  The present work introduces a rigorous stochastic model, named Generalized
Stochastic Microdosimetric Model (GSM2), to describe biological damage induced
by ionizing radiation. Starting from 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 radiation in a cell nucleus. The resulting probability distribution
is not required to satisfy any a priori assumption. Furthermore, 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.
