A Penalization Approach in Breast Cancer Chemotherapy: Preliminary Numerical Simulations

In this paper, we discuss preliminary numerical simulation results that stem from an optimal control problem in breast cancer chemotherapy. The objective of this control problem is to minimize the growth of tumor cells while minimizing damage to normal tissue, considering that chemotherapeutic agents affect both tumor cells and healthy cells. The control variable is drug concentration, and the state variable is the tumor density in the breast. We first formulate the optimal control problem by specifying a performance criterion and various constraints and then investigate the necessary optimality conditions. Next, we present an optimization algorithm for solving the control problem. Finally, we present and discuss numerical simulations to demonstrate the importance of the suggested optimal control strategy for tumor cell eradication.