ADAPTATION OF A BETATRON FOR RESEARCH IN BIOLOGY AND MEDICINE

V. A. MOSKALEV

(Presented by the scientific seminar of the Faculty of Physics and Engineering)

INTRODUCTION

The betatron, as a source of superhard rays, has already found fairly wide application in foreign medical practice for the treatment of tumors. Published data indicate that 36% of patients are completely cured by betatron rays, 34% of patients show a significant improvement in health, and only 30% of patients do not respond to cure. This 30% includes patients suffering from radioresistant tumors and patients with advanced tumors that have produced numerous metastases in various regions of the organism.

Our work is an attempt to adapt the betatron specifically for medical research, with subsequent clinical use.

The purpose of the present article is to acquaint the reader briefly, first, with the advantages of the betatron over the ordinary X-ray apparatus and, second, with part of the investigations carried out by the author with a betatron in the laboratory of the Tomsk Polytechnic Institute.

X-ray installations have long been used in the fields of diagnosis, radiography, and superficial therapy. However, these installations have very limited capabilities when it comes to treating organs located at great depth beneath the surface of the skin. The hard gamma rays generated by betatrons possess a number of important properties that distinguish them favorably from the radiation of ordinary X-ray tubes [1].

First, the maximum dose of irradiation by betatron rays falls not on the surface of the object being irradiated, but on layers of tissue lying at a certain depth below the surface. This phenomenon is due to the fact that a beam of hard rays, passing from air into tissue, releases a large number of secondary electrons possessing high kinetic energy. The secondary electrons, in turn, produce ionization, knocking out tertiary electrons, and so on. Thus the total flux of electrons rapidly increases up to a certain depth from the surface of the body. When the energy of the electrons becomes insufficient for further ionization, the increase in the electron flux, and consequently in the radiation dose, ceases, and the electron flux begins slowly to decrease. For a 10 MeV betatron (on which the present work was carried out), the max-

The maximum dose is obtained at a depth of 20 mm beneath the surface of the irradiated object.

When irradiation is carried out with ordinary X-rays, the maximum dose is obtained at the surface of the patient’s body. This surface dose greatly limits the use of X-rays in deep therapy, restricting the magnitude of the dose delivered to the tumor. For the betatron, no such limitation exists.

Second, betatron radiation has an extremely high penetrating power, which is very important for the clinical use of the betatron.

Third, at high radiation energy the secondary electrons move predominantly in the direction of propagation of the primary beam of γ-quanta. Therefore, the diffusion of radiation beyond the geometrical limits of the beam is negligibly small. For the same reason, the dimensions of the irradiation field have little effect on the distribution of isodoses in tissue, which makes it possible to localize the radiation inside the body more precisely.

Fourth, in contrast to low-energy radiation, the degree of ionization in bone differs very little from ionization in tissue; consequently, it becomes possible to penetrate into any part of the organism without the danger of damaging bone that may lie in the path of the rays.

As a result of the ionization produced by γ-rays in tissue, some of the cells composing the tissue are destroyed. It has been found that, under the action of rays on cancer cells, the latter perish more rapidly than normal cells and in greater numbers; moreover, normal cells are capable of regeneration, whereas cancer cells do not exhibit this ability. The use of radiation for the treatment of malignant tumors is based on this fact. The elementary effect produced by betatron rays on the human organism is no different from that of X-rays, and in this sense the betatron is not a fundamentally new therapeutic installation.

However, the advantages of its rays indicated above provide full grounds for considering the use of the betatron for treating patients with deeply situated tumors to be a matter of primary importance. In addition, the betatron proves to be a very useful apparatus in the study of total irradiation of the living organism.

Collimation of the γ-ray Beam

The therapeutic use of the betatron requires the presence of a sharply defined beam of rays, outside the geometrical boundaries of which the radiation dose must not exceed the limiting safe dose, which according to standards is 0.05 roentgen per session. In addition, it may be necessary to change the transverse dimensions of the beam depending on the size of the tumor being irradiated.

To obtain a sharply defined beam of rays, a system of lead diaphragms is used, the so-called collimator.

Because of the high energy of betatron rays, the thickness of the collimator in the direction of radiation propagation reaches considerable dimensions and in our case is equal to 17 cm. The distribution of radiation intensity relative to the beam axis is symmetric if the beam axis exactly coincides with the axis of the collimator opening. The procedure of mounting and adjusting the collimator relative to the beam axis takes much time and requires painstaking work. Therefore, repeated performance of this procedure is wholly impractical.

However, if it is necessary to change the dimensions of the beam cross-section, we must install a collimator with the corresponding aperture. To...

to avoid an unproductive expenditure of time on adjusting the collimator when changing the irradiation field, the central part of the collimator is made in the form of a separate bushing, which can be freely replaced by another one with a new aperture. If a set of ready-made bushings with different apertures is available, it is possible to vary the dimensions of the irradiation field over a wide range.

Since betatron radiation propagates predominantly in the “forward” direction, there is no need to surround the target with lead on all sides (as, for example, when using a radioactive source). The results of measurements of the spatial distribution of ray intensity showed that if the collimator subtends 24° in the horizontal plane, then it absorbs the greater part of the total radiation from the betatron.

Superhard betatron radiation, passing through the diaphragm, knocks out from the walls of the latter a large number of secondary electrons, which “contaminate” the beam of rays, increasing the surface dose. The most convenient way to remove electrons from the beam is by a magnetic field produced by a system of induction coils placed in the path of the collimated beam. If the collimator is placed closer to the target¹, removal of the electrons is carried out automatically by the fringe field of the betatron magnetizing coils. The desire to place the collimator as close as possible to the target is also justified by the fact that the dimensions of the collimator are correspondingly reduced, since the beam near the target has a small cross section. However, excessive approach of the collimator to the accelerating chamber may cause a disturbance of the conditions for electron acceleration owing to the presence of eddy currents in the collimator material, which can distort the magnetic field in the working zone. In order to reduce eddy currents in the collimator, it should be assembled from thin sheets of lead. It is possible to make the collimator from a solid lead block provided that the collimator is located sufficiently far from the working zone of the betatron (on the order of 10 cm), as was done in the present work.

Calculation and Design of the Collimator

The basis for calculating the collimator is the spatial pattern of the radiation distribution of the betatron, determined experimentally. A preliminary calculation may be made either on the basis of a theoretical pattern of ray distribution, or on the basis of experimental data obtained earlier on analogous installations.

The spatial distribution of the radiation of our betatron was determined experimentally by the author and is given in Table 1.

Table 1

Here the radiation intensity for various angles is given as a percentage of the intensity on the beam axis, taken as 100%.

The attenuation of the radiation intensity in the absorber, taking into account the inverse-square law, is expressed by the well-known equation

\[ I_x = I_0 \cdot e^{-\mu x}\left(\frac{f}{f+x}\right)^2, \tag{1}* \]

where \(I_0\) is the intensity of the “falling” (primary) radiation at a given point,

\(I_x\) is the intensity at the same point when, in the path of the rays, there is a layer of absorber of thickness \(x\),

\(\mu\) is the coefficient of attenuation of the rays in the absorber material,

\(f\) is the distance from the radiation source to the absorber.

Equation (1) is valid for monochromatic radiation. Its use in calculations with radiation of a continuous spectrum is possible provided that the attenuation coefficient for radiation of the given composition and the given absorber is determined experimentally.

From (1), after taking logarithms and simplifying, we find the thickness of the absorber layer:

\[ x = \ln \frac{I_0}{I_x} \cdot \frac{1}{\mu}. \tag{2} \]

Setting the goal of reducing the radiation level outside the collimated beam to 0.05% of the intensity on the beam axis, from formula (2) we find the thickness of the lead collimator in the region immediately adjacent to the beam of rays. This thickness is equal to 15.5 cm. In the collimator actually constructed, its thickness is 17 cm.

The design of the collimator and its dimensions are presented in Fig. 1. Here 1 is the collimator, 2 is the replaceable part of the collimator.

The collimator is placed between the coils of the electromagnet and is screwed to a special frame fixed on the magnetic circuit. The mounting of the collimator permits adjustment of its position in order to align the axes of the beam of rays and the collimator. It should be noted that, when adjusting the collimator relative to the beam axis, one should use a thimble ionization chamber with thick walls. The betatron radiation, passing through the collimator aperture, knocks a large number of secondary electrons out of its walls and gives soft X-radiation, which is registered by a thin-walled ionization chamber and greatly complicates the procedure of installing the collimator. These secondary radiations have very low energy and are filtered out by aluminum 1 mm thick. The use of a thick-walled ionization chamber (wall thickness 3.3 cm for our betatron) eliminates the need to filter the radiation when installing the collimator.

Figure 2 shows the radiation distribution obtained with our collimator. Curve 1 is without the collimator. The presence of a replaceable central sleeve in the collimator makes it possible to change quickly the dimensions of the irradiation-field cross section.

Filtration of the Betatron Beam of Rays

Owing to the sharp directionality of the betatron radiation, its distribution over the cross section of the collimated beam is extremely nonuniform. In our case the dose at the edge of the beam is 66% of the value of the dose on the beam axis.

Fig. 1

Fig. 2

Vertical axis: Intensity
Horizontal axis: degrees

If the beam of rays is intended for therapy, such nonuniformity of the radiation over the surface of the irradiation field is inadmissible, since it creates unequal irradiation of the tissue regions encompassed by the cross section of the beam.

To eliminate this nonuniformity we used a copper equalizing filter of special configuration.

In view of the high energy of betatron radiation in comparison with ordinary X-rays, the question of choosing the filter material acquires especially important significance. Lead, a material widely used in X-ray technology for filters, proves unsatisfactory for betatron radiation for the following reasons. The attenuation of radiation in lead is due to photoelectric absorption of quanta and to coherent and incoherent scattering. These processes are decreasing functions of the radiation energy, and when the quantum energy reaches 1 MeV a new process arises—the formation of electron–positron pairs. Pair production is a function increasing with increasing quantum energy and, at several MeV, becomes predominant in the process of attenuation of radiation intensity as the radiation passes through lead. Because of this dependence of the indicated processes on the radiation energy, lead most readily transmits rays with an energy of about 3 MeV and is not a good filter for radiation with a larger energy value. The mean energy of the radiation after passing through a layer of lead becomes smaller. The process of pair production increases with increasing atomic number of the element; therefore such a pattern of ray attenuation occurs for all heavy elements.

Therefore, for effective filtering of high-energy rays it is desirable to use light elements—aluminum or carbon (graphite), for which the effective cross section of the pair-production process is small. However, in order to appreciably attenuate the rays with an aluminum or graphite filter, a very large filter thickness on the beam axis would be required, which makes the filter very inconvenient in operation.

Copper has an intermediate atomic number between lead and carbon and possesses a good property: it attenuates radiation uniformly in the range from 5 to 25 MeV, leaving the spectral composition of the radiation almost unchanged. The thickness of the copper layer required for attenuation of the radiation is small; the filter is very compact, is easily and simply fastened in a special slot of the collimator, and can be manufactured in any mechanical workshop. Therefore we chose copper as the material for making the filter.

The equalizing filter is placed in the path of the collimated beam of rays, completely covering its cross section. In using the filter, our aim is to reduce the radiation intensity in the beam to a specified value at any point of its cross section. Since the intensity of the rays falls off with distance from the beam axis, the filter thickness is greatest on the beam axis, then gradually decreases, and at the edge of the beam cross section has a minimum value. Thus the equalizing filter must have the form of a truncated cone, similar to the curve of the radiation distribution in the collimated beam shown in Fig. 2. On the basis of this curve we made a preliminary calculation of the copper equalizing filter, using the analytically calculated value of the radiation attenuation coefficient in copper. A repeated calculation of the filter, carried out using the experimentally found value of the attenuation coefficient in copper, gave results in good agreement with the results of the first calculation. The calculated profile of the cross section of the equalizing filter along the longitudinal axis is given in Fig. 3 (1).

Subsequently the filter is subjected to experimental verification and correction. Our filter is made in the form of a pyramid of copper disks 1.5 mm thick. The diameter of the largest disk is 43 mm. When placed in a special groove of the collimator, the disk completely intercepts the beam of rays.

Fig. 3

The maximum thickness of the experimentally selected filter is 7.5 mm.

Table 2 gives the dimensions of the equalizing filter as a function of distance from the beam axis, obtained analytically and as a result of experiments. A comparison of the data given indicates good agreement between the calculated and experimental values.

Table 2

Figure 3 (2 and 3) shows the profile of the copper filter used in the work, and Fig. 4 (1) shows the distribution of radiation over the cross section of the collimated beam after filtration.

Fig. 4

The distribution obtained may be considered quite satisfactory for using the beam for purposes of deep...

therapy, since here the intensity reaches its maximum value at a distance of 5 mm from the edge of the beam and then remains constant, forming a kind of “plateau.” When installing the filter it is necessary to align its axis exactly with the axis of the ray beam, since even a slight deviation of the filter axis from the beam axis (3–4 mm) causes a sharp distortion of the symmetrical distribution of radiation over the beam cross section, Fig. 4 (2).

Distribution of Isodoses of Betatron Radiation in a Physiological Medium

Quantitative determination of the radiation dose inside an organism is difficult, and in practice measurements are made on models of the human body—phantoms. Phantoms are made from materials whose density is close to that of physiological tissue. Such materials include bakelite, pressed wood, plexiglass, and water. For our measurements we used water as a medium replacing physiological tissue. The water was poured into a textolite tank; the beam entered the phantom through an aluminum window with a wall thickness of 0.5 mm. Measurements in the water phantom were carried out using a thimble ionization chamber with graphite walls 3 mm thick and a working volume of 1 cm³. The radiation dose was measured in the direction of propagation of the radiation as a function of the thickness of the water layer and in the direction perpendicular to the propagation of the rays at various depths, as a function of the angle between the beam axis and the given direction in the horizontal and vertical planes. A special device made it possible, by remote control, to move the radiation detector in the beam in steps of 2 mm.

Measurements of the radiation dose as a function of the thickness of the water layer showed that the maximum dose is obtained at a depth of 20 mm below the water surface, Fig. 5. The dose at the surface of the phantom was not measured for technical reasons.

On the basis of the radiation measurements, curves of the isodose distribution in water were constructed, Fig. 6 (2). For comparison, the isodose distribution of an X-ray installation with a radiation energy of 400 kV is given, Fig. 6 (1). From comparison of the graphs it is evident that the depth doses for betatron radiation are considerably higher than for the X-ray installation. The increased depth dose makes it possible to deliver much larger doses to a tumor than in ordinary X-ray therapy. In addition, in deep therapy the method of cross-irradiation is often used, with separate positions for the entrance and exit of the beam. When a betatron is used, this makes it possible to create a very large dose in the region where the beams intersect, while the total dose in all the other irradiated areas of the body taken together will not exceed 10% of the maximum.

A preliminary calculation of the depth dose of radiation can be carried out analytically [2]. We do not present the calculations here for reasons of saving space.

Protection of the operating personnel and the patient from the harmful action of scattered radiation is provided by specially designed lead screens that cover the betatron from the front side. The design and calculation of the protective devices are set forth in work [3].

The relative arrangement of the collimator, filter, protective screens, and betatron components is shown schematically in Fig. 7. On our betatron, together with staff of the Tomsk Medical Institute, a series of studies was carried out on the action of radiation on the organism of animals, as well as on microorganisms. These investigations yielded interesting results.

Fig. 5

Fig. 6. Thickness of the water layer in cm

In conclusion, it should be said that betatrons, as sources of superhard X-ray radiation, can and should find broad application in Soviet medicine for the treatment of malignant tumors. To this end, broad circles of medical workers must be acquainted with

Fig. 7. Layout of the betatron components
M—target, 1—magnetic circuit, 2—electromagnet coil, 3—vacuum toroidal chamber, 4—collimator, 5—lead protective shields, 6—plexiglass blocks for absorbing scattered radiation and electrons

the advantages of betatron beams in therapy, with the results of the clinical use of the betatron abroad, and also with the work being carried out in the Soviet Union.

LITERATURE

1. Moskalev V. A. An installation for the therapy of deeply situated tumors. Vrachebnoe delo No. 4, Medgiz, 1954.

2. H. E. Johns, et al. Depth dose data and isodose distribution for radiation from a 22 MeV betatron. Am. J. Rad., Roent. 62, 257, 1949.

3. Moskalev V. A. Development of a betatron for medicine and biology. Dissertation. Tomsk, 1953.

1. By target we mean the tungsten plate onto which the accelerated electrons are “dumped” and subsequently decelerated, i.e., the source of superhard X-ray radiation. ↩