A Riemannian Framework for Longitudinal Analysis of Resting-State Functional Connectivity

Reconfigurations of cortical manifold structure during reward-based motor learning

Adaptive motor behavior depends on the coordinated activity of multiple neural systems distributed across the brain. While the role of sensorimotor cortex in motor learning has been well established, how higher-order brain systems interact with sensorimotor cortex to guide learning is less well understood. Using functional MRI, we examined human brain activity during a reward-based motor task where subjects learned to shape their hand trajectories through reinforcement feedback. We projected patterns of cortical and striatal functional connectivity onto a low-dimensional manifold space and examined how regions expanded and contracted along the manifold during learning. During early learning, we found that several sensorimotor areas in the dorsal attention network exhibited increased covariance with areas of the salience/ventral attention network and reduced covariance with areas of the default mode network (DMN). During late learning, these effects reversed, with sensorimotor areas now exhibiting increased covariance with DMN areas. However, areas in posteromedial cortex showed the opposite pattern across learning phases, with its connectivity suggesting a role in coordinating activity across different networks over time. Our results establish the neural changes that support reward-based motor learning and identify distinct transitions in the functional coupling of sensorimotor to transmodal cortex when adapting behavior.

Distinct patterns of cortical manifold expansion and contraction underlie human sensorimotor adaptation

Sensorimotor learning is a dynamic, systems-level process that involves the combined action of multiple neural systems distributed across the brain. Although much is known about the specialized cortical systems that support specific components of action (such as reaching), we know less about how cortical systems function in a coordinated manner to facilitate adaptive behavior. To address this gap, our study measured human brain activity using functional MRI (fMRI) while participants performed a classic sensorimotor adaptation task and used a manifold learning approach to describe how behavioral changes during adaptation relate to changes in the landscape of cortical activity. During early adaptation, areas in the parietal and premotor cortices exhibited significant contraction along the cortical manifold, which was associated with their increased covariance with regions in the higher-order association cortex, including both the default mode and fronto-parietal networks. By contrast, during Late adaptation, when visuomotor errors had been largely reduced, a significant expansion of the visual cortex along the cortical manifold was associated with its reduced covariance with the association cortex and its increased intraconnectivity. Lastly, individuals who learned more rapidly exhibited greater covariance between regions in the sensorimotor and association cortices during early adaptation. These findings are consistent with a view that sensorimotor adaptation depends on changes in the integration and segregation of neural activity across more specialized regions of the unimodal cortex with regions in the association cortex implicated in higher-order processes. More generally, they lend support to an emerging line of evidence implicating regions of the default mode network (DMN) in task-based performance.

Taking the 4D Nature of fMRI Data Into Account Promises Significant Gains in Data Completion

Functional magnetic resonance imaging (fMRI) is a powerful, noninvasive tool that has significantly contributed to the understanding of the human brain. FMRI data provide a sequence of whole-brain volumes over time and hence are inherently four dimensional (4D). Missing data in fMRI experiments arise from image acquisition limits, susceptibility and motion artifacts or during confounding noise removal. Hence, significant brain regions may be excluded from the data, which can seriously undermine the quality of subsequent analyses due to the significant number of missing voxels. We take advantage of the four dimensional (4D) nature of fMRI data through a tensor representation and introduce an effective algorithm to estimate missing samples in fMRI data. The proposed Riemannian nonlinear spectral conjugate gradient (RSCG) optimization method uses tensor train (TT) decomposition, which enables compact representations and provides efficient linear algebra operations. Exploiting the Riemannian structure boosts algorithm performance significantly, as evidenced by the comparison of RSCG-TT with state-of-the-art stochastic gradient methods, which are developed in the Euclidean space. We thus provide an effective method for estimating missing brain voxels and, more importantly, clearly show that taking the full 4D structure of fMRI data into account provides important gains when compared with three-dimensional (3D) and the most commonly used two-dimensional (2D) representations of fMRI data.

Analyzing Dynamical Brain Functional Connectivity as Trajectories on Space of Covariance Matrices

Human brain functional connectivity (FC) is often measured as the similarity of functional MRI responses across brain regions when a brain is either resting or performing a task. This paper aims to statistically analyze the dynamic nature of FC by representing the collective time-series data, over a set of brain regions, as a trajectory on the space of covariance matrices, or symmetric-positive definite matrices (SPDMs). We use a recently developed metric on the space of SPDMs for quantifying differences across FC observations, and for clustering and classification of FC trajectories. To facilitate large scale and high-dimensional data analysis, we propose a novel, metric-based dimensionality reduction technique to reduce data from large SPDMs to small SPDMs. We illustrate this comprehensive framework using data from the Human Connectome Project (HCP) database for multiple subjects and tasks, with task classification rates that match or outperform state-of-the-art techniques.

Variational Autoencoder with Truncated Mixture of Gaussians for Functional Connectivity Analysis

Resting-state functional connectivity states are often identified as clusters of dynamic connectivity patterns. However, existing clustering approaches do not distinguish major states from rarely occurring minor states and hence are sensitive to noise. To address this issue, we propose to model major states using a non-linear generative process guided by a Gaussian-mixture distribution in a low-dimensional latent space, while separately modeling the connectivity patterns of minor states by a non-informative uniform distribution. We embed this truncated Gaussian-Mixture model in a Variational Autoencoder framework to obtain a general joint clustering and outlier detection approach, tGM-VAE. When applied to synthetic data with known ground-truth, tGM-VAE is more accurate in clustering connectivity patterns than existing approaches. On the rs-fMRI of 593 healthy adolescents, tGM-VAE identifies meaningful major connectivity states. The dwell time of these states significantly correlates with age.