Granger Causality Mapping Research Articles

Inferring species interactions using Granger causality and convergent cross mapping

Identifying directed interactions between species from time series of their population densities has many uses in ecology. This key statistical task is equivalent to causal time series inference, which connects to the Granger causality (GC) concept: $x$ causes $y$ if $x$ improves the prediction of $y$ in a dynamic model. However, the entangled nature of nonlinear ecological systems has led to question the appropriateness of Granger causality, especially in its classical linear Multivariate AutoRegressive (MAR) model form. Convergent-cross mapping (CCM), a nonparametric method developed for deterministic dynamical systems, has been suggested as an alternative. Here, we show that linear GC and CCM are able to uncover interactions with surprisingly similar performance, for predator-prey cycles, 2-species deterministic (chaotic) or stochastic competition, as well as 10- and 20-species interaction networks. There is no correspondence between the degree of nonlinearity of the dynamics and which method performs best. Our results therefore imply that Granger causality, even in its linear MAR($p$) formulation, is a valid method for inferring interactions in nonlinear ecological networks; using GC or CCM (or both) can instead be decided based on the aims and specifics of the analysis.

Toward Mechanism-Directed Electrophenotype-Based Treatments for Atrial Fibrillation.

Current treatment approaches for persistent atrial fibrillation (AF) have a ceiling of success of around 50%. This is despite 15 years of developing adjunctive ablation strategies in addition to pulmonary vein isolation to target the underlying arrhythmogenic substrate in AF. A major shortcoming of our current approach to AF treatment is its predominantly empirical nature. This has in part been due to a lack of consensus on the mechanisms that sustain human AF. In this article, we review evidence suggesting that the previous debates on AF being either an organized arrhythmia with a focal driver or a disorganized rhythm sustained by multiple wavelets, may prove to be a false dichotomy. Instead, a range of fibrillation electrophenotypes exists along a continuous spectrum, and the predominant mechanism in an individual case is determined by the nature and extent of remodeling of the underlying substrate. We propose moving beyond the current empirical approach to AF treatment, highlight the need to prescribe AF treatments based on the underlying AF electrophenotype, and review several possible novel mapping algorithms that may be useful in discerning the AF electrophenotype to guide tailored treatments, including Granger Causality mapping.

Evaluation of Methods for Causal Discovery in Hydrometeorological Systems

AbstractUnderstanding causal relations is of utmost importance in hydrology and climate research for systems identification, prediction, and understanding systems behavior in a changing climate. Traditionally, researchers in hydrometeorology attempted to study causal questions by conducting controlled experiments using numerical models. This approach, however, in most cases of interest provides uncertain results because the models are approximate representation of the natural system. An alternative approach that has recently drawn significant attention in several fields is to infer causal relations from purely observational data. It possesses several traits to its utility particularly in hydrometeorology due to the rapid accumulation of in situ and remotely sensed data records. The first objective of this study is to present a brief description of four causal discovery methods (Granger causality, Transfer Entropy, graph‐based algorithms, and Convergent Cross Mapping) with special emphasis on the assumptions on which they are built. Second, using synthetic data generated from a hydrological model, we assess their performance in retrieving causal information taking into account sensitivity to sample size and presence of noise. Last, we use causal analysis to examine and formulate hypotheses on causal drivers of evapotranspiration in a shrubland region during summer and winter seasons. An interpretation of the hypotheses based on canopy seasonal dynamics and evapotranspiration processes is presented. It is hoped that the results presented here can be useful in guiding researchers studying hydrometeorological systems as to which causal method is most appropriate to the characteristics of the system under study.

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

BackgroundThe 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 methodWe 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. ResultsWe 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. ConclusionsIn 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.

Distinct neural processes support post-success and post-error slowing in the stop signal task

Executive control requires behavioral adaptation to environmental contingencies. In the stop signal task (SST), participants exhibit slower go trial reaction time (RT) following a stop trial, whether or not they successfully interrupt the motor response. In previous fMRI studies, we demonstrated activation of the right-hemispheric ventrolateral prefrontal cortex, in the area of inferior frontal gyrus, pars opercularis (IFGpo) and anterior insula (AI), during post-error slowing (PES). However, in similar analyses we were not able to identify regional activities during post-success slowing (PSS). Here, we revisited this issue in a larger sample of participants (n=100) each performing the SST for 40 min during fMRI. We replicated IFGpo/AI activation to PES (p≤0.05, FWE corrected). Further, PSS engages decreased activation in a number of cortical regions including the left inferior frontal cortex (IFC; p≤0.05, FWE corrected). We employed Granger causality mapping to identify areas that provide inputs each to the right IFGpo/AI and left IFC, and computed single-trial amplitude (STA) of stop trials of these input regions as well as the STA of post-stop trials of the right IFGpo/AI and left IFC. The STAs of the right inferior precentral sulcus and supplementary motor area (SMA) and right IFGpo/AI were positively correlated and the STAs of the left SMA and left IFC were positively correlated (slope>0, p’s≤0.01, one-sample t test), linking regional responses during stop success and error trials to those during PSS and PES. These findings suggest distinct neural mechanisms to support PSS and PES.

Causality analysis detects the regulatory role of maternal effect genes in the early Drosophila embryo

In developmental studies, inferring regulatory interactions of segmentation genetic network play a vital role in unveiling the mechanism of pattern formation. As such, there exists an opportune demand for theoretical developments and new mathematical models which can result in a more accurate illustration of this genetic network. Accordingly, this paper seeks to extract the meaningful regulatory role of the maternal effect genes using a variety of causality detection techniques and to explore whether these methods can suggest a new analytical view to the gene regulatory networks. We evaluate the use of three different powerful and widely-used models representing time and frequency domain Granger causality and convergent cross mapping technique with the results being thoroughly evaluated for statistical significance. Our findings show that the regulatory role of maternal effect genes is detectable in different time classes and thereby the method is applicable to infer the possible regulatory interactions present among the other genes of this network.

Diffusion of responsibility attenuates altruistic punishment: A functional magnetic resonance imaging effective connectivity study.

Humans altruistically punish violators of social norms to enforce cooperation and pro-social behaviors. However, such altruistic behaviors diminish when others are present, due to a diffusion of responsibility. We investigated the neural signatures underlying the modulations of diffusion of responsibility on altruistic punishment, conjoining a third-party punishment task with event-related functional magnetic resonance imaging and multivariate Granger causality mapping. In our study, participants acted as impartial third-party decision-makers and decided how to punish norm violations under two different social contexts: alone (i.e., full responsibility) or in the presence of putative other third-party decision makers (i.e., diffused responsibility). Our behavioral results demonstrated that the diffusion of responsibility served as a mediator of context-dependent punishment. In the presence of putative others, participants who felt less responsible also punished less severely in response to norm violations. Our neural results revealed that underlying this behavioral effect was a network of interconnected brain regions. For unfair relative to fair splits, the presence of others led to attenuated responses in brain regions implicated in signaling norm violations (e.g., AI) and to increased responses in brain regions implicated in calculating values of norm violations (e.g., vmPFC, precuneus) and mentalizing about others (dmPFC). The dmPFC acted as the driver of the punishment network, modulating target regions, such as AI, vmPFC, and precuneus, to adjust altruistic punishment behavior. Our results uncovered the neural basis of the influence of diffusion of responsibility on altruistic punishment and highlighted the role of the mentalizing network in this important phenomenon. Hum Brain Mapp 37:663-677, 2016. © 2015 Wiley Periodicals, Inc.

Control over the strength of connections between modules: a double dissociation between stimulus format and task revealed by Granger causality mapping in fMRI.

Drawing on theoretical and computational work with the localist dual route reading model and results from behavioral studies, Besner et al. (2011) proposed that the ability to perform tasks that require overriding stimulus-specific defaults (e.g., semantics when naming Arabic numerals, and phonology when evaluating the parity of number words) necessitate the ability to modulate the strength of connections between cognitive modules for lexical representation, semantics, and phonology on a task- and stimulus-specific basis. We used functional magnetic resonance imaging to evaluate this account by assessing changes in functional connectivity while participants performed tasks that did and did not require such stimulus-task default overrides. The occipital region showing the greatest modulation of BOLD signal strength for the two stimulus types was used as the seed region for Granger causality mapping (GCM). Our GCM analysis revealed a region of rostromedial frontal cortex with a crossover interaction. When participants performed tasks that required overriding stimulus type defaults (i.e., parity judgments of number words and naming Arabic numerals) functional connectivity between the occipital region and rostromedial frontal cortex was present. Statistically significant functional connectivity was absent when the tasks were the default for the stimulus type (i.e., parity judgments of Arabic numerals and reading number words). This frontal region (BA 10) has previously been shown to be involved in goal-directed behavior and maintenance of a specific task set. We conclude that overriding stimulus-task defaults requires a modulation of connection strengths between cognitive modules and that the override mechanism predicted from cognitive theory is instantiated by frontal modulation of neural activity of brain regions specialized for sensory processing.

FMRI evidence for areas that process surface gloss in the human visual cortex

Surface gloss is an important cue to the material properties of objects. Recent progress in the study of macaque’s brain has increased our understating of the areas involved in processing information about gloss, however the homologies with the human brain are not yet fully understood. Here we used human functional magnetic resonance imaging (fMRI) measurements to localize brain areas preferentially responding to glossy objects. We measured cortical activity for thirty-two rendered three-dimensional objects that had either Lambertian or specular surface properties. To control for differences in image structure, we overlaid a grid on the images and scrambled its cells. We found activations related to gloss in the posterior fusiform sulcus (pFs) and in area V3B/KO. Subsequent analysis with Granger causality mapping indicated that V3B/KO processes gloss information differently than pFs. Our results identify a small network of mid-level visual areas whose activity may be important in supporting the perception of surface gloss.

A network analysis of audiovisual affective speech perception

In this study we were interested in the neural system supporting the audiovisual (AV) integration of emotional expression and emotional prosody. To this end normal participants were exposed to short videos of a computer-animated face voicing emotionally positive or negative words with the appropriate prosody. Facial expression of the face was either neutral or emotionally appropriate. To reveal the neural network involved in affective AV integration, standard univariate analysis of functional magnetic resonance (fMRI) data was followed by a random-effects Granger causality mapping (RFX-GCM). The regions that distinguished emotional from neutral facial expressions in the univariate analysis were taken as seed regions. In trials showing emotional expressions compared to neutral trials univariate analysis showed activation primarily in bilateral amygdala, fusiform gyrus, middle temporal gyrus/superior temporal sulcus and inferior occipital gyrus. When employing either the left amygdala or the right amygdala as a seed region in RFX-GCM we found connectivity with the right hemispheric fusiform gyrus, with the indication that the fusiform gyrus sends information to the Amygdala. These results led to a working model for face perception in general and for AV-affective integration in particular which is an elaborated adaptation of existing models.

Combining independent component analysis and Granger causality to investigate brain network dynamics with fNIRS measurements

In this study a new strategy that combines Granger causality mapping (GCM) and independent component analysis (ICA) is proposed to reveal complex neural network dynamics underlying cognitive processes using functional near infrared spectroscopy (fNIRS) measurements. The GCM-ICA algorithm implements the following two procedures: (i) extraction of the region of interests (ROIs) of cortical activations by ICA, and (ii) estimation of the direct causal influences in local brain networks using Granger causality among voxels of ROIs. Our results show that the use of GCM in conjunction with ICA is able to effectively identify the directional brain network dynamics in time-frequency domain based on fNIRS recordings.

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.

Predicting depression based on dynamic regional connectivity: A windowed Granger causality analysis of MEG recordings

Abnormal inter-regional causalities can be mapped for the objective diagnosis of various diseases. These inter-regional connectivities are usually calculated over an entire scan and used to characterize the stationary strength of the connections. However, the connectivity within networks may undergo substantial changes during a scan. In this study, we developed an objective depression recognition approach using the dynamic regional interactions that occur in response to sad facial stimuli. The whole time-period magnetoencephalography (MEG) signals from the visual cortex, amygdala, anterior cingulate cortex (ACC) and inferior frontal gyrus (IFG) were separated into sequential time intervals. The Granger causality mapping method was used to identify the pairwise interaction pattern within each time interval. Feature selection was then undertaken within a minimum redundancy-maximum relevance (mRMR) framework. Typical classifiers were utilized to predict those patients who had depression. The overall performances of these classifiers were similar, and the highest classification accuracy rate was 87.5%. The best discriminative performance was obtained when the number of features was within a robust range. The discriminative network pattern obtained through support vector machine (SVM) analyses displayed abnormal causal connectivities that involved the amygdala during the early and late stages. These early and late connections in the amygdala appear to reveal a negative bias to coarse expression information processing and abnormal negative modulation in patients with depression, which may critically affect depression discrimination.

Corticostriatal Contributions to Musical Expectancy Perception

This study investigates the functional neuroanatomy of harmonic music perception with fMRI. We presented short pieces of Western classical music to nonmusicians. The ending of each piece was systematically manipulated in the following four ways: Standard Cadence (expected resolution), Deceptive Cadence (moderate deviation from expectation), Modulated Cadence (strong deviation from expectation but remaining within the harmonic structure of Western tonal music), and Atonal Cadence (strongest deviation from expectation by leaving the harmonic structure of Western tonal music). Music compared with baseline broadly recruited regions of the bilateral superior temporal gyrus (STG) and the right inferior frontal gyrus (IFG). Parametric regressors scaled to the degree of deviation from harmonic expectancy identified regions sensitive to expectancy violation. Areas within the BG were significantly modulated by expectancy violation, indicating a previously unappreciated role in harmonic processing. Expectancy violation also recruited bilateral cortical regions in the IFG and anterior STG, previously associated with syntactic processing in other domains. The posterior STG was not significantly modulated by expectancy. Granger causality mapping found functional connectivity between IFG, anterior STG, posterior STG, and the BG during music perception. Our results imply the IFG, anterior STG, and the BG are recruited for higher-order harmonic processing, whereas the posterior STG is recruited for basic pitch and melodic processing.

Functional integration of parietal lobe activity in early Alzheimer's disease

Objectives: Parietal lobe dysfunction is an important characteristic of early Alzheimer’s disease (AD). Functional studies have shown conflicting parietal activation patterns indicative of either compensatory or dysfunctional mechanisms. This study aimed at examining activation differences in early AD using a visuospatial task. We focused on functional characteristics of the parietal lobe and examined compensation or disconnection mechanisms by combining a fMRI task with effective connectivity measures from Granger Causality Mapping (GCM). Methods: Eighteen male patients with amnestic mild cognitive impairment (aMCI) and 18 male cognitively healthy older individuals were given a mental rotation task with different rotation angles. Results: There were no behavioral group differences on the fMRI task. Separate measurements at each angle revealed widespread activation group differences. More temporal and parietal activation in the higher angle condition was observed in aMCI patients. The parametric modulation, which identifies regions associated with increasing angle, confirmed these results. The GCM showed increased connectivity within the parietal lobe and between parietal and temporal regions in aMCI patients. Decreased connectivity was found between the inferior parietal lobule and posterior cingulate gyrus. Connectivity patterns correlated with memory performance scores in aMCI patients. Conclusions: Our results demonstrate increased effective temporo-parietal connectivity in aMCI patients, while maintaining intact behavioral performance. This might be a compensational mechanism to counteract a parietal-posterior cingulate gyrus disconnection. These findings highlight the importance of connectivity changes in the pathophysiology of AD. In addition, effective connectivity may be a promising method for evaluating interventions aimed at the promotion of compensatory mechanisms.

Amygdala activity and prefrontal cortex–amygdala effective connectivity to emerging emotional faces distinguish remitted and depressed mood states in bipolar disorder

Few studies have employed effective connectivity (EC) to examine the functional integrity of neural circuitry supporting abnormal emotion processing in bipolar disorder (BD), a key feature of the illness. We used Granger Causality Mapping (GCM) to map EC between the prefrontal cortex (PFC) and bilateral amygdala and a novel paradigm to assess emotion processing in adults with BD. Thirty-one remitted adults with BD [(remitted BD), mean age = 32 years], 21 adults with BD in a depressed episode [(depressed BD), mean age = 33 years], and 25 healthy control participants [(HC), mean age = 31 years] performed a block-design emotion processing task requiring color-labeling of a color flash superimposed on a task-irrelevant face morphing from neutral to emotional (happy, sad, angry, or fearful). GCM measured EC preceding (top-down) and following (bottom-up) activity between the PFC and the left and right amygdalae. Our findings indicated patterns of abnormally elevated bilateral amygdala activity in response to emerging fearful, sad, and angry facial expressions in remitted-BD subjects versus HC, and abnormally elevated right amygdala activity to emerging fearful faces in depressed-BD subjects versus HC. We also showed distinguishable patterns of abnormal EC between the amygdala and dorsomedial and ventrolateral PFC, especially to emerging happy and sad facial expressions in remitted-BD and depressed-BD subjects. EC measures of neural system level functioning can further understanding of neural mechanisms associated with abnormal emotion processing and regulation in BD. Our findings suggest major differences in recruitment of amygdala-PFC circuitry, supporting implicit emotion processing between remitted-BD and depressed-BD subjects, which may underlie changes from remission to depression in BD.

Functional integration of parietal lobe activity in early Alzheimer disease

Parietal lobe dysfunction is an important characteristic of early Alzheimer disease (AD). Functional studies have shown conflicting parietal activation patterns indicative of either compensatory or dysfunctional mechanisms. This study aimed at examining activation differences in early AD using a visuospatial task. We focused on functional characteristics of the parietal lobe and examined compensation or disconnection mechanisms by combining a fMRI task with effective connectivity measures from Granger causality mapping (GCM). Eighteen male patients with amnestic mild cognitive impairment (aMCI) and 18 male cognitively healthy older individuals were given a mental rotation task with different rotation angles. There were no behavioral group differences on the fMRI task. Separate measurements at each angle revealed widespread activation group differences. More temporal and parietal activation in the higher angle condition was observed in patients with aMCI. The parametric modulation, which identifies regions associated with increasing angle, confirmed these results. The GCM showed increased connectivity within the parietal lobe and between parietal and temporal regions in patients with aMCI. Decreased connectivity was found between the inferior parietal lobule and posterior cingulate gyrus. Connectivity patterns correlated with memory performance scores in patients with aMCI. Our results demonstrate increased effective temporoparietal connectivity in patients with aMCI, while maintaining intact behavioral performance. This might be a compensational mechanism to counteract a parietal-posterior cingulate gyrus disconnection. These findings highlight the importance of connectivity changes in the pathophysiology of AD. In addition, effective connectivity may be a promising method for evaluating interventions aimed at the promotion of compensatory mechanisms.

Interactions within and between Corticostriatal Loops during Component Processes of Category Learning

We examined dynamic interactions between cortex and BG during stimulus-response and feedback processing phases of categorization. First, we dissociated stimulus-response processing from feedback processing using "jittered" intervals of time between response and feedback to examine how each recruits the four primary corticostriatal loops (motor, executive, visual, and motivational). Second, we examined dynamic interactions within and between corticostriatal loops using Granger causality mapping. On each trial, subjects viewed one of six abstract visual stimuli, pressed a button indicating category membership, and then received feedback as to whether the decision was right or wrong. Stimulus-response processing was associated with greater activity in the visual loop, whereas feedback processing resulted in activity in the executive loop that was sensitive to feedback valence. Granger causality mapping showed patterns of directed influence within corticostriatal loops and between loops from the motor to the executive, to the visual, and finally to the motivational loop. These patterns of interaction are consistent with functional integration of motor processing in the motor loop with feedback processing in the executive loop and maintenance of stimulus-response history for future responses in the motivational loop.

Dissociating hippocampal and basal ganglia contributions to category learning using stimulus novelty and subjective judgments

We identified factors leading to hippocampal and basal ganglia recruitment during categorization learning. Subjects alternated between blocks of a standard trial and error category learning task and a subjective judgment task. In the subjective judgments task subjects categorized the stimulus and then instead of receiving feedback they indicated the basis of their response using 4 options: Remember: Conscious episodic memory of previous trials. Know-Automatic: Automatic, rapid response accompanied by conscious awareness of category membership. Know-Intuition: A “gut feeling” without fully conscious knowledge of category membership. Guess: Guessing. In addition, new stimuli were introduced throughout the experiment to examine effects of novelty. Categorization overall recruited both the basal ganglia and posterior hippocampus. However, basal ganglia activity was found during Know judgments (both Automatic and Intuition), whereas posterior hippocampus activity was found during Remember judgments. Granger causality mapping indicated interactions between the basal ganglia and hippocampus, with the putamen exerting directed influence on the posterior hippocampus, which in turn exerted directed influence on the posterior caudate nucleus. We also found a region of anterior hippocampus that showed decreased activity relative to baseline during categorization overall, and showed a strong novelty effect. Our results indicate that subjective measures may be effective in dissociating basal ganglia from hippocampal dependent learning, and that the basal ganglia are involved in both conscious and unconscious learning. They also indicate a dissociation within the hippocampus, in which the anterior regions are sensitive to novelty, and the posterior regions are involved in memory based categorization learning.

Granger Causality Mapping during Joint Actions Reveals Evidence for Forward Models That Could Overcome Sensory-Motor Delays

Studies investigating joint actions have suggested a central role for the putative mirror neuron system (pMNS) because of the close link between perception and action provided by these brain regions [1], [2], [3]. In contrast, our previous functional magnetic resonance imaging (fMRI) experiment demonstrated that the BOLD response of the pMNS does not suggest that it directly integrates observed and executed actions during joint actions [4]. To test whether the pMNS might contribute indirectly to the integration process by sending information to brain areas responsible for this integration (integration network), here we used Granger causality mapping (GCM) [5]. We explored the directional information flow between the anterior sites of the pMNS and previously identified integrative brain regions. We found that the left BA44 sent more information than it received to both the integration network (left thalamus, right middle occipital gyrus and cerebellum) and more posterior nodes of the pMNS (BA2). Thus, during joint actions, two anatomically separate networks therefore seem effectively connected and the information flow is predominantly from anterior to posterior areas of the brain. These findings suggest that the pMNS is involved indirectly in joint actions by transforming observed and executed actions into a common code and is part of a generative model that could predict the future somatosensory and visual consequences of observed and executed actions in order to overcome otherwise inevitable neural delays.