Identification of vortex structures in a cohort of 204 intracranial aneurysms

Abstract

An intracranial aneurysm (IA) is a cerebrovascular pathology that can lead to death or disability if ruptured. Abnormal wall shear stress (WSS) has been associated with IA growth and rupture, but little is known about the underlying flow physics related to rupture-prone IAs. Previous studies, based on analysis of a few aneurysms or partial views of three-dimensional vortex structures, suggest that rupture is associated with complex vortical flow inside IAs. To further elucidate the relevance of vortical flow in aneurysm pathophysiology, we studied 204 patient IAs (56 ruptured and 148 unruptured). Using objective quantities to identify three-dimensional vortex structures, we investigated the characteristics associated with aneurysm rupture and if these features correlate with previously proposed WSS and morphological characteristics indicative of IA rupture. Based on the Q-criterion definition of a vortex, we quantified the degree of the aneurysmal region occupied by vortex structures using the volume vortex fraction (vVF) and the surface vortex fraction (sVF). Computational fluid dynamics simulations showed that the sVF, but not the vVF, discriminated ruptured from unruptured aneurysms. Furthermore, we found that the near-wall vortex structures co-localized with regions of inflow jet breakdown, and significantly correlated to previously proposed haemodynamic and morphologic characteristics of ruptured IAs.

Keywords: image-based computational fluid dynamics; intracranial aneurysms; rupture; vortex structures.

Figure 1.

An illustration of the classification of aneurysm flow modes based on the inflow jet. Aneurysms were classified to have either (a) Continuous Jet Mode, or (b) Jet Breakdown Mode. Both flow modes can exist in sidewall or bifurcation aneurysms.

Figure 2.

A representative sidewall aneurysm case with the Continuous Jet Mode at five time points throughout the cardiac cycle (t/T = 0, 0.04, 0.08, 0.15 and 0.50). (a) Velocity streamlines and (b) out-of-plane vorticity shows a single organized vortex entering distally. This flow resulted in a low fraction of (c) vortex structures near the surface (coloured by positive Q contours). Both surface vortex structures and (d) vortex structures in the three-dimensional volume (coloured by positive Q contours) do not change throughout the cardiac cycle.

Figure 3.

A representative bifurcation aneurysm case with the Continuous Jet Mode at five time points throughout the cardiac cycle (t/T = 0, 0.04, 0.08, 0.15 and 0.50). The single organized vortex is shown by (a) velocity streamlines and (b) out-of-plane vorticity. (c) This flow results in a low fraction of vortex structures near the surface (coloured by positive Q contours). Both vortex structures near the surface and (d) vortex structures in the three-dimensional volume (coloured by positive Q contours) do not change throughout the cardiac cycle.

Figure 4.

A representative sidewall aneurysm case with the Jet Breakdown Mode at five time points throughout the cardiac cycle (t/T = 0, 0.04, 0.08, 0.15 and 0.50). (a) Velocity streamlines with a solid black arrow showing the main inflow jet and dashed arrows showing the counter-rotating vortices, and (b) out-of-plane vorticity. (c) Vortex structures near the surface (coloured by positive Q contours) co-localize with the impingement jet site. Vortex structures near the surface and (d) vortex structures in the three-dimensional volume (coloured by positive Q contours) do not change throughout the cardiac cycle.

Figure 5.

A representative bifurcation aneurysm case with the Jet Breakdown Mode at five time points throughout the cardiac cycle (t/T = 0, 0.04, 0.08, 0.15 and 0.50). (a) Velocity streamlines with a solid black arrow showing the main inflow jet and dashed arrows showing the counter-rotating vortices, and (b) out-of-plane vorticity. This impingement co-localizes with (c) vortex structures near the surface (coloured by positive Q contours). Surface vortex structures and (d) vortex structures in the three-dimensional volume (coloured by positive Q contours) do not change throughout the cardiac cycle.

Figure 6.

The results of the sensitivity analysis performed on two ruptured (R1 and R2) and two unruptured (UR1 and UR2) patient IA cases. The metrics vVF (left) and sVF (right) were monitored. (a) The results of a grid independence study where the wall element thickness was refined. An average change of less than 0.01 was observed at a maximum wall element size of 25 µm (dashed line). (b) The results of a spatial discretization sensitivity study that quantified the effect of first- and second-order discretization schemes. Between first- and second-order discretization schemes an average change of 0.05 and less than 0.01 were observed for the vVF and the sVF, respectively. (c) The results of a non-Newtonian viscosity model. An average change of less than 0.01 was observed when the Carreau–Yasuda (C-Y) model was used. (d) vVF and sVF are shown during one cardiac cycle. Peak systole is denoted with the dashed line. Each case showed minimal changes in regions of positive Q. The average standard deviation of the vVF and the sVF was 0.02 and 0.01, respectively.

Figure 7.

Vortex structures (coloured by positive Q contours) for six representative unruptured (UR, top) and six representative ruptured (R, bottom) cases. (a) Vortex structures in the three-dimensional volume and (b) vortex structures near the surface are shown.

Figure 8.

A boxplot showing the results of the comparison of the sVF and the vVF for the 204 aneurysms by a Mann–Whitney U-test. (a) The 148 unruptured (UR) and 56 ruptured (R) cases showed no statistical difference in the vVF, with a group average of 0.29 and 0.30, respectively (p = 0.32). (b) sVF was found to be statistically different between ruptured and unruptured aneurysms, with a group average of 0.13 and 0.09, respectively (p < 0.001). n.s., not significant; *S, statistically significant (defined as p < 0.01).

Figure 9.

A boxplot showing the results of the comparison of the sVF between unruptured and ruptured aneurysms with the Continuous Jet Mode and the Jet Breakdown Mode. Ruptured aneurysms had the highest sVF, which was significantly higher than that of unruptured aneurysms with the same flow mode (unruptured: 0.11 ± 0.04, ruptured: 0.14 ± 0.06, p = 0.008). *S, statistically significant (defined as p < 0.01).

Figure 10.

Comparison of velocity streamlines, surface layer vortex structures (Q > 0), WSS and OSI for two unruptured (UR3, RR4) and two ruptured (R3, R4) aneurysms.

Figure 11.

Correlation between previous rupture indicators and sVF by Pearson correlation analysis. (a) WSS versus sVF (p < 0.001; r = 0.43), (b) OSI versus sVF (p = 0.019; r = 0.17) and (c) SR versus sVF (p < 0.001; r = 0.49). Decrease in the WSS and increase in the SR were significantly correlated to increase in the sVF.