Strain-rate imaging uses large velocity encoding gradients to obtain m
easurements of velocity that are extremely insensitive to the effects
of random noise. The spatial differential of velocity yields the veloc
ity gradient from which the strain-rate and twist-rate tensors can be
determined. These tensors represent the distortion of the material and
are of interest in the analysis of the dynamic behavior of living tis
sue (e.g., that of the myocardium). This work presents a new technique
that uses the magnitude of the signal in the velocity encoded data to
measure through-plane velocity variations at the resolution of the vo
xel size. The magnitude of the MR signal contains information about th
e range of phases present within a voxel. When the phase is dependent
on the velocity (as in phase velocity imaging), the magnitude contains
information about the range of velocities within a voxel. The method
presented in this work uses unbalanced slice-refocusing gradients to s
ample the magnitude variation introduced by the interaction of velocit
y encoding gradients with spatially dependent velocities. The previous
ly developed in-plane velocity gradient methods can be easily integrat
ed with this new through-plane measurement to characterize the deforma
tion of the myocardium in three spatial dimensions with high accuracy.
The applicability of these methods is demonstrated theoretically, in
phantoms and in vivo.