School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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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


© 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (

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Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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AIMS Biophysics



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Mathematics Commons



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