Comparison of Brain Networks based on Predictive Models of Connectivity

In this study we adopt predictive modelling to identify simultaneously commonalities and differences in multi-modal brain networks acquired within subjects. Typically, predictive modelling of functional connectomes from structural connectomes explores commonalities across multimodal imaging data. However, direct application of multivariate approaches such as sparse Canonical Correlation Analysis (sCCA) applies on the vectorised elements of functional connectivity across subjects and it does not guarantee that the predicted models of functional connectivity are Symmetric Positive Matrices (SPD). We suggest an elegant solution based on the transportation of the connectivity matrices on a Riemannian manifold, which notably improves the prediction performance of the model. Randomised lasso is used to alleviate the dependency of the sCCA on the lasso parameters and control the false positive rate. Subsequently, the binomial distribution is exploited to set a threshold statistic that reflects whether a connection is selected or rejected by chance. Finally, we estimate the sCCA loadings based on a de-noising approach that improves the estimation of the coefficients. We validate our approach based on resting-state fMRI and diffusion weighted MRI data. Quantitative validation of the prediction performance shows superior performance, whereas qualitative results of the identification process are promising.Comment: 7 pages, 4 figure

Exploration of Balanced Metrics on Symmetric Positive Definite Matrices

International audienceSymmetric Positive Definite (SPD) matrices have been usedin many fields of medical data analysis. Many Riemannian metrics havebeen defined on this manifold but the choice of the Riemannianstructurelacks a set of principles that could lead one to choose properly the met-ric. This drives us to introduce the principle of balanced metrics that re-late the affine-invariant metric with the Euclidean and inverse-Euclideanmetric, or the Bogoliubov-Kubo-Mori metric with the Euclidean and log-Euclidean metrics. We introduce two new families of balanced metrics,the mixed-power-Euclidean and the mixed-power-affine metrics and wediscuss the relation between this new principle of balanced metrics and the concept of dual connection in information geometry

Exploration of Balanced Metrics on Symmetric Positive Definite Matrices

International audienceSymmetric Positive Definite (SPD) matrices have been usedin many fields of medical data analysis. Many Riemannian metrics havebeen defined on this manifold but the choice of the Riemannianstructurelacks a set of principles that could lead one to choose properly the met-ric. This drives us to introduce the principle of balanced metrics that re-late the affine-invariant metric with the Euclidean and inverse-Euclideanmetric, or the Bogoliubov-Kubo-Mori metric with the Euclidean and log-Euclidean metrics. We introduce two new families of balanced metrics,the mixed-power-Euclidean and the mixed-power-affine metrics and wediscuss the relation between this new principle of balanced metrics and the concept of dual connection in information geometry

Geometric learning of functional brain network on the correlation manifold

The correlation matrix is a typical representation of node interactions in functional brain network analysis. The analysis of the correlation matrix to characterize brain networks observed in several neuroimaging modalities has been conducted predominantly in the Euclidean space by assuming that pairwise interactions are mutually independent. One way to take account of all interactions in the network as a whole is to analyze the correlation matrix under some geometric structure. Recent studies have focused on the space of correlation matrices as a strict subset of symmetric positive definite (SPD) matrices, which form a unique mathematical structure known as the Riemannian manifold. However, mathematical operations of the correlation matrix under the SPD geometry may not necessarily be coherent (i.e., the structure of the correlation matrix may not be preserved), necessitating a post-hoc normalization. The contribution of the current paper is twofold: (1) to devise a set of inferential methods on the correlation manifold and (2) to demonstrate its applicability in functional network analysis. We present several algorithms on the correlation manifold, including measures of central tendency, cluster analysis, hypothesis testing, and low-dimensional embedding. Simulation and real data analysis support the application of the proposed framework for brain network analysis.ope

From Connectivity Models to Region Labels: Identifying Foci of a Neurological Disorder

We propose a novel approach to identify the foci of a neurological disorder based on anatomical and functional connectivity information. Specifically, we formulate a generative model that characterizes the network of abnormal functional connectivity emanating from the affected foci. This allows us to aggregate pairwise connectivity changes into a region-based representation of the disease. We employ the variational expectation-maximization algorithm to fit the model and subsequently identify both the afflicted regions and the differences in connectivity induced by the disorder. We demonstrate our method on a population study of schizophrenia.National Alliance for Medical Image Computing (U.S.) (Grant NIH NIBIB NAMIC U54-EB005149)Neuroimaging Analysis Center (U.S.) (Grant NIH NCRR NAC P41-RR13218)Neuroimaging Analysis Center (U.S.) (Grant NIH NCRR NAC P41-EB015902)National Science Foundation (U.S.) (CAREER Grant 0642971)National Institutes of Health (U.S.) (R01MH074794)National Institutes of Health (U.S.). Advanced Multimodal Neuroimaging Training Progra

Relating resting-state fMRI and EEG whole-brain connectomes across frequency bands.

Whole brain functional connectomes hold promise for understanding human brain activity across a range of cognitive, developmental and pathological states. So called resting-state (rs) functional MRI studies have contributed to the brain being considered at a macroscopic scale as a set of interacting regions. Interactions are defined as correlation-based signal measurements driven by blood oxygenation level dependent (BOLD) contrast. Understanding the neurophysiological basis of these measurements is important in conveying useful information about brain function. Local coupling between BOLD fMRI and neurophysiological measurements is relatively well defined, with evidence that gamma (range) frequency EEG signals are the closest correlate of BOLD fMRI changes during cognitive processing. However, it is less clear how whole-brain network interactions relate during rest where lower frequency signals have been suggested to play a key role. Simultaneous EEG-fMRI offers the opportunity to observe brain network dynamics with high spatio-temporal resolution. We utilize these measurements to compare the connectomes derived from rs-fMRI and EEG band limited power (BLP). Merging this multi-modal information requires the development of an appropriate statistical framework. We relate the covariance matrices of the Hilbert envelope of the source localized EEG signal across bands to the covariance matrices derived from rs-fMRI with the means of statistical prediction based on sparse Canonical Correlation Analysis (sCCA). Subsequently, we identify the most prominent connections that contribute to this relationship. We compare whole-brain functional connectomes based on their geodesic distance to reliably estimate the performance of the prediction. The performance of predicting fMRI from EEG connectomes is considerably better than predicting EEG from fMRI across all bands, whereas the connectomes derived in low frequency EEG bands resemble best rs-fMRI connectivity

Re-visiting Riemannian geometry of symmetric positive definite matrices for the analysis of functional connectivity

Common representations of functional networks of resting state fMRI time series, including covariance, precision, and cross-correlation matrices, belong to the family of symmetric positive definite (SPD) matrices forming a special mathematical structure called Riemannian manifold. Due to its geometric properties, the analysis and operation of functional connectivity matrices may well be performed on the Riemannian manifold of the SPD space. Analysis of functional networks on the SPD space takes account of all the pairwise interactions (edges) as a whole, which differs from the conventional rationale of considering edges as independent from each other. Despite its geometric characteristics, only a few studies have been conducted for functional network analysis on the SPD manifold and inference methods specialized for connectivity analysis on the SPD manifold are rarely found. The current study aims to show the significance of connectivity analysis on the SPD space and introduce inference algorithms on the SPD manifold, such as regression analysis of functional networks in association with behaviors, principal geodesic analysis, clustering, state transition analysis of dynamic functional networks and statistical tests for network equality on the SPD manifold. We applied the proposed methods to both simulated data and experimental resting state fMRI data from the human connectome project and argue the importance of analyzing functional networks under the SPD geometry. All the algorithms for numerical operations and inferences on the SPD manifold are implemented as a MATLAB library, called SPDtoolbox, for public use to expediate functional network analysis on the right geometry.ope

A probabilistic framework to infer brain functional connectivity from anatomical connections

We present a novel probabilistic framework to learn across several subjects a mapping from brain anatomical connectivity to functional connectivity, i.e. the covariance structure of brain activity. This prediction problem must be formulated as a structured-output learning task, as the predicted parameters are strongly correlated. We introduce a model selection framework based on cross-validation with a parametrization-independent loss function suitable to the manifold of covariance matrices. Our model is based on constraining the conditional independence structure of functional activity by the anatomical connectivity. Subsequently, we learn a linear predictor of a stationary multivariate autoregressive model. This natural parameterization of functional connectivity also enforces the positive-definiteness of the predicted covariance and thus matches the structure of the output space. Our results show that functional connectivity can be explained by anatomical connectivity on a rigorous statistical basis, and that a proper model of functional connectivity is essential to assess this link

Generative models of brain connectivity for population studies

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 131-139).Connectivity analysis focuses on the interaction between brain regions. Such relationships inform us about patterns of neural communication and may enhance our understanding of neurological disorders. This thesis proposes a generative framework that uses anatomical and functional connectivity information to find impairments within a clinical population. Anatomical connectivity is measured via Diffusion Weighted Imaging (DWI), and functional connectivity is assessed using resting-state functional Magnetic Resonance Imaging (fMRI). We first develop a probabilistic model to merge information from DWI tractography and resting-state fMRI correlations. Our formulation captures the interaction between hidden templates of anatomical and functional connectivity within the brain. We also present an intuitive extension to population studies and demonstrate that our model learns predictive differences between a control and a schizophrenia population. Furthermore, combining the two modalities yields better results than considering each one in isolation. Although our joint model identifies widespread connectivity patterns influenced by a neurological disorder, the results are difficult to interpret and integrate with our regioncentric knowledge of the brain. To alleviate this problem, we present a novel approach to identify regions associated with the disorder based on connectivity information. Specifically, we assume that impairments of the disorder localize to a small subset of brain regions, which we call disease foci, and affect neural communication to/from these regions. This allows us to aggregate pairwise connectivity changes into a region-based representation of the disease. Once again, we use a probabilistic formulation: latent variables specify a template organization of the brain, which we indirectly observe through resting-state fMRI correlations and DWI tractography. Our inference algorithm simultaneously identifies both the afflicted regions and the network of aberrant functional connectivity. Finally, we extend the region-based model to include multiple collections of foci, which we call disease clusters. Preliminary results suggest that as the number of clusters increases, the refined model explains progressively more of the functional differences between the populations.by Archana Venkataraman.Ph.D