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

Abstract

SUMMARYWe present an efficient implementation of the proper (in vivo) outlet boundary conditions in detailed, threedimensional (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 TM , 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.

Analysis of drag effects on pulsatile blood flow in a right coronary artery by using Eulerian multiphase model

“…This is done using the pressure in the cell located at (or nearest to) the reference pressure location. In situations where there is only one outlet or the outlet vessels are symmetric, simply treating the outlet(s) as a reference location for zero pressure is sufcient to produce accurate results (Johnson et al, 2010). In this study, the FLUENT's outflow boundary condition at the exit of coronary artery was used to cover a range of physiological blood pressures, where the reference pressure was set to 75 mmHg above atmospheric pressure, which is an average aortic pressure taken from the in vivo measurements (Poppas et al, 1997), as previously used by Jung et al (2006a) and Huang et al (2009).…”

Geometric multiscale modeling of the cardiovascular system, between theory and practice

“…See [138] for more details, while recently an alternative formulation has been proposed in [42]. We also mention [100] and [189] where proper outflow conditions for the coronary tree and cerebral aneurysms, respectively, are discussed.…”

Non-Newtonian effects in simulations of coronary arterial blood flow

“…However, the information obtained in each case reflects specific data of a specific case, at a specific time. These technologies therefore cannot be used to examine what-if scenarios for modeling practices [Johnson et al (2011a); Taylor and Draney (2004)]. Thus, imposing the appropriate BCs in simulations of arterial flow requires special attention.…”

“…The proper implementation of outlet BCs in simulations of flow in a specific artery requires that the impact of the rest of the arterial network be taken into consideration [Formaggia et al (2009)]. This can be achieved by using boundary conditions that, instead of absolute pressure or velocity values, describe a correlation between outlet flow and pressure [Johnson et al (2011a); Formaggia et al (2009)]. Such correlations represent flow information for the arterial network that extends beyond the boundary points of the simulation.…”