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Theoretical Study of Atherosclerosis in Coronary Arteries

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Identification of the vulnerable plaque, at high risk for rupturing, is the critical issue in the diseased coronary arteries. Despite the fact that imaging of coronary arteries has been enormously progressed during recent decades, it cannot yet definitively determine the risk of the disease inside the coronary arteries. Existing of a realistic, precise, and applicable biomechanical model contributing to prevent the imposed irreversible damages stemming from high-risk arteries would be a precious asset. 

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There are many studies from different disciplines including medicine and engineering on the biomechanics of atherosclerotic coronary arteries both theoretically and experimentally. The focus of experimental efforts including both in-vivo and in-vitro studies was on either imaging or extracting mechanical properties. The second group of the literature is concerned with theoretical and numerical modelling of the atherosclerotic coronary arteries. In the theoretical investigations, to date, the structure (plaque and artery), the fluid, and the fluid-structure interaction model have been studied independently.

In the case of structural analyses, which is based on the finite element method (FEM), the main focus of studies are on the effect of morphology parameters of the diseased coronary artery on the initiation of plaque rupture [2-10]. Although most of these studies provide valuable information to develop biomechanical models, they are mostly limited to the straight or cylindrical arteries and also they did not appropriately incorporate the effect of fluid part. Meanwhile, some researchers focused on the hemodynamic conditions of blood to predict vessel inflammation and atherosclerosis initiation/progression. 

Two and three-dimensional modelling is employed to investigate blood role as an important part of arteries in the plaque rupture, progression and establishing of thrombus. None of these studies are able to simulate atherosclerosis precisely. Purely fluid based analyses were mainly conducted through CFD, and they mostly considered the structural part as a rigid body. Due to the complexity of the problem resulting from the nonlinear geometry and material properties as well as different forces and boundary conditions exerted on the plaque it is vital to consider both the solid and fluid parts of the coronary arteries and their interactions as well. 

In the primary studies the solid material has been considered hyper-elastic homogenous and isotropic and the fluid characteristics were defined as Newtonian, laminar, viscous, and incompressible, and a 3D FSI model has been solved for thick and thin arterial walls. Other factors such as nonlinear time-dependent fluid model microcalcification, and pulsatile flow have also been taken into account in the literature for 2D and 3D analyses. None of the previous studies modelled the plaque considering all the effective factors combined. Gholipour are believed to be the first researchers that have developed a 3-D biomechanics model incorporating various parameters. In their studies more realistic model compared with previous studies have been investigated. However, a complete model is yet to be developed which can reliably predict different types of failures. 

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