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.     

Mammalian spontaneous otoacoustic emissions are amplitude-stabilized cochlear standing waves

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

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.     

Delays of stimulus-frequency otoacoustic emissions and cochlear vibrations contradict the theory of coherent reflection filtering

When stimulated by tones, the ear appears to emit tones of its own, stimulus-frequency otoacoustic emissions (SFOAEs). SFOAEs were measured in 17 chinchillas and their group delays were compared with a place map of basilar-membrane vibration group delays measured at the characteristic frequency. The map is based on Wiener-kernel analysis of responses to noise of auditory-nerve fibers corroborated by measurements of vibrations at several basilar-membrane sites. SFOAE group delays were similar to, or shorter than, basilar-membrane group delays for frequencies >4 kHz and <4 kHz, respectively. Such short delays contradict the generally accepted "theory of coherent reflection filtering" [Zweig and Shera, J. Acoust. Soc. Am. 98, 2018-2047 (1995)], which predicts that the group delays of SFOAEs evoked by low-level tones approximately equal twice the basilar-membrane group delays. The results for frequencies higher than 4 kHz are compatible with hypotheses of SFOAE propagation to the stapes via acoustic waves or fluid coupling, or via reverse basilar membrane traveling waves with speeds corresponding to the signal-front delays, rather than the group delays, of the forward waves. The results for frequencies lower than 4 kHz cannot be explained by hypotheses based on waves propagating to and from their characteristic places in the cochlea.     

Modeling cochlear dynamics: interrelation between cochlea mechanics and psychoacoustics

A model of the cochlea was used to bridge the gap between model approaches commonly used to investigate phenomena related to otoacoustic emissions and more filter-based model approaches often used in psychoacoustics. In the present study, a nonlinear and active one-dimensional transmission line model was developed that accounts for several aspects of physiological data with a single fixed parameter set. The model shows plausible excitation patterns and an input-output function similar to the linear-compressive-linear function as hypothesized in psychoacoustics. The model shows realistic results in a two-tone suppression paradigm and a plausible growth function of the 2f(1)-f(2) component of distortion product otoacoustic emissions. Finestructure was found in simulated stimulus-frequency otoacoustic emissions (SFOAE) with realistic levels and rapid phase rotation. A plausible "threshold in quiet" including finestructure and spontaneous otoacoustic emissions (SOAE) could be simulated. It is further shown that psychoacoustical data of modulation detection near threshold can be explained by the mechanical dynamics of the modeled healthy cochlea. It is discussed that such a model can be used to investigate the representation of acoustic signals in healthy and impaired cochleae at this early stage of the auditory pathway for both, physiological as well as psychoacoustical paradigms.     

Low-frequency characteristics of human and guinea pig cochleae

Previous physiological studies investigating the transfer of low-frequency sound into the cochlea have been invasive. Predictions about the human cochlea are based on anatomical similarities with animal cochleae but no direct comparison has been possible. This paper presents a noninvasive method of observing low frequency cochlear vibration using distortion product otoacoustic emissions (DPOAE) modulated by low-frequency tones. For various frequencies (15-480 Hz), the level was adjusted to maintain an equal DPOAE-modulation depth, interpreted as a constant basilar membrane displacement amplitude. The resulting modulator level curves from four human ears match equal-loudness contours (ISO226:2003) except for an irregularity consisting of a notch and a peak at 45 Hz and 60 Hz, respectively, suggesting a cochlear resonance. This resonator interacts with the middle ear stiffness. The irregularity separates two regions of the middle ear transfer function in humans: A slope of 12 dB/octave below the irregularity suggests mass-controlled impedance resulting from perilymph movement through the helicotrema; a 6-dB/octave slope above the irregularity suggests resistive cochlear impedance and the existence of a traveling wave. The results from four guinea pig ears showed a 6-dB/octave slope on either side of an irregularity around 120 Hz, and agree with published data.     

Effects of low-frequency biasing on spontaneous otoacoustic emissions: amplitude modulation

The dynamic effects of low-frequency biasing on spontaneous otoacoustic emissions (SOAEs) were studied in human subjects under various signal conditions. Results showed a combined suppression and modulation of the SOAE amplitudes at high bias tone levels. Ear-canal acoustic spectra demonstrated a reduction in SOAE amplitude and growths of sidebands while increasing the bias tone level. These effects varied depending on the relative strength of the bias tone to a particular SOAE. The SOAE magnitudes were suppressed when the cochlear partition was biased in both directions. This quasi-static modulation pattern showed a shape consistent with the first derivative of a sigmoid-shaped nonlinear function. In the time domain, the SOAE amplitudes were modulated with the instantaneous phase of the bias tone. For each biasing cycle, the SOAE envelope showed two peaks each corresponded to a zero crossing of the bias tone. The temporal modulation patterns varied systematically with the level and frequency of the bias tone. These dynamic behaviors of the SOAEs are consistent with the shifting of the operating point along the nonlinear transducer function of the cochlea. The results suggest that the nonlinearity in cochlear hair cell transduction may be involved in the generation of SOAEs.     

Manifestations of intense noise stimulation on spontaneous otoacoustic emission and threshold microstructure: experiment and model.

Comparison between changes that occur simultaneously on spontaneous otoacoustic emissions (SOAEs) and on other cochlear origin phenomena can contribute to the understanding of cochlear micromechanical activity. The temporary changes that arise after short noise exposure are investigated in the following paper. The effects of noise exposure on the threshold microstructure near an SOAE and on the amplitude and frequency of the SOAE were measured. These experimental results indicate the following: (1) exposure to wideband noise for a short time causes a temporary reduction in the SOAE frequency and amplitude, and alters reversibly the threshold microstructure in the vicinity of the SOAE. The difference between the minimum and maximum in the threshold microstructure is reduced, and the frequency that yields the minimum threshold decreases; (2) the threshold at the SOAE frequency is most sensitive to noise exposure; (3) intense stimulation causes a relatively small increase, or even a decrease, in threshold at frequencies near the SOAE. The experimental results are interpreted in terms of a nonlinear transmission line model which includes nonlinear amplifiers. The effect of the noise exposure is modeled by reduction in the cochlear partition amplification term. Most of the experimental results are predicted by this model.     

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.     

A model for active elements in cochlear biomechanics

A linear, mathematical model of cochlear biomechanics is presented in this paper. In this model, active elements are essential for simulating the high sensitivity and sharp tuning characteristic of the mammalian cochlea. The active elements are intended to represent the motile action of outer hair cells; they are postulated to be mechanical force generators that are powered by electrochemical energy of the cochlear endolymph, controlled by the bending of outer hair cell stereocilia, and bidirectionally coupled to cochlear partition mechanics. The active elements are spatially distributed and function collectively as a cochlear amplifier. Excessive gain in the cochlear amplifier causes spontaneous oscillations and thereby generates spontaneous otoacoustic emissions.     

Acoustics of the human middle-ear air space

The impedance of the middle-ear air space was measured on three human cadaver ears with complete mastoid air-cell systems. Below 500 Hz, the impedance is approximately compliance-like, and at higher frequencies (500-6000 Hz) the impedance magnitude has several (five to nine) extrema. Mechanisms for these extrema are identified and described through circuit models of the middle-ear air space. The measurements demonstrate that the middle-ear air space impedance can affect the middle-ear impedance at the tympanic membrane by as much as 10 dB at frequencies greater than 1000 Hz. Thus, variations in the middle-ear air space impedance that result from variations in anatomy of the middle-ear air space can contribute to inter-ear variations in both impedance measurements and otoacoustic emissions, when measured at the tympanic membrane.     

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.     

Theory of forward and reverse middle-ear transmission applied to otoacoustic emissions in infant and adult ears

The purpose of this study is to understand why otoacoustic emission (OAE) levels are higher in normal-hearing human infants relative to adults. In a previous study, distortion product (DP) OAE input/output (I/O) functions were shown to differ at f2 = 6 kHz in adults compared to infants through 6 months of age. These DPOAE I/0 functions were used to noninvasively assess immaturities in forward/reverse transmission through the ear canal and middle ear [Abdala, C., and Keefe, D. H., (2006). J. Acoust Soc. Am. 120, 3832-3842]. In the present study, ear-canal reflectance and DPOAEs measured in the same ears were analyzed using a scattering-matrix model of forward and reverse transmission in the ear canal, middle ear, and cochlea. Reflectance measurements were sensitive to frequency-dependent effects of ear-canal and middle-ear transmission that differed across OAE type and subject age. Results indicated that DPOAE levels were larger in infants mainly because the reverse middle-ear transmittance level varied with ear-canal area, which differed by more than a factor of 7 between term infants and adults. The forward middle-ear transmittance level was -16 dB less in infants, so that the conductive efficiency was poorer in infants than adults.     

Investigating the wave-fixed and place-fixed origins of the 2f(1)-f(2) distortion product otoacoustic emission within a micromechanical cochlear model

The 2f(1)-f(2) distortion product otoacoustic emission (DPOAE) arises within the cochlea due to the nonlinear interaction of two stimulus tones (f(1) and f(2)). It is thought to comprise contributions from a wave-fixed source and a place-fixed source. The generation and transmission of the 2f(1)-f(2) DPOAE is investigated here using quasilinear solutions to an elemental model of the human cochlea with nonlinear micromechanics. The micromechanical parameters and nonlinearity are formulated to match the measured response of the cochlea to single- and two-tone stimulation. The controlled introduction of roughness into the active micromechanics of the model allows the wave- and place-fixed contributions to the DPOAE to be studied separately. It is also possible to manipulate the types of nonlinear suppression that occur within the quasilinear model to investigate the influence of stimulus parameters on DPOAE generation. The model predicts and explains a variety of 2f(1)-f(2) DPOAE phenomena: The dependence of emission amplitude on stimulus parameters, the weakness of experiments designed to quantify cochlear amplifier gain, and the predominant mechanism which gives rise to DPOAE fine structure. In addition, the model is used to investigate the properties of the wave-fixed source and how these properties are influenced by the stimulus parameters.     

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

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

Explosive synchronization enhances selectivity: Example of the cochlea

Acoustical signal transduction in the cochlea is an active process that involves nonlinear amplification and spontaneous otoacoustic emissions. Signal transduction involves individual subunits composed of globally coupled hair cells, which can be modeled as oscillators close to a Hopf bifurcation. The coupling may induce a transition toward synchronization, which in turn leads to a strong nonlinear response. In the model studied here, the synchronization transition of the subunit is discontinuous (explosive) in the absence of an external stimulus. We show that, in the presence of an external stimulus and for a coupling strength slightly lower than the critical value leading to explosive synchronization, the response of the subunit has better frequency selectivity and a larger signal-to-noise ratio. From physiological observations that subunits are themselves coupled together, we further propose a model of the complete cochlea, accounting for the ensemble of frequencies that the organ is able to detect.     

The breaking of cochlear scaling symmetry in human newborns and adults

Scaling symmetry appears to be a fundamental property of the cochlea as evidenced by invariant distortion product otoacoustic emission (DPOAE) phase above ～1-1.5 kHz when using frequency-scaled stimuli. Below this frequency demarcation, phase steepens. Cochlear scaling and its breaking have been described in the adult cochlea but have not been studied in newborns. It is not clear whether immaturities in cochlear mechanics exist at birth in the human neonate. In this study, DPOAE phase was recorded with a swept-tone protocol in three, octave-wide segments from 0.5 to 4 kHz. The lowest-frequency octave was targeted with increased signal averaging to enhance signal-to-noise ratio (SNR) and focus on the apical half of the newborn cochlea where breaks from scaling have been observed. The results show: (1) the ear canal DPOAE phase was dominated by the distortion-source component in the low frequencies; thus, the reflection component cannot explain the steeper slope of phase; (2) DPOAE phase-frequency functions from adults and infants showed an unambiguous discontinuity around 1.4 and 1 kHz when described using two- and three-segment fits, respectively, and (3) newborns had a significantly steeper slope of phase in the low-frequency portion of the function which may suggest residual immaturities in the apical half of the newborn cochlea.     

Longitudinal endolymph movements and endocochlear potential changes induced by stimulation at infrasonic frequencies.

The inner ear is continually exposed to pressure fluctuations in the infrasonic frequency range (< 20 Hz) from external and internal body sources. The cochlea is generally regarded to be insensitive to such stimulation. The effects of stimulation at infrasonic frequencies (0.1 to 10 Hz) on endocochlear potential (EP) and endolymph movements in the guinea pig cochlea were studied. Stimuli were applied directly to the perilymph of scala tympani or scala vestibuli of the cochlea via a fluid-filled pipette. Stimuli, especially those near 1 Hz, elicited large EP changes which under some conditions exceeded 20 mV in amplitude and were equivalent to a cochlear microphonic (CM) response. Accompanying the electrical responses was a cyclical, longitudinal displacement of the endolymph. The amplitude and phase of the CM varied according to which perilymphatic scala the stimuli were applied to and whether a perforation was made in the opposing perilymphatic scala. Spontaneously occurring middle ear muscle contractions were also found to induce EP deflections and longitudinal endolymph movements comparable to those generated by perilymphatic injections. These findings suggest that cochlear fluid movements induced by pressure fluctuations at infrasonic frequencies could play a role in fluid homeostasis in the normal state and in fluid disturbances in pathological states.     

A comparative study of distortion-product-otoacoustic-emission fine structure in human newborns and adults with normal hearing

Distortion product otoacoustic emissions (DPOAE) measured in human newborns are not adult-like. More than a decade of work from various investigators has created a well-developed body of evidence describing these differences but the putative anatomy or physiology has only been partially explained. Recently, Abdala and Keefe [J. Acoust. Soc. Am. 120, 3832-3842 (2006)] have identified outer and middle ear immaturities that at least partially describe the differences observed between newborn and adult input-output functions and suppression tuning curves. DPOAE fine structure characteristics and their maturation have not been examined to any extent in the literature. Fine structure characteristics in two groups of ten newborns and young adults with normal hearing sensitivity are compared here. Consistent with previous reports, the newborns show higher DPOAE levels; greater fine structure depth and wider fine structure spacing is also observed in the newborns. Differences in fine structure morphology are also observed between the two age groups. While some of these findings are attributable to an immature outer and middle ear system in the newborns, it is argued that some observed differences in fine structure characteristics might be due to remnant immaturities in passive motion of the basilar membrane in the newborn cochlea.     

Stimulus-frequency-emission group delay: a test of coherent reflection filtering and a window on cochlear tuning

This paper tests and applies a key prediction of the theory of coherent reflection filtering for the generation of reflection-source otoacoustic emissions. The theory predicts that reflection-source-emission group delay is determined by the group delay of the basilar-membrane (BM) transfer function at its peak. This prediction is tested over a seven-octave frequency range in cats and guinea pigs using measurements of stimulus-frequency-emission (SFOAE) group delay. A comparison with group delays calculated from published measurements of BM mechanical transfer functions supports the theory at the basal end of the cochlea. A comparison across the whole frequency range based on variations in the sharpness of neural tuning with characteristic frequency (CF) suggests that the predicted relation holds in the basal-most 60% of the cochlea. At the apical end of the cochlea, however, the measurements disagree with neural and mechanical group delays. This disagreement suggests that there are important differences in cochlear mechanics and/or mechanisms of emission generation between the base and apex of the cochlea. Measurements in humans over a four-octave range indicate that human SFOAE group delays are roughly a factor of 3 longer than their counterparts in cat and guinea pig but manifest similar trends across CF. The measurements thus reveal global deviations from scaling whose form appears quantitatively similar in all three species. Interpreted using the theory of coherent reflection filtering, the group delay measurements indicate that the wavelength at the peak of the traveling wave decreases with increasing CF at a rate of roughly 25% per octave in the base of the cochlea. The measurements and analysis reported here illustrate the rich potential inherent in OAE measurements for obtaining valuable information about basic cochlear properties such as tuning.