Auditory nerve phase-locked response recorded from normal hearing adults using electrocochleography.

OBJECTIVE: The auditory nerve overlapped waveform response (ANOW), a new measure that can be recorded non-invasively from humans, holds promise for providing more accurate assessment of low frequency hearing thresholds than currently used objective measures. This research aims to investigate the robustness and the nature of the ANOW response in humans. DESIGN: Repeated within-session recordings of the ANOW response using low-frequency Tone Bursts (TBs) were obtained at multiple stimulus levels. ANOW's absolute amplitude and phase locking value (PLV) measures were analysed to obtain normative data and to test the reliability of the ANOW response. STUDY SAMPLE: Thirteen normal hearing adults within the age range of 25 to 40 years. RESULTS: ANOW response was obtained to both 250 Hz and 500 Hz TBs and was traced down to 30-40 dB nHL. ANOW response showed significantly higher amplitude and stronger phase locking using 250 Hz TB compared to 500 Hz TB. High degree of test retest reliability of the ANOW response was found using 250 Hz TB at presentation levels higher than 40 dB nHL. CONCLUSIONS: ANOW response is recordable noninvasively using low-frequency TBs and shows higher robustness as the stimulus frequency decreases.

Medial Olivocochlear Reflex Effect on Cochlear Response in Humans: Elicitor Side and Level.

BACKGROUND: Understanding the functional differences between crossed and uncrossed medial olivocochlear (MOC) neurons has been of interest to researchers for decades. Previous reports revealed conflicting results about which MOC pathway, crossed or uncrossed, is stronger in humans. Both crossed and uncrossed MOC neurons synapse at the base of the outer hair cells (OHCs) in each ear. OHCs generate the cochlear microphonic, which is a major contributor to the cochlear response (CR) PURPOSE: The current study investigated the effects of eliciting the crossed and uncrossed MOC reflex (MOCR) on CR in humans with three levels of noise. RESEARCH DESIGN: Normal-hearing, young adults (n = 16) participated in this study. The CR was recorded using 500 Hz tone-burst stimuli presented at 80 dB nHL. To examine the crossed and uncrossed MOCR, CR was recorded without and with continuous ipsilateral or contralateral broadband noise (BBN) at three levels (40, 50, and 60 dB SPL). DATA ANALYSIS: Analysis of the CR was completed using the amplitude of the response extracted using fast Fourier transform. Statistical analysis was completed using repeated measures analysis of variance and post-hoc analysis. RESULTS: Compared with baseline, the presentation of BBN, specifically contralaterally, resulted in CR enhancement with no significant difference as a function of the three BBN levels. Greater enhancement of the CR amplitude was observed with contralateral than ipsilateral BBN elicitor. CONCLUSIONS: The current findings suggest that a contralateral elicitor of the uncrossed MOC pathway results in a larger CR amplitude enhancement compared with an ipsilateral elicitor of the crossed MOC pathway, regardless of the elicitor level. Eliciting the MOCR appears to modulate the OHCs function. Furthermore, assessing the MOCR with the 500 Hz CR with BBN elicitors at moderate levels should separate its effects (i.e., increase response amplitude) from those associated with the middle ear muscle reflex (i.e., reduce response amplitude).

Human medial olivocochlear reflex: Contralateral activation effect on low and high frequency cochlear response.

The role of the medial olivocochlear (MOC) reflex has been investigated by assessing changes of cochlear responses (CR) in humans. The CR consists of pre-neural and neural potentials originating from the inner ear, and at high signal levels is dominated by cochlear microphonic (CM). The CM originates from the outer hair cells, where the MOC fibers synapse, and there is little research about using it to investigate the MOC reflex in humans. The current study aimed to investigate the effect of contralateral activation of the MOC reflex on the CR in humans. The CR was recorded in female adults (n = 16) to 500 and 2000 Hz tone burst stimuli presented at 80 dB nHL with and without contralateral broadband noise (CBBN) at 40 dB SPL. Two different methods were utilized to quantify and analyze the CR data: peak amplitude and power spectrum. Results revealed enhancement of the CR amplitude with activation of the MOC reflex. Furthermore, on average, enhancement in the CR amplitude was observed to 500 Hz, but not 2000 Hz stimulus. The CR power spectrum findings revealed similar findings to the peak amplitude. These findings indicate the MOC effect is measurable when using a low frequency stimulus, but not high frequency. Moreover, the CR could be used as a potential tool to study the MOC reflex in humans.

A Novel Nonlinear System Identification for Cerebral Autoregulation in Human: Computer Simulation and Validation.

Cerebral autoregulation in healthy humans was studied using a novel methodology adapted from Bendat nonlinear analysis technique. A computer simulation of a high-pass filter in parallel with a cubic nonlinearity followed by a low-pass filter was analyzed. A linear system transfer function analysis showed an incorrect estimate of the gain, cut-off frequency, and phase of the high-pass filter. By contrast, using our nonlinear systems identification, yielded the correct gain, cut-off frequency, and phase of the linear system, and accurately quantified the nonlinear system and following low-pass filter. Adding the nonlinear and linear coherence function indicated a complete description of the system. Cerebral blood flow velocity and arterial pressure were measured in six data sets. Application of the linear and nonlinear systems identification techniques to the data showed a high-pass filter, like the linear transfer function, but the gain was smaller. The phase was similar between the two techniques. The linear coherence was low for frequencies below 0.1 Hz but improved by including a nonlinear term. The linear + nonlinear coherence was approximately 0.9 across the frequency bandwidth, indicating an improved description over the linear system analysis of the cerebral autoregulation system.

An analytic approach to identifying the sources of the low-frequency round window cochlear response.

The cochlear microphonic, traditionally thought of as an indication of electrical current flow through hair cells, in conjunction with suppressing high-pass noise or tones, is a promising method of assessing the health of outer hair cells at specific locations along the cochlear partition. We propose that the electrical potential recorded from the round window in gerbils in response to low-frequency tones, which we call cochlear response (CR), contains significant responses from multiple cellular sources, which may expand its diagnostic purview. In this study, CR is measured in the gerbil and modeled to identify its contributing sources. CR was recorded via an electrode placed in the round window niche of sixteen Mongolian gerbils and elicited with a 45 Hz tone burst embedded in 18 high-pass filtered noise conditions to target responses from increasing regions along the cochlear partition. Possible sources were modeled using previously-published hair cell and auditory nerve response data, and then weighted and combined using linear regression to produce a model response that fits closely to the mean CR waveform. The significant contributing sources identified by the model are outer hair cells, inner hair cells, and the auditory nerve. We conclude that the low-frequency CR contains contributions from several cellular sources.

The Middle Ear Muscle Reflex in Rat: Developing a Biomarker of Auditory Nerve Degeneration.

OBJECTIVES: The long-term goal of this research is to determine whether the middle ear muscle reflex can be used to predict the number of healthy auditory nerve fibers in hearing-impaired ears. In this study, we develop a high-impedance source and an animal model of the middle ear muscle reflex and explore the influence of signal frequency and level on parameters of the reflex to determine an optimal signal to examine auditory nerve fiber survival. DESIGN: A high-impedance source was developed using a hearing aid receiver attached to a 0.06 diameter 10.5-cm length tube. The impedance probe consisted of a microphone probe placed near the tip of a tube coupled to a sound source. The probe was calibrated by inserting it into a syringe of known volumes and impedances. The reflex in the anesthetized rat was measured with elicitor stimuli ranging from 3 to 16 kHz presented at levels ranging from 35 to 100 dB SPL to one ear while the reflex was measured in the opposite ear containing the probe and probe stimulus. RESULTS: The amplitude of the reflex increased with elicitor level and was largest at 3 kHz. The lowest threshold was approximately 54 dB SPL for the 3-kHz stimulus. The rate of decay of the reflex was greatest at 16 kHz followed by 10 and 3 kHz. The rate of decay did not change significantly with elicitor signal level for 3 and 16 kHz, but decreased as the level of the 10-kHz elicitor increased. A negative feedback model accounts for the reflex decay by having the strength of feedback dependent on auditory nerve input. The rise time of the reflex varied with frequency and changed with level for the 10- and 16-kHz signals but not significantly for the 3-kHz signal. The latency of the reflex increased with a decrease in elicitor level, and the change in latency with level was largest for the 10-kHz stimulus. CONCLUSIONS: Because the amplitude of the reflex in rat was largest with an elicitor signal at 3 kHz, had the lowest threshold, and yielded the least amount of decay, this may be the ideal frequency to estimate auditory nerve survival in hearing-impaired ears.

A novel auditory ossicles membrane and the development of conductive hearing loss in Dmp1-null mice.

Genetic mouse models are widely used for understanding human diseases but we know much less about the anatomical structure of the auditory ossicles in the mouse than we do about human ossicles. Furthermore, current studies have mainly focused on disease conditions such as osteomalacia and rickets in patients with hypophosphatemia rickets, although the reason that these patients develop late-onset hearing loss is unknown. In this study, we first analyzed Dmp1 lac Z knock-in auditory ossicles (in which the blue reporter is used to trace DMP1 expression in osteocytes) using X-gal staining and discovered a novel bony membrane surrounding the mouse malleus. This finding was further confirmed by 3-D micro-CT, X-ray, and alizarin red stained images. We speculate that this unique structure amplifies and facilitates sound wave transmissions in two ways: increasing the contact surface between the eardrum and malleus and accelerating the sound transmission due to its mineral content. Next, we documented a progressive deterioration in the Dmp1-null auditory ossicle structures using multiple imaging techniques. The auditory brainstem response test demonstrated a conductive hearing loss in the adult Dmp1-null mice. This finding may help to explain in part why patients with DMP1 mutations develop late-onset hearing loss, and supports the critical role of DMP1 in maintaining the integrity of the auditory ossicles and its bony membrane.

The potential use of low-frequency tones to locate regions of outer hair cell loss.

Current methods used to diagnose cochlear hearing loss are limited in their ability to determine the location and extent of anatomical damage to various cochlear structures. In previous experiments, we have used the electrical potential recorded at the round window -the cochlear response (CR) -to predict the location of damage to outer hair cells in the gerbil. In a follow-up experiment, we applied 10 mM ouabain to the round window niche to reduce neural activity in order to quantify the neural contribution to the CR. We concluded that a significant proportion of the CR to a 762 Hz tone originated from phase-locking activity of basal auditory nerve fibers, which could have contaminated our conclusions regarding outer hair cell health. However, at such high concentrations, ouabain may have also affected the responses from outer hair cells, exaggerating the effect we attributed to the auditory nerve. In this study, we lowered the concentration of ouabain to 1 mM and determined the physiologic effects on outer hair cells using distortion-product otoacoustic emissions. As well as quantifying the effects of 1 mM ouabain on the auditory nerve and outer hair cells, we attempted to reduce the neural contribution to the CR by using near-infrasonic stimulus frequencies of 45 and 85 Hz, and hypothesized that these low-frequency stimuli would generate a cumulative amplitude function (CAF) that could reflect damage to hair cells in the apex more accurately than the 762 stimuli. One hour after application of 1 mM ouabain, CR amplitudes significantly increased, but remained unchanged in the presence of high-pass filtered noise conditions, suggesting that basal auditory nerve fibers have a limited contribution to the CR at such low frequencies.

Predicting the location of missing outer hair cells using the electrical signal recorded at the round window.

The electrical signal recorded at the round window was used to estimate the location of missing outer hair cells. The cochlear response was recorded to a low frequency tone embedded in high-pass filtered noise conditions. Cochlear damage was created by either overexposure to frequency-specific tones or laser light. In animals with continuous damage along the partition, the amplitude of the cochlear response increased as the high-pass cutoff frequency increased, eventually reaching a plateau. The cochlear distance at the onset of the plateau correlated with the anatomical onset of outer hair cell loss. A mathematical model replicated the physiologic data but was limited to cases with continuous hair cell loss in the middle and basal turns. The neural contribution to the cochlear response was determined by recording the response before and after application of Ouabain. Application of Ouabain eliminated or reduced auditory neural activity from approximately two turns of the cochlea. The amplitude of the cochlear response was reduced for moderate signal levels with a limited effect at higher levels, indicating that the cochlear response was dominated by outer hair cell currents at high signal levels and neural potentials at low to moderate signal levels.

SOD1-G93A mice exhibit muscle-fiber-type-specific decreases in glucose uptake in the absence of whole-body changes in metabolism.

BACKGROUND: Skeletal muscles play an important role in systemic glucose homeostasis and are purported to be the origin of the altered metabolic state observed in amyotrophic lateral sclerosis (ALS). OBJECTIVE: The purpose of this study was to evaluate whole-body and muscle-specific glucose metabolism in the SOD1-G93A mouse model of ALS. METHODS: We assessed glucose tolerance in early-, middle-, and late-stage SOD1-G93A and control mice using an intraperitoneal glucose tolerance test. We then measured the respiratory exchange ratio (CO2 production/O2 consumption) as a function of fasting and feeding using indirect calorimetry in a subset of male mice at these time points. Finally, muscles from all mice were harvested to evaluate basal and insulin-stimulated glucose transport in fast- and slow-twitch muscles. RESULTS: No changes in systemic glucose clearance were observed in SOD1-G93A mice at any stage, nor were there changes in fasting insulin levels. Indirect calorimetry revealed an increase in the respiratory exchange ratio during the fed state at middle, but not at early or late stages of disease. Middle-stage SOD1-G93A mice exhibited decreased insulin-stimulated glucose uptake in fast-twitch, but not slow-twitch, skeletal muscle. Late-stage SOD1-G93A mice exhibited decreased insulin-stimulated glucose uptake in both fast- and slow-twitch muscle, as well as increased basal (non-insulin-stimulated) glucose uptake. CONCLUSIONS: These results suggest that alterations in muscle metabolism occur in a fiber-type-specific manner in ALS, but do not necessarily lead to whole-body metabolic changes in SOD1-G93A mice.

Analysis of the cochlear microphonic to a low-frequency tone embedded in filtered noise.

The cochlear microphonic was recorded in response to a 733 Hz tone embedded in noise that was high-pass filtered at 25 different frequencies. The amplitude of the cochlear microphonic increased as the high-pass cutoff frequency of the noise increased. The amplitude growth for a 60 dB SPL tone was steeper and saturated sooner than that of an 80 dB SPL tone. The growth for both signal levels, however, was not entirely cumulative with plateaus occurring at about 4 and 7 mm from the apex. A phenomenological model of the electrical potential in the cochlea that included a hair cell probability function and spiral geometry of the cochlea could account for both the slope of the growth functions and the plateau regions. This suggests that with high-pass-filtered noise, the cochlear microphonic recorded at the round window comes from the electric field generated at the source directed towards the electrode and not down the longitudinal axis of the cochlea.

Mapping auditory nerve firing density using high-level compound action potentials and high-pass noise masking.

Future implementation of regenerative treatments for sensorineural hearing loss may be hindered by the lack of diagnostic tools that specify the target(s) within the cochlea and auditory nerve for delivery of therapeutic agents. Recent research has indicated that the amplitude of high-level compound action potentials (CAPs) is a good predictor of overall auditory nerve survival, but does not pinpoint the location of neural damage. A location-specific estimate of nerve pathology may be possible by using a masking paradigm and high-level CAPs to map auditory nerve firing density throughout the cochlea. This initial study in gerbil utilized a high-pass masking paradigm to determine normative ranges for CAP-derived neural firing density functions using broadband chirp stimuli and low-frequency tonebursts, and to determine if cochlear outer hair cell (OHC) pathology alters the distribution of neural firing in the cochlea. Neural firing distributions for moderate-intensity (60 dB pSPL) chirps were affected by OHC pathology whereas those derived with high-level (90 dB pSPL) chirps were not. These results suggest that CAP-derived neural firing distributions for high-level chirps may provide an estimate of auditory nerve survival that is independent of OHC pathology.

Within-session analysis of amphetamine-elicited rotation behavior reveals differences between young adult and middle-aged F344/BN rats with partial unilateral striatal dopamine depletion.

Preclinical modeling of Parkinson's disease using 6-hydroxydopamine (6-OHDA) has been valuable in developing and testing therapeutic strategies. Recent efforts have focused on modeling early stages of disease by infusing 6-OHDA into the striatum. The partial DA depletion that follows intrastriatal 6-OHDA is more variable than the near-complete depletion following medial forebrain bundle infusion, and behavioral screening assays are not as well characterized in the partial lesion model. We compared relationships between amphetamine-elicited rotation behavior and DA depletion following intrastriatal 6-OHDA (12.5 microg) in 6 month vs. 18 month F344/BN rats, at 2-weeks and 6-weeks post-lesion. We compared the total number of rotations with within-session (bin-by-bin) parameters of rotation behavior as indicators of DA depletion. Striatal DA depletion was greater in the young adult than in the middle-aged rats at 2 weeks but not at 6 weeks post-lesion. The total number of rotations for the whole session and striatal DA depletion did not differ between the two age groups. Regression analysis revealed a greater relationship between within-session parameters of rotation behavior and DA depletion in the middle-aged group than in the young adult group. These results have implications for estimating DA depletion in preclinical studies using rats of different ages.

Effects of universal newborn hearing screening on an early intervention program for children with hearing loss, birth to 3 yr of age.

BACKGROUND: Universal Newborn Hearing Screening (UNHS) was introduced in Kansas in 1999. Prior to UNHS a small percentage of newborns were screened for and identified with hearing loss. PURPOSE: The purpose of this study was to determine the effects of UNHS on a local early intervention (EI) program for young children with hearing loss. RESEARCH DESIGN: This was a retrospective study based on the chart review of children enrolled in the EI program during target years before and after the establishment of UNHS. STUDY SAMPLE: Charts for 145 children were reviewed. DATA COLLECTION AND ANALYSIS: The chart review targeted the following aspects of the EI program: caseload size, percentage of caseload identified by UNHS, age of diagnosis, age of enrollment in EI, degree of hearing loss, etiology of hearing loss, late onset of hearing loss, age of hearing aid fit, percentage of children fit with hearing aids by 6 mo, percentage of children with profound hearing loss with cochlear implants, and percentage of children with additional disabilities. RESULTS: Changes in the EI program that occurred after UNHS were increases in caseload size, percentage of caseload identified by UNHS, percentage of children fit with hearing aids by 6 mo of age, and percentage of children with profound hearing loss with cochlear implants. There were decreases in age of diagnosis, age of enrollment in EI, and age of hearing aid fit. Before UNHS, the majority of children had severe and profound hearing loss; after UNHS there were more children with mild and moderate hearing loss. The percentage of known etiology and late-onset hearing loss was approximately the same before and after UNHS, as was the percentage of children with additional disabilities. CONCLUSION: UNHS had a positive impact on caseload size, age of diagnosis, age of enrollment in EI, and age of hearing aid fit. The percentage of the caseload identified in the newborn period was about 25% before UNHS and over 80% after its implementation. After UNHS, the EI caseload included as many children with mild and moderate hearing loss as with severe and profound loss. By the last reporting year in the study (academic year 2005-2006) all children with profound hearing losses had cochlear implants.

Predicting auditory nerve survival using the compound action potential.

OBJECTIVE: Advances in cochlear hair-cell regeneration, neural regeneration, and genetic therapy encourage continued development of diagnostic tests that can accurately specify the appropriate target within the cochlea and auditory nerve for delivery of therapeutic agents. In this study, we test the hypothesis that the morphology of the acoustically evoked compound action potential (CAP) may reflect the condition of the auditory nerve in individuals with sensorineural hearing loss. DESIGN: CAPs to tone burst stimuli at octave frequencies from 1 to 16 kHz were recorded at low- to high-stimulus levels from sedated Mongolian gerbils with partial lesions of the auditory nerve (n = 10). Distortion-product otoacoustic emissions were measured to ensure preservation of normal outer hair-cell function. CAPs were analyzed with conventional measures of N1 latency and amplitude and by fitting the CAPs with a mathematical model that includes a parameter (N) representing the number of nerve fibers contributing to the CAP and a parameter (f) representing the oscillation frequency of the CAP waveform. Nerve fiber density and percent normal nerve area were estimated from cross-sections of the auditory nerve bundle. RESULTS: Despite substantial lesions in the auditory nerve, CAP thresholds remained within normal or were only moderately elevated and were not correlated with histological measures of nerve fiber density and normal nerve area. At high-stimulus levels, the model parameter N was strongly correlated with nerve fiber density for three of the five test frequencies and with normal nerve area for all five test frequencies. Correlations between N1 amplitude measures at high-stimulus levels and our histological measures were also significant for the majority of test frequencies, but they were generally weaker than the correlations for the model parameter N. The model parameter f, at low- and high-stimulus levels, was also positively correlated with measures of normal nerve area. CONCLUSIONS: Consistent with previous findings, physiological measures of threshold were not correlated with partial lesions of the auditory nerve. The model parameter N at high-stimulus levels was strongly correlated with normal nerve area suggesting, that it is a good predictor of auditory nerve survival. The model parameter N also seemed to be a better predictor of the condition of the auditory nerve than the conventional measure of N1 amplitude. Because the model parameter f was correlated with normal nerve area at low- and high-stimulus levels, it may provide information on the functional status of the auditory nerve.

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.

Columella footplate motion and the cochlear microphonic potential in the embryo and hatchling chicken.

A piezoelectric (PZE) vibrator was used to mechanically drive the columella footplate and stimulate the cochlea of chicken embryos and hatchlings. Our objectives were to characterize the motion of the PZE driver and determine the relationship between columella footplate motion (displacement/ velocity) and the cochlear microphonic recorded from the recessus scala tympani (CMrst). At each frequency, displacement of the PZE driver probe tip was linearly related to the applied voltage over a wide range of attenuation levels (-60 to -20 dBre:50 Vp-p). The mean displacement across frequencies (100-4000 Hz) was 0.221+/-0.042 micromp-p for a constant applied voltage level of -20 dBre:50 Vp-p. Displacement was within 1.5 dB of the mean for this stimulus level at all frequencies except for 4000 Hz, where it was approximately 3 dB higher (p < 0.01). CMrst amplitudes in hatchlings were larger than amplitudes in embryos (p=0.003). For a given frequency, CM was linearly related to footplate displacement and velocity at both ages. The transform ratio of CMrst/A (CM amplitude/displacement) increased at approximately 6 dB/octave at frequencies between 100 and 1000 Hz in hatchlings suggesting that cochlear impedance (Zc) was resistive at these frequencies. In a large fraction of the embryos, Zc exhibited reactive behavior.

Predicting severity of cochlear hair cell damage in adult chickens using DPOAE input-output functions.

Distortion product otoacoustic emissions (DPOAE) were recorded from the ear canal of aged broiler chickens which have been shown to present with age-related cochlear degeneration [Hear. Res. 166 (2002) 82]. We describe the relationship between the shape of the DPOAE input-output (I/O) function and the type of hair cell damage present at and between the cochlear frequency places of the DPOAE primary tones (f1 and f2). The mid stimulus level compressive growth of the mean DPOAE I/O functions is reduced in a graded fashion relative to the severity of hair cell damage. However, individual DPOAE I/O functions within most hair cell damage groups show large variability from this characteristic. Various least squares regression models were used to predict hair cell density from indices derived from the DPOAE I/O function (area, threshold and slope). The results showed that no simple linear relationship exists between hair cell density and the DPOAE I/O function indices. Multivariate binary logistic regression used DPOAE I/O function indices to predict membership in hair cell damage groups. The logistic model revealed that DPOAE threshold can be used to predict the occurrence of severe/total hair cell damage with good specificity though poor sensitivity.

Constructing a cochlear transducer function from the summating potential using a low-frequency bias tone.

A new method is developed to construct a cochlear transducer function using modulation of the summating potential (SP), a dc component of the electrical response of the cochlea to a sinusoid. It is mathematically shown that the magnitude of the SP is determined by the even-order terms of the power series representing a nonlinear function. The relationship between the SP magnitudes and the second derivative of the transducer function was determined by using a low-frequency bias tone to position a high-frequency probe tone at different places along the cochlear transducer function. Two probe tones (6 kHz and 12 kHz) ranging from 70 to 90 dB SPL and a 25-Hz bias tone at 130 dB SPL were simultaneously presented. Electric responses from the cochlea were recorded by an electrode placed at the round window to obtain the SP magnitudes. The experimental results from eight animals demonstrated that the SP magnitudes as a function of bias levels are essentially proportional to the second derivative of a sigmoidal Boltzmann function. This suggests that the low-frequency modulated SP amplitude can be used to construct a cochlear transducer function.