Fitting pole-zero micromechanical models to cochlear response measurements

Fast time-domain solution of a nonlinear three-dimensional cochlear model using the fast Fourier transform

A fast numerical time-domain solution of a nonlinear three-dimensional (3D) cochlear model is proposed. In dynamical systems, a time-domain solution can determine nonlinear responses, and the human faculty of hearing depends on nonlinear behaviors of the microscopically structured organs of the cochlea. Thus, time-domain 3D modeling can help explain hearing. The matrix product, an n² operation, is a central part of the time-domain solution procedure in cochlear models. To solve the cochlear model faster, the fast Fourier transform (FFT), an n log n operation, is used to replace the matrix product. Numerical simulation results verified the similarity of the matrix product and the FFT under coarse grid settings. Furthermore, applying the FFT reduced the computation time by a factor of up to 100 owing to the computational complexity of the proposed approach being reduced from n² to n log n. Additionally, the proposed method successfully computed 3D models under moderate and fine grid settings that were unsolvable using the matrix product. The 3D cochlear model exhibited nonlinear responses for pure tones and clicks under various gain distributions in a time-domain simulation. Thus, the FFT-based method provides fast numerical solutions and supports the development of 3D models for cochlear mechanics.

Low-passed outer hair cell response and apical-basal transition in a nonlinear transmission-line cochlear model

The low-pass characteristic of the outer hair cell (OHC) voltage response to mechanical stimulation could be considered a serious problem for cochlear models aiming at explaining high-frequency active amplification by introducing instantaneous nonlinear terms because active gain would dramatically decrease at high frequency. Evidence from experimental studies by Nam and Fettiplace [(2012). PloS One 7, e50572] suggests that the local cutoff frequency significantly increases approaching the cochlear base, somehow mitigating this problem. In this study, low-pass filtering of an internal force term, derived from a physiologically plausible OHC schematization by Lu, Zhak, Dallos, and Sarpeshkar [(2006). Hear. Res. 214, 45-67] is included in a simple one-dimensional (1-D) two-degrees-of-freedom transmission-line model by Sisto, Shera, Altoè, and Moleti [(2019). J. Acoust. Soc. Am. 146, 1685-1695] The frequency dependence of the low-pass filter phase-shift naturally yields a transition from sharp tuning and wide dynamical gain range in the basal cochlea to low tuning and poor dynamical range in the apical region. On the other hand, the frequency-dependent attenuation of low-pass filtering makes it more difficult to obtain the high gain (40-50 dB) of the basal basilar membrane response that is experimentally measured in mammals at low stimulus levels. Pressure focusing in the short-wave resonant region, which is not accounted for in this 1-D model, may help in acquiring the additional gain necessary to match the experimental data.

Pole-Zero REM Modeling with Application in EEG Artifact Removal

A new approach of pole-zero modeling in the presence of white noise is proposed. While the model estimate is calculated through the conventional least square estimation, the choice of number of poles and zeros in this scenario is critical and a challenging task. A wrong choice can overfit the additive noise in larger orders or underfit and discard parts of the noiseless data in smaller orders. To overcome this issue, we choose the order through RE Minimization (REM). RE is the error between the observed noisy data and the unavailable noiseless output. Using the available output error, the method provides a probabilistic worst case upperbound for RE and optimizes it. Simulation results on generated synthetic data show advantages of REM compared to existing order selection methods such as AIC and BIC. The results show that the proposed method avoids over or under parametrizing of AIC and BIC. The results in a practical application of EOG artifacts removal of eye blinks from EEG data provides an efficient modeling of the true background EEG with optimal eye blink removal.

Does the "Reticular Lamina Nonlinearity" Contribute to the Basal DPOAE Source?

The spatial extent of the cochlear region that actually contributes to the DPOAE signal measured in the ear canal may be evaluated experimentally using interference tones or computed numerically using nonlinear cochlear models. A nonlinear transmission-line cochlear model is used in this study to evaluate whether the recently reported nonlinear behavior of the reticular lamina (RL) over a wide basal region may be associated with generation of a significant distortion product otoacoustic emission (DPOAE) component. A two-degrees-of-freedom 1-D nonlinear model was used as discussed by Sisto et al. (2019), in which each local element consists of two coupled oscillators, roughly representing the basilar membrane (BM) and the RL. In this model, the RL shows a strongly nonlinear response over a wide region basal to the characteristic place, whereas the BM response is linear outside the narrow peak region. Such a model may be considered as that using the minimal number of degrees of freedom necessary to separately predict the motion of the BM and RL, while preserving important cochlear symmetries, such as the zero-crossing invariance of the impulse response. In the numerical simulations, the RL nonlinearity generates indeed a large intracochlear distortion product source, extended down to very basal cochlear regions. Nevertheless, due to the weak and indirect coupling between the RL motion and the differential fluid pressure in the basal part of the traveling wave path, no significant contribution from this mechanism is predicted by the model to the generation of the DPOAE signal that is eventually measured in the ear canal.

Suppression tuning curves in a two-degrees-of-freedom nonlinear cochlear model

A two-degrees-of-freedom nonlinear cochlear model [Sisto, Shera, Altoè, and Moleti (2019). J. Acoust. Soc. Am. 146, 1685-1695] correctly predicts that the reticular lamina response is nonlinear over a wide basal region. Numerical simulations of suppression tuning curves agree with a recent experiment [Dewey, Applegate, and Oghalai (2019). J. Neurosci. 39, 1805-1816], supporting the idea that the strong susceptibility of the reticular lamina response to suppression by high-frequency tones does not imply that the total traveling wave energy builds-up in correspondingly basal regions. This happens because the reticular lamina is the lightest element of a coupled-oscillators system, only indirectly coupled to the differential pressure.

Nonlinear cochlear mechanics without direct vibration-amplification feedback

Recent in vivo recordings from the mammalian cochlea indicate that although the motion of the basilar membrane appears actively amplified and nonlinear only at frequencies relatively close to the peak of the response, the internal motions of the organ of Corti display these same features over a much wider range of frequencies. These experimental findings are not easily explained by the textbook view of cochlear mechanics, in which cochlear amplification is controlled by the motion of the basilar membrane (BM) in a tight, closed-loop feedback configuration. This study shows that a simple phenomenological model of the cochlea inspired by the work of Zweig [J. Acoust. Soc. Am. 138, 1102 (2015)] can account for recent data in mouse and gerbil. In this model, the active forces are regulated indirectly, through the effect of BM motion on the pressure field across the cochlear partition, rather than via direct coupling between active-force generation and BM vibration. The absence of strong vibration-amplification feedback in the cochlea also provides a compelling explanation for the observed intensity invariance of fine time structure in the BM response to acoustic clicks.

Constraints imposed by zero-crossing invariance on cochlear models with two mechanical degrees of freedom

The zero crossings of basilar-membrane (BM) responses to clicks are nearly independent of stimulus intensity. This work explores the constraints that this invariance imposes on one-dimensional nonlinear cochlear models with two degrees of freedom (2DoF). The locations of the poles and zeros of the BM admittance, calculated for a set of linear models in which the strength of the active force is progressively decreased, provides a playground for evaluating the behavior of a corresponding nonlinear model at increasing stimulus levels. Mathematical constraints on the model parameters are derived by requiring that the poles of the admittance move horizontally in the s-plane as the active force is varied. These constraints ensure approximate zero-crossing invariance over a wide stimulus level range in a nonlinear model in which the active force varies as a function of the local instantaneous BM displacement and velocity. Two different 2DoF models are explored, each capable of reproducing the main qualitative characteristics of the BM response to tones (i.e., the tall and broad activity pattern at low stimulus levels, the large gain dynamics, and the partial decoupling between gain and phase). In each model, the motions of the two masses are compared with response data from animal experiments.

Cochlear impulse responses resolved into sets of gammatones: the case for beating of closely spaced local resonances

Gammatones have had a long history in auditory studies, and recent theoretical work suggests they may play an important role in cochlear mechanics as well. Following this lead, the present paper takes five examples of basilar membrane impulse responses and uses a curve-fitting algorithm to decompose them into a number of discrete gammatones. The limits of this ‘sum of gammatones’ (SOG) method to accurately represent the impulse response waveforms were tested and it was found that at least two and up to six gammatones could be isolated from each example. Their frequencies were stable and largely independent of stimulus parameters. The gammatones typically formed a regular series in which the frequency ratio between successive members was about 1.1. Adding together the first few gammatones in a set produced beating-like waveforms which mimicked waxing and waning, and the instantaneous frequencies of the waveforms were also well reproduced, providing an explanation for frequency glides. Consideration was also given to the impulse response of a pair of elastically coupled masses—the basis of two-degree-of-freedom models comprised of coupled basilar and tectorial membranes—and the resulting waveform was similar to a pair of beating gammatones, perhaps explaining why the SOG method seems to work well in describing cochlear impulse responses. A major limitation of the SOG method is that it cannot distinguish a waveform resulting from an actual physical resonance from one derived from overfitting, but taken together the method points to the presence of a series of closely spaced local resonances in the cochlea.