Measuring Diffusion in the Presence of Material Strain

Abstract

Material strain during the course of diffusion encoding by MRI will in general change the observed diffusional signal losses. These changes will occur even when the material returns cyclically to its initial location during the diffusion-evolution period. This effect derives from the modification of the local spatial modulation k of spin phase within a sample by a material deformation \font\serif=cmss10 at 10pt $\hbox{\serif F}$ as k --> $\hbox{\serif F}^{\rm 1T}$ k, resulting in an observed diffusion tensor $\hbox{\serif D}^{\rm obs} = {{1}\over{\Delta}} \int^{\Delta}_0 \hbox{\serif U}(t)^{-1} \hbox{\serif DU}(t)^{-1}dt,$ where $\hbox{\serif{U}}$ is the material stretch tensor. For example, when a material is compressed during pulsed-gradient diffusion encoding, the compression acts to increase the attenuation due to diffusion just as if a larger gradient were used. By using a simple gelatin phantom, the existence of this effect is demonstrated, and an effective method for its correction based on an MRI mapping of the material strain is presented. This correction is particularly relevant for inferring myofiber structure in the beating in vivo human heart, since the measurement of $\hbox{\serif{D}}$ is perturbed by the deformation of myocardium during the heart's contraction.