Optimal control applied to cell-cycle-specific cancer chemotherapy

We propose a mathematical model for the growth of cell-cycle-specific dose limiting bone marrow. In an attempt to determine effective methods of treatment without overdestruction of the bone marrow we implement optimal control theory. We design the control functional to maximize both the bone marrow mass and the dose over the treatment interval. Next we show that an optimal control exists for this problem, and then we characterize our optimal control in terms of the solutions to the optimality system, which is the state system coupled with the adjoint system. We show that the optimality system is unique for suitably small time intervals. Finally, we analyze the optimal control and the optimality system using numerical techniques. This allows us to suggest optimal methods of treatment that prevent excessive destruction of the bone marrow based on the specific weights in our objective functional.