Network inference with confidence from multivariate time series

Robust disruptions in electroencephalogram cortical oscillations and large-scale functional networks in autism

BACKGROUND

Autism spectrum disorders (ASD) are increasingly prevalent and have a significant impact on the lives of patients and their families. Currently, the diagnosis is determined by clinical judgment and no definitive physiological biomarker for ASD exists. Quantitative biomarkers obtainable from clinical neuroimaging data - such as the scalp electroencephalogram (EEG) - would provide an important aid to clinicians in the diagnosis of ASD. The interpretation of prior studies in this area has been limited by mixed results and the lack of validation procedures. Here we use retrospective clinical data from a well-characterized population of children with ASD to evaluate the rhythms and coupling patterns present in the EEG to develop and validate an electrophysiological biomarker of ASD.

METHODS

EEG data were acquired from a population of ASD (n = 27) and control (n = 55) children 4-8 years old. Data were divided into training (n = 13 ASD, n = 24 control) and validation (n = 14 ASD, n = 31 control) groups. Evaluation of spectral and functional network properties in the first group of patients motivated three biomarkers that were computed in the second group of age-matched patients for validation.

RESULTS

Three biomarkers of ASD were identified in the first patient group: (1) reduced posterior/anterior power ratio in the alpha frequency range (8-14 Hz), which we label the "peak alpha ratio", (2) reduced global density in functional networks, and (3) a reduction in the mean connectivity strength of a subset of functional network edges. Of these three biomarkers, the first and third were validated in a second group of patients. Using the two validated biomarkers, we were able to classify ASD subjects with 83 % sensitivity and 68 % specificity in a post-hoc analysis.

CONCLUSIONS

This study demonstrates that clinical EEG can provide quantitative biomarkers to assist diagnosis of autism. These results corroborate the general finding that ASD subjects have decreased alpha power gradients and network connectivities compared to control subjects. In addition, this study demonstrates the necessity of using statistical techniques to validate EEG biomarkers identified using exploratory methods.

Electrical Brain Responses to an Auditory Illusion and the Impact of Musical Expertise

The presentation of two sinusoidal tones, one to each ear, with a slight frequency mismatch yields an auditory illusion of a beating frequency equal to the frequency difference between the two tones; this is known as binaural beat (BB). The effect of brief BB stimulation on scalp EEG is not conclusively demonstrated. Further, no studies have examined the impact of musical training associated with BB stimulation, yet musicians' brains are often associated with enhanced auditory processing. In this study, we analysed EEG brain responses from two groups, musicians and non-musicians, when stimulated by short presentation (1 min) of binaural beats with beat frequency varying from 1 Hz to 48 Hz. We focused our analysis on alpha and gamma band EEG signals, and they were analysed in terms of spectral power, and functional connectivity as measured by two phase synchrony based measures, phase locking value and phase lag index. Finally, these measures were used to characterize the degree of centrality, segregation and integration of the functional brain network. We found that beat frequencies belonging to alpha band produced the most significant steady-state responses across groups. Further, processing of low frequency (delta, theta, alpha) binaural beats had significant impact on cortical network patterns in the alpha band oscillations. Altogether these results provide a neurophysiological account of cortical responses to BB stimulation at varying frequencies, and demonstrate a modulation of cortico-cortical connectivity in musicians' brains, and further suggest a kind of neuronal entrainment of a linear and nonlinear relationship to the beating frequencies.

EEG functional connectivity is partially predicted by underlying white matter connectivity

Over the past decade, networks have become a leading model to illustrate both the anatomical relationships (structural networks) and the coupling of dynamic physiology (functional networks) linking separate brain regions. The relationship between these two levels of description remains incompletely understood and an area of intense research interest. In particular, it is unclear how cortical currents relate to underlying brain structural architecture. In addition, although theory suggests that brain communication is highly frequency dependent, how structural connections influence overlying functional connectivity in different frequency bands has not been previously explored. Here we relate functional networks inferred from statistical associations between source imaging of EEG activity and underlying cortico-cortical structural brain connectivity determined by probabilistic white matter tractography. We evaluate spontaneous fluctuating cortical brain activity over a long time scale (minutes) and relate inferred functional networks to underlying structural connectivity for broadband signals, as well as in seven distinct frequency bands. We find that cortical networks derived from source EEG estimates partially reflect both direct and indirect underlying white matter connectivity in all frequency bands evaluated. In addition, we find that when structural support is absent, functional connectivity is significantly reduced for high frequency bands compared to low frequency bands. The association between cortical currents and underlying white matter connectivity highlights the obligatory interdependence of functional and structural networks in the human brain. The increased dependence on structural support for the coupling of higher frequency brain rhythms provides new evidence for how underlying anatomy directly shapes emergent brain dynamics at fast time scales.

Assessing dynamics, spatial scale, and uncertainty in task-related brain network analyses

The brain is a complex network of interconnected elements, whose interactions evolve dynamically in time to cooperatively perform specific functions. A common technique to probe these interactions involves multi-sensor recordings of brain activity during a repeated task. Many techniques exist to characterize the resulting task-related activity, including establishing functional networks, which represent the statistical associations between brain areas. Although functional network inference is commonly employed to analyze neural time series data, techniques to assess the uncertainty-both in the functional network edges and the corresponding aggregate measures of network topology-are lacking. To address this, we describe a statistically principled approach for computing uncertainty in functional networks and aggregate network measures in task-related data. The approach is based on a resampling procedure that utilizes the trial structure common in experimental recordings. We show in simulations that this approach successfully identifies functional networks and associated measures of confidence emergent during a task in a variety of scenarios, including dynamically evolving networks. In addition, we describe a principled technique for establishing functional networks based on predetermined regions of interest using canonical correlation. Doing so provides additional robustness to the functional network inference. Finally, we illustrate the use of these methods on example invasive brain voltage recordings collected during an overt speech task. The general strategy described here-appropriate for static and dynamic network inference and different statistical measures of coupling-permits the evaluation of confidence in network measures in a variety of settings common to neuroscience.

The maturation of cortical sleep rhythms and networks over early development

OBJECTIVE

Although neuronal activity drives all aspects of cortical development, how human brain rhythms spontaneously mature remains an active area of research. We sought to systematically evaluate the emergence of human brain rhythms and functional cortical networks over early development.

METHODS

We examined cortical rhythms and coupling patterns from birth through adolescence in a large cohort of healthy children (n=384) using scalp electroencephalogram (EEG) in the sleep state.

RESULTS

We found that the emergence of brain rhythms follows a stereotyped sequence over early development. In general, higher frequencies increase in prominence with striking regional specificity throughout development. The coordination of these rhythmic activities across brain regions follows a general pattern of maturation in which broadly distributed networks of low-frequency oscillations increase in density while networks of high frequency oscillations become sparser and more highly clustered.

CONCLUSION

Our results indicate that a predictable program directs the development of key rhythmic components and physiological brain networks over early development.

SIGNIFICANCE

This work expands our knowledge of normal cortical development. The stereotyped neurophysiological processes observed at the level of rhythms and networks may provide a scaffolding to support critical periods of cognitive growth. Furthermore, these conserved patterns could provide a sensitive biomarker for cortical health across development.

Assortative mixing in functional brain networks during epileptic seizures

We investigate assortativity of functional brain networks before, during, and after one-hundred epileptic seizures with different anatomical onset locations. We construct binary functional networks from multi-channel electroencephalographic data recorded from 60 epilepsy patients; and from time-resolved estimates of the assortativity coefficient, we conclude that positive degree-degree correlations are inherent to seizure dynamics. While seizures evolve, an increasing assortativity indicates a segregation of the underlying functional network into groups of brain regions that are only sparsely interconnected, if at all. Interestingly, assortativity decreases already prior to seizure end. Together with previous observations of characteristic temporal evolutions of global statistical properties and synchronizability of epileptic brain networks, our findings may help to gain deeper insights into the complicated dynamics underlying generation, propagation, and termination of seizures.

Nonrandomness, nonlinear dependence, and nonstationarity of electroencephalographic recordings from epilepsy patients

To derive tests for randomness, nonlinear-independence, and stationarity, we combine surrogates with a nonlinear prediction error, a nonlinear interdependence measure, and linear variability measures, respectively. We apply these tests to intracranial electroencephalographic recordings (EEG) from patients suffering from pharmacoresistant focal-onset epilepsy. These recordings had been performed prior to and independent from our study as part of the epilepsy diagnostics. The clinical purpose of these recordings was to delineate the brain areas to be surgically removed in each individual patient in order to achieve seizure control. This allowed us to define two distinct sets of signals: One set of signals recorded from brain areas where the first ictal EEG signal changes were detected as judged by expert visual inspection ("focal signals") and one set of signals recorded from brain areas that were not involved at seizure onset ("nonfocal signals"). We find more rejections for both the randomness and the nonlinear-independence test for focal versus nonfocal signals. In contrast more rejections of the stationarity test are found for nonfocal signals. Furthermore, while for nonfocal signals the rejection of the stationarity test increases the rejection probability of the randomness and nonlinear-independence test substantially, we find a much weaker influence for the focal signals. In consequence, the contrast between the focal and nonfocal signals obtained from the randomness and nonlinear-independence test is further enhanced when we exclude signals for which the stationarity test is rejected. To study the dependence between the randomness and nonlinear-independence test we include only focal signals for which the stationarity test is not rejected. We show that the rejection of these two tests correlates across signals. The rejection of either test is, however, neither necessary nor sufficient for the rejection of the other test. Thus, our results suggest that EEG signals from epileptogenic brain areas are less random, more nonlinear-dependent, and more stationary compared to signals recorded from nonepileptogenic brain areas. We provide the data, source code, and detailed results in the public domain.

Small-world topology of functional connectivity in randomly connected dynamical systems

Characterization of real-world complex systems increasingly involves the study of their topological structure using graph theory. Among global network properties, small-world property, consisting in existence of relatively short paths together with high clustering of the network, is one of the most discussed and studied. When dealing with coupled dynamical systems, links among units of the system are commonly quantified by a measure of pairwise statistical dependence of observed time series (functional connectivity). We argue that the functional connectivity approach leads to upwardly biased estimates of small-world characteristics (with respect to commonly used random graph models) due to partial transitivity of the accepted functional connectivity measures such as the correlation coefficient. In particular, this may lead to observation of small-world characteristics in connectivity graphs estimated from generic randomly connected dynamical systems. The ubiquity and robustness of the phenomenon are documented by an extensive parameter study of its manifestation in a multivariate linear autoregressive process, with discussion of the potential relevance for nonlinear processes and measures.

Inferring biochemical reaction pathways: the case of the gemcitabine pharmacokinetics

BACKGROUND

The representation of a biochemical system as a network is the precursor of any mathematical model of the processes driving the dynamics of that system. Pharmacokinetics uses mathematical models to describe the interactions between drug, and drug metabolites and targets and through the simulation of these models predicts drug levels and/or dynamic behaviors of drug entities in the body. Therefore, the development of computational techniques for inferring the interaction network of the drug entities and its kinetic parameters from observational data is raising great interest in the scientific community of pharmacologists. In fact, the network inference is a set of mathematical procedures deducing the structure of a model from the experimental data associated to the nodes of the network of interactions. In this paper, we deal with the inference of a pharmacokinetic network from the concentrations of the drug and its metabolites observed at discrete time points.

RESULTS

The method of network inference presented in this paper is inspired by the theory of time-lagged correlation inference with regard to the deduction of the interaction network, and on a maximum likelihood approach with regard to the estimation of the kinetic parameters of the network. Both network inference and parameter estimation have been designed specifically to identify systems of biotransformations, at the biochemical level, from noisy time-resolved experimental data. We use our inference method to deduce the metabolic pathway of the gemcitabine. The inputs to our inference algorithm are the experimental time series of the concentration of gemcitabine and its metabolites. The output is the set of reactions of the metabolic network of the gemcitabine.

CONCLUSIONS

Time-lagged correlation based inference pairs up to a probabilistic model of parameter inference from metabolites time series allows the identification of the microscopic pharmacokinetics and pharmacodynamics of a drug with a minimal a priori knowledge. In fact, the inference model presented in this paper is completely unsupervised. It takes as input the time series of the concetrations of the parent drug and its metabolites. The method, applied to the case study of the gemcitabine pharmacokinetics, shows good accuracy and sensitivity.

Emergence of stable functional networks in long-term human electroencephalography

Functional connectivity networks have become a central focus in neuroscience because they reveal key higher-dimensional features of normal and abnormal nervous system physiology. Functional networks reflect activity-based coupling between brain regions that may be constrained by relatively static anatomical connections, yet these networks appear to support tremendously dynamic behaviors. Within this growing field, the stability and temporal characteristics of functional connectivity brain networks have not been well characterized. We evaluated the temporal stability of spontaneous functional connectivity networks derived from multi-day scalp encephalogram (EEG) recordings in five healthy human subjects. Topological stability and graph characteristics of networks derived from averaged data epochs ranging from 1 s to multiple hours across different states of consciousness were compared. We show that, although functional networks are highly variable on the order of seconds, stable network templates emerge after as little as ∼100 s of recording and persist across different states and frequency bands (albeit with slightly different characteristics in different states and frequencies). Within these network templates, the most common edges are markedly consistent, constituting a network "core." Although average network topologies persist across time, measures of global network connectivity, density and clustering coefficient, are state and frequency specific, with sparsest but most highly clustered networks seen during sleep and in the gamma frequency band. These findings support the notion that a core functional organization underlies spontaneous cortical processing and may provide a reference template on which unstable, transient, and rapidly adaptive long-range assemblies are overlaid in a frequency-dependent manner.

Epilepsy as a disorder of cortical network organization

The brain is naturally considered as a network of interacting elements which, when functioning properly, produces an enormous range of dynamic, adaptable behavior. However, when elements of this network fail, pathological changes ensue, including epilepsy, one of the most common brain disorders. This review examines some aspects of cortical network organization that distinguish epileptic cortex from normal brain as well as the dynamics of network activity before and during seizures, focusing primarily on focal seizures. The review is organized around four phases of the seizure: the interictal period, onset, propagation, and termination. For each phase, the authors discuss the most common rhythmic characteristics of macroscopic brain voltage activity and outline the observed functional network features. Although the characteristics of functional networks that support the epileptic seizure remain an area of active research, the prevailing trends point to a complex set of network dynamics between, before, and during seizures.

Emergence of persistent networks in long-term intracranial EEG recordings

Over the past two decades, the increased ability to analyze network relationships among neural structures has provided novel insights into brain function. Most network approaches, however, focus on static representations of the brain's physical or statistical connectivity. Few studies have examined how brain functional networks evolve spontaneously over long epochs of continuous time. To address this, we examine functional connectivity networks deduced from continuous long-term electrocorticogram recordings. For a population of six human patients, we identify a persistent pattern of connections that form a frequency-band-dependent network template, and a set of core connections that appear frequently and together. These structures are robust, emerging from brief time intervals (~100 s) regardless of cognitive state. These results suggest that a metastable, frequency-band-dependent scaffold of brain connectivity exists from which transient activity emerges and recedes.

Characterizing brain cortical plasticity and network dynamics across the age-span in health and disease with TMS-EEG and TMS-fMRI

Brain plasticity can be conceptualized as nature's invention to overcome limitations of the genome and adapt to a rapidly changing environment. As such, plasticity is an intrinsic property of the brain across the lifespan. However, mechanisms of plasticity may vary with age. The combination of transcranial magnetic stimulation (TMS) with electroencephalography (EEG) or functional magnetic resonance imaging (fMRI) enables clinicians and researchers to directly study local and network cortical plasticity, in humans in vivo, and characterize their changes across the age-span. Parallel, translational studies in animals can provide mechanistic insights. Here, we argue that, for each individual, the efficiency of neuronal plasticity declines throughout the age-span and may do so more or less prominently depending on variable 'starting-points' and different 'slopes of change' defined by genetic, biological, and environmental factors. Furthermore, aberrant, excessive, insufficient, or mistimed plasticity may represent the proximal pathogenic cause of neurodevelopmental and neurodegenerative disorders such as autism spectrum disorders or Alzheimer's disease.

Unraveling spurious properties of interaction networks with tailored random networks

We investigate interaction networks that we derive from multivariate time series with methods frequently employed in diverse scientific fields such as biology, quantitative finance, physics, earth and climate sciences, and the neurosciences. Mimicking experimental situations, we generate time series with finite length and varying frequency content but from independent stochastic processes. Using the correlation coefficient and the maximum cross-correlation, we estimate interdependencies between these time series. With clustering coefficient and average shortest path length, we observe unweighted interaction networks, derived via thresholding the values of interdependence, to possess non-trivial topologies as compared to Erdös-Rényi networks, which would indicate small-world characteristics. These topologies reflect the mostly unavoidable finiteness of the data, which limits the reliability of typically used estimators of signal interdependence. We propose random networks that are tailored to the way interaction networks are derived from empirical data. Through an exemplary investigation of multichannel electroencephalographic recordings of epileptic seizures--known for their complex spatial and temporal dynamics--we show that such random networks help to distinguish network properties of interdependence structures related to seizure dynamics from those spuriously induced by the applied methods of analysis.

Noninvasive brain stimulation in Alzheimer's disease: systematic review and perspectives for the future

BACKGROUND

A number of studies have applied transcranial magnetic stimulation (TMS) to physiologically characterize Alzheimer's disease (AD) and to monitor effects of pharmacological agents, while others have begun to therapeutically use TMS and transcranial direct current stimulation (tDCS) to improve cognitive function in AD. These applications are still very early in development, but offer the opportunity of learning from them for future development.

METHODS

We performed a systematic search of all studies using noninvasive stimulation in AD and reviewed all 29 identified articles. Twenty-four focused on measures of motor cortical reactivity and (local) plasticity and functional connectivity, with eight of these studies assessing also effects of pharmacological agents. Five studies focused on the enhancement of cognitive function in AD.

RESULTS

Short-latency afferent inhibition (SAI) and resting motor threshold are significantly reduced in AD patients as compared to healthy elders. Results on other measures of cortical reactivity, e.g. intracortical inhibition (ICI), are more divergent. Acetylcholine-esterase inhibitors and dopaminergic drugs may increase SAI and ICI in AD. Motor cortical plasticity and connectivity are impaired in AD. TMS/tDCS can induce acute and short-duration beneficial effects on cognitive function, but the therapeutic clinical significance in AD is unclear. Safety of TMS/tDCS is supported by studies to date.

CONCLUSIONS

TMS/tDCS appears safe in AD, but longer-term risks have been insufficiently considered. TMS holds promise as a physiologic biomarker in AD to identify therapeutic targets and monitor pharmacologic effects. In addition, TMS/tDCS may have therapeutic utility in AD, though the evidence is still very preliminary and cautious interpretation is warranted.

Uniform approach to linear and nonlinear interrelation patterns in multivariate time series

Currently, a variety of linear and nonlinear measures is in use to investigate spatiotemporal interrelation patterns of multivariate time series. Whereas the former are by definition insensitive to nonlinear effects, the latter detect both nonlinear and linear interrelation. In the present contribution we employ a uniform surrogate-based approach, which is capable of disentangling interrelations that significantly exceed random effects and interrelations that significantly exceed linear correlation. The bivariate version of the proposed framework is explored using a simple model allowing for separate tuning of coupling and nonlinearity of interrelation. To demonstrate applicability of the approach to multivariate real-world time series we investigate resting state functional magnetic resonance imaging (rsfMRI) data of two healthy subjects as well as intracranial electroencephalograms (iEEG) of two epilepsy patients with focal onset seizures. The main findings are that for our rsfMRI data interrelations can be described by linear cross-correlation. Rejection of the null hypothesis of linear iEEG interrelation occurs predominantly for epileptogenic tissue as well as during epileptic seizures.

Directed differential connectivity graph of interictal epileptiform discharges

In this paper, we study temporal couplings between interictal events of spatially remote regions in order to localize the leading epileptic regions from intracerebral EEG (iEEG). We aim to assess whether quantitative epileptic graph analysis during interictal period may be helpful to predict the seizure onset zone of ictal iEEG. Using wavelet transform, cross-correlation coefficient, and multiple hypothesis test, we propose a differential connectivity graph (DCG) to represent the connections that change significantly between epileptic and nonepileptic states as defined by the interictal events. Postprocessings based on mutual information and multiobjective optimization are proposed to localize the leading epileptic regions through DCG. The suggested approach is applied on iEEG recordings of five patients suffering from focal epilepsy. Quantitative comparisons of the proposed epileptic regions within ictal onset zones detected by visual inspection and using electrically stimulated seizures, reveal good performance of the present method.

Coalescence and fragmentation of cortical networks during focal seizures

Epileptic seizures reflect a pathological brain state characterized by specific clinical and electrical manifestations. The proposed mechanisms are heterogeneous but united by the supposition that epileptic activity is hypersynchronous across multiple scales, yet principled and quantitative analyses of seizure dynamics across space and throughout the entire ictal period are rare. To more completely explore spatiotemporal interactions during seizures, we examined electrocorticogram data from a population of male and female human patients with epilepsy and from these data constructed dynamic network representations using statistically robust measures. We found that these networks evolved through a distinct topological progression during the seizure. Surprisingly, the overall synchronization changed only weakly, whereas the topology changed dramatically in organization. A large subnetwork dominated the network architecture at seizure onset and preceding termination but, between, fractured into smaller groups. Common network characteristics appeared consistently for a population of subjects, and, for each subject, similar networks appeared from seizure to seizure. These results suggest that, at the macroscopic spatial scale, epilepsy is not so much a manifestation of hypersynchrony but instead of network reorganization.

Estimating the directed information to infer causal relationships in ensemble neural spike train recordings

Advances in recording technologies have given neuroscience researchers access to large amounts of data, in particular, simultaneous, individual recordings of large groups of neurons in different parts of the brain. A variety of quantitative techniques have been utilized to analyze the spiking activities of the neurons to elucidate the functional connectivity of the recorded neurons. In the past, researchers have used correlative measures. More recently, to better capture the dynamic, complex relationships present in the data, neuroscientists have employed causal measures-most of which are variants of Granger causality-with limited success. This paper motivates the directed information, an information and control theoretic concept, as a modality-independent embodiment of Granger's original notion of causality. Key properties include: (a) it is nonzero if and only if one process causally influences another, and (b) its specific value can be interpreted as the strength of a causal relationship. We next describe how the causally conditioned directed information between two processes given knowledge of others provides a network version of causality: it is nonzero if and only if, in the presence of the present and past of other processes, one process causally influences another. This notion is shown to be able to differentiate between true direct causal influences, common inputs, and cascade effects in more two processes. We next describe a procedure to estimate the directed information on neural spike trains using point process generalized linear models, maximum likelihood estimation and information-theoretic model order selection. We demonstrate that on a simulated network of neurons, it (a) correctly identifies all pairwise causal relationships and (b) correctly identifies network causal relationships. This procedure is then used to analyze ensemble spike train recordings in primary motor cortex of an awake monkey while performing target reaching tasks, uncovering causal relationships whose directionality are consistent with predictions made from the wave propagation of simultaneously recorded local field potentials.

Estimating complex cortical networks via surface recordings- a critical note

We discuss potential caveats when estimating topologies of 3D brain networks from surface recordings. It is virtually impossible to record activity from all single neurons in the brain and one has to rely on techniques that measure average activity at sparsely located (non-invasive) recording sites. Effects of this spatial sampling in relation to structural network measures like centrality and assortativity were analyzed using multivariate classifiers. A simplified model of 3D brain connectivity incorporating both short- and long-range connections served for testing. To mimic M/EEG recordings we sampled this model via non-overlapping regions and weighted nodes and connections according to their proximity to the recording sites. We used various complex network models for reference and tried to classify sampled versions of the "brain-like" network as one of these archetypes. It was found that sampled networks may substantially deviate in topology from the respective original networks for small sample sizes. For experimental studies this may imply that surface recordings can yield network structures that might not agree with its generating 3D network.

Analyzing spatio-temporal patterns of genuine cross-correlations

In multivariate time series analysis, the equal-time cross-correlation is a classic and computationally efficient measure for quantifying linear interrelations between data channels. When the cross-correlation coefficient is estimated using a finite amount of data points, its non-random part may be strongly contaminated by a sizable random contribution, such that no reliable conclusion can be drawn about genuine mutual interdependencies. The random correlations are determined by the signals' frequency content and the amount of data points used. Here, we introduce adjusted correlation matrices that can be employed to disentangle random from non-random contributions to each matrix element independently of the signal frequencies. Extending our previous work these matrices allow analyzing spatial patterns of genuine cross-correlation in multivariate data regardless of confounding influences. The performance is illustrated by example of model systems with known interdependence patterns. Finally, we apply the methods to electroencephalographic (EEG) data with epileptic seizure activity.

From brain to earth and climate systems: small-world interaction networks or not?

We consider recent reports on small-world topologies of interaction networks derived from the dynamics of spatially extended systems that are investigated in diverse scientific fields such as neurosciences, geophysics, or meteorology. With numerical simulations that mimic typical experimental situations, we have identified an important constraint when characterizing such networks: indications of a small-world topology can be expected solely due to the spatial sampling of the system along with the commonly used time series analysis based approaches to network characterization.

Coupling among electroencephalogram gamma signals on a short time scale

An important goal in neuroscience is to identify instances when EEG signals are coupled. We employ a method to measure the coupling strength between gamma signals (40-100 Hz) on a short time scale as the maximum cross-correlation over a range of time lags within a sliding variable-width window. Instances of coupling states among several signals are also identified, using a mixed multivariate beta distribution to model coupling strength across multiple gamma signals with reference to a common base signal. We first apply our variable-window method to simulated signals and compare its performance to a fixed-window approach. We then focus on gamma signals recorded in two regions of the rat hippocampus. Our results indicate that this may be a useful method for mapping coupling patterns among signals in EEG datasets.

Identifying the brain's most globally connected regions

Recent advances in brain connectivity methods have made it possible to identify hubs-the brain's most globally connected regions. Such regions are essential for coordinating brain functions due to their connectivity with numerous regions with a variety of specializations. Current structural and functional connectivity methods generally agree that default mode network (DMN) regions have among the highest global brain connectivity (GBC). We developed two novel statistical approaches using resting state functional connectivity MRI-weighted and unweighted GBC (wGBC and uGBC)-to test the hypothesis that the highest global connectivity also occurs in the cognitive control network (CCN), a network anti-correlated with the DMN across a variety of tasks. High global connectivity was found in both CCN and DMN. The newly developed wGBC approach improves upon existing methods by quantifying inter-subject consistency, quantifying the highest GBC values by percentage, and avoiding arbitrarily connection strength thresholding. The uGBC approach is based on graph theory and includes many of these improvements, but still requires an arbitrary connection threshold. We found high GBC in several subcortical regions (e.g., hippocampus, basal ganglia) only with wGBC despite the regions' extensive anatomical connectivity. These results demonstrate the complementary utility of wGBC and uGBC analyses for the characterization of the most highly connected, and thus most functionally important, regions of the brain. Additionally, the high connectivity of both the CCN and the DMN demonstrates that brain regions outside primary sensory-motor networks are highly involved in coordinating information throughout the brain.