Target size variation in microdosimetric distributions and its impact on the linear-quadratic parameterization of cell survival.

The linear-quadratic (LQ) parameterization of survival fraction SF(D) inherently assumes that all cells in a population get the same dose D, albeit the distribution of specific energy z over the individual cells f(z,D) can be very wide. From these microdosimetric distributions, which are target size dependent, we estimate the size of the cellular sensitive volume by analysing its influence on the LQ parameterization of cell survival. A Monte Carlo track structure code was used to simulate detailed tracks from a 60Co source as well as proton and carbon ions of various energies. From these tracks, f(z,D) distributions were calculated for spherical targets with diameters ranging from 10 nm to 12 µm. A cell survival function based on f(z,D) was fitted to published experimental LQ α values, revealing an intrinsic limitation that target size imposes on the usage of f(z,D) to describe the linear term of the LQ parameterization. The results indicate that such threshold volume arises naturally from the relationship between the particle´s probability of no-hit and the probability of cell survival. Further analysis led to the proposal of a radiobiological property yf,MID, defined as the mean lineal energy corresponding to the target size that allows equivalence between the mean inactivation dose (MID) and the mean specific energy z1. The fact that z1 is an increasing continuous function of target size within the range of biological targets of interest in radiobiology, ensures the uniqueness of yf,MID for any radiation quality, thus, its potential usefulness in modelling. In conclusion, an accurate estimation of such threshold volumes may be useful for improving modelling of cell survival curves