Proefschrift

1.8 Evolutionary Game Theory of mCRPC More specifically for this thesis, evolutionary game theory (EGT) is used as a foundation for the mathematical modeling (Maynard Smith and Price, 1973; Maynard Smith, 1982; Hofbauer et al., 1998), which helps to model situations where multiple organisms interact and where interactions with individuals of different properties largely determine one’s chances of survival (fitness). Unlike in classical game theory (Nash et al., 1950; von Neumann and Morgenstern, 1944), individuals are not expected to be overtly rational, and their ‘strategies’ are properties that they inherit from their predecessors. These EGT models have been shown to be quite useful in developing and testing the fundamental understanding of the dynamical interactions underlying tumor population dynamics (Tomlinson, 1997; Gatenby and Vincent, 2003a; Vincent and Gatenby, 2005; Dingli et al., 2009a; McEvoy, 2009; Gallaher et al., 2018). Evolutionary game theory is particularly adept in providing a framework to study both the ecological density dependence and the evolutionary frequency dependence between players. The EGT model developed in this thesis was used to inform and open a first of its kind clinical trial at the Moffitt Cancer Center using adaptive therapy of abiraterone in men with mCRPC. This led to increasing the median time to radiographic progression of these men from 14.3 months in the control group to 30.4 months on the trial (Zhang et al., 2017, 2019). This was achieved by a relatively simple protocol. When a patient is enrolled on trial, their baseline prostate specific antigen (PSA) level is recorded. Abiraterone is then administered and when that patient’s PSA drops to 50% of their personal baseline PSA, abiraterone is discontinued. Off treatment, the PSA levels will rise and abiraterone is re-administered when the patient reaches their original baseline PSA. Based on the success of this trial (NCT02415621), more trials on adaptive therapies have been opened (e.g. in melanoma - NCT03543969, in thyroid - NCT03630120, second Zhang trial in mCRPC - NCT03511196). 1.9 Optimal Control of mCRPC The initial success in theory and in practice of the abiraterone clinical trial invited an exploration of more sophisticated time-dependent applications of abiraterone. It is likely that there are significant opportunities to further improve patient outcomes beyond that seen in the clinical trial with sufficient understanding of the underlying dynamics. In this way, this thesis frames the clinical outcome of the patient as an optimal control problem of the mathematical model. Optimal control for time-dependent problems involves recognizing dynamic state variables (sensitive and resistant cell densities), an objective (i.e. tumor size) and a controller that can be varied in time (abiraterone dose schedule). Optimization techniques can isolate values of the controller which minimizes the objective over some fixed or varied time horizon of the model. The majority of past optimal control models of cancer therapy define the objective as minimizing total tumor burden following the standard goal of “treat to cure.” Swan and Vincent (1977), Swan (1980), and Swan (1988) provide the first applications of optimal control theory to treating cancer (Swan and Vincent, 1977; Swan, 1980, 1988). Optimal control theory has since been used to investigate cytotoxic chemotherapies, cell cycle 13