Optimal Control for Cancer Chemotherapy under Tumor Heterogeneity

Designing an effective chemotherapeutic treatment for cancer is of practical interest, and challenging due to the mutation between tumor cells and tumor heterogeneity. Recent studies, in the areas of systems science and engineering, have modeled the cancer cell population as a dynamic system and thus the chemotherapeutic treatment can be considered as the control acts on this population. In this model, tumor heterogeneity, which is the main obstacle that complicates the dynamics of the cancer cell population, can be characterized by the cell's drug-resistance levels. As a result, an optimal ensemble control problem can be formulated to minimize the combination of tumor volumes and drugs' side effects, which guarantees the effectiveness of the designed treatment. In this work, we extend our studies on optimal control for cancer chemotherapy by considering the mutations between cells. We first briefly describe the corresponding mathematical model, and then derive the optimal treatment protocols for such a cancer cell population. Several numerical examples are included to illustrate the impact of mutations and discuss the optimal cancer treatment scenarios.