Limitations of the Concept of Linear Energy Transfer (LET)

Abstract

Variations in the relative biological effectiveness of ionizing radiations are commonly attributed to differences in specific ionization or linear energy transfer (LET). The implication has been that for each radiation field there exists one definite distribution of dose in LET (LET spectrum) that may be computed from an analysis of the existent particle energies and corresponding values of specific energy loss. Thus Boag (1) has furnished LET spectra in water for neutrons of various energies. We have designed a proportional counter instrument (2) for the experimental determination of LET spectra and performed measurements (3) that show a certain discrepancy with Boag's computations. Recent experiments indicate, moreover, that the LET spectrum recorded by the instrument depends on the internal gas pressure, which implies a change of LET spectrum with change of the length of track that is sampled. We believe that this effect is real and is caused by the existence of statistical fluctuations that must affect biological systems as much as the physical measuring device. Computations exist that provide a theoretical value of — (dE/dx), the specific energy loss of a particle of given charge and speed. This representation, however, is an idealization, since in reality the charged particle loses energy discontinuously and hence the energy ΔE lost in traversing a thickness Δx will fluctuate because of variations in both the number of collisions and the energy expended per collision. Thus, the real quantity — (ΔE/Δx) has a range of values for identical particles of the same energy, and the spread becomes wider as Δx is decreased, since statistical variations are larger in smaller samples. On the other hand, if Δx is increased, the spread becomes less, but since a greater number of collisions is involved, δE is larger and the energy of the particle may change sufficiently so that the average value of —(ΔE/Δx) obtained in the sample may differ. For example, the theoretical value of —(dE/dx) for a proton at the peak of the Bragg curve is about 91 Kev/μ. When a small section of proton track is examined, a distribution of values will be observed which has the above figure as a mean value. As the test interval is increased, the distribution curve will become more peaked but the mean value will drop below 91 Kev/μ. Our experimental data indicate that, in the case of LET spectra produced by neutrons, these effects are sufficiently marked that appreciable deviations from the theoretical distribution must occur, no matter what sample is chosen. The further conclusion must be drawn that the LET spectrum is a function of the size of the biological test object and is, in fact, rather different in biological structures of different dimensions. Because of these complications, the analysis we perform to obtain the LET spectra is itself affected by second-order errors, but these should be less than the actual discrepancy between theoretical and practical distributions.