Egbert de Boer

High-frequency electromotile responses in the cochlea

Mammalian outer hair cells (OHCs) convert electrical energy into mechanical energy. The significance of this electromotility rests in the ability of the OHCs to modulate the vibrations of the cochlear partition in vivo. While high-frequency electromotility of isolated OHCs has been demonstrated at frequencies up to 100 kHz, a similar measure of the effect of OHC electromotility on motion of the sensory epithelium has not been made in vivo. In this study, in vivo electrical stimulation of the guinea pig cochlea is found to induce a mechanical response of the basilar membrane for frequencies to at least 100 kHz, nearly twice the upper limit of hearing for the guinea pig. The perfusion of salicylate in the cochlea reversibly reduces the electromotile response, indicating that an OHC-mediated process is the key contributor.

Self‐suppression in a locally active nonlinear model of the cochlea: A quasilinear approach

Mechanical input-output functions of the cochlea for pure-tone stimuli are nonlinear for frequencies around the characteristic frequency. To simulate these functions, a long-wave model of the cochlea containing a saturating pressure generator (located at the site of the outer hair cells) is solved in the frequency domain with a quasilinear method. In this method distortion products in the basilar-membrane (BM) response are treated as perturbations and the nonlinear pressure waveform is approximated by the first-order Fourier component. Because the saturating pressure generator forms part of a feedback loop the solution of the model is achieved in a number of iteration steps. Model results show flattening of the BM response at higher input pressures; this property, called self-suppression, is due to saturation of the pressure generator. The resulting input-output functions display the main features of experimental curves. The third-order distortion product in the BM velocity is always more than 25 dB below the primary BM velocity and does not influence the results of the computation; this justifies the use of the quasilinear method.

The ‘‘inverse problem’’ solved for a three‐dimensional model of the cochlea. I. Analysis

With nonactive cochlear models of the ‘‘classical’’ type, it is impossible to simulate the characteristic type of frequency selectivity that is revealed by modern mechanical measurements of the motion of the basilar membrane (BM). Locally active models of the cochlea have been proposed to alleviate this problem but it remains uncertain whether the real cochlea is active in this sense. The present study was undertaken to investigate this subject in a more general and systematic way than has hitherto been done. The ‘‘inverse’’ problem is solved for a three‐dimensional (3‐D) model and a procedure is developed for recovering the BM impedance needed to simulate the given BM response function. In the present paper the theoretical basis of the procedure is presented, and an analysis is given of the validity of the method and the errors involved. It is shown why the inverse problem is ‘‘ill‐posed’’ and why the results of our procedure are more accurate in the region of the response peak than in the more basal reg...

TWO-TONE SUPPRESSION IN A LOCALLY ACTIVE NONLINEAR MODEL OF THE COCHLEA

In auditory nerve, inner-hair cell and basilar-membrane responses, it has been found that the response to one tone can be suppressed by another tone. This phenomenon, called two-tone suppression, is examined on the level of the basilar membrane with a locally active long-wave model of the cochlea in which the active mechanism is nonlinear. The model is solved in the frequency domain by means of a quasi-linear solution method. Several phenomena, such as difference in growth of suppression for low-side and high-side suppressors and critical dependence of the phase of the probe response on suppressor parameters, have been replicated. The attenuation hypothesis which states that the presence of a suppressor has the same effect on the probe response as attenuation of probe level is shown to be insufficient in explaining the experimental data. This model, in which suppression is simply reduction of power amplification due to saturation of the active mechanism, is more successful in this respect.

Realistic mechanical tuning in a micromechanical cochlear model

Two assumptions were made in the formulation of a recent cochlear model [P.J. Kolston, J. Acoust. Soc. Am. 83, 1481-1487 (1988)]: (1) The basilar membrane has two radial modes of vibration, corresponding to division into its arcuate and pectinate zones; and (2) the impedance of the outer hair cells (OHCs) greatly modifies the mechanics of the arcuate zone. Both of these assumptions are strongly supported by cochlear anatomy. This paper presents a revised version of the outer hair cell, arcuate-pectinate (OHCAP) model, which is an improvement over the original model in two important ways: First, a model for the OHCs is included so that the OHC impedance is no longer prescribed functionally; and, second, the presence of the OHCs enhances the basilar membrane motion, so that the model is now consistent with observed response changes resulting from trauma. The OHCAP model utilizes the unusual spatial arrangement of the OHCs, the Deiters cells, their phalangeal processes, and the pillars of Corti. The OHCs do not add energy to the cochlear partition and hence the OHCAP model is passive. In spite of the absence of active processes, the model exhibits mechanical tuning very similar to those measured by Sellick et al. [Hear. Res. 10, 93-100 (1983)] in the guinea pig cochlea and by Robles et al. [J. Acoust. Soc. Am. 80, 1364-1374 (1986)] in the chinchilla cochlea. Therefore, it appears that mechanical response tuning and response changes resulting from trauma should not be used as justifications for the hypothesis of active processes in the real cochlea.

The ‘‘inverse problem’’ solved for a three‐dimensional model of the cochlea. II. Application to experimental data sets

With ‘‘classical’’ nonactive models of the cochlea it is impossible to simulate the degree of frequency selectivity that is revealed by modern mechanical measurements of the motion of the basilar membrane (BM). Locally active models have been proposed to alleviate this problem, but it remains uncertain whether the actual cochlea is active in this sense. In the first paper of this series [E. de Boer, J. Acoust. Soc. Am. 98, 896–903 (1995)], the ‘‘inverse’’ problem is solved for a (classical) three‐dimensional model and a procedure is developed for recovering the BM impedance needed to simulate a given BM response function. It was found that the results of this procedure will be more accurate in the region of the response peak than in the more basal region of the model. In the present paper the same procedure is applied to data of recent mechanical experiments. For the peak region the outcome is unequivocal: Recent measurement results can only be simulated by the classical model when it is made locally acti...

What type of force does the cochlear amplifier produce

Recent experimental measurements suggest that the mechanical displacement of the basilar membrane (BM) near threshold in a viable mammalian cochlea is greater than 10(-8) cm, for a stimulus sound-pressure level at the eardrum of 20 microPa. The associated response peak is very sensitive to the physiological condition of the cochlea. In the formulation of all recent cochlear models, it has been explicitly assumed that this peak is produced by the cochlear amplifier injecting a large amount of energy into the cochlea, thereby altering the real component of the BM impedance. In this paper, a new cochlear model is described which produces a realistic response by assuming that the cochlear amplifier force acts at a phase such that the main effect is to reduce the imaginary component of the BM impedance. In this new model, the magnitude of the cochlear amplifier force required to produce a realistic response is much smaller than in the previous models. It is suggested that future experimental investigations should attempt to determine both the magnitude and the phase of the forces associated with the cochlear amplifier.

The Allen-Fahey experiment extended

An ingenious experiment has been performed by Allen and Fahey [J. Acoust. Soc. Am. 92, 178-188 (1992)], in which they attempted to estimate the gain of the cochlear amplifier by comparing responses to the 2 f1-f2 distortion product (DP) in the outer ear canal (otoacoustic emissions) and from an auditory-nerve fiber. Results were essentially negative: no evidence of cochlear amplification was found in that experiment. A variation of that experiment is reported here, where DP responses in the outer ear canal are compared with mechanical responses of the basilar membrane. This variation does not suffer from the major limitation in the original experiment in the choice of possible frequency ratios. Results confirm and extend those of Allen and Fahey entirely. Apparently, the gain of the cochlear amplifier cannot be measured in this way. It is argued that the retrograde wave going to the stapes is most likely reduced in magnitude by wave interference when the two primary frequencies approach each other. Such a reduction does not take place in the forward-going wave to the location tuned to the DP frequency. This explanation is illustrated on the basis of results of earlier experiments on the movements of the basilar membrane.

Classical and non-classical models of the cochlea

In a “classical” model of the cochlea the response is controlled by a local parameter function, for instance, the BM impedance. In a non-classical model, the response is controlled by parameters that are distributed over space. In this note it is shown to which extent classical and non-classical models are equivalent. To each non-classical model there exists one classical model that yields the same response. However, the BM impedance of that classical model does not necessarily obey the requirements of a driving-point impedance.

The sulcus connection. On a mode of participation of outer hair cells in cochlear mechanicsa)

Motile outer hair cells (OHCs) can only participate well in cochlear mechanics when one end of the hair cells is more restrained in its movements than the other. On this thought a model of the organ of Corti (OoC) is developed in which (in every cross section) the tectorial membrane (TM) is considered to consist of two stiff segments connected by a hinge. Movements of the TM then induce movements of the fluid contained in the inner spiral sulcus (ISS) and the fluid dynamics of the sulcus will play an important part in restraining the top ends of the hair cells. Since the model is meant to reflect low‐level phenomena, it is conceived as linear. For simplicity, it operates in the long‐wave mode. The sulcus is considered as a narrow channel that is closed at both ends. Since the sulcus fluid is an independent energy‐storage element of the system, the entire cochlear model, consisting of two main fluid channels, the organ of Corti (OoC), the three‐element TM and the sulcus, and equipped with motile OHCs, can ...