Proefschrift

metastatic disease, essentially abandoning the idea of a cure. In Chapter 3 , a mathematical model utilizing evolutionary game theory is developed to quantitatively frame the cancer eco-evolutionary dynamics of mCRPC under abiraterone treatment. The mathematical model developed here does not attempt to fully describe every underlying biological process of mCRPC, but instead focuses on the sensitive and resistant clinically known cell types and their interaction with the drug abiraterone. In this way, this mathematical model is not intended to exactly recreate clinical data. Instead, the mathematical model is used to identify critical parameters that affect system dynamics, generate experimentally testable hypotheses, and generally provide an increased understanding of the first principles of evolution of resistance to treatment with abiraterone. This model is the foundation for the remaining chapters where alternative treatment strategies with the goal of, not curing, but managing mCRPC as a chronic condition are developed, tested, and discussed. In Chapter 4 , initial analysis of the mathematical model compares the eco-evolutionary dynamics and subsequent simulated patient outcomes between various treatment strategies of abiraterone including the current standard of care MTD, a common clinical protocol known as intermittent therapy, and a novel strategy known as adaptive therapy which explicitly aims to manage the proliferation of resistant cancer cells. In this adaptive therapy, when a patient is enrolled on trial, their baseline prostate cancer blood marker known as 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. These results were used to open a first of its kind clinical trial at the Moffitt Cancer Center using this adaptive therapy protocol of abiraterone in 16 men with mCRPC. Adaptive therapy resulted in a median time to progression of 30.4 months for these men, compared to only 14.3 months for a cohort of 16 men receiving MTD abiraterone. Furthermore, this doubling of time to progression was achieved using on average 59% less cumulative abiraterone than MTD. The initial success of the clinical trial invited an exploration of more sophisticated time-dependent applications of abiraterone. In Chapter 5 , the clinical outcome of a patient is framed as an optimal control problem to identify abiraterone dosing schedules using nonlinear constrained optimization. The patient outcomes from standard clinical treatments are compared to those with other treatment objectives, such as maintaining a constant total tumor volume or minimizing the fraction of resistant cancer cells within the tumor. The model showed that continuous high doses of abiraterone as well as other dosing strategies aimed at curing the patient resulted in accelerated competitive release of the resistant cancer cells and rapid subsequent tumor progression. Results suggested that only when a patient is approaching their personal limit of tumor burden should treatment be initiated, and then only the minimum dose required to provide the patient acceptable measures of blood markers and quality of life should be administered. Finally, in Chapter 6, the mathematical model is used to identify what is coined as an ‘evolutionary stable therapy’ for mCRPC. The objective of this therapy is to maintain a 119