Mathematical modeling can offer valuable insights into the behavior of biological systems upon treatment. Different mathematical models (empirical, semi-empirical, and mechanistic) have been designed to predict the efficacy of either hyperthermia (HT), radiotherapy (RT), or their combination. However, mathematical approaches capable of modeling cell survival from shared general principles for both mono-treatments alone and their co-application are rare. Moreover, some cell cultures show dose-dependent saturation in response to HT or RT, manifesting in survival curve flattenings. An advanced survival model must, therefore, appropriately reflect such behavior.

Approach: We propose a mathematical approach to model the effect of both treatments based on the general principle of sublethal damage (SLD) accumulation for the induction of cell death and irreversible proliferation arrest. Our approach extends Jung's model on heat-induced cellular inactivation by incorporating dose-dependent recovery rates that delineate changes in SLD restoration.

Main results: The resulting unified model (Umodel) accurately describes HT and RT survival outcomes, applies to simultaneous thermoradiotherapy modeling, and is particularly suited to reproduce survival curve flattening phenomena. We demonstrate the Umodel's robust performance (R2 ≳0.95) based on numerous clonogenic cell survival data sets from the literature and our experimental studies.

Significance: The proposed Umodel allows using a single unified mathematical function based on generalized principles of accumulation of sublethal damage with implemented radiosensitization, regardless of the type of energy deposited and the mechanism of action. It can reproduce various patterns of clonogenic survival curves, including any flattening, thus encompassing the variability of cell reactions to therapy, thereby potentially better reflecting overall tumor responses. Our approach opens a range of options for further model developments and strategic therapy outcome predictions of sequential treatments applied in different orders and varying recovery intervals between them.
Keywords: Cell survival flattening; Hiperthermia treatment; Mathematical model; Sublethal damage; Thermoradiotherapy.
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