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

Article Contents

2021, Volume 11, Issue 3: 643-652. Doi: 10.3934/mcrf.2021016

This issue Previous Article External polyhedral estimates of reachable sets of discrete-time systems with integral bounds on additive terms Next Article Second order directional shape derivatives of integrals on submanifolds

Modeling the pressure distribution in a spatially averaged cerebral capillary network

1.
Technische Universität München, 81675 Munich, Germany
2.
Far Eastern Federal University, 690950 Vladivostok, Russia
3.
Institute for Applied Mathematics, FEB RAS, 690041 Vladivostok, Russia

^* Corresponding author: Andrey Kovtanyuk
^* Corresponding author: Andrey Kovtanyuk

Received: February 28, 2019

Revised: February 29, 2020

Early access: March 2021

Published: September 2021

The work was supported by the Klaus Tschira Foundation, Buhl-Strohmaier Foundation, and Würth Foundation

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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.

Keywords:

Inverse problem for the Poisson equation,
unique solvability,
cerebral blood flow circulation.

Mathematics Subject Classification: Primary: 58J05; Secondary: 92B05.

Citation:

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Figure 1. Stencil corresponding to the cubic topology

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Figure 2. The pressure distribution

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Figure 3. The absolute velocity distribution

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