The present work introduces a rigorous stochastic model, called the generalized stochastic microdosimetric model (${\mathrm{GSM}}^2$), to describe biological damage induced by ionizing radiation. Starting from the microdosimetric spectra of energy deposition in tissue, we derive a master equation describing the time evolution of the probability density function of lethal and potentially lethal DNA damage induced by a given radiation to a cell nucleus. The resulting probability distribution is not required to satisfy any a priori conditions. After the initial assumption of instantaneous irradiation, we generalized the master equation to consider damage induced by a continuous dose delivery. In addition, spatial features and damage movement inside the nucleus have been taken into account. In doing so, we provide a general mathematical setting to fully describe the spatiotemporal damage formation and evolution in a cell nucleus. Finally, we provide numerical solutions of the master equation exploiting Monte Carlo simulations to validate the accuracy of ${\mathrm{GSM}}^2$. Development of ${\mathrm{GSM}}^2$ can lead to improved modeling of radiation damage to both tumor and normal tissues, and thereby impact treatment regimens for better tumor control and reduced normal tissue toxicities.

• Received 20 October 2020
• Accepted 6 January 2021

DOI:https://doi.org/10.1103/PhysRevE.103.012412