Date of Award

2007

Level of Access Assigned by Author

Open-Access Thesis

Degree Name

Master of Science in Mechanical Engineering (MSME)

Department

Mechanical Engineering

Advisor

Kiran Bhaganagar

Second Committee Member

Michael Boyle

Third Committee Member

William Davids

Abstract

In a normal coronary artery, the flow is laminar and the velocity is parabolic in nature. Over time, plaques deposit along the artery wall, narrowing the artery and creating an obstruction, a stenosis. As the stenosis grows, the characteristics of the flow change and transition occurs, resulting in turbulent flow distal to the stenosis. To date, direct numerical simulation (DNS) of turbulent flow has been performed in a number of studies to understand how stenosis modifies flow dynamics. However, the effect of the actual shape and size of the obstruction has been disregarded in these DNS studies. An ideal approach is to obtain geometrical information of the stenotic channel using medical imaging methods such as IVUS (Intravascular Ultrasound) and couple them with numerical solvers that simulate the flow in the stenotic channel. The purpose of the present thesis is to demonstrate the feasibility of coupling the IVUS geometry with DNS solver. This preliminary research will provide the necessary tools to achieve the long term goal of developing a framework for the morphological features of the stenosis on the flow modifications in a diseased coronary artery. In the present study, the geometrical information of the stenotic plaque has been provided by the medical imaging team at the Cleveland Clinic Foundation for 42 patients who underwent IVUS. The integration of the geometrical information of the stenotic plaque with the DNS was performed in 3 stages 1) fuzzy logic scheme was used to group the 42 patients into categories, 2) meshing algorithm was generated to interface with the DNS solver, and 3) the existing DNS for channel flow was modified to account for inhomogeneity in the streamwise direction. A plaque classification system was developed using statistical k-means clustering with fuzzy logic. Four distinct morphological categories were found in plaque measurements obtained from the 42 patients. Patients were then assigned a degree of membership to each category based on a fuzzy evaluation system. Flow simulations showed distinct turbulent flow characteristics when comparing the four categories, and similar characteristics within each category. An existing DNS solver that used the fourth-order velocity second-order vorticity formulation of the Navier-Stokes equations was modified to account for inhomogeneity in the streamwise direction. A multigrid method was implemented, using Green's method to compute unknown boundary conditions at the walls in using an influence matrix approach. The inflow is the free stream laminar flow condition; the outflow is computed explicitly with a buffer domain and by parabolizing the Navier Stokes equation. The transitional flow solver was tested using blowing and suction disturbances at the wall to generate the Tollmien-Schlichting waves predicted by linear stability theory. The toolset developed as a part of this thesis demonstrates the feasibility of integrating realistic geometry with DNS. This tool can be used for patient-specific simulation of stenotic flow in coronary and carotid arteries. Additionally, within the field of fluid dynamics, this framework will contribute to the understanding of transition and turbulence in stenotic flows.

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