Optimal control of tumor size used to maximize survival time when cells are resistant to chemotherapy.

The high failure rates encountered in the chemotherapy of some cancers suggest that drug resistance is a common phenomenon. In the current study, the tumor burden during therapy is used to slow the growth of the drug-resistant cells, thereby maximizing the survival time of the host. Three types of tumor growth model are investigated--Gompertz, logistic, and exponential. For each model, feedback controls are constructed that specify the optimal tumor mass as a function of the size of the resistant subpopulation. For exponential and logistic tumor growth, the tumor burden during therapy is shown to have little impact upon survival time. When the tumor is in Gompertz growth, therapies maintaining a large tumor burden double and sometimes triple the survival time under aggressive therapies. Aggressive therapies aim for a rapid reduction in the sensitive cell subpopulation. These conclusions are not dependent upon the values of the model constants that determine the mass of resistant cells. Since treatments maintaining a high tumor burden are optimal for Gompertz tumor growth and close to optimal for exponential and logistic tumor growth, it may no longer be necessary to know the growth characteristics of a tumor to schedule anticancer drugs.