Stochastic resonance (sensory neurobiology)

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Stochastic resonance is a phenomenon that occurs in a threshold measurement system (e.g. a man-made instrument or device; a natural cell, organ or organism) when an appropriate measure of information transfer (signal-to-noise ratio, mutual information, coherence, d', etc.) is maximized in the presence of a non-zero level of stochastic input noise thereby lowering the response threshold; [1] the system resonates at a particular noise level.

Contents

The three criteria that must be met for stochastic resonance to occur are:

  1. Nonlinear device or system: the input-output relationship must be nonlinear
  2. Weak, periodic signal of interest: the input signal must be below threshold of measurement device and recur periodically
  3. Added input noise: there must be random, uncorrelated variation added to signal of interest

Stochastic resonance occurs when these conditions combine in such a way that a certain average noise intensity results in maximized information transfer. A time-averaged (or, equivalently, low-pass filtered) output due to signal of interest plus noise will yield an even better measurement of the signal compared to the system's response without noise in terms of SNR.

The idea of adding noise to a system in order to improve the quality of measurements is counter-intuitive. Measurement systems are usually constructed or evolved to reduce noise as much as possible and thereby provide the most precise measurement of the signal of interest. Numerous experiments have demonstrated that, in both biological and non-biological systems, the addition of noise can actually improve the probability of detecting the signal; this is stochastic resonance. The systems in which stochastic resonance occur are always nonlinear systems. The addition of noise to a linear system will always decrease the information transfer rate. [1] [2]

History

Stochastic resonance was first discovered in a study of the periodic recurrence of Earth's ice ages. [2] [3] The theory developed out of an effort to understand how the Earth's climate oscillates periodically between two relatively stable global temperature states, one "normal" and the other an "ice age" state. The conventional explanation was that variations in the eccentricity of Earth's orbital path occurred with a period of about 100,000 years and caused the average temperature to shift dramatically. The measured variation in the eccentricity had a relatively small amplitude compared to the dramatic temperature change, however, and stochastic resonance was developed to show that the temperature change due to the weak eccentricity oscillation and added stochastic variation due to the unpredictable energy output of the Sun (known as the solar constant) could cause the temperature to move in a nonlinear fashion between two stable dynamic states.

Images

The above 256-grayscale-level images of the Arc result when the original is modified by the addition of noise and carrying out a nonlinear threshold operation; each panel shows a different level of noise variance, with a standard deviation of 10 grayscale levels in the top left, 50 levels in the top right, 100 in the bottom left and 150 in the bottom right. Different panels allow the best detection of different features; for example, the designs on the pillars are best seen in the top right, while the full outline of the arc is best seen in the bottom left. The appearance of features also changes with the size of the image as a result of averaging of the image; this can be observed by viewing the image at different distances. Arcfour2.png
The above 256-grayscale-level images of the Arc result when the original is modified by the addition of noise and carrying out a nonlinear threshold operation; each panel shows a different level of noise variance, with a standard deviation of 10 grayscale levels in the top left, 50 levels in the top right, 100 in the bottom left and 150 in the bottom right. Different panels allow the best detection of different features; for example, the designs on the pillars are best seen in the top right, while the full outline of the arc is best seen in the bottom left. The appearance of features also changes with the size of the image as a result of averaging of the image; this can be observed by viewing the image at different distances.

As an example of stochastic resonance, consider the following demonstration after Simonotto et al. [4]

The Arc de Triomphe ArcFull2.png
The Arc de Triomphe

The image to the left shows an original picture of the Arc de Triomphe in Paris. If this image is passed through a nonlinear threshold filter in which each pixel detects light intensity as above or below a given threshold, a representation of the image is obtained as in the images to the right. It can be hard to discern the objects in the filtered image in the top left because of the reduced amount of information present. The addition of noise before the threshold operation can result in a more recognizable output. The image below shows four versions of the image after the threshold operation with different levels of noise variance; the image in the top right hand corner appears to have the optimal level of noise allowing the Arc to be recognized, but other noise variances reveal different features.

The quality of the image resulting from stochastic resonance can be improved further by blurring, or subjecting the image to low-pass spatial filtering. This can be approximated in the visual system by squinting one's eyes or moving away from the image. This allows the observer's visual system to average the pixel intensities over areas, which is in effect a low-pass filter. The resonance breaks up the harmonic distortion due to the threshold operation by spreading the distortion across the spectrum, and the low-pass filter eliminates much of the noise that has been pushed into higher spatial frequencies.

A similar output could be achieved by examining multiple threshold levels, so in a sense the addition of noise creates a new effective threshold for the measurement device.

Animal physiology

Cuticular mechanoreceptors in crayfish

Evidence for stochastic resonance in a sensory system was first found in nerve signals from the mechanoreceptors located on the tail fan of the crayfish (Procambarus clarkii). [5] An appendage from the tail fan was mechanically stimulated to trigger the cuticular hairs that the crayfish uses to detect pressure waves in water. The stimulus consisted of sinusoidal motion at 55.2 Hz with random Gaussian noise at varying levels of average intensity. Spikes along the nerve root of the terminal abdominal ganglion were recorded extracellularly for 11 cells and analyzed to determine the SNR.

Two separate measurements were used to estimate the signal-to-noise ratio of the neural response. The first was based on the Fourier power spectrum of the spike time series response. The power spectra from the averaged spike data for three different noise intensities all showed a clear peak at the 55.2 Hz component with different average levels of broadband noise. The relatively low- and mid-level added noise conditions also show a second harmonic component at about 110 Hz. The mid-level noise condition clearly shows a stronger component at the signal of interest than either low- or high-level noise, and the harmonic component is greatly reduced at mid-level noise and not present in the high-level noise. A standard measure of the SNR as a function of noise variance shows a clear peak at the mid-level noise condition. The other measure used for SNR was based on the inter-spike interval histogram instead of the power spectrum. A similar peak was found on a plot of SNR as a function of noise variance for mid-level noise, although it was slightly different from that found using the power spectrum measurement.

These data support the claim that noise can enhance detection at the single neuron level but are not enough to establish that noise helps the crayfish detect weak signals in a natural setting. Experiments performed after this at a slightly higher level of analysis establish behavioral effects of stochastic resonance in other organisms; these are described below.

Cercal mechanoreceptors in crickets

A similar experiment was performed on the cricket (Acheta domestica), an arthropod like the crayfish. [6] The cercal system in the cricket senses the displacement of particles due to air currents utilizing filiform hairs covering the cerci, the two antenna-like appendages extending from the posterior section of the abdomen. Sensory interneurons in terminal abdominal ganglion carry information about intensity and direction of pressure perturbations. Crickets were presented with signal plus noise stimuli and the spikes from cercal interneurons due to this input were recorded.

Two types of measurements of stochastic resonance were conducted. The first, like the crayfish experiment, consisted of a pure tone pressure signal at 23 Hz in a broadband noise background of varying intensities. A power spectrum analysis of the signals yielded maximum SNR for a noise intensity equal to 25 times the signal stimulus resulting in a maximum increase of 600% in SNR. 14 cells in 12 animals were tested, and all showed an increased SNR at a particular level of noise, meeting the requirements for the occurrence of stochastic resonance.

The other measurement consisted of the rate of mutual information transfer between the nerve signal and a broadband stimulus combined with varying levels of broadband noise uncorrelated with the signal. The power spectrum SNR could not be calculated in the same manner as before because there were signal and noise components present at the same frequencies. Mutual information measures the degree to which one signal predicts another; independent signals carry no mutual information, while perfectly identical signals carry maximal mutual information. For varying low amplitudes of signal, stochastic resonance peaks were found in plots of mutual information transfer rate as a function of input noise with a maximum increase in information transfer rate of 150%. For stronger signal amplitudes that stimulated the interneurons in the presence of no noise, however, the addition of noise always decreased the mutual information transfer demonstrating that stochastic resonance only works in the presence of low-intensity signals. The information carried in each spike at different levels of input noise was also calculated. At the optimum level of noise, the cells were more likely to spike, resulting in spikes with more information and more precise temporal coherence with the stimulus.

Stochastic resonance is a possible cause of escape behavior in crickets to attacks from predators that cause pressure waves in the tested frequency range at very low amplitudes, like the wasp Liris niger. Similar effects have also been noted in cockroaches. [6]

Cutaneous mechanoreceptors in rats

Another investigation of stochastic resonance in broadband (or, equivalently, aperiodic) signals was conducted by probing cutaneous mechanoreceptors in the rat. [7] A patch of skin from the thigh and its corresponding section of the saphenous nerve were removed, mounted on a test stand immersed in interstitial fluid. Slowly adapting type 1 (SA1) mechanoreceptors output signals in response to mechanical vibrations below 500 Hz.

The skin was mechanically stimulated with a broadband pressure signal with varying amounts of broadband noise using the up-and-down motion of a cylindrical probe. The intensity of the pressure signal was tested without noise and then set at a near sub-threshold intensity that would evoke 10 action potentials over a 60-second stimulation time. Several trials were then conducted with noise of increasing amplitude variance. Extracellular recordings were made of the mechanoreceptor response from the extracted nerve.

The encoding of the pressure stimulus in the neural signal was measured by the coherence of the stimulus and response. The coherence was found to be maximized by a particular level of input Gaussian noise, consistent with the occurrence of stochastic resonance.

Electroreceptors in paddlefish

The paddlefish (Polyodon spathula) hunts plankton using thousands of tiny passive electroreceptors located on its extended snout, or rostrum. The paddlefish is able to detect electric fields that oscillate at 0.5–20 Hz, and large groups of plankton generate this type of signal.

Due to the small magnitude of the generated fields, plankton are usually caught by the paddlefish when they are within 40 mm of the fish's rostrum. An experiment was performed to test the hunting ability of the paddlefish in environments with different levels of background noise. [8] It was found that the paddlefish had a wider distance range of successful strikes in an electrical background with a low level of noise than in the absence of noise. In other words, there was a peak noise level, implying effects of stochastic resonance.

In the absence of noise, the distribution of successful strikes has greater variance in the horizontal direction than in the vertical direction. With the optimal level of noise, the variance in the vertical direction increased relative to the horizontal direction and also shifted to a peak slightly below center, although the horizontal variance did not increase.

Another measure of the increase in accuracy due to the optimal noise background is the number of plankton captured per unit time. For four paddlefish tested, two showed no increase in capture rate, while the other two showed a 50% increase in capture rate.

Separate observations of the paddlefish hunting in the wild have provided evidence that the background noise generated by plankton increase the paddlefish's hunting abilities. Each individual organism generates a particular electrical signal; these individual signals cause massed groups of plankton to emit what amounts to a noisy background signal. It has been found that the paddlefish does not respond to only noise without signals from nearby individual organisms, so it uses the strong individual signals of nearby plankton to acquire specific targets, and the background electrical noise provides a cue to their presence. For these reasons, it is likely that the paddlefish takes advantage of stochastic resonance to improve its sensitivity to prey.

Individual model neurons

Stochastic resonance was demonstrated in a high-level mathematical model of a single neuron using a dynamical systems approach. [9] The model neuron was composed of a bi-stable potential energy function treated as a dynamical system that was set up to fire spikes in response to a pure tonal input with broadband noise and the SNR is calculated from the power spectrum of the potential energy function, which loosely corresponds to an actual neuron's spike-rate output. The characteristic peak on a plot of the SNR as a function of noise variance was apparent, demonstrating the occurrence of stochastic resonance.

Inverse stochastic resonance

Another phenomenon closely related to stochastic resonance is inverse stochastic resonance. It happens in the bistable dynamical systems having the limit cycle and stable fixed point solutions. In this case the noise of particular variance could efficiently inhibit spiking activity by moving the trajectory to the stable fixed point. It has been initially found in single neuron models, including classical Hodgkin-Huxley system. [10] [11] Later inverse stochastic resonance has been confirmed in Purkinje cells of cerebellum, [12] where it could play the role for generation of pauses of spiking activity in vivo.

Multi-unit systems of model neurons

An aspect of stochastic resonance that is not entirely understood has to do with the relative magnitude of stimuli and the threshold for triggering the sensory neurons that measure them. If the stimuli are generally of a certain magnitude, it seems that it would be more evolutionarily advantageous for the threshold of the neuron to match that of the stimuli. In systems with noise, however, tuning thresholds for taking advantage of stochastic resonance may be the best strategy.

A theoretical account of how a large model network (up to 1000) of summed FitzHugh–Nagumo neurons could adjust the threshold of the system based on the noise level present in the environment was devised. [13] [14] This can be equivalently conceived of as the system lowering its threshold, and this is accomplished such that the ability to detect suprathreshold signals is not degraded.

Stochastic resonance in large-scale physiological systems of neurons (above the single-neuron level but below the behavioral level) has not yet been investigated experimentally.

Human perception

Psychophysical experiments testing the thresholds of sensory systems have also been performed in humans across sensory modalities and have yielded evidence that our systems make use of stochastic resonance as well.

Vision

The above demonstration using the Arc de Triomphe photo is a simplified version of an earlier experiment. A photo of a clocktower was made into a video by adding noise with a particular variance a number of times to create successive frames. This was done for different levels of noise variance, and a particularly optimal level was found for discerning the appearance of the clocktower. [4] Similar experiments also demonstrated an increased level of contrast sensitivity to sine wave gratings. [4]

Tactility

Human subjects who undergo mechanical stimulation of a fingertip are able to detect a subthreshold impulse signal in the presence of a noisy mechanical vibration. The percentage of correct detections of the presence of the signal was maximized for a particular value of noise. [15]

Audition

The auditory intensity detection thresholds of a number of human subjects were tested in the presence of noise. [16] The subjects include four people with normal hearing, two with cochlear implants and one with an auditory brainstem implant.

The normal subjects were presented with two sound samples, one with a pure tone plus white noise and one with just white noise, and asked which one contained the pure tone. The level of noise which optimized the detection threshold in all four subjects was found to be between -15 and -20 dB relative to the pure tone, showing evidence for stochastic resonance in normal human hearing.

A similar test in the subjects with cochlear implants only found improved detection thresholds for pure tones below 300 Hz, while improvements were found at frequencies greater than 60 Hz in the brainstem implant subject. The reason for the limited range of resonance effects are unknown. Additionally, the addition of noise to cochlear implant signals improved the threshold for frequency discrimination. The authors recommend that some type of white noise addition to cochlear implant signals could well improve the utility of such devices.

Related Research Articles

In physiology, nociception, also nocioception; from Latin nocere 'to harm/hurt') is the sensory nervous system's process of encoding noxious stimuli. It deals with a series of events and processes required for an organism to receive a painful stimulus, convert it to a molecular signal, and recognize and characterize the signal to trigger an appropriate defensive response.

<span class="mw-page-title-main">Stimulus (physiology)</span> Detectable change in the internal or external surroundings

In physiology, a stimulus is a detectable change in the physical or chemical structure of an organism's internal or external environment. The ability of an organism or organ to detect external stimuli, so that an appropriate reaction can be made, is called sensitivity (excitability). Sensory receptors can receive information from outside the body, as in touch receptors found in the skin or light receptors in the eye, as well as from inside the body, as in chemoreceptors and mechanoreceptors. When a stimulus is detected by a sensory receptor, it can elicit a reflex via stimulus transduction. An internal stimulus is often the first component of a homeostatic control system. External stimuli are capable of producing systemic responses throughout the body, as in the fight-or-flight response. In order for a stimulus to be detected with high probability, its level of strength must exceed the absolute threshold; if a signal does reach threshold, the information is transmitted to the central nervous system (CNS), where it is integrated and a decision on how to react is made. Although stimuli commonly cause the body to respond, it is the CNS that finally determines whether a signal causes a reaction or not.

A mechanoreceptor, also called mechanoceptor, is a sensory receptor that responds to mechanical pressure or distortion. Mechanoreceptors are innervated by sensory neurons that convert mechanical pressure into electrical signals that, in animals, are sent to the central nervous system.

<span class="mw-page-title-main">Sensory neuron</span> Nerve cell that converts environmental stimuli into corresponding internal stimuli

Sensory neurons, also known as afferent neurons, are neurons in the nervous system, that convert a specific type of stimulus, via their receptors, into action potentials or graded receptor potentials. This process is called sensory transduction. The cell bodies of the sensory neurons are located in the dorsal ganglia of the spinal cord.

Stochastic resonance (SR) is a phenomenon in which a signal that is normally too weak to be detected by a sensor, can be boosted by adding white noise to the signal, which contains a wide spectrum of frequencies. The frequencies in the white noise corresponding to the original signal's frequencies will resonate with each other, amplifying the original signal while not amplifying the rest of the white noise – thereby increasing the signal-to-noise ratio, which makes the original signal more prominent. Further, the added white noise can be enough to be detectable by the sensor, which can then filter it out to effectively detect the original, previously undetectable signal.

<span class="mw-page-title-main">Caridoid escape reaction</span> Innate escape mechanism by crustaceans

The caridoid escape reaction, also known as lobstering or tail-flipping, refers to an innate escape mechanism in marine and freshwater crustaceans such as lobsters, krill, shrimp and crayfish.

A gamma wave or gamma rhythm is a pattern of neural oscillation in humans with a frequency between 25 and 140 Hz, the 40 Hz point being of particular interest. Gamma rhythms are correlated with large-scale brain network activity and cognitive phenomena such as working memory, attention, and perceptual grouping, and can be increased in amplitude via meditation or neurostimulation. Altered gamma activity has been observed in many mood and cognitive disorders such as Alzheimer's disease, epilepsy, and schizophrenia.

In audiology and psychoacoustics the concept of critical bands, introduced by Harvey Fletcher in 1933 and refined in 1940, describes the frequency bandwidth of the "auditory filter" created by the cochlea, the sense organ of hearing within the inner ear. Roughly, the critical band is the band of audio frequencies within which a second tone will interfere with the perception of the first tone by auditory masking.

<span class="mw-page-title-main">Neural oscillation</span> Brainwaves, repetitive patterns of neural activity in the central nervous system

Neural oscillations, or brainwaves, are rhythmic or repetitive patterns of neural activity in the central nervous system. Neural tissue can generate oscillatory activity in many ways, driven either by mechanisms within individual neurons or by interactions between neurons. In individual neurons, oscillations can appear either as oscillations in membrane potential or as rhythmic patterns of action potentials, which then produce oscillatory activation of post-synaptic neurons. At the level of neural ensembles, synchronized activity of large numbers of neurons can give rise to macroscopic oscillations, which can be observed in an electroencephalogram. Oscillatory activity in groups of neurons generally arises from feedback connections between the neurons that result in the synchronization of their firing patterns. The interaction between neurons can give rise to oscillations at a different frequency than the firing frequency of individual neurons. A well-known example of macroscopic neural oscillations is alpha activity.

<span class="mw-page-title-main">Neuronal noise</span> Random electric fluctuations in neurons

Neuronal noise or neural noise refers to the random intrinsic electrical fluctuations within neuronal networks. These fluctuations are not associated with encoding a response to internal or external stimuli and can be from one to two orders of magnitude. Most noise commonly occurs below a voltage-threshold that is needed for an action potential to occur, but sometimes it can be present in the form of an action potential; for example, stochastic oscillations in pacemaker neurons in suprachiasmatic nucleus are partially responsible for the organization of circadian rhythms.

<span class="mw-page-title-main">Noise (electronics)</span> Random fluctuation in an electrical signal

In electronics, noise is an unwanted disturbance in an electrical signal.

Neural coding is a neuroscience field concerned with characterising the hypothetical relationship between the stimulus and the neuronal responses, and the relationship among the electrical activities of the neurons in the ensemble. Based on the theory that sensory and other information is represented in the brain by networks of neurons, it is believed that neurons can encode both digital and analog information.

<span class="mw-page-title-main">Biological neuron model</span> Mathematical descriptions of the properties of certain cells in the nervous system

Biological neuron models, also known as spiking neuron models, are mathematical descriptions of neurons. In particular, these models describe how the voltage potential across the cell membrane changes over time. In an experimental setting, stimulating neurons with an electrical current generates an action potential, that propagates down the neuron's axon. This axon can branch out and connect to a large number of downstream neurons at sites called synapses. At these synapses, the spike can cause release of a biochemical substance (neurotransmitter), which in turn can change the voltage potential of downstream neurons, potentially leading to spikes in those downstream neurons, thus propagating the signal. As many as 85% of neurons in the neocortex, the outermost layer of the mammalian brain, consist of excitatory pyramidal neurons, and each pyramidal neuron receives tens of thousands of inputs from other neurons. Thus, spiking neurons are a major information processing unit of the nervous system.

Coincidence detection is a neuronal process in which a neural circuit encodes information by detecting the occurrence of temporally close but spatially distributed input signals. Coincidence detectors influence neuronal information processing by reducing temporal jitter and spontaneous activity, allowing the creation of variable associations between separate neural events in memory. The study of coincidence detectors has been crucial in neuroscience with regards to understanding the formation of computational maps in the brain.

Recurrent thalamo-cortical resonance is an observed phenomenon of oscillatory neural activity between the thalamus and various cortical regions of the brain. It is proposed by Rodolfo Llinas and others as a theory for the integration of sensory information into the whole of perception in the brain. Thalamocortical oscillation is proposed to be a mechanism of synchronization between different cortical regions of the brain, a process known as temporal binding. This is possible through the existence of thalamocortical networks, groupings of thalamic and cortical cells that exhibit oscillatory properties.

Synaptic noise refers to the constant bombardment of synaptic activity in neurons. This occurs in the background of a cell when potentials are produced without the nerve stimulation of an action potential, and are due to the inherently random nature of synapses. These random potentials have similar time courses as excitatory postsynaptic potentials (EPSPs) and inhibitory postsynaptic potentials (IPSPs), yet they lead to variable neuronal responses. The variability is due to differences in the discharge times of action potentials.

<span class="mw-page-title-main">Somatosensory system</span> Nerve system for sensing touch, temperature, body position, and pain

In physiology, the somatosensory system is the network of neural structures in the brain and body that produce the perception of touch, as well as temperature (thermoception), body position (proprioception), and pain. It is a subset of the sensory nervous system, which also represents visual, auditory, olfactory, gustatory and vestibular stimuli.

A sense is a biological system used by an organism for sensation, the process of gathering information about the world through the detection of stimuli. Although in some cultures five human senses were traditionally identified as such, many more are now recognized. Senses used by non-human organisms are even greater in variety and number. During sensation, sense organs collect various stimuli for transduction, meaning transformation into a form that can be understood by the brain. Sensation and perception are fundamental to nearly every aspect of an organism's cognition, behavior and thought.

Transcranial random noise stimulation (tRNS) is a non-invasive brain stimulation technique and a form of transcranial electrical stimulation (tES). Terney et al from Göttingen University was the first group to apply tRNS in humans in 2008. They showed that by using an alternate current along with random amplitude and frequency in healthy subjects, the motor cortex excitability increased for up to 60 minutes after 10 minutes of stimulation. The study included all the frequencies up to half of the sampling rate i.e. 640 Hz, however the positive effect was limited only to higher frequencies. Although tRNS has shown positive effects in various studies the optimal parameters, as well as the potential clinical effects of this technique, remain unclear.

The spike response model (SRM) is a spiking neuron model in which spikes are generated by either a deterministic or a stochastic threshold process. In the SRM, the membrane voltage V is described as a linear sum of the postsynaptic potentials (PSPs) caused by spike arrivals to which the effects of refractoriness and adaptation are added. The threshold is either fixed or dynamic. In the latter case it increases after each spike. The SRM is flexible enough to account for a variety of neuronal firing pattern in response to step current input. The SRM has also been used in the theory of computation to quantify the capacity of spiking neural networks; and in the neurosciences to predict the subthreshold voltage and the firing times of cortical neurons during stimulation with a time-dependent current stimulation. The name Spike Response Model points to the property that the two important filters and of the model can be interpreted as the response of the membrane potential to an incoming spike (response kernel , the PSP) and to an outgoing spike (response kernel , also called refractory kernel). The SRM has been formulated in continuous time and in discrete time. The SRM can be viewed as a generalized linear model (GLM) or as an (integrated version of) a generalized integrate-and-fire model with adaptation.

References

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  16. ↑ Zeng FG, Fu QJ, Morse R (June 2000). "Human hearing enhanced by noise". Brain Research. 869 (1–2): 251–5. doi:10.1016/S0006-8993(00)02475-6. PMID   10865084. S2CID   11934512.
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