Numerical Simulation of Blood Flow through Tortuous and Stenotic Coronary Arteries using Multiphase Approach

Abstract

The cardiovascular pathologies such as atherosclerosis and thrombosis are vascular diseases involving fluid-dynamical, mechanical, and biological factors. In past few years, the study of numerical blood flow dynamic studies within anatomically complex arteries has garnered great interest among cardiologists, clinicians and biomedical engineers. The evolution in computational fluid dynamics (CFD) and high computing performance have helped us to identify the probable arterial regions for the presence of cardiovascular diseases (CVDs) and to understand and predict how this disease may develop. The presence of tortuosity and stenosis in coronary artery (CA) disturbs the local wall shear stress (WSS) which is considered as an influential hemodynamic descriptor (HD) for the growth of atherosclerotic sites. Different WSS based HDs have been formulated over the years to understand the hemodynamic flow conditions as predictors of endothelial wall dysfunction which is precursor for all CVDs. In general, these HDs have been numerically determined using ‘single phase’ approach. In single phase approach, the flow-dependent cell transport and their interactions with the carrier fluid are generally ignored by considering blood as a single phase fluid. In the present work, numerical investigation of two phase blood flow through stenotic and tortuous left coronary arteries (LCAs) was performed using Eulerian multiphase mixture theory model for the modeling of blood flow in multiphase mixture model, plasma is modeled as continuous liquid phase and Red Blood Cells (RBCs) as the dispersed phase. The model of interest is first validated and the results of multiphase and single phase modeling of blood were compared with experiment results in order to evaluate the performance of multiphase mixture model for blood flow. The multiphase mixture theory approach performed better than single phase approach and showed good agreement with the experimental results. With the confidence gained, the mixture theory multiphase approach is then used for pulsatile blood flow simulations through four idealized CA geometries having varying degrees of stenosis (DOS) severities viz., 30, 50, 70, and 85% diameter reduction stenosis and through several tortuous artery models by varying three morphological indices namely,curvature radius (CR), distance between two bends (DBB) and the angle of bend (AoB). The geometric models of both stenosed and tortuous idealized LCAs were designed in the commercial program SolidWorks and the CFD simulations were carried out with the use of commercial program Ansys Fluent (V14.5). The aim of this study was to understand the effect of stenosis and tortuosity in coronary artery hemodynamics. This interaction between artery geometry and flow is examined in two ways; initially by investigating the influence of stenosis severity and tortuosity parameters on various WSS based hemodynamic descriptors and then on RBC concentration. In addition, a detailed hemodynamic study was performed to determine the influence of the stenosis severity and tortuosity on flow and vice versa. In large blood vessels (millimeter to centimeter size) such as in coronary and carotid arteries, the RBCs shear induced migration affects the transport of oxygen to the arterial endothelial cells (ECs). Hence, in this work we also investigated the locations where hydrodynamic diffusion of RBCs occurs and the effects of stenosis severity on shear induced diffusion (SID) of RBCs, concentration distribution and WSS. For the first time, multiphase mixture theory approach along with modified Phillips shearinduced diffusive flux model and coupled with Quemada non-Newtonian viscosity model has been applied to numerically simulate the RBCs macroscopic behavior in four different degrees of stenosis (DOS) geometries viz. 30, 50, 70, and 85%. The capability to describe the blood flow through a stenosed and tortuous artery for varying degrees of stenosis (DOS) severity and tortuosity morphological indices combined with imaging modalities provides the medical practitioners the ability to diagnose the severity of disease with high accuracy in its early stages and the opportunity of treatment before the ailment becomes fatal.