Deriving a cochlear transducer function from low-frequency modulation of distortion product otoacoustic emissions

In this paper, a new method is introduced to derive a cochlear transducer function from measuring distortion product otoacoustic emissions (DPOAEs). It is shown that the cubic difference tone (CDT, 2f1-f2) is produced from the odd-order terms of a power series that approximates a nonlinear function characterizing cochlear transduction. Exploring the underlying mathematical formulation, it is found that the CDT is proportional to the third derivative of the transduction function when the primary levels are sufficiently small. DPOAEs were measured from nine gerbils in response to two-tone signals biased by a low-frequency tone with different amplitudes. The CDT magnitude was obtained at the peak regions of the bias tone. The results of the experiment demonstrated that the shape of the CDT magnitudes as a function of bias levels was similar to the absolute value of the third derivative of a sigmoidal function. A second-order Boltzmann function was derived from curve fitting the CDT data with an equation that represents the third derivative of the Boltzmann function. Both the CDT-bias function and the derived nonlinear transducer function showed effects of primary levels. The results of the study indicate that the low-frequency modulated DPOAEs can be used to estimate the cochlear transducer function.     

Cochlear compression: effects of low-frequency biasing on quadratic distortion product otoacoustic emission

Distortion product otoacoustic emissions (DPOAEs) are generated from the nonlinear transduction n cochlear outer hair cells. The transducer function demonstrating a compressive nonlinearity can be estimated from low-frequency modulation of DPOAEs. Experimental results from the gerbils showed that the magnitude of quadratic difference tone (QDT, f2-f1) was either enhanced or suppressed depending on the phase of the low-frequency bias tone. Within one period of the bias tone, QDT magnitudes exhibited two similar modulation patterns, each resembling the absolute value of the second derivative of the transducer function. In the time domain, the center notches of the modulation patterns occurred around the zero crossings of the bias pressure, whereas peaks corresponded to the increase or decrease in bias pressure. Evaluated with respect to the bias pressure, modulated QDT magnitude displayed a double-modulation pattern marked by a separation of the center notches. Loading/unloading of the cochlear transducer or rise/fall in bias pressure shifted the center notch to positive or negative sound pressures, indicating a mechanical hysteresis. These results suggest that QDT arises from the compression that coexists with the active hysteresis in cochlear transduction. Modulation of QDT magnitude reflects the dynamic regulation of cochlear transducer gain and compression.     

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.     

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.     

The influence of transducer operating point on distortion generation in the cochlea

Distortion generated by the cochlea can provide a valuable indicator of its functional state. In the present study, the dependence of distortion on the operating point of the cochlear transducer and its relevance to endolymph volume disturbances has been investigated. Calculations have suggested that as the operating point moves away from zero, second harmonic distortion would increase. Cochlear microphonic waveforms were analyzed to derive the cochlear transducer operating point and to quantify harmonic distortions. Changes in operating point and distortion were measured during endolymph manipulations that included 200-Hz tone exposures at 115-dB SPL, injections of artificial endolymph into scala media at 80, 200, or 400 nl/min, and treatment with furosemide given intravenously or locally into the cochlea. Results were compared with other functional changes that included action potential thresholds at 2.8 or 8 kHz, summating potential, endocochlear potential, and the 2 f1-f2 and f2-f1 acoustic emissions. The results demonstrated that volume disturbances caused changes in the operating point that resulted in predictable changes in distortion. Understanding the factors influencing operating point is important in the interpretation of distortion measurements and may lead to tests that can detect abnormal endolymph volume states.     

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.     

Cochlear transducer operating point adaptation

The operating point (OP) of outer hair cell (OHC) mechanotransduction can be defined as any shift away from the center position on the transduction function. It is a dc offset that can be described by percentage of the maximum transduction current or as an equivalent dc pressure in the ear canal. The change of OP can be determined from the changes of the second and third harmonics of the cochlear microphonic (CM) following a calibration of its initial value. We found that the initial OP was dependent on sound level and cochlear sensitivity. From CM generated by a lower sound level at 74 dB SPL to avoid saturation and suppression of basal turn cochlear amplification, the OHC OP was at constant 57% of the maximum transduction current (an ear canal pressure of -0.1 Pa). To perturb the OP, a constant force was applied to the bony shell of the cochlea at the 18 kHz best frequency location using a blunt probe. The force applied over the scala tympani induced an OP change as if the organ of Corti moved toward the scala vestibuli (SV) direction. During an application of the constant force, the second harmonic of the CM partially recovered toward the initial level, which could be described by two time constants. Removing the force induced recovery of the second harmonic to its normal level described by a single time constant. The force applied over the SV caused an opposite result. These data indicate an active mechanism for OHC transduction OP.     

Lateralization and frequency selectivity in normal and impaired hearing

The onset-time difference delta T required to lateralize a 30-ms bifrequency tone burst toward the leading ear was measured as a function of the frequency difference delta F between the tone in the left ear and the tone in the right ear. At center frequencies of 0.5 and 4 kHz, four normal listeners tested at 80 and 100 dB SPL had delta Ts that were relatively constant at subcritical delta Fs, but increased at delta Fs wider than a critical band. At 1 kHz, delta T increased with delta F even at subcritical delta Fs. Ten listeners with cochlear impairments were tested at 100 dB SPL. Seven had normal delta Ts at 4 kHz, despite hearing losses between 50 and 70 dB. At 0.5 and 1 kHz, mildly impaired listeners had nearly normal lateralization functions, whereas more severely imparied listeners had very large delta Ts and no frequency selectivity. These and other findings indicate that listeners even with moderate to severe hearing losses can lateralize normally on the basis of interaural differences in onset envelope, but not on the basis of temporal differences in the fine structure.     

Attenuation and protection provided by ossicular removal

Behavioral studies of hearing loss produced by exposure to ototraumatic agents in experimental animals, combined with the anatomical evaluation of end-organ pathology, have provided useful information about the relation between dysfunction and pathology. However, in order to attribute a given hearing loss to some pattern of cochlear damage, it is necessary to test each ear independently. The objective of the present study was to evaluate attenuation measured behaviorally and protection to the cochlea provided by removal of the malleus and incus in noise-exposed chinchillas. Results from one behaviorally trained chinchilla with ossicular removal indicated a conductive hearing loss that varied from 41 dB at 0.125 kHz to 81 dB at 4.8 kHz and averaged 60 dB. Counts of missing sensory cells in ears of seven chinchillas with unilateral ossicular removal and exposure to noise (octave band centered at 0.5 kHz, 95 dB SPL, for durations up to 216 days, or centered at 4.0 kHz, 108 dB SPL, for 1.75 h) showed no more cell loss on the protected side than in age-matched control ears. From these data it is concluded that ossicular removal provides enough attenuation to protect the chinchilla cochlea from damage during these noise exposures, and that it will insure monaural responses behaviorally as long as the hearing loss in the test ear does not exceed that in the ear with ossicular removal by approximately 50 dB at any frequency.     

Spectral fine-structures of low-frequency modulated distortion product otoacoustic emissions

Biasing of the cochlear partition with a low-frequency tone can produce an amplitude modulation of distortion product otoacoustic emissions (DPOAEs) in gerbils. In the time domain, odd- versus even-order DPOAEs demonstrated different modulation patterns depending on the bias tone phase. In the frequency domain, multiple sidebands are presented on either side of each DPOAE component. These sidebands were located at harmonic multiples of the biasing frequency from the DPOAE component. For odd-order DPOAEs, sidebands at the even-multiples of the biasing frequency were enhanced, while for even-order DPOAEs, the sidebands at the odd-multiples were elevated. When a modulation in DPOAE magnitude was presented, the magnitudes of the sidebands were enhanced and even greater than the DPOAEs. The amplitudes of these sidebands varied with the levels of the bias tone and two primary tones. The results indicate that the maximal amplitude modulations of DPOAEs occur at a confined bias and primary level space. This can provide a guide for optimal selections of signal conditions for better recordings of low-frequency modulated DPOAEs in future research and applications. Spectral fine-structure and its unique relation to the DPOAE modulation pattern may be useful for direct acquisition of cochlear transducer nonlinearity from a simple spectral analysis.     

The effects of sensory hearing loss on cochlear filter times estimated from auditory brainstem response latencies.

Derived-band auditory brainstem responses (ABRs) were obtained in 43 normal-hearing and 80 cochlear hearing-impaired individuals using clicks and high-pass noise masking. The response times across the cochlea [the latency difference between wave V's of the 5.7- and 1.4-kHz center frequency (CF) derived bands] were calculated for five levels of click stimulation ranging from 53 to 93 dB p.-p.e. SPL (23 to 63 dB nHL) in 10-dB steps. Cochlear response times appeared to shorten significantly with hearing loss, especially when the average pure tone (1 to 8 kHz) hearing loss exceeded 30 dB. Examination of derived-band latencies indicates that this shortening is due to a dramatic decrease of wave V latency in the lower CF derived band. Estimates of cochlear filter times in terms of the number of periods to maximum response (Nmax) were calculated from derived-band latencies corrected for gender-dependent cochlear transport and neural conduction times. Nmax decreased as a function of hearing loss, especially for the low CF derived bands. The functions were similar for both males and females. These results are consistent with broader cochlear tuning due to peripheral hearing loss. Estimating filter response times from ABR latencies enhances objective noninvasive diagnosis and allows delineation of the differential effects of pathology on the underlying cochlear mechanisms involved in cochlear transport and filter build-up times.     

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

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

Nonlinear interactions that could explain distortion product interference response areas

Suppression and/or enhancement of third- and fifth-order distortion products by a third tone that can have a frequency more than an octave above and a level more than 40 dB below the primary tones have recently been measured by Martin et al. [Hear. Res. 136, 105-123 (1999)]. Contours of iso-suppression and iso-enhancement that are plotted as a function of third-tone frequency and level are called interference response areas. After ruling out order aliasing, two possible mechanisms for this effect have been developed, a harmonic mechanism and a catalyst mechanism. The harmonic mechanism produces distortion products by mixing a harmonic of one of the primary tones with the other primary tone. The catalyst mechanism produces distortion products by mixing one or more intermediate distortion products that are produced by the third tone with one or more of the input tones. The harmonic mechanism does not need a third tone and the catalyst mechanism does. Because the basilar membrane frequency response is predicted to affect each of these mechanisms differently, it is concluded that the catalyst mechanism will be dominant in the high-frequency regions of the cochlea and the harmonic mechanism will have significant strength in the low-frequency regions of the cochlea. The mechanisms are dependent on the existence of both even- and odd-order distortion, and significant even- and odd-order distortion have been measured in the experimental animals. Furthermore, the nonlinear part of the cochlear mechanical response must be well into saturation when input tones are 50 or more dB SPL.     

Spectral and level effects in noise-on-tone suppression

The effective internal level of a 1-kHz tone at 50 dB SPL was estimated by measuring the forward masking produced on a 10-ms signal tone of the same frequency. Noise containing a spectral notch was then added to the masker tone, and its influence on the effective level of the tone was measured with a variety of noise levels, notch widths, and notch shapes. In experiment 1, the masker tone was centered in the spectral notch, itself centered in a 2-kHz band of noise. As the spectrum level in the noise passbands increased from 6 dB/Hz to 36 dB/Hz, signal threshold decreased, indicating a decrease in masking by the masker tone. This "unmasking" effect of the noise was attributed to suppression of the masker tone by the components in the noise. Unmasking was greatest with the narrowest spectral notch (250 Hz), and decreased to zero as the notch widened to 1500 Hz. Compared to its level when presented alone, the effective internal level of the masker tone could be reduced by up to 30 dB (250-Hz notch, 36 dB/Hz). The relative suppressive strength of individual noise components was estimated in experiment 2, in which the 1-kHz masker tone was located at one edge of a spectral notch, rather than in the center. Noise spectrum level was fixed at 16 dB/Hz. As notch width decreased to zero, on either the high-frequency or low-frequency side of the masker tone, its effective internal level was again reduced by approximately 30 dB. In a tentative analysis, the first derivative of the smoothed threshold function was taken, to provide an estimate of the relative contributions to suppression at 1 kHz of noise components between 250 and 1740 Hz.(ABSTRACT TRUNCATED AT 250 WORDS)     

The fine structure of the recovering auditory detection threshold.

Detection thresholds were gathered for a 2 kHz Gaussian-shaped probe (standard deviation = 0.5 ms), centered at intervals of as little as half a millisecond over 0-30 ms following a 200 ms, 97 dB SPL, 2 kHz tone. Surprisingly, there were small, sudden rises and falls superimposed on each subject's generally smooth recovery. Even more obvious were nonmonotonicities in the standard deviation of the cumulative normal fitted to each threshold's psychometric function.     

Tuning curves and pitch matches in a listener with a unilateral, low-frequency hearing loss

Psychoacoustical tuning curves and interaural pitch matches were measured in a listener with a unilateral, moderately severe hearing loss of primarily cochlear origin below 2 kHz. The psychoacoustical tuning curves, measured in a simultaneous-masking paradigm, were obtained at 1 kHz for probe levels of 4.5-, 7-, and 13-dB SL in the impaired ear, and 7-dB SL in the impaired ear, and 7-dB SL in the normal ear. Results show that as the level of the probe increased from 4.5- to 13-dB SL in the impaired ear, (1) the frequency location of the tip of the tuning curve decreased from approximately 2.85 to 2.20 kHz and (2) the lowest level of the masker required to just mask the probe increased from 49- to 83-dB SPL. The tuning curve in the normal ear was comparable to data from other normal listeners. The interaural pitch matches were measured from 0.5 to 6 kHz at 10-dB SL in the impaired ear and approximately 15- to 20-dB SL in the normal ear. Results show reasonable identity matches (e.g., a 500-Hz tone in the impaired ear was matched close to a 500-Hz tone in the normal ear), although variability was significantly greater for pitch matches below 2 kHz. The results are discussed in terms of their implications for models of pitch perception.     

The influence of systematic primary-tone level variation L2-L1 on the acoustic distortion product emission 2f1-f2 in normal human ears

The purpose of the present study was to determine the effect of primary-tone level variation, L2--L1, on the amplitude of distortion-product otoacoustic emissions (DPOAEs). The DPOAE at the frequency 2f1--f2 (f2 greater than f1) was measured in 20 ears of ten normally hearing subjects. Acoustic distortion products were generated by primaries f1 and f2 with geometric mean frequencies of 1, 2, and 4 kHz. The f2/f1 ratios were 1.25 (1 kHz), 1.23 (2 kHz), and 1.21 (4 kHz). The primary-tone level L1 was kept constant at either 65 or 75 dB SPL while the second primary-tone level L2 was varied between 20 and 90 dB SPL in 5-dB steps. The level differences L2--L1 generating maximal DPOAE amplitudes depended on L1 and on the geometric mean frequency of f1 and f2. There were large interindividual differences. Overall, the L2--L1 evoking maximal mean DPOAE amplitudes was --10 dB for geometric mean frequencies of 1 and 2 kHz with both L1 = 65 dB SPL and L1 = 75 dB SPL. For 4 kHz, L2-L1 was --5 dB with L1 = 65 dB SPL and 0 dB with L1 = 75 dB SPL. The mean slopes of the DPOAE growth functions in the initial linearly increasing portions were steeper at higher stimulus frequencies, increasing from 0.52 at 1 kHz to 0.72 at 4 kHz for L1 = 65 dB SPL and from 0.48 at 1 kHz to 0.72 at 4 kHz for L1 = 75 dB SPL.     

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

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

Group delay measurement from spiral ganglion cells in the basal turn of the guinea pig cochlea

Measurements of group delay were made extracellularly from spiral ganglion cells in the 3.7 to 5.0-mm region of the guinea pig cochlea, using sinusoidally amplitude modulated tones with constant modulating frequency (100 Hz) and depth of modulation (0.19). Threshold cochlear tuning was accompanied by frequency-dependent group delays. The group delay on the low-frequency tail was independent of carrier frequency; the interunit variation was 0.28-1.28 ms. The difference in group delay between CF and the low-frequency tail decreased as the CF threshold increased (-0.09 +/- 0.02 ms per 10 dB, beginning at 0.62 +/- 0.07 ms at 0 dB SPL). The group delay decreased above CF; at the units' maximum frequency it was less than the low-frequency tail value, and was sometimes negative. Following arterial injections of furosemide the CF threshold increased and the group delay peak decreased; the low-frequency tail was unaffected. The group delay decreased with increasing intensity; the reduction near and above CF was not only larger than that on the low-frequency tail, but also the change at 5-10 dB above threshold was far greater than expected from the Q10dB of the suprathreshold iso-rate tuning curves. A minimum-phase analysis suggested that the group delay response above CF, together with its nonlinear behavior, can be accounted for by a high-frequency, level-independent, amplitude plateau, in combination with the single unit, amplitude nonlinearity which is known to exist above CF.     

Asymmetry of masking between complex tones and noise: the role of temporal structure and peripheral compression

Thresholds for the detection of harmonic complex tones in noise were measured as a function of masker level. The rms level of the masker ranged from 40 to 70 dB SPL in 10-dB steps. The tones had a fundamental frequency (F0) of 62.5 or 250 Hz, and components were added in either cosine or random phase. The complex tones and the noise were bandpass filtered into the same frequency region, from the tenth harmonic up to 5 kHz. In a different condition, the roles of masker and signal were reversed, keeping all other parameters the same; subjects had to detect the noise in the presence of a harmonic tone masker. In both conditions, the masker was either gated synchronously with the 700-ms signal, or it started 400 ms before and stopped 200 ms after the signal. The results showed a large asymmetry in the effectiveness of masking between the tones and noise. Even though signal and masker had the same bandwidth, the noise was a more effective masker than the complex tone. The degree of asymmetry depended on F0, component phase, and the level of the masker. The maximum difference between masked thresholds for tone and noise was about 28 dB; this occurred when the F0 was 62.5 Hz, the components were in cosine phase, and the masker level was 70 dB SPL. In most conditions, the growth-of-masking functions had slopes close to 1 (on a dB versus dB scale). However, for the cosine-phase tone masker with an F0 of 62.5 Hz, a 10-dB increase in masker level led to an increase in masked threshold of the noise of only 3.7 dB, on average. We suggest that the results for this condition are strongly affected by the active mechanism in the cochlea.