Numerical Modeling of Blood Flow in Bioresorbable Vascular Stents Open Access

Abstract

This study focuses on the numerical simulation of blood flow in vessels with Bioresorbable Vascular Stents (BVS). BVS is a recent invention that has only been approved for clinical practices in Europe. BVS has considerable advantages over the traditional metal stents, since it is flexible and resorbable. Patients may take less medication once it is completely dissolved, for it is not a permanent implant. However, BVS also has several limitations that have caught the attention of researchers. One of these limitations, the potential formation of vortexes behind the strut, is investigated in this study.

The structure and fluid in this problem, the vessel wall and the blood flow, have complicated biomechanical properties. The vascular wall is elastic and change in length over time. The blood flow is pulsatile and features a complex rheology. In this project, the blood flow is assumed to be Newtonian fluid and the vascular wall is assumed to be rigid. Under such assumptions, Incompressible Navier-Stokes equations (INS) are implemented. The boundary conditions at the inflow end of vessel segment, at the outflow end and on the vascular wall are prescribed as patient-specific blood flow data, 'free' or so-called 'do-nothing condition', and 0, respectively.

LifeV, an open source library of algorithms and data structures for the numerical solution of partial differential equations, is then employed to solve the INS numerically. ParaView, a three-dimensional visualization tool, is used to visualize the numerical results dynamically. The variables of interest, including the pressure, the velocity and the Wall Sheer Stress (WSS) can be observed in the result figures and animations.

Based on the simulation results, the WSS is low in the vicinity of the strut but high in the region between the ring struts. This distribution pattern of the WSS suggests there is a possibility that the blood flow may be turbulent behind the strut, but no obvious circulate streamlines of blood flow are observed in the velocity streamline figures. Potential paths of continued study could include simulations with sufficiently fine meshes and having the vascular wall more involved in the study of fluid-dynamic influence from the vascular wall.

Table of Contents

Table of Contents

1. Introduction..................................................................................................................... 1

1.1 Background........................................................................................................................ 1

1.2 Concerns and Limitations.................................................................................................. 2

1.3 Prior study........................................................................................................................... 4

1.4 Summary............................................................................................................................... 5

2. Mathematical modeling.............................................................................................. 6

2.1 Assumptions regarding Blood Flow............................................................................... 6

2.2 Assumptions regarding the vascular wall.................................................................... 8

2.3 The Fluid equations......................................................................................................... 10

2.4 boundary condition......................................................................................................... 12

2.5 Quantities of Interest: the WSS...................................................................................... 15

3. The numerical Engine................................................................................................... 17

3.1 The Geometry and Meshing of the Vascular Wall and the Stent........................... 17

3.2 LifeV.................................................................................................................................... 19

3.3 The visualization software: ParaView.......................................................................... 20

3.4 The environment in which the computation is conducted........................................... 21

4. Numerical Tests.............................................................................................................. 23

4.1 Process............................................................................................................................... 23

4.2 The Visualization Results and Interpretation............................................................. 27

4.3 Discussion.......................................................................................................................... 40

4.4 insights............................................................................................................................... 42

Reference................................................................................................................................ 45

About this Honors Thesis

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School	Emory College
Department	Mathematics
Degree	BS
Submission	Honors Thesis
Language	English
Research Field	Mathematics Engineering, Biomedical Biophysics, Medical
Keyword	lifeV Navier-Stokes equation Wall Shear Stress Streamline Bioresorbable stent
Committee Chair / Thesis Advisor	Veneziani, Alessandro, Emory University
Committee Members	Benzi, Michele, Emory University Kesar, Trisha M, Emory University

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