A cochlear model using feed-forward outer-hair-cell forces

Optogenetics Reveals Roles for Supporting Cells in Force Transmission to and From Outer Hair Cells in the Mouse Cochlea

Outer hair cells (OHCs) of the organ of Corti (OoC), acting as bidirectional cellular mechanoelectrical transducers, generate, receive, and exchange forces with other major elements of the cochlear partition, including the sensory inner hair cells (IHCs). Force exchange is mediated via a supporting cell scaffold, including Deiters' (DC) and outer pillar cells (OPC), to enable the sensitivity and exquisite frequency selectivity of the mammalian cochlea and to transmit its responses to the auditory nerve. To selectively activate DCs and OPCs in male and female mice, we conditionally expressed in them a hyperpolarizing halorhodopsin (HOP), a light-gated inward chloride ion pump, and measured extracellular receptor potentials (ERPs) and their DC component (ERPDCs) from the cortilymph, which fills the OoC fluid spaces, and compared the responses with similar potentials from HOP-/- littermates. The compound action potentials (CAP) of the auditory nerve were measured as an indication of IHC activity and transmission of cochlear responses to the CNS. HOP light-activated hyperpolarization of DCs and OPCs suppressed cochlear amplification through changing the timing of its feedback, altered basilar membrane (BM) responses to tones at all measured levels and frequencies, and reduced IHC excitation. HOP activation findings reported here complement recent studies that revealed channelrhodopsin activation depolarized DCs and OPCs and effectively bypassed, rather than blocked, the control of OHC mechanical and electrical responses to sound and their contribution to timed and directed electromechanical feedback to the mammalian cochlea. Moreover, our findings identify DCs and OPCs as potential targets for the treatment of noise-induced hearing loss.

Otoacoustic emissions reveal the micromechanical role of organ-of-Corti cytoarchitecture in cochlear amplification

The intricate, crystalline cytoarchitecture of the mammalian organ of Corti presumably plays an important role in cochlear amplification. As currently understood, the oblique, Y-shaped arrangement of the outer hair cells (OHCs) and phalangeal processes of the Deiters cells serves to create differential "push-pull" forces that drive the motion of the basilar membrane via the spatial feedforward and/or feedbackward of OHC forces. In concert with the cochlear traveling wave, the longitudinal separation between OHC sensing and forcing creates phase shifts that yield a form of negative damping, amplifying waves as they propagate. Unlike active forces that arise and act locally, push-pull forces are inherently directional-whereas forward-traveling waves are boosted, reverse-traveling waves are squelched. Despite their attractions, models based on push-pull amplification must contend with otoacoustic emissions (OAEs), whose existence implies that amplified energy escapes from the inner ear via mechanisms involving reverse traveling waves. We analyze hybrid local/push-pull models to determine the constraints that reflection-source OAEs place on the directionality of cochlear wave propagation. By implementing a special force-mixing control knob, we vary the mix of local and push-pull forces while leaving the forward-traveling wave unchanged. Consistency with stimulus-frequency OAEs requires that the active forces underlying cochlear wave amplification be primarily local in character, contradicting the prevailing view. By requiring that the oblique cytoarchitecture produce predominantly local forces, we reinterpret the functional role of the Y-shaped geometry, proposing that it serves not as a push-pull amplifier, but as a mechanical funnel that spatially integrates local OHC forces.

Stimulus-frequency otoacoustic emissions and middle-ear pressure gains in a finite-element mouse model

For evoked otoacoustic emissions (OAEs), the stimulus and emission signals traverse the middle ear (ME) in forward and reverse directions, respectively. In this study, a fully coupled three-dimensional finite-element model of the mouse ear canal (EC), ME, and cochlea was used to calculate ME pressure gains, impedances, and reflectances at the EC-entrance and stapes-footplate-cochlear-fluid interfaces. The cochlear model incorporates a series of interdigitated Y-shaped structures sandwiched between the basilar membrane and reticular lamina, each comprised of a Deiters' cell, its phalangeal-process extension, and an outer hair cell (OHC). By introducing random perturbations to the OHC gains, stimulation-frequency otoacoustic emissions (SFOAEs) were generated. Raising the perturbation magnitude from 10% to 80% increased the SFOAE magnitude by up to 24 dB in the 10-30 kHz frequency range. Increasing or decreasing the stiffness of the stapes annular ligament and eardrum by a factor of 8 changed the SFOAEs by up to 30 dB, but the round-trip ME gain as measured could not account for this. A modified round-trip ME gain, with reflections removed at the EC-entrance and stapes-cochlea boundaries, eliminated a ±10 dB discrepancy and allowed ME changes to be quantitatively associated with changes in measured OAEs.

Cochlear supporting cells require GAS2 for cytoskeletal architecture and hearing

In mammals, sound is detected by mechanosensory hair cells that are activated in response to vibrations at frequency-dependent positions along the cochlear duct. We demonstrate that inner ear supporting cells provide a structural framework for transmitting sound energy through the cochlear partition. Humans and mice with mutations in GAS2, encoding a cytoskeletal regulatory protein, exhibit hearing loss due to disorganization and destabilization of microtubule bundles in pillar and Deiters' cells, two types of inner ear supporting cells with unique cytoskeletal specializations. Failure to maintain microtubule bundle integrity reduced supporting cell stiffness, which in turn altered cochlear micromechanics in Gas2 mutants. Vibratory responses to sound were measured in cochleae from live mice, revealing defects in the propagation and amplification of the traveling wave in Gas2 mutants. We propose that the microtubule bundling activity of GAS2 imparts supporting cells with mechanical properties for transmitting sound energy through the cochlea.

Broadband nonreciprocal linear acoustics through a non-local active metamaterial

The ability to create linear systems that manifest broadband nonreciprocal wave propagation would provide for exquisite control over acoustic signals for electronic filtering in communication and noise control. Acoustic nonreciprocity has predominately been achieved by approaches that introduce nonlinear interaction, mean-flow biasing, smart skins, and spatio-temporal parametric modulation into the system. Each approach suffers from at least one of the following drawbacks: the introduction of modulation tones, narrow band filtering, and the interruption of mean flow in fluid acoustics. We now show that an acoustic media that is non-local and active provides a new means to break reciprocity in a linear fashion without these deleterious effects. We realize this media using a distributed network of interlaced subwavelength sensor-actuator pairs with unidirectional signal transport. We exploit this new design space to create a stable metamaterial with non-even dispersion relations and electronically tunable nonreciprocal behavior over a broad range of frequencies.

Nonlinear cochlear mechanics without direct vibration-amplification feedback

Recent in vivo recordings from the mammalian cochlea indicate that although the motion of the basilar membrane appears actively amplified and nonlinear only at frequencies relatively close to the peak of the response, the internal motions of the organ of Corti display these same features over a much wider range of frequencies. These experimental findings are not easily explained by the textbook view of cochlear mechanics, in which cochlear amplification is controlled by the motion of the basilar membrane (BM) in a tight, closed-loop feedback configuration. This study shows that a simple phenomenological model of the cochlea inspired by the work of Zweig [J. Acoust. Soc. Am. 138, 1102 (2015)] can account for recent data in mouse and gerbil. In this model, the active forces are regulated indirectly, through the effect of BM motion on the pressure field across the cochlear partition, rather than via direct coupling between active-force generation and BM vibration. The absence of strong vibration-amplification feedback in the cochlea also provides a compelling explanation for the observed intensity invariance of fine time structure in the BM response to acoustic clicks.

Cochlear Frequency Tuning and Otoacoustic Emissions

Otoacoustic emissions (OAEs) evoked from the inner ear are the barely audible, signature byproduct of the delicate hydromechanical amplifier that evolved within its bony walls. Compared to the sounds evoked from the ears of common laboratory animals, OAEs from human ears have exceptionally long delays, typically exceeding those of cats, guinea pigs, and chinchillas by a factor of two to three. This review asks "Why are human OAE delays so long?" and recounts efforts to locate answers in the characteristics of mechanical frequency selectivity in the inner ear. The road to understanding species differences in OAE delay leads to the identification of new invariances and to the emergence of new questions.

Amplification and Suppression of Traveling Waves along the Mouse Organ of Corti: Evidence for Spatial Variation in the Longitudinal Coupling of Outer Hair Cell-Generated Forces

Mammalian hearing sensitivity and frequency selectivity depend on a mechanical amplification process mediated by outer hair cells (OHCs). OHCs are situated within the organ of Corti atop the basilar membrane (BM), which supports sound-evoked traveling waves. It is well established that OHCs generate force to selectively amplify BM traveling waves where they peak, and that amplification accumulates from one location to the next over this narrow cochlear region. However, recent measurements demonstrate that traveling waves along the apical surface of the organ of Corti, the reticular lamina (RL), are amplified over a much broader region. Whether OHC forces accumulate along the length of the RL traveling wave to provide a form of "global" cochlear amplification is unclear. Here we examined the spatial accumulation of RL amplification. In mice of either sex, we used tones to suppress amplification from different cochlear regions and examined the effect on RL vibrations near and far from the traveling-wave peak. We found that although OHC forces amplify the entire RL traveling wave, amplification only accumulates near the peak, over the same region where BM motion is amplified. This contradicts the notion that RL motion is involved in a global amplification mechanism and reveals that the mechanical properties of the BM and organ of Corti tune how OHC forces accumulate spatially. Restricting the spatial buildup of amplification enhances frequency selectivity by sharpening the peaks of cochlear traveling waves and constrains the number of OHCs responsible for mechanical sensitivity at each location.SIGNIFICANCE STATEMENT Outer hair cells generate force to amplify traveling waves within the mammalian cochlea. This force generation is critical to the ability to detect and discriminate sounds. Nevertheless, how these forces couple to the motions of the surrounding structures and integrate along the cochlear length remains poorly understood. Here we demonstrate that outer hair cell-generated forces amplify traveling-wave motion on the organ of Corti throughout the wave's extent, but that these forces only accumulate longitudinally over a region near the wave's peak. The longitudinal coupling of outer hair cell-generated forces is therefore spatially tuned, likely by the mechanical properties of the basilar membrane and organ of Corti. Our findings provide new insight into the mechanical processes that underlie sensitive hearing.

Vibration hotspots reveal longitudinal funneling of sound-evoked motion in the mammalian cochlea

The micromechanical mechanisms that underpin tuning and dynamic range compression in the mammalian inner ear are fundamental to hearing, but poorly understood. Here, we present new, high-resolution optical measurements that directly map sound-evoked vibrations on to anatomical structures in the intact, living gerbil cochlea. The largest vibrations occur in a tightly delineated hotspot centering near the interface between the Deiters' and outer hair cells. Hotspot vibrations are less sharply tuned, but more nonlinear, than basilar membrane vibrations, and behave non-monotonically (exhibiting hyper-compression) near their characteristic frequency. Amplitude and phase differences between hotspot and basilar membrane responses depend on both frequency and measurement angle, and indicate that hotspot vibrations involve longitudinal motion. We hypothesize that structural coupling between the Deiters' and outer hair cells funnels sound-evoked motion into the hotspot region, under the control of the outer hair cells, to optimize cochlear tuning and compression.

Cochlear amplification and tuning depend on the cellular arrangement within the organ of Corti

The field of cochlear mechanics has been undergoing a revolution due to recent findings made possible by advancements in measurement techniques. While it has long been assumed that basilar-membrane (BM) motion is the most important determinant of sound transduction by the inner hair cells (IHCs), it turns out that other parts of the sensory epithelium closer to the IHCs, such as the reticular lamina (RL), move with significantly greater amplitude for weaker sounds. It has not been established how these findings are related to the complex cytoarchitecture of the organ of Corti between the BM and RL, which is composed of a lattice of asymmetric Y-shaped elements, each consisting of a basally slanted outer hair cell (OHC), an apically slanted phalangeal process (PhP), and a supporting Deiters' cell (DC). Here, a computational model of the mouse cochlea supports the hypothesis that the OHC micromotors require this Y-shaped geometry for their contribution to the exquisite sensitivity and frequency selectivity of the mammalian cochlea. By varying only the OHC gain parameter, the model can reproduce measurements of BM and RL gain and tuning for a variety of input sound levels. Malformations such as reversing the orientations of the OHCs and PhPs or removing the PhPs altogether greatly reduce the effectiveness of the OHC motors. These results imply that the DCs and PhPs must be properly accounted for in emerging OHC regeneration therapies.

An elemental approach to modelling the mechanics of the cochlea

The motion along the basilar membrane in the cochlea is due to the interaction between the micromechanical behaviour of the organ of Corti and the fluid movement in the scalae. By dividing the length of the cochlea into a finite number of elements and assuming a given radial distribution of the basilar membrane motion for each element, a set of equations can be separately derived for the micromechanics and for the fluid coupling. These equations can then be combined, using matrix methods, to give the fully coupled response. This elemental approach reduces to the classical transmission line model if the micromechanics are assumed to be locally-reacting and the fluid coupling is assumed to be entirely one-dimensional, but is also valid without these assumptions. The elemental model is most easily formulated in the frequency domain, assuming quasi-linear behaviour, but a time domain formulation, using state space method, can readily incorporate local nonlinearities in the micromechanics. Examples of programs are included for the elemental model of a human cochlea that can be readily modified for other species.

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General formulation of an elemental model for cochlear mechanics.

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Reduce to the transmission line model for locally-reacting micromechanical and 1D fluid coupling.

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Incorporation of non-uniform areas, 3D fluid coupling and non locally-reacting micromechanics.

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MATLAB programs for the elemental model in the frequency domain and time domain.

Hair Cell Transduction, Tuning, and Synaptic Transmission in the Mammalian Cochlea

Sound pressure fluctuations striking the ear are conveyed to the cochlea, where they vibrate the basilar membrane on which sit hair cells, the mechanoreceptors of the inner ear. Recordings of hair cell electrical responses have shown that they transduce sound via submicrometer deflections of their hair bundles, which are arrays of interconnected stereocilia containing the mechanoelectrical transducer (MET) channels. MET channels are activated by tension in extracellular tip links bridging adjacent stereocilia, and they can respond within microseconds to nanometer displacements of the bundle, facilitated by multiple processes of Ca2+-dependent adaptation. Studies of mouse mutants have produced much detail about the molecular organization of the stereocilia, the tip links and their attachment sites, and the MET channels localized to the lower end of each tip link. The mammalian cochlea contains two categories of hair cells. Inner hair cells relay acoustic information via multiple ribbon synapses that transmit rapidly without rundown. Outer hair cells are important for amplifying sound-evoked vibrations. The amplification mechanism primarily involves contractions of the outer hair cells, which are driven by changes in membrane potential and mediated by prestin, a motor protein in the outer hair cell lateral membrane. Different sound frequencies are separated along the cochlea, with each hair cell being tuned to a narrow frequency range; amplification sharpens the frequency resolution and augments sensitivity 100-fold around the cell's characteristic frequency. Genetic mutations and environmental factors such as acoustic overstimulation cause hearing loss through irreversible damage to the hair cells or degeneration of inner hair cell synapses. © 2017 American Physiological Society. Compr Physiol 7:1197-1227, 2017.

Two-Dimensional Cochlear Micromechanics Measured In Vivo Demonstrate Radial Tuning within the Mouse Organ of Corti

The exquisite sensitivity and frequency discrimination of mammalian hearing underlie the ability to understand complex speech in noise. This requires force generation by cochlear outer hair cells (OHCs) to amplify the basilar membrane traveling wave; however, it is unclear how amplification is achieved with sharp frequency tuning. Here we investigated the origin of tuning by measuring sound-induced 2-D vibrations within the mouse organ of Corti in vivo Our goal was to determine the transfer function relating the radial shear between the structures that deflect the OHC bundle, the tectorial membrane and reticular lamina, to the transverse motion of the basilar membrane. We found that, after normalizing their responses to the vibration of the basilar membrane, the radial vibrations of the tectorial membrane and reticular lamina were tuned. The radial tuning peaked at a higher frequency than transverse basilar membrane tuning in the passive, postmortem condition. The radial tuning was similar in dead mice, indicating that this reflected passive, not active, mechanics. These findings were exaggerated in Tecta(C1509G/C1509G) mice, where the tectorial membrane is detached from OHC stereocilia, arguing that the tuning of radial vibrations within the hair cell epithelium is distinct from tectorial membrane tuning. Together, these results reveal a passive, frequency-dependent contribution to cochlear filtering that is independent of basilar membrane filtering. These data argue that passive mechanics within the organ of Corti sharpen frequency selectivity by defining which OHCs enhance the vibration of the basilar membrane, thereby tuning the gain of cochlear amplification.

SIGNIFICANCE STATEMENT

Outer hair cells amplify the traveling wave within the mammalian cochlea. The resultant gain and frequency sharpening are necessary for speech discrimination, particularly in the presence of background noise. Here we measured the 2-D motion of the organ of Corti in mice and found that the structures that stimulate the outer hair cell stereocilia, the tectorial membrane and reticular lamina, were sharply tuned in the radial direction. Radial tuning was similar in dead mice and in mice lacking a tectorial membrane. This suggests that radial tuning comes from passive mechanics within the hair cell epithelium, and that these mechanics, at least in part, may tune the gain of cochlear amplification.

Consequences of Location-Dependent Organ of Corti Micro-Mechanics

The cochlea performs frequency analysis and amplification of sounds. The graded stiffness of the basilar membrane along the cochlear length underlies the frequency-location relationship of the mammalian cochlea. The somatic motility of outer hair cell is central for cochlear amplification. Despite two to three orders of magnitude change in the basilar membrane stiffness, the force capacity of the outer hair cell’s somatic motility, is nearly invariant over the cochlear length. It is puzzling how actuators with a constant force capacity can operate under such a wide stiffness range. We hypothesize that the organ of Corti sets the mechanical conditions so that the outer hair cell’s somatic motility effectively interacts with the media of traveling waves—the basilar membrane and the tectorial membrane. To test this hypothesis, a computational model of the gerbil cochlea was developed that incorporates organ of Corti structural mechanics, cochlear fluid dynamics, and hair cell electro-physiology. The model simulations showed that the micro-mechanical responses of the organ of Corti are different along the cochlear length. For example, the top surface of the organ of Corti vibrated more than the bottom surface at the basal (high frequency) location, but the amplitude ratio was reversed at the apical (low frequency) location. Unlike the basilar membrane stiffness varying by a factor of 1700 along the cochlear length, the stiffness of the organ of Corti complex felt by the outer hair cell remained between 1.5 and 0.4 times the outer hair cell stiffness. The Y-shaped structure in the organ of Corti formed by outer hair cell, Deiters cell and its phalange was the primary determinant of the elastic reactance imposed on the outer hair cells. The stiffness and geometry of the Deiters cell and its phalange affected cochlear amplification differently depending on the location.

Modeling auditory coding: from sound to spikes

Models are valuable tools to assess how deeply we understand complex systems: only if we are able to replicate the output of a system based on the function of its subcomponents can we assume that we have probably grasped its principles of operation. On the other hand, discrepancies between model results and measurements reveal gaps in our current knowledge, which can in turn be targeted by matched experiments. Models of the auditory periphery have improved greatly during the last decades, and account for many phenomena observed in experiments. While the cochlea is only partly accessible in experiments, models can extrapolate its behavior without gap from base to apex and with arbitrary input signals. With models we can for example evaluate speech coding with large speech databases, which is not possible experimentally, and models have been tuned to replicate features of the human hearing organ, for which practically no invasive electrophysiological measurements are available. Auditory models have become instrumental in evaluating models of neuronal sound processing in the auditory brainstem and even at higher levels, where they are used to provide realistic input, and finally, models can be used to illustrate how such a complicated system as the inner ear works by visualizing its responses. The big advantage there is that intermediate steps in various domains (mechanical, electrical, and chemical) are available, such that a consistent picture of the evolvement of its output can be drawn. However, it must be kept in mind that no model is able to replicate all physiological characteristics (yet) and therefore it is critical to choose the most appropriate model—or models—for every research question. To facilitate this task, this paper not only reviews three recent auditory models, it also introduces a framework that allows researchers to easily switch between models. It also provides uniform evaluation and visualization scripts, which allow for direct comparisons between models.

Microstructures in the organ of Corti help outer hair cells form traveling waves along the cochlear coil

According to the generally accepted theory of mammalian cochlear mechanics, the fluid in the cochlear scalae interacts with the elastic cochlear partition to generate transversely oscillating displacement waves that propagate along the cochlear coil. Using a computational model of cochlear segments, a different type of propagating wave is reported, an elastic propagating wave that is independent of the fluid-structure interaction. The characteristics of the propagating wave observed in the model, such as the wavelength, speed, and phase lag, are similar to those observed in the living cochlea. Three conditions are required for the existence of the elastic propagating wave in the cochlear partition without fluid-interaction: 1), the stiffness gradient of the cochlear partition; 2), the elastic longitudinal coupling; and 3), the Y-shaped structure in the organ of Corti formed by the outer hair cell, the Deiters cell, and the Deiters cell phalangeal process. The elastic propagating waves in the cochlear partition disappeared without the push-pull action provided by the outer hair cell and Deiters cell phalangeal process. The results suggest that the mechanical feedback of outer hair cells, facilitated by the organ of Corti microstructure, can control the tuning and amplification by modulating the cochlear traveling wave.

Tyrosine motifs are required for prestin basolateral membrane targeting

Prestin is targeted to the lateral wall of outer hair cells (OHCs) where its electromotility is critical for cochlear amplification. Using MDCK cells as a model system for polarized epithelial sorting, we demonstrate that prestin uses tyrosine residues, in a YXXΦ motif, to target the basolateral surface. Both Y520 and Y667 are important for basolateral targeting of prestin. Mutation of these residues to glutamine or alanine resulted in retention within the Golgi and delayed egress from the Golgi in Y667Q. Basolateral targeting is restored upon mutation to phenylalanine suggesting the importance of a phenol ring in the tyrosine side chain. We also demonstrate that prestin targeting to the basolateral surface is dependent on AP1B (μ1B), and that prestin uses transferrin containing early endosomes in its passage from the Golgi to the basolateral plasma membrane. The presence of AP1B (μ1B) in OHCs, and parallels between prestin targeting to the basolateral surface of OHCs and polarized epithelial cells suggest that outer hair cells resemble polarized epithelia rather than neurons in this important phenotypic measure.

Cytoarchitecture of the mouse organ of corti from base to apex, determined using in situ two-photon imaging

The cells in the organ of Corti are highly organized, with a precise 3D microstructure hypothesized to be important for cochlear function. Here we provide quantitative data on the mouse organ of Corti cytoarchitecture, as determined using a new technique that combines the imaging capabilities of two-photon microscopy with the autofluorescent cell membranes of the genetically modified mTmG mouse. This combination allowed us to perform in situ imaging on freshly excised tissue, thus minimizing any physical distortions to the tissue that extraction from the cochlea and chemical fixation and staining might have caused. 3D image stacks of the organ of Corti were obtained from base to apex in the cochlear duct, from which 3D lengths and relative angles for inner and outer hair cells, Deiters' cells, phalangeal processes, and inner and outer pillars were measured. In addition, intercellular distances, diameters, and stereocilia shapes were obtained. An important feature of this study is the quantitative reporting of the longitudinal tilts of the outer hair cells towards the base of the cochlea, the tilt of phalangeal processes towards the apex, and Deiters' cells that collectively form a Y-shaped building block that is thought to give rise to the lattice-like organization of the organ of Corti. The variations of this Y-shaped element along the cochlear duct and between the rows of outer hair cells are shown with the third row morphologically different from the other rows, and their potential importance for the cochlear amplifier is discussed.

Modelling cochlear mechanics

The cochlea plays a crucial role in mammal hearing. The basic function of the cochlea is to map sounds of different frequencies onto corresponding characteristic positions on the basilar membrane (BM). Sounds enter the fluid-filled cochlea and cause deflection of the BM due to pressure differences between the cochlear fluid chambers. These deflections travel along the cochlea, increasing in amplitude, until a frequency-dependent characteristic position and then decay away rapidly. The hair cells can detect these deflections and encode them as neural signals. Modelling the mechanics of the cochlea is of help in interpreting experimental observations and also can provide predictions of the results of experiments that cannot currently be performed due to technical limitations. This paper focuses on reviewing the numerical modelling of the mechanical and electrical processes in the cochlea, which include fluid coupling, micromechanics, the cochlear amplifier, nonlinearity, and electrical coupling.

Vibration of the organ of Corti within the cochlear apex in mice

The tonotopic map of the mammalian cochlea is commonly thought to be determined by the passive mechanical properties of the basilar membrane. The other tissues and cells that make up the organ of Corti also have passive mechanical properties; however, their roles are less well understood. In addition, active forces produced by outer hair cells (OHCs) enhance the vibration of the basilar membrane, termed cochlear amplification. Here, we studied how these biomechanical components interact using optical coherence tomography, which permits vibratory measurements within tissue. We measured not only classical basilar membrane tuning curves, but also vibratory responses from the rest of the organ of Corti within the mouse cochlear apex in vivo. As expected, basilar membrane tuning was sharp in live mice and broad in dead mice. Interestingly, the vibratory response of the region lateral to the OHCs, the "lateral compartment," demonstrated frequency-dependent phase differences relative to the basilar membrane. This was sharply tuned in both live and dead mice. We then measured basilar membrane and lateral compartment vibration in transgenic mice with targeted alterations in cochlear mechanics. Prestin(499/499), Prestin(-/-), and Tecta(C1509G/C1509G) mice demonstrated no cochlear amplification but maintained the lateral compartment phase difference. In contrast, Sfswap(Tg/Tg) mice maintained cochlear amplification but did not demonstrate the lateral compartment phase difference. These data indicate that the organ of Corti has complex micromechanical vibratory characteristics, with passive, yet sharply tuned, vibratory characteristics associated with the supporting cells. These characteristics may tune OHC force generation to produce the sharp frequency selectivity of mammalian hearing.

Selective ablation of pillar and deiters' cells severely affects cochlear postnatal development and hearing in mice

Mammalian auditory hair cells (HCs) are inserted into a well structured environment of supporting cells (SCs) and acellular matrices. It has been proposed that when HCs are irreversibly damaged by noise or ototoxic drugs, surrounding SCs seal the epithelial surface and likely extend the survival of auditory neurons. Because SCs are more resistant to damage than HCs, the effects of primary SC loss on HC survival and hearing have received little attention. We used the Cre/loxP system in mice to specifically ablate pillar cells (PCs) and Deiters' cells (DCs). In Prox1CreER(T2)+/-;Rosa26(DTA/+) (Prox1DTA) mice, Cre-estrogen receptor (CreER) expression is driven by the endogenous Prox1 promoter and, in presence of tamoxifen, removes a stop codon in the Rosa26(DTA/+) allele and induces diphtheria toxin fragment A (DTA) expression. DTA produces cell-autonomous apoptosis. Prox1DTA mice injected with tamoxifen at postnatal days 0 (P0) and P1 show significant DC and outer PC loss at P2-P4, that reaches ∼70% by 1 month. Outer HC loss follows at P14 and is almost complete at 1 month, while inner HCs remain intact. Neural innervation to the outer HCs is disrupted in Prox1DTA mice and auditory brainstem response thresholds in adults are 40-50 dB higher than in controls. The hearing deficit correlates with loss of cochlear amplification. Remarkably, in Prox1DTA mice, the auditory epithelium preserves the ability to seal the reticular lamina and spiral ganglion neuron counts are normal, a key requirement for cochlear implant success. In addition, our results show that cochlear SC pools should be appropriately replenished during HC regeneration strategies.

A three-dimensional finite element model of round window membrane vibration before and after stapedotomy surgery

Piston stapes prostheses are implanted in patients with refractory conductive or mixed hearing loss due to stapes otosclerosis to stimulate the perilymph with varying degrees of success. The overclosure effect described by the majority of researchers affects mainly low and medium frequencies, and a large number of patients report a lack of satisfactory results for frequencies above 2 kHz. The mechanics of perilymph stimulation with the piston have not been studied in a systematic manner. The objective of this study was to assess the influence of stapedotomy surgery on round window membrane vibration and to estimate the postoperative outcomes using the finite element (FE) method. The study hypothesis is that the three-dimensional FE model developed of the human inner ear, which simulates the round window (RW) membrane vibration, can be used to assess the influence of stapedotomy on auditory outcomes achieved after the surgical procedure. An additional objective of the study was to enable the simulation of RW membrane vibration after stapedotomy using a new type of stapes prosthesis currently under investigation at Warsaw University of Technology. A three-dimensional finite element (FE) model of the human inner ear was developed and validated using experimental data. The model was then used to simulate the round window membrane vibration before and after stapedotomy surgery. Functional alterations of the RW membrane vibration were derived from the model and compared with the results of experimental measurements from temporal bones of a human cadaver. Piston stapes prosthesis implantation causes an approximately fivefold (14 dB) lower amplitude of the RW membrane vibrations compared with normal anatomical conditions. A satisfactory agreement between the FE model and the experimental data was found. The new prosthesis caused an increase of 20–30 dB in the RW displacement amplitude compared with the 0.4-mm piston prosthesis. In all frequencies, the FE model predicted a RW displacement curve that was above the experimental curves for the normal ear. The stapedotomy can be well simulated by the FE model to predict the auditory outcomes achieved following this otosurgery procedure. The 3D FE model developed in this study may be used to optimize the geometry of a new type of stapes prosthesis in order to achieve a similar sound transmission through the inner ear as for a normal middle ear. This should provide better auditory outcomes for patients with stapedial otosclerosis.

A mouse model for human deafness DFNB22 reveals that hearing impairment is due to a loss of inner hair cell stimulation

The gene causative for the human nonsyndromic recessive form of deafness DFNB22 encodes otoancorin, a 120-kDa inner ear-specific protein that is expressed on the surface of the spiral limbus in the cochlea. Gene targeting in ES cells was used to create an EGFP knock-in, otoancorin KO (Otoa(EGFP/EGFP)) mouse. In the Otoa(EGFP/EGFP) mouse, the tectorial membrane (TM), a ribbon-like strip of ECM that is normally anchored by one edge to the spiral limbus and lies over the organ of Corti, retains its general form, and remains in close proximity to the organ of Corti, but is detached from the limbal surface. Measurements of cochlear microphonic potentials, distortion product otoacoustic emissions, and basilar membrane motion indicate that the TM remains functionally attached to the electromotile, sensorimotor outer hair cells of the organ of Corti, and that the amplification and frequency tuning of the basilar membrane responses to sounds are almost normal. The compound action potential masker tuning curves, a measure of the tuning of the sensory inner hair cells, are also sharply tuned, but the thresholds of the compound action potentials, a measure of inner hair cell sensitivity, are significantly elevated. These results indicate that the hearing loss in patients with Otoa mutations is caused by a defect in inner hair cell stimulation, and reveal the limbal attachment of the TM plays a critical role in this process.

Von Békésy and cochlear mechanics

Georg Békésy laid the foundation for cochlear mechanics, foremost by demonstrating the traveling wave that is the substrate for mammalian cochlear mechanical processing. He made mechanical measurements and physical models in order to understand that fundamental cochlear response. In this tribute to Békésy we make a bridge between modern traveling wave observations and those of Békésy, discuss the mechanical properties and measurements that he considered to be so important, and touch on the range of computational traveling wave models.

Analysis of the cochlear amplifier fluid pump hypothesis

We use analysis of a realistic three-dimensional finite-element model of the tunnel of Corti (ToC) in the middle turn of the gerbil cochlea tuned to the characteristic frequency (CF) of 4 kHz to show that the anatomical structure of the organ of Corti (OC) is consistent with the hypothesis that the cochlear amplifier functions as a fluid pump. The experimental evidence for the fluid pump is that outer hair cell (OHC) contraction and expansion induce oscillatory flow in the ToC. We show that this oscillatory flow can produce a fluid wave traveling in the ToC and that the outer pillar cells (OPC) do not present a significant barrier to fluid flow into the ToC. The wavelength of the resulting fluid wave launched into the tunnel at the CF is 1.5 mm, which is somewhat longer than the wavelength estimated for the classical traveling wave. This fluid wave propagates at least one wavelength before being significantly attenuated. We also investigated the effect of OPC spacing on fluid flow into the ToC and found that, for physiologically relevant spacing between the OPCs, the impedance estimate is similar to that of the underlying basilar membrane. We conclude that the row of OPCs does not significantly impede fluid exchange between ToC and the space between the row of OPC and the first row of OHC-Dieter's cells complex, and hence does not lead to excessive power loss. The BM displacement resulting from the fluid pumped into the ToC is significant for motion amplification. Our results support the hypothesis that there is an additional source of longitudinal coupling, provided by the ToC, as required in many non-classical models of the cochlear amplifier.

Unification and extension of monolithic state space and iterative cochlear models

Time domain cochlear models have primarily followed a method introduced by Allen and Sondhi [J. Acoust. Soc. Am. 66, 123-132 (1979)]. Recently the "state space formalism" proposed by Elliott et al. [J. Acoust. Soc. Am. 122, 2759-2771 (2007)] has been used to simulate a wide range of nonlinear cochlear models. It used a one-dimensional approach that is extended to two dimensions in this paper, using the finite element method. The recently developed "state space formalism" in fact shares a close relationship to the earlier approach. Working from Diependaal et al. [J. Acoust. Soc. Am. 82, 1655-1666 (1987)] the two approaches are compared and the relationship formalized. Understanding this relationship allows models to be converted from one to the other in order to utilize each of their strengths. A second method to derive the state space matrices required for the "state space formalism" is also presented. This method offers improved numerical properties because it uses the information available about the model more effectively. Numerical results support the claims regarding fluid dimension and the underlying similarity of the two approaches. Finally, the recent advances in the state space formalism [Bertaccini and Sisto, J. Comp. Phys. 230, 2575-2587 (2011)] are discussed in terms of this relationship.

In vivo outer hair cell length changes expose the active process in the cochlea

Background

Mammalian hearing is refined by amplification of the sound-evoked vibration of the cochlear partition. This amplification is at least partly due to forces produced by protein motors residing in the cylindrical body of the outer hair cell. To transmit power to the cochlear partition, it is required that the outer hair cells dynamically change their length, in addition to generating force. These length changes, which have not previously been measured in vivo, must be correctly timed with the acoustic stimulus to produce amplification.

Methodology/Principal Findings

Using in vivo optical coherence tomography, we demonstrate that outer hair cells in living guinea pigs have length changes with unexpected timing and magnitudes that depend on the stimulus level in the sensitive cochlea.

Conclusions/Significance

The level-dependent length change is a necessary condition for directly validating that power is expended by the active process presumed to underlie normal hearing.

Auditory nerve excitation via a non-traveling wave mode of basilar membrane motion

Basilar membrane (BM) motion and auditory nerve fiber (ANF) tuning are generally very similar, but the ANF had appeared to be unresponsive to a plateau mode of BM motion that occurs at frequencies above an ANF's characteristic frequency (CF). We recorded ANF responses from the gerbil, concentrating on this supra-CF region. We observed a supra-CF plateau in ANF responses at high stimulus level, indicating that the plateau mode of BM motion can be excitatory.

Feed-forward and feed-backward amplification model from cochlear cytoarchitecture: an interspecies comparison

The high sensitivity and wide bandwidth of mammalian hearing are thought to derive from an active process involving the somatic and hair-bundle motility of the thousands of outer hair cells uniquely found in mammalian cochleae. To better understand this, a biophysical three-dimensional cochlear fluid model was developed for gerbil, chinchilla, cat, and human, featuring an active "push-pull" cochlear amplifier mechanism based on the cytoarchitecture of the organ of Corti and using the time-averaged Lagrangian method. Cochlear responses are simulated and compared with in vivo physiological measurements for the basilar membrane (BM) velocity, V(BM), frequency tuning of the BM vibration, and Q₁₀ values representing the sharpness of the cochlear tuning curves. The V(BM) simulation results for gerbil and chinchilla are consistent with in vivo cochlea measurements. Simulated mechanical tuning curves based on maintaining a constant V(BM) value agree with neural-tuning threshold measurements better than those based on a constant displacement value, which implies that the inner hair cells are more sensitive to V(BM) than to BM displacement. The Q₁₀ values of the V(BM) tuning curve agree well with those of cochlear neurons across species, and appear to be related in part to the width of the basilar membrane.

Basilar membrane velocity in a cochlea with a modified organ of Corti

Many cochlear models assign zero longitudinal coupling in the cochlea. Although this is consistent with the transverse basilar membrane (BM) fibers, the cochlear partition contains cellular longitudinal coupling. In cochlear models, longitudinal coupling diminishes passive BM tuning; however, it has recently been employed in theories of active mechanics to enhance tuning. Our goal in this study was to probe passive longitudinal coupling by comparing BM responses in damaged cochleae with passive responses in normal cochleae. The cochleae of gerbils were damaged with intratympanic neomycin followed by a waiting period to ensure that all of the cells of the partition were missing or severely disrupted. We then measured BM motion and examined the cochleae histologically. In comparison with passive responses in normal cochleae, we observed a downward shift in characteristic frequency, an expected consequence of reduced stiffness from cellular damage. However, we did not observe enhanced passive tuning in the damaged cochleae, as would be expected if longitudinal coupling were substantially greater in the normal cochleae. Thus, we conclude that cell-based longitudinal coupling is not large enough to influence passive cochlear mechanics. This finding constrains theories of active mechanics.

Tectorial membrane travelling waves underlie abnormal hearing in Tectb mutant mice

Remarkable sensitivity and exquisite frequency selectivity are hallmarks of mammalian hearing, but their underlying mechanisms remain unclear. Cochlear insults and hearing disorders that decrease sensitivity also tend to broaden tuning, suggesting that these properties are linked. However, a recently developed mouse model of genetically altered hearing (Tectb(-/-)) shows decreased sensitivity and sharper frequency selectivity. In this paper, we show that the Tectb mutation reduces the spatial extent and propagation velocity of tectorial membrane (TM) travelling waves and that these changes in wave propagation are likely to account for all of the hearing abnormalities associated with the mutation. By reducing the spatial extent of TM waves, the Tectb mutation decreases the spread of excitation and thereby increases frequency selectivity. Furthermore, the change in TM wave velocity reduces the number of hair cells that effectively couple energy to the basilar membrane, which reduces sensitivity. These results highlight the importance of TM waves in hearing.

Force transmission in the organ of Corti micromachine

Auditory discrimination is limited by the performance of the cochlea whose acute sensitivity and frequency tuning are underpinned by electromechanical feedback from the outer hair cells. Two processes may underlie this feedback: voltage-driven contractility of the outer hair cell body and active motion of the hair bundle. Either process must exert its mechanical effect via deformation of the organ of Corti, a complex assembly of sensory and supporting cells riding on the basilar membrane. Using finite element analysis, we present a three-dimensional model to illustrate deformation of the organ of Corti by the two active processes. The model used available measurements of the properties of structural components in low-frequency and high-frequency regions of the rodent cochlea. The simulations agreed well with measurements of the cochlear partition stiffness, the longitudinal space constant for point deflection, and the deformation of the organ of Corti for current injection, as well as displaying a 20-fold increase in passive resonant frequency from apex to base. The radial stiffness of the tectorial membrane attachment was found to be a crucial element in the mechanical feedback. Despite a substantial difference in the maximum force generated by hair bundle and somatic motility, the two mechanisms induced comparable amplitudes of motion of the basilar membrane but differed in the polarity of their feedback on hair bundle position. Compared to the hair bundle motor, the somatic motor was more effective in deforming the organ of Corti than in displacing the basilar membrane.

Different models of the active cochlea, and how to implement them in the state-space formalism

The state-space formalism [Elliott S. J., et al. (2007). J. Acoust. Soc. Am. 122, 2759-2771] allows one to discretize cochlear models in a straightforward matrix form and to modify the main physical properties of the cochlear model by changing the position and functional form of a few matrix elements. Feed-forward and feed-backward properties can be obtained by simply introducing off-diagonal terms in the matrixes expressing the coupling between the dynamical variables and the additional active pressure on the basilar membrane. Some theoretical issues related to different cochlear modeling choices, their implementation in a state-space scheme, and their physical consequences on the cochlear phenomenology, as predicted by numerical simulations, are discussed. Different schematizations of the active term describing the behavior of the outer hair cell's feedback mechanism, including nonlinear and nonlocal dependences on either pressure or basilar membrane displacement, are also discussed, showing their effect on some measurable cochlear properties.

Otoacoustic estimation of cochlear tuning: validation in the chinchilla

We analyze published auditory-nerve and otoacoustic measurements in chinchilla to test a network of hypothesized relationships between cochlear tuning, cochlear traveling-wave delay, and stimulus-frequency otoacoustic emissions (SFOAEs). We find that the physiological data generally corroborate the network of relationships, including predictions from filter theory and the coherent-reflection model of OAE generation, at locations throughout the cochlea. The results support the use of otoacoustic emissions as noninvasive probes of cochlear tuning. Developing this application, we find that tuning ratios-defined as the ratio of tuning sharpness to SFOAE phase-gradient delay in periods-have a nearly species-invariant form in cat, guinea pig, and chinchilla. Analysis of the tuning ratios identifies a species-dependent parameter that locates a transition between "apical-like" and "basal-like" behavior involving multiple aspects of cochlear physiology. Approximate invariance of the tuning ratio allows determination of cochlear tuning from SFOAE delays. We quantify the procedure and show that otoacoustic estimates of chinchilla cochlear tuning match direct measures obtained from the auditory nerve. By assuming that invariance of the tuning ratio extends to humans, we derive new otoacoustic estimates of human cochlear tuning that remain mutually consistent with independent behavioral measurements obtained using different rationales, methodologies, and analysis procedures. The results confirm that at any given characteristic frequency (CF) human cochlear tuning appears sharper than that in the other animals studied, but varies similarly with CF. We show, however, that the exceptionality of human tuning can be exaggerated by the ways in which species are conventionally compared, which take no account of evident differences between the base and apex of the cochlea. Finally, our estimates of human tuning suggest that the spatial spread of excitation of a pure tone along the human basilar membrane is comparable to that in other common laboratory animals.

A silicon cochlea with active coupling

We present a mixed-signal very-large-scale-integrated chip that emulates nonlinear active cochlear signal processing. Modeling the cochlea's micromechanics, including outer hair cell (OHC) electromotility, this silicon (Si) cochlea features active coupling between neighboring basilar membrane (BM) segments-a first. Neighboring BM segments, each implemented as a class AB log-domain second-order section, exchange currents representing OHC forces. This novel active-coupling architecture overcomes the major shortcomings of existing cascade and parallel filter-bank architectures, while achieving the highest number of digital outputs in an Si cochlea to date. An active-coupling architecture Si cochlea with 360 frequency channels and 2160 pulse-stream outputs occupies 10.9 mm(2) in a five-metal 1-poly 0.25-mum CMOS process. The chip's responses resemble that of a living cochlea's: Frequency responses become larger and more sharply tuned when active coupling is turned on. For instance, gain increases by 18 dB and Q 10 increases from 0.45 to 1.14. This enhancement decreases with increasing input intensity, realizing frequency-selective automatic gain control. Further work is required to improve performance by reducing large variations from tap to tap.

Multiple roles for the tectorial membrane in the active cochlea

This review is concerned with experimental results that reveal multiple roles for the tectorial membrane in active signal processing in the mammalian cochlea. We discuss the dynamic mechanical properties of the tectorial membrane as a mechanical system with several degrees of freedom and how its different modes of movement can lead to hair-cell excitation. The role of the tectorial membrane in distributing energy along the cochlear partition and how it channels this energy to the inner hair cells is described.

A COCHLEAR MODEL USING THE TIME-AVERAGED LAGRANGIAN AND THE PUSH-PULL MECHANISM IN THE ORGAN OF CORTI

In our previous work, the basilar membrane velocity V(BM) for a gerbil cochlea was calculated and compared with physiological measurements. The calculated V(BM) showed excessive phase excursion and, in the active case, a best-frequency place shift of approximately two fifths of an octave higher. Here we introduce a refined model that uses the time-averaged Lagrangian for the conservative system to resolve the phase excursion issues. To improve the overestimated best-frequency place found in the previous feed-forward active model, we implement in the new model a push-pull mechanism from the outer hair cells and phalangeal process. Using this new model, the V(BM) for the gerbil cochlea was calculated and compared with animal measurements, The results show excellent agreement for mapping the location of the maximum response to frequency, while the agreement for the response at a fixed point as a function of frequency is excellent for the amplitude and good for the phase.

Inverse-solution method for a class of non-classical cochlear models

Measurements of distortion-product (DP) waves inside the cochlea have led to a conception of wave propagation that is at variance with the "classical" attitude. Of the several alternatives that have been proposed to remedy this situation, the feed-forward model could be a promising one. This paper describes a method to apply the inverse solution with the aim to attain a feed-forward model that accurately reproduces a measured response. It is demonstrated that the computation method is highly successful. Subsequently, it is shown that in a feed-forward model a DP wave generated by a two-tone stimulus is almost exclusively a forward-traveling wave which property agrees with the nature of the experimental findings. However, the amplitude of the computed DP wave is only substantial in the region where the stimulation patterns of the two primary tones overlap. In addition, the model developed cannot explain coherent reflection for single tones. It has been suggested that a forward transversal DP wave induced by a (retrograde) compression wave could be involved in DP wave generation. This topic is critically evaluated.

Inverted direction of wave propagation (IDWP) in the cochlea

The "classical" view on wave propagation is that propagating waves are possible in both directions along the length of the basilar membrane and that they have identical properties. Results of several recently executed experiments [T. Ren, Nat. Neurosci. 2, 333-334 (2004) and W. X. He, A. L. Nuttall, and T. Ren, Hear. Res., 228, 112-122 (2007)] appear to contradict this view. In the current work measurements were made of the velocity of the guinea-pig basilar membrane (BM). Distortion products (DPs) were produced by presenting two primary tones, with frequencies below the characteristic frequency f(0) of the BM location at which the BM measurements were made, with a constant frequency ratio. In each experiment the phase of the principal DP, with frequency 2f(1)-f(2), was recorded as a function of the DP frequency. The results indicate that the DP wave going from the two-tone interaction region toward the stapes is not everywhere traveling in the reverse direction, but also in the forward direction. The extent of the region in which the forward wave occurs appears larger than is accounted for by classical theory. This property has been termed "inverted direction of wave propagation." The results of this study confirm the wave propagation findings of other authors. The experimental data are compared to theoretical predictions for a classical three-dimensional model of the cochlea that is based on noise-response data of the same animal. Possible physical mechanisms underlying the findings are discussed.

Laser amplification with a twist: traveling-wave propagation and gain functions from throughout the cochlea

Except at the handful of sites explored by the inverse method, the characteristics-indeed, the very existence-of traveling-wave amplification in the mammalian cochlea remain largely unknown. Uncertainties are especially pronounced in the apex, where mechanical and electrical measurements lack the independent controls necessary for assessing damage to the preparation. At a functional level, the form and amplification of cochlear traveling waves are described by quantities known as propagation and gain functions. A method for deriving propagation and gain functions from basilar-membrane mechanical transfer functions is presented and validated by response reconstruction. Empirical propagation and gain functions from locations throughout the cochlea are obtained in mechanically undamaged preparations by applying the method to published estimates of near-threshold basilar membrane responses derived from Wiener-kernel (chinchilla) and zwuis analysis (cat) of auditory-nerve responses to broadband stimuli. The properties of these functions, and their variation along the length of the cochlea, are described. In both species, and at all locations examined, the gain functions reveal a region of positive power gain basal to the wave peak. The results establish the existence of traveling-wave amplification throughout the cochlea, including the apex. The derived propagation and gain functions resemble those characteristic of an active optical medium but rotated by 90 degrees in the complex plane. Rotation of the propagation and gain functions enables the mammalian cochlea to operate as a wideband, hydromechanical laser analyzer.

The role of organ of Corti mass in passive cochlear tuning

The mechanism for passive cochlear tuning remains unsettled. Early models considered the organ of Corti complex (OCC) as a succession of spring-mass resonators. Later, traveling wave models showed that passive tuning could arise through the interaction of cochlear fluid mass and OCC stiffness without local resonators. However, including enough OCC mass to produce local resonance enhanced the tuning by slowing and thereby growing the traveling wave as it approached its resonant segment. To decide whether the OCC mass plays a role in tuning, the frequency variation of the wavenumber of the cochlear traveling wave was measured (in vivo, passive cochleae) and compared to theoretical predictions. The experimental wavenumber was found by taking the phase difference of basilar membrane motion between two longitudinally spaced locations and dividing by the distance between them. The theoretical wavenumber was a solution of the dispersion relation of a three-dimensional cochlear model with OCC mass and stiffness as the free parameters. The experimental data were only well fit by a model that included OCC mass. However, as the measurement position moved from a best-frequency place of 40 to 12 kHz, the role of mass was diminished. The notion of local resonance seems to only apply in the very high-frequency region of the cochlea.

Intracochlear pressure and derived quantities from a three-dimensional model

Intracochlear pressure is calculated from a physiologically based, three-dimensional gerbil cochlea model. Olson [J. Acoust. Soc. Am. 103, 3445-3463 (1998); 110, 349-367 (2001)] measured gerbil intracochlear pressure and provided approximations for the following derived quantities: (1) basilar membrane velocity, (2) pressure across the organ of Corti, and (3) partition impedance. The objective of this work is to compare the calculations and measurements for the pressure at points and the derived quantities. The model includes the three-dimensional viscous fluid and the pectinate zone of the elastic orthotropic basilar membrane with dimensional and material property variation along its length. The arrangement of outer hair cell forces within the organ of Corti cytoarchitecture is incorporated by adding the feed-forward approximation to the passive model as done previously. The intracochlear pressure consists of both the compressive fast wave and the slow traveling wave. A Wentzel-Kramers-Brillowin asymptotic and numerical method combined with Fourier series expansions is used to provide an efficient procedure that requires about 1 s to compute the response for a given frequency. Results show reasonably good agreement for the direct pressure and the derived quantities. This confirms the importance of the three-dimensional motion of the fluid for an accurate cochlear model.

Forward and reverse waves in nonclassical models of the cochlea

In "classical" models of the cochlea the mechanical properties of the cochlear partition (in which the basilar membrane plays a dominant role) depend only on the local longitudinal coordinate. Wave propagation in such models is the same for both propagation directions, towards the apex and towards the base. "Nonclassical" models contain mechanical properties that depend on variables at more than one location. In such models the properties of wave propagation may well be asymmetrical. This note presents an analysis of feed-forward and feed-backward models, with the emphasis on the properties of forward and reverse waves. In both of these classes of model, wave amplification for forward waves turns into wave attenuation for reverse waves. The slope of the phase pattern is nearly the same for the two types of waves, it is increased in feed-forward models and decreased in feed-backward models-with respect to a model without feedback.

A mechano-electro-acoustical model for the cochlea: response to acoustic stimuli

A linear, physiologically based, three-dimensional finite element model of the cochlea is developed. The model integrates the electrical, acoustic, and mechanical elements of the cochlea. In particular, the model includes interactions between structures in the organ of Corti (OoC), piezoelectric relations for outer hair cell (OHC) motility, hair bundle (HB) conductance that changes with HB deflection, current flow in the cross section and along the different scalae, and the feed-forward effect. The parameters in the model are based on guinea-pig data as far as possible. The model is vetted using a variety of experimental data on basilar membrane motion and data on voltages and currents in the OoC. Model predictions compare well, qualitatively and quantitatively, with experimental data on basilar membrane frequency response, impulse response, frequency glides, and scala tympani voltage. The close match of the model predictions with experimental data demonstrates the validity of the model for simulating cochlear response to acoustic input and for testing hypotheses of cochlear function. Analysis of the model and its results indicates that OHC somatic motility is capable of powering active amplification in the cochlea. At the same time, the model supports a possible synergistic role for HB motility in cochlear amplification.

Evidence for outer hair cell driven oscillatory fluid flow in the tunnel of corti

Outer hair cell (OHC) somatic motility plays a key role in mammalian cochlear frequency selectivity and hearing sensitivity, but the mechanism of cochlear amplification is not well understood and remains a matter of controversy. We have visualized and quantified the effects of electrically evoked OHC somatic motility within the gerbil organ of Corti using an excised cochlear preparation. We found that OHC motility induces oscillatory motion of the medial olivocochlear fibers where they cross the tunnel of Corti (ToC) in their course to innervate the OHCs. We show that this motion is present at physiologically relevant frequencies and remains at locations distal to the OHC excitation point. We interpret this fiber motion to be the result of oscillatory fluid flow in the ToC. We show, using a simple one-dimensional hydromechanical model of the ToC, that a fluid wave within the tunnel can travel without significant attenuation for distances larger than the wavelength of the cochlear traveling wave at its peak. This ToC fluid wave could interact with the cochlear traveling wave to amplify the motion of the basilar membrane. The ToC wave could also provide longitudinal coupling between adjacent sections of the basilar membrane, and such coupling may be critical for cochlear amplification.

Imaging electrically evoked micromechanical motion within the organ of corti of the excised gerbil cochlea

The outer hair cell (OHC) of the mammalian inner ear exhibits an unusual form of somatic motility that can follow membrane-potential changes at acoustic frequencies. The cellular forces that produce this motility are believed to amplify the motion of the cochlear partition, thereby playing a key role in increasing hearing sensitivity. To better understand the role of OHC somatic motility in cochlear micromechanics, we developed an excised cochlea preparation to visualize simultaneously the electrically-evoked motion of hundreds of cells within the organ of Corti (OC). The motion was captured using stroboscopic video microscopy and quantified using cross-correlation techniques. The OC motion at approximately 2-6 octaves below the characteristic frequency of the region was complex: OHC, Deiter's cell, and Hensen's cell motion were hundreds of times larger than the tectorial membrane, reticular lamina (RL), and pillar cell motion; the inner rows of OHCs moved antiphasic to the outer row; OHCs pivoted about the RL; and Hensen's cells followed the motion of the outer row of OHCs. Our results suggest that the effective stimulus to the inner hair cell hair bundles results not from a simple OC lever action, as assumed by classical models, but by a complex internal motion coupled to the RL.

Fast cochlear amplification with slow outer hair cells

In mammalian cochleas, outer hair cells (OHCs) produce mechanical amplification over the entire audio-frequency range (up to 100 kHz). Under the 'somatic electro-motility' theory, mechano-electrical transduction modulates the OHC transmembrane potential, driving an OHC mechanical response which generates cycle-by-cycle mechanical amplification. Yet, though the OHC motor responds up to at least 70 kHz, the OHC membrane RC time constant (in vitro upper limit approximately 1000 Hz) reduces the potential driving the motor at high frequencies. Thus, the mechanism for high-frequency amplification with slow OHCs has been a two-decade-long mystery. Previous models fit to experimental data incorporated slow OHCs but did not explain how the OHC time constant limitation is overcome. Our key contribution is showing that negative feedback due to organ-of-Corti functional anatomy with adequate OHC gain significantly extends closed-loop system bandwidth and increases resonant gain. The OHC gain-bandwidth product, not just bandwidth, determines if high-frequency amplification is possible. Due to the cochlea's collective traveling-wave architecture, a single OHC's gain need not be great. OHC piezoelectricity increases the effectiveness of negative-feedback but is not essential for amplification. Thus, emergent closed-loop network dynamics differ significantly from open-loop component dynamics, a generally important principle in complex biological systems.