COnstrained Reference frame diffusion TEnsor Correlation Spectroscopic (CORTECS) MRI: A practical framework for high-resolution diffusion tensor distribution imaging

Diffusion MRI studies with resolutions of a few hundred micrometers have consistently shown that in the cortex water diffusion occurs preferentially along radial and tangential orientations with respect to the cortical surface, in agreement with histology. These dominant orientations do not change significantly even if the relative contributions from microscopic water pools to the net voxel signal vary across studies that use different diffusion times, b-values, TEs, and TRs. With this in mind, we propose a practical new framework for measuring non-parametric diffusion tensor distribution (DTD) MRI by constraining the microscopic diffusion tensors of the DTD to be diagonalized using the same orthonormal reference frame of the mesoscopic voxel. In each voxel, the constrained DTD (cDTD) is completely determined by the correlation spectrum of the microscopic principal diffusivities associated with the axes of the voxel reference frame. Consequently, all cDTDs are inherently limited to the domain of positive definite tensors and can be reconstructed efficiently with numerical methods for solving Inverse Laplace Transform problems. Moreover, cDTDs can be measured using only data acquired with conventional single diffusion encoding, which can be obtained more efficiently than measurements with multiple diffusion encoding. In tissues with radial symmetry, such as the cortex, we can further constrain the cDTD to contain only cylindrically symmetric diffusion tensors and measure the 2D correlation spectra of radial and tangential diffusivities. To demonstrate this framework, we perform numerical simulations and analyze high-resolution dMRI data. We image 2D cDTDs in the cortex and derive marginal distributions of radial and tangential diffusivities, distributions of the microscopic fractional anisotropies and mean diffusivities, as well as their 2D correlation spectra to quantify the shape-size characteristics of the microscopic diffusion tensors. Signal components corresponding to specific bands in the measured correlation spectra show high specificity to cortical laminar structures observed with histology. Our framework drastically simplifies the measurement of non-parametric DTDs and may be applied retrospectively to analyze existing high-resolution dMRI data. Moreover, the framework provides a non-parametric generalization of DTI and subsumes existing diffusion signal representations and tissue models, enabling their harmonization, cross-validation, and optimization in specific clinical applications characterizing tissue changes.