McGehee, Cordelia2023-01-042023-01-042022-05https://hdl.handle.net/11299/250396University of Minnesota M.S. thesis. May 2022. Major: Mathematics. Advisor: Yoichiro Mori. 1 computer file (PDF); vii, 51 pages.Adaptive therapy of cytotoxic (cell killing) chemotherapy has been proposed as a method to prolong progression-free survival in certain cancers when underlying cell-cell competition between sensitive and resistant cancer cells is present. Traditionally, cytotoxic chemotherapy dosing is administered at the maximal tolerated dose with the goal of rapidly shrinking tumor growth. In the case of a tumor where underlying intratumoral cell-cell competition between a drug sensitive and drug resistant population leads to competition for resources, it is hypothesized that maximally killing the sensitive cell population allows for competitive release of the resistant cell population and outgrowth of a chemotherapy resistant tumor. In adaptive therapy, chemotherapy is administered when a tumor reaches a certain upper threshold and then is discontinued when the tumor shrinks to a specified lower threshold. The purpose of this strategy is to use the sensitive cell population to inhibit the growth of the resistant cell population and increase the length of time to competitive release and outgrowth of the resistant cell population. In this thesis, a modified Lotka-Volterra competition model is explored across competition parameters in order to analytically address 1) the optimality of continuous fixed dose versus adaptive dosing schedules and 2) the role of drug dose and mechanism of action in the choice of dosing regime. Using this model, several novel results are shown. First, for certain parameters, complete tumor eradication can be achieved in the presence of a resistant subpopulation under adaptive cytotoxic or continuous antiproliferative (decreasing growth rate) dosing schedules. Second, in this parameter space, fixed dose antiproliferative dosing schedules are more robust than cytotoxic adaptive regimes to uncertainty in initial conditions. Third, in parameter spaces where eradication of the resistant cell population is not feasible, both fixed dose antiproliferative schedules and cytotoxic adaptive therapy schedules may result in delayed resistant cell outgrowth over maximum tolerated dose and are comparable in their benefits. Overall, these results indicate that both antiproliferative continuous fixed dose therapy and cytotoxic adap-tive therapy can be used for tumor management in the case of underlying intratumoral competition between chemotherapy sensitive and chemotherapy resistant cells.enAdaptive TherapyCancerControl TheoryDynamical SystemsEvolutionPharmacologyThesis or Dissertation