# A one dimensional model of blood flow through a curvilinear artery

F. Berntsson, A. Ghosh, V. A. Kozlov, S. A. Nazarov

Research output: Contribution to journalArticleResearchpeer-review

### Abstract

We present a one-dimensional model describing the blood flow through a moderately curved and elastic blood vessel. We use an existing two dimensional model of the vessel wall along with Navier−Stokes equations to model the flow through the channel while taking factors, namely, surrounding muscle tissue and presence of external forces other than gravity into account. Our model is obtained via a dimension reduction procedure based on the assumption of thinness of the vessel relative to its length. Results of numerical simulations are presented to highlight the influence of different factors on the blood flow.

Original language English 633-643 11 Applied Mathematical Modelling 63 https://doi.org/10.1016/j.apm.2018.07.019 Published - 1 Nov 2018

### Keywords

• Asymptotic analysis
• Blood flow
• Curvilinear vessel
• Dimension reduction
• Numerical simulation

### Scopus subject areas

• Modelling and Simulation
• Applied Mathematics

### Cite this

Berntsson, F. ; Ghosh, A. ; Kozlov, V. A. ; Nazarov, S. A. / A one dimensional model of blood flow through a curvilinear artery. In: Applied Mathematical Modelling. 2018 ; Vol. 63. pp. 633-643.
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A one dimensional model of blood flow through a curvilinear artery. / Berntsson, F.; Ghosh, A.; Kozlov, V. A.; Nazarov, S. A.

In: Applied Mathematical Modelling, Vol. 63, 01.11.2018, p. 633-643.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - A one dimensional model of blood flow through a curvilinear artery

AU - Berntsson, F.

AU - Ghosh, A.

AU - Kozlov, V. A.

AU - Nazarov, S. A.

PY - 2018/11/1

Y1 - 2018/11/1

N2 - We present a one-dimensional model describing the blood flow through a moderately curved and elastic blood vessel. We use an existing two dimensional model of the vessel wall along with Navier−Stokes equations to model the flow through the channel while taking factors, namely, surrounding muscle tissue and presence of external forces other than gravity into account. Our model is obtained via a dimension reduction procedure based on the assumption of thinness of the vessel relative to its length. Results of numerical simulations are presented to highlight the influence of different factors on the blood flow.

AB - We present a one-dimensional model describing the blood flow through a moderately curved and elastic blood vessel. We use an existing two dimensional model of the vessel wall along with Navier−Stokes equations to model the flow through the channel while taking factors, namely, surrounding muscle tissue and presence of external forces other than gravity into account. Our model is obtained via a dimension reduction procedure based on the assumption of thinness of the vessel relative to its length. Results of numerical simulations are presented to highlight the influence of different factors on the blood flow.

KW - Asymptotic analysis

KW - Blood flow

KW - Curvilinear vessel

KW - Dimension reduction

KW - Numerical simulation

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