Weak electric fields detectability in a noisy neural network

We investigate the detectability of weak electric field in a noisy neural network based on Izhikevich neuron model systematically. The neural network is composed of excitatory and inhibitory neurons with similar ratio as that in the mammalian neocortex, and the axonal conduction delays between neurons are also considered. It is found that the noise intensity can modulate the detectability of weak electric field. Stochastic resonance (SR) phenomenon induced by white noise is observed when the weak electric field is added to the network. It is interesting that SR almost disappeared when the connections between neurons are cancelled, suggesting the amplification effects of the neural coupling on the synchronization of neuronal spiking. Furthermore, the network parameters, such as the connection probability, the synaptic coupling strength, the scale of neuron population and the neuron heterogeneity, can also affect the detectability of the weak electric field. Finally, the model sensitivity is studied in detail, and results show that the neural network model has an optimal region for the detectability of weak electric field signal.     

Emergence of resonances in neural systems: the interplay between adaptive threshold and short-term synaptic plasticity

In this work we study the detection of weak stimuli by spiking (integrate-and-fire) neurons in the presence of certain level of noisy background neural activity. Our study has focused in the realistic assumption that the synapses in the network present activity-dependent processes, such as short-term synaptic depression and facilitation. Employing mean-field techniques as well as numerical simulations, we found that there are two possible noise levels which optimize signal transmission. This new finding is in contrast with the classical theory of stochastic resonance which is able to predict only one optimal level of noise. We found that the complex interplay between adaptive neuron threshold and activity-dependent synaptic mechanisms is responsible for this new phenomenology. Our main results are confirmed by employing a more realistic FitzHugh-Nagumo neuron model, which displays threshold variability, as well as by considering more realistic stochastic synaptic models and realistic signals such as poissonian spike trains.     

STOCHASTIC RESONANCE MEASURED BY THEMUTUAL INFORMATION IN THE NEURONSTHAT TRANSMIT CHAOTIC SPIKE TRAINS

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双层Hodgkin-Huxley神经元网络中的随机共振

随机共振是一种非零噪声优化系统响应的现象。运用信噪比的评价方式,研究单个Hodgkin-Huxley神经元及其所构建的双层神经元网络中的随机共振,来模拟生物感觉系统中检测微弱信号的随机共振现象。结果表明,单个神经元在阈值下存在噪声优化系统检测性能的随机共振现象,但是最优的噪声强度却随外部信号性质的改变而变化;双层神经元网络不但可以在固定的噪声强度上对一定幅度范围内的阈下信号进行优化检测,而且噪声的存在并没有降低网络对阈上信号的检测能力。     

STOCHASTIC RESONANCE MEASURED BY THEMUTUAL INFORMATION IN THE NEURONSTHAT TRANSMIT CHAOTIC SPIKE TRAINS

The spike trains generated by a neuron model are studied by the methods of nonlinear time series analysis. The results show that the spike trains are chaotic. To investigate effect of noise on transmission of chaotic spike trains, this chaotic spike trains are used as a discrete subthreshold input signal to the integrate-and-fire neuronal model and the FitzHugh-Nagumo(FHN) neuronal model working in noisy environment. The mutual information between the input spike trains and the output spike trains is calculated, the result shows that the transformation of information encoded by the chaotic spike trains is optimized by some level of noise, and stochastic resonance(SR) measured by mutual information is a property available for neurons to transmit chaotic spike trains.     

Stochastic resonance in a single neuron model: theory and analog simulation.

Here, we consider a noisy, bistable, single neuron model in the presence of periodic external modulation. The modulation induces a correlated switching between states driven by the noise. The information flow through the system, from the modulation, or signal, to the output switching events, leads to a succession of strong peaks in the power spectrum. The signal-to-noise ratio (SNR) obtained from this power spectrum is a measure of the information content in the neuron response. With increasing noise intensity, the SNR passes through a maximum: an effect which has been called stochastic resonance, and which was first advanced as a possible explanation of the observed periodicity in the recurrences of the Earth's ice ages. We treat the problem within the framework of a recently developed approximate theory, valid in the limits of weak noise intensity, weak periodic forcing and low forcing frequency, for both additive and multiplicative noise. Moreover, we have constructed an analog simulator of the neuron which demonstrates the stochastic resonance effect, and with which we have measured the SNRs for comparison with the theoretical results. Our model should be of interest in situations where a single inherently noisy neuron is the receptor of a periodic signal, which is itself noisy, either from the network or from an external source.     

Aperiodic stochastic resonance in neural information processing with Gaussian colored noise

The aim of this paper is to explore the phenomenon of aperiodic stochastic resonance in neural systems with colored noise. For nonlinear dynamical systems driven by Gaussian colored noise, we prove that the stochastic sample trajectory can converge to the corresponding deterministic trajectory as noise intensity tends to zero in mean square, under global and local Lipschitz conditions, respectively. Then, following forbidden interval theorem we predict the phenomenon of aperiodic stochastic resonance in bistable and excitable neural systems. Two neuron models are further used to verify the theoretical prediction. Moreover, we disclose the phenomenon of aperiodic stochastic resonance induced by correlation time and this finding suggests that adjusting noise correlation might be a biologically more plausible mechanism in neural signal processing.     

Izhikevich神经元网络的同步与联想记忆

联想记忆是人脑的一项重要功能。以Izhikevich神经元模型为节点,构建神经网络,神经元之间采用全连结的方式;以神经元群体的时空编码（spatio-temporal coding）理论研究所构建神经网络的联想记忆功能。在加入高斯白噪声的情况下,调节网络中神经元之间的连接强度的大小,当连接强度和噪声强度达到一个阈值时网络中部分神经元同步放电,实现了存储模式的联想记忆与恢复。仿真结果表明,神经元之间的连接强度在联想记忆的过程中发挥了重要的作用,噪声可以促使神经元间的同步放电,有助于神经网络实现存储模式的联想记忆与恢复。     

Role of refractory period in homoclinic models of neural synchronization

We study the properties of a homoclinic model of neuron by introducing a suitable one-dimensional map. We show that the system is characterized by a response time to external signals which is a decreasing function of the signal strength, in contrast to excitable models whose response time is signal-independent. In a one-dimensional array of these systems with bidirectional coupling, we observe a sudden transition to a synchronized state at a certain value of the coupling strength. The transition occurs when the response time of a site to the signals of the adjacent sites is of the order of refractory time. Near the transition, we find an intermittent behavior due to the competition between a turbulent and a synchronized state. The observed behavior distinguishes homoclinic systems from excitable systems.     

Noise enhances subthreshold oscillations in injured primary sensory neurons

Noise can play a constructive role in the detection of weak signals in various kinds of peripheral receptors and neurons. What the mechanism underlying the effect of noise is remains unclear. Here, the perforated patch-clamp technique was used on isolated cells from chronic compression of the dorsal root ganglion (DRG) model. Our data provided new insight indicating that, under conditions without external signals, noise can enhance subthreshold oscillations, which was observed in a certain type of neurons with high-frequency (20-100 Hz) intrinsic resonance from injured DRG neurons. The occurrence of subthreshold oscillation considerably decreased the threshold potential for generating repetitive firing. The above effects of noise can be abolished by blocking the persistent sodium current (I(Na, P)). Utilizing a mathematical neuron model we further simulated the effect of noise on subthreshold oscillation and firing, and also found that noise can enhance the electrical activity through autonomous stochastic resonance. Accordingly, we propose a new concept of the effects of noise on neural intrinsic activity, which suggests that noise may be an important factor for modulating the excitability of neurons and generation of chronic pain signals.     

Frequency sensitivity in Hodgkin–Huxley systems

 The frequency sensitivity of weak periodic signal detection has been studied via numerical simulations for both a single neuron and a neuronal network. The dependence of the critical amplitude of the signal upon its frequency and a resonance between the intrinsic oscillations of a neuron and the signal could account for the frequency sensitivity. In the presence of both a subthreshold periodic signal and noise, the signal-to-noise ratio (SNR) of the output of either a single neuron or a neuronal network present the typical characteristics of stochastic resonance. In particular, there exists a frequency-sensitive range of 30–100 Hz, and for signals with frequencies within this range the SNRs have large values. This implies that the system under consideration (a single neuron or a neuronal network) is more sensitive to the detection of periodic signals, and the frequency sensitivity may be of a functional significance to signal processing. Received: 26 October 1999 / Accepted in revised form: 25 July 2000     

Enhancement of information transmission of sub-threshold signals applied to distal positions of dendritic trees in hippocampal CA1 neuron models with stochastic resonance

Stochastic resonance (SR) has been shown to enhance the signal-to-noise ratio and detection of low level signals in neurons. It is not yet clear how this effect of SR plays an important role in the information processing of neural networks. The objective of this article is to test the hypothesis that information transmission can be enhanced with SR when sub-threshold signals are applied to distal positions of the dendrites of hippocampal CA1 neuron models. In the computer simulation, random sub-threshold signals were presented repeatedly to a distal position of the main apical branch, while the homogeneous Poisson shot noise was applied as a background noise to the mid-point of a basal dendrite in the CA1 neuron model consisting of the soma with one sodium, one calcium, and five potassium channels. From spike firing times recorded at the soma, the mutual information and information rate of the spike trains were estimated. The simulation results obtained showed a typical resonance curve of SR, and that as the activity (intensity) of sub-threshold signals increased, the maximum value of the information rate tended to increased and eventually SR disappeared. It is concluded that SR can play a key role in enhancing the information transmission of sub-threshold stimuli applied to distal positions on the dendritic trees.     

Ubiquitous crossmodal Stochastic Resonance in humans: auditory noise facilitates tactile, visual and proprioceptive sensations

Background

Stochastic resonance is a nonlinear phenomenon whereby the addition of noise can improve the detection of weak stimuli. An optimal amount of added noise results in the maximum enhancement, whereas further increases in noise intensity only degrade detection or information content. The phenomenon does not occur in linear systems, where the addition of noise to either the system or the stimulus only degrades the signal quality. Stochastic Resonance (SR) has been extensively studied in different physical systems. It has been extended to human sensory systems where it can be classified as unimodal, central, behavioral and recently crossmodal. However what has not been explored is the extension of this crossmodal SR in humans. For instance, if under the same auditory noise conditions the crossmodal SR persists among different sensory systems.

Methodology/Principal Findings

Using physiological and psychophysical techniques we demonstrate that the same auditory noise can enhance the sensitivity of tactile, visual and propioceptive system responses to weak signals. Specifically, we show that the effective auditory noise significantly increased tactile sensations of the finger, decreased luminance and contrast visual thresholds and significantly changed EMG recordings of the leg muscles during posture maintenance.

Conclusions/Significance

We conclude that crossmodal SR is a ubiquitous phenomenon in humans that can be interpreted within an energy and frequency model of multisensory neurons spontaneous activity. Initially the energy and frequency content of the multisensory neurons'' activity (supplied by the weak signals) is not enough to be detected but when the auditory noise enters the brain, it generates a general activation among multisensory neurons of different regions, modifying their original activity. The result is an integrated activation that promotes sensitivity transitions and the signals are then perceived. A physiologically plausible model for crossmodal stochastic resonance is presented.     

Effect of syncytium structure of receptor systems on stochastic resonance induced by chaotic potential fluctuation.

To study a role of syncytium structure of sensory receptor systems in the detection of weak signals through stochastic resonance, we present a model of a receptor system with syncytium structure in which receptor cells are interconnected by gap junctions. The apical membrane of each cell includes two kinds of ion channels whose gating processes are described by the deterministic model. The membrane potential of each cell fluctuates chaotically or periodically, depending on the dynamical state of collective channel gating. The chaotic fluctuation of membrane potential acts as internal noise for the stochastic resonance. The detection ability of the system increases as the electric conductance between adjacent cells generated by the gap junction increases. This effect of gap junctions arises mainly from the fact that the synchronization of chaotic fluctuation of membrane potential between the receptor cells is strengthened as the density of gap junctions is increased.     

Stochastic resonance in the LIF models with input or threshold noise

In this paper, two stochastic versions of the LIF neural model are considered: one with the noise signal applied to the firing threshold, the other having it added to the input current. Then, adopting a discontinuous stepwise noise whose innovations are uncorrelated and gaussian distributed, the behaviours of the two models pertaining to the stochastic resonance (SR) are analysed and compared. Furthermore, it is shown that introducing a suitable time correlation into the noise signal brings us from the first model to the second one.     

A linear model for characterization of synchronization frequencies of neural networks

The synchronization frequency of neural networks and its dynamics have important roles in deciphering the working mechanisms of the brain. It has been widely recognized that the properties of functional network synchronization and its dynamics are jointly determined by network topology, network connection strength, i.e., the connection strength of different edges in the network, and external input signals, among other factors. However, mathematical and computational characterization of the relationships between network synchronization frequency and these three important factors are still lacking. This paper presents a novel computational simulation framework to quantitatively characterize the relationships between neural network synchronization frequency and network attributes and input signals. Specifically, we constructed a series of neural networks including simulated small-world networks, real functional working memory network derived from functional magnetic resonance imaging, and real large-scale structural brain networks derived from diffusion tensor imaging, and performed synchronization simulations on these networks via the Izhikevich neuron spiking model. Our experiments demonstrate that both of the network synchronization strength and synchronization frequency change according to the combination of input signal frequency and network self-synchronization frequency. In particular, our extensive experiments show that the network synchronization frequency can be represented via a linear combination of the network self-synchronization frequency and the input signal frequency. This finding could be attributed to an intrinsically-preserved principle in different types of neural systems, offering novel insights into the working mechanism of neural systems.     

Uncovering chaotic structure in mechanomyography signals of fatigue biceps brachii muscle

The mechanomyography (MMG) signal reflects mechanical properties of limb muscles that undergo complex phenomena in different functional states. We undertook the study of the chaotic nature of MMG signals by referring to recent developments in the field of nonlinear dynamics. MMG signals were measured from the biceps brachii muscle of 5 subjects during fatigue of isometric contraction at 80% maximal voluntary contraction (MVC) level. Deterministic chaotic character was detected in all data by using the Volterra–Wiener–Korenberg model and noise titration approach. The noise limit, a power indicator of the chaos of fatigue MMG signals, was 22.20±8.73. Furthermore, we studied the nonlinear dynamic features of MMG signals by computing their correlation dimension D₂, which was 3.35±0.36 across subjects. These results indicate that MMG is a high-dimensional chaotic signal and support the use of the theory of nonlinear dynamics for analysis and modeling of fatigue MMG signals.     

Didactic discussion of stochastic resonance effects and weak signals

A simple, paradigmatic, model is used to illustrate some general properties of effects subsumed under the label “stochastic resonance.” In particular, analyses of the transparent model show that 1) a small amount of noise added to a much larger signal can greatly increase the response to the signal, but 2) a weak signal added to much larger noise will not generate a substantial added response. The conclusions drawn from the model illustrate the general result that stochastic resonance effects do not provide an avenue for signals that are much smaller than noise to affect biology. A further analysis demonstrates the effects of small signals in the shifting of biologically important chemical equilibria under conditions where stochastic resonance effects are significant. © 1996 Wiley-Liss, Inc.     

Stochastic resonance modulates neural synchronization within and between cortical sources

Neural synchronization is a mechanism whereby functionally specific brain regions establish transient networks for perception, cognition, and action. Direct addition of weak noise (fast random fluctuations) to various neural systems enhances synchronization through the mechanism of stochastic resonance (SR). Moreover, SR also occurs in human perception, cognition, and action. Perception, cognition, and action are closely correlated with, and may depend upon, synchronized oscillations within specialized brain networks. We tested the hypothesis that SR-mediated neural synchronization occurs within and between functionally relevant brain areas and thus could be responsible for behavioral SR. We measured the 40-Hz transient response of the human auditory cortex to brief pure tones. This response arises when the ongoing, random-phase, 40-Hz activity of a group of tuned neurons in the auditory cortex becomes synchronized in response to the onset of an above-threshold sound at its "preferred" frequency. We presented a stream of near-threshold standard sounds in various levels of added broadband noise and measured subjects' 40-Hz response to the standards in a deviant-detection paradigm using high-density EEG. We used independent component analysis and dipole fitting to locate neural sources of the 40-Hz response in bilateral auditory cortex, left posterior cingulate cortex and left superior frontal gyrus. We found that added noise enhanced the 40-Hz response in all these areas. Moreover, added noise also increased the synchronization between these regions in alpha and gamma frequency bands both during and after the 40-Hz response. Our results demonstrate neural SR in several functionally specific brain regions, including areas not traditionally thought to contribute to the auditory 40-Hz transient response. In addition, we demonstrated SR in the synchronization between these brain regions. Thus, both intra- and inter-regional synchronization of neural activity are facilitated by the addition of moderate amounts of random noise. Because the noise levels in the brain fluctuate with arousal system activity, particularly across sleep-wake cycles, optimal neural noise levels, and thus SR, could be involved in optimizing the formation of task-relevant brain networks at several scales under normal conditions.