Abstract
A model of autoregulation of cerebral blood flow is under consideration. The flow is described using a blood vessel network, and blood is considered as a micropolar fluid. Sudden changes in partial pressure of oxygen and carbon dioxide in the arterial blood are considered as disturbances, and medicines dilating or restricting blood vessels are referred as control. A viability approach is applied as follows. An appropriate safety domain (ASD) is chosen in the space of state variables, and the discriminating kernel, the largest subset of ASD, where the state vector can be kept, is computed. Feedback controls forcing the state vector to remain in the discriminating kernel are constructed.
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Acknowledgements
The authors are thankful to Christine Klindt-Schuster (clinic “Rechts der Isar,” Technical University of Munich) for her help with collecting the experimental data. Financial supports of the Klaus Tschira Foundation, Würth Foundation, and Buhl-Strohmaier-Foundation are gratefully acknowledged. Computer resources have been provided by the Gauss Centre for Supercomputing/Leibniz Supercomputing Centre under grant: pr74lu.
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Turova, V., Botkin, N., Alves-Pinto, A., Blumenstein, T., Rieger-Fackeldey, E., Lampe, R. (2017). Modeling Autoregulation of Cerebral Blood Flow Using Viability Approach. In: Apaloo, J., Viscolani, B. (eds) Advances in Dynamic and Mean Field Games. ISDG 2016. Annals of the International Society of Dynamic Games, vol 15. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-70619-1_16
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