Quantitative assessment of diffusional kurtosis anisotropy

Abstract

Diffusional kurtosis imaging (DKI) measures the diffusion and kurtosis tensors to quantify restricted, non-Gaussian diffusion that occurs in biological tissue. By estimating the kurtosis tensor, DKI accounts for higher order diffusion dynamics, when compared with diffusion tensor imaging (DTI), and consequently can describe more complex diffusion profiles. Here, we compare several measures of diffusional anisotropy which incorporate information from the kurtosis tensor, including kurtosis fractional anisotropy (KFA) and generalized fractional anisotropy (GFA), with the diffusion tensor-derived fractional anisotropy (FA). KFA and GFA demonstrate a net enhancement relative to FA when multiple white matter fiber bundle orientations are present in both simulated and human data. In addition, KFA shows net enhancement in deep brain structures, such as the thalamus and the lenticular nucleus, where FA indicates low anisotropy. Thus, KFA and GFA provide additional information relative to FA with regard to diffusional anisotropy, and may be particularly advantageous for the assessment of diffusion in complex tissue environments.

Keywords: DKI; FA; GFA; KFA; anisotropy; diffusion; kurtosis; non-Gaussian.

Fig. 1

Multiple Gaussian compartment model for one WM fiber bundle orientation with only anisotropic diffusion (A) and an additional isotropic compartment (B). Numbers at the top of each column represent the ratio λ_⊥/λ_‖ for that column. The fiber bundle orientation depicts the orientation the diffusion ellipsoid for each of the separate compartments, where the colored ellipsoid represents simulated WM fiber bundles and the gray spheres represent simulated isotropic diffusion. The blue diffusion ellipsoid is taken from the net diffusion tensor and is a way of visualizing FA. The dODF is used to calculate GFA and is taken from Eq. [10], using the kurtosis dPDF representation (10). W(n̂) illustrates the directional dependence of the kurtosis tensor and is calculated by Eq. [6]. The plots at the bottom of each column represent the anisotropy parameter values for λ_⊥/λ_‖ ratios between 0 and 1. Renderings of the diffusion ellipsoid, dODF, and W(n̂) are not shown to scale to emphasize anisotropic features, as FA, KFA, or GFA are not affected by the overall scaling. In panel A, KA_λ and KA_σ are always zero, as discussed in the text.

Fig. 2

Multiple Gaussian compartment model for 2 crossing fibers with only anisotropic diffusion (A) and an additional isotropic compartment (B). Numbers at the top of each column represent the crossing angle for that column, and the 3D renderings depicted in Fig. 2 are calculated from the same equations as those in Fig. 1. The plots at the bottom of each column represent the anisotropy parameter values for simulated crossing angles for each integer value between 1 and 90 degrees.

Fig. 3

Multiple Gaussian compartment model for 3 crossing fibers with only anisotropic diffusion (A) and an additional isotropic compartment (B). Numbers at the top of each column represent the crossing angle for that column, and the 3D renderings depicted in Fig. 2 are calculated from the same equations as those in Fig. 1. The plots at the bottom of each column represent the anisotropy parameter values for simulated crossing angles for each integer value between 1 and 90 degrees. For this example, both FA and KA_μ drop to zero at 90 degrees, while all other measures are non-zero.

Fig. 4

Representative anisotropy maps from a healthy volunteer. (A) Anisotropy maps for two slices taken from a healthy volunteer. MPRAGE and GFA color map (16) for the first slice (B) and second slice (C) point out a few regions of interest. (D) Sagittal MPRAGE image with white bars indicates the slice location for the parameter maps.

Fig. 5

Anisotropy difference maps. Representative transverse (A) and (B), sagittal (C), and coronal (D) slices from the difference maps highlight differences in the anisotropy parameters. The first column illustrates the average of the normalized GFA colormaps (16) illustrating WM structures in the normalized data. The second column overlays the template ROIs on the mean GFA map. The ROIs shown are CC (red), CB (green), SLF (blue), CR and IC (yellow), EC (orange), other WM structures (magenta), Thal (light grey), and LN (dark grey). The anisotropy difference maps shown are indicated at the top of each column, and the NFD column shows the NFD map averaged across all subjects. There is a strong correlation between regions enhanced in the KFA-FA difference map and regions with multiple fiber bundle orientations detected, depicted in the NFD maps.

Fig. 6

Representative transverse, sagittal, and coronal slices from the ICBM WM template as well as the mean of the normalized FA, GFA, and KFA parameter maps across all 5 subjects.

Fig. 7

(A) Inter- and (B) Intra-subject variability maps for FA, GFA, and KFA for the same slices depicted in Fig. 6. Inter-subject variability is calculated as the voxel-wise coefficient of variation of the parameter across all 5 subjects. Intra-subject variability is calculated as the voxel-wise coefficient of variation of the parameter for each of the 3 independent DKI acquisitions from each subject, which is then averaged across all 5 subjects. Inter-subject variability is comparable for each of the three parameters, although GFA inter-subject variability is slightly lower. However, intra-subject variability is higher for KFA than for FA or GFA, which may reflect the lower relative precision for the kurtosis tensor compared to the diffusion tensor.