On the relationships between the fixed-f1, fixed-f2, and fixed-ratio phase derivatives of the 2f1-f2 distortion product otoacoustic emission.

For primary frequency ratios, f2/f1, in the range 1.1-1.3, the fixed-f1 ("f2-sweep") phase derivative of the 2f1-f2 distortion product otoacoustic emission (DPOAE) is larger than the fixed-f2("f1-sweep") one. It has been proposed by some researchers that part or all of the difference between these delays may be attributed to the so-called cochlear filter "build-up" or response time in the DPOAE generation region around the f2 tonotopic site. The analysis of an approximate theoretical expression for the DPOAE signal [Talmadge et al., J. Acoust. Soc. Am. 104, 1517-1543 (1998)] shows that the contributions to the phase derivatives associated with the cochlear filter response is small. It is also shown that the difference between the phase derivatives can be qualitatively accounted for by assuming the approximate scale invariance of cochlear mechanics. The effects of DPOAE fine structure on the phase derivative are also explored, and it is found that the interpretation of the phase derivative in terms of the phase variation of a single DPOAE component can be quite problematic.

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.

Interrelations among distortion-product phase-gradient delays: their connection to scaling symmetry and its breaking.

Distortion-product-otoacoustic-emission (DPOAE) phase-versus-frequency functions and corresponding phase-gradient delays have received considerable attention because of their potential for providing information about mechanisms of emission generation, cochlear wave latencies, and characteristics of cochlear tuning. The three measurement paradigms in common use (fixed-f1, fixed-f2, and fixed-f2/f1) yield significantly different delays, suggesting that they depend on qualitatively different aspects of cochlear mechanics. In this paper, theory and experiment are combined to demonstrate that simple phenomenological arguments, which make no detailed mechanistic assumptions concerning the underlying cochlear mechanics, predict relationships among the delays that are in good quantitative agreement with experimental data obtained in guinea pigs. To understand deviations between the simple theory and experiment, a general equation is found that relates the three delays for any deterministic model of DPOAE generation. Both model-independent and exact, the general relation provides a powerful consistency check on the measurements and a useful tool for organizing and understanding the structure in DPOAE phase data (e.g., for interpreting the relative magnitudes and intensity-dependencies of the three delays). Analysis of the general relation demonstrates that the success of the simple, phenomenological approach can be understood as a consequence of the mechanisms of emission generation and the approximate local scaling symmetry of cochlear mechanics. The general relation is used to quantify deviations from scaling manifest in the measured phase-gradient delays; the results indicate that deviations from scaling are typically small and that both linear and nonlinear mechanisms contribute significantly to these deviations. Intensity-dependent mechanisms contributing to deviations from scaling include cochlear-reflection and wave-interference effects associated with the mixing of distortion- and reflection-source emissions (as in DPOAE fine structure). Finally, the ratio of the fixed-f1 and fixed-f2 phase-gradient delays is shown to follow from the choice of experimental paradigm and, in the scaling limit, contains no information about cochlear physiology whatsoever. These results cast considerable doubt on the theoretical basis of recent attempts to use relative DPOAE phase-gradient delays to estimate the bandwidths of peripheral auditory filters.

Modeling the combined effects of basilar membrane nonlinearity and roughness on stimulus frequency otoacoustic emission fine structure.

A theoretical framework for describing the effects of nonlinear reflection on otoacoustic emission fine structure is presented. The following models of cochlear reflection are analyzed: weak nonlinearity, distributed roughness, and a combination of weak nonlinearity and distributed roughness. In particular, these models are examined in the context of stimulus frequency otoacoustic emissions (SFOAEs). In agreement with previous studies, it is concluded that only linear cochlear reflection can explain the underlying properties of cochlear fine structures. However, it is shown that nonlinearity can unexpectedly, in some cases, significantly modify the level and phase behaviors of the otoacoustic emission fine structure, and actually enhance the pattern of fine structures observed. The implications of these results on the stimulus level dependence of SFOAE fine structure are also explored.

Experimental confirmation of the two-source interference model for the fine structure of distortion product otoacoustic emissions.

High-resolution measurements of distortion product otoacoustic emissions (DPOAEs) from three different experimental paradigms are shown to be in agreement with the implications of a realistic "two-source" cochlear model of DPOAE fine structure. The measurements of DPOAE amplitude and phase imply an interference phenomenon involving one source in the region of strong nonlinear interaction of the primary waves (the strong "overlap" or generation region), and the other source region around the DPOAE tonotopic place. The component from the DPOAE place can be larger than the one from the generator region. These findings are supported by the analysis of the onset and offset of the DPOAE when the higher-frequency primary is pulsed on and off. The two-source hypothesis was further tested by adding a third tone closer in frequency to the DPOAE which modifies the amplitude of the component from the DPOAE place and leaves the one from the generator region unchanged. The results agree well with the model prediction that the variation with frequency, and implied latency, of the phase of the DPOAE tonotopic-place component are greater than the corresponding quantities for the component from the generation region.

Modeling otoacoustic emission and hearing threshold fine structures.

A class of cochlear models which account for much of the characteristic variation with frequency of human otoacoustic emissions and hearing threshold microstructure is presented. The models are based upon wave reflections via distributed spatial cochlear inhomogeneities and tall and broad cochlear activity patterns, as suggested by Zweig and Shera [J. Acoust. Soc. Am. 98, 2018-2047 (1995)]. They successfully describe in particular the following features: (1) the characteristic quasiperiodic frequency variations (fine structures) of the hearing threshold, synchronous and click-evoked emissions, distortion-product emissions, and spontaneous emissions; (2) the relationships between these fine structures; and (3) the distortion product emission filter shape. All of the characteristic frequency spacings are approximately the same (0.4 bark) and are mainly determined by the phase behavior of the apical reflection function. The frequency spacings for spontaneous emissions and threshold microstructure are predicted to be the same, but some deviations from these values are predicted for synchronous and click-evoked and distortion-product emissions. The analysis of models is aided considerably by the use of the solutions of apical, and basal, moving solutions (basis functions) of the cochlear wave equation in the absence of inhomogeneities.

Ear canal reflectance in the presence of spontaneous otoacoustic emissions. I. Limit-cycle oscillator model.

Allen et al. [Abstract in Eighteenth Midwinter Research Meeting of the Association for Research in Otolaryngology, Des Moines, IA (1995)] have found that the ear canal reflectance passes through a minimum around the frequency of a spontaneous otoacoustic emission (SOAE). They considered this result to constitute evidence against active nonlinear cochlear function as the basis for SOAEs. In order to investigate theoretically the expected behavior of ear canal reflectance in the neighborhood of a SOAE associated with an active-nonlinear cochlea, we use a simplified model in which the ear drum end of the ear canal is effectively terminated by a nonlinear-active element. Under the influence of a sinusoidal driver at the entrance of the ear canal, this element will, to a good approximation, either (1) oscillate at both the frequency of the driver (at which the reflectance is determined) and the SOAE (at a suppressed level, corresponding to nonentrainment), or (2) be entrained and only oscillate at the driving frequency. The magnitude of the nonlinear ear canal reflectance is found to exceed unity only at sufficiently low stimulus levels, and occurs under conditions of entrainment and nonentrainment of the spontaneous emission. Otherwise, the reflectance is less than unity and, as a function of frequency, has a minimum around the SOAE frequency.

Spontaneous otoacoustic emission frequency is modulated by heartbeat.

Detailed analysis of spontaneous otoacoustic emissions (SOAEs) in human subjects revealed that all stable SOAEs sufficiently above the noise floor to permit appropriate analysis have sidebands at multiples of approximately 1 Hz. This is consistent with the hypothesis that SOAEs are modulated by heartbeat. Simultaneous measurement of the rate of blood flow to the thumb and the separation of the spectral sidebands demonstrated that they covary (r = 0.982, p < 5 x 10(-10)). An adaptive least-squares fit (LSF) paradigm was developed to facilitate the measurement of the instantaneous frequency and amplitude of the signals. A combination of traditional spectral analyses and new LSF analyses showed that the sideband generation stems from frequency modulation of the emissions. If there is any amplitude modulation correlated with the blood flow, it is below the noise floor of the analysis. The frequency of the emission was at a minimum when the blood flow was maximal. Examination of alternative mechanisms using computer simulations suggests that these changes stem from changes of 10-100 ppm in the mass of the basilar membrane.

Relaxation dynamics of spontaneous otoacoustic emissions perturbed by external tones. III. Response to a single tone at multiple suppression levels.

The relaxation dynamics of spontaneous otoacoustic emissions (SOAEs) interacting with an external tone have been successfully described using a van der Pol limit cycle oscillator model [Murphy et al., J. Acoust. Soc. Am. 97, 3702-3710 (1995) and Murphy et al., J. Acoust. Soc. Am. 97, 3711-3720 (1995)]. Data were collected for an SOAE interacting with a single-frequency ipsilateral suppressor. Transitions between different suppressed states were achieved by adding or removing signal at the suppressor frequency. The relaxation dynamics of the van der Pol model provided a good fit to the data.

Relaxation dynamics of spontaneous otoacoustic emissions perturbed by external tones. I. Response to pulsed single-tone suppressors.

The dynamic aspects of the suppression of spontaneous otoacoustic emissions by external tones are evaluated. A Van der Pol oscillator driven by an external tone is used as an interpretive model for data on the pulsed suppression of spontaneous emissions obtained from six female subjects. Typical results for both the onset of, and recovery from suppression yield 1/r1 (where -r1 is the negative linear component of the damping function) in the range of 2-25 ms. In accordance with the predictions of the model, (a) the relaxation time for the onset of suppression increases with the amount of suppression induced by the external tone, (b) the values of r1 and the amplitudes of the unsuppressed emissions exhibit an inverse correlation, (c) the values inferred for r1 are not significantly dependent on the frequency of the pulsed suppressor tone, and (d) the inferred r1 values are not significantly dependent upon the amount of suppression.

Relaxation dynamics of spontaneous otoacoustic emissions perturbed by external tones. II. Suppression of interacting emissions.

The level of a spontaneous otoacoustic emission (SOAE) during recovery from suppression by an external tone sometimes exhibits a prominent overshoot before reaching its normal level. At the onset of suppression, a less prominent undershoot is sometimes observed before the emission level stabilizes. The overshoot and undershoot are described in terms of the variable amount suppression produced by a neighboring higher-frequency SOAE which is responding more slowly to the modulation of the external tone. The variation of the SOAE amplitude during pulsed suppression is modeled by a pair of Van der Pol limit-cycle oscillators with the primary oscillator linearly coupled to the displacement of the secondary high-frequency one. We have found relaxation time constants for the onset of suppression of the order of 4.5 and 7.4 ms for the primary and secondary SOAEs, respectively, and for the recovery from suppression 4.8 and 10.48 ms for the primary and secondary SOAEs, respectively. The same model is also successful in describing the release from suppression of the primary SOAE by the secondary SOAE when the latter is partially suppressed by the external tone. Aspirin administration reduces the magnitude of the overshoot by reducing the level of the higher-frequency SOAE and thereby eliminating the suppression of the lower-frequency one.

Correlation between amplitude and frequency fluctuations of spontaneous otoacoustic emissions.

The normalized cross-correlation function between the amplitude and frequency fluctuations of 11 spontaneous otoacoustic emissions was measured. A significant correlation was found in seven subjects. The correlation coefficient ranged from -0.37 to +0.65 across subjects. In four subjects, the amplitude fluctuation lagged the frequency fluctuation. The time lag was between 1.6 and 5.5 ms. The results were interpreted using a noise-perturbed limit-cycle oscillator with nonlinear (Duffing) stiffness as a model for a spontaneous emission. The data show that the relative increase of the nonlinear stiffness in this model was between -0.010 and +0.015. This indicates that an even-order nonlinear stiffness plays a minor role in the emission generator.

New off-line method for detecting spontaneous otoacoustic emissions in human subjects.

Spontaneous otoacoustic emissions were evaluated in 36 female and 40 male subjects. In agreement with the results of previous surveys, emissions were found to be more prevalent in female subjects and there was a tendency for the male subjects to have fewer emissions in their left ears. The digitization of five minute samples of ear canal signals, combined with sophisticated data analysis, produced a substantial reduction in the emission detection threshold. 588 emissions were detected in 72% of the subjects and 56% of the ears. Of the observed emissions, 18 could be identified with cubic distortion products of other emissions, and 11 could be identified as harmonic products (i.e., integral frequency multiples of other emissions). The large number of emissions detected (one subject had 32 in her right ear and 25 in her left) permitted evaluation of the pattern of separation of emissions. The average effective separation along the basilar membrane (according to the Greenwood frequency map) for adjacent emissions of all ears was 0.427 mm with interquartile values of 0.387 mm and 0.473 mm. The relationship between emission power, frequency, and full width at half maximum appears to be in agreement with the implications of a noise perturbed Van der Pol oscillator model of spontaneous emissions.

Are spontaneous otoacoustic emissions generated by self-sustained cochlear oscillators?

Theoretical analyses supporting the assumption that spontaneous otoacoustic emissions (SOAEs) can be described as self-sustained oscillations (requiring a power source) are reviewed and extended. Spectral and statistical properties of spontaneous otoacoustic emissions are examined and shown to be consistent with this assumption. Several alternative models of spontaneous emissions (noise-driven saturating memoryless nonlinearity, noise-driven nonlinear-stiffness oscillator) are examined. Although some of these models are able to produce the types of statistical distributions of amplitude and displacement similar to those observed in the experimental data, this similarity is destroyed upon narrow-band filtering.