With the advancement of computer power, computational solution is considered as a useful predictive tool for study of the blood flow through a diseased artery. The blood flow is governed by the continuity and Navier-Stokes equations. Womersley number and Reynolds number are physiologically important non-dimensional flow parameters and have existence in the non-dimensional governing equations. In the computational solution, the mathematical flow modelled is established considering some boundary conditions, and then it is solved by numerical simulations. The governing equations are converted to discretised form and then solved numerically by readily available commercial CFD software and/or by in-house developed CFD code using appropriate algorithms. Grid independence test and validation of CFD model are the crucial parts of computational solutions. The chapter delivers the knowledge on impact of fluid mechanics on arterial diseases and computational solution techniques.
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Motivation on blood flow study through the diseased artery and to write a book chapter is felt by the need in obtaining a better understanding of the influence of flow phenomena on initialization, progression, and formation of atherosclerosis. It is hoped that such type of chapter may provide the comparative necessary information to achieve the basic fluid mechanical phenomena in the arterial circulation system. This chapter helps to enhance the knowledge of hemodynamics reference to cardiovascular response, which may help to design of prosthetic devices rationally. With the increasing performances of computer hardware and software, at present days, a computational study is being increasingly used in biomedical research of diseased arteries. Understanding flow dynamics and flow disorders due to flow restriction called stenosis is essential to study yet now numerically and experimentally. The disease is due to the formation of stenosis commonly called atherosclerosis. It is a complex problem as the artery is elliptical, elastic, porous; the shape of the stenosis is asymmetrical; inlet flow is pulsatile, blood is non-Newtonian and heterogeneous, blood property varies concerning human beings. This study of flow dynamics and hemodynamics parameters may be solved by CFD (due to the invention of commercial software) by using high-speed computer.
Last few decades, researchers are working on this area numerically or experimentally. Among them, Zendehbudi and Moayeri have compared the velocity distributions, streamline contours and wall shear stresses for physiological flow and pulsatile flow through an axisymmetrical constricted (61% area) artery. (Zendehbudi & Moayeri, 1999) They have performed the relevant numerical computations considering the blood as Newtonian and laminar flow. The constitutive equations have been solved by using the SIMPLER (Semi-Implicit Method for Pressure Linked Equations Revised) algorithm (Patankar, 1980). Apart from that, they have also discussed the pressure drop across 56% area reduction (PR=33.33) of the cosine-shaped restriction with for steady flow with Reynolds number varying from 50 to 250 to validate their results with the earlier experimental observation (Young & Tsai, 1973), which was found to be having good agreement. Lee and Xu have analysed the flow behaviour of pulsatile flow through trapezoidal-shaped (45% restriction by area) considering the fluid to be incompressible and Newtonian. (Lee & Xu, 2002) They have used two separate commercial codes CFX 4.2 and ABAQUS7 for the analysis. They have investigated velocity profiles, wall shear stress for the rigid and compliant tube. From their wall shear stress representation, it is obvious that the wall shear stress (WSS) curves for the rigid and compliant tube are identical. Pressure and flow separation is investigated numerically for different shaped restrictions (Mandal & Chakraborty, 2007a, 2007b, 2007c).
Reynolds-averaged Navier-Stokes approach is used for modelling of pulsatile and turbulent flow by Varghese and Frankel (2003) in stenotic vessels. CFD, Ansys FLUENT has been used and it has been has noted that the minimum wall shear stress occurs at distal to the stenosis. The effect of symmetrical and asymmetrical bell-shaped stenosis has been investigated numerically on haemodynamic parameters for the progression of the disease in steady and pulsatile situations. (Mandal et al., 2010b, 2011) This study revealed that asymmetrical-shaped stenosis predicts higher impact on flow characteristics as observed from their study. Two-dimensional rigid models by assuming unsteady, incompressible, and homogeneous blood flow with double stenosis is also solved numerically (Rabby et al., 2014), where cosine-shaped stenosis, inlet sinusoidal pulsatile laminar flow conditions has been chosen. The effect of stricture length of stenosis and its flow circulation is studied numerically and it has been found that restriction is the main component of disease progression. (Mandal & Chakraborty, 2008, 2009)