On modeling arterial blood flow with or without solute transport and in presence of atherosclerosis

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

doi:10.3934/biophy.2024005

AIMS Biophysics

2024, Volume 11, Issue 1: 66-84. doi: 10.3934/biophy.2024005

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On modeling arterial blood flow with or without solute transport and in presence of atherosclerosis

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

1.
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801; d-riahi@illinois.edu
2.
School of Mathematical & Statistical Sciences, University of Texas Rio Grande Valley, Brownsville, Texas 78520; riahid@oal.com
3.
Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM 87801

Received: 16 November 2023 Revised: 08 January 2024 Accepted: 15 January 2024 Published: 30 January 2024

In this article, we review previous studies of modeling problems for blood flow with or without transport of a solute in a section of arterial blood flow and in the presence of atherosclerosis. Moreover, we review problems of bio-fluid dynamics within the field of biophysics. In most modeling cases, the presence of red blood cells in the plasma is taken into account either by using a two-phase flow approach, where blood plasma is considered as one phase and red blood cells are counted as another phase, or by using a variable viscosity formula that accounts for the amount of hematocrit within the blood. Both analytical and computational methods were implemented to solve the governing equations for blood flow in the presence of solute transport, which, depending on the type of the investigated problem, could contain momentum, mass conservation, and solute concentration, which were mostly subjected to reasonable approximations. The form of atherosclerosis implemented in the modeling system either was either based on the experimental data for an actual human or was due to a reasonable mathematical modeling for both steady and unsteady atherosclerosis cases. For the wall of the artery itself, which is elastic in nature, modeling equations for the displacement of the artery wall has previously been used, even though their effects on the blood flow inside the artery were shown to be rather small. In some cases, thermal effects were also taken into account by including a temperature equation in the investigation. In the case of the presence of solutes in the blood, various blood flow parameters such as blood pressure force, blood speed, and solute transport were mostly determined or approximated for different values of the parameters that could represent hematocrit, solute diffusion, atherosclerosis height, solute reaction, and pulse frequency. In some studies, available experimental results and data were used in the modeling system that resulted in a more realistic outcome for the blood flow parameters, such as blood pressure force and blood flow resistance. Results have been found for variations of blood flow parameters and solute transport when compared to different values of the parameters. Effects that can increase or decrease the blood flow parameters and solute transport in the artery have mostly been determined, with particular applications for further understanding efforts to improve the patients' health care.
- solute concentration,
- blood flow,
- atherosclerosis,
- artery,
- hematocrit
Citation: Daniel N. Riahi, Saulo Orizaga. On modeling arterial blood flow with or without solute transport and in presence of atherosclerosis[J]. AIMS Biophysics, 2024, 11(1): 66-84. doi: 10.3934/biophy.2024005

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Abstract

In this article, we review previous studies of modeling problems for blood flow with or without transport of a solute in a section of arterial blood flow and in the presence of atherosclerosis. Moreover, we review problems of bio-fluid dynamics within the field of biophysics. In most modeling cases, the presence of red blood cells in the plasma is taken into account either by using a two-phase flow approach, where blood plasma is considered as one phase and red blood cells are counted as another phase, or by using a variable viscosity formula that accounts for the amount of hematocrit within the blood. Both analytical and computational methods were implemented to solve the governing equations for blood flow in the presence of solute transport, which, depending on the type of the investigated problem, could contain momentum, mass conservation, and solute concentration, which were mostly subjected to reasonable approximations. The form of atherosclerosis implemented in the modeling system either was either based on the experimental data for an actual human or was due to a reasonable mathematical modeling for both steady and unsteady atherosclerosis cases. For the wall of the artery itself, which is elastic in nature, modeling equations for the displacement of the artery wall has previously been used, even though their effects on the blood flow inside the artery were shown to be rather small. In some cases, thermal effects were also taken into account by including a temperature equation in the investigation. In the case of the presence of solutes in the blood, various blood flow parameters such as blood pressure force, blood speed, and solute transport were mostly determined or approximated for different values of the parameters that could represent hematocrit, solute diffusion, atherosclerosis height, solute reaction, and pulse frequency. In some studies, available experimental results and data were used in the modeling system that resulted in a more realistic outcome for the blood flow parameters, such as blood pressure force and blood flow resistance. Results have been found for variations of blood flow parameters and solute transport when compared to different values of the parameters. Effects that can increase or decrease the blood flow parameters and solute transport in the artery have mostly been determined, with particular applications for further understanding efforts to improve the patients' health care.

Acknowledgments

S.O thanks NMT for the research facilities. S.O also thanks Thomas Witelski (Duke University) for hosting a four-week research visit. D.N.R. Thanks both UTRGV and UIUC for continued support. We thank the SI editors (Dr. Yavuz, and Dr. Usta) for their time and contributions. S.O thanks UTRGV (Dr. Huber, Dr. Villalobos and Elda Leal) for the provided office space during the winter break 2023-2024. The authors also thank the anonymous reviewer who made suggestions that improved the quality of the paper.

Conflict of interest

Authors declare no conflict of interest.

Author contributions

Both authors contributed equally in the preparation and completion of this manuscript.

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