White matter characterization with diffusional kurtosis imaging

Abstract

Diffusional kurtosis imaging (DKI) is a clinically feasible extension of diffusion tensor imaging that probes restricted water diffusion in biological tissues using magnetic resonance imaging. Here we provide a physically meaningful interpretation of DKI metrics in white matter regions consisting of more or less parallel aligned fiber bundles by modeling the tissue as two non-exchanging compartments, the intra-axonal space and extra-axonal space. For the b-values typically used in DKI, the diffusion in each compartment is assumed to be anisotropic Gaussian and characterized by a diffusion tensor. The principal parameters of interest for the model include the intra- and extra-axonal diffusion tensors, the axonal water fraction and the tortuosity of the extra-axonal space. A key feature is that these can be determined directly from the diffusion metrics conventionally obtained with DKI. For three healthy young adults, the model parameters are estimated from the DKI metrics and shown to be consistent with literature values. In addition, as a partial validation of this DKI-based approach, we demonstrate good agreement between the DKI-derived axonal water fraction and the slow diffusion water fraction obtained from standard biexponential fitting to high b-value diffusion data. Combining the proposed WM model with DKI provides a convenient method for the clinical assessment of white matter in health and disease and could potentially provide important information on neurodegenerative disorders.

Copyright © 2011 Elsevier Inc. All rights reserved.

Figures

Fig. 1

Illustration of the b-value dependence of the criterion of Eq. (6) for determining whether the diffusion is effectively Gaussian in an axonal compartment consisting of two crossing fibers oriented at polar angles (θA ,θB) relative to a particular diffusion direction of interest, as illustrated in Fig. 1(a). Depending on the polar angles (shown in degrees), this system can be considered a “Gaussian compartment” when the (Dab) is smaller than the plotted values in Fig. 1(b), with Da the free intra-axonal diffusivity. The central portion of the plot and the corner regions correspond to the most Gaussian diffusion.

Fig. 2

WM parametric transversal maps as overlays on the MPRAGE image of a healthy young control: (a) the AWF according to Eq. (7); (b) the axonal diffusivity according to Eq. (12); (c) the axial EAS diffusivity according to Eq. (13); (d) the radial EAS diffusivity according to (Eq. (14); (e) the tortuosity of the EAS accordign to Eq. (15). A mask was applied to the parametric maps that selects regions with aligned fibers according to Eq. (16).

Fig. 3

Histograms of the WM parameters of a healthy young control over all WM voxels consisting of aligned fibers (according to Eqn. (16)): (a) the AWF according to Eq. (7); (b) the axonal diffusivity according to Eq. (12); (c) the axial EAS diffusivity according to (Eq. (13); (d) the radial EAS diffusivity according to Eq. (14); (e) the tortuosity of the EAS according to Eq. (15). The histograms of the other 2 subjects look very similar (not shown here).

Fig. 4

Mean values of the WM indices in 3 healthy young adults: (a) the AWF according to Eq. (7); (b) the axonal diffusivity according to Eq. (12); (c) the axial EAS diffusivity according to (Eq. (13); (d) the radial EAS diffusivity according to Eq. (14); (e) the tortuosity of the EAS according to Eq. (15). The error bars represent the standard variation for all WM voxels consisting of aligned fibers (mask according to Eqn. (16)).

Fig. 5

The decay of the DWI-signal relative to the b = 0 – signal for different fiber bundles with the diffusion gradient applied in the direction perpendicular to the fiber bundle. The solid lines represent the optimal biexponential fits.

Fig. 6

Comparison between the parameters obtained from biexponential fitting to high b-value diffusion data in the slice direction of the patient coordinate system and the DKI-WM model parameters for ROIs with the main fiber direction parallel to the AC-PC plane. Bland-Altman plots are shown assessing the agreement between: (a) the slow diffusion coefficient, Ds, and IAS diffusivity, Da,slice; (b) the fast diffusion coefficient, Df, and EAS diffusivity, De,slice; (c) the biexponential slow component volume fraction fbiexp, and the AWF fKmax (Eq. (7)); (d) the biexponential slow component volume fraction fbiexp, and the AWF fROI (Eq. (8)). In each plot, the mean bias and limits of agreement are indicated by the solid and dashed lines, respectively. The radial EAS diffusivity is lower, and the AWF higher, in the ROIs in the corpus callosum (□) than in the ROIs of the forceps major (●) and inferior occipital fasciculus (●).

Fig. B.1

Histograms of (a) η1, and (b) η2, as defined in Eq. (B.7), and (c) Kmin (the minimum kurtosis minimum for all directions) over all non-CSF voxels of the brain of a healthy young control. The η-values show a reasonably narrow distribution centered around 1 (with standard deviations SD = 0.3), which corresponds to the upper sign solution of Eqn. (B.3) and (B.4) and indicates that De,i ≥ Da,i in the brain. The finite SD may reflect measurement noise as well as the approximate nature of our model. We also noted negative η-values in a very small number of voxels of the corpus callosum (< 0.2 % of all WM-voxels), but neglected those voxels as the corresponding D3-values were very small which makes the corresponding kurtosis tensor elements difficult to be determine accurately. The Kmin values show a distribution of predominantly positive values centered around 0.58 (with standard deviation SD = 0.22), indicating that De,i ≥ Da,i in any frame of reference.