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.     

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.     

Longitudinal endolymph movements and endocochlear potential changes induced by stimulation at infrasonic frequencies.

The inner ear is continually exposed to pressure fluctuations in the infrasonic frequency range (< 20 Hz) from external and internal body sources. The cochlea is generally regarded to be insensitive to such stimulation. The effects of stimulation at infrasonic frequencies (0.1 to 10 Hz) on endocochlear potential (EP) and endolymph movements in the guinea pig cochlea were studied. Stimuli were applied directly to the perilymph of scala tympani or scala vestibuli of the cochlea via a fluid-filled pipette. Stimuli, especially those near 1 Hz, elicited large EP changes which under some conditions exceeded 20 mV in amplitude and were equivalent to a cochlear microphonic (CM) response. Accompanying the electrical responses was a cyclical, longitudinal displacement of the endolymph. The amplitude and phase of the CM varied according to which perilymphatic scala the stimuli were applied to and whether a perforation was made in the opposing perilymphatic scala. Spontaneously occurring middle ear muscle contractions were also found to induce EP deflections and longitudinal endolymph movements comparable to those generated by perilymphatic injections. These findings suggest that cochlear fluid movements induced by pressure fluctuations at infrasonic frequencies could play a role in fluid homeostasis in the normal state and in fluid disturbances in pathological states.     

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.     

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.     

Comparison of WKB calculations and experimental results for three-dimensional cochlear models.

The WKB asymptotic method is applied to the calculation of cochlear models with square scala cross section, for which the fluid motion is fully three dimensional. The analysis begins with the exact solution for wave propagation in a duct with constant properties. This solution is somewhat tedious but straightforward, since it requires a Fourier series expansion across the duct. Then with the formulation of Whitham [Linear and Nonlinear Waves (Wiley, New York, 1974)], the approximate solution is readily generated for the duct with properties which vary slowly along the length. Numerical calculations are carried out for the experimental models of Cannel [Ph.D. thesis, Univ. of Warwick (1969)] and Helle [Dr.-Ing. disser., Technische Univ., Müchen (1974)] who furnish quantitative details of both "basilar membrane" response and model parameters. Without any free parameters for adjusting, the present WKB solution shows quite satisfactory agreement with the experimental model results. Computer time is reasonable; the calculation of displacement envelope and phase at a number of stations along the cochlea for a given frequency requires only one second of CPU time. Thus the credibility and practically of the approach is established for the investigation of yet more realistic and more elaborate cochlear models.     

Mechanical passive and active models of the human basilar membrane

Simple three-dimensional passive and active models of the human basilar membrane were built, solved using the Finite Element Method and tested. In the active model an active mechanism connected with electromotility of outer hair cells was included. In the active model the active mechanism was incorporated in the form of additional, local pressure load. In the passive model the active mechanism was neglected. Hydrodynamic coupling between the cochlear partition and cochlear fluid was excluded in both models. Geometrical and physical parameters of the model were chosen to be adequate to those of humans in the best possible way. However, some of these parameters had to be estimated. The models were tested by calculation of typical curves known from cochlear measurements performed mostly on animals. For the passive model a linear input-output function and very small values of the basilar membrane velocities were obtained. This behaviour is to be expected for the passive model and for the basilar membrane in the poor physiological condition. For the active model the compressed input-output functions, tuning curves, isointensity curves and reasonable BM velocities were obtained. Possible inadequacies, which could explain the differences between numerical results and measurements were described.     

Differential electrical excitation of the auditory nerve

The multichannel cochlear prosthesis requires an electrode stimulus configuration which produces a stimulus field spatially localized to each electrode. In this paper, a three-dimensional discrete resistance model of the cochlea was developed which exhibits electrical response properties similar to those observed during electrical stimulation of the cochlea. The model results suggest that the spatial attenuation of current within the cochlea varies greatly in magnitude, depending on the stimulus configuration. In addition, the model suggests that the spatial attenuation of current in both the auditory nerve fiber endings in the organ of Corti and in the myelinated fibers within the cochlear ground paths is different from the voltage attenuation in the scalar fluids. Therefore the efficacy with which a particular stimulus configuration differentially excites local terminal auditory nerve fiber populations cannot be deduced from scalar voltage measurements which have previously been recorded in the literature. Consequently physiological experiments were performed in the cat to measure the current distributions in the terminal nerve fiber region for monopolar and bipolar stimulation of the scala tympani, and also for stimulation between the scala tympani and the scala vestibuli. The mean length constants measured in the basal turn for these stimuli were found to be 12, 3, and 7.5 mm, respectively.     

Cochlear mechanics: analysis for a pure tone

A three-dimensional hydroelastic model of the cochlea is analyzed, in which the fluid is viscous and the basilar membrane is an inhomogeneous orthotropic elastic plate. After the solution is obtained using a multiple-scale approximation, comparison is made with experiment for the human cochlea.     

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.     

Intracochlear pressure and derived quantities from a three-dimensional model

Intracochlear pressure is calculated from a physiologically based, three-dimensional gerbil cochlea model. Olson [J. Acoust. Soc. Am. 103, 3445-3463 (1998); 110, 349-367 (2001)] measured gerbil intracochlear pressure and provided approximations for the following derived quantities: (1) basilar membrane velocity, (2) pressure across the organ of Corti, and (3) partition impedance. The objective of this work is to compare the calculations and measurements for the pressure at points and the derived quantities. The model includes the three-dimensional viscous fluid and the pectinate zone of the elastic orthotropic basilar membrane with dimensional and material property variation along its length. The arrangement of outer hair cell forces within the organ of Corti cytoarchitecture is incorporated by adding the feed-forward approximation to the passive model as done previously. The intracochlear pressure consists of both the compressive fast wave and the slow traveling wave. A Wentzel-Kramers-Brillowin asymptotic and numerical method combined with Fourier series expansions is used to provide an efficient procedure that requires about 1 s to compute the response for a given frequency. Results show reasonably good agreement for the direct pressure and the derived quantities. This confirms the importance of the three-dimensional motion of the fluid for an accurate cochlear model.     

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.     

Two-dimensional analysis of fluid motion in the cochlea resulting from compressional bone conduction

Fluid motion resulting from the compressional excitation of the cochlear capsule due to bone conduction is examined in this paper. Vibrations of the skull deform the shape of the cochlear capsule and give rise to motion the fluid. A two-dimensional channel having a height to length ratio equal to ε is used to model the cochlea. The cochlear pressure is expressed as an integral equation in the cochlear partition velocity. In the limit as ε approaches zero the integral equation is solved and the cochlear pressure is expressed as an asymptotic expansion in ε. Rapid spatial variation in the velocity of the cochlear partition requires one to treat high-order fluid modes within the cochlear fluid. Hence, evanescent pressure modes are included in the analysis. Asymmetry in the oval and the round window velocity is shown to give rise to a pressure gradient across the cochlear partition and basilar membrane displacement. The vibration amplitude of the cochlear partition is shown to depend on the value of the ratio of the oval and the round window impedance.     

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.     

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.     

The application of a capacitive probe technique for direct observation of electromechanical processes in the guinea pig cochlea

The demonstration of evoked mechanical responses of the outer hair cells in the mammalian cochlea by indirect measurements introduces a new range of problems into direct mechanical measurements. Direct and indirect measurements indicate that the frequency spectra of evoked electromechanical responses may extend well into the range of audio frequencies, revealing a need to develop terminology and protocols for distinguishing evoked mechanical responses from the traditional traveling wave when both are apparently superimposed on the motion of the basilar membrane in the normally functioning cochlea. Details are presented of a frequency-modulation capacitive probe technique for measurement of vibrating structures of the guinea pig ear. Considerations include the design of the transducer, calibration, sensitivity, linearity, and sources of noise, as well as the influence of the technique upon the animal preparation, and in particular the issues associated with draining scala tympani for the measurement. Relative advantages and disadvantages of the technique are compared with salient features of other techniques currently available. In view of the apparent complexity of cochlear mechanics some preliminary experiments are required to elucidate some of the key questions about reverse-transduction processes in general. A "simple" first experiment is to test existence of any rectifying or motile response.     

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.     

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.     

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.