Influences of Axial Symmetry of Arterial Stenosis on Pressure Distribution Based on Computational Fluid Dynamics Simulations Público

Abstract

In this thesis, we want to find the degree of impact stenosis geometric features, especially the axial symmetry, can have on the pressure drop along the side walls of stenotic arterial vessels. Computational fluid dynamics (CFD) simulations are applied to solve the three-dimensional steady Navier-Stokes equations, a time-independent system characterizing incompressible, Newtonian, homogeneous flow and commonly used in blood flow models. The numerical solutions are computed using Finite Element approximation, and linearization of the system is done by Picard iteration method. As a result, we found that pressure drop can serve as an indicator for the geometric shape, especially the axial symmetricity, in cases of significant arterial stenosis. While for mild stenosis, pressure drop is not sufficiently informative in distinguishing between axisymmetric and nonsymmetric stenosis geometries.

Table of Contents

Acknowledgement III
1 Introduction 1
1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Related work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 The 3-D Navier-Stokes Equations 4
2.1 Navier-Stokes problem at a glance . . . . . . . . . . . . . . . . . . . . . 4
2.1.1 Preliminary theorems . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.2 Conservation of mass . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.3 Conservation of momentum . . . . . . . . . . . . . . . . . . . . 6
2.2 Steady Navier-Stokes equations . . . . . . . . . . . . . . . . . . . . . . 8
3 Numerical Approaches 10
3.1 The Weak Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 Finite Element Approximation . . . . . . . . . . . . . . . . . . . . . . . 11
3.3 Linearization: Picard Iteration . . . . . . . . . . . . . . . . . . . . . . . 14
3.3.1 Incremental analysis . . . . . . . . . . . . . . . . . . . . . . . . 14
3.3.2 Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4 Modeling and CFD Simulations 16
4.1 Stenosis geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.1.1 Geometry description . . . . . . . . . . . . . . . . . . . . . . . . 16
4.1.2 Construction and meshing . . . . . . . . . . . . . . . . . . . . . 19
4.2 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.3 Numerical solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5 Results, Discussion and Follow-ups 24
5.1 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5.2 Comparison with experimental results . . . . . . . . . . . . . . . . . . . 28
5.3 Future works and applications . . . . . . . . . . . . . . . . . . . . . . . 28
Bibliography 30

About this Honors Thesis

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School	Emory College
Department	Mathematics
Degree	BS
Submission	Honors Thesis
Language	English
Research Field	Applied Mathematics
Palabra Clave	CFD Computational math Blood flow
Committee Chair / Thesis Advisor	Veneziani, Alessandro, Emory University Viguerie, Alex, Emory University
Committee Members	Ruthotto, Lars , Emory University Page, Michael, Emory University

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