Efficient implementation of the proper outlet flow conditions in blood flow simulations through asymmetric arterial bifurcations

We present an efficient implementation of the proper ( in vivo ) outlet boundary conditions in detailed, three‐dimensional (3D) and time‐periodic simulations of blood flow through arteries. This is achieved through the intermediate use of an approximate ‘simulant’ model of the outlet pressure/flow relationship corresponding to the full 3D and time‐dependent numerical simulation. This model allows us to efficiently couple the 3D outlet pressure/flow conditions to the equivalent relations due to the downstream arterial network, as obtained from a one‐dimensional approximate model in the form of Fourier frequency impedance coefficients. An adjustable time‐periodic function correction term in the simulant model requires input from the full 3D model that has to run iteratively until convergence. The advantage of the proposed numerical scheme is that it decouples the upstream detailed simulation from the downstream approximate network model offering exceptional versatility. This approach is demonstrated here in a series of detailed 3D simulations of blood flow, performed using the commercial software FLUENT™, through an asymmetric arterial bifurcation. Two cases are considered: first a healthy system patterned after the left main coronary arterial bifurcation, and second a diseased case where an occlusion has developed in one of the daughter vessels, resulting in strengthening the asymmetry of the bifurcation. Rapid convergence of the iterative process was achieved in both cases. Subtle changes occur in the shear patterns of the daughter vessels, whereas the flow distribution is quite different. In the presence of a stenosis additional regions of low shear develop due to inertial effects.