The apparent stiffness tensor is relevant for characterizing trabecular bone quality. Previous studies have used morphology-stiffness relationships for estimating the apparent stiffness tensor. In this paper, we propose to train spherical convolutional neural networks (SphCNNs) to estimate this tensor. Information of the edges, trabecular thickness, and spacing are summarized in functions on the unitary sphere used as inputs for the SphCNNs. The concomitant dimensionality reduction makes it possible to train neural networks on relatively small datasets. The predicted tensors were compared to the stiffness tensors computed by using the micro-finite element method (mu FE), which was considered as the gold standard, and models based on fourth-order fabric tensors. Combining edges and trabecular thickness yields significant improvements in the accuracy compared to the methods based on fourth-order fabric tensors. From the results, SphCNNs are promising for replacing the more expensive mu FE stiffness estimations.

ObjectiveSurvival Rate Prediction (SRP) is a valuable tool to assist in the clinical diagnosis and treatment planning of lung cancer patients. In recent years, deep learning (DL) based methods have shown great potential in medical image processing in general and SRP in particular. This study proposes a fully-automated method for SRP from computed tomography (CT) images, which combines an automatic segmentation of the tumor and a DL-based method for extracting rotational-invariant features. MethodsIn the first stage, the tumor is segmented from the CT image of the lungs. Here, we use a deep-learning-based method that entails a variational autoencoder to provide more information to a U-Net segmentation model. Next, the 3D volumetric image of the tumor is projected onto 2D spherical maps. These spherical maps serve as inputs for a spherical convolutional neural network that approximates the log risk for a generalized Cox proportional hazard model. ResultsThe proposed method is compared with 17 baseline methods that combine different feature sets and prediction models using three publicly-available datasets: Lung1 (n=422), Lung3 (n=89), and H&N1 (n=136). We observed comparable C-index scores compared to the best-performing baseline methods in a 5-fold cross-validation on Lung1 (0.59 +/- 0.03 vs. 0.62 +/- 0.04). In comparison, it slightly outperforms all methods in inter-data set evaluation (0.64 vs. 0.63). The best-performing method from the first experiment reduced its performance to 0.61 and 0.62 for Lung3 and H&N1, respectively. DiscussionThe experiments suggest that the performance of spherical features is comparable with previous approaches, but they generalize better when applied to unseen datasets. That might imply that orientation-independent shape features are relevant for SRP. The performance of the proposed method was very similar, using manual and automatic segmentation methods. This makes the proposed model useful in cases where expert annotations are not available or difficult to obtain.

Brain tractography involves mapping diffusion-weighted images (DWI) onto streamlines representing neural fibre bundles. Recent research avenues have framed tractography into a reinforcement learning (RL) framework with actor-critic models. However, previous RL-based methods may compromise geometrical relations between the input (DWI) and output (tractogram).

More specifically, 3D rotations applied to the input of RL-based tractography are not adequately reflected in the output, indicating a lack of SO3 equivariance. This study aims to restore the equivariance present in previous non-learning-based methods (e.g., iFOD2 from MRtrix3) to RL-based tractography.

To achieve this, we introduce SO3 equivariant and invariant components for the actors (direction prediction model) and critics (q-value prediction model), respectively. We employ an SE3-equivariant transformer as the next direction prediction function. The fact that both the input DWI and the output directional update can be represented as spherical tensors and transform under representations of SO3 makes this formulation a natural fit for the present problem. 

Another benefit of RL-based tractography is that incorporating local neighbourhoods can help mitigate well-known tractography problems (e.g. kissing, crossing, fanning). Our proposed algorithm extracts neighbourhood information as a predefined graph with spherical signals on the nodes.

The contribution of this work is threefold. First, we discuss rotational equivariance in streamlined tractography on a theoretical level. Second, we propose a method that combines RL-based tractography with an equivariant model. Third, we evaluate the equivariance of the proposed method both locally and globally.

Structural connectomics derives subject-specific brain connectivity from diffusion-weighted MRI and has potential as a biomarker for clinical Parkinson’s disease (PD) detection. In this study, we applied probabilistic tractography (iFOD2) to derive different types of connectomes and analyzed group discriminability between PD patients and healthy controls from the Parkinson's Progression Markers Initiative (PPMI) dataset (n = 233). Particular emphasis was placed on the streamline filtering stage with SIFT2 and the comparison of different connectivity metrics, including streamline count, fractional anisotropy (FA), axial diffusivity (AD), mean diffusivity (MD), and radial diffusivity (RD). We performed a three-level analysis comprising 1) connection-level statistical analysis, 2) graph theory measures at the node and whole-brain levels, and 3) classification using support vector machines (SVM) and graph neural networks. We did not find any statistical difference at any level after correction for multiple comparisons. Also, the classifiers performed poorly with AUC values close to chance levels. However, we found differences between filtered and unfiltered tractograms at the node level, which could suggest that filtering is a necessary step in structural connectivity analyses. Our findings suggest that structural connectivity analysesfor PD are highly sensitive to specific pipeline configurations and fine-tuning.