By now chemotherapy with maximum tolerated doses (MTD) is conventional treatment for cancer. The MTD based therapies imply that patients get the highest doses they can safely tolerate. It is known that after such a therapy relapse is nearly inevitable due to the emergence of therapeutic resistance: the MTD-based chemotherapy kills off the chemotherapy-sensitive cells and chemo-refractory cells eventually dominate in the tumor. Ten years ago the idea of using adaptive therapy (AT) was proposed. According to the new concept, the doses of therapy should be administered according to the current state of tumor and its anticipated evolution, alternating maximum tolerated doses with low doses or even “no therapy” periods, to give the normal tissue time to recover. Recently, the AT has shown promise in clinical trials, but the adaptive policies examined so far have been largely ad hoc and sub-optimal.
In this talk we consider an evolutionary game theory model of lung cancer dynamics under chemotherapy. Given a set of treatment objectives, we use the framework of dynamic programming to find the optimal adaptive treatment strategies. In particular, we optimize the total drug usage and time to recovery by numerically solving a Hamilton-Jacobi-Bellman equation.

Based on joint work with Alexander Vladimirsky and Jacob G. Scott.