Probing white-matter microstructure with higher-order diffusion tensors and susceptibility tensor MRI

Abstract

Diffusion MRI has become an invaluable tool for studying white matter microstructure and brain connectivity. The emergence of quantitative susceptibility mapping and susceptibility tensor imaging (STI) has provided another unique tool for assessing the structure of white matter. In the highly ordered white matter structure, diffusion MRI measures hindered water mobility induced by various tissue and cell membranes, while susceptibility sensitizes to the molecular composition and axonal arrangement. Integrating these two methods may produce new insights into the complex physiology of white matter. In this study, we investigated the relationship between diffusion and magnetic susceptibility in the white matter. Experiments were conducted on phantoms and human brains in vivo. Diffusion properties were quantified with the diffusion tensor model and also with the higher order tensor model based on the cumulant expansion. Frequency shift and susceptibility tensor were measured with quantitative susceptibility mapping and susceptibility tensor imaging. These diffusion and susceptibility quantities were compared and correlated in regions of single fiber bundles and regions of multiple fiber orientations. Relationships were established with similarities and differences identified. It is believed that diffusion MRI and susceptibility MRI provide complementary information of the microstructure of white matter. Together, they allow a more complete assessment of healthy and diseased brains.

Keywords: MRI; cumulant; diffusion tensor imaging; generalized diffusion tensor imaging; higher order tensor; kurtosis; susceptibility tensor imaging; white matter.

Figure 1

Signal behavior of diffusion weighted images of a phantom. (A) A T2-weighted image shows the crossing fiber structure of the phantom. Four voxels highlighted regions of fiber crossing (green), single fiber in a 45°-angle (blue), vertical fiber (magenta) and isotropic fluid (red). (B) Diffusion-weighted signals as a function of the b-values showed distinctive characteristics for the four voxels highlighted in (A). In the fluid and the single fiber along the direction of [0, 0, 1], the signals approached the noise floor when b > 2000 s/mm² (arrow).

Figure 2

Higher-order tensors estimated with and without Tikhonov regularization. (A,B) Eigenvalues of the second and the fourth order tensor estimated without regularization. The fourth order tensor was overestimated for the fluid (arrows). (C,D) Corresponding eigenvalues of the second and the fourth order tensor estimated with regularization. The contrast between regions of fiber crossing and surrounding areas was significantly improved.

Figure 3

Comparison of HOT (A,B) and AMS (C,D) glyphs in fiber crossing. (A) A T2-weighted image illustrated a region of complex fiber structures with both single fibers and crossing fibers (red box). (B) The PDF glyphs over this ROI reconstructed by HOT agreed with the known phantom structure. (C) An illustration of myelinated axons crossing at 45°. Each voxel in the myelin sheath contained an anisotropic susceptibility tensor. (D) The distribution of AMS depicted a 45° crossing.

Figure 4

Comparison of frequency maps measured experimentally and those fitted with susceptibility tensors. (A) Comparison of representative experimental and fitted frequency maps along three orientations. Fitted maps were slightly smoothed but showing similar contrast. (B) A representative root-mean-squared-error (RMSE) map between the experimental and fitted frequency along one orientation. Significant errors were only observed around tissue boundaries. (C) Line profiles of experimental and fitted frequency maps for the same three orientations as in (A). (D) Experimental and fitted frequency values along the line shown in (C) demonstrating high correlation.

Figure 5

Comparison of fiber orientations reconstructed by HOT and the orientation dependence of AMS. (A) Color coded FA map reconstructed by DTI (left) and fiber orientations of selected ROI reconstructed by HOT. The color scheme was: red representing left-right, green representing anterior-posterior and blue representing superior-inferior. In the top row, fiber orientations were primarily unidirectional in the left-right direction; in the bottom row, fiber crossings were extensive and clearly visible in the PDF glyphs. (B) STI eigenvector orientation map (left) and corresponding AMS plot as a function of fiber angle over the same ROI in (A). AMS was calculated using the adjacent green ROI as a reference to reduce global heterogeneity of magnetic susceptibility. Fiber angles were computed as the angles between DTI fiber orientations and the B₀ field (superior-inferior).