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Model-based medical decision support in terms of computer simulations, predictions and optimization gains increasing importance in health care systems worldwide. This work deals with the control of the glucose balance in intensive care unit (ICU) patients providing nutrition and insulin. The basis of the investigations is the bio-medical model GlucoSafe by Pielmeier et al. (Comput. Methods Programs Biomed. 97(3):211-222, 2010) that describes the temporal evolution of the blood glucose and insulin concentrations in the human body by help of a nonlinear dynamic system of first-order ordinary differential equations. This paper aims at the theoretical analysis and numerical treatment of the arising optimal control problem. Numerical results demonstrate the controllability and applicability of the model, in particular critical hyper-and hypoglycemic initial states are considered.

Studying the heat exchange of small, slender objects in a surrounding flow, we approximate the impact of extended heat sources by Dirac-distributions (point sources) with appropriate amplitudes in the context of slender-body theory. The proposed model for the source strength functions is deduced from analytical considerations (Green's functions) of the stationary two-dimensional heat equation. Numerical simulations show the L2-approximation quality of the strategy

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