Optimal Control Applied to Cell-Cycle-Specific Chemotherapy Drugs Focusing on Bone Marrow Preservation

Abstract

Chemotherapy is an essential cancer treatment, but it often causes severe bone marrow toxicity. Cell-cycle-specific drugs target proliferating cells more selectively, yet inappropriate dosing can still lead to bone marrow toxicity. This study develops an optimal control framework to design chemotherapy strategies that balance treatment effectiveness and bone marrow preservation. A compartmental model based on ordinary differential equations describes the dynamics of proliferating and quiescent bone marrow cells under chemotherapy. Treatment intensity is introduced as a bounded control acting on proliferating cells only. An objective function is defined to minimize chemotherapy-induced bone marrow damage while regulating drug administration. Pontryagin’s Maximum Principle is employed to derive the optimal treatment control, resulting in a coupled state-adjoint system. The optimality system is solved numerically using the forward-backward sweep method in conjunction with the fourth-order Runge-Kutta scheme. Numerical results demonstrate that optimal dosing strategies can significantly reduce bone marrow damage while maintaining effective chemotherapy treatment.