A stochastic reaction–diffusion modeling investigation of FLASH ultra-high dose rate response in different tissues - Abolfath, Ramin; Baikalov, Alexander; Fraile, Alberto; Bartzsch, Stefan; Schüler, Emil; Mohan, Radhe (Frontiers in Physics, 2023)
Purpose: To propose a theory for the differential tissue sparing of FLASH ultra-high dose rate (UHDR) through the inter-track reaction-diffusion mechanism. Methods: We calculate the time evolution of particle track structures using a system of coupled reaction-diffusion equations on a random network designed for molecular transport in porous and disorder media. The network is representative of the intra- and inter-cellular diffusion channels in tissues. Results: We demonstrate the occurrence of phase separation among the tracks as the complexity in intra- and inter-cellular structural increases. The tracks evolve individually like isolated islands with negligible inter-track overlap at the strong limit of disorder as they propagate like localized waves in space, resembling the localized distribution of nano-plasmonic excitations in tumors. In contrast, in a homogeneous media and at the limit of weak disorder such as in water and normal tissues, the neighboring tracks melt into each other and form a percolated network of non-reactive species. Thus, the extent of chemically active domains and their time evolution depends on tissue types such that the spatio-temporal correlation among the chemical domains vanishes as the inter-cellular complexity of the tissues increases from normal to fractal-type malignancy. Conclusions: FLASH normal tissue sparing is a result of the interplay of the proximity of the track over intra- and inter-cellular landscape, a transition in the spatial distribution of chemical reactivity, and molecular crowding. In this context, insensitivities in the radiobiological responses of the tumors to the high dose rate at FLASH-UHDR are interpreted via a lack of geometrical correlation among isolated tracks. The structural and geometrical complexities of cancerous cells prevent clustering of the tracks over a timescale that inter-track chemical reactivities presumably prevail in normal tissues. This theoretical study presents proof of principle in a hypothetical scenario in which cellular complexity influences dramatically the geometrical correlations of the track structures. We provide a logical interpretation of the experimentally observed differential FLASH-UHDR sparing of tissues. A series of systematic experiments on radiolysis diffusibility and reactivity on actual normal and cancerous tissues must be carried out to classify the tissues potentially spared by FLASH-UHDR and verify our theory.