Relating the Variability of Tone-Burst Otoacoustic Emission and Auditory Brainstem Response Latencies to the Underlying Cochlear Mechanics

Abstract

Forward and reverse cochlear latency and its relation to the frequency tuning of the auditory filters can be assessed using tone bursts (TBs). Otoacoustic emissions (TBOAEs) estimate the cochlear roundtrip time, while auditory brainstem responses (ABRs) to the same stimuli aim at measuring the auditory filter buildup time. Latency ratios are generally close to two and controversy exists about the relationship of this ratio to cochlear mechanics. We explored why the two methods provide different estimates of filter buildup time, and ratios with large inter-subject variability, using a time-domain model for OAEs and ABRs. We compared latencies for twenty models, in which all parameters but the cochlear irregularities responsible for reflection-source OAEs were identical, and found that TBOAE latencies were much more variable than ABR latencies. Multiple reflection-sources generated within the evoking stimulus bandwidth were found to shape the TBOAE envelope and complicate the interpretation of TBOAE latency and TBOAE/ABR ratios in terms of auditory filter tuning.

INTRODUCTION

Wave-V latency of auditory brainstem responses (τ_ABR) recorded to narrow-band tone-bursts have been used to derive the forward cochlear latency τ_BM(x) in humans [4, 8, 10, 12]. τ_BM(x), defined as the group delay of the basilar-membrane (BM) response at cochlear location x, appears related to the frequency tuning of the underlying auditory filter [15]. The cochlear roundtrip time τ_OAE(f) can be derived using tone-burst OAE (TBOAE) latency [4, 8, 10, 12], and is defined as the time it takes a particular frequency component in the evoking stimulus to travel to the region where the emission is generated and back to the eardrum.

When emissions are generated through coherent reflection filtering occurring near the peak of the forward traveling wave, theoretical predictions map τ_OAE to 1.8–2τ_BM [14]. A recent study measuring simultaneous ABR and OAEs to tone-bursts found ratios closer to 1 for stimulus frequencies (CFs) below 1.5 kHz and ratios above 2 for higher CFs [12]. These findings contradict earlier studies reporting ratios close to two (2 [8]; 2.08 ± 0.19 [5]; 1.92 ± 0.42 ms [4]). Reasons for these discrepancies are in part due to the methods adopted to separate the stimulus from the TBOAE onset. τ_OAE suffers from an inter-subject variability as large as 10–30% [4, 10], a variability that is five times higher than for ABRs recorded in the same listeners [12].

The present study investigates the sources giving rise to inter-subject variations of the TBOAE and ABR latency methods using a modeling approach that is free from experimental TBOAE onset-separation errors. Implementations of a time-domain model for OAE and ABR generation were used to simulate ears from 20 listeners, in which all parameters but the random cochlear irregularities leading to coherent reflection-source OAEs were identical. The simulated TBOAE and ABR latency estimates aid in understanding why both methods can provide different estimates of auditory filter buildup time, leading to ratios that are not necessarily 1.8–2, even in a model based on emission generation through slow forward and reverse traveling waves.

METHODS

A nonlinear time-domain model of the middle ear and cochlea that generates reflection- and distortion-source OAEs [16] was used as a preprocessor to an auditory-nerve (AN) model [19], after which a functional model for the ventral cochlear nucleus (VCN) and inferior colliculus (IC) was included [9]. Simulated ABR wave-I, III and V were obtained by summing the model responses across 500 simulated Greenwood spaced CFs at the level of the AN, CN and IC, respectively. To match the outputs of the cochlear model to the inputs of the AN model, several adjustments were made to the existing AN model implementation [19]: (i) BM vibration was translated into inner-hair-cell (IHC) bundle deflection using a transformation gain constant, after which a 2^nd order Boltzmann function and a 2^nd order low-pass filter with cut-off frequency of 1 kHz were adopted to simulate the IHC receptor potential. (ii) AN fiber thresholds were made independent of CF, (iii) and made dependent on the spontaneous-rate (SR) of the fiber, and (iv), SR-dependence of the AN equations was modified to match the original implementation of the three-store diffusion model [17]. These adjustments lead to a 2-ms latency decrease in ABR wave-V latency for a 40-dB click level increase, a feature that is not accounted for in existing ABR models that only account for a ~0.5 ms decrease [1, 13].

τ_ABR was calculated as the peak latency of the simulated ABR wave-V minus the synaptic delays introduced in the CN and IC model stages, comparable to the experimental ABR forward-latency method [12]. τ_OAE was calculated using the energy-weighted group delay (EWGD) [2, 12] of the OAE waveform in a window starting at a latency equal to the stimulus duration (4 ms) plus 0.5 ms, as in [12]. Simulated ear-canal pressure PEC consists of 3 components: STIM, representing the passive components of the response; and OAE_RS and OAE_DS, representing the reflection- and distortion-source OAE components. STIM was estimated by rescaling PEC computed in the low-level linear regime (20 dB SPL) using a model without micromechanical irregularities (i.e., no OAE_RS and no OAE_DS), leading to the OAE = OAE_DS +OAE_RS = PEC−STIM. OAE_RS was obtained subtracting PEC from a model simulation where irregularities were first turned on, and then turned off: OAE_RS = PEC_irr −PEC_{no irr}. OAE_DS can then readily be obtained using OAE_DS = OAE−OAE_RS = PEC_{no irr} −STIM. In addition to calculating the EWGD identically to the method used in [12], EWGDs were also calculated using the whole waveforms of the simulated OAE, OAE_RS and OAE_DS. τ_BM was calculated from the EWGD of the simulated BM velocity waveform of the 1-kHz CF channel.

RESULTS

To demonstrate that the model is suited to study TBOAE and ABR latency, Fig. 1 shows a direct comparison between the simulated TBOAE and ABR latencies and those obtained experimentally to 1-kHz TBs (t_dur= 4 ms) of increasing intensity. When using the same latency method, simulated τ_ABR fell within the bounds of the experimental standard deviations of the experimental study [12] for stimulus levels above 40 dB peSPL, demonstrating decreased ABR latencies for increased stimulus levels. Simulated τ_OAE were found to match the experimental data well when calculating EWGDs over the whole derived waveform, but overestimate the latencies for stimulus levels above 60 dB peSPL when using the same analysis method employed in [12].

FIGURE 1.

(A) Experimental and simulated τ_OAE to 4-ms long 1-kHz tone bursts (no plateau), using the methods in [12] for 14 human subjects, and 20 frozen model subjects. Additionally, τ_OAE calculated over the whole derived OAE, OAE_RS and OAE_DS waveforms are also shown. (B) τ_ABR for the same stimuli and subjects as in panel A. Simulated τ_BM calculated as the EWGD of the BM velocity response of the 1-kHz CF cochlear channel. (C) Experimental [12] and simulated τ_OAE/τ_ABR ratios. Ratios for OAE,OAE_RS,OAE_DS were calculated using the whole derived waveforms.

Variability of latency estimates

The standard deviations of the simulated τ_ABR across 20 frozen model implementations were small compared to those found experimentally (Fig. 1B). Because the models were identical except for the micromechanical irregularities, experimental variability stemming from background noise and/or probe and electrode placement were not captured, and hence would not introduce variability in the simulated τ_ABR. Because the variability was so small, we conclude that the ABR latency estimates were not affected by changes in the micromechanical irregularity patterns in the cochlea that were used to simulate different model subjects. The story is different when we evaluate the standard deviations of the simulated τ_OAE in Fig. 1A. Even though our methods of deriving τ_OAE are free from measurement noise, standard deviations up to 1.3 ms were found. Differences in experimental methods alone are thus not able to explain why five times larger standard deviations are found for τ_OAE than for τ_BM in the experimental data plotted [12]. The simulations in Fig. 1A and B indicate that differences in the generator mechanisms of both types of responses may explain the large variability in the latency estimates because the only difference in the frozen models implementation was the placement of the random irregularities on the BM giving rise to reflection-source OAEs.

Indeed, when plotting waveforms of the simulated TBOAEs for different model subjects (Fig. 2), it is clear that the envelopes of the waveforms show little similarity between subjects. The EWGD estimates (indicated by the white markers) are able to compensate for some of the variability in the waveform envelopes, but variation in τ_OAE across frozen models is still apparent. For low stimulus levels, the OAE_RS component is responsible for the variations in waveform envelopes across subjects (left panel). For higher stimulation levels where a prominent OAE_DS component appears, the variations in τ_OAE are smaller, because the variation on the latency of the dominating OAE_DS component is next to zero. Latencies τ_OAE and standard deviations for the OAE, OAE_RS, and OAE_DS waveforms are summarized Fig. 1A. The variation in τ_OAE is due to variations in the OAE_RS envelope, and becomes smaller at larger stimulation levels, for which the OAE_DS component dominates the response, and τ_OAEDS variations are absent.

FIGURE 2.

TBOAE waveforms and envelopes to 4-ms long 1-kHz tone bursts, simulated for 4 frozen model subjects and two stimulus levels. Derived OAE, OAE_RS and OAE_DS waveforms are shown and EWGDs are indicated by white markers.

Reflection-source generators

Variations in the simulated TBOAE_RS envelopes arise through differences in the placement of the random irregularities along the BM. Thus, it is possible that emission components are generated at different cochlear locations, leading to different τ_OAE(f) contributing to the total OAE. This idea was tested in a model that had one point-source BM irregularity (M₁) placed at the cochlear location corresponding to the frequency of a peak of the simulated CEOAE spectrum. As a result, a relatively narrow band emission was generated in response to simulation with a click. A second point-source BM irregularity (M₂), was added at a frequency corresponding to the nearest peak in the click-evoked OAE (CEOAE) spectrum of that model subject when all random irregularities were present. M₁ and M₂ thus investigate the influence of two distinct reflection-sources on the OAE waveform.

Figure 3 shows OAE_RS waveform envelopes and corresponding magnitude and phase spectra for different stimulus levels and three model versions with one or two point-sources present: M₁, and M₂ alone, and both sources together M₁₂. Envelope maxima of the single source models decreased as stimulus level increased. This latency-decrease with level reflects group-delay changes of the forward traveling wave as observed from the fixed location of the reflector source (i.e., as judged from the shallower slopes of the phase patterns with level evaluated at the frequency corresponding to the source location M). When two point-sources are present simultaneously, the relationship between latency and group delay becomes less apparent. At low stimulus levels, the OAE_RS envelope shows two bumps with neither maximum occurring at latencies corresponding to the maxima of the OAE envelopes in the single source models. As stimulus level increases, the first bump becomes more prominent than the second, with corresponding growth of the first bump more linear than that of the second (analysis not shown), in agreement with experimental filtered click CEOAE waveforms [3, 6, 11]. Additional analysis with TB stimuli and different source frequencies revealed that as long as the two sources were located within the stimulus bandwidth (i.e., 250 Hz for the 1-kHz TBs in this study), behavior qualitatively similar to that of the double source waveform in Fig. 3 was obtained. Note that the mechanism giving rise to a latency of the first envelope bump shorter than that of either one of the point-source emissions (M₁₂ vs M₁ or M₂) occurred here through beating of two emission components that travel out of the cochlea together. The exact phase and amplitude ratio between the emission components determines the envelope shape regardless of their exact relation to the center frequency of the stimulus. Waveform shapes and associated latencies did thus not need to arise from specific generators at more basal locations, as often referred to in other studies [7, 18]. The varying envelope shapes in Fig. 2 for different frozen model implementations, and associated variability in the τ_OAE were in this model framework explained by beating between OAEs arising from multiple sources located within the peak region of the traveling wave.

FIGURE 3.

Envelopes and spectra for three point-source models stimulated with clicks (20–90 dB peSPL). Responses are normalized to their maximum amplitude. M₁ and M₂ represent single reflector sources at 1290 Hz and 1370 Hz; model M₁₂ has both. Results are shown for the OAE_RS component.

Latency ratios

Because subject-dependent reflection-source emission generators shape the envelope of the TBOAEs causing variability on τ_OAE, the ratios between τ_OAE and τ_ABR are also affected. As shown in Fig. 1, experimental ratios and those obtained using the whole simulated OAE waveform show ratios close to two for low stimulus levels, that increase towards 3 for higher stimulus levels. For the simulated results, the ratio is dominated by the latency of the reflection-source OAE component at low stimulus levels whereas it is dominated by the latency of the invariable distortion-source OAE component for the high levels. This also influences the variability of the ratio by showing larger variability for low stimulus levels. The experimental results do not show decreased variability of the ratio as stimulus level increases, which is likely due to the adopted windowing method that zero pads 4.5 ms of the recorded ear-canal-pressure to obtain the OAE waveform. Because for higher stimulus levels, the simulated τ_OAEDS was close to or shorter than 4.5 ms, it is possible that the experimental analysis was not able to include this emission component in τ_OAE or the latency ratios.

Relationship to τ_BM

The model approach allows for a direct comparison of simulated τ_OAE and τ_ABR to τ_BM. Even though the model is able to capture the experimental forward-latency decrease with level derived from the ABR wave-V (Fig. 1B), τ_ABR overestimates the model τ_BM(1kHz) derived from the simulated BM velocity waveform. For stimulus levels below 50 dB SPL the deviation is largest, whereas for high stimulus levels, the two waveforms run parallel. The deviation between the two measures arises because whereas τ_BM(1kHz) is a single channel estimate of filter build-up time, τ_ABR is obtained from a population response shaped by excitation (and associated build-up times) along much of the BM. Comparison between τ_BM(1kHz) and τ_OAE yields cochlear roundtrip times up to 8 times larger than τ_BM(1kHz) for τ_OAERS and up to 3 times larger for τ_OAEDS. A quantitative comparison between latency estimates and ratios is limited by the overall quality of the model, and is not pursued at this stage. At this point, we conclude that even though our model simulates experimental data of 1-kHz TBOAE and ABRs well, neither the ratios nor the latency estimates derived from τ_OAE and τ_ABR capture well the underlying filter build-up time derived from τ_BM(1kHz).

DISCUSSION

τ_OAE and τ_OAE/τ_ABR ratios are affected by the reflection-source generator mechanisms giving rise to subject-dependent envelope shapes of the TBOAEs. This τ_OAE variability, together with experimental difficulties in separating the stimulus from the TBOAE onset, imply that τ_OAE and τ_OAE/τ_ABR are difficult to relate to auditory filter build-up time. The variability of τ_OAE was due to the subject-dependent variations in the OAE_RS envelopes. Even though OAE_RS was generated through coherent reflection in the peak region of the traveling wave, the measure cannot easily be related to filter build-up time when multiple sources are present within the stimulus bandwidth. The double-bump behavior demonstrated here can account for the filtered click OAE data of [3], since the 1/3rd octave bandwidth adopted in that study allows for multiple CEOAE spectral peaks within the analysis window. Beating between multiple reflection sources within the evoking stimulus bandwidth can, even for TB stimuli, make it difficult to use this method to estimate individual filter build-up time. However, though the variability of the τ_OAE method is much larger than that of the τ_ABR, the τ_OAE method has successfully demonstrated a frequency-dependence of auditory filter build-up time of the human auditory system, as calculated from the mean over a large body of subjects [4, 5, 8, 12].

τ_OAEDS and τ_ABR demonstrated little variability across frozen model implementation, and thus appear to be more robust measures. The relationship between τ_ABR and the underlying single-channel filter build-up time remains unclear because τ_ABR depends on simultaneous summing of energy across the excited channels. Though our simulations fell within bounds of experimental studies, the model may not accurately capture this cross-channel summation. In addition, we have not examined whether the current simulations correctly predict the relative amplitudes of the OAE_DS and OAE_RS components at higher stimulus levels. In the model, these relative amplitudes are determined by the form of the compressive nonlinearity and the roughness pattern, respectively. Simulated τ_OAEDS were closest to twice the modeled τ_BM(1kHz), and showed little variability across model subjects, making them a promising measure for cochlear roundtrip time. However, experimental demonstration of the OAE_DS response to TBs is difficult because of temporal overlap with the stimulus waveform. Nevertheless, it would be interesting to re-analyse existing data for evidence of this component and to test its relation to filter build-up times.