A minimalistic model of the ultra high dose rate effect of ionizing radiation: insights in the flash effect

In phenomenological stochastic models of the biological cellular effect of ionizing radiation, e.g. the multiple target multiple hit model (MTMH), one uses the concept of threshold – the effect happens if at least M critical cellular targets are hit by at least N ionizing particles each, the effect doesn’t take place otherwise. A notable sigmoidal shape of the biological effect versus absorbed dose curve originates from the spatial inhomogeneity of the cellular regions hit by the radiation - some regions are hit many times and contribute to the possible cellular effect, the others aren’t. The active radicals and ions created by the ionizing particles and eventually (directly or indirectly) causing the biological damage also have spatially inhomogeneous concentration, – mesoscopic spatial fluctuations around the average value. The fluctuations of the radical concentration dissipate due to the diffusion and the recombination processes in competition with creation of new radicals due to the dose deposition at a given dose rate, and this kinetics affects the eventual biological effect. We present a simple theory of the diffusive relaxation of the mesoscopic, non-thermodynamic fluctuations of radical concentration and its application within a MTMH-type model to the FLASH effect. We will also discuss the matching points of the model with atomistic simulations. The conclusions of the model are in qualitative agreement with the recent review [1] collecting the available in vivo experimental results of the FLASH sparing effect for normal tissue complications probability, pooling different tissues, and animals. In particular, the model succeeds in predicting the onset and increase of the FLASH effect at higher doses and also the threshold dose below which the FLASH sparing is not observed. We acknowledge PNRR-M4C2-I1.5-ECS00000017-Tuscany Health Ecosystem (THE); INFN-CSN5 Minibeam Radiotherapy (MIRO) project.