Generalized, sublethal damage-based mathematical approach for improved modeling of clonogenic survival curve flattening upon hyperthermia, radiotherapy, and beyond

Abstract

Mathematical modeling can offer valuable insights into the behavior of biological systems upon treatment. Different mathematical models have been designed to predict the efficacy of hyperthermia (HT), radiotherapy (RT), or their combination. However, approaches capable of modeling cell survival from shared general principles for both mono-treatments and their co-application are rare. Moreover, some cell cultures show dose-dependent saturation in response to HT or RT, manifesting in survival curve flattening. An advanced survival model must, therefore, appropriately reflect such behavior. 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. 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 survival datasets from the literature and experiments. The proposed Umodel allows the use of a single mathematical function based on generalized SLD accumulation principles with implemented radiosensitization, regardless of energy type or mechanism of action. It reproduces various clonogenic survival curve patterns, including flattening, thus encompassing treatment variability and potentially better reflecting tumor responses. Our approach opens options for further model development and therapy outcome predictions of sequential treatments in different orders and recovery intervals.