A mathematical model for angiogenic signaling formulated by Hahnfeldt et al. is combined with the classical equations for tumor immune system interactions by Stepanova to form a minimally parameterized model that captures these aspects of the tumor microenvironment. The resulting 3-compartment model that takes into account cancerous cells, the tumor vasculature and tumor immune-system interactions, is considered under metronomic chemotherapy. This is the regular, almost continuous administration of chemotherapeutic agents at low dose, possibly with small interruptions to increase the efficacy of the drugs. There exists medical evidence that such administrations of specific cytotoxic agents (e.g., cyclophosphamide) have both anti-angiogenic and immune stimulatory effects. The model exhibits bistable behavior with the existence of both benign and malignant locally asymptotically stable equilibrium points. The transfer of states from the malignant into the benign regions is used as a motivation for the construction of an objective functional that induces this process and the corresponding optimal control problem is analyzed.
|Commitee:||Leem, Koung Hee, Staples, Stacey|
|School:||Southern Illinois University at Edwardsville|
|Department:||Mathematics and Statistics|
|School Location:||United States -- Illinois|
|Source:||MAI 55/01M(E), Masters Abstracts International|
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