Browsing by Subject "Hamilton-Jacobi-Bellman equation"

Cancer is a dynamic and complex microevolutionary process. All attempts of curing cancer thus rely on successfully controlling also the evolving future cancer cell population. Since the emergence of drug resistance severely limits the success of many anti-cancer therapies, especially in the case of the promising targeted therapies, we need urgently better ways of controlling cancer evolution with our treatments to avoid resistance. This thesis characterizes acquired drug resistance as an evolutionary rescue and uses optimal control theory to critically investigate the rationale of aggressive maximum tolerated dose (MTD) therapies that represent the standard of care for first line treatment. Unlike the previous models of drug resistance, which mainly concentrate on minimizing the tumor volume, herein the optimal control problem is reformulated to explicitly minimize the probability of evolutionary rescue, or equivalently, maximizing the extinction probability of the cancer cells. Furthermore, I investigate the effects of drug-induced resistance, where the rate of gaining new resistant cells increases with the dose due to increased genome-wide mutation rate and non-genetic adaptations (such as epigenetic regulation and phenotypic plasticity). This approach not only reflects the biological realism, but also allows to model the cost of control in a quantifiable manner instead of using some ambiguous and incomparable penalty parameter for the cost of treatment. The major finding presented in this thesis is that MTD-style therapies may actually increase the likelihood of an evolutionary rescue even when only modest drug-induced effects are present. This suggests that significant improvements to treatment outcomes may be accomplished at least in some cases by treatment optimization. The resistance promoting properties of different anti-cancer therapies should therefore be properly investigated in experimental and clinical settings.