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Diffusion MRI uses the random displacement of water molecules to sensitize the signal to brain microstructure and to properties such as the density and shape of cells. Microstructure modeling techniques aim to estimate these properties from acquired data by separating the signal between virtual tissue 'compartments' such as the intra-neurite and the extra-cellular space. A key challenge is that the diffusion MRI signal is relatively featureless compared with the complexity of brain tissue. Another challenge is that the tissue microstructure is wildly different within the gray and white matter of the brain. In this review, we use results from multidimensional diffusion encoding techniques to discuss these challenges and their tentative solutions. Multidimensional encoding increases the information content of the data by varying not only the b-value and the encoding direction but also additional experimental parameters such as the shape of the b-tensor and the echo time. Three main insights have emerged from such encoding. First, multidimensional data contradict common model assumptions on diffusion and T 2 relaxation, and illustrates how the use of these assumptions cause erroneous interpretations in both healthy brain and pathology. Second, many model assumptions can be dispensed with if data are acquired with multidimensional encoding. The necessary data can be easily acquired in vivo using protocols optimized to minimize Cramér-Rao lower bounds. Third, microscopic diffusion anisotropy reflects the presence of axons but not dendrites. This insight stands in contrast to current 'neurite models' of brain tissue, which assume that axons in white matter and dendrites in gray matter feature highly similar diffusion. Nevertheless, as an axon-based contrast, microscopic anisotropy can differentiate gray and white matter when myelin alterations confound conventional MRI contrasts., Competing Interests: Declaration of Competing Interest Markus Nilsson and Filip Szczepankiewicz declare ownership interests in Random Walk Imaging, which holds patents pertaining to the methods presented herein. Remaining authors declare no conflict of interest., (Copyright © 2023. Published by Elsevier Inc.)

Specific features of white matter microstructure can be investigated by using biophysical models to interpret relaxation-diffusion MRI brain data. Although more intricate models have the potential to reveal more details of the tissue, they also incur time-consuming parameter estimation that may converge to inaccurate solutions due to a prevalence of local minima in a degenerate fitting landscape. Machine-learning fitting algorithms have been proposed to accelerate the parameter estimation and increase the robustness of the attained estimates. So far, learning-based fitting approaches have been restricted to microstructural models with a reduced number of independent model parameters where dense sets of training data are easy to generate. Moreover, the degree to which machine learning can alleviate the degeneracy problem is poorly understood. For conventional least-squares solvers, it has been shown that degeneracy can be avoided by acquisition with optimized relaxation-diffusion-correlation protocols that include tensor-valued diffusion encoding. Whether machine-learning techniques can offset these acquisition requirements remains to be tested. In this work, we employ artificial neural networks to vastly accelerate the parameter estimation for a recently introduced relaxation-diffusion model of white matter microstructure. We also develop strategies for assessing the accuracy and sensitivity of function fitting networks and use those strategies to explore the impact of the acquisition protocol. The developed learning-based fitting pipelines were tested on relaxation-diffusion data acquired with optimal and sub-optimal acquisition protocols. Networks trained with an optimized protocol were observed to provide accurate parameter estimates within short computational times. Comparing neural networks and least-squares solvers, we found the performance of the former to be less affected by sub-optimal protocols; however, model fitting networks were still susceptible to degeneracy issues and their use could not fully replace a careful design of the acquisition protocol., (Copyright © 2021. Published by Elsevier Inc.)

In diffusion MRI (dMRI), microscopic diffusion anisotropy can be obscured by orientation dispersion. Separation of these properties is of high importance, since it could allow dMRI to non-invasively probe elongated structures such as neurites (axons and dendrites). However, conventional dMRI, based on single diffusion encoding (SDE), entangles microscopic anisotropy and orientation dispersion with intra-voxel variance in isotropic diffusivity. SDE-based methods for estimating microscopic anisotropy, such as the neurite orientation dispersion and density imaging (NODDI) method, must thus rely on model assumptions to disentangle these features. An alternative approach is to directly quantify microscopic anisotropy by the use of variable shape of the b-tensor. Along those lines, we here present the 'constrained diffusional variance decomposition' (CODIVIDE) method, which jointly analyzes data acquired with diffusion encoding applied in a single direction at a time (linear tensor encoding, LTE) and in all directions (spherical tensor encoding, STE). We then contrast the two approaches by comparing neurite density estimated using NODDI with microscopic anisotropy estimated using CODIVIDE. Data were acquired in healthy volunteers and in glioma patients. NODDI and CODIVIDE differed the most in gray matter and in gliomas, where NODDI detected a neurite fraction higher than expected from the level of microscopic diffusion anisotropy found with CODIVIDE. The discrepancies could be explained by the NODDI tortuosity assumption, which enforces a connection between the neurite density and the mean diffusivity of tissue. Our results suggest that this assumption is invalid, which leads to a NODDI neurite density that is inconsistent between LTE and STE data. Using simulations, we demonstrate that the NODDI assumptions result in parameter bias that precludes the use of NODDI to map neurite density. With CODIVIDE, we found high levels of microscopic anisotropy in white matter, intermediate levels in structures such as the thalamus and the putamen, and low levels in the cortex and in gliomas. We conclude that accurate mapping of microscopic anisotropy requires data acquired with variable shape of the b-tensor., (Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.)