Low-intensity combination chemotherapy maximizes host survival time for tumors containing drug-resistant cells

Recent clinical trials have shown that for some cancers, high-intensity alternating chemotherapy does not significantly improve either survival times or response rates compared with nonalternating therapy. The current study uses optimal control to determine the best way to treat a tumor that contains drug-resistant cells that cannot be destroyed. The delivery of two non-cross-resistant chemotherapeutic agents is limited by bounds on the drug concentration and the dose intensity. This ensures that the drug toxicity stays within a tolerable range. The aim of the therapy is to maximize the host survival time, defined as the time over which the tumor burden can be kept below a fixed bound. The model is posed as a free terminal time, optimal parameter selection problem in which the constraints are continuously parametrized by time and the number of courses of therapy is free to vary. New theory is developed so that the optimal parameter selection problem can be solved as a sequence of fixed terminal time problems using existing optimal control software. Numerical simulations of Gompertz tumor growth showed that a treatment maintaining a high tumor burden doubled and sometimes tripled with survival time under aggressive therapy. When these simulations were repeated using exponential and logistic tumor growth models, the tumor burden during treatment had little influence upon survival time. In all simulations, survival time was not extended by delivering the anticancer drugs concurrently instead of staggering the treatment arms.