Generalized concept of the LET-RBE relationship of radiation-induced chromosome aberration and cell death.

The frequency of chromosome aberrations per traversal of a nucleus by a charged particle at the low dose limit increases proportionally to the square of the linear energy transfer (LET), peaks at about 100 keV/micron and then decreases with further increase of LET. This has long been interpreted as an excessive energy deposition over the necessary energy required to produce a biologically effective event. Here, we present an alternative interpretation. Cell traversed by a charged particle has certain probability to receive lethal damage leading to direct death. Such events may increase with an increase of LET and the number of charged particles traversing the cell. Assuming that the lethal damage is distributed according to a Poisson distribution, the probability that a cell has no such damage is expressed by e-cLx, where c is a constant, L is LET, and x is the number of charged particles traversing the cell. From these assumptions, the frequency of chromosome aberration in surviving cells can be described by Y = alpha SD + beta S2D2 with the empirical relation Y = alpha D + beta D2 in the low LET region, where S = e-cL, alpha is a value proportional to LET, beta is a constant, and D is the absorbed dose. This model readily explains the empirically established relationship between LET and relative biological effectiveness (RBE). The model can also be applied to clonogenic survival. If cells can survive and they have neither unstable chromosome aberrations nor other lethal damage, the LET-RBE relationship for clonogenic survival forms a humped curve. The relationship between LET and inactivation cross-section becomes proportional to the square of LET in the low LET region when the frequency of a directly lethal events is sufficiently smaller than unity, and the inactivation cross-section saturates to the cell nucleus cross-sectional area with an increase in LET in the high LET region.