Abstract
Vestibular evoked myogenic potentials (VEMPs) are widely used clinical vestibular tests and their interpretation is derived from the original proposal by Colebatch that the cVEMP is due to saccular activation by air conducted sound (ACS). This was based on previous extensive evidence that sounds selectively activate saccular afferent neurons and not semicircular canal neurons at clinical testing conditions. We revisit that earlier data and the results since. Despite that evidence, a recent partial review of the neural basis of cVEMPs has raised the possibility that canal afferents may be activated at clinical test frequencies and intensities and contribute to VEMPs, which would weaken their clinical specificity. This possibility is largely based on evidence that ACS clicks activate canal afferents in the rat – but not in the guinea pig. We show that result from the rat study is due to the very high sound pressure levels used – intensities which were far higher than those in the guinea pig study. When ACS stimuli of comparable intensity are used for both species at comparable clinically effective frequencies and intensities (~110 dB SPL), otolithic neurons are activated in both species but canal activation by ACS clicks is negligible (and so most probably in humans also). Furthermore, the evidence from lesion and electrical stimulation studies and human clinical data complements the neural evidence and confirms the cVEMP to ACS is a specific test of saccular function. Audibility curves show rats have very high thresholds for frequencies most commonly used for human VEMP testing (500–1000 Hz). That result questions the applicability of results of sound evoked vestibular responses from rat for understanding human vestibular function. There is a range of stimulus intensities and frequencies appropriate for measuring VEMPs. Using stimulus values within this range, neural evidence from rats and guinea pigs shows minimal contribution of canal afferents, meaning that VEMPs are specific tests of otolith function and that any contribution from semicircular canals to human cVEMPs (tones at 500 Hz, clicks at 100 dB nHL) is negligible. Using stimulus values outside that range will stimulate semicircular canal afferents as well as otolith afferents, thus compromising the otolithic specificity of VEMPs.
Introduction
The traditional ways of clinical testing of vestibular function using angular and linear acceleration have now been complemented by methods which measure vestibular evoked myogenic potentials (VEMPs) in response to air conducted sound (ACS) or bone conducted vibration (BCV). For recent reviews see (). In what was a remarkable development Colebatch et al. showed that ACS click stimulation or BCV from light taps with a tendon hammer caused small myogenic potentials recorded by surface electrodes on the tensed sternocleidomastoid muscle (SCM) (, ). This response is now known as the cervical VEMP (cVEMP). Prior histopathological and neural data from Aran, Didier and Cazals (reviewed below) together with data from human clinical neurophysiology (, ) led Colebatch to propose that cVEMPs were probably caused by saccular receptors and afferents. This was a remarkable discovery because Colebatch had suddenly introduced a clinical test of a part of the vestibular labyrinth whose function clinicians had not been able to assess before. cVEMPs were rapidly adopted and are now part of routine clinical vestibular testing. Later it was shown cVEMPs are more effectively elicited by brief (7 ms) 500 Hz tone bursts of either ACS or BCV than clicks (, ). About 10 years after the introduction of cVEMPs, Rosengren et al. reported another VEMP recorded by surface electrodes close to the inferior oblique (IO) eye muscles in response to ACS and BCV termed the ocular vestibular evoked myogenic potential – the oVEMP – and suggested that its origin may be from utricular macula ().
These two types of VEMPs are distinctly different. The cVEMP in response to ACS clicks or BCV stimuli is a short latency positive (inhibitory) myogenic potential recorded on the tensed sternocleidomastoid (SCM) muscle (Figure 1). The ocular VEMP (oVEMP) is a small negative (excitatory) myogenic potential recorded by surface electrodes beneath the eyes as the person looks up. Both VEMPs are extremely fast: in humans the latency from stimulus onset to the onset of the diagnostically important p13 potential of the cVEMP is only about 8 ms (). The latency from the onset of the stimulus to the foot of the diagnostically important negative n10 potential of the oVEMP is about 6–7 ms (). In dealing with the neural origin of VEMPs this extremely fast response must be explained.
Figure 1
Are these VEMPs really measures of vestibular function? Colebatch et al. answered that conclusively by showing that patients without hearing exhibited cVEMPs and conversely patients after selective vestibular nerve section and who could hear the stimuli, had no cVEMPs (
Vestibular evoked myogenic potentials are of particular clinical value since they test the function of receptors at the striolae of the otolithic maculae which are such key indicators of vestibular function. Type I receptors at the striola are the most metabolically vulnerable of all otolithic receptors – they are the first to show signs of injury after vestibulotoxic antibiotics such as gentamicin (
Afferents from utricular and saccular macula have many complex overlapping but differential neural projections (
Figure 2

To show the fast and highly repeatable eye movement responses of humans and guinea pigs to 500 Hz BCV stimulation. (A) 3D eye position records from the right eye in one human subject during successive presentations of right mastoid stimulation by 7 ms tone bursts of 500 Hz BCV by a B71 bone oscillator. The bottom record in each panel shows the mean values and 95% confidence intervals of the individual responses above. Horizontal vertical and torsional eye movement components (from top to bottom) were measured by pupil and iris tracking using high resolution video acquired at 180 Hz. At a short latency in response to the 500 Hz tone burst (vertical lines) the eye moves horizontally and torsionally away from the side of stimulation. The vertical component is downwards. Replotted from data published in (
Given that VEMPs are vestibular in origin, which vestibular sensory regions are activated by sound and vibration? That requires evidence from single neuron recordings of primary vestibular afferents. As noted above, some early neural evidence was available to Colebatch et al. and much more has appeared since, as we discuss below.
Didier and Cazals
Colebatch proposed that the cVEMP was due to saccular activation (
Probably the strongest evidence for the role of the saccule came from the electrophysiological evidence from the Bordeaux group over a period of 10 years of research. These researchers reported that in response to ACS click stimuli in guinea pigs, compound action potentials to ACS clicks were recorded on the saccular nerve after total ablation of cochlear receptors by various ototoxic antibiotics including amikacin and sisomycin (
In an amazingly foresightful conclusion, they stated: “these data favor the hypothesis of a hearing function of the saccule in a mammal possibly involving type 1 cells and electrical synapses.” (
It is surprising and puzzling that this very extensive and directly relevant evidence of the saccular origin of sound evoked vestibular responses by the Bordeaux group was not referenced in a recent review purportedly of the neural origin of cVEMPs (
Translating data from animal physiological experiments to human clinical vestibular function requires careful consideration of many aspects (
Neurophysiological evidence from different species
What is the neural basis of these responses to ACS and BCV which could drive an eye movement response at such a remarkably short latency? Clearly it is the transduction and transmission at the onset of the stimulus which is of paramount important since cVEMPs and oVEMPs are elicited so quickly after the onset of transient stimuli such as brief (2 ms) tone bursts or ACS clicks (
Figure 3

Neural responses to ACS clicks. Time series of responses of 3 guinea pig primary vestibular neurons to ACS clicks, to show the short latency of activation of primary neurons. Each line is the superimposed responses of the neuron to 5 or so stimuli. The latencies of spike activation are 0.5 ms in (a) and (c) and 1.0 ms in (b). Time scales are 1.0 ms. Reproduced from (
Different groups studying the vestibular neural response to ACS and BCV have used different species, different stimuli, different criteria of activation to determine whether single primary otolith or canal neurons are activated in response to ACS or BCV. In most of these studies, vestibular neurons are identified by their response to angular or linear accelerations and then ACS or BCV stimuli are presented to test if the neuron responds. If possible, the site of origin of activated neurons is verified by staining the neurons, processing the tissue and so identifying their site of origin, although this is an extremely difficult technique. Since these studies seek to explain the basis of a human response, the stimulus parameters in animal experiments should be selected where possible to be comparable to those used for human clinical testing and the animal species should have comparable sensory characteristics to those of human subjects.
The approach of the Curthoys group has been to record from single neurons in the vestibular nerve in guinea pigs (
A recent review has raised the issue of the possible activation of semicircular canal neurons by ACS and BCV and whether this canal activation may contribute to standard clinical cVEMPs (
There is a long history showing that vibration is an effective stimulus for otolithic receptors and neurons going back to Ross in 1936 in frogs (
Neural evidence from squirrel monkey
Young et al. studied the response of primary vestibular neurons in squirrel monkeys and found single vestibular neurons with irregular resting discharge were activated by ACS and BCV (
The inconsistency of the results of Young et al. using the two criteria is shown by their summary of the results which emphasized that canal afferents had higher phase-locking thresholds than saccular afferents: “In contrast, almost all saccular afferents were affected by sound stimulation; median thresholds at 250 and 350 Hz are between 106 and 110 db. The corresponding values for canal units were at least 120 dB at these frequencies” (
We contend that the widely held belief that the Young et al. study showed canal afferents are more sensitive than otolith afferents should be set aside because it is inconsistent with their textual summary of their own results and because it is based on the use of a criterion of activation which is not relevant for the initiation of the fast neural response to the stimuli within the first 0.5 ms which is crucial for the generation of VEMPs (Figure 3). As they stated themselves, the major result from the Young et al. study is that otolithic neurons are activated at substantially lower intensities compared to canal neurons.
Neural evidence from guinea pig (ACS)
Murofushi and Curthoys set out to find the cause of cVEMPs to high intensity ACS clicks (
Figure 4

Audibility curves (plots of the sound intensity at threshold in dB SPL for various frequencies) for the chinchilla and human (upper panel) and the guinea pig and rat (lower panel). The rat and guinea pig data shows the free field hearing threshold determined by behavioral audiometery for ACS tones of increasing frequency in dB SPL. At 500 Hz the guinea pig threshold is about 15 dB SPL, whereas the rat threshold is about 60 dB SPL – a difference between species of 45 dB. The human threshold at 500 Hz is 8 dB SPL. Reproduced from (
A crucial decision in this and later studies was the stimulus intensity which corresponded to the high, but not extreme, values being used in the concurrent development of the VEMP for human vestibular testing. If a single high intensity were to be used (such as 130 dB SPL) it would not take account of animals with possible conductive hearing loss and may, as we now know, cause vestibular damage (
The Murofushi study tested the response of a large number of single neurons from various vestibular sensory regions to identify if they were activated by ACS clicks. What constitutes activation? This is really fundamental since some stimuli may deflect the cilia of vestibular receptors, and so technically activate receptors, but fail to generate stimulus-locked action potentials in primary vestibular afferents that trigger responses in later neurons. Such a stimulus technically activates the receptor, but it is functionally irrelevant for generating the myogenic response we sought to explain, since it does not result in action potentials reaching the myogenic target. We used the simplest most direct indicator of activation, which was a stimulus-locked audible increase in firing rate - a rate change - in response to ACS or BCV stimuli. The results of Murofushi et al. in the guinea pig demonstrated the selectivity of saccular neurons for ACS clicks and the insensitivity of canal neurons for ACS clicks at clinical test intensities.
We demonstrated that otolithic neurons with irregular resting discharge were most likely to be activated by ACS clicks. In the Murofushi et al. study, 102 otolithic neurons were activated by ACS clicks but not one of 300 canal neurons were activated (
Neural evidence from cat
McCue and Guinan recorded from irregular afferents in the inferior vestibular nerve of cats and demonstrated that 229 irregular afferent neurons were activated by ACS stimuli (both rate change and phase-locking criteria were used (
Neural evidence from chinchilla
In a study of the effect of semicircular canal dehiscence (SCD) on semicircular canal afferent responses, Carey recorded many primary semicircular canal afferents in chinchillas to ACS stimulation and showed activation of canal afferents before SCD by ACS at very high intensities – 135 dB SPL (
Neural evidence from guinea pig (BCV)
Halmagyi et al. had shown that BCV from gentle taps by a tendon hammer at the midline of the forehead at the hairline (a location called Fz) is an effective way of generating cVEMPs (
In the 2006 study a large number of primary vestibular afferents in guinea pigs were recorded, testing the response of every one to brief (7 ms) 500 Hz tone burst stimuli - the same frequency Welgampola et al. had used to test cVEMPs to BCV in human patients (
The results of BCV stimulation showed 82.8% of irregular otolithic afferents tested, but only 4.7% of irregular canal neurons tested were activated by the 500 Hz stimulus (see Figure 5). In later studies using lower frequencies, discussed below, we (
Figure 5

Numbers of regular and irregular primary vestibular afferent neurons tested (open bars) and activated (closed bars) by 500 Hz bone conducted vibration at 80 dB above guinea pig ABR threshold. Lat, horizontal canal; Ant, anterior canal; Post, posterior canal. The otolith neurons are divided into Pitch static and Roll static. The results show that only a small proportion of semicircular canal neurons were activated at this intensity, in contrast a large proportion of otolithic irregular neurons tested were activated. Otolith and canal regular neurons were rarely activated. Reproduced from (
Neurons with irregular resting discharge showed a clear increase in firing rate to 500 Hz BCV at low stimulus levels and staining and tracing showed that these irregular afferents originated from the striola of the utricular macula as Goldberg et al. had reported (
Neural evidence from rat (ACS)
In 2011 Zhu et al. published a paper showing that ACS clicks at a single high intensity (130 dB SPL) activated both irregular otolith and canal neurons in rats (
The results of the Zhu et al. (
In the original Zhu 2011 paper only one high intensity test stimulus was used −130 dB SPL which was called 80 dB SL (
That suggestion is confirmed by the later published data from the Zhu group (
Figure 6

Plots of neural activation (CPE - cumulative probability of evoking a spike) of rat canal and otolith neurons in response to ACS clicks as a function of regularity of resting discharge (CV*). The rows show the results for 4 levels of ACS click intensity: 50, 60, 70, 80 dB above the rat ABR threshold (SL). In every graph each dot shows the probability of firing of an individual neuron to 150 click presentations. The four columns show the results for neurons of the anterior (AC), horizontal (HC), and posterior canals (PC) and otoliths. At high intensity (top row at 80 dB SL) many anterior canal as well as otolithic neurons show a high probability of activation, corresponding to the results at that stimulus intensity reported earlier by (
Recently the Zhu group have published evidence using their characteristic testing paradigm reporting the effects of ACS stimulus frequency on primary vestibular neural activation. Huang et al. used a range of frequencies to explore activation of vestibular neurons by ACS in rats (
Relating neural data to VEMPs
The early neural and clinical evidence was assembled in a review in which the following hypothesis was proposed: that cVEMPs are mainly due to saccular function and oVEMPs are mainly due to utricular function (
The independence of oVEMPs and cVEMPs was confirmed by the fact that some patients have present oVEMPs but reduced or absent cVEMPs and other patients show exactly the converse (
Discussion
Canal contributions to VEMPs—after SCD
While a main conclusion of this paper is that saccular function is tested by the cVEMP, perhaps canal neurons may also contribute to the cVEMP? Can semicircular canal neurons be activated at all by sound and vibration? The answer is yes - depending on the stimulus and bony canal characteristics. That capability is shown by the evidence from responses of canal neurons to high intensity click stimuli (
Figure 7

The response of an irregular primary anterior canal neuron to high-frequency ACS before and after a small (0.1 mm diameter) dehiscence (SCD) in the bony wall of the anterior canal. (A) The response of the neuron to pitch angular acceleration (lower record) shows that the neuron is an anterior canal afferent. (B) Before SCD an 8 s burst of 1,483 Hz ACS has no effect on the neural response. (C) After the SCD a 10 s burst of 1,479 ACS causes strong stimulus-locked activation in this anterior canal Hz neuron. The lower records in (B,C) show the stimulus command voltage. After resealing the SCD, the response to ACS stimulation disappears (not shown). Reproduced from (
Figure 8

(A) Schematic diagram of the projections from the otoliths to the inferior oblique (IO) and sternocleidomastoid muscle (SCM) which likely underlie the oVEMP and cVEMP, respectively. Both schematics are based on the results of (
Canal contributions to VEMPs–low frequency vibration
Recently it was possible to record artefact-free responses from single semicircular canal neurons to low frequency skull vibration (100 Hz BCV) in animals with intact normally encased labyrinths. These results show that canal afferent neurons (and also otolithic neurons) were activated by low frequency stimuli (
Figure 9

To show that low frequency skull vibration (100 Hz) activates canal neurons in animals with intact bony labyrinths. Time series of an anterior semicircular canal neuron with irregular resting discharge to low frequency bone conducted vibration at 200 Hz (A) and 150 Hz (B). A triaxial linear accelerometer cemented to the animal’s skull was used to measure head acceleration (in three dimensions x, y, and z – shown beneath the neural activation) during stimulus application, which is shown by the command voltage in the bottom trace. At 150 Hz BCV, the increase in the neuron’s firing rate is closely locked to the onset and offset of the stimulus – the stimulus intensity corresponding to 0.35 g linear head acceleration. At the higher frequency of 200 Hz there is modest increase in firing rate although the stimulus magnitudes are identical. There was no activation at 500 Hz. Reproduced from (
Vestibular projections to SCM
Anatomical and physiological evidence shows that all five vestibular end organs have projections to the SCM and so all are potentially capable of producing an ipsilateral vestibular evoked myogenic potential on the SCM (
ABR threshold as a reference for stimulus intensity
In retrospect, using the physical intensity of ACS or BCV at ABR threshold as a baseline reference level for stimulus intensity for vestibular research requires reconsideration. ABR threshold is the outcome of cochlear mechanical and neural operation, whereas in vestibular studies ABR threshold has been used to equilibrate physical stimulus intensities for vestibular (not cochlear) stimulation between animals and between species. The large species differences in cochlear function (as shown by extremely large differences in audibility curves and also ABR threshold values of rats vs. guinea pigs; Figure 4) bring into question the appropriateness of using a cochlear reference as the baseline for measuring and comparing the intensity of vestibular stimuli especially when that baseline is used to compare the results of stimulation between species. Sensitivity to sound in terms of audibility reflects cochlear function and varies between species. Using ABR threshold as a reference/baseline leads to extremely different physical sound pressure levels delivered to the vestibular neurons. The same number of dB above ABR threshold entails completely different physical intensities of vestibular stimulation in rats and guinea pigs.
Experimental and clinical evidence that cVEMPs are saccular
Is the cVEMP a specific test of saccular function? The above has shown the physiological evidence from animal studies indicates that at standard frequencies and intensities used in clinical testing, any contribution from semicircular canals is negligible and experimental and clinical evidence agrees with that indication.
Tsubota et al. conducted experiments in monkeys where in one animal they sectioned the entire vestibular nerve and, in another animal, just the superior vestibular nerve (
That result was complemented by results from 7 human patients during schwannoma surgery where the inferior vestibular nerve was electrically stimulated and recordings made of the cVEMP. Stimulation of the inferior vestibular nerve generated a cVEMP response in the ipsilateral SCM and no response in the contralateral SCM (95). These results of lesioning and electrical stimulation complement each other, and both show that the cVEMP response is saccular.
Sheykholeslami et al. reported cVEMP recordings from a human patient where there was total anatomical absence of all the semicircular canals bilaterally, whereas the remainder of the membranous labyrinth, including the otolithic structures, was intact (96). With no semicircular canals this patient showed clear cVEMPs to ACS stimulation, once again showing the selective saccular origin of cVEMPs and the negligible contribution of semicircular canal input to cVEMP under clinical testing conditions.
We now have the opportunity to identify whether activation of canal afferents which Zhu al reported in rat primary semicircular canal afferents (2011) has a significant role in clinical testing of otolith function. The opportunity arises because of the development of the video head impulse test (vHIT) of the function of all semicircular canals (97, 98). It is now well established using vHIT that some patients have all semicircular canals functioning normally but have reduced or absent utricular or saccular responses (oVEMPs or cVEMPs) (99–106). The fact that the canals are fully operational yet there is reduced or absent cVEMP points strongly to the fact that whatever canal neurons may be activated by sound or vibration, their contribution to standard cVEMP tests is negligible. Of course, the testing of cVEMPs requires careful attention to technical details in testing, such as SCM tension (
Kjaersgaard et al. claimed that cVEMPs in response to electrical stimulation of ampullary nerves in human patients supported the role of semicircular canal afferents in cVEMPs, whilst acknowledging the issue of current spread (
As we have stressed the cVEMP is a short latency response to a single stimulus rather than a change in firing during a maintained stimulus. It is the earliest part of the stimulus within the first few milliseconds which is vital to the generation of the response (
Conclusion
Physiology and human clinical results show VEMP tests are specific tests of otolith function for 500 Hz and clicks at 100 dB nHL in the intact labyrinth. At this intensity in standard clinical testing there is likely little contribution if any, from semicircular canals. The evidence of the saccular activation by sound and vibration at clinical test frequencies and intensities and the failure of canal afferents to affect cVEMPs with intact bony labyrinths leads to the conclusion that clinical cVEMPs are a specific test of saccular otolith function. This is supported by strong evidence from stimulation and lesion studies for the primary role of the saccule in generating the cVEMP response to ACS.
We have shown that the apparent disagreement between guinea pig and rat data about canal activation by ACS stimuli is most likely due to the very high physical intensities used for the rat compared to the guinea pig. Comparable stimulus intensities for both rat and guinea pig show comparable results with minimal canal contributions at standard clinical testing levels.
A recent review stated, “All in all, common application and interpretation of the cVEMP as a specific test of saccular and inferior vestibular nerve integrity in clinical practice needs to be reconsidered, until more evidence is provided.” (
New and noteworthy
Does semicircular canal activation contribute to vestibular tests of otolith function (VEMPs) using sound or vibration with clinical testing conditions? The answer is no. The physiological evidence is that there is negligible contribution from semicircular canal activation when VEMP tests are conducted with standard clinical stimulus frequencies and levels. The one study (in rats) that reported extensive canal activation used very high stimulus intensities. When intensity is restricted to values used in the clinic, canal activation is minimal and VEMPs are specific tests of otolith function. In contrast to guinea pigs, rats have very high auditory thresholds for frequencies of sounds used for human clinical VEMP testing (500-1000 Hz) which brings into question the applicability of results of sound evoked vestibular responses from the rat for understanding human vestibular function.
Statements
Author contributions
IC: Methodology, Writing – review & editing, Writing – original draft, Conceptualization. LF: Methodology, Writing – review & editing, Conceptualization. LMc: Writing – review & editing. LMa: Writing – review & editing. SI: Writing – review & editing. JD: Conceptualization, Writing – review & editing, Methodology. GH: Writing – review & editing.
Funding
The author(s) declare that no financial support was received for the research and/or publication of this article.
In memoriam
We dedicate this paper to the memory of Professor Toshihisa Murofushi. Toshi made many contributions to the understanding of vestibular function and was a leader in the field in Japan. In particular with regard to cVEMPs both in terms of basic physiology of vestibular afferents and clinical testing. He was a leader and a pioneer and Toshi was an exceptionally nice guy and everyone in the Sydney labs loved him, and we are sad at his loss. He persevered in the face of continued lack of results until things did work. He had undaunted, steadfast, focused attention to the question at hand. That is borne out by his papers reporting the guinea pig data and all the papers that he published since because when he went back to Japan, he became one of the world’s foremost experts on VEMPs. He had very firm ideas about their cause, and he was steadfast in defending his ideas. He really was a pioneer of vestibular physiology in Japan uniting clinical understanding with basic vestibular physiology. Toshi passed away on 13 May 2024. Thank you and Vale Toshi.
Conflict of interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
The author(s) declared that they were an editorial board member of Frontiers, at the time of submission. This had no impact on the peer review process and the final decision.
Generative AI statement
The authors declare that no Gen AI was used in the creation of this manuscript.
Publisher’s note
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Abbreviations
ABR, auditory brainstem response; ACS, air conducted sound; BCV, bone conducted vibration; cVEMP, cervical vestibular evoked myogenic potential; Fz, the skull location at the midline at the hairline; IO, inferior oblique; oVEMP, ocular vestibular evoked myogenic potential; SCD, semicircular canal dehiscence; SCM, sternocleidomastoid muscle; SL, sensation level; SPL, sound pressure level; SVIN, skull vibration induced nystagmus.; VEMP, vestibular evoked myogenic potential; vHIT, video head impulse test; VOR, vestibulo-ocular response.
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Summary
Keywords
VEMP, rat, guinea pig, otolith, utricular, semicircular canal
Citation
Curthoys IS, Fröhlich L, McGarvie L, Manzari L, Iwasaki S, Dlugaiczyk J and Halmagyi GM (2025) The neural basis of vestibular evoked myogenic potentials. The cVEMP is a specific indicator of saccular function. Front. Neurol. 16:1644120. doi: 10.3389/fneur.2025.1644120
Received
09 June 2025
Accepted
11 July 2025
Published
05 August 2025
Volume
16 - 2025
Edited by
Bryan Kevin Ward, Johns Hopkins University, United States
Reviewed by
Erin Gillikin Piker, James Madison University, United States
Sendhil Govender, University of New South Wales, Australia
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© 2025 Curthoys, Fröhlich, McGarvie, Manzari, Iwasaki, Dlugaiczyk and Halmagyi.
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*Correspondence: Ian S. Curthoys, ian.curthoys@sydney.edu.au
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