Modeling the pressure distribution in a spatially averaged cerebral capillary network

Andrey Kovtanyuk; Alexander Chebotarev; Nikolai Botkin; Varvara Turova; Irina Sidorenko; Renée Lampe

doi:10.3934/MCRF.2021016

Modeling the pressure distribution in a spatially averaged cerebral capillary network

Andrey Kovtanyuk, Alexander Chebotarev, Nikolai Botkin, Varvara Turova, Irina Sidorenko, Renée Lampe

Associate Professorship of Paediatric Neuroorthopaedics, Main Research: Cerebral Palsy

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

A boundary value problem for the Poisson’s equation with unknown intensities of sources is studied in context of mathematical modeling the pressure distribution in cerebral capillary networks. The problem is formulated as an inverse problem with finite-dimensional overdetermination. The unique solvability of the problem is proven. A numerical algorithm is proposed and implemented.

Original language	English
Pages (from-to)	643-652
Number of pages	10
Journal	Mathematical Control and Related Fields
Volume	11
Issue number	3
DOIs	https://doi.org/10.3934/MCRF.2021016
State	Published - Sep 2021

Keywords

Cerebral blood flow circulation
Inverse problem for the Poisson equation
Unique solvability

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10.3934/MCRF.2021016

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abstract = "A boundary value problem for the Poisson{\textquoteright}s equation with unknown intensities of sources is studied in context of mathematical modeling the pressure distribution in cerebral capillary networks. The problem is formulated as an inverse problem with finite-dimensional overdetermination. The unique solvability of the problem is proven. A numerical algorithm is proposed and implemented.",

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AU - Botkin, Nikolai

AU - Turova, Varvara

AU - Sidorenko, Irina

AU - Lampe, Renée

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AB - A boundary value problem for the Poisson’s equation with unknown intensities of sources is studied in context of mathematical modeling the pressure distribution in cerebral capillary networks. The problem is formulated as an inverse problem with finite-dimensional overdetermination. The unique solvability of the problem is proven. A numerical algorithm is proposed and implemented.

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KW - Inverse problem for the Poisson equation

KW - Unique solvability

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Modeling the pressure distribution in a spatially averaged cerebral capillary network

Abstract

Keywords

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