Modeling and computation for unsteady blood flow and solute concentration in a constricted porous artery

Daniel N. Riahi; Saulo Orizaga; Daniel N. Riahi; Saulo Orizaga

doi:10.3934/bioeng.2023007

AIMS Bioengineering

2023, Volume 10, Issue 1: 67-88. doi: 10.3934/bioeng.2023007

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Research article

Modeling and computation for unsteady blood flow and solute concentration in a constricted porous artery

Daniel N. Riahi ^1,2,
Saulo Orizaga ^{3
,
,}

1.
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, 61801, IL
2.
School of Mathematical & Statistical Sciences, University of Texas Rio Grande Valley, Brownsville, 78520, Texas
3.
Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, 87801, New Mexico

Received: 20 November 2022 Revised: 23 February 2023 Accepted: 24 February 2023 Published: 07 March 2023

We investigated a physical system for unsteady blood flow and solute transport in a section of a constricted porous artery. The aim of this study was to determine effects of hematocrit, stenosis, pulse oscillation, diffusion, convection and chemical reaction on the solute transport. The significance of this study was uncovering combined roles played by stenosis height, hematocrit, pulse oscillation period, reactive rate, blood speed, blood pressure force and radial and axial extent of the porous artery on the solute transported by the blood flow in the described porous artery. We used both analytical and computational methods to determine blood flow quantities and solute transport for different parametric values of the described physical system. We found that solute transport increases with increasing stenosis height, blood pulsation period, convection and blood pressure force. However, transportation of solute reduces with increasing hematocrit, chemical reactive rate and radial or axial distance.
- constricted artery,
- porous medium,
- blood flow,
- solute concentration,
- stenosis
Citation: Daniel N. Riahi, Saulo Orizaga. Modeling and computation for unsteady blood flow and solute concentration in a constricted porous artery[J]. AIMS Bioengineering, 2023, 10(1): 67-88. doi: 10.3934/bioeng.2023007

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Abstract

We investigated a physical system for unsteady blood flow and solute transport in a section of a constricted porous artery. The aim of this study was to determine effects of hematocrit, stenosis, pulse oscillation, diffusion, convection and chemical reaction on the solute transport. The significance of this study was uncovering combined roles played by stenosis height, hematocrit, pulse oscillation period, reactive rate, blood speed, blood pressure force and radial and axial extent of the porous artery on the solute transported by the blood flow in the described porous artery. We used both analytical and computational methods to determine blood flow quantities and solute transport for different parametric values of the described physical system. We found that solute transport increases with increasing stenosis height, blood pulsation period, convection and blood pressure force. However, transportation of solute reduces with increasing hematocrit, chemical reactive rate and radial or axial distance.

Abbreviations

L₀

length of damaged stenotic region

location of stenosis

r, z

radial and axial coordinates, respectively

R(z)

radius of stenotic region

R₀

radius of non-stenotic region

maximum radius of stenotic region

blood velocity vector along the axial direction

blood velocity vector along the radial direction

solute concentration

D₀

diffusivity coefficient

E₀

reaction constant

density

blood pressure

permeability of the porous medium

µ_s

variable blood

dynamic viscosity of the plasma in the blood

maximum hematocrit at the center of cylindrical tube

parameter used for the formula's constriction

small parameter defined as the ratio of R₀ to L₀

F₁

flow resistance

τ_w0

wall shear stress of zeroth order

τ_w1

wall shear stress of 1st order

Acknowledgments

The authors are thankful for reviewers' comments and suggestions for an earlier version of this work that improved the quality of the present paper. S.O. thanks UTRGV for the office space and hospitality during summer of 2022 and winter of 2022.

Conflict of interest

The authors declare no conflict of interest.

Author contributions

The authors contributed equally on the completion of this manuscript.

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