Numerical Simulations of Blood Flow in Coronary Arteries Investigating Sensitivity of Numerical Results to Different Boundary Pressures at Outflow Open Access

Abstract

Atherosclerosis develops when cholesterol containing deposits (plaque) build up, and growth of such plaques can slowly narrow and harden the arteries throughout the body. Serious problems occur because narrowing of coronary arteries causes heart to receive less blood and leads to the heart attack. Coronary heart disease has been the leading cause of death in the developed world and nearly the leading cause in the developing world. As it has been found that atherosclerosis is strongly associated with local hemodynamic of blood flow, mathematical modeling is applied to build the relationship between pressures the velocities. As a result, predictions of atherosclerosis for a specific patient can be made based on the solutions to those mathematical equations. Blood in this study is considered being incompressible unsteady Newtonian fluid, and Navier Stokes equations are applied for modeling. Computational dynamic modeling (CFD) is applied to solve those problems numerically. However, to obtain reliable clinical results, the required accurate patient specific boundary conditions are hard to measure due to technical difficulties, especially the pressures on the outflow boundary. This study aimed to investigate how inaccurate pressures at outflow boundaries would affect the numerical results.

In this study, five cases with different outflow pressures (baseline pressure was from patient specific measurements; two cases were with pressures increased by 10% and 20% from the baseline; the other two cases were with pressures decreased by 10% and 20% from the baseline) and the same inflow velocities were simulated within a complete cardiac cycle 0. 833s. The coronary artery geometry, velocities and baseline pressures were acquired from a specific patient.

The results showed obvious pressure increases as the boundary pressures increased, whereas velocity distribution remained identical visually (clinically). Atherosclerosis risk indices, wall shear stress (WSS) and oscillatory shear index (OSI) were the clinically the same as well. At this point of study, it can be concluded that changes on the outflow boundary pressures clinically have no effect on the resulting velocities, wall shear stress and oscillatory shear index, and thus the prediction of atherosclerosis.

Table of Contents

Contents

1 Introduction 1 1.1 Coronary Arteries and Atherosclerosis . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Computational Fluid Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Ingredients of a CFD analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Objective and Signicance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Methods 8 2.1 Simplied Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 The Governing Mathematical Model . . . . . . . . . . . . . . . . . . . . . . 10 2.3 Quantitative Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4 CFD workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.5 Numerical Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.5.1 Underlying Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.5.2 Softwares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3 Results 15 3.1 Physical Properties of Blood . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.2 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4 Discussion 25 5 Conclusion 34 6 Biliography 42

About this Honors Thesis

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School	Emory College
Department	Mathematics
Degree	BS
Submission	Honors Thesis
Language	English
Research Field	Mathematics
Keyword	Atherosclerosis Computational Fluid Dynamics Numerical Simulation
Committee Chair / Thesis Advisor	Veneziani, Alessandro, Emory University
Committee Members	Chang, Howard, Emory University Yang, Shanshuang, Emory University

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