right. No discontinuity can be perceived in its edge because all the cells in column d are stimulated. The upper diagram in Fig. Ill— 14 indicates that the horizontal displacement of the broken edge of the image can be as small as x and still excite two parallel columns of cells. If x is as small as 0.00087 mm for the hexagonal close- packed cone system in the retina, then x sub- tends an arc of 12 seconds at the nodal points re ti na , of the eye, which are at an average distance of 16.8 mm from the retinal image. The results are supported by the experimental evidence. It has been shown experimentally that the minimum separation of a break in a line detectable by unaided vision is as low as 12 ± 4 seconds of arc. The conclusion is, therefore, that visual acuity for the positions and movements of contours is about five times greater than it is for resolu- tion of double points and lines. Therefore, where interpolation methods Fig. 111-14. Hering's mosaic pattern of the 126 BIOPHYSICAL CHARACTERISTICS OF THE EYE of measurement are used, as in the estimation of the position of a slide rule, or of a meniscus of a barometer or chemical burette, the observa- tions are much less accurate than those obtained by a coincidence method as is used in mensuration. Variation of Acuity with Distance from Fovea The acuity of vision rapidly decreases as the image moves away from the fovea. Figure III— 15 shows this decrease in visual acuity and its variation with angular departure from perpendicular incidence on the 1.0 0.9 0.8 IT Temporal 40 30 20 30 40 10 10 Degrees from visual axis Fig. Ill— 15. Variation of acuity with distance from the fovea centralis in direct vision. Composite curve after Helmholtz, Handbuch der physiologischen Optik. fovea. At 5° from the fovea it falls to one third of its maximum. The broken line represents the visual acuity under very low intensities of illumination. On the other hand, when the eyes are used for fine work at high-level brightness, the visual acuity is very high at the center of the fovea. The drop in visual acuity across the fovea at low intensities, apparent in the depression of the dotted curve, indicates why we see. a faint star in the night sky better near the rim of vision than when it is focused on the fovea. The crossing of the blind spot is shown by the gap in the two lines at the nasal side of the axis. MEASURES OF ACUITY OF VISION Measures of Acuity of Vision 127 From the theoretical standpoint the simplest measure of acuity or " sharpness " of vision is the minimum angular separation which per- mits of resolution for two point objects. As mentioned above, this value for the normal eye is taken as 1 minute of arc. Hooke first pointed out in 1671 that the resolving power of the normal eye for such an object as a double star is about 1 minute of arc. The double star, Fig. 111-16. The upper letter E should be read by a normal eye at 50 ft. lower line and upper letter C should be read at 40 ft. The imaged on the fovea of the retina, can be perceived as two point sources if a relatively unstimulated cone lies between two others on which more energy is received. Vision is usually tested at 6 meters or about 20 feet. For this pur- pose a " page of type " is usually employed as a test object. In 1862 Snellen published a chart of test letters based on the assumption that 1 minute of arc is characteristic of the minimum separable. Figure III— 16 illustrates the principle of construction of a typical test-chart letter. Each letter in one row has a diameter subtending 5 minutes of arc at a distance marked on the chart against the row, and the stroke of the letter has a width subtending 1 minute of arc. A person with normal vision should be able to read the letters of any row at the distance indicated by the numerals set at the end of the row. The types are printed for distances from 20 to 200 feet. The illumination should be above 50 ft-candles, and glare must be avoided. 128 BIOPHYSICAL CHARACTERISTICS OF THE EYE The " broken ring " of Landolt [1876] aims at providing a test less variable than that of the letters. The ring has a diameter which sub- tends 5 minutes of arc at the standard distance, while its width and a gap in the ring each subtend 1 minute of arc. The observer must be able to recognize the position of the gap in any relative position of the letter. Although the measurement of acuity by such a broken ring may be rendered more difficult in the presence of uncorrected visual astig- matism, a greater consistency can be claimed in tests with this type of standardized object. Color Variables Color is an experienced sensation. The color variables are bright- ness, hue, and saturation. At ordinary levels of illumination intensity or of brightness, one can see about the same brightness-difference of colored surfaces as of color- less ones. Between a perfect white and a perfect black one perceives about 60 perceptible shades of neutral grays for an intensity of illumina- tion of about 50 ft-candles. Thus, one can distinguish about 125 hues in the spectrum of sunlight. Hue is a property of color which varies with changes in the frequency of the stimulating light. The ability to detect a difference in saturation (tint) is not very well developed. It is estimated that 20 different degrees of saturation represent the average number of tints of a color actually distinguishable. Therefore, multiplying the number of distinguishable hues (125) by the distinguishable shades (30) under a given high intensity of illumina- tion by the distinguishable tints (20) gives 75,000 as the approximate number of different color sensations. If, in addition, the intensity of illumination is changed so as to introduce a range of brightness, it is seen that the number of distinctly different visual sensations which one can experience, excluding those of form, runs into the millions. The Fundamental Colors It can be shown experimentally that three frequencies may be selected o from a continuous spectrum — one from the red end at about 6800 A, o one from the blue end at about 4500 A, and one from the middle at o about 5560 A — whose combinations in different proportions will give a sensation of white, any of the intermediate shades, or purple. Con- sidered physically, these three frequencies may be designated as funda- mental color arousers, but it is to be remembered that color is a term used to indicate a reaction in consciousness, and it is therefore not strictly applicable to the physical stimuli. THEORIES OF COLOR VISION 129 The fundamental color sensations according to some theories are red, green, and blue; according to others, they are red, yellow, green, and blue. Theories of Color Vision It is doubtful that any subject in science has given rise to so much speculation as the cause of color vision. The earliest historical period of speculation on how color is experienced, 640 B.C. to a.d. 1671, con- tains such great names as Pythagoras, Epicurus, Aristotle. The second great period, 1671 to 1801, of color theory was dominated by Newton's corpuscular theories. During the third period, 1801 to 1874, the con- tributions of the great minds of Young, Helmholtz, and Maxwell were added. The fourth period, which began with Hering's outstanding contribution, extended from 1874 to the early nineteen hundreds and culminated in the quantum interpretation of the photoelectric effect and applications of the quantum theory to photo-chemistry of the photoreceptor processes in the retina. The Young-Helmholtz theory, as Troland [1920] points out, is pre- ferred by physicists because it lays emphasis primarily upon the stimuli to vision, while the Hering theory receives more attention from the psychologists because its fundamental conceptions are derived from introspective analysis. These theories postulate the existence in the photoreceptors of the retina of a number of specific chemical substances which are acted upon by light. According to the Young-Helmholtz theory, there are three of these substances which are decomposed at a maximum rate by red, green, and blue light, respectively, and less so by the remainder of the visual spectrum. The rates of photochemical decomposition of these three chemical substances are supposed to be reported individually to the brain via the optic nerve, and the ratio between the three decom- position products determines the nature of the sensation. This ratio accounts satisfactorily for the laws of " color mixture " for normal, and also for some forms of color-defective vision, but it does very little more than this. It fails completely to explain the changes in the nature of the colors when the combination of red and green forms yellow, or when the combination of yellow and blue forms white. The theory of Hering also postulates the presence in the entire retino- cerebral apparatus of three substances. One of these substances is decomposed by light of all frequencies, although to the greatest extent by yellow-green light. This substance is then supposed to accumulate during the absence of light, owing to a reversible chemical reaction. 130 BIOPHYSICAL CHARACTERISTICS OF THE EYE The other two substances are supposed to be decomposed at a maxi- mum rate by red and yellow lights, and recomposed by green and blue lights. TABLE III-5 Photochemical Substance Retinal Process Sensation A. Red-green Disassimilation Red Assimilation Green B. Yellow-blue Disassimilation Yellow Assimilation Blue C. White-black Disassimilation White Assimilation Black The six psychological primary colors, red, green, yellow, blue, white, and black, are correlated directly with six distinctive rates of change in the three basic photochemical substances, as shown in Table III— 5. This system of relationships satisfactorily explains the manner in which the psychological primaries combine with one another, and accounts especially for the " antagonistic " behavior of red and green, and yellow and blue. Troland [1920] points out that the three weakest points in this theory are: (1) the failure of opposite processes in the black- white substance actually to cancel each other while those in the other two substances always leave a residual gray; (2) the fact that psychologically primary red and green do not in fact combine to pro- duce gray, but rather a yellow; and (3) the failure of continuous stimula- tion of a single region of the retina to reduce the sensory effects of all stimuli to a neutral mid-gray. Apparently, therefore, the essentially antagonistic natures of the processes underlying respective members of the three pairs of primary colors are not supported by the experimental facts. To meet these and other criticisms, Mrs. Ladd-Franklin [1892] pro- posed a theory based essentially on the existence of a single light- sensitive substance located in the retina. She also assumed a gradual evolution of the color sense of the retina from a primitive condition of colorless vision such as still exists in the periphery of the retina to a high degree of specialization by the fovea to reactions of color. Thus the retina is supposed to preserve a complete record of the historical changes of the anatomical development of rods into cones and also a comparable development of the rod-pigment sensitizer. In man only is there an additional intermediate cleavage stage, the visual yellow. According to the Ladd-Franklin theory a hypothetical light-sensitive substance must be assumed to break down in three stages. In stage I its decomposition by light leads to the initiation of nerve impulses THEORIES OF COLOR VISION 131 in such a manner as to produce various gradations of achromatic lumi- nosity in the visual sensation ranging from black, which is associated with the absence of excitation, to a white associated with the maximum rate of decomposition. In stage II of differentiation, the substance presents to the action of light two separate parts, corresponding, for example, " with two different radicals involved in the constitution of its original complex molecules." One of these parts is decomposed at a maximum rate by yellow light, and the other by blue light. The prod- ucts of decomposition act upon the optic nerve to produce the colors yellow and blue in consciousness. Simultaneous and equivalent decom- position of the two parts of the substance, however, generates a gray in consciousness. Stage III of evolution of the substance involves a differentiation of the yellow-sensitive component into red-sensitive and green-sensitive constituents. When these are acted upon separately, they produce a psychologically primary red and green in consciousness, but when simultaneously and equally decomposed they yield the original value. Hecht [1928] objects to the assumption that the sensations yellow and white are unique. He points out that if Young's idea is correct then yellow is a phenomenon which is produced where red and green receptor substances respond simultaneously. Similarly, white is identified when all three — red, green, and blue — receptor substances respond simultaneously. Both Hering and Ladd-Franklin have devised theories that assume the existence of separate receptor substances for yellow and for white. Hecht raised the question as to which of these two conceptions of yellow and white is correct. His answer was obtained by means of a simple experiment of binocular color mixing. He placed a red filter (Wratten 29) in front of one eye and a green filter (Wratten 58) in front of the other eye, and then viewed a brightly illuminated white surface about 20 cm square placed on a black background. He found that with one eye open the surface appears red ; with the other open, it appears green; with both eyes open, the surface appears yellow. In this experiment red light falls on a part of the retina of one eye and green light falls on the corresponding portion of the retina of the other eye, and the result is a yellow sensation; hence, Hecht concludes that only Young's theory is tenable. If the green and red Wratten filters are replaced by yellow (16) and blue (44A), a reasonably good white is produced binocularly. The binocular formation of yellow and white shows that theories which require special sensitive substances in the retina for yellow and white are untenable. 132 BIOPHYSICAL CHARACTERISTICS OF THE EYE One must, therefore, conclude that no theory of color sensation is deserving of consideration which is not built on the fact discovered by Thomas Young, and confirmed by Helmholtz, that three radiant- energy stimuli are sufficient as a physical cause to start the retinal photochemical processes, which probably initiate the nerve impulses transmitted along the optic nerve to the brain, and the result is an experienced sensation called color vision. BIBLIOGRAPHY 1876 Landolt, E., Ann. d'Ocul, 75, 207. 1892 Ladd-Franklin, C. For summary see Science, 60, 555 (1922). 1909 Gullstrand's Schematic Eye. For complete data see H. von Helmholtz, Handbuch der physiologischen Optik, 3rd Ed., Vol. 1, p. 335. 1912 Stilling, J., Ophthalmoscope, 10, 519; see also Southall [1937]. 1912 Duane, A., Ophthalmoscope, 10, 486. 1918 Reeves, P., Astrophijs. J., 47, 141. 1920 Nutting, P. G., J. Optical Soc. Am., 4, 55. 1920 Reeves, P., J. Optical Soc. Am., 4, 35. 1920 Troland, L. T., Am. J. Physiol. Optics, 1, 317. 1921 Luckiesh, M., A. H. Taylor, and R. H. Sinden, J. Franklin Inst., 192, 757. 1921 Luckiesh, M., Am. J. Physiol. Optics, 2, 3. 1924 Burge, W. E., Am. J. Physiol. Optics, 5, 231. (Referred to by Sheard [1924].) 1924 Sheard, C, Am. J. Physiol. Opics, 5, 214. 1926 Fincham, E. F., Am. J. Physiol. Optics, 7, 469. 1927 Duke-Elder, W. S., /. Physiol, 62, 315. 1928 Hecht, S., Proc. Natl. Acad. Sci., 14, 237. 1930 Luckiesh, M., Artificial Sunlight, D. Van Nostrand Company, New York. 1932 Barnes, R. B., and M. Czerny, Z. Physik, 79, 436. 1935 Hartline, H. K., Cold Spring Harbor Symposia Quant. Biol., 3, 245; also H. K. Hartline and C. H. Graham, J. Gen. Physiol., 18, 917. 1935 Hecht, S., " The Nature of the Photoreceptor Process," Murchison's Hand- book of General Experimental Psychology, Clark University Press, Worcester, Mass. 1937 Southall, J. P. C, Introduction to Physiological Optics, Oxford University Press. 1938 Dartnall, H. J. A., C. F. Goodeve, and R. J. Lythgoe, Proc. Roy. Soc. London, A164, 216. 1938 Hecht, S., " A Review of The Photochemical Basis of Vision," J. Applied Phys., 9, 156. 1938 Hecht, S., " The Nature of the visual Process," The Harvey Lectures, New York Acad. Med., Series XXXIII. 1938 Hevesy, G., and F. A. Paneth, Radioactivity, p. 30, Oxford University Press. 1941 Bartley, S. H., Vision. A Study of its basis, D. Van Nostrand Company, New York. 1941 Granit, R., Ann. Rev. Physiol, III, 461 Part II, " Visual Receptors." 1941 Polyak, S. L., The Retina, University of Chicago Press. Chapter IV EMISSION AND ABSORPTION OF BIOPHYSICALLY ACTIVE LIGHT Statistics yield much evidence that sunlight is of direct benefit to human beings. During the winter the sun is at lower altitudes and the maximum possible duration of sunshine is much less than in summer. Furthermore, the solar radiation must pass through a greater air mass since it reaches the earth more obliquely. As a consequence, the photo- biologic radiations in sunlight are greatly weakened in winter. There is some evidence that sunlight increases the resistance to infection. Sunlight tends continually to sterilize earth and water because of the resulting photochemical activity. Perhaps the most out- standing importance of sunlight, or its artificial equivalent, is in its rela- tion to the prevention and cure of rickets. Rickets occurs with marked frequency during the winter and spring and almost disappears in mid- summer. Sunlight or its equivalent is also known to promote calcium anabolism, and the most important function of all is that chlorophyll, the green coloring matter in the leaves of the plants, makes use of cer- tain wavelengths in fixing the carbon from carbon dioxide gas in plant structure. Spectral Transmission of the Atmosphere The atmosphere serves as a gigantic filter for the sun's radiant energy. The short-wave ultraviolet energy is absorbed by the ozone in the upper strata, and smoke, water vapor, and the dense gases near the earth's surface all act as scattering agents of light. The visual proof is the clear blue color and the brightness of the sky. Without this scattering, the sky would be as dark as it is at night. As a result of absorption of solar radiation by the atmosphere, the spectral nature and the intensity of the sunlight vary with the altitude of the sun. In order to give an idea of the spectral distribution of direct solar radiation, curve A, Fig. IV- 1, has been plotted from Abbot's data, which clearly shows the prominent atmospheric absorption bands 133 134 BIOPHYSICALLY ACTIVE LIGHT Spectral distribution of radiation from the sun at Washington, D.C. appearing as depressions in the curve. Their depths indicate to what degree the atmosphere is opaque to these wavelengths. Those in the infra-red are due chiefly to water vapor which was slightly above average when these data were obtained. There is a rapid decrease between 5000 and 4000 A, indicating a rapid increase in opacity of the atmosphere in this violet region. Although the short-wavelength limit of the solar spectrum as recorded on earth is set close to o 2885 A, for all practical purposes, owing to smoke, it is usually ac- cepted as 2950 A in summer and o 3100 A in winter. In order to appreciate the absorption effect of the atmosphere, curve B in Fig. IV-1 has been introduced to show the relatively greater inten- sity of the energy at very high altitudes where absorption is a negligible factor. 4000 H 8000 12,000 16.000 o Wavelengths in A 20,000 Fig. IV-1. The spectral distribution of radiation from the sun. A, as measured at Washington, D. C, with 1.37 cm water vapor in the atmosphere, for the sun at zenith. B, similar measurements made at altitudes so great that absorbing atmosphere is negligible. Shaded area shows visible spectral region with maximum visibility at 5560 A. (By courtesy of J. H. Clark [1931].) Figure IV-2 shows the fluctuations of the ultraviolet content of sunlight during a typical clear day at different times of the year. It was found that the ultraviolet content of sunlight rises more sharply to a 11 12 1 Hour Fig. IV-2. Ultraviolet con- tent of sunlight on a typical clear day in the months indi- maximum and then decreases more rapidly cated (By courtesy of j H than the total radiation. This difference is ciark [1931].) due to the relatively greater atmospheric absorption for the ultraviolet radiation. The predominance of the ultraviolet content between 11 a.m. and summer, is apparent from these curves. 1 p.m., especially during the DEGREE OF ERYTHEMA 135 Degree of Erythema o Using the homogeneous emission line of mercury at 2967 A as a source, a minimum perceptible erythema is denned as that produced by 180,000 ergs per square centimeter. For an exposure of 15 minutes a radiant flux intensity of 20 microwatts per square centimeter would be required (Council on Physical Therapy [1932], [1934]). Medical authorities usually recognize four stages of erythema. From the viewpoint of therapy the first three stages may be beneficial, depend- ing upon the objective sought. The final blistering stage may even be curative locally; it is, however, in general pathological. The first three vary visually from a faint redness to a vivid redness which is the more lasting. For midsummer sunlight the relative exposure times, for an assumed average untanned skin, are as follows : Degree 1 , minimum perceptible erythema 1 . Degree 2, vivid, producing moderate tan 2.5 Degree 3, painful " burn " 5.0 Degree 4, blistering 10.0 From this point of view the minimum perceptible erythema is one that disappears in 24 hours. These relative values are only approximate and are modified by the degree of pigmentation, but in general they represent a good working range for time of exposure and erythema pro- duced. In order to save time of exposure ultraviolet-ray therapy has been generally investigated and practiced with high-intensity sources of ultraviolet radiations in which exposures of a few minutes are usually resorted to. The conclusions gained from high-energy exposures for short periods of time, however, cannot be applied to the production of erythema by moderately intense sources over longer periods of time. TABLE IV-1 Erythemal Effectiveness of Radiation in Range 2400 to 3300 A, 2967 A Taken as Unity Wavelengths o A Relative Effectiveness Wavelengths A Relative Effectiveness 2400 56 2967 100 2500 57 3000 83 2600 42 3050 33 2700 14 3100 11 2800 6 3150 1 2900 31 3200 0.5 2950 98 3250 0.3 3300 0.0 136 BIOPHYSICALLY ACTIVE LIGHT TABLE IV-2 Minutes Required for the Production op Erythema prom Artificial Sources Degree of Erythema Artificial Sources 76 cm from Skin Minimum Perceptible Vivid Sunlight and skylight (noon, midsummer) Quartz mercury arc (3.5 amperes, 110 volts) Sunlight lamp (Type S-l), Corex D bulb (400-watt tung- sten mercury arc) Bare carbon arc (1000-watt) 8 mm, " Sunshine car- bons " 20 7 8.5 16 50 17 21 40 By courtesy of M. Luckiesh. It should be kept in mind that a value of erythemal effectiveness (Table IV-1) expressed in watts per square centimeter remains un- changed only as long as the physical characteristics of the radiation do not change. For example, such a factor established for a bare source of radiation ceases to hold when the source is placed in a reflector which does not reflect the ultraviolet rays as well as the visible rays. In Table IV-2 is indicated the exposure time required to produce two degrees of erythema, with common commercial artificial sources placed at a distance of 76 cm (30 in.) from average untanned skin. Erythemal measurements are semiquantitative and uncertain, since the untanned skins of individuals vary over a wide range, and it is essen- tial to recognize a skin of approximately average sensibility. An approach to a quantitative method of detecting " degree of erythema " is attained by means of a strip of tape in which is punched a series of holes \ to ^ in. in diameter. This is attached to the untanned skin of the back, chest, or abdomen. The source is placed at a measured dis- tance from the skin and then the effect of the incident energy is observed at a given skin distance. As the time passes, the holes are successively covered; the result is a series of exposures of various durations. For accurate work a second series of holes should be used adjacent to the first as a check. The intensity of illumination is varied according to the inverse square law, and the minimum perceptible erythema is fairly easy to establish. Luckiesh, during an extensive study of the reciprocity law over a range of 25 to 400 ft-candles with the " Sunlight (Type S-l) Lamp " (Fig. IV-3), found that the equality of products of exposure time and ft-candles holds very well for this type of mercury-arc radiation, and TANNING 137 Mercury arc Tungsten filament Corex D glass Tungsten electrode Argon gas Pool of mercury Fig. IV-3. "Sunlight Lamp" (Type S-l) General Electric Company. (By courtesy of Forsythe, Barnes, and Easley [1931].) that the minimum perceptible degree is very definite. The second degree is described as " vivid," but a moderate tan results from it and the relative time of exposure is about 2.5 times that of degree 1. Tanning The color of normal human skin depends upon its pigment content and the back-scatter of that part of the incident energy which has succeeded in penetrating without absorption (Edwards and Duntley [1939]). Below the external horny layer (corneum) is found the basal cell layer in which the principal concentration of photoactive pig- ments is located. A network of blood vessels is found in the layers below these basal cells. The next deeper layer is called the derma, below which lie the subcutaneous tissues. It has been suggested that the tanning mechanism is probably a photodynamic action in the presence of oxygen and is due to the oxida- tion of pigments already present in a colorless reduced state. The bleaching of tanned skin shows it to be a reversible process quite inde- pendent of the formation of new pigment. The major pigments are found to be melanin and an allied diffuse substance melanoid. Carotene was also found in the subcutaneous tissues. In different races the melanin content of the skin is found to increase in the following order: Japanese, Hindu, mulatto, and negro. Albino skins apparently do not have the ability to produce pigmentation even with the aid of long-wave ultraviolet light. Irradiation of the normal skin with long-wave ultraviolet light from o the spectral region extending from 3000 to 4500 A produces a darken- ing of the pigment found in the skin. The maximal effect is obtained o from the narrow band of energy lying near 3400 A, according to Henschke and Schulze [1939], or at 3850 A according to Hausser [1938]. It is doubtful that an erythema accompanies the tanning when this spectral range is used conservatively. Owing to the filter action of the cumulative darkening pigment, it seems reasonable to expect that the erythema threshold accompanying tanning is very much greater. It o was found, for instance, that if a normal skin was irradiated with 3850 A it took 18 X 10 7 ergs/cm 2 or 3.4 X 10 19 photons/cm 2 of skin to produce 138 BIOPHYSICALLY ACTIVE LIGHT o . the erythema threshold ; if irradiated with 2967 A, it took 34 X 10 ergs/ cm 2 , or 5.1 X 10 16 photons/cm 2 . Apparently the erythema accom- panying gradual tanning by long-wave ultraviolet light is a negligible o factor if no 2967 A radiation is present. If the intensities of these two radiations are so chosen that the same o final degree of erythema is developed, that at 3850 A reaches its maxi- mum in 2 to 3 hours, but that at 2967 A is just becoming visible at the end of this period of time. Twelve hours after irradiation each shows its maximal reddening; the former has developed into a brown red, the latter into a pronounced carmine red color. After 48 hours the former is still maximal red and the latter is strongly brown. After 5 weeks the o erythema has subsided; the 2967 A exposure is slightly pigmented, and the 3850 A exposure has developed into a deep brown pigmentation. As yet the photochemical reactions involved in these biophysical activities are only slightly understood. The trend of the evidence (Blum [1941]) seems to indicate that an active substance is liberated which is responsible for the erythemal response as an indirect capillary reaction. Apart from the vasodilatation, which appears after a latent period, the structural injuries are limited almost entirely to the first 0.1 mm when wavelength 3000 A was used. Penetration by 7500 A is only about 2.5 mm, although a wavelength of about 11,500 A can penetrate to a depth of 5 mm. Artificial Sources of Ultraviolet Radiation A typical mercury-vapor arc is illustrated in Fig. IV-4. This is a Cooper Hewitt quartz-enclosed mercury-vapor arc. The luminous tube of the burner is made of clear fused quartz of high ultraviolet trans- Anode Fig. IV-4. Sectional view of a " Cooper Hewitt " quartz mercury arc. 110-volt burner. Length 6f in. Luminous tube diameter f in. mission. The leads are flexible stranded wire insulated with porcelain beads because of the high temperature attained by the terminals. The anode, or positive electrode, of the burner consists of a tungsten wire coiled into a target. In operation it is heated white hot by the arc which extends from it to the surface of the mercury cathode-, or negative electrode. The cathode chamber serves to keep the mercury at the ARTIFICIAL SOURCES OF ULTRAVIOLET RADIATION 139 proper temperature and to store up the mercury used in starting the burner to arc. The arc is started by tilting the burner so that a series of mercury globules runs from the cathode to the anode and back to the cathode chamber. The arc first strikes between these globules, and when the device is operating with sufficient resistance in series (it is a low-pressure 80 60 40 20 350 _ - c »*- o o l\ I '■0 S 300 E 3 _ o N CO 3 High-intensity quartz mercury-vapor arc 143 v-4.5 a E 3 E X CO /I 1 l\\ CM E § 250 CM - 1 CM 1 CO E CO E / **"" 1 / *o 1 / 3 \ CO - (0 E CD / ° \ S E <3 x: 4-* / f» \ >\ ° 200 E u 1! Lethal to bacteria n maximum at 2660 A Q. CO o E •*-* ».— LU / o< / f- 1 r to \ bfl \ ca \ •a ' bo CB C LU _ S 150 Z-Sa~ CD o , ' =>l t J= 3 CT> CM 1 | / E \ E \ ° >> 1 fl "E 1 / E 1 o 3 1 / S 100 1 1 CO 1 1 / 1/ «-• i — ^ ai 1 1 /o< 1 1 1/ L \ " "5 50 to 1 1 / CD 1 / \ / V V 1 /l II |CM is 1 m J=l / CM \ / CM \ / 1 1 < } ^*r V J CD 1 I 1 *• 1 1 1 1 /l 1 1 1 ,1 i 2300 2500 2700 2 o 900 Wavelengths A 3100 3300 Fig. IV-5. Distribution of the energy among the wavelengths emitted by a quartz mercury-vapor arc. The right-hand axis shows the relative erythemal effectiveness of the various wavelengths at 50 cm from the arc. arc) the light column appears to fill the whole arc tube uniformly. In this condition its spectrum shows only the strongest mercury lines and no continuous spectrum is visible. When the arc is adjusted for opera- tion at high intensity, it starts as a low-pressure arc but, as it heats, changes to the high-pressure condition. In this state, indicated by an apparent concentration of the light into a narrow thread of great inten- sity in the axis of the arc tube, a continuous spectrum is superimposed upon the mercury line spectrum, several additional mercury lines become visible, and the ultraviolet radiation is greatly intensified. The quartz mercury arc from which the data for Fig. IV-5 were obtained was rated and operated at 143 volts and 4.5 amperes. It radiated considerable energy shorter than 2537 A, and, notwithstanding the low intensity of these short wavelengths, considerable erythema can be produced by them. In substituting this arc for ultraviolet sunlight, the radiations shorter than 3150 A are of primary importance. The quartz mercury arc radiates strongly in the following groups of wave- 140 BIOPHYSICALLY ACTIVE LIGHT lengths: 2536, 2652, 2894, 2967, 3021, and 3130 A; less strongly at 2752 and 2804 A; and weakly at 2378, 2399, 2482, and 2698 A. The newer high-potential " SC-2537 Hanovia " mercury-vapor arc has as much as 85 per cent or more of its energy of emission concentrated at 2537 A. " Sterilamp " This lamp was designed and constructed by the Westinghouse Lamp Company to emit its predominant radiations at wavelengths having the highest bactericidal properties and the least erythemal effect. Radi- ations from these lamps produce a mercury spectrum with the greater o portion of the radiant energy in the region of 2537 A. There is also some radiation in the region of 1849 to 1960 A. The shortest radiations are readily absorbed by the surrounding air but are very strong in bactericidal action. These lamps are tubular and are made in various lengths. A typical example has an overall length of 14 in. and a f -in. diameter. Its start- ing potential is 400 volts alternating current, operating, however, at 275 volts with a current of about 0.03 amp. They have two terminals, one at each end, and burn in any position when connected to the 110- volt a-c circuit with proper transformers. Hart and Gardner [1937] and others have used this type of lamp for sterilization of the air in the surgical operative region. " Sunlight Lamp " Of the number of tungsten-mercury arcs that have been patented, the only one which has been commercialized is the sunlight (Type S-l) lamp, developed by the General Electric Company. It consists of two tungsten button electrodes at the terminals of a tungsten filament sup- port, as shown in Fig. IV-3, a pool of mercury, and an argon-filled " Corex D Glass " globe. The lamp starts in any position. When the proper voltage is applied, the filament heats and the arc strikes between the button terminals. The biologically active radiation becomes more intensive as the bulb increases in temperature. It is essentially a low- voltage lamp, and the attached transformer must deliver 9.5 amp at approximately 30 volts in order to heat the filament. When the arc is completed, the current rises to 30 amp and the voltage drops to about 11 volts. The lamp consists of two primary sources of energy, incan- descent tungsten and mercury vapor. The emitted radiant energy of the former consists of a continuous spectrum of all wavelengths extending o from the long-wave infra-red to about 3500 A in the violet region. The THE ELECTRIC ARC 141 mercury vapor emits energy of only the characteristic wavelengths of mercury, comparable to those shown in Fig. IV-6. / + / f*» 1 (D 0.7 ^-* 0.6 - u 01 0> / CO *o TO 1 E 0.5 "Sunlight lamp" E / 0> J o range o * / Ik I ■+-> 2800-3200 A 0) 1 E / E / TO 1 ° 0.4 c u 2.45% of total energy E E » CD / o< DO >5 0.2 en 1 CM 1 !/c CM CO t^ CO \Tanning Maximum 1 I 0.1 - 1/ c J\ 1 1 i I i 2600 2800 3000 Wavelengths in A 3200 3400 Fig. IV-6. Distribution of energy curve of the " Sunlight Lamp " from data by A. H. Taylor [1931]. The following average values for the ultraviolet output are obtain- able when the arc strikes in a mixture of mercury vapor and argon gas enclosed by a Corex D bulb of about 1-mm thickness: Relative Ultraviolet Output Wavelength Output 3657 198 3130 100 3024 28 2967 A 17 If a shallow oxidized aluminum reflector, about 13 in. in diameter, is used over the bulb, then at 30 in. a minimum perceptible erythema is produced on average untanned skin by exposures of 8 to 10 minutes. At a distance of 1 meter this type of lamp emits an energy flux one third o as great as midday summer sunlight in the spectral range 2800 to 3100 A. o The Corex D glass transmits about 59 per cent of the 3000-A wavelength. The Electric Arc Carbon arcs produce the highest available artificial temperatures, 4000° K being obtainable. The positive crater of a direct-current arc is used as a source of continuous radiation. By introducing salts into 142 BIOPHYSICALLY ACTIVE LIGHT the core of the carbon, selective emission in the hot gases may be utilized to enrich different parts of the spectrum. If the lower terminal of such an arc, set in a vertical position, is made of a large cylinder of iron with a shallow depression in its center, the arc is termed an " iron arc " and is extraordinarily rich in ultraviolet radiations. In the commercial types of carbon arc the amount of ultraviolet radiation between 2800 o and 3100 A varies considerably. For example, the energy distribution 15 10 ,~\ ll ' \ s \ \ \ 1 \ A ll L \ \ s \ s ^ — _ njj 1' 1 l 1 V — — ~-> . B ^ Hf__ 2000 3000 4000 Wavelengths in A 5000 6000 Fig. IV-7. Emission of " Sunshine S " carbon and " Therapeutic B " carbon arcs as compared with quartz mercury arc. S and B, bare arc without reflector, 30 amp, alternating current, 50 volts across arc. Hg, quartz tube mercury arc, no reflector, average voltage 140 and 170, alternating current, and 4 amp. Each square represents 250 microwatts of radiant flux per square centimeter at 1-meter distance from the arcs. (Data by courtesy of the National Carbon Company.) of the radiation obtained from the " therapeutic carbons " of the Na- tional Carbon Company as determined by Greider and Dowries are shown in Fig. IV-7. The " Eveready therapeutic B carbons " and the " Sunshine carbons " are marked B and S, respectively. The B carbon supplies more biologically active radiation than the S carbon. The B carbon contains iron. It gives light with a slightly bluish tinge but in the visible range has a candlepower less than one fourth that of the S carbon. The spectrum of B carbon is characterized by many lines that extend o from the visible through the ultraviolet region to 2300 A or shorter. It is very intense in the long-ultraviolet region. In order to avoid con- junctivitis during exposure with this type of carbon arc it is necessary to protect the eyes with glass goggles. Finsen Unit Inasmuch as interest in the biological effectiveness of ultraviolet radiation arose first in therapy, powerful sources of ultraviolet radiation ABSORPTION OF RADIANT ENERGY 143 have been studied and exploited primarily for their therapeutic effective- ness. It must be emphasized, however, that there is no necessary rela- tion between erythemal effectiveness and therapeutic value. As a result, the establishment of a system of units based on erythemal effec- tiveness must not be viewed as a solution to the problem of measurement of energy in the ultraviolet region for general biological application. The practical necessity of establishing some criterion for the compara- tive evaluation of different types of ultraviolet sources for medical purposes cannot be escaped. This has led to the adoption of certain standard units. The Council on Physical Therapy [1934] has tentatively adopted the Finsen unit (F.U.) as a beam of homogeneous radiation of wavelength 2967 A with flux density of 10 /iw/cm 2 . It has been observed that 2 F.U. for 15 minutes is a representative requirement for minumum perceptible erythema. Therefore it has been proposed that 1 erythemal unit be denned as 2 F.U., or 20 juw/cm 2 o for 15 minutes of homogeneous radiation of wavelength 2967 A. In the use of such a unit it must be borne in mind that even small changes in operating conditions of a source will change the energy-wave- length output and hence the radiation erythemal equivalents. Absorption of Radiant Energy The transmission of radiant energy through a medium is always accompanied by a certain amount of absorption, regardless of the wave- length incident on the medium. Media which are commonly referred to as transparent, if not employed in too great thickness, transmit with- out appreciable absorption the range of wavelengths comprised within the region of the visible spectrum. In general, however, thej^ show powerful absorption in the infra-red and ultraviolet regions, and if a sufficiently great thickness is employed absorption will be found present even in the range of visible radiations. Pure water, which is one of the most transparent of the common sub- stances, appears distinctly blue in long columns, showing that it absorbs more or less completely the red end of the spectrum. It is conventional to distinguish between two types of absorption: general, in which the absorbing power is very nearly the same for all wavelengths ; and selective, in which the absorption is more or less limited to a narrow spectral region. Lampblack, developed photographic films, neutral filters, and some forms of close-meshed rocking wire screens represent the first type. Analine dyes, inorganic colored salts, blood, bile, and generally all colored media represent the second type, in which 144 BIOPHYSICALLY ACTIVE LIGHT certain waveleDgths are freely transmitted while others are strongly absorbed. Law of General Absorption When radiant energy passes through a homogeneous medium, the medium absorbs part of the energy and the amount of this absorption is generally different for various wavelengths. If a monochromatic beam of light has its intensity (the energy per square centimeter per second of a plane parallel beam of monochromatic light) decreased by an amount dl in passing through a distance dx in the material, and if the loss is the same at all depths, then dl r» dx. If at the same time the decrease in intensity is proportional to the intensity itself (dl o* I), then dl = —aldx On integration this becomes I = constant e~ ax where a is the constant of proportionality whose magnitude depends on the material and wavelength of the beam of radiant energy. The nega- tive sign is used to indicate that the change in I is a decrease. If Jo denotes the constant intensity of the beam which enters the surface of a slab of absorbing material, where x = 0, then the constant in the above relation is the intensity of the incident energy, 7 . It follows that the intensity of the beam after passing through a thickness x = d has an intensity I d given by the relation Id = he~ ad where a is known as the coefficient of absorption. This law implies that the absorption increases in geometrical progression as the thickness increases in arithmetical progression. To illustrate the law, let us consider the slab d composed of five layers, each of unit thickness, and made of a material having an absorption coefficient equal to yo- Let the incident energy I = 100 units. In traversing the first layer, this value is reduced y 1 ^- by absorption so that 90 units leave the first and enter the next layer. The 90 units lose Yq of their magnitude in the second layer, so that 81 units are incident on layer three. Then layer three absorbs 8.1 units, leaving 72.9 units, etc. The energy leaving the final surface of the fifth layer is only 59.0 units. Hence the total energy loss through absorption is 41 units. The per cent transmission or transmissivity is T = 100 y PRESENTATION OF DATA 145 Beer's Law of Absorption The absorption law is used in various forms. Beer (1852) used it for solutions to describe the absorption of monochromatic light in which the solvent contributed nothing to the absorption. If we con- sider the absorbing layers as having molecular structure, and if we can say that each molecule absorbs an equal fraction of the energy which passes over it, then Beer's law expresses the absorptions in terms of concentrations of the absorbing layers. Let c be the concentration of a solution; then, if 7 is the entering intensity and Id the reduced intensity upon leaving an absorbing layer of thickness d, Beer's law states that Id = he~ acd where a is called the absorption coefficient. Beer's law holds only when the absorbing property of a molecule is not influenced by the proximity of its neighbors, which condition is not always true. It must be emphasized that the laws of absorption apply only to monochromatic radiation and cannot be rigorously applied to the absorption of narrow bands of spectral wavelengths or to the absorption of extended spectral regions. Extinction Coefficient A common practice (after Bunsen and Roscoe) is to express the absorption as the reciprocal of the thickness which is necessary to weaken the light to one tenth of its incident value. This definition gives I d = I Q lQT kd and I d = I l(T tCd or logio — = kd and logi — = eCd Id id where k is called the extinction coefficient, and e is the molecular extinction coefficient. The extinction coefficient (k) is used when the molecular weight of the absorbing material is not known, The concentration C is expressed in moles per liter. Presentation of Data Figure IV-8 illustrates the use of transmissivity (Id/Io) in presenting data. Graph 1 in this figure shows how the transparency of an 0.08-mm thickness of human epidermis varies with the incident energy at the wavelengths designated (Lucas [1931]). Superimposed is graph 2, 8U - -06O >-1 - - ■8 A - 2» E 09 C — - 20 d i i i i 2500 30 35 □ Wavelength A 4000 2300 25 27 o Wavelength A 3000 Fig. IV-8. Curve 1 shows how the transmissivity of an 0.08-mm layer of human epidermis varies with wavelength. Note its rapid rise in transparency near 3000 A. Curve 2 shows the relative greater transparency of human sweat, 1 mm thick, in the ultraviolet. The lower curves show how the extinction coefficient k can be used to compare the absorption of (3) egg albumin, pH 1.65 (L. E. Arnow [1935]), with (4) serum pseudoglobulin, and (5) serum albumin. Note characteristic absorption band at 2790 A. (F. C. Smith [1929].) 146 ABSORPTION SPECTROPHOTOMETRY 147 32 ,28 £24 20 = 16 Calculated ^/\ Thymus Z*^"' ^ nucleic /"' \ acid \ x / / <7 \ ' 1 \ \ \\ Experimental \\ \\ Adenine \ \ Guanine / ^-\ Thymine\\ 1 1 Cytosine \\\ i i i X\ 2200 2400 2600 Wavelength A 2800 Fig. IV-9. The ultraviolet absorp- showing the comparable transmis- sivity of human sweat about 1 mm thick (Crew and Whittle [1938]). The lower series of graphs illus- trates how the extinction coefficient k can be used to show the relative absorption of (3) egg albumin, (4) serum pseudoglobulin, and (5) serum albumin. Note that they all have « a pronounced absorption band at =12 2790 A, which is common to proteins, and are rather transparent to radia- o tion around 2500 A. Figure IV-9 illustrates the use of the molecular extinction coefficient to show that the combined absorp- tion of several constituent molecular , ,1 1 ,• tion spectrum of thymus nucleic acid groups is equal to the absorption , ..,., , ^ M ^ as compared with the absorption spec- of the composite molecule. The tra of its purine and pyr i m i d i ne con- broken graph shows how closely the stituents. The graphical sum of the sums of the extinction coefficients absorbing constituents is the upper of the products of hydrolysis of broken . curve - Note how closel y [t ., , . • i r • / • approximates the experimental value. thymus nucleic acid [purine (guanine (% courtegy of j R Loofbourow and adenine), and pyrimidine con- 1940].) stituents (thymine and cytosine)] resemble the experimental values obtained from the composite molecule, thymus nucleic acid. Absorption Spectrophotometry The essential pieces of apparatus for absorption spectrophotometry are: (1) a constant source of radiation, (2) an optical instrument for resolving the radiation into a spectrum, and (3) a means of evaluating the relative intensities of the incident and transmitted energy passing through an absorption cell. When absorption measurements in the visible spectral regions are made, incandescent linear-filament lamps are used. For the ultraviolet, the condensed under-water spark between molybdenum terminals gives a nearly continuous strong spectrum containing wavelengths as low as 2000 A. Figure IV-20 shows the limits of transmission set by very pure water. Recently developed high-pressure mercury arcs (Buttolph [1939]) emit a practically continuous spectrum in the long-wave ultra- violet. 148 BIOPHYSICALLY ACTIVE LIGHT Fig. IV-10. Diagram of a " Spekker " photometer placed in front of the spectrograph slit G. A prism monochromator or prism spectrograph is preferably used to resolve the visible beam of light into its spectrum. For exploring the ultraviolet, the above instruments are provided with quartz lenses and prisms. A means of evaluating the relative intensities of the various wave- lengths before and after they have passed through the absorption cell constitutes the photometric phase of the absorption measurements. A photoelectric cell or a linear thermocouple may be used for this purpose in connection with a monochromator. The in- tensities are evaluated from a developed photographic plate when a spectrograph is used. One of the simpler precision absorption instruments now much in use is the split beam " Spekker " absorption pho- tometer (Twyman and Allsopp [1934]), illustrated in Fig. IV-10. The light source Q, and the " Spekker " photometer containing the absorp- tion cells C\ and C 2 , are adjusted so that the two emerging beams are focused one above the other on the slit of the spectrograph G. The spectrograph resolves these two sources and focuses them as two contacting spectral images on the photographic plate. The light from source Q is internally reflected from the faces of the two rhombs Ri and R 2 . Thus two beams of equal intensity are pro- duced. One beam is diverted upward, and the other downward; both are reflected forward through the lenses L\ and L 2 . The upper beam passes through a precision slit S\ and an absorption cell C\ containing the solvent, and thence through the lens L 3 via the rhomb R% into the upper half of the spectrograph slit G. An identical optical path is traced by the downard deflected beam in passing through the absorption cell C 2 containing the solution. The image of the adjustable slit S 2 falls below that of Si on the spectrograph slit. The slits Si and S 2 control the intensity of the two beams. The slit S 2 is variable in size by means of a precision micrometer push screw. By proper adjustment of the light energy passing through S 2 the photographed spectrum of this beam may be matched for intensity at any desired wavelength with a similar wavelength in the spectrum photographed just above it by means of the light passing through S\. Slits aSi and S 2 are illuminated with equal fluxes of uniform radiation, which may be represented by 7 (per unit area). Let Ai and A 2 be the COLORIMETER FOR MONOCHROMATIC LIGHT 149 areas of the apertures of the slits S\ and S 2 when an intensity match for a given wavelength is produced on the photographic plate. The quanti- ties of radiation transmitted by the apertures and incident on the absorption cells C\ and C 2 are Ail and A 2 Io, respectively. After trans- mission through the absorption cells, both these quantities are reduced to Id. The matched intensities for a given wavelength are given in the Bunsen-Roscoe notation I d = Ai/ l(T* ld = A 2 J 1(T*** where d is the length of the matched absorption cells. Then logio ~r = (k 2 - h)d Ai The screw regulating the size of the slit S 2 , if calibrated to read log (A 2 /Ai) for a fixed value of A\ and d, will give the optical density of the absorbing substance with reference to that of the comparison liquid (the solvent) for a given wavelength. If the extinction coefficient of the solvent is known, the extinction coefficient of the solution may be obtained. Colorimeter for Monochromatic Light Colorimetric methods of analysis consist of treating a solution of a substance whose absorption characteristics are desired with a reagent so as to produce a color which is proportional in intensity to the amount of the substance present in the solution. If Beer's law is applicable, then the concentration must be directly proportional to the logarithm of the transmitted light intensity (Fig. IV-11). In the usual colori- metric analysis it is desirable to determine the amount of colored material in the sample as compared with a standard. The amount of material present is measured by the amount of light absorbed. Accurate meas- urements can be made only by a spectrophotometric determination at that wavelength which corresponds with the maximum of its absorption band. A very good first approximation can be attained if one uses a narrow band of wavelengths as a source coinciding with the maximum absorption in the absorption band of the colored solution. Figure IV-12 shows a simple way in which this analysis may be accomplished. The basic design developed by Moll [1919] uses a nearly monochro- matic illumination obtained by means of a direct-vision spectroscope or Amici prism. A straight horizontal-filament lamp L is placed in the focal plane of an achromatic objective 0\. The beam of parallel light passes through an Amici prism train from which it emerges as a con- 1.0 .8 .6 M O _ "S .2 60 O o .1 "o a * .08 1.06 E W 1.04 .02 1 i i ¥\ V\ X \ i\ i X^ V \ ! \ 1 \ 1 k \ 1 \ \ 1 \ \' \7200 A \ \ i\ \ \ \ 7100 A \ V \ \ \ • 15600 A \ ] \4800 \ ' \ \>o6o A\ \ i \ \ i \ a\ \i 12 3 4 Concentration or depth Fig. IV-11. Relation between spectral transmission-factor and depth or concen- tration of a solution of methyl green. (From data by M. Luckiesh [1917].) 6 C, 3 Fig. IV-12. Optical system of a colorimeter or nethelometer for monochromatic light. (By courtesy of Kipp and Zonen.) 150 COLORIMETER FOR MONOCHROMATIC LIGHT 151 tinuous spectrum, which is focused by the second objective 2 on the horizontal slit S. The filament acts as a primary slit of the monochroma- tor. A selected narrow part of the spectrum, after passing through the slit, is reflected by two rectangular prisms (P), one half to the right and the other half to the left. These two beams are now made parallel by the objectives O3 and O4. Identical beams therefore pass through absorption cells C\ and C 2 . The transmitted beams are focused by means of objectives. O5 and 06 on the vacuum thermocouples I and II. The thermocouples are connected in opposition through the resistances to the galvanometer. The resistances are adjusted so that the galva- nometer reads zero. Now if a semitransparent solution is introduced in absorption cell C\ and the solvent into C 2 , the current generated by the thermocouple I decreases and the galvanometer deflects. The equilibrium is restored by reducing the current in circuit II in the follow- ing manner. Each thermocouple is shunted with a 50-ohm resistance. The shunt of II is a variable-resistance box R 2 connected in such a way that a known fraction of the drop in potential across R 2 can be removed from the galvanometer circuit. This fraction is adjusted so as to balance the current through the galvanometer to read zero. The resistance between the two keys K\ and K 2 then indicates the percentage of the drop in potential which has been made inoperative. This number is thus equal to the percentage extinction caused by the absorbing solute for the wavelength under examination. The accuracy obtainable is claimed to be of the order of 0.01 per cent. The sensitivity of such an instrument is dependent largely on the spectral region used. For the shorter wavelengths, the radiant energy emitted by an incandescent lamp burning at its normal voltage is small. The dispersive power of the Amici prism, however, is higher in the blue than in the red. Since the slit width per 100 A is smaller in the red than in the blue, a wider slit may be used in the blue than in the red end of the spectrum. To test the applicability of Beer's law to any solution, a preliminary test (Fig. IV-11) should be made to show that the logarithm of the transmissivity for a given wavelength (log 7\) is proportional to C. For this test a cell of known thickness is filled with the solution, and a spectral absorption analysis is obtained. If a sufficiently thin cell is chosen, most wavelengths available will be appreciably transmitted. On coordinate paper having a logarithmic scale ruled along the vertical axis and a uniform scale of concentration on the horizontal axis, as in Fig. IV-11, a plot of log 7\ is made for a given wavelength with change in concentration. Unity on the log scale is chosen as 100 per cent transmission. Straight lines are drawn through the data. Any varia- 152 BIOPHYSICALLY ACTIVE LIGHT tions from a linear relation show departures from Beer's law. If cor- rections have been made for surface reflections in the cell, the extrap- olated line will pass through transmission factor 1.0 at zero concentra- tion. If this correction has not been made, the common point will be near 0.92 on the " transmission axis " (Luckiesh [1917]) if two surface reflections must be accounted for. Each straight line represents the relation of log 7\ and concentration or depth for the wavelength used. By extending these lines to intersect the concentration axis the spectral characteristic of any depth or concentration may be read from the graph. Some lines are very steep; the larger the absorption coefficient the steeper (greater slope) the transmission curves for a particular wave- length of the incident energy. DlCHROMATISM It will be seen from Fig. IV-11 that the slopes of the lines labeled 4800 A, 5000 A, and 5600 A increase, while those labeled 7100 A and o 7200 A decrease with increase in wavelength. This change indicates that the dye is dichroic. This means that the color of a solution is composed of two or more maxima of transparency, and, if the rate of change of these maxima is not the same, dichromatism occurs with change in concentration. Suppose that in a solution the transmission color of the molecule is yellow and the ion blue. The color of the solution with decrease in concentration would vary from yellow through green to blue. Com- parison of sample and standard at concentrations differing to any con- siderable extent would be impossible since a deep column of dilute solution would be blue and a shallow column of a more concentrated solution would be green. From the figure it may be seen that methyl green dye in solutions of high concentration or of great depth will be not green but red. This change in color is indicated by the large transmission factor of wave- o length 7200 A (red) at concentration 3 on the graph as compared with o the very low transmission of 5000 A (green), indicating that the solution o has an absorptive band between 5600 and 7100 A. It follows that comparison of sample and standard at concentrations differing by anj r considerable extent would be impossible. Duboscq Colorimeter The Duboscq colorimeter is designed so that light from an even source of illumination R, Fig. IV-13, is reflected from a fine ground- glass surface. The two glass cups G are inserted in the beam of reflected DUBOSCQ COLORIMETER 153 light; they contain the solutions to be tested. Two solid cylindrical plungers of optical glass, matched for color and with optically plane and parallel ends, are lowered to various depths into the cups. These plungers can be set independently so that various depths of liquid may be examined. The two beams of light which pass through the glass ii in'-*" -=3=; (&) Fig. IV-13. (a) Path of light rays through a Duboscq colorimeter, (b) Path of light rays through a hemoglobinometer. (By courtesy of Bausch and Lomb Opti- cal Company.) plungers are brought to a common axis by means of the rhombohedral prisms D. The biprism refracting system C places the two images side by side so that the light from each cup illuminates half the field. The eyepiece BA by which the observer sees both fields with one eye is focused on the line of separation of the two fields. The depth of the two columns of liquid may thus be altered by moving the plungers independently in their respective cups until the two halves of the field are identical in brightness. When these conditions are ful- filled, the concentrations of the two solutions are inversely proportional to the depths, which are read on the scales of the instrument. Such a subjective setting is good to 1 per cent. For best results the source must not vary in intensity or color-tempera- ture. Artificial illumination is therefore recommended. To increase the sensitivity of color match in working with a blue field, a yellow filter is added over the eye lens, so as to work with a neutral green. Under these circumstances, should the layer of the 154 BIOPHYSICALLY ACTIVE LIGHT variable thickness be too thin, it will appear not only brighter but more yellow-green. If too thick, it will appear darker and more blue-green. In a similar way one may use a red filter that produces a neutral violet. Hemoglobinometer The hemoglobinometer is a colorimeter with which the amount of hemoglobin in a sample of arterial blood is determined without resort- ing to chemical analyses. To 5.7 32 28 24 £ 20 1 16 lj 12 4 - 3760 A 4146 Oxyhemoglobin Absorption spectra 76 gm/ liter] Acid 0.1 AT HC1 3000 4000 5000 Wavelengths in A 6000 7000 Fig. IV-14. Absorption spectrum of oxyhemoglobin with a and /3 band indicated. The /3 band disappears first on dilution. (From data by Newcomer [1919].) Whole blood, as well as its various chemical modifications, shows marked spectral absorption bands which cannot be matched by using any single filter. A good match may be obtained, however, by convert- ing the hemoglobin to acid hematin, in which the absorption bands are less prominent, and choosing a yellow glass filter, placed below the cups, whose absorption curve runs as a mean through that of the acid hematin. Acid hematin (globin hemochromogen) has, according to Newcomer [1919], an absorption band near 6620 A and two weak bands extending from 5100 A to 5900 A (Fig. IV-14). A " blue " filter can be inserted o to absorb most of the light having wavelengths greater than 5000 A. THE BARRIER-LAYER PHOTOELECTRIC CELL 155 o o This filter transmits 60 per cent at 4500 A and 70 at 4250 A, so that the brightness match is made in terms of the blue transmitted light. The number of grams of hemoglobin per 100 cc of blood may be read directly off a scale to 0.5 gram and estimated to 0.1 gram. The filter should transmit those wavelengths corresponding as nearly as possible to the absorption maximum of the solution. Photoelectric Colorimeters In the design of modern colorimeters the aim is to embody rigorous physical principles and to avoid all empirical procedures. The photo- electric method of measuring light intensities can be used to give quanti- tative results under the requirements laid down by Beer's law. Since Beer's law requires that the log 7\ be proportional to the thick- ness d and the concentration C, for a constant incident intensity, it follows that for a fixed thickness of solution the log 7\ ~ C There are two ways of approaching the design of a colorimeter which uses a photoelectric cell and a galvanometer as an indicator of the trans- missivity. The deflections may be observed on a logarithmic scale with the inevitable crowding of the engraved divisions at large-scale deflection, or else the electrical instrument may be a logarithmic device with its deflections observed on an equally spaced or linear scale. The Barrier-Layer Photoelectric Cell The barrier-layer photoelectric cell is of the photoemissive type requiring no vacuum-tube amplification. In the trade these types are called " photronic cells." A photronic cell consists of a metal support- ing disk upon which has been deposited a layer of photosensitive material. Upon this is placed a special kind of metallic grid acting at once as electrode and as collector for the current set up by the electrons freed from the light-sensitive material. The light reaches this material through the grid itself. Figure IV-15 shows the construction of a Weston Photronic Cell, and Fig. IV-16 indicates the relative sensitivity to various wavelengths of light as compared with the visibility curve of the eye. Under full sun- light such a cell may deliver as much as 10 milliamperes current. The response is linear, i.e., 100 ft-candles generates 100 times as much as 1 ft-candle when a current-indicating instrument having a resistance of about 100 ohms or less is used to measure the current. A typical sensitivity curve of the average photronic cell indicates 156 BIOPHYSICALLY ACTIVE LIGHT that the cell is most sensitive to yellow light of wavelength 5800 A, while the eye's sensitivity as shown by the dotted curve is in the yellow- green at 5560 A. Note, however, how much more sensitive it is in the blue than the eye. Fig. IV-15. Weston photronic photoelectric cell and its component parts, Model 594. (By courtesy of Weston Electrical Instrument Corporation.) Should it be desirable to use such a cell to simulate the human eye, it will be necessary to place a special filter, made for this purpose, over the cell so as to absorb the radiant energy represented by the area between the visibility curve and sensitivity curve of the cell. „ 90 300 400 , 500 i /500 . Ultra violetl f I Blue I Green If' \ I Red Violet Yellow Orange 700 x 10" 7 cm=X I Infra-red Fig. IV-16. Spectral sensitivity of the Weston photronic cell. (By courtesy of Weston Electrical Instrument Corporation.) A typical example of the use of a photronic cell in a colorimeter is fouDd in the instruments designed by Armstrong and Kuder [1935], or that of Evelyn [1936]. The so-called Kuder Photoelectric Model (Fisher Scientific Company) is a colorimeter operating with a direct- THE BARRIER-LAYER PHOTOELECTRIC CELL 157 reading scale. The operator can plot his own transmissivity concentra- tion curve on the attached scale, graduated from to 100 arbitrary units. Standardizing scale fPry sl'd | | Zero | mg./lQO ml 20 40 Sugar in blood or urine |Lam P | 60 80 100 120 140 160 180 200 220 240 260 280 320 360 4^0 k Length of each scale 111 mm A brief statement of the technique used for each scale a Accurate quantitative albumin determinations using a modified Exton's Reagent. b Calcium by Brigg's method, modified by Roe and Kahn. Phosphorus by Benedict's method. c Turbidimetric test using silver nitrate. Rapid and accurate. d Cholesterol determination by the modified Bloor or Leiboff methods. e Creatinine determination by the commonly accepted Folin and Wu method. / Employs acid hematin method. Scale standardized by Van Slyke oxygen capacity method. 9 Determination by the well known phenolsulphonphthalein method. h Sugar determinations by the commonly accepted Folin and Wu method. i Urea nitrogen or nonprotein nitrogen determinations by Folin and Wu method. Fig. IV-17. A set of nine colorimetric calibration scales, for clinical laboratory determinations. (By courtesy of Fisher Scientific Company, Pittsburgh, Pa.) In this instrument, other scales which are engraved by the maker to read directly the concentrations in milligrams per 100 ml may also be 158 BIOPHYSICALLY ACTIVE LIGHT used. Examples of such scales used in clinical work are shown in Fig. IV-17. Photronic Cell Colorimeters A photronic cell colorimeter of very simple design as suggested by- Evelyn [1936] is shown in Fig. IV-18. Since the light transmitted by the absorption cells is a logarithmic function of the concentration, one may obtain linear readings by using a circuit which reacts with a loga- rithmic response to the transmitted light. A device of this kind is the logarithmic response vacuum-tube voltmeter used by Muller and Kin- ney [1925] in their design of a photoelectric colorimeter. Absorption of Ultraviolet diation by Proteins Ra- Fig. IV-18. Colorimeter design after Evelyn [1936] showing use of a pho- tronic cell. Source of light L, with reflector, produces near parallel beam through filter F. Light beam limited by external stops in opaque cover over a 6-cc parallel fused absorption cell C. Energy incident on photronic cell (PC) directly connected to microammeter, of less than 50 ohms resistance, which reads current developed by PC. The absorption of ultraviolet ra- diation by serum proteins was inves- tigated as early as 1922 by Judd Lewis. Improvements in design of the rotating sector quartz spectro- photometer made it possible for F. C. Smith [1929] to obtain the absorp- tion spectrum of horse and human serum proteins with a great de- gree of precision. These results are shown in Fig. IV-8. It will be noticed that as the wavelength decreases o o from 3000 A to 2790 A the extinction coefficient rises very rapidly, indicating the approach to a sharp opacity at 2790 A. Then, with decreasing wavelength, the material becomes more transparent, and o reaches a relatively high transparency at 2500 A, from which minimum o it rises very rapidly to high absorption values at 2000 A. These graphs indicate that the absorption spectra of these proteins are the same, o except that the extinction coefficient for globulin at 2790 A is nearly double that of albumin. It is possible by means of such absorption measurements to determine the ratio of albumin to globulin in small amounts of cerebrospinal fluid. This type of curve may also be used to indicate the purity of a given o sample of protein by comparing the values obtained for k at 2790 A with those at 2500 A. ABSORPTION OF ULTRAVIOLET RADIATION BY PROTEINS 159 Notice the striking resemblance between the absorption of serum albumin and egg albumin. An analogous absorption curve was obtained by Gates [1934] for pepsin of pH 2.06. These data place the maximum absorption at 2775 A. The energy required to inactivate 50 per cent of pepsin, for the wave- length band between 2640 and 2820 A, is 230,000 ergs/mm 2 , and between 2425 and 2570 A is 305,000 ergs/mm 2 ; between 2300 and 2400 A it falls to 77,500 ergs/mm 2 . The most striking and important change produced by absorbed ultra- violet light in all proteins, whether globulins or albumins, and whether positively or negatively charged, is a change in solubility or denaturation. v o It should follow that the wavelengths from 2650 to 2900 A, which in- o elude the absorption maximum at 2790 A, are highly efficient denaturat- ing agents. o The absorption band of blood serum around 2800 A is apparently due to the proteins present, and the tyrosin and tryptophan constituents of the proteins are mainly responsible for this band. In conclusion some relations between the absorption of proteins and some of the amino acids should be pointed out which support the theory that the ultraviolet absorptions of the proteins in the 2800 A region are due to the aromatic acids. An extensive analysis by Coulter, Stone, and Kabat [1935] shows o that all the narrow absorption bands between 2530 and 2690 A found in all protein may be assigned to phenylalanine, while the bands at 2700, and 2850 to 2900 A, may be attributed to tryptophan and tyrosin, respectively. Their conclusions were drawn from an examination of serum albumin, egg albumin, thyroglobulin, englobulin, pseudoglobulin, pneumococci antibody, gelatin, insulin, tyrosin, tryptophan, and phenylalanine. The general evidence suggests that ultraviolet radiation and soft x-rays cause liberation of material of low molecular weight which with albumin residues undergo photo-oxidation reactions, due to the absorp- tion of ultraviolet energy. In order to illustrate what a powerful tool the spectroscopist has made available to the biochemist attention is called to the work of Wald [1934], who demonstrated the presence of vitamin A in ox and pig retina, in sheep pigment-choroid, and in sheep retina by means of the ultraviolet absorption band of vitamin A with maximum at 3280 A. The standard method of determining the vitamin-A content of cod- liver oil is by the extinction coefficient of its absorption spectrum band at 3280 A. 160 BIOPHYSICALLY ACTIVE LIGHT TABLE IV-3 Maximum Lethal Author Effect at Wavelength Bacteria Gates, F. L. [1929] [1930] 2600 to 2700 A S. aureus Ehrismann and 2510 Eresch. coli (B. coli) Noethling [1931] 2810 Serratia marcescens (B. prodigiosus) 2650 Pseudomonas aeruginosa (B. pyocyaneus) 2650 Micrococcus candidus 2650 S. aureus 2696 Vibrio Finkler Wyckoff [1931] 2696 S. aureus 2652 Eresch. coli (B. coli) 2652 Salmonella aertrycke (B. aertrycke) Hollaender and Clauss [1935] 2600 Eresch. coli (B. coli) Landen and Uber [1939] 2650 Sacc. ellipsoideus Burge [1915] 2650 Coagulates egg albumin Effect of Ultraviolet Radiation on Bacteria Finsen and Dreyer (1903) were probably the first to show that light of short wavelengths is virucidal. Except in the more recent investiga- tions in this field, monochromatic radiation has not been used, nor has the amount of energy which is associated with the lethal wavelengths been determined. In a study of the ultraviolet effect upon vaccine virus by Rivers and Gates [1928], a series of experiments showed that the effect of monochromatic ultraviolet radiation in terms of the incident energy required to inactivate all of a given specimen of vaccine virus is a maximum at about 2650 A. More significant than the involved absolute energies is the general shape of these lethal curves. They exhibit a rapid drop in the required lethal energy between 3000 and 2800 A, a minimum at 2650, and a rise towards 2250 A corresponding closely to the curve representing the absorption of ultraviolet energy by protein substances. In an attempt to narrow the energy band that is required for a lethal exposure the results obtained by others as shown in Table IV-3 must be examined. The maximum lethal effects for Escherichia coli o „ are obtained on the average near 2650 A, and it takes about 14 X 10~° erg per bacterium to produce death. Inactivation data by Hollaender and Emmons [1939] on the skin fungus Trichophyton mentagrophytes indicate that 2537 A is the most effective region. It takes about 7 X 10 -4 erg to obtain 50 per cent inactivation of these spores. EFFECT OF ULTRAVIOLET RADIATION ON BACTERIA 161 Erythema In the destruction of yeast, Saccharomyces cerevisiae, the inhibitory and lethal effects, according to Oster [1934], are approximately the same for all wavelengths, while the destruction efficiency on the basis of a 50 per cent killing is a maximum at wavelengths between 2600 and o 2700 A. The energy required to suppress budding of 50 per cent of the cells irradiated ranges from 457 ergs/mm 2 at 2652 A to 23,500 ergs/mm 2 at 3022 A. Landen and Uber [1939] obtained 500 ergs/mm 2 as the o destructive efficiency of 2650 A for the yeast Sacc. ellipsoideus. Similar results were obtained by Sharp [1938], for Bacillus anthraci using the strong ultraviolet mercury line 2537 A. Summer sunlight cannot pro- duce comparable effects since the normal atmosphere absorbs all lethal radiation shorter than 2950 A. Gates [1929] concludes from his study of the bactericidal action of ultraviolet light on S. aureus that : (1) in the initial period of exposure no bacteria succumb; (2) after this initial exposure a considerable number of bacteria, between 20 and 30 per cent, are destroyed, and in this group are found the young ones ; (3) the remainder to about 70 or 80 per cent of the total number succumb along an energy gradient that ap- pears to have an exponential rela- tionship to the lethal effects; and finally (4) a number of organisms remain which require an excess of energy to kill them. The evidence, therefore, shows that the most effective bacterici- dal region lies in the range 2500 o to 2650 A, with a possible maxi- o ^^ mum effectiveness at 2650 A. The absorption maxima for proteins, yeast, and pepsin also extend from 2700 to 2800 A, from which it may be inferred that bacteria are de- stroyed by the photochemical ioni- zation induced in the protein body material of the bacterium (Fig. IV-19), if the |surface of the bacte- rium and the medium in which it is investigated are excluded. Since at 2700 Ait takes about 25 X 10~ 6 erg per bacterium (Hercik [1936]) to _ o -a < - 2400 2600 2800 Wavelength 3000 3200 A Fig. IV-19. The antirachitic response for an equal energy spectrum is shown as compared with the spectral absorption of ergosterol and the average erythemic re- action of the untanned skin to an equal energy spectrum. Antirachitic data from Knudson and Benford [1938]. Ergosterol data from Bills, Honeywell, and MacNair [1928]. Erythema data from Luckiesh, Holla- day, and Taylor [1930] or Coblentz, Starr, and Hogue [1932]. 162 BIOPHYSICALLY ACTIVE LIGHT to produce death, it follows that about three million photons are necessary to cause death. The lethal action of the ultraviolet energy is not brought about by a chemical change of the medium surrounding the organism. The funda- mental reaction which causes death is produced inside the cell by the radiant energy that can penetrate to this depth. The reaction is prob- ably unimolecular, on the basis of the assumption that the number of bacteria killed should be proportional to the radiant energy intercepted by a critical volume in the organism. Rentschler [1940] found that the bactericidal action is determined by the amount of radiant energy to which the bacterium is exposed, regard- less of whether a high intensity is applied for a short time or a low intensity is applied for a correspondingly long time, provided that the product, intensity X time, is the same. The lethal action is independent of the temperature of the bacteria at the time of exposure. The sensitivity of an organism to ultraviolet radiation varies appre- ciably at different stages of its life cycle. It has been found that younger cells are more sensitive than older cells to all forms of absorbed ionizing radiations. Ultraviolet Activation In 1924 Hess and Steenbock independently and almost simultaneously announced the discovery that exposure of edible materials to ultraviolet light endows them with antirachitic activity. It has developed that this activation is relatively permanent and that it is not a process of oxidation. The second stage in the development was reached when it was demon- strated that sterols became antirachitic upon irradiation. With the introduction of the quartz spectrograph for investigating the spectral absorption of the material under examination the problem entered its quantitative phase. It was found that in foodstuffs the sterol fraction contained the " acceptor " of the activating rays. The trend of the investigation then turned to the solution of the chemical changes induced by the radiation in the sterols. It was found that ordinary cholesterol was somewhat opaque to ultraviolet light and that irradiation decreased its opacity. Schultz and Morse, working with cod-liver oil in 1925, found that the absorption spectrum of ordinary cholesterol contained a definite band structure, with maxima of absorption at about 2940 and 2830 A. The bands disappeared after irradiation and only general absorption remained. They assumed that the cholesterol was contaminated by a ORIGIN OF MOLECULAR ABSORPTION BANDS 163 small amount of an impurity which produced the selective absorption. In December, 1926, reports fram three separate laboratories confirmed the contamination hypothesis. The contamination was subsequently identified as ergosterol. The names of Rosenheim, Webster, Heilbron, Kamm, Morton, and Pohl are associated with the work of identifying the absorption spectrum of ergosterol. Heilbron, Kamm, and Morton [1927] reported that the fractional crystallization of cholesterol led to the accumulation in the least-soluble fraction of the substance responsible for the characteristic absorption spectrum, and identified three absorp- tion bands at 2935, 2820, and 2690 A. Irradiation destroyed the three bands, leaving only a general absorption. Subsequently, Bills, Honeywell, and MacNair [1928] showed that ergosterol was the contaminant provitamin. With the aid of a continu- ous ultraviolet source of radiation supplied by a hydrogen discharge tube, they found that ordinary cholesterol possessed a fourth absorption band at 2600 A (Fig. IV-19), and that ergosterol possessed similar o absorption bands at 2935, 2820, and 2700 A. This absorption dis- appears under irradiation, which produces activation that yields thera- peutically valuable vitamin D. In Fig. IV-19, the spectral antirachitic efficiency curve of ultraviolet radiation is plotted. Along with this curve, the absorption curve of ergosterol and the erythema curve are given. Note how the antirachitic curve follows the general contours of the absorption curve of ergosterol, o and that the most effective antirachitic wavelength, 2804 A, gives the least erythema. One may conclude that a measurement of the erythema effectiveness does not give an index to the effectiveness of ultraviolet irradiation in the cure or prevention of rickets. Origin of Molecular Absorption Bands If the irradiated atoms or molecules of the tissue become ionized, it is possible that this ionization will lead to chemical changes resulting in the destruction of the cell. On what part of the living cell the radiation acts and what primary changes result are still some of the questions to be answered. The primary process may consist in absorption by a com- plex molecule which is part of the nucleus. Since the molecules are relatively close together and interact strongry with each other, the absorption will not be limited to a sharply defined wavelength, but will spread over a more or less narrow band of wavelengths. A single absorption band is characterized by a group of absorption lines so close together that in a spectrogram obtained with a spectro- graph of small dispersion the lines fuse together. With higher disper- 164 BIOPHYSICALLY ACTIVE LIGHT sion the band will be found to have its lines crowded closer together at one end, called the band head. The complex organic molecules that have been considered as partici- pating in absorption are said to be in their lowest molecular energy state, E . A photon of energy content hv, absorbed by such a molecule, will alter its energy state from E to Ex. This means that the molecule absorbs energy Ex — E from the radiant energy passing over it, in which these E's are definite energy states characteristic of the molecule and not of the radiant energy. Thus a molecule in a liquid might absorb light of frequency v in such a way that v = (Ex — E )/h, where h is the usual Planck's constant. For simplicity's sake, let us consider a molecule of hydrochloric acid in which the hydrogen and chlorine atoms are a definite distance apart. This molecule, by acquiring additional energy through absorption, can respond in three ways: (1) There may result a vibration of the two atoms along their axis of connection. (2) There may result a rotation about an axis at right angles to the above axis. (3) There may be changes in radii of the orbital electrons of the atoms, i.e., quantized changes in the electron energies. The spectroscopic evidence shows that the vibrational energy E v = in + \)hv vi where n can take on only integer values 0, 1, 2, etc. This implies that the vibrational energy is quantized and that, the larger n, the farther the electron is removed from the nucleus. The rotational energy is also quantized so that increase in its energy states proceeds as (r + b 2 h 2 E r = 8x 2 / where r changes by integers 0, 1, 2, etc. /, the moment of inertia, is included because the rotational characteristic of the molecule changes with increase in orbital radii of the electrons. The electronic energy E e may also change, owing to electronic rearrangements when a quantum is absorbed by either atom. Thus the total energy of the molecule may initially be E = E e + E v + E r Now, changes in any one, any two, or all three may take place when energy is absorbed. The absorption bands under consideration are found in the near ultraviolet; as a result the energy of the absorbed photon is chiefly used in electronic excitation. We may picture the energy change involved thus: the initial energy of subscript zero, E e0 + E v0 + E r0 becomes E en + E v0 + E r x- The STERILIZATION OF WATER WITH ULTRAVIOLET RADIATION 165 energy changes involved in the vibrational changes may be compara- tively small and do not enter into the picture; hence, E v0 is very small. Therefore, for some one electron change from its lowest energy state n = to some higher energy state n = 1, the frequency of the absorbed energy is v = v e + B ± 2Br + Cr 2 where v e is due to an electronic change, B and C are constants for the band, and r takes successive values of 0, 1, 2, 3, etc. Thus each line in such a band corresponds to the same electronic shift and to the same vibrational shift. If this relation is plotted for various values of r a parabola of two branches is obtained. The theoretical band for a dia- tomic molecule has the appearance of possessing a sharp edge at the long-wavelength end and gradually decreasing in intensity towards the short-wavelength end. Somewhat similar properties are exhibited by the experimental absorption bands previously discussed. Instead of computing the theoretical energy values and from them the spectral frequencies, the problem usually is the converse, viz., obtaining the energy values from the experimentally determined spectrum and trying to arrive at their theoretical significance through an equation similar to that developed above. The observed facts, however, have far outstripped our understanding of the mechanism of absorption. Although only a superficial elementary analysis of electronic band spectra has been given, it should be sufficient to enable the reader to appreciate the difficulties and the direction in which progress in this field is now being made. Sterilization of Water with Ultraviolet Radiation In order to appreciate the limitations set by water, either as a solvent or for immersion, on the lethal action of ultraviolet radiation, it is necessary to examine the transmission factors of water for ultraviolet spectral radiation. Information on the absorption characteristics of water in the ultraviolet is meager. o In general it is known that an absorption band exists at 6000 A with o probably two weaker bands at 6500 and 5200 A. These give to water the predominant blue color when viewed through thick layers. In the ultraviolet the absorption has been traced from 3000 A to its o opaque limit just below 1800 A. These results are summarized in Fig. IV-20. This curve shows why water becomes opaque near 1800 A. o Since midsummer sunlight is limited at 2950 A by the opacity of the atmosphere, it becomes apparent that sunlight cannot exert a lethal action on bacteria immersed in water at any great depth. To sterilize 166 BIOPHYSICALLY ACTIVE LIGHT water it would be necessary to use a source of ultraviolet radiation from a quartz mercury-vapor lamp of high intensity. This type of lamp is o especially rich in ultraviolet radiation at 2536, and 2654 A, and even 50 - 45 - Ultraviolet absorption 40 " by water 35 - 1.7-cm layer c o 'a30 - o CO c JD ro *-- "25 tZ 0) u -c= -C |_He rmful to plants 1 lesst sunlig £20 - o<. Q- 15 - 3 a. O 1 00 lAbsorbed by air g j™ X -, 1 CT> 1 bx \ 1 T cvj , rt %>• 3 i /0 Strongly absorbed | by bacteria 10 ^ r — 1 5 1 1 1 1 1 1 1 1 1 1 1800 2200 2600 Wavelengths in A 3000 Fig. IV-20. This curve is constructed from data by Kreusler [1901]. It shows the opacity of a layer of water 1.7 cm thick to a source of artificial ultraviolet radi- ation. Air does not transmit sunlight below 2950 A. Note that bacteria cannot be killed by wavelength region around 2600 A, if immersed in water to any great depth. Coefficient of absorption is 0.0025 for water at 2600 A. this form of radiation cannot be efficient if water is treated in layers greater than 2 cm thick, and if the flow is so fast that a single bacterium erg. cannot absorb its lethal dose of 25 X 10 6 Ultraviolet Absorption in Air In the ultraviolet the absorption at atmospheric pressure of a layer of o air 1 meter thick is negligible for wavelengths greater than 2300 A. It is about 1 per cent at 2200 A and 2 per cent at 2050 A, and increases rapidly towards shorter wavelengths. This absorption is due to the presence of oxygen. It sets a lower limit of about 1850 A to the wave- length of the ultraviolet radiation which can be recorded with an optical instrument in which the beam traverses 50 cm of air at atmospheric pressure. STERILIZATION OF AIR WITH RADIANT ENERGY 167 If air 1 meter thick at 760 mm pressure shows a negligible absorption o for wavelengths greater than 2050 A, why is it that we find a rather sharp o cut-off in transmission of sunlight at 2950 A, so that no rays lethal to o bacteria (2500 to 2800 A) reach the earth? This opacity of the atmos- phere is attributable to the presence of ozone at high altitudes. Ozone o shows a pronounced absorption band extending from 2200 to 2900 A. o Below 2200 A ozone is transparent again, but the dense oxygen in the lower atmosphere is relatively opaque to wavelengths 2200 to 2000 so that the opacity increases rapidly from 1850 to shorter wavelengths. It, therefore, follows that midsummer sunlight reaches the earth without containing an appreciable amount of ultraviolet energy destruc- tive to bacteria. Apparently, sunlight as a means of sterilizing the lower strata of air is of questionable value. For this task, therefore, one must resort to other ultraviolet sources which possess pronounced o energy radiations near 2650 A. Sterilization of Air with Ultraviolet Radiant Energy The sterilization of the air in an operating room has been successfully accomplished with the aid of a Westinghouse " Sterilamp " by Hart and Gardner [1937]. Their work proved that the presence of staphylococci in the air in the operating room was a source of wound contamination rather than contamination from the skin of the patient or personnel, or by other contacts. They showed that the transportation of pathogenic bacteria through the air to the wound can be eliminated to a great extent by laying down a barrage of ultraviolet radiant energy around the operative incision and exposed sterile supplies. Barriers of ultraviolet rays have been shown to be effective in prevent- ing the spread of infection in an isolation ward. Wells' work [1940] shows that an organism in air is about 20 times more vulnerable to the o ultraviolet range 2000 to 3000 A than when suspended in water. Vul- nerability values were found to be reduced tenfold paralleling an increase in relative humidity from 46 to 91 per cent. For this effect no acceptable explanation has been proposed. The available information indicates that bacteria are killed by about the same amount of ionizing energy no matter what its wavelength. The cell damage caused by ionizing radiations must be attributed directly to the liberated ions and to the chemical changes that these ions induce. The nature of these changes has been the subject of much experimentation. Tentatively, we may state that the number of ions produced by lethal doses of radiation is small compared with the enor- mous number of atoms in the tissue that is radiated. Ionic recombina- 168 BIOPHYSICALLY ACTIVE LIGHT tions take place so rapidly that the chemical changes leading to the death of the cell are minimal, but they are of such a nature that the metabolism of the cell does not readily repair them. In spite of the large amount of work that has already been done, it will probably take a long time to solve so complex a problem. BIBLIOGRAPHY 1901 Kreusler, H., Ann. Physik, 6, 412. 1915 Burge, W. E., Am. J. Physiol, 36, 21. 1917 Luckiesh, M., J. Franklin Inst., 184, 227. 1919 Moll, W. J. H., Colorimetry and Nephelometry, Verlag Akad. Wet. Amsterdam, 28, 1001. 1919 Newcomer, H. S., J. Biol. Chem., 37, 465. 1925 Muller, R. H., and G. F. Kinney, J. Optical Soc. Am., 25, 342. 1925 Report of the Optical Society of America, Committee on Spectrophotometry, J. Optical Soc. Am., 10, 169. 1927 Heilbron, I. M., E. D. Kamm, and R. A. Morton, Biochem. J., 21, 78. 1928 Bills, C. E., E. M. Honeywell, and W. A. MacNair, J. Biol. Chem., 76, 251. 1928 Clark, W. M., Determination of Hydrogen Ions, Williams and Wilkins Com- pany, Baltimore, Md. 1928 Rivers, T. M., and F. L. Gates, J. Exptl. Med., 47, 45. 1928 Yoe, H. H., Photometric Chemical Analysis, Colorimetry, Vol. I; Nephelometry, Vol. II; John Wiley & Sons, New York. 1929 Gates, F. L., J. Gen. Physiol, 13, 231; 13, 249. 1929 Smith, F. C, Proc. Roy. Soc. London, B104, 198. 1930 Gates, F. L., J. Gen. Physiol, 14, 31. 1930 Luckiesh, M., L. L. Holladay, and A. H. Taylor, J. Optical Soc. Am., 421, 20. 1930 Wyckoff, R. W. G., J. Exptl. Med., 52, 769. 1931 Clark, J. H., J". Optical Soc. Am., 21, 240. 1931 Ehrismann, O., and W. Noethling, Z. Hyg. Infektionskrakh., 113, 597. 1931 Forsythe, W. E., B. T. Barnes, and M. A. Easley, J. Optical Soc. Am., 21, 30. 1931 Lucas, N. S., Biochem. J., 25, 57. 1931 Taylor, A. H., J. Optical Soc. Am., 21, 20. 1931 Wyckoff, R. W. G, J. Gen. Physiol, 15, 351. 1932 Coblentz, W. W., R. Starr, and J. M. Hogue, J. Research Natl. Bur. Sta7id- ards, 8, 541. 1932 Council on Physical Therapy, " Acceptance of Sunlamps," J. Am. Med. Assoc, 99, 31 ; 100, 1863. 1933 Gates, F. L., J. Gen. Physiol, 17, 797. 1934 Coblentz, W. W., /. Am. Med. Assoc, 103, 183 and 254. 1934 Council on Physical Therapy, J. Am. Med. Assoc, 102, 42. 1934 Gates, F. L., J. Gen. Physiol, 18, 265. 1934 Giese, A. C, and P. A. Leighton, J. Gen. Physiol, 18, 557. 1934 Oster, R. H., J. Gen. Physiol, 18, 251. 1934 Twyman, F., and C. B. Allsopp, Absorption Spectrophotometry with Hilger Instruments, 2d Ed., Adam Hilger, London. BIBLIOGRAPHY 169 1934 Wald, G., J". Gen. Physiol, 18, 905. 1935 Armstrong, E. L., and M. L. Kuder, J. Lab. Clin. Med., 21, 181. 1935 Arnow, L. E., J. Biol. Chem., 110, 43. 1935 Coulter, C. B., F. M. Stone, and E. A. Kabat, J. Gen. Physiol, 19, 739. 1935 Hollaender, A., and W. D. Claus, J. Gen. Physiol, 19, 753. 1935 Morton, R. A., The Application of Absorption Spectra to the Study of Vitamins and Hormones, Adam Hilger, London. 1936 Circular Letter LC-473, KSG : AEH IV-3, U. S. Dept. Commerce, Natl. Bur. Standards, Washington, D. C. 1936 Evelyn, K. A., J. Biol. Chem., 115, 65; 117, 365 (1937)..' 1936 Herci'k, F., J. Gen. Physiol, 20, 589. 1936 Snell, D. S., Methods of Colorimetric Analysis, D. Van Nostrand Company, New York. 1937 Hart, D., and C. E. Gardner, Trans. South. Surg. Assoc, 49, 377. 1938 Coblentz, W. W., J. Am. Med. Assoc, 111, 419. 1938 Crew, W. H., and C. H. Whittle, J. Phijsiol, 93, 335. 1938 Hausser, I., Strahlentherapie, 62, 315. 1938 Hecht, S., /. Applied Phys., 9, 156. 1938 Knudson, A., and F. Benford, J. Biol. Chem., 124, 287. 1938 Sharp, D. G., J. Bad., 37, 447. 1939 Brode, W. R., Chemical Spectrophotometry and Its Application, Adam Hilger, London. 1939 Buttolph, L. J., J. Optical Soc Am., 29, 124. 1939 Edwards, E. A., and S. Q. Duntley, Am. J. Anal, 65, 1. 1939 Henschke, U., and R. Schulze, Strahlentherapie, 64, 14. 1939 Hollaender, A., and C. W. Emmons, J. Cellular Comp. Physiol, 13, 391. 1939 Landen, E. W., and F. M. Uber, Proc Soc. Exptl Biol. Med., 42, 559. 1940 Loofbourow, J. R., " Borderland Problems in Biology and Physics," Rev. Modern Phys., 12, 270. 1940 Rentschler, H. C, Trans. III. Eng. Soc, 35, 960. 1940 Wells, W. F., J. Franklin Inst., 229, 347. 1941 Blum, H. F., Photodynamic Action and Diseases Caused by Light, Am. Chem. Soc. Mono. 85. Reinhold Publishing Corporation, New York. 1941 Ellis, C, and A. A. Wells, The Chemical Action of Ultraviolet Rays, 2d Ed. F. F. Heyroth, Reinhold Publishing Corporation, New York. 1941 Laurens, H., " The Physiological Effects of Radiant Energy," Ann. Rev. Physiol, 3, 21. Chapter V THE STRUCTURE AND PROPERTIES OF SURFACES AND MEMBRANES In the previous chapters some of the fundamental phenomena causing the destruction of the metabolic equilibrium of the normal cell after x-radiation and gamma radiation absorption were examined. Many substances will also decompose as the result of absorption of ultraviolet rays. If these radiations can produce a modification in the surrounding medium in which a cell is embedded, the resulting toxic products may affect the life history of the cell. On the other hand, the energy may be absorbed in such a way as to change directly the colloidal states of the cytoplasm, causing a modification of the surface structure of the cell and the accompanying alteration of the normal cellular permeability. These modifications will permit the entrance of toxic chemical sub- stances which are normally unable to enter the cell. A great deal of information exists regarding the passage of dissolved substances into living cells and the accompanying changes in osmotic pressure, but the interpretation of the data, particularly in regard to the possible existence of plasmatic membranes, is rendered difficult by the complexity of the system involved. In general, two points of view have developed: (1) that the cytoplasmic surface is covered with a thin layer of specially differentiated substances of a lipoid nature or with a mosaic of alternate lipoid and protein material; (2) that no special membrane exists on the surface of a cell, but that permeability phenomena are governed by absorption of water by colloids and by the difference in electrical potential which is developed as a result of the Concentration of ions unable to cross the border of the cell. How far the membrane hypothesis is adaptable as an explanation of cellular permeability and osmosis is left to the judgment of the reader after he has acquainted himself with the phenomena contributing to the changes in surface energy of liquids, existing either as free surfaces or as surfaces of separation associated with partitions through which osmo- sis can take place. Liquid Surfaces A liquid in a large-surfaced open container at rest and under the influence of gravity develops a free horizontal surface. Below this free 170 SURFACE ENERGY 171 surface of the liquid the molecules exert an attractive force on one another. This attractive force is appreciable because the molecules are within very minute distances of one another. Since in the interior of the liquid each molecule is surrounded by others on every side, it is therefore subject to attraction in all directions. On the average, over long periods of time as compared with the molecular temperature vibra- tions, the attraction of any molecule is uniform in all directions; hence the molecule is in equilibrium. At the surface, however, the molecules of the liquid are attracted only inward and to each side by their neighbors; there is no outward attrac- tion to balance the inward force. The result is that every surface mole- cule is subjected to a resultant inward attraction directed perpendicular to the surface. It is this inward attraction that causes a free surface to maintain its unique shape for given external conditions. It is also this resultant inward attraction that produces the reduction of the area of a free surface. The fundamental property of liquid surfaces is that they tend to contract to the smallest possible area permissible by their environment. This tendency is illustrated by the spherical form assumed by small drops of liquid and small gas bubbles, and the shapes assumed by soap films. The departure from spherical forms, noticed in larger liquid drops or gas bubbles, is due to the gravitational effect. The diskoidal form of the mammalian erythrocyte is not well understood, and no satisfactory mathematical expression for the contour has been found. Surface Energy The fact that an undisturbed liquid surface tends to contract shows that surface energy is associated with it, for energy must be expended to extend such a surface. If we view this extension of the surface from an internal point and in terms of the molecules which form the surface, we observe that, as the surface is extended, more and more molecules must be brought from the interior to be added to the expanding surface. In this molecular rearrangement, work is done to move the internal mole- cules into the surface; hence energy is being expended against the inward-directed molecular forces. An expanding surface is therefore accumulating a greater potential surface energy, and a contracting sur- face is accompanied by a loss in surface energy. When a surface con- tracts, either it must wrinkle, or molecules must be forced out of it. If an appreciable surface molecular attraction comparable to what might be called tangential tension exists, then a liquid surface must wrinkle on contraction. This result is contrary to experimental evidence; hence no tangential surface force can exist. 172 SURFACES AND MEMBRANES Adam [1930] has shown at great length that the surface energy due to the inward pull on the molecules forming the surface is the fundamental property of surfaces. This potential surface energy is of fundamental importance, for a large number of problems relating to the equilibrium of surfaces can be solved without a knowledge of more than the magni- tude of this surface energy. In the solution of such problems a mathe- matical device is used to simplify the analysis. We substitute for the surface energy a hypothetical tension acting in all directions tangent to the surface, and equal to the magnitude of the surface energy per unit area. This hypothetical tension is what is generally understood by the term surface tension. The surface energy per unit area is denoted by the number of ergs per square centimeter. This is analogous in dimensions to surface tension expressed in dynes per centimeter. To illustrate its usage by an ele- mentary example, let us analyze the surface energy of a circular surface of radius r having an area irr 2 . Next, let us assume a hypothetical force acting at right angles to the circumference of the surface. This force will act along the radii of the circle tending to shrink the surface. Let its magnitude be T dynes per centimeter of circumference. In order to increase the area, energy must be expended. Let the available energy be sufficient to expand it to an area having a radius (r + dr) cm. The energy used to produce this expansion is dE = 2-n-rTdr, which upon inte- gration becomes E = irr 2 T. Hence the energy per unit area measured in ergs per square centimeter has the same dimensions as T, the so-called surface tension measured in dynes per centimeter. This hypothetical surface tension which is supposed to act in the face of the plane surface is also treated as acting tangentially to any curved surface. To treat it as a vector will often lead to fallacious results. Its use may be illus- trated in calculating the surface energy of a spherical bubble immersed in a liquid, a common biophysical phenomenon. The pressure inside a bubble of gas immersed in a liquid must be greater than the external pressure existing at the surface by an amount equal to the internally directed molecular forces per unit area. If T is the hypothetical surface tension in dynes per centimeter at the liquid- gas interface of a bubble of area 4xr 2 , then the surface energy at this interface is E = 4irr 2 T. If the bubble is allowed to expand so that its radius increases to r + dr, then the work done in this expansion is dE = 8irrTdr. If the pressure directed along the radius of the bubble is p dynes per square centimeter, and an increase in volume dV results, then the work done is dE = pdV, or p • 4irr 2 dr = 8irrTdr. Hence 2T V = — r LIQUID-GAS INTERFACE 173 If, as in the structure of a soap bubble, two surfaces of external radius R 2 and internal radius R\ are involved, then the internal pressure is p = 2T \R 2 + Rj or for very thin soap bubbles where R\ may be considered equal to R 2 AT t Temperature Effects on Surface Energy As the temperature of a liquid rises, the kinetic agitations of the mole- cules increase. It has been found experimentally that the surface energy decreases with rising temperature. Table V-l shows that the reduction in surface-energy measurements with rise in temperature, TABLE V-l Temperature Effects on Surface Energy A liquid-air interface. Changes in T indicated in ergs per square centimeter. Standard T for water-air interface at 20° C is 72.75 ± 0.05 erg/cm 2 . Air pressure, standard conditions. * — t°C 10 15 20 25 30 35 40 50 100 Water T y4 22 ?3 4Q ?2 ?5 ?1 g7 ?1 lg 7Q 3g 6g 56 6? gl 5g g5 (°C 20 50 100 Benzene T 1? Q1 13A7 ? ^ 7 over long ranges of temperature, is practically linear. The tempera- ture effect is caused by a decrease in the inward pull on the surface mole- cules which results in a decrease in surface energy. Liquid-Gas Interface Under ideal conditions surface-energy measurements are made on an uncontaminated liquid surface subjected to a gas pressure of 1 atmosphere at 20° C. The surface is then referred to as a liquid-gas interface. The accepted reference standard of interface-energy measure- ments is water in the presence of air at 20° C and 760 mm pressure. Its magnitude is 72.75 ± 0.05 erg/cm 2 . Benzene, which is sometimes used as a reference standard, has under the same conditions an interface surface energy equal to 28.88 ± 0.03 erg/cm 2 . Water has the highest interface surface energy of the liquids except mercury, which may pos- 174 SURFACES AND MEMBRANES sess as high a value as 465 ergs/cm 2 . The surface energy possessed by some of the more common physiological fluids is shown in Table V-2, each of which has a surface energy lower than water. TABLE V-2 Liquid-Liquid Interface Surface Energy Interfacial energy E in ergs per square centimeter, 20° C T . . . Liquid- Water Liquid- Air Liquid E M E Water 72.75 Aniline 5.8 42.90 Benzene 35.0 28.88 Carbon disulphide 45.0 32.33 Carbon tetrachloride 45.0 26.77 Chloroform 32.8 27.14 Ethyl ether 10.7 17.01 Bile 48 Milk 50 Serum (mammalian) 60 Urine (normal) 66 Urine (icteric) 55 Liquid-Liquid Interface Interface energy also exists at the surface between two immiscible liquids. It has been found that the interfacial energy between two liquids is less than the energy of the liquid possessing the higher surface energy when in contact with air. In this case the reduction in energy is a measure of the reduction of the surface energy of the boundary due to the presence of the superimposed liquid. Here one liquid surface is in close contact with a second liquid surface. The molecules of one liquid surface attract the molecules lying in the opposite face of the adjoining liquid across the contact boundary. This attraction diminishes the effective pull exerted by each of the liquids on its own surface molecules. The condition for complete miscibility of two liquids is that this interfacial energy shall be zero. Table V-2 shows how much the interfacial energy of water in contact with an organic liquid has been reduced below that of water in contact with air. Effects of Substances in Solution on Surface Energy Substances dissolved in a liquid may either lower or raise the surface energy at the interface between liquid and air. When many inorganic EFFECTS OF SUBSTANCES IN SOLUTION ON SURFACE ENERGY 175 salts, such as sodium and potassium chloride, are dissolved in water, the interface energy is raised to a marked degree. This rise is shown in Table V-3. On the other hand, bile salts, tannic acid, starch, and lecithin reduce the surface energy of water. Kopaczewski's [1933] experiments show that " human serum at 20° C has a tension of 67.7 dynes per cm," which increases to " 68.3 dynes per cm on dilution with water to form a 50 per cent concentration." If a dissolved substance lowers the surface energy of the solvent, it will tend to become concen- trated in the surface layer. It has been observed that the surface energy of stored samples of serum falls slowly with time. This decrease in surface energy may be due to adsorption of air or other gases at the liquid-gas interface. Substances which cause a decrease in surface energy and are as a result concentrated at the surface of the solvent can produce very large changes in surface energy for very minute quantities dissolved. TABLE V-3 Surface Energy of Aqueous Solutions Interface, liquid-air. For M moles per kilogram of solvent an increase in T is shown. Units of AT, ergs per square centimeter. Temperature 20° C. NaCl KC1 M AT AT 0.025 0.055 0.05 0.09 . . . 0.10 0.17 0.16 0.25 0.42 0.35 0.5 0.82 0.70 1.0 1.64 1.4 2.0 3.28 2.8 3.0 4.90 4.2 4.0 6.50 5.5 5.0 8.17 7.0 A substance which increases the surface energy of the solvent, as for instance sodium chloride, will tend to flow out of the surface layer, leaving it less concentrated than the solution in the interior of the solvent. The Hay test for the presence of bile in urine takes advantage of the fact that the surface energy is decreased because of the concentration of bile salts in the surface layer. If sublimed sulphur is sprinkled on the surface of normal urine or pure water, the sulphur is not wetted but floats on the surface. If the sublimed sulphur is sprinkled on icteric urine, from patients suffering from jaundice, the sulphur sinks to the 176 SURFACES AND MEMBRANES bottom of the urine. The surface energy of the normal urine, because of the presence of the bile salts, is changed from about 66 to 55 ergs/cm 2 . Oil is sprayed on water as a larvicide to suppress mosquitoes. The larvae of mosquitoes normally suspend themselves from the water-air interface by means of three hairlike appendages attached to their breath- ing tubes. Substituting a water-oil interface for the water-air interface reduces the surface energy. To be effective the oil must reduce the surface energy sufficiently to prevent the larvae from suspending them- selves by their breathing tubes, so that they sink and suffocate. Surface Energy in Living Systems Since living cells are immersed in liquids, it follows that the interface surface energy must be much less than that found at air-water inter- faces. Recent work shows that invariable, very low tensions exist between the cell and liquid interface. Protoplasm in sea water, for instance, may have a surface energy as low as 1 erg/cm 2 . The work by Harvey [1938] on the physical properties of protoplasm shows that such " naked " cells as amebas, leucocytes, and plant cells removed from their cellulose walls possess surface energies even less than 1 erg/cm 2 . With the microscope centrifuge, first constructed by Harvey in 1932, some very low values for this interface tension were found for numerous invertebrate eggs. Plateau's Principle of Minimal Area When the disturbing effects of gravity are absent to distort the shape of a fluid body at rest, liquid surfaces always assume a curvature such that the mean curvature along two planes at right angles is constant. — + — = Constant where #1 and R 2 are these principal radii of curvature at any point. Hence, when one decreases the other must increase to keep the reciprocals of the sum constant. A spherical soap bubble, for example, has two equal curvatures along two planes at right angles. If this bubble is stretched, one radius of curvature increases as the one at right angles decreases. Geometrically it can be shown that surfaces to which this equation applies are surfaces of minimum area. The forms of living cells and protoplasmic masses, such as vacuoles, plasmolyzed protoplasts, and amebas, are also illustrations of this principle. Barnes [1937] even found that fatty material in such cells as intestinal epithelium occurs as spherical droplets. THE COALESCENCE OF LIQUID SPHERES 177 This law of constant mean curvature is also illustrated by the struc- ture of emulsions. Emulsions are systems of two liquids insoluble in each other, consisting of small globules of one liquid suspended in a second liquid with which it does not mix. The conditions necessary to produce a stable emulsion are such that, when two incompletely miscible liquids are mechanically agitated so as to disperse one in the o ther in the form of globules, a minimum of work must be done upon the system, which is equal to the product of the interfacial surface energy per unit area by the increase in surface due to the globule formation. That this is an appreciable amount of energy, and that the resulting dispersion is unstable, can be shown by the fact that as the coalescence of the globules takes place a measurable amount of energy is liberated. To stabilize an emulsion, it is necessary to add a third substance (the emulsifier) which will form an adsorbed film on the globules. This will prevent their coalescence if the surface energy of each globule is reduced to a mini- mum. In general, the more the emulsifier decreases this surface energy, the more stable is the resulting emulsion. The most effective emulsifiers for fat-water systems are polysaccharide gums, proteins, soaps, lipoids, bile salts, and saponins. The Coalescence of Liquid Spheres The coalescence of spherical droplets in suspension is primarily attribu- table to the reduction in the potential surface energy. Taylor's [1921] study of this problem convinced him that coalescence of liquid spheres is not due to a molecular attraction, so long as the spheres do not touch. When contact occurs, a " force " comes into play which causes them to coalesce and become one sphere. This occurs with all liquids, independ- ent of the relative size of the spheres, and at all temperatures. A fundamental property of the surface energy is to maintain the area of a liquid surface at a minimum. The minimum area that can be attained by any unconstrained mass is spherical. Therefore, if several small spheres, each of surface energy e, were to coalesce, a new sphere, having surface energy E, must be formed. Upon the large sphere a redistribution of surface energy must take place in such a way that the surface energy E is less than the sum of the surface energies of the small spheres. Taylor [1921] calculated this redistribution of energy for the coales- cence of three spheres of water whose diameters were 0.3, 0.4, and 0.5 cm. The potential surface energy of these three spheres is E= tt{(0.3) 2 + (0.4) 2 + (0.5) 2 }!T or 0.50x7" ergs per square centimeter, where T is the interface tension in 178 SURFACES AND MEMBRANES dynes per centimeter. If these spheres are brought in contact they will coalesce to form one sphere whose diameter is 0.6 cm and whose potential surface energy is E = O.SQtT ergs per square centimeter. The differ- ence, or 0.14wT, is the loss in potential surface energy that has been transformed into kinetic energy, which manifests itself as a rise in temperature of the newly formed sphere. For water, where T = 72.75 ergs/cm 2 at 20° C, this rise amounts to 7.5 X 10 -7 calorie. The con- verse case possesses physiological interest. How much energy would be used to break the above drop into ten thousand equal spherical fragments? Surface Energy of Spreading Cells In the response of living cells to contact with solid bodies, the surface energy and contact angles developed at the interfaces play an important part, if not a major one, in determining the physical response of cells to changes in environment. The behavior of a cell towards a horizontal flat surface with which it may come in contact and attain an equilibrated shape or, if surface con- ditions are favorable, spread to molecular film thickness has many biological implications. The familiar adhesiveness exhibited by blood cells and the spreading of phagocytes in the process of ingesting small particles are typical examples. CP interface P PG interface Plasma G Glass ~~ ) Fig. V-l. Cell immersed in plasma before contact with glass surface. The complex phenomena of the response of a living cell to a flat surface or spherical particle with which it makes contact is best under- stood if an idealized simple case is first analyzed and examined for the physical implications involved. The existence of a perfect fluid is assumed which is immersed in plasma of the same density as the cell. SURFACE ENERGY OF SPREADING CELLS 179 Plasma y-CP interface Tcp / j/" h Cell \\ To A T-GC f\ G f a \^^ / Glass R-h ■^a ^^GC interface 1 GP interface Fig. V-2. Cell immersed in plasma in equi- librium position with respect to glass surface. 6 = contact angle. In this environment the cell is spherical and possesses potential surface energy equal to 4irr 2 Tcp ergs per square centimeter, where Top is the tension attributed to the cell-plasma interface. The spherical cell is then allowed to come in contact with a glass plate G shown in Fig. V-l, which is also immersed in plasma. As the cell makes contact with the glass sur- face it exchanges a cell- plasma (CP) interface, of area to, 2 , for a cell-glass (CG) interface of equal area (Fig. V-2). If the cell spreads over the glass surface, this area increases until the cell has expanded and formed a layer one molecule thick. The fundamental question is whether the cell will always spread to monomolecular thickness or whether an intermediate equilibrium posi- tion will be attained, owing to the character of the interfaces. Fenn's [1921] theoretical analysis of this situation showed that for a given environment the surface energy of the cell, while spreading, would decrease and reach a minimum value when the cell attained its equi- librium position on a given surface. To verify this analysis the spherical cell C is represented as in Fig. V-l. This cell with cell-plasma interface and of unit radius is about to come in contact with the surface G in the presence of the plasma P. As the cell touches the glass surface it assumes the shape shown in Fig. V-2. The problem is to determine the height h of the distorted cell above the hori- zontal surface G at equilibrium in terms of its surface energy. In its new environment it now possesses cell-plasma (CP), cell-glass (CG), and glass-plasma (GP) interfaces differing in area from those in Fig. V-l. In assuming the equilibrium position on the glass surface, part of the cell-plasma interface, of area to, 2 , is replaced by an equal area of cell- glass interface. At the circular edge of contact between the three media are located the tensions T G p due to the glass-plasma interface, T GC due to the glass-cell interface, and Tqp due to the cell-plasma interface. At the junction of these three phases the cell-plasma interface makes an angle with the glass-cell interface, which defines the contact angle. The cell, if free to spread, must decrease its potential surface energy in the act of spreading. This act of spreading enlarges the glass-cell con- tact area until equilibrium has been attained. In this state the surface energy is at a minimum. The surface energy of the contacted cell is 180 SURFACES AND MEMBRANES made up of two parts: the area of the curved surface of the spherical segment with surface energy equal to (irh 2 + ira 2 )Tcp, and the circular interface with surface energy equal to Ta 2 (T GC — T GP ) ergs per square centimeter. Then the total energy is E = T(h 2 + a 2 )T CP + *a 2 (T 0C - T GP ) where T represents the tensions designated by the three different inter- facial subscripts. Let Tcp — n and T GC ~ Top — w. The above equation may then be rewritten as E = nir(h 2 + a 2 ) + rrnra 2 where, because the volume of the cell remains constant, 3/i 3 a 2 In the process of spreading, the volume of the cell is assumed to remain constant, so that the problem reduces itself to ascertaining the magnitude of the height h of the cell at equilibrium for given values of cell, surface, and plasma characteristics, i.e., for values of m and n or values of m/n. Substituting for a its values in terms of h in the above equation for E, and differentiating the result with respect to h, gives ,a[ 2n _ |(m + n) _8 f(m + n) ] dE_ dh ' 3/i 2 Since at equilibrium the surface energy must be a minimum, i.e., 4(w ~\~ 7l) dE/dh = 0, it follows that h 3 = — . Geometrically it can be 2n — m seen from Fig. V-2 that 4 - 2h 3 cos 6 = 3 4 + h 6 Substituting the above value of h z in this relation, we find that m T GP - T GC cos 6 = = n T CP It is possible to use this expression to predict what will happen when a cell of uniform density, immersed in plasma of the same density, makes contact with a horizontal surface. Suppose that it spreads until its contact angle is 90°. What is the height of the cell under these circum- PHAGOCYTOSIS 181 stances? This height may be obtained by setting 8 = 90°, cos = 0, -m/n = 0. Then h 3 = 2, and h = 1.26. The cell has therefore assumed the shape of a hemisphere having a volume equal to the original spherical cell. If the nature of the surface G is then changed so that the contact angle = 0, then cos = +1; hence — m/n = +1, i.e., the cell spreads " to infinity." If the surface G is such that the cell does not spread at all, then 8 = 180° and cos 8 = —1; hence — m/n = — 1. The cell is a free sphere. The conclusions are that values of —m/n between +1 and —1 will produce all possible degrees of spreading and that the surface characteris- tics of cell, plasma, and plane determine the magnitude of the contact angle in its equilibrium position. To produce further spreading of the cell, either work must be done on it or the surface characteristics of the interfaces must be changed. Phagocytosis If a small spherical insoluble particle is substituted for the plane sur- face, comparable changes in the contact area of the cell and particle will take place because of the spreading of the cell over the particle. This factor led Fenn to propose the above analysis as a method of approach in the understanding of the very important biological phenomenon known as phagocytosis. Phagocytosis may be defined as the ingestion of a particle by a living cell. The particle may be a non-living piece of matter, a bacterium, or other cell structure. The problem is not to investigate the fate of the ingested particle, but to attempt to analyze the mechanism of phagocyto- sis in terms of the surface energy existing at the interfaces created by the contact of the cell with the particle in the presence of plasma. The above theory of cell spreading may be extended to cover cases where the surface G over which the cell spreads is curved to such an extent that G may be considered a small sphere. Under these circum- stances the following questions may arise. What is the physical adjust- ment of the cell, and how does the total surface energy vary as the small spherical particle is progressively ingested? It frequently happens in phagocytosis that the cell is about ten times greater in radius than the particle to be ingested, as for instance when a particle in the form of a Staphylococcus aureus of average diameter from 0.7 to 1.0 m is about to make contact with a large mononuclear lympho- cyte with average diameter 12 to 15 m- In this example, according to Lyddane and Stuhlman [1940], the above theory shows that the surface 182 SURFACES AND MEMBRANES energy of the expanding cell, as it progressively ingests the particle, drops to a minimum at some specific depth of penetration, where the cell and particle are then in equilibrium. Under these conditions, whether the particle is partly or completely ingested, the surface energy between coccus and cell is at a minimum. If as a result of ingestion the cell- particle interface changes, it is possible that further ingestion goes on at the expense of the internal energy of the cell, or that the particle is ejected. Phagocytosis a Phenomenon of Spreading The above analysis is supported by experimental evidence (Mudd [1933]), which proves that the ability of a phagocyte to spread over the surface of a particle undergoing ingestion is one of the principal factors in determining phagocytosis. It has been found that, in the presence of dilute sensitizing serum, adhesion of particles to the phagocytes may take place with little evidence of complete ingestion. If the sensitizing serum is more concentrated, however, the particles adhere to the phago- cytes and are subsequently covered by their cytoplasm. The conclu- sion that may be drawn is that the phagocytosis-promoting substances of immune sera, opsonin or bacteriotropin, resurface the particles with at least a monomolecular layer of an interfacial-surface-energy depressant, a surface deposit upon which phagocytes can spread very readily. Phagocytosis in the body can be promoted by the deposition, on the particle or on a bacterium, of a film of serum globulin which gives the surface a low interfacial tension against the leucocyte and a high inter- facial tension against the medium in which the particle is suspended. Since it is practically impossible to measure the three interfacial tensions in a phagocyte-particle-liquid system, inferences must be drawn from such theoretical situations and indirect experimental evidence as out- lined above (Mudd, McCutcheon, and Lucke [1934]). The influence of sulphanilamide upon phagocytic activity is still uncertain. Recent work, however, indicates that sulphanilamide and sulphapyridine are more effective therapeutically in conjunction with immune serum than if either drug or serum is given alone, a result sug- gesting that phagocytosis may play a part in the final disposal of the infective agents. Stalagmometer A rather usual method for measuring surface energy is by determining the weight of the drops which detach themselves slowly from the tip of a calibrated vertical glass tube of small bore. A rather crude formula is STALAGMOMETER 183 then applied in which the weight of the drop W is proportional to the surface energy and radius of the tube. W = 2-irrT It is assumed that the tension of the liquid acts vertically around the rim of the tube from which the drop is suspended and subsequently necks off. It can be shown theoretically and verified experimentally that drops necking off from a vertical tube are always smaller than 2-irrT, often by Ky o Fig. V-3. Progressive stages in the formation of a drop of water separating itself from a clean polished surface at the end of a glass capillary tube. Freehand sketch. more than 40 per cent. High-speed photographs by Guye and Perrot [1903] show that the suspended drop becomes unstable before it leaves the end of the tube. Then a constricted portion develops, as seen in Fig. V-3, which narrows and subsequently allows the drop to form after breaking off near the end. The stretched column between the lower drop and the tube then separates itself from the tube and forms an additional small drop; finally, the remainder of the column retracts, allowing some of the liquid to remain suspended from the end of the tube. In any drop-weight method both the large and small drops must be counted together as " one drop." Harkins and Brown [1919] showed by careful measurements that the weight of a drop is conditioned by the radius of the tube from which the drop falls and is also a function of the inverse cube root of V, the volume of the drop. The more exact relation between these quantities is or more simply W = 2-rrrTf T= m F \v 1/3 ) 184 SURFACES AND MEMBRANES where F is a correction factor and equal to and m is the mass of ... B 27r/(r/T 1/3 ) the drop falling from a tube of radius r. A table of correction factors compiled by Harkins and Brown can be found in the International Criti- cal Tables, Vol. 4, p. 435. With the aid of these tables the error in deter- mining the surface energy is reducible to 0.1 per cent. A convenient form of dropping tube, or stalagmom- eter, is shown in Fig. V-4. It is essentially a capil- lary tube the end of which is flattened by compression, carefully ground flat, and polished. The tube is filled, with the liquid under examination, to the major en- graving A. The number of drops which break away from the lower plane surface C are counted while the liquid level falls from the upper mark A to the lower mark B. Since the measured surface energy decreases in mag- nitude with rise in temperature, all observations must be made at constant temperature. The experimental results that can be obtained by this method are least subject to error when the lower polished flat release- surface possesses a sharp edge and the drops are allowed to form slowly. Adam [1930] recommends a total time of about ten minutes for the formation of each drop. The surface-energy values will be found too large if the drop forms too rapidly. The time of formation can be shortened if the initial stages of drop formation are rapid and if the final necking is allowed to develop very slowly, for example during one minute, so that the drop eases off very gently. In the use of a stalagmometer great care must be exercised to avoid the contamination of the polished release-surface by grease. The slightest trace of grease greatly lowers the surface energy of the water which is used to calibrate the stalagmometer. In order that determinations may be carried out at constant temperature and in the presence of saturated vapor, drops must be allowed to form in a closed, temperature-controlled vessel. Fig. V-4 agmometer Traube. Zjla c , Stal- after The Suspended-Ring Method If a biological fluid possesses a low content of surface-active solute, a tensiometer method, which measures the force required to detach a cir- cular ring from the surface, is highly recommended. A metal ring THE SUSPENDED-RING METHOD 185 dipped below the surface and then carefully pulled vertically upwards will drag with it a film of the liquid. If we assume that this film becomes vertical before rupture takes place, then the downward pull P on the ring must be equal to twice the product of mean circumference of ring by surface energy. To the first approximation P = 4tRT To increase the accuracy, the exact dimensions of the ring and the diameter 2r of the wire of which it is made must be taken into considera- tion. On account of the incompleteness of the theory, Harkins, Young, and Cheng [1926] have increased the reliability of the method to better than 1 per cent by introducing an experimental correction factor F, so that the working equation becomes T = mg ™ 4wR To obtain an unknown surface energy the maximum pull in dynes to raise the ring when the surface is on the point of rupture is obtained, experimentally, as p = mg/^irR, where R is the mean radius of the ring. The volume of the liquid V raised by means of the ring above the plane surface of the liquid, which corresponds with the above maximum pull, is V = m/(d — p), where d is the density of the liquid, p is the density of air saturated with vapor of the liquid, and m is the mass of the raised liquid. It was found that for the proper values of the ratio of R/r the correc- tion factor F is determined by the value of R 3 /V. Hence, the values of R, r, and the experimentally determined value of V being known, the surface energy may be determined to a high degree of precision with the aid of a table of these correction factors as T = p-F In the hands of du Nouy [1919] this method was brought to a high degree of precision. He adopted a ring of platinum (10 per cent iridium) which hangs from an inverted V frame of the same kind of wire fused to the ring. This ring can be cleaned by simply heating it white hot. It is suspended from the arm of a specially designed torsion balance, as in the Cenco-du Notiy tensiometer (Fig. V-5). The wire ring is of circular section about 0.3 mm in diameter with a mean circumference of 4 cm. The torsion wire is made of steel piano wire of diameter 0.25 mm. The liquid is placed in a shallow crystallizing dish or watch glass into which the ring is allowed to dip. The pointer attached to the torsion wire rotates over a fixed circular scale as the ring is raised to the point where it 186 SURFACES AND MEMBRANES breaks through the liquid surface. The liquid surface is adjusted so that, for its final reading at rupture, the beam lies in a horizontal position. If the ring has a mean circumference of 4.00 cm and is used on pure water at room temperature, the value of the correction factor F will be approximately 0.990. Since F can be determined for any given case, the apparatus is sensitive to a force of about 0.1 dyne and has the advantage of being able to use small quantities of liquid at high operat- ing speeds. Certain experimental precautions are essential if a moderately high degree of precision is desired in the use of this instrument: 1. The liquid should be covered by an inverted glass funnel to pre- vent cooling by evaporation. 2. The liquid and the vapor above it must be kept at a con- stant temperature. 3. The vessel used to contain the sample should be of such a shape and size that the surface need not be corrected for curvature of meniscus of the liquid. 4. The design of the vessel should be such that the surface of the liquid may be renewed or swept by a clean glass bar. Tables of correc- tion factors are supplied by the manufacturers of this instrument for the particular ring adopted. Since the surface energy of water and other liquids increases appreci- ably with a decrease in temperature, it is necessary to know the tem- perature and the temperature coefficient of the liquid under test. The temperature coefficient of water between 15 and 25° C is, according to Harkins, 0.154 erg/cm 2 /°C; between 10 and 60° C its surface energy may be expressed by T = 75.796 Fig. V-5. Cenco-duNouy precision tensiometer. (Courtesy Central Scien- tific Company.) 0.145* - 0.00024* 2 The Effect of Surface Impurities on Surface-Energy Measure- ments In determining the speed with which a substance spreads over the surface of a liquid, the ring method of measuring surface energy is used PERMEABILITY OF STATIC MEMBRANES 187 to compare the surface energy at points on the circumference of a circle at whose center the spreading substance touches the liquid. Substances like myristic acid are found to spread in two stages. In the first stage the surface is covered by a unimolecular " expanded " film under no compression. The second stage follows when the expanded film becomes more closely packed and still maintains its unimolecular thickness. The ring method was used by Cary and Rideal [1925] to follow surface- energy changes as illustrated by the progressive film formation of a crystal of a fatty acid, as, for instance, myristic acid, when it was brought into contact with the surface of a 0.01 N solution of hydrochloric acid in water. The velocity of spreading on water was found to be of the order of 20 cm/sec. Water, having a high cohesion, does not spread on organic liquids. Organic liquids of moderately high cohesion spread on water. Any diminution of the surface energy of the water, by an adsorbed film, diminishes the tendency of the upper liquid to spread. The property of castor oil to spread rapidly as a thin film would seem to help explain the rapidity and thoroughness with which it coats the intestinal walls when it is used as a purgative. It has also been demon- strated that castor oil is a better lubricant for machinery than mineral oil of equal viscosity. Permeability of Static Membranes It has been found possible to construct partitions which, when used to separate pure water from a solution of crystalloids like sugar or salt, will allow the water to diffuse through them, but not the dissolved crystalloids. A film of colloid (glue-like) material such as starch coated on a supporting sheet of porous paper, if used as a partition between pure water and a solution of crystalloids and colloids, will allow the crystal- loids to pass through and diffuse into the water, but it will entirely block the passage of the colloids. If the partition is a structure which allows only the solvents to pass through, it is designated as semi-permeable. Some animal bladders and parchment sheets will allow water and dissolved crystalloids to pass through but will prevent the passage of colloidal substances. Animal and vegetable membranes that have the property of allowing the solvent to pass through them and of preventing some or all of the solute from passing are also considered semi-permeable. The botanist de Vries [1888] was one of the first to attribute the shrink- age of plant cells, placed in dilute sugar solutions, to the semi-permea- bility of the cell membrane. He observed, with the aid of a microscope, that plant cells had comparatively rigid cellulose walls enclosing a mem- brane filled with protoplasm. Reproductions of his original osmotic 188 SURFACES AND MEMBRANES experiments on the middle nerve leaf of Tradescantia discolor are shown in Fig. V-6. In diagram A note how the sap fills the normal cell until its bulging sides touch the cellulose walls. When such a structure was immersed in a 10 per cent sugar solution, the protoplasm was found to shrink gradually and draw away from the walls, as shown in B. When the cell was immersed in a strong solution of potassium nitrate, the sap was observed to shrink into globular masses like those shown in C. A Fig. V-6. Cells from the middle nerve leaf Tradescantia discolor. A, normal cell. B, plasmolysis started, cytoplasm shrinks from cell wall. C, strong plasmolysis due to 1.0 M potassium nitrate. (After H. de Vries [1888].) De Vries found that such a shrinkage was produced by the passage of the water content of the cell through the cell membrane while the leaf was immersed in a sugar or salt solution. He also discovered that many plant cells, after having undergone what he termed -plasmolysis, could be restored to their natural fluid conditions by placing them in pure water. This experiment proved that the mem- brane was permeable to water in either direction. He concluded that the dead cellulose walls were freely permeable to the sugar and salt solutions, but that the membrane boundary of the cell protoplasm was impermeable to the crystalloids but permeable to water. A familiar example of membrane permeability is the swelling of seeds when steeped in pure water. They will increase as much as 70 per cent in weight from the transmission of water through the semi-permeable covering with which they are surrounded. The apparent " selective " permeability of seed coverings to certain substances is illustrated by the use of copper sulphate as a fungicide for wheat. This salt, though highly poisonous for the fungus spores adher- ing to it, will not affect the vitality of the wheat seed because the seed covering is impermeable to it. Other examples of selective permeability are furnished by the many marine forms in which the sodium-potassium ratio of the cell content is very different from that found in sea water. The marine plant Valonia, for instance, was found by Osterhout [1936] OSMOSIS 189 to possess a cell content which has about one fifth the sodium concen- tration and fifty times the potassium concentration of sea water in which it normally exists. In a certain sense, the human skin may be considered as functioning like a semi-permeable membrane. The work of Whitehouse, Hancock, and Haldane [1932] has shown that a large proportion of the moisture which is given off from the skin during rest under ordinary conditions of temperature passes through the skin by osmosis or diffusion. The osmotic loss was demonstrated through different effects of baths in pure water and strong salt solutions. They foimd that osmotic loss increased very rapidly as the temperature of the skin rose, but that, with a suffi- cient rise, a point was reached where the presence of liquid sweat over the whole skin interrupted the process completely. Since the introduction of the cell theory in 1838 the general conclusion that living matter must be enclosed in a protective membrane in order to survive in its environment has become definitely established. A fundamental property of a living cell is the semi-permeability of its limiting membrane. Upon the death of the cell the semi-permeability of its membrane is usually entirely lost. The limiting membrane of protoplasm is not a dead partition, but an intricate dynamic structure maintaining the control between its internal and external environment. The external environment is usually a dilute solution containing a changing amount of nutrient material. Osmosis Osmosis may be defined as the passage of a fluid or fluids through a membrane which separates two liquid phases consisting of a common solvent and one or more solutes with different concentrations in the two phases. The unfertilized eggs of the sea urchin are typical natural osmometers. They are normally spherical in shape, which readily permits their change in volume to be determined by measuring their diameters. The eggs can be swollen by introducing them into diluted sea water. Shrinkage will take place when they are transferred from diluted to concentrated sea water. McCutcheon and Lucke [1927] discovered that the rate at which water passed through the membrane in exosmosis as well as endosmosis in the unfertilized sea-urchin egg followed the same law as that expressing the velocity of a monomolecular chemical reaction, namely, that dx it ^ - = k(o - x) 190 SURFACES AND MEMBRANES where x was the change of volume during time t, c the original volume, and k the velocity constant. It was also found that the speed of osmosis was greatly increased as the temperature increased. The speed of pene- tration was found to be much greater than if simple diffusion through a membrane took place. Osmotic Pressure The osmotic pressure of a solution can be defined as the maximum hydrostatic pressure (P = hdg) produced when a solution and solvent are separated by a perfect semi-permeable membrane. It may also be defined as the equivalent of the external pressure which must be applied to a solution in order to prevent the passage of the solvent into it through a perfect semi-permeable membrane. Measurements of Osmotic Pressure In the search for an ideal semi-permeable partition, Traube, as early as 1867, discovered that a flexible film of cupric ferrocyanide has semi- permeable properties. He found that, when a dilute solution of copper sulphate is mixed with a dilute solution of potassium ferrocyanide, a brown precipitate of cupric ferrocyanide is formed. This precipitate, if used as a partition, will permit the passage of water, but will prevent the passage of both copper sulphate and potassium ferrocyanide, as well as of many other crystalloids. A very realistic model of a growing cell may be constructed by intro- ducing a moderately concentrated solution of potassium ferrocyanide, in the form of a drop, below the surface of a dilute copper sulphate solu- tion. A brown precipitated film of cupric ferrocyanide is formed around the drop, which subsequently ruptures at some point as the result of the increasing osmotic pressure caused by osmotic flow of water through the membrane. The rupture, however, is rapidly mended by a new patch of precipitated cupric ferrocyanide. The osmotic pressure again enlarges the drop until by a succession of ruptures and subsequent repairs the drop has grown until its internal and external pressures have attained equilibrium. Since this type of unsupported membrane is rather fragile, the botanist Pfeffer (1877) supported the gelatinous cupric ferrocyanide film by the framework of a porous earthenware pot. He used an unglazed porcelain cylindrical vessel from which he had removed the air occluded in the pores and then allowed them to fill with water. By placing this water- saturated pot in a 3 per cent solution of copper sulphate and pouring into the interior a 3 per cent solution of potassium ferrocyanide, he succeeded MEASUREMENTS OF OSMOTIC PRESSURE 191 in precipitating the semi-permeable membrane in the framework of the vessel, where the two liquids met in the porous wall. Figure V-7 shows the form of the apparatus used by Pfeffer to measure osmotic pressures. The earthenware pot was a white unglazed porcelain cell z with the glass pieces v and t inserted as air-tight stoppers. The Distilled water bath Fig. V-7. A precision method for measuring osmotic pressures according to Pfeffer. porcelain cell was about 4.6 cm high and had an internal diameter of about 1.6 cm with walls from 1.25 to 2 mm thick. A manometer m was attached to measure the pressure. The tube g was sealed off after air bubbles had been removed at the joints t. The solution whose osmotic pressure was to be determined was introduced into the apparatus through g. The porous cell was then totally immersed in distilled water, and 192 SURFACES AND MEMBRANES after osmotic equilibrium had been attained the pressure was read on the manometer. Using dilute solutions of cane sugar, Pfeffer discovered that the os- motic pressures developed by them were proportional to their concentra- tions and that the osmotic pressure increased with rise in temperature. He found that the osmotic forces developed by his solutions were aston- ishingly large. A 10 per cent sugar solution, for instance, actually developed an osmotic pressure of nearly 7 atmospheres, or a force of more than 100 lb/in. 2 Van't Hoff's Discovery Ten years later van't Hoff pointed out the remarkable parallelism between the properties of gases and the osmotic behavior of dilute solu- tions. The experimental evidence showed that the osmotic pressure of a dilute solution was directly proportional (1) to the concentration of the solute and (2) to the absolute temperature. If it could be proved that the ultimate material particles in the solvent behave as if they were entities having the properties of gas molecules, the application of the general gas law to osmotic-pressure phenomena would be justified. Or, conversely, if the general gas law could be used to predict the osmotic pressure of a solution, the conclusion is that, to the first approximation, the entities in the solvent of a dilute solution had properties analogous to those of gas molecules. The first step is the justification of Boyle's law. In order to apply it the pressure must be shown to be inversely proportional to the volume, provided that the temperature is kept constant. Since the measured hydrostatic pressure P = hdg and the density of this column of liquid d = m/V, it follows that PV = hmg. When the osmotic pressure developed by sucrose, as indicated in Table V-4, is examined, it can be seen that a 0.2 M concentration develops a pressure of 5.11 atmospheres at 20° C. It should follow that a 0.4 M concentration must develop a pressure of 10.22 atmospheres, and 0.6 M concentration, a pressure of 15.33 atmospheres. The corresponding experimental values are 10.22 and 15.52 atmospheres, respectively. The agreement is surprisingly good. The conclusion is that the osmotic pressure is proportional to the concentration expressed in gram-molecular weights per 1000 grams of water; i.e., P is proportional to mg/V. The gram-molecular weight is the weight of a substance in grams numerically equal to its molecular weight. A gram-molecular weight of any substance contains the same number of molecules (6.064 X 10 23 ) as a gram-molecular weight of any other substance. The concentration ISOTONIC SOLUTIONS 193 of a substance is defined as the number of gram-molecular weights M contained in 1000 grams of water. As a second step another aspect of the general gas law must be justi- fied, namely : the pressure developed by a given mass of gas, at constant volume, is proportional to the absolute temperature. The restatement of the law as applied to dilute solutions would read : the osmotic pressure developed by a given concentration is proportional to the absolute temperature. Table V-4 shows that a sucrose concentration of 0.4 M TABLE V-4 Osmotic Pressure of Sucrose Concentrations in gram-molecular weights per 1000 grams water. Sucrose C12H22O11. Temperatures in degrees Centigrade. Osmotic pressure in atmospheres, standard conditions. C = M/1000, where M = 342.2. Temperai ture, °C -J c 10 20 30 40 0.1 2.48 2.52 2.61 2.50 2.58 0.2 4.76 4.93 5.11 5.09 5.21 0.3 7.14 7.39 7.67 7.71 7.91 0.4 9.52 9.87 10.22 10.38 10.69 0.5 12.00 12.40 12.86 13.09 13.47 0.6 1 14.50 14.98 15.52 15.85 16.28 By Courtesy of Morse, Holland, Myers, Cash, and Zinn, Am. Chem., J., 48, 29 {1912). at 10° C can develop an osmotic pressure of 9.87 atmospheres while the same concentration at 20° C should, according to the general gas law, develop a pressure of 10.21 atmospheres. The data show that this sucrose solution can develop an osmotic pressure of 10.22 atmosphere. The conclusion is that, at any given temperature, all equal concentra- tions of dilute solutions of non-electrolytes have the same osmotic pres- sure. Hence, the molecular weight of a non-electrolyte being known, the general gas law can be used to calculate the amount of a substance that must be dissolved in 1000 grams of solvent to obtain any desired osmotic pressure. Isotonic Solutions Solutions developing the same osmotic pressure are isosmotic or iso- tonic. Hypotonic solutions are solutions that have a lower osmotic pressure, and hypertonic solutions possess a greater osmotic pressure, 194 SURFACES AND MEMBRANES than plant or animal cell contents when the cells are placed in such solutions. If a cell is placed in a solution having a higher osmotic pressure (hyper- tonic solution) than the cell contents, water tends to flow out of the cell, thus reducing its internal osmotic pressure. The cell therefore shrinks in size. If the solution in which a cell is introduced has a lower osmotic pressure (hypotonic solution), then water tends to flow into the cell, which expands, eventually bursting as the result of the increased internal osmotic pressure. Hamburger, a Dutch physiologist, was probably the first to apply physical laws to animal physiology. He showed, as early as 1886, that erythrocytes from different species of animals have different limits of fragibility and that in no case was the solution producing hemolysis (stretching of red blood cells so that pigment escapes) isotonic with the cell content. He found that an isotonic solution of sodium chloride containing 0.951 gram of NaCl per 100 grams of water could be used to prevent the rupture of the membrane of human red corpuscles. Osmotic Pressure of Electrolytes We find experimentally that an aqueous solution of sucrose (M = 342.2) having a molar concentration of 0.2 M at 0° C develops an osmotic pressure equal to 4.76 atmospheres. A similar concentration of sodium chloride (M = 58.5) develops an osmotic pressure of 8.75 atmospheres. The sodium chloride behaves osmotically as if its concen- tration were nearly twice as great as that of sucrose. This abnormal osmotic activity of salt solutions was first observed by the botanist de Vries during his investigation of the previously men- tioned experiments on the plasmolysis of plant cells. If " normal " means the values calculated in accordance with the van't Hoff laws of osmotic pressure and molecular weights of non- electrolytes, then electrolytes may be said to possess an abnormally high osmotic pressure. This abnormality is found to become more pro- nounced by diluting the solution. The explanation is found in the fact that salts, acids, and alkalies dissociate when dissolved in water. The molecules in solution dissociate into positively and negatively charged entities called ions. These ions participate in creating the osmotic pressure just as if they were individ- ual particles. Sodium chloride, in water, dissociates into one positively charged entity, the sodium ion, and one negatively charged entity, the chloride ion. If all the molecules which make up a solution of sodium chloride in water were completely dissociated, then such a salt solution OSMOTIC PRESSURE OF ELECTROLYTES 195 should have an osmotic pressure twice that of a sugar solution of the same molecular concentration. TABLE V-5 Degree of Ionization of Sodium Chloride in Water with Changes in Concentration C = the concentration in gram-molecules per 1000 grams water. a = the degree of ionization or the fraction dissociated. i = the isotonic coefficient. /°C C a i 1.000 0.5 0.2 0.1 0.05 0.02 0.01 0.001 0.0001 18° C 0.68 1.68 0.77 0.82 1.77 1.82 0.85 1.85 0.88 1.88 0.92 1.92 0.94 0.96 1.94 1.96 0.99 1.99 25° C a i 0.847 1.847 0.828 0.849 1.828 1.849 0.874 1.874 0.899 1.899 0.929 1.929 0.944 0.96 1.944 1.96 0.99 1.99 TABLE V-6 Degree of Ionization of Electrolytes a = the degree of ionization or fraction dissociated. n = the number of ions into which the molecule dissociates. Concentration of all solutions 0.01 M at 25° C. NaCl KC1 MgSC-4 Na 2 S0 4 HC1 M 58.46 74.56 60.19 71.03 36.47 a 0.944 0.940 0.596 0.87 0.952 n 2 2 2 3 2 i 1.944 1.940 1.596 1.87 1.952 It has been found that the situation is more complex inasmuch as the salt in solution is ionized to a greater degree in a dilute solution than in a concentrated solution, and both the ions and also the undissociated salt molecules participate additively to produce the osmotic pressure. The experimental evidence to support these statements is indicated in Tables V-5 and V-6, which show, respectively, the degree of ionization of sodium chloride with decreasing concentration and the degree of ionization as the molecular structure changes. According to Table V-4, the osmotic pressure developed by a 0.5 M sugar solution at 18° C is 12.8 atmospheres, while a similar sodium chlo- ride solution develops an osmotic pressure 1.77 times as great, or 22.7 atmospheres. If the dissolved sodium chloride dissociates completely, the solution will produce a pressure of 2 times 12.8 atmospheres. The 196 SURFACES AND MEMBRANES sodium chloride is apparently not completely dissociated. Table V-5 shows that its degree of ionization a is 77 per cent, that this degree of ionization increases with dilution, and that only at infinite dilutions would one expect the degree of ionization to be 100 per cent. The os- motic pressure of a 0.5 M sodium chloride solution is due to 77 positive ions, 77 negative ions, and 23 undissociated molecules per 100 sodium chloride molecules found in the solvent at this concentration. These ions additively develop an osmotic pressure equal to 1.77 times 12.8 or 22.7 atmospheres. Isotonic Coefficient The van't Hoff isotonic coefficient 00 is a number by which the osmotic pressure, calculated from the general gas law, must be multiplied in order to give the expected osmotic pressure of an acid, base, or salt. If n is the number of ions into which the molecule dissociates when introduced into a solvent and a is the fraction of the molecules ionized at a given concentration, called the degree of ionization, then the isotonic coefficient is defined by i = na + (1 — a) Table V-5 shows some typical results obtained from sodium chloride dissolved in water; of special importance is the fact that the isotonic coefficient increases with dilution because of the increase in degree of ionization. Only for very dilute solutions (C < 0.0001) is the dissocia- tion so complete that each molecule appears as two ions in the solvent to produce the expected osmotic pressure. The Freezing Point The construction of an adequate semi-permeable membrane with which to determine the osmotic pressure of most physiological liquids has often entailed insurmountable difficulties. An indirect method can be resorted to which will give adequate quantitative results. Advan- tage is taken of the relation that exists between the freezing point of a solution and its molal concentration on the one hand and its molal concentration and osmotic pressure on the other hand. The temperature at which a liquid substance exists in equilibrium with its solid crystalline state is termed its freezing 'point. This must not be confused with the melting point; for instance, a fat like mutton tallow solidifies between 36° and 41° C, but melts around 44° C; butter solidifies near 21.5° C, but melts at about 30° C. Both the melting point of ice and the freezing point of water are 0° C under standard conditions. FREEZING POINT OF A DILUTE SOLUTION 197 In a mixture of ice and water at 0° C, the less dense ice (0.91674 gram/cc) floats on the water (0.99987 gram/cc). Since water expands on solidification, increasing the pressure will lower the freezing point. If the material contracts on freezing, like paraffin, then an increase in pressure will raise the freezing point. For water, an increase in pressure of 1 atmosphere will lower the freezing point 0.0075° C. Therefore, in making freezing-point measurements which involve water as a solvent, the very minute correction due to changes in atmospheric pressure can be disregarded. The freezing point of any solution is invariably lower than that of the pure solvent. The temperature at which a solution freezes is lower the greater the amount of substance dissolved. When such a solution begins to freeze, it is only the solvent which freezes out at first. As a result, the remainder of the solute is more concentrated. The freezing point of this concentrate is in turn still lower. The process continues until the solution becomes saturated. At this point the dissolved substance and the solvent freeze out so that the concentration of both remains un- changed during solidification. Freezing Point of a Dilute Solution of a Non-Electrolyte When a solid like sugar is dissolved in water to form a dilute solution the freezing point of the solution is below the freezing point of pure water. We refer to this lowered freezing temperature as the depressed freezing point. It is designated by A and is expressed in terms of the number of Centigrade degrees below the freezing point of distilled water taken as zero. Experimentally it is found that a solution containing 3.42 grams of sucrose dissolved in 1000 grams of water, i.e., a concen- tration of 0.01 M, freezes at —0.0186° C. The depression of the freezing point A = 0.0186. As the concentration is decreased, the freezing-point depression is proportionally decreased. At concentra- tion 0.001 (Table V-7), A = 0.00186, and proportionally lower values are obtained as the concentration decreases until at infinite dilution (zero concentration) the freezing-point depression is zero. If other non-electrolytes are dissolved in water and examined in a similar manner, it is found that all those solutions containing 0.01 gram-molecular weight per 1000 grams of water have a common freezing point, namely, —0.0186° C. They all possess A values which are smaller for proportionally smaller concentrations. As a result of such experiments Blagden formulated a law which states that the depression of the freezing point of a dilute non-electrolyte is proportional to the concentration of the solute. Raoult later found 198 SURFACES AND MEMBRANES that, for the same solvent, equimolecular amounts of different solute depressed the freezing point to the same extent, so that the conclusion is that equimolecular dilute solutions have the same freezing point or the same A value. TABLE V-7 Freezing Points of Some Common Salts of Physiological Importance, Compared with Sucrose Concentration in gram-molecular weights per 1000 grams water A value of Concentration M 0.001 0.01 0.1 Sucrose 0.00186 0.0186 0.188 342.2 NaCl 0.00366 0.0360 0.348 58.46 KC1 0.00366 0.0361 0.345 74.56 BaCl 2 0.00530 0.0503 0.470 208 . 29 MgSO-4 0.00338 0.0285 0.225 60.19 0.1 M is not considered a dilute solution. Glucose, M = 180.09, C = 0.1 M, A = 0.192. Morse, Frazer, and Lovelace [1907]. Osmotic-pressure experiments have furnished data showing that all equimolecular dilute solutions of non-electrolytes have the same osmotic pressure. Another conclusion is that dilute non-electrolyte solutions of equimolecular concentrations have freezing points that are directly pro- portional to their osmotic pressure. According to the van't Hoff's law, the osmotic pressure of a dilute solution containing 0.01 gram molecule of non-electrolyte in 1000 grams of water will develop an osmotic pressure of 0.224 atmosphere at 0° C. It will freeze at —0.0186° C. Hence a depression of the freezing point of 0.1° corresponds with an increase in osmotic pressure of 1.204 atmos- pheres or 915 mm of mercury (1219.5 millibars) at 0° C. Freezing Point of a Dilute Solution of Electrolyte Equimolecular dilute solutions of electrolytes do not freeze at the same temperature. This departure from the simple relations obtained for non-electrolytes can be observed in Table V-7. Here are tabulated some of the common salts of physiological importance which have freezing points differing from the freezing point of sucrose by as much as a factor of 2 or 3. Since the freezing point depends on the number of entities in solution, it must follow that the molecule of a salt like sodium chloride, which dissociates into a sodium ion and a chloride ion, would, for example, at EXPERIMENTAL DETERMINATION OF THE FREEZING POINT 199 0.001 M concentration produce a lowering of the freezing point equal to twice that of a non-electrolyte, i.e., 2 X 0.00186° or 0.00372°. A similar solution of barium chloride which dissociates into three ions should show a freezing-point lowering equal to 3 X 0.00186°, or 0.00558°. The corresponding experimental values shown in Table V-7 are 0.00366° and 0.00530°. Since the experimental values are smaller than the theoretical values, it follows that not all the molecules in the solvent are dissociated into ions, so that at all concentrations we must allow for the fraction of undissociated molecules found even in verjr dilute solutions. In the classical theory of solution the undissociated entities are mole- cules; in the Debye-Huckel theory they are supposed to be ions sur- rounded by an atmosphere of oppositely charged ions, and under the influence of an electric field it is this atmosphere that is constantly chang- ing instead of the ionic entities. In either theory a knowledge of the degree of dissociation is essential to determine the requisite freezing point and from it to calculate the expected osmotic pressure. The degree of ionization of NaCl at 0.001 M concentration is 96 per cent. This means that out of every 100 sodium chloride molecules in the solvent 96 dissociate into sodium and chloride ions and 4 remain undisso- ciated. It should follow that the expected freezing-point depression is 1.96 X 0.00186°, or 0.00365°, which is in close agreement with the experimental value of 0.00366° of Table V-7. Since a depression of the freezing point of 0.1° corresponds with an increase in osmotic pressure of 1.204 atmospheres, the above solution can develop an osmotic pressure of 33.5 mm of mercury. How many millibars is this mercury pressure equivalent to? Experimental Determination of the Freezing Point One of the most practical indirect methods for determining the osmotic pressure, and one almost exclusively used by physiologists and in medical practice, is the cryoscopic method. Since most physiological fluids are in reality dilute solutions, as seen in Table V-8, they readily lend them- selves to freezing-point determinations. An additional advantage is founded upon the fact that it makes practically no difference whether gross material is in suspension or whether more or less protein material is present. The freezing point of blood, for instance, may be obtained by using whole blood, blood plasma, or serum, since the corpuscles act as particles in suspension. ) Since a change in the freezing point of 0.01° corresponds with an osmotic-pressure change of 91.5 mm of mercury, it is necessary to use a thermometer calibrated to 0.01° so that an estimated change of plus or 200 SURFACES AND MEMBRANES minus one tenth of a calibrated division will introduce an error of not more than 9.15 mm of mercury in the osmotic-pressure observations. TABLE V-8 Physiological Fluids Data show mean per cent water content. Normal sea water 98.8 Bladder bile 84 Valonia sap 98.4 Liver bile 97 Ringer solution 99 Cow's milk 87.1 Cell sap 97-98 Human milk 88.5 Blood plasma 91 Horse's serum* 93.32 Gastric juice 99.5 Horse aqueous humor* 99.69 Pancreatic juice 99.5 Horse vitreous humor* 99.68 Saliva 99.5 Red blood corpuscles 64 * W. S. Duke-Elder, Physiol. Rev., 14, 483 (1934). In physiological or medical investigations, if the quantities of fluids available are not too small, a thermocouple or Beckmann thermometer having a range of 3° C with intervals calibrated in hundredths of a degree can be used. If only small quantities of fluid are available, a micro- Beckmann thermometer can be used. The micro-Beckmann thermome- ter has an overall length of 28 cm with a linear spread of 3.5 cm per degree. Since each tenth degree is calibrated into 10 divisions, it is possible, with the aid of a reading glass, to obtain a reliable freezing- point reading to 0.002° C. The freezing-point apparatus as assembled is shown in Fig. V-8. The Beckmann thermometer B and stirrer C are inserted into the freezing- TABLE V-9 Freezing Mixtures Proportion of substance I to be added to proportion of substance II to produce a freezing mixture having temperature t° C Substance 1 II fC Ammonium chloride 3 10 water -5.1 Potassium iodide 14 10 water -11.7 Calcium chloride 3 10 ice -10.9 Ammon um chloride 1 4 ice -15.4 Sodium nitrate 1 2 ice -17.75 Sodium chloride 1 3 ice -21.3 CaCl 2 + 6H 2 100 7 ice -54.9 Chloroform Solid C0 2 -77.0 Ether Solid CO-2 -77.0 Courtesy Chemical Rubber Publishing Company, Cleveland, Ohio. EXPERIMENTAL DETERMINATION OF THE FREEZING POINT 201 point tube F. This tube is surrounded by an air chamber A, which assures a slower and more uniform rate of cooling of the liquid under examination. A stirrer S and thermometer T are introduced into the beaker E which contains the freezing mixture of the desired tempera- WM//v/w?w///M/////// l >/////////w/w/w/////;?VM/;/j////r. Fig. V-8. An assembled freezing-point apparatus. ture as predetermined from Table V-9. A metal drain G is used to collect the moisture condensed on E. The Beckmann is a mercury-in-glass differential thermometer, with scale readings in degrees Centigrade. It seldom happens that the dis- tribution of mercury between its reservoir and bulb will be such that this thermometer will read exactly 0° C when water freezes. In order to locate this zero point on the Beckmann scale, distilled water is introduced into the freezing tube by way of the side arm D and the zero point is located experimentally. It will be observed that the temperature will fall until ice is formed and then remain constant. This constant- 202 SURFACES AND MEMBRANES temperature reading is identified on the scale and constitutes 0° C. If there is a tendency to supercooling, a tiny crystal of ice may be added through the side tube D to start the crystallization of the water. If supercooling has taken place, the mercury in the thermometer will rise rapidly on crystallization to the true freezing point, where it will remain stationary for a time. The water is then removed from the freezing tube, and the tube is dried and reassembled. About 25 cc of the solution whose freezing point is to be determined is then introduced through the arm D and the freezing point is determined in the same way as for water. TABLE V-10 Freezing Point of Mammalian Blood A indicates the average freezing-point depression in degrees Centigrade. O.P. the osmotic pressure calculated for body temperature, 37° C. The unit of O.P. is the atmosphere. Mammal Man Ox Horse Rabbit Sheep Pig Dog Cat Mean A°C O.P. 0.560 7.7 0.585 7.9 0.564 7.7 0.592 8.1 0.619 8.5 0.615 8.5 0.571 7.8 • 0.638 ■ 8.7 0.59 8.0 A = 0.1° C corresponds with an increase in 1.204 atmospheres at 0° C. A = 0.59 is equivalent to 8.0 atmospheres at 37° C. A point to be emphasized is that at no time does mammalian blood exert such a pressure; all that is meant is that this is the osmotic pressure that would be produced by blood if it were separated from pure water by a semi-permeable membrane. The difference between these two freezing points as read on the thermometer is the desired depression A of the freezing point, from which the osmotic pressure can be calculated. Some freezing-point-depression data obtained by cryoscopic methods from mammalian blood are shown in Table V-10. The conclusion drawn from these data is that the blood of all these mammals develops about the same osmotic pressure, and that under normal circumstances the osmotic pressure of blood never departs from this mean value. It has been observed that shortly after meals the osmotic pressure of the blood is slightly higher; it is reduced slightly by large ingestion of water. The kidney as a mechanism exists for regulating the osmotic pressure of the blood so that the tissues may remain immersed in a fluid of constant osmotic pressure. This constancy of the osmotic pressure is attained through the excretion of the necessary amounts of water and solids. Osmotic Pressure of Proteins Proteins are complex organic compounds of high molecular weight. The serum albumins, for example, have a molecular weight of 68,000, OSMOTIC PRESSURES OF SOME BIOLOGICAL FLUIDS 203 and the serum globulins have a higher value, averaging 175,000. They are formed by living matter and occur in the tissues and liquids of plants and animals. They are composed of carbon (50-55 per cent), hydrogen (6-7 per cent), nitrogen (15-18 per cent), oxygen (19-24 per cent), with some sulphur, phosphorus, or iron. Since proteins are colloids they do not penetrate the semi-permeable boundaries of living cells and tissue structures, yet despite their giant molecular forms they can develop a small osmotic pressure. As early as 1861 Graham suggested that plasma colloids might exert an osmotic pressure in the vascular system, but it remained for Starling [1896] to measure the osmotic pressure of colloidal solutions directly. He took advantage of the fact that colloidal membranes, while permitting the passage of water and salts, are impermeable to colloids in solution. With this technique Starling [1936] found that blood serum containing about 7 per cent proteins developed, owing to the presence of the pro- teins, an excess osmotic pressure of about 35 mm mercury. The osmotic pressure developed by blood plasma, which is about 6.4 atmospheres at 37° C, is due primarily to the presence of sodium chloride. Its colloid osmotic pressure, which is of prime importance for the transfer of fluids from tissue to blood to urine, is mainly due to the presence of plasma proteins and is approximately 28 mm of mercury. Equally low values were found by Pfeffer for egg albumen (1.25 weight per cent at 20° C), 22.4 mm of mercury. Since a A change of 0.01° corresponds to a pressure change of 91.5 mm mercury, it can be concluded that the presence of proteins will change the freezing point only 0.0034°. This quantity lies just within the limit of accuracy of the micro-Beckmann thermometer. For all practical pur- poses, in the osmotic-pressure determinations of blood, the presence of proteins adds a negligible magnitude to the depression of the freezing- point determination. Osmotic Pressures of Some Biological Fluids One interesting hypothesis that has been used in discussing the theory that life originated in the sea is that in the blood of all vertebrates the content of sodium, potassium, calcium, and magnesium is proportional to that of Archean sea water. In certain marine invertebrates the body fluids contain the ions of the above salts in almost the same concentrations in which they occur in sea water. The tissue fluids of the j elly fish are very mu ch like sea water when one compares their relative concentrations of sodium, potassium, calcium, and magnesium ions. The serum cf the lobster, which is of a higher order in the scale of evolution, contains a concentration of sodium and 204 SURFACES AND MEMBRANES magnesium between that of the jellyfish and the mammal. Macallum [1917] suggested that these and a mass of other data point to the pos- sibility that an animal not possessed of a kidney, or analogous organ, cannot accurately regulate the concentration of ions in its body fluids, and must through osmosis approximate the total ionic concentrations of its surrounding medium. It is possible, for instance, to introduce a spider crab (Maia verrucosa) into diluted or concentrated sea water and find that the crab's body fluid can adjust itself through osmosis to its new environment. The fiddler crab (Portunus depurator), commonly found on our southern beaches, also has no regulative osmotic pressure capacity; hence, the osmotic pressure of its body fluid is that of normal sea water (A = 2.30). As we ascend the animal scale and examine the migratory forms, such as the salmon, which leaves the deep sea to go up into fresh water, or the eel, which migrates thousands of miles into the Sargasso Sea in order to spawn, it is found that the osmotic pressure of their blood is only slightly modified. The blood of the sand shark has a freezing point whose A value is slightly below that of sea water. The blood of whales and other marine mammals, on the other hand, has the same freezing point as the blood of land mammals. Apparently, the more specialized the animal form, the more perfectly is it adapted to regulate the osmotic pressure of its fluids. In the higher animal forms the kidney plays a very important role in regulating the osmotic pressure of the blood. The theories of kidney secretion, however, are outside the scope of this subject and can be reviewed in any textbook on general physiology, such as that by Mitchell [1938]. Model of a Cell Membrane Despite the extensive research of the past years, the constitution and functions of the limiting surfaces of cells remain on the whole unsolved. As a rule, the limiting surfaces are ill defined, probably highly variable in structure and properties, and so closely bound up with the protoplasm of which they form a part that they cannot be clearly recognized as mem- branes. There is a body of evidence suggesting that the limiting layer of the protoplast is a thin membrane composed largely of fatty sub- stances containing submicroscopic compartments composed of an aque- ous phase which is chiefly responsible for determining the entrance or exclusion of substances into the cell. Another well-supported view is that the cell envelope is a fluid bimolecular layer of lipoid (fatlike) mole- cules. This membrane, however, cannot be homogeneous, since water penetrates with ease into cells. MODEL OF A CELL MEMBRANE 205 Various optical attempts at measuring the thickness of the transition layer have given values that are less than 0.2 X 10 -4 cm, i.e., unresolv- able by a compound microscope (see Chapter VIII). That bacteria of the genus Bacillus possess cell walls was recently verified with the aid of the electron microscope. The photomicrograph (Fig. VIII-22) of human tubercle bacilli made with an RCA electron microscope shows the bacilli to be surrounded by what appears to be a membrane having a thickness less than 0.1 X 10 -4 cm. Oil layer monomolecular Fig. V-9. (a) A conventionalized picture of a drop of water covered with a monomolecular layer of oil, suspended in air. (6) A drop of oil suspended in water with oil molecules forming bounding phase. (By courtesy of W. D. Harkins and Chemical Catalog Company. [Reinhold Publishing Corporation], New York.) These dimensions may be compared with those found by Langmuir [1925] for palmitic acid molecules when these molecules were steeply oriented to form a monomolecular surface film. Palmitic acid with its chain of sixteen carbons to the molecule has a cross section of 20.5 sq A and a length measured perpendicular to a supporting surface of about 24.2 A. The relative order of magnitudes indicates that the membrane of the cell is at most about 100 molecules thick. If a closed membrane were one molecule thick, it could be pictured as in Fig. V-9. This highly conventionalized picture, used by Harkins [19251 in discussing the orientation of molecules in the surface of spheri- cal liquid drops, shows a small spherical drop of water, Fig. V-9 (a), covered with a monomolecular layer of oil suspended in air. Its surface can be represented as composed of closely packed molecules with their polar ends turned toward the water phase and the non-polar ends point- 206 SURFACES AND MEMBRANES ing outward. If, however, a drop of oil is suspended in water as in (b), the oil molecules orient themselves in the opposite direction. The fundamental principles involved in the structure of the interfaces are : The molecules in the surfaces of liquids seem to be arranged in such a way that the least polar groups are oriented towards the vapor phase. At the water-air interface the hydrogen atoms turn towards the vapor phase and the oxygen atoms toward the liquid phase. At the liquid surfaces of organic paraffin derivatives the CH 3 groups turn outward, and the more active groups, such as N0 2 , CN, COOH, CHO, OH, or groups which contain double bonds, turn toward the interior of the liquid. If the organic compounds are soluble in water, their orientation is such as to place the active groups inward. The stability of emulsoid particles seems to be brought about by the orientation of molecules at the interface. In order to have the emulsoid particles stable, the molecules which make the transition from the inte- rior of the drop to the dispersion medium must form what may be termed a bounding membrane. If the thermal agitation is taken into consideration, it may be assumed that the molecules in a bounding surface, composed of flexible hydro- carbon chains, will orient themselves at any angle. The only restriction on their motion is imposed by the condition that the lower end of each molecule must remain in contact with the underlying water. Langmuir found that palmitic acid could be spread to form an expanded structure 13.6 A thick, and that the film could also be compressed to form a struc- ture 22.5 A thick. Thus an expanded film may be pictured in contra- distinction to a compressed film, in which the oriented molecules, though still anchored to the underlying water, are set at any angle and hence loosely packed. If for the sake of simplicity such a monomolecular structure is used to represent the superficial wall of a cell, then, to a good approximation, the cell wall may be represented as an expanded organic molecular film with a transition thickness of less than one hundred molecules. Such a structure could possess semi-permeable properties and even change its surface energy by the reorientation of its structure. Under the action of the temperature kinetic agitation it would be possible to find, on the average, areas not covered with molecules. Such a membrane would allow for a shifting lattice structure and the adoption of a modified sieve theory for the basic pattern of a semi-permeable living membrane. Some data may now be examined in support of the view that a cell has an outer boundary or cell wall (cell membrane) which fundamentally may have the structure of an expanded molecular film. It has been shown that the walls of cells are made of substances which are colloidal in MODEL OF A CELL MEMBRANE 207 solution and more or less swollen by water. Overton suggested that lipoids have a tendency to concentrate at interfaces, where the sub- stances could participate in producing the membrane structure. He then added that only those substances which are soluble in this lipoid structure were able to penetrate the interior. Overton's experiments support the view of the existence of such a structural framework. Later work by Loeb and others indicated that lipoid-soluble fatty acids readily penetrated the cell wall; on the other hand, acids which are practically lipoid-insoluble did not penetrate. Except for its static structural point of view a lipoid-solubility theory is as acceptable as any proposed to date. In general, it has been found that living cells are readily permeable to lipoid-soluble non-electrolytes which possess an appreciable degree of water solubility. The work of Collander and Barlund [1933] shows, however, that the penetration is limited to molecular sizes which are relatively small. It was found, for instance, that the relatively smaller molecules like formamide, acetimide, and ethylene glycol penetrated much more readily than much larger colloid molecules like albumin and hemoglobin. Apparently the average lattice spaces are therefore about 5 X 10 — 8 cm in diameter. The existence of lattice spaces explains why those gases that are readily soluble in plvysiological fluids can success- fully pass through living membranes. It has been found that both red cells and paramecia are affected by agents which penetrate or are adsorbed as lipoid and protein mono- molecular layers; therefore, it can be concluded that their surface struc- tures must contain lipoproteins or consist of a lipoid protein mosaic. A cell wall cannot be smooth but must have distributed over its sur- face a multitude of irregular hills and valleys of atomic dimensions, an excellent surface for the adsorption of atoms, ions, and ion clusters. This structure can develop a difference in ionic concentration on the opposite sides of its wall. The result is a polarized ionic barrier acting as an effective control for ionic migrations. It has been found, however, that cells are more permeable, on the average, to electrically neutral molecules than to ions. It is necessary therefore to have a structure that is electrically polarizable. It must, however, be able to change its degree and form of polarity in accordance with the kind of electrolyte in which the cell may be immersed. The wall of the living cell has been found to be impermeable to polar compounds but permeable to a weak polar group such as the hydroxyl. The rate of entrance was found to be proportional to the ratio of the number of non-polar groups to the polar groups. A static structure, namely, a group of oriented molecules as found in the condensed stage of a film, cannot change its polarity very readily. The previously pro- 208 SURFACES AND MEMBRANES posed expanded stage of a film membrane would conform to the demands of polarity made upon it as the result of the mosaic of pores and its rela- tively flexible molecular orientation. It would depend for its degree of TABLE V-ll Chemical Analyses op Sap Compared with Normal Sea Water Contents Bermuda Sea Water Valonia Sap 1 Halicystis Sap 2 CI + Br 0.580 0.597 0.603 Na 0.498 0.09 0.557 K 0.012 0.5 0.0064 Ca 0.012 0.0017 0.008 Mg 0.057 Trace? 0.0167 SO4 0.036 Trace? Trace 1 Valonia macrophysa. 2 Halicystis Osterhoutii. Mean Ionic Content of Blood Expressed in Per Cent and Milliequivalent Per Cent Milliequivalent Contents per 1000 cc* Whole Blood Plasma Corpuscles Serum Cells Na 0.20 * 0.335 0.065 135.1±1.7 16.8 ±3.5 K 0.20 0.019 0.42 4.6±0.7 82.5±4.9 Ca 0.006 0.011 0.001 5.3±0.3 0.2±0.3 Mg 0.003 0.0027 0.0066 1.6±0.3 4.6±0.5 Fe 0.5 0.00 0.10 CI 0.294 0.37 0.20 HC0 3 0.164 0.002 Total solids 22.0 9.3 34.6 Hemoglobin 14.5 0.0 34.0 Specific gravity- 1.054-1 060 1.062 1.090 Water 79-80 90-92 64-65 By Courtesy of W. J. V. Osterhout [1936]. * By Courtesy of P. M. Hald and A. J. Eisenman [1937]. For effects and changes due to high altitude see D. B. Dill, J. H. Talbot, and W. V. Consolazio 119371. polarity on the relative concentration of adsorbed ions and polar mole- cules at the two faces of the bounding film. A shrinkage of such an expanded film would also more nearly orient the molecules to produce an increase in the degree of polarity and at the same time decrease the size and number of the pores of the mosaic. In this connection Osterhout has shown that isotonic calcium chloride BIBLIOGRAPHY 209 solution can render cells nearly impermeable to all ions, and that any- excess of calcium over its normal sea-water concentration (Table V-ll) tends to decrease the permeability of the cell. If the calcium salts react chemically with the mobile external surface molecules in the presence of fatty acid molecules to form a calcium soap, the surface becomes more polarized for the soap molecules are more soluble in water than the original fatty acid molecules. The molecular structure may then be pictured as more closely packed and the openings of the mosaic pattern so reduced in area as to exclude the possibility of infiltration of most solute molecules. A further important matter must be taken into consideration in setting up a hypothetical model of a semi-permeable dynamic cell wall, namely, the selective accumulative property of certain cells. This may be appre- ciated after examining the data of Table V-ll. Of interest is the analysis of the cell sap of Valonia macrophysa by Osterhout [1936], which shows an unusually high potassium content as compared with sea water. Note also the amount of potassium in red corpuscles as com- pared with their plasma environment. It is difficult to explain these results since there can be no apparent differentiation by the membrane between sodium and potassium ions on the basis of their dimensions, mobility, or electric charge. Jacques' recent work on the nature of the protoplasmic surface of the cell in the marine plants Valonia and Halicys- tis and in the fresh-water Nitella indicates that the cell membranes are composed of non-aqueous layers at the inner and outer surfaces of the protoplasm which possess different solubilities for various salts, potas- sium being absorbed more rapidly than sodium in Valonia. In any case the structure and the structural changes that account for the normal semi-permeability of the wall of the living cell (Rideal [1939]) await final analysis* and must remain matters of speculation until the biochemist and the biophysicist can furnish the necessary infor- mation about the chemical composition and electrical properties of plasma membranes. BIBLIOGRAPHY 1888 de Vries, Hugo, Z. physik. Chem., 2, 415. 1896 Starling, E. H., J. Physiol, 19, 312, and 24, 317 (1899). 1903 Guye, P. A., and F. L. Perrot, Bull. univ. arch. sci. phys. nat., 15, 132. Also H. E. Edgerton and K. J. Germeshausen [1934]. 1907 Morse, H. N., J. C. W. Frazer, and B. F. Lovelace, Am. Chem. J., 37, 324. 1917 Macallum, A. B., Trans. Coll. Physicians Phila., 39, 289. 1919 du Nouy, P. L., /. Gen. Physiol, 1, 521. * For a comprehensive discussion of the properties and functions of membranes and cell walls see " General Discussion " [1937]. 210 SURFACES AND MEMBRANES 1919 Haekins, W. D., and F. E. Brown, J. Am. Chem. Soc., 41, 499. 1921 Fenn, W. O., J. Gen. Physiol, 4, 373. 1921 Taylor, W., Phil. Mag., 41, 877. 1922 Osterhout, W. J. V., Injury, Recovery and Death in Relation to Conductivity and Permeability, J. B. Lippincott Company, Philadelphia, Pa. 1925 Cary, A., and E. K. Rideal, Proc. Roy. Soc. London, A109, 301. 1925 Harkins, W. D., Colloid Symposium Monograph, II, 141, Chemical Catalog Company, (Reinhold Publishing Corporation), New York. 1925 Langmuir, I., Colloid Symposium Monograph, III, 48, Chemical Catalog Company, New York. 1926 Harkins, W. D., T. F. Young, and L. H. Cheng, Science, 64, 333. 1926 McClendon, J. F., Colloid Symposium Monograph, IV, 224, Chemical Catalog Company, New York. 1927 McCutcheon, M., and B. Lucre, /. Gen. Physiol, 10, 659. 1930 Adam, N. K., The Physics and Chemistry of Surfaces, Clarendon Press, Oxford. 1930 Harkins, W. D., and H. F. Jordan, J. Am. Chem. Soc, 52, 1751. 1932 Harvey, E. N., J. Franklin Inst, 214, 1. 1932 Lillie, R. S., Protoplasmic Action and Nervous Action, University of Chicago Press. 1932 Lucre, B., and M. McCutcheon, " The Living Cell as an Osmotic System and Its Permeability to Water," Physiol. Rev., 12, 68. 1932 Whitehouse, A. G. R., W. Hancock, and J. S. Haldane, Proc. Roy. Soc. London, Bill, 412. 1933 Collander, R., and H. Barlund, Acta Bot. Fennica, 11, 2. 1933 Kopaczewski, W., Protoplasma, 19, 255. 1933 Mudd, S., Cold Spring Harbor Symposia Quant. Biol, 1, 77. 1934 Edgerton, H. E., and K. J. Germeshausen, Am. hist. Chem. Eng. Trans., 30, 420. 1934 Mudd, S., M. McCutcheon, and B. Lucre, Physiol. Rev., 14, 210. 1935 Jacques, A. G., and W. J. V. Osterhout, J. Gen. Physiol, 18, 967. 1936 Osterhout, W. J. V., Botan. Rev., 2, 283. 1936 Starling, Principles of Human Physiology, 7th Ed., Churchill, London. (Revised by C. L. Evans.) 1937 Baldwin, E., An Introduction to Comparative Biochemistry, Cambridge University Press. 1937 Barnes, T. C, Textbook of General Physiology, P. Blakiston's Son, Philadel- phia, Pa. 1937 Dill, D. B., J. H. Talbot, and W. V. Consolazio, J. Biol Chem., 118, 649. 1937 General Discussion, " The Properties and Functions of Membranes, Natural and Artificial," Trans. Faraday Soc, 33, 911. 1937 Hald, P. M., and A. J. Eisenman, J. Biol. Chem., 118, 275. 1938 Harvey, E. N., J. Applied Phys., 9, 68. 1938 Mitchell, P. H., A Text Book of General Physiology, 3rd Ed., McGraw-Hill Book Company, New York. 1939 Rideal, E. K., Science, 90, 217. 1940 Cole, K. S., Cold Spring Harbor Symposia Quant. Biol, 8, 110. (Electrical properties of cell membranes.) 1940 Lyddane, R. H., and O. Stuhlman, Jr., J. Gen. Physiol, 23, 521. 1941 Mudd, S., K. Polevitzry, J. F. Anderson, and L. A. Chambers, J. Bad., 42, 251. Chapter VI THE BIOPHYSICAL PROBLEM OF NERVE CONDUCTION A sensation invoked in the brain has no resemblance to the physical events which redirect the activity of the nervous system. The sensa- tion of light may be aroused not only through absorption by the retinal receptors of radiant energy of a limited group of frequencies, but also by electrical or mechanical stimulation of the retina. The sensation called sound may be experienced by placing a low-frequency tuning fork with its base in contact with the head so that the vibrations are communicated to the bones of the skull. The same fork pressed to the surface of the skin produces a sensation of vibration, that is, a series of tactile impres- sions repeated at rapid intervals. The experienced sensations are not the reproductions of the physical stimuli; they are, however, symbols of the stimuli that can be used to inform us of events occurring in our physical environment. Therefore it is important to inquire how nerves transport quantitative information about these stimuli to the central nervous system. The experienced sensations are aroused by messages which are trans- mitted from the excited receptors by means of the nerves to the cere- brum. The problems of the kind of messages or nerve impulses and of the speed of their propagation have been under investigation since the time of Galvani and Volta, but not until 1908 did the researches initi- ated by Gotch and Keith Lucas make it possible to give a quantitative interpretation to the problem of nerve conduction. The most general features of the so-called moving nerve impulses are best studied by first examining those irritable tissues or cells which can develop quantitatively interpretable responses to mechanical, thermal, chemical, or electrical stimulation, such as excised nerves and muscles of higher animals. The impulse set up in response to an electric stimulus applied to tissue isolated from its normal environment is an artificial effect. The accumu- lated evidence, however, shows that its counterpart must be the funda- mental activity of the nerve fiber in the body. Relation of Stimulus to Response The word " stimulus " will be used to mean any local artificial change in the environment of tissues which causes an excitatory process to be set up in the tissues localized at the point of stimulation. 211 212 THE BIOPHYSICAL PROBLEM OF NERVE CONDUCTION The threshold value or minimal stimulus of a particular kind has a magnitude which is just sufficient to excite. A stimulus greater than threshold value will not produce a greater response. The magnitude of the response is independent of the magnitude of the stimulus, provided that it is not smaller than threshold. This general relation is known as the all-or-none-law. The implication is that the response is characteristic of the reacting structure and not of the energy employed to disturb the state of that structure. Most living cells can be used as reacting structures in which the proper stimulus will set up a disturbance, or nervous impulse. With modern technique it is even possible to study the impulses set up in sensory nerve fibers by the appropriate stimulation of the sense organs so as to deter- mine the frequency, the form, and the speed with which the messages are transmitted to the brain. Various forms of energy can be employed as stimuli. In biophysical investigations of the excitability of nerve fibers it has become general practice to use a brief electric current as stimulus, for it is highly probable that the process of excitation itself is electrical. Electrical Stimuli Physiologists agree that an impulsive electrical discharge is by far the most effective and convenient means of artificially stimulating nerve fibers to set upa" nerve impulse," which travels over the whole length of the nerve fiber in both directions from the point of stimulation. Be- cause the intensity and duration of an electric current can be very accu- rately controlled, it has become common practice to study the activity of an isolated nerve when stimulated by a brief electric shock. It has the advantage that such stimulation can be repeated without producing appreciable damage in the nerve fiber. In most experimental work on the response of nerves to electric stimu- lation, current taken off the secondary of a mechanically interrupted induction coil has been used. A commercial 60-cycle alternating current has also been employed. For precision work, impulsive currents should be used with pulses timed by means of a mechanical regulator or more accurately by a variable-frequency stimulator. Induction Coil Discharge In every properly designed induction coil with mechanical interrupter a condenser is connected across the interrupter. Its capacitance must be so chosen as to quench the spark as quickly as possible when the mechanical interrupter opens the primary circuit. As a result, the break of the primary current is much quicker than the make. For a given STIMULATING ELECTRODE 213 primary current there is a corresponding capacitance which makes the po- tential across the terminals of the spark gap a maximum. The primary current I p rises exponentially on the closing of the interrupter, as shown in Fig. VI-1. When the circuit is suddenly opened at C the current rapidly drops to D. Without the condenser this slope would be less steep. Since the current builds up more slowly than it diminishes, the associated magnetic field builds up more slowly than it col- lapses. The induced electromotive force, and therefore the induced current in the secondary, are smaller when the primary cir- cuit is closed than when it is open. This / Time — 0.01 sec ~ Fig. VI-1. An ideal rise and fall of the current in the primary and accompanying changes in current in the sec- ondary of an induction coil condition is illustrated by the broken-line with proper condenser con- curve I s . The larger induced electromotive nected across the mechanical force at the break therefore lasts a shorter mterru P ter - time than the smaller induced electromotive force at the make. The voltage across the terminals of the secondary, to which a stimu- lating electrode may be attached, is alternately positive and negative, but one cycle does not consist of two equal alternations of opposite sign. Therefore the discharge across the terminals of the stimulating electrode is, as seen in Fig. VI-1, predominantly in one direction. pt 2 cm Stimulating Electrode The electric stimulus can be applied to the irritable tissue with the aid of the two-prongecl metal electrode shown in Fig. VI-2. The binding posts B are attached to the high-po- tential terminals of an induction coil or variable-frequency stimulator. The handle S is an insulating cover Fig. VI-2. A form of stimulating of hard mbber tQ faciHtate han . electrode m which the electrodes are „. t->i , • n r>. i pronged into a holder including a cord dhn %- Platinum needles, Pt, spaced about 2.5 mm, are placed in direct contact with the tissue. If the response of an excised nerve is to be investigated, the platinum needle-electrodes are placed across and near one end of the preparation. When an adequate electrical discharge passes between the terminals of the electrodes, an excitatory impulse travels away from the point of stimulation. and plug. They can be sterilized. Overall length 4 in., tip length 1 in., tip spacing 0.1 in. Also available with longer electrodes. (By courtesy of Allen B. DuMont Laboratories, Passaic, New Jersey.) 214 THE BIOPHYSICAL PROBLEM OF NERVE CONDUCTION The Detection of Nerve Impulses As the impulse moves along the nerve, it is possible to detect its pas- sage by placing in parallel with a section of the nerve a sensitive electrical- potential-recording instrument (see " Cathode-Ray Oscillograph "), terminating at two Ag|AgCl| Isotonic NaCl non-polarizable electrodes in contact with the surface of the nerve. For most purposes silver wires, freshly coated by electrolysis, are placed in direct contact with the tissues.* Structure of Nerve Fibers A nerve is a bundle of separate nerve fibers. Each is a thread of protoplasm (Fig. VI-3), either myelinated or unmyelinated, which functions as the conducting element of the nervous system. The myeli- nated nerve consists of an axis cylinder surrounded by the myelin Node of Ranvier Nucleus Fibrillar sheath Myelin sheath Axis cylinder Fig. VI-3. Very much enlarged myelinated nerve fiber of frog, semi-diagram- matic longitudinal section. Axis cylinder appears structureless. The neurilemma (n) is visible chiefly at a node as a thin delicate membrane. sheath, which is a complex fatty substance of high specific resistance. External to it lies the neurilemma sheath. At regular intervals along the fiber, constrictions occur in the sheath, which are known as nodes of Ranvier. The unmyelinated fibers have no apparent myelin sheath. Those in the central nervous system are naked axis cylinders, but in the periphery they are covered by a very thin neurilemma sheath. The axis cylinder is a soft, transparent, jelly like substance having much the same composition as that found inside other living cells. Its specific resistance is low. Its osmotic pressure is the same as that of blood. The evidence seems to support the view that the axis cylinder is limited by a plasma membrane. This limiting membrane is semi -per- meable and electrically polarized, and it is probably the structure that participates in the propagation of the energy known as the nerve impulses. The living fiber maintains a difference of potential across its surface which disappears when the nerve is deprived of oxygen. It maintains * Those designed by Adrian and Bronk [1929] are made of hypodermic needles with an insulated silver or copper core, the end of which is flush with the bevel of the needle. DEMARCATION CURRENT OR CURRENT OF INJURY 215 its normal steady state only through a continuous expenditure of oxida- tive energy. The electrolytic composition on the inside of the fiber differs from that on the outside primarily by its potassium-ion content. This difference as estimated by Fenn is about 65 times larger inside than out- side. Such a difference in a concentration cell, according to Gasser's [1938] calculations, would produce about 100 millivolts. That such large differences of potential do exist was verified by Hodgkin [1939] from a single nerve fiber of a crab preparation. Such potentials may be accounted for by assuming the existence of a concentration gradient or of a diffusion gradient across the cell membrane in which the mobility of the potassium cation is the dominant factor. A mode of exploring the cause of such a difference of potential is to investigate whether or not most of the potential may arise as the result of the existence of a possible polarized film of molecules at the surface of the fiber. A simple experiment involving the measurement of what is called the demarcation current proves the existence of a polarized surface possessing a difference of potential across its membrane-like covering. Demarcation Current or Current of Injury If a nerve fiber is removed from the body, and two non-polarizable electrodes, in series with a sensitive electrometer, are applied to the + + + + + + + + + + + + + + «-s 1 + + + + + + ^p* +~+ + + -i- + [ : > /bW <£> Fig. VI-4. The polarized state of a diagrammatic nerve fiber. Injury at the right end. V2 — V\ about 50 millivolts. nerve in such a way that one is in contact with the surface of the nerve and the other is in contact with an injured end of the fiber (Fig. VI-4), a constant deflection of the electrometer will result as long as the tissue is alive. Such a deflection indicates that a difference of potential exists between the outside cell membrane and the exposed axis cylinder. The direction in which the electrometer deflects will indicate that the uninjured surface is at a higher potential than the injured end. This difference in potential is very small, usually about 50 millivolts. Until recently these small differences of potential have been measured by means of an Einthoven string galvanometer or a capillary electrometer. Millivolt potentials can now be measured with precision with modern 216 THE BIOPHYSICAL PROBLEM OF NERVE CONDUCTION galvanometers; if necessary, the potential may be amplified by means of a vacuum-tube voltage amplifier. The difference in potential main- tains itself as long as the " injury " as such does not undergo a change in its physicochemical nature due to degeneration of the tissue. The injury does not produce the difference in potential; it merely allows the difference of potential to manifest itself as an active source of electro- motive force. The Action Potential Our definite knowledge of the response of living tissue to electrical excitation began with the celebrated investigations of du Bois-Reymond, extending from 1846 to 1860 and published under the title " Unter- suchungen uber thierische Elektrizitat." By 1871 Bernstein had Stimulating electrodes HI + I 5 mV Direction of activity H I I I I I M ill -*-i a Localized bioelectric current -■*• — . . — ■*■ a it G Fig. VI-5. Monophasic action current pulse is shown traveling from the stimu- lating electrode G. Shading simulates degree of depolarization. Injury potential between A and B neutralized by counter emf from potentiometer P. If E is an oscillograph, the fluorescent screen will show the above monophasic action potential pulse as it passes the contact B. demonstrated that when an excised muscle or nerve was stimulated at any point along the tissue a wave of activity ran along the nerve. This wave was identified as a negative pulse of an electrical activity rising to a potential of about 5 millivolts. The existence of a traveling pulse of activity may be demonstrated as illustrated in Fig. VI-5. An excised nerve with its active end A placed in contact with a small metal electrode is connected through a potentiometer P and an electrometer E to a duplicate electrode B attached to the passive surface of the nerve sheath. The normal demarcation current is neutralized by a counter electro- motive force from the potentiometer until the electrometer deflection is zero. At G, several centimeters to the left of contact B, is placed a pair of stimulating electrodes. The two platinum points are connected to the DIPHASIC ACTION POTENTIAL 217 high-potential output of a small induction coil. When the key in the primary circuit of the induction coil is rapidly closed and opened, one or more 0.2-milliampere high-potential induction discharges stimulate the nerve fiber at this point and set up a nerve impulse i a which travels away from G in both directions. This impulse, in a thick mammalian nerve fiber, having a diameter of about 20 microns, may attain a speed of 100 meters per second; in unmyelinated nerve it may be as low as 1 meter per second. The arrival of the pulse at B is shown by a deflection of the electric impulse recorder E. The successive changes in the deflections indicate that the external surface at the electrode B has been subjected to a rapid drop in potential, followed by a slower recovery to its former value. A record of the fall and rise of this action potential is inserted in the figure. The action is designated as monophasic. The inference is that the nerve impulse is an activity that travels with moderate speed, that it has an electrical origin, and that it is a pulse of activity with a rather steep wave front. It manifests itself as a local decrease and a slower recovery in the surface potential of the nerve. Diphasic Action Potential Another method of approach is to investigate the propagation of the nerve impulse uninfluenced by the complications introduced by the demarcation current. The experiment may be modified as shown in Oh • \-\ In 1=1- V-/ To induction coil Fig. VI-6. Diphasic action potential i\, ii, due to a wave pulse i a passing under contact c and then under contact d. The potential is amplified and presented as viewed on the fluorescent face of a cathode-ray oscillograph as two successive op- positely directed pulses. Fig. VI-6. This diagram shows a normal nerve with the pick-up elec- trodes placed on its surface at the points x\ — x 2 . Under these cir- cumstances no current flows through E either from c to d or from d to c, 218 THE BIOPHYSICAL PROBLEM OF NERVE CONDUCTION showing that the external surface of the nerve is an electric equipotential surface. If, however, the stimulus, an electric discharge across A, is adjusted so as to excite a single nerve impulse (i a ), it signals its arrival at x\ by a recordable impulsive deflection of the electric recorder E. The deflec- tion takes place in such a direction as to indicate that a unidirectional impulsive current i\ is traveling in the external circuit from d to c. After o OL Direction of motion Time Current flows from c to d 2 4 Current flows from d toe -2 -4 Units of time l/lOOO sec J | | | L Fig. VI-7. record. Diphasic action potential reproduced to scale from an oscillograph a very short interval of time a second impulsive electric deflection is observed, indicating that another momentary current pulse i 2 has passed in the opposite direction, i.e., from c to d. This reversed electric deflection takes place the instant the pulse of nerve excitation passes the point x 2 . These externally recordable successive impulses of current, with the two phases of change in potential, are called the diphasic action -potential. A scale drawing of this diphasic action is shown in Fig. VI-7. The time interval from crest to crest is proportional to the distance between the contacts c to d. The electrical implication is that the pulse of nerve excitation lowers the normal potential V 2 to V\ on passing under the contact x\ ; hence, a flow of current i\ from d to c through the external circuit takes place. After the destructive activity has passed the point X\, restoration sets in, accompanied by a slower return of the potential to its original value V 2 . After a short interval, depending on the distance X\ — x 2 , the nerve pulse reaches x 2 , where in turn the normal surface potential V 2 at d is lowered to V\, accompanied by the reversal of the previous electrical phenomena. PHYSICAL CHARACTERISTICS OF THE ACTION POTENTIAL 219 Physical Characteristics of the Action Potential The present evidence supports the hypothesis that the electric response is a true indication of the normal activity of the nerve and that it is not an artificial effect due to the type of stimulus employed. The energy manifesting itself as the nerve pulse is not obtained from the artificial stimulus. This stimulus only appears to upset an equilibrated electro- chemical boundary condition, which may take the form of a destruction of a polarized electrical double layer and a subsequent slower repolariza- tion at the expense of osmotic and chemical actions. 40 - 30 = 20 10 1 1 1 1 i i i i - - Rising phase / \ Falling phase - - - Direction J of motion / — / - / Maximum attained N. - Si in 0.135tr >v T i . i i i l t 0.2 0.4 0.6 Time • '14 m/sec 10 20 30 Time in milliseconds 0.7 m/sec 200 Fig. VI-9. The complete action potential of a bullfrog's peroneal nerve recon- structed semi-diagrammatically from oscillograph records. The electrical shock was strong enough to excite all the fibers. Composite curve drawn from data by Erlanger and Gasser [1937]. Insert, similar results from a single mammalian (group A) nerve fiber. After-potentials vary as to form, size, and duration, depending on the kind of fiber. The complete sequence is a spike and a negative after- potential followed by a positive potential in the A and C fibers. In the B fibers the negative after-potential is extremely small in single responses but can be developed by special procedures. Table VI-1 shows this classification applied by Grundfest [1940] to mammalian nerve fibers. Comparable correlations are not available for the action potentials of invertebrate nerves. Grundfest points to two noteworthy correlations in the table: (1) the spike duration is constant for all A fibers within the experimental limits of 0.45 ± 0.5 millisecond and is independent of the size of these 222 THE BIOPHYSICAL PROBLEM OF NERVE CONDUCTION fibers; (2) the absolute refractory period is not independent of fiber size in group A, but increases as the fiber size decreases. Note that the positive after-potentials of the three groups persist more definitely as the fibers decrease in size. It is particularly noteworthy that no nega- tive after-potential follows the action potential response of the group B fibers. TABLE VI-1 Properties of Three Groups of Mammalian Nerve Fibers Group A B C Diameters of fibers, m 20 to l*f <3j unmyelinated Velocity propagation, meters per second 100 to < 5*f 14 to < 3| <2§ Spike duration, msec 0.4 to 0.5* 1.2} 2.0§ Negative after-potential Amount, per cent of spike Duration, msec 3 to 5|| 12 to 20 1| H NoneJ 3 to5§ 50 to 80 § Positive after-potential Amount, per cent of spike Duration, msec 0.2|| 40 to 60 1| IT 1.5 to4.0J 100 to 300 % 1.5§ 300 to > 1000§ Absolute refractory period, msec 0.4 alpha* || 0.6 delta, cat* 1 . delta, rabbit* 1.2J 2.0J Order of susceptibility to asphyxiaj 2 1 3 By Courtesy of H. Grundfest [1940], *Gasser and Grundfest [1939]. Delta (cat) are small A fibers. tHursh [1939]. J Grundfest [1939]. § Grundfest and Gasser [1938]. || Gasser and Grundfest [1936]. 1 Lehmann [1937]. After-Potentials In recording the monophasic action potential from a single nerve fiber (group A) as shown in the insert in Fig. VI-9, it has been found that the SUMMATION OF INADEQUATE STIMULI 223 after-potentials run a course characteristic of the fiber. The spike potential in normal mammalian nerve fibers (group A) does not drop vertically back to the resting potential, but is followed by another nega- tive potential (after the spike has passed) lasting about 15 milliseconds. This potential has a rising phase of its own and begins before the spike potential has returned to normality. The negative after-potential is a separate phenomenon. The present evidence shows it to be depressed by lack of oxygen. It is abnormally prolonged by veratrine and depressed by carbon monoxide poisoning; its duration is decreased by monovalent ions (K + ) or increased by diva- lent cations such as Ca. Its basic significance, however, is still in doubt. The overall action potential drops below the resting potential, becomes positive, and returns to its normal value in about 50 milliseconds. The positive after-potential is probably intimately related to the spike poten- tial, which is unquestionably the sign of the nerve impulse itself. As an impulse travels along a nerve, the region of breakdown is in an absolute refractory state and the region immediately behind this is in a relatively refractory state. The importance of all these phenomena lies in the fact that they determine the excitability of the nerve. Excitability is defined as the reciprocal of the threshold magnitude necessary to excite the tissue. Summation of Inadequate Stimuli If the stimulus is subliminal, no nerve impulse is developed. How- ever, if a second subliminal stimulus follows the first within 1 millisecond or less and a nerve impulse is developed, the impulse is said to be due to the summation of inadequate stimuli. To account for this it has been suggested that any stimulus gives rise in a nerve fiber to a local excitatory process which does one of two things: if it is sufficiently great, it initiates a nerve impulse; if not, it reverses itself and subsides. If, during the reversal, a second subliminal stimulus is applied to bring the intensity of the process up to or above threshold, it will give rise to an impulse. Hence a stimulus, however weak or briefly applied, leaves the point of application in the nerve fiber in an altered state of excitability after the stimulus has ceased to act, and a time interval must elapse before com- plete recovery has set in. If the stimulus is threshold so that a nerve impulse is initiated by the excitatory process, the excitability drops to zero immediately after the response has occurred: the cell or organ passes through an unexcitable state called the completely refractory stage. This absolute refractory period during which excitation is impossible is followed by a relatively 224 THE BIOPHYSICAL PROBLEM OF NERVE CONDUCTION refractory period. The excitability during this period of time is lower than normal; it is possible to set up an impulse, but the stimulus to accomplish it must be more intense than that which was needed to excite the normal pulse. Frequency of Impulses The relatively refractory period spaces the impulses so that the normal impulses are a minimum distance apart, making overlapping or continu- ous activity impossible. For instance, in the phrenic nerve of the cat, at 37° C under electric shock stimulation, it was found impossible to excite more than 1000 spike potentials per second. The frequency of innervation of the motor units of muscle is ordinarily only 5 to 50 per second, depending on the intensity of muscular contrac- tion (Adrian and Bronk [1929]). Even in extreme conditions it does not rise above 100 per second. In sensory fibers the frequencies of inner- vation are of about the same order of magnitude. Thus, for example, Adrian [1932] found that, when pressure was applied to the pad of a cat's foot, the nerve impulses propagated in single fibers varied from 9 to 100 per second, according to the magnitude of the pressure applied. * In general, it has been found that the rate of recovery of excitability in the most rapidly conducting and most excitable mammalian fibers is such that it would prevent conduction of as many as 1000 impulses per second. Speed of Propagation It has been known since 1913, from the work of Lapique and Legendre, that the speed of propagation of nerve impulses increases with increase in fiber size. Direct measurements on nerve fibers, ranging in diameter from 1 to 16 microns, have shown the speed of propagation of the nerve impulses to be proportional to the diameter of the fiber. Hursh [1939] found that in the nerves of four-day-old kittens the maximal velocity of propagation is 11 meters per second, as compared with 80 to 90 meters per second in the saphenous nerve of full-grown cats. As the kitten grows to maturity, the maximal velocity increases at a rate directly proportional to the diameter of the largest fibers. Gasser and Grundfest [1939], using myeli- nated fibers in the phrenic nerve of the cat, which vary in diameter from 1 to 14 microns, also found that the speed of propagation was propor- tional to the diameters of these fibers. From the evidence on the relation between velocity of propagation and amplitudes of the recorded axon potentials, they concluded that the A CCO M MO DA TION 225 maximum axon potential was approximately directly proportional to the diameter of the active fiber. This conclusion is supported by theoretical considerations. Whether the simple relation — the velocity of propagation of the nerve impulse is directly proportional to the diameter of the nerve fiber — can be extended to cover a much wider range of fiber diameters is still an open question in view of the measurements by Pumphrey and Young [1938]. These show that in cephalopod (squid) nerves, which contain fibers varying in diameter from 30 to 700 microns, measurements of the velocity of propagation were nearly proportional to the square root of the diameter, and that the smaller nerves of vertebrates (1 to 20 microns) gave values of velocity which were proportional to the diameter of the fiber. The conduction properties of a nerve may be reduced by a drop in temperature to such an extent that a local application of ice acts as a nearly complete depressent to the nerve impulse as it passes through the low-temperature nerve section. The velocity of propagation, however, will be restored when the nerve regains its original temperature. Anesthetics and narcotics, such as ether, chloroform, cocain, chloral, phenol, and alcohol, may be applied locally to a nerve trunk to decrease the conductivity and irritability, which are restored when the narcotic is removed. Accommodation When a stimulus in the form of an electric current is applied to a nerve for a short time, the critical value of current strength to excite — that is, the threshold value — is constant. Under these experimental condi- tions the applied current builds up a local excitatory process which sets the nerve impulse in motion when it reaches a critical value. If a stimu- lating electric current, insufficiently large to excite, is removed from a nerve, the excitatory process is assumed to revert to its resting value, according to the law of exponential decay. If a subthreshold direct current is used as a stimulus and allowed to increase slowly with time, it is found that the current may attain a very high value without producing a response in the form of a moving nerve pulse. This result is possible if the rate at which the excitatory process decays is equal to, or greater than, its rate of increase. If a constant subthreshold direct current passes through a length of nerve, the excitability of the nerve is increased at the cathode contact- point and decreased at the place where the anode makes contact. If the excitability at the cathode contact is examined as a function of time of application of a stimulus (Bishop [1928]), it is found that the excitability 226 THE BIOPHYSICAL PROBLEM OF NERVE CONDUCTION rapidly increases with time and passes through a maximum, from which it at first rapidly falls, and then decreases more slowly to attain a con- stant value. In frog nerve this maximum is attained in 3 milliseconds; in large mammalian nerve it is a fraction of a millisecond. On breaking of the current, the excitability of the nerve abruptly decreases to a large value of inexcitability, from which it rapidly recovers to attain its resting value exponentially with time (Erlanger and Blair [1931]). At the anode the inverse of this phenomenon takes place. This change in excitability is called accommodation. Complete accommodation means that the excitability of the nerve has returned completely to its resting value during the passage of a con- stant current. This is probably due to the neutralization of the depolar- izing effect of the current by the repolarization activity of the nerve so that the two effects cancel, leaving the membrane at its resting value. Sequence of Events From the above experimental evidence we may roughly piece together an explanation of the sequence of events which in the final analysis may lead to a correct interpretation of the origin and method of propagation of the impulsive wave of the nerve fiber. In general, the biological potentials are of two types : the static poten- tials of the resting nerve indicating the relative difference of potential between the two points under examination, and the transient potentials accompanying the activity associated with pulse propagation. Structurally the nerve fiber has the form of a cylindrical condenser or " submarine cable." The transmission of message pulses in an electrical cable, however, is entirely different from the propagation of pulse mes- sages in nerve fiber. The condenser-like properties of the nerve sheath and its potential difference between the axis cylinder and the outer surface are probably due to a difference in ionic concentration on the two sides of the bound- ary. This difference in potential gradually disappears when the nerve is deprived of oxygen. An explanation of this disappearance may be found in the associated osmotic-pressure phenomenon, for part of the potential is very probably due to the orientation of the organic molecules forming a polar boundary at the surface of the axis cylinder. Suppose that these molecules are of the palmitic acid (C15H31 — COOH) type, composed of a long (21 X 10 -8 cm) cylindrical carbon chain termi- nating in an active polar group having a — COOH configuration. In a closely packed array* they stand upright so that a maximum number of * Shaffer and Dingle [1938] find the monomolecular layer of crystalline egg albumin to be 40 X 10 -8 cm thick. SEQUENCE OF EVENTS 227 active — COOH groups bury themselves in the water phase of the axis cylinder. If an increase in hydrogen-ion concentration of the water phase should now take place, it would diminish the attraction of the — COOH group for the water, and thus cause a change in the surface energy of the monomolecular array and consequently a change in potential. When the nerve fiber becomes locally active a rearrangement in the monomolecular array may take place. The normal difference of poten- tial suffers a transient decrease followed by a slower restoration so that a sensitive voltage-measuring device in contact with the point of excitation on the external surface of the nerve will show a pulse-like variation of potential with time. This transient lasts about 0.004 second. About one tenth of this time is used for the potential to rise to its maximum value. The change in the state of the fiber that permits the development of this transient is not known. Any theory that may be proposed must be based on the following well-established facts. The duration of the spike- like pulse is constant for a restricted range of speeds of propagation and fiber diameters (Table VI-1). If the spike appears at all, it appears with the maximum size which the intrinsic properties of the nerve permit. The nerve pulse is independent of the nature of the stimulus which starts it. Its speed of propagation increases with the diameter of the fiber and increases with a rise in temperature. If its amplitude is locally depressed, it attains its full size when it emerges into a subsequent nor- mal nerve section. The energy with which the action is maintained is supplied locally. At various times, as the experimental data have accumulated, models of nerve excitation have been developed to coordinate the existing data. One of the early models designed to illustrate pulse propagation consisted of a wire-core axis cylinder while the interstitial fluid was replaced by an envelope of electrolytic solution. This was the so-called core con- ductor model which, however, lacks the equivalence of a bioelectrical membrane. Hermann used it to show that it duplicated the " passive " electrical properties of the nerve. In spite of the perfected physical analogies attained by such models, one can duplicate biophysical conditions only very approximately, by substituting a polarizable organic interfacial membrane for the oxide film and a fluid conductor of physiological composition for the metallic core. Labes and Zain's [1927] model approached these conditions by using collodion sacs filled with a neutral solution of potassium phosphate for the cores, which were surrounded with sodium chloride solution isotonic with the phosphate mixture. The inner and outer solutions of a series of these collodion cells were placed in communication with each other 228 THE BIOPHYSICAL PROBLEM OF NERVE CONDUCTION through and with the external fluid by a series of fine glass capillaries with which the semi-permeable nature of the membrane was simulated. The iron- wire model developed by Lillie [1923] carries the analogy into the dynamic stage, and it is generally accepted as the most complete model of the propagated nerve pulse. Lillie's Iron- Wire Model of Nerve Propagation The model developed by Lillie to illustrate impulse transmission in a nerve fiber uses a pure iron wire that had been " conditioned " in strong nitric acid, which coated it with a layer of iron oxide. If such a wire is then placed in dilute nitric acid, no further chemical activity will take place; it is now said to be in its " passive " state. If the passive wire, in its dilute nitric acid bath, is scratched so that the oxide coating is pene- trated, the dilute acid will attack the exposed underlying clean iron surface at this point. It is found that the exposed iron becomes electri- cally positive with respect to the adjacent edge of the oxide-coated sur- face. The electric eddy currents flowing across the edge of this surface fracture reduce the oxide coating to iron and oxidize the adjacent free iron surface, thus causing the exposed iron to become coated with an inactive surface. This reduction-oxidation process travels along the wire, in both direc- tions from the scratch, in the form of a local pulse-like electrical disturb- ance with the speed of about 15 cm/sec. This speed may be decreased by increasing the concentration of the acid. After the initial formation of the passive surface on the iron wire a pro- longed phase follows, during which a reexcitation of the wire by scratch- ing produces only imperfect oxidation-reduction pulses. By degrees, however, the oxide-coated wire regains its original property of a recovered passive wire. Similar properties are, as we have seen, exhibited by nerve fibers dur- ing their refractory period and again in the relative refractory period in which the speed of propagation gradually regains its normal value. If the wire is enclosed in a tube filled with nitric acid, the velocity of transmission of the oxidation-reduction pulse is found to vary with the diameter of the tube. In a narrow tube the resistance through the elec- trolyte of neighboring points, between which the eddy currents flow, is increased. Hence, the currents are smaller and the time required to reduce the film is increased. This decrease in velocity with decrease in diameter is also one of the properties of nerve fibers. The model is an excellent one provided that its limitations are realized. It is not, however, a theory of nerve activity, and it does not suggest one. PHYSICOMATHEMATICAL THEORY 229 Physicomathematical Aspects of Excitation and Propagation of Nerve Impulses Throughout the development of any physical experiment, one may observe the accumulated data presented in the form of tables. One column usually contains the independent variable and a parallel column the dependent variable. Another way of presenting the data is by drawing a graph or by expressing the results in a mathematical formula. If, as in the problem of nerve conduction, one suspects that a basic physical law is involved, statements of relations are generally proposed between the rate of change of some quantity and other quantities developed by the experimental evidence. Such a relation presented in rigid mathematical terms is called a differential equation; it will contain derivatives of functions and also the functions themselves. For instance, Newton's second law of motion states that the force equals the time rate of change of the momentum. Written in mathe- matical terms, this law is d(mv) f = ' — i — dt where mv is the momentum. If the mass is constant we can rewrite the equation as „ dv F = m — dt which may be solved by direct integration. On the other hand, if an effort is to be made to find relations between two phenomena, as, for instance, between the local excitatory process of a nerve and the stimulus, then the method of approach is as follows : 1. We start by assuming a working hypothesis. The data provide the clue. 2. We next set up a mathematical expression representing the rate of change of the two variables to be examined. 3. Then we integrate the equation in order to reproduce the working hypothesis in a mathematical form su