Evaluation of different measures of functional connectivity using a neural mass model

Computational and dynamic models in neuroimaging

This article reviews the substantial impact computational neuroscience has had on neuroimaging over the past years. It builds on the distinction between models of the brain as a computational machine and computational models of neuronal dynamics per se; i.e., models of brain function and biophysics. Both sorts of model borrow heavily from computational neuroscience, and both have enriched the analysis of neuroimaging data and the type of questions we address. To illustrate the role of functional models in imaging neuroscience, we focus on optimal control and decision (game) theory; the models used here provide a mechanistic account of neuronal computations and the latent (mental) states represent by the brain. In terms of biophysical modelling, we focus on dynamic causal modelling, with a special emphasis on recent advances in neural-mass models for hemodynamic and electrophysiological time series. Each example emphasises the role of generative models, which embed our hypotheses or questions, and the importance of model comparison (i.e., hypothesis testing). We will refer to this theme, when trying to contextualise recent trends in relation to each other.

Mutual information analysis of EEG signals indicates age-related changes in cortical interdependence during sleep in middle-aged versus elderly women

Elderly subjects exhibit declining sleep efficiency parameters with longer time spent awake at night and greater sleep fragmentation. In this article, we report on the changes in cortical interdependence during sleep stages between 15 middle-aged (range: 42-50 years) and 15 elderly (range: 71-86 years) women subjects. Cortical interdependence assessed from EEG signals typically exhibits increasing levels of correlation because human subjects progress from wake to deeper stages of sleep. EEG signals acquired from previously existing polysomnogram datasets were subjected to mutual information analysis to detect changes in information transmission associated with change in sleep stage and to understand how age affects the interdependence values. We observed a significant reduction in the interdependence between central EEG signals of elderly subjects in nonrapid eye movement and rapid eye movement stage sleep in comparison with middle-aged subjects (age group effect: elderly versus middle aged P < 0.001, sleep stage effect: P < 0.001, interaction effect between age group and sleep stage: P = 0.007). A narrowband analysis revealed that the reduction in mutual information was present in delta, theta, and sigma frequencies. These findings suggest that the lowered cortical interdependence in sleep of elderly subjects may indicate independently evolving dynamic neural activities at multiple cortical sites. The loss of synchronization between neural activities during sleep in the elderly may make these women more susceptible to localized disturbances that could lead to frequent arousals.

Modulus and direction of the neural current vector identify distinct functional connectivity modes between human MT+ areas

Reconstruction of neural current sources from magnetoencephalography (MEG) data provides two independent estimates of the instantaneous current modulus and its direction. Here, we explore how different information on the modulus and direction affects the inter-hemisphere connectivity of the human medial temporal complex (hMT+). Connectivity was quantified by mutual information values of paired time series of current moduli or directions, with the joint probability distribution estimated with an optimized Gaussian kernel. These time series were obtained from tomographic analysis of single-trial MEG responses to a visual motion stimulus. With a high-contrast stimulus, connectivity measures based on the modulus were relatively strong in the prestimulus period, continuing until 100 ms after stimulus onset. The strongest modulus connectivity was produced with a long lag (19 ms) of the right hMT+ after the left hMT+. On the other hand, connectivity measures based on direction were relatively strong after 100 ms, with a short delay of less than 6 ms. These results suggest that nonspecific and probably indirect communication between the homologous areas is turned, by the stimulus arrival, into more precise and direct communication through the corpus callosum. The orientation of the estimated current vector for the strong connectivity can be explained by the curvature of the active cortical sheet. The temporal patterns of modulus and directional connectivity were different at low contrast, but similar to those at high contrast. We conclude that the modulus and direction indicate distinct functional connectivity modes.

Influence of coherence between multiple cortical columns on alpha rhythm: a computational modeling study

In electroencephalographic (EEG) and magnetoencephalographic (MEG) signals, stimulus-induced amplitude increase and decrease in the alpha rhythm, known as event-related synchronization and desynchronization (ERS/ERD), emerge after a task onset. ERS/ERD is assumed to reflect neural processes relevant to cognitive tasks. Previous studies suggest that several sources of alpha rhythm, each of which can serve as an alpha rhythm generator, exist in the cortex. Since EEG/MEG signals represent spatially summed neural activities, ERS/ERD of the alpha rhythm may reflect the consequence of the interactions between multiple alpha rhythm generators. Two candidates modulate the magnitude of ERS/ERD: (1) coherence between the activities of the alpha rhythm generators and (2) mean amplitude of the activities of the alpha rhythm generators. In this study, we use a computational model of multiple alpha rhythm generators to determine the factor that dominantly causes ERS/ERD. Each alpha rhythm generator is modeled based on local column circuits in the primary visual cortex and made to interact with the neighboring generators through excitatory connections. We observe that the model consistently reproduces spontaneous alpha rhythms, event-related potentials, phase-locked alpha rhythms, and ERS/ERD in a specific range of connectivity coefficients. Independent analyses of the coherence and amplitude of multiple alpha rhythm generators reveal that the ERS/ERD in the simulated data is dominantly caused by stimulus-induced changes in the coherence between multiple alpha rhythm generators. Nonlinear phenomena such as phase-resetting and entrainment of the alpha rhythm are related to the neural mechanism underlying ERS/ERD.

Estimation of genuine and random synchronization in multivariate neural series

Synchronization is an important mechanism that helps in understanding information processing in a normal or abnormal brain. In this paper, we propose a new method to estimate the genuine and random synchronization indexes in multivariate neural series, denoted as GSI (genuine synchronization index) and RSI (random synchronization index), by means of a correlation matrix analysis and surrogate technique. The performance of the method is evaluated by using a multi-channel neural mass model (MNMM), including the effects of different coupling coefficients, signal to noise ratios (SNRs) and time-window widths on the estimation of the GSI and RSI. Results show that the GSI and the RSI are superior in description of the synchronization in multivariate neural series compared to the S-estimator. Furthermore, the proposed method is applied to analyze a 21-channel scalp electroencephalographic recording of a 35 year-old male who suffers from mesial temporal lobe epilepsy. The GSI and the RSI at different frequency bands during the epileptic seizure are estimated. The present results could be helpful for us to understand the synchronization mechanism of epileptic seizures.

A method for the estimation of functional brain connectivity from time-series data

A central issue in cognitive neuroscience is which cortical areas are involved in managing information processing in a cognitive task and to understand their temporal interactions. Since the transfer of information in the form of electrical activity from one cortical region will in turn evoke electrical activity in other regions, the analysis of temporal synchronization provides a tool to understand neuronal information processing between cortical regions. We adopt a method for revealing time-dependent functional connectivity. We apply statistical analyses of phases to recover the information flow and the functional connectivity between cortical regions for high temporal resolution data. We further develop an evaluation method for these techniques based on two kinds of model networks. These networks consist of coupled Rössler attractors or of coupled stochastic Ornstein-Uhlenbeck systems. The implemented time-dependent coupling includes uni- and bi-directional connectivities as well as time delayed feedback. The synchronization dynamics of these networks are analyzed using the mean phase coherence, based on averaging over phase-differences, and the general synchronization index. The latter is based on the Shannon entropy. The combination of these with a parametric time delay forms the basis of a connectivity pattern, which includes the temporal and time lagged dynamics of the synchronization between two sources. We model and discuss potential artifacts. We find that the general phase measures are remarkably stable. They produce highly comparable results for stochastic and periodic systems. Moreover, the methods proves useful for identifying brief periods of phase coupling and delays. Therefore, we propose that the method is useful as a basis for generating potential functional connective models.

Drug effect on EEG connectivity assessed by linear and nonlinear couplings

Quantitative analysis of human electroencephalogram (EEG) is a valuable method for evaluating psychopharmacological agents. Although the effects of different drug classes on EEG spectra are already known, interactions between brain locations remain unclear. In this work, cross mutual information function and appropriate surrogate data were applied to assess linear and nonlinear couplings between EEG signals. The main goal was to evaluate the pharmacological effects of alprazolam on brain connectivity during wakefulness in healthy volunteers using a cross-over, placebo-controlled design. Eighty-five pairs of EEG leads were selected for the analysis, and connectivity was evaluated inside anterior, central, and posterior zones of the scalp. Connectivity between these zones and interhemispheric connectivity were also measured. Results showed that alprazolam induced significant changes in EEG connectivity in terms of information transfer in comparison with placebo. Trends were opposite depending on the statistical characteristics: decreases in linear connectivity and increases in nonlinear couplings. These effects were generally spread over the entire scalp. Linear changes were negatively correlated, and nonlinear changes were positively correlated with drug plasma concentrations; the latter showed higher correlation coefficients. The use of both linear and nonlinear approaches revealed the importance of assessing changes in EEG connectivity as this can provide interesting information about psychopharmacological effects.

A comparative study of pattern synchronization detection between neural signals using different cross-entropy measures

Cross-approximate entropy (X-ApEn) and cross-sample entropy (X-SampEn) have been employed as bivariate pattern synchronization measures for characterizing interdependencies between neural signals. In this study, we proposed a new measure, cross-fuzzy entropy (X-FuzzyEn), to describe the synchronicity of patterns. The performances of three statistics were first quantitatively tested using five different coupled systems including both deterministic and stochastic models, i.e., coupled broadband noises, Lorenz-Lorenz, Rossler-Rossler, Rossler-Lorenz, and neural mass model. All the measures were compared with each other with respect to their ability to distinguish between different levels of coupling and their robustness against noise. The three measures were then applied to a real-life problem, pattern synchronization analysis of left and right hemisphere rat electroencephalographic (EEG) signals. Both simulated and real EEG data analysis results showed that the X-FuzzyEn provided an improved evaluation of bivariate series pattern synchronization and could be more conveniently and powerfully applied to different neural dynamical systems contaminated by noise.

Time-Varying Cortical Connectivity Estimation from Noninvasive, High-Resolution EEG Recordings

Objective: In this paper, we propose a body of techniques for the estimation of rapidly changing connectivity relationships between EEG signals estimated in cortical areas, based on the use of adaptive multivariate autoregressive modeling (AMVAR) for the estimation of a time-varying partial directed coherence (PDC). This approach allows the observation of rapidly changing influences between the cortical areas during the execution of a task, and does not require the stationarity of the signals. Methods: High resolution EEG data were recorded from a group of spinal cord injured (SCI) patients during the attempt to move a paralyzed limb. These data were compared with the time-varying connectivity patterns estimated in a control group during the real execution of the movement. Connectivity was estimated with the use of realistic head modeling and the linear inverse estimation of the cortical activity in a series of regions of interest by using time-varying PDC. Results: The SCI population involved a different cortical network than those generated by the healthy subjects during the task performance. Such a network differs for the involvement of the parietal cortices, which increases in strength near to the movement imagination onset for the SCI when compared to the normal population. Conclusions: The application of time-varying PDC allows tracking the evolution of the connectivity between cortical areas in the analyzed populations during the proposed tasks. Such details about the temporal evolution of the connectivity patterns estimated cannot be obtained with the application of the standard estimators of connectivity.

Functional brain imaging in schizophrenia: selected results and methods

Functional brain imaging studies of patients with schizophrenia may be grouped into those that assume that the signs and symptoms of schizophrenia are due to disordered circuitry within a critical brain region and studies that assume that the signs and symptoms are due to disordered connections among brain regions. Studies have investigated the disordered functional brain anatomy of both the positive and negative symptoms of schizophrenia. Studies of spontaneous hallucinations find that although hallucinations are associated with abnormal brain activity in primary and secondary sensory areas, disordered brain activation associated with hallucinations is not limited to sensory systems. Disordered activation in non-sensory regions appear to contribute to the emotional strength and valence of hallucinations, to be a factor underlying an inability to distinguish ongoing mental processing from memories, and to reflect the brain's attempt to modulate the intensity of hallucinations and resolve conflicts with other processing demands. Brain activation studies support the view that auditory/verbal hallucinations are associated with an impaired ability of internal speech plans to modulate neural activation in sensory language areas. In early studies, negative symptoms of schizophrenia were hypothesized to be associated with impaired function in frontal brain areas. In support of this hypothesis meta-analytical studies have found that resting blood flow or metabolism in frontal cortex is reduced in schizophrenia, though the magnitude of the effect is only small to moderate. Brain activation studies of working memory (WM) functioning are typically associated with large effect sizes in the frontal cortex, whereas studies of functions other than WM generally reveal smaller effects. Findings from some functional connectivity studies have supported the hypothesis that schizophrenia patients experience impaired functional connections between frontal and temporal cortex, although the nature of the disordered connectivity is complex. More recent studies have used functional brain imaging to study neural compensation in schizophrenia, to serve as endophenotypes in genetic studies and to provide biomarkers in drug development studies. These emerging trends in functional brain imaging research are likely to help stimulate the development of a general neurobiological theory of the complex symptoms of schizophrenia.

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.

Influences of bilateral ischemic stroke on the cortical synchronization

Stroke has been one of the leading causes of mortality and long-term morbidity around the world. Describing the cortical synchrony has been useful in understanding of central nervous system disorders after brain injury. In this paper, we investigated the large scale cortical phase synchronization derived from multichannel electroencephalogram (EEG) recordings of bilateral ischemic stroke patients(n = 9). Compared with the results from the age- and gender-matched control subjects (n = 8), stroke patients showed 1) there were not significant changes of the intra-hemispheric synchronization after the bilateral stroke; and however, 2) both global and inter-hemispheric synchronization are vulnerable to the ischemic injury. Our preliminary results indicated that synchrony analysis of the spontaneous scalp EEG during at resting state provided new insight into cortical functional disorder following stroke.

Random fields--union intersection tests for detecting functional connectivity in EEG/MEG imaging

Electrophysiological (EEG/MEG) imaging challenges statistics by providing two views of the same underlying spatio-temporal brain activity: a topographic view (EEG/MEG) and tomographic view (EEG/MEG source reconstructions). It is a common practice that statistical parametric mapping (SPM) for these two situations is developed separately. In particular, assessing statistical significance of functional connectivity is a major challenge in these types of studies. This work introduces statistical tests for assessing simultaneously the significance of spatio-temporal correlation structure between ERP/ERF components as well as that of their generating sources. We introduce a greatest root statistic as the multivariate test statistic for detecting functional connectivity between two sets of EEG/MEG measurements at a given time instant. We use some new results in random field theory to solve the multiple comparisons problem resulting from the correlated test statistics at each time instant. In general, our approach using the union-intersection (UI) principle provides a framework for hypothesis testing about any linear combination of sensor data, which allows the analysis of the correlation structure of both topographic and tomographic views. The performance of the proposed method is illustrated with real ERP data obtained from a face recognition experiment.

Human brain networks in health and disease

PURPOSE OF REVIEW

Recent developments in the statistical physics of complex networks have been translated to neuroimaging data in an effort to enhance our understanding of human brain structural and functional networks. This review focuses on studies using graph theoretical measures applied to structural MRI, diffusion MRI, functional MRI, electroencephalography, and magnetoencephalography data.

RECENT FINDINGS

Complex network properties have been identified with some consistency in all modalities of neuroimaging data and over a range of spatial and time scales. Conserved properties include small worldness, high efficiency of information transfer for low wiring cost, modularity, and the existence of network hubs. Structural and functional network metrics have been found to be heritable and to change with normal aging. Clinical studies, principally in Alzheimer's disease and schizophrenia, have identified abnormalities of network configuration in patients. Future work will likely involve efforts to synthesize structural and functional networks in integrated models and to explore the interdependence of network configuration and cognitive performance.

SUMMARY

Graph theoretical analysis of neuroimaging data is growing rapidly and could potentially provide a relatively simple but powerful quantitative framework to describe and compare whole human brain structural and functional networks under diverse experimental and clinical conditions.

Detection of neural correlates of self-paced motor activity using empirical mode decomposition phase locking analysis

Transient episodes of synchronisation of neuronal activity in particular frequency ranges are thought to underlie cognition. Empirical mode decomposition phase locking (EMDPL) analysis is a method for determining the frequency and timing of phase synchrony that is adaptive to intrinsic oscillations within data, alleviating the need for arbitrary bandpass filter cut-off selection. It is extended here to address the choice of reference electrode and removal of spurious synchrony resulting from volume conduction. Spline Laplacian transformation and independent component analysis (ICA) are performed as pre-processing steps, and preservation of phase synchrony between synthetic signals, combined using a simple forward model, is demonstrated. The method is contrasted with use of bandpass filtering following the same pre-processing steps, and filter cut-offs are shown to influence synchrony detection markedly. Furthermore, an approach to the assessment of multiple EEG trials using the method is introduced, and the assessment of statistical significance of phase locking episodes is extended to render it adaptive to local phase synchrony levels. EMDPL is validated in the analysis of real EEG data, during finger tapping. The time course of event-related (de)synchronisation (ERD/ERS) is shown to differ from that of longer range phase locking episodes, implying different roles for these different types of synchronisation. It is suggested that the increase in phase locking which occurs just prior to movement, coinciding with a reduction in power (or ERD) may result from selection of the neural assembly relevant to the particular movement.

Duration of coherence intervals in electrical brain activity in perceptual organization

We investigated the relationship between visual experience and temporal intervals of synchronized brain activity. Using high-density scalp electroencephalography, we examined how synchronized activity depends on visual stimulus information and on individual observer sensitivity. In a perceptual grouping task, we varied the ambiguity of visual stimuli and estimated observer sensitivity to this variation. We found that durations of synchronized activity in the beta frequency band were associated with both stimulus ambiguity and sensitivity: the lower the stimulus ambiguity and the higher individual observer sensitivity the longer were the episodes of synchronized activity. Durations of synchronized activity intervals followed an extreme value distribution, indicating that they were limited by the slowest mechanism among the multiple neural mechanisms engaged in the perceptual task. Because the degree of stimulus ambiguity is (inversely) related to the amount of stimulus information, the durations of synchronous episodes reflect the amount of stimulus information processed in the task. We therefore interpreted our results as evidence that the alternating episodes of desynchronized and synchronized electrical brain activity reflect, respectively, the processing of information within local regions and the transfer of information across regions.

Dynamic Causal Models for phase coupling

This paper presents an extension of the Dynamic Causal Modelling (DCM) framework to the analysis of phase-coupled data. A weakly coupled oscillator approach is used to describe dynamic phase changes in a network of oscillators. The use of Bayesian model comparison allows one to infer the mechanisms underlying synchronization processes in the brain. For example, whether activity is driven by master-slave versus mutual entrainment mechanisms. Results are presented on synthetic data from physiological models and on MEG data from a study of visual working memory.

Cognitive fitness of cost-efficient brain functional networks

The human brain's capacity for cognitive function is thought to depend on coordinated activity in sparsely connected, complex networks organized over many scales of space and time. Recent work has demonstrated that human brain networks constructed from neuroimaging data have economical small-world properties that confer high efficiency of information processing at relatively low connection cost. However, it has been unclear how the architecture of complex brain networks functioning at different frequencies can be related to behavioral performance on cognitive tasks. Here, we show that impaired accuracy of working memory could be related to suboptimal cost efficiency of brain functional networks operating in the classical beta frequency band, 15-30 Hz. We analyzed brain functional networks derived from magnetoencephalography data recorded during working-memory task performance in 29 healthy volunteers and 28 people with schizophrenia. Networks functioning at higher frequencies had greater global cost efficiency than low-frequency networks in both groups. Superior task performance was positively correlated with global cost efficiency of the beta-band network and specifically with cost efficiency of nodes in left lateral parietal and frontal areas. These results are consistent with biophysical models highlighting the importance of beta-band oscillations for long-distance functional connections in brain networks and with pathophysiological models of schizophrenia as a dysconnection syndrome. More generally, they echo the saying that "less is more": The information processing performance of a network can be enhanced by a sparse or low-cost configuration with disproportionately high efficiency.

Repetition suppression and plasticity in the human brain

The suppression of neuronal responses to a repeated event is a ubiquitous phenomenon in neuroscience. However, the underlying mechanisms remain largely unexplored. The aim of this study was to examine the temporal evolution of experience-dependent changes in connectivity induced by repeated stimuli. We recorded event-related potentials (ERPs) during frequency changes of a repeating tone. Bayesian inversion of dynamic causal models (DCM) of ERPs revealed systematic repetition-dependent changes in both intrinsic and extrinsic connections, within a hierarchical cortical network. Critically, these changes occurred very quickly, over inter-stimulus intervals that implicate short-term synaptic plasticity. Furthermore, intrinsic (within-source) connections showed biphasic changes that were much faster than changes in extrinsic (between-source) connections, which decreased monotonically with repetition. This study shows that auditory perceptual learning is associated with repetition-dependent plasticity in the human brain. It is remarkable that distinct changes in intrinsic and extrinsic connections could be quantified so reliably and non-invasively using EEG.

MATLAB toolbox for functional connectivity

The term "functional connectivity" is used to denote correlations in activation among spatially-distinct brain regions, either in a resting state or when processing external stimuli. Functional connectivity has been extensively evaluated with several functional neuroimaging methods, particularly PET and fMRI. Yet these relationships have been quantified using very different measures and the extent to which they index the same constructs is unclear. We have implemented a variety of these functional connectivity measures in a new freely available MATLAB toolbox. These measures are categorized into two groups: whole time-series and trial-based approaches. We evaluate these measures via simulations with different patterns of functional connectivity and provide recommendations for their use. We also apply these measures to a previously published fMRI data set (Siegle, G.J., Thompson, W., Carter, C.S., Steinhauer, S.R., Thase, M.E., 2007. Increased amygdala and decreased dorsolateral prefrontal BOLD responses in unipolar depression: related and independent features. Biol. Psychiatry 610 (2), 198-209) in which activity in dorsal anterior cingulate cortex (dACC) and dorsolateral prefrontal cortex (DLPFC) was evaluated in 32 control subjects during a digit sorting task. Though all implemented measures demonstrate functional connectivity between dACC and DLPFC activity during event-related tasks, different participants appeared to display qualitatively different relationships.

Persistent neural states: stationary localized activity patterns in nonlinear continuous n-population, q-dimensional neural networks

Neural continuum networks are an important aspect of the modeling of macroscopic parts of the cortex. Two classes of such networks are considered: voltage and activity based. In both cases, our networks contain an arbitrary number, n, of interacting neuron populations. Spatial nonsymmetric connectivity functions represent cortico-cortical, local connections, and external inputs represent nonlocal connections. Sigmoidal nonlinearities model the relationship between (average) membrane potential and activity. Departing from most of the previous work in this area, we do not assume the nonlinearity to be singular, that is, represented by the discontinuous Heaviside function. Another important difference from previous work is that we relax the assumption that the domain of definition where we study these networks is infinite, that is, equal to R or R2. We explicitly consider the biologically more relevant case of a bounded subset omega of Rq, q = 1, 2, 3, a better model of a piece of cortex. The time behavior of these networks is described by systems of integro-differential equations. Using methods of functional analysis, we study the existence and uniqueness of a stationary (i.e., time-independent) solution of these equations in the case of a stationary input. These solutions can be seen as 'persistent'; they are also sometimes called bumps. We show that under very mild assumptions on the connectivity functions and because we do not use the Heaviside function for the nonlinearities, such solutions always exist. We also give sufficient conditions on the connectivity functions for the solution to be absolutely stable, that is, independent of the initial state of the network. We then study the sensitivity of the solutions to variations of such parameters as the connectivity functions, the sigmoids, the external inputs, and, last but not least, the shape of the domain of existence omega of the neural continuum networks. These theoretical results are illustrated and corroborated by a large number of numerical experiments in most of the cases 2 < or = n < or = 3, 2 < or = q < or = 3.

Dynamic causal modeling of the response to frequency deviants

This article describes the use of dynamic causal modeling to test hypotheses about the genesis of evoked responses. Specifically, we consider the mismatch negativity (MMN), a well-characterized response to deviant sounds and one of the most widely studied evoked responses. There have been several mechanistic accounts of how the MMN might arise. It has been suggested that the MMN results from a comparison between sensory input and a memory trace of previous input, although others have argued that local adaptation, due to stimulus repetition, is sufficient to explain the MMN. Thus the precise mechanisms underlying the generation of the MMN remain unclear. This study tests some biologically plausible spatiotemporal dipole models that rest on changes in extrinsic top-down connections (that enable comparison) and intrinsic changes (that model adaptation). Dynamic causal modeling suggested that responses to deviants are best explained by changes in effective connectivity both within and between cortical sources in a hierarchical network of distributed sources. Our model comparison suggests that both adaptation and memory comparison operate in concert to produce the early (N1 enhancement) and late (MMN) parts of the response to frequency deviants. We consider these mechanisms in the light of predictive coding and hierarchical inference in the brain.

Identifying neural drivers with functional MRI: an electrophysiological validation

Whether functional magnetic resonance imaging (fMRI) allows the identification of neural drivers remains an open question of particular importance to refine physiological and neuropsychological models of the brain, and/or to understand neurophysiopathology. Here, in a rat model of absence epilepsy showing spontaneous spike-and-wave discharges originating from the first somatosensory cortex (S1BF), we performed simultaneous electroencephalographic (EEG) and fMRI measurements, and subsequent intracerebral EEG (iEEG) recordings in regions strongly activated in fMRI (S1BF, thalamus, and striatum). fMRI connectivity was determined from fMRI time series directly and from hidden state variables using a measure of Granger causality and Dynamic Causal Modelling that relates synaptic activity to fMRI. fMRI connectivity was compared to directed functional coupling estimated from iEEG using asymmetry in generalised synchronisation metrics. The neural driver of spike-and-wave discharges was estimated in S1BF from iEEG, and from fMRI only when hemodynamic effects were explicitly removed. Functional connectivity analysis applied directly on fMRI signals failed because hemodynamics varied between regions, rendering temporal precedence irrelevant. This paper provides the first experimental substantiation of the theoretical possibility to improve interregional coupling estimation from hidden neural states of fMRI. As such, it has important implications for future studies on brain connectivity using functional neuroimaging.

Our understanding of how the brain works relies on the development of neuropsychological models, which describe how brain activity is coordinated among different regions during the execution of a given task. Knowing the directionality of information transfer between connected regions, and in particular distinguishing neural drivers, or the source of forward connections in the brain, from other brain regions, is critical to refine models of the brain. However, whether functional magnetic resonance imaging (fMRI), the most common technique for imaging brain function, allows one to identify neural drivers remains an open question. Here, we used a rat model of absence epilepsy, a form of nonconvulsive epilepsy that occurs during childhood in humans, showing spontaneous spike-and-wave discharges (nonconvulsive seizures) originating from the first somatosensory cortex, to validate several functional connectivity measures derived from fMRI. Standard techniques estimating interactions directly from fMRI data failed because blood flow dynamics varied between regions. However, we were able to identify the neural driver of spike-and-wave discharges when hemodynamic effects were explicitly removed using appropriate modelling. This study thus provides the first experimental substantiation of the theoretical possibility to improve interregional coupling estimation from hidden neural states of fMRI. As such, it has important implications for future studies on connectivity in the functional neuroimaging literature.

Neural long-range interactions can be distinguished from hemodynamic confounds in functional magnetic resonance imaging using new data analysis techniques that will allow experimental validation of models of brain function.

Brain network analysis from high-resolution EEG recordings by the application of theoretical graph indexes

The extraction of the salient characteristics from brain connectivity patterns is an open challenging topic since often the estimated cerebral networks have a relative large size and complex structure. Since a graph is a mathematical representation of a network, which is essentially reduced to nodes and connections between them, the use of a theoretical graph approach would extract significant information from the functional brain networks estimated through different neuroimaging techniques. The present work intends to support the development of the "brain network analysis:" a mathematical tool consisting in a body of indexes based on the graph theory able to improve the comprehension of the complex interactions within the brain. In the present work, we applied for demonstrative purpose some graph indexes to the time-varying networks estimated from a set of high-resolution EEG data in a group of healthy subjects during the performance of a motor task. The comparison with a random benchmark allowed extracting the significant properties of the estimated networks in the representative Alpha (7-12 Hz) band. Altogether, our findings aim at proving how the brain network analysis could reveal important information about the time-frequency dynamics of the functional cortical networks.

Interpretation of the auto-mutual information rate of decrease in the context of biomedical signal analysis. Application to electroencephalogram recordings

The mutual information (MI) is a measure of both linear and nonlinear dependences. It can be applied to a time series and a time-delayed version of the same sequence to compute the auto-mutual information function (AMIF). Moreover, the AMIF rate of decrease (AMIFRD) with increasing time delay in a signal is correlated with its entropy and has been used to characterize biomedical data. In this paper, we aimed at gaining insight into the dependence of the AMIFRD on several signal processing concepts and at illustrating its application to biomedical time series analysis. Thus, we have analysed a set of synthetic sequences with the AMIFRD. The results show that the AMIF decreases more quickly as bandwidth increases and that the AMIFRD becomes more negative as there is more white noise contaminating the time series. Additionally, this metric detected changes in the nonlinear dynamics of a signal. Finally, in order to illustrate the analysis of real biomedical signals with the AMIFRD, this metric was applied to electroencephalogram (EEG) signals acquired with eyes open and closed and to ictal and non-ictal intracranial EEG recordings.

Persistent Neural States: Stationary Localized Activity Patterns in Nonlinear Continuous n-Population, q-Dimensional Neural Networks

Neural continuum networks are an important aspect of the modeling of macroscopic parts of the cortex. Two classes of such networks are considered: voltage and activity based. In both cases, our networks contain an arbitrary number, n, of interacting neuron populations. Spatial nonsymmetric connectivity functions represent cortico-cortical, local connections, and external inputs represent nonlocal connections. Sigmoidal nonlinearities model the relationship between (average) membrane potential and activity. Departing from most of the previous work in this area, we do not assume the nonlinearity to be singular, that is, represented by the discontinuous Heaviside function. Another important difference from previous work is that we relax the assumption that the domain of definition where we study these networks is infinite, that is, equal to [Formula: see text] or [Formula: see text]. We explicitly consider the biologically more relevant case of a bounded subset Ω of [Formula: see text], a better model of a piece of cortex. The time behavior of these networks is described by systems of integro-differential equations. Using methods of functional analysis, we study the existence and uniqueness of a stationary (i.e., time-independent) solution of these equations in the case of a stationary input. These solutions can be seen as ‘persistent’; they are also sometimes called bumps. We show that under very mild assumptions on the connectivity functions and because we do not use the Heaviside function for the nonlinearities, such solutions always exist. We also give sufficient conditions on the connectivity functions for the solution to be absolutely stable, that is, independent of the initial state of the network. We then study the sensitivity of the solutions to variations of such parameters as the connectivity functions, the sigmoids, the external inputs, and, last but not least, the shape of the domain of existence Ω of the neural continuum networks. These theoretical results are illustrated and corroborated by a large number of numerical experiments in most of the cases 2 ⩽ n ⩽ 3, 2 ⩽ q ⩽ 3.

Estimation of effective and functional cortical connectivity from neuroelectric and hemodynamic recordings

In this paper, different linear and nonlinear methodologies for the estimation of cortical connectivity from neuroelectric and hemodynamic measurements are reviewed and applied on common data set in order to highlight similarities and differences in the results. Different effective and functional connectivity methods were applied to motor and cognitive data sets, including structural equation modeling (SEM), directed transfer function (DTF), partial directed coherence (PDC), and direct directed transfer function (dDTF). Comparisons were made between the results in order to understand if, for a same dataset, effective and functional connectivity estimators can return the same cortical connectivity patterns. An application of a nonlinear method [phase synchronization index (PSI)] to similar executed and imagined movements was also reviewed. Connectivity patterns estimated with the use of the neuroelectric information and of the information from the multimodal integration of neuroelectric and hemodynamic data were also compared. Results suggests that the estimation of the cortical connectivity patterns performed with the linear methods (SEM, DTF, PDC, dDTF) or with the nonlinear method (PSI) on movement related potentials returned similar cortical networks. Differences in cortical connectivity were noted between the patterns estimated with the use of multimodal integration and those estimated by using only the neuroelectric data.

Approximate entropy and auto mutual information analysis of the electroencephalogram in Alzheimer's disease patients

We analysed the electroencephalogram (EEG) from Alzheimer's disease (AD) patients with two nonlinear methods: approximate entropy (ApEn) and auto mutual information (AMI). ApEn quantifies regularity in data, while AMI detects linear and nonlinear dependencies in time series. EEGs from 11 AD patients and 11 age-matched controls were analysed. ApEn was significantly lower in AD patients at electrodes O1, O2, P3 and P4 (p < 0.01). The EEG AMI decreased more slowly with time delays in patients than in controls, with significant differences at electrodes T5, T6, O1, O2, P3 and P4 (p < 0.01). The strong correlation between results from both methods shows that the AMI rate of decrease can be used to estimate the regularity in time series. Our work suggests that nonlinear EEG analysis may contribute to increase the insight into brain dysfunction in AD, especially when different time scales are inspected, as is the case with AMI.

Bayesian estimation of synaptic physiology from the spectral responses of neural masses

We describe a Bayesian inference scheme for quantifying the active physiology of neuronal ensembles using local field recordings of synaptic potentials. This entails the inversion of a generative neural mass model of steady-state spectral activity. The inversion uses Expectation Maximization (EM) to furnish the posterior probability of key synaptic parameters and the marginal likelihood of the model itself. The neural mass model embeds prior knowledge pertaining to both the anatomical [synaptic] circuitry and plausible trajectories of neuronal dynamics. This model comprises a population of excitatory pyramidal cells, under local interneuron inhibition and driving excitation from layer IV stellate cells. Under quasi-stationary assumptions, the model can predict the spectral profile of local field potentials (LFP). This means model parameters can be optimised given real electrophysiological observations. The validity of inferences about synaptic parameters is demonstrated using simulated data and experimental recordings from the medial prefrontal cortex of control and isolation-reared Wistar rats. Specifically, we examined the maximum a posteriori estimates of parameters describing synaptic function in the two groups and tested predictions derived from concomitant microdialysis measures. The modelling of the LFP recordings revealed (i) a sensitization of post-synaptic excitatory responses, particularly marked in pyramidal cells, in the medial prefrontal cortex of socially isolated rats and (ii) increased neuronal adaptation. These inferences were consistent with predictions derived from experimental microdialysis measures of extracellular glutamate levels.

Mutual-information-based approach for neural connectivity during self-paced finger lifting task

Frequency-dependent modulation between neuronal assemblies may provide insightful mechanisms of functional organization in the context of neural connectivity. We present a conjoined time-frequency cross mutual information (TFCMI) method to explore the subtle brain neural connectivity by magnetoencephalography (MEG) during a self-paced finger lifting task. Surface electromyogram (sEMG) was obtained from the extensor digitorum communis. Both within-modality (MEG-MEG) and between-modality studies (sEMG-MEG) were conducted. The TFCMI method measures both the linear and nonlinear dependencies of the temporal dynamics of signal power within a pre-specified frequency band. Each single trial of MEG across channels and sEMG signals was transformed into time-frequency domain with use of the Morlet wavelet to obtain better temporal spectral (power) information. As compared to coherence approach (linear dependency only) in broadband analysis, the TFCMI method demonstrated advantages in encompassing detection for the mesial frontocentral cortex and bilateral primary sensorimotor areas, clear demarcation of event- and non-event-related regions, and robustness for sEMG - MEG between-modality study, i.e., corticomuscular communication. We conclude that this novel TFCMI method promises a possibility to better unravel the intricate functional organizations of brain in the context of oscillation-coded communication.

Tracking the time-varying cortical connectivity patterns by adaptive multivariate estimators

The directed transfer function (DTF) and the partial directed coherence (PDC) are frequency-domain estimators that are able to describe interactions between cortical areas in terms of the concept of Granger causality. However, the classical estimation of these methods is based on the multivariate autoregressive modelling (MVAR) of time series, which requires the stationarity of the signals. In this way, transient pathways of information transfer remains hidden. The objective of this study is to test a time-varying multivariate method for the estimation of rapidly changing connectivity relationships between cortical areas of the human brain, based on DTF/PDC and on the use of adaptive MVAR modelling (AMVAR) and to apply it to a set of real high resolution EEG data. This approach will allow the observation of rapidly changing influences between the cortical areas during the execution of a task. The simulation results indicated that time-varying DTF and PDC are able to estimate correctly the imposed connectivity patterns under reasonable operative conditions of signal-to-noise ratio (SNR) ad number of trials. An SNR of five and a number of trials of at least 20 provide a good accuracy in the estimation. After testing the method by the simulation study, we provide an application to the cortical estimations obtained from high resolution EEG data recorded from a group of healthy subject during a combined foot-lips movement and present the time-varying connectivity patterns resulting from the application of both DTF and PDC. Two different cortical networks were detected with the proposed methods, one constant across the task and the other evolving during the preparation of the joint movement.

Dynamic causal modelling of induced responses

This paper describes a dynamic causal model (DCM) for induced or spectral responses as measured with the electroencephalogram (EEG) or the magnetoencephalogram (MEG). We model the time-varying power, over a range of frequencies, as the response of a distributed system of coupled electromagnetic sources to a spectral perturbation. The model parameters encode the frequency response to exogenous input and coupling among sources and different frequencies. The Bayesian inversion of this model, given data enables inferences about the parameters of a particular model and allows us to compare different models, or hypotheses. One key aspect of the model is that it differentiates between linear and non-linear coupling; which correspond to within and between-frequency coupling respectively. To establish the face validity of our approach, we generate synthetic data and test the identifiability of various parameters to ensure they can be estimated accurately, under different levels of noise. We then apply our model to EEG data from a face-perception experiment, to ask whether there is evidence for non-linear coupling between early visual cortex and fusiform areas.

Contribution of exploratory methods to the investigation of extended large-scale brain networks in functional MRI: methodologies, results, and challenges

A large-scale brain network can be defined as a set of segregated and integrated regions, that is, distant regions that share strong anatomical connections and functional interactions. Data-driven investigation of such networks has recently received a great deal of attention in blood-oxygen-level-dependent (BOLD) functional magnetic resonance imaging (fMRI). We here review the rationale for such an investigation, the methods used, the results obtained, and also discuss some issues that have to be faced for an efficient exploration.

On the application of the auto mutual information rate of decrease to biomedical signals

The auto mutual information function (AMIF) evaluates the signal predictability by assessing linear and non-linear dependencies between two measurements taken from a single time series. Furthermore, the AMIF rate of decrease (AMIFRD) is correlated with signal entropy. This metric has been used to analyze biomedical data, including cardiac and brain activity recordings. Hence, the AMIFRD can be a relevant parameter in the context of biomedical signal analysis. Thus, in this pilot study, we have analyzed a synthetic sequence (a Lorenz system) and real biosignals (electroencephalograms recorded with eyes open and closed) with the AMIFRD. We aimed at illustrating the application of this parameter to biomedical time series. Our results show that the AMIFRD can detect changes in the non-linear dynamics of a sequence and that it can distinguish different physiological conditions.