The mechanical waveform of the basilar membrane. III. Intensity effects

Mechanical responses in the basal turn of the guinea-pig cochlea were measured with broad-band noise stimuli and expressed as input-output cross-correlation functions. The experiments were performed over the full range of stimulus intensities in order to try to understand the influence of cochlear nonlinearity on frequency selectivity, tuning, signal compression and the impulse response. The results are interpreted within the framework of a nonlinear, locally active, three-dimensional model of the cochlea. The data have been subjected to inverse analysis in order to recover the basilar-membrane (BM) impedance, a parameter function that, when inserted into the (linearized version of that) model, produces a model response that is similar to the measured response. This paper reports details about intensity effects for noise stimulation, in particular, the way the BM impedance varies with stimulus intensity. In terms of the underlying cochlear model, the decrease of the "activity component" in the BM impedance with increasing stimulus level is attributed to saturation of transduction in the outer hair cells. In the present paper this property is brought into a quantitative form. According to the theory [the EQ-NL theorem, de Boer, Audit. Neurosci. 3, 377-388 (1997)], the BM impedance is composed of two components, both intrinsically independent of stimulus level. One is the passive impedance Zpass and the other one is the "extra" impedance Zextra. The latter impedance is to be multiplied by a real factor gamma (0 < or = gamma < or = 1) that depends on stimulus level. This concept about the composition of the BM impedance is termed the "two-component theory of the BM impedance." In this work both impedances are entirely derived from experimental data. The dependence of the factor gamma on stimulus level can be derived by using a unified form of the outer-hair-cell transducer function. From an individual experiment, the two functions Zpass and Zextra are determined, and an approximation (Zpass + gamma Zextra) to the BM impedance constructed. Next, the model response (the "resynthesized" response) corresponding to this "artificial" impedance is computed. The same procedure is executed for several stimulus-level values. For all levels, the results show a close correspondence with the original experimental data; this includes correct prediction of the compression of response amplitudes, the reduction of frequency selectivity, the shift in peak frequency and, most importantly, the preservation of timing in the impulse response. All these findings illustrate the predictive power of the underlying model.     

The "inverse problem" solved for a three-dimensional model of the cochlea. III. Brushing-up the solution method.

In two earlier papers [de Boer, J. Acoust. Soc. Am. 98, 896-903 and 904-910 (1995)] the inherent problems of the inverse-solution method in cochlear mechanics were described. The present paper shows results obtained with a more universal solution method. With the new method it is possible to construct a three-dimensional model of the cochlea producing a response that accurately simulates a measured mechanical basilar-membrane response. With earlier methods this could not be done. The inverse solution invariably yields that, with low stimulus levels, the model simulating a viable cochlea must be locally active. For the response of a dead animal a passive model is sufficient. Once more the inherent intricacies and problems of the inverse-solution method are discussed. Conservation of fluid volume leads to the concept of the "virtual stapes velocity." For best results, the input signal to the inverse-solution procedure should be acquired in the form of a "composite cross-correlation spectrum." Inverse analysis can, under certain circumstances, produce aberrant results. In this paper it is shown why the resulting impedance function is the most accurate in the region of the response peak. Therefore, it is unlikely that a passive model would exist of which the response simulates the data obtained from a healthy animal.     

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.     

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).     

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.     

Transmission properties of bone conducted sound: measurements in cadaver heads

In the past, only a few investigations have measured vibration at the cochlea with bone conduction stimulation: dry skulls were used in those investigations. In this paper, the transmission properties of bone conducted sound in human head are presented, measured as the three-dimensional vibration at the cochlear promontory in six intact cadaver heads. The stimulation was provided at 27 positions on the skull surface and two close to the cochlea; mechanical point impedance was measured at all positions. Cochlear promontory vibration levels in the three perpendicular directions were normally within 5 dB. With the stimulation applied on the ipsilateral side, the response decreased, and the accumulated phase increased, with distance between the cochlea and the excitation position. No significant changes were obtained when the excitations were on the contralateral side. In terms of vibration level, the best stimulation position is on the mastoid close to the cochlea; the worst is at the midline of the skull. The transcranial transmission was close to 0 dB for frequencies up to 700 Hz; above it decreased at 12 dB/decade. Wave transmission at the skull-base was found to be nondispersive at frequencies above 2 kHz whereas it altered with frequency at the cranial vault.     

Multicomponent stimulus interactions observed in basilar-membrane vibration in the basal region of the chinchilla cochlea.

Multicomponent stimuli consisting of two to seven tones were used to study suppression of basilar-membrane vibration at the 3-4-mm region of the chinchilla cochlea with a characteristic frequency between 6.5 and 8.5 kHz. Three-component stimuli were amplitude-modulated sinusoids (AM) with modulation depth varied between 0.25 and 2 and modulation frequency varied between 100 and 2000 Hz. For five-component stimuli of equal amplitude, frequency separation between adjacent components was the same as that used for AM stimuli. An additional manipulation was to position either the first, third, or fifth component at the characteristic frequency (CF). This allowed the study of the basilar-membrane response to off-CF stimuli. CF suppression was as high as 35 dB for two-tone combinations, while for equal-amplitude stimulus components CF suppression never exceeded 20 dB. This latter case occurred for both two-tone stimuli where the suppressor was below CF and for multitone stimuli with the third component=CF. Suppression was least for the AM stimuli, including when the three AM components were equal. Maximum suppression was both level- and frequency dependent, and occurred for component frequency separations of 500 to 600 Hz. Suppression decreased for multicomponent stimuli with component frequency spacing greater than 600 Hz. Mutual suppression occurred whenever stimulus components were within the compressive region of the basilar membrane.     

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.     

Basilar-membrane responses to multicomponent (Schroeder-phase) signals: understanding intensity effects

Harmonic complexes comprised of the same spectral components in either positive-Schroeder (+Schr) or negative-Schroeder (-Schr) phase [see Schroeder, IEEE Trans. Inf. Theory 16, 85-89 (1970)] have identical long-term spectra and similar waveform envelopes. However, localized patterns of basilar-membrane (BM) excitation can be quite different in response to these two stimuli. Measurements in chinchillas showed more modulated (peakier) BM excitation for +Schr than -Schr complexes [Recio and Rhode, J. Acoust. Soc. Am. 108, 2281-2298 (2000)]. In the current study, laser velocimetry was used to examine BM responses at a location tuned to approximately 17 kHz in the basal turn of the guinea-pig cochlea, for +Schr and -Schr complexes with a 203-Hz fundamental frequency and including 101 equal-amplitude components from 2031 to 22,344 Hz. At 35-dB SPL, +Schr response waveforms showed greater amplitude modulation than -Schr responses. With increasing stimulation level, internal modulation decreased for both complexes. To understand the observed phenomena quantitatively, responses were predicted on the basis of a linearized model of the cochlea. Prediction was based on an "indirect impulse response" measured in the same animal. Response waveforms for Schroeder-phase signals were accurately predicted, provided that the level of the indirect impulse used in prediction closely matched the level of the Schroeder-phase stimulus. This result confirms that the underlying model, which originally was developed for noise stimuli, is valid for stimuli that produce completely different response waveforms. Moreover, it justifies explanation of cochlear filtering (i.e., differential treatment of different frequencies) in terms of a linear system.     

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.     

A macro-mechanical model of the guinea pig cochlea with realistic parameters

The post-mortem transfer function of the cochlea of the guinea pig was compared to the transfer function generated by a model with parameters derived from physical measurements of the guinea pig cochlea. Both the formulation and parameters of the model were carefully chosen to be realistic using evidence from published measurements. The fit between the transfer function of the model and recent mechanical measurements of the passive guinea pig cochlear response was good, with a root mean square ratio of 6.3 dB in amplitude and 0.33 pi rad in phase. The model was used to explore the effect of cochlear partition mode factor and duct geometry upon the mechanical response of the cochlea. Possible inadequacies of the model which could explain the remaining differences between the output of the model and measurements are discussed.     

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.     

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.     

Nonlinear interactions that could explain distortion product interference response areas

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

Effects of background noise level on behavioral estimates of basilar-membrane compression

Hearing-impaired (HI) listeners often show poorer performance on psychoacoustic tasks than do normal-hearing (NH) listeners. Although some such deficits may reflect changes in suprathreshold sound processing, others may be due to stimulus audibility and the elevated absolute thresholds associated with hearing loss. Masking noise can be used to raise the thresholds of NH to equal the thresholds in quiet of HI listeners. However, such noise may have other effects, including changing peripheral response characteristics, such as the compressive input-output function of the basilar membrane in the normal cochlea. This study estimated compression behaviorally across a range of background noise levels in NH listeners at a 4 kHz signal frequency, using a growth of forward masking paradigm. For signals 5 dB or more above threshold in noise, no significant effect of broadband noise level was found on estimates of compression. This finding suggests that broadband noise does not significantly alter the compressive response of the basilar membrane to sounds that are presented well above their threshold in the noise. Similarities between the performance of HI listeners and NH listeners in threshold-equalizing noise are therefore unlikely to be due to a linearization of basilar-membrane responses to suprathreshold stimuli in the NH listeners.     

The effects of neural synchronization and peripheral compression on the acoustic-reflex threshold

This study investigates the acoustic reflex threshold (ART) dependency on stimulus phase utilizing low-level reflex audiometry [Neumann et al., Audiol. Neuro-Otol. 1, 359-369 (1996)]. The goal is to obtain optimal broadband stimuli for elicitation of the acoustic reflex and to obtain objective determinations of cochlear hearing loss. Three types of tone complexes with different phase characteristics were investigated: A stimulus that compensates for basilar-membrane dispersion, thus causing a large overall neural synchrony (basilar-membrane tone complex-BMTC), the temporally inversed stimulus (iBMTC), and random-phase tone complexes (rTC). The ARTs were measured in eight normal-hearing and six hearing-impaired subjects. Five different conditions of peak amplitude and stimulus repetition rate were used for each stimulus type. The results of the present study suggest that the ART is influenced by at least two different factors: (a) the degree of synchrony of neural activity across frequency, and (b) the fast-acting compression mechanism in the cochlea that is reduced in the case of a sensorineural hearing loss. The results allow a clear distinction of the two subjects groups based on the different ART for the utilized types and conditions of the stimuli. These differences might be useful for objective recruitment detection in clinical diagnostics.     

铁镓单晶Janus-Helmholtz换能器

针对深水、低频、宽带换能器的技术需求,结合Janus-Helmholtz换能器的结构特点和铁镓单晶材料低场应变大及机械强度高的特性,提出了铁镓单晶Janus-Helmholtz换能器设计方案。采用永磁偏磁场和环形闭合磁路,建立了一系列铁镓单晶磁致伸缩换能器理论分析模型,包括对磁致伸缩材料参数进行线性化处理,设计了换能器最佳工作点,结合静态磁场和动态磁场分布情况分段细化换能器驱动等效参数,以及利用全阻抗模型通过电感损耗等效计算换能器静态阻抗,然后通过二维有限元分析等效模型,优化分析了换能器的结构参数与电声性能。最后制作了换能器样机,并进行了测试与分析。对比仿真和测试结果表明:全阻抗模型得到的阻抗曲线与样机测试结果相一致,有限元等效模型计算的发送电流响应与样机测试结果良好吻合。换能器样机水中谐振基频为1000 Hz,谐振频率下发送电流响应176.4 dB;在875～2300 Hz频率范围内,发送电流响应起伏不大于6 dB;增加驱动电流有效值到16.2 A,最大声源级可以达到196.2 dB。     

Reflection of retrograde waves within the cochlea and at the stapes

A number of authors [de Boer and Viergever, Hear. Res. 13, 101-112 (1984); de Boer et al., in Peripheral Auditory Mechanisms (Springer-Verlag, Berlin, 1986); Hear. Res. 23, 1-7 (1986); Viergever, in Auditory Frequency Selectivity (Plenum, New York, 1986), pp. 31-38; Kaernbach et al., J. Acoust. Soc. Am. 81, 408-411 (1987)] have argued that backward-traveling waves, in striking contrast to waves traveling forward towards the helicotrema, suffer appreciable reflection as they move through the basal turns of the cochlea. Such reflection, if present, would have important consequences for understanding the nature and strength of otoacoustic emissions. The apparent asymmetry in reflection of cochlear waves is shown, however, to be an artifact of the boundary condition those authors impose at the stapes: conventional cochlear models are found not to generate reflections of waves traveling in either direction even when the wavelength changes rapidly and the WKB approximation breaks down. Although backward-traveling waves are not reflected by the secular variation of the geometrical and mechanical characteristics of the cochlea, they are reflected when they reach the stapes. The magnitude of that boundary reflection is computed for the cat and shown to be a large, rapidly varying function of frequency.     

The trapped fluid transducer: modeling and optimization

Exact and approximate formulas for calculating the sensitivity and bandwidth of an electroacoustic transducer with an enclosed or trapped fluid volume are developed. The transducer is composed of a fluid-filled rectangular duct with a tapered-width plate on one wall emulating the biological basilar membrane in the cochlea. A three-dimensional coupled fluid-structure model is developed to calculate the transducer sensitivity by using a boundary integral method. The model is used as the basis of an optimization methodology seeking to enhance the transducer performance. Simplified formulas are derived from the model to estimate the transducer sensitivity and the fundamental resonant frequency with good accuracy and much less computational cost. By using the simplified formulas, one can easily design the geometry of the transducer to achieve the optimal performance. As an example design, the transducer achieves a sensitivity of around -200 dB (1 VmuPa) at 10 kHz frequency range with piezoelectric sensing. In analogy to the cochlea, a tapered-width plate design is considered and shown to have a more uniform frequency response than a similar plate with no taper.