Stochastic resonance in the sensory systems and its applications in neural prosthetics

(cid:1) In stochastic resonance, optimal noise enhances the performance of a system. (cid:1) The applications of stochastic resonance have been demonstrated in medical devices to improve sensory function. (cid:1) Stochastic resonance can help improve existing technologies in the medical ﬁeld.


Introduction
The counterintuitive idea that noise (random variability) which is generally considered disruptive (Shannon, 1948;Von Neumann, 1956), might, in the right circumstances, be helpful to information transfer and processing, is known as stochastic resonance (SR) (Moss et al., 2004).As noise is inherent in biological systems, enthusiasm has grown around the potential applications of SR in sensory biology, neuroscience, and medical science (Moss et al., 2004).Several previous review papers have covered growing research output surrounding SR and its applications, particularly in biological and sensory systems (Anishchenko et al., 1999;McDonnell and Abbott, 2009;McDonnell and Ward, 2011;Moss et al., 2004;Wiesenfeld and Moss, 1995).The purpose of the present narrative review is to examine and evaluate advances in the use of SR in human sensory prosthetic applications.
We begin with an overview of noise in the nervous system and introduce SR (also covered in previous reviews (Anishchenko et al., 1999;McDonnell and Abbott, 2009;McDonnell and Ward, 2011;Moss et al., 2004;Wiesenfeld and Moss, 1995)).We then explore occurrences and applications of SR in hearing, somatosensory or tactile sensation, and vision.We also explore examples and applications of cross-modal SR wherein subthreshold noise from one sensory system enhances performance in another (Manjarrez et al., 2007).We emphasise the prevalence of sensory-related impairments in each modality and consider the prospects SR offers to inform the development of technologies designed to improve the lives of individuals who experience such deficits.Finally, we aim to identify areas where more research is required, highlighting future directions that could maximise the impact SR research can have on neural prosthetics and other similar sensory technologies.

What is noise?
Noise is a term used to describe background disturbances that distort the desired measurement and cause variability in measured data (McDonnell and Abbott, 2009).When we think of noise, we typically think of auditory noise, which is formally defined as ''unwanted sound."However, noise is also a broad term used to describe different forms of random interference from several different sources.Examples of non-auditory noise include the static snow on an untuned television set, random movement of small particles within a liquid, and even volatility in stock prices.In many instances, random variability is destructive.For example, telecommunication processes are interrupted by noise appearing as electronic fluctuations or electromagnetic interference (McDonnell and Abbott, 2009).Similarly, random variability in neural firing (or neural noise) in the human brain is associated with disruption of cognitive functions and symptoms of various neurological disabilities, such as dyslexia (Hancock et al., 2017) and autism (Rubenstein and Merzenich, 2003).
There are many examples in human psychophysics research, which investigates sensation and perception of physical stimuli, of variability in sensory and neural signals being destructive to sensory and perceptual processes (Moss et al., 2004).In such circumstances, noise has a masking effect on stimuli, as the additive impact of the signal and noise (mask) makes it more difficult to identify weak signals.In visual perception, the joint presentation of a visual test stimulus and a visual masking stimulus usually degrades the image (Kahneman, 1968).For example, in word recognition, the presentation of an overlaid random visual pattern slowed down the recognition process which suggested that words should have been presented for longer before they could be accurately identified (Scharf et al., 1966).In another example, sinusoidal electrovibration signals presented on a touch screen were effectively masked by bursts of electrovibratory noise (Vardar et al., 2018).Performance on the detection task was a linear function of the noise level, with signal thresholds increasing as noise level increased.There is also evidence that even the natural random motion of the hair cells in the inner ear might disrupt auditory perception near threshold (De Vries, 1948;Harris, 1968).However, later research has challenged this finding (Jaramillo and Wiesenfeld, 1998).Nonetheless, overall, there is compelling evidence that excessive noise disrupts signal detection and processing in various sensory modalities.

What is stochastic resonance?
Considering that noise causes significant disruption in most circumstances (Shannon, 1948;Von Neumann, 1956), it might be surprising to hear that random variability is pervasive in natural and manufactured systems.For example, the brain is inherently noisy, with a significant proportion of its electrical activity arising from random neural firing (Neri, 2010).Yet, despite the abundance of random neural excitation, the brain appears adapted to these occurrences, and important cognitive processes are undeterred by this variability and could even benefit from it (McDonnell and Ward, 2011;Ward and Greenwood, 2016).
The first mention of SR was in a series of papers examining the periodic occurrences of ice ages (Benzi et al., 1982;Benzi et al., 1981;Nicolis, 1982Nicolis, , 1993)).Several forms of SR feature in the scientific literature; the version described in these early examples is known as dynamical SR.Dynamical SR features the co-occurrence of weak periodic forcing and noise (either internal or environmental), which drives a system between two stable states separated by an unstable intermediate state (Benzi et al., 1981).The system must acquire sufficient energy to change between states.In the ice age example, the stable states are a glacial stage and an interglacial stage.The weak periodic forcing is solar radiation, which varies according to the earth's orbit and the noise results from fluctuations in temperature due to atmospheric and oceanic circulations.In this model, the combination of random temperature fluctuations and periodic solar radiation produces sufficient energy to generate a shift between the two climatic states (Benzi et al., 1982).Based on this principle, SR models for perceptual/cognitive phenomena that display two conflicting states, such as binocular rivalry, have also been developed (Kim et al., 2006;Moreno-Bote et al., 2007).
Contemporary research has expanded the definition of SR beyond its original conceptualisation in climatological models.A threshold model of SR is particularly popular in biological systems.This model includes three essential components: a threshold, a subthreshold stimulus, and noise (Moss et al., 2004).In this model, the probability of the subthreshold stimulus surpassing the detection threshold increases when combined with some optimal nonzero level of noise (Fig. 1).
The effect occurs as the variability offered by the noise interacts with the stimulus such that it boosts the subthreshold stimulus above the threshold (Moss et al., 2004).Less than optimal noise does not boost the signal over the threshold, whereas the addition of more noise than the optimal level is detrimental to performance, leading to an inverted U-shaped performance graph (Fig. 1).This model applies well to biological systems because neuronal networks are characteristically noisy, and neurons require excitation to surpass a threshold to generate an impulse (Koch and Segev, 2000;McCulloch and Pitts, 1943).We also note that the threshold need not be a step function -it can be what is called a ''soft threshold" such as an S-shaped (i.e., logistic or tanh) function (Chapeau-Blondeau and Godivier, 1997;Greenwood et al., 2004).In the soft threshold case, the threshold function should be noninvertible, i.e., the response saturates above a certain signal or energy level.
For noise to be beneficial (i.e., for SR to be present), it must be present at an optimal level, regardless of its type and form (auditory, vibrational, visual, neural, electrical, etc., Gaussian, 1/f-like, etc.), and there must be a relevant nonlinearity in the system, such as a hard or soft threshold, with which the noise interacts, as in Fig. 1.Too little or too much noise can have the opposite effect from SR, reducing performance.The optimal noise may depend on task (Raul et al., 2023), and individual (Aihara et al., 2008(Aihara et al., , 2010)).In other words, no ''specific" type of noise is required for SR to occur-any noise can induce SR if used in a suitable context.

Early examples in sensory biology
A growing body of research investigates the SR phenomenon in biological systems.Some of the first demonstrations of SR in biological systems came from studies of neural activation in crayfish (Douglass et al., 1993;Pei et al., 1996).One such study found that the probability of neural responses of crayfish mechanoreceptors to weak stimuli increased with optimal intensities of external noise applied to mechanoreceptor cells (Douglass et al., 1993).Another study found transmission of mechanosensory information improved when interneurons were stimulated using light energy (i.e., varying intensities of light shone on the sixth ganglion) (Pei et al., 1996).Since the early studies with crayfish, there have been multiple demonstrations of SR in biological systems (Funke et al., 2007;Martínez et al., 2007;Russell et al., 1999).Given the extremely broad literature covering SR in biological systems, we focus on the utility of noise in three human-relevant sensory modalities (hearing, touch, and vision) for the remainder of this review.2

Stochastic resonance in the auditory system
Although noise is generally a nuisance in the auditory system (De Vries, 1948;Harris, 1968), some research suggests that random variability sometimes may benefit auditory processing.For example, there is significant evidence that auditory sensation and processing naturally exploits SR via a similar mechanism to the early dynamical models of SR.A study using hair cells from the cochlea of leopard frogs (Rana pipiens) found that the inner hair cells naturally exploit SR to achieve greater sensitivity to weak sounds (Jaramillo and Wiesenfeld, 1998).This effect occurs because the action of inner hair cells depends on the activation of mechanically gated ion channels to convert mechanical energy into action potentials (Cunningham and Müller, 2019).Although the mechanical stimulation generated by weak auditory stimuli alone is not sufficient to open or close a channel, the addition of some noise can amplify the mechanical stimulation to reach the activation barrier.Furthermore, noise occurs naturally in the auditory system via the random motion of inner hair cells in the surrounding fluid.This noise increases the mechanoelectrical transduction of weak signals and improves hearing.Thus, it is likely that this adaptation offered a survival advantage at some evolutionary stage (Jaramillo and Wiesenfeld, 1998).what kind of searches were done.We conducted a search in Google Scholar for studies on 'noise in prosthesis', 'stochastic resonance in prosthesis', 'noise in devices', 'stochastic resonance in auditory prosthesis', 'stochastic resonance in visual prosthesis', 'stochastic resonance for balance', and 'noisy galvanic vestibular stimulation'.Note that the literature for noisy galvanic vestibular stimulation is too vast for a narrative review and therefore, we included some systematic review studies for evidence.Studies involving transcranial random noise stimulation (tRNS) were excluded as they were beyond the scope of this review.Additionally, we also searched Google Scholar for 'inconsistent evidence for stochastic resonance in prostheses', 'inconsistent evidence for stochastic resonance in devices', 'no evidence for stochastic resonance in prosthesis', 'no stochastic resonance' and searched PubMed database for '"no stochastic resonance" prostheses' and '"no stochastic resonance" devices.','"no stochastic resonance" clinical' to include studies where stochastic resonance was not observed.A few studies were also identified by hand-searching references from key articles.Note that the quotations were not used for the Google Scholar searches.
More recent studies have found further evidence of SR in auditory processes.In these studies, however, the SR effect appears to occur in the Central Nervous System (CNS) rather than in the cochlea, and via threshold rather than dynamical SR.Auditory Evoked Potentials (AEP) are a measure of electrical activity in the CNS in response to auditory stimuli and can be used to measure hearing thresholds (Paulraj et al., 2015).The Auditory Steady-State Response (ASSR) is an AEP that specifically measures hearing sensitivity (Korczak et al., 2012).A study of normal-hearing individuals demonstrated that synchronisation of neural activation with a periodic auditory stimulus applied to the left ear improved with additive white noise applied to the right ear (measured via the ASSR) (Tanaka et al., 2010).Another study using the auditory 40-Hz transient response (ATR), closely related to the ASSR, found that the ATR in bilateral auditory cortex, left posterior cingulate cortex and left superior frontal gyrus, as well as phase coherence (phase synchronization) between these areas, was maximal for optimal levels of added broadband auditory noise (Ward et al., 2010).These results occurred especially for alpha (10 Hz) and gamma (40 Hz) frequency spectral power, regardless of whether the noise was mixed with the stimulus or presented to the opposite ear from the stimulus.In addition, better synchronisation (phase coherence) of neural activation with an auditory stimulus leads to more accurate auditory perception and clearer hearing.In contrast, a lack of synchronisation occurs with auditory impairment (Nash-Kille and Sharma, 2014).
An experimental study with normal hearing individuals revealed a positive effect of added noise on pitch discrimination (Oh and Lee, 2021).In the study, participants wore headphones and were required to distinguish between a constant reference tone and a second tone applied to the other ear.In addition, participants' task was to indicate whether they heard two different tones or a single tone.Results suggested that the addition of lowintensity background noise at approximately 5 dB resulted in better pitch discrimination (Oh and Lee, 2021).Thus, findings from this experimental study and earlier research (Tanaka et al., 2010;Ward et al., 2010) suggest a benefit of additive noise to auditory functions for healthy hearing individuals via the SR phenomenon.In contrast to the studies just described, however, another recent paper reported that SR was absent in the human auditory system when noise was applied acoustically or electrically via transcranial random noise stimulation (or tRNS) (Rufener et al., 2020).

Hearing impairments and stochastic resonance
Over 430 million people worldwide experience a disabling level of hearing loss, and these numbers are likely to increase to over 700 million by 2050 (WHO, 2021b).There are several causes of hearing impairment, most of which relate to damage to the sensory cells within the inner ear (sensorineural hearing loss).Sensorineural hearing loss can result from disease, age, injury, extended exposure to loud sounds, and certain medications (Baek, 2015).Individuals with sensorineural impairment have difficulty hearing sounds at lower levels and distinguishing one sound from another, especially when one rapidly follows the other (Dillon, 2012).Depending on the severity, hearing impairment can cause difficulties with communication (Knutson and Lansing, 1990) and in everyday activities such as work (Morata et al., 2005).Moreover, long-term hearing impairment has been associated with decreases in brain volume both in the right temporal lobe as well as brainwide (Lin et al., 2014), and with increased risk of dementia (Powell et al., 2021).
Hearing aids and cochlear implants are technologies designed to overcome some of the deficits experienced by people with partial sensorineural hearing loss.Hearing aids work by amplifying sounds entering the ear, facilitating their detection by remaining hair cells (Dillon, 2012).While hearing aids are helpful for individuals with mild to moderate hearing loss, individuals experiencing severe to profound hearing loss have attained greater benefits from cochlear implants (Dillon, 2012).Consequently, cochlear implants are an option for individuals with more comprehensive hearing loss.Cochlear implants function by imitating the role of sensory cells in the ear and converting sound energy into electrical impulses that stimulate the auditory nerve (Zeng et al., 2008).Cochlear implants are widely considered to be the most effective neural prosthetic (Zeng et al., 2008).Hearing aids and cochlear implants significantly reduce the difficulties with communication (Knutson and Lansing, 1990) and in everyday activities (Morata et al., 2005) associated with hearing loss (Dillon, 2012;Zeng et al., 2008).
Ongoing research in bioengineering offers a pathway to continue to improve auditory prosthetic technologies.Several studies (Morse and Evans, 1996;Morse et al., 2007;Rubinstein and Hong, 2003;Zeng et al., 2000) have supported the application of SR for improving the effectiveness of cochlear implants.Early work used nerve cells (sciatic nerve) from toads (Xenopus laevis) to model the response of the human cochlear nerve to vowel sounds delivered via a cochlear implant (Morse and Evans, 1996).Results indicated that the addition of noise to the vowel sounds produced by the cochlear implant led to greater sensitivity in neural excitation and improved discriminability of vowel sounds from the neural recordings (Morse and Evans, 1996).Further research investigating auditory stimulus detection and discrimination among a sample of human participants (nine with normal hearing, one with a cochlear implant and one with a brain stem implant) found that performance improved for all participants with additive noise (Zeng et al., 2000).Similar results of SR were also observed in cochlear implant listeners in a similar study (Chatterjee and Robert, 2001).
Examination of a larger sample of thirty participants, all with cochlear implants, revealed that for almost all participants, the addition of auditory noise (high-frequency pulses) enabled them to hear much softer sounds (Rubinstein and Hong, 2003).More recent evidence has also shown that adding noise to cochlear implants of deaf adults improved participants' ability to categorise various vowels based on their sounds, but it did not significantly improve vowel recognition (Morse et al., 2022).Some recent research investigates specific techniques to leverage SR to improve the effectiveness of cochlear implants.One technique that features prominently in the literature is a specialised process called stochastic beamforming.Stochastic beamforming involves presenting different levels of Gaussian noise to each cochlear implant electrode, leading to different responses in each of the receiving nerve fibres, allowing greater information transmission (Morse et al., 2007).Morse et al. (2007) through modelling and experiments, showed that the stochastic beamforming technique results in increased dynamic range thus leading to enhanced speech comprehension.Stochastic beamforming represents one novel innovation motivated by research in SR with the potential to substantially improve cochlear implants' functionality.However, further research with larger samples is required before it can be implemented for general use.

Stochastic resonance in the somatosensory system
The somatosensory system detects and processes physical sensations, including pain, pressure, movement, and temperature.It relies upon the transfer of tactile information gathered by sensory neurons to the CNS via neural impulses (Abraira and Ginty, 2013).Somatosensory information is important for responding to internal and external stimuli and contributes, for example, to balance and proprioception (Abraira and Ginty, 2013).There is evidence of SR in various functions of the somatosensory system.
Experimental evidence has demonstrated SR in somatosensory processing at the peripheral (Ivey et al., 1998) and spinocortical level (Manjarrez et al., 2002;Manjarrez et al., 2003).Behavioural studies with human participants have revealed that the addition of noise at optimal levels assists in detecting weak tactile signals (Collins et al., 1996), motor precision (Mendez-Balbuena et al., 2012), and balance (Collins et al., 2003;Priplata et al., 2002).For example, participants' ability to exert a controlled level of force against a static opposing force was more precise and consistent when mechanical noise (low-pass filtered to the range 0-15 Hz) was applied to the index finger (Mendez-Balbuena et al., 2012).Further research confirmed that noise benefits occurred for weak/near-threshold stimuli, but that noise hindered the detection of above-threshold stimuli (Collins et al., 1997).Also, multiple studies have found that mechanical noise applied to the feet improved balance while standing (Collins et al., 2003;Priplata et al., 2002).These examples demonstrate that external noise at optimal intensities offers opportunities to improve the performance of the somatosensory system.

Uses of stochastic resonance for proprioceptive and neurodegenerative conditions
Impairments in tactile sensation and proprioception are associated with poorer balance and mobility, which can have significant consequences.Falls are the second largest contributor to accidental death worldwide, behind road accidents, and disproportionately affect the elderly (Heinrich et al., 2010;WHO, 2021a).Falls also have a significant social and psychological impact on the elderly; falls are associated with anxiety and depressive symptoms, isolation, and social withdrawal (Pin and Spini, 2016).
Good balance involves integrating information from the visual, somatosensory, and vestibular systems.As we age, however, these systems deteriorate, leading to disturbances in gait and balance (Horak, 2006;Wells et al., 2003).Sensory deficits among the elderly can be attributed to higher thresholds caused by loss of receptor density, decreased skin elasticity, and decreased neural activity (Kenshalo Sr, 1986).There is strong evidence that lack of tactile sensation beneath the feet is associated with poorer balance among the elderly (Lord et al., 1994) and in diabetic individuals (Kars et al., 2009).Lower limb amputees also experience mobility challenges attributed to the loss of sensory feedback required for proprioception (Likens et al., 2020).Falls cause a significant burden at individual and societal levels, and individuals with deficits in tactile sensation and proprioception are most at risk.SR might offer an opportunity to improve tactile sensation in the feet, resulting in better outcomes for individuals vulnerable to falls.Several studies (Likens et al., 2020;Moon et al., 2020;Priplata et al., 2002;Wells et al., 2005) have investigated the possibility of increasing the sensitivity of sensory receptors in the feet to tactile stimuli via the addition of mechanical noise.After the initial finding that mechanical noise applied to the feet improved balance while standing on a vibrating plate (Priplata et al., 2002), it was suggested that vibrating shoe inserts might overcome balance difficulties caused by deficits in sensation.The following year, the impact of vibrating insoles on balance showed that vibrating insoles led to improved balance among participants of all ages (Priplata et al., 2003).Five years later, a similar set of vibrating insoles was tested on individuals with diabetic neuropathy, again with some encouraging results (Hijmans et al., 2008;Orlando et al., 2024) (see Table 1).Lastly, a recent pilot study showed that vibrating insoles helped improve plantar sensation in diabetic peripheral neuropathy participants (Ennion and Hijmans, 2024).
As research continues, the design of vibrating insoles continues to develop.For example, a recent study tested a set of vibrating insoles with a more user-friendly design (Moon et al., 2020).The design included insoles that fit comfortably within the shoes' body and a smartphone app to control the noise intensity (Fig. 2).Research is also beginning to test whether mechanical noise could improve balance among unilateral lower-limb amputees.A pilot study with twenty unilateral transtibial amputees revealed optimal noise intensities led to greater consistency in step length and reductions in postural sway whilst standing (Likens et al., 2020).Thus, the vibrating insoles are a simple, SR-based sensory prosthetic that can improve outcomes among many individuals experiencing impaired tactile sensation and proprioception.Zandiyeh et al. (2019) studied the effect of SR (mechanical vibration) on improving knee somatosensory acuity (proprioception and kinaesthesia) in females who had their ACL (anterior cruciate ligament) reconstructed (three months post-surgery), and in healthy controls.The authors found that SR stimulation improved somatosensory acuity in both the ACL reconstructed group and in healthy controls.They also showed that proprioception (measured with joint position sense) was improved via SR (the ACL reconstructed group showed a more profound effect), but the effect on kinaesthesia (measured with the threshold to detection of passive movement) did not reach significance.Overall, this study showed that SR can be beneficial in individuals who have had ACL reconstructive surgery.However, proprioception (measured by joint reposition sense) was not improved in participants with chronic ankle instability when a customised SR stimulation device was used in an earlier study (Ross et al., 2018).
SR also helped improve balance in some neurological disorders.For example, a case-control study showed that SR electrical stimulation was an effective stimulation approach for reducing postural sway and improving balance in children diagnosed with cerebral palsy (spastic diplegia) (Zarkou et al., 2018).More recently, Lynn et al. (2023) tested a stochastic resonance stimulation (SRS) device in a pilot study to investigate the effects of SR on manual abilities in children with hemiplegic cerebral palsy.In this study, the children donned wrist and arm bands that delivered SRS via embedded piezoelectric actuators in two randomly assigned conditions (i.e., sham: device off) and subthreshold stimulation (SBT-SRS).In both conditions, participants were required to complete uni-manual and bimanual tasks.The authors showed that the children with hemiplegic cerebral palsy demonstrated improved uni-manual abilities and increased function of the impaired hand on bimanual tasks when receiving a single session of SBT-SRS.Additionally, in a subset of participants, the authors also conducted the task in an above-threshold stimulation (AT-SRS) condition.Here the authors found that some children also benefited (i.e., improvement in manual abilities) with a single session of AT-SRS.
Noise might also alleviate sensorimotor symptoms caused by neurodegenerative conditions such as Parkinson's disease (Liu et al., 2018).Common motor symptoms of Parkinson's disease, such as the characteristic tremor, result from the failure of neurons in the thalamus to send accurate sensorimotor signals (Schiff, 2010).Modelling suggests that SR may reduce Parkinson's symptoms via the addition of appropriate noise stimulation to neurons in the basal ganglia (Liu et al., 2018).Currently, treatment of Parkinson's symptoms occurs via deep brain stimulation, which involves the introduction of high-frequency electrical pulses.However, these electrical pulses take a lot of energy to produce.Modelling suggests that SR stimulation could instead reduce the energy cost by using low-frequency, low-intensity noise which comes at a low energy cost and is more likely to induce normal neural firing (Liu et al., 2018).In addition, further modelling suggests that SR might assist in the treatment of other neurological diseases with motor symptoms such as dystonia and refractory epilepsy (Liu Table 1 The applications of SR across various modalities summarised. (continued on next page) P. Matthews, P. Raul, L.M. Ward et al. Clinical Neurophysiology 165 (2024) 182-200 et al., 2018).In addition to modelling studies, experimental evidence for non-invasive SR via whole-body vibrations (Kaut et al., 2011;Kaut et al., 2016;Rogan and Taeymans, 2023) and stochastic vestibular stimulation (Bergquist, 2015) has shown promise in improving Parkinson-related symptoms.SR has also been illustrated in neurodegenerative conditions through noisy galvanic vestibular stimulation (nGVS).Wuehr et al. (2022) investigated the effects of low-intensity vestibular noise stimulation on postural instability in participants with Parkinson's disease.They found that at least half of their participants showed improvements in postural balance due to SR when treated with low-intensity nGVS.This suggests that low-intensity nGVS can be useful for improving postural stability for individuals with Parkinson's disease.In a more recent study, nGVS resulted in a beneficial balance response but did not affect gait parameters for participants with Parkinson's disease (Peto et al., 2024).
In another study, Wuehr et al. (2023) also showed that lowintensity nGVS improved vestibular motion perception performance in patients diagnosed with bilateral vestibulopathy.A systematic review and meta-analysis also showed moderate evidence for SR induced via nGVS in people with bilateral vestibulopathy (McLaren et al., 2022), although this improvement was context specific (outlined in Table 1).More recently, Wuehr et al. (2024) showed that nGVS resulted in a strong SR effect such that postural symptoms were drastically reduced in people with progressive supranuclear palsy indicating clinical relevance.Interestingly, however, no clear strong SR was found on standing balance when nGVS was applied to healthy adults (Assländer et al., 2021;Keywan et al., 2020;Rice, 2021).Therefore, SR can be used as an effective non-invasive therapeutic tool for various clinical conditions in the proprioceptive domain.

Stochastic resonance in visual perception
Perception and processing of visual stimuli rely upon the stimulation of photoreceptors surpassing a threshold (Maunsell and Essen, 1983a;Maunsell and Essen, 1983b).For example, in ideal artificial conditions, the absolute threshold for detecting light is about six photons (Hecht et al., 1942).The existence of such thresholds makes SR possible.Similar to the finding in the auditory system, there is evidence that the visual system exploits SR.For Note.Coloured rows show studies where no clear SR effect was reported.
P. Matthews, P. Raul, L.M. et al. Clinical Neurophysiology 165 (2024) 182-200 example, micro-movements of cats' eyes can lead to improved transmission of visual signals and improved visual acuity (Hennig et al., 2002).A similar phenomenon occurs in human vision wherein constant tiny eye movements, called microsaccades, result in greater clarity of peripheral vision (Hennig and Wörgötter, 2003).Indeed, some evidence suggests that additive noise can optimise the performance of the human visual system.Computational models demonstrate that visual noise enhances the discriminability of ambiguous visual stimuli (Riani and Simonotto, 1994).A functional magnetic resonance imaging (fMRI) study indicated that, at optimal external noise levels, the volume of visual cortical activity passes through a maximum whilst completing a task of processing noisy images (Simonotto et al., 1999).Several behavioural studies in humans and animals have found that visual functions, including contrast sensitivity (Anderson et al., 2000), threedimensional perception (Ditzinger et al., 2000), motion discrimination (Treviño et al., 2016) and letter recognition (Itzcovich et al., 2017;Piana et al., 2000;Raul et al., 2023), benefit from the introduction of optimal levels of external noise.
These effects are not universal, however, and some research findings (Aihara et al., 2008(Aihara et al., , 2010) ) implicate individual differences in responses to additive noise on sensory processes.The perceptual system itself has a significant amount of internal noise and the amount of internal noise differs from person to person, thereby affecting whether SR will occur (e.g., there is an optimal amount of noise) or not (there is too much noise (Aihara et al., 2008;Raul et al., 2023;van Boxtel, 2019)).

Stochastic resonance and visual impairment
Globally, over 285 million people are visually impaired; of those, 39 million are blind, and 246 million experience low vision (Pascolini and Mariotti, 2011).Common causes of visual impairment include cataracts, glaucoma, age-related macular degeneration (AMD), corneal opacities and diabetic retinopathy (Pascolini and Mariotti, 2011).A variety of measures are available for reducing the deficits caused by visual impairment.Corrective lenses are helpful in most cases, and surgical interventions have proved effective in restoring vision among with cataracts (Lubin ´ski et al., 2014) and glaucoma (Coleman, 2012).Retinal disorders such as age-related macular degeneration and retinitis pig-mentosa cause damage to photoreceptor cells on the retina that is not easily corrected with existing therapies (Cho et al., 2021;Weiland and Humayun, 2008), although there are some promising approaches involving natural products (Cho et al., 2021).There is some evidence that stem cell therapy (MacLaren and Pearson, 2007) and retinal implantation (Radtke et al., 2008) could help improve vision for individuals with retinal degeneration.Several studies (Dobelle et al., 1974;Humayun et al., 2012;Schiller and Tehovnik, 2008;Veraart et al., 1998;Weiland and Humayun, 2008) have investigated the feasibility of a visual prosthesis that uses electrical activation of sensory neurons in the visual system to restore visual function among individuals with severe impairments.
A visual prosthesis that restores some sense of vision to individuals with retinal disorders is currently under development.The proposed visual prosthesis would need to replace the role of the damaged photoreceptors and stimulate the appropriate retinal ganglion cells to carry visual information to the CNS for processing (Schiller and Tehovnik, 2008).Clinical trials (Humayun et al., 2012) have revealed that the Argus II Retinal Prosthesis System (Fig. 3) improves users' object localisation, motion discrimination, and visual acuity whilst using the implant.However, the visual experience offered is markedly different from natural vision.Thus, SR research might also offer an opportunity to improve this technology.
Research among a clinical cohort suggests that individuals with visual impairments might benefit from SR (Itzcovich et al., 2017).A trial investigating letter recognition among participants diagnosed with retinal disorders (optic atrophy, degenerative myopia, and retinitis pigmentosa) found the percentage of correct letter identifications was higher with additive luminance noise (Gaussian white noise).Based on these findings, noise might enhance a visual prosthetic such as the Argus II Retinal Prosthesis System similar to how auditory noise has enhanced the effectiveness of cochlear implants (Morse and Evans, 1996;Morse et al., 2007;Rubinstein and Hong, 2003;Zeng et al., 2000).

Cross-modal stochastic resonance and its uses
Until this point in the review, we have considered SR as occurring when the noise and stimulus are part of the same sensory system, such as auditory noise improving hearing, mechanical noise improving sensorimotor performance, and visual noise improving visual perception.This unimodal conceptualisation of SR has dominated research.However, some research (Huang et al., 2017;Krauss et al., 2018;Lugo et al., 2008;Manjarrez et al., 2007) has revealed that noise originating from one sensory system can result in SR in another sensory system.This phenomenon is known as cross-modal SR.There is a growing literature providing diverse examples of cross-modal SR, including electro-tactile stimulation of the index finger leading to improved speech perception among cochlear implant users (Huang et al., 2017).Fig. 4 shows the experimental paradigm used in that study, in which participants simultaneously received tactile stimulation and auditory stimuli.The observed effect is likely the result of the integration of tactile and auditory information occurring along the auditory pathway (Kayser et al., 2005;Shore, 2011).A thorough review of the mechanisms behind cross-modal SR is available in Krauss and colleagues' study (Krauss et al., 2018).
Cross-modal SR significantly expands the opportunities to use noise productively in sensory systems.For example, subthreshold auditory white (Gaussian) noise can enhance healthy participants' sensitivity to weak tactile, visual, and proprioceptive stimuli (Lugo et al., 2008).The auditory noise used in this study was below the threshold and could not be detected.It was, however, sufficient to cause a general excitation of cortical sensory neurons, increasing their sensitivity.Similar evidence was also reported by Yashima et al. (2021) in the proprioceptive domain.There the authors showed that adding weak auditory noise improved balance control in young healthy participants.This suggests that subthreshold auditory white noise might improve sensory perception among individuals experiencing a deficit in one or more sensory modalities.The evidence of SR occurring across sensory modalities reveals new ways that noise might assist with sensory impairments.
For convenient reference, Table 1 provides a summary of the assistive and clinically relevant SR studies reviewed in the preceding pages.

Discussion
In this manuscript, we have reviewed the applications of SR in neural prosthetics.Noise is pervasive in natural and manufactured systems, and the SR phenomenon offers an opportunity to take advantage of this.SR is beginning to have a significant impact on sensory prosthetic technologies, encouraging future research in this area.For example, devices such as hearing aids and cochlear implants effectively address impairments in the auditory system.Research in SR (Morse and Evans, 1996;Morse et al., 2007;Rubinstein and Hong, 2003;Zeng et al., 2000) has already identified how noise can improve these existing devices.Stochastic beamforming also shows some promise although further research should test different versions of the beamforming algorithm in various settings before it can be implemented in everyday medical use.
In the somatosensory system, the benefits of SR implementation through vibrating inserts are clear (Anishchenko et al., 1999;Moss et al., 2004;Wiesenfeld and Moss, 1995).Additionally, its beneficial effects in neurological (Zarkou et al., 2018) and neurodegenerative conditions (Wuehr et al., 2023;Wuehr et al., 2022) suggest that SR can be used to improve the performance of somatosensory systems in various clinical settings.This benefit of noise in the somatosensory system is also supported by computational research (Liu et al., 2018).Whilst SR (via nGVS) shows some benefit in clinical groups for somatosensory systems, current research suggests that its effect in the healthy group is limited (Assländer et al., 2021).
Finally, in the visual system, despite strong evidence for SR in visual processes, the implementation of these findings to improve visual performance among individuals with visual impairments remains a challenge.There has not been as much success translating advancements in research to technological advancement in vision as other modalities.In fact, a noise-based visual device does  not exist in the literature.Therefore, future research should investigate how SR might be leveraged to improve visual performance among visually impaired individuals and across a broader range of visual functions.Additional research could investigate applications of cross-modal SR in vision.Given the evidence that eye micro-movements naturally improve visual performance among humans (Hennig and Worgotter, 2004) and cats (Hennig et al., 2002), a visual prosthetic could be fashioned to mimic these eye movements.
There are also limitations to this review.As a narrative review, we may have overlooked additional studies that provide further evidence or highlight alternative devices where noise enhances sensory function.Furthermore, we only found a few studies where SR was ineffective.While it is possible that we missed some studies demonstrating the negative results of SR in certain devices, we also believe that negative results are not often reported in this area of research due to the file drawer problem.Some of these limitations could be mitigated by conducting a systematic review in the future.Our aim with this review, however, was to present an overview of the progress made in clinically-relevant SR research across various sensory domains.
Additionally, this review did not discuss the applications of tRNS.tRNS is a very broad topic that would benefit from having a separate discussion on how tRNS-induced SR could be effective as a therapeutic device.
Whereas the evidence supporting the applications of SR in neural prosthetics is promising, noise/SR is not yet considered to be a standard therapeutic option.This may be because the clinical exploration of SR's practical uses is still in its early stages and, as mentioned earlier, SR depends on various other factors such as neural (or internal) noise level, which make standardisation challenging.Future research with larger sample sizes is needed before a standardised approach for SR can be recommended for clinical medical use.These studies should also investigate how different types of noise (e.g., white or coloured) and their properties can be optimised to maximise clinical benefits.Additionally, the potential use of noise, including visual and cross-modal noise methods, in existing visual prosthetics should be explored to assist individuals with various visual impairments.

Conclusion
SR, the counterintuitive phenomenon that optimal levels of random variability in sensory and neural signals can help rather than hinder the detection and processing of stimuli, has demonstrated applications in various scientific fields.Although high noise levels are detrimental to important sensory processes (Kahneman, 1968;Scharf et al., 1966), the evidence that weaker, and optimal, noise levels can improve detection and processing of weak stimuli continues to grow.Moreover, cross-modal SR presents a new area of SR to be explored, and offers new insights into the mechanism of SR and the integration of sensory information in the brain (Krauss et al., 2018).Now over forty years since its first mention as a possible explanation for ice ages (Benzi et al., 1982;Benzi et al., 1981;Nicolis, 1982Nicolis, , 1993)), research into SR continues to offer new applications that may be able to assist where current standards of care fail.

Fig. 1 .
Fig. 1.Depiction of the threshold model of SR.Panel (a) shows the combination of signal and noise surpassing the sensory threshold and generating information about the signal.Panel (b) shows the inverted U-shaped curve characteristic of SR.Image used with permission.This article was published in Clinical Neurophysiology, vol 115, Issue 2, F. Moss, L.M. Ward, & W.G. Sannita, Stochastic resonance and sensory information processing: a tutorial and review of application, 267-281, Copyright International Federation of Clinical Neurophysiology (2003).

Fig. 3 .
Fig. 3. Argus II Retinal Prosthesis System.The effects of Argus II Retinal Prosthesis System could potentially be further enhanced by SR.Image used with permission.This article was published in Ophthalmology, vol 119, Issue 4, M.S. Humayun and colleagues, Interim Results from the International Trial of Second Sight's Visual Prosthesis, 779-788, Copyright American Academy of Ophthalmology (2012).