Steep and shallow phase gradient distortion product otoacoustic emissions arising basal to the primary tones

Abstract

Distortion product otoacoustic emission (DPOAE) level∕phase maps were collected in humans with and without an interference tone (IT) near the DPOAE frequency place (f_dp) at primary-tone levels of 75 dB SPL. A DPOAE component with the expected steep phase gradient could be extracted at f_dp, however, considerable vertical-phase banding, presumably indicative of reflection emissions, remained. An IT placed 0.33 oct above f₂ removed most of this banding, revealing DPOAE components originating basal to the IT frequency place. These findings suggest that the commonly accepted two-source model of DPOAE generation may need to be qualified when higher primary-tone levels are utilized.

Introduction

Kim (1980) first proposed that distortion-product otoacoustic emissions (DPOAEs) are produced by a combination of two emission-generator components, one originating at the f₂ place and the other arising from the DPOAE frequency place (f_dp). The now commonly accepted two-source model (e.g., Zwieg and Shera, 1995; Talmadge et al., 1998) for apical DPOAE generation (i.e., f_dp<f₁; e.g., 2f₁-f₂ DPOAE), supported by numerous studies in humans (e.g., Talmadge et al., 1999; Knight and Kemp, 2000, 2001; Kalluri and Shera, 2001; Konrad-Martin et al., 2001; Dhar et al., 2005), proposes that within the cochlea, there are two separate contributors to the DPOAE levels and phases measured in the ear canal when elicited by low- to moderate-level primaries. The first contributor, referred to as the “generator” or “distortion” source, is thought to arise from the nonlinear interaction between the f₁ and f₂ primary tones. The primary-tone “overlap” region for apical DPOAEs is assumed to be near the tonotopic location on the basilar membrane (BM) of the higher-frequency f₂ primary tone, which creates energy at the DPOAE frequency that then travels both apically and basally within the cochlea. The apically traveling energy reaches the f_dp place on the BM and is then reflected back basally, thereby providing the second source (reflection) of the otoacoustic emission (OAE) measured in the ear canal. This energy reflection is attributed to the presence of randomly distributed inhomogeneities on the BM in the f_dp region. The interaction of these two sources results in the commonly observed fine structure in human DP-grams.

Emissions that Kemp and Knight (2000, 2001) called “place-fixed” and “wave-fixed” OAEs correspond to the more mechanistic terms “coherent linear reflection” and “nonlinear distortion,” respectively, adopted by Shera and Guinan (1999) to refer to these same emission properties. The Shera and Guinan (1999) formulation emphasizes the unique phase characteristics of the DPOAE, depending upon the site of emission generation. For example, for the wave-fixed component, a constant f₂∕f₁-ratio sweep maintains the relative phases of the f₁ and f₂ primary tones and the DPOAE. Thus, because of the property of cochlear-scale invariance, DPOAE phase remains relatively unvarying for a constant f₂∕f₁-ratio sweep resulting in shallow phase gradients. Because the DPOAE-place component (reflection) comes from the f_dp, for a constant f₂∕f₁-ratio sweep, the phase for this constituent changes rapidly and is associated with steep phase gradients.

In the DPOAE level∕phase (L∕P) maps described by Knight and Kemp (2000, 2001), when DPOAE phase is plotted as a function of DPOAE frequency, a constant vertical-phase band for a given DPOAE frequency presumably indicates a place-fixed (reflection) source. In contrast, a constant horizontal-phase band for a fixed f₂∕f₁-ratio sweep as a function of DPOAE frequency is considered indicative of a wave-fixed (distortion) source.

It is important to emphasize that the majority of the research designed to explore the two-source DPOAE model in humans has been conducted in exceptional subjects having very robust DPOAEs (e.g., Dhar et al., 2005) using low to moderate primary-tone levels (e.g., Konrad-Martin et al., 2001; Kalluri and Shera, 2001). Recently, our laboratory assembled DPOAE L∕P maps like those described by Knight and Kemp (2000, 2001), at similar higher primary-tone levels with L₁,L₂=75,75 dB SPL. These higher primary-tone levels are required to obtain robust 2f₁-f₂ and 2f₂-f₁ DPOAEs across a wide range of f₂∕f₁ ratios, especially in subjects with various types of sensorineural hearing loss (e.g., Stagner et al., 2007). In these L∕P maps, both horizontal- and vertical-phase banding were obtained that were very similar to that originally described by Knight and Kemp (2000, 2001).

In an attempt to “unmix” the two DPOAE components presumably indicative of the two emission mechanisms, interference tones (ITs) were placed near the f_dp, and DPOAE L∕P maps were obtained with and without the IT. Vector differences computed between the two conditions extracted a reflection component at f_dp for both the 2f₁-f₂ and 2f₂-f₁ DPOAEs; however, significant vertical banding still remained. In subsequent experiments, ITs placed 0.33 oct above f₂ removed most of the observable vertical-phase banding for both DPOAEs. The present report describes these theoretically important findings consistent with the presence of other DPOAE sources at higher primary-tone levels in humans.

Methods

Subjects

DPOAEs were measured in three ears of three normal-hearing human subjects between 18 and 30 years of age. Each subject had normal DPOAEs as compared to our laboratory’s database. All subjects provided informed consent and received monetary compensation for participation in the study. DPOAEs were obtained with subjects seated comfortably in a reclining chair within a single-walled sound booth situated in a quiet laboratory setting. The human-research protocol was approved by the institutional review board (IRB) of the VA Loma Linda Healthcare System.

DPOAE measures

To assure normal baseline DPOAEs, “DP-grams” as a function of f₂ frequency were measured with f₂ ranging from 0.275 to 15.3 kHz in 0.1-oct steps with L₁,L₂=55,55; 65,65; 75,75; and 65,55 dB SPL. Primary tones were produced by two digital-to-analog (D∕A) channels of a digital-signal processing (DSP) board (Digidesign, Audiomedia), mounted in a microcomputer (Apple, Macintosh Quadra 700). The f₁ and f₂ signals were presented using two ear-speakers (Etymotic Research, ER-2), and the level of the ear-canal sound pressure was measured using a low-noise microphone assembly (Etymotic Research, ER-10B+). The ear-canal signal was synchronously sampled at 44,100 kHz and averaged (n=4) by an analog-to-digital (A∕D) channel of the DSP board. A 4096-point fast Fourier transform (FFT) of the averaged time sample was performed by customized software. The 2f₁-f₂ and 2f₂-f₁ DPOAEs and associated noise-floor (NF) levels were extracted from the FFT. The NF was based upon the average of eight frequency bins on either side of the DPOAE frequency bin, excluding the first bin on either side of the DPOAE frequency.

DPOAE level∕phase (L∕P) maps

To generate DPOAE L∕P maps, DPOAEs were measured in response to constant f₂∕f₁ ratio sweeps varied in 0.025 increments from f₂∕f₁=1.025 to 1.5, with DPOAE frequency steps of ∼43 Hz, from 0.5 to 6 kHz for both 2f₁-f₂ and 2f₂-f₁, resulting in f₁ ranging from 0.258 to 12.016 kHz and f₂ from 0.366 to 18.023 kHz. For this study, the L∕P maps were collected at primary-tone levels of L₁,L₂=75,75 dB SPL, using a 2048-point FFT and four- or eight-time averages. DPOAE level was directly plotted (Microsoft Excel 2003, v.11.5), while phase was corrected for primary-tone phase variation and unwrapped by “looking” in two directions (f₂∕f₁ ratio and DPOAE frequency) using custom-developed Excel-based routines before plotting. Final, more detailed analysis and plotting were performed in MATLAB.

DPOAE L∕P maps were obtained with and without an IT placed at either 44 Hz below f_dp (IT=65 dB SPL) or at 0.33 oct above f₂ (IT=75 dB SPL). ITs were presented on alternate trials throughout the protocol to minimize any effects due to time-dependent changes in DPOAEs. The IT, which was digitally mixed with f₁, was rotated in phase by 90° over the four presentations and then time averaged to eliminate the majority of emission components produced by the IT. Vector differences were computed between control (no IT) and IT conditions to produce residual DPOAE L∕P maps consisting of DPOAE components removed by the IT. DP-grams with and without the IT and for the residual were extracted from the DPOAE L∕P maps for wide (f₂∕f₁=1.20) and narrow (f₂∕f₁=1.025) primary-tone ratios. The phase of the residual was unwrapped in the frequency direction and plotted as a function of DPOAE frequency and phase in cycles. Plotted this way, the slope is in units of time and can be thought of as a delay. The contrast of these delays suggests different physical mechanisms of emission production.

Results

The results of obtaining DPOAE L∕P maps with and without an IT near f_dp are shown for a representative subject in Fig. 1. Similar results were found for the other subjects, but the subject illustrated had the most robust DPOAEs, making it more straightforward to appreciate the findings in the DPOAE L∕P maps. On the left of Fig. 1 are six DPOAE L∕P maps [Figs. 1a, 1c, 1e =level; Figs. 1b, 1d, 1f =phase] corresponding to the control [Figs. 1a, 1b], IT [Figs. 1c, 1d], and residual [Figs. 1e, 1f] experimental conditions. In the control condition of Fig. 1a, DPOAE fine structure is evident in the level plot at f₂∕f₁ ratios of ∼1.2 (upper dashed black line) as peaks and valleys (arrows). In the corresponding phase plot of Fig. 1b, the two frequently observed phase behaviors for the 2f₁-f₂ DPOAE are clearly evident. That is, horizontal-phase banding dominates at wide f₂∕f₁ ratios, which presumably represents distortion emissions, while vertical-phase banding associated with reflection emissions is apparent at f₂∕f₁ ratios less than about 1.1. For the 2f₂-f₁ DPOAE [bottom half of Fig. 1b], vertical-phase banding was obtained for all f₂∕f₁ ratio values. In the IT condition shown in the level plot of Fig. 1c, DPOAE fine structure is substantially reduced (arrows). However, in the corresponding phase plot of Fig. 1d for the 2f₁-f₂ DPOAE, significant vertical banding remained, especially above 3 kHz. Likewise, much of the vertical-phase structure associated with the 2f₂-f₁ DPOAE remained in this frequency region. In the residual map of Fig. 1e, based upon the vector difference between the control (no IT) and IT maps, patchy residuals are evident where the IT removed DPOAE components for the 2f₁-f₂ (white arrows) and for the 2f₂-f₁ (black arrows). Finally, in the corresponding phase map of Fig. 1f, the phase behavior of these residuals showed vertical banding as commonly described for a reflection component from f_dp. It should be emphasized that the phase banding was notably much narrower (i.e., steeper phase gradient) for the residual 2f₁-f₂ DPOAEs at wide ratios [Fig. 1f, white arrows] as compared to the narrow ratio 2f₁-f₂ or 2f₂-f₁ for all conditions [Figs. 1b, 1d, 1f].

Figure 1.

DPOAE L∕P maps obtained with and without an IT placed 44 Hz below f_dp. The residual map in (e) demonstrates that DPOAE components can be extracted near f_dp that have vertical-phase banding properties in (f) (arrows). Red∕gray dashed line in (h) demonstrates that these emissions have the expected steep phase gradients consistent with a DPOAE-reflection component. However, in the presence of the IT, large DPOAE components remain (c) associated with similar vertical banding (d) and phase gradients as indicated by the blue∕gray line in (i). Black dashed lines on the DPOAE L∕P maps indicate f₂∕f₁ ratios where data were extracted for the plots in (g) and (h) (see text for complete details of this and Fig. 2).

The four plots to the right of the DPOAE L∕P maps illustrate more familiar analyses. For example, Fig. 1g demonstrates DP-grams extracted from these maps at an f₂∕f₁ ratio of 1.2 for the 2f₁-f₂ DPOAE without (solid black line) and with (solid blue∕gray line) the IT near f_dp. It is clear that in this situation the IT essentially eliminated the fine structure supporting the visual impression gained by comparing the central regions (white arrows) of the control [Fig. 1a] and IT [Fig. 1c] DPOAE L∕P maps.

The remaining three plots show phase curves extracted for the 2f₁-f₂ DPOAE at wide [Fig. 1h] and narrow [Fig. 1i] f₂∕f₁ ratios, as well as for the 2f₂-f₁ DPOAE at a narrow ratio [Fig. 1j] for control, IT, and residual conditions. For the 2f₁-f₂ at a standard ratio (f₂∕f₁=1.2), shallow phase slopes [Fig. 1h] were obtained for both the control (solid black line) and IT (solid blue∕gray line) conditions, consistent with the horizontal-phase bands seen in the corresponding phase maps at this ratio [Figs. 1b, 1d]. For this same f₂∕f₁ ratio, the residual showed a steep phase slope (dashed red∕gray line) associated with the vertical-phase banding [Fig. 1f, white arrows] extracted by the IT near f_dp. These findings illustrate the ability to extract a reflection component from the f_dp. However, most notably, significant vertical-phase banding remained [Fig. 1d] that could not be removed by the IT.

At narrow f₂∕f₁ ratios of 1.025 [Fig. 1i], steep phase-gradient DPOAEs were obtained for both the control (solid black line) and IT (solid blue∕gray line) conditions accompanied by vertical-phase structure. However, at this narrow ratio setting, the residual was too near the NF to measure its phase characteristics. This more conventional analysis confirms the observations noted above on the L∕P maps that the slopes of the phase gradients for the wide ratio 2f₁-f₂ DPOAE residual [white arrows in Fig. 1h] are roughly twice those of the narrow ratio 2f₁-f₂ [Fig. 1i], or 2f₂-f₁ [Fig. 1j] components for the control, IT, or residual (black arrows) conditions suggesting that the 2f₁-f₂ DPOAE from f_dp has a much longer latency than these narrow-ratio 2f₁-f₂ and 2f₂-f₁ components associated with steep phase gradients.

Phase curves for the 2f₂-f₁ DPOAE are shown in Fig. 1j for the narrow f₂∕f₁-ratio condition (1.025) equidistant below the white dashed centerline at f₂∕f₁=0. For this DPOAE, all conditions revealed steep phase gradients associated with the vertical-phase banding observed in the phase maps, which is consistent with the place-fixed behavior of this emission.

Figure 2 displays the results of repeating the same experiment depicted in Fig. 1 in the same subject in a different session, but with the IT placed 0.33 oct above f₂. First, the striking similarity of the DPOAE L∕P maps between Figs. 1a, 2a with respect to DPOAE level should be noted thus demonstrating the excellent test∕retest reliability of these maps within the same individual. In the control condition of Fig. 2a, fine structure is again evident in the DPOAE levels at wide f₂∕f₁ ratios of ∼1.2 as peaks and valleys. In the corresponding phase plot of Fig. 2b, the two phase behaviors can again be observed for the 2f₁-f₂ DPOAE. For the 2f₂-f₁ DPOAE (bottom half of plot), the phase banding is vertical, which supports the presence of a reflection-based generation mechanism. In the IT condition illustrated in Figs. 2c, 2d, as compared to Fig. 1c, it can be seen that the fine structure at f₂∕f₁=1.2 in the level plot [Fig. 2c] is not affected by the IT, when it is placed 0.33 oct above f₂. This outcome suggests that the IT had minimal effects on the f₂ source at this distance basal to f₂, otherwise the DPOAE fine structure would be modified by a reduction in this DPOAE component. In contrast to the previous experiment, in the related phase plot of Fig. 2d, a significant amount of the vertical-phase banding that was present in the control condition [Fig. 2b] is removed by the IT for both DPOAEs. In the residual maps of Figs. 2e, 2f, a large residual DPOAE for both the 2f₁-f₂ and 2f₂-f₁ emissions is evident in Fig. 2e, which is indicative of the DPOAE components removed by the IT that presumably originate, or are modified, from BM regions situated basal to the IT place. In the corresponding phase map of Fig. 2f, the phase behavior of these residuals shows both horizontal- and vertical-phase banding for the 2f₁-f₂ DPOAE, and vertical-phase banding for the 2f₂-f₁ DPOAE.

Figure 2.

DPOAE maps obtained with and without an IT placed 0.33 oct above f₂. The residual map in (e) demonstrates that by placing the IT above f₂, large DPOAE components can be extracted that have phase properties of both distortion and reflection emissions, depending upon the f₂∕f₁ ratio (f). Shallow and steep phase gradients associated with these two components were confirmed by extracting the phase curves at a wide f₂∕f₁ ratio in (h), and at a narrow ratio in (i) (dashed red∕gray lines). In (d), almost all of the narrow f₂∕f₁-ratio vertical-phase banding was removed by the IT for the narrow ratio 2f₁-f₂ DPOAE, and similarly for the 2f₂-f₁ DPOAE, suggesting that both of these reflectionlike components originate in regions of the cochlea that are basal to the IT place.

The top plot of Fig. 2g at the right of the DPOAE L∕P maps shows DP-grams extracted for an f₂∕f₁ ratio of 1.2 for the 2f₁-f₂ emission collected without (solid black line) and with an IT (solid blue∕gray line) placed 0.33 oct above f₂. These DP-grams traverse the center of the fine structure regions in Figs. 1a, 1c (dashed black line at 1.2). It is clear that both DP-grams superimposed on one another convincingly indicate that in this situation the 75 dB SPL IT did not influence DPOAE sources originating from the f₂ place that interact with the source reflected from the f_dp to produce this fine structure. This observation reinforces the notion that the modifications produced by the IT resulted from its influence on DPOAE components located basal to the IT place.

The other three plots depict DPOAE phase gradients extracted from the DPOAE L∕P maps for the 2f₁-f₂ and 2f₂-f₁ DPOAEs for wide (1.2) and narrow (1.025) f₂∕f₁ ratios for the control, IT, and residual experimental conditions. Figure 2h shows phase curves for the wide 1.2-ratio condition, a circumstance where all the phase curves have shallow slopes that are in agreement with the horizontal-phase banding observed across all three experimental conditions. At this ratio, the IT presumably removed a distortion component, which is in accord with the shallow phase slope for the residual (red∕gray dashed line) constituent. However, this component apparently was not generated at f₂, but rather basal to the IT frequency place above f₂.

For the narrow ratio situation at 1.025 shown in Fig. 2i, steep phase gradients were obtained for all conditions. The phase gradient for the residual (red∕gray dashed line) seen in Fig. 2f as vertical banding is consistent with the IT removing a DPOAE source with reflection-like phase properties that does not arise from the f_dp.

In Fig. 2j, the phase slopes are steep for all three experimental conditions as commonly observed for the place-fixed behavior of the 2f₂-f₁ DPOAE. However, in this situation, the IT was considerably above the f_dp until the f₂∕f₁ ratio values were equal to or >1.3 in contrast to Fig. 1j where it is just below the f_dp for all ratios. Thus, these place-fixed components also appear to originate from regions that are substantially basal to the f_dp.

Discussion

A number of studies in human subjects (e.g., Talmadge et al., 1999; Knight and Kemp, 2000, 2001; Kalluri and Shera, 2001; Konrad-Martin et al., 2001; Dhar et al., 2005) have supported the two-source model of DPOAE generation synthesized by Shera and Guinan (1999) for low- to moderate-level primaries. The present results from human subjects also confirm that a steep phase gradient DPOAE component can be extracted with ITs near f_dp. Presumably, this emission corresponds to the reflection component arising from randomly distributed inhomogeneities on the BM in the f_dp region. However, significant vertical-phase banding remained in the DPOAE L∕P maps that was shown to be associated with steep phase gradients. By placing the IT 0.33 oct above f₂, most, if not all, of this remaining vertical banding, along with a significant component associated with wave-fixed phase behavior, was extracted [Fig. 2f]. It is noteworthy that the high-frequency IT did not alter the pattern of DPOAE fine structure at wide f₂∕f₁ ratios, which is due to the interaction of the f₂ and f_dp emission components. This finding suggests that the IT acted by removing or modifying components basal to the f₂ that were responsible for the remaining place-fixed phase behavior. These results are in agreement with evidence that other emissions, such as the 2f₂-f₁ DPOAE, can be generated basal to the f₂ place (e.g., Martin et al., 1998). The fact that placing the IT 0.33 above f₂ strongly influenced the 2f₂-f₁ DPOAE supports the earlier findings for this emission. These remaining steep phase gradient emissions also cannot be attributed to suppression of multiple internal reflections, since Dhar et al. (2002) demonstrated that the presence of such reflections interact to significantly alter DPOAE fine structure, which, in this case, remained unchanged when these emissions were removed by the IT. It is possible that these basal source contributions could somehow be reflected from f_dp. In this latter situation, the high-frequency IT at 0.33 oct above f₂ eliminates the basal source and consequently the reflected component from f_dp associated with vertical-phase behavior. However, the observations that this component cannot be affected by the IT at f_dp [Figs. 1c, 1d] and that the fine structure remains unchanged [Fig. 2c] in the presence of the high-frequency IT seem to support the notion that this particular DPOAE component associated with vertical-phase banding comes from a region basal to f₂.

Overall, the present findings suggest that the two-source model of DPOAE generation in humans may be limited to situations where the primary tones are kept at low to moderate levels. As primary-tone levels are increased to higher levels, as in the present case, it appears that other emission components are generated basal to f₂ for the case of the 2f₁-f₂ DPOAE, and even well basal to the emission place for the upper sideband 2f₂-f₁ DPOAE. These basal components have phase properties that have previously been attributed strictly to distortion or reflection emissions generated at f₂ or f_dp, respectively. Knight and Kemp (2000) obtained DPOAE L∕P maps in two human subjects in response to 70-dB SPL primary-tone levels that were very similar to the ones illustrated here. They subsequently attempted to extract the place-fixed and wave-fixed components (Knight and Kemp, 2001) using temporal windowing and inverse fast Fourier transform (IFFT) techniques. The resulting outcomes led these authors to conclude that both emission types were widely distributed, a finding that is contradictory to the current results. Recently, Dhar et al. (2005) also discovered over a very restricted frequency range of 400 Hz that the reflection component dominated at narrow ratios and low primary-tone levels. Interestingly, this outcome was not observed over the large frequency span encompassed by the current DPOAE L∕P maps. It is important to emphasize that the present results were obtained using IT techniques that directly remove emission components by the suppressive effects of a third tone in a nonlinear system.

The other more frequently employed strategy of using time windowing and IFFT filtering assumes that only two components are to be separated, and that this approach can be utilized, because their corresponding phase behaviors result in unique and separable latencies in the pseudotime domain. It appears likely that under the conditions used in the present study, these methods would also extract two components, but the assumption that one of the components arose entirely from f_dp and the other from f₂ would be incorrect. Of course, this circumstance represents an important issue that needs to be tested by comparing the distribution of components that can be extracted with the two techniques at these higher primary-tone levels. Overall, if other investigators can confirm these findings, then the commonly accepted two-source model of DPOAE generation in humans may require further qualifications based upon primary-tone levels.