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Strain-rate imaging uses large velocity encoding gradients to obtain measurements of velocity that are extremely insensitive to the effects of random noise. The spatial differential of velocity yields the velocity 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 tissue (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 voxel size. The magnitude of the MR signal contains information about the 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 sample the magnitude variation introduced by the interaction of velocity encoding gradients with spatially dependent velocities. The previously developed in-plane velocity gradient methods can be easily integrated with this new through-plane measurement to characterize the deformation of the myocardium in three spatial dimensions with high accuracy. The applicability of these methods is demonstrated theoretically, in phantoms and in vivo.


Journal article


Magn Reson Med

Publication Date





537 - 546


Echo-Planar Imaging, Heart, Humans, Magnetic Resonance Imaging, Models, Theoretical, Myocardium, Phantoms, Imaging