Computational studies leading to a mechanical model for atherosclerotic plaque growth

Nookala, Nanda Kumar (2017) Computational studies leading to a mechanical model for atherosclerotic plaque growth. PhD thesis, Indian Institute of Technology Hyderabad.

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Abstract

We simulated steady and unsteady flow of blood through a two-dimensional channel with single and double stenosis using a self-written code. We model blood using the shear thinning relation proposed by Yeleswarapu in 1996, while the stenosis is approximated using a cosine shaped taper. The stream function-vorticity formulation of the flow equations are solved using a finite difference scheme in conjunction with a full multigrid algorithm that reduces computational time, and this is coded in FORTRAN. The presence of stenosis leads to a recirculation zone immediately downstream of the stenosis. The effects of stenosis size (upto 25% radial occlusion), length (L0), Reynolds number (Re ≤ 4000) on steady flow, and Womersley number (Wo ≤ 16) on pulsatile flow, of blood through a twodimensional channel with single stenosis as well as double stenosis are investigated, and the results are compared with the Newtonian case. In steady flow, the shear-thinning fluid predicts higher peak wall shear stress than the Newtonian fluid: the difference between the predictions, expressed as a percentage of the Newtonian wall shear stress, decreases as percentage stenosis and Reynolds number increase (∼ 5% at 25% stenosis, Re = 4000). For a given percentage stenosis and Reynolds number, the percentage difference between the shear thinning fluid and Newtonian fluid decreases as theWomersley number increases (corresponding to increasing pulsatile nature of the flow)(< 6% atWo= 16). In the case of double stenosis, peak wall shear stress increases with both length of stenosis and gap between stenosis; however, the effect of increasing length is much more compared to gap. Pulsatility plays a key role by shifting the location of peak wall shear stress from the primary to the secondary stenosis, and back again, during a cycle. This result suggests that, plaque growth dynamics are uniquely determined by the pulsatile shear stress history at a particular location. Based on this finding, and based on the distinct scatter of the experimental data, individual equations are developed to predict plaque growth at two separate locations in the arterial tree, distinct phenomenological equations are developed to predict plaque growth at those locations. Additionally, ANSYS FLUENT is used to simulate 3D flow of shear thinning fluid in a single and double stenosed pipe, and the velocity profiles and wall shear stress variation along the length are obtained: these showed excellent match with the graphs obtained for 2D flow using the code. Further, The peak WSS predicted by ANSYS FLUENT is within 6% of that predicted by the 2D simulation: this demonstrated the reliability of the code. ANSYS FLUENT is also used to obtain flow profiles in a non-axisymmetric 3D pipe geometry.

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