Authors: Christopher Bergevin, Rebecca E. Whiley, Hero Wit, Geoffrey A. Manley, Pim van Dijk
Categories: Articles
Source: Biophysical Journal
Authors: Christopher Bergevin, Rebecca E. Whiley, Hero Wit, Geoffrey A. Manley, Pim van Dijk
As a sound pressure detector that uses energy to boost both its sensitivity and selectivity, the inner ear is an active nonequilibrium system. The collective processes of the inner ear that give rise to this exquisite functionality remain poorly understood. One manifestation of the active ear across the animal kingdom is the presence of spontaneous otoacoustic emission (SOAE), idiosyncratic arrays of spectral peaks that can be measured using a sensitive microphone in the ear canal. Current SOAE models attempt to explain how multiple peaks arise, and generally assume a spatially distributed tonotopic system. However, the nature of the generators, their coupling, and the role of noise (e.g., Brownian motion) are hotly debated, especially given the inner ear morphological diversity across vertebrates. One means of probing these facets of emission generation is studying fluctuations in SOAE peak properties, which produce amplitude and frequency modulations (AM and FM, respectively). These properties are likely related to the presence of noise affecting active cellular generation elements, and the coupling between generators. To better biophysically constrain models, this study characterizes the fluctuations in filtered SOAE peak waveforms, focusing on interrelations within and across peaks. A systematic approach is taken, examining three species that exhibit disparate inner ear humans, barn owls, and green anole lizards. To varying degrees across all three groups, SOAE peaks have intrapeak (IrP) and interpeak (IPP) correlations indicative of interactions between generative elements. Activity from anole lizards, whose auditory sensory organ is relatively much smaller than that of humans or barn owls, showed a much higher incidence of nearest-neighbor IPP correlations. We propose that these data reveal characteristics of SOAE cellular generators acting cooperatively, allowing the ear to function as an optimized detector.
The inner ear is a complex biomechanical system whose function is not well understood. To further elucidate the role of coupling in emission generation, this study systematically compares fluctuations in sound emitted spontaneously from the ear (spontaneous otoacoustic emission [SOAE]) across three vertebrates. Ultimately these data serve to illustrate that the inner ear is a nonequilibrium, active system whose cellular elements work together. A clearer understanding of SOAE generation and how it manifests across the animal kingdom will significantly advance our understanding of both normal and impaired auditory function.
Most researchers recognize the ear to be an “active system.” That is, metabolic energy is used to improve the ear’s sensitivity and (frequency) selectivity to external sound (e.g., (1,2), see also (3,4,5) for additional considerations). This cellular-based biomechanical power amplification is generally considered to be a systems-level phenomenon, where elements collectively use energy to influence responses. Thereby, in a broader sense, the inner ear can be regarded as an example of “active matter” (6). An oft-cited hallmark of the active ear is the generation of spontaneous otoacoustic emission (SOAE), sound emitted by the (healthy) ear and measurable noninvasively using a sensitive microphone inserted in the ear canal (7). Emission typically manifests as an array of narrow spectral peaks that are unique to a given ear and have a close relationship to perception (e.g., threshold microstructure, see (8)). SOAE activity is readily observable in humans, and some nonmammals such as barn owls and lizards, but conspicuously absent in most mammals commonly used for auditory neuroscience. Many SOAE peaks exhibit statistical properties consistent with self-sustained oscillations rather than (passively) filtered noise, thus providing evidence of the ear being a nonequilibrium, active system (9,10,11,12). More specifically, such a characterization is chiefly made by virtue of their “modality”: Are filtered SOAE peak pressure distributions bimodal (consistent with a sinusoid) or unimodal (characteristic of noise)?
There is a broad consensus that SOAE is primarily the result of mechanical work being done by the hair cells, which act as the primary site for mechano-electro-transduction. A key impediment to our understanding of the underlying biomechanics of emission generation is uncertainty of how individual generative elements are effectively coupled together, so as to work cooperatively (13). We consider auditory cellular cooperativity as the collective effects of an active medium leading to improved hearing function (e.g., the ear’s overall sensitivity and selectivity emerges from hair cells using energy together). The notion of cooperativity is a general one in that it can arise at different spatial scales, such as the molecular level (e.g., collective effort of mechano-electro-transduction channels in a given bundle; (14)), or mesocellularly (e.g., bidirectionally oriented hair cells at a given longitudinal location in the lizard (15)). More colloquially, cooperativity indicates that the ear as whole is different from the sum of the parts, and has been implicit in previous studies that consider features such as the tectorial membrane (TM) (e.g., (16,17)).
The role of coupling in emission generation is poorly understood, especially in the face of SOAE being relatively universal across the animal kingdom. That is, seemingly disparate morphological differences at the level of the inner ear give rise to ubiquitous SOAE characteristics (Fig. 1; see also (18)). Given that the biomechanics of SOAE generation are thought to be closely associated with cochlear morphology, a systematic comparative approach to identify empirical similarities and differences is desirable to elucidate core principles at work in all ears. Furthermore, this approach can yield a greater understanding of what features are necessary for a model of emission generation to demonstrably capture the underlying biomechanics of the inner ear.Figure 1Representative SOAE spectra from humans (A), barn owls (B), and green anole lizards (C). Each species has data from two different individuals. The top row shows spectra from an ear exhibiting moderate SOAE activity, while the bottom row exhibits relatively robust activity. A visual approximation of the microphone noise floor, expected to be roughly similar across experiments, is shown for the bottom row (red dashed lines). Ordinate units are in dB. For an approximate absolute reference, the microphone noise floor when coupled to a tube is typically around −20 dB SPL at 3 kHz. See the supporting material (including Fig. S1) for further rationale, as well as SOAE plots as spectral-temporal maps (Fig. S2). Short colored horizontal lines in the inset refer to the colors used in subsequent figures.
Historically, individual SOAE peaks were well described by first order “single-source” models, such as a van der Pol oscillator (e.g., (19)). Here, an implicit foundational assumption is that an individual element somehow behaves as a self-sustained oscillator (20). Subsequent studies (e.g., (21)) have expanded upon single-source models to provide possible biophysical explanations of the source of active power. However, these models are ultimately too simple to describe the unique array of SOAE peaks that emerge from a given ear, and more comprehensive approaches are needed. Shera (22) summarized the current state of SOAE modeling and proposed two broad, but fundamentally different, 1) wave-based reflection frameworks, where an otherwise stable system gives rise to SOAE somewhat analogously to a laser cavity (e.g., (11)) and 2) limit-cycle oscillator arrays that are somehow coupled to form frequency clusters, or “plateaus,” that give rise to SOAE peaks (23). Regardless of whether such a delineation clarifies the biophysical origins of emissions, the ear is a coupled system and the cellular components work cooperatively. Thus, the goal is to elucidate how this cooperativity arises.
Given the assumption that SOAE is telling us important information about how the active ear works, there is a clear need for an empirical-based thread tying together SOAE evidence to help guide modeling efforts aimed at explaining auditory function near threshold. Various characteristics of SOAE spectra, such as interpeak (IPP) frequency spacing (11) and the presence of “baseline activity” (24,25,26), have helped constrain theoretical models. One aspect that has been relatively less well characterized is the rich temporal properties exhibited by SOAE activity. For example, (27) briefly reported upon an array of complex interactions between SOAE peaks. While these features have been further studied (e.g., (28)), the temporal dynamics of SOAE are still not well understood and remain underutilized.
Some degree of noisiness is present in SOAE peaks, causing fluctuations in their observable properties. Specifically, a given peak exhibits time domain variations that give rise to amplitude (AM) and frequency modulations (FMs), thereby affecting the peak’s spectral shape (24). A small number of studies have examined correlations between SOAE peaks (10,29,30). These generally reported limited correlations for fluctuations in AM and FMs within a given peak (“intrapeak” [IrP]) and between AM or FMs between different peaks (IPP). However, a clear systematic picture has yet to emerge about the nature of what these correlations are telling us and how they arise. This is in part due to a lack of understanding as to the cause(s) of these fluctuations.
While SOAE activity is typically noted as occurring in the absence of any external sounds, the inner ear is always subject to noise. Possible sources of noise that could cause the observed fluctuations include noise internal to the ear (e.g., Brownian motion of hair cell bundles due to thermal fluid agitation) that could act locally and/or globally, stochastic aspects of active force generation (e.g., channel clatter, (31)), and external sounds (e.g., intrinsic thermal motion of air molecules, respiration) that could affect eardrum motion (or act through bone conduction) and thereby affect the inner ear. Such noise could drive the observed AM and FM fluctuations. When we consider SOAE as the product of cellular cooperatively, which works in the presence of noise, a critical unknown to address is the nature of the coupling between oscillatory elements. We evaluate the presence of correlations between AM and FMs with the goal of providing data that can elucidate how different SOAE sources interact and clarify the distinctions (or lack thereof) between different modeling frameworks.
By examining several animal groups, this study systematically characterizes IrP and IPP correlations, including how such relate to general statistical properties of individual peaks. We compare SOAE properties from three terrestrial humans, barn owls (Tyto alba), and green anole lizards (Anolis carolinensis). This allows us to capitalize off of the wide degree of morphological variation across vertebrate classes for properties thought to play key roles in the underlying biomechanics. Two specific considerations relevant to the three groups of this study warrant mention. First is the size of the inner ear. The human cochlea contains roughly 15,000 hair cells spread over about 35 mm of length, whereas the barn owl has 16,000 hair cells over 12 mm. The inner ear of the green anole contains only about 150–180 hair cells over a papillar length of 0.5 mm. Second is the presence and structure of the TM. The TM is a gelatinous, charged matrix that sits atop the stereovillar bundles of the hair cells, near the mechanically gated transduction channels. It is considered crucial for longitudinal coupling in the mammalian cochlea (e.g., (17,32)). In birds, the TM takes on a more massive form. In lizards, it exhibits a wide variety of shapes across classes, and is altogether absent over the vast majority (>90%) of the green anole’s hair cells (33).
Despite morphological variations, the simplest assumption is that SOAE generation mechanisms are fundamentally similar across species. We would expect that the generative elements would be affected by the same types of noise, such that AM and FM fluctuations would be similar across species, and the coupling of these elements would be preserved. Thus, one might predict that fluctuation correlations would generally be congruent across species.
We first provide a broad overview of the basic approach. Time waveforms from the microphone signal were obtained, from which averaged spectra could be produced (e.g., Fig. 1). A central approach to the analysis presented here is that individual SOAE peaks could then be filtered in the spectral domain (Fig. S3), providing an “isolated” component of the overall SOAE activity from which fluctuations could be extracted. The basic process is shown in Fig. S4. With the filtered waveforms (Fig. S4 B), we extracted two key metrics. First is that we sought to characterize peak modality (e.g., Fig. S4 C), as described below. We also computed the fluctuations in the envelope as well as in the instantaneous frequency (IF), referred to as AM and FM, respectively. That is, the AM is the “modulation” time course of envelope fluctuations while FM describes the IF fluctuations. These are indicated in Fig. S4 D. These waveforms then led to the second basic measure, whether correlations existed between various signals. A principal distinction made is that IrP analyses concern the properties unique to a particular SOAE peak (including modality), versus IPP that concern the properties between a given pair of peaks. A visual overview of this is shown in Fig. S6. Additional acronyms and terms associated with these quantities are indicated in Table 1. For both key measures, we sought to make an objective binary classification (e.g., this peak is either unimodal or bimodal, these two peaks do or do not show a cross correlation between their AM fluctuations).Table 1Acronyms used to describe various peak characteristics and analysesCFCharacteristic frequency (i.e., where peak p has largest averaged magnitude, ≡fp)AMamplitude modulation from analytic signal envelope [≡ENVp(t)=|ap(t)|]FMfrequency modulation from analytic signal instantaneous frequency [≡IFp(t)=12πddt(∠ap(t))]IrPintrapeak relationshipIPPinterpeak (paired) relationshipNNnearest neighbor (i.e., two adjacent peaks without any other peaks between)Unimodal (IrP)Gaussian-like xp(t) distributionBimodal (IrP)sinusoidal-like (i.e., double-peaked) xp(t) distributionIrPxcintrapeak AM and FM correlation [ENV1 re IF1]IPPxcAMinterpeak AM correlation [ENV1 re ENV2]IPPxcFMinterpeak FM correlation [IF1 re IF2]
Data reported here were obtained from humans, barn owls, and green anole lizards (hereafter, anole lizards) using methods consistent with previous reports (e.g., (12,34,35)). Human (n=8) and anole lizard (n=8) data were collected in Canada, while barn owl (n=8) data were collected in Germany (12). All data were collected in an acoustic isolation booth, using an Etymotic ER-10C probe that was nonsurgically coupled to the meatus. Human subjects were awake and asked to sit motionless. Both nonhuman species were lightly anesthetized (owls with ketamine at 10 mg/kg and xylazine 3 mg/kg; lizards with sodium pentobarbital at 36 mg/kg). Anesthesia was maintained as necessary and animals recovered after the experiments. Body temperature was stabilized before recording in owls (39°C) and lizards (∼23°C) via a heating blanket. For some lizards, the heating blanket was left off (ambient temperature was usually ∼21°C). The sample rate for data acquisition was 44.1 kHz for humans and lizards and 48 kHz for owls. Recorded waveforms were typically 120 s long (two human subjects had 60-s waveforms). Attempts were made to ensure that the obtained SOAE waveform was suitably “artifact-free” (e.g., no presence of respiratory or cardiac modulations), although not all SOAE waveforms were strictly free of artifacts (see Fig. S2). All work was approved by the York University institutional committees (protocol 2012-19) and the authorities of Lower Saxony, Germany, permit number AZ 33.9-42502-04-13/1182. All recorded time waveforms, as well as analysis codes and filtered waveforms, are freely at Database: Dryad (https://datadryad.org/).
Let x(t) represent the entire (“long”) waveform collected for a given ear at time t. The averaged spectra shown in Fig. 1 were obtained by parsing x(t) into shorter consecutive segments s that were 186 ms long (8192 samples). The magnitude of the fast Fourier transform (FFT) of xs(t) was averaged for 300 segments. Thus, the spectra shown in Fig. 1 were acquired over approximately 1 min. For this choice of parameters, the frequency bin width was 5.38 Hz. The choice of parameters for computing the FFT can affect the absolute peak height but not the overall spectral structure (see supporting material, specifically Fig. S1).
To extract objective measures of peak features, we fit each peak with a Lorentzian function L(f) of the general form(1)L(f)=α(f−β)2+γwhere f is the frequency and β is the peak’s characteristic frequency (CF). The function was fit to the amplitude values in dB, with a linear frequency scale. The fit was “local” in that no more than 50 frequency bins about the CF were used, and was computed via nonlinear regression using MATLAB’s fminsearch.m function. An example of the fitting for all three groups is shown in Fig. S3 and further details can be found in the supporting material. From the fit, the peak “height” (not area) was determined as the difference between L(f) computed at the peak CF and a frequency far away from CF (e.g., 10 kHz). Peak “width” was calculated as the fullwidth at half-maximum from L(f) as 2γ.
Individual SOAE peaks were analyzed by computing the FFT of x(t) and applying a recursive exponential narrowband filter (see green curve in Fig. S4 A, leading to the red curve by multiplication (11,36)). Filter center frequency was manually chosen to align with the frequency of maximum amplitude (i.e., the top of the peak), while the bandwidth was chosen to capture the entire width of the SOAE peak, designated as where horizontal flanks emerged atop the noise floor. Filters of adjacent peaks did not overlap. The filtered signal was inverse transformed back to the time domain (e.g., blue trace in Fig. S4 B), producing a long filtered waveform for a given peak (typically being 95 s long), which was designated xp(t).
We used the analytic signal representation to determine AM and FM. Let ap(t) represent the analytic signal of peak xp(t), as computed via a Hilbert transform. We obtained the AM waveform for a given peak from the magnitude of the analytic signal, commonly referred to as the envelope (red traces in Fig. S4, B and D). Thus, we defined the AM of a peak ENVp(t)≡|ap(t)|. We obtained the FM waveform by estimating the IF as the temporal gradient of the unwrapped phase of the analytic signal (blue trace in Fig. S4 D, (37)). Thus, we define the FM of a peak IFp(t)≡12πddt[∠ap(t)]. The ratio between the average IF and the filter bandwidth was found to be close to unity within ±0.01% for all peaks, indicative that the filter center frequency serves as a suitable proxy measure of peak CF (e.g., Fig. 2 A), although we ultimately used Lorentzian fits to define CF. See Table 1 for an overview of acronyms used in these analyses.Figure 2General IrP features of filtered SOAE peaks from anole lizards (green circles), barn owls (orange diamonds), and humans (blue crosses). (A) Normalized SOAE peak width (Hz) via the Lorentzian fit full-width half-maximum versus peak center frequency (kHz). Widths were normalized by dividing by center frequency (e.g., a value of 10 at 3 kHz corresponds to a 30 Hz width). (B) SOAE peak height (in dB) versus peak width as derived from the Lorentzian fits. (C) Comparison among classifiers for whether a given SOAE peak’s amplitude distribution was unimodal or bimodal (as per Hartigans’ dip statistic, p<0.05) relative to whether an IrPxc was observed (| IrPxc |>0.03). A small amount of vertical and horizontal jitter was added to improve visualization. (D) SOAE peak width relative to the presence of an IrPxc and the filtered peak’s amplitude distribution, creating four categories for each species. Each box represents the interquartile range with a central mark at the median, and whiskers showing the minimum and maximum values. Values beyond the boundaries of the whiskers were considered outliers. (E) Same as (D), but for SOAE peak height across species relative to IrPxc presence and peak amplitude distribution classification. Note that in (D) and (E), horizontal jitter was added to improve visualization. (F) For SOAE peaks with an IrPxc that was localized in time (i.e., a singular peak in the cross correlation), the associated delay is plotted as a function of the SOAE peak’s center frequency.
Once a filtered waveform for a given peak was obtained, as noted previously, analysis was bifurcated along two IrP analyses focused solely on that specific SOAE peak, and IPP analyses that examined relationships between a pair of SOAE peaks extracted from the same waveform. For IrP analysis, we characterized both modality and whether there was a correlation between the AM and FM fluctuations (IrPxc). To objectively assess peak modality, we created a histogram of all values of xp(t) as the basis to determine whether an SOAE peak’s amplitude distribution was unimodal or bimodal (e.g., Fig. S4 C). Such measures are commonly interpreted as whether a peak is indicative of filtered noise versus a self-sustained oscillation, respectively (9,11). We classified distributions as unimodal or bimodal via Hartigans’ dip statistic (38), as described previously by (39), with a p value of 0.05 across 5000 bootstraps. This method provided a conservative estimate of distribution modality. By conservative, we mean that the use of Hartigans’ dip statistic is underestimating the fraction of bimodal peaks, given limitations inherent to the method itself. This is justified by visual examination of the (filtered peak) analytic signal as a 2D histogram in the complex plane. For example, inspection suggests that nearly two-thirds of anole SOAE peaks are bimodal, rather than about one-quarter as indicated in Table 3. We evaluated how distribution modality related to SOAE peak properties as determined by Lorentzian fitting. The second IrP analysis concerned whether a correlation was present between AM and FM traces for that peak (IrPxc). Correlation methodology is described below.
For IPP analyses, we first classified whether a given pair were nearest neighbors (NNs) (e.g., 0.93 and 1.1 kHz peaks in the top left in Fig. 1) or not. That is, NNs were peak pairs without other peaks between them. We then performed two types of analyses to evaluate IPP relationships. First, we assessed properties related to frequency spacing between peaks (e.g., f2−f1), including how these related to peak CF. Second, we considered potential correlations in AM or FM between peaks. Correlative behavior between AM for two different peaks was abbreviated as IPPxcAM, whereas IPPxcFM designated correlations in FM. The analyses described here were not applied to all SOAE peaks identified. SOAE peaks identified for IPP spacing analysis were only included if the amplitude at CF was at least 1 dB above the noise floor.
The potential correlations (denoted by ⋆) between two isolated waveforms (e.g., AM of peak 1 as ENVp1(t) and AM of peak 2 as ENVp2(t)) were assessed to ascertain relationships between fluctuations and how in localized time such relationships are when present. We note that a key underlying assumption for standard correlation techniques is stationarity (40). That is, whether or not the signals exhibit stability in their statistical properties over time. This is addressed further in supporting material, section S0.6, and the results. While we considered various methods for correlation analyses, our primary approach was carried out in the time domain and is described here. See supporting material, section S0.4, for a discussion of alternate methods and cross-validations between methods.
Similar to the spectral averaging described previously, we parsed the (long) AM and FM waveforms derived from xp(t) into shorter consecutive segments s. For each segment, we then subtracted out the mean value of the signal to isolate the (real-valued) residual fluctuations (ϕ) for subsequent correlation analyses. For example, consider a short AM segment from a given peak (ENVps) comprised of length, l, samples. Then ϕps(t)=ENVps(t)−ENV¯ps, where ENV¯ps is the mean value of the envelope over the time interval spanned by the segment. Each correlation segment was 93 ms long for lizards and owls, and 372 ms for humans due to their slower fluctuation rates (see Fig. S5), related to the generally narrower filter widths used for their peaks. For a 95 s waveform, 1022 correlation segments were averaged for lizards and owls, and 255 segments for humans. Averaging shorter segments reduced the chance of spurious correlations occurring due to artifacts (e.g., coughing, cardiac pulsing; see also Fig. S11).
The time domain cross-covariance between the residual fluctuations for two peaks (i.e., ϕ1s⋆ϕ2s≡Tcc) was computed using MATLAB’s xcorr.m function as(2)Tccs(τ)=∑nϕ1s(t+τ)ϕ2s(t)where n represents the total number of overlapping samples (∼2l−1) comprising the segments and τ is the “lag.” τ was defined such that negative values meant that peak2 was delayed relative to peak1 (i.e., temporally shifted to the right along the positive time axis). We normalized Tccs using the autocorrelations at zero lag (computed as Aps(τ)=∑ϕps(t+τ)ϕps(t)) to obtain the cross correlation Txcs as(3)Txcs(τ)=Tccs(τ)A1s(0)A2s(0)
We averaged Txcs(τ) across segments to obtain an averaged, normalized cross correlation Txc(τ), where Txc∈[−1,1]. Negative values indicated that when one fluctuation showed an increase, the other a decrease, whereas positive values indicate both varied in a similar fashion. To cross-validate, additional correlation methods (including a spectral domain method) were also computed and were described further in supporting material, section S0.4.
Initial observations indicated that, when present, correlations were relatively weak (i.e., typically |Txc|<0.1), necessitating a classification metric to determine whether a correlation was present. To create a quantitative benchmark, we effectively bootstrapped the correlation to obtain Tb as Tbs(τ)≡∑nϕ1s(t+τ+ξ)ϕ2s(t), where ξ is a randomized indexing offset for each τ value to scramble the correlation reference times. We computed an averaged Tb(τ) as done for Txc(τ) in Eq. 3. If a fluctuation correlation was present, this had the effect of averaging it out to create control measure Tb . Such a measure provides a useful visual indication of correlation presence, as indicated in Fig. S6 (there, Txc is blue and Tb is red). Second, we created an objective determination for the presence of a correlation by examining whether the maximum value of |Txc(τ)| exceeded a threshold value derived from Tb. Based upon the typical range of Tb values, a conservative threshold of 0.03 was typically employed (see black dashed horizontal lines in Fig. S6, B and C). Rationale and justification for the choice of this value is covered in supporting material, section S0.4 and Fig. S8. Ultimately, this process provided a binary measure as to whether the two waveforms were correlated.
If a correlation Txc was deemed present based on the threshold criterion, it was categorized in several respects. First, we ascertained if Txc(τ) was singly peaked (i.e., the cross correlation had a clear maximum or minimum localized to a particular instant; e.g., Fig. S6 C). Otherwise, it was deemed indeterminate (e.g., Fig. S6 B; see Fig. S13) with regard to the subsequent metrics. Second, singly peaked Txc were classified as exhibiting positive or negative correlations based on the sign of the peak. Third, delays were determined to be positive, negative, or zero based on τ at the peak of Txc. A negative delay meant peak2 had to be shifted back in time to match peak1 (i.e., peak2 lagged behind peak1). We used the convention that, for IrP correlations, peak1 was the AM and peak2 was the FM. For IPP, peak1 was always the peak lower in frequency relative to peak2. Taken together, these considerations form the criteria for the classifications in Table 3.
Unique spectra of SOAE peaks were apparent in all subjects, a subset of which is illustrated in Fig. 1. Details regarding the quantity of SOAE peaks observed for each species and how they were used for spectral and correlation analyses are outlined in Table 2. We divide the results into several different sections, starting each off with a general overview to describe what is to be examined and how that relates to understanding SOAE generation.Table 2Table of values from SOAE peak correlation analysisPropertyHumanOwlLizardTotal number of unique individuals considered888Total number of SOAE peaks considered739487Average number of SOAE peaks/ear9.1 (4.6)11.8 (2.7)10.9 (2.2)Number of SOAE peaks that were (Lorentzian) fit729081Number of SOAE peaks filtered for correlation analysis595969When two values are indicated, unless noted otherwise, the first is the mean value and the second (in parentheses) is the standard deviation.
Given the signal processing techniques employed here, establishing SOAE stationarity is a key consideration we describe first. That is, ascertaining the consistency of the statistical properties of the underlying signals across time (40,41). It is well established that lizard SOAE activity can vary with body temperature (24), and anecdotal observations suggest that human SOAE can change if a subject is in a noisy environment just before a measurement session. Thus, we attempted to account for potential variability in our experimental paradigm by providing time for the subject to adjust to the quiet environment in the booth before measurements (>15 min), recording SOAE signals over a relatively short period (typically 120 s), and using waveforms without acoustical or electrical artifacts. SOAE patterns were reasonably stable across recordings when using 46 ms windows to compute a short-time Fourier transform to observe gross temporal variations (Fig. S2). When present, artifacts could be visibly discerned in the entire SOAE waveform, or identified as brief excursions in phase-plane plots of the ENVp or IFp signals (see Fig. S10). Analytic signal distributions likewise supported spectral stability (see supporting material, section S0.5); if an emission was turning on/off, we might expect a superposition of caldera and molehill distributions, which were only very rarely observed (e.g., Fig. S4 C; see Fig. S14 for an usual case of superimposed distributions in a human subject).
We also examined the autocorrelation of both the AM and FM waveforms for a given filtered SOAE peak. In general, these responses were well localized in time (e.g., Fig. S9), being strongly singly peaked at zero lag as might be expected for a stationary noisy signal. The AM autocorrelation curves appeared Gaussian-like (i.e., continuously differentiable with zero gradient at zero lag), whereas the FM autocorrelations commonly had a singularity at zero lag (i.e., like two negative exponentials pasted together; see Fig. S9). The autocorrelations could exhibit some degree of sinc-like “ringing” (Fig. S9), which was typically small for lizards and owls but could be more substantial in humans (see peaks along the diagonal in Fig. 4 denoted with !). Such may arise from the narrowband filtering of the SOAE peak. We note that the Fourier transform of a rectangular pulse is a sinc function and, although the (recursive exponential) filter shape employed in this study is not rectangular per se (see green curve in Fig. S4 A), it is rectangular-like enough to expect this ringing behavior to first order. While there were some deviations from stationarity that likely warrant further study, especially for humans, those aspects will not be considered further here and the rest of the analyses detailed in the results focus on methodologies that assume SOAE stationarity.
As noted in the materials and methods, we computed cross correlations using both time domain (Txc) and spectral-domain (Sxc) approaches. The results reported here are exclusively from the time domain, although we typically found excellent agreement between correlation patterns for both methods. In addition, we examined how the averaged cross correlations for shorter time segments (i.e., Txc) compared with the response where the entire (typically 95 s) waveform was used (TxcL, where L indicates a “long” waveform used). In some cases, TxcL had a strong correlative peak but Txc did not. This typically occurred when the entire SOAE waveform contained a large broadband artifact that could allow for sufficient overlap to produce a correlation in TxcL, which would be otherwise averaged out in Txc. Thus, we have no reason to expect that correlations were not detected due to the choice of shorter time segments for calculations.
Here, we focus on properties unique to a given (filtered) SOAE peak, such as modality classification correlative behavior in fluctuation in AM and FM (i.e., IrPxc). Across the three species, normalized peak width decreased as peak center frequency increased (R=−0.36,p<0.01; Fig. 2 A). Generally, taller peaks had narrower widths (R=−0.55,p<0.001; Fig. 2 B). As seen in Table 3 and Fig. 2 C, approximately one-fifth of lizard and human SOAE peaks filtered for analysis had bimodal distributions (anoles: 22.6±18.8%; 20.4±15.9%). However, only one peak from barn owls was classified as bimodal (1.4±3.9%). While a peak could be identified as unimodal as per Hartigans’ dip statistic, visual inspection of a 2D histogram of the analytic signal could show “ringing” that was indicative of sinusoidal-like (i.e., bimodal) statistics (see right panel of Fig. S4 C). The conservative nature of this classification overestimated the number of peaks that were identified as unimodal, particularly in anoles, despite having flat-top distributions that were suggestive of sinusoidal statistics obscured by noise (see left panel of Fig. S4 C).Table 3Table of values from SOAE peak correlation analysisPropertyHumanOwlLizardIntrapeak (IrP) valuesAverage fraction of filtered peaks/ear with bimodal distributions (%)20.4 (15.9)1.4 (3.9)22.6 (18.8)Average fraction of peaks/ear showing IrPxc (%)33.9 (14.3)7.3 (13.7)58.5 (24.0)Average fraction of bimodal peaks/ear showing IrPxc (%)88.9 (27.2)100.0 (0.0)100.0 (0.0)Fraction of peaks/ear showing IrPxc and singly peaked (%)3.6 (9.4)16.7 (23.6)44.9 (26.9)Fraction of peaks showing (singly peaked) IrPxc that were negatively correlated (%)88.9 (27.2)100.0 (0.0)100.0 (0.0)Average (signed) IrPxc delay (ms)−4.9 (6.3)0.02 (0.0)−1.7 (1.7)Interpeak (IPP) valuesAverage spacing between neighboring peaks (kHz)0.42 (0.48)0.49 (0.18)0.29 (0.12)Fraction of analyzed peak pairs showing IPPxcAM (%)24.35.013.6Fraction of peaks showing IPPxcAM that were bimodal (%)25.910.029.7Fraction of peak pairs showing IPPxcAM that were NNs (%)39.370.091.9Fraction of NN peak pairs that show IPPxcAM (%)43.113.755.7Fraction of peak showing both IPPxcAM and IrPxc (%)48.215.067.6Fraction of peaks/ear showing IPPxcAM and singly peaked (%)94.6100.097.3Fraction of peaks showing (singly peaked) IPPxcAM that were negatively correlated (%)47.2100.016.7Average (signed) IPPxcAM delay (ms)3.5 (9.7)2.1 (0.92)0.28 (0.77)Average (unsigned) IPPxcAM delay (ms)8.4 (5.8)2.1 (0.92)0.63 (0.52)Fraction of analyzed peak pairs showing IPPxcFM (%)0.40.02.2Peaks/ear showing IPPxcFM that were bimodal (%)100.0–66.7Fraction of NN peak pairs that show IPPxcFM (%)100.00 .09.8Fraction of peak pairs showing IPPxcFM that were NNs (%)100.0–100.0Fraction of peak showing both IPPxcFM and IrPxc (%)0.0–91.7Fraction of peaks/ear showing IPPxcFM and singly peaked (%)0.0–100.0Fraction of peaks showing (singly peaked) IPPxcFM that were negatively correlated (%)––0.0Average (signed) IPPxcFM delay (ms)––0.29 (1.4)Average (unsigned) IPPxcFM delay (ms)––0.98 (0.92)When two values are indicated, unless noted otherwise, the first is the mean value and the second (in parentheses) is the standard deviation. Note that values here represent those extracted across eight different individuals for each group. Note that the lizard group is specific to Anolis. Several acronyms are used and defined in Table 1. Note that delay values are only included for correlations localized in time (i.e., for those singly peaked). Also note that, as described in the materials and methods, the fraction of peaks classified as bimodal is likely an underestimate (especially for anoles) due to limitations associated with Hartigans’ dip statistic.
Several examples of the AM and FM time waveforms as extracted from the filtered SOAE peaks are shown in Fig. S5. IrPxc were observed in all eight individuals for humans and lizards but were rare for owls, occurring in only two of the eight individuals. As indicated in Fig. S4 D, sometimes the amplitude would approach zero, causing a corresponding spike in the FM. Such might be expected to give rise to increased IrPxc, by virtue of increased uncertainty in the IF of the signal at those instants. We explored this to a limited extent by varying filter bandwidth, which had the effect of reducing/shifting these AM minima around, and observed very little effect on IrPxc or IPPxcFM. We interpret this as the correlation measures involving FM as being relatively insensitive to envelopes approaching zero.
In owls and lizards, all SOAE peaks with bimodal distributions exhibited IrPxc (Fig. 2 C). All but one of the human SOAE peaks with bimodal distributions exhibited IrPxc. However, only a minority of SOAE peaks that exhibited IrPxc were also classified as bimodal (anoles: 41.5%; barn 25.0%; 48.0%; Fig. 2 C). We conducted three-way ANOVAs to evaluate whether peak properties were affected by amplitude distribution modality and the presence of IrPxc across species. When evaluating peak width (Fig. 2 D), there was a statistically significant effect of species (F(2,171)=52.3,p<0.001) and a weak effect of amplitude distribution (F(1,177)=2.9,p=0.09), but no effect of IrPxc presence (F(1,177)=0.3,p=0.57) nor of the interactions between factors (all p>0.1). Peak widths were significantly narrower in humans (19.2±14.5 Hz) than in anoles (88.4±31.2 Hz, p<0.001) or barn owls (110.3±37.6 Hz, p<0.001), but not significantly different between anoles and barn owls (p=0.92). While not statistically significant, widths were generally narrower in peaks with bimodal amplitude distributions (42.2±28.4 Hz) than those with unimodal distributions (79.7±48.8 Hz).
All SOAE peaks from barn owls had unimodal distributions except for the tallest peak (Fig. 2 E). Such was in strong contrast to lizards, where peaks with much smaller amplitudes exhibited bimodal distributions. For SOAE peak height (Fig. 2 E), there were statistically significant effects of species (F(2,171)=15.6,p<0.001), amplitude distribution (F(1,177)=25.4,p<0.001), and the interaction between these factors (F(2,177)=3.05,p=0.05). Across all three species, SOAE peaks with bimodal amplitude distributions were taller than those with unimodal distributions (anoles: bi., 12.5±2.1 dB; uni., 6.5±2.5 dB, p=0.004; barn bi., 20.0 dB; uni., 5.3±4.0 dB, p=0.016; bi., 19.5±3.6 dB; uni., 7.4±4.1 dB, p<0.001). SOAE peaks were significantly taller in humans than in anoles (p<0.001), but there was no difference between humans and barn owls (p=0.997). While peaks tended to be taller in barn owls than in anoles, this was not significant (p=0.058). It should be noted that anole peak heights may be underestimated, since the presence of baseline activity could create elevated flanks (e.g., lizard in bottom panel of Fig. 1 C has a broad hump from 2 to 4.2 kHz, which affects the Lorentzian fitting as shown in Fig. S3). There was no effect of IrPxc presence (F(1,177)=1.24,p=0.27) nor of the interactions between IrPxc and species or amplitude distribution (both p>0.10) on SOAE peak height.
In some instance, when an IrPxc occurred, it was not localized in time. That is, there was not a clear singular “peak” in the cross correlation (see supporting material, section S0.6, including Fig. S7). Such was typically the case for humans and owls. For lizards, IrPxc was localized as a single peak in approximately half the cases. Across all three species, singly peaked IrPxc were almost always negative (only one positive IrPxc was observed in humans) such that increases in AM corresponded to decreases in FM. The corresponding delays were not related to SOAE peak frequency (R=0.08,p=0.68). For lizards, the delays for singly peaked IrPxc were always negative (Fig. 2 F), such that the FM lagged behind the AM (i.e., correlative features occurred earlier in time for AM by several milliseconds). IrPxc delays could only be determined for four peaks from humans and one peak from owls. There were numerous cases where an IrPxc was clearly present but not suitably localized in time to allow for a delay to be determined (e.g., Fig. S6 B), making it difficult to characterize broad trends in the relationships between AM and FM fluctuations across species.
In this section, we focus on the relationship(s) between peaks in the SOAE spectrum, considering general spectral features (e.g., frequency spacing between peaks) as well of those of (filtered) peaks (e.g., IPPxc). We first considered IPP relationships derived from the spacing between SOAE peaks in the averaged spectra (Fig. 3 A). The average distance between peak pairs (IPP spacing) was significantly different across species (F(2,702)=22.75,p<0.001). IPP spacing was significantly lower in anoles (1.11±0.71 kHz) than in barn owls (1.81±1.15 kHz, p<0.001) or humans (1.70±1.71 kHz, p<0.001), but was not significantly different between barn owls and humans (p=0.65). The distribution of IPP ratios (computed as an SOAE peak’s CF divided by all lower peak CFs) in Fig. 3 B illustrates that this spacing was not the consequence of harmonic relationships between peaks. If a given peak pair was harmonically related, an integer ratio (≥2) would be obtained. Most ratios were less than two, with no clustering about integers, indicative that SOAE peaks were rarely (if ever) harmonic distortions of others. We computed the ratio of frequency differences among triplets of SOAE peaks (Fig. 3 C) to evaluate whether spacing was driven by peaks colocating at cubic intermodulation distortion frequencies, which occurs when this ratio is equal to unity. While some localization about one was present for both lizards and humans, there was a broad spread suggestive that the majority of peaks were not distortions of others. However, a prominent maximum about unity was observed in owls. While decreasing the bin width demonstrated that values about 0.9–0.95 contributed this maximum, the clustering remained. This localization could be consistent with SOAE peaks being more likely to be related as intermodulation distortions in owls. Alternately, localization about one could arise by virtue of the more temporally uniform spacing between adjacent SOAE peaks in owls.Figure 3General IPP relationships. (A) IPP frequency spacing relative to the geometric mean (GM) frequency of the pair for all SOAE peaks. (B) Distribution of IPP frequency ratios (i.e., CF divided by other peak frequencies below it) between all SOAE peaks from each ear. All values are greater than unity (i.e., no peaks were compared with themselves). Vertical gray line indicates a factor of two for visual reference. (C) Distribution of intermodulation difference ratios. These were computed by considering triplets of consecutive peak frequencies (f1<f2<f3), counting the resulting frequency difference ratios (f3−f2)/(f2−f1). The vertical gray line, placed for visual reference, shows the ratio value that would result if f1=2f2−f3 or f3=2f2−f1. The total count has been divided by two to eliminate redundancies. (D) Reciprocal of IPP frequency spacing (hence units of ms) relative to the GM frequency of the pair for adjacent peaks. (E) IPP delay plotted in number of cycles (NSOAE) relative to the GM frequency of the pair for adjacent peaks. (F) Associated delays for peak pairs with an IPP AM cross correlation (IPPxcAM) that was singly peaked, plotted as a function of the GM frequency of the pair. Here, a negative delay indicates that the correlated fluctuations in the lower frequency peak preceded those for the higher one.
IPP spacing may be indicative of a time delay (e.g., standing wave interference). For example, SOAE-derived measures such as NSOAE (defined as the geometric mean of the pair’s CFs divided by their frequency difference, (11)) have been shown to correlate well to time delay measures such as the SFOAE phase-gradient delay. A comparison across species of delays estimated by IPP spacing is shown in Fig. 3 E. We found that delays between adjacent peaks (i.e., NN) were significantly different across species (F(2,227)=30.83,p<0.001). Barn owls had relatively uniform time delays between 1 and 3 ms (2.2±0.063 ms), which were significantly shorter than those in anole lizards (4.1±1.9 ms, p<0.001) and humans (5.1±3.7 ms, p<0.001; Fig. 3 D). Delays in anole lizards were also significantly shorter than those in humans (p=0.034). While delays were frequency dependent in anole lizards (R=−0.28,p=0.012) and humans (R=−0.45,p<0.001), this was not the case in owls (R=0.043,p=0.6936). There were still significant differences in delays between species (F(2,227)=35.6,p<0.001; humans and barn p<0.001, humans and p=0.92, barn owls and anole p<0.001), but delays for owls showed greater variability and frequency dependence in this form (R=0.61205,p<0.01).
Overall, a relatively small fraction of SOAE peak pairs showed IPP correlations (Table 3). IPP FM correlations (IPPxcFM) were observed in six pairs in anoles (2.2% of peak pairs) and only once in humans (0.4%), but never in barn owls. IPPxcFM were only observed in SOAE peak pairs that were NNs. In anoles, IPPxcFM occurred in pairs where most SOAE peaks had amplitude distributions classified as bimodal (66.7%) and IrPxc were present (91.7%). All of the IPPxcFM in anoles had a single temporally confined peak that was positive, such that increases in FM in one peak were associated with increases in the other (see example in bottom panel of Fig. 4 C between peaks at 1.7 and 1.9 kHz, see Fig. S6 C right for correlation curve). However, their delays could be positive or negative, ranging from −0.98 to 2.68 ms (0.29±1.40 ms). For the one IPPxcFM that was observed in a human ear, both associated SOAE peaks were bimodal but neither had an IrPxc. This IPPxcFM was not localized in time and neither a direction nor a delay could be obtained.Figure 4SOAE correlation maps for the same SOAE spectra shown in Fig. 1 (and using the same paneling layout). Here, SOAE peak spacing is plotted logarithmically, mirrored about both the horizontal and vertical axes. Thus, if the tonotopic map is approximately exponential in nature, the line spacing would match spatial distance along the basilar membrane. IrP relations are shown along the diagonal. Nearest-neighbor IPP relations are in the upper half and all other peak pair relations are in the lower half. At any given intersection, a pair of symbols is present to describe the correlations, as defined visually in the legend at the bottom. The left symbol in a given pair describes the AM correlations and the right symbol describes the FM correlations. For IPP cases where neither an AM or FM correlation was detected, there is a single red x. In IrP cases where either the AM or FM waveform autocorrelations showed a significant degree of ringing, there is an ! inside the circle symbol.
While IPP AM correlations (IPPxcAM) were more common than IPPxcFM, they still occurred in the minority of SOAE peaks for each species (anoles: 13.6%; barn 5.0%; 24.3%). We evaluated whether SOAE peak amplitude distribution modality or the presence of an IrPxc in a pair affected the presence of IPPxcAM across species in a three-way ANOVA. This identified significant main effects of species (F(2,695)=4.72,p=0.009) but not amplitude distribution (F(1,695)=0.05,p=0.83), the presence of IrPxc (F(1,695)=2.27,p=0.13), nor the interactions between these factors (all p>0.30). IPPxcAM were significantly more common in humans (24.35%) than in anole lizards (13.55%, p=0.007), but there was no difference between humans and barn owls (4.95%, p=0.38) nor anole lizards and barn owls (p=0.89). While many NN pairs did not show IPPxcAM, they were significantly more common between NNs in anoles (91.9%) and barn owls (70.0%), but not in humans (39.3%). We constructed “correlation maps” to combine correlation and tonotopic information visually (Fig. 4). These assumed that the frequency region associated with SOAE generation (above ∼1 kHz) has an exponential tonotopic map, consistent with auditory nerve fiber tracing studies (e.g., (42,43)). Overall, these plots indicate the relative sparse nature of IPP correlative behavior and how such varies across groups, and also the relatively limited spatial range over which such occurs.
A visual comparison across species of both peak width and height versus frequency, relative to whether a given peak pair showed IPPxcAM or was NN, is shown in Fig. S15. A three-way ANOVA with peak width as the dependent variable identified statistically significant effects of species (F(2,695)=348.5,p<0.001), IPPxcAM presence (F(1,695)=11.3,p<0.001), and their interaction (F(2,695)=13.9,p<0.001), but no effect of NNs (F(1,695)=0.48,p=0.49) nor the other interactions (both p>0.20). SOAE peaks with IPPxcAM were narrower than those without correlations in barn owls (p<0.001), but not in anoles or humans (both p>0.80). We also conducted a three-way ANOVA with peak height as the dependent variable and found statistically significant effects of species (F(2,695)=10.23,p<0.001), IPPxcAM presence (F(1,695)=36.5,p<0.001), and their interaction (F(2,695)=9.9,p<0.001), but no effect of NNs (F(1,695)=0.56,p=0.46) or the other interactions (both p>0.40). SOAE peaks with IPPxcAM were significantly taller than those without correlations in barn owls (p<0.001), but not in anoles (p=0.90) or humans (p=0.07).
In general, human IPPxcAM peaks were wider (i.e., less temporally localized) than those in lizards or owls (Fig. S17), which is consistent with human SOAE peaks being comparatively narrower in the spectral domain (Fig. 1). When IPPxcAM were deemed present, the majority of correlation waveforms (≥74%) had a single temporally confined peak (e.g., Fig. S4). Other correlation waveforms exhibited more complex shapes (e.g., Fig. S12), and we could not readily infer if a correlation was positive or negative nor calculate its associated delay. For owls, all IPPxcAM were negative, whereas the majority of correlations were positive for lizards (83.3%). For humans, the fraction was roughly evenly split (52.8%). IPPxcAM delays were not frequency dependent in any species (all p>0.10), and were on the order of 0–10 ms (Fig. 3 F). Delays were statistically significantly different between species (F(2,100)=12.5,p<0.001), being significantly longer in humans (3.5±9.7 ms) than in anoles (0.28±0.77 ms; p<0.001) or barn owls (2.1±0.92 ms; p=0.006). There was no difference in delays from anoles and barn owls (p=0.93). Delays tended to be positive, meaning that the SOAE peak with a higher CF led the other.
First we summarize the general findings from the study, drawing attention to similarities and differences across the three groups (humans, barn owls, anole lizards). Each subject had a unique array of SOAE peaks. The properties of individual SOAE peaks were generally consistent across species with respect to their frequency dependence (Fig. 2). However, other peak properties were variable. Our evaluation of the effects of temporal properties (amplitude distribution modality, the presence of IrPxc or IPPxc) on SOAE peaks indicated that taxonomic class was the strongest determinant of differences in peak properties, with human SOAE peaks being consistently taller and narrower than those from barn owls and anole lizards. The presence of IrPxc had no effect on SOAE peak height or width, but IPPxcAM presence did. In particular, IPPxcAM were associated with taller, narrower peaks in barn owls, but had no relationship with peak properties in humans or anole lizards.
Across all three species, peak height was inversely related to peak width, and taller peaks were more likely to have bimodal amplitude distributions (Fig. 2, B and E). The relationship between amplitude distribution modality and peak height may be a consequence of higher signal/noise ratios in such peaks, which could explain the classification of many SOAE peak amplitude distributions as unimodal, despite features that suggested sinusoidal-like statistics in both the amplitude and analytic signal distributions. However, comparatively shorter and wider peaks from anole lizards were classified as bimodal more often than taller and narrower peaks from humans or barn owls (Fig. 2, D and E), indicative that signal/noise ratios cannot wholly explain the observed results. Rather, these variations are likely connected to morphological differences between the species examined here, further elaborated on below. With regard to modality classification, one consideration is that such is not in fact strictly binary. That is, there may be more of a continuous distribution between unimodal and bimodal extremes (44). Seen through this lens, both filtered noise and self-sustained oscillations could be simultaneously present with respect to an SOAE generator mechanism(s) within in a given ear.
SOAE only rarely creates observable harmonic distortion (e.g., a large SOAE peak at frequency f does not lead to another SOAE peak at 2f). However, for the owls, IPP spacing was relatively more uniform (see Fig. 3 C), suggestive that either intermodulation distortion was common and/or that some sort of characteristic delay was present. Despite this uniformity, there was relatively little correlative behavior between peaks (e.g., lack of clear IPPxcAM). We interpret this as that peak pairs are either less likely to be primary and associated distortion products (e.g., uniform spacing related to a standing wave effect), or some noise sources obscure such a (correlative) relation (see also (30,45)). In addition, a significant fraction of correlations deemed present were not singularly peaked. That is, their relationship could not be well localized to a particular instant (e.g., Fig. S12). For these cases, gradient-related considerations may be at play, such that the time derivative(s) of one waveform that might relate to the other (see Fig. S13). Further study is needed to explore these relationships.
There were clear differences in IPPxc across the three groups (Figs. 3 and 4). AM correlations (IPPxcAM) were equally common for humans and lizards, but less likely for owls. IPPxcAM were always negative for owls, whereas for lizards they were mostly positive (Table 3). For humans, IPPxcAM could be in either direction. In humans, IPPxcAM delays could be tens of ms; nearly an order of magnitude longer than those observed for nonmammals (Fig. 3 F). While IPPxcAM delays could be positive or negative (albeit always positive in barn owls), they tended to be positive such that the SOAE peak with a higher CF led the other, which is consistent with previous observations for humans (30).
A feature of SOAE activity that appears unique to lizards was the presence of “baseline” activity (24,25,26), as visually apparent in Fig. 1. Baseline emissions could contribute SOAE energy in the filter in addition to the peaks, which could explain the higher incidence of correlations between smaller amplitude peaks in anole lizards. This persistent underlying broadband activity could act as a catalyst to synchronization, giving rise to both IrPxc and IPPxc. Future work should address whether correlative behavior is exclusively confined to peaks. While not systematically explored, it is possible that “intervalley” correlative behavior could occur and could be related to the presence of the broad baseline SOAE present for anoles (see Fig. S20).
The inner ear morphological differences across the three species studied here needs to be considered, as there were sufficient differences in correlative behavior to suggest that SOAE generation could occur differently among species. For example, can the expanded size and more complex morphology of humans and owls relative to anoles be indicative of richer dynamics and interactions occurring (or not) over different timescales in those ears? Further, to what extent can different interelement coupling via the TM explain the present results?
To expand upon this point, consider how the spatial extent of the relevant portion of the tonotopic (i.e., frequency-space) map varies across the three groups. To first approximation, this would amount to the number of hair cells per octave. In general, the diameter of a hair cell and the spacing between cells is similar across species. For simplicity, consider human SOAE activity as occurring over the frequency range of 0.5–8 kHz (46). This corresponds to four octaves, which would spatially span an extent of about 15–20 mm, depending upon assumptions made about the specific form of the tonotopic map. For barn owls, SOAE occurs from ∼2 to 12 kHz, or roughly 2.6 octaves (47). In light of the underlying tonotopic fovea (48), this amounts to a spatial distance of about 8–9 mm. Now consider the anole lizard at about 20°C, where SOAE frequencies are ∼0.5–5 kHz, or 3.3 octaves. This range only spans about 0.25 mm (26,49). (There is an error in (49). There is a passage that reads “The length of the organ is 3.5 mm.” Their Fig. 3 clearly shows that value should be 0.35 mm, or 350 μm.) If the longitudinal spatial extent of a hair cell can be taken as 10 μm, assumed to be roughly constant across species, then clearly there are significantly fewer cells per octave for anole lizards. Thus, presumably fewer cells are contributing to SOAE generation overall, as well as fewer cells per peak. Since these cells are more closely localized together, our finding that anole lizards had a higher degree of correlative behavior (e.g., large fraction of NN peaks showing IPPxcAM, and even IPPxcFM to a lesser extent) is not unexpected, as interactions might be expected to decrease over longer distances. In addition, smaller groups of cells contributing to SOAE peaks, packed together just as closely, might lead to greater fluctuations between groups and/or less synchronization within a group. Such could explain the relatively wider SOAE peaks in the anoles compared with humans and a spatially localized group of more frequency-disparate cells do not synchronize as coherently. Thus, tonotopic considerations could be sufficient to account for differences in the degree of SOAE peak interactions observed, including possibly explaining peak widths and the presence of baseline SOAE activity (e.g., poor intragroup synchronization).
Expanding further, two morphological differences unique to the Anolis basilar papilla (relative to owls and humans) warrant consideration. First, (free-standing) anole hair cell bundles are relatively large, with maximum heights ranging from several μm to upward of 30 μm (26,49). Since the intercell spacing is not relatively enlarged, the bundles thus are densely packed together, forming what appears as a continuum of stereovilli, akin to a phalanx (49). Given boundary layer considerations, this suggests that individual bundles would be predominantly viscously coupled to their NNs. This is consistent with the observed IPPxcAM occurring most often between adjacent SOAE peaks. Second, they are embedded in the underlying papilla, which appears to be relatively rigid along the longitudinal (i.e., tonotopic) axis due the presence of a “fundus” (50). This aspect may introduce a degree of “global” coupling that could affect how the cells work together (51,52,53). For example, the rigid papilla, which prevents the longitudinal traveling wave along the basilar membrane (BM) as present for mammals, may act as a spatial integrator to allow for a coherent response among contributors. Such an effect might be similar to a “a mechanical funnel,” which has been proposed for localized BM regions in the mammalian cochlea (54). Thus, this would give rise to IPPxcAM between more spatially distributed SOAE peaks.
Overall, correlations within a peak for a given ear (IrPxc) were much more common than between peaks in a given ear (IPPxcAM or IPPxcFM; Table 3). We used a threshold to make a binary classification of whether a correlation was present and did not explicitly report (normalized) cross correlation values. When correlations were present, the values observed were typically small (∼0.1 or less; see Fig. S11 B) and were only attainable through averaging (or long timescales). This suggests that some source of noise obscures (or affects) how SOAE fluctuations interrelate. One interpretation is that correlations, if present, are relatively weak. Notably, SOAE signals themselves are typically small in terms of filtered energy in the peak” relative to the underlying noise floor (see Fig. 1 of (10)), which would likely affect the observed correlation strength. More IPP correlations may emerge (especially for humans) when using improved time-series analysis techniques, including both linear (55) and nonlinear methods (40). These could include modern entropy-related analyses (e.g., maximum entropy spectral estimation) (56,57,58) and higher-order spectral analysis (59). Further, inclusion of techniques specifically addressing nonstationarity (40,41) could prove valuable.
SOAE peaks appeared stationary to a first degree, but human SOAE had greater deviations from stationarity than anole lizards or barn owls. It is presently unclear if this observation is related to humans being unanesthetized. The narrower peak widths observed in humans could underlie these deviations. While not systematically explored, anecdotal observations indicated that the choice of filter bandwidth did have some effect upon the observed correlations. As long as the filter width captured the bulk of the energy about the SOAE peak, making the filter slightly narrower or wider had little effect upon the qualitative shape of a correlation (if present), causing only slight changes in the correlation height or delay. This occurred even despite clear visual changes in the fluctuations (e.g., widened filters for human peaks meant faster fluctuation waveforms that differed by visual comparison with the standard narrower filters). Several different correlation methods are shown in Fig. S7, indicating that all lead to qualitatively similar endpoints, except in rare instances. These observations suggest that filter parameters do play an important role, but do not critically affect the correlative features as reported here.
One final consideration is that the SOAE data reported here can be roughly categorized into “low” and “high” frequency groups, with a dividing line around 4–5 kHz (Fig. 2 A). Anoles are on the low side, owls on the high side, with humans straddling the two (although predominantly in the low-frequency category). This dichotomy is notable within the context of a broader variety of auditory neuroscience “transitions” that occur around 3–5 kHz (see Fig. 17 of (60)) and that high-frequency SOAE occurs in mutant mice (17), upward of 25 kHz. Further consideration is needed to explore the possibility that there might be a distinction between “slow” and “fast” SOAE generation mechanisms, and how such might factor into differences in cochlear processing between the base and apex (61).
The data reported here stem from acoustic measurements that are essentially made outside of the head. Yet we are concerned with what is occurring at the cellular (and molecular level) inside the ear. A rough analog would be trying to ascertain what is transpiring at a cocktail party, taking place in a room behind a closed door, while we are listening for snatches of conversation at the opposite end of a long and twisted hallway. Currently, very little is known empirically about what is actually oscillating spontaneously inside the inner ear. For example, the following questions remain open.1)What is the source of the oscillations in the inner ear that generates SOAE activity?2)How do these oscillations arise given the spatially distributed nature of the inner ear?3)How are generative elements coupled together to affect each other’s behavior?4)What causes the (amplitude and frequency) fluctuations in SOAE activity, giving rise to a peak’s width?5)What are the relevant sources of noise (e.g., Brownian motion, channel clatter) that affect SOAE generation?
Given that these are foundational questions with regard to the modeling assumption underlying SOAE generation, we briefly review what has been reported, as such could provide context for interpreting the data reported here. Nuttal et al. (62) directly observed spontaneous BM motion in a guinea pig that corresponded to SOAE measured in the ear canal. This fortuitous observation was made in a single animal and unfortunately has not been replicated to the best of our knowledge. Their subsequent study (63) found that BM motion exhibited noise that was band limited to the tonotopic measurement site and was also affected by physiological factors (e.g., decreasing with or and efferent stimulation). However, the source of the noise remains unknown; it could be caused by external sound pressure on the eardrum, internal Brownian motion of fluid, and/or something else entirely. Spontaneous vibrations of the eardrum for anole lizards have been shown to directly correlate to SOAE (64). In addition, indirect measurements offer further insights on spontaneous oscillations in the cochlea (e.g., (65,66,67)). For example, (66) found that genetic mutations that affect the TM significantly affected the presence of SOAE in mice. Lastly, one influential reported measurement is the observation of spontaneous oscillations of bullfrog saccular hair bundles (e.g., (39,68)), which have formed the basis of one class of SOAE models, namely the “local oscillator” group. However, it is unclear if these types of motions, which occur at tens of Hz, extend to the auditory range of several kHz or higher where fluid forces may be very different (69,70,71). Consider for example that SOAE activity has been observed up to 63 kHz in bats, a frequency region important for echolocation in that species (72).
To provide context for further interpreting the data reported here and connecting to models, we suggest a useful heuristic is that SOAE generators are acting cooperatively (13). This notion is implicit in many descriptions of cochlear amplification, yet many active cochlear models do not address SOAE generation. Consider that older model classes for “simpler” ears tended to be passive, one comprehensive lizard-centric example being a cascade of linear time-invariant filters including a static nonlinearity (73). While it is still unclear whether these models can plausibly capture the sharp tuning and nonlinear features observed physiologically, they certainly are not capable of describing SOAE generation. Subsequent models included some sort of active contribution, although this would manifest in a wide variety of different ways (e.g., regions of negative damping, hair cell bundles acting as limit-cycle oscillators). Early SOAE models often focused on a single peak described by a single limit-cycle oscillator (e.g., van der Pol, (19)), including noise to create fluctuations (9). They were able to capture many basic features of isolated SOAE peaks, such as their general Lorentzian shape. Later SOAE models incorporated two or more self-sustained oscillators (e.g., (74)), leading toward several classes of models that attempt to explain multiple SOAE peaks (e.g., (11,23,75,76,77,78,79)). However, it is unclear if any of these models are able to reasonably capture the characteristics of SOAE fluctuations as reported here.
To frame how the current results can help constrain models of SOAE generation, we briefly expand upon the proposed modeling dichotomy (22) described in the introduction. The following rhetorical question serves as a launch Where is the cochlea/a hair cell “poised”? (13). In essence, this distinction revolves around whether an individual element can self-oscillate (i.e., and thereby the spontaneous oscillation is local; see (80)), or whether it is necessary to embed the element into a distributed system for such spontaneous oscillations to manifest (and thus it is global). Applied to SOAE generation, the local limit-cycle oscillator array formulation assumes that the various generation elements individually behave as limit-cycle oscillators. Conversely, the global wave-based reflection framework posits that SOAE is intrinsically an emergent systems-level response; the (inner) ear is a collective system that is wholly different than the sum of the parts. In essence, this dichotic framework ties back to arguments about the parameter regime for models.
Ultimately, we would argue that this proposed distinction is useful, but is not a suitable heuristic for understanding SOAE generation. First, the dichotomy is predicated upon the unknown answer to the question of precisely what is oscillating and what are the forces causing such. This blurs the boundary between the two sides. For example, a “system” of limit-cycle oscillators can sit in an “amplitude death” regime when coupled together (81,82). Even a single limit-cycle oscillator (e.g., van der Pol system), subject to strong positive damping and/or a constant force pushing it way from the region where a negative damping occurs, may not self-oscillate. Thus, there are myriad scenarios where a limit-cycle oscillator is quiescent. Stochastic forces complicate things further (e.g., (83)). Further, waves may naturally arise in a limit-cycle oscillator array given coupling in a spatial-temporal system (e.g., (84)). Conversely, a wave-based reflection framework can produce plateaus (85). Second, the distinction is a potentially confounding choice of global versus local can mistakenly be interpreted as referring only to (interelement) coupling. Nonetheless, examples of each modeling approach have both merits and drawbacks. A standing wave-based reflection framework (11) has made several predictions that reasonably hold, although it has not been placed in a more comprehensive computational scheme to test how robust the model is for predicting a wider range of SOAE phenomena. A limit-cycle oscillator array (23) describes a variety of features via “frequency clustering,” but does not yet produce realistic SOAE spectra (e.g., peaks are too narrow). Furthermore, to reiterate, it is unknown if the hair cells in nonmammalian ears do in fact act as local oscillators at frequencies corresponding to SOAE activity (i.e., several kHz). Thus, a key central assumption has yet to be empirically validated.
Ultimately, we suggest that the two proposed model classes appear just as different facets of the same essential a theoretical description of a spatially distributed system of coupled active (i.e., some sort of internal energy source) oscillatory elements. The key challenge is to properly describe that coupling to elucidate how the cellular elements work together to create self-sustained motion, giving rise to individual SOAE peaks, and further characterize the precise role of key aspects such as nonlinearity and noise.
We propose that the data reported here demonstrating the presence of both IrP and IPP correlations are indicative of fluctuations arising due to both different SOAE generator sources interacting and the presence of intrinsic physical noise (e.g., Brownian motion). So the AM and FM variations observed for a given peak, which appear “noisy,” could derive from the noisy influence of a nearby generator as well as purely stochastic forces due to thermal considerations. Thereby, assuming that different sources of “noise” cause SOAE fluctuations, one might expect differences in correlative behavior across a limit-cycle oscillator array viewpoint (e.g., NN coupling) might expect correlations to be localized to neighboring peaks, whereas a wave-based reflection framework perspective might predict broader correlations due to a noisy reflection boundary that is shared across generation sites (e.g., the stapes as driven by external noise affecting the eardrum).
To better connect the current results with future modeling efforts, we pose several lines of inquiry that revolve around what sort of interelement mechanical coupling should be considered, as well as what role stochastic considerations play.1)What is the dominant source of noise to which an individual generator element is subject (e.g., Brownian motion affecting displacement, channel “clatter” in the mechanically gated ion channels, etc.)?2)Given the relatively limited tonotopic extent of correlative behavior (i.e., predominantly confined to NN peaks), is the basis for energy flow diffusive or wave based in nature (86)? More generally, how spatially localized is the noise, such that forces experienced are correlated to some extent along the tonotopic axis?3)To what extent can stochastic processes be used to understand the effective “bandwidth” of SOAE peaks, and why are human peaks relatively so narrow?4)Why is correlative behavior, while present, rare? Is it because (weaker) correlations may in fact be present, but some source of measurement noise serves to mask the effect? Or are their only correlations between specific generators, perhaps due to some underlying network connectivity (e.g., NNs, Fig. 4)?5)Despite the ear likely having sufficient (nonlinear) complexity, SOAE appears generally stable with regard to external stimuli ((87,88), Fig. S19). Is such an observation in contrast to models suggestive of chaotic dynamics in the inner ear?6)How can SOAE interactions inform how “roughness” (23,89) should be properly included so to lead to a testable predictions?
Ultimately, these questions can be viewed as a means to help guide models in terms of their falsifiability (13) with respect to the SOAE interactions as described in the current paper.
To summarize, while many questions still remain about the physiological underpinnings of SOAE generation, we interpret the current data as indicative of SOAE arising by virtue of cooperative behavior, where cellular elements work together as active force generators to improve both the sensitivity and selectivity of the ear. One specific suggestion is that an SOAE peak is a manifestation of a tonotopically localized group of cells working together (e.g., (26)), akin to a form of synchronization (90). The presence of correlations in the fluctuations (whether it be IrP or IPP) as reported here can be attributed to those groups perturbing one another to varying extents by virtue of being in the same vicinity.
Finally, we briefly argue that nonmammalian models are particularly well suited for future SOAE experiments and modeling, as well as auditory neurophysiology, especially when placed in a broader evolutionary context (e.g., (91)). By clarifying processes in these relatively simpler ears, key principles should become apparent that constrain and inform assumptions for the more complex mammalian cochlea (18). With respect to barn owls, they are known to be auditory specialists with exceptional sound localization acuity and have a well-established history as a model for auditory research (e.g., (47,92,93,94)). The barn owl’s auditory epithelium is also notable in that almost half of its length is devoted to the highest octave (from 5 to 10 kHz), thus an unusually large number of hair cells will be responsive to such frequencies. It is presently unclear to what extent SOAE activity can be observed in other bird species, however.
Future work in lizards could be a particularly valuable avenue to characterize how various morphological traits could be associated with fluctuation correlations and their properties. First, consider that papillar morphology varies significantly across lizard families (e.g., number of hair cells/ear, structure/presence of tectorial membrane; see (18,33,50)). This variability motivates the application of the correlation methodology employed here to study SOAE IPP correlations for other lizard groups. Second, we further rationalize the choice of Anolis as lizard for the SOAE data presented here. Anoles are an iguanid species with a small basilar papilla containing relatively few auditory hair cells (≈150), whose bundles are predominantly free standing (i.e., lack an overlying tectorium). The cells are densely packed together, forming what appears as a continuum of stereovilli, akin to a phalanx (49). Given boundary layer considerations, this suggests that individual bundles would be predominantly viscously coupled to their NNs. However, they are also embedded in the underlying papilla, which would effectively introduce a degree of global coupling that could affect how the cells work together (51,52). Given morphological differences relative to the mammalian cochlea, the very small ears of anole lizards bring into focus the important question central to this How does energy, whether it comes from external sound and/or is injected internally by active mechanisms, spatially propagate throughout the inner ear?
The lizard’s BM/papilla appear to be relatively rigid in that it prevents a longitudinal traveling wave along the BM (as traditionally present for mammals). This feature may in turn act as a spatial integrator that allows for a coherent response among contributors, perhaps similar to a “a mechanical funnel” as has been proposed for localized BM regions in the mammalian cochlea (54). Conversely, there may be less conventional roles that waves play in the anole lizard’s inner ear (aside from acoustic fluid propagation) that could affect phase relationships between generators. For example, diffusive waves (86) might provide a means by which energy injected in one location affects only nearby generation sites. Lastly, lizards provide an opportunity to consider acoustic cross talk between the two ears via the interaural canal (95,96). This pathway allows for mechanical coupling between the two ears, which broadens the notion of global across the head to the bilateral domain and how such may affect SOAE correlation analyses.
This study took a comparative approach to systematically characterize SOAE peak fluctuations and their associated correlations. More specifically, we examined three species whose inner ears differ characteristically in their anatomy. Key differences include the size of the epithelium (from 0.5 to 35 mm in length) and the corresponding number of hair cells (150–15,000), both of which presumably affect the coupling of hair cells. For example, whereas hair cells that respond to frequencies where peaks occur in the SOAE spectrum completely lack a tectorial covering in anole lizards, both barn owls and humans possess a thick, continuous tectorium. All three types of ears show SOAE activity as an idiosyncratic array of peaks of varying heights and widths. These peaks can show clear evidence of self-sustained sinusoidal oscillation (i.e., bimodal amplitude distributions), a hallmark feature of the active ear. However, the extent to which this characteristic was present was variable, being more common in humans and anole lizards than in barn owls. Further, SOAE peaks from all three groups exhibited fluctuations in amplitude and frequency that could show both IrP and IPP correlative behavior. Overall, these correlations were rare in barn owls. IrP behavior was most common in anole lizards and moderately present in humans. Conversely, IPP correlations were most common in humans and less so in anole lizards. This latter IPP aspect, when present, was generally localized to adjacent SOAE peaks in barn owls and anole lizards. However, in humans, IPP behavior was more likely to occur between more distant SOAE peaks than those that were directly adjacent. We argue that IPP correlations could be attributed to how coupling might be affected by spatial aspects such as number of hair cells and of intercell spacing, with anole lizards at one end of the coupling spectrum and humans near the other end.
This work was supported by the 10.13039/501100000038Natural Sciences and Engineering Research Council of Canada (10.13039/501100000038NSERC) to C.B. and R.E.W. Input from Andrew Bell, Michele Bergevin, Julien Meaud, and Daibhid O Maoileidigh is gratefully acknowledged. Detailed comments from several reviewers significantly improved the manuscript.
C.B. designed the research, analyzed the data, and wrote the article. R.E.W., H.W., and P.v.D. analyzed the data and edited the article. G.A.M. contributed data and edited the article.
All authors declare no competing interests.