Physics-constrained unsupervised deep learning for accelerated diffusion MRI

Abstract

Diffusion Magnetic Resonance Imaging (dMRI) is a noninvasive technique that probes the microscopic Brownian movement of water molecules within neural tissues, providing insights into the underlying microstructural architecture. In dMRI, the displacement of spins is encoded in a domain called q-space through the use of diffusion-sensitizing gradients. Classical dMRI models, such as diffu sion tensor imaging (DTI), require only a few samples in q-space, but fall short in resolving crossing or diverging fiber bundles. To address these limitations, High Angular Resolution Diffusion Imaging (HARDI) was introduced to enhance f iber characterization by densely sampling the q-space across multiple spherical shells defined by different b-values, thereby detecting several fiber orientations within a single voxel. Building on this framework, advanced multi-shell tech niques such as Multi-Shell Spherical Deconvolution (MSMT-CSD) and Neurite Orientation Dispersion and Density Imaging (NODDI) have been developed, of fering refined insights into complex microstructural features. Nevertheless, the requirement for densely sampling q-space renders advanced dMRI techniques ex tremely time-consuming and impractical for clinical use. This thesis proposes a deep unsupervised Q-space Upsampling via physics-Constrained Coordinate based Implicit network (QUCCI) to accelerate multi-shell dMRI. QUCCI models the underlying volume as a continuous function in both spatial coordinates and q-space, enabling the sampling of q-space along arbitrary directions without the constraints of fixed sampling schemes. An encoder maps coordinates to a la tent code, and an MLP predicts the signal, allowing arbitrary q-space sampling without large training datasets or vendor harmonization. Physics-based regu larization stabilizes learning. Tested on 10 subjects at R = 10, 15, 22.5, and extended to joint q-space interpolation plus in-plane super-resolution for submil limeter whole-brain dMRI, QUCCI surpasses a recent deep-learning competitor, a least-squares baseline, and raw undersampled data. Slice-, subject-, and metric level evaluations, and downstream DTI, MSMT-CSD, and NODDI maps confirm its superior fidelity. QUCCI enables accelerated dMRI with minimal information loss, advancing the clinical feasibility of advanced multi-shell methods.