Neuroscience

Dynamics underlying epileptic seizures span multiple scales in space and time, therefore, understanding seizure mechanisms requires identifying the relations between seizure components within and across these scales, together with the analysis of their dynamical repertoire. In this view, mathematical models have been developed, ranging from single neuron to neural population. In this study, we consider a neural mass model able to exactly reproduce the dynamics of heterogeneous spiking neural networks. We combine mathematical modeling with structural information from non invasive brain imaging, thus building large-scale brain network models to explore emergent dynamics and test the clinical hypothesis. We provide a comprehensive study on the effect of external drives on neuronal networks exhibiting multistability, in order to investigate the role played by the neuroanatomical connectivity matrices in shaping the emergent dynamics. In particular, we systematically investigate the conditions under which the network displays a transition from a low activity regime to a high activity state, which we identify with a seizure-like event. This approach allows us to study the biophysical parameters and variables leading to multiple recruitment events at the network level. We further exploit topological network measures in order to explain the differences and the analogies among the subjects and their brain regions, in showing recruitment events at different parameter values. We demonstrate, along with the example of diffusion-weighted magnetic resonance imaging (dMRI) connectomes of 20 healthy subjects and 15 epileptic patients, that individual variations in structural connectivity, when linked with mathematical dynamic models, have the capacity to explain changes in spatiotemporal organization of brain dynamics, as observed in network-based brain disorders. In particular, for epileptic patients, by means of the integration of the clinical hypotheses on the epileptogenic zone (EZ), i.e., the local network where highly synchronous seizures originate, we have identified the sequence of recruitment events and discussed their links with the topological properties of the specific connectomes. The predictions made on the basis of the implemented set of exact mean-field equations turn out to be in line with the clinical pre-surgical evaluation on recruited secondary networks.

The counterintuitive phenomenon of coherence resonance describes a nonmonotonic behavior of the regularity of noise-induced oscillations in the excitable regime, leading to an optimal response in terms of regularity of the excited oscillations for an intermediate noise intensity. We study this phenomenon in populations of FitzHugh-Nagumo (FHN) neurons with different coupling architectures. For networks of FHN systems in an excitable regime, coherence resonance has been previously analyzed numerically. Here we focus on an analytical approach studying the mean-field limits of the globally and locally coupled populations. The mean-field limit refers to an averaged behavior of a complex network as the number of elements goes to infinity. We apply the mean-field approach to the globally coupled FHN network. Further, we derive a mean-field limit approximating the locally coupled FHN network with low noise intensities. We study the effects of the coupling strength and noise intensity on coherence resonance for both the network and the mean-field models. We compare the results of the mean-field and network frameworks and find good agreement in the globally coupled case, where the correspondence between the two approaches is sufficiently good to capture the emergence of coherence resonance, as well as of anticoherence resonance.

An inverse procedure is proposed and tested which aims at recovering the a priori unknown functional and structural information from global signals of living brains activity. To this end, we consider a Leaky-Integrate and Fire (LIF) model with short term plasticity neurons, coupled via a directed network. Neurons are assigned a specific current value, which is heterogenous across the sample, and sets the firing regime in which the neuron is operating in. The aim of the method is to recover the distribution of incoming network degrees, as well as the distribution of the assigned currents, from global field measurements. The proposed approach to the inverse problem implements the reductionist Heterogenous Mean-Field approximation. This amounts in turn to organizing the neurons in different classes, depending on their associated degree and current. When tested against synthetic data, the method returns accurate estimates of the sought distributions, while managing to reproduce and interpolate almost exactly the time series of the supplied global field. Finally, we also applied the proposed technique to longitudinal wide-field fluorescence microscopy data of cortical functionality in awake Thy1-GCaMP6f mice. Mice are induced a photothrombotic stroke in the primary motor cortex and their recovery monitored in time. An all-to-all LIF model which accommodates for currents heterogeneity allows to adequately explain the recorded patterns of activation. Altered distributions in neuron excitability are in particular detected, compatible with the phenomenon of hyperexcitability in the penumbra region after stroke.

A synaptic theory of Working Memory (WM) has been developed in the last decade as a possible alternative to the persistent spiking paradigm. In this context, we have developed a neural mass model able to reproduce exactly the dynamics of heterogeneous spiking neural networks encompassing realistic cellular mechanisms for short-term synaptic plasticity. This population model reproduces the macroscopic dynamics of the network in terms of the firing rate and the mean membrane potential. The latter quantity allows us to gain insight of the Local Field Potential and electroencephalographic signals measured during WM tasks to characterize the brain activity. More specifically synaptic facilitation and depression integrate each other to efficiently mimic WM operations via either synaptic reactivation or persistent activity. Memory access and loading are related to stimulus-locked transient oscillations followed by a steady-state activity in the β-γ band, thus resembling what is observed in the cortex during vibrotactile stimuli in humans and object recognition in monkeys. Memory juggling and competition emerge already by loading only two items. However more items can be stored in WM by considering neural architectures composed of multiple excitatory populations and a common inhibitory pool. Memory capacity depends strongly on the presentation rate of the items and it maximizes for an optimal frequency range. In particular we provide an analytic expression for the maximal memory capacity. Furthermore, the mean membrane potential turns out to be a suitable proxy to measure the memory load, analogously to event driven potentials in experiments on humans. Finally we show that the γ power increases with the number of loaded items, as reported in many experiments, while θ and β power reveal non monotonic behaviours. In particular, β and γ rhythms are crucially sustained by the inhibitory activity, while the θ rhythm is controlled by excitatory synapses.

Epilepsy is characterized by perturbed dynamics that originate in a local network before spreading to other brain regions. In this paper we studied studied patient-specific brain network models of epilepsy patients, comprising 88 nodes equipped with region specific neural mass models capable of demonstrating epileptiform discharges. Applying stability analysis led to a seizure control strategy that is significantly less invasive than the traditional surgery, which typically resects the epileptogenic regions. The invasiveness of the procedure correlates with graph theoretical importance of the nodes. The novel method subsequently removes the most unstable links, a procedure possible by advent of novel surgery techniques. Our approach is entirely based on structural data, allowing creation of a brain model based on purely non-invasive data prior to any surgery.

This article simulates how neuronal populations in the brain work together to distinguish different sensory inputs from the real world (e.g. visual images). More specifically, it proposes two new algorithms (one where each neuron acts on its own and one where they all work together) to find among a large neuronal population the one subpopulation that discriminates different stimuli best.

Background

Spike trains of multiple neurons can be analyzed following the summed population (SP) or the labeled line (LL) hypothesis. Responses to external stimuli are generated by a neuronal population as a whole or the individual neurons have encoding capacities of their own. The SPIKE-distance estimated either for a single, pooled spike train over a population or for each neuron separately can serve to quantify these responses.

New method

For the SP case we compare three algorithms that search for the most discriminative subpopulation over all stimulus pairs. For the LL case we introduce a new algorithm that combines neurons that individually separate different pairs of stimuli best.

Results

The best approach for SP is a brute force search over all possible subpopulations. However, it is only feasible for small populations. For more realistic settings, simulated annealing clearly outperforms gradient algorithms with only a limited increase in computational load. Our novel LL approach can handle very involved coding scenarios despite its computational ease.

Comparison with existing methods

Spike train distances have been extended to the analysis of neural populations interpolating between SP and LL coding. This includes parametrizing the importance of distinguishing spikes being fired in different neurons. Yet, these approaches only consider the population as a whole. The explicit focus on subpopulations render our algorithms complimentary.

Conclusions

The spectrum of encoding possibilities in neural populations is broad. The SP and LL cases are two extremes for which our algorithms provide correct identification results.

The detection of directional couplings between dynamics based on measured spike trains is a crucial problem in the understanding of many different systems. In particular, in neuroscience it is important to assess the connectivity between neurons.One of the approaches that can estimate directional coupling from the analysis of point processes is the nonlinear interdependence measure L. Although its efficacy has already been demonstrated, it still needs to be tested under more challenging and realistic conditions prior to an application to real data. Thus, in this paper

we use the Hindmarsh-Rose model system to test the method in the presence of noise and for different spiking regimes.We also examine the influence of different parameters and spike train distances. Our results show that the measure L is versatile and robust to various types of noise, and thus suitable for application to experimental data.

Background: Measures of spike train synchrony are widely used in both experimental and computational neuroscience. Time-scale independent and parameter-free measures, such as the ISI-distance, the SPIKE-distance and SPIKE-synchronization, are preferable to time scale parametric measures, since by adapting to the local firing rate they take into account all the time scales of a given dataset.

New method: In data containing multiple time scales (e.g. regular spiking and bursts) one is typically less interested in the smallest time scales and a more adaptive approach is needed. Here we propose the A-ISI-distance, the A-SPIKE-distance and A-SPIKE-synchronization, which generalize the original measures by considering the local relative to the global time scales. For the A-SPIKE-distance we also introduce a rate-independent extension called the RIA-SPIKE-distance, which focuses specifically on spike timing.

Results: The adaptive generalizations A-ISI-distance and A-SPIKE-distance allow to disregard spike time differences that are not relevant on a more global scale. A-SPIKE-synchronization does not any longer demand an unreasonably high accuracy for spike doublets and coinciding bursts. Finally, the RIA-SPIKE-distance proves to be independent of rate ratios between spike trains.

Comparison with existing methods: We find that compared to the original versions the A-ISI-distance and the A-SPIKE-distance yield improvements for spike trains containing different time scales without exhibiting any unwanted side effects in other examples. A-SPIKE-synchronization matches spikes more efficiently than SPIKE-synchronization.

Conclusions: With these proposals we have completed the picture, since we now provide adaptive generalized measures that are sensitive to firing rate only (A-ISI-distance), to timing only (ARI-SPIKE-distance),and to both at the same time (A-SPIKE-distance).

Repetitive spatio-temporal propagation patterns are encountered in fields as wide-ranging as climatology, social communication and network science. In neuroscience, perfectly consistent repetitions of the same global propagation pattern are called a synfire pattern. For any recording of sequences of discrete events (in neuroscience terminology: sets of spike trains) the questions arise how closely it resembles such a synfire pattern and which are the spike trains that lead/follow. Here we address these questions and introduce an algorithm built on two new indicators, termed SPIKE-order and spike train order, that define the synfire indicator value, which allows to sort multiple spike trains from leader to follower and to quantify the consistency of the temporal leader-follower relationships for both the original and the optimized sorting. We demonstrate our new approach using artificially generated datasets before we apply it to analyze the consistency of propagation patterns in two real datasets from neuroscience (giant depolarized potentials in mice slices) and climatology (El Niño sea surface temperature recordings). The new algorithm is distinguished by conceptual and practical simplicity, low computational cost, as well as flexibility and universality.

Measures of spike train synchrony have proven a valuable tool in both experimental and computational neuroscience. Particularly useful are time-resolved methods such as the ISI- and the SPIKE-distance, which have already been applied in various bivariate and multivariate contexts. Recently, SPIKE-Synchronization was proposed as another time-resolved synchronization measure. It is based on Event-Synchronization and has a very intuitive interpretation. Here, we present a detailed analysis of the mathematical properties of these three synchronization measures. For example, we were able to obtain analytic expressions for the expectation values of the ISI-distance and SPIKE-Synchronization for Poisson spike trains. For the SPIKE-distance we present an empirical formula deduced from numerical evaluations. These expectation values are crucial for interpreting the synchronization of spike trains measured in experiments or numerical simulations, as they represent the point of reference for fully randomized spike trains.

In a first step toward the comprehension of neural activity, one should focus on the stability of the possible dynamical states. Even the characterization of an idealized regime, such as that of a perfectly periodic spiking activity, reveals unexpected difficulties. In this paper we discuss a general approach to linear stability of pulse-coupled neural networks for generic phase-response curves and post-synaptic response functions. In particular, we present: (1) a mean-field approach developed under the hypothesis of an infinite network and small synaptic conductances; (2) a “microscopic” approach which applies to finite but large networks. As a result, we find that there exist two classes of perturbations: those which are perfectly described by the mean-field approach and those which are subject to finite-size corrections, irrespective of the network size. The analysis of perfectly regular, asynchronous, states reveals that their stability depends crucially on the smoothness of both the phase-response curve and the transmitted post-synaptic pulse. Numerical simulations suggest that this scenario extends to systems that are not covered by the perturbative approach. Altogether, we have described a series of tools for the stability analysis of various dynamical regimes of generic pulse-coupled oscillators, going beyond those that are currently invoked in the literature.

The detection of a nonrandom structure from experimental data can be crucial for the classification, understanding, and interpretation of the generating process. We here introduce a rank-based nonlinear predictability score to detect determinism from point process data. Thanks to its modular nature, this approach can be adapted to whatever signature in the data one considers indicative of deterministic structure. After validating our approach using point process signals from deterministic and stochastic model dynamics, we show an application to neuronal spike trains recorded in the brain of an epilepsy patient. While we illustrate our approach in the context of temporal point processes, it can be readily applied to spatial point processes as well.

The SPIKE-distance is an estimator of the dissimilarity between two (or more) spike trains. In contrast to most other spike train distances (such as the Victor-Purpura distance) it is time-resolved and is able to track changes in instantaneous clustering, i.e., time-localized patterns of (dis)similarity among two or more spike trains. Additional features include selective and triggered temporal averaging as well as the instantaneous comparison of spike train groups. The SPIKE-distance can also be formulated as a causal measure which is defined such that the instantaneous values of dissimilarity rely on past information only so that time-resolved spike train synchrony can be estimated in real-time.

The final definition presented here is the one introduced in Kreuz et al., 2013, which improves considerably on the original proposal (Kreuz et al., 2011). Mathematical properties and expectation values for Poisson spike train can be found in Mulansky et al., 2015.

Measures of neuronal signal synchrony are estimators of the synchrony between two or sometimes more continuous time series of brain activity which yield low values for independent time series and high values for correlated time series. A complementary class of approaches comprises measures of spike train synchrony which quantify the degree of synchrony between discrete signals.

Synchronization of continuous time series can manifest itself in many different ways. The simplest case of complete synchronization (Fujisaka and Yamada, 1983) can be attained if identical systems are coupled sufficiently strongly so that their states coincide after transients have died out. The concept of generalized synchronization (Afraimovich et al., 1986) introduced for uni-directionally coupled systems, describes the presence of some functional relation between the states of the two systems. Finally, phase synchronization, first described for chaotic oscillators (Rosenblum et al., 1996), is defined as the global entrainment of the phases while the amplitudes may remain uncorrelated.

Following this variety of concepts many different approaches to quantify the degree of synchronization between two continuous signals have been proposed. These approaches comprise linear ones like the cross correlation or the spectral coherence function as well as nonlinear measures like mutual information (Gray, 1990), transfer entropy (Schreiber, 2000), Granger causality (Granger, 1969), or the nonlinear interdependence (Arnhold et al., 1999; Quian Quiroga et al., 2002; Andrzejak et al., 2003). Furthermore, different indices of phase synchronization such as the mean phase coherence (Kuramoto, 1984; Mormann et al., 2000) have been introduced.

Experimental data comprising both time-continuous flows and point processes are recorded in many scientific disciplines. The characterization of causal interactions from such signals is key to an advanced understanding of the underlying dynamics. We therefore introduce a unified approach to characterize unidirectional couplings between point processes, between flows, as well as between point processes and flows. For this purpose we show and exploit the generality of the asymmetric state similarity conditioning principle. We use Hindmarsh-Rose neuron models and Lorenz oscillators to illustrate the high sensitivity and specificity of our approach.

A wide variety of approaches to estimate the degree of synchrony between two or more spike trains have been proposed. One of the most recent methods is the ISI-distance which extracts information from the interspike intervals (ISIs) by evaluating the ratio of the instantaneous firing rates. In contrast to most previously proposed measures it is parameter free and time-scale independent. However, it is not well suited to track changes in synchrony that are based on spike coincidences. Here we propose the SPIKE-distance, a complementary measure which is sensitive to spike coincidences but still shares the fundamental advantages of the ISI-distance. In particular, it is easy to visualize in a time-resolved manner and can be extended to a method that is also applicable to larger sets of spike trains. We show the merit of the SPIKE-distance using both simulated and real data.

Measures of multiple spike train synchrony are essential in order to study issues such as spike timing reliability, network synchronization, and neuronal coding. These measures can broadly be divided in multivariate measures and averages over bivariate measures. One of the most recent bivariate approaches, the ISI-distance, employs the ratio of instantaneous interspike intervals (ISIs). In this study we propose two extensions of the ISI-distance, the straightforward averaged bivariate ISI-distance and the multivariate ISI-diversity based on the coefficient of variation. Like the original measure these extensions combine many properties desirable in applications to real data. In particular, they are parameter-free, time scale independent, and easy to visualize in a time-resolved manner, as we illustrate with in vitro recordings from a cortical neuron. Using a simulated network of Hindemarsh–Rose neurons as a controlled configuration we compare the performance of our methods in distinguishing different levels of multi-neuron spike train synchrony to the performance of six other previously published measures. We show and explain why the averaged bivariate measures perform better than the multivariate ones and why the multivariate ISIdiversity is the best performer among the multivariate methods. Finally, in a comparison against standard methods that rely on moving window estimates, we use single-unit monkey data to demonstrate the advantages of the instantaneous nature of our methods.

We study the regularity of noise-induced excitations in the FitzHugh–Nagumo (FHN) neuronal model subject to excitatory and inhibitory high-frequency input with and without correlations. For each value of the correlation a relative maximum of spike coherence can be observed for intermediate noise strengths (coherence resonance). Moreover, the FHN system exhibits an absolute maximum of coherent spiking for intermediate values of both the noise amplitude and the strength of correlation (double coherence resonance). The underlying mechanisms can be explained by means of the discrete input statistics.

The investigation of synchronization phenomena on measured experimental data such as biological time series has recently become an increasing focus of interest. Different approaches for measuring synchronization have been proposed that rely on certain characteristic features of the dynamical system under investigation. For experimental data the underlying dynamics are usually not completely known, therefore it is difficult to decide a priori which synchronization measure is most suitable for an analysis. In this study we use three different coupled model systems to create a ‘controlled’ setting for a comparison of six different measures of synchronization. All measures are compared to each other with respect to their ability to distinguish between different levels of coupling and their robustness against noise. Results show that the measure to be applied to a certain task can not be chosen according to a fixed criterion but rather pragmatically as the measure which most reliably yields plausible information in test applications, although certain dynamical features of a system under investigation (e.g., power spectra, dimension) may render certain measures more suitable than others.

The response of the Hodgkin-Huxley neuronal model subjected to stochastic uncorrelated spike trains originating from a large number of inhibitory and excitatory post-synaptic potentials is analyzed in detail. The model is examined in its three fundamental dynamical regimes: silence, bistability, and repetitive firing. Its response is characterized in terms of statistical indicators interspike-interval distributions and their first moments as well as of dynamical indicators autocorrelation functions and conditional entropies. In the silent regime, the coexistence of two different coherence resonances is revealed: one occurs at quite low noise and is related to the stimulation of subthreshold oscillations around the rest state; the second one at intermediate noise variance is associated with the regularization of the sequence of spikes emitted by the neuron. Bistability in the low noise limit can be interpreted in terms of jumping processes across barriers activated by stochastic fluctuations. In the repetitive firing regime a maximization of incoherence is observed at finite noise variance. Finally, the mechanisms responsible for the different features appearing in the interspike-interval distributions like multimodality and exponential tails are clearly identified in the various regimes.

Objective: An important issue in epileptology is the question whether information extracted from the EEG of epilepsy patients can be used for the prediction of seizures. Several studies have claimed evidence for the existence of a pre-seizure state that can be detected using different characterizing measures. In this paper, we evaluate the predictability of seizures by comparing the predictive performance of a variety of univariate and bivariate measures comprising both linear and non-linear approaches.

Methods: We compared 30 measures in terms of their ability to distinguish between the interictal period and the pre-seizure period. After completely analyzing continuous inctracranial multi-channel recordings from five patients lasting over days, we used ROC curves to distinguish between the amplitude distributions of interictal and preictal time profiles calculated for the respective measures. We compared different evaluation schemes including channelwise and seizurewise analysis plus constant and adaptive reference levels. Particular emphasis was placed on statistical validity and significance.

Results: Univariate measures showed statistically significant performance only in a channelwise, seizurewise analysis using an adaptive baseline. Preictal changes for these measures occurred 5–30 min before seizures. Bivariate measures exhibited high performance values reaching statistical significance for a channelwise analysis using a constant baseline. Preictal changes were found at least 240 min before seizures. Linear measures were found to perform similar or better than non-linear measures.

Conclusions: Results provide statistically significant evidence for the existence of a preictal state. Based on our findings, the most promising approach for prospective seizure anticipation could be a combination of bivariate and univariate measures.

Significance: Many measures reported capable of seizure prediction in earlier studies are found to be insignificant in performance, which underlines the need for statistical validation in this field.

We demonstrate by means of a simple example that the arbitrariness of defining a phase from an aperiodic signal is not just an academic problem, but is more serious and fundamental. Decomposition of the signal into components with positive phase velocities is proposed as an old solution to this new problem.

We agree with the Comment by Duckrow and Albano [Phys. Rev. E 67, 063901 (2003)] that mutual information, estimated with an optimized algorithm, can be a useful tool for studying synchronization in real data. However, we point out that the improvement they found is mainly due to an interesting but nonstandard embedding technique used, and not so much due to the algorithm used for the estimation of mutual information itself. We also address the issue of stationarity of electroencephalographic (EEG) data

The exact mechanisms leading to the occurrence of epileptic seizures in humans are still poorly understood. It is widely accepted, however, that the process of seizure generation is closely associated with an abnormal synchronization of neurons. In order to investigate this process, we here measure phase synchronization between different regions of the brain using intracranial EEG recordings. Based on our preliminary finding of a preictal drop in synchronization, we investigate whether this phenomenon can be used as a sensitive and specific criterion to characterize a preseizure state and to distinguish this state from the interictal interval.

Applying an automated technique for detecting decreased synchronization to EEG recordings from a group of 18 patients with focal epilepsy comprising a total of 117 h, we observe a characteristic decrease in synchronization prior to 26 out of 32 analyzed seizures at a very high specificity as tested on interictal recordings. The duration of this preictal state is found to range from several minutes up to a few hours. Investigation of the spatial distribution of preictal desynchronization indicates that the process of seizure generation in focal epilepsy is not necessarily confined to the focus itself but may instead involve more distant, even contralateral areas of the brain. Finally, we demonstrate an intrahemispheric asymmetry in the spatial dynamics of preictal desynchronization that is found in the majority of seizures and appears to be an immanent part of the mechanisms underlying the initiation of seizures in humans.

Attempting to Increase Insight into the Spatio-Temporal Dynamics of the Epileptogenic Process to Address One of the Greatest Challenges in Epileptology

We propose a simple method to measure synchronization and time-delay patterns between signals. It is based on the relative timings of events in the time series, defined, e.g., as local maxima. The degree of synchronization is obtained from the number of quasisimultaneous appearances of events, and the delay is calculated from the precedence of events in one signal with respect to the other. Moreover, we can easily visualize the time evolution of the delay and synchronization level with an excellent resolution. We apply the algorithm to short rat electroencephalogram (EEG) signals, some of them containing spikes. We also apply it to an intracranial human EEG recording containing an epileptic seizure, and we propose that the method might be useful for the detection of epileptic foci. It can be easily extended to other types of data and it is very simple and fast, thus being suitable for on-line implementations.

Several recent studies emphasize the high value of nonlinear EEG analysis particularly for improved characterization of epileptic brain states. In this review the authors report their work to increase insight into the spatial and temporal dynamics of the epileptogenic process. Specifically, they discuss possibilities for seizure anticipation, which is one of the most challenging aspects of epileptology. Although there are numerous studies exploring basic neuronal mechanisms that are likely to be associated with seizures, to date no definite information is available regarding how, when, or why a seizure occurs. Nonlinear EEG analysis now provides strong evidence that the interictal–ictal state transition is not an abrupt phenomenon. Rather, findings indicate that it is indeed possible to detect a preseizure phase. The unequivocal definition of such a state with a sufficient length would enable investigations of basic mechanisms leading to seizure initiation in humans, and development of adequate seizure prevention strategies.