Graduate Thesis Or Dissertation
 

Mathematical modeling and the control of immune processes with application to cancer

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/s1784p76v

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  • A foundation for the control of tumors is presented, based upon the formulation of a realistic, knowledge-based mathematical model of the interaction between tumor cells and the immune system. The parametric control variables relevant to the latest experimental data, e.g., the sigmoidal dose-response relationship and Michaelis-Menten dynamics, are also considered. The model consists of 12 states, each composed of first-order, nonlinear differential equations based on cellular kinetics and each of which can be modeled bilinearly. In recent years a great deal of clinical progress has been achieved in the use of optimal controls to improve cancer therapy patient care. For this study, a cancer immunotherapy problem is investigated in which the aim is to minimize the tumor burden at the end of the treatment period, while penalizing excessive administration of interleukin-2 as a limit of toxicity. The optimal solution developed for this investigation is a mixture of an initially large dose of interleukin-2, followed by a gradually decreased dosage and a continuing infusion to maintain the tumor cell population at its allowable limit. Sensitivity analysis is applied to an investigation of the influences of system parameters. It has been found that the immune system is influenced greatly by several parameters such as macrophage level, tumor killing rate, tumor growth rate, and IL-2 level. The simulation results suggest that parametric control variables are important in the destruction of tumors and that the application of exacerbation theory is a good method of tumor control.
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