A multiscale symbolic approach to decoding delta and ripple oscillation bands as biomarkers for epileptiform discharges.

We use a multiscale symbolic approach to study the complex dynamics of temporal lobe refractory epilepsy employing high-resolution intracranial electroencephalogram (iEEG). We consider the basal and preictal phases and meticulously analyze the dynamics across frequency bands, focusing on high-frequency oscillations up to 240 Hz. Our results reveal significant periodicities and critical time scales within neural dynamics across frequency bands. By bandpass filtering neural signals into delta, theta, alpha, beta, gamma, and ripple high-frequency bands (HFO), each associated with specific neural processes, we examine the distinct nonlinear dynamics. Our method introduces a reliable approach to pinpoint intrinsic time lag scales τ within frequency bands of the basal and preictal signals, which are crucial for the study of refractory epilepsy. Using metrics such as permutation entropy (H), Fisher information (F), and complexity (C), we explore nonlinear patterns within iEEG signals. We reveal the intrinsic τmax that maximize complexity within each frequency band, unveiling the nonlinear subtle patterns of the temporal structures within the basal and preictal signal. Examining the H×F and C×F values allows us to identify differences in the delta band and a band between 200 and 220 Hz (HFO 6) when comparing basal and preictal signals. Differences in Fisher information in the delta and HFO 6 bands before seizures highlight their role in capturing important system dynamics. This offers new perspectives on the intricate relationship between delta oscillations and HFO waves in patients with focal epilepsy, highlighting the importance of these patterns and their potential as biomarkers.

Neural Dynamics Associated with Biological Variation in Normal Human Brain Regions.

The processes involved in encoding and decoding signals in the human brain are a continually studied topic, as neuronal information flow involves complex nonlinear dynamics. This study examines awake human intracranial electroencephalography (iEEG) data from normal brain regions to explore how biological sex influences these dynamics. The iEEG data were analyzed using permutation entropy and statistical complexity in the time domain and power spectrum calculations in the frequency domain. The Bandt and Pompe method was used to assess time series causality by associating probability distributions based on ordinal patterns with the signals. Due to the invasive nature of data acquisition, the study encountered limitations such as small sample sizes and potential sources of error. Nevertheless, the high spatial resolution of iEEG allows detailed analysis and comparison of specific brain regions. The results reveal differences between sexes in brain regions, observed through power spectrum, entropy, and complexity analyses. Significant differences were found in the left supramarginal gyrus, posterior cingulate, supplementary motor cortex, middle temporal gyrus, and right superior temporal gyrus. This study emphasizes the importance of considering sex as a biological variable in brain dynamics research, which is essential for improving the diagnosis and treatment of neurological and psychiatric disorders.

Chaotic dynamics of the Hénon map and neuronal input-output: A comparison with neurophysiological data.

In this study, the Hénon map was analyzed using quantifiers from information theory in order to compare its dynamics to experimental data from brain regions known to exhibit chaotic behavior. The goal was to investigate the potential of the Hénon map as a model for replicating chaotic brain dynamics in the treatment of Parkinson's and epilepsy patients. The dynamic properties of the Hénon map were compared with data from the subthalamic nucleus, the medial frontal cortex, and a q-DG model of neuronal input-output with easy numerical implementation to simulate the local behavior of a population. Using information theory tools, Shannon entropy, statistical complexity, and Fisher's information were analyzed, taking into account the causality of the time series. For this purpose, different windows over the time series were considered. The findings revealed that neither the Hénon map nor the q-DG model could perfectly replicate the dynamics of the brain regions studied. However, with careful consideration of the parameters, scales, and sampling used, they were able to model some characteristics of neural activity. According to these results, normal neural dynamics in the subthalamic nucleus region may present a more complex spectrum within the complexity-entropy causality plane that cannot be represented by chaotic models alone. The dynamic behavior observed in these systems using these tools is highly dependent on the studied temporal scale. As the size of the sample studied increases, the dynamics of the Hénon map become increasingly different from those of biological and artificial neural systems.

High-frequency oscillations in the ripple bands and amplitude information coding: Toward a biomarker of maximum entropy in the preictal signals.

Intracranial electroencephalography (iEEG) can directly record local field potentials (LFPs) from a large set of neurons in the vicinity of the electrode. To search for possible epileptic biomarkers and to determine the epileptogenic zone that gives rise to seizures, we investigated the dynamics of basal and preictal signals. For this purpose, we explored the dynamics of the recorded time series for different frequency bands considering high-frequency oscillations (HFO) up to 240 Hz. We apply a Hilbert transform to study the amplitude and phase of the signals. The dynamics of the different frequency bands in the time causal entropy-complexity plane, H × C, is characterized by comparing the dynamical evolution of the basal and preictal time series. As the preictal states evolve closer to the time in which the epileptic seizure starts, the, H × C, dynamics changes for the higher frequency bands. The complexity evolves to very low values and the entropy becomes nearer to its maximal value. These quasi-stable states converge to equiprobable states when the entropy is maximal, and the complexity is zero. We could, therefore, speculate that in this case, it corresponds to the minimization of Gibbs free energy. In this case, the maximum entropy is equivalent to the principle of minimum consumption of resources in the system. We can interpret this as the nature of the system evolving temporally in the preictal state in such a way that the consumption of resources by the system is minimal for the amplitude in frequencies between 220-230 and 230-240 Hz.

Spike Timing-Dependent Plasticity with Enhanced Long-Term Depression Leads to an Increase of Statistical Complexity.

Synaptic plasticity is characterized by remodeling of existing synapses caused by strengthening and/or weakening of connections. This is represented by long-term potentiation (LTP) and long-term depression (LTD). The occurrence of a presynaptic spike (or action potential) followed by a temporally nearby postsynaptic spike induces LTP; conversely, if the postsynaptic spike precedes the presynaptic spike, it induces LTD. This form of synaptic plasticity induction depends on the order and timing of the pre- and postsynaptic action potential, and has been termed spike time-dependent plasticity (STDP). After an epileptic seizure, LTD plays an important role as a depressor of synapses, which may lead to their complete disappearance together with that of their neighboring connections until days after the event. Added to the fact that after an epileptic seizure the network seeks to regulate the excess activity through two key mechanisms: depressed connections and neuronal death (eliminating excitatory neurons from the network), LTD becomes of great interest in our study. To investigate this phenomenon, we develop a biologically plausible model that privileges LTD at the triplet level while maintaining the pairwise structure in the STPD and study how network dynamics are affected as neuronal damage increases. We find that the statistical complexity is significantly higher for the network where LTD presented both types of interactions. While in the case where the STPD is defined with purely pairwise interactions an increase is observed as damage becomes higher for both Shannon Entropy and Fisher information.

Higher-Order Cumulants Drive Neuronal Activity Patterns, Inducing UP-DOWN States in Neural Populations.

A major challenge in neuroscience is to understand the role of the higher-order correlations structure of neuronal populations. The dichotomized Gaussian model (DG) generates spike trains by means of thresholding a multivariate Gaussian random variable. The DG inputs are Gaussian distributed, and thus have no interactions beyond the second order in their inputs; however, they can induce higher-order correlations in the outputs. We propose a combination of analytical and numerical techniques to estimate higher-order, above the second, cumulants of the firing probability distributions. Our findings show that a large amount of pairwise interactions in the inputs can induce the system into two possible regimes, one with low activity ("DOWN state") and another one with high activity ("UP state"), and the appearance of these states is due to a combination between the third- and fourth-order cumulant. This could be part of a mechanism that would help the neural code to upgrade specific information about the stimuli, motivating us to examine the behavior of the critical fluctuations through the Binder cumulant close to the critical point. We show, using the Binder cumulant, that higher-order correlations in the outputs generate a critical neural system that portrays a second-order phase transition.

Information Theoretic Measures and Their Applications.

The concept of entropy, an ever-growing physical magnitude that measured the degree of decay of order in a physical system, was introduced by Rudolf Clausius in 1865 through an elegant formulation of the second law of thermodynamics [...].

Rhythmic activities of the brain: Quantifying the high complexity of beta and gamma oscillations during visuomotor tasks.

Electroencephalography (EEG) signals depict the electrical activity that takes place at the surface of the brain and provide an important tool for understanding a variety of cognitive processes. The EEG is the product of synchronized activity of the brain, and variations in EEG oscillations patterns reflect the underlying changes in neuronal synchrony. Our aim is to characterize the complexity of the EEG rhythmic oscillations bands when the subjects perform a visuomotor or imagined cognitive tasks (imagined movement), providing a causal mapping of the dynamical rhythmic activities of the brain as a measure of attentional investment. We estimate the intrinsic correlational structure of the signals within the causality entropy-complexity plane H×C, where the enhanced complexity in the gamma 1, gamma 2, and beta 1 bands allows us to distinguish motor-visual memory tasks from control conditions. We identify the dynamics of the gamma 1, gamma 2, and beta 1 rhythmic oscillations within the zone of a chaotic dissipative behavior, whereas in contrast the beta 2 band shows a much higher level of entropy and a significant low level of complexity that correspond to a non-invertible cubic map. Our findings enhance the importance of the gamma band during attention in perceptual feature binding during the visuomotor/imagery tasks.

Causal Shannon-Fisher Characterization of Motor/Imagery Movements in EEG.

The electroencephalogram (EEG) is an electrophysiological monitoring method that allows us to glimpse the electrical activity of the brain. Neural oscillations patterns are perhaps the best salient feature of EEG as they are rhythmic activities of the brain that can be generated by interactions across neurons. Large-scale oscillations can be measured by EEG as the different oscillation patterns reflected within the different frequency bands, and can provide us with new insights into brain functions. In order to understand how information about the rhythmic activity of the brain during visuomotor/imagined cognitive tasks is encoded in the brain we precisely quantify the different features of the oscillatory patterns considering the Shannon-Fisher plane H × F . This allows us to distinguish the dynamics of rhythmic activities of the brain showing that the Beta band facilitate information transmission during visuomotor/imagined tasks.

A symbolic information approach to determine anticipated and delayed synchronization in neuronal circuit models.

The phenomenon of synchronization between two or more areas of the brain coupled asymmetrically is a relevant issue for understanding mechanisms and functions within the cerebral cortex. Anticipated synchronization (AS) refers to the situation in which the receiver system synchronizes to the future dynamics of the sender system while the intuitively expected delayed synchronization (DS) represents exactly the opposite case. AS and DS are investigated in the context of causal information formalism. More specifically, we use a multi-scale symbolic information-theory approach for discriminating the time delay displayed between two areas of the brain when they exchange information.

Rényi entropy-complexity causality space: a novel neurocomputational tool for detecting scale-free features in EEG/iEEG data.

Scale-free brain activity, linked with learning, the integration of different time scales, and the formation of mental models, is correlated with a metastable cognitive basis. The spectral slope, a key aspect of scale-free dynamics, was proposed as a potential indicator to distinguish between different sleep stages. Studies suggest that brain networks maintain a consistent scale-free structure across wakefulness, anesthesia, and recovery. Although differences in anesthetic sensitivity between the sexes are recognized, these variations are not evident in clinical electroencephalographic recordings of the cortex. Recently, changes in the slope of the power law exponent of neural activity were found to correlate with changes in Rényi entropy, an extended concept of Shannon's information entropy. These findings establish quantifiers as a promising tool for the study of scale-free dynamics in the brain. Our study presents a novel visual representation called the Rényi entropy-complexity causality space, which encapsulates complexity, permutation entropy, and the Rényi parameter q. The main goal of this study is to define this space for classical dynamical systems within theoretical bounds. In addition, the study aims to investigate how well different time series mimicking scale-free activity can be discriminated. Finally, this tool is used to detect dynamic features in intracranial electroencephalography (iEEG) signals. To achieve these goals, the study implementse the Bandt and Pompe method for ordinal patterns. In this process, each signal is associated with a probability distribution, and the causal measures of Rényi entropy and complexity are computed based on the parameter q. This method is a valuable tool for analyzing simulated time series. It effectively distinguishes elements of correlated noise and provides a straightforward means of examining differences in behaviors, characteristics, and classifications. For the iEEG experimental data, the REM state showed a greater number of significant sex-based differences, while the supramarginal gyrus region showed the most variation across different modes and analyzes. Exploring scale-free brain activity with this framework could provide valuable insights into cognition and neurological disorders. The results may have implications for understanding differences in brain function between the sexes and their possible relevance to neurological disorders.

Characterizing the information transmission of inverse stochastic resonance and noise-induced activity amplification in neuronal systems.

Purkinje cells exhibit a reduction of the mean firing rate at intermediate-noise intensities, which is somewhat reminiscent of the response enhancement known as "stochastic resonance" (SR). Although the comparison with the stochastic resonance ends here, the current phenomenon has been given the name "inverse stochastic resonance" (ISR). Recent research has demonstrated that the ISR effect, like its close relative "nonstandard SR" [or, more correctly, noise-induced activity amplification (NIAA)], has been shown to stem from the weak-noise quenching of the initial distribution, in bistable regimes where the metastable state has a larger attraction basin than the global minimum. To understand the underlying mechanism of the ISR and NIAA phenomena, we study the probability distribution function of a one-dimensional system subjected to a bistable potential that has the property of symmetry, i.e., if we change the sign of one of its parameters, we can obtain both phenomena with the same properties in the depth of the wells and the width of their basins of attraction subjected to Gaussian white noise with variable intensity. Previous work has shown that one can theoretically determine the probability distribution function using the convex sum between the behavior at small and high noise intensities. To determine the probability distribution function more precisely, we resort to the "weighted ensemble Brownian dynamics simulation" model, which provides an accurate estimate of the probability distribution function for both low and high noise intensities and, most importantly, for the transition of both behaviors. In this way, on the one hand, we show that both phenomena emerge from a metastable system where, in the case of ISR, the global minimum of the system is in a state of lower activity, while in the case of NIAA, the global minimum is in a state of increased activity, the importance of which does not depend on the width of the basins of attraction. On the other hand, we see that quantifiers such as Fisher information, statistical complexity, and especially Shannon entropy fail to distinguish them, but they show the existence of the mentioned phenomena. Thus, noise management may well be a mechanism by which Purkinje cells find an efficient way to transmit information in the cerebral cortex.

Automatic online spike sorting with singular value decomposition and fuzzy C-mean clustering.

BACKGROUND: Understanding how neurons contribute to perception, motor functions and cognition requires the reliable detection of spiking activity of individual neurons during a number of different experimental conditions. An important problem in computational neuroscience is thus to develop algorithms to automatically detect and sort the spiking activity of individual neurons from extracellular recordings. While many algorithms for spike sorting exist, the problem of accurate and fast online sorting still remains a challenging issue. RESULTS: Here we present a novel software tool, called FSPS (Fuzzy SPike Sorting), which is designed to optimize: (i) fast and accurate detection, (ii) offline sorting and (iii) online classification of neuronal spikes with very limited or null human intervention. The method is based on a combination of Singular Value Decomposition for fast and highly accurate pre-processing of spike shapes, unsupervised Fuzzy C-mean, high-resolution alignment of extracted spike waveforms, optimal selection of the number of features to retain, automatic identification the number of clusters, and quantitative quality assessment of resulting clusters independent on their size. After being trained on a short testing data stream, the method can reliably perform supervised online classification and monitoring of single neuron activity. The generalized procedure has been implemented in our FSPS spike sorting software (available free for non-commercial academic applications at the address: http://www.spikesorting.com) using LabVIEW (National Instruments, USA). We evaluated the performance of our algorithm both on benchmark simulated datasets with different levels of background noise and on real extracellular recordings from premotor cortex of Macaque monkeys. The results of these tests showed an excellent accuracy in discriminating low-amplitude and overlapping spikes under strong background noise. The performance of our method is competitive with respect to other robust spike sorting algorithms. CONCLUSIONS: This new software provides neuroscience laboratories with a new tool for fast and robust online classification of single neuron activity. This feature could become crucial in situations when online spike detection from multiple electrodes is paramount, such as in human clinical recordings or in brain-computer interfaces.

Abnormal EEG signal energy in the elderly: A wavelet analysis of event-related potentials during a stroop task.

BACKGROUND: Previous work showed that elderly with excess in theta activity in their resting state electroencephalogram (EEG) are at higher risk of cognitive decline than those with a normal EEG. By using event-related potentials (ERP) during a counting Stroop task, our prior work showed that elderly with theta excess have a large P300 component compared with normal EEG group. This increased activity could be related to a higher EEG signal energy used during this task. NEW METHOD: By wavelet analysis applied to ERP obtained during a counting Stroop task we quantified the energy in the different frequency bands of a group of elderly with altered EEG. RESULTS: In theta and alpha bands, the total energy was higher in elderly subjects with theta excess, specifically in the stimulus categorization window (258-516 ms). Both groups solved the task with similar efficiency. COMPARISON WITH EXISTING METHODS: The traditional ERP analysis in elderly compares voltage among conditions and groups for a given time window, while the frequency composition is not usually examined. We complemented our previous ERP analysis using a wavelet methodology. Furthermore, we showed the advantages of wavelet analysis over Short Time Fourier Transform when exploring EEG signal during this task. CONCLUSIONS: The higher EEG signal energy in ERP might reflect undergoing neurobiological mechanisms that allow the elderly with theta excess to cope with the cognitive task with similar behavioral results as the normal EEG group. This increased energy could promote a metabolic and cellular dysregulation causing a greater decline in cognitive function.

Heterogeneity across neural populations: Its significance for the dynamics and functions of neural circuits.

Neural populations show patterns of synchronous activity, as they share common correlated inputs. Neurons in the cortex that are connected by strong synapses cause rapid firing explosions. In addition, areas that are connected by weaker synapses have a slower dynamics and they can contribute to asymmetries in the input distributions. The aim of this work is to develop a neural model to investigate how the heterogeneities in the synaptic input distributions affect different levels of organizational activity in the brain dynamics. We analytically show how small changes in the correlation inputs can cause large changes in the interactions of the outputs that lead to a phase transition, demonstrating that a simple variation in the direction of a biased skewed distribution in the neuronal inputs can generate a transition of states in the firing rate, passing from spontaneous silence ("down state") to an absolute spiking activity ("up state"). We present an exact quantification of the dynamics of the output variables, showing that when considering a biased skewed distribution in the inputs of neuronal population, the critical point is not in an asynchronous or synchronous state but rather at an intermediate value.

The role of correlations in direction and contrast coding in the primary visual cortex.

The spiking activity of nearby cortical neurons is not independent. Numerous studies have explored the importance of this correlated responsivity for visual coding and perception, often by comparing the information conveyed by pairs of simultaneously recorded neurons with the sum of information provided by the respective individual cells. Pairwise responses typically provide slightly more information so that encoding is weakly synergistic. The simple comparison between pairwise and summed individual responses conflates several forms of correlation, however, making it impossible to judge the relative importance of synchronous spiking, basic tuning properties, and stimulus-independent and stimulus-dependent correlation. We have applied an information theoretic approach to this question, using the responses of pairs of neurons to drifting sinusoidal gratings of different directions and contrasts that have been recorded in the primary visual cortex of anesthetized macaque monkeys. Our approach allows us to break down the information provided by pairs of neurons into a number of components. This analysis reveals that, although synchrony is prevalent and informative, the additional information it provides frequently is offset by the redundancy arising from the similar tuning properties of the two cells. Thus coding is approximately independent with weak synergy or redundancy arising, depending on the similarity in tuning and the temporal precision of the analysis. We suggest that this would allow cortical circuits to enjoy the stability provided by having similarly tuned neurons without suffering the penalty of redundancy, because the associated information transmission deficit is compensated for by stimulus-dependent synchrony.

Common inputs in subthreshold membrane potential: The role of quiescent states in neuronal activity.

Experiments in certain regions of the cerebral cortex suggest that the spiking activity of neuronal populations is regulated by common non-Gaussian inputs across neurons. We model these deviations from random-walk processes with q-Gaussian distributions into simple threshold neurons, and investigate the scaling properties in large neural populations. We show that deviations from the Gaussian statistics provide a natural framework to regulate population statistics such as sparsity, entropy, and specific heat. This type of description allows us to provide an adequate strategy to explain the information encoding in the case of low neuronal activity and its possible implications on information transmission.

Superlinear Summation of Information in Premotor Neuron Pairs.

Whether premotor/motor neurons encode information in terms of spiking frequency or by their relative time of firing, which may display synchronization, is still undetermined. To address this issue, we used an information theory approach to analyze neuronal responses recorded in the premotor (area F5) and primary motor (area F1) cortices of macaque monkeys under four different conditions of visual feedback during hand grasping. To evaluate the sensitivity of spike timing correlation between single neurons, we investigated the stimulus dependent synchronization in our population of pairs. We first investigated the degree of correlation of trial-to-trial fluctuations in response strength between neighboring neurons for each condition, and second estimated the stimulus dependent synchronization by means of an information theoretical approach. We compared the information conveyed by pairs of simultaneously recorded neurons with the sum of information provided by the respective individual cells. The information transmission across pairs of cells in the primary motor cortex seems largely independent, whereas information transmission across pairs of premotor neurons is summed superlinearly. The brain could take advantage of both the accuracy provided by the independency of F1 and the synergy allowed by the superlinear information population coding in F5, distinguishing thus the generalizing role of F5.

Effect of interacting second- and third-order stimulus-dependent correlations on population-coding asymmetries.

Spike correlations among neurons are widely encountered in the brain. Although models accounting for pairwise interactions have proved able to capture some of the most important features of population activity at the level of the retina, the evidence shows that pairwise neuronal correlation analysis does not resolve cooperative population dynamics by itself. By means of a series expansion for short time scales of the mutual information conveyed by a population of neurons, the information transmission can be broken down into firing rate and correlational components. In a proposed extension of this framework, we investigate the information components considering both second- and higher-order correlations. We show that the existence of a mixed stimulus-dependent correlation term defines a new scenario for the interplay between pairwise and higher-than-pairwise interactions in noise and signal correlations that would lead either to redundancy or synergy in the information-theoretic sense.

Causal information quantification of prominent dynamical features of biological neurons.

Neurons tend to fire a spike when they are near a bifurcation from the resting state to spiking activity. It is a delicate balance between noise, dynamic currents and initial condition that determines the phase diagram of neural activity. Many possible ionic mechanisms can be accounted for as the source of spike generation. Moreover, the biophysics and the dynamics behind it can usually be described through a phase diagram that involves membrane voltage versus the activation variable of the ionic channel. In this paper, we present a novel methodology to characterize the dynamics of this system, which takes into account the fine temporal 'structures' of the complex neuronal signals. This allows us to accurately distinguish the most fundamental properties of neurophysiological neurons that were previously described by Izhikevich considering the phase-space trajectory, using a time causal space: statistical complexity versus Fisher information versus Shannon entropy.