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

Analyzing asymmetry in brain hierarchies with a linear state-space model of resting-state fMRI data

This study challenges the traditional focus on zero-lag statistics in resting-state functional magnetic resonance imaging (rsfMRI) research. Instead, it advocates for considering time-lag interactions to unveil the directionality and asymmetries of the brain hierarchy. Effective connectivity (EC), the state matrix in dynamical causal modeling (DCM), is a commonly used metric for studying dynamical properties and causal interactions within a linear state-space system description. Here, we focused on how time-lag statistics are incorporated within the framework of DCM resulting in an asymmetric EC matrix. Our approach involves decomposing the EC matrix, revealing a steady-state differential cross-covariance matrix that is responsible for modeling information flow and introducing time-irreversibility. Specifically, the system's dynamics, influenced by the off-diagonal part of the differential covariance, exhibit a curl steady-state flow component that breaks detailed balance and diverges the dynamics from equilibrium. Our empirical findings indicate that the EC matrix's outgoing strengths correlate with the flow described by the differential cross covariance, while incoming strengths are primarily driven by zero-lag covariance, emphasizing conditional independence over directionality.

Dynamic brain states in spatial neglect after stroke

Previous studies indicated that spatial neglect is characterized by widespread alteration of resting-state functional connectivity and changes in the functional topology of large-scale brain systems. However, whether such network modulations exhibit temporal fluctuations related to spatial neglect is still largely unknown. This study investigated the association between brain states and spatial neglect after the onset of focal brain lesions. A cohort of right-hemisphere stroke patients (n = 20) underwent neuropsychological assessment of neglect as well as structural and resting-state functional MRI sessions within 2 weeks from stroke onset. Brain states were identified using dynamic functional connectivity as estimated by the sliding window approach followed by clustering of seven resting state networks. The networks included visual, dorsal attention, sensorimotor, cingulo-opercular, language, fronto-parietal, and default mode networks. The analyses on the whole cohort of patients, i.e., with and without neglect, identified two distinct brain states characterized by different degrees of brain modularity and system segregation. Compared to non-neglect patients, neglect subjects spent more time in less modular and segregated state characterized by weak intra-network coupling and sparse inter-network interactions. By contrast, patients without neglect dwelt mainly in more modular and segregated states, which displayed robust intra-network connectivity and anti-correlations among task-positive and task-negative systems. Notably, correlational analyses indicated that patients exhibiting more severe neglect spent more time and dwelt more often in the state featuring low brain modularity and system segregation and vice versa. Furthermore, separate analyses on neglect vs. non-neglect patients yielded two distinct brain states for each sub-cohort. A state featuring widespread strong connections within and between networks and low modularity and system segregation was detected only in the neglect group. Such a connectivity profile blurred the distinction among functional systems. Finally, a state exhibiting a clear separation among modules with strong positive intra-network and negative inter-network connectivity was found only in the non-neglect group. Overall, our results indicate that stroke yielding spatial attention deficits affects the time-varying properties of functional interactions among large-scale networks. These findings provide further insights into the pathophysiology of spatial neglect and its treatment.

GeneNetTools: tests for Gaussian graphical models with shrinkage

MOTIVATION

Gaussian graphical models (GGMs) are network representations of random variables (as nodes) and their partial correlations (as edges). GGMs overcome the challenges of high-dimensional data analysis by using shrinkage methodologies. Therefore, they have become useful to reconstruct gene regulatory networks from gene-expression profiles. However, it is often ignored that the partial correlations are 'shrunk' and that they cannot be compared/assessed directly. Therefore, accurate (differential) network analyses need to account for the number of variables, the sample size, and also the shrinkage value, otherwise, the analysis and its biological interpretation would turn biased. To date, there are no appropriate methods to account for these factors and address these issues.

RESULTS

We derive the statistical properties of the partial correlation obtained with the Ledoit-Wolf shrinkage. Our result provides a toolbox for (differential) network analyses as (i) confidence intervals, (ii) a test for zero partial correlation (null-effects) and (iii) a test to compare partial correlations. Our novel (parametric) methods account for the number of variables, the sample size and the shrinkage values. Additionally, they are computationally fast, simple to implement and require only basic statistical knowledge. Our simulations show that the novel tests perform better than DiffNetFDR-a recently published alternative-in terms of the trade-off between true and false positives. The methods are demonstrated on synthetic data and two gene-expression datasets from Escherichia coli and Mus musculus.

AVAILABILITY AND IMPLEMENTATION

The R package with the methods and the R script with the analysis are available in https://github.com/V-Bernal/GeneNetTools.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Reliability and subject specificity of personalized whole-brain dynamical models

Dynamical whole-brain models were developed to link structural (SC) and functional connectivity (FC) together into one framework. Nowadays, they are used to investigate the dynamical regimes of the brain and how these relate to behavioral, clinical and demographic traits. However, there is no comprehensive investigation on how reliable and subject specific the modeling results are given the variability of the empirical FC. In this study, we show that the parameters of these models can be fitted with a "poor" to "good" reliability depending on the exact implementation of the modeling paradigm. We find, as a general rule of thumb, that enhanced model personalization leads to increasingly reliable model parameters. In addition, we observe no clear effect of the model complexity evaluated by separately sampling results for linear, phase oscillator and neural mass network models. In fact, the most complex neural mass model often yields modeling results with "poor" reliability comparable to the simple linear model, but demonstrates an enhanced subject specificity of the model similarity maps. Subsequently, we show that the FC simulated by these models can outperform the empirical FC in terms of both reliability and subject specificity. For the structure-function relationship, simulated FC of individual subjects may be identified from the correlations with the empirical SC with an accuracy up to 70%, but not vice versa for non-linear models. We sample all our findings for 8 distinct brain parcellations and 6 modeling conditions and show that the parcellation-induced effect is much more pronounced for the modeling results than for the empirical data. In sum, this study provides an exploratory account on the reliability and subject specificity of dynamical whole-brain models and may be relevant for their further development and application. In particular, our findings suggest that the application of the dynamical whole-brain modeling should be tightly connected with an estimate of the reliability of the results.

SPROUT: spectral sparsification helps restore the spatial structure at single-cell resolution

Single-cell RNA sequencing thoroughly quantifies the individual cell transcriptomes but renounces the spatial structure. Conversely, recently emerged spatial transcriptomics technologies capture the cellular spatial structure but skimp cell or gene resolutions. Ligand-receptor interactions reveal the potential of cell proximity since they are spatially constrained. Cell–cell affinity values estimated by ligand–receptor interaction can partially represent the structure of cells but falsely include the pseudo affinities between distant or indirectly interacting cells. Here, we develop a software package, SPROUT, to reconstruct the single-cell resolution spatial structure from the transcriptomics data through diminished pseudo ligand–receptor affinities. For spatial data, SPROUT first curates the representative single-cell profiles for each spatial spot from a candidate library, then reduces the pseudo affinities in the intercellular affinity matrix by partial correlation, spectral graph sparsification, and spatial coordinates refinement. SPROUT embeds the estimated interactions into a low-dimensional space with the cross-entropy objective to restore the intercellular structures, which facilitates the discovery of dominant ligand–receptor pairs between neighboring cells at single-cell resolution. SPROUT reconstructed structures achieved shape Pearson correlations ranging from 0.91 to 0.97 on the mouse hippocampus and human organ tumor microenvironment datasets. Furthermore, SPROUT can solely de novo reconstruct the structures at single-cell resolution, i.e., reaching the cell-type proximity correlations of 0.68 and 0.89 between reconstructed and immunohistochemistry-informed spatial structures on a human developing heart dataset and a tumor microenvironment dataset, respectively.

The 'un-shrunk' partial correlation in Gaussian graphical models

BACKGROUND

In systems biology, it is important to reconstruct regulatory networks from quantitative molecular profiles. Gaussian graphical models (GGMs) are one of the most popular methods to this end. A GGM consists of nodes (representing the transcripts, metabolites or proteins) inter-connected by edges (reflecting their partial correlations). Learning the edges from quantitative molecular profiles is statistically challenging, as there are usually fewer samples than nodes ('high dimensional problem'). Shrinkage methods address this issue by learning a regularized GGM. However, it remains open to study how the shrinkage affects the final result and its interpretation.

RESULTS

We show that the shrinkage biases the partial correlation in a non-linear way. This bias does not only change the magnitudes of the partial correlations but also affects their order. Furthermore, it makes networks obtained from different experiments incomparable and hinders their biological interpretation. We propose a method, referred to as 'un-shrinking' the partial correlation, which corrects for this non-linear bias. Unlike traditional methods, which use a fixed shrinkage value, the new approach provides partial correlations that are closer to the actual (population) values and that are easier to interpret. This is demonstrated on two gene expression datasets from Escherichia coli and Mus musculus.

CONCLUSIONS

GGMs are popular undirected graphical models based on partial correlations. The application of GGMs to reconstruct regulatory networks is commonly performed using shrinkage to overcome the 'high-dimensional problem'. Besides it advantages, we have identified that the shrinkage introduces a non-linear bias in the partial correlations. Ignoring this type of effects caused by the shrinkage can obscure the interpretation of the network, and impede the validation of earlier reported results.

Bayesian Estimation for Gaussian Graphical Models: Structure Learning, Predictability, and Network Comparisons

Gaussian graphical models (GGM; "networks") allow for estimating conditional dependence structures that are encoded by partial correlations. This is accomplished by identifying non-zero relations in the inverse of the covariance matrix. In psychology the default estimation method uses ℓ1-regularization, where the accompanying inferences are restricted to frequentist objectives. Bayesian methods remain relatively uncommon in practice and methodological literatures. To date, they have not yet been used for estimation and inference in the psychological network literature. In this work, I introduce Bayesian methodology that is specifically designed for the most common psychological applications. The graphical structure is determined with posterior probabilities that can be used to assess conditional dependent and independent relations. Additional methods are provided for extending inference to specific aspects within- and between-networks, including partial correlation differences and Bayesian methodology to quantify network predictability. I first demonstrate that the decision rule based on posterior probabilities can be calibrated to the desired level of specificity. The proposed techniques are then demonstrated in several illustrative examples. The methods have been implemented in the R package BGGM.

Joint Bayesian Estimation of Voxel Activation and Inter-regional Connectivity in fMRI Experiments

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 groups 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 parallel factorization 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, showing the effectiveness of the model in providing interpretable joint inference on voxel-level activations and inter-regional connectivity associated with how the brain processes risk. The proposed method is also validated through simulation studies and comparisons to other methods used within the neuroscience community.

Learning in brain-computer interface control evidenced by joint decomposition of brain and behavior

OBJECTIVE

Motor imagery-based brain-computer interfaces (BCIs) use an individual's ability to volitionally modulate localized brain activity, often as a therapy for motor dysfunction or to probe causal relations between brain activity and behavior. However, many individuals cannot learn to successfully modulate their brain activity, greatly limiting the efficacy of BCI for therapy and for basic scientific inquiry. Formal experiments designed to probe the nature of BCI learning have offered initial evidence that coherent activity across spatially distributed and functionally diverse cognitive systems is a hallmark of individuals who can successfully learn to control the BCI. However, little is known about how these distributed networks interact through time to support learning.

APPROACH

Here, we address this gap in knowledge by constructing and applying a multimodal network approach to decipher brain-behavior relations in motor imagery-based brain-computer interface learning using magnetoencephalography. Specifically, we employ a minimally constrained matrix decomposition method - non-negative matrix factorization - to simultaneously identify regularized, covarying subgraphs of functional connectivity, to assess their similarity to task performance, and to detect their time-varying expression.

MAIN RESULTS

We find that learning is marked by diffuse brain-behavior relations: good learners displayed many subgraphs whose temporal expression tracked performance. Individuals also displayed marked variation in the spatial properties of subgraphs such as the connectivity between the frontal lobe and the rest of the brain, and in the temporal properties of subgraphs such as the stage of learning at which they reached maximum expression. From these observations, we posit a conceptual model in which certain subgraphs support learning by modulating brain activity in sensors near regions important for sustaining attention. To test this model, we use tools that stipulate regional dynamics on a networked system (network control theory), and find that good learners display a single subgraph whose temporal expression tracked performance and whose architecture supports easy modulation of sensors located near brain regions important for attention.

SIGNIFICANCE

The nature of our contribution to the neuroscience of BCI learning is therefore both computational and theoretical; we first use a minimally-constrained, individual specific method of identifying mesoscale structure in dynamic brain activity to show how global connectivity and interactions between distributed networks supports BCI learning, and then we use a formal network model of control to lend theoretical support to the hypothesis that these identified subgraphs are well suited to modulate attention.

Sleep spindles mediate hippocampal-neocortical coupling during long-duration ripples

Sleep is pivotal for memory consolidation. According to two-stage accounts, memory traces are gradually translocated from hippocampus to neocortex during non-rapid-eye-movement (NREM) sleep. Mechanistically, this information transfer is thought to rely on interactions between thalamocortical spindles and hippocampal ripples. To test this hypothesis, we analyzed intracranial and scalp Electroencephalography sleep recordings from pre-surgical epilepsy patients. We first observed a concurrent spindle power increase in hippocampus (HIPP) and neocortex (NC) time-locked to individual hippocampal ripple events. Coherence analysis confirmed elevated levels of hippocampal-neocortical spindle coupling around ripples, with directionality analyses indicating an influence from NC to HIPP. Importantly, these hippocampal-neocortical dynamics were particularly pronounced during long-duration compared to short-duration ripples. Together, our findings reveal a potential mechanism underlying active consolidation, comprising a neocortical-hippocampal-neocortical reactivation loop initiated by the neocortex. This hippocampal-cortical dialogue is mediated by sleep spindles and is enhanced during long-duration hippocampal ripples.

Heterogeneity of Preictal Dynamics in Human Epileptic Seizures

It is generally understood that there is a preictal phase in the development of a seizure and this precictal period is the basis for seizure prediction attempts. The focus of this study is the preictal global spatiotemporal dynamics and its intra-patient variability. We analyzed preictal broadband brain connectivity from human electrocorticography (ECoG) recordings of 185 seizures (which included 116 clinical seizures) collected from 12 patients. ECoG electrodes record from only a part of the cortex, leaving large regions of the brain unobserved. Brain connectivity was therefore estimated using the sparse-plus-latent-regularized precision matrix (SLRPM) method, which calculates connectivity from partial correlations of the conditional statistics of the observed regions given the unobserved latent regions. Brain connectivity was quantified using eigenvector centrality (EC), from which a degree of heterogeneity was calculated for the preictal periods of all seizures in each patient. Results from the SLRPM method are compared to those from the sparse-regularized precision matrix (SRPM) and correlation methods, which do not account for the unobserved inputs when estimating brain connectivity. The degree of heterogeneity estimated by the SLRPM method is higher than those estimated by the SRPM and correlation methods for the preictal periods in most patients. These results reveal substantial heterogeneity or desynchronization among brain areas in the preictal period of human epileptic seizures. Furthermore, the SLRPM method identifies more onset channels from the preictal active electrodes compared to the SRPM and correlation methods. Finally, the correlation between the degree of heterogeneity and seizure severity of patients for SLRPM and SRPM methods were lower than that obtained from the correlation method. These results support recent findings suggesting that inhibitory neurons can have anti-seizure effects by inducing variability or heterogeneity across seizures. Understanding how this variability is linked to seizure initiation may lead to better predictions and controlling therapies.

Capturing the Forest but Missing the Trees: Microstates Inadequate for Characterizing Shorter-Scale EEG Dynamics

The brain is known to be active even when not performing any overt cognitive tasks, and often it engages in involuntary mind wandering. This resting state has been extensively characterized in terms of fMRI-derived brain networks. However, an alternate method has recently gained popularity: EEG microstate analysis. Proponents of microstates postulate that the brain discontinuously switches between four quasi-stable states defined by specific EEG scalp topologies at peaks in the global field potential (GFP). These microstates are thought to be “atoms of thought,” involved with visual, auditory, salience, and attention processing. However, this method makes some major assumptions by excluding EEG data outside the GFP peaks and then clustering the EEG scalp topologies at the GFP peaks, assuming that only one microstate is active at any given time. This study explores the evidence surrounding these assumptions by studying the temporal dynamics of microstates and its clustering space using tools from dynamical systems analysis, fractal, and chaos theory to highlight the shortcomings in microstate analysis. The results show evidence of complex and chaotic EEG dynamics outside the GFP peaks, which is being missed by microstate analysis. Furthermore, the winner-takes-all approach of only one microstate being active at a time is found to be inadequate since the dynamic EEG scalp topology does not always resemble that of the assigned microstate, and there is competition among the different microstate classes. Finally, clustering space analysis shows that the four microstates do not cluster into four distinct and separable clusters. Taken collectively, these results show that the discontinuous description of EEG microstates is inadequate when looking at nonstationary short-scale EEG dynamics.

Sleep Spindle-dependent Functional Connectivity Correlates with Cognitive Abilities

EEG studies have shown that interindividual differences in the electrophysiological properties of sleep spindles (e.g., density, amplitude, duration) are highly correlated with trait-like "reasoning" abilities (i.e., "fluid intelligence"; problem-solving skills; the ability to employ logic or identify complex patterns), but not interindividual differences in STM or "verbal" intellectual abilities. Previous simultaneous EEG-fMRI studies revealed brain activations time-locked to spindles. Our group has recently demonstrated that the extent of activation in a subset of these regions was related to interindividual differences in reasoning intellectual abilities, specifically. However, spindles reflect communication between spatially distant and functionally distinct brain areas. The functional communication among brain regions related to spindles and their relationship to reasoning abilities have yet to be investigated. Using simultaneous EEG-fMRI sleep recordings and psychophysiological interaction analysis, we identified spindle-related functional communication among brain regions in the thalamo-cortical-BG system, the salience network, and the default mode network. Furthermore, the extent of the functional connectivity of the cortical-striatal circuitry and the thalamo-cortical circuitry was specifically related to reasoning abilities but was unrelated to STM or verbal abilities, thus suggesting that individuals with higher fluid intelligence have stronger functional coupling among these brain areas during spontaneous spindle events. This may serve as a first step in further understanding the function of sleep spindles and the brain network functional communication, which support the capacity for fluid intelligence.

Characterizing Brain Connectivity From Human Electrocorticography Recordings With Unobserved Inputs During Epileptic Seizures

Epilepsy is a neurological disorder characterized by the sudden occurrence of unprovoked seizures. There is extensive evidence of significantly altered brain connectivity during seizure periods in the human brain. Research on analyzing human brain functional connectivity during epileptic seizures has been limited predominantly to the use of the correlation method. However, spurious connectivity can be measured between two brain regions without having direct connection or interaction between them. Correlations can be due to the apparent interactions of the two brain regions resulting from common input from a third region, which may or may not be observed. Hence, researchers have recently proposed a sparse-plus-latent-regularized precision matrix (SLRPM) when there are unobserved or latent regions interacting with the observed regions. The SLRPM method yields partial correlations of the conditional statistics of the observed regions given the latent regions, thus identifying observed regions that are conditionally independent of both the observed and latent regions. We evaluate the performance of the methods using a spring-mass artificial network and assuming that some nodes cannot be observed, thus constituting the latent variables in the example. Several cases have been considered, including both sparse and dense connections, short-range and long-range connections, and a varying number of latent variables. The SLRPM method is then applied to estimate brain connectivity during epileptic seizures from human ECoG recordings. Seventy-four clinical seizures from five patients, all having complex partial epilepsy, were analyzed using SLRPM, and brain connectivity was quantified using modularity index, clustering coefficient, and eigenvector centrality. Furthermore, using a measure of latent inputs estimated by the SLRPM method, it was possible to automatically detect 72 of the 74 seizures with four false positives and find six seizures that were not marked manually.

Towards artificial intelligence in mental health by improving schizophrenia prediction with multiple brain parcellation ensemble-learning

In the literature, there are substantial machine learning attempts to classify schizophrenia based on alterations in resting-state (RS) brain patterns using functional magnetic resonance imaging (fMRI). Most earlier studies modelled patients undergoing treatment, entailing confounding with drug effects on brain activity, and making them less applicable to real-world diagnosis at the point of first medical contact. Further, most studies with classification accuracies >80% are based on small sample datasets, which may be insufficient to capture the heterogeneity of schizophrenia, limiting generalization to unseen cases. In this study, we used RS fMRI data collected from a cohort of antipsychotic drug treatment-naive patients meeting DSM IV criteria for schizophrenia (N = 81) as well as age- and sex-matched healthy controls (N = 93). We present an ensemble model -- EMPaSchiz (read as ‘Emphasis’; standing for ‘Ensemble algorithm with Multiple Parcellations for Schizophrenia prediction’) that stacks predictions from several ‘single-source’ models, each based on features of regional activity and functional connectivity, over a range of different a priori parcellation schemes. EMPaSchiz yielded a classification accuracy of 87% (vs. chance accuracy of 53%), which out-performs earlier machine learning models built for diagnosing schizophrenia using RS fMRI measures modelled on large samples (N > 100). To our knowledge, EMPaSchiz is first to be reported that has been trained and validated exclusively on data from drug-naive patients diagnosed with schizophrenia. The method relies on a single modality of MRI acquisition and can be readily scaled-up without needing to rebuild parcellation maps from incoming training images.