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Mathematical model for the thermal enhancement of radiation response: Thermodynamic approach

Radiotherapy can effectively kill malignant cells, but the doses required to cure cancer patients may inflict severe collateral damage to adjacent healthy tissues. Hyperthermia (HT) is a promising option to improve the outcome of radiation treatment (RT) and is increasingly applied in hospital. However, the synergistic effect of simultaneous thermoradiotherapy is not well understood yet, while its mathematical modelling is essential for treatment planning. To better understand this synergy, we propose a theoretical model in which the thermal enhancement ratio (TER) is explained by the fraction of cells being radiosensitised by the infliction of sublethal damage through mild HT. Further damage finally kills the cell or inhibits its proliferation in a non-reversible process. We suggest the TER to be proportional to the energy invested in the sensitisation, which is modelled as a simple rate process. Assuming protein denaturation as the main driver of HT-induced sublethal damage and considering the temperature dependence of the heat capacity of cellular proteins, the sensitisation rates were found to depend exponentially on temperature; in agreement with previous empirical observations. Our predictions well reproduce experimental data from in-vitro and in-vivo studies, explaining the thermal modulation of cellular radioresponse for simultaneous thermoradiotherapy.