Causal visual interactions as revealed by an information theoretic measure and fMRI

Identifying Effective Connectivity between Stochastic Neurons with Variable-Length Memory Using a Transfer Entropy Rate Estimator

Information theory explains how systems encode and transmit information. This article examines the neuronal system, which processes information via neurons that react to stimuli and transmit electrical signals. Specifically, we focus on transfer entropy to measure the flow of information between sequences and explore its use in determining effective neuronal connectivity. We analyze the causal relationships between two discrete time series, X:=Xt:t∈Z and Y:=Yt:t∈Z, which take values in binary alphabets. When the bivariate process (X,Y) is a jointly stationary ergodic variable-length Markov chain with memory no larger than k, we demonstrate that the null hypothesis of the test-no causal influence-requires a zero transfer entropy rate. The plug-in estimator for this function is identified with the test statistic of the log-likelihood ratios. Since under the null hypothesis, this estimator follows an asymptotic chi-squared distribution, it facilitates the calculation of p-values when applied to empirical data. The efficacy of the hypothesis test is illustrated with data simulated from a neuronal network model, characterized by stochastic neurons with variable-length memory. The test results identify biologically relevant information, validating the underlying theory and highlighting the applicability of the method in understanding effective connectivity between neurons.

Local similarity of activity patterns during auditory and visual processing

Neuroimaging studies have shown that brain activity is variable and changes according to stimuli and the environmental context, reflecting brain coding or information representations at different processing levels. However, little is known about activity organization that reflects coding strategies. Here, we explored and compared two different coding approaches, spatial via cross-correlation and intensity-based coding using mutual information. Using two fMRI datasets and different seeds, we searched for the spatial and intensity-based similarities with the seeds in brain activity. Our results showed that, apart from the seed regions, significant regions detected by intensity-based similarity analysis differ completely from those found using cross-correlation. These findings may indicate that information shared through spatial coding differs from that transmitted via non-spatial coding processes. Our results suggest that brain coding is organized in several different ways to optimize information processing.

Reproducible Inter-Personal Brain Coupling Measurements in Hyperscanning Settings With functional Near Infra-Red Spectroscopy

Despite a huge advancement in neuroimaging techniques and growing importance of inter-personal brain research, few studies assess the most appropriate computational methods to measure brain-brain coupling. Here, we focus on the signal processing methods to detect brain-coupling in dyads. From a public dataset of functional Near Infra-Red Spectroscopy signals (N=24 dyads), we derived a synthetic control condition by randomization, we investigated the effectiveness of four most used signal similarity metrics: Cross Correlation, Mutual Information, Wavelet Coherence and Dynamic Time Warping. We also accounted for temporal variations between signals by allowing for misalignments up to a maximum lag. Starting from the observed effect sizes, computed in terms of Cohen's d, the power analysis indicated that a high sample size ([Formula: see text]) would be required to detect significant brain-coupling. We therefore discuss the need for specialized statistical approaches and propose bootstrap as an alternative method to avoid over-penalizing the results. In our settings, and based on bootstrap analyses, Cross Correlation and Dynamic Time Warping outperform Mutual Information and Wavelet Coherence for all considered maximum lags, with reproducible results. These results highlight the need to set specific guidelines as the high degree of customization of the signal processing procedures prevents the comparability between studies, their reproducibility and, ultimately, undermines the possibility of extracting new knowledge.

Time-Frequency Maximal Information Coefficient Method and its Application to Functional Corticomuscular Coupling

An important challenge in the study of functional corticomuscular coupling (FCMC) is an accurate capture of the coupling relationship between the cerebral cortex and the effector muscle. The coherence method is a linear analysis method, which has certain limitations in further revealing the nonlinear coupling between neural signals. Although mutual information (MI) and transfer entropy (TE) based on information theory can capture both linear and nonlinear correlations, the equitability of these algorithms is ignored and the nonlinear components of the correlation cannot be separated. The maximal information coefficient (MIC) is a suitable method to measure the coupling between neurophysiological signals. This study extends the MIC to the time-frequency domain, named time-frequency maximal information coefficient (TFMIC), to explore the FCMC in a specific frequency band. The effectiveness, equitability, and robustness of the algorithm on the simulation data was verified and compared with coherence, TE- and MI- based methods. Simulation results showed that the TFMIC could accurately detect the coupling for different functional relationships at low noise levels. The dorsiflexion experimental results revealed that the beta-band (14-30 Hz) significant coupling was observed at channels Cz, C4, FC4, and FCz. Additionally, the results showed that the coupling was higher in the alpha-band (8-13 Hz) and beta-band (14-30 Hz) than in the gamma-band (31-45 Hz). This might be related to a transition between sensorimotor states. Specifically, the nonlinear component of FCMC was also observed at channels Cz, C4, FC4, and FCz. This study expanded the research on nonlinear coupling components in FCMC.

Multi-Dimensional Dynamics of Human Electromagnetic Brain Activity

Magnetoencephalography (MEG) and electroencephalography (EEG) are invaluable neuroscientific tools for unveiling human neural dynamics in three dimensions (space, time, and frequency), which are associated with a wide variety of perceptions, cognition, and actions. MEG/EEG also provides different categories of neuronal indices including activity magnitude, connectivity, and network properties along the three dimensions. In the last 20 years, interest has increased in inter-regional connectivity and complex network properties assessed by various sophisticated scientific analyses. We herein review the definition, computation, short history, and pros and cons of connectivity and complex network (graph-theory) analyses applied to MEG/EEG signals. We briefly describe recent developments in source reconstruction algorithms essential for source-space connectivity and network analyses. Furthermore, we discuss a relatively novel approach used in MEG/EEG studies to examine the complex dynamics represented by human brain activity. The correct and effective use of these neuronal metrics provides a new insight into the multi-dimensional dynamics of the neural representations of various functions in the complex human brain.

Neural correlates of visual motion processing without awareness in patients with striate cortex and pulvinar lesions

Patients with striate cortex lesions experience visual perception loss in the contralateral visual field. In few patients, however, stimuli within the blind field can lead to unconscious (blindsight) or even conscious perception when the stimuli are moving (Riddoch syndrome). Using functional magnetic resonance imaging (fMRI), we investigated the neural responses elicited by motion stimulation in the sighted and blind visual fields of eight patients with lesions of the striate cortex. Importantly, repeated testing ensured that none of the patients exhibited blindsight or a Riddoch syndrome. Three patients had additional lesions in the ipsilesional pulvinar. For blind visual field stimulation, great care was given that the moving stimulus was precisely presented within the borders of the scotoma. In six of eight patients, the stimulation within the scotoma elicited hemodynamic activity in area human middle temporal (hMT) while no activity was observed within the ipsilateral lesioned area of the striate cortex. One of the two patients in whom no ipsilesional activity was observed had an extensive lesion including massive subcortical damage. The other patient had an additional focal lesion within the lateral inferior pulvinar. Fiber-tracking based on anatomical and functional markers (hMT and Pulvinar) on individual diffusion tensor imaging (DTI) data from each patient revealed the structural integrity of subcortical pathways in all but the patient with the extensive subcortical lesion. These results provide clear evidence for the robustness of direct subcortical pathways from the pulvinar to area hMT in patients with striate cortex lesions and demonstrate that ipsilesional activity in area hMT is completely independent of conscious perception.

Lag-based effective connectivity applied to fMRI: a simulation study highlighting dependence on experimental parameters and formulation

A vast repertoire of methods is currently available to study effective brain connectivity based on neuroimaging data, among which lag-based measures can be distinguished. Although several studies have previously assessed the performance of such measures, their validity in different conditions remains unclear. In the current study, several lag-based effective connectivity measures are tested and benchmarked using simulated fMRI data, conceived to reflect a broad range of different situations with practical interest. The main goal is two-fold: 1) to provide a thorough overview of lag-based effective connectivity measures, and 2) to assess their performance in specific experimental conditions, thereby providing guidance for future effective connectivity studies involving fMRI. We focus on well-known lag-based measures, cover existing improvements and alternative formulations in some cases: Granger causality (GC), Geweke's Granger causality (GGC), directed transfer function (DTF), partial directed coherence (PDC), phase slope index (PSI), and transfer entropy (TE). Benchmarking consists in identifying causal relations in local field potential (LFP) networks that have their output convolved with a canonical hemodynamic response function (HRF) with varying node number, topology, coupling strength, neuronal delay, repetition time (TR), signal-to-noise ratio (SNR) and HRF variability. In a first set of simulations, we cover all possible combinations of discretized values of the previous variables, for networks with 2 and 3 nodes, and find that the measure with best performance (time-domain Granger Causality) is able to detect neuronal delays of a few hundreds of milliseconds with TRs between 0.25 and 2s and neuronal delays below 100ms for TRs that are also below 100ms, with more than 80% accuracy in realistic conditions. For networks with more than 3 nodes, we find that the number of nodes and the density of causal links degrade sensitivity, especially if the number of observations does not compensate for the increase in nodes, and that clustered networks can be more easily identified. In conclusion, this study argues in favor of the applicability of lag-based measures in the context of fMRI, provided that a stringent set of experimental specifications is met and that the chosen measure is applied with full knowledge of its limitations and specific constraints.

Confounding effects of phase delays on causality estimation

Linear and non-linear techniques for inferring causal relations between the brain signals representing the underlying neuronal systems have become a powerful tool to extract the connectivity patterns in the brain. Typically these tools employ the idea of Granger causality, which is ultimately based on the temporal precedence between the signals. At the same time, phase synchronization between coupled neural ensembles is considered a mechanism implemented in the brain to integrate relevant neuronal ensembles to perform a cognitive or perceptual task. Phase synchronization can be studied by analyzing the effects of phase-locking between the brain signals. However, we should expect that there is no one-to-one mapping between the observed phase lag and the time precedence as specified by physically interacting systems. Specifically, phase lag observed between two signals may interfere with inferring causal relations. This could be of critical importance for the coupled non-linear oscillating systems, with possible time delays in coupling, when classical linear cross-spectrum strategies for solving phase ambiguity are not efficient. To demonstrate this, we used a prototypical model of coupled non-linear systems, and compared three typical pipelines of inferring Granger causality, as established in the literature. Specifically, we compared the performance of the spectral and information-theoretic Granger pipelines as well as standard Granger causality in their relations to the observed phase differences for frequencies at which the signals become synchronized to each other. We found that an information-theoretic approach, which takes into account different time lags between the past of one signal and the future of another signal, was the most robust to phase effects.

Transfer entropy as a log-likelihood ratio

Transfer entropy, an information-theoretic measure of time-directed information transfer between joint processes, has steadily gained popularity in the analysis of complex stochastic dynamics in diverse fields, including the neurosciences, ecology, climatology, and econometrics. We show that for a broad class of predictive models, the log-likelihood ratio test statistic for the null hypothesis of zero transfer entropy is a consistent estimator for the transfer entropy itself. For finite Markov chains, furthermore, no explicit model is required. In the general case, an asymptotic χ2 distribution is established for the transfer entropy estimator. The result generalizes the equivalence in the Gaussian case of transfer entropy and Granger causality, a statistical notion of causal influence based on prediction via vector autoregression, and establishes a fundamental connection between directed information transfer and causality in the Wiener-Granger sense.

Identification of Directed Influence: Granger Causality, Kullback-Leibler Divergence, and Complexity

Detecting and characterizing causal interdependencies and couplings between different activated brain areas from functional neuroimage time series measurements of their activity constitutes a significant step toward understanding the process of brain functions. In this letter, we make the simple point that all current statistics used to make inferences about directed influences in functional neuroimage time series are variants of the same underlying quantity. This includes directed transfer entropy, transinformation, Kullback-Leibler formulations, conditional mutual information, and Granger causality. Crucially, in the case of autoregressive modeling, the underlying quantity is the likelihood ratio that compares models with and without directed influences from the past when modeling the influence of one time series on another. This framework is also used to derive the relation between these measures of directed influence and the complexity or the order of directed influence. These results provide a framework for unifying the Kullback-Leibler divergence, Granger causality, and the complexity of directed influence.

Analysis of fMRI time series with mutual information

Neuroimaging plays a fundamental role in the study of human cognitive neuroscience. Functional magnetic resonance imaging (fMRI), based on the Blood Oxygenation Level Dependent signal, is currently considered as a standard technique for a system level understanding of the human brain. The problem of identifying regionally specific effects in neuroimaging data is usually solved by applying Statistical Parametric Mapping (SPM). Here, a mutual information (MI) criterion is used to identify regionally specific effects produced by a task. In particular, two MI estimators are presented for its use in fMRI data. The first one uses a Parzen probability density estimation, and the second one is based on a K Nearest Neighbours (KNN) estimation. Additionally, a statistical measure has been introduced to automatically detect the voxels which are relevant to the fMRI task. Experiments demonstrate the advantages of MI estimators over SPM maps; firstly, providing more significant differences between relevant and irrelevant voxels; secondly, presenting more focalized activation; and, thirdly, detecting small areas related to the task. These findings, and the improved performance of KNN MI estimator in multisubject and multistimuli studies, make the proposed methods a good alternative to SPM.

Empirical and theoretical aspects of generation and transfer of information in a neuromagnetic source network

Variability in source dynamics across the sources in an activated network may be indicative of how the information is processed within a network. Information-theoretic tools allow one not only to characterize local brain dynamics but also to describe interactions between distributed brain activity. This study follows such a framework and explores the relations between signal variability and asymmetry in mutual interdependencies in a data-driven pipeline of non-linear analysis of neuromagnetic sources reconstructed from human magnetoencephalographic (MEG) data collected as a reaction to a face recognition task. Asymmetry in non-linear interdependencies in the network was analyzed using transfer entropy, which quantifies predictive information transfer between the sources. Variability of the source activity was estimated using multi-scale entropy, quantifying the rate of which information is generated. The empirical results are supported by an analysis of synthetic data based on the dynamics of coupled systems with time delay in coupling. We found that the amount of information transferred from one source to another was correlated with the difference in variability between the dynamics of these two sources, with the directionality of net information transfer depending on the time scale at which the sample entropy was computed. The results based on synthetic data suggest that both time delay and strength of coupling can contribute to the relations between variability of brain signals and information transfer between them. Our findings support the previous attempts to characterize functional organization of the activated brain, based on a combination of non-linear dynamics and temporal features of brain connectivity, such as time delay.

A model selection method for nonlinear system identification based FMRI effective connectivity analysis

In this paper a model selection algorithm for a nonlinear system identification method is proposed to study functional magnetic resonance imaging (fMRI) effective connectivity. Unlike most other methods, this method does not need a pre-defined structure/model for effective connectivity analysis. Instead, it relies on selecting significant nonlinear or linear covariates for the differential equations to describe the mapping relationship between brain output (fMRI response) and input (experiment design). These covariates, as well as their coefficients, are estimated based on a least angle regression (LARS) method. In the implementation of the LARS method, Akaike's information criterion corrected (AICc) algorithm and the leave-one-out (LOO) cross-validation method were employed and compared for model selection. Simulation comparison between the dynamic causal model (DCM), nonlinear identification method, and model selection method for modelling the single-input-single-output (SISO) and multiple-input multiple-output (MIMO) systems were conducted. Results show that the LARS model selection method is faster than DCM and achieves a compact and economic nonlinear model simultaneously. To verify the efficacy of the proposed approach, an analysis of the dorsal and ventral visual pathway networks was carried out based on three real datasets. The results show that LARS can be used for model selection in an fMRI effective connectivity study with phase-encoded, standard block, and random block designs. It is also shown that the LOO cross-validation method for nonlinear model selection has less residual sum squares than the AICc algorithm for the study.

Dynamics of large-scale cortical interactions at high gamma frequencies during word production: event related causality (ERC) analysis of human electrocorticography (ECoG)

Intracranial EEG studies in humans have shown that functional brain activation in a variety of functional-anatomic domains of human cortex is associated with an increase in power at a broad range of high gamma (>60Hz) frequencies. Although these electrophysiological responses are highly specific for the location and timing of cortical processing and in animal recordings are highly correlated with increased population firing rates, there has been little direct empirical evidence for causal interactions between different recording sites at high gamma frequencies. Such causal interactions are hypothesized to occur during cognitive tasks that activate multiple brain regions. To determine whether such causal interactions occur at high gamma frequencies and to investigate their functional significance, we used event-related causality (ERC) analysis to estimate the dynamics, directionality, and magnitude of event-related causal interactions using subdural electrocorticography (ECoG) recorded during two word production tasks: picture naming and auditory word repetition. A clinical subject who had normal hearing but was skilled in American Signed Language (ASL) provided a unique opportunity to test our hypothesis with reference to a predictable pattern of causal interactions, i.e. that language cortex interacts with different areas of sensorimotor cortex during spoken vs. signed responses. Our ERC analyses confirmed this prediction. During word production with spoken responses, perisylvian language sites had prominent causal interactions with mouth/tongue areas of motor cortex, and when responses were gestured in sign language, the most prominent interactions involved hand and arm areas of motor cortex. Furthermore, we found that the sites from which the most numerous and prominent causal interactions originated, i.e. sites with a pattern of ERC "divergence", were also sites where high gamma power increases were most prominent and where electrocortical stimulation mapping interfered with word production. These findings suggest that the number, strength and directionality of event-related causal interactions may help identify network nodes that are not only activated by a task but are critical to its performance.

What's behind a face: person context coding in fusiform face area as revealed by multivoxel pattern analysis

The identification of a face comprises processing of both visual features and conceptual knowledge. Studies showing that the fusiform face area (FFA) is sensitive to face identity generally neglect this dissociation. The present study is the first that isolates conceptual face processing by using words presented in a person context instead of faces. The design consisted of 2 different conditions. In one condition, participants were presented with blocks of words related to each other at the categorical level (e.g., brands of cars, European cities). The second condition consisted of blocks of words linked to the personality features of a specific face. Both conditions were created from the same 8 × 8 word matrix, thereby controlling for visual input across conditions. Univariate statistical contrasts did not yield any significant differences between the 2 conditions in FFA. However, a machine learning classification algorithm was able to successfully learn the functional relationship between the 2 contexts and their underlying response patterns in FFA, suggesting that these activation patterns can code for different semantic contexts. These results suggest that the level of processing in FFA goes beyond facial features. This has strong implications for the debate about the role of FFA in face identification.

A phase synchrony measure for quantifying dynamic functional integration in the brain

The temporal coordination of neural activity within structural networks of the brain has been posited as a basis for cognition. Changes in the frequency and similarity of oscillating electrical potentials emitted by neuronal populations may reflect the means by which networks of the brain carry out functions critical for adaptive behavior. A computation of the phase relationship between signals recorded from separable brain regions is a method for characterizing the temporal interactions of neuronal populations. Recently, different phase estimation methods for quantifying the time-varying and frequency-dependent nature of neural synchronization have been proposed. The most common method for measuring the synchronization of signals through phase computations uses complex wavelet transforms of neural signals to estimate their instantaneous phase difference and locking. In this article, we extend this idea by introducing a new time-varying phase synchrony measure based on Cohen's class of time-frequency distributions. This index offers improvements over existing synchrony measures by characterizing the similarity of signals from separable brain regions with uniformly high resolution across time and frequency. The proposed measure is applied to both synthesized signals and electroencephalography data to test its effectiveness in estimating phase changes and quantifying neural synchrony in the brain.

Multivariate information-theoretic measures reveal directed information structure and task relevant changes in fMRI connectivity

The human brain undertakes highly sophisticated information processing facilitated by the interaction between its sub-regions. We present a novel method for interregional connectivity analysis, using multivariate extensions to the mutual information and transfer entropy. The method allows us to identify the underlying directed information structure between brain regions, and how that structure changes according to behavioral conditions. This method is distinguished in using asymmetric, multivariate, information-theoretical analysis, which captures not only directional and non-linear relationships, but also collective interactions. Importantly, the method is able to estimate multivariate information measures with only relatively little data. We demonstrate the method to analyze functional magnetic resonance imaging time series to establish the directed information structure between brain regions involved in a visuo-motor tracking task. Importantly, this results in a tiered structure, with known movement planning regions driving visual and motor control regions. Also, we examine the changes in this structure as the difficulty of the tracking task is increased. We find that task difficulty modulates the coupling strength between regions of a cortical network involved in movement planning and between motor cortex and the cerebellum which is involved in the fine-tuning of motor control. It is likely these methods will find utility in identifying interregional structure (and experimentally induced changes in this structure) in other cognitive tasks and data modalities.

A novel model-free data analysis technique based on clustering in a mutual information space: application to resting-state FMRI

Non-parametric data-driven analysis techniques can be used to study datasets with few assumptions about the data and underlying experiment. Variations of independent component analysis (ICA) have been the methods mostly used on fMRI data, e.g., in finding resting-state networks thought to reflect the connectivity of the brain. Here we present a novel data analysis technique and demonstrate it on resting-state fMRI data. It is a generic method with few underlying assumptions about the data. The results are built from the statistical relations between all input voxels, resulting in a whole-brain analysis on a voxel level. It has good scalability properties and the parallel implementation is capable of handling large datasets and databases. From the mutual information between the activities of the voxels over time, a distance matrix is created for all voxels in the input space. Multidimensional scaling is used to put the voxels in a lower-dimensional space reflecting the dependency relations based on the distance matrix. By performing clustering in this space we can find the strong statistical regularities in the data, which for the resting-state data turns out to be the resting-state networks. The decomposition is performed in the last step of the algorithm and is computationally simple. This opens up for rapid analysis and visualization of the data on different spatial levels, as well as automatically finding a suitable number of decomposition components.

Testing methodologies for the nonlinear analysis of causal relationships in neurovascular coupling

We investigated the use and implementation of a nonlinear methodology for establishing which changes in neurophysiological signals cause changes in the blood oxygenation level-dependent (BOLD) contrast measured in functional magnetic resonance imaging. Unlike previous analytical approaches, which used linear correlation to establish covariations between neural activity and BOLD, we propose a directed information-theoretic measure, the transfer entropy, which can elucidate even highly nonlinear causal relationships between neural activity and BOLD signal. In this study we investigated the practicality of such an analysis given the limited data samples that can be collected experimentally due to the low temporal resolution of BOLD signals. We implemented several algorithms for the estimation of transfer entropy and we tested their effectiveness using simulated local field potentials (LFPs) and BOLD data constructed to match the main statistical properties of real LFP and BOLD signals measured simultaneously in monkey primary visual cortex. We found that using the advanced methods of entropy estimation implemented and described here, a transfer entropy analysis of neurovascular coupling based on experimentally attainable data sets is feasible.

Causal relationships between frequency bands of extracellular signals in visual cortex revealed by an information theoretic analysis

Characterizing how different cortical rhythms interact and how their interaction changes with sensory stimulation is important to gather insights into how these rhythms are generated and what sensory function they may play. Concepts from information theory, such as Transfer Entropy (TE), offer principled ways to quantify the amount of causation between different frequency bands of the signal recorded from extracellular electrodes; yet these techniques are hard to apply to real data. To address the above issues, in this study we develop a method to compute fast and reliably the amount of TE from experimental time series of extracellular potentials. The method consisted in adapting efficiently the calculation of TE to analog signals and in providing appropriate sampling bias corrections. We then used this method to quantify the strength and significance of causal interaction between frequency bands of field potentials and spikes recorded from primary visual cortex of anaesthetized macaques, both during spontaneous activity and during binocular presentation of naturalistic color movies. Causal interactions between different frequency bands were prominent when considering the signals at a fine (ms) temporal resolution, and happened with a very short (ms-scale) delay. The interactions were much less prominent and significant at coarser temporal resolutions. At high temporal resolution, we found strong bidirectional causal interactions between gamma-band (40–100 Hz) and slower field potentials when considering signals recorded within a distance of 2 mm. The interactions involving gamma bands signals were stronger during movie presentation than in absence of stimuli, suggesting a strong role of the gamma cycle in processing naturalistic stimuli. Moreover, the phase of gamma oscillations was playing a stronger role than their amplitude in increasing causations with slower field potentials and spikes during stimulation. The dominant direction of causality was mainly found in the direction from MUA or gamma frequency band signals to lower frequency signals, suggesting that hierarchical correlations between lower and higher frequency cortical rhythms are originated by the faster rhythms.

Quantifying auditory event-related responses in multichannel human intracranial recordings

Multichannel intracranial recordings are used increasingly to study the functional organization of human cortex. Intracranial recordings of event-related activity, or electrocorticography (ECoG), are based on high density electrode arrays implanted directly over cortex, combining good temporal and spatial resolution. Developing appropriate statistical methods for analyzing event-related responses in these high dimensional ECoG datasets remains a major challenge for clinical and systems neuroscience. We present a novel methodological framework that combines complementary, existing methods adapted for statistical analysis of auditory event-related responses in multichannel ECoG recordings. This analytic framework integrates single-channel (time-domain, time–frequency) and multichannel analyses of event-related ECoG activity to determine statistically significant evoked responses, induced spectral responses, and effective (causal) connectivity. Implementation of this quantitative approach is illustrated using multichannel ECoG data from recent studies of auditory processing in patients with epilepsy. Methods described include a time–frequency matching pursuit algorithm adapted for modeling brief, transient cortical spectral responses to sound, and a recently developed method for estimating effective connectivity using multivariate autoregressive modeling to measure brief event-related changes in multichannel functional interactions. A semi-automated spatial normalization method for comparing intracranial electrode locations across patients is also described. The individual methods presented are published and readily accessible. We discuss the benefits of integrating multiple complementary methods in a unified and comprehensive quantitative approach. Methodological considerations in the analysis of multichannel ECoG data, including corrections for multiple comparisons are discussed, as well as remaining challenges in the development of new statistical approaches.

Linear and nonlinear information flow based on time-delayed mutual information method and its application to corticomuscular interaction

OBJECTIVE

To propose a model-free method to show linear and nonlinear information flow based on time-delayed mutual information (TDMI) by employing uni- and bi-variate surrogate tests and to investigate whether there are contributions of the nonlinear information flow in corticomuscular (CM) interaction.

METHODS

Using simulated data, we tested whether our method would successfully detect the direction of information flow and identify a relationship between two simulated time series. As an experimental data application, we applied this method to investigate CM interaction during a right wrist extension task.

RESULTS

Results of simulation tests show that we can correctly detect the direction of information flow and the relationship between two time series without a prior knowledge of the dynamics of their generating systems. As experimental results, we found both linear and nonlinear information flow from contralateral sensorimotor cortex to muscle.

CONCLUSIONS

Our method is a viable model-free measure of temporally varying causal interactions that is capable of distinguishing linear and nonlinear information flow. With respect to experimental application, there are both linear and nonlinear information flows in CM interaction from contralateral sensorimotor cortex to muscle, which may reflect the motor command from brain to muscle.

SIGNIFICANCE

This is the first study to show separate linear and nonlinear information flow in CM interaction.

Exploring transient transfer entropy based on a group-wise ICA decomposition of EEG data

This paper presents a data-driven pipeline for studying asymmetries in mutual interdependencies between distinct components of EEG signal. Due to volume conductance, estimating coherence between scalp electrodes may lead to spurious results. A group-based independent component analysis (ICA), which is conducted across all subjects and conditions simultaneously, is an alternative representation of the EEG measurements. Within this approach, the extracted components are independent in a global sense while short-lived or transient interdependencies may still be present between the components. In this paper, functional roles of the ICA components are specified through a partial least squares (PLS) analysis of task effects within the time course of the derived components. Functional integration is estimated within the information-theoretic approach using transfer entropy analysis based on asymmetries in mutual interdependencies of reconstructed phase dynamics. A secondary PLS analysis is performed to assess robust task-specific changes in transfer entropy estimates between functionally specific components.

Confounding effects of indirect connections on causality estimation

Addressing the issue of effective connectivity, this study focuses on effects of indirect connections on inferring stable causal relations: partial transfer entropy. We introduce a Granger causality measure based on a multivariate version of transfer entropy. The statistic takes into account the influence of the rest of the network (environment) on observed coupling between two given nodes. This formalism allows us to quantify, for a specific pathway, the total amount of indirect coupling mediated by the environment. We show that partial transfer entropy is a more sensitive technique to identify robust causal relations than its bivariate equivalent. In addition, we demonstrate the confounding effects of the variation in indirect coupling on the detectability of robust causal links. Finally, we consider the problem of model misspecification and its effect on the robustness of the observed connectivity patterns, showing that misspecifying the model may be an issue even for model-free information-theoretic approach.

Quantifying the causal interactions in the brain using a measure of directed transinformation

Most of the brain's cognitive functions rely on the coordinated interactions of neuronal sources that are distributed within and across specialized brain areas. It is important to quantify these temporal interactions directly from neuroimaging data such as the electroencephalogram (EEG). A variety of measures have been proposed to quantify the neural interactions including linear correlation measures and nonlinear information theoretic measures. An important aspect of neural interactions is the direction of the information flow, i.e., the causal interaction between the different regions. In this paper, we propose using a directed transinformation measure (T measure) to quantify these causal interactions. This measure is a generalization of Granger causality and quantifies both the linear and nonlinear interactions between the signals. The proposed measure is applied to both simulated and real EEG signals and is shown to be sensitive to the dependencies between signals.

Combining structural connectivity and response latencies to model the structure of the visual system

Several approaches exist to ascertain the connectivity of the brain, and these approaches lead to markedly different topologies, often incompatible with each other. Specifically, recent single-cell recording results seem incompatible with current structural connectivity models. We present a novel method that combines anatomical and temporal constraints to generate biologically plausible connectivity patterns of the visual system of the macaque monkey. Our method takes structural connectivity data from the CoCoMac database and recent single-cell recording data as input and employs an optimization technique to arrive at a new connectivity pattern of the visual system that is in agreement with both types of experimental data. The new connectivity pattern yields a revised model that has fewer levels than current models. In addition, it introduces subcortical–cortical connections. We show that these connections are essential for explaining latency data, are consistent with our current knowledge of the structural connectivity of the visual system, and might explain recent functional imaging results in humans. Furthermore we show that the revised model is not underconstrained like previous models and can be extended to include newer data and other kinds of data. We conclude that the revised model of the connectivity of the visual system reflects current knowledge on the structure and function of the visual system and addresses some of the limitations of previous models.

Visual perception is very important to us, something we can easily come to realize if we imagine ourselves blind. The visual system consists of numerous interconnected brain areas. If we are to understand the functioning of the visual system, then we will need to understand the connectivity between these areas. Current models of the visual system have a number of limitations. One of these is that the time it takes for the neural signal to reach a certain area often seems inconsistent with the place of that area in the overall structure of the system; e.g., the signal might arrive relatively quickly at an area generally located “higher” in the visual system and slowly at an area located in the “lower” part. We combine data about the known connectivity in the monkey brain with timing data to find a network structure that is consistent with both kinds of data. The results show that the timing data can be explained when the network contains direct routes from subcortical areas to “higher” cortical areas. We show that our model has fewer limitations than previous models and might explain unresolved issues in the study of connectivity in the human brain.

Directed transfer function analysis of fMRI data to investigate network dynamics

In this work, we have adapted the directed transfer function (DTF) to fMRI for the analysis of cortical network dynamics. While modern fMRI sequences are capable of sampling at second or sub-second rates, the underlying hemodynamic response limits the true temporal resolution to the order of 6-12 seconds. Therefore, DTF analysis of fMRI is appropriate for characterizing dynamics in brain response which evolves more slowly than the fMRI response, such as those during learning, fatigue and habituation. In such cases, the response to repeated trials will change with time and a summary measure from each trial can be used as input to the DTF analysis because these summary measures are of appropriate sampling rates and are not affected by the sluggishness of the hemodynamic response. As an example, we investigated the dynamic effects of muscle fatigue on the motor network. Specifically, DTF was used as a multivariate measure of the strength and direction of information flow between the various nodes of the network. We found that the primary motor area had a causal influence on the supplementary motor area, pre-motor area and cerebellum, and this influence initially increased with time and diminished towards the end of the experiment, probably as a result of fatigue.

Directed information flow: a model free measure to analyze causal interactions in event related EEG-MEG-experiments

In a study that combined event related potential (ERP) and magnetic field (ERMF) data, we analyzed the timing and direction of information flow between striate (S) and extrastriate (ES) cortex by applying a generalized mutual information measure (DIT for "directed information transfer") during a visual spatial attention task. ERP and ERMF recordings showed that selective attention to stimulus arrays in one visual field enhanced late responses (around 200 ms after the stimulus presentation) that were localized in S (ERMF) and ES (ERP) cortex. The results of the DIT analysis indicate there is a significant attention related increase in the flow of information back from ES to S cortex at around 220 ms, with an associated decrease in the flow of information forward from S cortex to ES cortex. These results support the hypothesis that a feedback mechanism guides attention-related processing in primary visual cortex and provide evidence that DIT can by used to evaluate the direction of information flow between cortical areas.

The role of impaired neuronal communication in neurological disorders

PURPOSE OF REVIEW

Basic and translational neuroscience findings indicate that normal brain function depends on activity synchronization within distributed brain networks. This conclusion suggests a view of how brain injury causes behavioral deficits that differs from traditional localizationist views.

RECENT FINDINGS

Novel functional neuroimaging methods demonstrate coherent activity in large-scale networks not only during task performance but also, surprisingly, at rest (i.e. in the absence of stimuli, tasks, or overt responses). Furthermore, breakdown of activity coherence at rest, even in regions of the brain that are structurally intact, correlates with behavioral deficits and their recovery after injury. Breakdown of functional connectivity appears to occur not just after local injury but also in other conditions that affect large-scale neural communication.

SUMMARY

A network perspective is fundamental to appreciating the pathophysiology of brain injury at the systems level and the underlying mechanisms of recovery, and for developing novel strategies of rehabilitation.

Audiovisual temporal correspondence modulates human multisensory superior temporal sulcus plus primary sensory cortices

The brain should integrate related but not unrelated information from different senses. Temporal patterning of inputs to different modalities may provide critical information about whether those inputs are related or not. We studied effects of temporal correspondence between auditory and visual streams on human brain activity with functional magnetic resonance imaging (fMRI). Streams of visual flashes with irregularly jittered, arrhythmic timing could appear on right or left, with or without a stream of auditory tones that coincided perfectly when present (highly unlikely by chance), were noncoincident with vision (different erratic, arrhythmic pattern with same temporal statistics), or an auditory stream appeared alone. fMRI revealed blood oxygenation level-dependent (BOLD) increases in multisensory superior temporal sulcus (mSTS), contralateral to a visual stream when coincident with an auditory stream, and BOLD decreases for noncoincidence relative to unisensory baselines. Contralateral primary visual cortex and auditory cortex were also affected by audiovisual temporal correspondence or noncorrespondence, as confirmed in individuals. Connectivity analyses indicated enhanced influence from mSTS on primary sensory areas, rather than vice versa, during audiovisual correspondence. Temporal correspondence between auditory and visual streams affects a network of both multisensory (mSTS) and sensory-specific areas in humans, including even primary visual and auditory cortex, with stronger responses for corresponding and thus related audiovisual inputs.

Identifying mutual information transfer in the brain with differential-algebraic modeling: Evidence for fast oscillatory coupling between cortical somatosensory areas 3b and 1

Understanding information transfer in the brain is a major challenge in today's neurosciences. Commonly, information transfer between brain areas is analyzed with the help of correlation measures for electrophysiological data. However, such approaches cannot distinguish between mutual coupling and other mechanisms of creating correlations between responses, such as common input from other sources. Functional coupling is mandatory for information transfer. Here we propose to analyze coupling between active brain areas with the help of models described by a system of differential-algebraic equations. Comparing models with various degrees of coupling, we show that mutual information transfer can be distinguished from one-way information transfer for activated cortical areas estimated by source localization techniques. We exemplify the technique with fast oscillatory activity found in both cortical areas 3b and 1 after peripheral nerve stimulation.