Comparison of hemodynamics of intracranial aneurysms between MR fluid dynamics using 3D cine phase-contrast MRI and MR-based computational fluid dynamics

Abstract

Introduction: Hemodynamics is thought to play a very important role in the initiation, growth, and rupture of intracranial aneurysms. The purpose of our study was to compare hemodynamics of intracranial aneurysms of MR fluid dynamics (MRFD) using 3D cine PC MR imaging (4D-Flow) at 1.5 T and MR-based computational fluid dynamics (CFD).

Methods: 4D-Flow was performed for five intracranial aneurysms by a 1.5 T MR scanner. 3D TOF MR angiography was performed for geometric information. The blood flow in the aneurysms was modeled using CFD simulation based on the finite element method. We used MR angiographic data as the vascular models and MR flow information as boundary conditions in CFD. 3D velocity vector fields, 3D streamlines, shearing velocity maps, wall shear stress (WSS) distribution maps and oscillatory shear index (OSI) distribution maps were obtained by MRFD and CFD and were compared.

Results: There was a moderate to high degree of correlation in 3D velocity vector fields and a low to moderate degree of correlation in WSS of aneurysms between MRFD and CFD using regression analysis. The patterns of 3D streamlines were similar between MRFD and CFD. The small and rotating shearing velocities and higher OSI were observed at the top of the spiral flow in the aneurysms. The pattern and location of shearing velocity in MRFD and CFD were similar. The location of high oscillatory shear index obtained by MRFD was near to that obtained by CFD.

Conclusion: MRFD and CFD of intracranial aneurysms correlated fairly well.

Fig. 1

Calculation method of wall shear stress (WSS). For one arbitrary calculation point (S₀) on the wall surface, we choose three reference points (S₁ to S₃) of the normal to the wall inside of the lumen at regular interval d. Velocity vectors at S₁, S₂, and S₃ are interpolated by surrounding data points with the use of linear interpolation method. The slope of velocity profile (derivative value=f′ (S₀)) of S₀ is the velocity vector gradient at S₀. We set the velocity at S₀ to zero and the velocity vector gradient at the wall is estimated with Lagrange’s polynomial interpolation formula. WSS vector at S₀ is calculated by multiplying viscosity by the tangential velocity vector gradient perpendicular to the normal to the wall (i.e., tangential shearing velocity vector). WSS is the strength of the WSS vector. f′(S₀), velocity vector gradient at the wall

Fig. 2

Examples of correlation charts of 3D velocity vector fields and WSS of BA-SCA aneurysm (temporal average) for MRFD and CFD. a X-component of velocity vectors. b Y-component of velocity vectors. c Z-component of velocity vectors. d Magnitude of velocity vectors. e WSS. BA-SCA basilar artery-superior cerebellar artery, WSS wall shear stress, MRFD MR fluid dynamics, CFD computational fluid dynamics

Fig. 3

Fifty-one-year-old female with right IC-PC aneurysm with a diameter of 6 mm. a A left posterior oblique view of surface rendered image shows a right IC-PC aneurysm with two outlets. C1 C1 segment of ICA, C2 C2 segment of ICA, Pcom posterior communicating artery. b 3D velocity vector fields (at the systolic phase when the velocities of parent artery is maximum during one cardiac cycle). c 3D streamlines (at the systolic phase when the velocities of parent artery is maximum during one cardiac cycle). d 3D WSS distribution map (temporal average). e Shearing velocity image facing the apex of the spiral flow (temporal average). f 3D OSI maps facing the apex of the spiral flow. Images in b, c, e, f, from the left to the right, present MRFD and CFD. Images in d, from the left to the right, present WSS obtained by MRFD, CFD with the regular interval of the WSS calculation point and the three reference points of 0.575 mm, and WSS by the shearing velocities calculated from the flow velocities of nodes located at the outermost layer of the vasculature (the distance of nodes from the wall, 0.009 mm) in CFD. 3D velocity vector fields (b) and 3D streamlines (c) demonstrate that blood flow enter via the distal aneurysmal neck, rotate very smoothly, and create one spiral flow in the aneurysm. 3D velocity vector fields (b) and 3D streamlines (c) of MRFD and CFD are similar. WSS distribution map (d) obtained from MRFD shows wider area with low WSS around the top of the spiral flow than that from CFD. WSS distribution maps (d) obtained from CFD with the different interval between the calculation point and the reference point(s) are similar. Small and rotating shearing velocities are noted at the top of the spiral flow in the aneurysm (e). This area in MRFD is near that in CFD, however, the magnitude of shearing velocities are different from each other (e). These areas correspond with the high OSI areas (f). IC-PC internal carotid-posterior communicating, ICA internal carotid artery, 3D three-dimensional, WSS wall shear stress, MRFD MR fluid dynamics, CFD computational fluid dynamics, OSI oscillatory shear index

Fig. 3

Fifty-one-year-old female with right IC-PC aneurysm with a diameter of 6 mm. a A left posterior oblique view of surface rendered image shows a right IC-PC aneurysm with two outlets. C1 C1 segment of ICA, C2 C2 segment of ICA, Pcom posterior communicating artery. b 3D velocity vector fields (at the systolic phase when the velocities of parent artery is maximum during one cardiac cycle). c 3D streamlines (at the systolic phase when the velocities of parent artery is maximum during one cardiac cycle). d 3D WSS distribution map (temporal average). e Shearing velocity image facing the apex of the spiral flow (temporal average). f 3D OSI maps facing the apex of the spiral flow. Images in b, c, e, f, from the left to the right, present MRFD and CFD. Images in d, from the left to the right, present WSS obtained by MRFD, CFD with the regular interval of the WSS calculation point and the three reference points of 0.575 mm, and WSS by the shearing velocities calculated from the flow velocities of nodes located at the outermost layer of the vasculature (the distance of nodes from the wall, 0.009 mm) in CFD. 3D velocity vector fields (b) and 3D streamlines (c) demonstrate that blood flow enter via the distal aneurysmal neck, rotate very smoothly, and create one spiral flow in the aneurysm. 3D velocity vector fields (b) and 3D streamlines (c) of MRFD and CFD are similar. WSS distribution map (d) obtained from MRFD shows wider area with low WSS around the top of the spiral flow than that from CFD. WSS distribution maps (d) obtained from CFD with the different interval between the calculation point and the reference point(s) are similar. Small and rotating shearing velocities are noted at the top of the spiral flow in the aneurysm (e). This area in MRFD is near that in CFD, however, the magnitude of shearing velocities are different from each other (e). These areas correspond with the high OSI areas (f). IC-PC internal carotid-posterior communicating, ICA internal carotid artery, 3D three-dimensional, WSS wall shear stress, MRFD MR fluid dynamics, CFD computational fluid dynamics, OSI oscillatory shear index