OPTIMAL-CONTROL PROBLEMS ARISING IN CELL-CYCLE-SPECIFIC CANCER-CHEMOTHERAPY

We explore mathematical properties of models of cancer chemotherapy in cluding cell-cycle dependence. Using the mathematical methods of contr ol theory, we demonstrate two assertions of interest for the biomedica l community: 1 Periodic chemotherapy protocols are close to the optimu m for a wide class of models and have additional favourable properties . 2 Two possible approaches, (a) to minimize the final count of malign ant cells and the cumulative effect of the drug on normal cells, or (b ) to maximize the final count of normal cells and the cumulative effec t of the drug on malignant cells, lead to similar principles of optimi zation. From the mathematical viewpoint, the paper provides a catalogu e of simplest mathematical models of cell-cycle dependent chemotherapy . They can be classified based on the number of compartments and types of drug action modelled. In all these models the optimal controls are complicated by the singular and periodic trajectories and multiple so lutions. However, efficient numerical methods have been developed. In simpler cases, it is also possible to provide an exhaustive classifica tion of solutions. We also discuss developments in estimation of cell cycle parameters and cell-cycle dependent drug action.