THE EFFECT OF INHOMOGENEITIES ON DOSE DISTRIBUTIONS OF HIGH-ENERGY ELECTRONS

M. Brenner, P. Karjalainen, A. Rytill, and H. Jungar

i b o Akademi, i b o , and Radiotherapy Clinic, University Central Hospital

Helsinki, Finland

INTRODUCTION

The evaluation of dose distributions of high-energy electrons behind and near small areas of high density or void causes considerable problems for the therapy physicists. The same can indeed be said about the distribution in areas of such a complicated structure as the head and neck, including the bone structures and voids a t the sinus maxillaris and sinus sphenoidalis.

We have started our studies of the effect of inhomogeneities with these special cases in mind, whereas the influence of large areas of low- or high-density tissue, such as the lungs and the regular bone layer of the skull, have not been covered by our investigations. Those problems, however, have been treated in other papers in this monograph.

In the special situations of our study, the scattering of the electrons plays a dominant role. Let me therefore start with a fairly simple consideration of the disturbance of a beam of strongly scattered particles by obstacles placed in the beam. We may assume that the particles are only scattered elastically, but not absorbed.

We consider first the shielding effect of a wall introduced in the beam of such radiation. We may take as an example a wall of lead used as a shield in a very broad, essentially parallel, beam of neutrons (FIGURE 1). If the lateral dimensions of the wall are just large enough to cover a small object to be shielded, the reduc- tion of the intensity of the radiation may be considerable in the shadow of the wall. Although no particles are absorbed and no reduction of their energy takes place in the elastic collisions with the atoms of the obstacle, their number in the shadow of the wall is still smaller. The reason is that they are scattered out from the parallel beam, i.e., they are removed from the parallel beam to a diverging bundle of rays. One may use the concept of a removal cross section for a quantitative evaluation of the effect.

It goes without saying that the particles that were removed will contribute t o the intensity a t both sides of the shielded objects.

What happens when the lateral dimensions of the wall are increased? Particles are now removed from a part of the beam, which originally passed the object a t some distance from it. Consequently, some of these will now be scattered into the position of the object, where they will cause a n increase of the intensity. If the lateral dimensions of the wall are increased to infinity, the wall will finally have n o

233

234 Annals New York Academy of Sciences

Finite wall I infinite wall FIGURE 1. Scattering of particles by a wall.

effect on the intensity of the radiation at all. This is true if the intensity is defined as the current density of the particles in the direction of the beam axis. The flux of the particles, however, is increased. The flux is defined as 4 = N - v, where N is the number of particles per unit volume and v the velocity of the particles. The number of particles passing the wall and their velocity is not changed, but they will spend a longer time travelling a certain distance in the direction of the beam axis. The den- sity, N, is therefore increased, thus causing the increase of the flux. The shielding

Finite window I InFinite window FIGURE 2. Scattering of particles at a window.

Brenner et al.: Inhomogeneities 235

property of the wall disappears. Its only effect is to change the direction of the particles.

The opposite situation obtains when the intensity behind a window in a wall is studied ( F I G U R E 2). A bundle of rays will pass unaffected through the window. The intensity of this is the same as the intensity without any wall, or with an infinite wall. However, particles are scattered in from the wall to this beam, thus causing an increase of the intensity. A corresponding decrease is expected at the sides of the unaffected bundle. The lack of scattering from the window area causes a loss in particle flux, as compared to the situation behind the infinite wall of FIGURE I .

The relevance to high-energy electron dose of the simple principles illustrated by FIGURES 1 and 2 has been pointed out before by Breitling and Vogel.'

I Beam

Skin to domain depth

Soft tissue wal I

FIGURE 3. An inhomogeneity as a domain in soft tissue.

How does the situation change when soft tissue is introduced around the ob- stacle and when the considered particles are electrons, which in addition to their scattering are retarded in the material as a result of its stopping power? The obsta- cle will be represented by bone structures embedded in soft tissue ( F I G U R E 3). The case of a window is realized by a cavity in soft tissue. A tissue layer taken perpen- dicularly to the beam and of equal depth as the cavity represents the wall of the simple picture. Let us, to facilitate the discussion, introduce the concept of a disturbing domain. A piece of bone represents there a high-density domain. Cor- respondingly, an area of low density is called a low-density domain, and a cavity is called a zero-density domain.

It is obvious that the beam will not be quite parallel when striking the domain, as was the case in the simple picture. Its divergence will increase with increasing skin to domain depth. Moreover, the energy of the beam is reduced by the passed layer of tissue. There is of course scattering and absorption in the domain and behind it as well. Instead of the intensity behind and near the domain, the ab- sorbed dose will be discussed.

236 Annals New York Academy of Sciences

Although the picture is considerably changed, the effect of scattering will remain, as has been shown by our experiments.

? r r ~ r r r r r r I I I I I I I r ~ r r r r r r r r r ~ surtma - - -

- - - - c -

- -5 - -

E !

MEASUREMENTS

v.

€ Boris pirm 34MeV' WxWm' :i 1 1 I 1 I 1 II 9

For the measurements, only special idealized phantoms were used. Dose dis- tributions were obtained by means of Kodak M films and Teflon@ thermolumi- nescent dosimetry (TLD) technique. For complete dose distribution, a polystyrene phantom was constructed. The films were exposed at ten different depths perpen- dicularly to the beam. The polystyrene used has a valid effective density value, which differs less from the corresponding value for water than does the value for the commonly used phantom material, LuciteB (Perspexm).

The Ejject o j a Small High-Density Domain

Generally, anatomical bones have an inhomogeneous structure. We preferred to make homogeneous pieces of bone-equivalent material to keep the measuring conditions easier t o interpret and reproduce. Powder of milled cattle bones was used in the complete dose-distribution measurements. In these measurements, the dimensions of the domain were kept unchanged. The powder was pressed in steel molds under a high pressure. The resulting material had a density of I .54 g/cm3. This compares fairly well with the density of the mandibula. FlGURE 4 shows the perturbation by a prism of bone. The curves show the perturbation in percents of

Brenner et al.: Inhomogeneities

1 I I l l I I I I 1 l I I I I

237

i t

1 1

U I I 1

FIGURE 5 . Perturbation of a 34-mev electron field by a 2 cm x 1.13 cm diameter cylinder of bone.

the dose in the dose maximum of the unperturbed distribution. The energy was 34 mev. A typical scattering picture for a small obstacle is seen. A minimum of 14% perturbation appears in the shadow and a maximum at the sides of somewhat over 5%. Corresponding curves were obtained for 20-mev and 15-mev electron energy, respectively. It was seen that the underdose in the shadow was somewhat more pronounced with the lower energies. The divergence of the overdose areas illus- trates an increase of the scattering angle by electrons with decreasing energy.

We found it interesting to see whether the shape of the domain would have any influence on the dose pattern. A cylindrical domain of the same volume as the prism was embedded in the polystyrene. As is seen in FIGURE 5, there was no change worthy of mention except for a small alteration of minor importance close to the domain. A more radical change of the ratio between the lateral and the depth dimensions is expected to affect the situation considerably.

The simple scattering picture is somewhat modified when the perturbing do- main is made of lead. At 20 and 15 mev all electrons are absorbed except for the backscattered or particles scattered from the surfaces at the sides. A complete shadow would prevail behind the lead piece, unless electrons were scattered from the sides into the shadow area. The lead domains give us an opportunity to study the plain scattering in effect of electrons from the surrounding tissue. The results obtained at 34 mev are shown in FIGURE 6. Backscattering is observed, as is a strong side scattering. In some applications of lead shields in therapy, the knowl- edge of the hot areas at the sides may be important.

To study how the perturbation depends on the lateral dimensions of the per- turbing body, we measured profiles behind pieces of sulfur. Pieces 1 cm thick were

238 Annals New Y ork Academy of Sciences

placed at a depth of 2 cm in a water phantom. Profiles were measured by means of 6 x 1 mm Teflon TLD samples at 3 cm:s distance from the disturbing bodies. To keep the sulfur bodies and the dosimeters in position, plates of polystyrene were used. FIGURE 7 shows the result. The lateral dimensions of the sulfur obstacles were first increased stepwise from 8 x 1 i cm size by i cm in both directions. Finally a large 6 x 7 cm piece was introduced.

To keep the shape of the electron field symmetric, two radiation-sensitive diodes were connected to a balancing circuit and kept at opposite sides of the field. Still it was difficult to keep the conditions stable. The broken curves show the undisturbedprofiles, and the solid curves show the effect of sulfur domains. In some cases, the solid curve seems to be tilted due to bad balance. The underdose behind the domain is about 20% and remains nearly the same from the smallest to the 2 x 3 cm piece. The variation is not significant. The large piece, however, shows the typical scattering picture of a large obstacle as described in our simple model. The dose in the shadow is higher than by a small obstacle, because the electrons scattered from the piece itself now reach the out-of-shadow area only in a reduced proportion. They remain mainly in the shadow, where they contribute to the dose. The underdose is possibly a few percent. The most useful information of this ex- ample is the dominant nature of the scattering by small obstacles. With obstacles of large lateral dimensions, on the other hand, the absorption is expected to be re- sponsible for the reduction of the dose in the center of the obstacle. The scattering gives then rather an edge effect. The underdose in the shadow is much more promi- nent with narrow pieces than with broad.

I I 1 I Y I 1 , I

FIGURE 6. Perturbation of a 34-mev electron field by a 1 x 1 x 2 cm3 prism of lead. Curves of more than 70% perturbation are not shown.

Brenner et al.: Inhomogeneities 239

240 Annals New Y ork Academy of Sciences

Using lead pieces instead of sulfur, a corresponding series of curves were ob- tained. The effect is now different. The underdose increases with increasing lateral dimension until a minimum of 84% is reached. Only bremsstrahlung should finally remain. The dose in the shadow is from the use of small lead obstacles, mainly due to electrons scattered in from the surrounding tissue. The picture is representative for a strongly absorbing domain.

By studying the dose behind lead, we can separate the effect of the electrons scattered in from the tissue. We can draw the depth-dose curve due to the scattered- in electrons. When this is subtracted from the undisturbed depth-dose curve, we get the depth-dose curve due to electrons, which have passed through the domain.' The same can be shown for the perturbed case. The method gives the partial doses due to scattered-in unperturbed electrons and electrons perturbed by the material of the domain.

Perturbation at a Cavity

We have studied the effect of a cavity as well. The cavity had the shape of a long channel of 2 x 2 cm cross section through the polystyrene phantom. It was chosen to simulate the trachea. The dose distribution at this cavity by 34-mev electrons is shown in FIGURE 8. The overdose behind the zero-density domain is 15%. A slight underdose is observed at the sides. These perturbations agree with the simple pic- ture of a window in a wall. Again, we expected a reduction of the overdose if the cavity had large lateral dimensions. This was, however, not verified by measure- ments because the case was not considered of any practical importance.

t i i Y \ \ -

FIGURE 8. Perturbation of a 34-mev electron field by a long cavity of 2 x 2 cmz cross section.

Brenner et af.: Inhomogeneities

r r r r r r I r r r r r r I r r I I r r I I I I ~m - 24 1

2 FIGURE 9. Perturbation of a Cobalt-60 field by a long cavity of 2 x 2 cm cross section.

We found it interesting to compare the distribution of the dose due to cobalt-60 radiation with that of electrons at the cavity. The results for cobalt radiation is seen in FIGURE 9. It is evident that the perturbation is much smaller than it is by elec- trons. We found that the build-up effect at the distal wall is negligible. The reason is that electrons from the proximal wall contribute to the dose behind the cavity and keep the conditions near electron equilibrium. The increased dose is ex- plained mainly by the absence of absorbing matter in the channel.

CONCLUSIONS

In our measurements it has been demonstrated that the perturbation of the electron isodose distribution by high-density domains of bone-equivalent material and cavities of limited lateral dimensions is due mainly to scattering. From this it follows that the dose at inhomogeneities of this type cannot be evaluated from depth-dose curves through infinitely wide layers along rays emanating from the source.

The underdose behind bone and the overdose behind cavities are more pro- nounced with narrow than with very broad domains. We got typically 20% under- dose and 15535% overdose, respectively, with the bone pieces and the cavities studied by us. With thicker domains, even larger effects are expected. Although only some special cases were studied, they illustrate the phenomena involved. One may by simple assumptions be able to generalize the results for the evaluation of distributions at domains of arbitrary thickness and density. The shape indepen- dence indicates that the integrated effect may be proportional to the volume. This

242 Annals New Y ork Academy of Sciences

is reasonable if we assume that the electrons mainly are scattered by a sizable angle only once within the domain.

REFERENCES

1 . BREITLING, G . & K . H . VOGEL. 1965. Uber den Einfluss der Streuung auf den Dosis- verlauf schneller Elektronen. I n Symposium on High-Energy Electron. A. Zuppinger & G . Poretti, Eds. : 20-26. Springer-Verlag. Berlin, Germany.

2. KARJALAINEN, P., M . BRENNER & A. RYTILA. 1968. Acta Radiologica 7: 129-140.