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

Nonlinear response to a click in a time-domain model of the mammalian ear

In this paper, a state-space implementation of a previously developed frequency-domain model of the cochlea is coupled to a lumped parameter model of the middle ear. After validation of the time-domain model by comparison of its steady-state response to results obtained with a frequency-domain formulation, the nonlinear response of the cochlea to clicks is investigated. As observed experimentally, a compressive nonlinearity progressively develops within the first few cycles of the response of the basilar membrane (BM). Furthermore, a time-frequency analysis shows that the instantaneous frequency of the BM response to a click progressively approaches the characteristic frequency. This phenomenon, called glide, is predicted at all stimulus intensities, as in experiments. In typical experiments with sensitive animals, the click response is characterized by a long ringing and the response envelope includes several lobes. In order to achieve similar results, inhomogeneities are introduced in the cochlear model. Simulations demonstrate the strong link between characteristics of the frequency response, such as dispersion and frequency-dependent nonlinearity, and characteristics of the time-domain response, such as the glide and a time-dependent nonlinearity. The progressive buildup of cochlear nonlinearity in response to a click is shown to be a consequence of the glide and of frequency-dependent nonlinearity.

Molecular organization and fine structure of the human tectorial membrane: is it replenished?

Auditory sensitivity and frequency resolution depend on the physical properties of the basilar membrane in combination with outer hair cell-based amplification in the cochlea. The physiological role of the tectorial membrane (TM) in hair cell transduction has been controversial for decades. New insights into the TM structure and function have been gained from studies of targeted gene disruption. Several missense mutations in genes regulating the human TM structure have been described with phenotypic expressions. Here, we portray the remarkable gradient structure and molecular organization of the human TM. Ultrastructural analysis and confocal immunohistochemistry were performed in freshly fixed human cochleae obtained during surgery. Based on these findings and recent literature, we discuss the role of human TMs in hair cell activation. Moreover, the outcome proposes that the α-tectorin-positive amorphous layer of the human TM is replenished and partly undergoes regeneration during life.

Two-compartment passive frequency domain cochlea model allowing independent fluid coupling to the tectorial and basilar membranes

The cochlea is a spiral-shaped, liquid-filled organ in the inner ear that converts sound with high frequency selectivity over a wide pressure range to neurological signals that are eventually interpreted by the brain. The cochlear partition, consisting of the organ of Corti supported below by the basilar membrane and attached above to the tectorial membrane, plays a major role in the frequency analysis. In early fluid-structure interaction models of the cochlea, the mechanics of the cochlear partition were approximated by a series of single-degree-of-freedom systems representing the distributed stiffness and mass of the basilar membrane. Recent experiments suggest that the mechanical properties of the tectorial membrane may also be important for the cochlea frequency response and that separate waves may propagate along the basilar and tectorial membranes. Therefore, a two-dimensional two-compartment finite difference model of the cochlea was developed to investigate the independent coupling of the basilar and tectorial membranes to the surrounding liquid. Responses are presented for models using two- or three-degree-of-freedom stiffness, damping, and mass parameters derived from a physiologically based finite element model of the cochlear partition. Effects of changes in membrane and organ of Corti stiffnesses on the individual membrane responses are investigated.

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.

Modified protein expression in the tectorial membrane of the cochlea reveals roles for the striated sheet matrix

The tectorial membrane (TM) of the mammalian cochlea is a complex extracellular matrix which, in response to acoustic stimulation, displaces the hair bundles of outer hair cells (OHCs), thereby initiating sensory transduction and amplification. Here, using TM segments from the basal, high-frequency region of the cochleae of genetically modified mice (including models of human hereditary deafness) with missing or modified TM proteins, we demonstrate that frequency-dependent stiffening is associated with the striated sheet matrix (SSM). Frequency-dependent stiffening largely disappeared in all three TM mutations studied where the SSM was absent either entirely or at least from the stiffest part of the TM overlying the OHCs. In all three TM mutations, dissipation of energy is decreased at low (<8 kHz) and increased at high (>8 kHz) stimulus frequencies. The SSM is composed of polypeptides carrying fixed charges, and electrostatic interaction between them may account for frequency-dependent stiffness changes in the material properties of the TM. Through comparison with previous in vivo measurements, it is proposed that implementation of frequency-dependent stiffening of the TM in the OHC attachment region facilitates interaction among tones, backward transmission of energy, and amplification in the cochlea.

A clinically oriented introduction and review on finite element models of the human cochlea

Due to the inaccessibility of the inner ear, direct in vivo information on cochlear mechanics is difficult to obtain. Mathematical modelling is a promising way to provide insight into the physiology and pathology of the cochlea. Finite element method (FEM) is one of the most popular discrete mathematical modelling techniques, mainly used in engineering that has been increasingly used to model the cochlea and its elements. The aim of this overview is to provide a brief introduction to the use of FEM in modelling and predicting the behavior of the cochlea in normal and pathological conditions. It will focus on methodological issues, modelling assumptions, simulation of clinical scenarios, and pathologies.

Porosity controls spread of excitation in tectorial membrane traveling waves

Cochlear frequency selectivity plays a key role in our ability to understand speech, and is widely believed to be associated with cochlear amplification. However, genetic studies targeting the tectorial membrane (TM) have demonstrated both sharper and broader tuning with no obvious changes in hair bundle or somatic motility mechanisms. For example, cochlear tuning of Tectb(-/-) mice is significantly sharper than that of Tecta(Y1870C/+) mice, even though TM stiffnesses are similarly reduced relative to wild-type TMs. Here we show that differences in TM viscosity can account for these differences in tuning. In the basal cochlear turn, nanoscale pores of Tecta(Y1870C/+) TMs are significantly larger than those of Tectb(-/-) TMs. The larger pore size reduces shear viscosity (by ∼70%), thereby reducing traveling wave speed and increasing spread of excitation. These results demonstrate the previously unrecognized importance of TM porosity in cochlear and neural tuning.

Effect of the attachment of the tectorial membrane on cochlear micromechanics and two-tone suppression

The mechanical stimulation of the outer hair cell hair bundle (HB) is a key step in nonlinear cochlear amplification. We show how two-tone suppression (TTS), a hallmark of cochlear nonlinearity, can be used as an indirect measure of HB stimulation. Using two different nonlinear computational models of the cochlea, we investigate the effect of altering the mechanical load applied by the tectorial membrane (TM) on the outer hair cell HB. In the first model (TM-A model), the TM is attached to the spiral limbus (as in wild-type animals); in the second model (TM-D model), the TM is detached from the spiral limbus (mimicking the cochlea of Otoa(EGFP/EGFP) mutant mice). As in recent experiments, model simulations demonstrate that the absence of the TM attachment does not preclude cochlear amplification. However, detaching the TM alters the mechanical load applied by the TM on the HB at low frequencies and therefore affects TTS by low-frequency suppressors. For low-frequency suppressors, the suppression threshold obtained with the TM-A model corresponds to a constant suppressor displacement on the basilar membrane (as in experiments with wild-type animals), whereas it corresponds to a constant suppressor velocity with the TM-D model. The predictions with the TM-D model could be tested by measuring TTS on the basilar membrane of the Otoa(EGFP/EGFP) mice to improve our understanding of the fundamental workings of the cochlea.

Basilar membrane and tectorial membrane stiffness in the CBA/CaJ mouse

The mouse has become an important animal model in understanding cochlear function. Structures, such as the tectorial membrane or hair cells, have been changed by gene manipulation, and the resulting effect on cochlear function has been studied. To contrast those findings, physical properties of the basilar membrane (BM) and tectorial membrane (TM) in mice without gene mutation are of great importance. Using the hemicochlea of CBA/CaJ mice, we have demonstrated that tectorial membrane (TM) and basilar membrane (BM) revealed a stiffness gradient along the cochlea. While a simple spring mass resonator predicts the change in the characteristic frequency of the BM, the spring mass model does not predict the frequency change along the TM. Plateau stiffness values of the TM were 0.6 ± 0.5, 0.2 ± 0.1, and 0.09 ± 0.09 N/m for the basal, middle, and upper turns, respectively. The BM plateau stiffness values were 3.7 ± 2.2, 1.2 ± 1.2, and 0.5 ± 0.5 N/m for the basal, middle, and upper turns, respectively. Estimations of the TM Young's modulus (in kPa) revealed 24.3 ± 25.2 for the basal turns, 5.1 ± 4.5 for the middle turns, and 1.9 ± 1.6 for the apical turns. Young's modulus determined at the BM pectinate zone was 76.8 ± 72, 23.9 ± 30.6, and 9.4 ± 6.2 kPa for the basal, middle, and apical turns, respectively. The reported stiffness values of the CBA/CaJ mouse TM and BM provide basic data for the physical properties of its organ of Corti.

Loss of the tectorial membrane protein CEACAM16 enhances spontaneous, stimulus-frequency, and transiently evoked otoacoustic emissions

α-Tectorin (TECTA), β-tectorin (TECTB), and carcinoembryonic antigen-related cell adhesion molecule 16 (CEACAM) are secreted glycoproteins that are present in the tectorial membrane (TM), an extracellular structure overlying the hearing organ of the inner ear, the organ of Corti. Previous studies have shown that TECTA and TECTB are both required for formation of the striated-sheet matrix within which collagen fibrils of the TM are imbedded and that CEACAM16 interacts with TECTA. To learn more about the structural and functional significance of CEACAM16, we created a Ceacam16-null mutant mouse. In the absence of CEACAM16, TECTB levels are reduced, a clearly defined striated-sheet matrix does not develop, and Hensen's stripe, a prominent feature in the basal two-thirds of the TM in WT mice, is absent. CEACAM16 is also shown to interact with TECTB, indicating that it may stabilize interactions between TECTA and TECTB. Although brain-stem evoked responses and distortion product otoacoustic emissions are, for most frequencies, normal in young mice lacking CEACAM16, stimulus-frequency and transiently evoked emissions are larger. We also observed spontaneous otoacoustic emissions (SOAEs) in 70% of the homozygous mice. This incidence is remarkable considering that <3% of WT controls have SOAEs. The predominance of SOAEs >15 kHz correlates with the loss of Hensen's stripe. Results from mice lacking CEACAM16 are consistent with the idea that the organ of Corti evolved to maximize the gain of the cochlear amplifier while preventing large oscillations. Changes in TM structure appear to influence the balance between energy generation and dissipation such that the system becomes unstable.

Light-induced vibration in the hearing organ

The exceptional sensitivity of mammalian hearing organs is attributed to an active process, where force produced by sensory cells boost sound-induced vibrations, making soft sounds audible. This process is thought to be local, with each section of the hearing organ capable of amplifying sound-evoked movement, and nearly instantaneous, since amplification can work for sounds at frequencies up to 100 kHz in some species. To test these fundamental precepts, we developed a method for focally stimulating the living hearing organ with light. Light pulses caused intense and highly damped mechanical responses followed by traveling waves that developed with considerable delay. The delayed response was identical to movements evoked by click-like sounds. This shows that the active process is neither local nor instantaneous, but requires mechanical waves traveling from the cochlear base toward its apex. A physiologically-based mathematical model shows that such waves engage the active process, enhancing hearing sensitivity.

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.

Phase of shear vibrations within cochlear partition leads to activation of the cochlear amplifier

Since Georg von Bekesy laid out the place theory of the hearing, researchers have been working to understand the remarkable properties of mammalian hearing. Because access to the cochlea is restricted in live animals, and important aspects of hearing are destroyed in dead ones, models play a key role in interpreting local measurements. Wentzel-Kramers-Brillouin (WKB) models are attractive because they are analytically tractable, appropriate to the oblong geometry of the cochlea, and can predict wave behavior over a large span of the cochlea. Interest in the role the tectorial membrane (TM) plays in cochlear tuning led us to develop models that directly interface the TM with the cochlear fluid. In this work we add an angled shear between the TM and reticular lamina (RL), which serves as an input to a nonlinear active force. This feature plus a novel combination of previous work gives us a model with TM-fluid interaction, TM-RL shear, a nonlinear active force and a second wave mode. The behavior we get leads to the conclusion the phase between the shear and basilar membrane (BM) vibration is critical for amplification. We show there is a transition in this phase that occurs at a frequency below the cutoff, which is strongly influenced by TM stiffness. We describe this mechanism of sharpened BM velocity profile, which demonstrates the importance of the TM in overall cochlear tuning and offers an explanation for the response characteristics of the Tectb mutant mouse.

Effect of metabolic presbyacusis on cochlear responses: a simulation approach using a physiologically-based model

In the presented model, electrical, acoustical, and mechanical elements of the cochlea are explicitly integrated into a signal transmission line where these elements convey physiological interpretations of the human cochlear structures. As a result, this physiologically-motivated model enables simulation of specific cochlear lesions such as presbyacusis. The hypothesis is that high-frequency hearing loss in older adults may be due to metabolic presbyacusis whereby age-related cellular/chemical degenerations in the lateral wall of the cochlea cause a reduction in the endocochlear potential. The simulations quantitatively confirm this hypothesis and emphasize that even if the outer and inner hair cells are totally active and intact, metabolic presbyacusis alone can significantly deteriorate the cochlear functionality. Specifically, in the model, as the endocochlear potential decreases, the transduction mechanism produces less receptor current such that there is a reduction in the battery of the somatic motor. This leads to a drastic decrease in cochlear amplification and frequency sensitivity, as well as changes in position-frequency map (tuning pattern) of the cochlea. In addition, the simulations show that the age-related reduction of the endocochlear potential significantly inhibits the firing rate of the auditory nerve which might contribute to the decline of temporal resolution in the aging auditory system.

Frequency-dependent properties of the tectorial membrane facilitate energy transmission and amplification in the cochlea

The remarkable sensitivity, frequency selectivity, and dynamic range of the mammalian cochlea relies on longitudinal transmission of minuscule amounts of energy as passive, pressure-driven, basilar membrane (BM) traveling waves. These waves are actively amplified at frequency-specific locations by a mechanism that involves interaction between the BM and another extracellular matrix, the tectorial membrane (TM). From mechanical measurements of isolated segments of the TM, we made the important new (to our knowledge) discovery that the stiffness of the TM is reduced when it is mechanically stimulated at physiologically relevant magnitudes and at frequencies below their frequency place in the cochlea. The reduction in stiffness functionally uncouples the TM from the organ of Corti, thereby minimizing energy losses during passive traveling-wave propagation. Stiffening and decreased viscosity of the TM at high stimulus frequencies can potentially facilitate active amplification, especially in the high-frequency, basal turn, where energy loss due to internal friction within the TM is less than in the apex. This prediction is confirmed by neural recordings from several frequency regions of the cochlea.

A wave finite element analysis of the passive cochlea

Current models of the cochlea can be characterized as being either based on the assumed propagation of a single slow wave, which provides good insight, or involve the solution of a numerical model, such as in the finite element method, which allows the incorporation of more detailed anatomical features. In this paper it is shown how the wave finite element method can be used to decompose the results of a finite element calculation in terms of wave components, which allows the insight of the wave approach to be brought to bear on more complicated numerical models. In order to illustrate the method, a simple box model is considered, of a passive, locally reacting, basilar membrane interacting via three-dimensional fluid coupling. An analytic formulation of the dispersion equation is used initially to illustrate the types of wave one would expect in such a model. The wave finite element is then used to calculate the wavenumbers of all the waves in the finite element model. It is shown that only a single wave type dominates the response until this peaks at the best place in the cochlea, where an evanescent, higher order fluid wave can make a significant contribution.

Electrokinetic properties of the mammalian tectorial membrane

The tectorial membrane (TM) clearly plays a mechanical role in stimulating cochlear sensory receptors, but the presence of fixed charge in TM constituents suggests that electromechanical properties also may be important. Here, we measure the fixed charge density of the TM and show that this density of fixed charge is sufficient to affect mechanical properties and to generate electrokinetic motions. In particular, alternating currents applied to the middle and marginal zones of isolated TM segments evoke motions at audio frequencies (1-1,000 Hz). Electrically evoked motions are nanometer scaled (∼5-900 nm), decrease with increasing stimulus frequency, and scale linearly over a broad range of electric field amplitudes (0.05-20 kV/m). These findings show that the mammalian TM is highly charged and suggest the importance of a unique TM electrokinetic mechanism.

Comparison of nonlinear mammalian cochlear-partition models

Various simple mathematical models of the dynamics of the organ of Corti in the mammalian cochlea are analyzed and their dynamics compared. The specific models considered are phenomenological Hopf and cusp normal forms, a recently proposed description combining active hair-bundle motility and somatic motility, a reduction thereof, and finally a model highlighting the importance of the coupling between the nonlinear transduction current and somatic motility. It is found that for certain models precise tuning to any bifurcation is not necessary and that a compressively nonlinear response over a range similar to experimental observations and that the normal form of the Hopf bifurcation is not the only description that reproduces compression and tuning similar to experiment.

Direction of wave propagation in the cochlea for internally excited basilar membrane

Otoacoustic emissions are an indicator of a normally functioning cochlea and as such are a useful tool for non-invasive diagnosis as well as for understanding cochlear function. While these emitted waves are hypothesized to arise from active processes and exit through the cochlear fluids, neither the precise mechanism by which these emissions are generated nor the transmission pathway is completely known. With regard to the acoustic pathway, two competing hypotheses exist to explain the dominant mode of emission. One hypothesis, the backward-traveling wave hypothesis, posits that the emitted wave propagates as a coupled fluid-structure wave while the alternate hypothesis implicates a fast, compressional wave in the fluid as the main mechanism of energy transfer. In this paper, we study the acoustic pathway for transmission of energy from the inside of the cochlea to the outside through a physiologically-based theoretical model. Using a well-defined, compact source of internal excitation, we predict that the emission is dominated by a backward traveling fluid-structure wave. However, in an active model of the cochlea, a forward traveling wave basal to the location of the force is possible in a limited region around the best place. Finally, the model does predict the dominance of compressional waves under a different excitation, such as an apical excitation.

Progress in cochlear physiology after Békésy

In the fifty years since Békésy was awarded the Nobel Prize, cochlear physiology has blossomed. Many topics that are now current are things Békésy could not have imagined. In this review we start by describing progress in understanding the origin of cochlear gross potentials, particularly the cochlear microphonic, an area in which Békésy had extensive experience. We then review progress in areas of cochlear physiology that were mostly unknown to Békésy, including: (1) stereocilia mechano-electrical transduction, force production, and response amplification, (2) outer hair cell (OHC) somatic motility and its molecular basis in prestin, (3) cochlear amplification and related micromechanics, including the evidence that prestin is the main motor for cochlear amplification, (4) the influence of the tectorial membrane, (5) cochlear micromechanics and the mechanical drives to inner hair cell stereocilia, (6) otoacoustic emissions, and (7) olivocochlear efferents and their influence on cochlear physiology. We then return to a subject that Békésy knew well: cochlear fluids and standing currents, as well as our present understanding of energy dependence on the lateral wall of the cochlea. Finally, we touch on cochlear pathologies including noise damage and aging, with an emphasis on where the field might go in the future.

Transmission of cochlear distortion products as slow waves: a comparison of experimental and model data

There is a long-lasting question of how distortion products (DPs) arising from nonlinear amplification processes in the cochlea are transmitted from their generation sites to the stapes. Two hypotheses have been proposed: (1) the slow-wave hypothesis whereby transmission is via the transverse pressure difference across the cochlear partition and (2) the fast-wave hypothesis proposing transmission via longitudinal compression waves. Ren with co-workers have addressed this topic experimentally by measuring the spatial vibration pattern of the basilar membrane (BM) in response to two tones of frequency f(1) and f(2). They interpreted the observed negative phase slopes of the stationary BM vibrations at the cubic distortion frequency f(DP) = 2f(1) - f(2) as evidence for the fast-wave hypothesis. Here, using a physically based model, it is shown that their phase data is actually in accordance with the slow-wave hypothesis. The analysis is based on a frequency-domain formulation of the two-dimensional motion equation of a nonlinear hydrodynamic cochlea model. Application of the analysis to their experimental data suggests that the measurement sites of negative phase slope were located at or apical to the DP generation sites. Therefore, current experimental and theoretical evidence supports the slow-wave hypothesis. Nevertheless, the analysis does not allow rejection of the fast-wave hypothesis.

Response to a pure tone in a nonlinear mechanical-electrical-acoustical model of the cochlea

In this article, a nonlinear mathematical model is developed based on the physiology of the cochlea of the guinea pig. The three-dimensional intracochlear fluid dynamics are coupled to a micromechanical model of the organ of Corti and to electrical potentials in the cochlear ducts and outer hair cells (OHC). OHC somatic electromotility is modeled by linearized piezoelectric relations whereas the OHC hair-bundle mechanoelectrical transduction current is modeled as a nonlinear function of the hair-bundle deflection. The steady-state response of the cochlea to a single tone is simulated in the frequency domain using an alternating frequency time scheme. Compressive nonlinearity, harmonic distortion, and DC shift on the basilar membrane (BM), tectorial membrane (TM), and OHC potentials are predicted using a single set of parameters. The predictions of the model are verified by comparing simulations to available in vivo experimental data for basal cochlear mechanics. In particular, the model predicts more amplification on the reticular lamina (RL) side of the cochlear partition than on the BM, which replicates recent measurements. Moreover, small harmonic distortion and DC shifts are predicted on the BM, whereas more significant harmonic distortion and DC shifts are predicted in the RL and TM displacements and in the OHC potentials.

Vibration responses of the organ of Corti and the tectorial membrane to electrical stimulation

Coupling of somatic electromechanical force from the outer hair cells (OHCs) into the organ of Corti is investigated by measuring transverse vibration patterns of the organ of Cori and tectorial membrane (TM) in response to intracochlear electrical stimulation. Measurement places at the organ of Corti extend from the inner sulcus cells to Hensen's cells and at the lower (and upper) surface of the TM from the inner sulcus to the OHC region. These locations are in the neighborhood of where electromechanical force is coupled into (1) the mechanoelectrical transducers of the stereocilia and (2) fluids of the organ of Corti. Experiments are conducted in the first, second, and third cochlear turns of an in vitro preparation of the adult guinea pig cochlea. Vibration measurements are made at functionally relevant stimulus frequencies (0.48-68 kHz) and response amplitudes (<15 nm). The experiments provide phase relations between the different structures, which, dependent on frequency range and longitudinal cochlear position, include in-phase transverse motions of the TM, counterphasic transverse motions between the inner hair cell and OHCs, as well as traveling-wave motion of Hensen's cells in the radial direction. Mechanics of sound processing in the cochlea are discussed based on these phase relationships.

Effects of a perilymphatic fistula on the passive vibration response of the basilar membrane

In this study, a three-dimensional finite-element model of the passive human cochlea was created. Dynamic behavior of the basilar membrane caused by the vibration of the stapes footplate was analyzed considering a fluid-structure interaction with the cochlear fluid. Next, the effects of a perilymphatic fistula (PLF) on the vibration of the cochlea were examined by making a small hole on the wall of the cochlea model. Even if a PLF existed in the scala vestibuli, a traveling wave was generated on the basilar membrane. When a PLF existed at the basal end of the cochlea, the shape of the traveling wave envelope showed no remarkable change, but the maximum amplitude became smaller at the entire frequency range from 0.5 to 5kHz and decreased with decreasing frequency. In contrast, when a PLF existed at the second turn of the cochlea, the traveling wave envelope showed a notch at the position of the PLF and the maximum amplitude also became smaller. This model assists in elucidating the mechanisms of hearing loss due to a PLF from the view of dynamics.

Nonlinear models of development, amplification and compression in the mammalian cochlea

This paper reviews current understanding and presents new results on some of the nonlinear processes that underlie the function of the mammalian cochlea. These processes occur within mechano-sensory hair cells that form part of the organ of Corti. After a general overview of cochlear physiology, mathematical modelling results are presented in three parts. First, the dynamic interplay between ion channels within the sensory inner hair cells is used to explain some new electrophysiological recordings from early development. Next, the state of the art is reviewed in modelling the electro-motility present within the outer hair cells (OHCs), including the current debate concerning the role of cell body motility versus active hair bundle dynamics. A simplified model is introduced that combines both effects in order to explain observed amplification and compression in experiments. Finally, new modelling evidence is presented that structural longitudinal coupling between OHCs may be necessary in order to capture all features of the observed mechanical responses.

Auditory mechanics of the tectorial membrane and the cochlear spiral

PURPOSE OF REVIEW

This review is timely and relevant because new experimental and theoretical findings suggest that cochlear mechanics from the nanoscale to the macroscale are affected by the mechanical properties of the tectorial membrane and the cochlea's spiral shape.

RECENT FINDINGS

Main tectorial membrane themes addressed in this review are composition and morphology, nanoscale mechanical interactions with the outer hair cell bundle, macroscale longitudinal coupling, fluid interaction with inner hair cell bundles, and macroscale dynamics and waves. Main cochlear spiral themes are macroscale, low-frequency energy focusing and microscale organ of Corti shear gain.

SUMMARY

Recent experimental and theoretical findings reveal exquisite sensitivity of cochlear mechanical performance to tectorial membrane structural organization, mechanics, and its positioning with respect to hair bundles. The cochlear spiral geometry is a major determinant of low-frequency hearing. These findings suggest a number of important research directions.

Biophysical mechanisms underlying outer hair cell loss associated with a shortened tectorial membrane

The tectorial membrane (TM) connects to the stereociliary bundles of outer hair cells (OHCs). Humans with an autosomal dominant C1509G mutation in alpha-tectorin, a protein constituent of the TM, are born with a partial hearing loss that worsens over time. The Tecta(C1509/+) transgenic mouse with the same point mutation has partial hearing loss secondary to a shortened TM that only contacts the first row of OHCs. As well, Tecta(C1509G/+) mice have increased expression of the OHC electromotility protein, prestin. We sought to determine whether these changes impact OHC survival. Distortion product otoacoustic emission thresholds in a quiet environment did not change to 6 months of age. However, noise exposure produced acute threshold shifts that fully recovered in Tecta (+/+) mice but only partially recovered in Tecta(C1509G/+) mice. While Tecta(+/+) mice lost OHCs primarily at the base and within all three rows, Tecta(C1509G/+) mice lost most of their OHCs in a more apical region of the cochlea and nearly completely within the first row. In order to estimate the impact of a shorter TM on the forces faced by the stereocilia within the first OHC row, both the wild type and the heterozygous conditions were simulated in a computational model. These analyses predicted that the shear force on the stereocilia is ~50% higher in the heterozygous condition. We then measured electrically induced movements of the reticular lamina in situ and found that while they decreased to the noise floor in prestin null mice, they were increased by 4.58 dB in Tecta(C1509G/+) mice compared to Tecta(+/+) mice. The increased movements were associated with a fourfold increase in OHC death as measured by vital dye staining. Together, these findings indicate that uncoupling the TM from some OHCs leads to partial hearing loss and places the remaining coupled OHCs at higher risk. Both the mechanics of the malformed TM and the increased prestin-related movements of the organ of Corti contribute to this higher risk profile.

Coupling active hair bundle mechanics, fast adaptation, and somatic motility in a cochlear model

One of the central questions in the biophysics of the mammalian cochlea is determining the contributions of the two active processes, prestin-based somatic motility and hair bundle (HB) motility, to cochlear amplification. HB force generation is linked to fast adaptation of the transduction current via a calcium-dependent process and somatic force generation is driven by the depolarization caused by the transduction current. In this article, we construct a global mechanical-electrical-acoustical mathematical model of the cochlea based on a three-dimensional fluid representation. The global cochlear model is coupled to linearizations of nonlinear somatic motility and HB activity as well as to the micromechanics of the passive structural and electrical elements of the cochlea. We find that the active HB force alone is not sufficient to power high frequency cochlear amplification. However, somatic motility can overcome resistor-capacitor filtering by the basolateral membrane and deliver sufficient mechanical energy for amplification at basal locations. The results suggest a new theory for high frequency active cochlear mechanics, in which fast adaptation controls the transduction channel sensitivity and thereby the magnitude of the energy delivered by somatic motility.

Fluid coupling in a discrete model of cochlear mechanics

A discrete model of cochlear mechanics is introduced that includes a full, three-dimensional, description of fluid coupling. This formulation allows the fluid coupling and basilar membrane dynamics to be analyzed separately and then coupled together with a simple piece of linear algebra. The fluid coupling is initially analyzed using a wavenumber formulation and is separated into one component due to one-dimensional fluid coupling and one comprising all the other contributions. Using the theory of acoustic waves in a duct, however, these two components of the pressure can also be associated with a far field, due to the plane wave, and a near field, due to the evanescent, higher order, modes. The near field components are then seen as one of a number of sources of additional longitudinal coupling in the cochlea. The effects of non-uniformity and asymmetry in the fluid chamber areas can also be taken into account, to predict both the pressure difference between the chambers and the mean pressure. This allows the calculation, for example, of the effect of a short cochlear implant on the coupled response of the cochlea.

Dual traveling waves in an inner ear model with two degrees of freedom

We calculate traveling waves in the mammalian cochlea, which transduces acoustic vibrations into neural signals. We use a WKB-based mechanical model with both the tectorial membrane (TM) and basilar membrane (BM) coupled to the fluid to calculate motions along the length of the cochlea. This approach generates two wave numbers that manifest as traveling waves with different modes of motion between the BM and TM. The waves add differently on each mass, producing distinct tuning curves and different characteristic frequencies (CFs) for the TM and the BM. We discuss the effect of TM stiffness and coupling on the waves and tuning curves. We also consider how the differential motions between the masses could influence the cochlear amplifier and how mode conversion could take place in the cochlea.

Measurement of cochlear power gain in the sensitive gerbil ear

The extraordinary sensitivity of the mammalian ear is commonly attributed to the cochlear amplifier, a cellular process thought to locally boost responses of the cochlear partition to soft sounds. However, cochlear power gain has not been measured directly. Here we use a scanning laser interferometer to determine the volume displacement and volume velocity of the cochlear partition by measuring its transverse vibration along and across the partition. We show the transverse displacement at the peak-response location can be >1,000 times greater than the displacement of the stapes, whereas the volume displacement of an area centred at this location is approximately tenfold greater than that of the stapes. Using the volume velocity and cochlear-fluid impedance, we discover that power at the peak-response area is >100-fold greater than that at the stapes. These results demonstrate experimentally that the cochlea amplifies soft sounds, offering insight into the mechanism responsible for the cochlear sensitivity.

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.