Analyzing the connectivity between regions of interest: an approach based on cluster Granger causality for fMRI data analysis

fMRI-based spatio-temporal parcellations of the human brain

PURPOSE OF REVIEW

Human brain parcellation based on functional magnetic resonance imaging (fMRI) plays an essential role in neuroscience research. By segmenting vast and intricate fMRI data into functionally similar units, researchers can better decipher the brain's structure in both healthy and diseased states. This article reviews current methodologies and ideas in this field, while also outlining the obstacles and directions for future research.

RECENT FINDINGS

Traditional brain parcellation techniques, which often rely on cytoarchitectonic criteria, overlook the functional and temporal information accessible through fMRI. The adoption of machine learning techniques, notably deep learning, offers the potential to harness both spatial and temporal information for more nuanced brain segmentation. However, the search for a one-size-fits-all solution to brain segmentation is impractical, with the choice between group-level or individual-level models and the intended downstream analysis influencing the optimal parcellation strategy. Additionally, evaluating these models is complicated by our incomplete understanding of brain function and the absence of a definitive "ground truth".

SUMMARY

While recent methodological advancements have significantly enhanced our grasp of the brain's spatial and temporal dynamics, challenges persist in advancing fMRI-based spatio-temporal representations. Future efforts will likely focus on refining model evaluation and selection as well as developing methods that offer clear interpretability for clinical usage, thereby facilitating further breakthroughs in our comprehension of the brain.

Directed physiological networks in the human prefrontal cortex at rest and post transcranial photobiomodulation

Cerebral infra-slow oscillation (ISO) is a source of vasomotion in endogenic (E; 0.005-0.02 Hz), neurogenic (N; 0.02-0.04 Hz), and myogenic (M; 0.04-0.2 Hz) frequency bands. In this study, we quantified changes in prefrontal concentrations of oxygenated hemoglobin (Δ[HbO]) and redox-state cytochrome c oxidase (Δ[CCO]) as hemodynamic and metabolic activity metrics, and electroencephalogram (EEG) powers as electrophysiological activity, using concurrent measurements of 2-channel broadband near-infrared spectroscopy and EEG on the forehead of 22 healthy participants at rest. After preprocessing, the multi-modality signals were analyzed using generalized partial directed coherence to construct unilateral neurophysiological networks among the three neurophysiological metrics (with simplified symbols of HbO, CCO, and EEG) in each E/N/M frequency band. The links in these networks represent neurovascular, neurometabolic, and metabolicvascular coupling (NVC, NMC, and MVC). The results illustrate that the demand for oxygen by neuronal activity and metabolism (EEG and CCO) drives the hemodynamic supply (HbO) in all E/N/M bands in the resting prefrontal cortex. Furthermore, to investigate the effect of transcranial photobiomodulation (tPBM), we performed a sham-controlled study by delivering an 800-nm laser beam to the left and right prefrontal cortex of the same participants. After performing the same data processing and statistical analysis, we obtained novel and important findings: tPBM delivered on either side of the prefrontal cortex triggered the alteration or reversal of directed network couplings among the three neurophysiological entities (i.e., HbO, CCO, and EEG frequency-specific powers) in the physiological network in the E and N bands, demonstrating that during the post-tPBM period, both metabolism and hemodynamic supply drive electrophysiological activity in directed network coupling of the prefrontal cortex (PFC). Overall, this study revealed that tPBM facilitates significant modulation of the directionality of neurophysiological networks in electrophysiological, metabolic, and hemodynamic activities.

Directed physiological networks in the human prefrontal cortex at rest and post transcranial photobiomodulation

Cerebral infra-slow oscillation (ISO) is a source of vasomotion in endogenic (E; 0.005-0.02 Hz), neurogenic (N; 0.02-0.04 Hz), and myogenic (M; 0.04-0.2 Hz) frequency bands. In this study, we quantified changes in prefrontal concentrations of oxygenated hemoglobin ( Δ [ H b O ] ) and redox-state cytochrome c oxidase ( Δ [ C C O ] ) as hemodynamic and metabolic activity metrics, and electroencephalogram (EEG) powers as electrophysiological activity, using concurrent measurements of 2-channel broadband near-infrared spectroscopy and EEG on the forehead of 22 healthy participants at rest. After preprocessing, the multi-modality signals were analyzed using generalized partial directed coherence to construct unilateral neurophysiological networks among the three neurophysiological metrics (with simplified symbols of HbO, CCO, and EEG) in each E/N/M frequency band. The links in these networks represent neurovascular, neurometabolic, and metabolicvascular coupling (NVC, NMC, and MVC). The results illustrate that the demand for oxygen by neuronal activity and metabolism (EEG and CCO) drives the hemodynamic supply (HbO) in all E/N/M bands in the resting prefrontal cortex. Furthermore, to investigate the effect of transcranial photobiomodulation (tPBM), we performed a sham-controlled study by delivering an 800-nm laser beam to the left and right prefrontal cortex of the same participants. After performing the same data processing and statistical analysis, we obtained novel and important findings: tPBM delivered on either side of the prefrontal cortex triggered the alteration or reversal of directed network couplings among the three neurophysiological entities (i.e., HbO, CCO, and EEG frequency-specific powers) in the physiological network in the E and N bands, demonstrating that during the post-tPBM period, both metabolism and hemodynamic supply drive electrophysiological activity in directed network coupling of the PFC. Overall, this study revealed that tPBM facilitates significant modulation of the directionality of neurophysiological networks in electrophysiological, metabolic, and hemodynamic activities.

Granger Causality among Graphs and Application to Functional Brain Connectivity in Autism Spectrum Disorder

Graphs/networks have become a powerful analytical approach for data modeling. Besides, with the advances in sensor technology, dynamic time-evolving data have become more common. In this context, one point of interest is a better understanding of the information flow within and between networks. Thus, we aim to infer Granger causality (G-causality) between networks' time series. In this case, the straightforward application of the well-established vector autoregressive model is not feasible. Consequently, we require a theoretical framework for modeling time-varying graphs. One possibility would be to consider a mathematical graph model with time-varying parameters (assumed to be random variables) that generates the network. Suppose we identify G-causality between the graph models' parameters. In that case, we could use it to define a G-causality between graphs. Here, we show that even if the model is unknown, the spectral radius is a reasonable estimate of some random graph model parameters. We illustrate our proposal's application to study the relationship between brain hemispheres of controls and children diagnosed with Autism Spectrum Disorder (ASD). We show that the G-causality intensity from the brain's right to the left hemisphere is different between ASD and controls.

Principles and open questions in functional brain network reconstruction

Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network representation involves often covert theoretical assumptions and methodological choices which affect the way networks are reconstructed from experimental data, and ultimately the resulting network properties and their interpretation. Here, we review some fundamental conceptual underpinnings and technical issues associated with brain network reconstruction, and discuss how their mutual influence concurs in clarifying the organization of brain function.

A technical review of canonical correlation analysis for neuroscience applications

Collecting comprehensive data sets of the same subject has become a standard in neuroscience research and uncovering multivariate relationships among collected data sets have gained significant attentions in recent years. Canonical correlation analysis (CCA) is one of the powerful multivariate tools to jointly investigate relationships among multiple data sets, which can uncover disease or environmental effects in various modalities simultaneously and characterize changes during development, aging, and disease progressions comprehensively. In the past 10 years, despite an increasing number of studies have utilized CCA in multivariate analysis, simple conventional CCA dominates these applications. Multiple CCA-variant techniques have been proposed to improve the model performance; however, the complicated multivariate formulations and not well-known capabilities have delayed their wide applications. Therefore, in this study, a comprehensive review of CCA and its variant techniques is provided. Detailed technical formulation with analytical and numerical solutions, current applications in neuroscience research, and advantages and limitations of each CCA-related technique are discussed. Finally, a general guideline in how to select the most appropriate CCA-related technique based on the properties of available data sets and particularly targeted neuroscience questions is provided.

Novel Regional Activity Representation With Constrained Canonical Correlation Analysis for Brain Connectivity Network Estimation

Inferring brain connectivity networks from fMRI data can take place at the Region of Interest (ROI) or voxel level. With most ROI-based approaches, the signals from same-ROI voxels are simply averaged, neglecting any inhomogeneity in each ROI and assuming that the same voxels will interact with different ROIs in a similar manner. In this paper, we propose a novel method of representing ROI activity and estimating brain connectivity that takes into account the regionally-specific nature of brain activity, the spatial location of concentrated activity, and activity in other ROIs. The proposed method is able to integrate intrinsic regional structures into a network modelling framework, which we call local activity constrained canonical correlation analysis (LA-cCCA). We evaluated LA-cCCA on both simulated and real fMRI data. The simulation results demonstrated that LA-cCCA had improved accuracy of the estimated brain connectivity networks compared to the average-signal or Principal Component Analysis (PCA)-based correlation methods and the Canonical Correlation Analysis (CCA) method. We further examined the performance of LA-cCCA on real fMRI data set from the Human Connectome Project. LA-cCCA outperformed the other three approaches in terms of connectivity reproducibility. The proposed method explores the potentials of regional activity representation and is a reliable model for connectivity network estimation. It may serve as a promising tool for studying both the healthy and diseased brain.

Permutation inference for canonical correlation analysis

Canonical correlation analysis (CCA) has become a key tool for population neuroimaging, allowing investigation of associations between many imaging and non-imaging measurements. As age, sex and other variables are often a source of variability not of direct interest, previous work has used CCA on residuals from a model that removes these effects, then proceeded directly to permutation inference. We show that a simple permutation test, as typically used to identify significant modes of shared variation on such data adjusted for nuisance variables, produces inflated error rates. The reason is that residualisation introduces dependencies among the observations that violate the exchangeability assumption. Even in the absence of nuisance variables, however, a simple permutation test for CCA also leads to excess error rates for all canonical correlations other than the first. The reason is that a simple permutation scheme does not ignore the variability already explained by previous canonical variables. Here we propose solutions for both problems: in the case of nuisance variables, we show that transforming the residuals to a lower dimensional basis where exchangeability holds results in a valid permutation test; for more general cases, with or without nuisance variables, we propose estimating the canonical correlations in a stepwise manner, removing at each iteration the variance already explained, while dealing with different number of variables in both sides. We also discuss how to address the multiplicity of tests, proposing an admissible test that is not conservative, and provide a complete algorithm for permutation inference for CCA.

The influence of COMT rs4680 on functional connectivity in healthy adults: A systematic review

The aim of this systematic review was to qualitatively synthesise the available research that investigated the influence of COMT genotype at SNP rs4680 on both task-based and resting-state connectivity in healthy adults. Thirty-five studies were identified that met inclusion criteria. Of the included studies, 20 studies reported resting-state findings and 16 studies reported task-based findings (emotion-processing, memory, working memory, reward-based learning and executive function). Studies were highly heterogeneous but an overall trend towards an association of the Val allele with greater resting-state connectivity and the Met allele with greater task-based connectivity is reported. A possible interpretation of current findings is discussed, whereby the Val allele is associated with improved cognitive flexibility allowing integration of novel relevant stimuli, and the Met allele allows improved sustained attention and targeted neural processing, particularly between limbic regions and prefrontal cortex. The most promising brain regions implicated in a COMT genotype influence on functional connectivity include prefrontal regions, amygdala and hippocampus.

Signature Patterns for Top-Down and Bottom-Up Information Processing via Cross-Frequency Coupling in Macaque Auditory Cortex

Predictive coding is a theoretical framework that provides a functional interpretation of top-down and bottom-up interactions in sensory processing. The theory suggests there are differences in message passing up versus down the cortical hierarchy. These differences result from the linear feedforward of prediction errors, and the nonlinear feedback of predictions. This implies that cross-frequency interactions should predominate top-down. But it remains unknown whether these differences are expressed in cross-frequency interactions in the brain. Here we examined bidirectional cross-frequency coupling across four sectors of the auditory hierarchy in the macaque. We computed two measures of cross-frequency coupling, phase-amplitude coupling (PAC) and amplitude-amplitude coupling (AAC). Our findings revealed distinct patterns for bottom-up and top-down information processing among cross-frequency interactions. Both top-down and bottom-up interactions made prominent use of low frequencies: low-to-low-frequency (theta, alpha, beta) and low-frequency-to-high- gamma couplings were predominant top-down, while low-frequency-to-low-gamma couplings were predominant bottom-up. These patterns were largely preserved across coupling types (PAC and AAC) and across stimulus types (natural and synthetic auditory stimuli), suggesting that they are a general feature of information processing in auditory cortex. Our findings suggest the modulatory effect of low frequencies on gamma-rhythms in distant regions is important for bidirectional information transfer. The finding of low-frequency-to-low-gamma interactions in the bottom-up direction suggest that nonlinearities may also play a role in feedforward message passing. Altogether, the patterns of cross-frequency interaction we observed across the auditory hierarchy are largely consistent with the predictive coding framework.

The impact of hemodynamic variability and signal mixing on the identifiability of effective connectivity structures in BOLD fMRI

PURPOSE

Multiple computational studies have demonstrated that essentially all current analytical approaches to determine effective connectivity perform poorly when applied to synthetic functional Magnetic Resonance Imaging (fMRI) datasets. In this study, we take a theoretical approach to investigate the potential factors facilitating and hindering effective connectivity research in fMRI.

MATERIALS AND METHODS

In this work, we perform a simulation study with use of Dynamic Causal Modeling generative model in order to gain new insights on the influence of factors such as the slow hemodynamic response, mixed signals in the network and short time series, on the effective connectivity estimation in fMRI studies.

RESULTS

First, we perform a Linear Discriminant Analysis study and find that not the hemodynamics itself but mixed signals in the neuronal networks are detrimental to the signatures of distinct connectivity patterns. This result suggests that for statistical methods (which do not involve lagged signals), deconvolving the BOLD responses is not necessary, but at the same time, functional parcellation into Regions of Interest (ROIs) is essential. Second, we study the impact of hemodynamic variability on the inference with use of lagged methods. We find that the local hemodynamic variability provide with an upper bound on the success rate of the lagged methods. Furthermore, we demonstrate that upsampling the data to TRs lower than the TRs in state-of-the-art datasets does not influence the performance of the lagged methods.

CONCLUSIONS

Factors such as background scale-free noise and hemodynamic variability have a major impact on the performance of methods for effective connectivity research in functional Magnetic Resonance Imaging.

Changes in Effective Connectivity Network Patterns in Drug Abusers, Treated With Different Methods

Introduction:

Various treatment methods for drug abusers will result in different success rates. This is partly due to different neural assumptions and partly due to various rate of relapse in abusers because of different circumstances. Investigating the brain activation networks of treated subjects can reveal the hidden mechanisms of the therapeutic methods.

Methods:

We studied three groups of subjects: heroin abusers treated with abstinent based therapy (ABT) method, heroin abusers treated with Methadone Maintenance Therapy (MMT) method, and a control group. They were all scanned with functional magnetic resonance imaging (fMRI), using a 6-block task, where each block consisted of the rest-craving-rest-neutral sequence. Using the dynamic causal modeling (DCM) algorithm, brain effective connectivity network (caused by the drug craving stimulation) was quantified for all groups. In this regard, 4 brain areas were selected for this analysis based on previous findings: ventromedial prefrontal cortex (VMPFC), dorsolateral prefrontal cortex (DLPFC), amygdala, and ventral striatum.

Results:

Our results indicated that the control subjects did not show significant brain activations after craving stimulations, but the two other groups showed significant brain activations in all 4 regions. In addition, VMPFC showed higher activations in the ABT group compared to the MMT group. The effective connectivity network suggested that the control subjects did not have any direct input from drug-related cue indices, while the other two groups showed reactions to these cues. Also, VMPFC displayed an important role in ABT group. In encountering the craving pictures, MMT subjects manifest a very simple mechanism compared to other groups.

Conclusion:

This study revealed an activation network similar to the emotional and inhibitory control networks observed in drug abusers in previous works. The results of DCM analysis also support the regulatory role of frontal regions on bottom regions. Furthermore, this study demonstrates the different effective connectivity patterns after drug abuse treatment and in this way helps the experts in the field.

Development of Effective Connectivity during Own- and Other-Race Face Processing: A Granger Causality Analysis

Numerous developmental studies have suggested that other-race effect (ORE) in face recognition emerges as early as in infancy and develops steadily throughout childhood. However, there is very limited research on the neural mechanisms underlying this developmental ORE. The present study used Granger causality analysis (GCA) to examine the development of children's cortical networks in processing own- and other-race faces. Children were between 3 and 13 years. An old-new paradigm was used to assess their own- and other-race face recognition with ETG-4000 (Hitachi Medical Co., Japan) acquiring functional near infrared spectroscopy (fNIRS) data. After preprocessing, for each participant and under each face condition, we obtained the causal map by calculating the weights of causal relations between the time courses of [oxy-Hb] of each pair of channels using GCA. To investigate further the differential causal connectivity for own-race faces and other-race faces at the group level, a repeated measure analysis of variance (ANOVA) was performed on the GCA weights for each pair of channels with the face race task (own-race face vs. other-race face) as the within-subject variable and the age as a between-subject factor (continuous variable). We found an age-related increase in functional connectivity, paralleling a similar age-related improvement in behavioral face processing ability. More importantly, we found that the significant differences in neural functional connectivity between the recognition of own-race faces and that of other-race faces were modulated by age. Thus, like the behavioral ORE, the neural ORE emerges early and undergoes a protracted developmental course.

Altered Effective Connectivity among Core Neurocognitive Networks in Idiopathic Generalized Epilepsy: An fMRI Evidence

Idiopathic generalized epilepsy (IGE) patients with generalized tonic-clonic seizures (GTCS) suffer long-term cognitive impairments, and present a higher incidence of psychosocial and psychiatric disturbances than healthy people. It is possible that the cognitive dysfunctions and higher psychopathological risk in IGE-GTCS derive from disturbed causal relationship among core neurocognitive brain networks. To test this hypothesis, we examined the effective connectivity across the salience network (SN), default mode network (DMN), and central executive network (CEN) using resting-state functional magnetic resonance imaging (fMRI) data collected from 27 IGE-GTCS patients and 29 healthy controls. In the study, a combination framework of time domain and frequency domain multivariate Granger causality analysis was firstly proposed, and proved to be valid and accurate by simulation experiments. Using this method, we then observed significant differences in the effective connectivity graphs between the patient and control groups. Specifically, between-group statistical analysis revealed that relative to the healthy controls, the patients established significantly enhanced Granger causal influence from the dorsolateral prefrontal cortex to the dorsal anterior cingulate cortex, which is coherent both in the time and frequency domains analyses. Meanwhile, time domain analysis also revealed decreased Granger causal influence from the right fronto-insular cortex to the posterior cingulate cortex in the patients. These findings may provide new evidence for functional brain organization disruption underlying cognitive dysfunctions and psychopathological risk in IGE-GTCS.

Information Flow Between Resting-State Networks

The resting brain dynamics self-organize into a finite number of correlated patterns known as resting-state networks (RSNs). It is well known that techniques such as independent component analysis can separate the brain activity at rest to provide such RSNs, but the specific pattern of interaction between RSNs is not yet fully understood. To this aim, we propose here a novel method to compute the information flow (IF) between different RSNs from resting-state magnetic resonance imaging. After hemodynamic response function blind deconvolution of all voxel signals, and under the hypothesis that RSNs define regions of interest, our method first uses principal component analysis to reduce dimensionality in each RSN to next compute IF (estimated here in terms of transfer entropy) between the different RSNs by systematically increasing k (the number of principal components used in the calculation). When k=1, this method is equivalent to computing IF using the average of all voxel activities in each RSN. For k≥1, our method calculates the k multivariate IF between the different RSNs. We find that the average IF among RSNs is dimension dependent, increasing from k=1 (i.e., the average voxel activity) up to a maximum occurring at k=5 and to finally decay to zero for k≥10. This suggests that a small number of components (close to five) is sufficient to describe the IF pattern between RSNs. Our method--addressing differences in IF between RSNs for any generic data--can be used for group comparison in health or disease. To illustrate this, we have calculated the inter-RSN IF in a data set of Alzheimer's disease (AD) to find that the most significant differences between AD and controls occurred for k=2, in addition to AD showing increased IF w.r.t.

CONTROLS

The spatial localization of the k=2 component, within RSNs, allows the characterization of IF differences between AD and controls.

Is First-Order Vector Autoregressive Model Optimal for fMRI Data?

We consider the problem of selecting the optimal orders of vector autoregressive (VAR) models for fMRI data. Many previous studies used model order of one and ignored that it may vary considerably across data sets depending on different data dimensions, subjects, tasks, and experimental designs. In addition, the classical information criteria (IC) used (e.g., the Akaike IC (AIC)) are biased and inappropriate for the high-dimensional fMRI data typically with a small sample size. We examine the mixed results on the optimal VAR orders for fMRI, especially the validity of the order-one hypothesis, by a comprehensive evaluation using different model selection criteria over three typical data types--a resting state, an event-related design, and a block design data set--with varying time series dimensions obtained from distinct functional brain networks. We use a more balanced criterion, Kullback's IC (KIC) based on Kullback's symmetric divergence combining two directed divergences. We also consider the bias-corrected versions (AICc and KICc) to improve VAR model selection in small samples. Simulation results show better small-sample selection performance of the proposed criteria over the classical ones. Both bias-corrected ICs provide more accurate and consistent model order choices than their biased counterparts, which suffer from overfitting, with KICc performing the best. Results on real data show that orders greater than one were selected by all criteria across all data sets for the small to moderate dimensions, particularly from small, specific networks such as the resting-state default mode network and the task-related motor networks, whereas low orders close to one but not necessarily one were chosen for the large dimensions of full-brain networks.

Synthetic neuronal datasets for benchmarking directed functional connectivity metrics

Background. Datasets consisting of synthetic neural data generated with quantifiable and controlled parameters are a valuable asset in the process of testing and validating directed functional connectivity metrics. Considering the recent debate in the neuroimaging community concerning the use of these metrics for fMRI data, synthetic datasets that emulate the BOLD signal dynamics have played a central role by supporting claims that argue in favor or against certain choices. Generative models often used in studies that simulate neuronal activity, with the aim of gaining insight into specific brain regions and functions, have different requirements from the generative models for benchmarking datasets. Even though the latter must be realistic, there is a tradeoff between realism and computational demand that needs to be contemplated and simulations that efficiently mimic the real behavior of single neurons or neuronal populations are preferred, instead of more cumbersome and marginally precise ones. Methods. This work explores how simple generative models are able to produce neuronal datasets, for benchmarking purposes, that reflect the simulated effective connectivity and, how these can be used to obtain synthetic recordings of EEG and fMRI BOLD signals. The generative models covered here are AR processes, neural mass models consisting of linear and nonlinear stochastic differential equations and populations with thousands of spiking units. Forward models for EEG consist in the simple three-shell head model while the fMRI BOLD signal is modeled with the Balloon-Windkessel model or by convolution with a hemodynamic response function. Results. The simulated datasets are tested for causality with the original spectral formulation for Granger causality. Modeled effective connectivity can be detected in the generated data for varying connection strengths and interaction delays. Discussion. All generative models produce synthetic neuronal data with detectable causal effects although the relation between modeled and detected causality varies and less biophysically realistic models offer more control in causal relations such as modeled strength and frequency location.

Sparse multivariate autoregressive modeling for mild cognitive impairment classification

Brain connectivity network derived from functional magnetic resonance imaging (fMRI) is becoming increasingly prevalent in the researches related to cognitive and perceptual processes. The capability to detect causal or effective connectivity is highly desirable for understanding the cooperative nature of brain network, particularly when the ultimate goal is to obtain good performance of control-patient classification with biological meaningful interpretations. Understanding directed functional interactions between brain regions via brain connectivity network is a challenging task. Since many genetic and biomedical networks are intrinsically sparse, incorporating sparsity property into connectivity modeling can make the derived models more biologically plausible. Accordingly, we propose an effective connectivity modeling of resting-state fMRI data based on the multivariate autoregressive (MAR) modeling technique, which is widely used to characterize temporal information of dynamic systems. This MAR modeling technique allows for the identification of effective connectivity using the Granger causality concept and reducing the spurious causality connectivity in assessment of directed functional interaction from fMRI data. A forward orthogonal least squares (OLS) regression algorithm is further used to construct a sparse MAR model. By applying the proposed modeling to mild cognitive impairment (MCI) classification, we identify several most discriminative regions, including middle cingulate gyrus, posterior cingulate gyrus, lingual gyrus and caudate regions, in line with results reported in previous findings. A relatively high classification accuracy of 91.89 % is also achieved, with an increment of 5.4 % compared to the fully-connected, non-directional Pearson-correlation-based functional connectivity approach.

Canonical information flow decomposition among neural structure subsets

Partial directed coherence (PDC) and directed coherence (DC) which describe complementary aspects of the directed information flow between pairs of univariate components that belong to a vector of simultaneously observed time series have recently been generalized as bPDC/bDC, respectively, to portray the relationship between subsets of component vectors (Takahashi, 2009; Faes and Nollo, 2013). This generalization is specially important for neuroscience applications as one often wishes to address the link between the set of time series from an observed ROI (region of interest) with respect to series from some other physiologically relevant ROI. bPDC/bDC are limited, however, in that several time series within a given subset may be irrelevant or may even interact opposingly with respect to one another leading to interpretation difficulties. To address this, we propose an alternative measure, termed cPDC/cDC, employing canonical decomposition to reveal the main frequency domain modes of interaction between the vector subsets. We also show bPDC/bDC and cPDC/cDC are related and possess mutual information rate interpretations. Numerical examples and a real data set illustrate the concepts. The present contribution provides what is seemingly the first canonical decomposition of information flow in the frequency domain.

Decreased small-world functional network connectivity and clustering across resting state networks in schizophrenia: an fMRI classification tutorial

Functional network connectivity (FNC) is a method of analyzing the temporal relationship of anatomical brain components, comparing the synchronicity between patient groups or conditions. We use functional-connectivity measures between independent components to classify between Schizophrenia patients and healthy controls during resting-state. Connectivity is measured using a variety of graph-theoretic connectivity measures such as graph density, average path length, and small-worldness. The Schizophrenia patients showed significantly less clustering (transitivity) among components than healthy controls (p < 0.05, corrected) with networks less likely to be connected, and also showed lower small-world connectivity than healthy controls. Using only these connectivity measures, an SVM classifier (without parameter tuning) could discriminate between Schizophrenia patients and healthy controls with 65% accuracy, compared to 51% chance. This implies that the global functional connectivity between resting-state networks is altered in Schizophrenia, with networks more likely to be disconnected and behave dissimilarly for diseased patients. We present this research finding as a tutorial using the publicly available COBRE dataset of 146 Schizophrenia patients and healthy controls, provided as part of the 1000 Functional Connectomes Project. We demonstrate preprocessing, using independent component analysis (ICA) to nominate networks, computing graph-theoretic connectivity measures, and finally using these connectivity measures to either classify between patient groups or assess between-group differences using formal hypothesis testing. All necessary code is provided for both running command-line FSL preprocessing, and for computing all statistical measures and SVM classification within R. Collectively, this work presents not just findings of diminished FNC among resting-state networks in Schizophrenia, but also a practical connectivity tutorial.

Canonical Granger causality between regions of interest

Estimating and modeling functional connectivity in the brain is a challenging problem with potential applications in the understanding of brain organization and various neurological and neuropsychological conditions. An important objective in connectivity analysis is to determine the connections between regions of interest in the brain. However, traditional functional connectivity analyses have frequently focused on modeling interactions between time series recordings at individual sensors, voxels, or vertices despite the fact that a single region of interest will often include multiple such recordings. In this paper, we present a novel measure of interaction between regions of interest rather than individual signals. The proposed measure, termed canonical Granger causality, combines ideas from canonical correlation and Granger causality analysis to yield a measure that reflects directed causality between two regions of interest. In particular, canonical Granger causality uses optimized linear combinations of signals from each region of interest to enable accurate causality measurements from substantially less data compared to alternative multivariate methods that have previously been proposed for this scenario. The optimized linear combinations are obtained using a variation of a technique developed for optimization on the Stiefel manifold. We demonstrate the advantages of canonical Granger causality in comparison to alternative causality measures for a range of different simulated datasets. We also apply the proposed measure to local field potential data recorded in a macaque brain during a visuomotor task. Results demonstrate that canonical Granger causality can be used to identify causal relationships between striate and prestriate cortexes in cases where standard Granger causality is unable to identify statistically significant interactions.

Upsampling to 400-ms resolution for assessing effective connectivity in functional magnetic resonance imaging data with Granger causality

Granger causality analysis of functional magnetic resonance imaging (fMRI) blood-oxygen-level-dependent signal data allows one to infer the direction and magnitude of influence that brain regions exert on one another. We employed a method for upsampling the time resolution of fMRI data that does not require additional interpolation beyond the interpolation that is regularly used for slice-timing correction. The mathematics for this new method are provided, and simulations demonstrate its viability. Using fMRI, 17 snake phobics and 19 healthy controls viewed snake, disgust, and neutral fish video clips preceded by anticipatory cues. Multivariate Granger causality models at the native 2-sec resolution and at the upsampled 400-ms resolution assessed directional associations of fMRI data among 13 anatomical regions of interest identified in prior research on anxiety and emotion. Superior sensitivity was observed for the 400-ms model, both for connectivity within each group and for group differences in connectivity. Context-dependent analyses for the 400-ms multivariate Granger causality model revealed the specific trial types showing group differences in connectivity. This is the first demonstration of effective connectivity of fMRI data using a method for achieving 400-ms resolution without sacrificing accuracy available at 2-sec resolution.

Functional clustering of time series gene expression data by Granger causality

Background

A common approach for time series gene expression data analysis includes the clustering of genes with similar expression patterns throughout time. Clustered gene expression profiles point to the joint contribution of groups of genes to a particular cellular process. However, since genes belong to intricate networks, other features, besides comparable expression patterns, should provide additional information for the identification of functionally similar genes.

Results

In this study we perform gene clustering through the identification of Granger causality between and within sets of time series gene expression data. Granger causality is based on the idea that the cause of an event cannot come after its consequence.

Conclusions

This kind of analysis can be used as a complementary approach for functional clustering, wherein genes would be clustered not solely based on their expression similarity but on their topological proximity built according to the intensity of Granger causality among them.

Prefrontal-occipitoparietal coupling underlies late latency human neuronal responses to emotion

Enhanced late positive potentials (LPPs) evoked by highly arousing unpleasant and pleasant stimuli have been consistently observed in event-related potential experiments in humans. Although the psychological factors modulating the LPP have been studied in detail, the neurobiological underpinnings of this response remain poorly understood. Current models suggest that the LPP is a product of both an automatic facilitation of perceptual activity, as well as postperceptual processing under cognitive control. Here we applied magnetoencephalography (MEG) and beamformer analysis combined with Granger causality measures to provide a mechanistic account for LPP generation that reconciles these two models. We demonstrate that the magnetic homolog of the LPP, mLPP, is localized within bilateral occipitoparietal and right prefrontal cortex. Critically, directed functional connectivity analysis between these brain regions, indexed by Granger causality, demonstrates stronger bidirectional influences between frontal and occipitoparietal cortex for high arousing emotional relative to low arousing neutral pictures. Thus, both bottom-up and top-down accounts of the late latency response to emotion derived from psychological studies can be explained by a reciprocal codependency between activity in prefrontal and occipitoparietal cortex.

Interaction of catechol O-methyltransferase and serotonin transporter genes modulates effective connectivity in a facial emotion-processing circuitry

Imaging genetic studies showed exaggerated blood oxygenation level-dependent response in limbic structures in carriers of low activity alleles of serotonin transporter-linked promoter region (5-HTTLPR) as well as catechol O-methyltransferase (COMT) genes. This was suggested to underlie the vulnerability to mood disorders. To better understand the mechanisms of vulnerability, it is important to investigate the genetic modulation of frontal-limbic connectivity that underlies emotional regulation and control. In this study, we have examined the interaction of 5-HTTLPR and COMT genetic markers on effective connectivity within neural circuitry for emotional facial expressions. A total of 91 healthy Caucasian adults underwent functional magnetic resonance imaging experiments with a task presenting dynamic emotional facial expressions of fear, sadness, happiness and anger. The effective connectivity within the facial processing circuitry was assessed with Granger causality method. We have demonstrated that in fear processing condition, an interaction between 5-HTTLPR (S) and COMT (met) low activity alleles was associated with reduced reciprocal connectivity within the circuitry including bilateral fusiform/inferior occipital regions, right superior temporal gyrus/superior temporal sulcus, bilateral inferior/middle prefrontal cortex and right amygdala. We suggest that the epistatic effect of reduced effective connectivity may underlie an inefficient emotion regulation that places these individuals at greater risk for depressive disorders.

Vector autoregression, structural equation modeling, and their synthesis in neuroimaging data analysis

Vector autoregression (VAR) and structural equation modeling (SEM) are two popular brain-network modeling tools. VAR, which is a data-driven approach, assumes that connected regions exert time-lagged influences on one another. In contrast, the hypothesis-driven SEM is used to validate an existing connectivity model where connected regions have contemporaneous interactions among them. We present the two models in detail and discuss their applicability to FMRI data, and their interpretational limits. We also propose a unified approach that models both lagged and contemporaneous effects. The unifying model, structural vector autoregression (SVAR), may improve statistical and explanatory power, and avoid some prevalent pitfalls that can occur when VAR and SEM are utilized separately.

Multiscale causal connectivity analysis by canonical correlation: theory and application to epileptic brain

Multivariate Granger causality is a well-established approach for inferring information flow in complex systems, and it is being increasingly applied to map brain connectivity. Traditional Granger causality is based on vector autoregressive (AR) or mixed autoregressive moving average (ARMA) model, which are potentially affected by errors in parameter estimation and may be contaminated by zero-lag correlation, notably when modeling neuroimaging data. To overcome this issue, we present here an extended canonical correlation approach to measure multivariate Granger causal interactions among time series. The procedure includes a reduced rank step for calculating canonical correlation analysis (CCA), and extends the definition of causality including instantaneous effects, thus avoiding the potential estimation problems of AR (or ARMA) models. We tested this approach on simulated data and confirmed its practical utility by exploring local network connectivity at different scales in the epileptic brain analyzing scalp and depth-EEG data during an interictal period.

Kernel canonical-correlation Granger causality for multiple time series

Canonical-correlation analysis as a multivariate statistical technique has been applied to multivariate Granger causality analysis to infer information flow in complex systems. It shows unique appeal and great superiority over the traditional vector autoregressive method, due to the simplified procedure that detects causal interaction between multiple time series, and the avoidance of potential model estimation problems. However, it is limited to the linear case. Here, we extend the framework of canonical correlation to include the estimation of multivariate nonlinear Granger causality for drawing inference about directed interaction. Its feasibility and effectiveness are verified on simulated data.