Biophysical modelling of proton radiation effects based on amorphous track models

To define a photon-equivalent dose in charged particle therapy one needs to know the RBE (Relative Biological Effectiveness) in the target region as well as in the surrounding tissue. RBE estimates are difficult since both the physical input parameters, i.e. LET distributions, and, even more so, the biological input parameters, i.e. cell nucleus size and local response, are not known in general. Track structure theory provides a basis for predicting dose-response curves for particle irradiation. There are (at least) two somewhat different algorithms: the Amorphous Track Partition model (ATP) and the Amorphous Track Local effect model (ATL). Both have been reported to give good agreement with observed radiobiological data. We were interested in a general comparison and in the predictive power of these models for protons.

We compared the principles of the two track structure approaches. The general dependencies of the model predictions on the input parameters are investigated. The model predictions for protons with respect to cell survival of V79 cells are compared with measurements.

Although based on similar assumptions, the application of track structure theory in terms of the computational procedure is different for the two models. The ATP model provides a set of equations to predict inter- and intratrack radiation response whereas the ATL model is based on Monte Carlo simulations. One conceptual difference is the use of average doses in subtargets in the ATP model compared with the use of local doses in infinitesimal compartments in the ATL model. The ATP concept introduces an empirical scaling of the cross-section from subcellular to cellular response. The ATL concept inherently requires a critical adjustment of parameters handling the high local dose region near the track centre. The models predict proton survival curves reasonably well but neither shows good agreement with experimental data over the entire range of proton energy and absorbed dose considered.

Designed for heavy ion applications, the models show weaknesses in the prediction of proton radiation effects. Amorphous track models are based on assumptions about the properties of the biological target and the radiation field that can be questioned. In particular, the assumption of subtargets and the multitarget/single-hit response function on one hand and the parameterization of radial dose and high dose cellular response on the other hand leave question marks.