Fast imaging of mean, axial and radial diffusion kurtosis

Abstract

Diffusion kurtosis imaging (DKI) is being increasingly reported to provide sensitive biomarkers of subtle changes in tissue microstructure. However, DKI also imposes larger data requirements than diffusion tensor imaging (DTI), hence, the widespread adaptation and exploration of DKI would benefit from more efficient acquisition and computational methods. To meet this demand, we recently developed a method capable of estimating mean kurtosis with only 13 diffusion weighted images. This approach was later shown to provide very accurate mean kurtosis estimates and to be more efficient in terms of contrast to noise per unit time. However, insofar, the computation of two other critical DKI parameters, radial and axial kurtosis, has required the estimation of all 22 variables parameterizing the full DKI signal expression. Here, we present two strategies for estimating all of DKI’s principal parameters – mean kurtosis, radial kurtosis, and axial kurtosis – using only 19 diffusion weighted images, compared to the current state-of-the-art acquisitions typically requiring about 60 images. The first approach is based on axially symmetric diffusion and kurtosis tensors, presented here for the first time, and referred to as axially symmetric DKI. The second approach is applicable in tissues with a priori known principal diffusion direction, and does not require fitting of any kind. The approaches are evaluated in human brain in vivo as well as in fixed rat spinal cord, and are demonstrated to provide metrics in good agreement with their full DKI counterparts estimated with nonlinear least squares. For small data sets and in white matter, axially symmetric DKI provides more accurate and robust estimates than unconstrained DKI. The significant acceleration achieved further paves the way to routine application of the technique.

Recent Developments in Fast Kurtosis Imaging

“…Note that in contrast to their diffusion tensor counterparts, they are not strictly rotationally invariant. The reason for this behavior is that in orthogonal fiber bundle crossings the diffusion eigenvalues may be degenerate (i.e., for such a 3D fiber arrangement there is no primary fiber direction and the diffusion tensor is isotropic) while the apparent kurtosis can differ among the fiber directions due to microstructural differences in the bundles [42]. Consequently, in this thought-experiment noise will determine which eigenvector will be deemed the primary direction thus causing the estimated directional kurtosis values to vary between measurements.…”

“…For estimation of D and W from reduced data sets (say a 1-9-9 acquisition, but in principle it could be other low angular resolution DKI acquisitions), a substantial reduction of parameters in the DKI signal expression would be needed. An effective strategy to achieve such a reduction was proposed in Hansen et al [42], and builds on the observation that if the system is assumed to possess axial symmetry, the apparent kurtosis W(n) can be expressed by only three independent parameters: lettingẑ be parallel to the symmetry axis, W(n) is characterized by W, W || = W(ẑ) (axial kurtosis), and W ⊥ (radial kurtosis). Stated in terms of the diffusion tensor eigenvectors (v 1 ,v 2 ,v 3 in decreasing order of the eigenvalues as above), the tensor-based directional kurtosis parameters are defined to be:…”

“…Rescaling of the axial and radial tensor kurtosis is convenient and causes the axial kurtosis definitions to become identical but radial kurtosis as defined in Equation (2.5.1) is in general different from the convention in Equation (2.1.4), unless there is axial symmetry [42].…”

“…Under axisymmetry, D and W share their symmetry axis so that D only adds two parameters. Finally, signal normalization adds one parameter, producing a total of eight free parameters for axisymmetric DKI [42]. Even in regions where axial symmetry is unlikely to hold in reality, the simplified DKI signal expression thus obtained yields reliable estimates of mean and directional kurtosis and diffusion metrics [42].…”

“…Here we review recent developments enabling fast kurtosis imaging based on small data sets (13 or 19 images) and with near-instant post-processing [37][38][39][40][41][42]. The review is structured such that first the theoretical foundation of DKI and WMTI is recapitulated briefly.…”