Diffusion MRI (dMRI) is the primary imaging modality used to study brain microstructure in vivo. Reliable and computationally efficient parameter inference for common dMRI biophysical models is a challenging inverse problem, due to factors such as variable dimensionalities (reflecting the unknown number of distinct white matter fiber populations in a voxel), low signal-to-noise ratios, and non-linear forward models. These challenges have led many existing methods to use biologically implausible simplified models to stabilize estimation, for instance, assuming shared microstructure across all fiber populations within a voxel. In this work, we introduce a novel sequential method for multi-fiber parameter inference that decomposes the task into a series of manageable subproblems. These subproblems are solved using deep neural networks tailored to problem-specific structure and symmetry, and trained via simulation. The resulting inference procedure is largely amortized, enabling scalable parameter estimation and uncertainty quantification across all model parameters. Simulation studies and real imaging data analysis using the Human Connectome Project (HCP) demonstrate the advantages of our method over standard alternatives. In the case of the standard model of diffusion, our results show that under HCP-like acquisition schemes, estimates for extra-cellular parallel diffusivity are highly uncertain, while those for the intra-cellular volume fraction can be estimated with relatively high precision.

The Orientation Distribution Function (ODF) characterizes key brain microstructural properties and plays an important role in understanding brain structural connectivity. Recent works introduced Implicit Neural Representation (INR) based approaches to form a spatially aware continuous estimate of the ODF field and demonstrated promising results in key tasks of interest when compared to conventional discrete approaches. However, traditional INR methods face difficulties when scaling to large-scale images, such as modern ultra-high-resolution MRI scans, posing challenges in learning fine structures as well as inefficiencies in training and inference speed. In this work, we propose HashEnc, a grid-hash-encoding-based estimation of the ODF field and demonstrate its effectiveness in retaining structural and textural features. We show that HashEnc achieves a 10 % enhancement in image quality while requiring 3 $$\times $$ less computational resources than current methods. Our code can be found at https://github.com/MunzerDw/NODF-HashEnc .

High angular resolution diffusion imaging (HARDI) is a type of diffusion magnetic resonance imaging (dMRI) that measures diffusion signals on a sphere in q-space. It has been widely used in data acquisition for human brain structural connectome analysis. To more accurately estimate the structural connectome, dense samples in q-space are often acquired, potentially resulting in long scanning times and logistical challenges. This paper proposes a statistical method to select q-space directions optimally and estimate the local diffusion function from sparse observations. The proposed approach leverages relevant historical dMRI data to calculate a prior distribution to characterize local diffusion variability in each voxel in a template space. For a new subject to be scanned, the priors are mapped into the subject-specific coordinate and used to help select the best q-space samples. Simulation studies demonstrate big advantages over the existing HARDI sampling and analysis framework. We also applied the proposed method to the Human Connectome Project data and a dataset of aging adults with mild cognitive impairment. The results indicate that with very few q-space samples (e.g., 15 or 20), we can recover structural brain networks comparable to the ones estimated from 60 or more diffusion directions with the existing methods.