Higher Order Tensor Diffusion Imaging of Complex White Matter Fiber Tracts

Resolving multiple fiber orientations within one imaging voxel is critical for accurate quantification of tissue microstructure and faithful reconstruction of the complex neural fiber pathways. It is recognized that the diffusion process in brain tissues is generally non-Gaussian and recently there have been multiple methods developed specifically to account for this non-Gaussian property. Many of these efforts, however, have been largely focused on improving fiber tracking algorithms rather than providing a quantitative assessment of the deviation from Gaussian diffusion. Consequently, fast and quantitative assessment of this non-Gaussian property is critically needed. Developing a quantitative measurement of the non-Gaussian diffusion processes may provide powerful tools to assess changes in white matter that are due to axonal damage or degeneration. Generalized diffusion tensor imaging (GDTI) with the use of higher order tensors (HOT) provides one such method to identify, characterize and visualize underlying fiber structures. An optimal scan protocol, which estimates the fourth-order diffusion tensor, is needed in order to maximize the efficiency and speed of the data acquisition. This optimization was investigated for a phantom that models crossing white matter fibers and compared to in vivo scans. The minimum number of b-values, b-value magnitudes, and the minimum number of gradient directions sufficient to estimate fourth order diffusion tensors was identified.

Gold standards were established by acquiring images using five b-values and a large number of gradient directions for both the phantom and in vivo data sets. The fourth order diffusion tensors were then calculated for one, two, and three b-value subsets of the original five b-value data for both phantom and in vivo cases. For each subset, the tensors were converted to a two-dimensional 9×9 matrix and decomposed using eigenvalue decomposition. Three scalar metrics were developed to characterize the non-Gaussian diffusion. The mean of the eigenvalues represents the fourth-order deviation from a Gaussian diffusion, the fourth order FA provides a measure of the variance within the fourth order diffusion distribution, and the variance-to-mean ratio (VMR) characterizes the signal distribution across the eigenvalues.

The scalar metrics for each b-value subset was compared to the gold standard by way of a Root Mean Square Error (RMSE). The normalized RMSE was then plotted for each metric across all subsets and the b-value magnitude combination corresponding to the lowest error was identified. It was found that a single b-value is not sufficient for the scalar representation of the fourth order diffusion tensor. While a three b-value subset had the lowest error, it was shown that two b-values provided acceptable image quality and fourth order diffusion information.