Improving treatment of metastatic cancers through game theory and dynamical systems theory

While great strides have been made in treating early stages of cancer, life expectancy of patients with metastatic cancer has remained about the same in the past decades. In our recent research we showed through the game-theoretical framework, that the Standard of Care (SoC) in metastatic cancers promotes the evolution of therapy-induced resistance and leads to subsequent treatment failure. As an alternative, we proposed the so-called evolutionary therapy, based on combination of evolutionary and Stackelberg (or leader-follower) game theory. This therapy foresees and steers resistance mechanisms in cancer cells so that the patient quality of life and time to disease progression can be both increased. Recent clinical trials show success of very simple evolutionary therapies in terms of both these criteria. However, the evolutionary therapy design is still in its infancy, as the underlying game-theoretical framework with a rational (Stackelberg) leader and followers driven by natural selection (playing evolutionary game) is not well explored and its properties, such as under what conditions the Stackelberg equilibrium is stable and can actually be reached, are therefore not well understood yet. In this proposal, we will develop the missing theory for the games with a rational leader and followers playing evolutionary game among each other, which we term Stackelberg evolutionary games. This theory will lead to a much more sophisticated design of evolutionary therapies. In our proposal, we will (i) analyze mathematics of eco-evolutionary cancer response to the physicianâ??s treatment choices, both in terms of evolutionary stable strategies (ESSs) and transient dynamics leading to these strategies ; (ii) determine for which initial conditions and treatment strategies of cancer various objectives of the leader (such as treating to cure vs. treating to contain) can be achieved, and analyze the sensitivity of these objectives to small deviations in the cancer dynamics; (iii) develop the methodology for calculating the treatment strategies and implement those numerically for ongoing clinical trials (evolutionary treatment of metastatic castrate-resistant prostate cancer and metastatic thyroid cancer) and laboratory experiments (involving MDA-MB-231/luc triple-negative and MCF7 estrogen receptor-positive breast cancers). These methods will be implemented algorithmically and will be organized in a publicly available software toolbox, including model predictive control algorithms for adjusting treatment strategies during clinical trials, based on new measurements. The theory that we will develop supports a paradigm shift in the treatment of metastatic cancers, by replacing the maximum tolerable dose treatment with more dynamic, adaptive treatment strategies based on game theory and dynamical systems theory.