Mark E. Chertoff

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.

Comparison of the envelope following response in the Mongolian gerbil using two‐tone and sinusoidally amplitude‐modulated tones

Two-tone (TT) and sinusoidally amplitude-modulated (SAM) signals, although differing in spectra, are both periodic; the period corresponds to the difference between the two frequencies (f2,1 = f2-f1) in the former and to the frequency of the modulation tone (fmod) in the latter. Here the results of a study comparing the steady-state electrophysiologic responses to TT and SAM stimuli recorded from Nembutal-anesthetized Mongolian gerbils are reported. In the first experiment a modulation rate transfer function (MRTF) was obtained for each stimulus type by setting the SAM carrier frequency (fc) and f1 of the TT signal at the same frequency while fmod and f2,1 were covaried. MRTFs were obtained for f1s and fcs of 1, 3, and 5 kHz, with envelopes which varied between 50 and 500 Hz in 50-Hz increments. Stimuli were presented at 75 dB peak sound-pressure level (pSPL). Responses to the two stimulus types yielded MRTFs which were very similar and generally low pass in shape. In the second experiment responses to the TT and SAM signals were recorded in the presence of a continuous interfering tone of 85-dB pSPL which was varied between 650 Hz and 3 kHz. In these experiments a maximum reduction in the response to the TT and SAM signals, measured at f2,1 and fmod as well as at fc and f1, occurred within a narrow frequency band above the frequency of the probe carrier and a broader region of reduced response extending to higher frequencies. This reduction in response was asymmetrical, spreading more to high than to low frequencies. The similarity of both MRTFs and interference response patterns supports the view that the envelope following responses to TT and SAM stimuli are manifestations of the same nonlinear phenomena.

Auditory nonlinearities measured with auditory‐evoked potentials

This article describes the use of auditory-evoked potentials (AEPs) as a tool to assess nonlinear processes in the auditory system. Two-tone signals were used as stimuli to obtain AEPs in both animal and human subjects. Frequency analysis of the physiologic waveforms revealed frequencies in the evoked potential that were not present in the acoustic signal. The largest distortion product in the evoked potential corresponded to the difference between the two primary frequencies (f2-f1). This distortion product was present in all subjects tested. Other distortion products at frequencies defined by n(f2-f1), where n less than 5, were also present in some individuals. These frequencies represent distortion components generated from an even-order nonlinear system. Extensive acoustic and electric calibration procedures provided substantial evidence that the distortion products recorded in the AEP were biologic in origin and not the result of acoustic or recording artifact.

Electrophysiological evidence of nonlinear distortion products to two-tone stimuli

Spectral analysis of auditory-evoked potential recordings from ten normal-hearing subjects to two-tone signals revealed energy at difference tone (DT = f2-f1) and cubic difference (CDT = 2f1-f2) frequencies that was not present in the acoustic signal. Control experiments and calibrations provided substantial evidence supportive of the biological nature of these auditory nonlinearities, suggesting that they are not the result of electromagnetic, acoustic, or analytic artifact. Amplitudes of DT- and CDT-evoked responses were evaluated for rarefaction and condensation signals with f1 = 510 and 800 Hz across frequency ratios (f2/f1) of 1.16, 1.26, 1.36, and 1.46. Additionally, time-domain summation and subtraction of separately collected evoked responses to rarefaction and condensation signals were performed to demonstrate that these electrophysiological DT and CDT responses reflect their expected quadratic and cubic nature. Suggestions for development of clinical applications of assessing auditory nonlinearities using this methodology are provided.

Cochlear hysteresis: Observation with low-frequency modulated distortion product otoacoustic emissions

Low-frequency modulation of distortion product otoacoustic emissions (DPOAEs) can be used to estimate a nonlinear transducer function (fTr) of the cochlea. From gerbils, DPOAEs were measured while presenting a high-level bias tone. Within one period of the bias tone, the magnitudes of the cubic difference tone (CDT, 2f1 - f2) demonstrated two similar modulation patterns (MPs) each resembled the absolute value of the third derivative of the fTr. The center peaks of the MPs occurred at positive sound pressures for rising in bias pressure or loading of the cochlear transducer, and more negative pressures while decreasing bias amplitude or unloading. The corresponding fTr revealed a sigmoid-shaped hysteresis loop with counterclockwise traversal. Physiologic indices that characterized the double MP varied with primary level. A Boltzmann-function-based model with negative damping as a feedback component was proposed. The model was able to replicate the experimental results. Model parameters that fit to the CDT data indicated higher transducer gain and more prominent feedback role at lower primary levels. Both physiologic indices and model parameters suggest that the cochlear transducer dynamically changes its gain with input signal level and the nonlinear mechanism is a time-dependent feedback process.

Click- and chirp-evoked human compound action potentials

In the experiments reported here, the amplitude and the latency of human compound action potentials (CAPs) evoked from a chirp stimulus are compared to those evoked from a traditional click stimulus. The chirp stimulus was created with a frequency sweep to compensate for basilar membrane traveling wave delay using the O-Chirp equations from Fobel and Dau [(2004). J. Acoust. Soc. Am. 116, 2213-2222] derived from otoacoustic emission data. Human cochlear traveling wave delay estimates were obtained from derived compound band action potentials provided by Eggermont [(1979). J. Acoust. Soc. Am. 65, 463-470]. CAPs were recorded from an electrode placed on the tympanic membrane (TM), and the acoustic signals were monitored with a probe tube microphone attached to the TM electrode. Results showed that the amplitude and latency of chirp-evoked N1 of the CAP differed from click-evoked CAPs in several regards. For the chirp-evoked CAP, the N1 amplitude was significantly larger than the click-evoked N1s. The latency-intensity function was significantly shallower for chirp-evoked CAPs as compared to click-evoked CAPs. This suggests that auditory nerve fibers respond with more unison to a chirp stimulus than to a click stimulus.

Temporary hearing loss influences post-stimulus time histogram and single neuron action potential estimates from human compound action potentials

An analytic compound action potential (CAP) obtained by convolving functional representations of the post-stimulus time histogram summed across auditory nerve neurons [P(t)] and a single neuron action potential [U(t)] was fit to human CAPs. The analytic CAP fit to pre- and postnoise-induced temporary hearing threshold shift (TTS) estimated in vivo P(t) and U(t) and the number of neurons contributing to the CAPs (N). The width of P(t) decreased with increasing signal level and was wider at the lowest signal level following noise exposure. P(t) latency decreased with increasing signal level and was shorter at all signal levels following noise exposure. The damping and oscillatory frequency of U(t) increased with signal level. For subjects with large amounts of TTS, U(t) had greater damping than before noise exposure particularly at low signal levels. Additionally, U(t) oscillation was lower in frequency at all click intensities following noise exposure. N increased with signal level and was smaller after noise exposure at the lowest signal level. Collectively these findings indicate that neurons contributing to the CAP during TTS are fewer in number, shorter in latency, and poorer in synchrony than before noise exposure. Moreover, estimates of single neuron action potentials may decay more rapidly and have a lower oscillatory frequency during TTS.

Differentiation of cochlear pathophysiology in ears damaged by salicylate or a pure tone using a nonlinear systems identification technique

Mongolian gerbils were exposed to either alpha-ketoglutarate, salicylate, or an 8-kHz pure tone. Cochlear microphonic (CM) was recorded from the round window in response to 68 and 88 dB SPL Gaussian noise. A nonlinear systems identification technique provided the frequency-domain parameters of a third-order polynomial model characterizing cochlear mechano-electric transduction (MET). A series of physiologic indices were derived from further exploration of the model. Exposure to the 8-kHz pure tone and round window application of salicylate resulted in different changes in the polynomial parameters and physiologic indices even though the threshold shifts were similar. A general reduction of CM magnitude was found after the tone exposure, and an increase at low-mid frequencies was demonstrated in the salicylate group especially at the lower signal level. The slope of the MET curve was reduced by the acoustic overstimulation. The root or the operating point of the MET was shifted in opposite directions after the two treatments. Sound-pressure levels that saturate MET expanded in the tone exposure group and narrowed in the salicylate group. The signal level also had effects on these indices.

Characterizing cochlear mechano-electric transduction using a nonlinear systems identification procedure.

A nonlinear systems identification technique [J. S. Bendat, Nonlinear System Analysis and Identification from Random Data (Wiley, New York, 1990)] provided the frequency-domain parameters of a third-order system polynomial equation describing cochlear mechano-electric transduction (MET) in Mongolian gerbils. The magnitude of the linear system term was the largest followed by the cubic and quadratic terms. The phase of the linear and cubic system terms differed by approximately 180 deg and the phase of the quadratic term lay between. Between-animal and within-animal variability was smallest for the linear and cubic terms, and largest for the quadratic term. Summing linear and nonlinear coherence functions revealed that the third-order system polynomial equation characterized approximately 83% of MET for low frequencies and 92% for high frequencies. Animals exposed to a 4-kHz pure tone at 100 dB SPL for 20 min showed changes in the magnitude and phase of the parameters of the third-order polynomial equation. An increase in linear coherence and a decrease in nonlinear coherence occurred at frequencies centered at the exposure frequency. Below the exposure frequency, linear coherence decreased and nonlinear coherence increased. Summation of the coherence functions showed that the third-order polynomial equation characterized MET better after exposure to the pure tone.

Analytic treatment of the compound action potential: Estimating the summed post-stimulus time histogram and unit response

The convolution of an equation representing a summed post-stimulus time histogram computed across auditory nerve fibers [P(t)] with an equation representing a single-unit wave form [U(t)], resulted in an analytic expression for the compound action potential (CAP). The solution was fit to CAPs recorded to low and high frequency stimuli at various signal levels. The correlation between the CAP and the analytic expression was generally greater than 0.90. At high levels the width of P(t) was broader for low frequency stimuli than for high frequency signals, but delays were comparable. This indicates that at high signal levels there is an overlap in the population of auditory nerve fibers contributing to the CAP for both low and high frequency stimuli but low frequencies include contributions from more apical regions. At low signal levels the width of P(t) decreased for most frequencies and delays increased. The frequency of oscillation of U(t) was largest for high frequency stimuli and decreased for low frequency stimuli. The decay of U(t) was largest at 8 kHz and smallest at 1 kHz. These results indicate that the hair cell or neural mechanisms involved in the generation of action potentials may differ along the cochlear partition.