Phenomenological toy model for flash effect in proton therapy

Abstract

We present a simple model based on general assumptions for the FLASH effect in radiotherapy, leading to a rate equation with only three free parameters. The model can predict the biological effect ratio between healthy and tumoral tissue for arbitrary input treatments, given as a dose rate versus time function. We analyze the behavior of the model and its sensitivity to its free parameters, and decide on suitable parameter values in accordance with available experimental data from the literature. Then we apply our model to study different sets of treatments, modeled as square pulse periodic functions with different pulse peak dose rate, pulse width and repetition period, in order to illustrate how it may be used to guide future experiment design. The model predicts that, for a given average dose rate above the FLASH threshold, a more prominent FLASH effect would be observed for continuous beams than for ultra-pulsated beams with an infinitely short irradiation time. This finding needs to be validated with suitable experiments.