MATHEMATICAL MODELING OF FLOW PROBLEMS IN ARTERIAL SYSTEM

Abstract

Cardiovascular disease is the leading cause of death in both developed and developing countries. Atherosclerosis is the most common manifestation of arterial disease and is characterized by deposits of yellowish plaques containing cholesterol, lipoid material, and lipophages formed within the intima and inner media of arteries. It is well known that, once such obstruction is formed, the blood flow is significantly altered and fluid dynamical factors play an important role as the stenosis continues to develop. In recent years, interest in hemodynamical studies grows since it seems that many cardiovascular diseases are related to the flow conditions in blood vessels. Blood is nonhomogeneous, anisotropic ionic, composite fluid composed of a suspension of many asymmetric, relatively large viscoelastic particles carried in a liquid that contains high molecular weight, asymmetric, ionic that behaves in a complicated way under shear .— type loading. Therefore, blood exhibits non Newtonian, time dependent deformation characteristics that can only be modeled by higher order constitutive equations. Blood flow in artery is commonly affected by the presence of stenosis, external body acceleration and magnetic field. Various surgeries like bypass and stenting are used to restore blood flow in the diseased artery. Restenosis is the major problem after these surgeries, which require repetition of the surgery. Various hemodynamic factors are respo c,sible for the restenosis after bypass surgery and stenting. Drug coated stents are widely used tz prevent restenosis. Clinician would like to obtain the uniform diffusion of drug from the coating on stent to artery wall. Experimentations on human body are not possible to find out the factors involved in the development of stenosis and restenosis in the artery. The thesis entitled Mathematical modeling of flow problems in arterial system deals with some problems related to blood flow in artery. Numerical solutions are obtained using finite difference method. Commercial CFD software- Fluent is used to solve the governing equations of flow in the arterial bypass model. The whole work is presented in the form of six chapters, as follows: Chapter 1 is introductory in nature ano gives a brief account for arterial system, diseases, blood flow, heat and mass transfer process, its mathematical formulation and numerical solution in the arterial system. At the "ond of the chapter, summary of the whole work embodied in the thesis is given. In chapter 2, the effect of tapering, non-Newtonian rehology, time dependent stenosis and external periodic body acceleration on the blood flow in artery has been analyzed numerically. In many situations of day to day life while travelling or driving in vehicles, in water ships, in airplanes and fast body movements in sports activities, the human body is often subjected to body accelerations or vibrations. The study is beneficial for analyzing the blood flow during such exposure. Results show that blood flow is strongly affected by the presence of stenosis, tapering and the periodic body acceleration. In chapter 3, effects of externally applied magnetic field on the blood flow in the multi-stenosed artery is studied. It is assumed th tt arterial segment to be rigid circular tube with multiple stenosis and the blood flowing through it is non-Newtonian characterized by generalized power law model. It is found that the :nagnetic field modifies the flow patterns in the stenotic artery. The results obtained from the study are useful to predict the changes in the blood flow during MRI and insertion of magnetic catheter in the diseased artery. In chapter 4, a numerical study is conducted to determine the influence of pulsatile blood flow and heat transfer on temperature distribution in the stenotic artery. The unsteady non-linear Navier-Stokes equations of motion governing blood flow and the heat flow equations coupled with the velocity field along with the suitable initial and boundary . conditions are solved by explicit finite difference scheme. The study is beneficial for analyzing the behaviour of temperature distribution inside artery during hyperthermia and cryosurgery. In chapter 5, a mathematical model has been developed to study the transport of drug from the drug coated stent to artery wall. Numerical simulation is used to study the effect of porosity, topcoat, diffusivity of drug in polymer coating and media layer of artery wall in the concentration of drug in polymer and media layer. Media layer of artery wall is assumed to be consisting of cell phase and extracellular fluid. It is observed that use of permeable membrane at the interface of polymer and media layer slows down drug diffusion process to get long term effects. In chapter 6, computational models have been developed for the blood flow,in arterial bypass surgery. The purpose of this study was to quantify the distribution of velocity and wall shear stress distribution in a stenosed artery with bypass graft. Blood flow and wall shear stress patterns were numerically computed in a complete bypass model of coronary artery. Effects of stenosis severity and angle of bypass have been analyzed. Commercial CFD software is used for the model formation, mesh generation and numerical simulation of blood flow in arterial bypass model. The results show that both the proximal and distal junctions are sensitive for the development of restenosis. The study will be helpful both for the clinicians and bypass graft manufacturers to design an optimized bypass graft. iii