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Voltage noise influences action potential duration in cardiac myocytes.

Stochastic gating of ion channels introduces noise to membrane currents in cardiac muscle cells (myocytes). Since membrane currents drive membrane potential, noise thereby influences action potential duration (APD) in myocytes. To assess the influence of noise on APD, membrane potential is in this study formulated as a stochastic process known as a diffusion process, which describes both the current-voltage relationship and voltage noise. In this framework, the response of APD voltage noise and the dependence of response on the shape of the current-voltage relationship can be characterized analytically. We find that in response to an increase in noise level, action potential in a canine ventricular myocytes is typically prolonged and that distribution of APDs becomes more skewed towards long APDs, which may lead to an increased frequency of early after-depolarization formation. This is a novel mechanism by which voltage noise may influence APD. The results are in good agreement with those obtained from more biophysically-detailed mathematical models, and increased voltage noise (due to gating noise) may partially underlie an increased incidence of early after-depolarizations in heart failure.

Action Potentials↗

Effect of noise on the contrast detection threshold in visual perception.

It has recently been shown that noise can improve the detection of stimuli in several sensory modalities. We herein investigated whether visual contrast detection sensitivity can be improved by adding a certain amount of noise. The contrast detection thresholds of a light changing brightness periodically were measured either with or without overlapping noise in 22 normal participants. Sinusoidal modulating light at 1 or 15 Hz was used as a signal. White noise was used to produce random flickering light as the noise. Participants were required to detect any changes in the brightness of the signal with or without noise. The contrast detection threshold, which was measured using a psychophysical method, decreased at around the threshold level of the noise intensity. The maximum facilitatory effect was obtained at a noise intensity of 5 dB. This effect was consistently observed regardless of the frequency of the signal (1 and 15 Hz). These findings indicate that noise can improve the signal detection in human visual perception.

Adult↗

Nonstationary noise estimation in functional MRI.

An important issue in functional MRI analysis is accurate characterisation of the noise processes present in the data. Whilst conventional fMRI noise representations often assume stationarity (or time-invariance) in the noise generating sources, such approaches may serve to suppress important dynamic information about brain function. As an alternative to these fixed temporal assumptions, we present in this paper two time-varying procedures for examining nonstationary noise structure in fMRI data. In the first procedure, we approximate nonstationary behaviour by means of a collection of simple but numerous time-varying parametric models. This is accomplished through the derivation of a locally parametric AutoRegressive (AR) plus drift model which tracks temporal covariance by allowing the model parameters to evolve over time. Before exploring time variation in these parameters, window-widths (bandwidths) that are well suited to the latent time-varying noise structure must be determined. To do this, we employ a bandwidth selection mechanism based on Stein's Unbiased Risk Estimator (SURE) criterion. In the second procedure, we describe the fMRI noise using a nonparametric method based on Functional Data Analysis (FDA). This process generates well-conditioned nonstationary covariance estimates that reflect temporal continuity in the underlying data structure whilst penalizing effective model dimension. We demonstrate both methods on simulated data and investigate the presence of nonstationary noise in resting fMRI data using the whitening capabilities of the locally parametric procedure. We evaluate the comparative behaviour of the stationary and nonstationary AR-based methods on data acquired at 1.5, 3 and 7 T magnetic field strengths and show that incorporation of time variation in the AR parameters leads to an overall decrease in the level of residual structure in the data. The FDA noise modelling technique is formulated within an activation mapping procedure and compared to the SPM (Statistical Parametric Mapping) toolbox on a cognitive face recognition task. Both the SPM and FDA methods show good sensitivity on this task, but we find that inclusion of the nonstationary FDA noise model seems to improve detection power in important task-related medial temporal regions.

Algorithms↗

Auditory noise can prevent increased extracellular acetylcholine levels in the hippocampus in response to aversive stimulation.

The intent of this study was to investigate neurochemical and behavioural effects of aversive stimulation and the impact of auditory background noise. Using in vivo microdialysis, hippocampal acetylcholine was extracted and subjected to HPLC analysis while male Wistar rats were exposed to aversive stimulation similar to that used in conventional procedures for aversive conditioning. Three groups of animals were used. Animals in the first group were exposed to a single tone/footshock pairing followed by a tone alone 2 h later. Animals in the second group served as controls and were only exposed to the tone without shock. A third group was exposed to the same tone/shock pairing and tone as the first group while being exposed to constant background noise during the whole experiment. The results showed, that the tone/shock combination led to pronounced behavioral and cholinergic activation. In contrast, exposure to background noise prevented the increase in hippocampal ACh levels to tone/shock stimulation. The unconditioned behavioural response, however, was not prevented suggesting that hippocampal ACh is not a necessary correlate of behavioural activation or arousal. A second experiment intended to investigate the effects of background noise in a shuttle box avoidance learning paradigm where rats were trained to avoid an aversive footshock, which was signalled by a tone. There, one group of rats was exposed to background noise during avoidance learning, and the other group was not exposed to noise. Whereas both groups learned to avoid the shock to some degree over training, the noise exposed animals did not show improvement in escape performance over the course of training, indicating that the noise hindered development of an adaptive response to the shock. In summary, our data indicate that background noise can prevent increased extracellular hippocampal ACh levels in response to an aversive stimulus, and can also lead to deficits in learning to escape from shock.

Acetylcholine↗

Effects of horizontal and vertical additive disparity noise on stereoscopic corrugation detection.

Stereoscopic corrugation detection in the presence of horizontal- and vertical- additive disparity noise was examined using a signal detection paradigm. Random-dot stereograms either represented a 3-D square-wave surface with various amounts of Gaussian-distributed additive disparity noise or had the same disparity values randomly redistributed. Stereoscopic detection of 2 arcmin peak amplitude corrugations was found to tolerate significantly greater amplitudes of vertical-disparity noise than horizontal-disparity noise--irrespective of whether the corrugations were horizontally or vertically oriented. However, this directional difference in tolerance to disparity noise was found to reverse when the corrugation and noise amplitudes were increased (so as to produce equivalent signal-to-noise ratios). These results suggest that horizontal- and vertical-disparity noise pose different problems for dot-matching and post-matching surface reconstruction as corrugation and noise amplitudes increase.

Adult↗

Upper displacement limits for spatially broadband patterns containing bandpass noise.

How is the spatial-frequency content of a moving broadband pattern analysed by the visual system? Observers were asked to discriminate the direction of motion in random-noise patterns containing equal energy in each two-dimensional octave band. Uncorrelated noise could be introduced into either low- or high-frequency bands in order to force the visual system to rely on the outputs of putative mechanisms tuned to a narrow frequency range of the stimulus. In two experiments the dependent measure was the magnitude of dmax, the largest discrete displacement whose direction could be discriminated reliably. It was found that dmax was unaffected by the presence of high-frequency noise reaching down to 0.67 c/deg, but that the task became impossible thereafter. In the case of low-frequency noise, dmax fell as the noise was moved up towards about 2 c/deg, at which point the task became impossible at any displacement. This pattern of results would be expected if the system were using information from the lowest signal frequencies in all conditions. In experiment 2, dmax was measured for stimuli in which the spectral position and quantity of high-frequency noise were manipulated. It was found that only noise spectrally-adjacent to the signal band has a detrimental effect on dmax. Three different single-filter models of motion detection each failed to provide a satisfactory account of the spatial-frequency range of good direction discrimination performance. Rather, the modelling shows that the visual system can access the outputs of a low-frequency channel when the noise is high and a high-frequency channel when the noise is low.

Contrast Sensitivity↗

Tuning non-linear adaptive compensators in non-ideal noise environment.

Adaptive compensation has been popular in a variety of biomedical signal processing applications. One of the major limitations of this method is the requirement for a primary signal + noise channel and a secondary noise channel, with the noises in the two channels being strongly correlated. In the majority of real-life biomedical applications this requirement can rarely be fulfilled since the secondary channel inevitably contains certain representation of the signal from the primary channel thus jeopardizing the adaptive compensation process. In the present work we describe a method for tuning an adaptive compensator containing a non-linear real-time multiplier in the reference channel in such non-ideal noise environment. The method is based on iterative adjustments of an exponential non-linear function which modifies in real-time the signal-to-noise balance in the reference channel in favor of the noise, preserving the correlation of the latter with the noise in the primary (signal + noise) channel but diminishing the signal content in the reference channel. Sets of model signals and noises are used to illustrate this methodology with a particular emphasis on biomedical signal applications. A quantitative description of the iterative tuning procedure is provided and the capabilities and limitations of this novel method for adaptive compensation are outlined.

Artifacts↗

Noise removal at the rod synapse of mammalian retina.

Mammalian rods respond to single photons with a hyperpolarization of about 1 mV which is accompanied by continuous noise. Since the mammalian rod bipolar cell collects signals from 20-100 rods, the noise from the converging rods would overwhelm the single-photon signal from one rod at scotopic intensities (starlight) if the bipolar cell summed signals linearly (Baylor et al., 1984). However, it is known that at scotopic intensities the retina preserves single-photon responses (Barlow et al., 1971; Mastronarde, 1983). To explore noise summation in the rod bipolar pathway, we simulated an array of rods synaptically connected to a rod bipolar cell using a compartmental model. The performance of the circuit was evaluated with a discriminator measuring errors in photon detection as false positives and false negatives, which were compared to physiologically and psychophysically measured error rates. When only one rod was connected to the rod bipolar, a Poisson rate of 80 vesicles/s was necessary for reliable transmission of the single-photon signal. When 25 rods converged through a linear synapse the noise caused an unacceptably high false positive rate, even when either dark continuous noise or synaptic noise where completely removed. We propose that a threshold nonlinearity is provided by the mGluR6 receptor in the rod bipolar dendrite (Shiells & Falk, 1994) to yield a synapse with a noise removing mechanism. With the threshold nonlinearity the synapse removed most of the noise. These results suggest that a threshold provided by the mGluR6 receptor in the rod bipolar cell is necessary for proper functioning of the retina at scotopic intensities and that the metabotropic domains in the rod bipolar are distinct. Such a nonlinear threshold could also reduce synaptic noise for cortical circuits in which sparse signals converge.

Animals↗

A signal-to-noise analysis of multifocal VEP responses: an objective definition for poor records.

Sixty local VEP records, called the multifocal VEP (mfVEP), can be obtained over a wide retinal area. From subject-to-subject, from day-to-day, and from location-to-location, these records can vary in quality presenting a challenge to quantitative analyses. Here three procedures are described for specifying the quality of mfVEP recordings in terms of signal-to-noise ratios. Monocular mfVEPs were recorded in two, 7-min runs. A '2-run signal-to-noise ratio' (2rSNR) was obtained as [RMS(RunA+RunB)]/[RMS(RunA-RunB)]-1, where RMS is the root-mean-square amplitude of the response over the period from 45 to 150 ms (signal window). Two 'noise-window signal-to-noise ratios' were obtained with the same numerator as the 2rSNR but with the denominators based upon the RMS of a signal-free window from 325 to 430 ms. In one case, inSNR, the denominator was the RMS of the record's noise window and in the other case, mnSNR, the denominator was the mean of the RMS amplitudes of all the signal-free noise windows for the subject. The SNRs were related to false-positive rates (i.e., detecting a signal when none was present) by recording mfVEPs with some of the sectors of the display occluded. In particular, the outer three rings (36 sectors) of the display were occluded so that only noise was recorded; false-positive rates for different values of SNR were calculated. The 2rSNR had the highest false-positive rate largely due to alpha in the records of some subjects. The mnSNR had a lower false-positive rate than did the inSNR because there was little correlation between the RMS of the noise in the signal-free window and the RMS of the noise within the signal window. Use of the mnSNR is recommended over the 2rSNR, especially where alpha contamination can not be eliminated. Ways to improve the SNR of the records are discussed.

Adult↗

Determining the visibility of noise in motion signals.

A procedure is described for generating stimuli to study the detection of noise components in motion signals. By using random dots with intensities distributed according to a Gaussian probability function, a temporally and spatially continuous mixture of signal and noise components can be realized in random dot kinematograms. These stimuli were used in a noise detection task, a signal detection task and a direction discrimination task. Signal-to-noise ratio ('coherence') thresholds for the signal detection and direction discrimination tasks were consistent with previous research. Noise can be detected at levels of approximately 0.5-2.5%, depending on the size of the motion stimulus. We argue that the noise in the motion stimulus becomes detectable when it exceeds the noise intrinsic to the various stages of motion processing. Therefore,the method provides a simple procedure for obtaining measures of equivalent input noise and can be used for estimating internal noise levels of motion processing mechanisms.

Adult↗

Noise and stochastic resonance in voltage-gated ion channels.

Using Monte Carlo techniques, I calculate the effects of internally generated noise on information transfer through the passage of action potential spikes along unmyelinated axons in a simple nervous system. I take the Hodgkin-Huxley (HH) description of Na and K channels in squid giant axons as the basis of the calculations and find that most signal transmission noise is generated by fluctuations in the channel open and closed populations. To bring the model closer to conventional descriptions in terms of thermal noise energy, kT, and to determine gating currents, I express the HH equations in the form of simple relations from statistical mechanics where the states are separated by a Gibbs energy that is modified by the action of the transmembrane potential on dipole moments held by the domains. Using the HH equations, I find that the output response (in the probability of action potential spikes) from small input potential pulses across the cell membrane is increased by added noise but falls off when the input noise becomes large, as in stochastic resonance models. That output noise response is sharply reduced by a small increase in the membrane polarization potential or a moderate increase in the channel densities. Because any reduction of noise incurs metabolic and developmental costs to an animal, the natural noise level is probably optimal and any increase in noise is likely to be harmful. Although these results are specific to signal transmission in unmyelinated axons, I suggest that the conclusions are likely to be general.

Action Potentials↗

Analysis of stochastic noise in intensity-modulated beams.

Inverse planning techniques are known to produce intensity-modulated beams (IMBs) that are highly modulated. They are characterized by the fact that they contain high-frequency modulations that are absent in the profiles that are easier to deliver. For the purpose of this study these clinically unwanted fluctuations are being defined as 'noise'. Although these highly modulated solutions are also optimal solutions, as soon as the profiles are being delivered, they become unfavourable with respect to delivery efficiency and the analysis and verification of treatment. The aim of this work was therefore to understand the origins of the structure and complexity of IMBs. Ultimately, if one can characterize the essential features in optimum beam profiles, it might be possible to control the frequency distribution of IMBs and simplify the IMRT planning and delivery process. The study was based on two common optimization techniques: simulated annealing (SA) and gradient-descent (GD). The assumptions made at the start of this work were that the stochastic noise caused by the SA optimization technique is dominant over other sources of noise and that it could be separated out from the essential modulation after convergence of the cost function by averaging minimum-cost fluence profiles. The results indicate that there are three possible sources of stochastic noise in IMBs, i.e. the optimization technique, the cost function and the definition of convergence of that cost function. In terms of the optimization technique itself, it was confirmed that the gradient-descent technique does not introduce stochastic noise in the IMBs. The SA technique does introduce stochastic noise but averaging of minimum-cost fluence profiles does not result in smoother beam profiles. This originates from the fact that this type of noise is not the dominant factor in the optimization, but rather the curvature of the cost function close to the global minimum. It is shown that the choice of initial temperature in the SA optimization technique is crucial for the convergence of the cost function and the frequency distribution of the fluence profiles. If the initial temperature is too small the stochastic noise will get frozen into the fluence profiles and become the dominant component of noise, resulting in very random-looking and difficult to deliver patterns.

Algorithms↗

Noise simulation in cone beam CT imaging with parallel computing.

We developed a computer noise simulation model for cone beam computed tomography imaging using a general purpose PC cluster. This model uses a mono-energetic x-ray approximation and allows us to investigate three primary performance components, specifically quantum noise, detector blurring and additive system noise. A parallel random number generator based on the Weyl sequence was implemented in the noise simulation and a visualization technique was accordingly developed to validate the quality of the parallel random number generator. In our computer simulation model, three-dimensional (3D) phantoms were mathematically modelled and used to create 450 analytical projections, which were then sampled into digital image data. Quantum noise was simulated and added to the analytical projection image data, which were then filtered to incorporate flat panel detector blurring. Additive system noise was generated and added to form the final projection images. The Feldkamp algorithm was implemented and used to reconstruct the 3D images of the phantoms. A 24 dual-Xeon PC cluster was used to compute the projections and reconstructed images in parallel with each CPU processing 10 projection views for a total of 450 views. Based on this computer simulation system, simulated cone beam CT images were generated for various phantoms and technique settings. Noise power spectra for the flat panel x-ray detector and reconstructed images were then computed to characterize the noise properties. As an example among the potential applications of our noise simulation model, we showed that images of low contrast objects can be produced and used for image quality evaluation.

Algorithms↗

Time-frequency modelling and discrimination of noise in the electrocardiogram.

In widely spread home care applications of ECG recorders, the traditional approach to the problem of noise immunity is no longer sufficient. This paper presents a new ECG-dedicated noise removal technique based on a time-frequency noise model computed in a quasi-continuous way. Our algorithm makes use of the local bandwidth variability of cardiac electrical representation and splits the discrete time sequence into two sub-planes. The background activities of any origin (muscle, power line interference, etc) are measured in the regions of the time-frequency plane, situated above the local bandwidth of the signal. The noise estimate on each particular scale is non-uniformly sampled and needs to be extrapolated to the regions where the components of cardiac representation are normally expected. On the lower scales, the noise contribution is computed with the use of square polynomial extrapolation. The time-frequency representation of noise, partially measured and partially calculated, is arithmetically subtracted from the noisy signal, and the inverse time-frequency transform yields a noise-free cardiac representation. The algorithm was tested with the use of CSE database records with the addition of MIT-BIH database noise patterns. The static and dynamic performance of the algorithm is sufficient to ameliorate the signal-to-noise ratio by more than 11 dB.

Algorithms↗

Stochastic resonance in a bistable system subject to multiplicative and additive noise

The stochastic resonance (SR) phenomenon in a bistable system under the simultaneous action of multiplicative and additive noise and periodic signal is studied by using the theory of signal-to-noise ratio (SNR) in the adiabatic limit. Two cases have been considered: the case of no correlations between multiplicative and additive noise and the case of correlations between two noises. The expressions of the SNR for both cases are obtained. The effects of intensity of multiplicative and additive noise and the intensity of the correlations between noises on the SNR are discussed for both cases, respectively. It is found that the existence of a maximum in the SNR is the identifying characteristic of the SR phenomenon. In the case of no correlations between multiplicative and additive noise, the SNR is independent of the initial condition of the system. However, the SNR is not only dependent on the intensity of correlations between noises, but also on the initial condition of the system in the presence of correlations between two noises.

Journal Article↗

Influence of colored noise on chaotic systems.

We focus on classical chaotic systems corrupted by white and colored noise. We study the dependence of the correlation dimension and the Kolmogorov entropy on the noise level and its spectral exponent. As is well known, white noise strongly reduces the width of the scaling region for the correlation dimension and entropy. On the contrary, we demonstrate that colored noise does not basically obscure the scaling region, changing only the shape of the correlation sum for length scales smaller than the noise level. The numerical results show that, even for a noise level as high as approximately 5%, a reasonably wide plateau for the correlation sum is still obtained, but the value of the calculated dimension is somewhat increased. The calculated correlation dimension is a bilinear function of the noise level and the dimension of the noise, which depends on the spectral exponent of the noise. On the other hand, the width of the scaling region for the correlation entropy depends on this spectral exponent, but the value of the plateau does not change substantially.

Journal Article↗

Stochastic resonance driven by two different kinds of colored noise in a bistable system.

The phenomenon of stochastic resonance in a bistable nonlinear system is investigated when both the multiplicative noise and the coupling between additive and multiplicative noise are colored with different values of noise correlation time tau(1) and tau(2). Combining the functional analysis and unified colored noise approximation, the two different kinds of colored noise in the nonlinear system can be simplified. The signal-to-noise ratio is calculated when a weakly periodic signal is added to the system. It is found that there appears a transition between one peak and two peaks in the curve of the signal-to-noise ratio when either the noise correlation time tau(1) and tau(2) or the coupling strength lambda between additive and multiplicative noise is increased. The transition between one and two peaks depending on tau(1) and lambda is more complex than that depending on tau(2).

Journal Article↗

Noise-level estimation of time series using coarse-grained entropy.

We present a method of noise-level estimation that is valid even for high noise levels. The method makes use of the functional dependence of coarse-grained correlation entropy K2(epsilon ) on the threshold parameter epsilon. We show that the function K2(epsilon ) depends, in a characteristic way, on the noise standard deviation sigma. It follows that observing K2 (epsilon ) one can estimate the noise level sigma. Although the theory has been developed for the Gaussian noise added to the observed variable we have checked numerically that the method is also valid for the uniform noise distribution and for the case of Langevin equation corresponding to the dynamical noise. We have verified the validity of our method by applying it to estimate the noise level in several chaotic systems and in the Chua electronic circuit contaminated by noise.

Journal Article↗