Mathematical Modeling of Cyclic Cancer Treatments

Abstract

We have so far discussed combination therapies as a means to overcome drug resistance. While the simultaneous administration of multiple drugs is the most effective way to avoid treatment failure, this might not always be possible, e.g., due to issues related to tolerance and toxicity. Here, we examine cyclic treatment regimes, which involve alternating applications of two (or more) different drugs, given one at a time. We discuss how mathematical methods can help us identify guidelines on optimal cyclic treatment scheduling, with the aim of minimizing resistance generation. We define a condition on the drugs’ potencies which allows for a relatively successful application of cyclic therapies. We find that the best strategy is to start with the stronger drug, but use longer cycle durations for the weaker drug. We further investigate the situation where a degree of cross-resistance is present, such that certain mutations cause cells to become resistant to both drugs simultaneously. We show that the general rule (best-drug-first, worst-drug-longer) is unchanged by the presence of cross-resistance. We design a systematic method to test all strategies and come up with the optimal timing and drug order. The role of various constraints on the optimal therapy design, and in particular, suboptimal treatment durations and drug toxicity, is considered.