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.     

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.     

Frequency-dependent self-induced bias of the basilar membrane and its potential for controlling sensitivity and tuning in the mammalian cochlea

A displacement-sensitive capacitive probe technique was used in the first turn of guinea pig cochleas to examine whether the motion of the basilar membrane includes a displacement component analogous to the dc receptor potentials of the hair cells. Such a "dc" component apparently exists. At a given location on the basilar membrane, its direction toward scala vestibuli (SV) or scala tympani (ST) varies systematically with frequency of the acoustic stimulus. Furthermore, it appears to consist of two parts: a small asymmetric offset response to each gated tone burst plus a progressive shift of the basilar membrane from its previous position. The mean position shift is cumulative, increasing with successive tone bursts. The amplitude of the immediate offset response, when plotted as a function of frequency, appears to exhibit a trimodal pattern. This displacement offset is toward SV at the characteristic frequency (CF) of the location of the probe, while at frequencies either above or below the CF the offset is relatively larger, and toward ST. The mechanical motion of the basilar membrane therefore appears to contain the basis for lateral suppression. The cumulative mean position shift, however, appears to peak toward ST at the apical end of the traveling wave envelope and appears to be associated with a resonance, not of the basilar membrane motion directly, but coupled to it. The summating potential, measured concurrently at the round window, shows a more broadly tuned peak just above the CF of the position of the probe. This seems to correspond to the peak at the CF of the mechanical bias. As the preparation deteriorates, the best frequency of the vibratory displacement response decreases to about a half-octave below the original CF. There is a corresponding decrease in the frequency of the peaks of the trimodal pattern of the asymmetric responses to tone bursts. The trimodal pattern also broadens. In previous experiments the basilar membrane has been forced to move in response to a low-frequency biasing tone. The sensitivity to high-frequency stimuli varies in phase with the biasing tone. The amplitudes of slow movement in these earlier experiments and in the present experiments are of the same order of magnitude. This suggests strongly that the cumulative shift toward ST to a high-frequency acoustic stimulus constitutes a substantial controlling bias on the sensitivity of the cochlea in that same high-frequency region. Its effect will be to reduce the slope of neural rate-level functions on the high-frequency side of CF.     

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.     

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.     

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.     

"Otoacoustic" emissions in a nonlinear cochlear hardware model with feedback

Spontaneous, simultaneous evoked as well as delayed evoked emissions are studied in a hardware model of peripheral preprocessing with nonlinear feedback. The results suggest many very close parallels to the data found for otoacoustic emissions in man. From these parallels and the additional data measurable only in the model, it can be concluded that: the cochlea acts in a similar way as established in the model; the three kinds of emissions stem from the same source; the phase response of the cochlea's hydromechanics is responsible for the frequency distance between neighboring emissions as well as for the additional tips in suppression tuning curves; the long delay of the delayed evoked emissions is due to the many decaying contributions from the places along the basilar membrane which cancel each other in the early part but sum up to the delayed emission in the later part; and the double-peaked shape of the suppression-period patterns produced by high-level, low-frequency tones reflects the symmetrically shaped saturating nonlinearity of the feedback loops in the model which correspond to the function of the outer hair cells.     

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.     

A computer model of medial efferent suppression in the mammalian auditory system

Stimulation of the olivocochlear bundle reduces basilar membrane displacement, driven auditory nerve activity, and compound action potential (CAP) response to acoustic stimulation. These effects were simulated using a computer model of the auditory periphery. The model simulates the medial efferent activity by attenuating the basilar membrane response. The model was evaluated against three animal studies reporting measurements at three levels of the auditory system; basilar membrane, single auditory nerve fibers and whole auditory nerve CAP. The CAP data included conditions where tones were masked by noise and "unmasked" by stimulation of the olivocochlear bundle. The model was able to simulate the data both qualitatively and quantitatively. As a consequence, it may be a suitable platform for studying the contribution of the efferent system to auditory processing of more complex auditory sounds in distracting backgrounds.     

Invariance principles for cochlear mechanics: hearing phases

A functional model of the cochlea is devised on the basis of the results from classical experiments. The basilar membrane filter is investigated in detail. Its phase is close to linear in the region around the peak of the amplification. On one side this has consequences for the time analysis and on the other side this has led to a prediction on phase perception for very simple combinations of tones, a prediction which is now confirmed by experiments. Equivariance under the dilation group permits one to describe the model by a wavelet transform [Daubechies, Ten Lectures on Wavelets (SIAM, Philadelphia, 1992)]. The wavelet is discussed in reference to the phase analysis of the basilar membrane filter.     

Wave propagation patterns in a "classical" three-dimensional model of the cochlea

The generation mechanisms of cochlear waves, in particular those that give rise to otoacoustic emissions (OAEs), are often complex. This makes it difficult to analyze wave propagation. In this paper two unusual excitation methods are applied to a three-dimensional stylized classical nonlinear model of the cochlea. The model used is constructed on the basis of data from an experimental animal selected to yield a smooth basilar-membrane impedance function. Waves going in two directions can be elicited by exciting the model locally instead of via the stapes. Production of DPOAEs was simulated by presenting the model with two relatively strong primary tones, with frequencies f1 and f2, estimating the driving pressure for the distortion product (DP) with frequency 2f1 - f2, and computing the resulting DP response pattern - as a function of distance along the basilar membrane. For wide as well as narrow frequency separations the resulting DP wave pattern in the model invariably showed that a reverse wave is dominant in nearly the entire region from the peak of the f2-tone to the stapes. The computed DP wave pattern was further analyzed as to its constituent components with the aim to isolate their properties.     

感性神经元模型及其动力学特性研究

神经元的大小属于介观尺度范围,本文考虑神经元的电感特性,建立了由细胞膜电感、膜电容、钾离子忆阻器和氯离子电阻构成的神经元经典电路模型和介观电路模型.利用经典电路理论和介观电路的量子理论,推导了在外部冲击激励下神经元细胞膜电压响应的表达式.将枪乌贼神经元的电生理参数代入膜电压表达式并计算可知,两种模型下的膜电压均先增大后减小,最后达到零值的静息状态,且其能量主要集中在0—30 Hz的脑电频率范围内.进一步比较发现,介观电路模型下膜电压的峰值及达到峰值所需的时间(达峰时间)均低于经典电路模型下的值,并与枪乌贼轴突受到刺激后的实验结果更接近,说明介观电路模型更能反应神经元受到刺激后的生理特征.基于介观电路模型,随着外部激励强度的增加,膜电压的峰值增加且达峰时间变短.膜电压峰值及达峰时间等参数更易受神经元膜电容的影响.神经元的介观电路模型对于理解神经元受到刺激后的兴奋性,推动受大脑功能启发的量子神经网络的发展等具有重要意义.     

Comment on "Mutual suppression in the 6 kHz region of sensitive chinchilla cochleae" [J. Acoust. Soc. Am. 121, 2805-2818 (2007)

Rhode [J. Acoust. Soc. Am. 121, 2805-2818 (2007)] acknowledges that two-tone neural rate responses for low-side suppression differ from those measured in basilar membrane mechanics, making one question whether this aspect of suppression has a mechanical correlate. It is suggested here that signal coding between mechanical and neural processing stages may be responsible for the fact that the total rate response (but not the basilar membrane response) for low-frequency suppressors is smaller than that for the probe-alone condition. For example, the velocity dependence of inner hair cell (IHC) transduction, membrane/synaptic filtering and the sensitivity difference between ac and dc components of the IHC receptor potential all serve to reduce excitability for low-side suppressors at the single-unit level. Hence, basilar membrane mechanics may well be the source of low-side suppression measured in the auditory nerve.     

感性神经元模型及其动力学特性研究

神经元的大小属于介观尺度范围,本文考虑神经元的电感特性,建立了由细胞膜电感、膜电容、钾离子忆阻器和氯离子电阻构成的神经元经典电路模型和介观电路模型.利用经典电路理论和介观电路的量子理论,推导了在外部冲击激励下神经元细胞膜电压响应的表达式.将枪乌贼神经元的电生理参数代入膜电压表达式并计算可知,两种模型下的膜电压均先增大后减小,最后达到零值的静息状态,且其能量主要集中在0—30 Hz的脑电频率范围内.进一步比较发现,介观电路模型下膜电压的峰值及达到峰值所需的时间(达峰时间)均低于经典电路模型下的值,并与枪乌贼轴突受到刺激后的实验结果更接近,说明介观电路模型更能反应神经元受到刺激后的生理特征.基于介观电路模型,随着外部激励强度的增加,膜电压的峰值增加且达峰时间变短.膜电压峰值及达峰时间等参数更易受神经元膜电容的影响.神经元的介观电路模型对于理解神经元受到刺激后的兴奋性,推动受大脑功能启发的量子神经网络的发展等具有重要意义.     

Histological evaluation of damage in cat cochleas used for measurement of basilar membrane mechanics

Cochleas utilized in basilar membrane vibration measurements were examined histologically using an epon-embedded surface preparation technique. The amount of damage observed at both the apical and basal ends of the cochleas was variable. The apical damage was probably caused by large, low-frequency movements of the basilar membrane. The basal damage was due to trauma produced directly by the surgical and experimental procedure. The sharpness of turning observed in the basilar membrane frequency response was found to be inversely related to the extent of histological damage.     

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.     

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.     

Physical model for the width distribution of axons

The distribution of widths of axons was recently investigated, and was found to have a distinct peak at an optimized value. The optimized axon width at the peak may arise from the conflicting demands of minimizing energy consumption and assuring signal transmission reliability. The distribution around this optimized value is found to have a distinct non-Gaussian shape, with an exponential “tail”. We propose here a mechanical model whereby this distribution arises from the interplay between the elastic energy of the membrane surrounding the axon core, the osmotic pressure induced by the neurofilaments inside the axon bulk, and active processes that remodel the microtubules and neurofilaments inside the axon. The axon’s radius of curvature can be determined by the cell’s control of the osmotic pressure difference across the membrane, the membrane tension or by changing the composition of the different components of the membrane. We find that the osmotic pressure, determined by the neurofilaments, seems to be the dominant control parameter.     

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.     

A composite auditory model for processing speech sounds

A composite inner-ear model, containing the middle ear, basilar membrane (BM), hair cells, and hair-cell/nerve-fiber synapses, is presented. The model incorporates either a linear-BM stage or a nonlinear one. The model with the nonlinear BM generally shows a high degree of success in reproducing the qualitative aspects of experimentally recorded cat auditory-nerve-fiber responses to speech. In modeling fiber population responses to speech and speech in noise, it was found that the BM nonlinearity allows bands of fibers in the model to synchronize strongly to a common spectral peak in the stimulus. A cross-channel correlation algorithm has been devised to further process the model's population outputs. With output from the nonlinear-BM model, the cross-channel correlation values are appreciably reduced only at those channels whose CFs coincide with the formant frequencies. This observation also holds, to a large extent, for noisy speech.