| Abstract | Modern biology and medicine deal with a wide variety of control and inverse problems. These issues are mostly computational intensive and in general ill-posed inverse problems. We like to showcase solutions and algorithms targeting these ill-posed problems. In this talk we will present a general framework on ordinary differential equations dealing with parameter estimation, numerical control, and design issues in mathematical biology. To illustrate our work we will investigate the glucose metabolism. The glucose metabolism is a tight regulated system providing energy in humans. Dysfunctions of this system may lead to pathologies like diabetes. Establishing mathematical control algorithms is therefore essential in imbalanced glucose metabolisms. Along with the classical Minimal Model we will present a novel glucose model incorporating new findings in the Selfish Brain Theory centering the brain as the main control element. We will demonstrate the potentialitiesof our inverse algorithms on clinical data of a IVGTT (intravenous glucose tolerance test). |
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