A convex optimization approach to cancer treatment to address tumor heterogeneity and imperfect drug penetration in physiological compartments

The clinical success of targeted cancer therapies is limited by the emergence of drug resistance often due to pre-existing tumor genetic heterogeneity and acquired, therapy-induced resistance. Targeted therapies have varied success in addressing metastatic disease, due to their ability to penetrate certain physiological compartments. This paper considers an evolutionary cancer model that incorporates tumor cell growth, mutation and compartmental migration and leverages recent results on the optimal control of monotone and convex systems to synthesize switching treatment strategies where a single drug or a predetermined combination of drugs is used at a given time. The need for switching is motivated by clinical considerations such as the limited effectiveness of any single targeted therapy against multiple resistance mechanisms arising in a single patient and the inability to design drug combinations at effective doses due to toxicity constraints. An optimal and clinically feasible switching therapy is obtained as the solution of a convex optimization problem that exploits the diagonally-dominant structure of the model. We demonstrate that this method yields an effective strategy in mitigating disease evolution in the presence of imperfect drug penetration in two compartments on an experimentally identified model of anaplastic lymphoma kinase (ALK)-rearranged lung carcinoma.