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In the present work, we develop a general spatial stochastic model todescribe the formation and repair of radiation-induced DNA damage. The model isdescribed mathematically as a measure-valued particle-based stochastic systemand extends in several directions the model developed in Cordoni et.al. 2021,Cordoni et.al. 2022a, Cordoni et.al. 2022b. In this new spatial formulation,radiation-induced DNA damage in the cell nucleus can undergo different pathwaysto either repair or lead to cell inactivation. The main novelty of the work isto rigorously define a spatial model that considers the pairwise interaction oflesions and continuous protracted irradiation. The former is relevant from abiological point of view as clustered lesions are less likely to be repaired,leading thus to cell inactivation. The latter instead describes the effects ofa continuous radiation field on biological tissue. We prove the existence anduniqueness of a solution to the above stochastic systems, characterizing itsprobabilistic properties. We further couple the model describing the biologicalsystem to a set of reaction-diffusion equations with random discontinuity thatmodel the chemical environment. At last, we study the large system limit of theprocess. The developed model can be applied to different contexts, withradiotherapy and space radioprotection being the most relevant. Further, thebiochemical system derived can play a crucial role in understanding anextremely promising novel radiotherapy treatment modality, named in thecommunity FLASH radiotherapy, whose mechanism is today largely unknown.

A spatial measure-valued model for radiation-induced DNA damage kinetics and repair under protracted irradiation condition