Protocol generalisation for brain tissue microstructure estimation via hypernetwork-controlled geometric deep learning
Authors: Andrea Brigliadori, Leevi Kerkela, Hui Zhang
Organizations: Hawkes Institute and Department of Computer Science, University College London, London, United Kingdom
Abstract
Brain tissue microstructure estimation with machine learning provides higher computational efficiency than conventional fitting. However, machine learning still presents important limitations that hamper its clinical utility. Specifically, current models typically lack generalisation across diffusion MRI acquisition protocols and require retraining whenever b-vectors or b-values change. Moreover, the recent machine learning methods that were developed to address protocol generalisation lack rotational equivariance. Particularly suitable for dMRI parameter estimation is a geometric deep learning model known as spherical convolutional neural network (SCNN), which guarantees rotational equivariance and b-vector generalisation. However, this architecture currently does not account for b-values. Therefore, obtaining a model that combines protocol generalisation and rotational equivariance remains an open challenge. In this paper, we directly address this issue by incorporating explicit b-value dependence into an SCNN architecture via a hypernetwork. This new approach is illustrated using NODDI as an example forward model for estimating brain tissue microstructure. To evaluate b-value generalisation, the original and newly proposed SCNN architectures are trained on synthetic data and tested on both synthetic and real data across different b-value pairs. Results demonstrate that the proposed method achieves reduced RMSE and bias on synthetic data, as well as higher agreement with conventional NODDI fitting on real data, indicating improved robustness to unseen b-values and a reduced need for retraining. By combining generalisation across b-values with generalisation across b-vectors and rotational equivariance, the proposed framework enhances the applicability of deep learning to clinical diffusion MRI parameter estimation. Code available at https://github.com/aerdnairo/arXiv\_generalisedSCNN.
Diffusion MRI enables non-invasive probing of tissue microstructure, but accurate parameter estimation is challenged by noise-related effects. In supervised machine learning frameworks trained on simulated data, discrepancies between the noise characteristics of simulated and acquired signals introduce a form of covariate shift, whereby the input signal distribution differs between training and inference. We investigated the impact of this mismatch on microstructure parameter estimation and propose a realistic noise synthesis (RNS) framework to mitigate it. RNS incorporates both the Rician expectation and the effective post-processing noise variance into simulated training signals. The Rician expectation was modelled using a noise standard deviation estimated with MPPCA, while the effective standard deviation was derived from spherical harmonic residuals of preprocessed data. The method was evaluated using the cylinder-zeppelin and the SANDI models on simulated datasets across multiple SNR levels and on in vivo diffusion data with repeated acquisitions. Sensitivity to noise misestimation was also assessed. Ignoring magnitude-induced noise effects during training produced systematic, SNR-dependent parameter bias, particularly at low SNR. Incorporating the Rician expectation substantially reduced bias to the level of noise-aware nonlinear least-squares fitting. Modelling the effective standard deviation further improved precision. Performance was largely independent of regression architecture but sensitive to accurate noise estimation. These findings demonstrate that realistic noise modelling in simulated training data mitigates signal-domain covariate shift and is essential for unbiased supervised microstructure estimation, particularly in low-SNR regimes associated with high b-values or high spatial resolution.
Understanding the human brain requires access to its microscopic tissue architecture. Diffusion magnetic resonance imaging (MRI) provides the only noninvasive window into whole-brain microstructure in vivo, yet reliable quantitative mapping remains confined to specialized research settings requiring dense sampling and optimized acquisition protocols. To address this gap, we present a physics-informed generative microstructure network (PIGMENT) that learns a universal generative prior of human brain microstructure and adapts it zero-shot to each participant's measured data to recover subject-specific maps. Trained on 11375 scans spanning multiple sites, vendors, and field strengths, PIGMENT enabled reliable quantitative mapping for tensor, kurtosis, and NODDI models across external datasets from five independent centers. It remains effective where conventional fitting becomes unreliable, recovering meaningful maps from extremely sparse acquisitions while supporting downstream tractography and structural connectivity mapping. PIGMENT estimates demonstrated strong biological validity, preserving submillimeter cortical microarchitectural patterns and early-childhood white matter developmental trajectories from 10-fold accelerated scans. Furthermore, PIGMENT enables reliable quantitative tensor mapping on cost-efficient low-field systems and the extraction of tumor-related biomarkers using ultra-fast clinical protocols. Together, these results establish PIGMENT as a physics-informed foundation model that extends quantitative diffusion MRI into regimes traditionally too sparse, heterogeneous, or clinically constrained for reliable analysis.
Diffusion MRI (dMRI) relies on diffusion-weighted echo-planar imaging, which is highly susceptible to eddy-current-induced geometric distortions. These distortions vary across diffusion volumes according to gradient strength and direction, causing between-volume misalignment that can bias downstream microstructural analyses. Current state-of-the-art correction methods, such as FSL Eddy, achieve high-quality correction through iterative prediction-correction schemes but are computationally expensive. We propose Eddeep, a deep-learning framework for fast eddy-current distortion correction in dMRI. Eddeep decomposes the problem into two stages. First, a supervised image translation network standardises the appearance of diffusion-weighted and b=0 images, removing contrast differences that hinder reliable registration. Second, an unsupervised registration network estimates both eddy-current distortion and between-volume head motion parameters under a physics-constrained quadratic distortion model, enabling correction in a single forward pass. The method was trained on UK Biobank data and evaluated on both in-domain (UK Biobank) and out-of-domain (Memodyn) datasets. Across a range of complementary metrics, including between-volume jitter, diffusion kurtosis imaging residuals, signal irregularity, and mutual information, Eddeep achieved correction quality comparable to that of FSL Eddy while substantially reducing inference time. These results demonstrate that deep learning can provide accurate and efficient eddy-current distortion correction without relying on iterative optimisation, supporting the development of faster diffusion MRI processing pipelines for large-scale studies and clinical deployment. The code is available at: https://github.com/CIG-UCL/eddeep.