Recovering high-quality FODs from a reduced number of diffusion-weighted images using a model-driven deep learning architecture

TL;DR

This paper tackles the problem of reconstructing high-quality fibre orientation distributions (FODs) from a reduced set of diffusion-weighted images to shorten scan time. It introduces SDNet, a spherical deconvolution framework that integrates forward-model data consistency blocks with learnable regularisation, and adds a fixel-classification penalty to improve downstream fixel-based analyses. Across experiments on HCP data, SDNet demonstrates competitive FOD-based performance versus FOD-Net and clear advantages over MSMT-CSD, with the κ-tuned penalty enhancing fixel separation in multi-fibre voxels. The approach offers a practical pathway to faster diffusion MRI workflows while preserving reliability in tract- and fixel-based analyses.

Abstract

Fibre orientation distribution (FOD) reconstruction using deep learning has the potential to produce accurate FODs from a reduced number of diffusion-weighted images (DWIs), decreasing total imaging time. Diffusion acquisition invariant representations of the DWI signals are typically used as input to these methods to ensure that they can be applied flexibly to data with different b-vectors and b-values; however, this means the network cannot condition its output directly on the DWI signal. In this work, we propose a spherical deconvolution network, a model-driven deep learning FOD reconstruction architecture, that ensures intermediate and output FODs produced by the network are consistent with the input DWI signals. Furthermore, we implement a fixel classification penalty within our loss function, encouraging the network to produce FODs that can subsequently be segmented into the correct number of fixels and improve downstream fixel-based analysis. Our results show that the model-based deep learning architecture achieves competitive performance compared to a state-of-the-art FOD super-resolution network, FOD-Net. Moreover, we show that the fixel classification penalty can be tuned to offer improved performance with respect to metrics that rely on accurately segmented of FODs. Our code is publicly available at https://github.com/Jbartlett6/SDNet .

Figures (7)

• Figure 1: SDNet architecture, made up of alternating deep regularisation blocks and DWI consistency blocks. Each DWI consistency block is made up of 3D convolution blocks, the values above each set of layers represents the number of channels, which increase as follows: $\{94,128, 192, 256, 320, 384, 448\}$. The DWI consistency block shows the matrix inversion that is solved for each voxel independently.
• Figure 2: Qualitative results showing reconstructed FODs for HCP subject 130821 centred at voxel [38,98,70]. The top row consists of the a. Fully Sampled, b. SDNet, c.${\text{SDNet}}_{\kappa}$, d. FOD-Net, and e. MSMT CSD FODs. The bottom row shows a zoomed-in area of FODs, corresponding to the region highlighted by the white square, consisting of the f. Fully Sampled, g. SDNet, h.${\text{SDNet}}_{\kappa}$, i. FOD-Net, and j. MSMT CSD FODs. Where $\kappa$ is the hyperparameter which balances the SH error and fixel classification penalty terms in the loss function as per Eq. \ref{['eq:Loss']}.
• Figure 3: FODs taken from HCP subject 130821, centred at voxel [84,110,70]. The top row are the a. Fully Sampled, b. SDNet, and c.${\text{SDNet}}_{\kappa}$ FODs. The second row consists a zoomed-in region of FODs, corresponding to the region highlighted by the white square the contain the d. Fully Sampled, e. SDNet, and f.${\text{SDNet}}_{\kappa}$. FODs. Where $\kappa$ balances the SH error and fixel classification penalty terms in the loss function as per Eq. \ref{['eq:Loss']}.
• Figure 4: SSE and fixel difference error maps for slice 72 from HCP subject 130821. Top row: SSE error maps between the fully sampled FODs and the FODs reconstructed by a. SDNet, b.${\text{SDNet}}_{\kappa}$, c. FOD-Net and d. MSMT CSD. Bottom row: Number of fixels calculated for the fully sampled FOD minus the number of fixels calculated from the FODs reconstructed by e. SDNet, f.${\text{SDNet}}_{\kappa}$, g. FOD-Net, and h. MSMT CSD. Where $\kappa$ balances the SH error and fixel classification penalty terms in the loss function as per Eq. \ref{['eq:Loss']}. Blue voxels indicate underestimates, and red areas overestimates, of the number of fixels. Large SSE and fixel differences are highlighted by the black and red arrows respectively.
• Figure 5: Mean test-time FOD-based performance (Left: ACC, Right: SSE) in the white matter (WM), ROI-1-CC: corpus callosum containing a single fixel, ROI-2-MCP: intersection between the middle cerebellar peduncle and superior longitudinal fascicle containing 2 fixels, and ROI-3-SLF: intersection between the superior longitudinal fascicle, corticospinal tract and the corpus callosum containing 3 fixels. $\kappa$ balances the SH error and fixel classification penalty terms in the loss function as per Eq. \ref{['eq:Loss']}. Error bars indicate the standard error of the metrics, which have been averaged over the 7 test subjects.