Cerebral aneurysm flow diverter modeled as a thin inhomogeneous porous medium in hemodynamic simulations

Abstract

Rapid and accurate simulation of cerebral aneurysm flow modifications by flow diverters (FDs) can help improving patient-specific intervention and predicting treatment outcome. However, when FD devices are explicitly represented in computational fluid dynamics (CFD) simulations, flow around the stent wires must be resolved, leading to high computational cost. Classic porous medium (PM) methods can reduce computational expense but cannot capture the inhomogeneous FD wire distribution once implanted on a cerebral artery and thus cannot accurately model the post-stenting aneurysmal flow. We report a novel approach that models the FD flow modification as a thin inhomogeneous porous medium (iPM). It improves over the classic PM approaches in two ways. First, the FD is more appropriately treated as a thin screen, which is more accurate than the classic 3D-PM-based Darcy-Forchheimer relation. Second, pressure drop is calculated cell-by-cell using the local FD geometric parameters across an inhomogeneous PM. We applied the iPM technique to simulating the post-stenting hemodynamics of three patient-specific aneurysms. To test its accuracy and speed, we compared the results from the iPM technique against CFD simulations with explicit FD devices. The iPM CFD ran 500% faster than the explicit CFD while achieving 94%-99% accuracy; thus, iPM is a promising clinical bedside modeling tool to assist endovascular interventions with FD and stents.

Keywords: CFD Simulation; Intracranial aneurysm; Porous media; Stent modeling; Stent simulation.

FIGURE 1:

Cross-sectional view of the 3D flow into an aneurysm through the FD pores, from a CFD simulation with the FD device explicitly present. Flow velocity vectors are mostly uniform in channels between the wires.

FIGURE 2:

Geometrical parameter definitions. (a) Definition of an FD cell, consisting of a pore and intersecting wires. (b) Relation of pore area (A_p) and wire area (A_w) to total area (A_t).

FIGURE 3:

Mapping the local PM parameters (viscous and inertial resistances) to a zero-thickness 3D model of the implanted FD. Zoomed views (with rescaled colors) show the similarity of each flow diverter pore size to their respective locally-homogeneous PM region.

FIGURE 4:

Mesh dependency study: Variation of aneurysm averaged velocity, shear rate, inflow rate, and turnover time as a function of cell count. The optimum base mesh size was determined to be 0.2mm.

FIGURE 5:

Workflow for modeling post-treatment IA hemodynamics with a flow diverter modeled as an inhomogeneous porous medium. The steps of the novel iPM approach are within the dashed bars.

FIGURE 6:

Three representative patient-specific ICA aneurysm geometries with virtually deployed FDs.

FIGURE 7:

Improvement in hemodynamics prediction of with progressively more refined FD inhomogeneity, in comparison with full simulation using an explicitly represented FD (Aneurysm B). Top row: PM properties were averaged over 1, 2, and 4 homogeneous regions in the aneurysm orifice. The black curved outline represents the flattened projection of the aneurysm orifice. Bottom row: WSS.

FIGURE 8:

Comparison of (a) Flow streamlines and (b) WSS for untreated (first column), FD-treated by iPM (second column), and FD-treated with explicit device (third column), in Aneurysms A, B, and C.

FIGURE 9.

Quantitative measurements of aneurysm averaged velocity, inflow rate, shear rate, and turnover time in Aneurysms A, B, and C for the untreated case, post-stenting using the iPM method, and post-stenting using explicitly modeled FD. The percent differences refer to flow modification by the FD for their respective post-stenting CFD methods