Outer hair cell active force generation in the cochlear environment

Outer hair cells are critical to the amplification and frequency selectivity of the mammalian ear acting via a fine mechanism called the cochlear amplifier, which is especially effective in the high-frequency region of the cochlea. How this mechanism works under physiological conditions and how these cells overcome the viscous (mechanical) and electrical (membrane) filtering has yet to be fully understood. Outer hair cells are electromotile, and they are strategically located in the cochlea to generate an active force amplifying basilar membrane vibration. To investigate the mechanism of this cell's active force production under physiological conditions, a model that takes into account the mechanical, electrical, and mechanoelectrical properties of the cell wall (membrane) and cochlear environment is proposed. It is shown that, despite the mechanical and electrical filtering, the cell is capable of generating a frequency-tuned force with a maximal value of about 40 pN. It is also found that the force per unit basilar membrane displacement stays essentially the same (40 pNnm) for the entire linear range of the basilar membrane responses, including sound pressure levels close to hearing threshold. Our findings can provide a better understanding of the outer hair cell's role in the cochlear amplifier.     

What type of force does the cochlear amplifier produce?

Recent experimental measurements suggest that the mechanical displacement of the basilar membrane (BM) near threshold in a viable mammalian cochlea is greater than 10(-8) cm, for a stimulus sound-pressure level at the eardrum of 20 microPa. The associated response peak is very sensitive to the physiological condition of the cochlea. In the formulation of all recent cochlear models, it has been explicitly assumed that this peak is produced by the cochlear amplifier injecting a large amount of energy into the cochlea, thereby altering the real component of the BM impedance. In this paper, a new cochlear model is described which produces a realistic response by assuming that the cochlear amplifier force acts at a phase such that the main effect is to reduce the imaginary component of the BM impedance. In this new model, the magnitude of the cochlear amplifier force required to produce a realistic response is much smaller than in the previous models. It is suggested that future experimental investigations should attempt to determine both the magnitude and the phase of the forces associated with the cochlear amplifier.     

New Evidence of Active Tuning in Cochlea

The wonderful performance of hearing systems is mainly attributed to the tuning tiltering of basilar membrane （BM）. Although theory of the cochlear mechanism has been greatly developed since the 1970s and the amplification or sensitivity of the cochlea has been concluded due to the out hair cells, the mechanics underlying the sharp-tuning or frequency selectivity of cochlea remains a puzzle. We use the cochlear translation function derived from the data of an experiment of the BM in vivo to calculate basilar responses to tone bursts, and find that there are resonant peaks with the characteristic frequency at the corresponding place in the initial and terminal part of the responses. However, when the translation function is shallower, there will be no resonant peaks in the responses. The result indicates that the sharp tuning is due to existence of the active resonant tuning mechanism.     

A Brownian energy depot model of the basilar membrane oscillation with a braking mechanism

High auditory sensitivity, sharp frequency selectivity, and spontaneous otoacoustic emissions are signatures of active amplification of the cochlea. The human ear can also detect very large amplitude sounds without being damaged, as long as the exposed time is not too long. The outer hair cells are believed to be the best candidate for the active force generator of the mammalian cochlea. In this paper, we propose a new model for the basilar membrane oscillation which describes both an active and a protective mechanism by employing an energy depot concept and a critical velocity of the basilar membrane. The compressive response of the basilar membrane at the characteristic frequency and the dynamic response to the stimulation are consistent with the experimental results. Although our model displays a Hopf bifurcation, our braking mechanism results in a hyper-compressive response to intense stimuli which is not generically observed near a Hopf bifurcation. Asymmetry seen in experimental recordings between the onset and the offset of the basilar membrane response to a sound burst is also observed in this model.     

Essential Role of Couplings between Hearing Nonlinearities

Hopf-type nonlinearities have been recently found to be the basic mechanism of the mammalian cochlear response. Physiology requires that these nonlinearities be coupled. By suitably implementing a biomorphic coupling scheme of cochlear nonlinearities, we obtain a simple cochlea model that faithfully reproduces measured basilar membrane response, validating the utility of the Hopf amplifier concept. Our results demonstrate that the correct coupling between nonlinearities is as important as the nonlinearities themselves.     

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

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

Finite element cochlear models and their steady state response

Numerical cochlear models are constructed by means of a finite element approach and their frequency and spatial responses are calculated. The cochlea is modelled as a coupled fluid-membrane system, for which both two- and three-dimensional models are considered. The fluid in the scala canals is assumed to be incompressible and the basilar membrane is assumed to be a locally reactive impedance wall or a lossy elastic membrane. With the three-dimensional models, the effects are examined of the spiral configuration of the cochlea, of the presence of the lamina and the ligament that narrows the coupling area between the two fluid canals (scala vestibuli and scala tympani), and of the extended reaction of the basilar membrane which cannot be included in case of the two-dimensional models. The conclusion is that these effects on the cochlear response and the inherent mechanism governing the cochlear behaviour are found to be rather secondary.     

Cochlear compression wave: an implication of the Allen-Fahey experiment

In order to measure the gain of the cochlear amplifier, de Boer and co-workers recently extended the Allen-Fahey experiment by measuring otoacoustic emissions and basilar membrane vibration [J. Acoust. Soc. Am. 117, 1260-1266 (2005)]. Although this new experiment overcame the limitation of the original Allen-Fahey experiment for using a low-frequency ratio, it confirmed the previous finding that there is no detectable cochlear amplification. This result was attributed to destructive interference of the otoacoustic emission over its generation site. The present letter provides an alternative interpretation of the results of the Allen-Fahey experiment based on the cochlear fluid compression-wave theory.     

Study of mechanical motions in the basal region of the chinchilla cochlea

Measurements from the 1-4-mm basal region of the chinchilla cochlea indicate the basilar membrane in the hook region (12-18 kHz) vibrates essentially as it does more apically, in the 5-9-kHz region. That is, a compressive nonlinearity in the region of the characteristic frequency, amplitude-dependent phase changes, and a gain relative to stapes motion that can attain nearly 10,000 at low levels. The displacement at threshold for auditory-nerve fibers in this region (20 dB SPL) was approximately 2 nm. Measurements were made at several locations in individual animals in the longitudinal and radial directions. The results indicate that there is little variability in the phase of motion radially and no indication of higher-order modes of vibration. The data from the longitudinal studies indicate that there is a shift in the location of the maximum with increasing stimulus levels toward the base. The cochlear amplifier extends over a 2-3-mm region around the location of the characteristic frequency.     

A parametric study of cochlear input impedance

In this paper various aspects of the cat cochlear input impedance Zc (omega) are implemented using a transmission line model having perilymph viscosity and a varying cross-sectional scalae area. These model results are then compared to the experimental results of Lynch et al. [J. Acoust. Soc. Am. 72, 108-130 (1982)]. From the model, the following observations are made about the cochlear input impedance: (a) Scalae area variations significantly alter the model Zc (omega); (b) the use of anatomically measured area improves the fits to the experimental data; (c) improved agreement between model and experimental phase is obtained when perilymph viscosity and tapering are included in the cochlear model for frequencies below approximately 150 Hz; (d) when model scalae tapering and perilymph viscosity are chosen to match physiological conditions, the effect of the helicotrema impedance on Zc (omega) is insignificant; and (e) the cochlear map, which is defined as the position of the basilar membrane peak displacement as a function of stimulus frequency, can have an important effect on Zc (omega) for frequencies below 500 Hz. A nonphysiological cochlear map can give rise to cochlear standing waves, which result in oscillations in Zc (omega). Scalae tapering and perilymph viscosity contribute significantly to the damping of these standing waves. These observations should dispel the previous notion that Zc (omega) is determined solely by parameters of the cochlea close to the stapes, and the notion that Zc (omega) is dominated by the helicotrema at low frequencies.     

A hydromechanical biomimetic cochlea: experiments and models

The construction, measurement, and modeling of an artificial cochlea (ACochlea) are presented in this paper. An artificial basilar membrane (ABM) was made by depositing discrete Cu beams on a piezomembrane substrate. Rather than two fluid channels, as in the mammalian cochlea, a single fluid channel was implemented on one side of the ABM, facilitating the use of a laser to detect the ABM vibration on the other side. Measurements were performed on both the ABM and the ACochlea. The measurement results on the ABM show that the longitudinal coupling on the ABM is very strong. Reduced longitudinal coupling was achieved by cutting the membrane between adjacent beams using a laser. The measured results from the ACochlea with a laser-cut ABM demonstrate cochlear-like features, including traveling waves, sharp high-frequency rolloffs, and place-specific frequency selectivity. Companion computational models of the mechanical devices were formulated and implemented using a circuit simulator. Experimental data were compared with simulation results. The simulation results from the computational models of the ABM and the ACochlea are similar to their experimental counterparts.     

One source for distortion product otoacoustic emissions generated by low- and high-level primaries

Distortion product otoacoustic emissions (DPOAE) elicited by tones below 60-70 dB sound pressure level (SPL) are significantly more sensitive to cochlear insults. The vulnerable, low-level DPOAE have been associated with the postulated active cochlear process, whereas the relatively robust high-level DPOAE component has been attributed to the passive, nonlinear macromechanical properties of the cochlea. However, it is proposed that the differences in the vulnerability of DPOAEs to high and low SPLs is a natural consequence of the way the cochlea responds to high and low SPLs. An active process boosts the basilar membrane (BM) vibrations, which are attenuated when the active process is impaired. However, at high SPLs the contribution of the active process to BM vibration is small compared with the dominating passive mechanical properties of the BM. Consequently, reduction of active cochlear amplification will have greatest effect on BM vibrations and DPOAEs at low SPLs. To distinguish between the "two sources" and the "single source" hypotheses we analyzed the level dependence of the notch and corresponding phase discontinuity in plots of DPOAE magnitude and phase as functions of the level of the primaries. In experiments where furosemide was used to reduce cochlear amplification, an upward shift of the notch supports the conclusion that both the low- and high-level DPOAEs are generated by a single source, namely a nonlinear amplifier with saturating I/O characteristic.     

Allen-Fahey and related experiments support the predominance of cochlear slow-wave otoacoustic emissions

Originally proposed as a method for measuring the power gain of the cochlear amplifier, Allen-Fahey experiments compare intracochlear distortion products and ear-canal otoacoustic emissions (OAEs) under tightly controlled conditions. In this paper Allen-Fahey experiments are shown to place significant constraints on the dominant mode of reverse energy propagation within the cochlea. Existing Allen-Fahey experiments are reviewed and shown to contradict the predictions of compression-wave OAE models recently proposed in the literature. In compression-wave models, distortion products propagate from their site of generation to the stapes via longitudinal compression waves in the cochlear fluids (fast waves); in transverse traveling-wave models, by contrast, distortion products propagate primarily via pressure-difference waves whose velocity and other characteristics depend on the mechanical properties of the cochlear partition (slow waves). Compression-wave models predict that the distortion-product OAEs (DPOAEs) measured in the Allen-Fahey paradigm increase at close primary-frequency ratios (or remain constant in the hypothetical absence of tuned suppression). The behavior observed experimentally is just the opposite-a pronounced decrease in DPOAE amplitude at close ratios. Since neither compression-wave nor simple conceptual "hybrid-wave" models can account for the experimental results--whereas slow-wave models can, via systematic changes in distortion-source directionality arising from wave-interference effects--Allen-Fahey and related experiments provide compelling evidence against the predominance of compression-wave OAEs in mammalian cochlear mechanics.     

Further studies on the dual-resonance nonlinear filter model of cochlear frequency selectivity: responses to tones

A number of phenomenological models that simulate the response of the basilar membrane motion can reproduce a range of complex features observed in animal measurements over different sites along its cochlea. The present report shows a detailed analysis of the responses to tones of an improved model based on a dual-resonance nonlinear filter. The improvement consists in adding a third path formed by a linear gain and an all-pass filter. This improvement allows the model to reproduce the gain and phase plateaus observed empirically at frequencies above the best frequency. The middle ear was simulated by using a digital filter based on the empirical impulse response of the chinchilla stapes. The improved algorithm is evaluated against observations of basilar membrane responses to tones at seven different sites along the chinchilla cochlear partition. This is the first time that a whole set of animal observations using the same technique has been available in one species for modeling. The resulting model was able to simulate amplitude and phase responses to tones from basal to apical sites. Linear regression across the optimized parameters for seven different sites was used to generate a complete filterbank.     

Suppression of distortion product otoacoustic emissions and hearing threshold

A distortion product otoacoustic emission (DPOAE) suppression tuning curve (STC) shows the minimum level of suppressor tone that is required to reduce DPOAE level by a fixed amount, as a function of suppressor frequency. Several years ago, Mills [J. Acoust. Soc. Am. 103, 507-523 (1998)] derived, theoretically, an approximately linear relationship between the tip-to-tail suppressor level difference on a DPOAE STC, and the gain of the cochlear amplifier, defined as the maximum increase in the active over the passive basilar membrane (BM) response. In this paper, preliminary data from adult human subjects are presented that establish a correlation between this tip-to-tail DPOAE STC difference and the threshold of hearing, the latter measured at the frequency of the f2 primary tone. Assuming that both suppression and the DPOAE are by-products of active, nonlinear BM dynamics, the above result suggests that threshold elevation in mild levels of hearing loss may be attributed, in part, to a reduction of cochlear amplifier gain, which is detectable with the suppression paradigm.     

The mechanical waveform of the basilar membrane. II. From data to models--and back

Mechanical responses in the basal turn of the guinea-pig cochlea are measured with low-level broad-band noise as the acoustical stimulus [for details see de Boer and Nuttall, J. Acoust. Soc. Am. 101, 3583-3592 (1997)]. Results are interpreted within the framework of a classical three-dimensional model of the cochlea that belongs to a very wide class of nonlinear models. The use of linear-systems analysis for this class of nonlinear models has been justified earlier [de Boer, Audit. Neurosci. 3, 377-388 (1997)]. The data are subjected to inverse analysis with the aim to recover the "effective basilar-membrane impedance." This is a parameter function that, when inserted into the model, produces a model response, the "resynthesized" response, that is similar to the measured response. With present-day solution methods, resynthesis leads back to an almost perfect replica of the original response in the spatial domain. It is demonstrated in this paper that this also applies to the response in the frequency domain and in the time domain. This paper further reports details with regard to geometrical properties of the model employed. Two three-dimensional models are studied; one has its dimensions close to that of the real cochlea, the other is a stylized model which has homogeneous geometry over its length. In spite of the geometric differences the recovered impedance functions are very similar. An impedance function computed for one model can be used in resynthesis of the response in the other one, and this leads to global amplitude deviations between original and resynthesized response functions not exceeding 8 dB. Discrepancies are much larger (particularly in the phase) when a two-dimensional model is compared with a three-dimensional model. It is concluded that a stylized three-dimensional model with homogeneous geometric parameters will give sufficient information in further work on unraveling cochlear function via inverse analysis. In all cases of a sensitive cochlea stimulated by a signal with a stimulus level of 50 dB SPL per octave or less, the resulting basilar-membrane impedance is found to be locally active, that is, the impedance function shows a region where the basilar membrane is able to amplify acoustic power or to reduce dissipation of power by the organ of Corti. Finally, the influence of deliberate errors added to the data is discussed in order to judge the accuracy of the results.     

No sharpening? a challenge for cochlear mechanics

Recent data on mechanical movements of the basilar membrane (BM) suggest that the part played in cochlear physiology by a sharpening mechanism is much less important than hitherto has been thought. In an extreme view, one could dispense with a sharpening mechanism completely and assume that (near the threshold) hair-cell excitation is proportional to BM velocity, or a very simple linear transform of it. In the present paper the consequences of this idea are worked out. A theoretical cochlear movement pattern is constructed that shows the same frequency selectivity as an average reverse-correlation function of an auditory nerve fiber. This response is called a revcor-spectrumlike response. Cochlear mechanics is then simplified to a pure shortwave model. It is shown that, if the cochlea model should present a revcor-spectrumlike response, this can only be achieved when the resistance component of the BM impedance is negative over a part of the length of the cochlea. This result is refined in several respects, and it is shown that a model equipped with the right kind of BM impedance function can have a response of the required type. It remains difficult to conceive of a physiological mechanism that would cause the desired effect on the BM impedance.     

Nonlinear interactions that could explain distortion product interference response areas

Suppression and/or enhancement of third- and fifth-order distortion products by a third tone that can have a frequency more than an octave above and a level more than 40 dB below the primary tones have recently been measured by Martin et al. [Hear. Res. 136, 105-123 (1999)]. Contours of iso-suppression and iso-enhancement that are plotted as a function of third-tone frequency and level are called interference response areas. After ruling out order aliasing, two possible mechanisms for this effect have been developed, a harmonic mechanism and a catalyst mechanism. The harmonic mechanism produces distortion products by mixing a harmonic of one of the primary tones with the other primary tone. The catalyst mechanism produces distortion products by mixing one or more intermediate distortion products that are produced by the third tone with one or more of the input tones. The harmonic mechanism does not need a third tone and the catalyst mechanism does. Because the basilar membrane frequency response is predicted to affect each of these mechanisms differently, it is concluded that the catalyst mechanism will be dominant in the high-frequency regions of the cochlea and the harmonic mechanism will have significant strength in the low-frequency regions of the cochlea. The mechanisms are dependent on the existence of both even- and odd-order distortion, and significant even- and odd-order distortion have been measured in the experimental animals. Furthermore, the nonlinear part of the cochlear mechanical response must be well into saturation when input tones are 50 or more dB SPL.     

Basilar membrane tension calculations for the gerbil cochlea

Anatomical studies suggest that the basilar membrane (BM) supports a radial tension, which is potentially important in cochlear mechanics. Assuming that the tension exists, we have calculated its magnitude from measurements of BM stiffness, longitudinal coupling, and geometry using a BM model. Results for the gerbil cochlea show that the tension decreases from the base to the apex of the cochlea and generates a tensile stress that is comparable in magnitude to the stress generated in other physiological systems. The model calculations are augmented by experiments that investigate the source of BM tension. The experimental results suggest that BM tension is maintained by the spiral ligament.