Generalized Stochastic Microdosimetric Model: The Main Formulation

The present work introduces a rigorous stochastic model, called the generalized stochastic microdosimetric model (GSM2), 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 GSM2. Development of GSM2 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.