The shape of the nonlinearity generating the combination tone 2f1-f2

If the level behavior of the cubic difference tone is explained by a static nonlinear characteristic, the correspondence between this characteristic and certain components and quantities of the basilar membrane must be clarified. This is attempted here for a nonlinearity compatible with the idea of an active undamping feedback mechanism saturating at high levels. The relation between asymptotic behavior of the nonlinearity and the measured CDT level dependence is established. Agreement with psychoacoustic data requires a very "softly" compressing characteristic; linear or logarithmic asymptotes are ruled out. The psychoacoustically known level dependence is well reproduced for small primary-frequency differences by cancellation experiments with a digitally simulated basilar-membrane model.     

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

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

A computational algorithm for computing nonlinear auditory frequency selectivity.

Computational algorithms that mimic the response of the basilar membrane must be capable of reproducing a range of complex features that are characteristic of the animal observations. These include complex input output functions that are nonlinear near the site's best frequency, but linear elsewhere. This nonlinearity is critical when using the output of the algorithm as the input to models of inner hair cell function and subsequent auditory-nerve models of low- and high-spontaneous rate fibers. We present an algorithm that uses two processing units operating in parallel: one linear and the other compressively nonlinear. The output from the algorithm is the sum of the outputs of the linear and nonlinear processing units. Input to the algorithm is stapes motion and output represents basilar membrane motion. The algorithm is evaluated against published chinchilla and guinea pig observations of basilar membrane and Reissner's membrane motion made using laser velocimetry. The algorithm simulates both quantitatively and qualitatively, differences in input/output functions among three different sites along the cochlear partition. It also simulates quantitatively and qualitatively a range of phenomena including isovelocity functions, phase response, two-tone suppression, impulse response, and distortion products. The algorithm is potentially suitable for development as a bank of filters, for use in more comprehensive models of the peripheral auditory system.     

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.     

Analysis of nonlinear oscillators using Volterra series in the frequency domain

The Volterra series representation is a direct generalisation of the linear convolution integral and has been widely applied in the analysis and design of nonlinear systems, both in the time and the frequency domain. The Volterra series is associated with the so-called weakly nonlinear systems, but even within the framework of weak nonlinearity there is a convergence limit for the existence of a valid Volterra series representation for a given nonlinear differential equation. Barrett (1965) [1] proposed a time domain criterion to prove that the Volterra series converges within a given region for a class of nonlinear systems with cubic stiffness nonlinearity. In this paper this time-domain criterion is extended to the frequency domain to accommodate the analysis of nonlinear oscillators subject to harmonic excitation. A common and severe nonlinear phenomenon called jump, a behavior associated with the Duffing oscillator and the multi-valued properties of the response solution, is investigated using the new frequency domain criterion of establishing the upper limits of the nonlinear oscillators, to predict the onset point of the jump, and the Volterra time and frequency domain analysis of this phenomenon are carried out based on graphical and numerical techniques.     

Forward masking: adaptation or integration?

The aim of this study was to attempt to distinguish between neural adaptation and persistence (or temporal integration) as possible explanations of forward masking. Thresholds were measured for a sinusoidal signal as a function of signal duration for conditions where the delay between the masker offset and the signal offset (the offset-offset interval) was fixed. The masker was a 200-ms broadband noise, presented at a spectrum level of 40 dB (re: 20 microPa), and the signal was a 4-kHz sinusoid, gated with 2-ms ramps. The offset-offset interval was fixed at various durations between 4 and 102 ms and signal thresholds were measured for a range of signal durations at each interval. A substantial decrease in thresholds was observed with increasing duration for signal durations up to about 20 ms. At short offset-offset intervals, the amount of temporal integration exceeded that normally found in quiet. The results were simulated using models of temporal integration (the temporal-window model) and adaptation. For both models, the inclusion of a peripheral nonlinearity, similar to that observed physiologically in studies of the basilar membrane, was essential in producing a good fit to the data. Both models were about equally successful in accounting for the present data. However, the temporal-window model provided a somewhat better account of similar data from a simultaneous-masking experiment, using the same parameters. This suggests that the linear, time-invariant properties of the temporal-window approach are appropriate for modeling forward masking. Overall the results confirm that forward masking can be described in terms of peripheral nonlinearity followed by linear temporal integration at higher levels in the auditory system. However, the difference in predictions between the adaptation and integration models is relatively small, meaning that influence of adaptation cannot be ruled out.     

Study of mechanical motions in the basal region of the chinchilla cochlea

Measurements from the 1-4-mm basal region of the chinchilla cochlea indicate the basilar membrane in the hook region (12-18 kHz) vibrates essentially as it does more apically, in the 5-9-kHz region. That is, a compressive nonlinearity in the region of the characteristic frequency, amplitude-dependent phase changes, and a gain relative to stapes motion that can attain nearly 10,000 at low levels. The displacement at threshold for auditory-nerve fibers in this region (20 dB SPL) was approximately 2 nm. Measurements were made at several locations in individual animals in the longitudinal and radial directions. The results indicate that there is little variability in the phase of motion radially and no indication of higher-order modes of vibration. The data from the longitudinal studies indicate that there is a shift in the location of the maximum with increasing stimulus levels toward the base. The cochlear amplifier extends over a 2-3-mm region around the location of the characteristic frequency.     

Individual and level-dependent differences in masking for adults with normal and impaired hearing

Simultaneous, on-frequency masking is commonly assumed to be linear with increasing noise intensity. However, some evidence suggests that, expressed in terms of signal-to-noise ratio changes with background level changes, masking slopes can vary from 0 dB/dB. These results and evidence from a large sample of subjects with normal and impaired hearing demonstrate level-dependent changes in masking, large individual differences in masking among subjects with similar thresholds in quiet, and significant correlations of masking slope with other estimates of auditory function measured in the same backgrounds.     

Basilar membrane mechanics at the base of the chinchilla cochlea. I. Input-output functions, tuning curves, and response phases

Basilar membrane (BM) velocity was measured at a site 3.5 mm from the basal end of the chinchilla cochlea using the M?ssbauer technique. The threshold of the compound action potential recorded at the round window in response to tone bursts was used as an indicator of the physiological state of the cochlea. The BM input-output functions display a compressive nonlinearity for frequencies around the characteristic frequency (CF, 8 to 8.75 kHz), but are linear for frequencies below 7 and above 10.5 kHz. In preparations with little surgical damage, isovelocity tuning curves at 0.1 mm/s are sharply tuned, have Q10's of about 6, minima as low as 13 dB SPL, tip-to-tail ratios (at 1 kHz) of 56 to 76 dB, and high-frequency slopes of about 300 dB/oct. These mechanical responses are as sharply tuned as frequency-threshold curves of chinchilla auditory nerve fibers with corresponding CF. There is a progressive loss of sensitivity of the mechanical response with time for the frequencies around CF, but not for frequencies on the tail of the tuning curve. In some experiments the nonlinearity was maintained for several hours, in spite of a considerable loss of sensitivity of the BM response. High-frequency plateaus were observed in both isovelocity tuning curves and phase-frequency curves.     

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 effect of a precursor on growth of forward masking

This study examined the effect of an on-frequency precursor on growth-of-masking (GOM) functions measured using an off-frequency masker. The signal was a 6-ms, 4-kHz tone. A GOM function was measured using a 40-ms, 2.8-kHz tone (the off-frequency masker). GOM functions were then measured with an on-frequency, fixed level precursor presented before the off-frequency masker. The precursor was 50 or 60 dB SPL, and 160 ms in duration. For the 60-dB SPL precursor, a 40-ms duration was also used. Two-line functions were fit to the GOM data to estimate the basilar membrane input-output function. The precursors reduced the gain of the input-output function, and this decrease was graded with precursor level. Both precursor durations had the same effect on gain. Changes in masking following a precursor were larger than would be predicted by additivity of masking. The observed decrease in gain may be consistent with activation of the medial olivocochlear reflex by the precursor.     

In vivo measurement of basilar membrane stiffness

Basilar membrane stiffness measurements were made in the base of the gerbil cochlea. Basilar membrane stiffness was determined by contacting the basilar membrane with a stainless steel needle (tip diameter 25 microns) attached to a force transducer, putting the needle/transducer structure through a low-frequency sinusoidal excursion with amplitude 5 or 25 nm, and measuring the restoring force exerted on the needle by the basilar membrane at the applied frequency. Stiffness was calculated as the amplitude of the restoring force divided by the amplitude of the excursion. Stiffness was measured over a 24-microns range of static displacements of the basilar membrane and is presented as stiffness versus static displacement. In cochleas that were not damaged during surgery the stiffness versus displacement characteristic usually had the following features: (1) an initial stiffness plateau with average stiffness 0.6 N/m; (2) a second plateau or level off with average stiffness 9.1 N/m; and (3) an increase in stiffness beyond the second plateau that was consistent with the theoretical stiffness-vs-displacement function of a beam. These features were present both pre- and post-mortem.     

Role of suppression and retro-cochlear processes in comodulation masking release

Recent physiological studies suggest that comodulation masking release (CMR) could be a consequence of wideband inhibition at the level of the cochlear nucleus. The present study investigates whether the existence region of psychophysical CMR is comparable to the inhibitory areas of units showing a physiological correlate of CMR. Since the inhibitory areas are similar to suppressive regions at the level of the basilar membrane, the amount of CMR that can be accounted for by suppression was determined by predicting the data with a model incorporating a peripheral nonlinearity. A CMR of up to 6 dB could still be experimentally observed for a flanking band (FB) four octaves below the on-frequency masker (OFM). For FB frequencies below the OFM, the suggested model predicts CMR equal to the measured CMR for high levels of the FB. The model underestimates the magnitude of CMR for midlevels of the FB, indicating that suppression alone cannot account for CMR. The data are consistent with the hypothesis that wideband inhibition plays a role in CMR.     

The influence of spread of excitation on the detection of amplitude modulation imposed on sinusoidal carriers at high levels

The improvement in amplitude modulation (AM) detection thresholds with increasing level of a sinusoidal carrier has been attributed to listening on the high-frequency side of the excitation pattern, where the growth of excitation is more linear, or to an increase in the number of "channels" via spread of excitation. In the present study, AM detection thresholds were measured using a 1000-Hz sinusoidal carrier. Thresholds for modulation frequencies of 4-64 Hz improved by about 10-20 dB as the carrier level increased from 10 dB SL (14.5 dB SPL on average) to 80 dB SPL. To minimize the use of spread of excitation with an 80-dB carrier, tonal "restrictors" with frequencies of 501, 801, 1210, and 1510 Hz were used alone and in combination. High-frequency restrictors elevated AM detection thresholds, whereas low-frequency restrictors did not, indicating that excitation on the high side is more important for detecting AM. Results of modeling suggest that the improvement in AM detection thresholds at high levels is likely due to the use of a relatively linear growth of response on the high-frequency side of the excitation pattern.     

Identification of the structure parameters using short-time non-stationary stochastic excitation

In this paper, we propose an approach to the flexural stiffness or eigenvalue frequency identification of a linear structure using a non-stationary stochastic excitation process. The idea of the proposed approach lies within time domain input-output methods. The proposed method is based on transforming the dynamical problem into a static one by integrating the input and the output signals. The output signal is the structure reaction, i.e. structure displacements due to the short-time, irregular load of random type. The systems with single and multiple degrees of freedom, as well as continuous systems are considered.     

On the loudness of complex stimuli and its relationship to cochlear excitation

Two experiments were conducted to reexamine the relation between loudness and the bandwidth of complex stimuli. In experiment 1, experimental stimuli consisting of a 2000-Hz pure tone and ten computer-generated multitonal complexes ranging in bandwidth from 0.26-3.16 oct, logarithmically centered at 2000 Hz, were matched in loudness to a 2000-Hz comparison pure tone presented at 90, 70, and 30 dB SPL. The SPL of the experimental stimuli required for equal loudness was linearly related to bandwidth (in octaves) for each of the three comparison stimulus levels. In experiment 2, the loudness behavior of narrow-bandwidth stimuli within the previously reported critical band region was examined. The results indicated a linear relation similar to that obtained in experiment 1. These results are consistent with an auditory filter concept in which frequency is continuously encoded along the basilar membrane and in which loudness of complex stimuli is linearly related to area of excitation.     

Modeling auditory-nerve responses for high sound pressure levels in the normal and impaired auditory periphery

This paper presents a computational model to simulate normal and impaired auditory-nerve (AN) fiber responses in cats. The model responses match physiological data over a wider dynamic range than previous auditory models. This is achieved by providing two modes of basilar membrane excitation to the inner hair cell (IHC) rather than one. The two modes are generated by two parallel filters, component 1 (C1) and component 2 (C2), and the outputs are subsequently transduced by two separate functions. The responses are then added and passed through the IHC low-pass filter followed by the IHC-AN synapse model and discharge generator. The C1 filter is a narrow-band, chirp filter with the gain and bandwidth controlled by a nonlinear feed-forward control path. This filter is responsible for low and moderate level responses. A linear, static, and broadly tuned C2 filter followed by a nonlinear, inverted and nonrectifying C2 transduction function is critical for producing transition region and high-level effects. Consistent with Kiang's two-factor cancellation hypothesis, the interaction between the two paths produces effects such as the C1/C2 transition and peak splitting in the period histogram. The model responses are consistent with a wide range of physiological data from both normal and impaired ears for stimuli presented at levels spanning the dynamic range of hearing.     

Middle-ear response in the chinchilla and its relationship to mechanics at the base of the cochlea

The responses of the malleus and the stapes to sinusoidal acoustic stimulation have been measured in the middle ears of anesthetized chinchillas using the M?ssbauer technique. With "intact" bullas (i.e., closed except for venting via capillary tubing), the vibrations of the tip of the malleus reach a maximal peak velocity of about 2 mm/s in responses to 100-dB SPL tones in the frequency range 500-6000 Hz; vibration velocity diminishes toward lower frequencies with a slope of about 6 dB/oct. Opening the bulla widely increases the responses to low-frequency stimuli by as much as 16 dB. At low frequencies, malleus response sensitivity with either open or intact bullas far exceeds all previous measurements in cats and matches or exceeds such measurements in guinea pigs. Whether measured in open or intact bullas, phase-versus-frequency curves closely approximate those predicted from the magnitude-versus-frequency curves by minimum phase theory. The stapes responses are similar to those of the malleus, except that stapes response magnitude is lower, on the average, by 7.5 dB at frequencies below 2 kHz and 10.7 dB at 2 kHz and above. Comparison of the responses of the middle ear with those of the basilar membrane at a site 3.5 mm from the stapes indicates that, at frequencies below 150 Hz, the basilar membrane displacement is proportional to stapes acceleration. At frequencies between 150 and 2000 Hz, basilar membrane displacement is proportional to stapes velocity.     

Distortion product otoacoustic emissions and basilar membrane vibration in the 6-9 kHz region of sensitive chinchilla cochleae

Distortion product otoacoustic emissions (DPOAEs) and basilar membrane (BM) vibration were measured simultaneously in the 6-9 kHz region of chinchilla cochleae. BM-Input-Output functions in a two-tone paradigm behaved similarly to DPOAEs for the 2f1-f2 component, nonmonotonic growth with the intensity of the lower frequency primary and a notch in the functions around 60 dB SPL. Ripples in frequency functions occur in both BM and OAE curves as a function of the distortion frequency. Optimum f2/f1 ratios for DPOAE generation are near 1.2. The slope of phase curves indicates that for low f2f1(<1.1) the emission source is the place location while for f2f1>1.1 the relative constancy of the phase function suggests that the place is the nonlinear region of f2, i.e., the wave location. Magnitudes of the DPOAEs increase rapidly above 60 dB SPL suggesting a different source or mechanism at high levels. This is supported by the observation that the high level DPOAE and BM-DP responses remain for a considerable period postmortem.     

A new procedure for measuring peripheral compression in normal-hearing and hearing-impaired listeners.

Forward-masking growth functions for on-frequency (6-kHz) and off-frequency (3-kHz) sinusoidal maskers were measured in quiet and in a high-pass noise just above the 6-kHz probe frequency. The data show that estimates of response-growth rates obtained from those functions in quiet, which have been used to infer cochlear compression, are strongly dependent on the spread of probe excitation toward higher frequency regions. Therefore, an alternative procedure for measuring response-growth rates was proposed, one that employs a fixed low-level probe and avoids level-dependent spread of probe excitation. Fixed-probe-level temporal masking curves (TMCs) were obtained from normal-hearing listeners at a test frequency of 1 kHz, where the short 1-kHz probe was fixed in level at about 10 dB SL. The level of the preceding forward masker was adjusted to obtain masked threshold as a function of the time delay between masker and probe. The TMCs were obtained for an on-frequency masker (1 kHz) and for other maskers with frequencies both below and above the probe frequency. From these measurements, input/output response-growth curves were derived for individual ears. Response-growth slopes varied from >1.0 at low masker levels to <0.2 at mid masker levels. In three subjects, response growth increased again at high masker levels (>80 dB SPL). For the fixed-level probe, the TMC slopes changed very little in the presence of a high-pass noise masking upward spread of probe excitation. A greater effect on the TMCs was observed when a high-frequency cueing tone was used with the masking tone. In both cases, however, the net effects on the estimated rate of response growth were minimal.