Mathematical model for dynamic interaction between tumor, immune system, and combined radiotherapy and chemotherapy based on experimental data

In this paper, a mathematical model is constructed to simulate the interaction between tumor, therapy, and immune cells. The therapy could be radiotherapy, chemotherapy, or a combined chemotherapy and radiotherapy. The model is designed to simulate an experiment designed to test the ability of therapeutic compounds to overcome radiation resistance. The chemotherapeutic drug used was vinblastine. The model starts with a logistic model for tumor growth which is extended to include the effect of radiotherapy, chemotherapy, and combined radiotherapy and chemotherapy. Parameters of the model have been obtained in each stage by fitting the model with the corresponding experimental data. The effect of body immune system is not included in the utilized experiment since it has not been performed in vivo. To overcome this weakness, the mathematical model for combined therapy is extended to include the immune cells. The simulation of the ultimate model illustrates that, for some cases, neither radiotherapy nor chemotherapy alone is sufficient to eliminate tumor, but the combined therapy can. The constructed model gives an insight to the cited experiment, highlights some shadow sites of it, and extend its applicability onto vivo. The model can be used in predicting the most effective treatment intervention strategies.