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.     

Distortion product otoacoustic emission (2f1-f2) amplitude growth in human adults and neonates

Distortion product otoacoustic emissions (DPOAEs) are thought to be by-products of an active amplification process in the cochlea and thus serve as a metric for evaluating the integrity of this process. Because the cochlear amplifier functions in a level-dependent fashion, DPOAEs recorded as a function of stimulus level (i.e., a DPOAE growth function) may provide important information about the range and operational characteristics of the cochlear amplifier. The DPOAE growth functions recorded in human adults and neonates may provide information about the maturation of these active cochlear processes. Two experiments were conducted. Experiment I included normal-hearing adults and term-born neonates. The 2f1-f2 DPOAE growth functions were recorded for both age groups at three f2 frequencies. Experiment II was an extension of the first experiment but added a subject group of premature neonates. The results of these studies indicate that DPOAE growth functions most often show amplitude saturation and nonmonotonic growth for all age groups. However, premature neonates show monotonic growth and the absence of amplitude saturation more often than adults. Those premature neonates who do show saturation also show an elevated threshold for amplitude saturation relative to adults. In contrast, term neonates are adultlike for most measures except that they show a larger percentage of nonsaturating growth functions than adults. These results may indicate immaturity in cochlear amplifier function prior to term birth in humans. Outer hair cell function and/or efferent regulation of outer hair cell function are hypothesized sources of this immaturity, although some contribution from the immature middle ear cannot be ruled out.     

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 cochlear model for acoustic emissions

Variability in cochlear emission properties among different species, particularly humans and small mammals, and within individuals in the same species, is modeled by a cochlear nonlinear transmission line. The difference between humans and animals is largely explained by a lower cochlear input impedance in human ears than in cats, gerbils, or chinchillas. Inconstancy in emission properties among individual human or animal subjects is related to structural variability among ears, which can be the result of a nonuniform connection between the outer hair cells cilia and the tectorial membrane. These structural differences are modeled by a nonuniform cochlear partition resistance along the cochlear length. The model predicts that an ear which has a uniform cochlear partition resistance and an adequate cochlear input impedance will emit acoustic distortion products (ADP), but not spontaneous acoustic emission (SAE), nor click-evoked emission (CE). Only a nonuniform cochlea emits SAE and CE in addition to enhanced ADPs. The model predictions agree quantitatively with cochlear emission data from humans and animals.     

The cochlear amplifier as a standing wave: "squirting" waves between rows of outer hair cells?

This paper draws attention to symmetric Lloyd-Redwood (SLR) waves-known in ultrasonics as "squirting" waves-and points out that their distinctive properties make them well-suited for carrying positive feedback between rows of outer hair cells. This could result in standing-wave resonance-in essence a narrow-band cochlear amplifier. Based on known physical properties of the cochlea, such an amplifier can be readily tuned to match the full 10-octave range of human hearing. SLR waves propagate in a thin liquid layer enclosed between two thin compliant plates or a single such plate and a rigid wall, conditions found in the subtectorial space of the cochlea, and rely on the mass of the inter-plate fluid interacting with the stiffness of the plates to provide low phase velocity and high dispersion. The first property means SLR wavelengths can be as short as the distance between rows of outer hair cells, allowing standing wave formation; the second permits wide-range tuning using only an order-of-magnitude variation in cochlear physical properties, most importantly the inter-row spacing. Viscous drag at the two surfaces potentially limits SLR wave propagation at low frequencies, but this can perhaps be overcome by invoking hydrophobic effects.     

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.     

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.     

Otoacoustic emissions without somatic motility: can stereocilia mechanics drive the mammalian cochlea?

Distortion product otoacoustic emissions (DPOAEs) evoked by low-level tones are a sensitive indicator of outer hair cell (OHC) function. High-level DPOAEs are less vulnerable to cochlear insult, and their dependence on the OHC function is more controversial. Here, the mechanism underlying high-level DPOAE generation is addressed using a mutant mouse line lacking prestin, the molecular motor driving OHC somatic motility, required for cochlear amplification. With prestin deletion, attenuated DPOAEs were measurable at high sound levels. DPOAE thresholds were shifted by approximately 50 dB, matching the loss of cochlear amplifier gain measured in compound action potentials. In contrast, at high sound levels, distortion products in the cochlear microphonic (CM) of mutants were not decreased re wildtypes (expressed re CM at the primaries). Distortion products in both CM and otoacoustic emissions disappeared rapidly after death. The results show that OHC somatic motility is not necessary for the production of DPOAEs at high SPLs. They also suggest that the small, physiologically vulnerable DPOAE that remains without prestin-based motility is due directly to the mechanical nonlinearity associated with stereociliary transduction, and that this stereocilia mechanical nonlinearity is robustly coupled to the motion of the cochlear partition to the extent that it can drive the middle ear.     

Effect of outer hair cell piezoelectricity on high-frequency receptor potentials

The low-pass voltage response of outer hair cells predicted by conventional equivalent circuit analysis would preclude the active force production at high frequencies. We have found that the band pass characteristics can be improved by introducing the piezoelectric properties of the cell wall. In contrast to the conventional analysis, the receptor potential does not tend to zero and at any frequency is greater than a limiting value. In addition, the phase shift between the transduction current and receptor potential tends to zero. The piezoelectric properties cause an additional, strain-dependent, displacement current in the cell wall. The wall strain is estimated on the basis of a model of the cell deformation in the organ of Corti. The limiting value of the receptor potential depends on the ratio of a parameter determined by the piezoelectric coefficients and the strain to the membrane capacitance. In short cells, we have found that for the low-frequency value of about 2-3 mV and the strain level of 0.1% the receptor potential can reach 0.4 mV throughout the whole frequency range. In long cells, we have found that the effect of the piezoelectric properties is much weaker. These results are consistent with major features of the cochlear amplifier.     

The structural and functional consequences of acoustic injury in the cochlea and peripheral auditory system: a five year update

This presentation considers important developments and new trends related to acoustic injury in the peripheral auditory system reported during the past 5 years. The discussion begins with the effect overstimulation has on the "active" cochlear process, and the associated loss in receptive field (tuning curve) selectivity. Exposure to intense sound also changes the structure and function of the tectorial membrane, sensory hair bundles, tip links, and intracellular organelles. All of these injuries may change the way in which energy is delivered to the transduction channels of the hair cell. Important new evidence describing the quantitative relation between hair cell loss and permanent hearing loss is reviewed, and the possibility that specific exposure conditions cause unique lesions to the inner or outer hair cells is explored. Finally, the importance of hair cell regeneration in the chick cochlea, changes in the CNS following acoustic injury, and the cochlear vascular system are considered.     

Intensity-invariance of fine time structure in basilar-membrane click responses: implications for cochlear mechanics

Basilar-membrane and auditory-nerve responses to impulsive acoustic stimuli, whether measured directly in response to clicks or obtained indirectly using cross- or reverse-correlation and/or Fourier analysis, manifest a striking symmetry: near-invariance with stimulus intensity of the fine time structure of the response over almost the entire dynamic range of hearing. This paper explores the origin and implications of this symmetry for cochlear mechanics. Intensity-invariance is investigated by applying the EQ-NL theorem [de Boer, Aud. Neurosci. 3, 377-388 (1997)] to define a family of linear cochlear models in which the strength of the active force generators is controlled by a real-valued, intensity-dependent parameter, gamma (with 0 < or = gamma < or = 1). The invariance of fine time structure is conjectured to imply that as gamma is varied the poles of the admittance of the cochlear partition remain within relatively narrow bands of the complex plane oriented perpendicular to the real frequency axis. Physically, the conjecture implies that the local resonant frequencies of the cochlear partition are nearly independent of intensity. Cochlear-model responses, computed by extending the model obtained by solution of the inverse problem in squirrel monkey at low sound levels [Zweig, J. Acoust. Soc. Am. 89, 1229-1254 (1991)] with three different forms of the intensity dependence of the partition admittance, support the conjecture. Intensity-invariance of cochlear resonant frequencies is shown to be consistent with the well-known "half-octave shift," describing the shift with intensity in the peak (or best) frequency of the basilar-membrane frequency response. Shifts in best frequency do not arise locally, via changes in the underlying resonant frequencies of the partition, but globally through the intensity dependence of the driving pressure. Near-invariance of fine time structure places strong constraints on the mechanical effects of force generation by outer hair cells. In particular, the symmetry requires that the feedback forces generated by outer hair cells (OHCs) not significantly affect the natural resonant frequencies of the cochlear partition. These results contradict many, if not most, cochlear models, in which OHC forces produce significant changes in the reactance and resonant frequencies of the partition.     

Mammalian spontaneous otoacoustic emissions are amplitude-stabilized cochlear standing waves

Mammalian spontaneous otoacoustic emissions (SOAEs) have been suggested to arise by three different mechanisms. The local-oscillator model, dating back to the work of Thomas Gold, supposes that SOAEs arise through the local, autonomous oscillation of some cellular constituent of the organ of Corti (e.g., the "active process" underlying the cochlear amplifier). Two other models, by contrast, both suppose that SOAEs are a global collective phenomenon--cochlear standing waves created by multiple internal reflection--but differ on the nature of the proposed power source: Whereas the "passive" standing-wave model supposes that SOAEs are biological noise, passively amplified by cochlear standing-wave resonances acting as narrow-band nonlinear filters, the "active" standing-wave model supposes that standing-wave amplitudes are actively maintained by coherent wave amplification within the cochlea. Quantitative tests of key predictions that distinguish the local-oscillator and global standing-wave models are presented and shown to support the global standing-wave model. In addition to predicting the existence of multiple emissions with a characteristic minimum frequency spacing, the global standing-wave model accurately predicts the mean value of this spacing, its standard deviation, and its power-law dependence on SOAE frequency. Furthermore, the global standing-wave model accounts for the magnitude, sign, and frequency dependence of changes in SOAE frequency that result from modulations in middle-ear stiffness. Although some of these SOAE characteristics may be replicable through artful ad hoc adjustment of local-oscillator models, they all arise quite naturally in the standing-wave framework. Finally, the statistics of SOAE time waveforms demonstrate that SOAEs are coherent, amplitude-stabilized signals, as predicted by the active standing-wave model. Taken together, the results imply that SOAEs are amplitude-stabilized standing waves produced by the cochlea acting as a biological, hydromechanical analog of a laser oscillator. Contrary to recent claims, spontaneous emission of sound from the ear does not require the autonomous mechanical oscillation of its cellular constituents.     

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.     

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.     

The mechanical waveform of the basilar membrane. IV. Tone and noise stimuli

Analysis of mechanical cochlear responses to wide bands of random noise clarifies many effects of cochlear nonlinearity. The previous paper [de Boer and Nuttall, J. Acoust. Soc. Am. 107, 1497-1507 (2000)] illustrates how closely results of computations in a nonlinear cochlear model agree with responses from physiological experiments. In the present paper results for tone stimuli are reported. It was found that the measured frequency response for pure tones differs little from the frequency response associated with a noise signal. For strong stimuli, well into the nonlinear region, tones have to be presented at a specific level with respect to the noise for this to be true. In this report the nonlinear cochlear model originally developed for noise analysis was modified to accommodate pure tones. For this purpose the efficiency with which outer hair cells modify the basilar-membrane response was made into a function of cochlear location based on local excitation. For each experiment, the modified model is able to account for the experimental findings, within 1 or 2 dB. Therefore, the model explains why the type of filtering that tones undergo in the cochlea is essentially the same as that for noise signals (provided the tones are presented at the appropriate level).     

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.     

Rate-intensity functions in the emu auditory nerve

Rate-versus-intensity functions recorded from mammalian auditory-nerve fibers have been shown to form a continuum of shapes, ranging from saturating to straight and correlating well with spontaneous rate and sensitivity. These variations are believed to be a consequence of the interaction between the sensitivity of the hair-cell afferent synapse and the nonlinear, compressive growth of the cochlear amplifier that enhances mechanical vibrations on the basilar membrane. Little is known, however, about the cochlear amplifier in other vertebrate species. Rate-intensity functions were recorded from auditory-nerve fibers in chicks of the emu, a member of the Ratites, a primitive group of flightless birds that have poorly differentiated short and tall hair cells. Recorded data were found to be well fitted by analytical functions which have previously been shown to represent well the shapes of rate-intensity functions in guinea pigs. At the fibers' most sensitive frequencies, rate-intensity functions were almost exclusively of the sloping (80.9%) or straight (18.6%) type. Flat-saturating functions, the most common type in the mammal, represented only about 0.5% of the total in the emu. Below the best frequency of each fiber, the rate-intensity functions tended more towards the flat-saturating type, as is the case in mammals; a similar but weaker trend was seen above best frequency in most fibers, with only a small proportion (18%) showing the reverse trend. The emu rate-intensity functions were accepted as supporting previous evidence for the existence of a cochlear amplifier in birds, the conclusion was drawn further that the nonlinearity observed is probably due to saturation of the hair-cell transduction mechanism.     

An auditory-periphery model of the effects of acoustic trauma on auditory nerve responses

Acoustic trauma degrades the auditory nerve's tonotopic representation of acoustic stimuli. Recent physiological studies have quantified the degradation in responses to the vowel /E/ and have investigated amplification schemes designed to restore a more correct tonotopic representation than is achieved with conventional hearing aids. However, it is difficult from the data to quantify how much different aspects of the cochlear pathology contribute to the impaired responses. Furthermore, extensive experimental testing of potential hearing aids is infeasible. Here, both of these concerns are addressed by developing models of the normal and impaired auditory peripheries that are tested against a wide range of physiological data. The effects of both outer and inner hair cell status on model predictions of the vowel data were investigated. The modeling results indicate that impairment of both outer and inner hair cells contribute to degradation in the tonotopic representation of the formant frequencies in the auditory nerve. Additionally, the model is able to predict the effects of frequency-shaping amplification on auditory nerve responses, indicating the model's potential suitability for more rapid development and testing of hearing aid schemes.     

Further evaluation of a model of loudness perception applied to cochlear hearing loss.

This paper describes further tests of a model for loudness perception in people with cochlear hearing loss. It is assumed that the hearing loss (the elevation in absolute threshold) at each audiometric frequency can be partitioned into a loss due to damage to outer hair cells (OHCs) and a loss due to damage to inner hair cells (IHCs) and/or neurons. The former affects primarily the active mechanism that amplifies the basilar membrane (BM) response to weak sounds. It is modeled by increasing the excitation level required for threshold, which results in a steeper growth of specific loudness with increasing excitation level. Loss of frequency selectivity, which results in broader excitation patterns, is also assumed to be directly related to the OHC loss. IHC damage is modeled by an attenuation of the calculated excitation level at each frequency. The model also allows for the possibility of complete loss of IHCs or functional neurons at certain places within the cochlea ("dead" regions). The parameters of the model (OHC loss at each audiometric frequency, plus frequency limits of the dead regions) were determined for three subjects with unilateral cochlear hearing loss, using data on loudness matches between sinusoids presented alternately to their two ears. Further experiments used bands of noise that were either 1-equivalent rectangular bandwidth (ERB) wide or 6-ERBs wide, centered at 1 kHz. Subjects made loudness matches for these bands of noise both within ears and across ears. The model was reasonably accurate in predicting the results of these matches without any further adjustment of the parameters.     

A state space model for cochlear mechanics

The stability of a linear model of the active cochlea is difficult to determine from its calculated frequency response alone. A state space model of the cochlea is presented, which includes a discretized set of general micromechanical elements coupled via the cochlear fluid. The stability of this time domain model can be easily determined in the linear case, and the same framework used to simulate the time domain response of nonlinear models. Examples of stable and unstable behavior are illustrated using the active micromechanical model of Neely and Kim. The stability of this active cochlea is extremely sensitive to abrupt spatial inhomogeneities, while smoother inhomogeneities are less likely to cause instability. The model is a convenient tool for investigating the presence of instabilities due to random spatial inhomogeneities. The number of unstable poles is found to rise sharply with the relative amplitude of the inhomogeneities up to a few percent, but to be significantly reduced if the spatial variation is smoothed. In a saturating nonlinear model, such instabilities generate limit cycles that are thought to produce spontaneous otoacoustic emissions. An illustrative time domain simulation is presented, which shows how an unstable model evolves into a limit cycle, distributed along the cochlea.