Structural Sensitivity of Control Models Arising in Combined Chemo-Radiotherapy

Simple mathematical models of tumor growth are commonly used to predict efficiency of different therapy protocols and to optimize therapy outcome. Nowadays, the focus is on personalized oncology, in which treatment strategy is tailored to an individual patient. Simple models with minimal number of parameters can be used to find appropriate treatment strategy. The main idea of this study is to describe effects of combined radio-chemotherapy by two control actions. In this work we compare results of different control strategies (treatment protocols) for a family of models of tumor growth. Using simulations in silico we analyse responses of a thousand patients to three possible therapy protocols. Comparing Kaplan-Meier survival curves obtained for two different tumor growth models indicates that while Gompertz model is slightly less sensitive to changes in control action than exponential and logistic models, the difference is negligible. The important finding is that the shapes of survival curves are similar in all cases. It suggests that the family of models is structurally insensitive. Obtained results imply that more attention should be paid on estimation of parameters for a tumor growth model, than on model selection.