Computational hemodynamic analysis of renal blood flow and the impact of outflow boundary conditions

Hemodynamic analysis is an essential tool for predicting the behavior of blood flows and assessing the risk of renovascular diseases. In this paper, by employing a CFD-based finite element method coupled with an efficient parallel algorithm for the unsteady incompressible Navier-Stokes equations, we conduct a comprehensive investigation of renal hemodynamics and the impact of outflow boundary conditions in patient-specific models of normal, stenotic, and aneurysmal arteries featuring rich small-branch networks. Based on the hemodynamic analysis for the severe stenosis (area stenosis $>87\%$ ) and the aneurysm (diameter $=13.3$  mm), we observe a pressure drop exceeding 10 mmHg and a distal-to-proximal pressure ratio below 0.9 for these lesions, which is considered hemodynamically significant and likely induces renovascular hypertension. Furthermore, we reveal that the low wall shear stress and complex vortices with bidirectional flow occur on the inner wall downstream of this stenosis, which play a critical role in driving atherosclerotic plaque formation. Through virtual aneurysm reconstruction and numerical simulation, we demonstrate that the presence of a renal aneurysm alters local flow patterns and pressure distributions. Numerical results for both healthy and pathological renal arteries show that outflow boundary conditions have a significant impact on the global distribution of pressure and local flow patterns near the outlets. Compared with constant pressure and resistance outflow boundary conditions, the two-element Windkessel model, through adjustments of its resistance and capacitance parameters, can provide more physiological flow and pressure distributions, particularly in capturing realistic pulsatile waveforms, pressure ranges, and distal flow patterns. Moreover, a sensitivity analysis of the resistance in the Windkessel boundary condition shows a negligible impact on the pressure drop and only a minor effect on the renal fractional flow reserve (a change of less than $3\%$ for a $20\%$ variation in resistance). When focusing solely on the hemodynamics within stenotic and aneurysmal lesions located far from the outlets, both the constant pressure and Windkessel boundary conditions yield comparable results for key lesion-specific hemodynamic indicators, including renal fractional flow reserve and pressure drop in the stenosis, and wall shear stress and oscillatory shear index in the aneurysm.