Correlation tensor magnetic resonance imaging.

Diffusional Kurtosis Magnetic Resonance Imaging (DKI) quantifies the extent of non-Gaussian water diffusion, which has been shown to be a sensitive biomarker for microstructure in health and disease. However, DKI is not specific to any microstructural property per se since kurtosis may emerge from several different sources. Q-space trajectory encoding schemes have been proposed for decoupling kurtosis arising from the variance of mean diffusivities (isotropic kurtosis) from kurtosis driven by microscopic anisotropy (anisotropic kurtosis). Still, these methods assume that the system is comprised of multiple Gaussian diffusion components with vanishing intra-compartmental kurtosis (associated with restricted diffusion). Here, we develop a more general framework for resolving the underlying kurtosis sources without relying on the multiple Gaussian diffusion approximation. We introduce Correlation Tensor MRI (CTI) - an approach harnessing the versatility of double diffusion encoding (DDE) and its sensitivity to displacement correlation tensors capable of explicitly decoupling isotropic and anisotropic kurtosis components from intra-compartmental kurtosis effects arising from restricted (and time-dependent) diffusion. Additionally, we show that, by subtracting these isotropic and anisotropic kurtosis components from the total diffusional kurtosis, CTI provides an index that is potentially sensitive to intra-compartmental kurtosis. The theoretical foundations of CTI, as well as the first proof-of-concept CTI experiments in ex vivo mouse brains at ultrahigh field of 16.4 T, are presented. We find that anisotropic and isotropic kurtosis can decouple microscopic anisotropy from substantial partial volume effects between tissue and free water. Our intra-compartmental kurtosis index exhibited positive values in both white and grey matter tissues. Simulations in different synthetic microenvironments show, however, that our current CTI protocol for estimating intra-compartmental kurtosis is limited by higher order terms that were not taken into account in this study. CTI measurements were then extended to in vivo settings and used to map heathy rat brains at 9.4 T. These in vivo CTI results were found to be consistent with our ex vivo findings. Although future studies are still required to assess and mitigate the higher order effects on the intra-compartmental kurtosis index, our results show that CTI's more general estimates of anisotropic and isotropic kurtosis contributions are already ripe for future in vivo studies, which can have significant impact our understanding of the mechanisms underlying diffusion metrics extracted in health and disease.

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