The effect of tectorial membrane and basilar membrane longitudinal coupling in cochlear mechanics

Evaluating the Correlation Between Stimulus Frequency Otoacoustic Emission Group Delays and Tuning Sharpness in a Cochlear Model

PURPOSE

A theoretical framework based on coherent reflection and filter theory predicts that the phase-gradient delays of stimulus frequency otoacoustic emissions (SFOAEs) are correlated with tuning sharpness in the mammalian cochlea. In this paper, we use a computational model of the cochlea to test this theory and to evaluate how SFOAE phase-gradient delays may be used to estimate the sharpness of cochlear tuning.

METHODS

This study is based on a physiologically motivated model which has been previously shown to predict key aspects of cochlear micromechanics. Cochlear roughness is introduced to model the reflection mechanism which underlies SFOAE generation. We then examine how varying the values of key model parameters or of the sound pressure level of the stimulus affects the relation between cochlear tuning and SFOAE delays. Finally, we quantify the ability of model simulations of SFOAE phase-gradient delays to provide reliable estimates of the tuning sharpness of the model.

RESULTS

We find that variations of model parameters that cause significant broadening of basilar membrane (BM) tuning typically give rise to a sizeable reduction in SFOAE phase-gradient delays. However, some changes in model parameters may cause a significant broadening of BM tuning with only a moderate decrease in SFOAE delays. SFOAE delays can be used to estimate the tuning sharpness of the model with reasonable accuracy only in cases where broadening of cochlear tuning is associated with a significant reduction in SFOAE delays.

CONCLUSION

The numerical results provide key insights about the correlations between cochlear tuning and SFOAE delays.

3D Computational Modeling of Blast Wave Transmission in Human Ear From External Ear to Cochlear Hair Cells: A Preliminary Study

INTRODUCTION

Auditory disabilities like tinnitus and hearing loss caused by exposure to blast overpressures are prevalent among military service members and veterans. The high-pressure fluctuations of blast waves induce hearing loss by injuring the tympanic membrane, ossicular chain, or sensory hair cells in the cochlea. The basilar membrane (BM) and organ of Corti (OC) behavior inside the cochlea during blast remain understudied. A computational finite element (FE) model of the full human ear was used by Bradshaw et al. (2023) to predict the motion of middle and inner ear tissues during blast exposure using a 3-chambered cochlea with Reissner's membrane and the BM. The inclusion of the OC in a blast transmission model would improve the model's anatomy and provide valuable insight into the inner ear response to blast exposure.

MATERIALS AND METHODS

This study developed a microscale FE model of the OC, including the OC sensory hair cells, membranes, and structural cells, connected to a macroscale model of the ear to form a comprehensive multiscale model of the human peripheral auditory system. There are 5 rows of hair cells in the model, each row containing 3 outer hair cells (OHCs) and the corresponding Deiters' cells and stereociliary hair bundles. BM displacement 16.75 mm from the base induced by a 31 kPa blast overpressure waveform was derived from the macroscale human ear model reported by Bradshaw et al. (2023) and applied as input to the center of the BM in the OC. The simulation was run for 2 ms as a structural analysis in ANSYS Mechanical.

RESULTS

The FE model results reported the displacement and principal strain of the OHCs, reticular lamina, and stereociliary hair bundles during blast transmission. The movement of the BM caused the rest of the OC to deform significantly. The reticular lamina displacement and strain amplitudes were highest where it connected to the OHCs, indicating that injury to this part of the OC may be likely due to blast exposure.

CONCLUSIONS

This microscale model is the first FE model of the OC to be connected to a macroscale model of the ear, forming a full multiscale ear model, and used to predict the OC's behavior under blast. Future work with this model will incorporate cochlear endolymphatic fluid, increase the number of OHC rows to 19 in total, and use the results of the model to reliably predict the sensorineural hearing loss resulting from blast exposure.

Advective mass transport along the cochlear coil

Mammalian auditory epithelium (the organ of Corti) stands out among different inner-ear epithelia in that it has large extracellular fluid spaces such as the tunnel of Corti, Nuel's space, outer tunnel, and spacing between outer hair cells. We tested the hypothesis that advective flow facilitates mass transport in the cochlear fluids, using computational simulations of cochlear fluid dynamics and ex vivo experiments to investigate mass transport in extracellular fluid spaces of the cochlea. Three model simulations were performed in series-cochlear mechanics, nonlinear fluid dynamics, and mass transport. In nonlinear fluid dynamics, we incorporated convection terms for more accurate computation of drift flow. For mass transport, both diffusion and advection were considered. For experiments, we measured vibrations of excised cochlear turns using optical coherence tomography. The excised OoC was subjected to acoustic and electrical stimulations.

Visualizing Collagen Fibrils in the Cochlea's Tectorial and Basilar Membranes Using a Fluorescently Labeled Collagen-Binding Protein Fragment

PURPOSE

A probe that binds to unfixed collagen fibrils was used to image the shapes and fibrous properties of the TM and BM. The probe (CNA35) is derived from the bacterial adhesion protein CNA. We present confocal images of hydrated gerbil TM, BM, and other cochlear structures stained with fluorescently labeled CNA35. A primary purpose of this article is to describe the use of the CNA35 collagen probe in the cochlea.

METHODS

Recombinant poly-histidine-tagged CNA35 was expressed in Escherichia coli, purified by cobalt-affinity chromatography, fluorescence labeled, and further purified by gel filtration chromatography. Cochleae from freshly harvested gerbil bullae were irrigated with and then incubated in CNA35 for periods ranging from 2 h - overnight. The cochleae were fixed, decalcified, and dissected. Isolated cochlear turns were imaged by confocal microscopy.

RESULTS

The CNA35 probe stained the BM and TM, and volumetric imaging revealed the shape of these structures and the collagen fibrils within them. The limbal zone of the TM stained intensely. In samples from the cochlear base, intense staining was detected on the side of the TM that faces hair cells. In the BM pectinate zone, staining was intense at the upper and lower boundaries. The BM arcuate zone was characterized by a prominent longitudinal collagenous structure. The spiral ligament, limbus and lamina stained for collagen, and within the spiral limbus the habenula perforata were outlined with intense staining.

CONCLUSION

The CNA35 probe provides a unique and useful view of collagenous structures in the cochlea.

Broad nonlinearity in reticular lamina vibrations requires compliant organ of Corti structures

In the mammalian cochlea, each longitudinal position of the basilar membrane (BM) has a nonlinear vibratory response in a limited frequency range around the location-dependent frequency of maximum response, known as the best frequency (BF). This nonlinear response arises from the electromechanical feedback from outer hair cells (OHCs). However, recent in vivo measurements have demonstrated that the mechanical response of other organ of Corti (OoC) structures, such as the reticular lamina (RL), and the electrical response of OHCs (measured in the local cochlear microphonic [LCM]) are nonlinear even at frequencies significantly below BF. In this work, a physiologically motivated model of the gerbil cochlea is used to demonstrate that the source of this discrepancy between the frequency range of the BM, RL, and LCM nonlinearities is greater compliance in the structures at the top of the OHCs. The predicted responses of the BM, RL, and LCM to pure tone and two-tone stimuli are shown to be in line with experimental evidence. Simulations then demonstrate that the sub-BF nonlinearity in the RL requires the structures at the top of the OHCs to be significantly more compliant than the BM. This same condition is also necessary for "optimal" gain near BF, i.e., high amplification that is in line with the experiment. This demonstrates that the conditions for OHCs to operate optimally at BF inevitably yield nonlinearity of the RL response over a broad frequency range.

Behavioral characteristics in sensing mechanism of the Corti

Some experiments can't be realized because the cochlea's Corti is the most delicate and complex sensory organ. In this paper, some typical and special behavioral characteristics in the process of sensation were found in medical clinic. Based on the interdisciplinary principles of medicine, physics and biology, a real numerical simulation model of Corti is established. On the basis of verifying the correctness of the model, the mechanism corresponding to these typical and special behavior characteristics in the process of sensation is explored through simulation calculation and analysis. This study provides theoretical and applied basis for people to better understand the sound sensing mechanism, and provides a numerical simulation platform for further analyzing Corti's sensing mechanism and good clinical application.

Deiters Cells Act as Mechanical Equalizers for Outer Hair Cells

The outer hair cells in the mammalian cochlea are cellular actuators essential for sensitive hearing. The geometry and stiffness of the structural scaffold surrounding the outer hair cells will determine how the active cells shape mammalian hearing by modulating the organ of Corti (OoC) vibrations. Specifically, the tectorial membrane and the Deiters cell are mechanically in series with the hair bundle and soma, respectively, of the outer hair cell. Their mechanical properties and anatomic arrangement must determine the relative motion among different OoC structures. We measured the OoC mechanics in the cochleas acutely excised from young gerbils of both sexes at a resolution fine enough to distinguish the displacement of individual cells. A three-dimensional finite element model of fully deformable OoC was exploited to analyze the measured data in detail. As a means to verify the computer model, the basilar membrane deformations because of static and dynamic stimulations were measured and simulated. Two stiffness ratios have been identified that are critical to understand cochlear physics, which are the stiffness of the tectorial membrane with respect to the hair bundle and the stiffness of the Deiters cell with respect to the outer hair cell body. Our measurements suggest that the Deiters cells act like a mechanical equalizer so that the outer hair cells are constrained neither too rigidly nor too weakly.SIGNIFICANCE STATEMENT Mammals can detect faint sounds thanks to the action of mammalian-specific receptor cells called the outer hair cells. It is getting clearer that understanding the interactions between the outer hair cells and their surrounding structures such as the tectorial membrane and the Deiters cell is critical to resolve standing debates. Depending on theories, the stiffness of those two structures ranges from negligible to rigid. Because of their perceived importance, their properties have been measured in previous studies. However, nearly all existing data were obtained ex situ (after they were detached from the outer hair cells), which obscures their interaction with the outer hair cells. We quantified the mechanical properties of the tectorial membrane and the Deiters cell in situ.

A Gap-Junction Mutation Reveals That Outer Hair Cell Extracellular Receptor Potentials Drive High-Frequency Cochlear Amplification

Cochlear amplification enables the enormous dynamic range of hearing through amplifying cochlear responses to low- to moderate-level sounds and compressing them to loud sounds. Amplification is attributed to voltage-dependent electromotility of mechanosensory outer hair cells (OHCs) driven by changing voltages developed across their cell membranes. At low frequencies, these voltage changes are dominated by intracellular receptor potentials (RPs). However, OHC membranes have electrical low-pass filter properties that attenuate high-frequency RPs, which should potentially attenuate amplification of high-frequency cochlear responses and impede high-frequency hearing. We made in vivo intracellular and extracellular electrophysiological measurements from the organ of Corti of male and female mice of the CBA/J strain, with excellent high-frequency hearing, and from the CD-1 mouse strain, which has sensitive hearing below 12 kHz but loses high-frequency hearing within a few weeks postpartum. The CD-1 mouse strain was transfected with an A88V mutation of the connexin 30 gap-junction protein. By blocking the action of the GJ protein to reduce input resistance, the mutation increased the OHC extracellular RP (ERP) magnitude and rescued high-frequency hearing. However, by increasing the organ of Corti resistance, the mutation rescued high-frequency hearing through preserving the OHC extracellular RP (ERP) magnitude. We measured the voltage developed across the basolateral membranes of OHCs, which controls their electromotility, for low- to high-frequency sounds in male and female mice of the CD-1 strain that expressed the A88V mutation. We demonstrate that ERPs, not RPs, drive OHC motility and cochlear amplification at high frequencies because at high frequencies, ERPs are not frequency attenuated, exceed RPs in magnitude, and are appropriately timed to provide cochlear amplification.SIGNIFICANCE STATEMENT Cochlear amplification, which enables the enormous dynamic range of hearing, is attributed to voltage-dependent electromotility of the mechanosensory outer hair cells (OHCs) driven by sound-induced voltage changes across their membranes. OHC intracellular receptor potentials are electrically low-pass filtered, which should hinder high-frequency hearing. We measured the intracellular and extracellular voltages that control OHC electromotility in vivo in a mouse strain with impaired high-frequency hearing. A gap-junction mutation of the strain rescued high-frequency hearing, increased organ of Corti resistance, and preserved large OHC extracellular receptor potentials but reduced OHC intracellular receptor potentials and impaired low-frequency hearing. We concluded intracellular potentials drive OHC motility at low frequencies and extracellular receptor potentials drive OHC motility and cochlear amplification at high frequencies.

Overturning the mechanisms of cochlear amplification via area deformations of the organ of Corti

The mammalian ear embeds a cellular amplifier that boosts sound-induced hydromechanical waves as they propagate along the cochlea. The operation of this amplifier is not fully understood and is difficult to disentangle experimentally. In the prevailing view, cochlear waves are amplified by the piezo-electric action of the outer hair cells (OHCs), whose cycle-by-cycle elongations and contractions inject power into the local motion of the basilar membrane (BM). Concomitant deformations of the opposing (or "top") side of the organ of Corti are assumed to play a minor role and are generally neglected. However, analysis of intracochlear motions obtained using optical coherence tomography calls this prevailing view into question. In particular, the analysis suggests that (i) the net local power transfer from the OHCs to the BM is either negative or highly inefficient; and (ii) vibration of the top side of the organ of Corti plays a primary role in traveling-wave amplification. A phenomenological model derived from these observations manifests realistic cochlear responses and suggests that amplification arises almost entirely from OHC-induced deformations of the top side of the organ of Corti. In effect, the model turns classic assumptions about spatial impedance relations and power-flow direction within the sensory epithelium upside down.

Link between stimulus otoacoustic emissions fine structure peaks and standing wave resonances in a cochlear model

In response to an external stimulus, the cochlea emits sounds, called stimulus frequency otoacoustic emissions (SFOAEs), at the stimulus frequency. In this article, a three-dimensional computational model of the gerbil cochlea is used to simulate SFOAEs and clarify their generation mechanisms and characteristics. This model includes electromechanical feedback from outer hair cells (OHCs) and cochlear roughness due to spatially random inhomogeneities in the OHC properties. As in the experiments, SFOAE simulations are characterized by a quasiperiodic fine structure and a fast varying phase. Increasing the sound pressure level broadens the peaks and decreases the phase-gradient delay of SFOAEs. A state-space formulation of the model provides a theoretical framework to analyze the link between the fine structure and global modes of the cochlea, which arise as a result of standing wave resonances. The SFOAE fine structure peaks correspond to weakly damped resonant modes because they are observed at the frequencies of nearly unstable modes of the model. Variations of the model parameters that affect the reflection mechanism show that the magnitude and sharpness of the tuning of these peaks are correlated with the modal damping ratio of the nearly unstable modes. The analysis of the model predictions demonstrates that SFOAEs originate from the peak of the traveling wave.

Inner hair cell stereocilia displacement in response to focal stimulation of the basilar membrane in the ex vivo gerbil cochlea

The inner hair cells in the mammalian cochlea transduce mechanical signals to electrical signals that provide input to the auditory nerve. The spatial-temporal displacement of the inner hair cell stereocilia (IHCsc) relative to basilar membrane (BM) displacement is central to characterizing the transduction process. This study specifically focuses on measuring displacement of the stereocilia hair bundles in the radial dimensions where they are most sensitive. To simplify the mechanical response of the cochlear partition, a mechanical probe was used to drive the BM. Optical imaging was used to measure radial displacement of the inner hair cell stereocilia local to the probe in ex vivo gerbil cochleae. The mechanical probe displaced the BM in the transverse direction using sinusoidal stimuli with frequencies ranging from 10 Hz to 42.5 kHz. IHCsc displacement measurements were made in the radial dimension as a function of their longitudinal location along the length of the BM. The results were used to quantify the frequency response, longitudinal space coupling, traveling wave velocity, and wavelength of the radial displacement of the stereocilia. The measurements were centered at two best frequency locations along the BM: Proximal to the round window (first turn), and in the second turn. At both locations, frequency tuning was seen that was consistent with published place maps. At both locations, traveling waves were observed simultaneously propagating basal and apical from the probe. The velocity of the traveling waves at the center frequency (CF) of the location was higher in the first turn than in the second. As the stimulus frequency increased and approached CF for a location, the traveling wavelength decreased. Differential motion of the BM and IHCsc was observed in the second turn as the stimulus frequency increased toward CF. The longitudinal coupling measured in this study was longer than observed in previous studies. In summary the results suggest that the shape of the wave patterns present on the BM are not sufficient to characterize the displacement of the IHCsc.

Age-related degradation of tectorial membrane dynamics with loss of CEACAM16

Studies of genetic disorders of sensorineural hearing loss have been instrumental in delineating mechanisms that underlie the remarkable sensitivity and selectivity that are hallmarks of mammalian hearing. For example, genetic modifications of TECTA and TECTB, which are principal proteins that comprise the tectorial membrane (TM), have been shown to alter auditory thresholds and frequency tuning in ways that can be understood in terms of changes in the mechanical properties of the TM. Here, we investigate effects of genetic modification targeting CEACAM16, a third important TM protein. Loss of CEACAM16 has been recently shown to lead to progressive reductions in sensitivity. Whereas age-related hearing losses have previously been linked to changes in sensory receptor cells, the role of the TM in progressive hearing loss is largely unknown. Here, we show that TM stiffness and viscosity are significantly reduced in adult mice that lack functional CEACAM16 relative to age-matched wild-type controls. By contrast, these same mechanical properties of TMs from juvenile mice that lack functional CEACAM16 are more similar to those of wild-type mice. Thus, changes in hearing phenotype align with changes in TM material properties and can be understood in terms of the same TM wave properties that were previously used to characterize modifications of TECTA and TECTB. These results demonstrate that CEACAM16 is essential for maintaining TM mechanical and wave properties, which in turn are necessary for sustaining the remarkable sensitivity and selectivity of mammalian hearing with increasing age.

Time-domain analysis of a three-dimensional numerical model of the human spiral cochlea at medium intensity

For the processing and detection of speech and music, the human cochlea has an exquisite sensitivity and selectivity of frequency and a dynamic range. How the cochlea performs these remarkable functions has fascinated auditory scientists for decades. Because it is not possible to measure sound-induced vibrations within the cochlea in a living human being, mathematical modeling has played an important role in cochlear mechanics. For this study, a three-dimensional human cochlear model with a fluid‒structure coupling was constructed. Time-domain analysis was performed to calculate the displacement, velocity, and stress of the basilar membrane (BM) and osseous spiral lamina (OSL) at different times in response to a pure tone stimulus. The model reproduced the traveling-wave motion of the BM. The model also showed that the cochlea's spiral shape can induce asymmetrical mechanical behavior of the BM and cause cochlear fluid to move in a radial direction; this may contribute to human sound perception. The cochlea's spiral shape not only enhances a low-frequency vibration of the BM but also changes the maximization of the positions of vibration. Therefore, the spiral's characteristics play a key role in the cochlea's frequency selectivity for low-frequency sounds. And this suggests that the OSL can react to sound as quickly as the BM. Furthermore, the basal region of the BM tends to have more stress than its other regions, and this may explain the clinical observation that human sensorineural hearing loss often occurs at high frequencies.

Intracochlear distortion products are broadly generated by outer hair cells but their contributions to otoacoustic emissions are spatially restricted

Detection of low-level sounds by the mammalian cochlea requires electromechanical feedback from outer hair cells (OHCs). This feedback arises due to the electromotile response of OHCs, which is driven by the modulation of their receptor potential caused by the stimulation of mechano-sensitive ion channels. Nonlinearity in these channels distorts impinging sounds, creating distortion-products that are detectable in the ear canal as distortion-product otoacoustic emissions (DPOAEs). Ongoing efforts aim to develop DPOAEs, which reflects the ear's health, into diagnostic tools for sensory hearing loss. These efforts are hampered by limited knowledge on the cochlear extent contributing to DPOAEs. Here, we report on intracochlear distortion products (IDPs) in OHC electrical responses and intracochlear fluid pressures. Experiments and simulations with a physiologically motivated cochlear model show that widely generated electrical IDPs lead to mechanical vibrations in a frequency-dependent manner. The local cochlear impedance restricts the region from which IDPs contribute to DPOAEs at low to moderate intensity, which suggests that DPOAEs may be used clinically to provide location-specific information about cochlear damage.

A role for tectorial membrane mechanics in activating the cochlear amplifier

The mechanical and electrical responses of the mammalian cochlea to acoustic stimuli are nonlinear and highly tuned in frequency. This is due to the electromechanical properties of cochlear outer hair cells (OHCs). At each location along the cochlear spiral, the OHCs mediate an active process in which the sensory tissue motion is enhanced at frequencies close to the most sensitive frequency (called the characteristic frequency, CF). Previous experimental results showed an approximate 0.3 cycle phase shift in the OHC-generated extracellular voltage relative the basilar membrane displacement, which was initiated at a frequency approximately one-half octave lower than the CF. Findings in the present paper reinforce that result. This shift is significant because it brings the phase of the OHC-derived electromotile force near to that of the basilar membrane velocity at frequencies above the shift, thereby enabling the transfer of electrical to mechanical power at the basilar membrane. In order to seek a candidate physical mechanism for this phenomenon, we used a comprehensive electromechanical mathematical model of the cochlear response to sound. The model predicts the phase shift in the extracellular voltage referenced to the basilar membrane at a frequency approximately one-half octave below CF, in accordance with the experimental data. In the model, this feature arises from a minimum in the radial impedance of the tectorial membrane and its limbal attachment. These experimental and theoretical results are consistent with the hypothesis that a tectorial membrane resonance introduces the correct phasing between mechanical and electrical responses for power generation, effectively turning on the cochlear amplifier.

Significance of the Microfluidic Flow Inside the Organ of Corti

We study the vibration modes of a short section in the middle turn of the gerbil cochlea including both longitudinal and radial interstitial fluid spaces between the pillar cells (PC) and the sensory hair cells to determine the role of the interstitial fluid flow within the organ of corti (OoC). Three detailed finite element (FE) models of the cochlear short section (CSS) are studied. In model 1, the CSS is without fluids; model 2 includes the OoC fluid, but not the exterior scalae fluids; and model 3 is the CSS with both scalae and OoC fluids. We find that: (1) the fundamental mode shape of models 1 or 3 is similar to the classical basilar membrane (BM) bending mode that includes pivoting of the arch of corti, and hence determines the low frequency vibrational mode shape of the cochlea in the presence of the cochlear wave. (2) The fundamental mode shape of model 2 is characterized by a cross-sectional shape change similar to the passive response of the cochlea. This mode shape includes a tilting motion of the inner hair cell (IHC) region, a fluid motion within the tunnel of corti (ToC) in the radial direction and along the OoC, and a bulging motion of the reticular lamina (RL) above the outer hair cell (OHC). Each of these motions provides a plausible mode of excitation of the sensory hair cells. (3) The higher vibrational modes of model 1 are similar to the electrically evoked response within the OoC and suggests that the higher vibrational modes are responsible for the active response of the cochlea. We also observed that the fluid flow through the OoC interstitial space is significant, and the model comparison suggests that the OoC fluid contributes to the biphasic BM motion seen in electrical stimulation experiments. The effect of fluid viscosity on cilium deflection was assessed by performing a transient analysis to calculate the cilium shearing gain. The gain values are found to be within the range of experimentally measured values reported by Dallos et al. (1996, The Cochlea, Springer-Verlag, New York).

Emilin 2 promotes the mechanical gradient of the cochlear basilar membrane and resolution of frequencies in sound

The detection of different frequencies in sound is accomplished with remarkable precision by the basilar membrane (BM), an elastic, ribbon-like structure with graded stiffness along the cochlear spiral. Sound stimulates a wave of displacement along the BM with maximal magnitude at precise, frequency-specific locations to excite neural signals that carry frequency information to the brain. Perceptual frequency discrimination requires fine resolution of this frequency map, but little is known of the intrinsic molecular features that demarcate the place of response on the BM. To investigate the role of BM microarchitecture in frequency discrimination, we deleted extracellular matrix protein emilin 2, which disturbed the filamentous organization in the BM. Emilin2 ^-/- mice displayed broadened mechanical and neural frequency tuning with multiple response peaks that are shifted to lower frequencies than normal. Thus, emilin 2 confers a stiffness gradient on the BM that is critical for accurate frequency resolution.

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.

The Tectorial Membrane: Mechanical Properties and Functions

The tectorial membrane (TM) is widely believed to play a critical role in determining the remarkable sensitivity and frequency selectivity that are hallmarks of mammalian hearing. Recently developed mouse models of human hearing disorders have provided new insights into the molecular, nanomechanical mechanisms that underlie resonance and traveling wave properties of the TM. Herein we review recent experimental and theoretical results detailing TM morphology, local poroelastic and electromechanical interactions, and global spread of excitation via TM traveling waves, with direct implications for cochlear mechanisms.

Constraints imposed by zero-crossing invariance on cochlear models with two mechanical degrees of freedom

The zero crossings of basilar-membrane (BM) responses to clicks are nearly independent of stimulus intensity. This work explores the constraints that this invariance imposes on one-dimensional nonlinear cochlear models with two degrees of freedom (2DoF). The locations of the poles and zeros of the BM admittance, calculated for a set of linear models in which the strength of the active force is progressively decreased, provides a playground for evaluating the behavior of a corresponding nonlinear model at increasing stimulus levels. Mathematical constraints on the model parameters are derived by requiring that the poles of the admittance move horizontally in the s-plane as the active force is varied. These constraints ensure approximate zero-crossing invariance over a wide stimulus level range in a nonlinear model in which the active force varies as a function of the local instantaneous BM displacement and velocity. Two different 2DoF models are explored, each capable of reproducing the main qualitative characteristics of the BM response to tones (i.e., the tall and broad activity pattern at low stimulus levels, the large gain dynamics, and the partial decoupling between gain and phase). In each model, the motions of the two masses are compared with response data from animal experiments.

Cochlear partition anatomy and motion in humans differ from the classic view of mammals

Mammals detect sound through mechanosensitive cells of the cochlear organ of Corti that rest on the basilar membrane (BM). Motions of the BM and organ of Corti have been studied at the cochlear base in various laboratory animals, and the assumption has been that the cochleas of all mammals work similarly. In the classic view, the BM attaches to a stationary osseous spiral lamina (OSL), the tectorial membrane (TM) attaches to the limbus above the stationary OSL, and the BM is the major moving element, with a peak displacement near its center. Here, we measured the motion and studied the anatomy of the human cochlear partition (CP) at the cochlear base of fresh human cadaveric specimens. Unlike the classic view, we identified a soft-tissue structure between the BM and OSL in humans, which we name the CP "bridge." We measured CP transverse motion in humans and found that the OSL moved like a plate hinged near the modiolus, with motion increasing from the modiolus to the bridge. The bridge moved almost as much as the BM, with the maximum CP motion near the bridge-BM connection. BM motion accounts for 100% of CP volume displacement in the classic view, but accounts for only 27 to 43% in the base of humans. In humans, the TM-limbus attachment is above the moving bridge, not above a fixed structure. These results challenge long-held assumptions about cochlear mechanics in humans. In addition, animal apical anatomy (in SI Appendix) doesn't always fit the classic view.

Unified cochlear model for low- and high-frequency mammalian hearing

The spatial variations of the intricate cytoarchitecture, fluid scalae, and mechano-electric transduction in the mammalian cochlea have long been postulated to provide the organ with the ability to perform a real-time, time-frequency processing of sound. However, the precise manner by which this tripartite coupling enables the exquisite cochlear filtering has yet to be articulated in a base-to-apex mathematical model. Moreover, while sound-evoked tuning curves derived from mechanical gains are excellent surrogates for auditory nerve fiber thresholds at the base of the cochlea, this correlation fails at the apex. The key factors influencing the divergence of both mechanical and neural tuning at the apex, as well as the spatial variation of mechanical tuning, are incompletely understood. We develop a model that shows that the mechanical effects arising from the combination of the taper of the cochlear scalae and the spatial variation of the cytoarchitecture of the cochlea provide robust mechanisms that modulate the outer hair cell-mediated active response and provide the basis for the transition of the mechanical gain spectra along the cochlear spiral. Further, the model predicts that the neural tuning at the base is primarily governed by the mechanical filtering of the cochlear partition. At the apex, microscale fluid dynamics and nanoscale channel dynamics must also be invoked to describe the threshold neural tuning for low frequencies. Overall, the model delineates a physiological basis for the difference between basal and apical gain seen in experiments and provides a coherent description of high- and low-frequency cochlear tuning.

Reducing tectorial membrane viscoelasticity enhances spontaneous otoacoustic emissions and compromises the detection of low level sound

The mammalian cochlea is able to detect faint sounds due to the presence of an active nonlinear feedback mechanism that boosts cochlear vibrations of low amplitude. Because of this feedback, self-sustained oscillations called spontaneous otoacoustic emissions (SOAEs) can often be measured in the ear canal. Recent experiments in genetically modified mice have demonstrated that mutations of the genes expressed in the tectorial membrane (TM), an extracellular matrix located in the cochlea, can significantly enhance the generation of SOAEs. Multiple untested mechanisms have been proposed to explain these unexpected results. In this work, a physiologically motivated computational model of a mammalian species commonly studied in auditory research, the gerbil, is used to demonstrate that altering the viscoelastic properties of the TM tends to affect the linear stability of the cochlea, SOAE generation and the cochlear response to low amplitude stimuli. These results suggest that changes in TM properties might be the underlying cause for SOAE enhancement in some mutant mice. Furthermore, these theoretical findings imply that the TM contributes to keeping the mammalian cochlea near an oscillatory instability, which promotes high sensitivity and the detection of low level stimuli.

Revealing the morphology and function of the cochlea and middle ear with optical coherence tomography

Optical coherence tomography (OCT) has revolutionized physiological studies of the hearing organ, the vibration and morphology of which can now be measured without opening the surrounding bone. In this review, we provide an overview of OCT as used in the otological research, describing advances and different techniques in vibrometry, angiography, and structural imaging.

Forward and Reverse Waves: Modeling Distortion Products in the Intracochlear Fluid Pressure

Distortion product otoacoustic emissions are sounds that are emitted by the cochlea due to the nonlinearity of the outer hair cells. These emissions play an important role both in clinical settings and research laboratories. However, how distortion products propagate from their generation location to the middle ear remains unclear; whether distortion products propagate as a slow reverse traveling wave, or as a fast compression wave, through the cochlear fluid has been debated. In this article, we evaluate the contributions of the slow reverse wave and fast compression wave to the propagation of intracochlear distortion products using a physiologically based nonlinear model of the gerbil cochlea. This model includes a 3D two-duct model of the intracochlear fluid and a realistic model of outer hair cell biophysics. Simulations of the distortion products in the cochlear fluid pressure in response to a two-tone stimulus are compared with published in vivo experimental results. Whereas experiments have characterized distortion products at a limited number of locations, this model provides a complete description of the fluid pressure at all locations in the cochlear ducts. As in experiments, the spatial variations of the distortion products in the fluid pressure have some similarities with what is observed in response to a pure tone. Analysis of the fluid pressure demonstrates that although a fast wave component is generated, the slow wave component dominates the response. Decomposition of the model simulations into forward and reverse wave components shows that a slow forward propagating wave is generated due to the reflection of the slow reverse wave at the stapes. Wave interference between the reverse and forward components sometimes complicates the analysis of distortion products propagation using measurements at a few locations.

The Competition between the Noise and Shear Motion Sensitivity of Cochlear Inner Hair Cell Stereocilia

Acoustical excitation of the organ of Corti induces radial fluid flow in the subtectorial space (STS) that excites the hair bundles (HBs) of the sensory inner hair cell of the mammalian cochlea. The inner hair cell HBs are bathed in endolymphatic fluid filling a thin gap in the STS between the tectorial membrane and the reticular lamina. According to the fluctuation dissipation theorem, the fluid viscosity gives rise to mechanical fluctuations that are transduced into current noise. Conversely, the stochastic fluctuations of the mechanically gated channels of the HBs also induce dissipation. We develop an analytic model of the STS complex in a cross section of the gerbil organ of Corti. We predict that the dominant noise at the apex is due to the channel stochasticity whereas viscous effects dominate at the base. The net root mean square fluctuation of the HB motion is estimated to be at least 1.18 nm at the base and 2.72 nm at the apex. By varying the HB height for a fixed STS gap, we find that taller HBs are better sensors with lower thresholds. An integrated active HB model is shown to reduce the hydrodynamic resistance through a cycle-by-cycle power addition through adaptation, reducing the thresholds of hearing, hinting at one potential role for HB activity in mammalian hearing. We determine that a Couette flow approximation in the STS underestimates the dissipation and that modeling the entire STS complex is necessary to correctly predict the low-frequency dissipation in the cochlea. Finally, the difference in the noise budget at the base and the apex of the cochlea indicate that a sensing modality other than the shear motion of the TM that may be used to achieve low-noise acoustic sensing at the apex.

Nanoscale Poroelasticity of the Tectorial Membrane Determines Hair Bundle Deflections

Stereociliary imprints in the tectorial membrane (TM) have been taken as evidence that outer hair cells are sensitive to shearing displacements of the TM, which plays a key role in shaping cochlear sensitivity and frequency selectivity via resonance and traveling wave mechanisms. However, the TM is highly hydrated (97% water by weight), suggesting that the TM may be flexible even at the level of single hair cells. Here we show that nanoscale oscillatory displacements of microscale spherical probes in contact with the TM are resisted by frequency-dependent forces that are in phase with TM displacement at low and high frequencies, but are in phase with TM velocity at transition frequencies. The phase lead can be as much as a quarter of a cycle, thereby contributing to frequency selectivity and stability of cochlear amplification.

Anisotropic Material Properties of Wild-Type and Tectb-/- Tectorial Membranes

The tectorial membrane (TM) is an extracellular matrix that is directly coupled with the mechanoelectrical receptors responsible for sensory transduction and amplification. As such, the TM is often hypothesized to play a key role in the remarkable sensory abilities of the mammalian cochlea. Genetic studies targeting TM proteins have shown that changes in TM structure dramatically affect cochlear function in mice. Precise information about the mechanical properties of the TMs of wild-type and mutant mice at audio frequencies is required to elucidate the role of the TM and to understand how these genetic mutations affect cochlear mechanics. In this study, images of isolated TM segments are used to determine both the radial and longitudinal motions of the TM in response to a harmonic radial excitation. The resulting longitudinally propagating radial displacement and highly spatially dependent longitudinal displacement are modeled using finite-element models that take into account the anisotropy and finite dimensions of TMs. An automated, least-square fitting algorithm is used to find the anisotropic material properties of wild-type and Tectb^-/- mice at audio frequencies. Within the auditory frequency range, it is found that the TM is a highly viscoelastic and anisotropic structure with significantly higher stiffness in the direction of the collagen fibers. Although no decrease in the stiffness in the fiber direction is observed, the stiffness of the TM in shear and in the transverse direction is found to be significantly reduced in Tectb^-/- mice. As a result, TMs of the mutant mice tend to be significantly more anisotropic within the frequency range examined in this study. The effects of the Tectb^-/- mutation on the TM's anisotropic material properties may be responsible for the changes in cochlear tuning and sensitivity that have been previously reported for these mice.

An analytic physically motivated model of the mammalian cochlea

In this paper, an analytic model of the mammalian cochlea is developed. A mixed physical-phenomenological approach by utilizing existing work on the physics of classical box-representations of the cochlea and behavior of recent data-derived wavenumber estimates is used. Spatial variation is incorporated through a single independent variable that combines space and frequency. This paper arrives at closed-form expressions for the organ of Corti velocity, its impedance, the pressure difference across the organ of Corti, and its wavenumber. Model tests using real and imaginary parts of chinchilla data from multiple locations and for multiple variables are performed. The model also predicts impedances that are qualitatively consistent with current literature. For implementation, the model can leverage existing efforts for both filter bank or filter cascade models that target improved algorithmic or analog circuit efficiencies. The simplicity of the cochlear model, its small number of model constants, its ability to capture the variation of tuning, its closed-form expressions for physically-interrelated variables, and the form of these expressions that allows for easily determining one variable from another make the model appropriate for analytic and digital auditory filter implementations as discussed here, as well as for extracting macromechanical insights regarding how the cochlea works.

Cochlear impulse responses resolved into sets of gammatones: the case for beating of closely spaced local resonances

Gammatones have had a long history in auditory studies, and recent theoretical work suggests they may play an important role in cochlear mechanics as well. Following this lead, the present paper takes five examples of basilar membrane impulse responses and uses a curve-fitting algorithm to decompose them into a number of discrete gammatones. The limits of this ‘sum of gammatones’ (SOG) method to accurately represent the impulse response waveforms were tested and it was found that at least two and up to six gammatones could be isolated from each example. Their frequencies were stable and largely independent of stimulus parameters. The gammatones typically formed a regular series in which the frequency ratio between successive members was about 1.1. Adding together the first few gammatones in a set produced beating-like waveforms which mimicked waxing and waning, and the instantaneous frequencies of the waveforms were also well reproduced, providing an explanation for frequency glides. Consideration was also given to the impulse response of a pair of elastically coupled masses—the basis of two-degree-of-freedom models comprised of coupled basilar and tectorial membranes—and the resulting waveform was similar to a pair of beating gammatones, perhaps explaining why the SOG method seems to work well in describing cochlear impulse responses. A major limitation of the SOG method is that it cannot distinguish a waveform resulting from an actual physical resonance from one derived from overfitting, but taken together the method points to the presence of a series of closely spaced local resonances in the cochlea.

Molding the asymmetry of localized frequency-locking waves by a generalized forcing and implications to the inner ear

Frequency locking to an external forcing frequency is a well-known phenomenon. In the auditory system, it results in a localized traveling wave, the shape of which is essential for efficient discrimination between incoming frequencies. An amplitude equation approach is used to show that the shape of the localized traveling wave depends crucially on the relative strength of additive versus parametric forcing components; the stronger the parametric forcing, the more asymmetric is the response profile and the sharper is the traveling-wave front. The analysis qualitatively captures the empirically observed regions of linear and nonlinear responses and highlights the potential significance of parametric forcing mechanisms in shaping the resonant response in the inner ear.

Mammalian Auditory Hair Cell Bundle Stiffness Affects Frequency Tuning by Increasing Coupling along the Length of the Cochlea

The stereociliary bundles of cochlear hair cells convert mechanical vibrations into the electrical signals required for auditory sensation. While the stiffness of the bundles strongly influences mechanotransduction, its influence on the vibratory response of the cochlear partition is unclear. To assess this, we measured cochlear vibrations in mutant mice with reduced bundle stiffness or with a tectorial membrane (TM) that is detached from the sensory epithelium. We found that reducing bundle stiffness decreased the high-frequency extent and sharpened the tuning of vibratory responses obtained postmortem. Detaching the TM further reduced the high-frequency extent of the vibrations but also lowered the partition's resonant frequency. Together, these results demonstrate that the bundle's stiffness and attachment to the TM contribute to passive longitudinal coupling in the cochlea. We conclude that the stereociliary bundles and TM interact to facilitate passive-wave propagation to more apical locations, possibly enhancing active-wave amplification in vivo.

Investigation of the 2f1-f2 and 2f2-f1 distortion product otoacoustic emissions using a computational model of the gerbil ear

In this work, a three-dimensional computational model of the gerbil ear is used to investigate the generation of the 2f₁-f₂ and 2f₂-f₁ distortion product otoacoustic emissions (DPOAEs). In order to predict both the distortion and reflection sources, cochlear roughness is modeled by introducing random inhomogeneities in the outer hair cell properties. The model was used to simulate the generation of DPOAEs in response to a two-tone stimulus for various primary stimulus levels and frequency ratios. As in published experiments, the 2f₁-f₂ DPOAEs are mostly dominated by the distortion component while the 2f₂-f₁ DPOAEs are dominated by the reflection component; furthermore, the influence of the levels and frequency ratio of the primaries are consistent with measurements. Analysis of the intracochlear response shows that the distortion component has the highest magnitude at all longitudinal locations for the 2f₁-f₂ distortion product (DP) while the distortion component only dominates close to the DP best place in the case of the 2f₂-f₁ DP. Decomposition of the intracochlear DPs into forward and reverse waves demonstrates that the 2f₁-f₂ DP generates reverse waves for both the distortion and reflection components; however, a reverse wave is only generated for the reflection component in the case of the 2f₂-f₁ DP. As in experiments in the gerbil, the group delay of the reflection component of the DPOAE is between 1× and 2× the forward group delay, which is consistent with the propagation of DP towards the stapes as slow reverse waves.

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.

Hydrostatic measurement and finite element simulation of the compliance of the organ of Corti complex

In the mammalian cochlea, the geometrical and mechanical properties of the organ of Corti complex (OCC, consisting of the tectorial membrane, the organ of Corti, and the basilar membrane) have fundamental consequences for understanding the physics of hearing. Despite efforts to correlate the mechanical properties of the OCC with cochlear function, experimental data of OCC stiffness are limited due to difficulties in measurement. Modern measurements of the OCC stiffness use microprobes exclusively, but suffer ambiguity when defining the physiologically relevant stiffness due to the high nonlinearity in the force-displacement relationship. The nonlinearity stems from two sources. First, microprobes apply local force instead of fluid pressure across the OCC. Second, to obtain the functionally relevant stiffness, the OCC is deformed well beyond in vivo levels (>10 μm). The objective of this study was to develop an alternative technique to overcome challenges intrinsic to the microprobe method. Using a custom-designed microfluidic chamber system, hydrostatic pressures were applied to the excised gerbil cochlea. Deformations of the OCC due to hydrostatic pressures were analyzed through optical-axis image correlation. The pressure-displacement relationship was linear within nanoscale displacement ranges (<1 μm). To compare the results in this paper with existing measurements, a three-dimensional finite element model was used.

A model and analysis for the nonlinear amplification of waves in the cochlea

A nonlinear three-dimensional model for the amplification of a wave in the cochlea is analyzed. Using the long-slender geometry of the cochlea, and the relatively high frequencies in the hearing spectrum, an asymptotic approximation of the solution is derived for linear, but spatially inhomogeneous, amplification. From this, a nonlinear WKB approximation is constructed for the nonlinear problem, and this is used to derive an efficient numerical method for solving the amplification problem. The advantage of this approach is that the very short waves needed to resolve the wave do not need to calculated as they are represented in the asymptotic solution.

A tectorin-based matrix and planar cell polarity genes are required for normal collagen-fibril orientation in the developing tectorial membrane

The tectorial membrane is an extracellular structure of the cochlea. It develops on the surface of the auditory epithelium and contains collagen fibrils embedded in a tectorin-based matrix. The collagen fibrils are oriented radially with an apically directed slant - a feature considered crucial for hearing. To determine how this pattern is generated, collagen-fibril formation was examined in mice lacking a tectorin-based matrix, epithelial cilia or the planar cell polarity genes Vangl2 and Ptk7 In wild-type mice, collagen-fibril bundles appear within a tectorin-based matrix at E15.5 and, as fibril number rapidly increases, become co-aligned and correctly oriented. Epithelial width measurements and data from Kif3acKO mice suggest, respectively, that radial stretch and cilia play little, if any, role in determining normal collagen-fibril orientation; however, evidence from tectorin-knockout mice indicates that confinement is important. PRICKLE2 distribution reveals the planar cell polarity axis in the underlying epithelium is organised along the length of the cochlea and, in mice in which this polarity is disrupted, the apically directed collagen offset is no longer observed. These results highlight the importance of the tectorin-based matrix and epithelial signals for precise collagen organisation in the tectorial membrane.

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.

Modeling signal propagation in the human cochlea

The level-dependent component of the latency of human auditory brainstem responses (ABR) to tonebursts decreases by about 38% for every 20-dB increase in stimulus level over a wide range of both frequency and level [Neely, Norton, Gorga, and Jesteadt (1998). J. Acoust. Soc. Am. 31, 87-97]. This level-dependence has now been simulated in an active, nonlinear, transmission-line model of cochlear mechanics combined with an adaptation stage. The micromechanics in this model are similar to previous models except that a dual role is proposed for the tectorial membrane (TM): (1) passive sharpening the tuning of sensory-cell inputs (relative to basilar-membrane vibrations) and (2) providing an optimal phase shift (relative to basilar-membrane vibrations) of outer-hair-cell feedback forces, so that amplification is restricted to a limited range of frequencies. The adaptation stage, which represents synaptic adaptation of neural signals, contributes to the latency level-dependence more at low frequencies than at high frequencies. Compression in this model spans the range of audible sound levels with a compression ratio of about 2:1. With further development, the proposed model of cochlear micromechanics could be useful both (1) as a front-end to functional models of the auditory system and (2) as a foundation for understanding the physiological basis of cochlear amplification.

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 passive mechanical conditions modulate power generation by the outer hair cells

In the mammalian cochlea, small vibrations of the sensory epithelium are amplified due to active electro-mechanical feedback of the outer hair cells. The level of amplification is greater in the base than in the apex of the cochlea. Theoretical studies have used longitudinally varying active feedback properties to reproduce the location-dependent amplification. The active feedback force has been considered to be proportional to the basilar membrane displacement or velocity. An underlying assumption was that organ of Corti mechanics are governed by rigid body kinematics. However, recent progress in vibration measurement techniques reveals that organ of Corti mechanics are too complicated to be fully represented with rigid body kinematics. In this study, two components of the active feedback are considered explicitly-organ of Corti mechanics, and outer hair cell electro-mechanics. Physiological properties for the outer hair cells were incorporated, such as the active force gain, mechano-transduction properties, and membrane RC time constant. Instead of a kinematical model, a fully deformable 3D finite element model was used. We show that the organ of Corti mechanics dictate the longitudinal trend of cochlear amplification. Specifically, our results suggest that two mechanical conditions are responsible for location-dependent cochlear amplification. First, the phase of the outer hair cell's somatic force with respect to its elongation rate varies along the cochlear length. Second, the local stiffness of the organ of Corti complex felt by individual outer hair cells varies along the cochlear length. We describe how these two mechanical conditions result in greater amplification toward the base of the cochlea.

Simulating the Chan-Hudspeth experiment on an active excised cochlear segment

Hearing relies on a series of coupled electrical, acoustical, and mechanical interactions inside the cochlea that enable sound processing. The local structural and electrical properties of the organ of Corti (OoC) and basilar membrane give rise to the global, coupled behavior of the cochlea. However, it is difficult to determine the root causes of important behavior, such as the mediator of active processes, in the fully coupled in vivo setting. An alternative experimental approach is to use an excised segment of the cochlea under controlled electrical and mechanical conditions. Using the excised cochlear segment experiment conducted by Chan and Hudspeth [Nat. Neurosci. 8, 149-155 (2005); Biophys. J. 89, 4382-4395 (2005)] as the model problem, a quasilinear computational model for studying the active in vitro response of the OoC to acoustical stimulation was developed. The model of the electrical, mechanical, and acoustical conditions of the experimental configuration is able to replicate some of the experiment results, such as the shape of the frequency response of the sensory epithelium and the variation of the resonance frequency with the added fluid mass. As in the experiment, the model predicts a phase accumulation along the segment. However, it was found that the contribution of this phase accumulation to the dynamics is insignificant. Taking advantage of the relative simplicity of the fluid loading, the three-dimensional fluid dynamics was reduced into an added mass loading on the OoC thereby reducing the overall complexity of the model.

Geometric Requirements for Tectorial Membrane Traveling Waves in the Presence of Cochlear Loads

Recent studies suggest that wave motions of the tectorial membrane (TM) play a critical role in determining the frequency selectivity of hearing. However, frequency tuning is also thought to be limited by viscous loss in subtectorial fluid. Here, we analyze effects of this loss and other cochlear loads on TM traveling waves. Using a viscoelastic model, we demonstrate that hair bundle stiffness has little effect on TM traveling waves calculated with physiological parameters, that the limbal attachment can cause small (<20%) increases in TM wavelength, and that viscous loss in the subtectorial fluid can cause small (<20%) decreases in TM wave decay constants. However, effects of viscous loss in the subtectorial fluid are significantly increased if TM thickness is decreased. In contrast, increasing TM thickness above its physiological range has little effect on the wave, suggesting that the TM is just thick enough to maximize the spatial extent of the TM traveling wave.

Feeling force: physical and physiological principles enabling sensory mechanotransduction

Organisms as diverse as microbes, roundworms, insects, and mammals detect and respond to applied force. In animals, this ability depends on ionotropic force receptors, known as mechanoelectrical transduction (MeT) channels, that are expressed by specialized mechanoreceptor cells embedded in diverse tissues and distributed throughout the body. These cells mediate hearing, touch, and proprioception and play a crucial role in regulating organ function. Here, we attempt to integrate knowledge about the architecture of mechanoreceptor cells and their sensory organs with principles of cell mechanics, and we consider how engulfing tissues contribute to mechanical filtering. We address progress in the quest to identify the proteins that form MeT channels and to understand how these channels are gated. For clarity and convenience, we focus on sensory mechanobiology in nematodes, fruit flies, and mice. These themes are emphasized: asymmetric responses to applied forces, which may reflect anisotropy of the structure and mechanics of sensory mechanoreceptor cells, and proteins that function as MeT channels, which appear to have emerged many times through evolution.

The Coda of the Transient Response in a Sensitive Cochlea: A Computational Modeling Study

In a sensitive cochlea, the basilar membrane response to transient excitation of any kind–normal acoustic or artificial intracochlear excitation–consists of not only a primary impulse but also a coda of delayed secondary responses with varying amplitudes but similar spectral content around the characteristic frequency of the measurement location. The coda, sometimes referred to as echoes or ringing, has been described as a form of local, short term memory which may influence the ability of the auditory system to detect gaps in an acoustic stimulus such as speech. Depending on the individual cochlea, the temporal gap between the primary impulse and the following coda ranges from once to thrice the group delay of the primary impulse (the group delay of the primary impulse is on the order of a few hundred microseconds). The coda is physiologically vulnerable, disappearing when the cochlea is compromised even slightly. The multicomponent sensitive response is not yet completely understood. We use a physiologically-based, mathematical model to investigate (i) the generation of the primary impulse response and the dependence of the group delay on the various stimulation methods, (ii) the effect of spatial perturbations in the properties of mechanically sensitive ion channels on the generation and separation of delayed secondary responses. The model suggests that the presence of the secondary responses depends on the wavenumber content of a perturbation and the activity level of the cochlea. In addition, the model shows that the varying temporal gaps between adjacent coda seen in experiments depend on the individual profiles of perturbations. Implications for non-invasive cochlear diagnosis are also discussed.

The fluid-structure-electrical interaction in the cochlea enable the basilar membrane, one of the most important structures in the cochlear partition, to display different dynamic patterns depending on the frequency content of the incoming sound. Interestingly, in a healthy cochlea the motion of the basilar membrane shows echoes upon an impulse acoustic stimulation delivered to the ear canal. The delay, duration, and shape of these echoes vary from one cochlea to another. A hypothesis that irregularities of the properties of the cochlear partition coherently scatter acoustic waves and generate echoes is examined. These irregularities are posited to arise, for example, the damage of the sensory cells or the natural randomness in the morphology of the cochlear partition. Here we build a physiologically-based mathematical model to understand the echoes observed in experiments by introducing irregularity to the properties of the sensory cells. We found that the patterns of the echoes depend on the individual profiles of the irregularities. Our work suggest that the ear canal recording, which is correlated to the dynamics of the basilar membrane, can be used as a non-invasive tool not only to diagnose the intracochlear damage but also to interpret these data given its idiosyncratic origin.

The vibrating reed frequency meter: digital investigation of an early cochlear model

The vibrating reed frequency meter, originally employed by Békésy and later by Wilson as a cochlear model, uses a set of tuned reeds to represent the cochlea’s graded bank of resonant elements and an elastic band threaded between them to provide nearest-neighbour coupling. Here the system, constructed of 21 reeds progressively tuned from 45 to 55 Hz, is simulated numerically as an elastically coupled bank of passive harmonic oscillators driven simultaneously by an external sinusoidal force. To uncover more detail, simulations were extended to 201 oscillators covering the range 1–2 kHz. Calculations mirror the results reported by Wilson and show expected characteristics such as traveling waves, phase plateaus, and a response with a broad peak at a forcing frequency just above the natural frequency. The system also displays additional fine-grain features that resemble those which have only recently been recognised in the cochlea. Thus, detailed analysis brings to light a secondary peak beyond the main peak, a set of closely spaced low-amplitude ripples, rapid rotation of phase as the driving frequency is swept, frequency plateaus, clustering, and waxing and waning of impulse responses. Further investigation shows that each reed’s vibrations are strongly localised, with small energy flow along the chain. The distinctive set of equally spaced ripples is an inherent feature which is found to be largely independent of boundary conditions. Although the vibrating reed model is functionally different to the standard transmission line, its cochlea-like properties make it an intriguing local oscillator model whose relevance to cochlear mechanics needs further investigation.

Longitudinal spread of mechanical excitation through tectorial membrane traveling waves

The mammalian inner ear separates sounds by their frequency content, and this separation underlies important properties of human hearing, including our ability to understand speech in noisy environments. Studies of genetic disorders of hearing have demonstrated a link between frequency selectivity and wave properties of the tectorial membrane (TM). To understand these wave properties better, we developed chemical manipulations that systematically and reversibly alter TM stiffness and viscosity. Using microfabricated shear probes, we show that (i) reducing pH reduces TM stiffness with little change in TM viscosity and (ii) adding PEG increases TM viscosity with little change in TM stiffness. By applying these manipulations in measurements of TM waves, we show that TM wave speed is determined primarily by stiffness at low frequencies and by viscosity at high frequencies. Both TM viscosity and stiffness affect the longitudinal spread of mechanical excitation through the TM over a broad range of frequencies. Increasing TM viscosity or decreasing stiffness reduces longitudinal spread of mechanical excitation, thereby coupling a smaller range of best frequencies and sharpening tuning. In contrast, increasing viscous loss or decreasing stiffness would tend to broaden tuning in resonance-based TM models. Thus, TM wave and resonance mechanisms are fundamentally different in the way they control frequency selectivity.

Stimulus Frequency Otoacoustic Emissions Provide No Evidence for the Role of Efferents in the Enhancement Effect

Auditory enhancement refers to the perceptual phenomenon that a target sound is heard out more readily from a background sound if the background is presented alone first. Here we used stimulus-frequency otoacoustic emissions (SFOAEs) to test the hypothesis that activation of the medial olivocochlear efferent system contributes to auditory enhancement effects. The SFOAEs were used as a tool to measure changes in cochlear responses to a target component and the neighboring components of a multitone background between conditions producing enhancement and conditions producing no enhancement. In the "enhancement" condition, the target and multitone background were preceded by a precursor stimulus with a spectral notch around the signal frequency; in the control (no-enhancement) condition, the target and multitone background were presented without the precursor. In an experiment using a wideband multitone stimulus known to produce significant psychophysical enhancement effects, SFOAEs showed no changes consistent with enhancement, but some aspects of the results indicated possible contamination of the SFOAE magnitudes by the activation of the middle-ear-muscle reflex. The same SFOAE measurements performed using narrower-band stimuli at lower sound levels also showed no SFOAE changes consistent with either absolute or relative enhancement despite robust psychophysical enhancement effects observed in the same listeners with the same stimuli. The results suggest that cochlear efferent control does not play a significant role in auditory enhancement effects.