Estimating time-dependent cell survival in particle beam thermoradiotherapy with the dynamic temperature-dependent stochastic microdosimetric kinetic model

<i>Objective.</i>Optimizing particle beam thermoradiotherapy is hindered by the lack of methods to quantify the biological effects of temporal temperature changes. This study proposes the 'dynamic Temperature-dependent Stochastic Microdosimetric Kinetic (TSMK) model,' which extends the conventional TSMK model to account for temporal temperature changes, and assesses its capability to predict cell survival by incorporating the temporal dynamics of hyperthermia (HT) after irradiation.<i>Approach.</i>We hypothesized that the kinetic parameters of the TSMK model hold valid at any given moment, even under time-varying temperature conditions. Based on this, we solved the kinetic differential equations for radiation damage to derive a formula for cell survival dependent on the temporal conditions of HT. To evaluate the dynamic TSMK model, we used survival data from human glioblastoma A-172/neo and A-172/mp53 cells irradiated with x-rays or carbon ions with varying HT durations, and human gastric adenocarcinoma MKN-45 cells irradiated with fast neutrons with varying intervals between irradiation and HT. Model parameters were fitted to the experimental results for each cell line to evaluate the model's accuracy. Subsequently, we estimated how the relationship between HT duration and cell survival changes with absorbed dose and the time interval between irradiation and HT.<i>Main results.</i>The dynamic TSMK model successfully reproduced cell survival fractions across varying HT durations and intervals relative to irradiation. The study demonstrated the model's ability to estimate the time window for synergistic effects of combined HT and radiation. Model calculations predicted that the degree of synergy and this time window vary significantly with radiation conditions.<i>Significance.</i>The dynamic TSMK model is the first biophysical model to quantitatively estimate cell survival fraction in particle beam thermoradiotherapy under time-varying temperatures. Providing a theoretical foundation for these biological effects, this model offers a potential tool for treatment planning systems to optimize thermoradiotherapy.