A Computational Hemodynamics Analysis on the Correlation Between Energy Loss and Clinical Outcomes for Flow Diverters Treatment of Intracranial Aneurysm

Abstract

The rupture of intracranial aneurysms might lead to permanent disability or even death. One possible endovascular treatment is the deployment of flow diverters (FDs), which reduces flow into the sac and promotes thrombosis. Computational fluid dynamics simulations were used to assess the flow patterns and dynamics. The concept of energy loss, as a measure of necessary work done to overcome flow resistance, was utilized to correlate with clinical outcome. If a surgical operation is successful, the flow would be diverted to a shorter path and energy loss should be reduced. Conversely, persistent flow in the sac, associated with treatment failure, would display an increased energy loss as blood is then squeezed through the stent pores. Four illustrative clinical cases, involving both bifurcation and sidewall aneurysms, were selected. To reduce the numerical complexity, earlier works in the literature had used a porous medium approximation for the FDs. Here, the FD was simulated explicitly as a virtual (or computer-generated) stent, which would likely provide a more accurate description. Furthermore, quantitative comparisons between the approaches of virtual stenting and a porous medium with typical parameters were conducted by examining the effective flow influx into the aneurysm.

Appendix

Some technical details concerning the quality assurance of the accuracy of the simulations are given here. Two columns of data are listed in the following table, which describes the number of cells used in all utilized meshes. The parameter ‘Energy Loss’ was calculated at a time point when β had the largest variation across different meshes. The adjectives, ‘Large’, ‘Medium’ and ‘Small’ were then used to designate these meshes. According to [44], the Grid Convergence Index (GCI) was calculated and recorded for one of the cases.

Case 1:

Successful case

Case 1a:

Pre-operation

Details of the grid size are tabulated in Table 6. The number of cells utilized in this study was 539,662.

Table 6 Number of cells and corresponding energy losses for different meshes

The ‘Energy Loss’ parameter was therefore quite insensitive to the number of cells (error < 0.5%) once a threshold was reached, a feature also illustrated in Fig. 12.

Fig. 12

Energy loss for the pre-operation condition at different mesh sizes versus time in one cardiac cycle of Patient 1

1.1 Analysis

The refinement ratio, r, was approximately 1.44, while the observed order of convergence, p, was very close to 2.50. For the three-grid study, a factor of safety (Fs), given by Fs = 1.25, was used to calculating the GCI for the finer grids [44]. Using these established procedures, the standard calculations yielded:

$${\text{GCI}}_{\text{Medium - Small}} = \, 0.459\% ,{\text{ GCI}}_{\text{Large - Medium}} = \, 1.136\% .$$

A quality assurance check was conducted to test whether the solutions were in the asymptotic range:

$${\text{GCI}}_{\text{Medium - Small}} / \, \left( {{\text{r}}^{\text{p}} {\text{GCI}}_{\text{Large - Medium}} } \right) \, = \, 0.9946.$$

This value of approximate unity thus confirmed that the solution was within the appropriate asymptotic range. Similar patterns were observed for other simulations reported in the text.