Spatial Image Gradient Estimation from the Diffusion MRI Profile
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Background
In the course of diffusion, water molecules experience varying values for the relaxation-time properties of the underlying tissue, a factor that has not been accounted for in diffusion MRI (dMRI) modeling.
Purpose
With the aim of mining the dMRI signal for information about the spatial variations in the tissue relaxation-time properties, we derive a new mathematical relationship between the diffusion signal and the spatial gradient of the image, which enables the estimation of the latter from the former.
Study Type
Retrospective and prospective.
Population
Human brain dMRI images: 617 healthy subjects from the public Human Connectome Project (HCP) Young Adults database, as well as 10 healthy volunteers and 1 ex vivo image scanned at our Center with stimulated-echo (STE) diffusion encoding and a long diffusion time of 1 second (which we will make publicly available).
Field Strength/Sequence
3T, standard spin-echo and STE dMRI.
Assessment
We validated our hypothesized relationship by evaluating the accuracy of the image spatial gradient estimated from the diffusion signal. Specifically, we compared it to the gold-standard spatial gradient approximated through finite difference, assessing the acute angle between the estimated and gold-standard gradient orientations. We furthermore measured the effects of the confounding factor of “fiber continuity”.
Statistical Tests
We used two-tailed t -tests (α=0.05) to compare the mean/median of the abovementioned acute angle across subjects to its null-hypothesis value (57.3°/60°), hypothesizing that it would be significantly smaller.
Results
We found the image gradient estimated from our diffusion model to be significantly related to that estimated via finite difference. The abovementioned acute angle had a mean/median of 51.3°/51.8° for the HCP and 53.0°/54.5° for our STE dataset, which were significantly smaller than those predicted by chance ( p = 0 and p < 10 −10 , respectively). The results of fiber continuity showed an effect that was stronger than but non-overlapping with our hypothesized effect.
Data Conclusion
Our results support our hypothesized relationship between within-voxel dMRI signal and image gradient, with an effect that was not explainable by the confounding factor of fiber continuity.
