An iterative algorithm for solving an initial boundary value problem of oxygen transport in brain

Andrey E. Kovtanyuk; Alexander Yu Chebotarev; Anastasiya A. Dekalchuk; Nikolai D. Botkin; Renee Lampe

doi:10.1109/DD46733.2019.9016443

An iterative algorithm for solving an initial boundary value problem of oxygen transport in brain

Andrey E. Kovtanyuk, Alexander Yu Chebotarev, Anastasiya A. Dekalchuk, Nikolai D. Botkin, Renee Lampe

Associate Professorship of Paediatric Neuroorthopaedics, Main Research: Cerebral Palsy

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

A non-stationary model of oxygen transport in brain is studied. The model comprises two coupled, non-linear partial differential equations describing the oxygen concentration in the blood and tissue phases. Thus, the model is the so-called continuum one, where the blood and tissue fractions occupy the same spatial domain. A priori estimates of solutions are obtained, and an iterative procedure for finding them is proposed. The convergence of this method to a unique weak solution of the problem is proven. A numerical example illustrates the theoretical analysis.

Original language	English
Title of host publication	Proceedings of the International Conference on Days on Diffraction 2019, DD 2019
Editors	Oleg V. Motygin, Aleksei P. Kiselev, Leonid I. Goray, A.A. Fedotov, A.Ya. Kazakov, Anna S. Kirpichnikova
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	99-104
Number of pages	6
ISBN (Electronic)	9781728158372
DOIs	https://doi.org/10.1109/DD46733.2019.9016443
State	Published - Jun 2019
Event	2019 International Conference on Days on Diffraction, DD 2019 - St. Petersburg, Russian Federation Duration: 3 Jun 2019 → 7 Jun 2019

Publication series

Name	Proceedings of the International Conference on Days on Diffraction 2019, DD 2019

Conference

Conference	2019 International Conference on Days on Diffraction, DD 2019
Country/Territory	Russian Federation
City	St. Petersburg
Period	3/06/19 → 7/06/19

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10.1109/DD46733.2019.9016443

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Kovtanyuk, A. E., Chebotarev, A. Y., Dekalchuk, A. A., Botkin, N. D., & Lampe, R. (2019). An iterative algorithm for solving an initial boundary value problem of oxygen transport in brain. In O. V. Motygin, A. P. Kiselev, L. I. Goray, A. A. Fedotov, A. Y. Kazakov, & A. S. Kirpichnikova (Eds.), Proceedings of the International Conference on Days on Diffraction 2019, DD 2019 (pp. 99-104). Article 9016443 (Proceedings of the International Conference on Days on Diffraction 2019, DD 2019). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/DD46733.2019.9016443

Kovtanyuk, Andrey E. ; Chebotarev, Alexander Yu ; Dekalchuk, Anastasiya A. et al. / An iterative algorithm for solving an initial boundary value problem of oxygen transport in brain. Proceedings of the International Conference on Days on Diffraction 2019, DD 2019. editor / Oleg V. Motygin ; Aleksei P. Kiselev ; Leonid I. Goray ; A.A. Fedotov ; A.Ya. Kazakov ; Anna S. Kirpichnikova. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 99-104 (Proceedings of the International Conference on Days on Diffraction 2019, DD 2019).

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title = "An iterative algorithm for solving an initial boundary value problem of oxygen transport in brain",

abstract = "A non-stationary model of oxygen transport in brain is studied. The model comprises two coupled, non-linear partial differential equations describing the oxygen concentration in the blood and tissue phases. Thus, the model is the so-called continuum one, where the blood and tissue fractions occupy the same spatial domain. A priori estimates of solutions are obtained, and an iterative procedure for finding them is proposed. The convergence of this method to a unique weak solution of the problem is proven. A numerical example illustrates the theoretical analysis.",

author = "Kovtanyuk, {Andrey E.} and Chebotarev, {Alexander Yu} and Dekalchuk, {Anastasiya A.} and Botkin, {Nikolai D.} and Renee Lampe",

note = "Publisher Copyright: {\textcopyright} 2019 IEEE.; 2019 International Conference on Days on Diffraction, DD 2019 ; Conference date: 03-06-2019 Through 07-06-2019",

year = "2019",

month = jun,

doi = "10.1109/DD46733.2019.9016443",

language = "English",

series = "Proceedings of the International Conference on Days on Diffraction 2019, DD 2019",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "99--104",

editor = "Motygin, {Oleg V.} and Kiselev, {Aleksei P.} and Goray, {Leonid I.} and A.A. Fedotov and A.Ya. Kazakov and Kirpichnikova, {Anna S.}",

booktitle = "Proceedings of the International Conference on Days on Diffraction 2019, DD 2019",

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Kovtanyuk, AE, Chebotarev, AY, Dekalchuk, AA, Botkin, ND & Lampe, R 2019, An iterative algorithm for solving an initial boundary value problem of oxygen transport in brain. in OV Motygin, AP Kiselev, LI Goray, AA Fedotov, AY Kazakov & AS Kirpichnikova (eds), Proceedings of the International Conference on Days on Diffraction 2019, DD 2019., 9016443, Proceedings of the International Conference on Days on Diffraction 2019, DD 2019, Institute of Electrical and Electronics Engineers Inc., pp. 99-104, 2019 International Conference on Days on Diffraction, DD 2019, St. Petersburg, Russian Federation, 3/06/19. https://doi.org/10.1109/DD46733.2019.9016443

An iterative algorithm for solving an initial boundary value problem of oxygen transport in brain. / Kovtanyuk, Andrey E.; Chebotarev, Alexander Yu; Dekalchuk, Anastasiya A. et al.
Proceedings of the International Conference on Days on Diffraction 2019, DD 2019. ed. / Oleg V. Motygin; Aleksei P. Kiselev; Leonid I. Goray; A.A. Fedotov; A.Ya. Kazakov; Anna S. Kirpichnikova. Institute of Electrical and Electronics Engineers Inc., 2019. p. 99-104 9016443 (Proceedings of the International Conference on Days on Diffraction 2019, DD 2019).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Botkin, Nikolai D.

AU - Lampe, Renee

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AB - A non-stationary model of oxygen transport in brain is studied. The model comprises two coupled, non-linear partial differential equations describing the oxygen concentration in the blood and tissue phases. Thus, the model is the so-called continuum one, where the blood and tissue fractions occupy the same spatial domain. A priori estimates of solutions are obtained, and an iterative procedure for finding them is proposed. The convergence of this method to a unique weak solution of the problem is proven. A numerical example illustrates the theoretical analysis.

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A2 - Kiselev, Aleksei P.

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Kovtanyuk AE, Chebotarev AY, Dekalchuk AA, Botkin ND, Lampe R. An iterative algorithm for solving an initial boundary value problem of oxygen transport in brain. In Motygin OV, Kiselev AP, Goray LI, Fedotov AA, Kazakov AY, Kirpichnikova AS, editors, Proceedings of the International Conference on Days on Diffraction 2019, DD 2019. Institute of Electrical and Electronics Engineers Inc. 2019. p. 99-104. 9016443. (Proceedings of the International Conference on Days on Diffraction 2019, DD 2019). doi: 10.1109/DD46733.2019.9016443

An iterative algorithm for solving an initial boundary value problem of oxygen transport in brain

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