Cerebral autoregulation is the ability to keep almost constant cerebral blood flow (CBF) for some range of changing the mean arterial pressure (MAP). In preterm infants, this range is usually very small, even absent, and a passive (linear) dependence of CBF on MAP is observed. Also, variations of the partial CO2 pressure and intracranial/venous pressure result in fluctuations of CBF. The absence of cerebral autoregulation may be a cause of intracranial hemorrhages due to instability of cerebral blood vessels, especially in the so-called germinal matrix which exists in a developing brain from 22 to 32 weeks of gestation. In the current paper, a mathematical model of impaired cerebral autoregulation is extended compared with previous works of the authors, and a heuristic feedback control that is able to keep deviations from a nominal CBF within a reasonable range is proposed. Viability theory is used to prove that this control can successfully work against a wide range of disturbances.
Keywords: Cerebral autoregulation; discriminating kernel; feedback control; grid method; leadership kernel; viability set.