Basilar Membrane Velocity Research Articles

Influence of the cochlear partition’s flexibility on the macro mechanisms in the inner ear

Recent studies have highlighted the anatomy of the cochlear partition (CP), revealing insights into the flexible nature of the osseous spiral lamina (OSL) and the existence of a flexible cochlear partition bridge (CPB) between the OSL and the basilar membrane (BM). However, most existing inner ear models treat the OSL as a rigid structure and ignore the CPB, neglecting their potential impact on intracochlear sound pressure and motion of the BM. In this paper, we investigate the effect of the CP’s flexibility by including the OSL and CPB as either rigid or flexible structures in a numerical anatomical model of the human inner ear. Our findings demonstrate that the flexibility of the OSL and the presence of the CPB significantly affect cochlear macro mechanisms, including differential intracochlear sound pressure, resistive behavior in cochlear impedances, CP stiffness, and BM velocity. These results emphasize the importance of considering the flexibility of the entire CP to enhance our understanding of cochlear function and to accurately interpret experimental data on inner ear mechanics.

Reference velocity of a human head in bone conduction hearing: Finite element study

A whole head or temporal bone has been used in experiments to understand the mechanism of bone conduction (BC) hearing. In these experiments, two assumptions are generally accepted: (1) a promontory can be a representative point to show the motion of a specimen in BC hearing, and (2) the promontory velocity is proportional to a cochlear response so that the higher the promontory velocity, the better the BC hearing. To confirm the two assumptions, we investigated the velocities of various points corresponding to different BC input types and directions in the head. In this investigation, we used the three-dimensional finite element model of a human head, including an auditory periphery. Results showed that a single promontory was insufficient to be a representative point to show the motion of a specimen because the specimen could have rotational motion at frequencies below 0.5 kHz and the localized deformation at frequencies above 3 kHz. The promontory velocity had the same pattern as the basilar membrane velocity at low and high frequencies. However, at mid-frequencies between 0.5 and 3 kHz, the promontory did not exhibit the same pattern of velocity as the basilar membrane. Therefore, one's BC hearing ability must be carefully determined on the basis of promontory velocity.

Fluid focusing and viscosity allow high gain and stability of the cochlear response.

This paper discusses the role of two-dimensional (2-D)/three-dimensional (3-D) cochlear fluid hydrodynamics in the generation of the large nonlinear dynamical range of the basilar membrane (BM) and pressure response, in the decoupling between cochlear gain and tuning, and in the dynamic stabilization of the high-gain BM response in the peak region. The large and closely correlated dependence on stimulus level of the BM velocity and fluid pressure gain [Dong, W., and Olson, E. S. (2013). Biophys. J. 105(4), 1067-1078] is consistent with a physiologically oriented schematization of the outer hair cell (OHC) mechanism if two hydrodynamic effects are accounted for: amplification of the differential pressure associated with a focusing phenomenon, and viscous damping at the BM-fluid interface. The predictions of the analytical 2-D Wentzel-Kramers-Brillouin (WKB) approach are compared to solutions of a 3-D finite element model, showing that these hydrodynamic phenomena yield stable high-gain response in the peak region and a smooth transition among models with different effectiveness of the active mechanism, mimicking the cochlear nonlinear response over a wide stimulus level range. This study explains how an effectively anti-damping nonlinear outer hair cells (OHC) force may yield large BM and pressure dynamical ranges along with an almost level-independent admittance.

Development of a finite element model of a human head including auditory periphery for understanding of bone-conducted hearing

A three-dimensional finite-element (FE) model of a human head including the auditory periphery was developed to obtain a better understanding of bone-conducted (BC) hearing. The model was validated by comparison of cochlear and head responses in both air-conducted (AC) and BC hearing with experimental data. Specifically, the FE model provided the cochlear responses such as basilar membrane velocity and intracochlear pressure corresponding to BC stimulations applied to the mastoid or the conventional bone-anchored-hearing-aid (BAHA) positions. This is a strength of the model because it is difficult to obtain the cochlear responses from experiments corresponding to the BC stimulation applied at a specific position on the head surface. In addition, there have been few studies based on an FE model that can calculate the head and cochlear responses simultaneously from a BC stimulation. Moreover, in this study, the intracochlear sound pressure at multi-positions along the BM length was calculated and used to clarify the effect of stimulating force direction on the cochlear and promontory velocities in BC hearing. Also, the relationship between BC and AC stimulation and the basilar membrane velocity in the FE model was used to calculate the stimulation level at hearing thresholds which has been investigated only by psychoacoustical methods.

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.

Asymmetry and Microstructure of Temporal-Suppression Patterns in Basilar-Membrane Responses to Clicks: Relation to Tonal Suppression and Traveling-Wave Dispersion.

The cochlea's wave-based signal processing allows it to efficiently decompose a complex acoustic waveform into frequency components. Because cochlear responses are nonlinear, the waves arising from one frequency component of a complex sound can be altered by the presence of others that overlap with it in time and space (e.g., two-tone suppression). Here, we investigate the suppression of basilar-membrane (BM) velocity responses to a transient signal (a test click) by another click or tone. We show that the BM response to the click can be reduced when the stimulus is shortly preceded or followed by another (suppressor) click. More surprisingly, the data reveal two curious dependencies on the interclick interval, Δt. First, the temporal suppression curve (amount of suppression vs. Δt) manifests a pronounced and nearly periodic microstructure. Second, temporal suppression is generally strongest not when the two clicks are presented simultaneously (Δt =0), but when the suppressor click precedes the test click by a time interval corresponding to one to two periods of the best frequency (BF) at the measurement location. By systematically varying the phase of the suppressor click, we demonstrate that the suppression microstructure arises from alternating constructive and destructive interference between the BM responses to the two clicks. And by comparing temporal and tonal suppression in the same animals, we test the hypothesis that the asymmetry of the temporal-suppression curve around Δt =0 stems from cochlear dispersion and the well-known asymmetry of tonal suppression around the BF. Just as for two-tone suppression, BM responses to clicks are most suppressed by tones at frequencies just above the BF of the measurement location. On average, the frequency place of maximal suppressibility of the click response predicted from temporal-suppression data agrees with the frequency at which tonal suppression peaks, consistent with our hypothesis.

Grenzschichtdämpfung von Wanderwellen in einem dreidimensionalen passiven Finite Elemente Modell der Cochlea des Menschen

A passive three-dimensional model of the human cochlea is described and analysed in the present article. One of its features is the implementation of a thermo-viscous boundary layer as a physically approved mechanism of mechanical damping. The model is solved numerically with the finite element method in ANSYS® and the simulation results are analysed with the help of MATLAB®. In this way curves of the basilar membrane's amplitude, phase and velocity for frequencies between 1000Hz and 8000Hz are calculated. A traveling wave develops on the basilar membrane and is damped after reaching its frequency-dependent maximum due to the boundary layer damping. A plot of the frequency-to-space transformation can be obtained which fits to the experimental data found in the literature. Furthermore, the study shows an energy analysis of the simulation verifying the boundary layer damping as a relevant physical effect for 3D-models of the cochlea.

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.

Temporal Suppression of Clicked-Evoked Otoacoustic Emissions and Basilar-Membrane Motion in Gerbils.

Otoacoustic emissions evoked by a click (CEOAEs) can be reduced if the evoking sound is preceded or followed by another ("suppressor") click. Studying the temporal suppression of CEOAEs can provide insights into the dynamics of cochlear nonlinearity. However, temporal suppression has never been measured in basilar-membrane (BM) motion. Thus, it remains unclear whether the characteristics of CEOAE temporal suppression are reflected in BM responses. Here we simultaneously measured ear-canal pressure and BM velocity (laser Doppler vibrometry) in response to clicks in gerbil. When the suppressor click preceded the evoking click, CEOAEs were maximally suppressed for interclick intervals (ICIs) equivalent to ~2 periods of the analyzed frequency (9-14 kHz). Maximal temporal suppression at nonzero ICIs has been previously observed in human CEOAEs. BM responses to clicks were maximally reduced when the suppressor click preceded the evoking one by ~1 period of the characteristic frequency (CF ~14 kHz). Thus, the "delayed" characteristics of CEOAE temporal suppression are reflected in BM motion, although on a different time scale. When the suppressor click followed the evoking click, CEOAEs were augmented rather than suppressed, while enhancement was not observed in BM motion at the CF. This result indicates that some aspects of CEOAE temporal suppression are intrinsic to CEOAE generation mechanisms and/or to places that are not reflected in a BM motion at a single-location.

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.

Auditory fatigue model applications to predict noise induced hearing loss in human and chinchilla

Noise induced hearing loss (NIHL) remains a severe health problem worldwide. Current noise metrics and models have assessment limitations on gradually developing NIHL (GDNIHL). In this study, we apply a complex velocity level (CVL) auditory fatigue model to quantitatively assess the impact of basilar membrane (BM) movement on GDNIHL. The transfer functions of chinchilla and human auditory systems, including the triple-path nonlinear (TRNL) filters to simulate the inner ear responses, are applied to obtain BM velocity distribution. Chinchilla and human experimental hearing loss data are used to validate the proposed CVL model’s effectiveness. The results reveal that the developed CVL model demonstrates high correlations with both chinchilla and human hearing loss data. The linear regression based correlation study indicates the proposed CVL model may accurately predict NIHL in both human and chinchilla.

Effects of basilar membrane arch and radial tension on the travelling wave in gerbil cochlea

The basilar membrane velocity of gerbil cochlea showed discrepancy between theoretical model and experimental measurements. We hypothesize that the reasons of such discrepancies are due to the arch towards the scala tympani and radial tension present in the basilar membrane of the gerbil cochlea. The arch changes the bending stiffness in the basilar membrane, reduces the effective fluid force on the membrane and increases the basilar membrane's inertia. The existence of the radial tension also dampens the acoustic travelling wave. In this paper, the wave number functions along the gerbil basilar membrane are calculated from experimentally measured physical parameters with the theoretical model as well as extracted from experimentally measured basilar membrane velocity with the wave number inversion formula. The two wave number functions are compared and the effects of the tension and membrane arch on the wave number are studied based on various parameters of the model. We found that the bending stiffness across the gerbil basilar membrane varies (1–2 orders along the cochlea in the section 2.2 mm–3 mm from base) more than the calculated value in the flat basilar membrane model and the radial tension increases the damping of the travelling wave in gerbil cochlea significantly (5 times more than that without radial tension). These effects of arch and radial tension in the basilar membrane elucidate the discrepancy between previous theoretical model and experimental measurements in gerbil cochlea.

The Importance of the Hook Region of the Cochlea for Bone-Conduction Hearing

For the most part, the coiled shape of the cochlea has been shown to have only minor importance for air-conducted hearing. It is hypothesized, however, that this coiled shape may play a more significant role for the bone-conducted (BC) route of hearing, through inertial forces exerted by the middle ear and cochlear fluid, and that this can be tested by comparing the results of applying BC stimuli in a variety of different directions. A three-dimensional finite element model of a human middle ear coupled to the inner ear was formulated. BC excitations were simulated by applying rigid-body vibrations normal to the surface of the basilar membrane (BM) at 0.8 (d1), 5.8 (d2), 15.6 (d3), and 33.1 (d4) mm from the base of the cochlea, such that relative motions of the fluid within the cochlea produced excitations of the BM. The vibrational direction normal to the BM surface at the base of the cochlea (d1) produced the highest BM velocity response across all tested frequencies—higher than an excitation direction normal to the BM surface at the nonbasal locations (d2–d4), even when the stimulus frequency matched the best frequency for each location. The basal part of the human cochlea features a well-developed hook region, colocated with the cochlear vestibule, that features the largest difference in fluid volume between the scala vestibuli (SV) and scala tympani (ST) found in the cochlea. The proximity of the hook region to the oval and round windows, combined with it having the biggest fluid-volume difference between the SV and ST, is thought to result in a maximization of the pressure difference between the SV and ST for BC stimuli normal to the BM in this region, and consequently a maximization of the resulting BM velocity.

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.

Carhart’s notch: A window into mechanisms of bone-conducted hearing

Otosclerosis is a disease process of the ear that stiffens the stapes annular ligament and results in footplate immobilization. This produces a characteristic loss in bone-conducted (BC) hearing of about 20 dB between 1 and 2 kHz, known as “Carhart’s notch,” for which the specific mechanisms responsible have not yet been well understood. In this study, it is hypothesized that this observed pattern of hearing loss results from interactions between compressional and inertial mechanisms of BC hearing. Differences in the basilar-membrane velocity between a normal and otosclerotic human ear were calculated in response to compressional vibration of the cochlear capsule, translational vibration of the skull bone in various directions, and combinations of the two, using an anatomically accurate 3-D finite element model of the middle ear, cochlea, and semicircular canals. Compressional and inertial BC stimuli were found to both be necessary to capture the full behavior of clinical data, with the compressional component dominating below 0.75 kHz, the inertial component dominating above 3 kHz, and the notch between 1 and 2 kHz resulting from the suppression of an ossicular resonance due to stapes fixation. [Work supported by grant R01-DC07910 and R01-DC05960 from the NIDCD of NIH.]

The coda of the transient response in a sensitive cochlea

In a sensitive cochlea, the basilar membrane (BM) velocity response due to transient external acoustic excitation or to localized transient internal bipolar electrical excitation gives rise not only to a primary impulse response, but also to a coda of delayed secondary responses (sometimes called echoes or ringing) with varying amplitudes but similar spectral content around the best frequency of the measurement location. 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 mathematical model to describe how the response at the point of excitation can be traced back to three sources. Surprisingly, the first BM response is due to a fast wave emergent from the point of excitation, reflected by the stapes and then repropagated (in amplified fashion) as a traveling wave back to the point of excitation; the second is due to a reverse, slow, traveling wave, which is likewise reflected at the stapes back to the measurement location by the stapes. The coda is also due to systematic (not random) perturbations of the organ of Corti properties. Implications for normal hearing and for the interpretation of otoacoustic emissions are discussed.

Superior-semicircular-canal dehiscence: Effects of location, shape, and size on sound conduction

The effects of a superior-semicircular-canal (SSC) dehiscence (SSCD) on hearing sensitivity via the air-conduction (AC) and bone-conduction (BC) pathways were investigated using a three-dimensional finite-element (FE) model of a human middle ear coupled to the inner ear. Dehiscences were modeled by removing a section of the outer bony wall of the SSC and applying a zero-pressure condition to the fluid surface thus exposed. At each frequency, the basilar-membrane velocity, vBM, was separately calculated for AC and BC stimulation, under both pre- and post-dehiscence conditions. Hearing loss was calculated as the difference in the maximum magnitudes of vBM between the pre- and post-dehiscence conditions representing a change in hearing threshold. In this study, BC excitations were simulated by applying rigid-body vibrations to the model along the directions of the (arbitrarily defined) x, y, and z axes of the model.Simulation results are consistent with previous clinical measurements on patients with an SSCD and with results from earlier lumped-element electrical-circuit modeling studies, with the dehiscence decreasing the hearing threshold (i.e., increasing vBM) by about 35 dB for BC excitation at low frequencies, while for AC excitation the dehiscence increases the hearing threshold (i.e., decreases vBM) by about 15 dB. A new finding from this study is that the initial width (defined as the width of the edge of the dehiscence where the flow of the fluid-motion wave from the oval window meets it for the first time) on the vestibular side of the dehiscence has more of an effect on vBM than the area of the dehiscence. Analyses of dehiscence effects using the FE model further predict that changing the direction of the BC excitation should have an effect on vBM, with vBM being about 20 dB lower due to BC excitation parallel to the longitudinal direction of the BM in the hook region (the x direction) as compared to excitations in other directions (y and z). BC excitation in the x direction and with a ‘center’ dehiscence located midway along the length of the SSC causes a reduction in the anti-symmetric component of the fluid pressure across the BM, as compared to the other directions of BC excitation, which results in a decrease in vBM at high frequencies.This article is part of a Special Issue entitled “MEMRO 2012”.

Effect of basilar membrane radial velocity profile on fluid coupling in the cochlea

The effects of different radial distributions of basilar membrane velocity on the fluid coupling in the cochlea are studied. Different mode shapes across the width of the basilar membrane, modeled as a beam, are simulated by assuming various boundary conditions. The results suggest that the fluid coupling is insensitive to the resulting differences in mode shape. This validates the assumption commonly made in cochlear models that the fluid coupling can be reasonably well predicted by assuming a single modal shape across the basilar membrane width, even if the exact form of the radial profile is not known.

Subharmonic Distortion in Ear Canal Pressure and Intracochlear Pressure and Motion

When driven at sound pressure levels greater than ~110 dB stimulus pressure level, the mammalian middle ear is known to produce subharmonic distortion. In this study, we simultaneously measured subharmonics in the ear canal pressure, intracochlear pressure, and basilar membrane or round window membrane velocity, in gerbil. Our primary objective was to quantify the relationship between the subharmonics measured in the ear canal and their intracochlear counterparts. We had two primary findings: (1) The subharmonics emerged suddenly, with a substantial amplitude in the ear canal and the cochlea; (2) at the stimulus level for which subharmonics emerged, the pressure in scala vestibuli/pressure in the ear canal amplitude relationship was similar for the subharmonic and fundamental components. These findings are important for experiments and clinical conditions in which high sound pressure level stimuli are used and could lead to confounding subharmonic stimulation.

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.