Purpose: The aim of the study was to propose a theory based on topology and geometry of diffusion channels in tissue to contribute to the mechanistic understanding of normal tissue sparing at ultra-high dose rates (UHDRs) and explore an interplay between intra- and inter-track radical recombination through a 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 disordered media. The network is representative of the intra- and inter-cellular diffusion channels in tissues. Spatial cellular heterogeneities over the scale of track spacing are constructed by incorporating random fluctuations in the connectivity between network sites, resembling molecular mass and charge heterogeneities at the cellular level.Results: We demonstrate the occurrence of phase separation among the tracks as the complexity in intra- and inter-cellular structure increases. At the strong limit of structural disorder, tracks evolve individually like isolated islands with negligible inter-track as they propagate like localized waves in space, analogous to the Anderson localization in quantum mechanics. In contrast, at the limit of weak disorder in a homogeneous medium, such as water, the neighboring tracks melt into each other and form a percolated network of non-reactive species. Thus, the spatiotemporal correlation among chemically active domains vanishes as the inter-cellular complexity of the tissue increases from normal tissue structure to fractal-type malignancy.Conclusion: Differential FLASH normal tissue sparing may result from the interplay of the proximity of tracks over the 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 FLASH-UHDR are interpreted via a lack of geometrical correlation among isolated tracks. The structural and geometrical complexities of cancerous cells prevent the clustering of tracks over a timescale, in which inter-track chemical reactivities presumably prevail in normal tissues. A series of systematic experiments on radiolysis-induced diffusivity and reactivity in actual normal and cancerous tissues must be performed to classify the tissues potentially spared by FLASH-UHDRs and verify our theory.
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