Continuum model of oxygen transport in brain

Kovtanyuk, Andrey E.; Chebotarëv, A. Yu.; Botkin, Nikolai D.; Turova, Varvara; Sidorenko, Irina; Lampe, Renée

doi:10.1016/j.jmaa.2019.02.020

Cited by 11 publications

(14 citation statements)

References 15 publications

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“…Following (Su, 2011;Kovtanyuk et. al., 2018;Kovtanyuk et. al., 2019), oxygen transport can be described by the following coupled equations:…”

Section: Problem Formulationmentioning

confidence: 99%

“…An iterative numerical procedure for finding solutions is proposed, along with the proof of its convergence. In (Kovtanyuk et. al., 2019), the investigation of the steady-state continuum model was continued, the existence and uniqueness of solutions for the boundary-value problem were established, and numerical examples illustrated the theoretical analysis were presented.…”

Section: Introductionmentioning

confidence: 99%

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The 32nd International Conference of the Jangjeon Mathematical Society, 17–21 July, 2019, Far Eastern Federal University, Vladivostok, Russia : abstracts

2019

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The study of the properties of analytical, social and economic networks marked the beginning of the study of complex networks in general. Typical studies of the network, the models of which are graphs, answered questions of centering and connectivity, finding the shortest paths, cycles or trees, minimal covers, or maximal matching. As one or another peak, an economic agent or person in the network in question is connected with another peak, an economic agent or another person, which or who of them has the most connections with others. The term "complex networks" appeared at the beginning of this century and refers to networks with a more complex architecture than classical networks with a given number of nodes and connections. Usually in such networks it is communications that largely determine their properties.

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“…Following (Su, 2011;Kovtanyuk et. al., 2018;Kovtanyuk et. al., 2019), oxygen transport can be described by the following coupled equations:…”

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The 32nd International Conference of the Jangjeon Mathematical Society, 17–21 July, 2019, Far Eastern Federal University, Vladivostok, Russia : abstracts

2019

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“…In the resulting model, the same spatial domain stands for blood and tissue fractions. A similar ansatz is used in [ 10 , 11 , 13 , 14 ], where continuum models governed by coupled partial differential equations are studied. In [ 10 , 11 ], numerical simulations of a nonstationary continuum model were performed in case of simple domains, and the comparison of results with those obtained for the original (nonhomogenized) model is done.…”

Section: Introductionmentioning

confidence: 99%

“…An iterative numerical procedure for finding solutions is proposed, along with the proof of its convergence. In [ 14 ], the investigation of steady-state continuum models is continued, the existence and uniqueness of solutions for the boundary-value problem are established, and numerical examples that illustrate the theoretical analysis are computed.…”

Section: Introductionmentioning

confidence: 99%

“…Despite the intensive numerical simulations of continuum models of oxygen transport, mathematical analysis of underlying partial differential equations is seldom addressed. The exception is a theoretical analysis of steady-state models considered in [ 13 , 14 ]. As for nonstationary models, theoretical issues related to the existence and uniqueness of solutions for underlying initial-boundary value problems are still open.…”

Section: Introductionmentioning

confidence: 99%

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Nonstationary Model of Oxygen Transport in Brain Tissue

Kovtanyuk

Chebotarëv

Botkin

et al. 2020

Computational and Mathematical Methods in Medicine

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The paper addresses the mathematical study of a nonstationary continuum model describing oxygen propagation in cerebral substance. The model allows to estimate the rate of oxygen saturation and stabilization of oxygen concentration in relatively large parts of cerebral tissue. A theoretical and numerical analysis of the model is performed. The unique solvability of the underlying initial-boundary value problem for a system of coupled nonlinear parabolic equations is proved. In the numerical experiment, the tissue oxygen saturation after hypoxia is analyzed for the case when a sufficient amount of oxygen begins to flow into the capillary network. A fast stabilization of the tissue oxygen concentration is demonstrated. The reliability of the results of the numerical simulation is discussed.

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