Modeling Autoregulation of Cerebral Blood Flow Using Viability Approach

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.