Optimizing adaptive cancer therapy: dynamic programming and evolutionary game theory

Abstract

BACKGROUND: Recent clinical trials have shown that the adaptive drug therapy can be more efficient than a standard MTD-based policy in treatment of cancer patients. The adaptive therapy paradigm is not based on a preset schedule; instead, the doses are administered based on the current state of tumor. But the adaptive treatment policies examined so far have been largely ad hoc. In this paper we propose a method for systematically optimizing the rules of adaptive policies based on an Evolutionary Game Theory model of cancer dynamics.METHODS: Given a set of treatment objectives, we use the framework of dynamic programming to find the optimal treatment strategies. In particular, we optimize the total drug usage and time to recovery by solving a Hamilton-Jacobi-Bellman equation based on a mathematical model of tumor evolution.RESULTS: We compare adaptive/optimal treatment strategy with MTD-based treatment policy. We show that optimal treatment strategies can dramatically decrease the total amount of drugs prescribed as well as increase the fraction of initial tumour states from which the recovery is possible. We also examine the optimization tradeoffs between the total administered drugs and recovery time.CONCLUSIONS: The adaptive therapy combined with optimal control theory is a promising concept in the cancer treatment and should be integrated into clinical trial design. * Other tumor regimes (fully angiogenic and glycolyctic) also exist outside of this parameter range. They are less interesting from the point of view of treatment strategies, but we still consider them for the sake of completeness in Section 6.3 of Supplementary Materials.

The contribution of evolutionary game theory to understanding and treating cancer

“…They adopted optimal control theory and showed analytically that to reduce the tumor volume while preserving its heterogeneity, one needs to apply lower than the MTD of drugs. Gluzman et al optimize treatment in the matrix model of interactions between glycolytic and acidic cells, introduced by Kaznatcheev et al (2017) [74]. The total drug usage and time to recovery are optimized, by solving the corresponding Hamilton–Jacobi–Bellman (HJB) equation, similarly to [48].…”

“…Additionally, there is evidence for selection for evolvability in tumor cells, e.g., hyper-mutators [37]. Recent works showed that a game-theoretic approach may help to provide an alternative to MTD, based on anticipating and steering the cancer eco-evolutionary dynamics in response to the treatment [74, 137].…”

Optimal control to reach eco-evolutionary stability in metastatic castrate-resistant prostate cancer

“…The ‘evolutionary stable therapies’ attempt to maintain a stable polymorphic tumor composition of cells sensitive and resistant to therapy, in order to prolong treatment efficacy and progression free survival [ 36 , 37 ]. Previous mathematical studies have developed examples of evolutionary stable therapies, by focusing only on stabilization of the frequency dynamics, while generally ignoring the density dynamics [ 38 , 39 ]. Stabilization of only the underlying frequency dynamics is inadequate in the case of long term stabilization of a growing tumor where tumor cell density is paramount to patient health [ 40 ].…”

Dosage strategies for delaying resistance emergence in heterogeneous tumors

“…The effectiveness of administering high dosages for a long period of time as an aggressive treatment versus a moderate strategy with low dosages in short duration has been compared through empirical studies [5]. In [6], the authors propose an adaptive therapy that is optimized based on an evolutionary game theoretic Abbreviations PKPD, pharmacokinetic/pharmacodynamic; MTD, maximum tolerated dose; MIC, minimum inhibiting concentration.…”