On the Biological Effects of Ionizing Radiation

K. Aglintsev

Numerous and often joint works by physicians, biologists, and physicists have been devoted to the study of the biological effects of ionizing radiation. The task of biologists consists in choosing the objects of investigation and developing methods for ascertaining one or another biological effect; the task of physicists is reduced to analyzing the mechanism of ionization and measuring the energy of the radiations employed. The subject of investigation is either the action of particles that directly cause ionization, such as $\alpha$-particles, electrons and positrons ($\alpha, \beta^{-}, \beta^{+}$), or the action of agents that produce ionization indirectly, such as X-rays and $\gamma$-rays, neutrons ($X, \gamma, n$).

The process of ionization of a medium, as is known, proceeds in the following manner: an $\alpha$-particle, electron, or positron, passing through a substance, loses a certain part of its energy in ionizing the molecules of the medium; the electron torn away in ionization usually leaves this molecule with insignificant energy, although sometimes with enough to produce secondary, tertiary, etc. ionization. Thus, along the path of the particle a chain of ions is formed. The number of ions per unit length of path depends on the mass and energy of the particles and on the nature of the ionized medium; for $\alpha$-particles this quantity is of the order of several thousand ion pairs per micron of path in tissues; along the path of fast electrons or positrons, over the length of one micron, only about ten ion pairs are formed. The ionizing action of fast neutrons is due to recoil nuclei, which are set in motion in collisions with neutrons; the ionizing action of neutrons therefore approaches that of $\alpha$-particles. Finally, X-rays and $\gamma$-rays, when absorbed by the medium, set electrons in motion, and these cause ionization of the medium. The range of fast electrons in tissue reaches a centimeter; the range of $\alpha$-particles is hundreds of times smaller. It should be noted that the formation of each ion pair is accompanied by the formation of several quanta of short-wavelength ultraviolet rays possessing high photochemical activity. If one adds that this ultraviolet radiation is obtained

within the tissue and need not overcome absorbing or reflecting layers of the substance, the essential importance of this factor, which always accompanies the ionization of a substance, becomes clear. The ionization process is represented schematically in Fig. 1, where circles denote primary, secondary, etc. ions, and crosses denote light quanta.

Experimental determinations and theoretical calculations make it possible, with satisfactory accuracy, to indicate the number of ions formed in the medium and their spatial distribution, but

Fig. 1.

these data are statistical in character; there can be no question of an absolutely exact picture of the ionization of the medium at a given instant of time. The biologist likewise often has to operate with mean values, since the presence of a large number of objects compels one to confine oneself to seeking regularities of a statistical character.

The physical aspect of a quantitative assessment of the biological action of radiation usually consists in measuring the ionization produced by it. In investigations with X-rays or γ-rays it is generally accepted to express the dose (i.e. the product of the radiation intensity by the time of irradiation of the object) in roentgens. As is known[^1], 1 roentgen (\(r\)) is that dose of X-rays or γ-rays at which in \(1 \text{ cm}^3\) of atmospheric air (at \(0^\circ\text{C}\) and \(76 \text{ cm}\) Hg) there is formed 1 CGS (electrostatic unit) of ions of each sign, i.e.

\[ \frac{1}{4.8 \cdot 10^{-10}} = 2.08 \cdot 10^9 \]

pairs of ions. Taking into account that the mean work required to form one pair of ions in air is approximately 33 electron-volts, we find that the dose of 1 roentgen corresponds to energy absorbed in \(1 \text{ cm}^3\) of air:

\[ W_r = 2.08 \cdot 10^9 \cdot 33 \cdot 1.6 \cdot 10^{-12} = 0.11 \ \text{erg}/\text{cm}^3 . \tag{1} \]

Naturally, in any medium differing from air, for a given intensity of incident X-rays or γ-rays, the amount

the amount of energy absorbed in \(1\ \mathrm{cm}^3\) of the medium will be different. Let \(I_0\) denote the intensity of the incident rays, i.e. the energy falling in \(1\ \mathrm{sec}\) on an area of \(1\ \mathrm{cm}^2\), and let \(\tau\) and \(\sigma_\beta\) be the coefficients of photoelectric absorption and absorption in incoherent scattering. Then, for the kinetic energy \(\Delta I_\beta\) of the electrons liberated in a thin layer \(d\) of the medium of area \(1\ \mathrm{cm}^2\) in \(1\ \mathrm{sec}\), we find

\[ \Delta I_\beta = I_0(\tau + \sigma_\beta)d . \tag{2} \]

The coefficients \(\tau\) and \(\sigma_\beta\) are proportional to the density of the medium, and their values depend on the atomic number \(Z\) of the medium. For air one may take \(Z_{\mathrm{eff}}=7.64\); for water, blood, and muscle \(Z_{\mathrm{eff}}=7.42\), for fatty tissue—5.92, and for bone—13.8². The closeness of the effective atomic numbers of air and of the principal types of tissue predetermined the choice of air as the “working substance” in ionization chambers for energy measurements in the region of x-rays and \(\gamma\)-rays. The principal advantage of using the roentgen as a unit of measurement is that the number of roentgens is almost strictly proportional to the kinetic energy of the electrons liberated in tissues. Since the density of tissue is approximately 770 times greater than the density of air under normal conditions, for a given beam of x-rays 1 roentgen absorbed in air will correspond to the absorption of 85 ergs of energy in \(1\ \mathrm{cm}^3\) of tissue \((85 \simeq 0.11\cdot770)\); sometimes the term “mass-roentgen” or “tissue roentgen” is used for a unit of this quantity.

The measurement of ionization caused by electrons or positrons can be carried out by the same methods as are used for measurements of x-rays or \(\gamma\)-rays; some authors are inclined to express the ionization due to electrons or even \(\alpha\)-particles also in roentgens. From the fundamental point of view this meets with serious objections, since the roentgen is a unit for measuring the dose only of radiant energy, but, in practice, it defines the observed ionization quite unambiguously. The unit for measuring the dose from neutron irradiation was chosen arbitrarily³: a Victoreen roentgenmeter, calibrated in roentgens, was used; its chamber, instead of being exposed to x-rays, was irradiated by a neutron flux, and the neutron flux corresponding to a reading of 1 roentgen on the scale of the instrument was regarded as the neutron unit of dose. Under identical conditions the readings of the instrument will be proportional to the number of neutrons, but under different conditions the results may prove incomparable with one another, since the interaction of neutrons of different energies with different media is determined by complex laws.

The complex of biological processes associated with the action of ionizing radiations is distinguished by extraordinary complexity and diversity.

…in a similar way. This is wholly determined by the fact that extremely varied objects are exposed to radiation, ranging from the simplest unicellular organisms and ending with highly organized animals, and, in X-ray therapy, with man. Naturally, the “radiosensitivity” of various organisms or cells is very different. The result of studying it is the construction of “damage curves” (mortality curve, Schädigungskurve), most often used to characterize biological action. In Fig. 2 such a curve is given, according to the data of Lachmann and Stube[^4], for bean sprouts. Along the abscissa axis the dose is plotted in roentgens; along the ordinate axis, the number of bean sprouts, expressed in percent, that died as a result of the action of X-rays.

Fig. 2.

The solid curve refers to the case of soft X-rays, the dotted one to hard X-rays. The value of the dose \(D_{1/2}\), causing the death of 50% of the irradiated objects, is especially significant; in Fig. 2 \(D_{1/2}\) is respectively equal to 150 r and 330 r. The apparent difference between the two curves is considerably smoothed out if, along the abscissa axis, instead of the dose \(D\), one plots the ratio \(D/D_{1/2}\). In Fig. 3 the curves of Fig. 2 are shown, plotted on the indicated scale; only an insignificant difference in the form of the curves is observed: one of them runs somewhat more steeply than the other.

Fig. 3.

In Fig. 4 the most frequently encountered types of “damage curves” are shown (dotted lines). Sometimes, instead of damage curves, “survival curves” are given, showing what fraction of the irradiated objects remains undamaged as a result of the action of a given dose; these curves in Fig. 4 are represented by solid lines. It is clear that the sum of the ordinates of the damage and survival curves is 1, and at \(D = D_{1/2}\) these curves intersect. Curves of type \(A\) (exponential) are encountered comparatively rarely; curves of type \(C\) are most often observed.

A significant feature of the biological action of ionizing radiations, sharply distinguishing biological processes from purely physical processes, is the violation of the law of proportionality between the absorbed radiation energy and the observed effect, which is especially pronounced in the case of the curves \(C\). This led to the conclusion that the action of the radiation energy “in vain” is associated with the accumulation of a certain effect. In other words, localization of the action of radiation is accompanied by an unproductive expenditure of energy in the biological medium in those cases when special “sensitive regions” are not affected, regions that react to the formation within them of ions (or light quanta).

Fig. 4.

Consideration of the physicochemical mechanism of the biological action of ionizing radiations and the construction of a theory explaining the observed forms of lesion curves have been carried out in many theoretical and experimental works. Dessauer\(^{5}\), for the first time, proceeding from the quantum character of the absorption of X-rays, developed the theory of “point heating,” assuming that the cause of biological changes is the heating of small volumes of tissue accompanying the absorption of a radiation quantum by the molecules of the biological medium. Condon and Terrill\(^{6}\), Curie, Holweck and Lacassagne\(^{7}\) also believed that injury occurs upon absorption of a radiation quantum. Blau and Altenburger\(^{8}\) developed the mathematical side of the theory of “multiple hits” (Hit theory, Treffer-theorie), according to which, for the death of a cell, many hits must be inflicted on that cell. The basic idea of their reasoning will be set forth below. According to Crowther\(^{9}\), cell death occurs upon the formation of at least one ion pair inside a special sensitive region of the cell. Zuppinger\(^{10}\) considered the influence of variability and biological non-equivalence of individual objects in the statistical study of injury in a series of objects of the same name. Glocker\(^{11}\) developed in detail a theory based on the hypothesis that cell death occurs as a result of the passage through the sensitive region of the cell of \(n\) electrons, where \(n\) is the number of hits causing death; thus, according to Glocker, a hit is the passage of an electron through the cell and the ionization caused by it. Zimmermeister\(^{12}\) somewhat supplemented Glocker’s theory by considering the role of ion concentration along the track. Koeneumann’s works\(^{13}\) contain generalizations of a mathematical character.

Biological action of neutrons has been investigated in a number of works, especially by Lawrence and collaborators[^14]. Zirkle[^15] and Gray and Read[^16] analyzed the question of the biological action of α-particles. Geweli[^17], Weiss[^18], and a number of other investigators considered the chemical side of the processes accompanying the ionization of tissue. It is possible that these processes are of decisive importance for understanding the mechanism of the biological action of ionizing radiations. Siewert[^19] examined the conditions under which periodic changes in the properties of irradiated objects may be observed.

From the phenomenological standpoint, in the theories listed it is assumed that in the cell there exists a special sensitive region, generally speaking, of very small dimensions. It probably occupies, in bacteria, less than 0.01 of their volume; in bean sprouts, less than 0.001; and in yeasts, less than 0.0001. In mutational changes in Drosophila it has a radius perhaps less than \(10^{-6}\) cm[^20]. The death of a cell or organism occurs from one or several \((n)\) hits delivered within this region. The presence of such a region is the main cause of the different radiosensitivity of different organisms.

The death of a given organism is a random event and, generally speaking, an improbable one. Thus, for example, if a culture is irradiated with X-rays of a fairly considerable intensity of \(1\ \text{r/sec}\), then, as was already indicated above, \(85\) ergs of energy are absorbed in \(1\ \text{cm}^3\) of tissue. In this case \(10^{-12}\) pairs of ions are formed, i.e., on the average in \(1\) sec. an ion pair is formed in a volume of order \(10^{-12}\ \text{cm}^3\), or \(1\mu^3\). Volumes smaller than \(1\mu^3\) are struck by one ion pair less often than once per second. The probability of the death of organisms is calculated as follows: let \(z_0, z_1, z_2, \ldots, z_k, \ldots, z_n \ldots\) denote the number of organisms that have experienced \(0, 1, 2, \ldots, k, \ldots, n, \ldots\) hits (we shall call them organisms of class \(0, 1, 2, \ldots, k, \ldots, n, \ldots\)), and suppose death occurs from \(n\) hits. Obviously, the number of organisms belonging to class \(k\), on the one hand, decreases because with each hit they experience they pass into class \(k+1\), and, on the other hand, increases at the expense of organisms of class \(k-1\) passing, upon a hit, from class \(k-1\) into class \(k\). Denoting by \(\sigma\) the probability of a hit, we have for \(k \ne 0\):

\[ dz_k=-\sigma z_k\,dt+\sigma z_{k-1}\,dt \tag{3} \]

and for class 0, i.e. for organisms that have not yet experienced a hit,

\[ dz_0=-\sigma z_0\,dt, \tag{4} \]

whence

\[ z_0=Ze^{-\sigma t}, \tag{5} \]

where \(Z\) is the initial number of organisms subjected to irradiation. Solving equation (3) successively for \(z_1, z_2,\ldots,z_{n-1}\), we find:

\[ z_1=\sigma t Ze^{-\sigma t}, \qquad z_2=\frac{(\sigma t)^2}{2!}Ze^{-\sigma t}, \ldots,\qquad z_{n-1}=\frac{(\sigma t)^{n-1}}{(n-1)!}Ze^{-\sigma t}. \tag{6} \]

Obviously, none of the organisms of class \(0, 1, 2,\ldots,(n-1)\) will die (death occurs from \(n\) hits), and therefore the sum \(z_0+z_1+z_2+\cdots z_{n-1}\) will give the number of organisms not yet dead, while the sum \(z_n+z_{n-1}+\cdots\) will give the number already dead from \(n, n+1\), etc. hits.

Accordingly, for the survival curve we find:

\[ Z_s=\sum_0^{n-1} z_k = Ze^{-\sigma t} \left[ 1+\sigma t+\frac{(\sigma t)^2}{2!}+\cdots+\frac{(\sigma t)^{n-1}}{(n-1)!} \right] \tag{7} \]

and for the injury curve:

\[ Z_a=Z-Z_s = Z-Ze^{-\sigma t} \left[ 1+\sigma t+\frac{(\sigma t)^2}{2!}+\cdots+\frac{(\sigma t)^{n-1}}{(n-1)!} \right]. \tag{8} \]

In Fig. 5 are shown the injury curves for \(n=1, 2, 3, 9, 18\), and 48. In Fig. 6 is presented the injury curve for \(n=11\) and the “variation curve” \(Z'\), depicting the number of organisms whose death occurs at a given value \(D\) of the dose; the variation curve has a maximum at the value \(D_b\), close to \(D_{1/2}\); the value \(D_{1/2}\) corresponds to the inflection point of the injury curve. The shaded area is equal to half the area of the variation curve and, for \(n=11\), is enclosed between ordinates differing by \(\pm 20\) from \(D_{1/2}\). Thus, most organisms die at values,

Fig. 5.

Fig. 6.

close to \(D_{1/2}\), and the value \(D_{1/2}\) is a convenient characteristic of the radiosensitivity of organisms. The higher the number \(n\), the steeper the lesion curve and the narrower the variation curve. Between the quantities \(D_b\) and \(D_{1/2}\) there is the relation

\[ \frac{D_b}{D_{1/2}}=\frac{n-1}{\,n-0.33\,}, \tag{9} \]

valid for \(n \gg 2\) and allowing one, when \(D_b\) and \(D_{1/2}\) are known, to determine the number \(n\).

Table I gives values of \(D_{1/2}\) for certain objects; as can be seen from the table, they vary within extremely wide limits.

Table I

Values of \(D_{1/2}\) for certain objects

There exist organisms that respond to a dose of \(0.001\ r\)—the unicellular fungi Phycomyces Blakesleeanus \(^{20}\).

Of considerable interest is the question of the dependence of the quantities \(n\) and \(D_{1/2}\) on the properties of ionizing radiations, for example, on the hardness of X-rays or the velocity of electrons. Glocker’s theory gives the correct qualitative picture. Glocker finds the following relation, connecting the probability of a hit, the dose \(D_{1/2}\), and the hit multiplicity \(n\):

\[ vN_0 \frac{a+R}{a}D_{1/2}\sim n-0.33 \simeq n, \tag{10} \]

where \(R\) is the range of the electron in tissues, \(a\) is the mean path length of the electron through the sensitive region of the cell, \(v\) is the total volume of sensitive regions in \(1\ \mathrm{cm}^3\) of tissue, and \(N_0\) is the total number of electrons arising in \(1\ \mathrm{cm}^3\) of tissue per \(1\ \mathrm{sec}\), i.e. a quantity proportional to the intensity of the radiation.

Table II gives the values of \(R\) of photoelectrons for relatively soft X-rays.

Table II

Dependence of the range of photoelectrons in tissue on the wavelength of the ionizing X-radiation

Formula (10) can be obtained from the following considerations: the factor at \(D_{1/2}\) is proportional to the probability of causing a hit and, according to Glocker, represents the total number of electron tracks causing damage to organisms; \(N\) is obtained as the sum \(N_i+N_a\), where \(N_i\) is the number of electron tracks arising inside the sensitive volumes \(v\), and \(N_a\) is the number of electron tracks crossing the volume \(v\) from outside. Obviously:

\[ N_i=vN_0. \]

To calculate \(N_a\), let us assume that in \(1\ \mathrm{cm}^3\) there are \(Z\) organisms (for simplicity we shall regard them as spheres of radius \(\rho\)). Then the probable number of organisms affected by a given electron track over the segment \(dr\) will be equal to:

\[ dZ_a=\frac{4\pi r^2\,dr\,Z\pi\rho^2}{4\pi r^2}=Z\pi\rho^2\,dr, \]

and the total number of organisms affected by a given track is

\[ (Z_a)_1=Z\pi\rho^2 R=\frac{4}{3}\pi\rho^3 Z\,\frac{R}{\frac{4}{3}\rho}=v\frac{R}{a}, \]

where \(a=\frac{4}{3}\rho\) is the mean path length of an electron track through the sensitive region. For the total number of organisms intersected by all tracks arising outside the sensitive region, we obtain:

\[ N_a=N_0\,v\,\frac{R}{a}, \]

whence

\[ N_i+N_a=N_0\,v\,\frac{R+a}{a}. \]

It is necessary to distinguish three possible cases in applying relation (10).

1) Ionization inside the sensitive region is sufficient to cause damage, independently of the wavelength of the radiation; in this case the indica-

multiplicity index $n=\mathrm{const.}$, i.e. the form of the lesion curve does not depend on the wavelength of the radiation. Relation (10) shows that the value of $D_{1/2}$ changes according to the law

\[ D_{1/2}=\frac{\mathrm{const.}}{N_0(a+R)}=\frac{\mathrm{const.}}{\lambda(a+R)}, \tag{11} \]

where $\lambda$ is the wavelength of the X-rays. As an example one may cite the values of $D_{1/2}$ for yeast (see Table III), $n=5$, $a=6\mu$.

Table III

Dependence of yeast $D_{1/2}$ on the wavelength of X-rays

2) Ionization within the sensitive region is insufficient for injury. In this case the form of the lesion curve changes, increasing as the wavelength decreases, while the value of $D_{1/2}$ remains constant. Examples of objects of this kind may be the bean seedlings mentioned above (Figs. 2, 3); for them, at $\lambda=0.56$ and $1.54$ Å, $n$ has the values 19 and 10. The data of Lachmann and Stubbe, showing that for soft rays $D_{1/2}$ is 2.5 times greater than for hard rays (see Fig. 2), require correction: the seedlings are covered with a skin about $0.25$ mm thick, absorbing about 60% of the soft rays and practically not absorbing the hard ones at all.

3) $D_{1/2}=\mathrm{const.}$ and $n=\mathrm{const.}$ This case occurs in mutations produced by X-rays. As Zimmermeyer has shown$^{12}$, constancy of $D_{1/2}$ and $n$ is observed when the sensitive region is extremely small, if its radius is less than the mean distance between neighboring pairs of ions along the electron track. It is possible that the cause of mutational changes is due to the excitation of individual molecules in genes. Sometimes a simultaneous change of $D_{1/2}$ and $n$ is also observed when $\lambda$ changes.

The question of the relative biological effectiveness of various kinds of ionizing radiation is of exceptional importance. The question of the action of $\alpha$-particles is of interest chiefly when considering organisms of small dimensions, in particular bacteria, since the ranges of $\alpha$-particles in water or tissue do not exceed several tens of microns. Neutrons possess high penetrating power, and their use proves very effective in the treatment of a number of diseases, in particular malignant tumors, and the problem of studying the biological action of neutron fluxes is very urgent.

A comparison of the biological action of $\alpha$-particles and neutrons with the biological action of X-rays and $\gamma$-rays leads to the following conclusions:

1. In a number of cases the biological effectiveness of $\alpha$-particles and neutrons proves to be several times greater than that of X-rays or $\gamma$-rays: one and the same dose of ionizing radiation corresponds to different biological effects. It is true that comparison of the dose in roentgens and neutron units, because of the insufficient definiteness of the latter, is associated with difficulties and, perhaps, even with errors.

The form of the injury curve under the action of X-rays and neutrons is either identical or differs only insignificantly; the hit exponent $n$ in passing from X-rays to neutrons either remains unchanged or decreases somewhat. Thus, Glocker, Langendorff, and Reuss[^22] found that in the yeast Saccaharomyces ellipsoides, for X-rays with wavelengths $0.56$ and $1.54$ Å the multiplicity exponent $n = 5$, while for radon $\alpha$-rays $n = 3$. Lawrence and co-workers, Zirkle and Ebersold, and Dempster did not find any substantial difference in the form of the injury curves from X-rays and neutrons for Drosophila eggs, wheat seedlings, and certain other objects; Zirkle and Lampe believe that the difference they observed in the course of the curves probably lies within the limits of statistical errors. Zirkle’s data for the action of $\alpha$-particles of different energies and, consequently, of different ionizing ability likewise do not make it possible to note differences in the form of the injury curves.

The values of the ratio $\eta_n^X$ or $\eta_\alpha^X$ of doses producing the same biological effect vary within wide limits, from $1.8$ to $12$ for different objects. Gray and Read, for bean seedlings, give $\eta_n^X = 8.7 \pm 1.6$ and $\eta_\alpha^X = 9.0 \pm 0.8$; in the work, neutrons with energy $2.4$–$2.8 \mathrm{MeV}$, excited as a result of the $(d, d)$ reaction, and radon $\alpha$-particles were used. According to Lawrence, the ratio $\eta_n^X$ has a value from $1.8$ to $3.5$ for Drosophila eggs, from $5$ to $12$ for wheat seedlings, etc.

Finally, comparing the action of $\alpha$-particles of different energies on spores of the fern Pteris longifolia, Zirkle established that the greatest relative effectiveness is possessed by $\alpha$-particles at the end of their path, i.e. particles with maximum ionizing ability.

1. In all the examples cited, a higher ionization density corresponds to a higher biological effectiveness; opposite cases are also observed. Organisms whose death occurs as a result of a single hit, for example, Bacteria coli, require a smaller dose in the case of hard X-rays and a larger one in the case of soft X-rays and $\alpha$-particles. For Bacteria coli the values of $D_{1/2}$ will respectively be equal to $4000$, $9000$, and $24000$ roentgens;

analogous picture occurs in mutations under the action of neutron irradiation \(^{23}\).

Some of the experimental facts cited are satisfactorily explained by the Glocker–Zimmermeier theory. Let us denote by \(w\) the number of sensitive centers within the sensitive region of volume \(v\), and suppose that death of the organism occurs when all these centers are excited. Let \(a\) be the mean path length of an ionizing particle through the volume \(v\) (if \(v\) has the form of a sphere, then \(a=\frac{4}{3}\rho\)); let \(b\) and \(R\) be the mean distance between neighboring ion pairs and the total range of the ionizing particle. Then \(\frac{a}{b}\) and \(\frac{R}{b}\) give the number of ion pairs within the sensitive volume and along the entire range \(R\). In Fig. 7, within the sensitive volume, seven sensitive centers are shown (\(w=7\)) and 11 ion pairs. Finally, let \(u\) be the number of centers that undergo excitation upon the formation, within the volume, of one ion pair. Zimmermeier assumes that

\[ u=\mathrm{const}. \]

Obviously, \(u\frac{a}{b}\) gives the number of sensitive centers that undergo excitation when the track of an ionizing particle passes through the sensitive region of the organism, and

\[ \frac{w}{u\frac{R}{b}} \]

gives the number of hits \(n\) necessary for the death of the organism.

Fig. 7.

All cases of the action (see above) of ionizing radiations are reduced by Zimmermeier to one of those presented in Table IV.

Each row of Table IV corresponds to definite assumptions regarding \(u\), \(a\), and \(b\), indicated in columns I—III of the table. Column IV gives the values of the multiplicity \(n\); column V gives the value \(D_{1/2}\) calculated by Zimmermeier on the basis of the formulas of Glocker’s theory for the conditions of columns I—IV; column VI indicates the resulting dependence of \(n\) and \(D_{1/2}\) on the properties of the ionizing radiations (for example, the wavelength \(\lambda\) of X-rays); the numbering in column VII corresponds to the classification of the various regularities of the action of ionizing radiations given above.

An extremely serious shortcoming of Zimmermeier’s theory is that this theory does not make it possible to establish the conditions for the realization of one of the three main particular cases: \(w=\mathrm{const.}\), \(D_{1/2}\) varies; according to Zimmermeier one necessarily obtains either \(n=1\)

Table IV

Various types of action of ionizing radiations according to Zimmermeyer.

or \(n\) changes. The source of the indicated shortcoming of Zimmermeyer’s scheme is the assumption \(u=\mathrm{const.}\), which is incorrect and contradicts the basic proposition of Glocker’s theory that a hit is obtained when the sensitive region is traversed by a single track. In fact, if instead of one track with \(\left(\dfrac{a}{b}\right)\) ion pairs two tracks with the same total number of ion pairs pass through the sensitive region, then, for sufficiently small \(b\), the probable number of excited sensitive centers in the second case will be twice as large; the assumption \(u=\mathrm{const.}\) gives the same value in both cases.

the value \(u\left(\dfrac{a}{b}\right)\) for the number of excited centers, since each track will already excite \(u\left(\dfrac{a}{2b}\right)\) centers.

Abandoning the assumption \(u=\mathrm{const.}\) makes it possible to estimate correctly the effectiveness of ionizing radiations with a high ionization density. Assuming that for a number of objects experiment gives \(n=\mathrm{const.}\ne 1\), we must take \(\dfrac{wb}{ua}=\mathrm{const.}\) and \(u\sim \dfrac{1}{\left(\dfrac{a}{b}\right)}\). Rows 2 or 6 of Table IV give:

\[ D_{1/2}=n\left(\frac{R}{b}\right)\frac{a}{a+R}\frac{1}{v}. \tag{12} \]

In the case of X-rays, with an increase in the wavelength \(\lambda\), the energy and range of the photoelectrons decrease, the total number of ion pairs \(\left(\dfrac{R}{b}\right)\) along the electron track falls, and in the region of soft X-rays \(D_{1/2}\) decreases, in full agreement with the data of Table III.

Application of formula (12) to the case of \(\alpha\)-particles and neutrons leads to an unexpected result contradicting the experimental data: since the total number of ions \(\dfrac{R}{b}\) along the track for \(\alpha\)-particles and recoil nuclei is very large, an enormous number would be obtained for \(D_{1/2}\), which contradicts the fact noted above of the higher biological effectiveness of \(\alpha\)-particles and neutrons in comparison with X-rays and \(\gamma\)-rays. It is easy to show that a simple statistical consideration cannot lead to any other result. The same ionization will be produced, for example, by one \(\alpha\)-particle with an energy of \(5\cdot 10^6\ \mathrm{eV}\) and by one hundred photoelectrons with an energy of \(5\cdot 10^4\ \mathrm{eV}\). The probability of injury to a cell in the second case will be approximately one hundred times greater, since the ranges of \(\alpha\)-particles and electrons of the given energy values are quantities of the same order (40 \(\mu\)).

Thus, consideration of only the mechanism of ionization gives, for the ratio of the biological effectiveness of neutrons and X-rays, a value of the order of 0.01, whereas experiment for a number of objects gives a value of the order of \(2—10\).

Clarification of this contradiction requires consideration of the method of measuring ionization. The ionizing action of neutrons, as well as of X-rays, is usually measured by means of a thimble ionization chamber with wall thickness of about 1 mm. The chamber is first calibrated in roentgens, and therefore in the case of X-rays the radiation intensity is obtained directly in roentgens per minute. In the case of neutron fluxes, the measured ionization is caused mainly by recoil protons knocked out of the chamber walls by neutrons, and in air the recoil nuclei—

recoil nuclei are practically not formed at all. Since the ionization of any volume of tissue is produced by recoil nuclei arising not only in the space surrounding this volume (in the “walls” of the volume), but also within the volume itself, a calculation of the number of ions formed in tissues, made on the basis of ionization measurements with the thimble ionization chamber of a roentgenometer, will be erroneous and will lead to an underestimated value of the ionization in tissues and, consequently, to an overestimated value of the biological effectiveness of neutrons. The error thus introduced will be close to

\[ \frac{a+R}{R}, \]

where \(a\) and \(R\) have the former meanings and refer to tissue; \(a\) corresponds to the volume of tissue whose linear dimensions are 770 times smaller than the volume of the air ionization chamber. Questions of the methodology of measuring neutron fluxes have been examined in detail by Ebersold and Henshaw \(^{24}\). The introduction of the necessary corrections will make it possible to obtain a relation between the biological action of neutrons and of x-rays closer to that following from the statistical theory of impacts.

Consideration of only the physical mechanism of tissue ionization makes it possible to understand chiefly the quantitative regularities. For a deeper penetration into the essence of the biological action, it is necessary to study in detail the complex and varied set of biochemical processes arising in living matter as a result of ionization. A detailed description of them lies beyond the scope of the present article, and here we shall confine ourselves to giving only a very brief list of some hypotheses and observed facts.

1. Transparent protoplasm becomes turbid and granular because of protein coagulation.

2. The viscosity of the protoplasm changes.

3. The ionic regime of the electrolytes entering into the composition of the cell changes.

4. Destruction or chemical alteration of complex protein molecules occurs, and new molecules appear within the cell that are not characteristic of the normal life cycle and poison the cell.

5. Suppression of the initial phase of cell division.

6. Disturbance of chromosome movement during cell division.

7. Some processes, for example keratinization of the epidermis, are accelerated.

The question of the radiosensitivity of the various organs and tissues of the human being is of enormous practical importance both for x-ray and radiotherapy and for problems of protecting radiologists and radiology workers. It has been established that lymphocytes and leukocytes possess the highest radiosensitivity, followed by germ cells, etc. A dose of \(700\,r\) already causes a painful reaction—erythema (a first-degree skin burn). It is generally accepted that persons constantly working with x-rays or \(\gamma\)-rays should not receive per day a dose greater than \(0.1\)—\(0.2\,r\); this value corresponds to a harmlessly tolera-

...over a long time an irradiation intensity of the order of \(10\,\mu r/\text{sec}\) \((1\,\mu r=10^{-6}r)\). In the case of the action of neutron fluxes it is possible that the value given should be reduced to \(10^{-5}\, n/\text{sec}\), or to \(0.01\)—\(0.02n\) per day (where \(n\) denotes the neutron unit mentioned above).

It is easy to pass from roentgens and neutron units to characteristics more convenient and customary for physicists: the number of quanta or the number of neutrons.

The ionizing capacity is related to the intensity by the relation

\[ I_p=I(\tau+\sigma_\beta), \tag{13} \]

and the intensity is expressed directly by the number of photons incident in 1 sec on \(1\ \text{cm}^2\):

\[ I=N\cdot h\nu . \]

Hence, if \(p\) is expressed in \(\dfrac{r}{\text{sec}}\), and \(h\nu\) in MeV, then:

\[ N=\frac{p\cdot 6.9\cdot 10^5}{h\nu(\tau+\sigma_\beta)} . \]

Table V gives the values of \(\tau\) and \(\sigma_\beta\) for several values of \(h\nu\). The last column of the table contains the value \(N_1\), the number of photons corresponding to a dose of 1 roentgen.

Table V

A sufficiently accurate determination of the number of neutrons is somewhat more complicated. It may be considered that neutrons from a radium-beryllium source at a distance of \(30\ \text{cm}\) produce 1500 ion pairs per second in \(1\ \text{cm}^3\) per curie of radon; this gives an ionization corresponding to \(0.75\cdot 10^{-6}\) neutron unit, i.e. close to the tolerance dose of neutrons. On the other hand, according to Amaldi, Hafstad, and Tuve,^25 such a source gives about \(2.5\cdot 10^7\) neutrons per second, i.e. about 2000 fast neutrons per \(1\ \text{cm}^2\) at a distance of \(30\ \text{cm}\).

The question of the “time factor” is of considerable interest, i.e. the dependence of the biological effect on the duration of exposure, and also the time of development of changes, in particular the duration of the latent period. In the simplest organisms, biological

changes are irreversible (the organism either dies or does not), and, within wide limits, the effect depends only on the dose, i.e., is proportional to the product of intensity by time and does not depend on the ratio of the factors at a constant product. In the case of highly organized organisms, reversible changes may also be observed: at small doses, “restoration” of damaged tissues occurs and, for example, under intermittent irradiation the effect may disappear. The duration of the latent period in a number of cases is shortened with increasing intensity. In general, this complex of questions is subject to further study.

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