Probing Apical-Basal Differences in the Human Cochlea Using Distortion-Product Otoacoustic Emission Phase

Abstract

Distortion-product otoacoustic emission (DPOAE) phase is shaped by interaction between the evoking stimulus waves. Near-invariant at high frequencies, DPOAE phase-vs-frequency functions measured at fixed ratios bend into sloping functions at low frequencies. The different phase behaviors observed suggest that the mechanics underlying the generation of OAEs differ in the halves of the cochlea. To map out the phenomenological extent of low-to-mid frequency phase bends, this study recorded DPOAE responses from 20 normal-hearing human adult ears for a wide range of stimulus frequencies, f₁ and f₂, where f₂ frequency sweeps from 0.25 to 8 kHz, and the f₂/ f₁ ratio varies from 1.05 to 1.49. Our preliminary results show two transitions in the phase slopes. One near 2.6 kHz in agreement with the literature, and another of opposite polarity near 0.75 kHz which has not been reported before. We find that the f₂ frequencies marking these defining phase features are invariant with stimulus ratio. Even as the underlying mechanics remain unknown, the invariance opens the door for DPOAE phase to reliably characterize apical-basal differences across age groups and species.

INTRODUCTION

Otoacoustic emissions (OAEs) at frequencies mapping to the apical half of the cochlea exhibit phase slopes unlike those at high frequencies. In response to two tones with frequencies f₁ and f₂, selected so that f₂/ f₁ is always 1.22, the phase of the distortion-product otoacoustic emission (DPOAE) at f_dp = 2 f₁−f₂ is nearly invariant above 1.4 kHz but clearly sloping below [5]. Similarly, the phase of stimulus-frequency OAEs (SFOAEs) bends into a steeper function of frequency near 1 kHz [11]. The bends occur not just in young human adults, but also in human newborns [2], and in other mammalian species for which data exist with high-enough resolution across a suciently wide frequency band.

Both DPOAE reflection-source phase and SFOAE phase rotate more steeply across frequency at lower stimulus levels, but the frequencies at which the bends occur appear roughly independent of level [1]. Placing a third tone—a suppressor tone—near the f_dp frequency suppresses the reflection-source contribution to the DPOAE specifically. Although the phase of that contribution is a relatively steep function of frequency [10], suppression of it does not eliminate the phase bends. The one reported way to influence the bend is to place the suppressor tone about one-third octave above the f₂ frequency, rather than near the f_dp itself [7].

Taken together, invariance with stimulus level and with suppression near 2 f₁−f₂, but not near f₂, suggests that bends in DPOAE phase stem from a mechanical transition in the region on the basilar membrane where the DPOAE is generated—as opposed to further apically where it is reflected. The generation region corresponds to the spatial extent of vibrations at the f₂ frequency interacting with those at the f₁ frequency. The observation that DPOAE phase rotates at low frequencies, and not at high frequencies, is consistent with the idea that the phase relationship between the stimulus waves undergoes a change as the generation region moves into the apical half of the cochlea. Presumably, SFOAEs are subject to the same “breaking of scaling symmetry” in the cochlear apex.

If the bend does indeed arise due to a transition in the DPOAE generation region, the bend should remain fixed over the same range of f₂ frequencies regardless of the stimulus ratio. Knight and Kemp [6] collected extensive frequency-vs-ratio “maps” of DPOAE phase to unveil the place- and wave-fixed nature of DPOAE sources. Martin et al. [8] showed for rabbits the same kind of phase maps to isolate contributions from DPOAE sources significantly basal to the characteristic place of the f₂ frequency. Ratio-independent phase bends can be seen in their data but they are not marked and the studies included only a limited number of subjects (two human subjects and three rabbits). The other studies of DPOAE phase referenced above include more subjects but only measurements with the stimulus ratio fixed at 1.22, and none of the studies go below f₂ = 0.78 kHz.

The present study explores in human subjects how bends in the DPOAE phase-vs-frequency function vary with the stimulus ratio f₂/ f₁ in five octaves of f₂ from 0.25 to 8 kHz. The wide frequency range gives, first, a high chance of detecting the bends across subjects, and second, a good basis for estimating the phase slopes above and below them. To keep the total measurement duration per subject feasible (< 90 min), we rely on both instrumental and methodological advances that previous studies did not have available.

METHODS

Subjects and Experimental Protocol

Twenty young adults with clinically normal hearing participated in the study. All were compensated at an hourly rate and had signed an informed consent before participating. The subjects were seated in a comfortable recliner in a double-walled soundbooth in the Hearing Research Lab at the University of Southern California. The OAE probe was fitted into one of the subject’s ear canals, selected at random if they did not have a preference, and the subject was instructed to breathe quietly and keep movement, swallowing, and so on at a minimum. A velcro band was placed around the subject’s head to hold the cable of the probe in place and reduce the tendency of the probe itself to slip out of the ear canal. Despite these measures, the stability of the setup required checking at regular intervals. Calibration was repeated every 6 minutes and the fit of the probe readjusted if deemed necessary by the experimenter. Readjustment or complete refitting was normally done once or twice within sessions lasting 70–90 minutes per subject.

Stimulus Parameters and Instrumentation

DPOAEs were recorded at the frequency and ratio parameters as shown in Fig. 1. The f₂ range from 0.25 to 8 kHz sets the range of 2 f₁−f₂ between 0.09 and 7.2 kHz, thus extending 1–2 octaves below previous measurements. Stimulus levels L₁/L₂ were 59/50 dB FPL across frequency, the reference pressure being an estimate of the pressure at the probe tip excluding the influence of the individual ear canal [9]. The stimulus frequencies were swept continuously at a rate increasing gradually from 0.07 oct/s to 2 oct/s in order to spend more averaging time at low frequencies where the noise is generally higher. The sweeps were 22 s each and noisy parts of them were identified and repeated to ensure that a minimum of 16 repetitions were within four standard deviations of one another around the median. The ER10X probe system (Etymotic Research Inc., Elk Grove Village, IL, USA) was used for all measurements with the preamplifier set at +20 dB and the highpass filter option disabled. Acquisition software written in Matlab (Mathworks Inc., Torrance, CA, USA) was used to interface with the probe system via an RME Babyface Pro audio interface (Audio AG, Haimhausen, Germany). System and ear-canal delays in recordings, as well as any drift in the calibration between conditions, were compensated for as part of the emitted-pressure level (EPL) calibration procedure invoked to compensate for the influence of individually shaped ear canals [4].

FIGURE 1:

Summary of fixed-ratio sweeps measured in each subject. Colors are used in subsequent plots to identify measurements at the corresponding ratio. Dots signify the third-octave bandwidth of our analysis.

Data Analysis

The DPOAE responses at the f_dp frequency were estimated by minimizing the squared error between a model of the response and the average of recorded responses which were not classified as noisy (similar to [3]). The effective stimulus pressures were estimated as well to verify the calibration and to enable the calculation of the DPOAE phase with reference to that of the stimuli, as in ϕ_dp = ϕ_measured −(2ϕ₁−ϕ₂). The noise was estimated using the same procedures used to obtain the DPOAE response but at 0.1 oct below f_dp frequency. Since the noise level increases at lower frequencies, this “neighbor” method probably somewhat overestimates the noise at the f_dp frequency.

The analyses were carried out with a bandwidth of 1/3 octaves at every 1/9 octaves. This choice implies that phase slopes greater than 3–9 cyc/oct contribute randomly. In effect, as outlined in Fig. 2, the steep phase slope associated with reflection-source DPOAEs is eliminated from the phase trend. Measurements with stimulus levels which had drifted from target levels by more than 3 dB, or with signal-to-noise ratios (SNRs) less than 3 dB, were excluded from further analysis. Points further than two standard deviations from the mean were considered outliers. A total of 25% of the data were excluded, almost exclusively due to noise at extreme frequencies and ratios.

FIGURE 2:

Heat plot of a complex-valued DPOAE response. Frequency is on the y axis and time is specified in cycles/octave on the x axis. This time unit is equivalent to the phase slope measured on a log₂ frequency axis. The distortion-source emission is assumed to be confined to the interval between the dashed lines indicating the windowing applied to exclude the reflection-source component from further analysis.

Phase is unwrapped point-by-point and so gaps in the data across frequency due to noise throw the procedure off the overall trend, as shown in black on Fig. 3. To correct for this, straight lines were fit to the three data points on either side of every gap. The phase value at the frequency in the middle of each gap was extrapolated from each of the lines. The difference between them, rounded to the nearest integer, determined how many cycles to shift the phase at frequencies higher than the gap. Example results are shown in blue in the figure. The procedure affected about 8% of the good-SNR data. Correcting them, rather than simply excluding them, reduced the variance of subsequent analyses but had no significant effect on the conclusions.

FIGURE 3:

Two example corrections of unwrapped phase curves.

RESULTS

To capture features of DPOAE phase that characterize the species rather than any one individual, we focus here on the averaged results shown in Fig. 4. They are qualitatively similar to what we see in individuals.

FIGURE 4:

Summary of average results. Panel A shows the SNR in different conditions. Panel B shows the averaged phase responses for all 8 ratio conditions. The phases were unwrapped, corrected for gaps as necessary, and then averaged across subjects. Panels C and D summarize the phase slopes measured in the low-, mid- and high-frequency regions of the measurements. Error bars signify 95% confidence intervals around the means.

Figure 4B illustrates that DPOAE phase is not generally invariant across frequency. The phase not only bends into a sloping function of frequency below a certain frequency—it is instead a transposed and elongated S-shape with two bends separated by a steepest slope in the middle octave. The is most sharply defined at ratios near 1.22 (0.3 oct), but generally, the phase straightens towards narrow ratios and flattens towards wide ratios. The low-frequency end of the data (< 0.75 kHz) and logarithmic frequency axes help visualize and extract these critical features of the phase.

Straight lines were fit to the low-, mid- and high-frequency octaves of the data and the slopes were extracted. That the confidence intervals do not overlap each other on the V-shapes of Fig. 4C demonstrate that the S-shape in the raw phase responses is real and not just a visual illusion. Furthermore, as illustrated most clearly in Fig. 4D, only the high-frequency slope is actually zero, and only for ratios above 1.2. If near-invariant DPOAE phase across frequency (near-zero slope) is the signature of scaling symmetry along the cochlea, it only holds above 3–4 frequencies.

To quantify the presence of bends in the phase, their frequencies were estimated in each individual from the intersections between the straight lines fit in the low, mid, and high octaves, see Fig. 5. A bend was considered present if the slopes on either side were significantly different in terms of non-overlapping 95% confidence intervals. Sometimes, when they were different but very similar, they intersected at very low or very high frequencies. These outlier cases were excluded by requiring, additionally, that the found bend frequencies be within the shaded ranges in the figure. We find that the f₂ frequencies at which the bends occur are approximately the same, regardless of the ratio, indicating that f₂, not 2 f₁−f₂, is the appropriate reference for it. There is a low-frequency bend at 0.75 kHz, a high-frequency bend at 2.6 kHz, and the geometric mean between them is 1.4 kHz. At a ratio of 1.22 specifically, the high-frequency bend is at 2.8 kHz which is similar to the 2.2 kHz found by Abdala et al. [2], although they used markedly different ways to measure and quantify the bends. There is no comparable reference data for the low-frequency bend. The transition has also been found in SFOAE measurements at 1 kHz in humans [11]. A closer correspondence between distortion- and reflection-source phase bends may appear if analyzed within the same subject.

FIGURE 5:

Phase response for f₂/ f₁ = 1.22 in an example subject and fit straight lines with intersections marking the “bend frequencies.” Bends across all subjects are summarized in figure to the right with the small numbers indicating how many of them out of 20 had bends present.

DISCUSSION

Our data extend 1–2 octaves lower in frequency than previous reports. We were able to go this low by taking high-pass filtering out of the acquisition change, except for filtering in the audio interface (cutoff about 0.02 kHz) and due to the rolloff of the microphone sensitivity (about 0.1 kHz). The noise increases more steeply at low frequencies than countered by fixed-rate frequency sweeps (> 6 dB/oct). Therefore, instead of keeping the rate fixed at say 0.5 oct/s, we started off at a very low rate, 0.07 oct/s at 0.25 kHz, and increased it gradually in correspondence with an assumed noise-floor decrease up to 2 oct/s at 8 kHz. Larger analysis windows could then be used to estimate the response at low frequencies and, to some extend, equalize the noise floor across frequency. This worked well for ratios below about 1.3, but above, the f_dp frequency swept between 0.08 and 0.13 kHz and our accelerated-sweep parameters did not equalize the noise floor at such low frequencies. We showed, nevertheless, that DPOAEs are typically present there, across a wide range of ratios. The rolloff one sees in the DPOAE level towards low frequencies (Fig. 4A) depends on the sound field of reference; in our case, an infinite tube as wide as the human ear canal [4].

Our preliminary estimates suggest that the phase rotates with an average slope of about −1 cyc/oct and also that it appears to flatten in the lowest and the highest octaves, significantly so within individuals as well as in general. Further verification is necessary as one possible explanation for the low-frequency bend is the increase in noise at low frequencies. Generally, the phase attributed to the signal is influenced by the noise, especially at low SNR. All measurements presented in this study have SNRs greater than 3 dB, which means that the signal dominates the noise. As long as the noise does not oscillate in sync with the response, it contributes only random variation around the signal phase. If the noise does correlate with the response, an artifactual slope can appear. The best verification contained within our current data is as shown in Fig. 6, that several of our subjects with good SNRs at low frequencies also show the flattening trend. The slopes remain significantly different, i.e. the bends remain present, when the SNR rejection criterion is set high enough (>> 3 dB) to exclude half of the data at each ratio.

FIGURE 6:

Three individual DPOAE responses with low-frequency phase bends and high SNRs. The presence of these low-frequency bends in data with high SNRs suggests that they are an intrinsic feature of DPOAE phase.

In conclusion, we extended DPOAE measurements down to f₂ = 0.25 kHz for a wide range of ratios. We used measurement methods that compensated for ear-canal acoustics (FPL and EPL) and for gaps of poor SNR. We find two bends in the phase: One in the 2–3 kHz range, largely consistent with previous reports, and a second about 2 octaves lower. The emergent S-shape of the phase discovered here resembles the phase response of a lightly underdamped resonator (Q ~ 0.75). The mechanisms responsible for this “resonance” remain unclear. Its location near the apical-basal transition suggests that it may involve contributions from both the apical and basal regions of the mammalian cochlea. Further study across age groups and species might elucidate this interesting feature of DPOAE phase.