A symmetry suppresses the cochlear catastrophe

When the independent spatial variable is defined appropriately, the empirical finding that the phase of the cochlear input impedance is small [Lynch et al., J. Acoust. Soc. Am. 72, 108-130 (1982)] is shown to imply that the wavelength of the pressure wave in the cochlea changes slowly with position near the stapes. As a result, waves traveling in either direction through the basal turn undergo little reflection, and the transfer of energy between the middle and inner ears remains efficient at low frequencies. The slow variation of the wavelength implies that the series impedance Z and shunt admittance Y of the cochlear transmission line are approximately proportional at low frequencies and thus requires that the width of the basilar membrane and the cross-sectional areas of the cochlear scalae taper in opposite directions. Maintenance of the symmetry between Z and Y is both necessary and sufficient to ensure that the spatial derivative of the wavelength, and hence the phase of the cochlear input impedance, remains small. Although introduced in another context, the model of Zweig ["Finding the impedance of the organ of Corti," J. Acoust. Soc. Am. 89, 1229-1254 (1991)] manifests the symmetry between Z and Y. In other transmission-line models of cochlear mechanics, however, that symmetry is absent, and the spatial derivative of the wavelength diverges at low frequencies--the "cochlear catastrophe." Those models therefore contradict the impedance measurements and predict little transfer of energy between the middle and inner ears.     

The effect of suppression on the periodicity of stimulus frequency otoacoustic emissions: experimental data

In a companion paper [Lineton and Lutman, J. Acoust. Soc. Am. 114, 859-870 (2003)], changes in the spectral period of stimulus frequency otoacoustic emissions (SFOAEs) during self-suppression and two-tone suppression were simulated using a nonlinear cochlear model based on the distributed roughness theory of otoacoustic emission generation [Zweig and Shera, J. Acoust. Soc. Am. 98, 2018-2047 (1995)1. The current paper presents the results of an experimental investigation of SFOAE suppression obtained from 20 human subjects. It was found that, in most subjects, the spectral period increased during self-suppression, but reduced during high-side two-tone suppression. This pattern of results is in close agreement with the predictions of the cochlear model, and therefore strongly supports the distributed roughness theory of Zweig and Shera. In addition, the results suggest that the SFOAE spectral period is sensitive to changes in the state of the cochlear amplifier.     

Unification and extension of monolithic state space and iterative cochlear models

Time domain cochlear models have primarily followed a method introduced by Allen and Sondhi [J. Acoust. Soc. Am. 66, 123-132 (1979)]. Recently the "state space formalism" proposed by Elliott et al. [J. Acoust. Soc. Am. 122, 2759-2771 (2007)] has been used to simulate a wide range of nonlinear cochlear models. It used a one-dimensional approach that is extended to two dimensions in this paper, using the finite element method. The recently developed "state space formalism" in fact shares a close relationship to the earlier approach. Working from Diependaal et al. [J. Acoust. Soc. Am. 82, 1655-1666 (1987)] the two approaches are compared and the relationship formalized. Understanding this relationship allows models to be converted from one to the other in order to utilize each of their strengths. A second method to derive the state space matrices required for the "state space formalism" is also presented. This method offers improved numerical properties because it uses the information available about the model more effectively. Numerical results support the claims regarding fluid dimension and the underlying similarity of the two approaches. Finally, the recent advances in the state space formalism [Bertaccini and Sisto, J. Comp. Phys. 230, 2575-2587 (2011)] are discussed in terms of this relationship.     

Modeling the effect of suppression on the periodicity of stimulus frequency otoacoustic emissions

The distributed roughness theory of the origins of spectral periodicity in stimulus frequency otoacoustic emissions (SFOAEs) predicts that the spectral period will be altered by suppression of the traveling wave (TW) [Zweig and Shera, J. Acoust. Soc. Am. 98, 2018-2047 (1995)]. In order to investigate this effect in more detail, simulations of the variation of the spectral period under conditions of self-suppression and two-tone suppression are obtained from nonlinear cochlear models based on this theory. The results show that during self-suppression the spectral period is increased, while during high-side two-tone suppression, the period is reduced, indicating that the detailed pattern of disruption of the cochlear amplifier must be examined if the nonlinear behavior of SFOAEs is to be understood. The model results suggest that the SFOAE spectral period may be sensitive to changes in the state of the cochlear amplifier. A companion paper [Lineton and Lutman, J. Acoust. Soc. Am. 114, 871-882 (2003)] presents experimental data which are compared with the results of the above models with a view to testing the underlying theory of Zweig and Shera.     

Analyzing reverse middle-ear transmission: noninvasive Gedankenexperiments.

The phenomenological framework outlined in the companion paper [C. A. Shera and G. Zweig, J. Acoust. Soc. Am. 92, 1356-1370 (1992)] characterizes both forward and reverse transmission through the middle ear. This paper illustrates its use in the analysis of noninvasive measurements of middle-ear and cochlear mechanics. A cochlear scattering framework is developed for the analysis of combination-tone and other experiments in which acoustic distortion products are used to drive the middle ear "in reverse." The framework is illustrated with a simple psychophysical Gedankenexperiment analogous to the neurophysiological experiments of P. F. Fahey and J. B. Allen [J. Acoust. Soc. Am. 77, 599-612 (1985)].     

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.     

Cochlear compression wave: an implication of the Allen-Fahey experiment

In order to measure the gain of the cochlear amplifier, de Boer and co-workers recently extended the Allen-Fahey experiment by measuring otoacoustic emissions and basilar membrane vibration [J. Acoust. Soc. Am. 117, 1260-1266 (2005)]. Although this new experiment overcame the limitation of the original Allen-Fahey experiment for using a low-frequency ratio, it confirmed the previous finding that there is no detectable cochlear amplification. This result was attributed to destructive interference of the otoacoustic emission over its generation site. The present letter provides an alternative interpretation of the results of the Allen-Fahey experiment based on the cochlear fluid compression-wave theory.     

Temporary threshold shifts after onset and offset of moderately loud low-frequency maskers

Moderately loud low-frequency maskers produce temporary threshold shifts which oscillate for a few minutes in reproducible patterns not only after their offset, but also after their onset. The temporal variations of threshold show "bounces" similar to those found by Hirsh and Ward [J. Acoust. Soc. Am. 24, 131-141 (1952)] after the offset of very loud maskers. In the present paper, threshold shifts of up to 30 dB are reported for pauses of 3-min duration in continuous maskers. These effects could originate in the internal cochlear metabolism, the steady-state condition of which seems to be influenced by the moderately loud low-frequency tones.     

Comparison of WKB and finite difference calculations for a two-dimensional cochlear model.

There are many points of uncertainty in the subject of cochlear models. In this paper only the question of efficient computing methods is addressed. For the cochlear model with a one-dimensional approximation for the fluid motion, Zweig, Lipes, and Pierce [J. Acoust. Soc. Am. 59, 975-982 (1976)] have shown that the WKB method agrees well with a direct numerical integration. For the two-dimensional fluid model, Neely [E.D. thesis, California Institute of Technology, Pasadena, CA (1977)] has shown that a direct finite difference solution is an order of magnitude faster than the integral equation approach used by Allen [J. Acoust. Soc. Am 61, 110-119 (1977)]. In the present work, a formal WKB solution is derived following Whitham [Linear and Nonlinear Waves (Wiley, New York, 1974)]. The advantage of this formulation is simplicity, but the disadvantage is that no error estimate is available. We find that the numerical results from the WKB solution agree well with those of Neely (1977), while the computer time is reduced by another order of magnitude. Thus, the WKB method seems to offer the satisfactory accuracy, efficiency, and flexibility for treating the more realistic cochlear models.     

A parametric model of the spectral periodicity of stimulus frequency otoacoustic emissions

A model for estimating the spectral period of stimulus frequency otoacoustic emissions (SFOAEs) is presented. The model characterizes the frequency spectrum of an SFOAE in terms of four parameters which can be directly related to cochlear mechanical quantities featuring in the theory of SFOAE generation proposed by Zweig and Shera [J. Acoust. Soc. Am. 98, 2018-2047 (1995)]. The results of applying the parametric model to SFOAEs generated by cochlear models suggest that it gives a sensitive measure of spectral period. It is concluded that the parametric model may be a useful tool for detecting small changes in cochlear function using SFOAE measurements.     

Suppression tuning in noise-exposed rabbits

Psychophysical, basilar-membrane (BM), and single nerve-fiber tuning curves, as well as suppression of distortion-product otoacoustic emissions (DPOAEs), all give rise to frequency tuning patterns with stereotypical features. Similarities and differences between the behaviors of these tuning functions, both in normal conditions and following various cochlear insults, have been documented. While neural tuning curves (NTCs) and BM tuning curves behave similarly both before and after cochlear insults known to disrupt frequency selectivity, DPOAE suppression tuning curves (STCs) do not necessarily mirror these responses following either administration of ototoxins [Martin et al., J. Acoust. Soc. Am. 104, 972-983 (1998)] or exposure to temporarily damaging noise [Howard et al., J. Acoust. Soc. Am. 111, 285-296 (2002)]. However, changes in STC parameters may be predictive of other changes in cochlear function such as cochlear immaturity in neonatal humans [Abdala, Hear. Res. 121, 125-138 (1998)]. To determine the effects of noise-induced permanent auditory dysfunction on STC parameters, rabbits were exposed to high-level noise that led to permanent reductions in DPOAE level, and comparisons between pre- and postexposure DPOAE levels and STCs were made. Statistical comparisons of pre- and postexposure STC values at CF revealed consistent basal shifts in the frequency region of greatest cochlear damage, whereas thresholds, Q10dB, and tip-to-tail gain values were not reliably altered. Additionally, a large percentage of high-frequency lobes associated with third tone interference phenomena, that were exhibited in some data sets, were dramatically reduced following noise exposure. Thus, previously described areas of DPOAE interference above f2 may also be studied using this type of experimental manipulation [Martin et al., Hear. Res. 136, 105-123 (1999); Mills, J. Acoust. Soc. Am. 107, 2586-2602 (2002)].     

A comparison of broadband models for sand sediments

Chotiros and Isakson [J. Acoust. Soc. Am. 116(4), 2011-2022 (2004)] recently proposed an extension of the Biot-Stoll model for poroelastic sediments that makes predictions for compressional wave speed and attenuation, which are in much better accord with the experimental measurements of these quantities extant in the literature than either those of the conventional Biot-Stoll model or the rival model of Buckingham [J. Acoust. Soc. Am. 108(6), 2796-2815 (2000)]. Using a local minimizer, the Nelder-Mead simplex method, it is shown that there are generally at least two choices of the Chotiros-Isakson parameters which produce good agreement with experimental measurements. Since one postulate of the Chotiros-Isakson model is that, due to the presence of air bubbles in the pore space, the pore fluid compressibility is greater than that of water, an alternative model based on a conjecture by Biot [J. Acoust. Soc. Am. 34(5), 1254-1264 (1962)], air bubble resonance, is considered. While this model does as well or better than the Chotiros-Isakson model in predicting measured values of wave speed and attenuation, the Rayleigh-Plesset theory of bubble oscillation casts doubt on its plausibility as a general explanation of large dispersion of velocity with respect to frequency.     

Spectral weighting strategies for sentences measured by a correlational method

Listeners' ability to understand speech in adverse listening conditions is partially due to the redundant nature of speech. Natural redundancies are often lost or altered when speech is filtered, such as done in AI/SII experiments. It is important to study how listeners recognize speech when the speech signal is unfiltered and the entire broadband spectrum is present. A correlational method [R. A. Lutfi, J. Acoust. Soc. Am. 97, 1333-1334 (1995); V. M. Richards and S. Zhu, J. Acoust. Soc. Am. 95, 423-424 (1994)] has been used to determine how listeners use spectral cues to perceive nonsense syllables when the full speech spectrum is present [K. A. Doherty and C. W. Turner, J. Acoust. Soc. Am. 100, 3769-3773 (1996); C. W. Turner et al., J. Acoust. Soc. Am. 104, 1580-1585 (1998)]. The experiments in this study measured spectral-weighting strategies for more naturally occurring speech stimuli, specifically sentences, using a correlational method for normal-hearing listeners. Results indicate that listeners placed the greatest weight on spectral information within bands 2 and 5 (562-1113 and 2807-11,000 Hz), respectively. Spectral-weighting strategies for sentences were also compared to weighting strategies for nonsense syllables measured in a previous study (C. W. Turner et al., 1998). Spectral-weighting strategies for sentences were different from those reported for nonsense syllables.     

Modeling the temporal behavior of distortion product otoacoustic emissions

The temporal behavior of the 2f1-f2 distortion product otoacoustic emission is theoretically investigated for the case in which the lower frequency (f1) primary tone is on continuously, and the higher frequency (f2) one is pulsed on and off [e.g., Talmadge et al., J. Acoust. Soc. Am. 105, 275-292 (1999)]. On physical grounds, this behavior is expected to be characterized by various group delays associated with the propagation of (1) the f2 cochlear primary wave between the cochlear base and the primary distortion product generation region around x2 (the f2 tonotopic place), and (2) the 2f1-f2 cochlear distortion product (DP) waves between the cochlear base, the primary generation region of the distortion product, and the region around the 2f1-f2 tonotopic place where the generated apical moving DP wave is reflected toward the cochlear base [e.g., Talmadge et al., J. Acoust. Soc. Am. 104, 1517-1543 (1998)]. An approximate analytic expression is obtained for this behavior from the analysis of the Fourier integral representation of the auditory peripheral response to the primary stimuli. This expression also approximately describes the transient build-up of the components of different latencies in terms of the damping properties of the cochlear partition. It is shown that considerable caution must be applied in attempting to relate phase derivatives of the distortion product otoacoustic emissions for steady state stimuli and the physical time delays which are associated with the temporal behavior of a distortion product emission in the case of a pulsed primary.     

On boundary conditions for the diffusion equation in room-acoustic prediction: Theory, simulations, and experiments

This paper proposes a modified boundary condition to improve the room-acoustic prediction accuracy of a diffusion equation model. Previous boundary conditions for the diffusion equation model have certain limitations which restrict its application to a certain number of room types. The boundary condition employing the Sabine absorption coefficient [V. Valeau et al., J. Acoust. Soc. Am. 119, 1504-1513 (2006)] cannot predict the sound field well when the absorption coefficient is high, while the boundary condition employing the Eyring absorption coefficient [Y. Jing and N. Xiang, J. Acoust. Soc. Am. 121, 3284-3287 (2007); A. Billon et al., Appl. Acoust. 69, (2008)] has a singularity whenever any surface material has an absorption coefficient of 1.0. The modified boundary condition is derived based on an analogy between sound propagation and light propagation. Simulated and experimental data are compared to verify the modified boundary condition in terms of room-acoustic parameter prediction. The results of this comparison suggest that the modified boundary condition is valid for a range of absorption coefficient values and successfully eliminates the singularity problem.     

On the interpretability of speech/nonspeech comparisons: a reply to Fowler

Fowler [J. Acoust. Soc. Am. 88, 1236-1249 (1990)] makes a set of claims on the basis of which she denies the general interpretability of experiments that compare the perception of speech sounds to the perception of acoustically analogous nonspeech sound. She also challenges a specific auditory hypothesis offered by Diehl and Walsh [J. Acoust. Soc. Am. 85, 2154-2164 (1989)] to explain the stimulus-length effect in the perception of stops and glides. It will be argued that her conclusions are unwarranted.     

Intensity perception. XIII. Perceptual anchor model of context-coding

In our preliminary theory of intensity resolution [e.g., see N. I. Durlach and L. D. Braida, J. Acoust. Soc. Am. 46, 372-383 (1969)], two modes of memory operation are postulated: the trace mode and the context-coding mode. In this paper, we present a revised model of the context-coding mode which describes explicitly a process by which sensations are coded relative to the context and which predicts a resolution edge effect [L. D. Braida and N. I. Durlach, J. Acoust. Soc. Am. 51, 483-502 (1972); J. E. Berliner, L. D. Braida, and N. I. Durlach, J. Acoust. Soc. Am. 61, 1256-1267 (1977)]. The sensation arising from a given stimulus presentation is coded by determining its distance from internal references or perceptual anchors. The noise in this process, combined with the sensation noise, constitutes the limitation on resolution in the model. In the revised model the probability density functions of the decision variable are not precisely Gaussian (and cannot be expressed analytically in closed form). This paper outlines the predictions of the model for one-interval paradigms and for fixed-level two-interval paradigms and derives estimates of the values of model parameters.     

Use of an adaptive-bandwidth protocol to measure importance functions for simulated cochlear implant frequency channels

The Articulation Index and Speech Intelligibility Index predict intelligibility scores from measurements of speech and hearing parameters. One component in the prediction is the frequency-importance function, a weighting function that characterizes contributions of particular spectral regions of speech to speech intelligibility. The purpose of this study was to determine whether such importance functions could similarly characterize contributions of electrode channels in cochlear implant systems. Thirty-eight subjects with normal hearing listened to vowel-consonant-vowel tokens, either as recorded or as output from vocoders that simulated aspects of cochlear implant processing. Importance functions were measured using the method of Whitmal and DeRoy [J. Acoust. Soc. Am. 130, 4032-4043 (2011)], in which signal bandwidths were varied adaptively to produce specified token recognition scores in accordance with the transformed up-down rules of Levitt [J. Acoust. Soc. Am. 49, 467-477 (1971)]. Psychometric functions constructed from recognition scores were subsequently converted into importance functions. Comparisons of the resulting importance functions indicate that vocoder processing causes peak importance regions to shift downward in frequency. This shift is attributed to changes in strategy and capability for detecting voicing in speech, and is consistent with previously measured data.