QUANTUM PHENOMENA IN THE BIOLOGICAL ACTION OF X-RAYS E. U. CONDON AND H. M. TERRILL

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1 QUANTUM PHENOMENA IN THE BIOLOGICAL ACTION OF X-RAYS E. U. CONDON AND H. M. TERRILL (From Department of Physics, Columbia University, N. Y., and Institute of Cancer Research, Columbia University, N. Y., F. C. Wood, Director) It is a well-known theory of experimental physics that X-rays, when absorbed by matter, are absorbed in discrete units or quanta of energy. The size of these quanta increases uith decreasing wave-length. Thus, while it is also true that visible light is absorbed in discrete quanta, still here the wave-lengths are so great and hence the quanta are so small that effects due to the discreteness may easily become negligible. In the case of the biological actions of X-rays, however, it appears that the quanta are of sufficient size to make it necessary to consider the effects of this discreteness in interpreting experiments. The present article offers an analysis of such effects and a discussion of the data taken from experiments at the Institute of Cancer Research by Dr. Francis C. Wood (1, 2) and his associates, on the killing of tumor tissue and other biological material by X-rays, and, in particular, of data taken by Packard (3, 4) on the killing of Drosophila eggs. The discreteness of absorption has for its consequence that a given small element of volume of biological material when exposed to the rays is only affected by them when such a discrete act of absorption happens in the volume. The quantum of X-ray energy, when absorbed, is taken up by one atom of the absorbing substance and a high-speed photo-electron is liberated. This electron moves about in the neighborhood of the place of its liberation, losing energy by collisions with atoms and causing a good deal of local ionization. It is presumably the disturbing effect of this ionization on certain colloid equilibria which causes biological action, but that question is outside the realm of this paper. The distance traversed by the electrons, physical ex- 324

2 QUANTUM PHENOMENA OF X-RAYS 325 periments show, depends in the main only on the density of the material through which they travel. Such measurements show that the range of electrons of various voltages is 200 KV mm. 185 KV mm. X-rays of wave-length of K line of Tungsten mm. so that the volume in which all of the ionization takes place is certainly at least as small as 0.1 mm. It is probably considerably smaller because the paths of the electrons are quite crooked, thus confirming the region of ionization to from one tenth to one hundredth of this volume. Since it has been shown that there is one pair of ions formed for about thirty to forty equivalent volts of energy, it follows that such an absorption of one quantum of 160 KV. X-ray is much like a highly localized burst of ionic shrapnel in which about 4,000 ion pairs are liberated in less than a millionth of a cubic centimeter. Any biological effect like the sterilization of an egg presumably happens when one or more of these bursts of ionization occurs in a certain sensitive volume of the egg. A burst of ionization occurring in another part of the egg may suffice to produce the chemical changes which result in the production of modified plants or animals such as have been studied recently by Muller (5) for Drosophila and Goodspeed and Olsen (6) for tobacco plants. Let v be the sensitive volume in which a quantum must be absorbed in order that sterilization may occur. Let I be the intensity of X-ray energy absorbed, measured in terms of 0.01 erg/sec. mm.3 as unit. Let V be the mean kilovolt equivalent of the X-rays in the radiation used, measured with 70 kilovolts as unit. The mean size of quantum is equal to 7 x 104 x v x 4.77 x = X lo-' X V ergs, so that the mean number of quanta absorbed per second per cubic mm. is 0.01I X lo-' X V I = - X X V quanta mm,3 set, -

3 326 E. U. CONDON AND H. M. TERRILL If the unit of time be ten minutes, then the mean number of quanta absorbed in time t per cubic millimeter is It X 600 X X lo6 = 7 X X lo7. V Now if the cell is the sensitive unit of volume, it is known that these are of the order of 5 p in diameter, that is, their volumes are of the order of 4 X 10-lo cc. = 4 X lov7 mm.8. Suppose this be chosen as the unit of volume for measuring the sensitive volume, v, of the egg. Then the mean number of quanta absorbed in such a volume in ten minutes is It Itv Itv - X X 4 = * V The choice of units in what precedes has been made in such a way that small numbers of these units would correspond to the quantities actually appearing in Packard s experiments on killing of Drosophila. The disappearance of any large power of ten from this final formula therefore means that the quanta are big enough so that their discreteness must play a r61e in the interpretation of the experiments. Thus Packard, when using an intensity corresponding to one or two in our units and a voltage of about two of our units, finds that about half the eggs are killed in half an hour (t = 3). Therefore if the killing was done by one or two quanta having been absorbed in the sensitive volume v, the value of v must have been about v = 1/60 or about 6 or 7 cubic microns. If the volume is considerably larger than this, then it follows that a good many separate quanta were absorbed in it before sterilization resulted. The mean number of quanta given by the last formula is equal to what in mathematical theory of probability is known as the ezpected number of absorptions. Because of the random nature of the absorption process the case becomes one to which the Poisson distribution law is applicable. The law requires that if the expected number of absorptions in the volume is n then the probability of exactly m absorptions occurring is equal to rimeml

4 QUANTUM PHENOMENA OF X-RAYS 327 where e is the base of the natural logarithms. Thus the probability that no absorptions occur even when the expected number is n is given by putting m = 0, i.e., it is e-n. Now if a single absorption is sufficient to kill, then it is evident that this probability of no absorptions is the probability of survival. Therefore if absorption of one quantum will kill the egg, the survival curve (number of eggs surviving after time t of exposure to rays) is given by

5 328 E. U. CONDON AND H. M. TERRILL in which N is the number surviving after time t and No is the number in the sample at t = 0. From this form it is evident that if log N/No is plotted against t the data should give a straight line whose slope is downward and from the value of which one could infer the size of the sensitive volume if I and V are known. Fig. 1 is such a plot of the data given in Table 2 of Packard's first article. The data are the same as those plotted by him in in his Fig. 2. It is clear that the data are well represented by a straight line indicating that the absorption of a single quantum in a particular part of the egg was responsible for a sterilization. However, for these data a measurement of I in absolute energy units is lacking so that the slope cannot be used to infer a value of the sensitive volume. In this case the X-ray tube was run at 190 KV. which makes the strongest part of the X-ray spectrum come at a wave-length corresponding to a quantum voltage of about 155 KV. This is the highest voltage, and hence the largest quanta, of any of the experiments. It is next of interest to consider the shape of the curve in the case that several quanta must be absorbed in the sensitive volume for sterilization to occur. Suppose for instance that m quanta have to be absorbed in the sensitive part before death occurs. Clearly the probability of survival is then equal to the probability that the sensitive volume was not the scene of the absorption of m or more quanta. This is equal to the probability that the number of quanta absorbed was 0 or 1 or 2 or 3 or... (m - l), and this is equal to the sum of the probabilities of each of these possibilities, that is, This expression, often called Poisson's exponential summation, is well known to students of the theory of probability for cases of this sort. An interesting reference in this connection is to a paper by F. Thorndike (7), in which it is applied numerically to a great many different cases, from the distribution of occurrence of visits from comets to the frequency with which wrong connections are made by telephone operat ors. This paper also gives

6 QUANTUM PHENOMENA OF X-RAYS 329 very full tables of the expression for different values of n and m. In Fig. 2 are given several theoretical curves, based on the formula of the preceding paragraph, the values of the formula being taken from the paper of Thorndike. The logarithm of the FIQ. 2 probability of survival is here plotted as a function of n, the expected number of quanta absorbed. Curve (a), a straight line, is for the case where only one quantum needs to be absorbed to cause death. Curve (b) is for the case in which every egg needs to absorb two quanta in its sensitive part to have death result. Similarly (c) and (d) are for the cases where three and four quanta

7 330 E. U. CONDON AND H. M. TERRILL are needed, respectively. When still more quanta are needed, the corresponding curves are similar, save that they have an even more gradual slope at the outset, but they ultimately become parallel to the rest. That these results of the mathematical theory are quite reasonable is seen from the following qualitative argument. Suppose a cell needs to have absorbed, say, ten quanta to be killed. Then for quite a while very few deaths will result, for it is unlikely that any one cell should receive ten quanta at the outset. What is happening in the initial period is that all of the cells are being hit but very few of them have been hit the necessary ten times. This goes on, with few cells dying, until most of the cells have been hit nine times. From now on each cell only requires one more quantum to kill it, so from here on the curve will behave much like the simpler curve for the case where only one quantum is required altogether. The greater the number of quanta needed the longer will be the period which is devoted to getting most of the cells hit just one less than the required number of times, after which the deaths occur at a rapid rate just as in the case where but one quantum suffices to kill. Of course there is the possibility, too, that the eggs show variation among themselves; that some of them require but one quantum while others require two. Under such circumstances the theoretical curves have the same general shape as in Fig. 2. However, it is not worth while to go into a detailed discussion of this at present. The data presented in Fig. 2 (Table 1) of Packard s second article when the logarithm of the number surviving is plotted against the X-ray exposure (intensity X time) gives a curve of the form of the theoretical curves of Fig. 2. These data have been plotted in this form in Fig. 3 where also the theoretical curves have been drawn in for the cases in which (a) one, (b) two, (c) three quanta are needed to cause death. From this we infer that between two and three quanta were needed in these experiments to kill the Drosophila eggs. The question immediately presents itself: Why does one set

8 QUANTUM PHENOMENA OF X-RAYS 331 of data indicate only one quantum, while the other set indicates that two or three are needed? The answer, we believe, lies in the difference between the hardness of the rays in the two sets of data. The second set of data is a composite curve taken with three different wave-lengths, namely, 0.22, 0.54 and 0.68 A. On the other hand, in the first set of data the tube was run at 190 FIG. 3 KV., giving the most intense radiation at a curve length of about 0.08 A,, which corresponds to about 155 KV. electrons. Since the size of the quanta is inversely proportional to the wave-length, it is seen that in the second set of data the quanta are only one third to one eighth as large as in the first set. It is not surprising that several of the smaller quanta were needed to do what one of the larger ones would do. This would suggest that the critical amount of energy to kill a Drosophila egg when released in the form of ionization in the sensitive part of the egg is roughly of the order of the quantum associated with 0.1 A. radiation, or 1.8 X lo- ergs. Naturally this value is only an order of magnitude result. In the case of the data presented in Fig. 3 absolute measurements of intensity have been made by Terrill, using a resistance thermometer method recently described (8). Here again the accuracy of the biological data seems to suffice merely for an order of magnitude determination of the size of the sensitive

332 E. U. CONDON AND H. M. TERRILL volume. A mean value for the absorbed energy in the wavelength range here used is.02 erg/sec. mmes or two of the units of this paper.

9 332 E. U. CONDON AND H. M. TERRILL volume. A mean value for the absorbed energy in the wavelength range here used is.02 erg/sec. mmes or two of the units of this paper. The slope of the straight portion of the experimental curve given in Fig. 3 (making allowance for the conversion factor from common to natural logarithms) is 0.468, so that for a voltage corresponding to the mean wave-length (0.48 A.) one infers that the sensitive volume is equal to 5 cubic microns. Crowther (9) has also discussed the statistical consequences of the discreteness of X-ray absorptions. He applies the formulas to some of his own observations on the killing of Colpidium Colpoda by X-rays. The survival curves for these are quite different in form, having a long period of raying with scarcely any deaths and then a period in which most of the specimens are killed very rapidly. Interpreted statistichlly his data indicate that between forty and fifty quanta are needed to cause a death. In such a case the discreteness of the absorption is not so much in evidence as in the case of the Drosophila. Another class of data for which the survival curve has a long horizontal part followed by a rapid dip-of the kind that indicates the need for many quanta-is that taken on the killing of various kinds of tumor tissue by Dr. F. C. Wood (1, 2) in the Institute of Cancer Research. This might come about not only through the possibility that such tumor cells, like the Colpidia, require many quanta to kill them, but also because in the nature of the case the portions of tissue employed had to consist of many cells. Survival of such a piece of tissue probably means survival of more than a certain minimum number of cells in the piece. For simplicity suppose only one cell need survive out of N. Let P be the probability that a cell survive, so 1 - P is the probability that it die. Then (1- P) is the probability that all of them die, so 1 - (1- P) is the probability that not all die, i.e., that one or more survive; but this is greater than P, as a simple algebraic treatment shows, being for P very small, about equal to NP. Hence to reduce the probability that any cell in the piece of tissue survive to a small value means that P must be about 1/N as great as if there were

10 QUANTUM PHENOMENA OF X-RAYS 333 but one cell, i.e., the dosage must be considerably greater, so that for this reason alone a complex piece of tissue would appear to require a larger number of quanta per cell than would a single cell. SUMMARY 1. A statistical theory of the survival curve for organisms subjected to X-rays, based on the quantum discreteness of the absorption process, is developed. 2. The theory is applied to data on the killing of Drosophila eggs. It appears that one quantum is sufficient to kill an egg when the wave-length is about 0.08 A., but that two or three are needed when the wave-length is three to eight times as great. 3. The relation of the theory to the killing of tumor tissue by X-rays is briefly discussed. REFEmNCES (1) WOOD, F. C.: Am. J. Roentgenol., 1924, xii, 474. (2) WOOD, F. C.: Radiology, 1925, v, 199. (3) PACKARD, C.: J. Cancer Res., 1926, x, 319. (4) PACKARD, C.: J. Cancer Res., 1927, xi, 1. (5) MULLER, H. J.: Science, 1927, Ixvi, 84. (6) GOODSPEED AND OLBEN: Science, 1928, IxVii, 46. (7) THORNDIKE, F.: Bell System Tech. Jour., 1926, v, 604. (8) TERRILL, H. M.: Phys. Rev., 1926, xxviii, 438. (9) CROWTHER, J. A.: Proc. Roy. SOC. (B), 1926, c, 390.

Chapter 30 X Rays GOALS. When you have mastered the material in this chapter, you will be able to:

Chapter 30 X Rays GOALS. When you have mastered the material in this chapter, you will be able to: Chapter 30 X Rays GOALS When you have mastered the material in this chapter, you will be able to: Definitions Define each of the following terms, and use it in an operational definition: hard and soft