Interpretation of the Precision Matrix and Its Application in Estimating Sparse Brain Connectivity during Sleep Spindles from Human Electrocorticography Recordings

The correlation method from brain imaging has been used to estimate functional connectivity in the human brain. However, brain regions might show very high correlation even when the two regions are not directly connected due to the strong interaction of the two regions with common input from a third region. One previously proposed solution to this problem is to use a sparse regularized inverse covariance matrix or precision matrix (SRPM) assuming that the connectivity structure is sparse. This method yields partial correlations to measure strong direct interactions between pairs of regions while simultaneously removing the influence of the rest of the regions, thus identifying regions that are conditionally independent. To test our methods, we first demonstrated conditions under which the SRPM method could indeed find the true physical connection between a pair of nodes for a spring-mass example and an RC circuit example. The recovery of the connectivity structure using the SRPM method can be explained by energy models using the Boltzmann distribution. We then demonstrated the application of the SRPM method for estimating brain connectivity during stage 2 sleep spindles from human electrocorticography (ECoG) recordings using an 8 x 8 electrode array. The ECoG recordings that we analyzed were from a 32-year-old male patient with long-standing pharmaco-resistant left temporal lobe complex partial epilepsy. Sleep spindles were automatically detected using delay differential analysis and then analyzed with SRPM and the Louvain method for community detection. We found spatially localized brain networks within and between neighboring cortical areas during spindles, in contrast to the case when sleep spindles were not present

Interpretation of the Precision Matrix and Its Application in Estimating Sparse Brain Connectivity during Sleep Spindles from Human Electrocorticography Recordings

The correlation method from brain imaging has been used to estimate functional connectivity in the human brain. However, brain regions might show very high correlation even when the two regions are not directly connected due to the strong interaction of the two regions with common input from a third region. One previously proposed solution to this problem is to use a sparse regularized inverse covariance matrix or precision matrix (SRPM) assuming that the connectivity structure is sparse. This method yields partial correlations to measure strong direct interactions between pairs of regions while simultaneously removing the influence of the rest of the regions, thus identifying regions that are conditionally independent. To test our methods, we first demonstrated conditions under which the SRPM method could indeed find the true physical connection between a pair of nodes for a spring-mass example and an RC circuit example. The recovery of the connectivity structure using the SRPM method can be explained by energy models using the Boltzmann distribution. We then demonstrated the application of the SRPM method for estimating brain connectivity during stage 2 sleep spindles from human electrocorticography (ECoG) recordings using an 8 x 8 electrode array. The ECoG recordings that we analyzed were from a 32-year-old male patient with long-standing pharmaco-resistant left temporal lobe complex partial epilepsy. Sleep spindles were automatically detected using delay differential analysis and then analyzed with SRPM and the Louvain method for community detection. We found spatially localized brain networks within and between neighboring cortical areas during spindles, in contrast to the case when sleep spindles were not present

Bayesian Mixed Effect Sparse Tensor Response Regression Model with Joint Estimation of Activation and Connectivity

Brain activation and connectivity analyses in task-based functional magnetic resonance imaging (fMRI) experiments with multiple subjects are currently at the forefront of data-driven neuroscience. In such experiments, interest often lies in understanding activation of brain voxels due to external stimuli and strong association or connectivity between the measurements on a set of pre-specified group of brain voxels, also known as regions of interest (ROI). This article proposes a joint Bayesian additive mixed modeling framework that simultaneously assesses brain activation and connectivity patterns from multiple subjects. In particular, fMRI measurements from each individual obtained in the form of a multi-dimensional array/tensor at each time are regressed on functions of the stimuli. We impose a low-rank PARAFAC decomposition on the tensor regression coefficients corresponding to the stimuli to achieve parsimony. Multiway stick breaking shrinkage priors are employed to infer activation patterns and associated uncertainties in each voxel. Further, the model introduces region specific random effects which are jointly modeled with a Bayesian Gaussian graphical prior to account for the connectivity among pairs of ROIs. Empirical investigations under various simulation studies demonstrate the effectiveness of the method as a tool to simultaneously assess brain activation and connectivity. The method is then applied to a multi-subject fMRI dataset from a balloon-analog risk-taking experiment in order to make inference about how the brain processes risk.Comment: 27 pages, 7 figure

Machine Learning Methods for Depression Detection Using SMRI and RS-FMRI Images

Major Depression Disorder (MDD) is a common disease throughout the world that negatively influences people’s lives. Early diagnosis of MDD is beneficial, so detecting practical biomarkers would aid clinicians in the diagnosis of MDD. Having an automated method to find biomarkers for MDD is helpful even though it is difficult. The main aim of this research is to generate a method for detecting discriminative features for MDD diagnosis based on Magnetic Resonance Imaging (MRI) data. In this research, representational similarity analysis provides a framework to compare distributed patterns and obtain the similarity/dissimilarity of brain regions. Regions are obtained by either data-driven or model-driven methods such as cubes and atlases respectively. For structural MRI (sMRI) similarity of voxels of spatial cubes (data-driven) are explored. For resting-state fMRI (rs-fMRI) images, the similarity of the time series of both cubes (data-driven) and atlases (model-driven) are examined. Moreover, the similarity method of the inverse of Minimum Covariant Determinant is applied that excludes outliers from patterns and finds conditionally independent regions given the rest of regions. Next, a statistical test that is robust to outliers, identifies discriminative similarity features between two groups of MDDs and controls. Therefore, the key contribution is the way to get discriminative features that include obtaining similarity of voxel’s cubes/time series using the inverse of robust covariance along with the statistical test. The experimental results show that obtaining these features along with the Bernoulli Naïve Bayes classifier achieves superior performance compared with other methods. The performance of our method is verified by applying it to three imbalanced datasets. Moreover, the similarity-based methods are compared with deep learning and regional-based approaches for detecting MDD using either sMRI or rs-fMRI. Given that depression is famous to be a connectivity disorder problem, investigating the similarity of the brain’s regions is valuable to understand the behavior of the brain. The combinations of structural and functional brain similarities are explored to investigate the brain’s structural and functional properties together. Moreover, the combination of data-driven (cube) and model-driven (atlas) similarities of rs-fMRI are looked over to evaluate how they affect the performance of the classifier. Besides, discriminative similarities are visualized for both sMRI and rs-fMRI. Also, to measure the informativeness of a cube, the relationship of atlas regions with overlapping cubes and vise versa (cubes with overlapping regions) are explored and visualized. Furthermore, the relationship between brain structure and function has been probed through common similarities between structural and resting-state functional networks