AUTHOR=Abolfath Ramin , Baikalov Alexander , Fraile Alberto , Bartzsch Stefan , Schüler Emil , Mohan Radhe 

TITLE=A stochastic reaction–diffusion modeling investigation of FLASH ultra-high dose rate response in different tissues

JOURNAL=Frontiers in Physics

VOLUME=Volume 11 - 2023

YEAR=2023

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2023.1060910

DOI=10.3389/fphy.2023.1060910

ISSN=2296-424X

ABSTRACT=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.