Diffusion Kurtosis MRI (DKI) quantifies the degree of non-Gaussian water diffusion, which has been shown to be a very sensitive biomarker for microstructure in health and disease.However, DKI is not specific to any microstructural property per se since kurtosis might emerge from several different sources. Q-space trajectory encoding schemes have been proposed to decouple kurtosis related with the variance of different diffusion magnitudes (isotropic kurtosis) from kurtosis related with microscopic anisotropy (anisotropic kurtosis), under explicit assumptions of vanishing intra-compartmental kurtosis and diffusion time independence. Here, we introduce correlation tensor imaging (CTI) an approach that can be used to more generally resolve different kurtosis sources. CTI exploits the versatility of the double diffusion encoding (DDE) sequence and its associated Z tensor to resolve the isotropic and anisotropic components of kurtosis; in addition, CTI also disentangles these two measures from restricted, time-dependent kurtosis, thereby providing an index for intra-compartmental kurtosis. The theoretical foundations of CTI are presented, as well as predictive numerical simulations. The first, proof-of-concept CTI ex vivo experiments were performed in mouse brain specimens revealing the underlying sources of diffusion kurtosis. We find that anisotropic kurtosis dominates in white matter regions, while isotropic kurtosis is low for both white and grey matter; by contrast, areas with substantial partial volume effects show high isotropic kurtosis. Intra-compartmental kurtosis estimates were found to have positive values suggesting that non-Gaussian, time-dependant restricted diffusion effects are not negligible, at least for our acquisition settings. We then performed in vivo CTI in heathy adult rat brains, and found the results to be consistent with the ex vivo findings, thereby demonstrating that CTI is readily incorporated into preclinical scanners. CTI can be thus used as a powerful tool for resolving kurtosis sources in vivo.

Purpose Microscopic fractional anisotropy (µFA) can disentangle microstructural information from orientation dispersion. While double diffusion encoding (DDE) MRI methods are widely used to extract accurate µFA, it has only recently been proposed that powder‐averaged single diffusion encoding (SDE) signals, when coupled with the diffusion standard model (SM) and a set of constraints, could be used for µFA estimation. This study aims to evaluate µFA as derived from the spherical mean technique (SMT) set of constraints, as well as more generally for powder‐averaged SM signals. Methods SDE experiments were performed at 16.4 T on an ex vivo mouse brain (Δ/δ = 12/1.5 ms). The µFA maps obtained from powder‐averaged SDE signals were then compared to maps obtained from DDE‐MRI experiments (Δ/τ/δ = 12/12/1.5 ms), which allow a model‐free estimation of µFA. Theory and simulations that consider different types of heterogeneity are presented for corroborating the experimental findings. Results µFA, as well as other estimates derived from powder‐averaged SDE signals produced large deviations from the ground truth in both gray and white matter. Simulations revealed that these misestimations are likely a consequence of factors not considered by the underlying microstructural models (such as intercomponent and intracompartmental kurtosis). Conclusion Powder‐averaged SMT and (2‐component) SM are unable to accurately report µFA and other microstructural parameters in ex vivo tissues. Improper model assumptions and constraints can significantly compromise parameter specificity. Further developments and validations are required prior to implementation of these models in clinical or preclinical research.

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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.