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. Author manuscript; available in PMC: 2022 Nov 1.
Published in final edited form as: Int J Audiol. 2021 Feb 22;60(11):890–899. doi: 10.1080/14992027.2021.1886352

Cochlear tuning estimates from level ratio functions of distortion product otoacoustic emissions

Uzma Shaheen Wilson a,*, Jenna Browning-Kamins a, Alessandra Spada Durante b, Sriram Boothalingam c, Arturo Moleti d, Renata Sisto e, Sumitrajit Dhar a,f
PMCID: PMC8380255  NIHMSID: NIHMS1687365  PMID: 33612052

Abstract

Distortion product otoacoustic emission (DPOAE) levels plotted as a function of stimulus frequency ratio demonstrate a bandpass shape. This bandpass shape is narrower at higher frequencies compared to lower frequencies and thus has been thought to be related to cochlear mechanical tuning. However, the frequency- and level-dependence of these functions above 8 kHz is largely unknown. Furthermore, how tuning estimates from these functions are related to behavioral tuning is not fully understood. From experiment 1, we report DPOAE level ratio functions (LRF) from seven normal-hearing, young-adults for f2 = 0.75-16 kHz and two stimulus levels of 62/52 and 52/37 dB FPL. We found that LRFs became narrower as a function of increasing frequency and decreasing level. Tuning estimates from these functions increased as expected from 1-8 kHz. In experiment 2, we compared tuning estimates from DPOAE LRF to behavioral tuning in 24 normal-hearing, young adults for 1 and 4 kHz and found that behavioral tuning generally predicted DPOAE LRF estimated tuning. Our findings suggest that DPOAE LRFs generally reflect the tuning profile consistent with basilar membrane, neural, and behavioral tuning. However, further investigations are warranted to fully determine the use of DPOAE LRF as a clinical measure of cochlear tuning.

Keywords: cochlear tuning, behavioral tuning, distortion product otoacoustic emissions, level ratio function

Introduction

An integral part of human hearing is the processing of complex signals, such as speech and music, both in quiet and in noise. Processing such complex signals demands both acute auditory sensitivity and fine frequency selectivity (Oxenham, 2018). In the cochlea, the sensory end organ of the auditory system, this complex task is achieved by a combination of passive and active biomechanics (Ashmore et al., 2010). However, the structures and properties of the cochlea that bestow the auditory system with extreme sensitivity and frequency selectivity are also highly vulnerable to various environmental and physiological insults (e.g. aging, noise exposure, drug toxicity, etc.). As the cochlea becomes a target for advanced regenerative and otoprotective therapies, it will become even more important to accurately evaluate various aspects of cochlear function, including its tuning properties.

Passive cochlear tuning is determined by the material properties of the basilar membrane (Békésy, 1947). This passive tuning is sharpened by the active processes related to outer hair cells (Brownell et al., 1985; Robles et al., 1986; Dallos, 2008). Evidence for the active cochlear processes comes from direct observation of highly sensitive and frequency specific mechanical vibrations of a specific location on the cochlear partition or the basilar membrane (see Robles & Ruggero, 2001 for a review). In humans, however, basilar membrane vibration measurements are not currently feasible due to their invasive nature. Fortunately, the active cochlear processes yield a byproduct, i.e. otoacoustic emissions, that are measurable in the ear canal and provide a window into cochlear mechanics (Kemp, 1978).

Distortion product otoacoustic emissions (DPOAE), evoked using two simultaneous tones (frequencies f1 and f2), are widely measured in clinics at a single stimulus frequency ratio (typically f2/f1 = 1.22). When DPOAE levels at a given f2 are measured at multiple stimulus frequency ratios, a bandpass shape is seen such that the DPOAE level is highest at an optimal ratio (Harris et al., 1989; Brown et al., 1993a; 1993b; Abdala, 1996; Stover et al., 1999; Dhar et al., 2005; Botti et al., 2016). This stereotypical bandpass shape of the DPOAE level as a function of stimulus frequency ratio is referred to as the DPOAE level-ratio function (LRF) in this manuscript.

The DPOAE LRF peaks at an optimal ratio which is dependent on the stimulus frequency and level (Harris et al., 1989; Johnson et al., 2006). DPOAE levels are reduced at ratios lower and higher than the optimal ratio giving the DPOAE LRF the aforementioned bandpass shape. At high ratios, the DPOAE recorded in the ear canal is reduced because the vibrations produced by the stimulus tones are spatially separated on the basilar membrane with minimal or no overlap to generate distortion. On the other hand, as the ratio approximates 1 and there is significant overlap between vibrations due to each stimulus tone, destructive phase interference and other nonlinear phenomena such as two-tone suppression contribute to the reduction seen in DPOAE level (Sisto et al., 2018).

Many studies have examined the DPOAE LRF in humans for the purposes of optimizing DPOAE measurement protocols (Harris et al., 1989), investigating frequency selectivity (Brown et al., 1993a), and understanding the generation mechanisms of DPOAEs (Stover et al., 1999). Harris et al. (1989) first showed the frequency- and level-dependence of the DPOAE LRF in five human ears and suggested that the filter-like properties of the LRF were related to cochlear mechanical tuning. Brown et al. (1993a) later compared tuning values obtained from DPOAE LRF to the bandwidth of auditory filters measured psychophysically and found a significant correlation between LRF and psychophysical tuning estimates. Extending these measurements in a larger sample of both normal and hearing-impaired individuals using a wide range of stimulus frequencies, Stover et al. (1999) suggested that the DPOAE LRF is sensitive to cochlear damage at the f2 region and thus could be used as an objective measure of tuning. Despite these early suggestions, the question remains: Can the DPOAE LRF be used clinically for estimating cochlear tuning? In order to address this question, the theoretical basis of the DPOAE LRF should be fully evaluated up to the highest frequencies, and the relationship of the DPOAE LRF to behavioral tuning estimates must be investigated, particularly for frequencies important for speech perception.

The theoretical and mechanical basis for the DPOAE LRF using direct measurements of basilar membrane and auditory nerve activity have been explored in laboratory animals (e.g. Allen & Fahey, 1992; Shera, 2003; de Boer et al., 2005; Shera & Guinan, 2007). Models of DPOAE link their generation to the extent of overlap between the vibration patterns created by the two stimulus tones. The spatial extent of these vibration patterns, and hence the overlap between them, is governed directly by the spatial tuning properties of the cochlear partition and its constituent structures. Thus, it is logical to expect tuning estimates derived from DPOAE LRF to be related to other estimates of auditory tuning that are driven by the basic mechanical properties of the cochlea. Sisto et al. (2018) proposed a model that assumes a simple relationship between tuning estimates from the distortion component DPOAE LRF and basilar membrane tuning based on the spatial width of the DPOAE generation region. If the model is representative of cochlear physiology, tuning estimates from the distortion component DPOAE LRF should manifest frequency- and level- dependent tuning characteristics observed in mechanical and neural measures. Furthermore, these DPOAE based tuning estimates should then also be related to other measures of tuning in humans.

Previous studies of the DPOAE LRF in humans almost exclusively report the entire DPOAE pressure recorded in the ear canal and not the individual components of the DPOAE. The DPOAE in the ear canal is composed of two major components from different locations of the cochlea generated by different mechanisms. The mixing of these components is known to lead to complexities in the DPOAE LRF (Shera, 2003). In order to test the predictions of the Sisto et al. (2018) model, the frequency- and level- dependence of the DPOAE LRF from the isolated distortion component needs to be characterized. Only two studies, to our knowledge, have separately characterized the ratio dependence of the two DPOAE components in humans (Dhar et al., 2005; Botti et al., 2016), albeit on a small number of ears and a limited frequency range (< 5 kHz). In the current study, we characterized tuning estimates from the distortion component DPOAE LRF for f2 up to 16 kHz and two different stimulus level pairs (experiment 1).

In order to assess the clinical potential of DPOAE LRFs, we also compared the tuning estimates derived from DPOAE LRF at 1 and 4 kHz to those obtained behaviorally (experiment 2). Behavioral measures of tuning are not utilized clinically because they are time-consuming, require excessive training in some individuals, and are simply unsuitable for certain populations such as very young children and special populations (Sęk & Moore 2011) . However, the need for an objective and quick measure of tuning (e.g. DPOAE LRF) as part of a diagnostic test battery is being realized, as links are discovered between broad auditory tuning and deficits in speech perception in noise, despite normal hearing sensitivity at frequencies important for speech (Badri et al., 2011). Therefore, the extent to which DPOAE LRF tuning is related to behavioral tuning needs to be evaluated so that the clinical and diagnostic value of this measure may be fully assessed.

Methods

All behavioral and otoacoustic measurements were performed in a sound-treated booth while participants sat comfortably in a reclining chair and watched a silent movie with captions during the OAE measurements. Participants were required to meet the following inclusion criteria: ear canals clear of excessive cerumen, normal middle ear function as defined by a Jerger Type A tympanogram (Jerger, 1970) and audiometric thresholds better than 25 dB HL between 0.25 - 8 kHz. Participants provided informed consent and were compensated for their participation in the study. All study procedures were approved by the Institutional Review Board at Northwestern University.

Experiment 1

(1) Participants:

Seven normal-hearing, young adults (age 16-22 years; 4 females, 3 males; 3 right ears, 4 left ears) were recruited from Northwestern University and surrounding areas.

(2) General Procedures:

Following screening measurements, stimulus calibration was performed by finding the Thévenin equivalent characteristics of the probe and estimating the load impedance of the ear with the probe inserted in the ear canal in order to equalize the forward pressure level (FPL) of the stimulus at the eardrum. DPOAEs were recorded using a fixed-f2 protocol where f1 was swept, and f2 was fixed at 0.75, 1, 2, 4, 6, 8, 10, 12.5, 14, and 16 kHz. Our goal was to probe the tuning properties of the overlap region of f1 and f2 excitation patterns. To achieve this, the f2 frequency was held constant and the f1 frequency changed gradually, to induce a systematic change in the overlap region responsible for generating the DPOAE. The sweep duration was approximately 8 seconds. This method resulted in DPOAE recordings across continuously varying f2/f1 between 1.05 and 1.5 (note that f1 was always lower in frequency than f2). Two primary level combinations were used (L1/L2 = 62/52 and 52/37 dB FPL or approximately 65/55 dB and 55/40 dB SPL respectively). The measurements for all f2 frequencies and both levels lasted ~ 2 hours.

(3) Equipment:

Stimulus generation and data acquisition were controlled using custom software running on a Macintosh computer (OS 10.10) at a sampling rate of 48 kHz and 24-bit resolution. Digital to analog and analog to digital conversions were performed with a Fireface 400 (RME, Haimhausen, Germany), and signals were amplified by an ER-H4C amplifier (Etymotic Research, Elk Grove Village, IL) before they were delivered to the ear by MB Quart 13.01 HX speakers (Maxxsonics, Chicago, IL). OAE measurements were recorded from one ear using an ER-10B+ probe microphone (Etymotic Research, Inc, Elk Grove Village, IL) coupled to the ear using a foam tip. The microphone’s frequency response was corrected to allow recording of OAEs up to 16 kHz (Rasetshwane & Neely, 2011).

(4) Signal processing:

Raw ear canal pressure recordings were first high-pass filtered using a 4th order digital Butterworth filter with a cutoff frequency of 0.4 kHz to remove low frequency noise artifact from the recordings. Artifact rejection was then employed using root-mean-square values of individual waveforms and setting a rejection criterion of 2 standard deviations above the mean RMS of all waveforms. Following artifact rejection, time domain averaging was performed across 32 (for f2 ≥ 3 kHz) or 64 recordings (for f2 < 3 kHz). A higher number of recordings was needed at frequencies below 3 kHz to improve signal to noise ratio, as physiological noise can be problematic at those frequencies in some ears. Individual recordings were split into odd and even buffers resulting in two sub-averages, which were added to yield a grand average of the signal and subtracted to provide an estimate of the noise. Emission and noise magnitudes and phases were estimated from the grand averages using a least-squares fit algorithm (Long & Talmadge, 1997). DPOAE components were then separated using inverse fast Fourier transform (IFFT) and time-domain filtering, and only the distortion/generator component was used in subsequent analyses. Details of the IFFT procedure are published elsewhere (Abdala & Dhar, 2012).

(5) Tuning estimates from LRF:

The tuning estimate Qerb can be defined as the sharpness or quality factor of a filter that passes the same amount of total power as a filter with an equivalent rectangular bandwidth. After separating the distortion/generator component (DPOAEgen) from the total ear canal DPOAE, the edge effects introduced by IFFT were removed. DPOAEgen LRF was then processed with the smooth function (MATLAB) using the loess method (50% span), and the peak response of the smoothed DPOAEgen LRF was identified using findpeaks (MATLAB). The smoothed DPOAEgen were interpolated at 1 Hz resolution. Only DPOAEgen levels greater than −20 dB SPL were kept before converting the DPOAEgen levels to power units for the Qerb estimation. To obtain the Qerb value of the smoothed DPOAEgen LRF, the height of the function was identified as the maximum of the DPOAEgen LRF and the area of the function was calculated using the trapz function (MATLAB). Lastly, Qerb was computed as follows:

Qerb=f2ERB;whereERB=area of the LRFheight of the LRF.

Next, we employed a mirroring method to mitigate the potential effects of two-tone suppression and/or destructive phase interference at ratios close to 1. Synthetic DPOAEgen LRFs were generated by mirroring the curve from the high ratio side of the LRF to the low ratio side. Unmirrored Qerb from the original DPOAEgen LRF and mirrored Qerb from the synthetic functions were computed and used for secondary analyses.

Experiment 2

(1) Participants:

24 normal-hearing young adults (mean age and standard deviation = 22.4 ± 2.2 years; 17 females and 7 males) were recruited from Northwestern University and surrounding areas.

(2) General Procedures:

Psychophysical tuning curves (PTCs) at 1 and 4 kHz were measured using the fast-swept PTC method described by Sęk & Moore (2011). DPOAEs for primary levels 55/40 dB SPL were obtained for f2 fixed at either 1.25 or 5 kHz and f1 was swept from 0.833 to 1.25 kHz or from 3.3 to 5 kHz, respectively. The sweep duration was 8 seconds. For f2 = 1.25 and 5 kHz, only data for 2f1-f2 DP frequencies (fdp) up to 1.2 and 4.5 kHz, respectively, were retained due to analysis artifact from f1, f2, and fdp being the same frequency at f2/f1 = 1. The combination of f1 and f2 frequencies yielded 2f1-f2 responses between 0.416–1.15 kHz and 1.6–4 kHz, roughly equating the cochlear regions being probed between DPOAEs and PTCs as schematized in Figure 1. The rough match between the cochlear regions being probed by the two measures should not influence the tuning estimates significantly as tuning is expected to vary smoothly along the cochlea. The potential implications for this slight mismatch will be discussed in later sections. The test and frequency order were randomized across participants. DPOAE and PTC measurements were repeated once within the same session and again in four weeks to assess repeatability. Qerb estimates were not found to be significantly different across sessions in a repeated-measures analysis of variance, and thus an average Qerb across all sessions was computed for each measure and frequency. PTCs for both probe frequencies took ~ 10 minutes to complete, whereas the DPOAE recordings lasted ~ 2 minutes.

Figure 1.

Figure 1.

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Top: Schematic illustrating the DPOAE LRF fixed-f2 paradigm, where dashed boxes indicate the range of f1 frequency sweep and dotted boxes indicate the range of the 2f1-f2 frequencies (fdp). Bottom: Schematic illustrating the probe frequency (fp) and masker frequency (fmasker) for PTC measurements.

(3) DPOAE Measurements:

DPOAEs were generally recorded and processed using the same procedure as Experiment 1 with two modifications. First, fewer number of recordings were obtained at each f2 in order to reduce the length of the session, so the grand average sent to the least-squares-fit program was based on an average of eight runs for each f2. Second, a faster sweep rate compared to experiment 1 was adopted in order to accommodate behavioral measures within the same testing session. Total ear canal DPOAE recordings were assessed for adequate signal to noise ratio (SNR) before IFFT component separation and distortion component LRF tuning estimation. Three participants had SNRs poorer than 10 dB for more than 25% of the total ear canal DPOAE data points and therefore, these participants were not included in subsequent group analyses.

(4) PTC measurements:

Participants were asked to listen for the probe tone while ignoring background noise. Signals were 500 ms pulsed pure tones with an inter-stimulus interval of 200 ms presented at 10 dB sensation level, while the maskers were narrowband noise with a bandwidth of 120 or 240 Hz, respectively, logarithmically swept in frequency between 0.5-1.5 kHz and 2-6 kHz for the 1 and 4 kHz probe tones, respectively. Noise level was controlled by the participant, such that depressing the space bar on a keyboard changed the noise level at the rate of 2 dB/s in 0.5 dB steps (Sęk & Moore, 2011; Charaziak et al., 2012; 2013). Raw PTCs were processed offline using custom written analysis scripts in MATLAB by smoothing the tuning curve using the loess method. Tuning estimates for PTCs were computed based on the height and area of the tuning curve (Charaziak et al., 2012; 2013).

(5) Statistical analyses:

Following signal processing, artifact rejection, and SNR determination, the number of observations were unequal across frequencies and levels for DPOAE LRFs because of poor signal to noise ratio at some frequency/level combinations, which prevented an accurate estimation of Qerb. Therefore, statistical analyses were not performed for experiment 1, due to the small sample size and unequal number of observations across frequencies and levels. In order to test for statistical differences between behavioral and DPOAE LRF tuning estimates obtained in experiment 2, a repeated-measures analysis of variance was conducted with frequency and measure as within-subjects variables for predicting Qerb and participant number as the random variable. Post-hoc paired-samples t-tests and correlational analyses using Pearson’s r were performed to further examine the effects of frequency (1 kHz vs. 4 kHz) and measure (behavioral vs. DPOAE). For post-hoc t-tests, a Bonferroni-correction was applied to alpha of 0.05 and significance level was set at p < 0.0125 for four comparisons (2 frequencies x 2 measures). For correlational analyses, significance level was set at p < 0.05. Analyses were performed in RStudio (R version 3.4.1) using {stats} and {ez} packages.

Results

Experiment 1

The peaks of the LRFs of the isolated DPOAEgen generally shifted towards lower ratios with increasing f2, in addition to becoming narrower and more asymmetrical such that the slope appeared to be steeper on the higher ratio side compared to the low ratio side from the LRF peak (Figure 2). This general trend notwithstanding, individual variability in magnitude and tuning of the response in these young, normal-hearing ears is noticeable. Furthermore, DPOAEgen decreased significantly in level at 14 kHz, particularly for the lower stimulus level pair (52/37 dB FPL), and data were only recordable in four study participants for f2 above 14 kHz.

Figure 2.

Figure 2.

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DPOAEgen levels (dB SPL) plotted as a function f2/f1 ratio for all subjects (indicated by line color) at all f2 frequencies from 0.75 (top) to 16 kHz (bottom) for L1/L2 = 52/37 dB FPL (left) and 62/52 dB FPL (right). Dashed lines indicate synthetic/mirrored LRFs whereas solid lines indicate original/unmirrored LRFs.

Eliminating the measured DPOAEgen at low ratios and mirroring the LRF from the high ratio side resulted in slightly sharper tuning in the majority of the cases, but in about a third of the observations, the LRFs became broader or remained the same after mirroring (Figure 2). Quantitatively, the Qerb values obtained from the mirrored LRFs were sharper than their original counterparts in 65.6% of the observations. In 34.4% of the observations, mirroring resulted in lower Qerb values consistent with broader tuning. Comparing mirrored vs unmirrored LRFs in Figure 2, these patterns appeared to be random, and not specific to a certain frequency or level combination within or across individuals. Although the tuning estimates from the synthetic/mirrored DPOAEgen and original/unmirrored DPOAEgen LRFs were highly correlated (r(129) = 0.805, p < 0.001), the correlation was not perfect. This observation was important when determining which tuning estimate (mirrored or unmirrored) to compare with behavioral tuning.

As shown in Figure 3, DPOAEgen tuning (Qerb) generally increased as a function of f2 from 1 – 8 kHz. A deviation from this relationship was seen at 0.75 kHz, where Qerb values were higher than at 1 kHz. Above 8 kHz, the Qerb values became broader and more variable for the lower stimulus levels of 52/37 dB FPL, likely due to fewer LRFs with good signal-to-noise ratio. Tuning estimates for the 62/52 dB FPL stimuli also increased as a function of f2 from 1–8 kHz, after which the loess fit line plateaued. A slight level dependence was observed for some frequencies such that tuning estimates were higher for lower stimulus levels; however, there was considerable variability across individuals and frequencies in this small sample.

Figure 3.

Figure 3.

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Qerb estimates, from the synthetic/mirrored DPOAEgen LRF, plotted as a function f2 frequencies for L1/L2 = 52/37 dB FPL (left) and 62/52 dB FPL (right). Circles indicate individual tuning estimates, whereas solid lines indicate loess fit to the data after excluding data at 0.75 kHz. Loess fit was chosen to demonstrate the trend of smoothly varying tuning as a function of frequency. Data from 0.75 kHz were excluded from the loess fit because of the unexpected sharper tuning below the apical-basal transition frequency.

Experiment 2

As shown in Figure 4, both DPOAEgen LRFs and PTCs generally demonstrate sharpening of tuning with increasing frequency. Based on our previous finding that tuning estimates from synthetic/mirrored DPOAEgen LRF were not entirely correlated with estimates from the original/unmirrored LRFs, we re-examined the relationship between tuning estimates from both methods and found a moderate correlation (r(43) = 0.768, p <0.001) after pooling data across both frequencies. Subsequent statistical analyses were performed using both synthetic/mirrored and original/unmirrored LRFs.

Figure 4.

Figure 4.

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Unmirrored DPOAEgen LRF (top) and PTCs (bottom) at 1 and 4 kHz from 21 participants. Only functions from which tuning estimates could be computed are shown. DPOAEgen LRFs are plotted as function of 2f1-f2 frequency, whereas PTCs are plotted as a function of masker frequency. Only smoothed PTCs are shown (raw tracings are published elsewhere [see Wilson et al., 2020]).

Qerb was sharper at 4 kHz than 1 kHz for both PTCs and DPOAEgen LRFs. This was true for both statistical models with mirrored DPOAEgen LRFs (F(1, 20) = 42.929, p < 0.001) and unmirrored DPOAEgen LRFs (F(1, 20) = 54.066, p < 0.001) tuning estimate as the dependent variable. Qerb was sharper for PTCs than DPOAEs using both mirrored LRF tuning estimates (F(1, 20) = 46.608, p <0.001) and unmirrored LRF tuning estimates (F(1, 20) = 56.740, p <0.001). Post-hoc t-tests revealed that PTC-based tuning was significantly sharper than mirrored DPOAE LRF tuning estimates at both 1 kHz (t(20) = 9.892, p <0.001) and 4 kHz (t(20) = 3.654, p<0.001). This difference was also significant for unmirrored DPOAE LRF tuning and behavioral tuning at 1 kHz (t(20) = 9.772, p <0.001) and 4 kHz (t(2) = 4.054, p <0.001). The average difference between PTC and LRF tuning estimate was slightly larger at 4 kHz than at 1 kHz; however, the interaction between frequency and measure was not significant for either mirrored LRF tuning (F(1, 20) = 0.035, p = 0.853) or unmirrored DPOAE LRF tuning (F(1, 20) = 0.120, p = 0.733).

Qerb estimates from mirrored and unmirrored LRFs were similar at both 1 kHz and 4 kHz. Mean and standard deviation was 3.99 ± 0.61 for mirrored LRFs and 3.97 ± 0.36 for unmirrored LRFs at 1 kHz, whereas the mean and standard deviation was 6.81 ± 1.92 for mirrored LRFs and 6.89 ± 1.13 for unmirrored LRFs at 4 kHz. The correlation between behavioral tuning and LRF tuning was not statistically significant (r(40) = 0.26, p = 0.102) for mirrored LRFs (Figure 5a), but was significant for unmirrored LRFs (r(40) = 0.36, p = 0.019) (Figure 5b), only when data from both frequencies were pooled together. When correlational analyses were done separately for each frequency, correlations were not significant for either 1 kHz or 4 kHz.

Figure 5.

Figure 5.

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Correlation plots for PTC and DPOAEgen tuning estimates from mirrored (A) and unmirrored (B) LRFs. Each point represents Qerb from 21 participants. Data from both 1 kHz and 4 kHz are included. Solid black line represents the linear fit to the data and dotted line represents unity. Note that the x-axis has been limited for better visualization.

Discussion

The overall objective of this study was to determine whether the bandpass shape of the distortion/generator LRF was related to behavioral tuning. We hypothesized that mechanical tuning becomes sharper with increasing frequency and decreasing level. Hence, the overlap between f1 and f2 excitation patterns would diminish at a specific ratio with increasing frequency and decreasing stimulus level. Thus, the prediction followed that the peak of the DPOAE LRF would shift towards lower ratios, and LRFs would become narrower with increasing frequency and decreasing level. Indeed, total ear canal DPOAE levels measured in 7 ears qualitatively demonstrated the predicted behavior. In experiment 1, the DPOAEgen LRF generally showed a frequency- and level- dependence consistent with known properties of cochlear mechanical tuning. The observation of narrower LRFs with increasing frequency and decreasing stimulus level, seen in the overall DPOAE level remained in the DPOAEgen LRFs. DPOAEgen LRFs were used to estimate tuning in all subsequent analyses. In experiment 2, we found that although the two measures were correlated when data for both frequencies were pooled, frequency-specific predictions of behavioral tuning from DPOAEgen LRF tuning could not be made at either 1 or 4 kHz.

Comparison to previous studies

We found that DPOAEgen LRF responses became narrower/sharper as f2 frequency increased. This sharpening of tuning from apex to base is consistent with tuning from neural and basilar membrane measurements (Cooper & Rhode, 1997; Liberman, 1978). The level dependence of the DPOAEgen LRF (sharper at lower stimulus levels) is also consistent with previous physiological and behavioral tuning reports. Perhaps the most detailed report of the frequency- and level-dependent tuning of DPOAEs comes from suppression tuning curve (STC) data from Gorga et al. (2011). The trend of sharpening of tuning as a function of increasing frequency and decreasing stimulus levels observed here was also observed in the Gorga et al. (2011) report.

Similar to Gorga et al. (2011), we found that Qerb increased as a function of f2 from 1 – 8 kHz and decreased with increasing primary levels. However, direct comparison of Qerb between the current study and Gorga et al. (2011) is not appropriate due to the varying methodologies used. Gorga et al. (2011) data are from iso-response measurements using a third suppressor tone that is varied in level and frequency, whereas the current data are from iso-input measurements of the DPOAE distortion/generator component while varying f2/f1 ratio for two different pairs of primary levels. Using a method similar to that of this study, Botti et al. (2016) examined the iso-input DPOAEgen LRF and showed a frequency- and level-dependence for f2 between 1 and 4 kHz. Our measurements extend to much higher frequencies than Botti et al. (2016).

Qerb was more variable across participants at high frequencies (>10 kHz) and at lower primary levels, likely due to poorer signal-to-noise ratio in some individuals for whom tuning estimates could not be computed. Similar variability of the tuned LRF at higher frequencies has been observed in rhesus monkeys (Lasky et al., 1995) and in primates (Valero et al., 2008). The variability may be related to the outer hair cell status in the cochlear base; however, high-frequency hearing was not assessed in our study and therefore, a second measure of cochlear health in the base is not available.

The trend of gradually increasing Qerb as a function of frequency was violated at 0.75 kHz where tuning was sharper than at 1 kHz. This violation from the general trend at 0.75 kHz may be related to the apical break in scaling of the cochlea, such that LRF functions measured using a fixed f2 of 0.75 kHz may be determined by very different cochlear mechanics than for f2 > 0.75 kHz (Cooper & Rhode, 1997; Robles & Ruggero, 2001, Dhar et al., 2011). Alternatively, there may be contributions from other regions of the cochlea contributing to the DPOAE recorded in the ear canal (Martin et al., 2011), thereby complicating the interpretation of tuning estimates at such low frequencies. Gorga et al. (2011) did not measure DPOAE STCs at 0.75 kHz; however, their DPOAE STCs at 0.5 kHz are not sharper than DPOAE STCs at 1 kHz. This difference between the results reported here and those reported by Gorga et al. (2011) cannot be explained easily other than to note the aforementioned methodological differences. Other psychoacoustical (e.g. Lopez-Poveda et al., 2007) and physiological (e.g. Cheatham and Dallos, 2001) studies of tuning in the apex have also observed difficult-to-interpret results, further highlighting that apical cochlear mechanics are not well understood.

Comparison to behavioral findings

We found a modest correlation between behavioral tuning and DPOAEgen tuning, which implicates a shared cochlear mechanical tuning as the basis for the relationship. However, behavioral tuning estimates were generally sharper than DPOAEgen tuning. The broader DPOAEgen tuning could be explained by individual differences in stimulus levels between the two measures: DPOAEgen were recorded at a fixed level combination of 55/40 dB SPL across individuals and PTCs were measured at near threshold stimulus levels (10 dB SL; ranging from 5 to 35 dB SPL). Behavioral tuning is nonlinearly dependent on the level of the signal (Moore, 1978; Heinz et al., 2002), with sharper tuning observed at low probe levels (~5-10 dB SL). The tuning curves at low levels shift 1 dB upward for every dB increase in signal level up to 20 dB SL, shifting nonlinearly at higher levels (Moore, 1978). Therefore, the differences in sharpness of tuning between DPOAE and psychophysical measures could simply be attributable to differences in stimulus levels.

Methodological differences could also have resulted in the differences in tuning estimates obtained from DPOAE LRFs and PTCs. The narrowband swept noise masker used in measuring the PTCs is expected to limit the response to the probe tone to a narrower region stimulating auditory nerve fibers. The DPOAE response, in contrast, is generated over a span of the basilar membrane responding to the two stimulus tones. Another important difference between the measures is in the fact that PTCs are an iso-response measure, whereas DPOAEs are an iso-input measure. This could lead to differences in tuning estimates obtained from the two measures, i.e. a small change in the masker may influence the input to the auditory nerve that would enhance or broaden behavioral tuning, whereas a large change in stimulus levels may be needed to enhance or broaden DPOAE LRF tuning. (Eustaquio-Martín & Lopez-Poveda 2011; Lopez-Poveda & Eustaquio-Martin 2013; Raufer & Verhulst 2016). Lastly, behavioral tuning estimates may include possible cues from off-frequency listening, although these effects were minimized using swept-noise maskers with wide bandwidths (Sęk & Moore 2011).

LRF theoretical framework

The well-known LRF was initially thought to be a result of a second filter in the cochlea that was tuned to a ratio yielding the maximum DPOAE level (Brown et al., 1992; Allen & Fahey, 1992). Although the presence of the second filter in the cochlea and its influence on DPOAE LRF remains elusive, many alternative hypotheses that do not involve a second filter have been proposed to explain the bandpass shape of the LRF (Talmadge et al., 1999; Knight & Kemp, 2000; Shera, 2003; Sisto et al., 2018). At high ratios, DPOAE levels are reduced as the excitation patterns of f1 and f2 are spatially separated with limited overlap between them. On the other hand, at low ratios close to 1, DPOAE levels are reduced, despite excitation patterns of f1 and f2 producing maximum mechanical overlap.

Empirical studies relating the behavior of DPOAE LRF to basilar membrane mechanics report a sustained basilar membrane response at the 2f1-f2 place at ratios close to 1; in contrast, the ear canal DPOAE LRF (Rhode, 2007) at these low ratios is reduced. The reduction in the ear canal DPOAE (Allen & Fahey, 1992) at low ratios is thought to be a result of either two-tone suppression of the f1, f2, and/or fdp on the basilar membrane (Kanis and deBoer, 1997) or destructive phase interference among multiple DPOAE sources (Talmadge et al., 1999; van Hengel and Duifhuis, 2000; Shera, 2003; deBoer et al., 2005). Indeed, when DPOAE components are separated, the reflection component resembles the intracochlear DPs measured directly on the basilar membrane, whereas the distortion/generator component shows the typical reduction at ratios close to 1 (Knight & Kemp, 2000; Dhar et al., 2005; Botti et al., 2006).

Given that DPOAEs mainly arise from activity within the overlap region where distortion is generated, it is arguably more desirable to understand and evaluate the distortion/generator component as a potential measure of cochlear mechanical tuning when the sharpness of the mechanical excitation patterns of f1 and f2 are of interest. Sisto et al. (2018) showed that measured and model-predicted Q increased as a function of increasing frequency and were similar to behavioral tuning estimates from Glasberg and Moore (1990) using simultaneous masking. The results presented here are consistent with the frequency-dependent tuning shown by Sisto et al. (2018) and other models, where LRF tuning is determined by mechanical tuning of the basilar membrane at high ratios and destructive phase interference and/or two-tone suppression at low ratios (Shera & Guinan, 2007; Sisto et al., 2018).

The current findings suggest that phase interference and/or two-tone suppression at low ratios is not likely to contribute significantly to the tuned LRF; tuning estimates from the synthetic/mirrored DPOAEgen LRF were not significantly different from the average tuning estimates from the original/unmirrored DPOAEgen LRF. The mirroring technique did not consistently sharpen the tuning of the LRF, likely due to the variable asymmetry of the LRF across frequencies and across individuals. The asymmetry likely arises from the relative strengths of the dominant mechanism or phase coherence of the wavelets as the f2/f1 changes from low to high ratio (Avan et al., 2013). While the estimates of tuning reported here are slightly broader than those reported by Sisto et al. (2018), the frequency dependence of the DPOAEgen LRF was similar in the two reports. The difference in sharpness of tuning from the two studies (only at 1 kHz) could be attributed to sampling biases in the two studies.

Limitations

Although the goal of the study was to determine whether DPOAEgen LRF can provide a non-invasive, objective, and quick estimate of cochlear mechanical tuning, the study was limited to a small sample of individuals with clinically normal hearing, in order to maximize the possibility of recording DPOAEs in our sample. Conclusions regarding the clinical utility of the DPOAEgen LRF cannot be made until additional investigations in ears with cochlear damage or deficits are performed. In the current study, PTCs were probed at 1 and 4 kHz and DPOAEs were measured for f2 = 1.25 and 5 kHz, hence, there is a slight mismatch in the cochlear frequency regions being assessed between the two measures. Although this may not influence tuning estimates derived from a normal cochlea in which tuning profile is expected to vary smoothly as a function of cochlear length, the slight mismatch could be a confounder in ears with an abrupt change in tuning, i.e. those with poor cochlear health due to aging, noise exposure, or other cochlear pathologies.

Conclusions

Tuning estimates from DPOAEgen LRFs exhibited level and frequency dependence similar to that observed in cochlear mechanics. Although behavioral tuning could not be predicted at a given frequency, there was a modest correlation between behavioral and LRF tuning when combined with the frequency dependence. These findings warrant further investigation of the clinical potential of this measure for the assessment of cochlear tuning.

Acknowledgments

Portions of this work were presented at the 44th Annual Scientific and Technology Conference of the American Auditory Society in Scottsdale, Arizona, the 41st Annual Mid-Winter Meeting of the Association for Research in Otolaryngology in San Diego, California, and the 2018 Hearing Across the Lifespan Conference in Lake Como, Italy. Funding for this work was provided by the National Institute on Deafness and Other Communication Disorders Grant F32 DC017352 (awarded to U.S.W.), The Graduate School and Knowles Hearing Center at Northwestern University and the INAIL grant BRiC 2016 ID17/2016.

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