Three-dimensional vortex characterization in small intracranial aneurysms based on four dimensional flow magnetic resonance imaging at 7 Tesla

Effective vectors and approaches are proposed to identify the three-dimensional (3D) vortex motion in small intracranial aneurysms (≤7 mm) based on four dimensional flow magnetic resonance imaging at 7 T. Six subjects with small intracranial aneurysms were scanned. The 3D vortex identification vector Γ2⃗ and scalar Ω are computed with velocity vectors. The high Γ2,magnitude region is defined using region growing based on the threshold value determined by an empirical nonlinear relation between Γ2,magnitude and the scalar Ω inside the aneurysmal sac, while the threshold of Ω = 0.6 is used to define the high Ω region. The spatially averaged vector Γ2⃗ and the vorticity vector ω⃗ over the defined high Γ2,magnitude and Ω regions are found to denote the corresponding vortex motion directions, respectively. With these two vectors, the 3D vector Γ1⃗ is invoked to localize vortex motion centers. Threshold values of region growing for the high Γ2,magnitude region from the nonlinear relation for each subject are in the range of 0.51 and 0.59. The volume of the defined high Γ2,magnitude region is close to that of the defined high Ω region. The angle between the generated two averaged vectors Γ2⃗ and ω⃗ is small for all subjects, with the maximum being 9.17°. The located vortex motion centers from Γ1⃗ based on Γ2⃗ and Ω(ω) are the same for each subject inside the aneurysm. The small angle between the two averaged vectors and the located same vortex center supports the effectiveness of the proposed method to characterize vortices in small unruptured intracranial aneurysms.