Measuring Granger causality between cortical regions from voxelwise fMRI BOLD signals with LASSO

Non-Asymptotic Guarantees for Reliable Identification of Granger Causality via the LASSO

Granger causality is among the widely used data-driven approaches for causal analysis of time series data with applications in various areas including economics, molecular biology, and neuroscience. Two of the main challenges of this methodology are: 1) over-fitting as a result of limited data duration, and 2) correlated process noise as a confounding factor, both leading to errors in identifying the causal influences. Sparse estimation via the LASSO has successfully addressed these challenges for parameter estimation. However, the classical statistical tests for Granger causality resort to asymptotic analysis of ordinary least squares, which require long data duration to be useful and are not immune to confounding effects. In this work, we address this disconnect by introducing a LASSO-based statistic and studying its non-asymptotic properties under the assumption that the true models admit sparse autoregressive representations. We establish fundamental limits for reliable identification of Granger causal influences using the proposed LASSO-based statistic. We further characterize the false positive error probability and test power of a simple thresholding rule for identifying Granger causal effects and provide two methods to set the threshold in a data-driven fashion. We present simulation studies and application to real data to compare the performance of our proposed method to ordinary least squares and existing LASSO-based methods in detecting Granger causal influences, which corroborate our theoretical results.

Classification of primary dysmenorrhea by brain effective connectivity of the amygdala: a machine learning study

BACKGROUND

The amygdala plays a crucial role in the central pathogenesis mechanism of primary dysmenorrhea (PDM). However, the detailed pain modulation principles of the amygdala in PDM remain unclear. Here, we applied the Granger causality analysis (GCA) to investigate the directional effective connectivity (EC) alterations in the amygdala network of PDM patients.

METHODS

Thirty-seven patients with PDM and 38 healthy controls were enrolled in this study and underwent resting-state functional magnetic resonance imaging scans during the pain-free stage. GCA was employed to explore the amygdala-based EC network alteration in PDM. A multivariate pattern analysis (MVPA)-based machine learning approach was used to explore whether the altered amygdala EC could serve as an fMRI-based marker for classifying PDM and HC participants.

RESULTS

Compared to the healthy control group, patients with PDM showed significantly decreased EC from the amygdala to the right superior frontal gyrus (SFG), right superior parietal lobe/middle occipital gyrus, and left middle cingulate cortex, whereas increased EC was found from the amygdala to the bilateral medial orbitofrontal cortex. In addition, increased EC was found from the bilateral SFG to the amygdala, and decreased EC was found from the medial orbitofrontal cortex, caudate nucleus to the amygdala. The increased EC from the right SFG to the amygdala was associated with a plasma prostaglandin E2 level in PDM. The MVPA based on an altered amygdala EC pattern yielded a total accuracy of 86.84% for classifying the patients with PDM and HC.

CONCLUSION

Our study is the first to combine MVPA and EC to explore brain function alteration in PDM. The results could advance understanding of the neural theory of PDM in specifying the pain-free period.

Adaptive Huber Regression on Markov-dependent Data

High-dimensional linear regression has been intensively studied in the community of statistics in the last two decades. For the convenience of theoretical analyses, classical methods usually assume independent observations and sub-Gaussian-tailed errors. However, neither of them hold in many real high-dimensional time-series data. Recently [Sun, Zhou, Fan, 2019, J. Amer. Stat. Assoc., in press] proposed Adaptive Huber Regression (AHR) to address the issue of heavy-tailed errors. They discover that the robustification parameter of the Huber loss should adapt to the sample size, the dimensionality, and the moments of the heavy-tailed errors. We progress in a vertical direction and justify AHR on dependent observations. Specifically, we consider an important dependence structure - Markov dependence. Our results show that the Markov dependence impacts on the adaption of the robustification parameter and the estimation of regression coefficients in the way that the sample size should be discounted by a factor depending on the spectral gap of the underlying Markov chain.

Stroke-related alterations in inter-areal communication

•

We used covariance-based Granger Causality on resting-state fMRI of stroke patients.

•

Stroke determines an overall decrease of homotopic Granger causality (GC)

•

Stroke determines a decrease of GC from and within the lesioned hemisphere.

•

Stroke causes imbalances in GC between the lesioned and the healthy hemisphere.

•

GC anomalies correlate with impaired performance in several behavioral domains.

Beyond causing local ischemia and cell damage at the site of injury, stroke strongly affects long-range anatomical connections, perturbing the functional organization of brain networks. Several studies reported functional connectivity abnormalities parallelling both behavioral deficits and functional recovery across different cognitive domains. FC alterations suggest that long-range communication in the brain is altered after stroke. However, standard FC analyses cannot reveal the directionality and time scale of inter-areal information transfer. We used resting-state fMRI and covariance-based Granger causality analysis to quantify network-level information transfer and its alteration in stroke. Two main large-scale anomalies were observed in stroke patients. First, inter-hemispheric information transfer was significantly decreased with respect to healthy controls. Second, stroke caused inter-hemispheric asymmetries, as information transfer within the affected hemisphere and from the affected to the intact hemisphere was significantly reduced. Both anomalies were more prominent in resting-state networks related to attention and language, and they correlated with impaired performance in several behavioral domains. Overall, our findings support the hypothesis that stroke provokes asymmetries between the affected and spared hemisphere, with different functional consequences depending on which hemisphere is lesioned.

Causality-Based Feature Fusion for Brain Neuro-Developmental Analysis

Human brain development is a complex and dynamic process caused by several factors such as genetics, sex hormones, and environmental changes. A number of recent studies on brain development have examined functional connectivity (FC) defined by the temporal correlation between time series of different brain regions. We propose to add the directional flow of information during brain maturation. To do so, we extract effective connectivity (EC) through Granger causality (GC) for two different groups of subjects, i.e., children and young adults. The motivation is that the inclusion of causal interaction may further discriminate brain connections between two age groups and help to discover new connections between brain regions. The contributions of this study are threefold. First, there has been a lack of attention to EC-based feature extraction in the context of brain development. To this end, we propose a new kernel-based GC (KGC) method to learn nonlinearity of complex brain network, where a reduced Sine hyperbolic polynomial (RSP) neural network was used as our proposed learner. Second, we used causality values as the weight for the directional connectivity between brain regions. Our findings indicated that the strength of connections was significantly higher in young adults relative to children. In addition, our new EC-based feature outperformed FC-based analysis from Philadelphia neurocohort (PNC) study with better discrimination of different age groups. Moreover, the fusion of these two sets of features (FC + EC) improved brain age prediction accuracy by more than 4%, indicating that they should be used together for brain development studies.

Construction of functional brain connectivity networks from fMRI data with driving and modulatory inputs: an extended conditional Granger causality approach

We propose a numerical-based approach extending the conditional MVAR Granger causality (MVGC) analysis for the construction of directed connectivity networks in the presence of both exogenous/stimuli and modulatory inputs. The performance of the proposed scheme is validated using both synthetic stochastic data considering also the influence of haemodynamics latencies and a benchmark fMRI dataset related to the role of attention in the perception of visual motion. The particular fMRI dataset has been used in many studies to evaluate alternative model hypotheses using the Dynamic Causal Modelling (DCM) approach. Based on the use of the Bayes factor, we show that the obtained GC connectivity network compares well to a reference model that has been selected through DCM analysis among other candidate models. Thus, our findings suggest that the proposed scheme can be successfully used as a stand-alone or complementary to DCM approach to find directed causal connectivity patterns in task-related fMRI studies.

Disordered directional brain network interactions during learning dynamics in schizophrenia revealed by multivariate autoregressive models

Directional network interactions underpin normative brain function in key domains including associative learning. Schizophrenia (SCZ) is characterized by altered learning dynamics, yet dysfunctional directional functional connectivity (dFC) evoked during learning is rarely assessed. Here, nonlinear learning dynamics were induced using a paradigm alternating between conditions (Encoding and Retrieval). Evoked fMRI time series data were modeled using multivariate autoregressive (MVAR) models, to discover dysfunctional direction interactions between brain network constituents during learning stages (Early vs. Late), and conditions. A functionally derived subnetwork of coactivated (healthy controls [HC] ∩ SCZ] nodes was identified. MVAR models quantified directional interactions between pairs of nodes, and coefficients were evaluated for intergroup differences (HC ≠ SCZ). In exploratory analyses, we quantified statistical effects of neuroleptic dosage on performance and MVAR measures. During Early Encoding, SCZ showed reduced dFC within a frontal–hippocampal–fusiform network, though during Late Encoding reduced dFC was associated with pathways toward the dorsolateral prefrontal cortex (dlPFC). During Early Retrieval, SCZ showed increased dFC in pathways to and from the dorsal anterior cingulate cortex, though during Late Retrieval, patients showed increased dFC in pathways toward the dlPFC, but decreased dFC in pathways from the dlPFC. These discoveries constitute novel extensions of our understanding of task‐evoked dysconnection in schizophrenia and motivate understanding of the directional aspect of the dysconnection in schizophrenia. Disordered directionality should be investigated using computational psychiatric approaches that complement the MVAR method used in our work.

Cardiorespiratory fitness predicts effective connectivity between the hippocampus and default mode network nodes in young adults

Rodent and human studies examining the relationship between aerobic exercise, brain structure, and brain function indicate that the hippocampus (HC), a brain region critical for episodic memory, demonstrates striking plasticity in response to exercise. Beyond the hippocampal memory system, human studies also indicate that aerobic exercise and cardiorespiratory fitness (CRF) are associated with individual differences in large-scale brain networks responsible for broad cognitive domains. Examining network activity in large-scale resting-state brain networks may provide a link connecting the observed relationships between aerobic exercise, hippocampal plasticity, and cognitive enhancement within broad cognitive domains. Previously, CRF has been associated with increased functional connectivity of the default mode network (DMN), specifically in older adults. However, how CRF relates to the magnitude and directionality of connectivity, or effective connectivity, between the HC and other DMN nodes remains unknown. We used resting-state fMRI and conditional Granger causality analysis (CGCA) to test the hypothesis that CRF positively predicts effective connectivity between the HC and other DMN nodes in healthy young adults. Twenty-six participants (ages 18-35 years) underwent a treadmill test to determine CRF by estimating its primary determinant, maximal oxygen uptake (V^. O_2max ), and a 10-min resting-state fMRI scan to examine DMN effective connectivity. We identified the DMN using group independent component analysis and examined effective connectivity between nodes using CGCA. Linear regression analyses demonstrated that CRF significantly predicts causal influence from the HC to the ventromedial prefrontal cortex, posterior cingulate cortex, and lateral temporal cortex and to the HC from the dorsomedial prefrontal cortex. The observed relationship between CRF and hippocampal effective connectivity provides a link between the rodent literature, which demonstrates a relationship between aerobic exercise and hippocampal plasticity, and the human literature, which demonstrates a relationship between aerobic exercise and CRF and the enhancement of broad cognitive domains including, but not limited to, memory.

Interregional causal influences of brain metabolic activity reveal the spread of aging effects during normal aging

During healthy brain aging, different brain regions show anatomical or functional declines at different rates, and some regions may show compensatory increases in functional activity. However, few studies have explored interregional influences of brain activity during the aging process. We proposed a causality analysis framework combining high dimensionality independent component analysis (ICA), Granger causality, and least absolute shrinkage and selection operator regression on longitudinal brain metabolic activity data measured by Fludeoxyglucose positron emission tomography (FDG-PET). We analyzed FDG-PET images from healthy old subjects, who were scanned for at least five sessions with an averaged intersession interval of 1 year. The longitudinal data were concatenated across subjects to form a time series, and the first-order autoregressive model was used to measure interregional causality among the independent sources of metabolic activity identified using ICA. Several independent sources with reduced metabolic activity in aging, including the anterior temporal lobe and orbital frontal cortex, demonstrated causal influences over many widespread brain regions. On the other hand, the influenced regions were more distributed, and had smaller age-related declines or even relatively increased metabolic activity. The current data demonstrated interregional spreads of aging on metabolic activity at the scale of a year, and have identified key brain regions in the aging process that have strong influences over other regions.

A Parsimonious Granger Causality Formulation for Capturing Arbitrarily Long Multivariate Associations

High-frequency neuroelectric signals like electroencephalography (EEG) or magnetoencephalography (MEG) provide a unique opportunity to infer causal relationships between local activity of brain areas. While causal inference is commonly performed through classical Granger causality (GC) based on multivariate autoregressive models, this method may encounter important limitations (e.g., data paucity) in the case of high dimensional data from densely connected systems like the brain. Additionally, physiological signals often present long-range dependencies which commonly require high autoregressive model orders/number of parameters. We present a generalization of autoregressive models for GC estimation based on Wiener–Volterra decompositions with Laguerre polynomials as basis functions. In this basis, the introduction of only one additional global parameter allows to capture arbitrary long dependencies without increasing model order, hence retaining model simplicity, linearity and ease of parameters estimation. We validate our method in synthetic data generated from families of complex, densely connected networks and demonstrate superior performance as compared to classical GC. Additionally, we apply our framework to studying the directed human brain connectome through MEG data from 89 subjects drawn from the Human Connectome Project (HCP) database, showing that it is able to reproduce current knowledge as well as to uncover previously unknown directed influences between cortical and limbic brain regions.

Estimation of Vector Autoregressive Parameters and Granger Causality From Noisy Multichannel Data

OBJECTIVE

The objective of this paper is to estimate the parameters of a multivariate autoregressive process from noisy multichannel data.

METHODS

Using a multivariate generalization of the Cadzow method, we propose a new method for estimating autoregressive parameters from noisy data: the nonlinear Cadzow method.

RESULTS

We show that our method outperforms existing multivariate methods such as higher order Yule-Walker method and Kalman EM method on simulated data. We apply our method to estimation of Granger causality from noisy data and again obtain superior results compared to previous methods. Finally, when applied to experimental local field potential data from monkey somatosensory and motor cortical areas, our method produces results consistent with cortical physiology.

CONCLUSION

The proposed nonlinear Cadzow method outperforms existing methods in obtaining denoised estimates of multivariate autoregressive parameters.

SIGNIFICANCE

Since multichannel recordings have become commonplace in biomedical applications ranging from discovering functional connectivity in the brain to speech data analysis and these recordings are inevitably contaminated by measurement noise, we believe our method has the potential for significant impact.

Response Hand and Motor Set Differentially Modulate the Connectivity of Brain Pathways During Simple Uni-manual Motor Behavior

We investigated the flexible modulation of undirected functional connectivity (uFC) of brain pathways during simple uni-manual responding. Two questions were central to our interests: (1) does response hand (dominant vs. non-dominant) differentially modulate connectivity and (2) are these effects related to responding under varying motor sets. fMRI data were acquired in twenty right-handed volunteers who responded with their right (dominant) or left (non-dominant) hand (blocked across acquisitions). Within acquisitions, the task oscillated between periodic responses (promoting the emergence of motor sets) or randomly induced responses (disrupting the emergence of motor sets). Conjunction analyses revealed eight shared nodes across response hand and condition, time series from which were analyzed. For right hand responses connectivity of the M1 ←→ Thalamus and SMA ←→ Parietal pathways was more significantly modulated during periodic responding. By comparison, for left hand responses, connectivity between five network pairs (including M1 and SMA, insula, basal ganglia, premotor cortex, parietal cortex, thalamus) was more significantly modulated during random responding. uFC analyses were complemented by directed FC based on multivariate autoregressive models of times series from the nodes. These results were complementary and highlighted significant modulation of dFC for SMA → Thalamus, SMA → M1, basal ganglia → Insula and basal ganglia → Thalamus. The results demonstrate complex effects of motor organization and task demand and response hand on different connectivity classes of fMRI data. The brain's sub-networks are flexibly modulated by factors related to motor organization and/or task demand, and our results have implications for assessment of medical conditions associated with motor dysfunction.

Sparse Estimation of Resting-State Effective Connectivity From fMRI Cross-Spectra

In functional magnetic resonance imaging (fMRI), functional connectivity is conventionally characterized by correlations between fMRI time series, which are intrinsically undirected measures of connectivity. Yet, some information about the directionality of network connections can nevertheless be extracted from the matrix of pairwise temporal correlations between all considered time series, when expressed in the frequency-domain as a cross-spectral density matrix. Using a sparsity prior, it then becomes possible to determine a unique directed network topology that best explains the observed undirected correlations, without having to rely on temporal precedence relationships that may not be valid in fMRI. Applying this method on simulated data with 100 nodes yielded excellent retrieval of the underlying directed networks under a wide variety of conditions. Importantly, the method did not depend on temporal precedence to establish directionality, thus reducing susceptibility to hemodynamic variability. The computational efficiency of the algorithm was sufficient to enable whole-brain estimations, thus circumventing the problem of missing nodes that otherwise occurs in partial-brain analyses. Applying the method to real resting-state fMRI data acquired with a high temporal resolution, the inferred networks showed good consistency with structural connectivity obtained from diffusion tractography in the same subjects. Interestingly, this agreement could also be seen when considering high-frequency rather than low-frequency connectivity (average correlation: r = 0.26 for f < 0.3 Hz, r = 0.43 for 0.3 < f < 5 Hz). Moreover, this concordance was significantly better (p < 0.05) than for networks obtained with conventional functional connectivity based on correlations (average correlation r = 0.18). The presented methodology thus appears to be well-suited for fMRI, particularly given its lack of explicit dependence on temporal lag structure, and is readily applicable to whole-brain effective connectivity estimation.

Top-down cortical interactions in visuospatial attention

The voluntary allocation of visuospatial attention depends upon top-down influences from the frontal eye field (FEF) and intraparietal sulcus (IPS)-the core regions of the dorsal attention network (DAN)-to visual occipital cortex (VOC), and has been further associated with within-DAN influences, particularly from the FEF to IPS. However, the degree to which these influences manifest at rest and are then modulated during anticipatory visuospatial attention tasks remains poorly understood. Here, we measured both undirected and directed functional connectivity (UFC, DFC) between the FEF, IPS, and VOC at rest and during an anticipatory visuospatial attention task, using a slow event-related design. Whereas the comparison between rest and task indicated FC modulations that persisted throughout the task duration, the large number of task trials we collected further enabled us to measure shorter timescale modulations of FC across the trial. Relative to rest, task engagement induced enhancement of both top-down influences from the DAN to VOC, as well as bidirectional influences between the FEF and IPS. These results suggest that task performance induces enhanced interaction within the DAN and a greater top-down influence on VOC. While resting FC generally showed right hemisphere dominance, task-related enhancement favored the left hemisphere, effectively balancing a resting hemispheric asymmetry, particularly within the DAN. On a shorter (within-trial) timescale, VOC-to-DAN and bidirectional FEF-IPS influences were transiently elevated during the anticipatory period of the trial, evincing phasic modulations related to changing attentional demands. In contrast to these task-specific effects, resting and task-related influence patterns were highly correlated, suggesting a predisposing role for resting organization, which requires minimal tonic and phasic modulations for control of visuospatial attention.

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.

Vector Autoregressive Models and Granger Causality in Time Series Analysis in Nursing Research: Dynamic Changes Among Vital Signs Prior to Cardiorespiratory Instability Events as an Example

BACKGROUND

Patients undergoing continuous vital sign monitoring (heart rate [HR], respiratory rate [RR], pulse oximetry [SpO2]) in real time display interrelated vital sign changes during situations of physiological stress. Patterns in this physiological cross-talk could portend impending cardiorespiratory instability (CRI). Vector autoregressive (VAR) modeling with Granger causality tests is one of the most flexible ways to elucidate underlying causal mechanisms in time series data.

PURPOSE

The purpose of this article is to illustrate the development of patient-specific VAR models using vital sign time series data in a sample of acutely ill, monitored, step-down unit patients and determine their Granger causal dynamics prior to onset of an incident CRI.

APPROACH

CRI was defined as vital signs beyond stipulated normality thresholds (HR = 40-140/minute, RR = 8-36/minute, SpO2 < 85%) and persisting for 3 minutes within a 5-minute moving window (60% of the duration of the window). A 6-hour time segment prior to onset of first CRI was chosen for time series modeling in 20 patients using a six-step procedure: (a) the uniform time series for each vital sign was assessed for stationarity, (b) appropriate lag was determined using a lag-length selection criteria, (c) the VAR model was constructed, (d) residual autocorrelation was assessed with the Lagrange Multiplier test, (e) stability of the VAR system was checked, and (f) Granger causality was evaluated in the final stable model.

RESULTS

The primary cause of incident CRI was low SpO2 (60% of cases), followed by out-of-range RR (30%) and HR (10%). Granger causality testing revealed that change in RR caused change in HR (21%; i.e., RR changed before HR changed) more often than change in HR causing change in RR (15%). Similarly, changes in RR caused changes in SpO2 (15%) more often than changes in SpO2 caused changes in RR (9%). For HR and SpO2, changes in HR causing changes in SpO2 and changes in SpO2 causing changes in HR occurred with equal frequency (18%).

DISCUSSION

Within this sample of acutely ill patients who experienced a CRI event, VAR modeling indicated that RR changes tend to occur before changes in HR and SpO2. These findings suggest that contextual assessment of RR changes as the earliest sign of CRI is warranted. Use of VAR modeling may be helpful in other nursing research applications based on time series data.

Potentiation of motor sub-networks for motor control but not working memory: Interaction of dACC and SMA revealed by resting-state directed functional connectivity

The dorsal Anterior Cingulate Cortex (dACC) and the Supplementary Motor Area (SMA) are known to interact during motor coordination behavior. We previously discovered that the directional influences underlying this interaction in a visuo-motor coordination task are asymmetric, with the dACC→SMA influence being significantly greater than that in the reverse direction. To assess the specificity of this effect, here we undertook an analysis of the interaction between dACC and SMA in two distinct contexts. In addition to the motor coordination task, we also assessed these effects during a (n-back) working memory task. We applied directed functional connectivity analysis to these two task paradigms, and also to the rest condition of each paradigm, in which rest blocks were interspersed with task blocks. We report here that the previously known asymmetric interaction between dACC and SMA, with dACC→SMA dominating, was significantly larger in the motor coordination task than the memory task. Moreover the asymmetry between dACC and SMA was reversed during the rest condition of the motor coordination task, but not of the working memory task. In sum, the dACC→SMA influence was significantly greater in the motor task than the memory task condition, and the SMA→dACC influence was significantly greater in the motor rest than the memory rest condition. We interpret these results as suggesting that the potentiation of motor sub-networks during the motor rest condition supports the motor control of SMA by dACC during the active motor task condition.

Multiregional integration in the brain during resting-state fMRI activity

Data-driven models of functional magnetic resonance imaging (fMRI) activity can elucidate dependencies that involve the combination of multiple brain regions. Activity in some regions during resting-state fMRI can be predicted with high accuracy from the activities of other regions. However, it remains unclear in which regions activity depends on unique integration of multiple predictor regions. To address this question, sparse (parsimonious) models could serve to better determine key interregional dependencies by reducing false positives. We used resting-state fMRI data from 46 subjects, and for each region of interest (ROI) per subject we performed whole-brain recursive feature elimination (RFE) to select the minimal set of ROIs that best predicted activity in the modeled ROI. We quantified the dependence of activity on multiple predictor ROIs, by measuring the gain in prediction accuracy of models that incorporated multiple predictor ROIs compared to models that used a single predictor ROI. We identified regions that showed considerable evidence of multiregional integration and determined the key regions that contributed to their observed activity. Our models reveal fronto-parietal integration networks, little integration in primary sensory regions, as well as redundancy between some regions. Our study demonstrates the utility of whole-brain RFE to generate data-driven models with minimal sets of ROIs that predict activity with high accuracy. By determining the extent to which activity in each ROI depended on integration of signals from multiple ROIs, we find cortical integration networks during resting-state activity.

Models of fMRI activity can elucidate underlying dependencies that involve the combination of multiple brain regions. However, it remains unclear in which regions activity depends on unique integration of multiple predictor regions. To address this question, sparse (parsimonious) models could serve to better determine key interregional dependencies by reducing false positives. We used resting-state fMRI data, and for each brain region we performed whole-brain recursive feature elimination to select the minimal set of regions that best predicted activity in the region. We identified integrator regions by quantifying the gain in prediction accuracy of models that incorporated multiple predictor regions compared to single predictor region. Our study provides data-driven models that use minimal sets of regions to predict activity with high accuracy. By determining the extent to which activity in each region depended on integration of signals from multiple sources, we find cortical integration networks during resting-state activity.

Functional split brain in a driving/listening paradigm

We often engage in two concurrent but unrelated activities, such as driving on a quiet road while listening to the radio. When we do so, does our brain split into functionally distinct entities? To address this question, we imaged brain activity with fMRI in experienced drivers engaged in a driving simulator while listening either to global positioning system instructions (integrated task) or to a radio show (split task). We found that, compared with the integrated task, the split task was characterized by reduced multivariate functional connectivity between the driving and listening networks. Furthermore, the integrated information content of the two networks, predicting their joint dynamics above and beyond their independent dynamics, was high in the integrated task and zero in the split task. Finally, individual subjects' ability to switch between high and low information integration predicted their driving performance across integrated and split tasks. This study raises the possibility that under certain conditions of daily life, a single brain may support two independent functional streams, a "functional split brain" similar to what is observed in patients with an anatomical split.

Multiscale modeling of brain dynamics: from single neurons and networks to mathematical tools

The extreme complexity of the brain naturally requires mathematical modeling approaches on a large variety of scales; the spectrum ranges from single neuron dynamics over the behavior of groups of neurons to neuronal network activity. Thus, the connection between the microscopic scale (single neuron activity) to macroscopic behavior (emergent behavior of the collective dynamics) and vice versa is a key to understand the brain in its complexity. In this work, we attempt a review of a wide range of approaches, ranging from the modeling of single neuron dynamics to machine learning. The models include biophysical as well as data-driven phenomenological models. The discussed models include Hodgkin-Huxley, FitzHugh-Nagumo, coupled oscillators (Kuramoto oscillators, Rössler oscillators, and the Hindmarsh-Rose neuron), Integrate and Fire, networks of neurons, and neural field equations. In addition to the mathematical models, important mathematical methods in multiscale modeling and reconstruction of the causal connectivity are sketched. The methods include linear and nonlinear tools from statistics, data analysis, and time series analysis up to differential equations, dynamical systems, and bifurcation theory, including Granger causal connectivity analysis, phase synchronization connectivity analysis, principal component analysis (PCA), independent component analysis (ICA), and manifold learning algorithms such as ISOMAP, and diffusion maps and equation-free techniques. WIREs Syst Biol Med 2016, 8:438-458. doi: 10.1002/wsbm.1348 For further resources related to this article, please visit the WIREs website.

Inference of biological networks using Bi-directional Random Forest Granger causality

The standard ordinary least squares based Granger causality is one of the widely used methods for detecting causal interactions between time series data. However, recent developments in technology limit the utilization of some existing implementations due to the availability of high dimensional data. In this paper, we are proposing a technique called Bi-directional Random Forest Granger causality. This technique uses the random forest regularization together with the idea of reusing the time series data by reversing the time stamp to extract more causal information. We have demonstrated the effectiveness of our proposed method by applying it to simulated data and then applied it to two real biological datasets, i.e., fMRI and HeLa cell. fMRI data was used to map brain network involved in deductive reasoning while HeLa cell dataset was used to map gene network involved in cancer.

Inferring the Dysconnection Syndrome in Schizophrenia: Interpretational Considerations on Methods for the Network Analyses of fMRI Data

Schizophrenia has long been considered one of the most intractable psychiatric conditions. Its etiology is likely polygenic, and its symptoms are hypothesized to result from complex aberrations in network-level neuronal activity. While easily identifiable by psychiatrists based on clear behavioral signs, the biological substrate of the disease remains poorly understood. Here, we discuss current trends and key concepts in the theoretical framework surrounding schizophrenia and critically discuss network approaches applied to neuroimaging data that can illuminate the correlates of the illness. We first consider a theoretical framework encompassing basic principles of brain function ranging from neural units toward perspectives of network function. Next, we outline the strengths and limitations of several fMRI-based analytic methodologies for assessing in vivo brain network function, including undirected and directed functional connectivity and effective connectivity. The underlying assumptions of each approach for modeling fMRI data are treated in some quantitative detail, allowing for assessment of the utility of each for generating inferences about brain networks relevant to schizophrenia. fMRI and the analyses of fMRI signals provide a limited, yet vibrant platform from which to test specific hypotheses about brain network dysfunction in schizophrenia. Carefully considered and applied connectivity measures have the power to illuminate loss or change of function at the network level, thus providing insight into the underlying neurobiology which gives rise to the emergent symptoms seen in the altered cognition and behavior of schizophrenia patients.

Foundational perspectives on causality in large-scale brain networks

A profusion of recent work in cognitive neuroscience has been concerned with the endeavor to uncover causal influences in large-scale brain networks. However, despite the fact that many papers give a nod to the important theoretical challenges posed by the concept of causality, this explosion of research has generally not been accompanied by a rigorous conceptual analysis of the nature of causality in the brain. This review provides both a descriptive and prescriptive account of the nature of causality as found within and between large-scale brain networks. In short, it seeks to clarify the concept of causality in large-scale brain networks both philosophically and scientifically. This is accomplished by briefly reviewing the rich philosophical history of work on causality, especially focusing on contributions by David Hume, Immanuel Kant, Bertrand Russell, and Christopher Hitchcock. We go on to discuss the impact that various interpretations of modern physics have had on our understanding of causality. Throughout all this, a central focus is the distinction between theories of deterministic causality (DC), whereby causes uniquely determine their effects, and probabilistic causality (PC), whereby causes change the probability of occurrence of their effects. We argue that, given the topological complexity of its large-scale connectivity, the brain should be considered as a complex system and its causal influences treated as probabilistic in nature. We conclude that PC is well suited for explaining causality in the brain for three reasons: (1) brain causality is often mutual; (2) connectional convergence dictates that only rarely is the activity of one neuronal population uniquely determined by another one; and (3) the causal influences exerted between neuronal populations may not have observable effects. A number of different techniques are currently available to characterize causal influence in the brain. Typically, these techniques quantify the statistical likelihood that a change in the activity of one neuronal population affects the activity in another. We argue that these measures access the inherently probabilistic nature of causal influences in the brain, and are thus better suited for large-scale brain network analysis than are DC-based measures. Our work is consistent with recent advances in the philosophical study of probabilistic causality, which originated from inherent conceptual problems with deterministic regularity theories. It also resonates with concepts of stochasticity that were involved in establishing modern physics. In summary, we argue that probabilistic causality is a conceptually appropriate foundation for describing neural causality in the brain.

Dorsal anterior cingulate cortex modulates supplementary motor area in coordinated unimanual motor behavior

Motor control is integral to all types of human behavior, and the dorsal Anterior Cingulate Cortex (dACC) is thought to play an important role in the brain network underlying motor control. Yet the role of the dACC in motor control is under-characterized. Here we aimed to characterize the dACC's role in adolescent brain network interactions during a simple motor control task involving visually coordinated unimanual finger movements. Network interactions were assessed using both undirected and directed functional connectivity analysis of functional Magnetic Resonance Imaging (fMRI) Blood-Oxygen-Level-Dependent (BOLD) signals, comparing the task with a rest condition. The relation between the dACC and Supplementary Motor Area (SMA) was compared to that between the dACC and Primary Motor Cortex (M1). The directed signal from dACC to SMA was significantly elevated during motor control in the task. By contrast, the directed signal from SMA to dACC, both directed signals between dACC and M1, and the undirected functional connections of dACC with SMA and M1, all did not differ between task and rest. Undirected coupling of dACC with both SMA and dACC, and only the dACC-to-SMA directed signal, were significantly greater for a proactive than a reactive task condition, suggesting that dACC plays a role in motor control by maintaining stimulus timing expectancy. Overall, these results suggest that the dACC selectively modulates the SMA during visually coordinated unimanual behavior in adolescence. The role of the dACC as an important brain area for the mediation of task-related motor control may be in place in adolescence, continuing into adulthood. The task and analytic approach described here should be extended to the study of healthy adults to examine network profiles of the dACC during basic motor behavior.

Granger causality analysis reveals distinct spatio-temporal connectivity patterns in motor and perceptual visuo-spatial working memory

We employed spectral Granger causality analysis on a full set of 56 electroencephalographic recordings acquired during the execution of either a 2D movement pointing or a perceptual (yes/no) change detection task with memory and non-memory conditions. On the basis of network characteristics across frequency bands, we provide evidence for the full dissociation of the corresponding cognitive processes. Movement-memory trial types exhibited higher degree nodes during the first 2 s of the delay period, mainly at central, left frontal and right-parietal areas. Change detection-memory trial types resulted in a three-peak temporal pattern of the total degree with higher degree nodes emerging mainly at central, right frontal, and occipital areas. Functional connectivity networks resulting from non-memory trial types were characterized by more sparse structures for both tasks. The movement-memory trial types encompassed an apparent coarse flow from frontal to parietal areas while the opposite flow from occipital, parietal to central and frontal areas was evident for the change detection-memory trial types. The differences among tasks and conditions were more profound in α (8–12 Hz) and β (12–30 Hz) and less in γ (30–45 Hz) band. Our results favor the hypothesis which considers spatial working memory as a by-product of specific mental processes that engages common brain areas under different network organizations.

Insular dysfunction within the salience network is associated with severity of symptoms and aberrant inter-network connectivity in major depressive disorder

Major depressive disorder (MDD) is characterized by altered intrinsic functional connectivity within (intra-iFC) intrinsic connectivity networks (ICNs), such as the Default Mode- (DMN), Salience- (SN) and Central Executive Network (CEN). It has been proposed that aberrant switching between DMN-mediated self-referential and CEN-mediated goal-directed cognitive processes might contribute to MDD, possibly explaining patients' difficulties to disengage the processing of self-focused, often negatively biased thoughts. Recently, it has been shown that the right anterior insula (rAI) within the SN is modulating DMN/CEN interactions. Since structural and functional alterations within the AI have been frequently reported in MDD, we hypothesized that aberrant intra-iFC in the SN's rAI is associated with both aberrant iFC between DMN and CEN (inter-iFC) and severity of symptoms in MDD. Twenty-five patients with MDD and 25 healthy controls were assessed using resting-state fMRI (rs-fMRI) and psychometric examination. High-model-order independent component analysis (ICA) of rs-fMRI data was performed to identify ICNs including DMN, SN, and CEN. Intra-iFC within and inter-iFC between distinct subsystems of the DMN, SN, and CEN were calculated, compared between groups and correlated with the severity of symptoms. Patients with MDD showed (1) decreased intra-iFC within the SN's rAI, (2) decreased inter-iFC between the DMN and CEN, and (3) increased inter-iFC between the SN and DMN. Moreover, decreased intra-iFC in the SN's rAI was associated with severity of symptoms and aberrant DMN/CEN interactions, with the latter losing significance after correction for multiple comparisons. Our results provide evidence for a relationship between aberrant intra-iFC in the salience network's rAI, aberrant DMN/CEN interactions and severity of symptoms, suggesting a link between aberrant salience mapping, abnormal coordination of DMN/CEN based cognitive processes and psychopathology in MDD.

Pattern-based Granger causality mapping in FMRI

Since its development, the multivoxel pattern analysis (MVPA) method has been widely used to study high-level cognitive function in the brain. The results of the MVPA indicate that the spatial pattern of functional MRI data contains useful information. In addition to the spatial pattern analysis of the brain functions, effective connectivity can also be analyzed between the spatial pattern-based information. In this article, we propose a multivoxel pattern-based causality mapping method to explore influences between the spatial pattern-based information in the brain. The method applies the Granger causality to interested regions of the brain in terms of spatiotemporal pattern-based data, which are known to play an important role in dealing with high-level functions of the brain. The method can compose a causality map throughout the entire brain for any specified region of interest. Both simulations and experiments were performed to show the performance of the proposed method, and the existence and analyzability of the connectivity between pattern-based information in the brain were verified.

Mapping the voxel-wise effective connectome in resting state FMRI

A network approach to brain and dynamics opens new perspectives towards understanding of its function. The functional connectivity from functional MRI recordings in humans is widely explored at large scale, and recently also at the voxel level. The networks of dynamical directed connections are far less investigated, in particular at the voxel level. To reconstruct full brain effective connectivity network and study its topological organization, we present a novel approach to multivariate Granger causality which integrates information theory and the architecture of the dynamical network to efficiently select a limited number of variables. The proposed method aggregates conditional information sets according to community organization, allowing to perform Granger causality analysis avoiding redundancy and overfitting even for high-dimensional and short datasets, such as time series from individual voxels in fMRI. We for the first time depicted the voxel-wise hubs of incoming and outgoing information, called Granger causality density (GCD), as a complement to previous repertoire of functional and anatomical connectomes. Analogies with these networks have been presented in most part of default mode network; while differences suggested differences in the specific measure of centrality. Our findings could open the way to a new description of global organization and information influence of brain function. With this approach is thus feasible to study the architecture of directed networks at the voxel level and individuating hubs by investigation of degree, betweenness and clustering coefficient.