Spherical convolutional neural networks can improve brain microstructure estimation from diffusion MRI data

TL;DR

This work tackles the inverse problem of estimating brain microstructure from diffusion MRI by introducing rotationally invariant spherical convolutional neural networks (sCNNs) that predict Gaussian-compartment parameters directly from full dMRI data. The authors validate the approach on simulated data and apply it to clinical scans, showing superior accuracy to the spherical mean technique and competitive performance with an MLP, while achieving substantially lower rotational variance. Importantly, the framework is extended to a three-compartment model that enables apparent neural soma density estimation using tensor-valued diffusion encoding, demonstrating generalizability to additional Gaussian compartments. The findings suggest that sCNNs can deliver robust, rotationally stable microstructure maps with practical implications for faster, more reliable diffusion MRI analyses in research and clinical settings.

Abstract

Diffusion magnetic resonance imaging is sensitive to the microstructural properties of brain tissue. However, estimating clinically and scientifically relevant microstructural properties from the measured signals remains a highly challenging inverse problem that machine learning may help solve. This study investigated if recently developed rotationally invariant spherical convolutional neural networks can improve microstructural parameter estimation. We trained a spherical convolutional neural network to predict the ground-truth parameter values from efficiently simulated noisy data and applied the trained network to imaging data acquired in a clinical setting to generate microstructural parameter maps. Our network performed better than the spherical mean technique and multi-layer perceptron, achieving higher prediction accuracy than the spherical mean technique with less rotational variance than the multi-layer perceptron. Although we focused on a constrained two-compartment model of neuronal tissue, the network and training pipeline are generalizable and can be used to estimate the parameters of any Gaussian compartment model. To highlight this, we also trained the network to predict the parameters of a three-compartment model that enables the estimation of apparent neural soma density using tensor-valued diffusion encoding.

Figures (5)

• Figure 1: Network for two-compartment model parameter prediction. The input is normalized two-shell data expanded using spherical harmonics up to degree eight. The signals undergo spherical convolutions, non-linearities, and spectral pooling to produce the predicted orientation distribution function. After the initial three convolutions, global mean pooling is applied in the signal domain, and the resulting arrays are concatenated to create a nearly rotationally invariant feature vector passed on to the FCN that outputs the predicted scalar parameter.
• Figure 2: Mean squared error of the estimated two-compartment model parameters on the test dataset for different values of intra-neurite diffusivity ($d$) and intra-neurite signal fraction ($f$). The first row (A-E) shows the results for $d$ and the second row (F-J) shows the results for $f$. Deep learning-based methods outperformed the spherical mean technique in all parts of the parameter space. The asterisk (*) refers to models trained with randomly rotated training data.
• Figure 3: Axial slices of the intra-neurite diffusivity (A-C) and intra-neurite signal fraction (G-I) maps generated using the spherical convolutional neural network, multi-layer perceptron, and spherical mean technique. The second row (D-F) shows the differences between the intra-neurite diffusivity maps and the fourth row (J-L) shows the differences between the intra-neurite signal fraction maps.
• Figure 4: Neurite orientation distribution functions overlaid on a map of intra-neurite signal fraction generated by the spherical convolutional neural network trained with randomly rotating the training data. The colour represents the principal direction, and the size is scaled according to neurite density. This coronal slice shows the intersection of the corticospinal tract and the corpus callosum.
• Figure 5: Axial slices of the intra-neurite diffusivity ($d_\text{i}$), spherical compartment diffusivity ($d_\text{sph}$), intra-neurite signal fraction ($f_\text{i}$), and spherical compartment signal fraction ($f_\text{sph}$) maps generated by the spherical convolutional neural network trained with randomly rotating the training data.