A three-dimensional off-lattice Boltzmann method for the simulation of blood flow through a model irregular stenosis

Abstract

In the present work, a three-dimensional characteristic-based off-lattice Boltzmann method is developed in general cylindrical curvilinear coordinates to handle body-fitted non-uniform meshes that typically arise in blood flow simulation of stenosed arteries. To handle the singularity point at r =  0, the azimuthal mapping approach together with a special periodic boundary condition is developed. The numerical solver is validated, using reference data from literature, for steady flow through a stenosed lumen and for pulsatile flow through an abdominal aortic aneurysm. Thereafter, the solver is applied to study pulsatile blood flow through a model irregular arterial stenosis with an aerial occlusion of 75%. The surface irregularity of the stenosis is modeled using a sine function while keeping the cosine-shaped occlusion. The degree of irregularity is controlled by the amplitude and frequency of the sine function. Flow characteristics such as wall shear stress (WSS), divergence of WSS, oscillatory shear index, relative residence time (RRT), the turbulence kinetic energy (TKE), and power spectral density are used to investigate the near-wall vascular remodeling caused by the resulting disturbed flow. The present study demonstrates that for a given areal occlusion, an increase in the amplitude and frequency of the surface irregularity increases the number of locations susceptible for perfusion of low-density lipoproteins and promotes flow disturbances in the stenotic and post-stenotic regions. An increase in the Reynolds number not only increases the peaks of the WSS but also brings the peaks together causing alternating stress in the stenosed region. Furthermore, a positive correlation is found between the Reynolds number and the TKE production. On the other hand, an increase in the Womersley number reduces the TKE production, curtails the disturbed flow, and reduces the RRT of the solutes, all of which further reduce the risk factors. Overall, the developed solver demonstrates the importance of shape of the stenosis on the blood flow dynamics for physiological inflow conditions.