Self-Sustaining Oscillations in Complex Networks of Excitable Elements

Random networks of symmetrically coupled, excitable elements can self-organize into coherently oscillating states if the networks contain loops (indeed loops are abundant in random networks) and if the initial conditions are sufficiently random. In the oscillating state, signals propagate in a single direction and one or a few network loops are selected as driving loops in which the excitation circulates periodically. We analyze the mechanism, describe the oscillating states, identify the pacemaker loops and explain key features of their distribution. This mechanism may play a role in epileptic seizures.Comment: 5 pages, 4 figures included, submitted to Phys. Rev. Let

A role for fast rhythmic bursting neurons in cortical gamma oscillations in vitro

Basic cellular and network mechanisms underlying gamma frequency oscillations (30–80 Hz) have been well characterized in the hippocampus and associated structures. In these regions, gamma rhythms are seen as an emergent property of networks of principal cells and fast-spiking interneurons. In contrast, in the neocortex a number of elegant studies have shown that specific types of principal neuron exist that are capable of generating powerful gamma frequency outputs on the basis of their intrinsic conductances alone. These fast rhythmic bursting (FRB) neurons (sometimes referred to as "chattering" cells) are activated by sensory stimuli and generate multiple action potentials per gamma period. Here, we demonstrate that FRB neurons may function by providing a large-scale input to an axon plexus consisting of gap-junctionally connected axons from both FRB neurons and their anatomically similar counterparts regular spiking neurons. The resulting network gamma oscillation shares all of the properties of gamma oscillations generated in the hippocampus but with the additional critical dependence on multiple spiking in FRB cells

The Neuronal Transition Probability (NTP) Model for the Dynamic Progression of Non-REM Sleep EEG: The Role of the Suprachiasmatic Nucleus

Little attention has gone into linking to its neuronal substrates the dynamic structure of non-rapid-eye-movement (NREM) sleep, defined as the pattern of time-course power in all frequency bands across an entire episode. Using the spectral power time-courses in the sleep electroencephalogram (EEG), we showed in the typical first episode, several moves towards-and-away from deep sleep, each having an identical pattern linking the major frequency bands beta, sigma and delta. The neuronal transition probability model (NTP) – in fitting the data well – successfully explained the pattern as resulting from stochastic transitions of the firing-rates of the thalamically-projecting brainstem-activating neurons, alternating between two steady dynamic-states (towards-and-away from deep sleep) each initiated by a so-far unidentified flip-flop. The aims here are to identify this flip-flop and to demonstrate that the model fits well all NREM episodes, not just the first. Using published data on suprachiasmatic nucleus (SCN) activity we show that the SCN has the information required to provide a threshold-triggered flip-flop for timing the towards-and-away alternations, information provided by sleep-relevant feedback to the SCN. NTP then determines the pattern of spectral power within each dynamic-state. NTP was fitted to individual NREM episodes 1–4, using data from 30 healthy subjects aged 20–30 years, and the quality of fit for each NREM measured. We show that the model fits well all NREM episodes and the best-fit probability-set is found to be effectively the same in fitting all subject data. The significant model-data agreement, the constant probability parameter and the proposed role of the SCN add considerable strength to the model. With it we link for the first time findings at cellular level and detailed time-course data at EEG level, to give a coherent picture of NREM dynamics over the entire night and over hierarchic brain levels all the way from the SCN to the EEG

Consistency and diversity of spike dynamics in the neurons of bed nucleus of Stria Terminalis of the rat: a dynamic clamp study

Neurons display a high degree of variability and diversity in the expression and regulation of their voltage-dependent ionic channels. Under low level of synaptic background a number of physiologically distinct cell types can be identified in most brain areas that display different responses to standard forms of intracellular current stimulation. Nevertheless, it is not well understood how biophysically different neurons process synaptic inputs in natural conditions, i.e., when experiencing intense synaptic bombardment in vivo. While distinct cell types might process synaptic inputs into different patterns of action potentials representing specific "motifs'' of network activity, standard methods of electrophysiology are not well suited to resolve such questions. In the current paper we performed dynamic clamp experiments with simulated synaptic inputs that were presented to three types of neurons in the juxtacapsular bed nucleus of stria terminalis (jcBNST) of the rat. Our analysis on the temporal structure of firing showed that the three types of jcBNST neurons did not produce qualitatively different spike responses under identical patterns of input. However, we observed consistent, cell type dependent variations in the fine structure of firing, at the level of single spikes. At the millisecond resolution structure of firing we found high degree of diversity across the entire spectrum of neurons irrespective of their type. Additionally, we identified a new cell type with intrinsic oscillatory properties that produced a rhythmic and regular firing under synaptic stimulation that distinguishes it from the previously described jcBNST cell types. Our findings suggest a sophisticated, cell type dependent regulation of spike dynamics of neurons when experiencing a complex synaptic background. The high degree of their dynamical diversity has implications to their cooperative dynamics and synchronization

Quantification of depth of anesthesia by nonlinear time series analysis of brain electrical activity

We investigate several quantifiers of the electroencephalogram (EEG) signal with respect to their ability to indicate depth of anesthesia. For 17 patients anesthetized with Sevoflurane, three established measures (two spectral and one based on the bispectrum), as well as a phase space based nonlinear correlation index were computed from consecutive EEG epochs. In absence of an independent way to determine anesthesia depth, the standard was derived from measured blood plasma concentrations of the anesthetic via a pharmacokinetic/pharmacodynamic model for the estimated effective brain concentration of Sevoflurane. In most patients, the highest correlation is observed for the nonlinear correlation index D*. In contrast to spectral measures, D* is found to decrease monotonically with increasing (estimated) depth of anesthesia, even when a "burst-suppression" pattern occurs in the EEG. The findings show the potential for applications of concepts derived from the theory of nonlinear dynamics, even if little can be assumed about the process under investigation.Comment: 7 pages, 5 figure

Does the 1/f frequency-scaling of brain signals reflect self-organized critical states?

Many complex systems display self-organized critical states characterized by 1/f frequency scaling of power spectra. Global variables such as the electroencephalogram, scale as 1/f, which could be the sign of self-organized critical states in neuronal activity. By analyzing simultaneous recordings of global and neuronal activities, we confirm the 1/f scaling of global variables for selected frequency bands, but show that neuronal activity is not consistent with critical states. We propose a model of 1/f scaling which does not rely on critical states, and which is testable experimentally.Comment: 3 figures, 6 page

Synaptic Transmission and Plasticity in an Active Cortical Network

BACKGROUND: The cerebral cortex is permanently active during both awake and sleep states. This ongoing cortical activity has an impact on synaptic transmission and short-term plasticity. An activity pattern generated by the cortical network is a slow rhythmic activity that alternates up (active) and down (silent) states, a pattern occurring during slow wave sleep, anesthesia and even in vitro. Here we have studied 1) how network activity affects short term synaptic plasticity and, 2) how synaptic transmission varies in up versus down states. METHODOLOGY/PRINCIPAL FINDINGS: Intracellular recordings obtained from cortex in vitro and in vivo were used to record synaptic potentials, while presynaptic activation was achieved either with electrical or natural stimulation. Repetitive activation of layer 4 to layer 2/3 synaptic connections from ferret visual cortex slices displayed synaptic augmentation that was larger and longer lasting in active than in silent slices. Paired-pulse facilitation was also significantly larger in an active network and it persisted for longer intervals (up to 200 ms) than in silent slices. Intracortical synaptic potentials occurring during up states in vitro increased their amplitude while paired-pulse facilitation disappeared. Both intracortical and thalamocortical synaptic potentials were also significantly larger in up than in down states in the cat visual cortex in vivo. These enhanced synaptic potentials did not further facilitate when pairs of stimuli were given, thus paired-pulse facilitation during up states in vivo was virtually absent. Visually induced synaptic responses displayed larger amplitudes when occurring during up versus down states. This was further tested in rat barrel cortex, where a sensory activated synaptic potential was also larger in up states. CONCLUSIONS/SIGNIFICANCE: These results imply that synaptic transmission in an active cortical network is more secure and efficient due to larger amplitude of synaptic potentials and lesser short term plasticity

Neocortical hyperexcitability in a genetic model of absence seizures and its reduction by levetiracetam

PURPOSE: To study the effect of the antiepileptic drug levetiracetam (LEV) on the patterns of intrinsic optical signals (IOSs) generated by slices of the somatosensory cortex obtained from 3- and 6-month-old WAG/Rij and age-matched, nonepileptic control (NEC) rats. METHODS: WAG/Rij and NEC animals were anesthetized with enfluorane and decapitated. Brains were quickly removed, and neocortical slices were cut coronally with a vibratome, transferred to a submerged tissue chamber, and superfused with oxygenated artificial cerebrospinal fluid (aCSF). Slices were illuminated with a dark-field condensor and examined with a x2.5 objective; images were processed with a real time digital video image-enhancement system. Images were acquired before (background) and during electrical stimulation with a temporal resolution of 10 images/s and were displayed in pseudocolors. Extracellular stimuli (200 micros; <4 V) were delivered through bipolar stainless steel electrodes placed in the white matter. RESULTS: IOSs recorded in NEC slices bathed in control aCSF became less intense and of reduced size with age (p < 0.05); this trend was not seen in WAG/Rij slices. Age-dependent decreases in IOS intensity and area size were also seen in NEC slices superfused with aCSF containing the convulsant 4-aminopyridine (4-AP, 5 microM); in contrast, significant increases in both parameters occurred with age in 4-AP-treated WAG/Rij slices (p < 0.05). Under any of these conditions, the IOS intensity and area size slices were larger in WAG/Rij than in NEC slices. LEV (50-500 microM) application to WAG/Rij slices caused dose-dependent IOS reductions that were evident both in control and in 4-AP-containing aCSF and were more pronounced in 6-month-old tissue. CONCLUSIONS: These data demonstrate age-dependent IOS modifications in NEC and WAG/Rij rat slices and identify a clear pattern of hyperexcitability that occurs in 6-month-old WAG/Rij neocortical tissue, an age when absence seizures occur in all animals. The ability of LEV to reduce these patterns of network hyperexcitability supports the potential use of this new antiepileptic drug in primary generalized epileptic disorders

Detecting K-complexes for sleep stage identification using nonsmooth optimisation

The process of sleep stage identification is a labour-intensive task that involves the specialized interpretation of the polysomnographic signals captured from a patient&rsquo;s overnight sleep session. Automating this task has proven to be challenging for data mining algorithms because of noise, complexity and the extreme size of data. In this paper we apply nonsmooth optimization to extract key features that lead to better accuracy. We develop a specific procedure for identifying K-complexes, a special type of brain wave crucial for distinguishing sleep stages. The procedure contains two steps. We first extract &ldquo;easily classified&rdquo; K-complexes, and then apply nonsmooth optimization methods to extract features from the remaining data and refine the results from the first step. Numerical experiments show that this procedure is efficient for detecting K-complexes. It is also found that most classification methods perform significantly better on the extracted features

Effective Reduced Diffusion-Models: A Data Driven Approach to the Analysis of Neuronal Dynamics

We introduce in this paper a new method for reducing neurodynamical data to an effective diffusion equation, either experimentally or using simulations of biophysically detailed models. The dimensionality of the data is first reduced to the first principal component, and then fitted by the stationary solution of a mean-field-like one-dimensional Langevin equation, which describes the motion of a Brownian particle in a potential. The advantage of such description is that the stationary probability density of the dynamical variable can be easily derived. We applied this method to the analysis of cortical network dynamics during up and down states in an anesthetized animal. During deep anesthesia, intracellularly recorded up and down states transitions occurred with high regularity and could not be adequately described by a one-dimensional diffusion equation. Under lighter anesthesia, however, the distributions of the times spent in the up and down states were better fitted by such a model, suggesting a role for noise in determining the time spent in a particular state