Active Cochlear Model Research Articles

The Shape of Noise to Come: Signal vs. Noise Amplification in the Active Cochlea.

According to the dominant view, the mammalian cochlea spatially amplifies signals by actively pumping energy into the traveling wave. That is, signals are amplified as they propagate through a region where the medium's resistance is effectively negative. While signal amplification has been extensively studied in active cochlear models, the same cannot be said for amplification of internal noise. According to transmission-line theory, signals are amplified more than internal noise in regions where the net resistance is negative. Here we generalize this finding by showing that a distributed system composed of cascaded "noisy" amplifiers boosts signals more rapidly than the internal noise; the larger the amplifier gain, the larger the signal-to-noise ratio (SNR) of the amplified signal. We further show that this mechanism operates in existing active cochlear models: the cochlear amplifier increases the SNR of cochlear responses, and thus enhances cochlear sensitivity. When considering also that the cochlear amplifier narrows the bandwidth of the "cochlear filters", activation of the cochlear amplifiers dramatically increases the SNR (by about one order of magnitude in our simulations) from the tail to the peak of the traveling wave. We further demonstrate that the tapered ear-horn-like cochlear geometry significantly improves the SNR of basilar-membrane responses.

Bio-Inspired Radio-Frequency Source Localization Based on Cochlear Cross-Correlograms.

This paper describes a bio-inspired radio frequency (RF) scene analysis system based on cross-correlating the outputs of two single-chip RF spectrum analyzers. The latter are implemented using digitally-programmable “RF cochlea” chips (in 65 nm CMOS) that integrate a transmission-line active cochlear model, consisting of 50 parallel exponentially-spaced stages for analyzing the radio spectrum from 1.0 to 8.3 GHz, together with an output encoding network. The encoders convert the analog outputs of all cochlear stages into parallel delta-sigma (Δ-Σ) modulated digital signals for real-time demodulation and analysis by a digital back-end processor. These outputs can also be multiplied with each other to generate cochlear correlation matrices (known as cross-correlograms). Simulation results demonstrate the use of cross-correlograms for wide-range time-delay estimation and real-time multi-source localization at different frequencies and input signal-to-noise (SNR) ratios. Over-the-air measurement results from an experimental two-channel RF scene analysis prototype confirm the use of such time-delay estimates, which are analogous to interaural time differences (ITDs) in the auditory system, for azimuthal source localization at 3.4 GHz. In addition, differences in received signal strength at the two cochleas, which are analogous to interaural level differences (ILD) in biology, are also used to localize RF sources.

A 1.0-8.3 GHz Cochlea-Based Real-Time Spectrum Analyzer With Δ-Σ-Modulated Digital Outputs

The biological inner ear, or cochlea, is a sophisticated signal processing system that performs spectrum analysis over an ultra-broadband frequency range of ~20 Hz to 20 kHz with exquisite sensitivity and high energy efficiency. Electronic cochlear models, which mimic the exponentially-tapered structure of the biological inner ear using bidirectional transmission lines or filter cascades, act as fast and hardware-efficient spectrum analyzers at both audio and radio frequencies. This paper describes a cochlea-based digitally-programmable single-chip radio frequency (RF) spectrum analyzer in 65 nm CMOS. This “RF cochlea” chip includes a transmission-line active cochlear model with 50 parallel exponentially-spaced stages that analyzes the radio spectrum from 1.0-8.3 GHz. The outputs of all stages are encoded in parallel as delta-sigma ( $\Delta - \Sigma $ ) modulated digital signals for real-time demodulation and analysis by a digital back-end processor. The chip consumes 418 mW and typically generates ~1 GS/s of total data at an ENOB of 5–6 bits. An artificial intelligence (AI)-driven single-channel cognitive radio (CR) receiver based on the RF cochlea has also been implemented and tested.

Evidence for apical-basal transition in the delay of the reflection components of otoacoustic emissions.

Stimulus-frequency, transient-evoked, and distortion product otoacoustic emissions (OAEs) have been measured in eight normal-hearing human ears over a wide stimulus level range, with high spectral resolution. The single-reflection component of the response was isolated using time-frequency filtering, and its average delay was measured as a function of frequency and stimulus level. The apical-basal transition was studied by fitting the average delay of the filtered single-reflection OAEs, expressed in number of cycles, to a three-slope power-law function with two knot frequencies. The results show that the scale-invariant prediction of constant dimensionless delay approximately holds only over a narrow intermediate frequency range (1-2.5 kHz). Below 1 kHz, and, to some extent, above 2.5 kHz, the dimensionless delay increases with frequency, at all stimulus levels. Comparison with the numerical simulations of a delayed-stiffness active cochlear model show that the increase of tuning with frequency reported by behavioral experiments only partly explains this result. The low-frequency scaling symmetry breaking associated with the deviation of the Greenwood tonotopic map from a pure exponential function is also insufficient to explain the steep low-frequency increase of the OAE delay. Other sources of symmetry breaking, not included in the model, could therefore play a role.

Localization of the Reflection Sources of Stimulus-Frequency Otoacoustic Emissions.

The generation of stimulus-frequency otoacoustic emission (SFOAE) residuals in humans is analyzed both theoretically and experimentally to investigate the relation between the frequency difference between the probe and the suppressor tone and the localization of the residual source. Experimental measurements of the SFOAE residual were performed using suppressors of increasing frequency to separate the otoacoustic response from the probe stimulus. From the response to the probe alone, the SFOAE response was also estimated, using spectral smoothing, and compared with the residuals obtained for different frequency suppressors. A nonlinear delayed-stiffness active cochlear model was used to compute the spatial distribution of the residual sources according to a recent model of the local reflectivity from roughness, as a function of the suppressor frequency. The simulations clarified the role of high-frequency suppressors, showing that in humans, with increasing suppressor frequency, the generation region of the residual is only slightly basally shifted with respect to the case of a near-frequency suppressor, near the basal edge of the peak of the resonant basilar membrane response. As a consequence, the hierarchy among different-delay components correspondingly changes, gradually favoring short-delay components, with increasing suppressor frequency. Good agreement between the experimental and theoretical dependence of the level of otoacoustic components of different delay on the frequency shift between probe and suppressor confirms the validity of this interpretation.

Application of the WKB method for an active cochlear model

The Wentzel-Kramers-Brillouin (WKB) method has been used to approximate the solution for systems with slowly varying properties. The analytic method is computationally efficient and provides insights into the physical problem by decomposing the solution into a dominant wavenumber and the associated amplitude [e.g., Steele and Taber (1978)]. Because of its computational efficiency, this method provides a convenient means to estimate parameters in a complicated cochlear model, through variation and optimization. In turn, these parameters can be used in a more complete approximation technique (like a finite element or boundary element method) where parameter estimation can be more cumbersome. In this paper, we extend the WKB approximation to an active cochlear model, including the micromechanics of the organ of Corti (OoC) and electromotility. The model involves the OoC structural elements, basilar membrane (BM), and tectorial membrane (TM), coupled to the electrical potentials in the cochlear ducts and fluid pressure. Model predictions are compared to numerical approximations using finite elements. [Work supported by NIH-NIDCD R01-04084 and NIH NIDCD-T32-000011.]

A Hopf Resonator for 2-D Artificial Cochlea: Piecewise Linear Model and Digital Implementation

The mammalian auditory system is able to process sounds over an extraordinarily large dynamic range, which makes it possible to extract information from very small changes both in sound amplitude and frequency. Evidently, response of the cochlea is essentially nonlinear, where it operates within Hopf bifurcation boundaries to maximize tuning and amplification. This paper presents a set of piecewise linear (PWL) and multiplierless piecewise linear (MLPWL1 and MLPWL2) active cochlear models, which mimic a range of behaviors, similar to the biological cochlea. These proposed models show similar dynamical characteristics of the Hopf equation for the active nonlinear artificial cochlea. Accordingly, a compact model structure is proposed upon which a 2-D cochlea is developed. The proposed models are investigated, in terms of their digital realization and hardware cost, targeting large scale implementation. Hardware synthesis and physical implementation on a FPGA show that the proposed models can reproduce precise active cochlea behaviors with higher performance and considerably lower computational costs in comparison with the original model. Results indicate that the MLPWL1 model has a lower computational overhead, precision, and hardware cost, while the PWL model has a higher precision and dynamically tracks the original model. On the other hand, the MLPWL2 model outperforms the others in terms of accuracy, dynamical tracking of the original model and implementation cost. The gain variations of the original, PWL, MLPWL1, and MLPWL2 models are 230, 100, 105, and 230 dB, respectively. The mean normalized root mean square errors (NRMSEs) of the PWL, MLPWL1, and MLPWL2 models are 0.11%, 11.97%, and 0.34%, respectively, as compared to the original cochlear model.

Generation place of the long- and short-latency components of transient-evoked otoacoustic emissions in a nonlinear cochlear model

Time-domain numerical solutions of a nonlinear active cochlear model forced by click stimuli are analyzed with a time-frequency wavelet technique to identify the components of the otoacoustic response associated with different generation mechanisms/places. Previous experimental studies have shown evidence for the presence of at least two components in the transient otoacoustic response: A long-latency response, growing compressively with increasing stimulus level, and a shorter-latency response, characterized by faster growth. The possible mechanisms for the generation of the two components are discussed using the results of the numerical simulations. The model is a one-dimensional (1-D) transmission line model with nonlinear and nonlocal active terms representing the anti-damping action of the "cochlear amplifier." The dependence on the stimulus level of latency and level was measured for the different components of the response. The generation mechanisms/places of the different components were identified by varying the stimulus level and by turning off the cochlear roughness in well-defined cochlear regions. The results suggest that reflections from roughness coming from basal regions of the cochlea may give a relevant contribution to the early otoacoustic response, whereas nonlinear mechanisms seem to produce a much smaller additional contribution.

Wave finite element analysis of an active cochlear model

The wave finite element method has previously been used to understand the various types of wave in a passive cochlear model. In this paper, the model is extended to give an initial representation of an active cochlea by making the real and imaginary components of the Young’s modulus, that defines the local dynamics of the plates representing the basilar membrane, position and frequency dependent. At a given excitation frequency, the distribution of the Young’s modulus is chosen so that the mechanical impedance of the plate elements correspond to that obtained from a lumped parameter model of the active cochlea. The types of wave predicted in this representation of the active cochlea are similar to those observed for the passive cochlea model and consist of a fast wave, a slow wave and a large number of higher-order fluid modes, which are evanescent. Although the results of the full finite element analysis for this active model are very different from the passive one, the decomposition into wave components still shows that the slow wave dominates the response along most of the cochlear length, until the response peaks, when a number of higher-order fluid modes are locally excited.

Basilar-membrane interference patterns from multiple internal reflection of cochlear traveling waves

At low stimulus levels, basilar-membrane (BM) mechanical transfer functions in sensitive cochleae manifest a quasiperiodic rippling pattern in both amplitude and phase. Analysis of the responses of active cochlear models suggests that the rippling is a mechanical interference pattern created by multiple internal reflection within the cochlea. In models, the interference arises when reverse-traveling waves responsible for stimulus-frequency otoacoustic emissions (SFOAEs) reflect off the stapes on their way to the ear canal, launching a secondary forward-traveling wave that combines with the primary wave produced by the stimulus. Frequency-dependent phase differences between the two waves then create the rippling pattern measurable on the BM. Measurements of BM ripples and SFOAEs in individual chinchilla ears demonstrate that the ripples are strongly correlated with the acoustic interference pattern measured in ear-canal pressure, consistent with a common origin involving the generation of SFOAEs. In BM responses to clicks, the ripples appear as temporal fine structure in the response envelope (multiple lobes, waxing and waning). Analysis of the ripple spacing and response phase gradients provides a test for the role of fast- and slow-wave modes of reverse energy propagation within the cochlea. The data indicate that SFOAE delays are consistent with reverse slow-wave propagation but much too long to be explained by fast waves.

Intracochlear fluid pressure and cochlear input impedance from push-pull amplification model

Intracochlear fluid pressure and cochlear input impedance are simulated and compared with in-vivo physiological measurements. The objective of this work is to compare the calculations and measurements for the cochlear fluid pressure (PST) and related cochlear input impedance (ZC) with “push-pull” active cochlear model involving cochlear cytoarchitecture. Presented three-dimensional cochlear hydro-dynamic model is developed by implementing an active “push-pull” cochlear amplifier mechanism based on Y-shaped organ of Corti cytoarchitecture and using the time-averaged Lagrangian method. For the gerbil PST magnitude, the model results shows (i) the nonlinearity with 10 dB gain, (ii) the 2/3 octave shift in the active case, and (iii) the presence of peaks and valleys which are observed in gerbil in vivo measurement. Additionally, simulation results of chinchilla and cat cochlear |ZC| reflect overall trend of animal measurements, while the gerbil and human cochlear |ZC| are 10 dB lower (> 2 kHz) and 7 dB lower (< 2 kHz) than the measurements respectively.

Biophysical Cochlear Model: Time-Frequency Analysis and Signal Reconstruction

The cochlea transforms incoming sound pressure into vibrations of the basilar membrane which give rise to neural impulses. Although it has been an object of research for several decades, complete understanding of its behavior is far from complete. Many experiments on real cochlea and many mathematical models have been developed in the past decades. In the biophysical cochlear model of Mammano and Nobili [1, 2], both mechanical and hydrodynamical aspects are treated at a level adequate to the complexity of realistic cochlear structures. In this paper, we analyze the time-frequency resolution of this biophysical cochlear model: analysis is first applied to the passive cochlear model and then extended to the active nonlinear model. Further, we propose the method for signal reconstruction from the cochlear time-frequency response. When applied to active cochlear model response, it could result with the signal which human ear actually hears (with some spectral enhancements and noise suppression).

Stimulus-frequency otoacoustic emission: Measurements in humans and simulations with an active cochlear model

An efficient method for measuring stimulus-frequency otoacoustic emissions (SFOAEs) was developed incorporating (1) stimulus with swept frequency or level and (2) the digital heterodyne analysis. SFOAEs were measured for 550-1450 Hz and stimulus levels of 32-62 dB sound pressure level in eight normal human adults. The mean level, number of peaks, frequency spacing between peaks, phase change, and energy-weighted group delays of SFOAEs were determined. Salient features of the human SFOAEs were stimulated with an active cochlear model containing spatially low-pass filtered irregularity in the impedance. An objective fitting procedure yielded an optimal set of model parameters where, with decreasing stimulus level, the amount of cochlear amplification and the base amplitude of the irregularity increased while the spatial low-pass cutoff and the slope of the spatial low-pass filter decreased. The characteristics of the human cochlea were inferred with the model. In the model, an SFOAE consisted of a long-delay component originating from irregularity in a traveling-wave peak region and a short-delay component originating from irregularity in regions remote from the peak. The results of this study should be useful both for understanding cochlear function and for developing a clinical method of assessing cochlear status.

A model of cochlear macro-, micro-, and nano-mechanics

Problem: Although previous cochlear models have been developed considering outer hair cell (OHC) electromotility as the cochlear amplifier, most do not consider several unique nanoscale biomechanical properties of the OHC. These include its orthotropic cytoskeleton, its intracellular turgor pressure, and the longitudinal and radial vectors related to force generation. This model was designed to incorporate these considerations. Methods: Cochlear macro-mechanics were modeled using a traditional one-dimensional transmission line model. Cochlear micro-mechanics were modeled using terms for basilar membrane, tectorial membrane, and hair cell stereocilia mass, stiffness, and damping. To model electromotility, the OHC receptor potential was first estimated using a linear approximation of mechanoelectrical transduction. Then, force generation was derived using parameters for various nanoscale mechanical properties of the OHC. These include the elastic moduli of the orthotropic OHC lateral wall, active length and radius changes, and cell turgor pressure. These parameters were obtained from published in vitro data. Results: Results from our active cochlear model showed that BM velocity increased up to 55 dB compared to a passive cochlear model. Normal-appearing sharp tuning curves can be accurately modeled. Conclusion: Future in vivo experiments are planned to test this cochlear model by modulating the biophysical properties of OHCs while measuring BM velocity in the guinea pig. Significance: This model improves our ability to accurately understand movements of the basilar membrane, tectorial membrane, stereocilia, and OHC electromotility. It can next be extended for use in modeling pathologic cochlear states, such as noise trauma, endolymphatic hydrops, or cochlear implantation. Support: None reported.

Response suppression and transient behavior in a nonlinear active cochlear model with feed-forward

A nonlinear active cochlear model is used to simulate the steady-state frequency response and transient response to clicks of the basilar membrane. The model includes the three-dimensional viscous fluid effects, an orthotropic cochlear partition with dimensional and material property variation along its length, and a nonlinear active feed-forward mechanism to represent the activity of the outer hair cells. A hybrid asymptotic and numerical method is used to provide a fast and efficient iterative procedure for modeling and simulation of the nonlinear responses in the active cochlea. The simulation results exhibit some of the characteristic nonlinear behavior of the basilar membrane commonly observed in experimental measurements, such as significant amplification and sustained “ringing” in the transient response at low stimulus level. The simple feed-forward mechanism is able to capture the properties of the noncausal active process in the cochlea without a second filter or resonance.

A three-dimensional nonlinear active cochlear model analyzed by the WKB-numeric method

A physiologically based nonlinear active cochlear model is presented. The model includes the three-dimensional viscous fluid effects, an orthotropic cochlear partition with dimensional and material property variation along its length, and a nonlinear active feed-forward mechanism of the organ of Corti. A hybrid asymptotic and numerical method combined with Fourier series expansions is used to provide a fast and efficient iterative procedure for modeling and simulation of the nonlinear responses in the active cochlea. The simulation results for the chinchilla cochlea compare very well with experimental measurements, capturing several nonlinear features observed in basilar membrane responses. These include compression of response with stimulus level, two-tone suppressions, and generation of harmonic distortion and distortion products.

Compression, gain, and nonlinear distortion in an active cochlear model with subpartitions.

The propagation of inhomogeneous, weakly nonlinear waves is considered in a cochlear model having two degrees of freedom that represent the transverse motions of the tectorial and basilar membranes within the organ of Corti. It is assumed that nonlinearity arises from the saturation of outer hair cell active force generation. I use multiple scale asymptotics and treat nonlinearity as a correction to a linear hydroelastic wave. The resulting theory is used to explain experimentally observed features of the response of the cochlear partition to a pure tone, including: the amplification of the response in a healthy cochlea vs a dead one; the less than linear growth rate of the response to increasing sound pressure level; and the amount of distortion to be expected at high and low frequencies at basal and apical locations, respectively. I also show that the outer hair cell nonlinearity generates retrograde waves.

Studies of the relationships between ear canal and cochlear signals for external tones and spontaneous and distortion product otoacoustic emissions, and their connection with middle ear transmission

Some knowledge about the transmission characteristics of the human middle ear may be obtained by comparing ear canal levels of external tones and spontaneous emissions of the same frequency, which when used with another tone give similar ear canal levels of distortion product otoacoustic emissions. It is assumed that the cochlear activity patterns of an external tone of frequency f2 and a spontaneous emission of frequency f2, which produce the same levels of ear canal cubic distortion products when used in conjunction with an external tone of frequency f1 and fixed level, are very similar. The degree of similarity is studied using nonlinear active cochlear models that give spontaneous emissions [Talmadge and Tubis (1993)]. The relationship of the cochlear activities at the place of peak excitation and at the base of the cochlea is also studied in detail. The model results indicate that the comparison of ear canal levels of external tones and spontaneous emissions, which are equivalent with respect to the production of distortion product emissions, may be used to give estimates of the reflection and transmission of cochlear waves at the stapes. [Work supported by the Deafness Research Foundation.]

An active cochlear model showing sharp tuning and high sensitivity.

Recent in vivo measurements of cochlear-partition motion indicate very high sensitivity and sharp mechanical tuning similar to the tuning of single cochlear nerve fibers. Our experience with mathematical models of the cochlea leads us to believe that this type of mechanical response requires the presence of active elements in the cochlea. We have developed an active cochlear model which incorporates negative damping components; this model produces partition displacement in good agreement with many of the mechanical and neural tuning characteristics which have been observed in vivo by other researchers. We suggest that the negative damping components of our model may represent an active mechanical behavior of the outer hair cells, functioning in the electromechanical environment of the normal cochlea.