  In the present work, we develop a general spatial stochastic model to
describe the formation and repair of radiation-induced DNA damage. The model is
described mathematically as a measure-valued particle-based stochastic system
and 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 pathways
to either repair or lead to cell inactivation. The main novelty of the work is
to rigorously define a spatial model that considers the pairwise interaction of
lesions and continuous protracted irradiation. The former is relevant from a
biological point of view as clustered lesions are less likely to be repaired,
leading thus to cell inactivation. The latter instead describes the effects of
a continuous radiation field on biological tissue. We prove the existence and
uniqueness of a solution to the above stochastic systems, characterizing its
probabilistic properties. We further couple the model describing the biological
system to a set of reaction-diffusion equations with random discontinuity that
model the chemical environment. At last, we study the large system limit of the
process. The developed model can be applied to different contexts, with
radiotherapy and space radioprotection being the most relevant. Further, the
biochemical system derived can play a crucial role in understanding an
extremely promising novel radiotherapy treatment modality, named in the
community FLASH radiotherapy, whose mechanism is today largely unknown.
