Proefschrift

CHAPTER 1. INTRODUCTION chemotherapies, radiotherapy, and immunotherapies (Coldman and Murray, 2000; Castiglione and Piccoli, 2006; Cappuccio et al., 2007; Castiglione and Piccoli, 2007; Ledzewicz and Sch¨attler, 2008; Villasana et al., 2010; Benzekry and Hahnfeldt, 2013; Ledzewicz and Sch¨attler, 2005; S´ wierniak and Smieja, 2005; Zhu et al., 2015; Murray, 1990a,b; Nanda et al., 2007; Ghaffari and Naserifar, 2010; A¨ınseba and Benosman, 2010; Ledzewicz et al., 2012; Kim et al., 2014; Ledzewicz and Sch¨attler, 2016). There are also optimal control studies in prostate cancer focusing on the optimal schedule of the first line androgen deprivation therapy (Hirata et al., 2018b). Engelhart (2011) and others have emphasized the importance of selecting the objective more carefully (Engelhart et al., 2011; Hadjiandreou and Mitsis, 2014; Wang and Scha¨ttler, 2016; Carr`ere, 2017). Since the “treat to cure” objective may be unfeasible, this thesis explores multiple alternative objectives with the goal of long-term tumor control. Firstly, optimal control is used to identify how to administer abiraterone with the objective of maintaining a constant tumor burden within a patient, irrespective of the underlying dynamics of sensitive and resistant cells. Then, the abiraterone treatment is identified with the objective to explicitly minimize the resistant cell population. Lastly, these two objectives are considered together to identify how to reach an evolutionary stable tumor, where both the total tumor burden and the frequencies of the sensitive and resistant cells types are held constant (Maynard Smith and Price, 1973; Maynard Smith, 1982; Hofbauer et al., 1998; Zeeman, 1980). If a stable equilibrium or multiple equilibria exist, the clinically relevant question is how can we use currently available drugs to arrive at these equilibria? Previous mathematical studies have focused only on stabilization of the frequency dynamics while generally ignoring the density dynamics (Gluzman et al., 2020; West et al., 2020). In this thesis, stabilization of both the underlying frequencies of sensitive and resistant cells and the total tumor cell density provides insight into novel dosing strategies. 1.10 Thesis Structure A detailed discussion using integrated pest management as an inspiration for long-term management of metastatic disease is discussed in Chapter 2 - “Until truly curative therapies for metastatic disease are developed, the similarity to the 1950s resistance crisis leads to a compelling question: can clinical oncology benefit from lessons learned in pest management?” This chapter qualitatively formalizes a clinical paradigm exploiting proven pest management techniques that could drastically reduce drug usage, delay or completely prevent evolution of resistance to available drugs, and lengthen the overall survival of patients with metastatic disease. In Chapter 3 the mathematical model that is used in chapters 4, 5, and 6 is presented. Details of the design of the Lotka–Volterra (LV) competition equations and the parameterization of them are discussed. The competition matrix that characterizes the evolutionary game between the cancer cell types is described and analyzed using linear stability analysis. Lastly, the specific implementation of this model in each chapter is described. 14