Dissertation/Thesis Abstract

Modeling and Control of Heterogeneous Tumors Under Chemotherapy
by Bratton, Kenneth John, M.S., Southern Illinois University at Edwardsville, 2014, 71; 1565478
Abstract (Summary)

Modeling and Control of Heterogeneous Tumors Under Chemotherapy Kenneth Bratton, Southern Illinois University Edwardsville joint research with Heinz Schaettler (Washington University) and Urszula Ledzewicz, (Southern Illinois University Edwardsville) Tumor cells typically are genetically highly unstable and as a response to mutations, they frequently consist of heterogeneous agglomerations of various cell populations that exhibit a wide range of sensitivities towards particular chemotherapeutic agents. However, in response to different growth and apoptosis rates as well as increasing tumor cell densities, specific traits become dominant. We consider a mathematical model for cancer chemotherapy with a single chemotherapeutic agent for three distinctly separate levels of drug sensitivity and analyze the dynamic properties of the system under metronomic (continuous low-dose) chemotherapy. More generally, the optimal control problem of minimizing the tumor burden over a prescribed therapy interval is considered. Interestingly, when several levels of drug sensitivity are taken into account in the model, lower time-varying dose rates become a viable option. For simpler models that only distinguish between sensitive and resistant subpopulations, this only holds once a significant residuum of resistant cells has developed. For heterogeneous tumor populations, a more modulated approach that varies the dose rates of the drugs may be more beneficial than the classical maximum tolerated dose approach pursued in medical practice.

Indexing (document details)
Advisor: Ledzewicz, Urszula
Commitee: Pelekanos, George, Schaettler, Heinz, Weyhaupt, Adam
School: Southern Illinois University at Edwardsville
Department: Mathematics and Statistics
School Location: United States -- Illinois
Source: MAI 53/06M(E), Masters Abstracts International
Subjects: Mathematics
Keywords: Cancer, Chemotherapy, Modeling, Mtd, Optimal control, Singular controls
Publication Number: 1565478
ISBN: 978-1-321-20418-6
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