Optimal control algorithms for antiangiogenic therapy based tumor treatment

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Supervisor:
Dr. Kovács Levente
Department of Control Engineering and Information Technology

Cancer diseases are one of the most lethal, incurable diseases today. Because of that, research and treatment of cancer is a very important mission for medicine. Beside classical methods there are a lot of new therapies, based on mathematical models, where human body works as a complex system. Antiangiogenic therapy applies an approach like that. This paper reviews the onco-pathological background of cancer therapies, especially targeted molecular therapy. After that the application and molecular background of antiangiogenic therapy was surveyed. While the focus of the current work lags on analysis of model-based therapies, a simplified form of Hahnfeldt model was used to investigate the tumor growth. Working point linearization to examine the steady states, stability, controllability and observability of the model was used. Several working points were analyzed. For the linearized model I designed several controllers: state feedback with pole placement, LQ control method, and I have realized both controllers with state observers. I made offline simulations using these four controllers. During the simulations, I examined how angiogenic inhibitor, working point and saturation effect the control and I also changed the parameters of the controllers. The controls were evaluated for three metrics: total value of administered inhibitor during the simulation, steady-state serum inhibitor level at the end of the simulation and steady-state tumor volume at the end of the simulation, considering the optimal time required to reach a minimal tumor volume. The scope of the work was to investigate how optimal solution can be obtained on the trade-off of optimal therapy and optimal time required to reach a minimal tumor volume.

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