Evidence for the distortion product frequency place as a source of distortion product otoacoustic emission (DPOAE) fine structure in humans. I. Fine structure and higher-order DPOAE as a function of the frequency ratio f2/f1

Critical experiments were performed in order to validate the two-source hypothesis of distortion product otoacoustic emissions (DPOAE) generation. Measurements of the spectral fine structure of DPOAE in response to stimulation with two sinusoids have been performed with normal-hearing subjects. The dependence of fine-structure patterns on the frequency ratio f2/f1 was investigated by changing f1 or f2 only (fixed f2 or fixed f1 paradigm, respectively), and by changing both primaries at a fixed ratio and looking at different order DPOAE. When f2/f1 is varied in the fixed ratio paradigm, the patterns of 2 f1-f2 fine structure vary considerably more if plotted as a function of f2 than as a function of fDP. Different order distortion products located at the same characteristic place on the basilar membrane (BM) show similar patterns for both, the fixed-f2 and fDP paradigms. Fluctuations in DPOAE level up to 20 dB can be observed. In contrast, the results from a fixed-fDP paradigm do not show any fine structure but only an overall dependence of DP level on the frequency ratio, with a maximum for 2f1-f2 at f2/f1 close to 1.2. Similar stimulus configurations used in the experiments have also been used for computer simulations of DPOAE in a nonlinear and active model of the cochlea. Experimental results and model simulations give strong evidence for a two-source model of DPOAE generation: The first source is the initial nonlinear interaction of the primaries close to the f2 place. The second source is caused by coherent reflection from a re-emission site at the characteristic place of the distortion product frequency. The spectral fine structure of DPOAE observed in the ear canal reflects the interaction of both these sources.     

Wave propagation patterns in a "classical" three-dimensional model of the cochlea

The generation mechanisms of cochlear waves, in particular those that give rise to otoacoustic emissions (OAEs), are often complex. This makes it difficult to analyze wave propagation. In this paper two unusual excitation methods are applied to a three-dimensional stylized classical nonlinear model of the cochlea. The model used is constructed on the basis of data from an experimental animal selected to yield a smooth basilar-membrane impedance function. Waves going in two directions can be elicited by exciting the model locally instead of via the stapes. Production of DPOAEs was simulated by presenting the model with two relatively strong primary tones, with frequencies f1 and f2, estimating the driving pressure for the distortion product (DP) with frequency 2f1 - f2, and computing the resulting DP response pattern - as a function of distance along the basilar membrane. For wide as well as narrow frequency separations the resulting DP wave pattern in the model invariably showed that a reverse wave is dominant in nearly the entire region from the peak of the f2-tone to the stapes. The computed DP wave pattern was further analyzed as to its constituent components with the aim to isolate their properties.     

In search of basal distortion product generators

The 2f1-f2 distortion product otoacoustic emission (DPOAE) is thought to arise primarily from the complex interaction of components that come from two different cochlear locations. Such distortion has its origin in the nonlinear interaction on the basilar membrane of the excitation patterns resulting from the two stimulus tones, f1 and f2. Here we examine the spatial extent of initial generation of the 2f1-f2 OAE by acoustically traumatizing the base of the cochlea and so eliminating the contribution of the basal region of the cochlea to the generation of 2f1-f2. Explicitly, amplitude-modulated, or continuously varying in level, stimulus tones with f2/f1= 1.2 and f2 =8000-8940 Hz were used to generate the 2f1-f2 DPOAE in guinea pig before and after acoustically traumatizing the basal region of the cochlea (the origin of any basal-to-f2 distortion product generators). It was found, based on correlation analysis, that there does not appear to be a basal-to-f2 distortion product generation mechanism contributing significantly to the guinea pig 2f1-f2 OAE up to L1 = 80 dB sound pressure level (SPL).     

Distortion product otoacoustic emissions and basilar membrane vibration in the 6-9 kHz region of sensitive chinchilla cochleae

Distortion product otoacoustic emissions (DPOAEs) and basilar membrane (BM) vibration were measured simultaneously in the 6-9 kHz region of chinchilla cochleae. BM-Input-Output functions in a two-tone paradigm behaved similarly to DPOAEs for the 2f1-f2 component, nonmonotonic growth with the intensity of the lower frequency primary and a notch in the functions around 60 dB SPL. Ripples in frequency functions occur in both BM and OAE curves as a function of the distortion frequency. Optimum f2/f1 ratios for DPOAE generation are near 1.2. The slope of phase curves indicates that for low f2f1(<1.1) the emission source is the place location while for f2f1>1.1 the relative constancy of the phase function suggests that the place is the nonlinear region of f2, i.e., the wave location. Magnitudes of the DPOAEs increase rapidly above 60 dB SPL suggesting a different source or mechanism at high levels. This is supported by the observation that the high level DPOAE and BM-DP responses remain for a considerable period postmortem.     

Investigating the wave-fixed and place-fixed origins of the 2f(1)-f(2) distortion product otoacoustic emission within a micromechanical cochlear model

The 2f(1)-f(2) distortion product otoacoustic emission (DPOAE) arises within the cochlea due to the nonlinear interaction of two stimulus tones (f(1) and f(2)). It is thought to comprise contributions from a wave-fixed source and a place-fixed source. The generation and transmission of the 2f(1)-f(2) DPOAE is investigated here using quasilinear solutions to an elemental model of the human cochlea with nonlinear micromechanics. The micromechanical parameters and nonlinearity are formulated to match the measured response of the cochlea to single- and two-tone stimulation. The controlled introduction of roughness into the active micromechanics of the model allows the wave- and place-fixed contributions to the DPOAE to be studied separately. It is also possible to manipulate the types of nonlinear suppression that occur within the quasilinear model to investigate the influence of stimulus parameters on DPOAE generation. The model predicts and explains a variety of 2f(1)-f(2) DPOAE phenomena: The dependence of emission amplitude on stimulus parameters, the weakness of experiments designed to quantify cochlear amplifier gain, and the predominant mechanism which gives rise to DPOAE fine structure. In addition, the model is used to investigate the properties of the wave-fixed source and how these properties are influenced by the stimulus parameters.     

Inverted direction of wave propagation (IDWP) in the cochlea

The "classical" view on wave propagation is that propagating waves are possible in both directions along the length of the basilar membrane and that they have identical properties. Results of several recently executed experiments [T. Ren, Nat. Neurosci. 2, 333-334 (2004) and W. X. He, A. L. Nuttall, and T. Ren, Hear. Res., 228, 112-122 (2007)] appear to contradict this view. In the current work measurements were made of the velocity of the guinea-pig basilar membrane (BM). Distortion products (DPs) were produced by presenting two primary tones, with frequencies below the characteristic frequency f(0) of the BM location at which the BM measurements were made, with a constant frequency ratio. In each experiment the phase of the principal DP, with frequency 2f(1)-f(2), was recorded as a function of the DP frequency. The results indicate that the DP wave going from the two-tone interaction region toward the stapes is not everywhere traveling in the reverse direction, but also in the forward direction. The extent of the region in which the forward wave occurs appears larger than is accounted for by classical theory. This property has been termed "inverted direction of wave propagation." The results of this study confirm the wave propagation findings of other authors. The experimental data are compared to theoretical predictions for a classical three-dimensional model of the cochlea that is based on noise-response data of the same animal. Possible physical mechanisms underlying the findings are discussed.     

Wave and place fixed DPOAE maps of the human ear

Human intermodulation distortion product otoacoustic emissions (DPOAE) can be a mixture of low and high latency components. They have different level, phase, and suppression characteristics, which indicate that emissions arise both from the frequency region of the primary tones directly and indirectly via the DP frequency place. Which component dominates the measured DPOAE in the ear canal depends on the stimulus parameters, especially the frequency ratio, f2/f1. Interference between the two emissions adds complexity to measurements of DPOAE. The behavior and even existence of whichever emission route is lower in level often cannot directly be deduced from the raw DPOAE data because the other emission covers it. It is therefore not known whether both emissions are present for all stimulus parameters or whether the trends seen in each emission when they are the dominant emission route continue under stimulus conditions when they are not dominant. In this study, the two DPOAE components are separated by a post-processing method. Previously, maps of raw DPOAE data against f2/f1 and DP frequency have been obtained. To separate the components, sets of data consisting of f2/f1 sweeps were transformed by an inverse Fourier transform into the time domain. The low and high latency components appeared as two distinct peaks because of their different phase gradients. These peaks were separated by windowing in the time domain and two frequency domain maps were reconstructed, representing the low and high latency DPOAEs. It was found that the low latency component of the 2 f1-f2 DP was only emitted strongly with f2/f1 between approximately 1.1 and 1.3. The removal of the high latency component revealed the low ratio edge of this region, at which the level falls sharply. However, the low latency emission has been traced at reduced amplitude over a wide range of stimulus parameters. Although previously only observed at small frequency ratios, the high latency component was found to be present widely in the lower sideband, its level reducing slowly at larger f2/f1. Its phase behavior changes in the lower sideband, being approximately constant with DP frequency at small ratios of f2/f1, but deviating from this at wider ratios. These results support the hypothesis that a DPOAE component which propagates to and is re-emitted from the DP frequency place (place fixed emission) is present across a wide parameter range. However, for all but the close primary condition the lower sideband DPOAE is dominated by direct emission from the region of f2 and f1 wave interaction (wave fixed emission). A simple transmission line model is presented to illustrate how the observed DPOAE maps can arise on the basis of this hypothesis.     

Modeling the temporal behavior of distortion product otoacoustic emissions

The temporal behavior of the 2f1-f2 distortion product otoacoustic emission is theoretically investigated for the case in which the lower frequency (f1) primary tone is on continuously, and the higher frequency (f2) one is pulsed on and off [e.g., Talmadge et al., J. Acoust. Soc. Am. 105, 275-292 (1999)]. On physical grounds, this behavior is expected to be characterized by various group delays associated with the propagation of (1) the f2 cochlear primary wave between the cochlear base and the primary distortion product generation region around x2 (the f2 tonotopic place), and (2) the 2f1-f2 cochlear distortion product (DP) waves between the cochlear base, the primary generation region of the distortion product, and the region around the 2f1-f2 tonotopic place where the generated apical moving DP wave is reflected toward the cochlear base [e.g., Talmadge et al., J. Acoust. Soc. Am. 104, 1517-1543 (1998)]. An approximate analytic expression is obtained for this behavior from the analysis of the Fourier integral representation of the auditory peripheral response to the primary stimuli. This expression also approximately describes the transient build-up of the components of different latencies in terms of the damping properties of the cochlear partition. It is shown that considerable caution must be applied in attempting to relate phase derivatives of the distortion product otoacoustic emissions for steady state stimuli and the physical time delays which are associated with the temporal behavior of a distortion product emission in the case of a pulsed primary.     

Multiple internal reflections in the cochlea and their effect on DPOAE fine structure

In recent years, evidence has accumulated in support of a two-source model of distortion product otoacoustic emissions (DPOAEs). According to such models DPOAEs recorded in the ear canal are associated with two separate sources of cochlear origin. It is the interference between the contributions from the two sources that gives rise to the DPOAE fine structure (a pseudoperiodic change in DPOAE level or group delay with frequency). Multiple internal reflections between the base of the cochlea (oval window) and the DP tonotopic place can add additional significant components for certain stimulus conditions and thus modify the DPOAE fine structure. DPOAEs, at frequency increments between 4 and 8 Hz, were recorded at fixed f2/f1 ratios of 1.053, 1.065, 1.08, 1.11, 1.14, 1.18, 1.22, 1.26, 1.30, 1.32, 1.34, and 1.36 from four subjects. The resulting patterns of DPOAE amplitude and group delay (the negative of the slope of phase) revealed several previously unreported patterns in addition to the commonly reported log sine variation with frequency. These observed "exotic" patterns are predicted in computational simulations when multiple internal reflections are included. An inverse FFT algorithm was used to convert DPOAE data from the frequency to the "time" domain. Comparison of data in the time and frequency domains confirmed the occurrence of these "exotic" patterns in conjunction with the presence of multiple internal reflections. Multiple internal reflections were observed more commonly for high primary ratios (f2/f1 > or = 1.3). These results indicate that a full interpretation of the DPOAE level and phase (group delay) must include not only the two generation sources, but also multiple internal reflections.     

Cochlear traveling-wave amplification, suppression, and beamforming probed using noninvasive calibration of intracochlear distortion sources

Originally developed to estimate the power gain of the cochlear amplifier, so-called "Allen-Fahey" and related experiments have proved invaluable for probing the mechanisms of wave generation and propagation within the cochlea. The experimental protocol requires simultaneous measurement of intracochlear distortion products (DPs) and ear-canal otoacoustic emissions (DPOAEs) under tightly controlled conditions. To calibrate the intracochlear response to the DP, Allen-Fahey experiments traditionally employ invasive procedures such as recording from auditory-nerve fibers or measuring basilar-membrane velocity. This paper describes an alternative method that allows the intracochlear distortion source to be calibrated noninvasively. In addition to the standard pair of primary tones used to generate the principal DP the noninvasive method employs a third, fixed tone to create a secondary DPOAE whose amplitude and phase provide a sensitive assay of the intracochlear value of the principal DP near its characteristic place. The method is used to perform noninvasive Allen-Fahey experiments in cat and shown to yield results in quantitative agreement with the original, auditory-nerve-based paradigm performed in the same animal. Data obtained using a suppression-compensated variation of the noninvasive method demonstrate that neither traveling-wave amplification nor two-tone suppression constitutes the controlling influence in DPOAE generation at close frequency ratios. Rather, the dominant factor governing the emission magnitude appears to be the variable directionality of the waves radiated by the distortion-source region, which acts as a distortion beamformer tuned by the primary frequency ratio.     

Linear and nonlinear distortion effects in direct detection 40 Gb/s MSK modulation formats multi-span optically amplified transmission

The generation of minimum shift keying (MSK) requires a linear variation of the phase, hence a constant frequency of the optical carrier. However, the generation of the optical phase may be preferred by driving an optical modulator using sinusoidal signal for practical implementation. Thus a nonlinear variation of the carrier phase, hence some distortion effects are produced. In this paper, we investigate the use of linear and nonlinear phase shaping filtering and their impacts on MSK modulated optical signals transmission over optically amplified long haul communications system. The evolution of the phasor of the in-phase and quadrature components is illustrated for lightwave-modulated signal transmission. The distinct features of three different MSK modulation formats: linear MSK, weakly nonlinear MSK and strongly nonlinear MSK and their transmission are simulated. Transmission performance obtained indicates the resilience of the MSK signals in transmission over multi-optically amplified multi-spans.     

Evidence for the distortion product frequency place as a source of distortion product otoacoustic emission (DPOAE) fine structure in humans. II. Fine structure for different shapes of cochlear hearing loss

Distortion product otoacoustic emissions (DPOAE) were recorded from eight human subjects with mild to moderate cochlear hearing loss, using a frequency spacing of 48 primary pairs per octave and at a level L1 = L2 = 60 dBSPL and with a fixed ratio f2/f1. Subjects with different shapes of hearing thresholds were selected. They included subjects with near-normal hearing within only a limited frequency range, subjects with a notch in the audiogram, and subjects with a mild to moderate high-frequency loss. If the primaries were located in a region of normal or near-normal hearing, but DP frequencies were located in a region of raised thresholds, the distortion product 2 f1-f2 was still observable, but the DP fine structure disappeared. If the DP frequencies fell into a region of normal thresholds, fine structure was preserved as long as DPOAE were generated, even in cases of mild hearing loss in the region of the primaries. These experimental results give further strong evidence that, in addition to the initial source in the primary region, there is a second source at the characteristic place of fDP. Simulations in a nonlinear and active computer model for DPOAE generation indicate different generation mechanisms for the two components. The disappearance of DPOAE fine structure might serve as a more sensitive indicator of hearing impairment than the consideration of DP level alone.     

Mechanisms of generation of the 2f2-f1 distortion product otoacoustic emission in humans

The 2f1-f2 distortion product otoacoustic emission (DPOAE) is considered to consist of two components in normally hearing ears, one having constant phase with changing DP frequency (wave fixed) and one having an increasing phase lag with increasing frequency (place fixed). The aim was to identify the wave-fixed and place-fixed components of both 2f1-f2 and 2f2-f1 DPs, and, in particular, to show whether a wave-fixed 2f2-f1 DP exists in normally hearing adults. DPOAE recordings were made in 20 ears of normally hearing young adults. Four frequency ratios were used and recording entailed fixed frequency-ratio sweeps. A separation into wave-fixed and place-fixed components was carried out using a time-window separation method. A method for estimating the noise floor after data processing was developed. Results confirmed the presence of wave-fixed and place-fixed components for 2f1-f2, consistent with previous studies. Both components were also present for 2f2-f1 in virtually all subjects. This latter finding conflicts with current models of DPOAE generation, and so a modified model is proposed. Unlike the 2f1-f2 emission, which has a wave-fixed component that is strongly dependent on the frequency ratio, neither component of the 2f2-f1 emission showed such a dependence. The proposed model explains these findings in terms of the overlap of the primary frequency traveling waves.     

Breaking away: violation of distortion emission phase-frequency invariance at low frequencies

The phase versus frequency function of the distortion product otoacoustic emission (DPOAE) at 2f(1) - f(2) is approximately invariant at frequencies above 1.5 kHz in human subjects when recorded with a constant f(2)/f(1). However, a secular break from this invariance has been observed at lower frequencies where the phase-gradient becomes markedly steeper. Apical DPOAEs, such as 2f(1)?- f(2), are known to contain contributions from multiple sources. This experiment asked whether the phase behavior of the ear canal DPOAE at low frequencies is driven by the phase of the component from the distortion product (DP) region at 2f(1)?- f(2), which exhibits rapid phase accumulation. Placing a suppressor tone close in the frequency to 2f(1)?- f(2) reduced the contribution of this component to the ear canal DPOAE in normal-hearing adult human ears. When the contribution of this component was reduced, the phase behavior of the ear canal DPOAE was not altered, suggesting that the breaking from DPOAE phase invariance at low frequencies is an outcome of apical-basal differences in cochlear mechanics. The deviation from DPOAE phase invariance appears to be a manifestation of the breaking from approximate scaling symmetry in the human cochlear apex.     

A second,low-frequency mode of vibration in the intact mammalian cochlea

The mammalian cochlea is a structure comprising a number of components connected by elastic elements. A mechanical system of this kind is expected to have multiple normal modes of oscillation and associated resonances. The guinea pig cochlear mechanics was probed using distortion components generated in the cochlea close to the place of overlap between two tones presented simultaneously. Otoacoustic emissions at frequencies of the distortion components were recorded in the ear canal. The phase behavior of the emissions reveals the presence of a nonlinear resonance at a frequency about a half octave below that of the high-frequency primary tone. The location of the resonance is level dependent and the resonance shifts to lower frequencies with increasing stimulus intensity. This resonance is thought to be associated with the tectorial membrane. The resonance tends to minimize input to the cochlear receptor cells at frequencies below the high-frequency primary and increases the dynamic load to the stereocilia of the receptor cells at the primary frequency when the tectorial membrane and reticular lamina move in counterphase.     

Allen-Fahey and related experiments support the predominance of cochlear slow-wave otoacoustic emissions

Originally proposed as a method for measuring the power gain of the cochlear amplifier, Allen-Fahey experiments compare intracochlear distortion products and ear-canal otoacoustic emissions (OAEs) under tightly controlled conditions. In this paper Allen-Fahey experiments are shown to place significant constraints on the dominant mode of reverse energy propagation within the cochlea. Existing Allen-Fahey experiments are reviewed and shown to contradict the predictions of compression-wave OAE models recently proposed in the literature. In compression-wave models, distortion products propagate from their site of generation to the stapes via longitudinal compression waves in the cochlear fluids (fast waves); in transverse traveling-wave models, by contrast, distortion products propagate primarily via pressure-difference waves whose velocity and other characteristics depend on the mechanical properties of the cochlear partition (slow waves). Compression-wave models predict that the distortion-product OAEs (DPOAEs) measured in the Allen-Fahey paradigm increase at close primary-frequency ratios (or remain constant in the hypothetical absence of tuned suppression). The behavior observed experimentally is just the opposite-a pronounced decrease in DPOAE amplitude at close ratios. Since neither compression-wave nor simple conceptual "hybrid-wave" models can account for the experimental results--whereas slow-wave models can, via systematic changes in distortion-source directionality arising from wave-interference effects--Allen-Fahey and related experiments provide compelling evidence against the predominance of compression-wave OAEs in mammalian cochlear mechanics.     

Testing coherent reflection in chinchilla: Auditory-nerve responses predict stimulus-frequency emissions

Coherent-reflection theory explains the generation of stimulus-frequency and transient-evoked otoacoustic emissions by showing how they emerge from the coherent "backscattering" of forward-traveling waves by mechanical irregularities in the cochlear partition. Recent published measurements of stimulus-frequency otoacoustic emissions (SFOAEs) and estimates of near-threshold basilar-membrane (BM) responses derived from Wiener-kernel analysis of auditory-nerve responses allow for comprehensive tests of the theory in chinchilla. Model predictions are based on (1) an approximate analytic expression for the SFOAE signal in terms of the BM traveling wave and its complex wave number, (2) an inversion procedure that derives the wave number from BM traveling waves, and (3) estimates of BM traveling waves obtained from the Wiener-kernel data and local scaling assumptions. At frequencies above 4 kHz, predicted median SFOAE phase-gradient delays and the general shapes of SFOAE magnitude-versus-frequency curves are in excellent agreement with the measurements. At frequencies below 4 kHz, both the magnitude and the phase of chinchilla SFOAEs show strong evidence of interference between short- and long-latency components. Approximate unmixing of these components, and association of the long-latency component with the predicted SFOAE, yields close agreement throughout the cochlea. Possible candidates for the short-latency SFOAE component, including wave-fixed distortion, are considered. Both empirical and predicted delay ratios (long-latency SFOAE delay/BM delay) are significantly less than 2 but greater than 1. Although these delay ratios contradict models in which SFOAE generators couple primarily into cochlear compression waves, they are consistent with the notion that forward and reverse energy propagation in the cochlea occurs predominantly by means of traveling pressure-difference waves. The compelling overall agreement between measured and predicted delays suggests that the coherent-reflection model captures the dominant mechanisms responsible for the generation of reflection-source otoacoustic emissions.     

Inner hair cell responses to the 2f1-f2 intermodulation distortion product

Recordings of dc and ac receptor potentials from pigmented guinea pig inner hair cells indicate strong responses to the 2f1-f2 intermodulation tone when f1 and f2 are greater than the hair cell characteristic frequency and do not cause a response when given individually. The effective magnitude of this cubic distortion product (CDP) was about 25-30 dB below equal sound level primaries over a 20-30-dB range of their sound levels. The relative strength of the CDP declined at a rate greater than 180-dB/oct separation of the primaries. When magnitude of f1 or f2 was held constant, the growth of CDP was nonmonotonic, exhibiting a distinct maximum. With a constant level of f1 or f2, optimal CDP was produced when the level of f2 was 10-15 dB greater than f1. Strong two-tone suppression from the primaries has a role in shaping the CDP growth. The ac receptor potentials of the CDP show a 150 degrees-200 degrees phase shift when the primaries are increased over a 50-dB range. These results support the hypothesis of a propagated CDP in the cochlea and are consistent with the major features of related studies of human psychoacoustic experiments, afferent nerve neural rate functions, and ear canal distortion products.     

Stimulus-frequency-emission group delay: a test of coherent reflection filtering and a window on cochlear tuning

This paper tests and applies a key prediction of the theory of coherent reflection filtering for the generation of reflection-source otoacoustic emissions. The theory predicts that reflection-source-emission group delay is determined by the group delay of the basilar-membrane (BM) transfer function at its peak. This prediction is tested over a seven-octave frequency range in cats and guinea pigs using measurements of stimulus-frequency-emission (SFOAE) group delay. A comparison with group delays calculated from published measurements of BM mechanical transfer functions supports the theory at the basal end of the cochlea. A comparison across the whole frequency range based on variations in the sharpness of neural tuning with characteristic frequency (CF) suggests that the predicted relation holds in the basal-most 60% of the cochlea. At the apical end of the cochlea, however, the measurements disagree with neural and mechanical group delays. This disagreement suggests that there are important differences in cochlear mechanics and/or mechanisms of emission generation between the base and apex of the cochlea. Measurements in humans over a four-octave range indicate that human SFOAE group delays are roughly a factor of 3 longer than their counterparts in cat and guinea pig but manifest similar trends across CF. The measurements thus reveal global deviations from scaling whose form appears quantitatively similar in all three species. Interpreted using the theory of coherent reflection filtering, the group delay measurements indicate that the wavelength at the peak of the traveling wave decreases with increasing CF at a rate of roughly 25% per octave in the base of the cochlea. The measurements and analysis reported here illustrate the rich potential inherent in OAE measurements for obtaining valuable information about basic cochlear properties such as tuning.