Numerical simulation of aneurysmal haemodynamics with calibrated porous-medium models of flow-diverting stents

Abstract

Modelling flow-diverting (FD) stents as porous media (PM) markedly improves the efficiency of computational fluid dynamics (CFD) simulations in the study of intracranial aneurysm treatment. Nonetheless, the parameters of PM models adopted for simulations up until now were rarely calibrated to match the represented FD structure. We therefore sought to evaluate the PM parameters for a representative variety of commercially available stents, so characterising the flow-diversion behaviours of different FD devices on the market.

We generated fully-resolved geometries for treatments using PED, Silk+, FRED, and dual PED stents. We then correspondingly derived the calibrated PM parameters—permeability (k) and inertial resistance factor (C₂)—for each stent design from CFD simulations, to ensure the calibrated PM model has identical flow resistance to the FD stent it represents. With each of the calibrated PM models respectively deployed in two aneurysms, we studied the flow-diversion effects of these stent configurations.

This work for the first time reported several sets of parameters for PM models, which is vital to address the current knowledge gap and rectify the errors in PM model simulations, thereby setting right the modelling protocol for future studies using PM models. The flow resistance parameters were strongly affected by porosity and effective thickness of the commercial stents, and thus accounted for in the PM models. Flow simulations using the PM stent models revealed differences in aneurysmal mass flowrate (MFR) and energy loss (EL) between various stent designs.

This study improves the practicability of FD simulation by using calibrated PM models, providing an individualised method with improved simulation efficiency and accuracy.

Introduction

As a vascular disorder with high rate of mortality and morbidity (Seibert et al., 2011), intracranial aneurysms (IAs) may severely threaten patients’ lives, because of the bleeding into the brain caused upon aneurysm rupture (Chalouhi et al., 2013). As an endovascular intervention that deploys a tubular metal mesh across the aneurysm neck, treatment with a flow-diverting (FD) stent aims at discouraging the blood from entering the aneurysm, thereby inducing aneurysm occlusion (Byrne et al., 2010).

The initiation, growth, and rupture of an aneurysm are believed to be associated inter alia with its local haemodynamics, which can be characterised by computational fluid dynamics (CFD) simulation (Chong et al., 2014, Penn et al., 2011). In CFD simulation of FD-stent treatment, modelling an FD stent as a porous medium (PM) can markedly improve the computational efficiency. In contrast to modelling the FD stent with fine meshes, which requires a high-resolution spatial discretisation around the stent’s thin wires, PM models mimic the resistance effect of an FD stent according to parameters that characterise a PM, including notably the permeability (k) and inertial resistance factor (C₂) (Augsburger et al., 2011, Ohta et al., 2015).

A number of studies have been performed to understand the correlation between PM models and fully-resolved wire-mesh FD stent models (Augsburger et al., 2011, Ohta et al., 2015, Raschi et al., 2014, Zhang et al., 2013). To obtain PM model parameters that could represent a FD stent, Augsburger et al. created a FD test model that had a geometry similar to the commercially available Silk FD stent (Balt Extrusion, Montmorency, France), and hence derived the k and C₂ values of the test model’s PM analogue.

Although the methodology of using the PM stent model was established, few studies have been carried out to specify the calibrated PM properties that could match different brands of FD stent available on the market, like the Pipeline embolization device (PED; ev3/Covidien, Irvine, USA), the Silk + FD stent (Silk+; Balt Extrusion), and the Flow Re-Directional Endoluminal Device (FRED; MicroVention, Tustin, USA) (Mohlenbruch et al., 2015, Wong et al., 2011). Furthermore, most of the published PM studies still utilised the PM properties derived by Augsburger et al. in the simulation of FD-stent treatment with other brands of device—and indeed often without correctly accounting for the PM model thickness (Li et al., 2017).

The objective of this study is to specify calibrated PM parameters for different treatment scenarios—single stent and multi-stent implantation, as well as for treatments with different brands of device (e.g. PED, Silk+, FRED, etc.). To meet this need, we first generated FD test models corresponding respectively to a single PED, Silk+, and FRED stent, as well as for two PED FDs (overlaid), and we considered regions or alignments with the lowest and highest porosities for each of these models. We derived the corresponding PM model properties—k and C₂—for each configuration, and applied them in the CFD simulation of treatments for two patient-specific cerebrovascular aneurysms to contrast the effects of different parameters as might realistically be encountered.