Elasticity and active force generation of cochlear outer hair cells.

The cochlear outer hair cell is described by a cylindrical membrane model, characterized by area and shear moduli for a passive elastic element and an active tension element dependent on the membrane potential. In passive experiments, these moduli are determined from the pressure-strain relations. The area modulus obtained is 0.07 N m-1, similar to a lipid bilayer and the shear modulus is 0.007 N m-1. These moduli combined with previous active experiments show that the active tension is nearly isotropic and is about 1.6 x 10(-2) N m-1 V-1, resulting in a 0.5 nN/mV force per cell. This implies that the receptor potential for acoustical stimulation produces an active force comparable to the acoustic force applied to the basilar membrane per outer hair cell. This finding supports the hypothesis that the outer hair cell acts as feedback motor in the fine tuning mechanism of the mammalian ear.     

A comparison between basilar membrane and inner hair cell receptor potential input-output functions in the guinea pig cochlea

Intracellular recordings were made from inner hair cells and basilar membrane motion was measured at a similar place, but in different preparations, in the first turn of the guinea pig cochlea. Potential recordings were made using glass microelectrodes and mechanical measurements were made using the M?ssbauer technique. Intensity functions of DC receptor potential and basilar membrane velocity in animals with good and poor thresholds are presented. In animals with good thresholds, stimuli at and above the characteristic frequency produce similarly compressive input-output functions for both inner hair cell receptor potentials and basilar membrane motion. However, for frequencies lower than the characteristic frequency, receptor potential input-output functions obtained from animals in good and poor condition show saturation at high stimulus intensities at which basilar membrane motion is linear. This discrepancy is believed to be due to a nonlinear inner hair cell transduction mechanism. We propose that nonlinearity observed in receptor potential input-output functions is a consequence of the simple cascading of a frequency-dependent nonlinear mechanical input and a frequency-independent nonlinear transduction process.     

Modelling of some mechanical malfunctions of the human basilar membrane

Numerical models of the human basilar membranes (BMs) with 0.4 × 10⁻³ and 2.8 × 10⁻³ m long ruptures and bosses were built and solved using the Finite Element Method. Possible reasons of such structural modifications were described. The models were tested by calculations of typical curves, e.g., input-output functions, isointensity curves, BM velocities and transfer functions. The numerical models predicted main characteristics of the modified BMs showing that all modifications might affect calculated curves in most cases. The results seem to be reasonable and although the models have some limitations, they may by use in further explaining of the BM malfunctions caused by physical changes or damages on the BM.     

Structural implications of basilar membrane compliance measurements

Static point-load measurements of basilar membrane compliance were made in the basal region of the excised guinea pig cochlea. Points on a radial line across the basilar membrane were displaced in one-half micron increments and the force required to maintain each increment recorded. The results are interpreted in terms of the material layers of the basilar membrane and displayed as compliance curves. In addition, a beam model of the basilar membrane, including the arches of Corti and the actual geometry of the pectinate zone, is constructed from anatomical data. The free parameters in this model are the modulus of elasticity of the transverse filaments and the effective spring stiffness of the arches. Compliance curves for the model are generated with a finite element approach and the parameters are obtained by requiring optimal agreement with the experimental measurements. The results show that the separation between fiber layers in the pectinate zone is relevant to the effective moment of inertia of the cross section and that the longitudinal coupling between the heads of the arches provides a rigidity to the arcuate zone not seen in the pectinate zone where longitudinal coupling is minimal. The elastic modulus calculated for the filaments is 1.8 GPa, approximately one-half that of keratin, while the cells and ground substance are five orders of magnitude softer.     

Using acoustic distortion products to measure the cochlear amplifier gain on the basilar membrane.

Most models of the cochlea developed during the last decade have explained frequency selectivity and sensitivity of the cochlea at threshold by the use of power amplification of the acoustic wave on the basilar membrane. This power amplification has been referred to as the cochlear amplifier (CA). In this paper, a method to measure the cochlear amplifier gain as a function of position along the basilar membrane is derived from a simple model. Next, experimental evidence is presented that strongly restricts the properties of these proposed cochlear amplifier models. Specifically, it is shown that small signals generated by mechanical nonlinearities in the basilar membrane motion are not amplified during basilar membrane propagation, contrary to what would be expected from the cochlear amplifier hypotheses. This paper describes a method of measuring the cochlear power gain as a function of frequency and position, from the stapes to within 2 mm of the place corresponding to the frequency being measured. Experimental results in the cat indicate that the total gain of the cochlear amplifier, over the range of positions measured, must be less than 10 dB. The simplest interpretation of the experimental results is that there is no cochlear amplifier. The results suggest that the cochlea must achieve its frequency selectivity by some other means.     

Comparison between otoacoustic and auditory brainstem response latencies supports slow backward propagation of otoacoustic emissions

Experimental measurements of the latency of transient evoked otoacoustic emission and auditory brainstem responses are compared, to discriminate between different cochlear models for the backward acoustic propagation of otoacoustic emissions. In most transmission-line cochlear models otoacoustic emissions propagate towards the base as a slow transverse traveling wave, whereas other models assume fast backward propagation via longitudinal compression waves in the fluid. Recently, sensitive measurements of the basilar membrane motion have cast serious doubts on the existence of slow backward traveling waves associated with distortion product otoacoustic emissions [He et al., Hear. Res. 228, 112-122 (2007)]. On the other hand, recent analyses of "Allen-Fahey" experiments suggest instead that the slow mechanism transports most of the otoacoustic energy [Shera et al., J. Acoust. Soc. Am. 122, 1564-1575 (2007)]. The two models can also be discriminated by comparing accurate estimates of the otoacoustic emission latency and of the auditory brainstem response latency. In this study, this comparison is done using human data, partly original, and partly from the literature. The results are inconsistent with fast otoacoustic propagation, and suggest that slow traveling waves on the basilar membrane are indeed the main mechanism for the backward propagation of the otoacoustic energy.     

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.     

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.     

Effect of coiling in a cochlear model

Transformation of the three-dimensional equations of fluid motion into cylindrical coordinates allowed analysis of a coiled cochlear model by the WKB technique. The model includes a single transverse mode of basilar membrane deflection and inviscid fluid. The results calculated using realistic parameters for the guinea pig show no significant difference in the basilar membrane amplitude and phase between the straight and coiled models. Some differences exist in the fluid pressure found in the scala. The conclusion is that the macromechanical response is not significantly affected by coiling.     

A comparison of various nonlinear models of cochlear compression

The vibration response of the basilar membrane in the cochlea to sinusoidal excitation displays a compressive nonlinearity, conventionally described using an input-output level curve. This displays a slope of 1 dB/dB at low levels and a slope m < 1 dB/dB at higher levels. Two classes of nonlinear systems have been considered as models of this response, one class with static power-law nonlinearity and one class with level-dependent properties (using either an automatic gain control or a Van der Pol oscillator). By carefully choosing their parameters, it is shown that all models can produce level curves that are similar to those measured on the basilar membrane. The models differ, however, in their distortion properties, transient responses, and instantaneous input-output characteristics. The static nonlinearities have a single-valued instantaneous characteristic that is the same at all input levels. The level-dependent systems are multi-valued with an almost linear characteristic, for a given amplitude of excitation, whose slope varies with the excitation level. This observation suggests that historical attempts to use functional modeling (i.e., Wiener of Volterra series) may be ill founded, as these methods are unable to represent level-dependent nonlinear systems with multi-valued characteristics of this kind.     

Three-dimensional numerical modeling for global cochlear dynamics

A hybrid analytical-numerical model using Galerkin approximation to variational equations has been developed for predicting global cochlear responses. The formulation provides a flexible framework capable of incorporating morphologically based mechanical models of the cochlear partition and realistic geometry. The framework is applied for a simplified model with an emphasis on application of hybrid methods for three-dimensional modeling. The resulting formulation is modular, where matrices representing fluid and cochlear partition are constructed independently. Computational cost is reduced using two methods, a modal-finite-element method and a boundary element-finite-element method. The first uses a cross-mode expansion of fluid pressure (2.5D model) and the second uses a waveguide Green's-function-based boundary element method (BEM). A novel wave number approach to the boundary element formulation for interior problem results in efficient computation of the finite-element matrix. For the two methods a convergence study is undertaken using a simplified passive structural model of cochlear partition. It is shown that basilar membrane velocity close to best place is influenced by fluid and structural discretization. Cochlear duct pressure fields are also shown demonstrating the 3D nature of pressure near best place.     

Realistic mechanical tuning in a micromechanical cochlear model

Two assumptions were made in the formulation of a recent cochlear model [P.J. Kolston, J. Acoust. Soc. Am. 83, 1481-1487 (1988)]: (1) The basilar membrane has two radial modes of vibration, corresponding to division into its arcuate and pectinate zones; and (2) the impedance of the outer hair cells (OHCs) greatly modifies the mechanics of the arcuate zone. Both of these assumptions are strongly supported by cochlear anatomy. This paper presents a revised version of the outer hair cell, arcuate-pectinate (OHCAP) model, which is an improvement over the original model in two important ways: First, a model for the OHCs is included so that the OHC impedance is no longer prescribed functionally; and, second, the presence of the OHCs enhances the basilar membrane motion, so that the model is now consistent with observed response changes resulting from trauma. The OHCAP model utilizes the unusual spatial arrangement of the OHCs, the Deiters cells, their phalangeal processes, and the pillars of Corti. The OHCs do not add energy to the cochlear partition and hence the OHCAP model is passive. In spite of the absence of active processes, the model exhibits mechanical tuning very similar to those measured by Sellick et al. [Hear. Res. 10, 93-100 (1983)] in the guinea pig cochlea and by Robles et al. [J. Acoust. Soc. Am. 80, 1364-1374 (1986)] in the chinchilla cochlea. Therefore, it appears that mechanical response tuning and response changes resulting from trauma should not be used as justifications for the hypothesis of active processes in the real cochlea.     

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.     

Nonlinear and active two-dimensional cochlear models: time-domain solution

A numerical solution method for two-dimensional (2-D) cochlear models in the time domain is presented. The method has particularly been designed for models with a cochlear partition having nonlinear and active mechanical properties. The 2-D cochlear model equations are reformulated as an integral equation for the acceleration of the basilar membrane (BM). This integral equation is discretized with respect to the spatial variable to yield a system of ordinary differential equations in the time variable. To solve this system, the variable step-size, fourth-order Runge-Kutta method described in Diependaal et al. [J. Acoust. Soc. Am. 82, 1655-1666 (1987)] is used. This method is robust and computationally efficient. The incorporation of a simple middle-ear model can be handled by this method. The method can also be extended to models in which the cochlear partition at each point along its length is represented by more than one degree of freedom.     

Distortion products and backward-traveling waves in nonlinear active models of the cochlea

This study explores the phenomenology of distortion products in nonlinear cochlear models, predicting their amplitude and phase along the basilar membrane. The existence of a backward-traveling wave at the distortion-product frequency, which has been recently questioned by experiments measuring the phase of basilar-membrane vibration, is discussed. The effect of different modeling choices is analyzed, including feed-forward asymmetry, micromechanical roughness, and breaking of scaling symmetry. The experimentally observed negative slope of basilar-membrane phase is predicted by numerical simulations of nonlinear cochlear models under a wide range of parameters and modeling choices. In active models, positive phase slopes are predicted by the quasi-linear analytical computations and by the fully nonlinear numerical simulations only if the distortion-product sources are localized apical to the observation point and if the stapes reflectivity is unrealistically small. The results of this study predict a negative phase slope whenever the source is distributed over a reasonably wide cochlear region and/or a reasonably high stapes reflectivity is assumed. Therefore, the above-mentioned experiments do not contradict "classical" models of cochlear mechanics and of distortion-product generation.     

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.     

Prediction of the characteristics of two types of pressure waves in the cochlea: theoretical considerations

The aim of this study was to predict the characteristics of two types of cochlear pressure waves, so-called fast and slow waves. A two-dimensional finite-element model of the organ of Corti (OC), including fluid-structure interaction with the surrounding lymph fluid, was constructed. The geometry of the OC at the basal turn was determined from morphological measurements of others in the gerbil hemicochlea. As far as mechanical properties of the materials within the OC are concerned, previously determined mechanical properties of portions within the OC were adopted, and unknown mechanical features were determined from the published measurements of static stiffness. Time advance of the fluid-structure scheme was achieved by a staggered approach. Using the model, the magnitude and phase of the fast and slow waves were predicted so as to fit the numerically obtained pressure distribution in the scala tympani with what is known about intracochlear pressure measurement. When the predicted pressure waves were applied to the model, the numerical result of the velocity of the basilar membrane showed good agreement with the experimentally obtained velocity of the basilar membrane documented by others. Thus, the predicted pressure waves appeared to be reliable. Moreover, it was found that the fluid-structure interaction considerably influences the dynamic behavior of the OC at frequencies near the characteristic frequency.     

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.     

On active and passive cochlear models--toward a generalized analysis

Simple cochlear models can show a peak in their response but only of a limited magnitude. The constraints limiting the size of this peak are studied in this note, for the short-wave as well as the long-wave case. It is found that a sharply rising response is impossible in a model in which the basilar membrane can only absorb acoustical energy. To attain a model response that is comparable to the response found in the most recent experiments, the basilar membrane must be assumed to be capable of adding acoustic energy to the fluid waves.     

A nonlinear filter-bank model of the guinea-pig cochlear nerve: rate responses

The aim of this study is to produce a functional model of the auditory nerve (AN) response of the guinea-pig that reproduces a wide range of important responses to auditory stimulation. The model is intended for use as an input to larger scale models of auditory processing in the brain-stem. A dual-resonance nonlinear filter architecture is used to reproduce the mechanical tuning of the cochlea. Transduction to the activity on the AN is accomplished with a recently proposed model of the inner-hair-cell. Together, these models have been shown to be able to reproduce the response of high-, medium-, and low-spontaneous rate fibers from the guinea-pig AN at high best frequencies (BFs). In this study we generate parameters that allow us to fit the AN model to data from a wide range of BFs. By varying the characteristics of the mechanical filtering as a function of the BF it was possible to reproduce the BF dependence of frequency-threshold tuning curves, AN rate-intensity functions at and away from BF, compression of the basilar membrane at BF as inferred from AN responses, and AN iso-intensity functions. The model is a convenient computational tool for the simulation of the range of nonlinear tuning and rate-responses found across the length of the guinea-pig cochlear nerve.