Exploring the 3D geometry of the diffusion kurtosis tensor—Impact on the development of robust tractography procedures and novel biomarkers

Highlights

• Geometry of the kurtosis tensor is elucidated using multi-compartmental models.

• Novel methods for estimating fibre direction and radial kurtosis are proposed.

• Position of kurtosis tensor maxima is related to the direction of crossing fibres.

• Kurtosis tensor direction estimates have small errors for large crossing angles.

• Kurtosis tensor can be used to accurately resolve corpus callosum fibres in vivo.

Abstract

Diffusion kurtosis imaging (DKI) is a diffusion-weighted technique which overcomes limitations of the commonly used diffusion tensor imaging approach. This technique models non-Gaussian behaviour of water diffusion by the diffusion kurtosis tensor (KT), which can be used to provide indices of tissue heterogeneity and a better characterisation of the spatial architecture of tissue microstructure. In this study, the geometry of the KT is elucidated using synthetic data generated from multi-compartmental models, where diffusion heterogeneity between intra- and extra-cellular media is taken into account, as well as the sensitivity of the results to each model parameter and to synthetic noise. Furthermore, based on the assumption that the maxima of the KT are distributed perpendicularly to the direction of well-aligned fibres, a novel algorithm for estimating fibre direction directly from the KT is proposed and compared to the fibre directions extracted from DKI-based orientation distribution function (ODF) estimates previously proposed in the literature. Synthetic data results showed that, for fibres crossing at high intersection angles, direction estimates extracted directly from the KT have smaller errors than the DKI-based ODF estimation approaches (DKI-ODF). Nevertheless, the proposed method showed smaller angular resolution and lower stability to changes of the simulation parameters. On real data, tractography performed on these KT fibre estimates suggests a higher sensitivity than the DKI-based ODF in resolving lateral corpus callosum fibres reaching the pre-central cortex when diffusion acquisition is performed with five b-values. Using faster acquisition schemes, KT-based tractography did not show improved performance over the DKI-ODF procedures. Nevertheless, it is shown that direct KT fibre estimates are more adequate for computing a generalised version of radial kurtosis maps.