Synchronization of spontaneous otoacoustic emissions to a 2f1-f2 distortion product

Synchronization of spontaneous otoacoustic emissions to a cubic distortion frequency fs = 2f1-f2 has been studied. Stimulus, consisting of two primary tones at frequency f1 and f2, could easily be filtered out of the microphone signal. This enabled us to monitor emission phase with respect to synchronization frequency fs, by recording zero-crossing moments of the microphone signal. When primaries were sufficiently loud (typically 30 dB SPL), phase fluctuated around a constant value: The emission was constantly synchronized to fs. Lowering primary levels (to typically 20 dB SPL) resulted in 2 pi-phase jumps at random moments: The emission occasionally slipped out of synchronization, trying to maintain its own natural frequency f0. This behavior can be described as synchronization of an oscillator (frequency f0) to a sinusoidal force (frequency fs) in the presence of noise.     

Amplitude and frequency fluctuations of spontaneous otoacoustic emissions

Amplitude and frequency fluctuations of spontaneous otoacoustic emissions have been studied. Spontaneous otoacoustic emissions were recorded from eight human ears and two frog ears (Rana esculenta). Record length typically was 80 s. For a recorded emission signal, the amplitude signal A(t) (average A0) and time intervals T(ti) between successive positive-going zero crossings (i counts zero crossings) were determined. Emission amplitude and period both showed small fluctuations: delta Arms/A0 ranged from 0.7 X 10(-2) to 6.3 X 10(-2) for human emissions and was 24 X 10(-2) for both frog emissions; delta Trms ranged from 1.4 to 6.9 X 10(-7) s for human emission and was 50.0 and 55.0 X 10(-7) s for the two frog emissions. There was a positive correlation between delta Arms/A0 and delta Trms as determined for different emissions (R = 0.9). Spectra of A(t) and T(ti) revealed that amplitude and period were slowly fluctuating functions: cutoff frequency delta f delta A of the amplitude spectrum ranged from 3 to 18 Hz; delta f delta T ranged from 7 to 32 Hz. Results have been compared to amplitude and frequency fluctuations of a second-order oscillator, that interacts with a noise source. It has been concluded that an oscillator with linear stiffness (for example a Van der Pol oscillator) driven by white Gaussian noise, cannot account for all experimental results. Other possible oscillators (e.g., nonlinear stiffness) and noise sources (e.g., narrow-band noise), that may account for the observed phenomena, are discussed.     

Objective estimates of cochlear tuning by otoacoustic emission analysis

A new method is presented for estimating cochlear tuning starting from measurements of either the transient evoked otoacoustic emission latency or the spontaneous otoacoustic emission minimal spacing. This method could be useful in obtaining indirect information about the tuning curve, particularly for subjects that, like neonates, cannot be studied with psycho-acoustical techniques. Theoretical models of the acoustic transmission along the cochlea based on the transmission line formalism predict a relation between the otoacoustic emission latency and the frequency. This relation depends on the tuning curve, i.e., the frequency dependence of the quality factor of the cochlear resonances. On the other hand, models for the generation of spontaneous emissions based on the concept of coherent scattering from cochlear random inhomogeneities imply an independent relation between the tuning curve and the minimal frequency spacing between spontaneous emissions. In this study, experimental measurements of the otoacoustic emission latency and of the minimal spacing between spontaneous emissions are presented. Theoretical relations are derived, which connect these two measured quantities and the tuning curve. The typically longer latency of neonates implies a higher degree of tuning at high levels of stimulation.     

Modification of spontaneous and evoked otoacoustic emissions and associated psychoacoustic microstructure by aspirin consumption

The discovery that aspirin consumption can abolish spontaneous otoacoustic emissions [D. McFadden and H.S. Plattsmier, J. Acoust. Soc. Am. 76, 443-448 (1984)] provides a technique for further exploring the relation between otoacoustic emissions (spontaneous and evoked) and psychoacoustic threshold microstructure. Spontaneous emissions, delayed evoked emissions, synchronous evoked emissions, and threshold microstructure in four subjects were monitored before, during, and after consumption of 3.9 g of aspirin per day (three 325-mg tablets every 6 h) for 3 or 4 days. The changes in spontaneous emissions are consistent with the findings of McFadden and Plattsmier except that one spontaneous emission appeared to plateau at a reduced level above the noise floor during the last day and a half of the 3-day period of aspirin consumption. Evoked emissions and threshold microstructure were also reduced by aspirin consumption but persisted longer and recovered sooner. In most instances, the initial change in threshold microstructure was a trend to increased sensitivity (reduced thresholds), with a greater increase near threshold maxima than at threshold minima. Further reduction in the levels of the evoked emissions was accompanied by the eventual decrease in sensitivity (elevation of all thresholds).     

Ear canal acoustic distortion at 2f1-f2 from human ears: relation to other emissions and perceived combination tones

Two aspects of the intermodulation distortion product at 2f1-f2 generated by normal human ears and measured acoustically in the ear canal were studied: (1) its relation to tone-evoked and spontaneous otoacoustic emissions, and (2) its relation to the perceived combination tone at the same frequency. With regard to (1), substantial differences among ears in the detectability of emissions were observed; ears tended to exhibit all or none of the emission types that were sought. Within ears possessing emissions, the magnitudes of tone-evoked emissions and acoustic distortion showed a similar dependence on frequency. With regard to (2), a three-primary-tone stimulus was employed to ask whether the ear canal acoustic distortion tone is canceled under the same stimulus conditions that produce perceptual cancellation. Simultaneous cancellation of perceptual and acoustic distortion was produced rarely. Results are interpreted qualitatively with a model in which primary tones produce distortion at their interaction region within the cochlea; this distortion propagates to the distortion-frequency place where it mediates perception. This same distortion wave produces emission components at additional locations, including the primary-tone interaction region, which sum vectorially to mediate the emitted acoustic distortion product.     

The dynamics of two coupled Van der Pol oscillators with attractive and repulsive coupling

We consider a variant of two coupled Van der Pol oscillators with both attractive and repulsive mean-field interactions. In the presence of attractive coupling, the system is in the complete synchrony, while repulsive coupling shows anti-synchronization state leading to suppression of oscillations with increasing interaction strength. The coupled system with both attractive and repulsive interactions shows competitive tendencies of being complete synchronization and anti-synchronization resulting in the stabilization of the fixed point. We have also studied the effect of the damping coefficient of the VdP oscillator on the nature of the transition from oscillatory to a steady-state. These oscillators stabilize to unstable equilibrium point or coupling dependent inhomogeneous steady state via second or first-order transitions respectively depending upon the damping coefficient and coupling strength. These transitions are analyzed in the parameter plane by analytical and numerical studies of the two coupled Van der Pol oscillators.     

Modeling the growth rate of distortion product otoacoustic emissions by active nonlinear oscillators

In this work, growth-rate curves of the 2 f1-f2 distortion product otoacoustic emission (DPOAE) are analyzed in a population of 30 noise exposed subjects, including both normal-hearing and hearing impaired subjects. A particular embedded limit-cycle oscillator equation is used to model the cochlear resonant response at the cochlear places of the primary and secondary tone frequencies (f2 and 2 f1-f2). The parameters of the oscillator equation can be directly interpreted in terms of effectiveness of the cochlear feedback mechanisms associated with the active filter amplification. A two-sources paradigm is included in the model, in agreement with experimental evidence and with the assumptions of more detailed full cochlear models based on the transmission line formalism. According to this paradigm, DPOAEs are nonlinearly generated at the cochlear place that is resonant at frequency f2, and coherently reflected at the 2 f1-f2 place. The analysis shows that the model, which had been previously used to describe the relaxation dynamics of transient evoked otoacoustic emissions (TEOAEs), also correctly predicts the observed growth rate of the DPOAE response as a function of the primary tones amplitude. A significant difference is observed between normal and impaired ears. The comparison between the growth rate curves at different frequencies provides information about the dependence of cochlear tuning on frequency.     

Projective synchronization of chaotic systems with bidirectional nonlinear coupling

This paper presents a new scheme for constructing bidirectional nonlinear coupled chaotic systems which synchronize projectively. Conditions necessary for projective synchronization (PS) of two bidirectionally coupled chaotic systems are derived using Lyapunov stability theory. The proposed PS scheme is discussed by taking as examples the so-called unified chaotic model, the Lorenz–Stenflo system and the nonautonomous chaotic Van der Pol oscillator. Numerical simulation results are presented to show the efficiency of the proposed synchronization scheme.     

Distortion-product otoacoustic-emission suppression tuning in human infants and adults using absorbed sound power

The greatest difference in distortion product otoacoustic emission (DPOAE) suppression tuning curves (STCs) in infant and adult ears occurs at a stimulus frequency of 6 kHz. These infant and adult STCs are much more similar when constructed using the absorbed power level of the stimulus and suppressor tones rather than using sound pressure level. This procedure incorporates age-related differences in forward and reverse transmission of sound power through the ear canal and middle ear. These results support the theory that the cochlear mechanics underlying DPOAE suppression are substantially mature in full-term infants.     

Transient-evoked stimulus-frequency and distortion-product otoacoustic emissions in normal and impaired ears

Transient-evoked stimulus-frequency otoacoustic emissions (SFOAEs), recorded using a nonlinear differential technique, and distortion-product otoacoustic emissions (DPOAEs) were measured in 17 normal-hearing and 10 hearing-impaired subjects using pairs of tone pips (pp), gated tones (gg), and for DPOAEs, continuous and gated tones (cg). Temporal envelopes of stimulus and OAE waveforms were obtained by narrow-band filtering at the stimulus or DP frequency. Mean SFOAE latencies in normal ears at 2.7 and 4.0 kHz decreased with increasing stimulus level and were larger at 4.0 kHz than latencies in impaired ears. Equivalent auditory filter bandwidths were calculated as a function of stimulus level from SFOAE latencies by assuming that cochlear transmission is minimum phase. DPOAE latencies varied less with level than SFOAE latencies. The ppDPOAEs often had two (or more) peaks separated in time with latencies consistent with model predictions for distortion and reflection components. Changes in ppDPOAE latency with level were sometimes explained by a shift in relative amplitudes of distortion and reflection components. The pp SFOAE SPL within the main spectral lobe of the pip stimulus was higher for normal ears in the higher-frequency half of the pip than the lower-frequency half, which is likely an effect of basilar membrane two-tone suppression.     

Practical time-delay synchronization of a periodically modulated self-excited oscillators with uncertainties

This paper studies time-delay synchronization of a periodically modulated Duffing Van der Pol (DVP) oscillator subjected to uncertainties with emphasis on complete synchronization. A robust adaptive response system is designed to synchronize with the uncertain drive periodically modulated DVP oscillator. Adaptation laws on the upper bounds of uncertainties are proposed to guarantee the boundedness of both the synchronization error and the estimated feedback coupling gains. Numerical results are presented to check the effectiveness of the proposed synchronization scheme. The results suggest that the linear and nonlinear terms in the feedback coupling play a complementary role in increasing the synchronization regime in the parameter space of the synchronization manifold. The proposed method can be successfully applied to a large variety of physical systems.     

Low-frequency modulation of distortion product otoacoustic emissions in humans

Low-frequency modulation of distortion product otoacoustic emissions (DPOAEs) was measured from the human ears. In the frequency domain, increasing the bias tone level resulted in a suppression of the cubic difference tone (CDT) and an increase in the magnitudes of the modulation sidebands. Higher-frequency bias tones were more efficient in producing the suppression and modulation. Quasi-static modulation patterns were derived from measuring the CDT amplitude at the peaks and troughs of bias tones with various amplitudes. The asymmetric bell-shaped pattern resembled the absolute value of the third derivative of a nonlinear cochlear transducer function. Temporal modulation patterns were obtained from inverse FFT of the spectral contents around the DPOAE. The period modulation pattern, averaged over multiple bias tone cycles, showed two CDT peaks each correlated with the zero-crossings of the bias tone. The typical period modulation pattern varied and the two CDT peaks emerged with the reduction in bias tone level. The present study replicated the previous experimental results in gerbils. This noninvasive technique is capable of revealing the static position and dynamic motion of the cochlear partition. Moreover, the results of the present study suggest that this technique could potentially be applied in the differential diagnosis of cochlear pathologies.     

Suppression of distortion product otoacoustic emissions and hearing threshold

A distortion product otoacoustic emission (DPOAE) suppression tuning curve (STC) shows the minimum level of suppressor tone that is required to reduce DPOAE level by a fixed amount, as a function of suppressor frequency. Several years ago, Mills [J. Acoust. Soc. Am. 103, 507-523 (1998)] derived, theoretically, an approximately linear relationship between the tip-to-tail suppressor level difference on a DPOAE STC, and the gain of the cochlear amplifier, defined as the maximum increase in the active over the passive basilar membrane (BM) response. In this paper, preliminary data from adult human subjects are presented that establish a correlation between this tip-to-tail DPOAE STC difference and the threshold of hearing, the latter measured at the frequency of the f2 primary tone. Assuming that both suppression and the DPOAE are by-products of active, nonlinear BM dynamics, the above result suggests that threshold elevation in mild levels of hearing loss may be attributed, in part, to a reduction of cochlear amplifier gain, which is detectable with the suppression paradigm.     

Method of studying the synchronization of self-sustained oscillations using continuous wavelet analysis of univariant data

A new method for detecting the synchronization of a self-sustained oscillator under an external action with a linearly increasing frequency is proposed. It is based on the continuous wavelet transformation of univariant data (scalar time series). The efficiency of the method is demonstrated with a modified asymmetric van der Pol oscillator, Rössler oscillator, and experimental physiological data. In the last case, synchronization between rhythmic processes of different order in the cardiovascular and respiratory systems of the man is demonstrated using only the time series of the R-R intervals.     

Transient evoked otoacoustic emission latency and cochlear tuning at different stimulus levels

Cochlear latency has been evaluated in young adults by time-frequency analysis of transient evoked otoacoustic emissions recorded using the nonlinear acquisition mode at different levels of the click stimulus. Objective, even if model-dependent, estimates of cochlear tuning have been obtained from the otoacoustic latency estimates. Transmission-line cochlear models predict that the transient-evoked otoacoustic emission latency is dependent on the stimulus level, because the bandwidth of the cochlear filter (tuning) depends on the local cochlear excitation level due to nonlinear damping. The results of this study confirm the increase of tuning with increasing frequency and show clearly the decrease of latency and tuning with increasing stimulus level. This decrease is consistent with the expected relation between the slowing down of the traveling wave near the tonotopic place and the cochlear excitation amplitude predicted by cochlear models including nonlinear damping. More specifically, these results support the models in which nonlinear damping consists of a quadratic term and a constant positive term.     

参数失配的受迫振动系统有误差界的同步判据

基于李雅普诺夫直接法和Sylvester准则,推导出外激励参数失配的受迫振动系统达到有误差界的同步的几种代数判据. 根据代数不等式,求得同步误差界的估计值. 通过控制同步误差界估计值,可以把实际的同步误差界值控制到小于预先给定的同步精确度. Duffing-Van der Pol受迫振动系统作为数值算例进一步验证了该方法是有效的. 关键词： 受迫振动系统 参数失配 同步误差界 代数判据     

Distortion product otoacoustic emission suppression tuning curves in normal-hearing and hearing-impaired human ears

Distortion product otoacoustic emission (DPOAE) suppression measurements were made in 20 subjects with normal hearing and 21 subjects with mild-to-moderate hearing loss. The probe consisted of two primary tones (f2, f1), with f2 held constant at 4 kHz and f2/f1 = 1.22. Primary levels (L1, L2) were set according to the equation L1 = 0.4 L2 + 39 dB [Kummer et al., J. Acoust. Soc. Am. 103, 3431-3444 (1998)], with L2 ranging from 20 to 70 dB SPL (normal-hearing subjects) and 50-70 dB SPL (subjects with hearing loss). Responses elicited by the probe were suppressed by a third tone (f3), varying in frequency from 1 octave below to 1/2 octave above f2. Suppressor level (L3) varied from 5 to 85 dB SPL. Responses in the presence of the suppressor were subtracted from the unsuppressed condition in order to convert the data into decrements (amount of suppression). The slopes of the decrement versus L3 functions were less steep for lower frequency suppressors and more steep for higher frequency suppressors in impaired ears. Suppression tuning curves, constructed by selecting the L3 that resulted in 3 dB of suppression as a function of f3, resulted in tuning curves that were similar in appearance for normal and impaired ears. Although variable, Q10 and Q(ERB) were slightly larger in impaired ears regardless of whether the comparisons were made at equivalent SPL or equivalent sensation levels (SL). Larger tip-to-tail differences were observed in ears with normal hearing when compared at either the same SPL or the same SL, with a much larger effect at similar SL. These results are consistent with the view that subjects with normal hearing and mild-to-moderate hearing loss have similar tuning around a frequency for which the hearing loss exists, but reduced cochlear-amplifier gain.     

Cortical responses to the 2f1-f2 combination tone measured indirectly using magnetoencephalography

The simultaneous presentation of two tones with frequencies f(1) and f(2) causes the perception of several combination tones in addition to the original tones. The most prominent of these are at frequencies f(2)-f(1) and 2f(1)-f(2). This study measured human physiological responses to the 2f(1)-f(2) combination tone at 500 Hz caused by tones of 750 and 1000 Hz with intensities of 65 and 55 dB SPL, respectively. Responses were measured from the cochlea using the distortion product otoacoustic emission (DPOAE), and from the auditory cortex using the 40-Hz steady-state magnetoencephalographic (MEG) response. The perceptual response was assessed by having the participant adjust a probe tone to cause maximal beating ("best-beats") with the perceived combination tone. The cortical response to the combination tone was evaluated in two ways: first by presenting a probe tone with a frequency of 460 Hz at the perceptual best-beats level, resulting in a 40-Hz response because of interaction with the combination tone at 500 Hz, and second by simultaneously presenting two f(1) and f(2) pairs that caused combination tones that would themselves beat at 40 Hz. The 2f(1)-f(2) DPOAE in the external auditory canal had a level of 2.6 (s.d. 12.1) dB SPL. The 40-Hz MEG response in the contralateral cortex had a magnitude of 0.39 (s.d. 0.1) nA m. The perceived level of the combination tone was 44.8 (s.d. 11.3) dB SPL. There were no significant correlations between these measurements. These results indicate that physiological responses to the 2f(1)-f(2) combination tone occur in the human auditory system all the way from the cochlea to the primary auditory cortex. The perceived magnitude of the combination tone is not determined by the measured physiological response at either the cochlea or the cortex.     

"Otoacoustic" emissions in a nonlinear cochlear hardware model with feedback

Spontaneous, simultaneous evoked as well as delayed evoked emissions are studied in a hardware model of peripheral preprocessing with nonlinear feedback. The results suggest many very close parallels to the data found for otoacoustic emissions in man. From these parallels and the additional data measurable only in the model, it can be concluded that: the cochlea acts in a similar way as established in the model; the three kinds of emissions stem from the same source; the phase response of the cochlea's hydromechanics is responsible for the frequency distance between neighboring emissions as well as for the additional tips in suppression tuning curves; the long delay of the delayed evoked emissions is due to the many decaying contributions from the places along the basilar membrane which cancel each other in the early part but sum up to the delayed emission in the later part; and the double-peaked shape of the suppression-period patterns produced by high-level, low-frequency tones reflects the symmetrically shaped saturating nonlinearity of the feedback loops in the model which correspond to the function of the outer hair cells.     

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.