Stochastic resonance is applied to quantitative analysis for weak chromatographic signal of roxithromycin in beagle dog plasma

Based on the theory of stochastic resonance, the signal to noise ratio (SNR) of HPLC/UV chromatographic signal of roxithromycin is enhanced by cooperation of signal, noise and nonlinear system. A simple new method for the determination of low concentration of roxithromycin in beagle dog plasma is presented. Using signal enhancement by stochastic resonance, this method extends the limit of quantitation from the reported 0.5 to 0.1 microg/ml. During validation of the new method, HPLC/MS was used as a comparison technique. The results indicate that the recovery and low concentrations of roxithromycin in beagle dog plasma were equivalent between the two methods (P>0.05). Stochastic resonance may be a promising tool for improving detection limits in trace analysis.     

EEG gamma-band activity during audiovisual speech comprehension in different noise environments

The presence of cross-modal stochastic resonance in different noise environments has been proved in previous behavioral and event-related potential studies, while it was still unclear whether the gamma-band oscillation study was another evidence of cross-modal stochastic resonance. The multisensory gain of gamma-band activity between the audiovisual (AV) and auditory-only conditions in different noise environments was analyzed. Videos of face motion articulating words concordant with different levels of pink noise were used as stimuli. Signal-to-noise ratios (SNRs) of 0, −4, −8, −12 and −16 dB were selected to measure the speech recognition accuracy and EEG activity for 20 healthy subjects. The power and phase of EEG gamma-band oscillations increased in a time window of 50–90 ms. The multisensory gains of evoked and total activity, as well as phase-locking factor, were greatest at the −12 dB SNR, which were consistent with the behavioral result. The multisensory gain of gamma-band activity showed an inverted U-shaped curve as a function of SNR. This finding confirmed the presence of cross-modal stochastic resonance. In addition, there was a significant correlation between evoked activity and phase-locking factor of gamma-band at five different SNRs. Gamma-band oscillation was believed to play a role in the rapid processing and information linkage strengthening of AV modalities in the early stage of cognitive processes.     

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。     

Multi-Reception Strategy with Improved SNR for Multichannel MR Imaging

A multi-reception strategy with extended GRAPPA is proposed in this work to improve MR imaging performance at ultra-high field MR systems with limited receiver channels. In this method, coil elements are separated to two or more groups under appropriate grouping criteria. Those groups are enabled in sequence for imaging first, and then parallel acquisition is performed to compensate for the redundant scan time caused by the multiple receptions. To efficiently reconstruct the data acquired from elements of each group, a specific extended GRAPPA was developed. This approach was evaluated by using a 16-element head array on a 7 Tesla whole-body MRI scanner with 8 receive channels. The in-vivo experiments demonstrate that with the same scan time, the 16-element array with twice receptions and acceleration rate of 2 can achieve significant SNR gain in the periphery area of the brain and keep nearly the same SNR in the center area over an eight-element array, which indicates the proposed multi-reception strategy and extended GRAPPA are feasible to improve image quality for MRI systems with limited receive channels. This study also suggests that it is advantageous for a MR system with N receiver channels to utilize a coil array with more than N elements if an appropriate acquisition strategy is applied.     

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.     

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.     

Improved Detection of Magnetic Signals by a MEMS Sensor Using Stochastic Resonance

We introduce the behavior of the electrical output response of a magnetic field sensor based on microelectromechanical systems (MEMS) technology under different levels of controlled magnetic noise. We explored whether a particular level of magnetic noise applied on the vicinity of the MEMS sensor can improve the detection of subthreshold magnetic fields. We examined the increase in the signal-to-noise ratio (SNR) of such detected magnetic fields as a function of the magnetic noise intensity. The data disclosed an inverted U-like graph between the SNR and the applied magnetic noise. This finding shows that the application of an intermediate level of noise in the environment of a MEMS magnetic field sensor improves its detection capability of subthreshold signals via the stochastic resonance phenomenon.     

Stochastic resonance in two simple compare-and-fire models

Two neural models are analysed and shown to exhibit the stochastic resonance effect. Namely, they respond to an underthreshold sinusoidal signal with an output signal whose signal-to-noise ratio (SNR) firstly increases then decreases as the intensity of noise affecting the system increases. The resonance curves are determined, analytically for the first and simplest model and by a synthetic method for the second one, and the respective resonant behaviours are illustrated and interpreted.     

Modeling nonlinear errors in surface electromyography due to baseline noise: A new methodology

The surface electromyographic (EMG) signal is often contaminated by some degree of baseline noise. It is customary for scientists to subtract baseline noise from the measured EMG signal prior to further analyses based on the assumption that baseline noise adds linearly to the observed EMG signal. The stochastic nature of both the baseline and EMG signal, however, may invalidate this assumption. Alternately, “true” EMG signals may be either minimally or nonlinearly affected by baseline noise. This information is particularly relevant at low contraction intensities when signal-to-noise ratios (SNR) may be lowest. Thus, the purpose of this simulation study was to investigate the influence of varying levels of baseline noise (approximately 2–40% maximum EMG amplitude) on mean EMG burst amplitude and to assess the best means to account for signal noise. The simulations indicated baseline noise had minimal effects on mean EMG activity for maximum contractions, but increased nonlinearly with increasing noise levels and decreasing signal amplitudes. Thus, the simple baseline noise subtraction resulted in substantial error when estimating mean activity during low intensity EMG bursts. Conversely, correcting EMG signal as a nonlinear function of both baseline and measured signal amplitude provided highly accurate estimates of EMG amplitude. This novel nonlinear error modeling approach has potential implications for EMG signal processing, particularly when assessing co-activation of antagonist muscles or small amplitude contractions where the SNR can be low.     

Models for spatially distributed populations: The effect of within-patch variability

This paper studies population models which have the following three ingredients: populations are divided into local subpopulations, local population dynamics are nonlinear and random events occur locally in space. In this setting local stochastic phenomena have a systematic effect on average population density and this effect does not disappear in large populations. This result is an outcome of the interaction of the three ingredients in the models and it says that stochastic models of systems of patches can be expected to give results for average population density that differ systematically from those of deterministic models. The magnitude of these differences is related to the degree of nonlinearity of local dynamics and the magnitude of local variability. These results explain those obtained from a number of previously published models which give conclusions that differ from those of deterministic models. Results are also obtained that show how stochastic models of systems of patches may be simplified to facilitate their study.     

The Effect of Loss of Immunity on Noise-Induced Sustained Oscillations in Epidemics

The effect of loss of immunity on sustained population oscillations about an endemic equilibrium is studied via a multiple scales analysis of a SIRS model. The analysis captures the key elements supporting the nearly regular oscillations of the infected and susceptible populations, namely, the interaction of the deterministic and stochastic dynamics together with the separation of time scales of the damping and the period of these oscillations. The derivation of a nonlinear stochastic amplitude equation describing the envelope of the oscillations yields two criteria providing explicit parameter ranges where they can be observed. These conditions are similar to those found for other applications in the context of coherence resonance, in which noise drives nearly regular oscillations in a system that is quiescent without noise. In this context the criteria indicate how loss of immunity and other factors can lead to a significant increase in the parameter range for prevalence of the sustained oscillations, without any external driving forces. Comparison of the power spectral densities of the full model and the approximation confirms that the multiple scales analysis captures nonlinear features of the oscillations.     

Stochastic resonance in psychophysics and in animal behavior

 A recent analysis of the energy detector model in sensory psychophysics concluded that stochastic resonance does not occur in a measure of signal detectability (d′), but can occur in a percent-correct measure of performance as an epiphenomenon of nonoptimal criterion placement [Tougaard (2000) Biol Cybern 83: 471–480]. When generalized to signal detection in sensory systems in general, this conclusion is a serious challenge to the idea that stochastic resonance could play a significant role in sensory processing in humans and other animals. It also seems to be inconsistent with recent demonstrations of stochastic resonance in sensory systems of both nonhuman animals and humans using measures of system performance such as signal-to-noise ratio of power spectral densities and percent-correct detections in a two-interval forced-choice paradigm, both closely related to d′. In this paper we address this apparent dilemma by discussing several models of how stochastic resonance can arise in signal detection systems, including especially those that implement a “soft threshold” at the input transform stage. One example involves redefining d′ for energy increments in terms of parameters of the spike-count distribution of FitzHugh–Nagumo neurons. Another involves a Poisson spike generator that receives an exponentially transformed noisy periodic signal. In this case it can be shown that the signal-to-noise ratio of the power spectral density at the signal frequency, which exhibits stochastic resonance, is proportional to d′. Finally, a variant of d′ is shown to exhibit stochastic resonance when calculated directly from the distributions of power spectral densities at the signal frequency resulting from transformation of noise alone and a noisy signal by a sufficiently steep nonlinear response function. All of these examples, and others from the literature, imply that stochastic resonance is more than an epiphenomenon, although significant limitations to the extent to which adding noise can aid detection do exist. Received: 22 January 2001 / Accepted in revised form: 8 March 2002     

Bistability in feedback circuits as a byproduct of evolution of evolvability

Noisy bistable dynamics in gene regulation can underlie stochastic switching and is demonstrated to be beneficial under fluctuating environments. It is not known, however, if fluctuating selection alone can result in bistable dynamics. Using a stochastic model of simple feedback networks, we apply fluctuating selection on gene expression and run in silico evolutionary simulations. We find that independent of the specific nature of the environment–fitness relationship, the main outcome of fluctuating selection is the evolution of increased evolvability in the network; system parameters evolve toward a nonlinear regime where phenotypic diversity is increased and small changes in genotype cause large changes in expression level. In the presence of noise, the evolution of increased nonlinearity results in the emergence and maintenance of bistability. Our results provide the first direct evidence that bistability and stochastic switching in a gene regulatory network can emerge as a mechanism to cope with fluctuating environments. They strongly suggest that such emergence occurs as a byproduct of evolution of evolvability and exploitation of noise by evolution.     

Behavioral stochastic resonance: how the noise from a Daphnia swarm enhances individual prey capture by juvenile paddlefish.

Zooplankton emit weak electric fields into the surrounding water that originate from their own muscular activities associated with swimming and feeding. Juvenile paddlefish prey upon single zooplankton by detecting and tracking these weak electric signatures. The passive electric sense in this fish is provided by an elaborate array of electroreceptors, Ampullae of Lorenzini, spread over the surface of an elongated rostrum. We have previously shown that the fish use stochastic resonance to enhance prey capture near the detection threshold of their sensory system. However, stochastic resonance requires an external source of electrical noise in order to function. A swarm of plankton, for example Daphnia, can provide the required noise. We hypothesize that juvenile paddlefish can detect and attack single Daphnia as outliers in the vicinity of the swarm by using noise from the swarm itself. From the power spectral density of the noise plus the weak signal from a single Daphnia, we calculate the signal-to-noise ratio, Fisher information and discriminability at the surface of the paddlefish's rostrum. The results predict a specific attack pattern for the paddlefish that appears to be experimentally testable.     

Intrinsic coherence resonance in excitable membrane patches

The influence of intrinsic channel noise on the spiking activity of excitable membrane patches is studied by use of a stochastic generalization of the Hodgkin-Huxley model. Internal noise stemming from the stochastic dynamics of individual ion channels does affect the electric properties of the cell-membrane patches. There exists an optimal size of the membrane patch for which the internal noise alone can cause a nearly regular spontaneous generation of action potentials. We consider the influence of intrinsic channel noise in presence of a constant and an oscillatory current driving for both, the mean interspike interval and the phenomenon of coherence resonance for neuronal spiking. Given small membrane patches, implying that channel noise dominates the excitable dynamics, we find the phenomenon of intrinsic coherence resonance. In this case, the relatively regular spiking behavior becomes essentially independent of an applied stimulus. We observed, however, the occurrence of a skipping of supra-threshold input events due to channel noise for intermediate patch sizes. This effect consequently reduces the overall coherence of the spiking.     

Signal detection theory,detectability and stochastic resonance effects

 Stochastic resonance is a phenomenon in which the performance of certain non-linear detectors can be enhanced by the addition of appropriate levels of random noise. Signal detection theory offers a powerful tool for analysing this type of system, through an ability to separate detection processes into reception and classification, with the former generally being linear and the latter always non-linear. Through appropriate measures of signal detectability it is possible to decide whether a local improvement in detection via stochastic resonance occurs due to the non-linear effects of the classification process. In this case, improvement of detection through the addition of noise can never improve detection beyond that of a corresponding adaptive system. Signal detection and stochastic resonance is investigated in several integrate-and-fire neuron models. It is demonstrated that the stochastic resonance observed in spiking models is caused by non-linear properties of the spike-generation process itself. The true detectability of the signal, as seen by the receiver part of the spiking neuron (the integrator part), decreases monotonically with input noise level for all signal and noise intensities. Received: 3 April 2001 / Accepted in revised form: 8 March 2002     

线性整合放电模型的相干共振

研究了神经递质以随机点序列释放和电压门控离子通道噪声共同作用下,线性整合放电模型的相干共振现象。基于分形布朗运动和改进的欧拉方法,得到了神经元膜电压分布和神经元放电峰峰间隔的信噪比。结果表明,神经元放电的峰峰间隔是神经递质的达到强度、离子通道噪声强度的非单调函数。适当的神经递质到达强度和离子通道噪声强度使峰峰间隔的信噪比出现最大值,即出现相干共振现象。     

Mechanisms of ventricular arrhythmias: a dynamical systems-based perspective

Defining the cellular electrophysiological mechanisms for ventricular tachyarrhythmias is difficult, given the wide array of potential mechanisms, ranging from abnormal automaticity to various types of reentry and kk activity. The degree of difficulty is increased further by the fact that any particular mechanism may be influenced by the evolving ionic and anatomic environments associated with many forms of heart disease. Consequently, static measures of a single electrophysiological characteristic are unlikely to be useful in establishing mechanisms. Rather, the dynamics of the electrophysiological triggers and substrates that predispose to arrhythmia development need to be considered. Moreover, the dynamics need to be considered in the context of a system, one that displays certain predictable behaviors, but also one that may contain seemingly stochastic elements. It also is essential to recognize that even the predictable behaviors of this complex nonlinear system are subject to small changes in the state of the system at any given time. Here we briefly review some of the short-, medium-, and long-term alterations of the electrophysiological substrate that accompany myocardial disease and their potential impact on the initiation and maintenance of ventricular arrhythmias. We also provide examples of cases in which small changes in the electrophysiological substrate can result in rather large differences in arrhythmia outcome. These results suggest that an interrogation of cardiac electrical dynamics is required to provide a meaningful assessment of the immediate risk for arrhythmia development and for evaluating the effects of putative antiarrhythmic interventions.