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Clinical Sports Medicine Collection. Davis AT Collection. Davis PT Collection. Murtagh Collection. Changes in length are accompanied by transverse motion due to the staircase gradient in stereocilia lengths and diagonal tip links.
Deflections are resisted by actin stiffness and polymerization at the tip, the angular stiffness at the base, and fluid drag in the axial and transverse directions. For maintained hair bundle displacements, the transduction current is known to adapt over multiple time courses due to kinetics of its molecular components. This electrical adaptation has a concomitant mechanical component that clearly contributes to active bundle movements [9].
Since flexoelectricity is downstream of the MET apparatus, the present analysis focuses on how flexoelectricity converts the current entering stereocilia, in whatever adapting temporal form it has, into useful mechanical work. Under physiological conditions, sound stimuli entering the ear leads to forces that deflect the hair bundles from rest Fig. As the bundle is pushed in the excitatory direction and the stereocilia are depolarized, flexoelectricity compels the radius to decrease 2b , length to increase, tip-link tension to increase, and finally a rapid bundle movement opposite in direction to that of the stimulation force.
As the stimulus cycle progresses, the applied bundle force reduces to zero 2c and then increases in the opposite, inhibitory direction producing hyperpolarization, a stereocilium radial increase, isovolumetric shortening 2d , and a further reduction in the tip-link tension that causes additional relaxation of the bundle in the inhibitory direction. Therefore, mechanical power provided by stereocilia flexoelectricity may interact with MET channel kinetics and nonlinearities to produce a limit cycle oscillation and amplify vibrations within the cochlea [10].
To investigate the feasibility of these ideas, we developed a relatively simple biophysical model to investigate power output of the flexoelectric mechanism see Methods. Therefore results only address efficiency of the flexoelectric motor and do not address coupling to mechanical activation of MET channels or self-excited motion that would be expected to occur under some conditions.
During excitatory stimulation, the bundle is pushed towards the tallest stereocilium causing opening of the MET channel and an influx of depolarizing current. This is accompanied by MET adaptation and associated nonlinearities. The efficiency of the electrical to mechanical conversion was estimated by dividing the output mechanical power by the input electrical power entering the stereocilia.
In terms of efficiency, the flexoelectric model is linear so the overall magnitude of the power will be affected by the voltage and current changes but the calculated efficiency predictions will not.
Efficiency predictions will be, however, affected by the degree of coupling between the stereocilia and accessory structures such as the tectorial membrane. Like skeletal muscle, the maximum power efficiency occurs for a load roughly half way between the zero-load condition and the maximum isometric force condition termed the impedance matched load [11].
Results shown in Fig. Input electrical MET power is lost to conductance of the soma and lost due to intrinsic mechanical properties of the stereocilia, including axial stiffness at low frequencies and entrained mass at high frequencies.
Efficiency is further limited at high frequencies primarily by transverse viscous drag light blue hatch. Tuning is reduced if axial length changes are not coupled to cause transverse bundle motion dashed curves. Raw data symbols showing the height of the tallest stereocilia for cochlear hair cells from mouse [2] , [44] , human [2] , [44] , guinea pig [45] , mustached bat [46] , chick [47] , alligator lizard [1] , [13] , [48] and the basilar papilla of turtle [49].
Flexoelectric model predictions show the frequency of peak efficiency for stereocilia of different heights that impart power to accessory structures e. TM but lose power to the fluid, and for freestanding stereocilia that impart power to the fluid through viscous pumping alone. The combination of these mechanisms results in a specific frequency for a given length stereocilia at which the electrical to mechanical power conversion is most efficient Fig.
Not surprisingly, the peak efficiency shifts to higher frequencies for shorter stereocilia. This tuning would be compromised if the MET channels were located uniformly along the length instead of at the stereocilia tips. In addition to the peak efficiency, the power output normalized to the input MET current was determined for a specific stereocilia length Fig.
The peak power output occurred at higher frequencies for shorter stereocilia while the magnitude of the output, not surprisingly, decreased with stereocilia height consistent with the decrease in membrane surface area available for electrical to mechanical power conversion.
Of further interest, it can be seen that axial length changes when transversely coupled are more sharply tuned to a specific best frequency solid line vs.
Numerous studies have measured stereocilia height along the length of the cochlea. Maps have been composed for numerous species to correlate best frequency with location along the sensory epithelium. We combined data from multiple physiological and anatomical studies to plot the height of the stereocilia as a function of best frequency Fig. The red curve TM coupled was computed using the approach in Fig. In the case of freestanding stereocilium, there are no accessory structures attached to the tips and therefore any useful power output must be delivered directly to the fluid.
Remarkably, by softening tip links and including power delivered to the fluid as useful mechanical output, the same model also predicts the relationship between best frequency and freestanding stereocilia length appearing in nature Fig. Results for freestanding stereocilium do not reflect a typical mechanical resonance balance between stiffness and mass [12] , [13] but, instead, reflect a balance between stiffness, the flexoelectric effect, and axial electrical resistance.
It is interesting that the bandwidth of freestanding stereocilia is quite narrow — this may be a key advantage of coupling hair bundles to a TM or similar accessory structure in hearing organs. Hence, if hair-bundle flexoelectricity were important at low frequencies, the motor would be inefficient.
This suggests that other motor mechanisms associated with the MET molecular apparatus, such as unconventional myosin motors showing climbing and sliding rate limitations of Hz and 44 Hz [14] , respectively, or somatic motility [15] might have advantages at low frequencies.
It is interesting that human hearing spans this range, as does hearing in many mammals including dogs, cats, guinea pigs and chinchillas. This opens the possibility that mammals may take advantage of one motor mechanism dominating at low frequencies and a different motor mechanism dominating at high frequencies. Present results show that stereocilia membrane flexoelectricity would be particularly tuned and efficient at high frequencies.
Support for the flexoelectric hypothesis also comes from genetic models of inherited hearing disorders. This is indeed the case. In adult myosin-XVa-deficient shaker 2 mice, the staircase architecture of hair bundles is lost and severe hearing loss occurs. Interestingly, these mice have nearly normal MET currents [16]. The present model predicts zero power output for these hair bundles because axial flexoelectric motion would not drive transverse deflection see Eq.
Similar results are found in stereocilin-deficient mice that lack horizontal top connectors, lateral links that connect adjacent stereocilia together [17]. The present analysis predicts hearing loss in both of these animal models due to disruption of the axial-transverse coupling normally exploited by the flexoelectric hair-bundle motor. There is evidence [18] suggesting that the tip-link insertion may not be near the top of the stereocilia, If this translates to the location of the MET current entering stereocilia, the primary effect would be to shorten the electrical path to the soma and thereby reduce the axial conductance.
Such an arrangement would shift the most efficient frequency up slightly — by approximately , where is the distance from the base to the MET channel and is the total length of the cilia. Mechanical amplification of sound signals in the inner ear is controlled by the brain, in most species, through extensive efferent synaptic contacts on hair cells. In mammals, activation of the efferent system decreases mechanical amplification within the cochlea primarily through efferent action on outer hair cells [19] — [21].
A similar amplification control strategy is present in birds where efferent neurons contact short hair cells while afferents exclusively contact long sensory hair cells. The short hair cells in birds do not exhibit prestin dependent electromotility [22] , but do have motile hair bundles thus implicating efferent innervation is controlling the hair bundle amplification in birds and other non-mammalian species.
Control of the bundle motor by the efferent system presents a challenge to hypotheses that attribute cochlear amplification to the MET molecular apparatus because a clear mechanism for fast control via efferent synaptic input is unclear.
In contrast, the power output of flexoelectric stereocilia described here is controlled by the electrical admittance of the hair cell soma, a parameter modulated by the efferent system [23]. In the present theoretical analysis, the power output at best frequency drops substantially when the somatic impedance is reduced. The reservoir comprises a long microchannel in series with a micropump, connected in parallel with the reciprocating flow network.
We characterized in vitro the response and repeatability of the planar pump and compared the results with a lumped element simulation. We also characterized the performance of the reservoir, including repeatability of dosing and range of dose modulation. Acute in vivo experiments were performed in which the reciprocating pump was used to deliver a test compound to the cochlea of anesthetized guinea pigs to evaluate short-term safety and efficacy of the system.
These advances are key steps toward realization of an implantable device for long-term therapeutic applications in humans. Kim, E. Gustenhoven, M. Mescher, E. Leary Pararas, K. Smith, A.
Spencer, V. Tandon, J. Borenstein and J. To request permission to reproduce material from this article, please go to the Copyright Clearance Center request page. If you are an author contributing to an RSC publication, you do not need to request permission provided correct acknowledgement is given. The head needs to be held in this position sufficiently long for sedimentation to complete, which, as described above, takes much longer for small particles.
Progress can usually be assessed by monitoring slow-phase eye movements. While still hanging, the head is rotated toward the opposite ear Fig.
The head is then tipped up and rotated further with the afflicted ear up Fig. It is important to keep the head tipped up to prevent particles from entering the anterior canal and converting to AC BPPV.
Once particles are in the common crus, the head is tipped further up Fig. Once in the utricular vestibule, pathological gravity sensitivity no longer occurs because the hydraulic lever is eliminated. Modified Epley canalith repositioning procedure. Sequence of 6 head positions A — F designed to move canaliths arrows from the long arm of the posterior canal in the right ear to the utricular vestibule. Hold times shown in each position are estimates based on relatively small, slowly sedimenting, canaliths.
A : initial seated position Epley 1. B : rotation into the Dix-Hallpike head hanging position toward the right ear to sediment particles as shown in Fig. Epley 2. C : rotation toward the left ear to sediment particles toward the common crus. D : head held up rotated left to move particles into crus avoiding conversion to the anterior canal Modified Epley 3. E : return toward upright position with particles sedimenting down the common crus. F : head tipped forward to move particles to nasal region of the utricular vestibule Epley 4.
A variety of CRPs have been devised to reposition canaliths from almost any sensitive location in the labyrinth. The clinical challenge is to determine the initial location of the canaliths based on observation of gravity-dependent slow-phase eye movements and to perform the appropriate CRP with effective orientations relative to gravity and sufficient hold times Helminski et al.
Although CRPs are highly successful in classical presentations Akin et al. Prominent 19th century scientists argued that the semicircular canals might be sensitive to air-conducted sound and potentially could play a role in directional hearing Camis Although we now know the canals are highly selective to angular motion and normally protected from stimulation by air-conducted sound, early experiments by Deetjen seemed to support the acoustic sensitivity hypothesis. Deetjen introduced aluminum powder into the perilymph and visualized both vibration and continuous flow of the fluid in response to sound.
According to Camis , Deetjen conjectured that forces and fluid motion in the perilymph might be transmitted through the membranous labyrinth to the endolymph providing a route for transduction by the crista, but Deetjen also noted evidence that mammalian vestibular organs are unlikely to be involved in auditory perception. Tullio demonstrated 30 yr later that the semicircular canals are normally insensitive to sound but can become pathologically sensitive if a fistula is opened in the bony labyrinth.
The experiments of Deetjen were correct, but the sound-evoked perilymph motion he observed was pathological and occurred only after opening the bony labyrinth.
Indeed, individuals with a perilymphatic fistula or dehiscence of the bone enclosing the labyrinth can experience pathological canal sensitivity to sound: a condition called Tullio phenomena. A fistula or dehiscence can also introduce other symptoms including conductive hearing loss, pressure sensitivity, and increased vestibular sensitivity to bone-conducted vibration Arts et al. Semicircular canal afferent nerve responses to auditory frequency stimuli in animal models of canal dehiscence syndrome have revealed two characteristic types of responses: 1 increases or decreases in action potential discharge rate that build up with the time constant of the canal, and 2 entrainment of the discharge rate to the auditory frequency stimulus with action potentials occurring at a precise phase relative to the stimulus Carey et al.
In mammals, neurons of the first type typically have regular interspike intervals at rest, while neurons with of the second type are calyx bearing and have irregular interspike intervals at rest Curthoys et al. Example single-unit afferent neuron responses in the toadfish model of canal dehiscence syndrome are shown in response to auditory frequency stimulation at Hz Fig.
Units shown in Fig. The same type of neural responses have been observed in a mammalian model of canal dehiscence syndrome Carey et al. Both types of auditory frequency responses arise directly from pathological hair bundle displacements in the compromised labyrinth. Auditory frequency responses with dehiscence or fistula. A — D : single-unit afferent neuron responses to auditory frequency stimuli in an animal model of dehiscence.
Insets i and ii : illustration of the slow component of cupula displacement M, black evoked by the auditory frequency driven endolymph pumping and cycle by cycle vibration around the deflected position AC, blue. Waves travel along the membranous labyrinth away from the site of the fistula causing vibration of hair bundles at the stimulus frequency and pumping of endolymph in either direction, ampullofugal for Hz E and ampullopetal for Hz F.
SW, standing waves; TW, traveling waves. Auditory frequency mechanics of semicircular canals is complex and nonlinear, involving the interaction of perilymph, endolymph, and the thin deformable membrane separating the two. The sensory organs themselves also play a role due to their location, morphology, and mechanical properties. A complete analysis of the deformable three-dimensional apparatus has not yet appeared in the literature, but some insight can be gained from analysis of simplified deformable canals.
Much like the cochlea, the semicircular canals consist of two fluids, endolymph and perilymph, separated by a flexible partition. The partition deforms if there is a pressure gradient across it, thus driving fluid displacement and ultimately leading to displacement of sensory hair bundles. The two fluids have density responsible for storing and releasing kinetic energy and viscosity responsible for dissipating power. The membrane has elasticity responsible for storing and releasing potential energy.
The interaction between kinetic energy and potential energy combined with viscosity results in a dispersive wave equation Grieser et al. Under normal conditions, the canals are protected from auditory frequency stimulation by the bony enclosure and hence waves are not generated in the canals. This protection is lost if the bony labyrinth is compromised.
Part of the sound energy entering the inner ear at the oval window is diverted toward the dehiscence, thus accounting for the conductive hearing loss Songer and Rosowski This diverted sound energy generates a pressure gradient in the vestibular apparatus that can excite traveling waves along the membranous labyrinth Grieser et al. Conservation of mass requires the perilymph volume displacement entering the affected canal near the utricular vestibule to be balanced by an equal volume displacement at the fistula.
Since the utricular vestibule is much larger than the fistula, the perilymph velocity at the fistula is much larger than near the utricle.
This generates a large pressure gradient acting across the membranous labyrinth between endolymph and perilymph at the site of the fistula. As a result, traveling waves are generated at the fistula and propagate toward the utricle Iversen et al. The direction of propagation is somewhat counterintuitive, because the waves travel toward the sound source rather than toward the fistula. This is illustrated based on the model of Iversen and Rabbitt in Fig.
Waves travel away from the site of the dehiscence and pump fluid in both directions generating pressure across the cupula that builds up following the slow time constant of the cupula. In addition to endolymph pumping, waves traveling ampullopetal from the site of the fistula pass through the ampulla thus vibrating sensory hair bundles at the auditory stimulus frequency.
This vibration modulates MET currents leading to transmitter release and action potential discharge locked in step with the vibration. In addition to the cycle-by-cycle vibration, traveling waves pump the endolymph due to nonlinear interaction of the fluid and the undulating membrane Grieser et al.
Since waves travel in both directions away from the fistula, the net direction of pumping depends on which wave dominates. Frequency-dependent reflection of the waves can generate standing waves in one direction that do not pump fluid Fig. The net result is a traveling wave pump that drives endolymph in a frequency-dependent way to slowly deflect the cupula in an excitatory or inhibitory direction, evoking responses like the examples shown in Fig.
Auditory frequency endolymph pumping has been directly observed in the semicircular canals of an animal model using particle imaging velocimetry Iversen et al.
This is a nonlinear effect with similarities to a classical Liebau valveless pump Liebau ; Thomann The only known treatments are surgical repair of the fistula or canal plugging Ward et al.
Encasement in rigid bone normally protects the membranous labyrinth from pressure gradients that would otherwise occur. Owing to complete enclosure, linear acceleration generates equal pressures in the endolymph and perilymph thus eliminating any pressure gradient across the membrane and rendering the canals insensitive to linear acceleration. Pressure applied to the oval window generates nearly uniform pressure in canal perilymph and endolymph Fig.
Opening the bony labyrinth breaks the balance and introduces stimulus-evoked transmembrane pressure gradients that normally would not exist.
Since the membranous labyrinth is thin, even small pressure gradients can deform it. The damaged canal becomes sensitive to sound, vibration, static pressure, blood pressure, and linear acceleration. However, a fistula or dehiscence are not the only conditions that generate important transmembrane pressure gradients. In the intact labyrinth, pressure gradients evoked in the endolymph and perilymph by sinusoidal angular head movements are not identical to each other simply because of differences in fluid mechanics associated with differing morphologies of the two ducts.
The pressure difference increases with stimulus frequency as the inertial force increases, eventually reaching a point where the membranous labyrinth deforms. This is likely to occur at frequencies above 6 Hz in humans, where perilymph fluid mechanics contributes to deform the membrane, thus driving endolymph displacement and increasing canal sensitivity to angular head rotation Fig. It is not clear if the increased high-frequency sensitivity provided by this mechanism offers an advantage to the animal or not.
Further evidence for membranous labyrinth deformation at high frequencies is the fact that surgically plugged semicircular canals continue to respond to high-frequency sinusoidal head rotation. Surgical plugging of a rigid canal would completely eliminate endolymph displacement and thereby completely eliminate sensitivity to angular motion stimulation.
Plugging often completely fails to eliminate responses above 6 Hz due to high inertial forces and pressure Hess et al. Sensitivity persists at high frequencies because stimulus-evoked pressure differences between endolymph and perilymph deform the membranous labyrinth, thus causing cupula deflection even when the canal is plugged.
Another example is provided by afferent responses to episodic increases in endolymph pressure, pressure possibly generated by a transient osmotic imbalance between the inner ear fluids. It has been shown in an animal model that a hydrostatic pressure increase in endolymph distends the ampulla and thereby evokes changes in the discharge rate of afferent neurons through hair bundle deflections Yamauchi et al.
Gross semicircular canal morphology is remarkably conserved through phylogenesis, with only relatively minor variations appearing across amniotes. Although there are significant differences in hair cells and synapses between species, the fundamental biomechanical contributions to canal selectivity to angular motion, frequency-dependent sensitivity, directional coding, and temporal coding are universal. The origins these sensory characteristics can be quantified using first principles of mechanics.
Decomposition of 3D movements into three vectoral components, one carried by each canal nerve, is the result of macromechanics Fig. The lower corner frequency defining the transition from angular acceleration sensitivity to angular velocity sensitivity and wave propagation responsible for sound and vibration sensitivity also result directly from macromechanics Fig.
Mechanical principles can be applied to understand substrates of a class of common vestibular disorders and in some cases can be used to devise effective therapeutic treatments. Future optimization of CRPs and other mechanical procedures therefore might benefit from subject-specific biomechanical analysis drawing from imaging modalities capable of resolving detailed morphology of the patient's membranous labyrinth.
On a finer scale, micro- and nanomechanics of long hair bundles and mechanical aspects of transduction have received relatively little attention to date in the semicircular canals and represent areas where current understanding is incomplete. No conflicts of interest, financial or otherwise, are declared by the authors.
National Center for Biotechnology Information , U. J Neurophysiol. Published online Dec Rabbitt 1, 2, 3. Author information Article notes Copyright and License information Disclaimer. Corresponding author. Address for reprint requests and other correspondence: R.
Rabbitt, 36 S. Wasatch Dr. This article has been cited by other articles in PMC. Abstract The semicircular canals are responsible for sensing angular head motion in three-dimensional space and for providing neural inputs to the central nervous system CNS essential for agile mobility, stable vision, and autonomic control of the cardiovascular and other gravity-sensitive systems.
Open in a separate window. Coding of Angular Motion The neural code transmitted to the CNS by semicircular canals is complex, with individual afferent neurons within each nerve bundle exhibiting diverse kinetics. Macromechanics As summarized above, each labyrinth includes three endolymph filled membranous tubes Fig. Light or Heavy Cupula Under normal physiological conditions the specific gravity of the cupula matches the endolymph, so tilting the head relative to gravity does not generate any buoyancy force in the cupula or gravity-dependent neural responses.
Alcohol Positional Nystagmus Money et al. Perilymphatic Fistula or Dehiscence of the Bone Prominent 19th century scientists argued that the semicircular canals might be sensitive to air-conducted sound and potentially could play a role in directional hearing Camis Additional Consequences of Membranous Labyrinth Compliance Encasement in rigid bone normally protects the membranous labyrinth from pressure gradients that would otherwise occur.
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