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Mathematical modelling plays a key role in modern medicine and the life sciences. Many physiological phenomena are very difficult to measure even in experimentally controllable situations. Thus mathematical modelling is often the only way to assess underlying mechanisms of complex biological systems. This text presents an elaborate deterministic model of the human cardiovascular system to simulate the effects of gravitationally induced hypovolemia, i.e. orthostatic stress, on the human body. Many clinical conditions arise from impaired physiological responses to this stress, e.g. orthostatic intolerance or postural orthostatic tachycardia syndrome. Hence a deeper understanding of the involved control mechanisms based on mathematical modelling is clinically relevant. Three control formulations representing popular techniques currently used in physiological modeling are investigated in the text: a straightforward differential equation using the arc tangent simulating basic correlations, a differential set point equation modelling not only saturation but also time decays, and an optimal control approach based on considerations coming from cybernetics.

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Stefan Fürtinger, Mag.: Study of Numerical Mathematics and Modeling at the Institute for Mathematics and Scientific Computing, Karl--Franzens--University--Graz, Austria. PhD-position in the field of mathematical image processing at the Karl--Franzens--University--Graz, Austria.

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