Basilar Membrane Frequency Research Articles

The effect of tectorial membrane and basilar membrane longitudinal coupling in cochlear mechanics

Most mathematical models of the mammalian cochlea neglect structural longitudinal coupling. However, recent experimental data suggest that viscoelastic longitudinal coupling, in the basilar membrane (BM) and the tectorial membrane (TM), is non-negligible. In this paper, mathematical models for BM and TM longitudinal coupling are presented to determine the influence of such a coupling on the tuning of the BM. The longitudinal coupling models are added to a macroscopic linear model of the guinea pig cochlea that includes the micromechanics of the organ of Corti and outer hair cell (OHC) somatic motility. The predictions of the BM response to acoustic stimulus show that the characteristic frequency is controlled by a TM radial resonance and that TM longitudinal coupling has a more significant effect than BM longitudinal coupling. TM viscoelasticity controls the sharpness of the BM frequency response and the duration of the impulse response. The results with realistic TM longitudinal coupling are more consistent with experiments. The model predicts that OHC somatic electromotility is able to supply power to the BM at frequencies well above the cutoff of the OHC basolateral membrane. Moreover, TM longitudinal coupling is predicted to stabilize the cochlea and enable a higher BM sensitivity to acoustic stimulation.

Modelling the temporal response of the auditory nerve to the pitch of complex tones in reverberation

A computational model of the auditory nerve has been used to investigate the effect of reverberation on the response to the fundamental frequency (F0) of frequency‐swept harmonic complexes. The model used a computationally efficient dual resonance non‐linear (DRNL) model of basilar membrane frequency selectivity. The DRNL architecture comprises two parallel filter paths providing linear and non‐linear responses. The model successfully reproduced the results of a physiological investigation using the same stimuli in a population of single units from the ventral cochlear nucleus (VCN). In particular the effect of reverberation was dependent upon unit best frequency, F0 and source‐to‐receiver distance. The model results suggest that the effects of reverberation observed at the level of the VCN are already present in the auditory periphery. The use of the model has also enabled us to examine the effect of hearing impairment by the removal of the non‐linear path response. This simulation of a sensorineural hearing loss accentuated the loss of the temporal representation of F0 in the presence of reverberation.

A mechano-electro-acoustical model for the cochlea: Response to acoustic stimuli

A linear, physiologically based, three-dimensional finite element model of the cochlea is developed. The model integrates the electrical, acoustic, and mechanical elements of the cochlea. In particular, the model includes interactions between structures in the organ of Corti (OoC), piezoelectric relations for outer hair cell (OHC) motility, hair bundle (HB) conductance that changes with HB deflection, current flow in the cross section and along the different scalae, and the feed-forward effect. The parameters in the model are based on guinea-pig data as far as possible. The model is vetted using a variety of experimental data on basilar membrane motion and data on voltages and currents in the OoC. Model predictions compare well, qualitatively and quantitatively, with experimental data on basilar membrane frequency response, impulse response, frequency glides, and scala tympani voltage. The close match of the model predictions with experimental data demonstrates the validity of the model for simulating cochlear response to acoustic input and for testing hypotheses of cochlear function. Analysis of the model and its results indicates that OHC somatic motility is capable of powering active amplification in the cochlea. At the same time, the model supports a possible synergistic role for HB motility in cochlear amplification.

Intensity-invariance of fine time structure in basilar-membrane click responses: implications for cochlear mechanics.

Basilar-membrane and auditory-nerve responses to impulsive acoustic stimuli, whether measured directly in response to clicks or obtained indirectly using cross- or reverse-correlation and/or Fourier analysis, manifest a striking symmetry: near-invariance with stimulus intensity of the fine time structure of the response over almost the entire dynamic range of hearing. This paper explores the origin and implications of this symmetry for cochlear mechanics. Intensity-invariance is investigated by applying the EQ-NL theorem [de Boer, Aud. Neurosci. 3, 377-388 (1997)] to define a family of linear cochlear models in which the strength of the active force generators is controlled by a real-valued, intensity-dependent parameter, gamma (with 0 < or = gamma < or = 1). The invariance of fine time structure is conjectured to imply that as gamma is varied the poles of the admittance of the cochlear partition remain within relatively narrow bands of the complex plane oriented perpendicular to the real frequency axis. Physically, the conjecture implies that the local resonant frequencies of the cochlear partition are nearly independent of intensity. Cochlear-model responses, computed by extending the model obtained by solution of the inverse problem in squirrel monkey at low sound levels [Zweig, J. Acoust. Soc. Am. 89, 1229-1254 (1991)] with three different forms of the intensity dependence of the partition admittance, support the conjecture. Intensity-invariance of cochlear resonant frequencies is shown to be consistent with the well-known "half-octave shift," describing the shift with intensity in the peak (or best) frequency of the basilar-membrane frequency response. Shifts in best frequency do not arise locally, via changes in the underlying resonant frequencies of the partition, but globally through the intensity dependence of the driving pressure. Near-invariance of fine time structure places strong constraints on the mechanical effects of force generation by outer hair cells. In particular, the symmetry requires that the feedback forces generated by outer hair cells (OHCs) not significantly affect the natural resonant frequencies of the cochlear partition. These results contradict many, if not most, cochlear models, in which OHC forces produce significant changes in the reactance and resonant frequencies of the partition.

Nonlinear interactions that could explain distortion product interference response areas.

Suppression and/or enhancement of third- and fifth-order distortion products by a third tone that can have a frequency more than an octave above and a level more than 40 dB below the primary tones have recently been measured by Martin et al. [Hear. Res. 136, 105-123 (1999)]. Contours of iso-suppression and iso-enhancement that are plotted as a function of third-tone frequency and level are called interference response areas. After ruling out order aliasing, two possible mechanisms for this effect have been developed, a harmonic mechanism and a catalyst mechanism. The harmonic mechanism produces distortion products by mixing a harmonic of one of the primary tones with the other primary tone. The catalyst mechanism produces distortion products by mixing one or more intermediate distortion products that are produced by the third tone with one or more of the input tones. The harmonic mechanism does not need a third tone and the catalyst mechanism does. Because the basilar membrane frequency response is predicted to affect each of these mechanisms differently, it is concluded that the catalyst mechanism will be dominant in the high-frequency regions of the cochlea and the harmonic mechanism will have significant strength in the low-frequency regions of the cochlea. The mechanisms are dependent on the existence of both even- and odd-order distortion, and significant even- and odd-order distortion have been measured in the experimental animals. Furthermore, the nonlinear part of the cochlear mechanical response must be well into saturation when input tones are 50 or more dB SPL.

A possibility of sharp tuning in a linear transversally inhomogeneous cochlear model

Considerable sharpening of basilar membrane frequency selectivity and simultaneous decreasing of phase lag can be obtained in a linear (‘passive’) hydromechanical three-dimensional cochlear model, if the transverse geometry of the cochlea is taken into account. Both the tuning qualities, Q 10, and the phase angles at CF of some transversally inhomogeneous linear models can be set into the range of experimental data [Sellick et al. (1983) Hear. Res. 10, 93–108; Robles et al. (1986) J. Acoust. Soc. Am. 80, 1364–1379.] The calculations are developed on the base of WKB-approximation. The integral coefficients of eiconal equation are the transversally averaged means of basilar membrane surface mass density and stiffness: ∝ b(x) o μ(x,y)η 2(y) dy, ∝ b(x) o D(x,y)( δ 2η δy 2 ) 2 dy , where η(y) is the major eigenfunction of basilar membrane cross-sectional vibrations. The classical Ritz's method is used for calculation of the cross-sectional eigenfunctions. The size and the form of cochlear cross-section are found also to alter the tuning. The rapid increase of the model response towards the peak is due to that damping remains negligible up to the peak position. where the imaginery part of the wave-number begins to increase sharply.

Simulating pitch perception and sensitivity to phase using a peripheral auditory model

The ability of neurophysiological studies to give an adequate account of human pitch perception was studied using a peripheral auditory model comprising (a) outer‐ear, low‐frequency attenuation, (b) a set of 60 digital filters to simulate basilar membrane frequency selectivity, (c) an array of inner hair cell simulators, and (d) a system based on Licklider's [Experientia 7, 128–133 (1951)] theory of pitch perception that generates running histograms of the time intervals among all spikes in fibers originating from adjacent sites on the membrane. The most frequently occurring time intervals were taken to represent the period of the perceived pitch, while the overall pattern of time intervals represented the perceived timbre. The model was tested, giving satisfactory results, using a wide range of harmonic, inharmonic, and noise stimuli known to give rise to pitch perceptions as well as stimuli, where the relative phase of the harmonic components affects stimulus timbre. [Work supported by SERC.]

Histological evaluation of damage in cat cochleas used for measurement of basilar membrane mechanics

Cochleas utilized in basilar membrane vibration measurements were examined histologically using an epon-embedded surface preparation technique. The amount of damage observed at both the apical and basal ends of the cochleas was variable. The apical damage was probably caused by large, low-frequency movements of the basilar membrane. The basal damage was due to trauma produced directly by the surgical and experimental procedure. The sharpness of turning observed in the basilar membrane frequency response was found to be inversely related to the extent of histological damage.