A Multivariate Granger Causality Concept towards Full Brain Functional Connectivity

Causal functional connectivity in Alzheimer's disease computed from time series fMRI data

Functional connectivity between brain regions is known to be altered in Alzheimer's disease and promises to be a biomarker for early diagnosis. Several approaches for functional connectivity obtain an un-directed network representing stochastic associations (correlations) between brain regions. However, association does not necessarily imply causation. In contrast, Causal Functional Connectivity (CFC) is more informative, providing a directed network representing causal relationships between brain regions. In this paper, we obtained the causal functional connectome for the whole brain from resting-state functional magnetic resonance imaging (rs-fMRI) recordings of subjects from three clinical groups: cognitively normal, mild cognitive impairment, and Alzheimer's disease. We applied the recently developed Time-aware PC (TPC) algorithm to infer the causal functional connectome for the whole brain. TPC supports model-free estimation of whole brain CFC based on directed graphical modeling in a time series setting. We compared the CFC outcome of TPC with that of other related approaches in the literature. Then, we used the CFC outcomes of TPC and performed an exploratory analysis of the difference in strengths of CFC edges between Alzheimer's and cognitively normal groups, based on edge-wise p-values obtained by Welch's t-test. The brain regions thus identified are found to be in agreement with literature on brain regions impacted by Alzheimer's disease, published by researchers from clinical/medical institutions.

Multivariate autoregressive model estimation for high dimensional intracranial electrophysiological data

Fundamental to elucidating the functional organization of the brain is the assessment of causal interactions between different brain regions. Multivariate autoregressive (MVAR) modeling techniques applied to multisite electrophysiological recordings are a promising avenue for identifying such causal links. They estimate the degree to which past activity in one or more brain regions is predictive of another region's present activity, while simultaneously accounting for the mediating effects of other regions. Including as many mediating variables as possible in the model has the benefit of drastically reducing the odds of detecting spurious causal connectivity. However, effective bounds on the number of MVAR model coefficients that can be estimated reliably from limited data make exploiting the potential of MVAR models challenging for even modest numbers of recording sites. Here, we utilize well-established dimensionality-reduction techniques to fit MVAR models to human intracranial data from ∼100 - 200 recording sites spanning dozens of anatomically and functionally distinct cortical regions. First, we show that high dimensional MVAR models can be successfully estimated from long segments of data and yield plausible connectivity profiles. Next, we use these models to generate synthetic data with known ground-truth connectivity to explore the utility of applying principal component analysis and group least absolute shrinkage and selection operator (gLASSO) to reduce the number of parameters (connections) during model fitting to shorter data segments. We show that gLASSO is highly effective for recovering ground-truth connectivity in the limited data regime, capturing important features of connectivity for high-dimensional models with as little as 10 seconds of data. The methods presented here have broad applicability to the analysis of high-dimensional time series data in neuroscience, facilitating the elucidation of the neural basis of sensation, cognition, and arousal.

Statistical Perspective on Functional and Causal Neural Connectomics: A Comparative Study

Representation of brain network interactions is fundamental to the translation of neural structure to brain function. As such, methodologies for mapping neural interactions into structural models, i.e., inference of functional connectome from neural recordings, are key for the study of brain networks. While multiple approaches have been proposed for functional connectomics based on statistical associations between neural activity, association does not necessarily incorporate causation. Additional approaches have been proposed to incorporate aspects of causality to turn functional connectomes into causal functional connectomes, however, these methodologies typically focus on specific aspects of causality. This warrants a systematic statistical framework for causal functional connectomics that defines the foundations of common aspects of causality. Such a framework can assist in contrasting existing approaches and to guide development of further causal methodologies. In this work, we develop such a statistical guide. In particular, we consolidate the notions of associations and representations of neural interaction, i.e., types of neural connectomics, and then describe causal modeling in the statistics literature. We particularly focus on the introduction of directed Markov graphical models as a framework through which we define the Directed Markov Property—an essential criterion for examining the causality of proposed functional connectomes. We demonstrate how based on these notions, a comparative study of several existing approaches for finding causal functional connectivity from neural activity can be conducted. We proceed by providing an outlook ahead regarding the additional properties that future approaches could include to thoroughly address causality.

Directed Network Defects in Alzheimer's Disease Using Granger Causality and Graph Theory

BACKGROUND

Few works studied the directed whole-brain interaction between different brain regions of Alzheimer's disease (AD). Here, we investigated the whole-brain effective connectivity and studied the graph metrics associated with AD.

METHODS

Large-scale Granger causality analysis was conducted to explore abnormal whole-brain effective connectivity of patients with AD. Moreover, graph-theoretical metrics including smallworldness, assortativity, and hierarchy, were computed from the effective connectivity network. Statistical analysis identified the aberrant network properties of AD subjects when compared against healthy controls.

RESULTS

Decreased small-worldness, and increased characteristic path length, disassortativity, and hierarchy were found in AD subjects.

CONCLUSION

This work sheds insight into the underlying neuropathological mechanism of the brain network of AD individuals such as less efficient information transmission and reduced resilience to a random or targeted attack.

The boundaries of state-space Granger causality analysis applied to BOLD simulated data: A comparative modelling and simulation approach

BACKGROUND

The analysis of connectivity has become a fundamental tool in human neuroscience. Granger Causality Mapping is a data-driven method that uses Granger Causality (GC) to assess the existence and direction of influence between signals, based on temporal precedence of information. More recently, a theory of Granger causality has been developed for state-space (SS-GC) processes, but little is known about its statistical validation and application on functional magnetic resonance imaging (fMRI) data.

NEW METHOD

We explored different multivariate computational frameworks to define the optimal combination for GC estimation. We hypothesized a new heuristic, combining SS-GC with a distinct statistical validation technique, Time Reversed Testing, validating it on synthetic data. We test its performance with a number of experimental parameters, including block structure, sampling frequency, noise and system mean pairwise correlation, using a statistical framework of binary classification.

RESULTS

We found that SS-GC with time reversed testing outperforms other frameworks. The results validate the application of SS-GC to generative models. When estimating reliable causal relations, SS-GC returns promising results, especially when considering synthetic data with a high impact of noise and sampling rate.

CONCLUSIONS

In this study, we empirically explored the boundaries of SS-GC with time reversed testing, a data-driven causality analysis framework with potential applicability to fMRI data.

Delayed correlations improve the reconstruction of the brain connectome

The brain works as a large-scale complex network, known as the connectome. The strength of the connections between two brain regions in the connectome is commonly estimated by calculating the correlations between their patterns of activation. This approach relies on the assumption that the activation of connected regions occurs together and at the same time. However, there are delays between the activation of connected regions due to excitatory and inhibitory connections. Here, we propose a method to harvest this additional information and reconstruct the structural brain connectome using delayed correlations. This delayed-correlation method correctly identifies 70% to 80% of connections of simulated brain networks, compared to only 5% to 25% of connections detected by the standard methods; this result is robust against changes in the network parameters (small-worldness, excitatory vs. inhibitory connection ratio, weight distribution) and network activation dynamics. The delayed-correlation method predicts more accurately both the global network properties (characteristic path length, global efficiency, clustering coefficient, transitivity) and the nodal network properties (nodal degree, nodal clustering, nodal global efficiency), particularly at lower network densities. We obtain similar results in networks derived from animal and human data. These results suggest that the use of delayed correlations improves the reconstruction of the structural brain connectome and open new possibilities for the analysis of the brain connectome, as well as for other types of networks.

Variability and Reproducibility of Directed and Undirected Functional MRI Connectomes in the Human Brain

A growing number of studies are focusing on methods to estimate and analyze the functional connectome of the human brain. Graph theoretical measures are commonly employed to interpret and synthesize complex network-related information. While resting state functional MRI (rsfMRI) is often employed in this context, it is known to exhibit poor reproducibility, a key factor which is commonly neglected in typical cohort studies using connectomics-related measures as biomarkers. We aimed to fill this gap by analyzing and comparing the inter- and intra-subject variability of connectivity matrices, as well as graph-theoretical measures, in a large (n = 1003) database of young healthy subjects which underwent four consecutive rsfMRI sessions. We analyzed both directed (Granger Causality and Transfer Entropy) and undirected (Pearson Correlation and Partial Correlation) time-series association measures and related global and local graph-theoretical measures. While matrix weights exhibit a higher reproducibility in undirected, as opposed to directed, methods, this difference disappears when looking at global graph metrics and, in turn, exhibits strong regional dependence in local graphs metrics. Our results warrant caution in the interpretation of connectivity studies, and serve as a benchmark for future investigations by providing quantitative estimates for the inter- and intra-subject variabilities in both directed and undirected connectomic measures.

Dynamic Neuromagnetic Network Changes of Seizure Termination in Absence Epilepsy: A Magnetoencephalography Study

Objective: With increasing efforts devoted to investigating the generation and propagation mechanisms of spontaneous spike and wave discharges (SWDs), little attention has been paid to network mechanisms associated with termination patterns of SWDs to date. In the current study, we aimed to identify the frequency-dependent neural network dynamics during the offset of absence seizures.

Methods: Fifteen drug-naïve patients with childhood absence epilepsy (CAE) were assessed with a 275-Channel Magnetoencephalography (MEG) system. MEG data were recorded during and between seizures at a sampling rate of 6,000 Hz and analyzed in seven frequency bands. Source localization was performed with accumulated source imaging. Granger causality analysis was used to evaluate effective connectivity networks of the entire brain at the source level.

Results: At the low-frequency (1–80 Hz) bands, activities were predominantly distributed in the frontal cortical and parieto–occipito–temporal junction at the offset transition periods. The high-frequency oscillations (HFOs, 80–500 Hz) analysis indicated significant source localization in the medial frontal cortex and deep brain areas (mainly thalamus) during both the termination transition and interictal periods. Furthermore, an enhanced positive cortico–thalamic effective connectivity was observed around the discharge offset at all of the seven analyzed bands, the direction of which was primarily from various cortical regions to the thalamus.

Conclusions: Seizure termination is a gradual process that involves both the cortices and the thalamus in CAE. Cortico–thalamic coupling is observed at the termination transition periods, and the cerebral cortex acts as the driving force.

Constructing the Microbial Association Network from Large-Scale Time Series Data Using Granger Causality

The increasing availability of large-scale time series data allows the inference of microbial community dynamics by association network analysis. However, correlation-based association network analyses are noninformative of causal, mediating and time-dependent relationships between microbial community functional factors. To address this insufficiency, we introduced the Granger causality model to the analysis of a recent marine microbial time series dataset. We systematically constructed a directed acyclic network, representing both internal and external causal relationships among the microbial and environmental factors. We further optimized the network by removing false causal associations using the conditional Granger causality. The final network was visualized as a Granger graph, which was analyzed to identify causal relationships driven by key functional operators in the environment, such as Gammaproteobacteria, which was Granger caused by total organic nitrogen and primary production (p < 0.05 and Q < 0.05).

Automated diagnosis of HIV-associated neurocognitive disorders using large-scale Granger causality analysis of resting-state functional MRI

HIV-associated neurocognitive disorders (HAND) represent an important source of neurologic complications in individuals with HIV. The dynamic, often subclinical, course of HAND has rendered diagnosis, which currently depends on neuropsychometric (NP) evaluation, a challenge for clinicians. Here, we present evidence that functional brain connectivity, derived by large-scale Granger causality (lsGC) analysis of resting-state functional MRI (rs-fMRI) time-series, represents a potential biomarker to address this critical diagnostic need. Brain graph properties were used as features in machine learning tasks to 1) classify individuals as HIV⁺ or HIV^- and 2) to predict overall cognitive performance, as assessed by NP scores, in a 22-subject (13 HIV^-, 9 HIV⁺) cohort. Over nearly all seven brain parcellation templates considered, support vector machine (SVM) classifiers based on lsGC-derived brain graph features significantly outperformed those based on conventional Pearson correlation (PC)-derived features (p<0.05, Bonferroni-corrected). In a second task for which the objective was to predict the overall NP score of each subject, the lsGC-based SVM regressors consistently outperformed the PC-based regressors (p<0.05, Bonferroni-corrected) on nearly all templates. With the widely used Automated Anatomical Labeling (AAL90) template, it was determined that the brain regions that figured most strongly in the SVM classifiers included those of the default mode network (posterior cingulate cortex, angular gyrus) and basal ganglia (caudate nucleus), dysfunction in both of which have been observed in previous structural and functional analyses of HAND.

Multivariate Granger causality unveils directed parietal to prefrontal cortex connectivity during task-free MRI

While a large body of research has focused on the study of functional brain "connectivity", few investigators have focused on directionality of brain-brain interactions which, in spite of the mostly bidirectional anatomical substrates, cannot be assumed to be symmetrical. We employ a multivariate Granger Causality-based approach to estimating directed in-network interactions and quantify its advantages using extensive realistic synthetic BOLD data simulations to match Human Connectome Project (HCP) data specification. We then apply our framework to resting state functional MRI (rs-fMRI) data provided by the HCP to estimate the directed connectome of the human brain. We show that the functional interactions between parietal and prefrontal cortices commonly observed in rs-fMRI studies are not symmetrical, but consists of directional connectivity from parietal areas to prefrontal cortices rather than vice versa. These effects are localized within the same hemisphere and do not generalize to cross-hemispheric functional interactions. Our data are consistent with neurophysiological evidence that posterior parietal cortices involved in processing and integration of multi-sensory information modulate the function of more anterior prefrontal regions implicated in action control and goal-directed behaviour. The directionality of functional connectivity can provide an additional layer of information in interpreting rs-fMRI studies both in health and disease.

Tracking the Reorganization of Module Structure in Time-Varying Weighted Brain Functional Connectivity Networks

Identification of module structure in brain functional networks is a promising way to obtain novel insights into neural information processing, as modules correspond to delineated brain regions in which interactions are strongly increased. Tracking of network modules in time-varying brain functional networks is not yet commonly considered in neuroscience despite its potential for gaining an understanding of the time evolution of functional interaction patterns and associated changing degrees of functional segregation and integration. We introduce a general computational framework for extracting consensus partitions from defined time windows in sequences of weighted directed edge-complete networks and show how the temporal reorganization of the module structure can be tracked and visualized. Part of the framework is a new approach for computing edge weight thresholds for individual networks based on multiobjective optimization of module structure quality criteria as well as an approach for matching modules across time steps. By testing our framework using synthetic network sequences and applying it to brain functional networks computed from electroencephalographic recordings of healthy subjects that were exposed to a major balance perturbation, we demonstrate the framework’s potential for gaining meaningful insights into dynamic brain function in the form of evolving network modules. The precise chronology of the neural processing inferred with our framework and its interpretation helps to improve the currently incomplete understanding of the cortical contribution for the compensation of such balance perturbations.

Assessment of resampling methods for causality testing: A note on the US inflation behavior

Different resampling methods for the null hypothesis of no Granger causality are assessed in the setting of multivariate time series, taking into account that the driving-response coupling is conditioned on the other observed variables. As appropriate test statistic for this setting, the partial transfer entropy (PTE), an information and model-free measure, is used. Two resampling techniques, time-shifted surrogates and the stationary bootstrap, are combined with three independence settings (giving a total of six resampling methods), all approximating the null hypothesis of no Granger causality. In these three settings, the level of dependence is changed, while the conditioning variables remain intact. The empirical null distribution of the PTE, as the surrogate and bootstrapped time series become more independent, is examined along with the size and power of the respective tests. Additionally, we consider a seventh resampling method by contemporaneously resampling the driving and the response time series using the stationary bootstrap. Although this case does not comply with the no causality hypothesis, one can obtain an accurate sampling distribution for the mean of the test statistic since its value is zero under H0. Results indicate that as the resampling setting gets more independent, the test becomes more conservative. Finally, we conclude with a real application. More specifically, we investigate the causal links among the growth rates for the US CPI, money supply and crude oil. Based on the PTE and the seven resampling methods, we consistently find that changes in crude oil cause inflation conditioning on money supply in the post-1986 period. However this relationship cannot be explained on the basis of traditional cost-push mechanisms.

Exploring connectivity with large-scale Granger causality on resting-state functional MRI

BACKGROUND

Large-scale Granger causality (lsGC) is a recently developed, resting-state functional MRI (fMRI) connectivity analysis approach that estimates multivariate voxel-resolution connectivity. Unlike most commonly used multivariate approaches, which establish coarse-resolution connectivity by aggregating voxel time-series avoiding an underdetermined problem, lsGC estimates voxel-resolution, fine-grained connectivity by incorporating an embedded dimension reduction.

NEW METHOD

We investigate application of lsGC on realistic fMRI simulations, modeling smoothing of neuronal activity by the hemodynamic response function and repetition time (TR), and empirical resting-state fMRI data. Subsequently, functional subnetworks are extracted from lsGC connectivity measures for both datasets and validated quantitatively. We also provide guidelines to select lsGC free parameters.

RESULTS

Results indicate that lsGC reliably recovers underlying network structure with area under receiver operator characteristic curve (AUC) of 0.93 at TR=1.5s for a 10-min session of fMRI simulations. Furthermore, subnetworks of closely interacting modules are recovered from the aforementioned lsGC networks. Results on empirical resting-state fMRI data demonstrate recovery of visual and motor cortex in close agreement with spatial maps obtained from (i) visuo-motor fMRI stimulation task-sequence (Accuracy=0.76) and (ii) independent component analysis (ICA) of resting-state fMRI (Accuracy=0.86).

COMPARISON WITH EXISTING METHOD(S)

Compared with conventional Granger causality approach (AUC=0.75), lsGC produces better network recovery on fMRI simulations. Furthermore, it cannot recover functional subnetworks from empirical fMRI data, since quantifying voxel-resolution connectivity is not possible as consequence of encountering an underdetermined problem.

CONCLUSIONS

Functional network recovery from fMRI data suggests that lsGC gives useful insight into connectivity patterns from resting-state fMRI at a multivariate voxel-resolution.

Quantify neuromagnetic network changes from pre-ictal to ictal activities in absence seizures

OBJECTIVE

The cortico-thalamo-cortical network plays a key role in childhood absence epilepsy (CAE). However, the exact interaction between the cortex and the thalamus remains incompletely understood. This study aimed to investigate the dynamic changes of frequency-dependent neural networks during the initialization of absence seizures.

METHODS

Magnetoencephalography data from 14 patients with CAE were recorded during and between seizures at a sampling rate of 6000Hz and analyzed in seven frequency bands. Neuromagnetic sources were volumetrically scanned with accumulated source imaging. Effective connectivity networks of the entire brain, including the cortico-thalamo-cortical network, were evaluated at the source level through Granger causality analysis.

RESULTS

The low-frequency (1-80Hz) activities showed significant frontal cortical and parieto-occipito-temporal junction source localization around seizures. The high-frequency (80-250Hz) oscillations showed predominant activities consistently localized in deep brain areas and medial frontal cortex. The increased cortico-thalamic effective connectivity was observed around seizures in both low- and high-frequency ranges. The direction was predominantly from the cortex to the thalamus at the early time, although the cortex that drove connectivity varied among subjects.

CONCLUSIONS

The cerebral cortex plays a key role in driving the cortico-thalamic connections at the early portion of the initialization of absence seizures. The oscillatory activities in the thalamus could be triggered by networks from various regions in the cortex.

SIGNIFICANCE

The dynamic changes of neural network provide evidences that absence seizures are probably resulted from cortical initialized cortico-thalamic network.

Altered Effective Connectivity Network in Childhood Absence Epilepsy: A Multi-frequency MEG Study

Using multi-frequency magnetoencephalography (MEG) data, we investigated whether the effective connectivity (EC) network of patients with childhood absence epilepsy (CAE) is altered during the inter-ictal period in comparison with healthy controls. MEG data from 13 untreated CAE patients and 10 healthy controls were recorded. Correlation analysis and Granger causality analysis were used to construct an EC network at the source level in eight frequency bands. Alterations in the spatial pattern and topology of the network in CAE were investigated by comparing the patients with the controls. The network pattern was altered mainly in 1-4 Hz, showing strong connections within the frontal cortex and weak connections in the anterior-posterior pathways. The EC involving the precuneus/posterior cingulate cortex (PC/PCC) significantly decreased in low-frequency bands. In addition, the parameters of graph theory were significantly altered in several low- and high-frequency bands. CAE patients display frequency-specific abnormalities in the network pattern even during the inter-ictal period, and the frontal cortex and PC/PCC might play crucial roles in the pathophysiology of CAE. The EC network of CAE patients was over-connective and random during the inter-ictal period. This study is the first to reveal the frequency-specific alteration in the EC network during the inter-ictal period in CAE patients. Multiple-frequency MEG data are useful in investigating the pathophysiology of CAE, which can serve as new biomarkers of this disorder.