FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
Modeling and simulation of cerebral blood flow autoregulation considered as an output regulation control problem |
A.E. Golubev |
2022, issue 2, P. 170-175 DOI: https://doi.org/10.47910/FEMJ202220 |
Abstract |
| A mathematical model of cerebral blood flow in the form of a system of nonlinear ordinary differential equations is studied. The cerebral blood flow autoregulation modeling problem is formulated as an output regulation automatic control problem. The nonlinear dynamics inversion based approach is applied to reveal the controllability properties of the model and construct the feedback control laws which describe mathematics behind the cerebrovascular autoregulation mechanism. |
Keywords: intracranial hemodynamics, cerebral autoregulation, nonlinear control, dynamics inversion, output regulation |
Download the article (PDF-file) |
References |
| [1] M. Ursino, C. A. Lodi, “A simple mathematical model of the interaction between intracranial pressure and cerebral hemodynamics", J. Appl. Physiol., 82, (1997), 1256-1269. [2] R. Lampe, N. Botkin, V. Turova, T. Blumenstein, A. Alves-Pinto, “Mathematical modeling of cerebral blood circulation and cerebral autoregulation: towards preventing intracranial hemorrhages in preterm newborns", Comp. Math. Meth. Med., 2014, (2014), 965275. [3] N. D. Botkin, A. E. Kovtanyuk, V. L. Turova, I. N. Sidorenko, R. Lampe, “Direct modeling of blood ow through the vascular network of the germinal matrix", Comput. Biol. Med., 92, (2018), 147-155. [4] A. Golubev, A. Kovtanyuk, R. Lampe, “Modeling of cerebral blood flow autoregulation using mathematical control theory", Mathematics, 10, (2022), 2060. [5] A. Isidori, Nonlinear control systems. 3rd edition. Springer-Verlag, 1995. [6] L. Rangel-Castilla, S. Gopinath, C. S. Robertson, “Management of intracranial hypertension", Neurol. clin., 26, (2008), 521-541. [7] A. E. Golubev, “Construction of programmed motions of constrained mechanical systems using third-order polynomials", J. Comput. Syst. Sci. Int., 60, (2021), 303-314. |