Mathematical models based on ordinary differential equations, with impulses, are used to describe tumor growth after different treatment combinations, including chemicals as well as radiation. The models are calibrated, using a nonlinear mixed-effects framework, based on time series data of tumor volume from animal experiments. Important features incorporated into the models include natural cell death, and short-term as well as long-term response to radiation treatment, with or without co-treatment with a radiosensitizing compound. Tumor Static Exposure, defined as the treatment combinations that yield stability of the trivial solution to the system model, is introduced as a prediction tool that can also be used to compare and optimize combination therapies.
The Tumor Static Exposure concept is illustrated practically, using calibrated models and data from animal experiments, as well as theoretically, using a linear cell cycle model to describe cancer growth subject to treatment with an arbitrary number of anticancer compounds.
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