Vectorial wall shear stress calculations in vessel structures using 4D PC-MRI

Methods Velocity data were corrected for aliasing and phase offsets and subsequently filtered using a median filter. Inward unit normal vectors were determined on the wall, after which a coordinate transformation was performed for each point at the wall such that the normal vector coincided with the z-axis of the transformed coordinate system. Velocities at fixed points along the normal were calculated using natural 3D interpolation in the original data. Any perpendicular velocity components were removed as only tangential velocity components contribute to the viscous forces at the wall. Smoothing splines were then fitted to the xand yvelocity components along the inward unit normals. The xand y-derivatives at the vessel wall were derived analytically and multiplied with the viscosity, which resulted in the WSS. Finally, all WSS vectors were transformed back to the original coordinate system. This method was validated using a synthetic dataset of a rigid straight tube (diameter 6mm) with parabolic flow, in which the theoretical WSS could be derived analytically (Poiseuille). Effects of resolution, segmentation errors and noise were assessed using this phantom data. Secondly the algorithm was tested in in-vivo PCMRI data. In vivo PC-MRI of the common carotid artery was performed on a 3T MRI system (Philips Healthcare, Best, The Netherlands) using a dedicated 8 channel carotid coil, 5 heart phases, FOV 80x80x12 mm, isotropic voxel size 0.4 mm (non-interpolated), sense factor 2, Venc of 30 (ap), 30 (rl) and 70 (fh) cm/s, scantime 10 minutes.