title: Mathematical modelling of cerebral blood circulation and cerebral autoregulation: towards preventing intracranial hemorrhages in preterm newborns.
abstract: Impaired cerebral autoregulation leads to fluctuations in cerebral blood flow, which can be especially dangerous for immature brain of preterm newborns. In this paper, two mathematical models of cerebral autoregulation are discussed. The first one is an enhancement of a vascular model proposed by Piechnik et al. We extend this model by adding a polynomial dependence of the vascular radius on the arterial blood pressure and adjusting the polynomial coefficients to experimental data to gain the autoregulation behavior. Moreover, the inclusion of a Preisach hysteresis operator, simulating a hysteretic dependence of the cerebral blood flow on the arterial pressure, is tested. The second model couples the blood vessel system model by Piechnik et al. with an ordinary differential equation model of cerebral autoregulation by Ursino and Lodi. An optimal control setting is proposed for a simplified variant of this coupled model. The objective of the control is the maintenance of the autoregulatory function for a wider range of the arterial pressure. The control can be interpreted as the effect of a medicament changing the cerebral blood flow by, for example, dilation of blood vessels. Advanced numerical methods developed by the authors are applied for the numerical treatment of the control problem.
authors.affiliation: Research Unit of Buhl-Strohmaier-Foundation for Children Orthopedics and Cerebral Palsy, Department of Orthopaedics, Clinic "Rechts der Isar", Technische Universität München, 81675 München, Germany.
authors.forename: Renée
authors.identifier: 0000-0002-1016-0249
authors.initials: R
authors.lastname: Lampe
authors.affiliation: Chair of Mathematical Modelling, Center for Mathematics, Technische Universität München, 85748 Garching, Germany.
authors.forename: Nikolai
authors.initials: N
authors.lastname: Botkin
authors.affiliation: Research Unit of Buhl-Strohmaier-Foundation for Children Orthopedics and Cerebral Palsy, Department of Orthopaedics, Clinic "Rechts der Isar", Technische Universität München, 81675 München, Germany.
authors.forename: Varvara
authors.identifier: 0000-0002-6613-3311
authors.initials: V
authors.lastname: Turova
authors.affiliation: Research Unit of Buhl-Strohmaier-Foundation for Children Orthopedics and Cerebral Palsy, Department of Orthopaedics, Clinic "Rechts der Isar", Technische Universität München, 81675 München, Germany.
authors.forename: Tobias
authors.identifier: 0000-0002-6997-5952
authors.initials: T
authors.lastname: Blumenstein
authors.affiliation: Research Unit of Buhl-Strohmaier-Foundation for Children Orthopedics and Cerebral Palsy, Department of Orthopaedics, Clinic "Rechts der Isar", Technische Universität München, 81675 München, Germany.
authors.forename: Ana
authors.initials: A
authors.lastname: Alves-Pinto
mesh_terms: D000465:Algorithms; D001783:Blood Flow Velocity / Q000502:physiology*; D001794:Blood Pressure / Q000502:physiology; D001921:Brain / Q000473:pathology*; D002560:Cerebrovascular Circulation; D003952:Diagnostic Imaging / Q000379:methods; D020342:Finite Element Analysis; D006439:Hemodynamics; D006706:Homeostasis / Q000502:physiology; D006801:Humans; D007231:Infant, Newborn; D007234:Infant, Premature; D020300:Intracranial Hemorrhages / Q000517:prevention & control*; D008962:Models, Theoretical