Modeling of Cerebral Blood Flow Autoregulation Using Mathematical Control Theory

Alexey Golubev, Andrey Kovtanyuk and Renée Lampe
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Alexey Golubev: Ishlinsky Institute for Problems in Mechanics RAS, Vernadskogo Av. 101(1), 119526 Moscow, Russia
Andrey Kovtanyuk: Fakultät für Mathematik, Technische Universität München, Boltzmannstr. 3, 85747 Garching bei München, Germany
Renée Lampe: Klinikum Rechts der Isar, Technische Universität München, Ismaningerstr. 22, 81675 München, Germany

Mathematics, 2022, vol. 10, issue 12, 1-14

Abstract: A mathematical model of cerebral blood flow in the form of a dynamical system is studied. The cerebral blood flow autoregulation modeling problem is treated as a nonlinear control problem and the potential and applicability of the nonlinear control theory techniques are analyzed in this respect. It is shown that the cerebral hemodynamics model in question is differentially flat. Then, the integrator backstepping approach combined with barrier Lyapunov functions is applied to construct the control laws that recover the cerebral autoregulation performance of a healthy human. Simulation results confirm the good performance and flexibility of the suggested cerebral blood flow autoregulation design. The conducted research should enrich our understanding of the mathematics behind the cerebral blood flow autoregulation mechanisms and medical treatments to compensate for impaired cerebral autoregulation, e.g., in preterm infants.

Keywords: intracranial hemodynamics; cerebral autoregulation; biomechanical system; nonlinear dynamics; nonlinear control; differential flatness; output tracking; integrator backstepping (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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