Feedback Control of Impaired Cerebral Autoregulation in Preterm Infants: Mathematical Modelling

Impaired cerebral autoregulation is often the cause of cerebral hemorrhage in preterm infants. The place of cerebral bleeding is most frequently the germinal matrix being a highly vascularized layer of neuronal and glial precursors. A passive, linear, dependency of the cerebral blood flow on the arterial mean pressure leads to damage of fragile blood vessels of the germinal matrix. A mathematical model of impaired cerebral autoregulation is proposed. Feedback controls, which are able to compensate fails of autoregulation, are constructed and their robustness against all unpredictable admissible disturbances is proven using techniques of viability theory.