# (193ac) Development of Mathematical Approach to Studying Cholesterol Deposition in the Artery for Different Fluid Models

Authors:
Tennessee Technological University
Tennessee Technological University
Tennessee Technological University
Atherosclerosis is an inflammatory disease that affects major arteries of the vasculature. It is a disease in which plaque builds up inside the arteries, narrowing of the arteries which are called stenosis. Atherosclerosis can lead to serious problems, including heart attack, stroke, or even death. A contributing factor in the growth and development of stenosis is the hydrodynamic point of view of blood where the development of atherosclerosis is often associated with local hemodynamics including shear stress and recirculation zones. There are many computational studies that have been addressed the blood flow behavior in such systems, but the modeling is not straightforward. This is due to the non-Newtonian nature of the blood at shear rates less than 100 s-1 , with the shear-thinning property of viscosity being considered to be the most significant non-Newtonian characteristic of blood.

In this work, the use of a mathematical model to analyze the effect of stenosis development on velocity profile and cholesterol deposition in the artery for different fluid models was explored. The results of this analysis indicated that in addition to the common parameters such as stenosis size, blood flow rate, stenosis height, blood viscosity is the most significant factor which has a substantial effect on the stenosis region. In summary, this work is a step forward towards the development of novel therapeutic and diagnostic approaches for atherosclerosis. An analytical mathematical approach is explained here that allows one to derive formulas for velocity profiles. Two main cases are considered in this research:

•  Newtonian flow

· Non- Newtonian flow based on the Power Law Model, Casson Model, Carreau Model, Walburn-Schneck model.

The analysis involves the solution of the equation of the Navier-Stokes which is coupled with continuity equation. The research proposed here will have a highly beneficial impact on the area of clinical diagnostics and medicine.

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