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The DPOAE response consists of the linear superposition of two components, a nonlinear distortion component generated in the overlap region, and a reflection component generated by roughness in the DP resonant region. Due to approximate scaling symmetry, the DPOAE distortion component has approximately constant phase. As the reflection component may be considered as a SFOAE generated by the forward DP traveling wave, it has rapidly rotating phase, relative to that of its source, which is also equal to the phase of the DPOAE distortion component. This different phase behavior permits effective separation of the DPOAE components (unmixing), using time-domain or time-frequency domain filtering. Departures from scaling symmetry imply fluctuations around zero delay of the distortion component, which may seriously jeopardize the accuracy of these filtering techniques. The differential phase-gradient delay of the reflection component obeys causality requirements, i.e., the delay is positive only, and the fine-structure oscillations of amplitude and phase are correlated to each other, as happens for TEOAEs and SFOAEs relative to their stimulus phase. Performing the inverse Fourier (or wavelet) transform of a modified DPOAE complex spectrum, in which a constant phase function is substituted for the measured one, the time (or time-frequency) distribution shows a peak at (exactly) zero delay and longlatency specular symmetric components, with a modified (positive and negative) delay, which is that relative to that of the distortion component in the original response. Component separation, applied to this symmetrized distribution, becomes insensitive to systematic errors associated with violation of the scaling symmetry in specific frequency ranges. [ABSTRACT FROM AUTHOR]

The issue of the relation between the tuning factor, the active gain, and the phase slope of the basilar membrane excitation is addressed. Different 1d-transmission line cochlear models are studied and compared. The active linear models are exactly solved in frequency domain whilst a fully nonlinear model is solved in time domain. An evident dependence of the phase slope on tuning is found in the linear models both in the passive and in the active cases. This dependence is much weaker for the nonlinear model solved in the time domain. This finding suggests that nonlinear behavior near the resonant place could play an important role in explaining the relation between tuning and phase gradient. The otoacoustic emissions generated by a linear backscattering mechanism, TEOAEs and SFOAEs, have also been studied. For a given roughness pattern, for all models, the OAE response was found to consist of a small set of place-fixed emission spots. As tuning increases, the latency of each spot is constant, whereas the relative intensity of the longest latency spots gradually increases. [ABSTRACT FROM AUTHOR]

The issue of the relation between the tuning factor, the active gain, and the phase slope of the basilar membrane excitation is addressed. Different 1d-transmission line cochlear models are studied and compared. The active linear models are exactly solved in frequency domain whilst a fully nonlinear model is solved in time domain. An evident dependence of the phase slope on tuning is found in the linear models both in the passive and in the active cases. This dependence is much weaker for the nonlinear model solved in the time domain. This finding suggests that nonlinear behavior near the resonant place could play an important role in explaining the relation between tuning and phase gradient. The otoacoustic emissions generated by a linear backscattering mechanism, TEOAEs and SFOAEs, have also been studied. For a given roughness pattern, for all models, the OAE response was found to consist of a small set of place-fixed emission spots. As tuning increases, the latency of each spot is constant, whereas the relative intensity of the longest latency spots gradually increases. [ABSTRACT FROM AUTHOR]

Two hydrodynamic effects are introduced in the standard transmission-line formalism, the focusing of the pressure and fluid velocity fields near the basilar membrane and the viscous damping at the fluid-basilar membrane interface, which significantly affect the cochlear response in the short-wave region. In this region, in which the wavelength is shorter than the cochlear duct height, only a layer of fluid of order of the wavelength is effectively involved in the traveling wave. This has been interpreted [8] as a reduced fluid contribution to the system inertia in the peak region, which is a viewpoint common to the 3-D FEM solutions. In this paper we propose an alternative approach, from a slightly different physical viewpoint. Invoking the fluid flux conservation along the traveling wave propagation direction, we can derive a rigorous propagation equation for the pressure integrated along the vertical axis. Consequently, the relation between the average pressure and the local pressure [4] at the fluid-BM interface can be written. The local pressure is amplified by a factor dependent on the local wavenumber with respect to the average pressure, a phenomenon we refer to as "fluid focusing", which plays a relevant role in the BM total amplification gain. This interpretation of the hydrodynamic boost to the pressure provides a physical justification to the strategy [10] of fitting the BM admittance with a polynomial containing both a conjugated pole and a zero. In the short-wave region, the sharp gradients of the velocity field yield a second important effect, a damping force on the BM motion, proportional to the local wavenumber, which stabilizes active models and shifts the peak of the response towards the base, with respect to the resonant place. This way, the peaked BM response is not that of a proper resonance, corresponding to a sharp maximum of the admittance, but rather a focusing-driven growth toward the resonant place, which is "aborted" before reaching it by the sharply increasing viscous losses. The large values of the wavenumber that ensure strong focusing are ultimately fueled, against viscosity, by the nonlinear OHC mechanism, hence the otherwise puzzling observation of a wide nonlinear gain dynamics with almost level-independent admittance. [ABSTRACT FROM AUTHOR]

Two different mechanisms are responsible for the DPOAE generation. The nonlinear distortion wave-fixed mechanism generates the DPOAE Zero-Latency (ZL) component, as a backward traveling wave from the "overlap" region. Linear reflection of the forward DP wave (IDP) generates the DPOAE Long-Latency (LL) component through a place-fixed mechanism. ZL and LL components add up vectorially to generate the DPOAE recorded in the ear canal. The 2 f1- f2 and 2f2- f1 DPOAE intensity depends on the stimulus level and on the primary frequency ratio r = f2/ f1, where f1 and f2 are the primary stimuli frequencies. Here we study the behavior of the ZL and LL DPOAE components as a function of r by both numerical and laboratory experiments, measuring DPAOEs with an equal primary levels (L1 = L2) paradigm in the range [35, 75] dB SPL, with r ranging in [1.1, 1.45]. Numerical simulations of a nonlocal nonlinear model have been performed without cochlear roughness, to suppress the linear reflection mechanism. In this way the model solution at the base represents the DPOAE ZL component, and the solution at the corresponding DPOAE tonotopic place corresponds to the IDP. This technique has been not effectual to study the 2f2-f1 DPOAE, as a consequence of its generation mechanism. While the 2f2-f1 generation place is known to be the tonotopic place x(f2), the 2f2-f1 DPOAE one has to be assumed basal to its corresponding reflection place. That is because ZL components generated in x(f2) cannot significantly pass through their resonant place. Moreover increasing the ratio r, 2f2-f1 ZL and LL generation place approach each other, because the overlap region of primary tones decreases. Consequently, the distinction between the two places becomes complicated. DPOAEs have been measured in six young normal-hearing subjects. DPOAE ZL and LL components have been separated by a time-frequency filtering method based on the wavelet transform [1] due to their different phase gradient delay. Amplitude/phase vs ratio and ratio-frequency maps have been analyzed both in numerical and laboratory data. As already observed in animal studies [4], the generation of 2f2-f1 DPOAE is around the f2 tonotopic place with a maximum around r = 1.2 for the ZL component, while the LL component shows a decreasing trend with r. Instead, 2 f2 - f1 DPOAEs show a decreasing trend with r for both ZL and LL components. [ABSTRACT FROM AUTHOR]

Two different mechanisms are responsible for the DPOAE generation. The nonlinear distortion wave-fixed mechanism generates the DPOAE Zero-Latency (ZL) component, as a backward traveling wave from the "overlap" region. Linear reflection of the forward DP wave (IDP) generates the DPOAE Long-Latency (LL) component through a place-fixed mechanism. ZL and LL components add up vectorially to generate the DPOAE recorded in the ear canal. The 2 f1- f2 and 2 f2- f1 DPOAE intensity depends on the stimulus level and on the primary frequency ratio r = f2/ f1, where f1 and f2 are the primary stimuli frequencies. Here we study the behavior of the ZL and LL DPOAE components as a function of r by both numerical and laboratory experiments, measuring DPAOEs with an equal primary levels (L1 = L2) paradigm in the range [35, 75] dB SPL, with r ranging in [1.1, 1.45]. Numerical simulations of a nonlocal nonlinear model have been performed without cochlear roughness, to suppress the linear reflection mechanism. In this way the model solution at the base represents the DPOAE ZL component, and the solution at the corresponding DPOAE tonotopic place corresponds to the IDP. This technique has been not effectual to study the 2 f2 - f1 DPOAE, as a consequence of its generation mechanism. While the 2 f1 - f2 generation place is known to be the tonotopic place x(f2), the 2 f2 - f1 DPOAE one has to be assumed basal to its corresponding reflection place. That is because ZL components generated in x(f2) cannot significantly pass through their resonant place. Moreover increasing the ratio r, 2f2 - f1 ZL and LL generation place approach each other, because the overlap region of primary tones decreases. Consequently, the distinction between the two places becomes complicated. DPOAEs have been measured in six young normal-hearing subjects. DPOAE ZL and LL components have been separated by a time-frequency filtering method based on the wavelet transform [1] due to their different phase gradient delay. Amplitude/phase vs ratio and ratio-frequency maps have been analyzed both in numerical and laboratory data. As already observed in animal studies [4], the generation of 2 f1 - f2 DPOAE is around the f2 tonotopic place with a maximum around r = 1.2 for the ZL component, while the LL component shows a decreasing trend with r. Instead, 2 f2 - f1 DPOAEs show a decreasing trend with r for both ZL and LL components. [ABSTRACT FROM AUTHOR]

Recent basilar-membrane (BM) vibration experiments show that the phase slope of the distortion product (DP) in the cochlear region in which a backward-traveling wave is expected is negative, which is typical of a forward-traveling wave, according to the predictions of quasi-linear approximate solutions of classical 1-D transmission-line cochlear models. This phase behavior has been interpreted as suggesting a strong deviation from the 'classical' models of the otoacoustic emission (OAE) generation and transmission. In this paper, the DP phase inversion phenomenon is approached from a conservative point of view. The DP phase is calculated in a classical cochlear model. The main conclusion is that deviations from the classical model are not necessary to account for the observed phase behavior. [ABSTRACT FROM AUTHOR]

Otoacoustic emissions are numerically simulated from a nonlinear nonlocal cochlear model solved in time domain by means of the space-state matrix technique. The feedback mechanism localized in the outer hair cells system is modeled as a nonlinear active force proportional to the total pressure acting on the basilar membrane or as an anti-damping nonlinear term proportional to the velocity of the membrane itself. The model seems to be a very good tool for simulating cochlear dynamics in different regimes of the cochlear parameters and in particular when strong nonlinearities are put into the model. [ABSTRACT FROM AUTHOR]

The 2f1-f2 distortion product otoacoustic emission (DPOAE) response, measured as a function of the primary frequency ratio r shows a bell-shaped curve, which depends, in principle, on the interplay among three factors: the dependence on r of the overlap between the basilar membrane (BM) responses to the primary tones, linear interference between the wavelets coming from spatially distributed sources, and nonlinear suppression phenomena. This issue has been investigated using a numerical nonlinear cochlear model, and an analytical linear cochlear model in which DPOAEs were generated as nonlinear perturbations, to assess the reliability of a method for estimating cochlear tuning from the width of the experimental DPOAE level vs. ratio function. A fixed-f2 acquisition paradigm was used, varying r continuously in the range 1-1.5, for two f2 values (1250 and 5000 Hz). The resulting experimental "spectra" have been time-frequency analyzed to select the distortion component, and compared with the models' simulations. The experimental results are well matched by both models, suggesting that the main features of the DPOAE vs. ratio curve are quite independent of nonlinear suppression phenomena. From the same model simulations, the basilar membrane BM tuning can be directly estimated. A strong linear correlation was found in the model between the width of the BM response and that of the DPOAE level vs. ratio relation, supporting the reliability of estimates of cochlear tuning obtained from the evaluation of the DP versus ratio experimental curves. [ABSTRACT FROM AUTHOR]

Stimulus-frequency otoacoustic emissions (SFOAEs) were measured in wild-type and TectaC1509/+ mice from 8-13 kHz via the two-tone suppression method. TectaC1509/+ mice have shorter SFOAE delays (0.1 ms) than wild-type (0.5 ms), suggesting broader mechanical tuning. [ABSTRACT FROM AUTHOR]