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Multielectrode neurophysiological recording and high-resolution neuroimaging generate multivariate data that are the basis for understanding the patterns of neural interactions. How to extract directions of information flow in brain networks from these data remains a key challenge. Research over the last few years has identified Granger causality as a statistically principled technique to furnish this capability. The estimation of Granger causality currently requires autoregressive modeling of neural data. Here, we propose a nonparametric approach based on widely used Fourier and wavelet transforms to estimate Granger causality, eliminating the need of explicit autoregressive data modeling. We demonstrate the effectiveness of this approach by applying it to synthetic data generated by network models with known connectivity and to local field potentials recorded from monkeys performing a sensorimotor task.

In a network of neuronal oscillators with time-delayed coupling, we uncover a phenomenon of enhancement of neural synchrony by time delay: a stable synchronized state exists at low coupling strengths for significant time delays. By formulating a master stability equation for time-delayed networks of Hindmarsh-Rose neurons, we show that there is always an extended region of stable synchronous activity corresponding to low coupling strengths. Such synchrony could be achieved in the undelayed system only by much higher coupling strengths. This phenomenon of enhanced neural synchrony by delay has important implications, in particular, in understanding synchronization of distant neurons and information processing in the brain.

Experiments in many fields of science and engineering yield data in the form of time series. The Fourier and wavelet transform-based nonparametric methods are used widely to study the spectral characteristics of these time series data. Here, we extend the framework of nonparametric spectral methods to include the estimation of Granger causality spectra for assessing directional influences. We illustrate the utility of the proposed methods using synthetic data from network models consisting of interacting dynamical systems. [Physical Review Letters, in press].PACS numbers: 45.30.+s, 02.70.Hm, 02.50.Sk, 02.30.Nw, Extracting information flow in networks of coupled dynamical systems from the time series measurements of their activity is of great interest in physical, biological and social sciences. Such knowledge holds the key to the understanding of phenomena ranging from turbulent fluids to interacting genes and proteins to networks of neural ensembles. [5,6,7,8], genetics [9], climate science [10,11], and economics [1,12]. However, the parametric modeling methods often encounter difficulties such as uncertainty in model parameters and inability to fit data with complex spectral contents [13]. On the other hand, the Fourier and wavelet transform-based nonparametric spectral methods are known to be free from such difficulties [13] and have been used extensively in the analysis of univariate and multivariate experimental time series [14,15]. A weakness of the current nonparametric framework is that it lacks the ability for estimating Granger causality. In this Letter, we overcome this weakness by proposing a nonparametric approach to estimate Granger causality directly from Fourier and wavelet transforms of data, eliminating the need of explicit AR modeling. Time-domain Granger causality can be obtained by integrating the corresponding spectral representation over frequency [3]. Below, we present the theory and apply it to simulated time series.Granger causality: the parametric estimation approach. Granger causality [1] is a measure of causal or directional influence from one time series to another and is based on linear predictions of time series. Consider two simultaneously recorded time series: X 1 : x 1 (1), x 1 (2), ..., x 1 (t), ...; X 2 : x 2 (1), x 2 (2), ..., x 2 (t), ... from two stationary stochastic processes (X 1 , X 2 ). Now, using AR representations, we construct bivariate linear prediction models for x 1 (t) and x 2 (t):(1)along with the univariate models: x 1 (t) = ∞ j=1 α j x 1 (t − j) + ǫ 1 (t) and x 2 (t) = ∞ j=1 β j x 2 (t − j) + ǫ 2 (t). Here, ǫ's are the prediction errors. If var(ǫ 1|2 (t)) < var(ǫ 1 (t)) in some suitable statistical sense, then X 2 is said to have a causal influence on X 1 . Similarly, if var(ǫ 2|1 (t)) < var(ǫ 2 (t)), then there is a causal influence from X 1 to X 2 . These causal influences are quantified in time domain [3] by F j→i = ln var(ǫ i (t)) var(ǫ i|j (t)) , where i = 1, 2 and j = 2, 1. Experimental processes are often rich in oscillatory content, lending themselv...

Although one proposed function of both the striatum and its major dopamine inputs is related to coding rewards and reward-related stimuli, an alternative view suggests a more general role of the striatum in processing salient events, regardless of their reward value. Here we define saliency as an event that both is unexpected and elicits an attentional-behavioral switch (i.e., arousing). In the present study, human striatal responses to nonrewarding salient stimuli were investigated. Using functional magnetic resonance imaging (fMRI), the blood oxygenation level-dependent signal was measured in response to flickering visual distractors presented in the background of an ongoing task. Distractor salience was manipulated by altering the frequency of distractor occurrence. Infrequently presented distractors were considered more salient than frequently presented distractors. We also investigated whether behavioral relevance of the distractors was a necessary component of saliency for eliciting striatal responses. In the first experiment (19 subjects), the distractors were made behaviorally relevant by defining a subset of them as targets requiring a button press. In the second experiment (17 subjects), the distractors were not behaviorally relevant (i.e., they did not require any response). The fMRI results revealed increased activation in the nucleus accumbens after infrequent (high salience) relative to frequent (low salience) presentation of distractors in both experiments. Caudate activity increased only when the distractors were behaviorally relevant. These results demonstrate a role of the striatum in coding nonrewarding salient events. In addition, a functional subdivision of the striatum according to the behavioral relevance of the stimuli is suggested.

Certain cells in the brain, for example, thalamic neurons during sleep, show spike-burst activity. We study such spike-burst neural activity and the transitions to a synchronized state using a model of coupled bursting neurons. In an electrically coupled network, we show that the increase of coupling strength increases incoherence first and then induces two different transitions to synchronized states, one associated with bursts and the other with spikes. These sequential transitions to synchronized states are determined by the zero crossings of the maximum transverse Lyapunov exponents. These results suggest that synchronization of spike-burst activity is a multi-time-scale phenomenon and burst synchrony is a precursor to spike synchrony.

Cognitively demanding goal-directed tasks in the human brain are thought to involve the dynamic interplay of several large-scale neural networks, including the default-mode network (DMN), salience network (SN), and central-executive network (CEN). Resting-state functional magnetic resonance imaging (rsfMRI) studies have consistently shown that the CEN and SN negatively regulate activity in the DMN, and this switching is argued to be controlled by the right anterior insula (rAI) of the SN. However, what remains to be investigated is the pattern of directed network interactions during difficult perceptual decision-making tasks. We recorded fMRI data while participants categorized the left-right motion of moving dots. We defined regions of interest, extracted fMRI time series, and performed directed connectivity analysis using Granger causality techniques. Our analyses demonstrated that the slow oscillation (0.07-0.19 Hz) mediated the interactions within and between the DMN, SN, and CEN nodes both for easier and harder decision-making tasks. We found that the rAI, a key node of the SN, played a causal control over the DMN and CEN for easier decision-making tasks. The combined effort of the rAI and dorsal anterior cingulate cortex of the SN had the causal control over the DMN and CEN for a harder task. These findings provide important insights into how a sensory signal organizes among the DMN, SN, and CEN during sensory information-guided, goal-directed tasks.

Brain areas within the motor system interact directly or indirectly during motor-imagery and motor-execution tasks. These interactions and their functionality can change following stroke and recovery. How brain network interactions reorganize and recover their functionality during recovery and treatment following stroke are not well understood. To contribute to answering these questions, we recorded blood oxygenation-level dependent (BOLD) functional magnetic resonance imaging (fMRI) signals from 10 stroke survivors and evaluated dynamical causal modeling (DCM)-based effective connectivity among three motor areas: primary motor cortex (M1), pre-motor cortex (PMC) and supplementary motor area (SMA), during motor-imagery and motor-execution tasks. We compared the connectivity between affected and unaffected hemispheres before and after mental practice and combined mental practice and physical therapy as treatments. The treatment (intervention) period varied in length between 14 to 51 days but all patients received the same dose of 60 h of treatment. Using Bayesian model selection (BMS) approach in the DCM approach, we found that, after intervention, the same network dominated during motor-imagery and motor-execution tasks but modulatory parameters suggested a suppressive influence of SM A on M1 during the motor-imagery task whereas the influence of SM A on M1 was unrestricted during the motor-execution task. We found that the intervention caused a reorganization of the network during both tasks for unaffected as well as for the affected hemisphere. Using Bayesian model averaging (BMA) approach, we found that the intervention improved the regional connectivity among the motor areas during both the tasks. The connectivity between PMC and M1 was stronger in motor-imagery tasks whereas the connectivity from PMC to M1, SM A to M1 dominated in motor-execution tasks. There was significant behavioral improvement (p = 0.001) in sensation and motor movements because of the intervention as reflected by behavioral Fugl-Meyer (FMA) measures, which were significantly correlated (p = 0.05) with a subset of connectivity. These findings suggest that PMC and M1 play a crucial role during motor-imagery as well as during motor-execution task. In addition, M1 causes more exchange of causal information among motor areas during a motor-execution task than during a motor-imagery task due to its interaction with SM A. This study expands our understanding of motor network involved during two different tasks, which are commonly used during rehabilitation following stroke. A clear understanding of the effective connectivity networks leads to a better treatment in helping stroke survivors regain motor ability.