AUTHOR=Alcocer-Ávila Mario , Monini Caterina , Cunha Micaela , Testa Étienne , Beuve Michaël TITLE=Formalism of the NanOx biophysical model for radiotherapy applications JOURNAL=Frontiers in Physics VOLUME=Volume 11 - 2023 YEAR=2023 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2023.1011062 DOI=10.3389/fphy.2023.1011062 ISSN=2296-424X ABSTRACT=NanOx is a theoretical framework developed to predict cell survival to ionizing radiation in the context of radiotherapy. Based on statistical physics, NanOx takes the stochastic nature of radiation at different spatial scales fully into account. It extends concepts from microdosimetry to nanodosimetry, and considers as well the primary oxidative stress. Cell death induction is attributed to two types of biological events: the local lethal events modeled by the inactivation of nanometric sensitive targets, and the global events, represented by the toxic accumulation of oxidative stress and sublethal lesions. This article presents in detail the general formalism behind NanOx. The model is structured into postulates, the theoretical bases compliant radiation physics and chemistry, and into simplifications and approximations, which are required for its implementation. The given details allow anyone to implement the model and modify it by introducing different approximations and simplifications in order to improve it, or even adapt it to other medical applications.