Fig. 7. Velocity encoding using a standard paradigm versus a non-coplanar multi-stack approach compatible with slice-to-volume registration (SVR).

a In standard velocity-encoding, such as using a spoiled gradient echo (SPGR) sequence, the imaging slice (black) is held fixed and additional dedicated velocity sensitizing gradients are added to create first moments (m) in specified spatial directions (m_x, m_y, m_z, where subscripts denote the spatial directions of the velocity encoding). Note that there are also typically first order moments associated with the native imaging gradients, which add a constant additional encoding, but this is not shown as it is usually subtracted out. b For each imaged voxel, the three velocity-encoding directions are orthogonal and conventionally aligned with the imaging axes. c Volumetric reconstruction using SVR requires the acquisition of non-coplanar stacks. In this case, the directionality of the first moment associated with the intrinsic imaging gradients is maintained relative to each acquired slice and this provides three-directional velocity-encoding. Slice selective imaging sequences generally have intrinsic velocity-sensitivity that is oblique to the slice plane. In the case of the bSSFP sequences deployed in this study senitization is along the slice and read directions (hence m_y,x, m_x,z, m_z,y in the figure). Combining three non-coplanar stacks of slices (d) provides data at the location of each voxel with three non-colinear velocity sensitizations, now oblique to the imaging axes. (Note that in this figure the coordinate axes show spatial directions. The arrows indicate only the directions in space of the relevant gradient moments).