Peripheral Auditory Mechanisms

The aim of this paper is to evaluate measures of acoustic-power transfer for comparisons of the performance of the auditory peripheries of different species. To do so we will define three power transfer measures that can be computed from available data. The measures also separate the auditory periphery into functional subunits so as to enable estimations of the roles of different auditory specializations.The three measures of power transfer are: the Tower Utilization Ratio at the TM” (PUR), the “Effective Area of the External Ear” (EA), and the “Middle Ear Efficiency” (MEE). The three power measures serve different purposes: PUR is an index of the impedance-matching performance of the external and middle ear; EA and MEE quantify power flow through the external and middle ears. The EA and MEE can be combined to obtain a single measure of the power into the cochlea that we call the “Net Effective Area” (NEA).Our analysis suggests (1) the impedances of external and middle ears are poorly matched, (2) an appreciable fraction of the sound power which enters the middle ear is absorbed before it reaches the cochlea, (3) cochlear function at auditory threshold for pure tones can be roughly approximated by a power detector, and (4) the quantification of power transfer through the ears of different species is a useful comparative tool.

For many experiments in physiological and psychological acoustics results are reported using, as a reference level, the sound pressure measured at the eardrum. However at higher frequencies there can be rather dramatic variations of sound pressure level within an ear canal and across the tympanic membrane. Different locations of a reference microphone can lead to quite different results, with the introduction of artifacts that relate only to peculiarities of the sound field. As a first step toward understanding this problem, measurements have been made of the spatial variation of sound pressure in scaled replicas of human ear canals and in the ear canals of live cats. The measured pressure distributions can be described reasonably well using a theoretical model that has been developed. This model is an extension of Webster’s horn equation, taking into account the curvature and variable cross section of the ear canal and the absorption of acoustic energy at the eardrum. From both theory and experiment it is clear that variations in sound pressure level of over 20 dB can occur over the surface of the tympanic membrane.

Acoustical Dirac impulses (15 μsec duration, sound energy from 600 Hz to 25 kHz) are used under free field conditions for evoking impulse responses in the tympanic membranes of awake, unrestrained human volunteers. The impulse responses are analysed in the time- and frequency domains. The impulse responses within different frequency bands add to a total impulse response of complex shape (Fig. 3). The frequency spectrum of the vibration velocity of the mallear handle (umbo) shows several maxima in amplitude and corresponding deflections of phase, but the maxima are mainly caused by changes in the spectrum of the sound travelling to the ear drum. In contrast, the transfer function of the umbo (sound pressure to vibration) is smooth with only little variation in amplitude and a gradual development of phase. It is argued that the common notion of the middle ear as a low-pass filter is misleading.

A dynamic continuum model of the tympanic membrane is formulated by accounting for its fibrous structure and including membrane type restoring mechanisms, internal structural damping, curvatures of the drum, and spatially varying properties. Accepted experimental observations are combined with the ultrastructure to argue that bending, torsional, and shear restoring forces are secondary at moderate to high sound pressure levels. The resulting model is sufficiently simple that closed form asymptotic solutions can be found which contain adequate physical content to address questions of the vibrational shape, the transient response, impulse failure, tympanoplasty effects, Eustachian tube coupling and similar related problems.

We describe our investigations of the mechanisms through which contractions of the stapedius muscle in the cat cause alterations in acoustic transmission through the middle ear. We have observed that stapedius contractions displace the stapes head along the direction of the stapedius tendon, which is perpendicular to the direction of stapes motion in response to sound. This stapes-head displacement (SHD) occurs without detectable displacement of the incus or malleus. This result suggests that the changes in transmission are solely caused by changes in the stapes impedance due to the SHD. Measurements of SHD were made together with the associated transmission changes. For SHDs up to 40 μm, the transmission was reduced up to 10 dB in the frequency range below 1.5 kHz with little change for higher frequencies. For SHDs larger than 40 μm, reductions in transmission up to 30 dB were observed in the low frequency range and up to 15 dB for high frequencies. We explore the possibility that changes in the configuration of the annular ligament at the stapes footplate are the source of the acoustic changes by comparing our results with other measurements of changes of stapes impedance. We conclude that this hypothesis is tenable.

In this paper we describe a system which we have developed to measure cat ear canal specific acoustic impedance Z _sp , magnitude and phase, as a function of frequency, for frequencies between 200 Hz and 33 kHz, and impedance magnitudes between 4.0 to 4.0×l05 rayles (MKS). The object to be measured is placed at the end of a 3.5 mm diameter sound delivery tube. After a simple calibration procedure, which determines the Thévenin parameters for the acoustic source transducer, the impedance may be calculated from the pressure measured at the orifice of the delivery tube with the unknown load in place. This procedure allows for a fast but accurate measure of a specific acoustic impedance. The system has been tested by measuring the impedance of a long cavity and comparing this response to the exact solution of the linearized Navier Stokes equations (acoustic equations including viscosity and thermal conduction). We have used this system to measure the impedance of the normal cat tympanic membrane in more than 30 cats. Healthy animals were found to have a real input impedance of ρc between 0.3 to 20.0 kHz. When the scala vestibuli was drained, the real part of the impedance dropped to less than ρc/10 for frequencies less than 3.0 kHz. Above 3 kHz, the impedance for the drained cochlea is best described by an open circuited transmission line.

In developing an artificial membrane in a total alloplastic middle ear (TAM) prosthesis (Grote 1984) one of the main research goals is mechanical compatibility (besides biological compatibility). First, micromechanically (≈10-9-10-6m), vibration amplitude spectra in response to sound must match that of the natural membrane in a sufficiently wide frequency range (between 200 and 10000 Hz). Second, macromechanically (≈10-3m), the elasticity modulus must be in the natural range for purposes of epithelial overgrowth and ingrowth. As ingrowth requires a porous material structure, porosity is a relevant structural variable, to be monitored by use of scanning electron micrographs. Finally, the material must sustain sterilization, at a temperature of about 120 °C.

Using a tiny magnet and a commercial SHE r.f. SQUID magnetometer setup, supplemented by an adjustable second order gradiometer, amplitude and phase spectra of vibrations of human middle ears were determined without disturbing the anatomy of middle ear and intact cochlea. The magnet had a mass of 1.5 mg and was positioned at the tip of the malleus (umbo), halfway the malleus near the processus brevis and on the anterior crus of the stapes. Post mortem changes of vibratory umbo displacements were measured in human temporal bones and guinea pigs. In a group of twelve ears the mean and standard deviation were determined at the three positions as mentioned above at 80 dB SPL stimulation level. These amplitude and phase spectra yielded information about the transfer characteristics of the middle ear and about the projection (into the tympanic plane) of a rotation axis.

This paper reviews macromechanical models of the cochlea. The emphasis is on two questions: (i) which geometrical and mechanical features should be included, and (ii) which experimental results can be matched.

The three-dimensional mathematical model of the cochlea developed by Steele and Taber (1979) is used as the basis for calculations of the transient response of the cochlea. The fast Fourier transform is employed to perform the actual calculations. Due to space limitations, only five experimental results are simulated and summarized here: click responses, pure tone transients, single-period pitch perception, time-separation pitch perception, and the response of the basilar membrane to speech signals.

The frequency selectivity of primary auditory afferents has been allocated preferentially to different structures in various classes of tetrapod animals: to the basilar membrane (BM) in mammals (Sellick et al., 1982; Khanna and Leonard, 1982), to the hair cell in the turtle (Crawford and Fettiplace, 1980) and to hair cell stereocilia in the alligator lizard (Holton and Weiss, 1983). We have investigated the motion of the BM in the pigeon using the Mössbauer technique because the avian inner ear structures possess features which compare to those in other tetrapods. The avian BM is short by comparison to the mammalian BM (4 mm in pigeon) and is only slightly bent. There are numerous hair cells per radial section (14 – 54 in pigeon) which are tightly packed over the BM and neural limbus (Takasaka and Smith, 1971). The tallest stereocilia are firmly embedded in a porous tectorial membrane. There is a second class of cells, called hyaline cells, which rest on the BM, are not covered by the tectorial membrane and are densely innervated by efferent fibres. On a physiological level, the effect of temperature on single unit frequency threshold curves in the pigeon is different to that in the mammal (Gummer and Klinke, 1983) — there is a 1-octave reduction of best frequency per 10 C reduction of cochlear temperature (Schermuly and Klinke, 1985). Von Békésy (1944) has shown that tonotopically mapped frequency tuning exists on the apical part of the chicken BM. It is not known, however, whether the avian BM supports travelling wave motion and whether it is capable of the frequency selectivity of primary auditory afferents.

The basilar membrane (BM) in the greater horseshoe bat has a peculiar thickness and width profile, which suggests that BM-stiffness in the basal half turn is more than one order of magnitude greater than in the second half turn and more apically. The transition is quite abrupt.Motivated by new data on the cochlear frequency map we analyse the possibility that the stiffer basal half turn acts as an acoustic interference filter. Its increased stiffness and impedance transitions at the stapes and at the transition mentioned, make this a feasible mechanism. We propose that 2¼ wavelengths of the reflected call frequency of the echolocating bat match the length of the interference filter. Using a scaled version of the middle ear description given by Matthews (1980) and linear, passive, long-wave, 1-dimensional cochlear mechanics we analyse the effect of the interference filter and compute the tympanic membrane input impedance. Experimental data on the latter (Wilson and Bruns, 1983a) are interpreted in terms of the proposed mechanism: fine structure in the input impedance appears to reflect the interference filter passbands.

A two-dimensional mathematical model of the cochlea of the greater horseshoe bat Rhinolophus ferrumequinum is constructed. From 0–4.5 mm, the partition has large, constant mass and stiffness with in vacuo resonance of 83 kHz, the bat’s emitted resting frequency. From 4.5–16 mm, partition mass is small and stiffness decreases exponentially with distance from the stapes. Solution is by VLFEM (Very Large Finite Element Method), an analytical/numerical hybrid technique designed for cochlear models with discontinuities.Basilar membrane amplitude is calculated for twenty input frequencies as a function of distance from the stapes. The specialized basal region attenuates amplitude at all frequencies, with a sharp minimum at 83 kHz. Reflection is significant for frequencies below 83 kHz. The results agree qualitatively with experimental measurements, indicating maximal neural stimulation at minimal basilar membrane motion.

In two-dimensional models of the cochlea, basilar membrane behaviour has to satisfy a mixed type boundary condition. In this paper this condition will be studied using the complex plane. Its solution is given in terms of the most general solution of Laplace’s equation for pressure. The result shows complex membrane pressure as a linear combination of two independent functions. Taking advantage of the well-known frequency to place mapping, the solution is written as a frequency invariant closed shape. This representation is useful in giving a physical interpretation of membrane motion in relation to fluid flow in cochlear models. Due to the frequency invariance, no time consuming numerical methods are necessary to find response curves for membrane pressure or velocity.

A one-dimensional computer model of the peripheral ear was explored using pure-tone inputs. This model was adopted after frequency-domain modeling showed that the differences between one- and two-dimensional models were small. The inner ear representation was the classical mass-spring-damper transmission line. In the time-domain simulations, this classical model was modified to have adjacent elements of the cochlear partition model lightly coupled to each other via springs.Simulation of the entire peripheral ear demonstrated that the parameters used in Neely’s (1981), Allen’s (1977) and our model were fairly well chosen. All three representations yielded cochlear input impedances that accurate approximated Lynch et al.’s (1982) results at higher frequencies, and they yielded sound pressure levels at the partition that approximated Nedzelnitsky’s (1980) measurements at low frequencies. In addition, very low values of cochlear partition damping resulted in highly peaked displacement curves that were approximately correct in amplitude (near 1 A at 0 dB SPL for 1 kHz).The effect of moderate longitudinal stiffness coupling was to broaden significantly the width of the resonant peak in the lightly damped case, at the cost of only slightly reducing the peak’s magnitude. Proper values of this longitudinal coupling resulted in tuning-curve shapes and values of Q₁₀ that were quite realistic.

Basilar membrane (BM) motion was measured at a site 3.5 mm from the basal end of the chinchilla cochlea using the Mössbauer technique. In preparations with little surgical damage, mechanical responses were as sharply tuned as auditory nerve fibers with the same characteristic frequency (CF, about 8.4 kHz). High-frequency plateaus were observed in both isovelocity tuning curves and phase-frequency curves. Input-output functions at frequencies around CF were strongly nonlinear. Another type of nonlinearlty, two-tone suppression, was also demonstrated in several cochleas, with suppression effects as large as 28 dB.

A mathematical model of cochlear processing is developed to describe the transformation from acoustic stimulus to intracellular hair cell potential. It incorporates a linear formulation of three-dimensional basilar membrane mechanics, subtectorial fluid-cilia displacement coupling, and a simplified description of the inner hair cell nonlinear transduction process. When the model parameters of the basilar membrane stage are set to values characteristic of the guinea pig, good agreement with experiment is obtained for single tone responses. When the parameters are varied, the basilar membrane tuning can change dramatically.

Cochlear micromechanics describes the radial displacement of hair bundles of the inner and outer hair cells in response to forces generated by fluid pressure gradients near the cochlear partition. A simple micromechanical model of a radial cross-section of the cochlear partition is a lumped mass, stiffness, and damping. This simple representation is adequate to simulate “traveling waves” and a frequency-to-place correspondence in a cochlear model, but inadequate to simulate “neural-like” tuning in cochlear mechanics. A second, coupled resonant element appears to be necessary to explain the sharp tuning which is typical of the cochlea. This second resonant element may be passive or may be part of a mechanical “cochlear amplifier” which contributes mechanical energy (at the expense of electrochemical energy) to provide high sensitivity at the threshold of hearing.

We assume that cochlear fluids are Newtonian and show that for physiological stimuli: fluid compressibility is negligible; convective non-linear inertial forces are small; and both viscous and linear inertial forces are appreciable. We examine the frequency dependence of viscous and inertial fluid forces that act on oscillating, isolated bodies of regular geometry. The mechanical admittance of such a body submerged in a fluid and supported by springs shows a geometry-dependent resonance. This resonance has a quality (Q_3dB ) that is less than 1 for an infinitesimally thin plate vibrating in its plane, but can be arbitrarily large both for a sphere and for a circular cylinder oscillating in a direction perpendicular to its long axis. From considerations of hair cells with free-standing stereocilia in the alligator lizard cochlea we conclude that stereociliary tufts in the cochlea could be resonant mechanical systems.

The feasibility of a resonant mechanical system in the cochlea, consisting of outer hair cells (OHCs) and the tectorial membrane (TM), playing a significant role in frequency selectivity has been investigated. As proposed initially by Zwislocki (J. Acoust. Soc. Am. 67, 1679–1688, 1980), such a resonant OHC-TM system, with stiffness provided by the sensory hairs of the three rows of OHC and mass by the overlying TM, would be mechanically coupled to the basilar membrane (BM) via the sensory hairs and would vibrate in a plane parallel to the reticular lamina. Since the TM mass is estimated to be 1/5 – 1/4 of the mass of the organ of Corti, OHC-TM vibrations would have a significant effect upon BM frequency selectivity if OHC-TM resonant frequency along the length of the cochlea were close to the BM frequency at the same location.Determination of the length and stiffness of OHC sensory hairs in the isolated guinea pig organ of Corti (Strelioff and Flock, Hearing Res., 15, 19–28, 1984) has made possible quantitative computations of OHC-TM resonant frequencies for the simple case where the effects of the TM attachement to the limbus are neglected. Computed OHC-TM resonant frequencies, assuming no variation in TM mass along the length of the cochlea, range from 1.2 kHz at the apex to 22 kHz at the base. These computed frequencies, based upon data from in vitro preparations, are sufficiently close to BM frequencies to demonstrate the feasibility of Zwislocki’s proposal. As more data on the mass and elasticity of the TM and the characteristics of its attachment to the limbus become available, it will be possible to more accurately evaluate the role of OHC-TM micromechanics in BM frequency selectivity.

The shape of the curve of the auditory sensitivity thresholds as a function of frequency is determined by the transfer function of the outer and middle ear. For a constant acoustic signal at the input to the cochlea the auditory sensitivity threshold is nearly constant. From theoretical results, it seems that the threshold of the neural responses appears always for the same velocity of the cochlear partition all along the cochlea.Concerning the auditory fatigue, we applied to the guinea pig’s cochlea a constant acoustic energy (pure tones of frequency from 2 kHz to 11,3 kHz) during 20 minutes and we measured the TTS by electrocochleography twenty minutes after the end of the exposure (from 2 to 32 kHz by half-octave steps). For each animal, the level of the stimulus at the input to the cochlea was adjusted by means of cochlear microphonic measurements.a)In order to obtain a constant TTS for each frequency of stimulation, the acoustic level at the input to the cochlea must decrease by about 4 dB/octave.b)A constant TTS at 16 kHz and at 22.6 kHz, whatever the stimulation frequency is, is obtained for an acoustic level at the input of the cochlea decreasing by about 10 dB/octave.Given the facts that, for a constant acoustic input to the cochlea: the amplitude of the displacements of the cochlear partition near the CF doubles each time that the frequency is halved and consequently the velocity of the cochlear partition is constant,the amplitude of the displacements of the cochlear partition at the base of the cochlea is constant for frequencies lower than CF and consequently the velocity of the cochlear partition at the base doubles with the frequency, the difference of slope between case a) and b), i.e. 6 dB/octave seems to indicate that the velocity of the cochlear partition is an important parameter which plays a significant role in the coming out of the auditory fatigue.

Experiments with physical models and hair cell damage data indicate that a significant steady flow issues from the spiral sulcus under high intensity sound conditions. A mathematical model describing the sulcus streaming flow induced by waves travelling along the basilar membrane was formulated. Preliminary results obtained for the guinea pig cochlea reveal that the streaming flow through the tectorial gap is significantly sharper than the corresponding basilar membrane displacement envelope. The steady flow passes through the inner hair cell row; this suggests that streaming is a possible passive filtering mechanism.

Receptor cells in many organs of the acoustico-lateralis system use active filtering mechanisms to detect sensory stimuli. The mechanisms appear to differ, but in each case feedback theory can be used to describe the filtering process. Changes in membrane potential appear to regulate electrical and/or electrical-mechanical changes in the receptor cell which lead to band-pass filtering of the sensory stimulus. An important feature of all these filtering processes appears to be a delay in the feedback loop which leads to a highly underdamped system.

We address the question of whether we can conclude just from basilar membrane (BM) vibration data that the cochlea is an active mechanical system. To this end we study an “inverse” problem for the cochlea in the framework of a short-wave model. Using the “inverse” problem formulation we compute the power flux through a channel cross-section from the BM velocity pattern. A rise in the power flux function indicates that the cochlea itself adds energy to the BM vibration. In order to avoid numerical errors as a result of too few data points, we have interpolated the BM velocity curves. The choice of interpolation method appears to influence the power flux function very much. Nonetheless, we conclude that the power flux method is able to determine from measured BM vibration patterns whether the underlying behaviour of the cochlea has been active or not.

A most important question concerns the stability of active cochlea models. We have addressed this question by studying effects occurring when a small section of the cochlea is made active and the remainder is left passive. In our study we determine the limiting value of the length Δ1 of the active section for which the system becomes unstable. The cochlea is modelled as a long-wave structure and described as a nonuniform transmission line. The principal parameter involved is the characteristic impedance of this line. At the resonance frequency of the emitter the characteristic impedance has a phase angle of π/4 radians (45°). The real part damps the emitter, and mainly determines the limiting length Δ1. The imaginary part is inductive and causes the emitter, if it becomes unstable, to oscillate at a frequency somewhat below its natural resonance frequency. It is found that for a given degree of activity, the length Δ1 must remain larger than a certain value for the system to remain stable. Several remarkable properties result from the analysis, these give really new insight into the requirements that an active cochlea model must meet. We have generalized the concept of characteristic impedance and have subjected the predictions of the analytical theory to test by carrying out numerical calculations in the time domain.

The question has been investigated whether or not it is possible to design a stable active model of the cochlea without using a second tuned structure. First a “learning” feedback model with negative damping in the cochlear partition is considered. This model, however, turned out to be unstable. The second model is characterized by a constant negative damping of the longitudinal fluid motion. An analysis of the energy flow shows that this simple model is stable as long as reflections at the helicotrema can be neglected. Consequently a second tuned structure seems not to be essential for the stability of a model.

Spontaneous otoacoustic emissions, delayed evoked emissions, synchronous evoked emissions and psychoacoustical threshold microstructure were monitored (in two subjects) before, during and after the consumption of 3.9g of aspirin per day for three consecutive days (12 doses of three 325mg tablets every 6 hours). Spontaneous emissions followed a pattern similar to that found by McFadden and Plattsmeir (1984). Evoked emissions were also reduced by aspirin consumption but persisted longer and recovered sooner. Reduction of psychoacoustic threshold microstructure associated with the emissions followed much the same time course as the evoked emissions. In most instances the reduction of threshold microstructure began with a lowering of threshold maxima (with threshold minima remaining relatively constant) and ended with all thresholds elevated.

Several properties of a spontaneous oto-acoustic emission are summarized (frequency spectrum, amplitude distribution, suppression, phase-lock). The emission is generated by an active filtering process in the inner ear. It can be described by a simple electronic model. Characteristics of the emission signal are compared with those of spontaneous voltage fluctuations in a hair cell.

Some hearing organs demonstrate frequency tuning that is strongly temperature-dependent whereas others do not. Previous experiments in mammals have shown little, if any, temperature-dependence. Spontaneous otoacoustic emissions (SOAEs) are very stable in some subjects and offer a sensitive indicator for temperature effects. SOAE frequency changes were investigated over the menstrual cycle, the diurnal cycle, and after irrigation of the ear canal. A consistent apparent negative correlation with temperature was found over the menstrual cycle. Over the diurnal cycle, however, different frequency components behaved differently with a negligible net temperature-dependence. Irrigation of the ear canal at 30°C indicated a slight negative temperature dependence, but further experiments on another subject gave opposite changes for 30°C but no change for 44°C. These latter effects may have been due to changes of middle-ear pressure, whereas the effects over the menstrual cycle may be due to changes of hormone level. The temperature dependence of human frequency tuning would appear to be less than 0.1%/°C, indicating a stiffness change of less than 0.2%/°C.

This paper reviews nonlinear and active cochlear models with special attention to the question whether a “second filter” is needed for modeling two-tone suppression below the characteristic frequency (CF). The concept of a unidirectionally coupled “second filter” is inconsistent with experimental evidence that major cochlear mechanical nonlinear phenomena are affected by alterations of the organ of Corti. A possible way of modeling the below-CF suppression is suggested in terms of an indirect effect mediated by a baseline shift of the cochlear partition.

Since the discovery of v. Békésy (1943) that frequency-place transformation in the cochlea of vertebrates is accomplished by traveling waves of the displacement of the basilar membrane, many experiments have been undertaken to add to the knowledge about the vibration patterns taking place in the inner ear. For almost three decades, the data elaborated post mortem in birds and vertebrates looking through a microscope by v.Békésy have been used to describe cochlea wave patterns at any sound level. Introducing the indirect, but much more sensitive Mössbauer probe new data from living animals could be obtained. Rhode (1971) was the first pointing to the level dependence of basilar membrane displacement. More data at even lower levels and smaller displacement values have been published meanwhile (for references see for example Patuzzi et al., 1984). The new animal data showed very clearly that the inner ear and its normal activity are very vulnerable. From this point of view it seems to be unlikely that equivalent data from humans may become available. The level dependent, i.e. nonlinear data of the traveling wave characteristics of man are, however, of great interest not only for the people working in physiology and psychology but also in ENT-departments. Therefore indirect methodes leading to the data of interest may be used in exchange. As mentioned earlier (Zwicker, 1983) oto-acoustic emissions (OAE’s) can be used as an effective tool to enlarge our knowledge about the inner ear’s signal processing especially at low and very low levels at which normal méthodes mostly fail.

Responses of a mechanical model of the peripheral auditory system are calculated for two-tone stimuli with primary frequencies chosen so that the frequency of the cubic difference tone (2f₁-f₂) is maintained constant for all pairs used. The comprehensive model explicitly includes linear characterizations of the earphone driver, acoustic coupler, and middle ear, and a passive cochlear model with nonlinear damping of the cochlear partition motion. The amplitude and phase plots of the (2f₁-f₂) distortion signal, determined both in the ear canal and at the (2f₁-f₂) characteristic place, show rapid variations with f₁, and quite different patterns depending on the stimulus level. These plots, as well as plots showing the spatial distribution of primary and distortion signals along the cochlea for six selected f₁ values, are interpretable as showing interactions between multiple propagating waves at the distortion product frequency.

Evidence has recently been obtained (Burns et al., 1984) for several interactions among spontaneous otoacoustic emissions (SOAEs) including intermodulation distortion products, mutual suppression, and noncontiguous-linked SOAEs which apparently share energy between two quasi-stable states. In this paper, we give an updated record of our findings on intermodulation distortion products and linked emissions, and give evidence that the former tend to occur when a distortion product frequency is close to that of a cochlear resonance. Computer simulations of the interactions among van der Pol oscillators, which represent nonlinear active elements in a simplified cochlear model, appear to qualitatively account for some of the observed features of SOAE interactions.

Direct mechanical measurements of the basilar membrane in the guinea pig cochlea have revealed that a dc component of basilar membrane motion exists and shows a systematic tendency to reverse polarity close to the best frequency (BF) of the ac response. The dc component is seen in time records as a change in the mean position of the basilar membrane with the onset of the tone burst. The offset is physiologically vulnerable and is substantially reduced as the preparation deteriorates. A computer model of the basilar membrane, employing nonlinear stiffness and damping elements, shows a pattern of rectification with polarity reversal not unlike the experimental data.

The response of a physical three chamber model of the cochlea is described in the present paper. The model is rectilinear, geometrically scaled 50:1 and supplied with train-gauge transducers to measure axial and cross components of oscillating fluid near the Corti organ. A continuous motion of fluid in the scala media was observed and a complete picture of the stream line distribution was obtained using fluorescent pow ders and black light. Some peculiar aspects of this continuous flow can be closely correlated with basilar membrane (B.M.) response.

Within the context of interest in analyzing ‘active’ and nonlinear processes in the cochlea we have been studying a model cochlea in which the local membrane impedance is described by a Van der Pol-oscillator. The behaviour of the undriven and sinusoidally driven discretized model is examined numerically. The undriven model describes the behaviour of a discrete number of coupled oscillators, which, if uncoupled, would have limit cycles gradually differing in frequency. In the coupled case the limit cycle behaviour is less predictable: it appears to exhibit quasi stochastic properties. In the driven model a sufficiently strong stimulus causes entrainment to the stimulus, and odd order harmonics appear. In the range where the driven response is small compared with the average limit cycle, the response is almost linear. The strict Van der Pol-damping function, which is parabolic in velocity, produces strong saturation. A generalized Van der Pol-damping term, which causes small-amplitude instability and large-amplitude stability, produces much the same general behaviour, but the intensity response can be modelled more realistically.

Discharge patterns of single auditory nerve fibers in adult cats were recorded in response to multi-component harmonic complexes. Stimuli possessed a variable number of equal-intensity harmonics of a common low-frequency fundamental. Data were analyzed by examining Fourier transforms of period histograms locked to the period of the stimulus fundamental. At low intensities transfer functions agreed with those defined by more traditional measures such as tuning curves. However, responses generally showed nonlinear level dependence at higher intensities, particularly above 60 dB SPL. In this, response spectra changed from resembling a bandpass filter to resembling a band-reject filter, i.e. responses were synchronized to components at the edges of the signal spectrum and to combination tones near the edges. The nonlinear effects became more pronounced as the number of components in the signal pass-band increased. Comparison of data from fibers with a wide range of thresholds indicated that the nonlinear behavior is mainly related to absolute stimulus level. This suggestes that the site of the nonlineari-ty is located prior to the spike generator.

Nonlinear interaction between close tones in the cochlea has been examined in gerbil via the multiple otoacoustic emissions this interaction generates. Tonal stimuli of near equal level yield a wide spread of up to 20 otoacoustic sidebands. The amplitude and relative phase of these components have been measured and these have provided new insights into cochlear mechanical nonlinearity and data on the reverse transmission of distortion products. Otoacoustic intermodulation and suppression characteristics differ in detail from those of the simple saturating nonlinear model presented. Demodulation of the wideband emissions reveals temporal attributes of the cochlear interaction to be the major difference from the model.

We have made extensive measurements of the lower frequency cubic intermodulation distortion product sound pressure in the external auditory meatus of cats. This distortion product has a frequency, f_D = 2f₁-f₂, where f₁ is the lower frequency of two pure tone input sounds. A₁ and A₂ are the amplitudes of the pure tone inputs at frequencies f₁ and f₂ respectively. The evidence is substantial that this distortion product is generated in the cochlea and that it propagates back out into the ear canal (e.g., Kim, 1980). Our data is presented here as Thevenin equivalent source pressures rather than as raw ear canal pressures. The Thevenin equivalent source pressure is a measurement of the properties of the source (assuming that a system is approximately linear in its overall characteristic) while the raw ear canal pressure depends upon not only the source but also the impedances of the sound delivery system and the animal’s input impedance at the place of pressure measurement. (In animal studies, this is frequently the input impedance at the tympanic membrane.)

The cubic distortion product, 2f₁ — f₂ (DP), was recorded in the cat ear canal as the levels of two primary tones (f₁=4.0, f₂=5.2 kHz here) were varied from approximately 40 to 90dB SPL. The DP level grows as the cube of the primary level at low and high levels, and usually exhibits a dip near L₁ = 65dB SPL, DP growth functions and N₁ amplitude-level functions were compared before and after exposure to either 4 kHz pure tones or to 500 Hz octave bands of noise. Pure-tone exposure produced a dose-dependent shift in the N₁ growth whereas the low-frequency noise exposure produced widely varying shifts in N₁ functions. In either case, however, changes in DP were correlated with changes in the neural responses. The level of the DP was compared before and after exposure at 2 levels below and one above the dip at L₁ = 65dB SPL. For all of these measures, the decrease in DP level was significantly correlated with the shift in the N₁ growth function. At both low and high primary levels, decrease in DP grows approximately as the square of the N₁ shift for shifts greater than 15dB.

Harmonics of moderate-level single tones can be measured in the earcanals of gerbils with healthy ears. The same harmonic components measured in a cavity are as much as 20 to 40 dB below those measured in the earcanal. Earcanal harmonics, specifically the second and third, are generated largely within the cochlea and are physiologically vulnerable. Harmonic magnitudes rapidly decrease for primary frequencies above about 3 kHz. High-frequency masking tones can have dramatic suppression effects on the harmonic structure of low frequency primaries. For example, a 2 or 4 kHz masker at moderate levels can totally suppress the third harmonic of a 200 Hz tone. Many of these results can be simulated by a vector-sum model. In this model harmonic emissions can be thought of as very gross potentials that convey little information concerning specific regions of the cochlea.

Electrical networks consisting of linear passive elements and many nonlinear resistors are often used to model the basilar membrane. The inputs to these networks are typically a sum of sinusoids switched on at t = 0, and the resulting quantities of interest because of their interpretation as analogs of experimental observables are the steady-state response components of a certain current and of certain voltages. In this paper, recently obtained mathematical results concerning the input-output representation of nonlinear systems are used to give, for the first time, a locally convergent expansion for all of the steady-state quantities of interest. Also given is a good deal of information concerning general properties of the expansion, and this establishes important properties of the nonlinear network’s response. Of particular practical interest is a term in the expansion that contains a component whose frequency is (2f₁-f₂) when the network’s input consists of a sum of two sinusoids, with frequencies f₁ and f₂. One of our main results is an explicit expression for this (2f₁-f₂) component.

The hair cells in the cochlea are divided into two morphologically distinct populations: a single row of inner hair cells (IHC) and three or four rows of outer hair cells (OHC). On the basis of differences in morphology, IHCs and OHCs have been attributed with different roles in mechano-electric transduction in the cochlea. The aim of this paper is to review recent studies on the electrophysiological properties of hair cells in the mammalian cochlea to see if there is any basis for this suggestion.

Tones produced by the injection of current into scala media were measured in the ear canal. The ear-canal emissions were substantially modified with the intravenous injection of a diuretic, furosemide. Changes in the endolymphatic potential and the cochlear microphonic were also measured.

Video enhanced microscopy is used to measure shape changes of isolated outer hair cells in response to transcellular electrical stimulation. Low frequency sinusoidal stimulation results in sinusoidal modulation of cell length about its resting value. Elongation is associated with positive potential gradients. Electrically evoked motility is unaffected by the presence of metabolic poisons that interfere with the production of ATP. Isotonic dilution of the bathing medium results in an increase in displacement magnitude. The symmetry of the displacements, their dependence on voltage gradients, independence of ATP, and evidence for an inverse relation between ionic concentration and magnitude of the movement argue against a contractile mechanism, but are compatible with electro-kinetic processes.

In order to obtain visual control over micromechanical and electrophysiological measurements on the sensory hair cells of the fish lateral line in vivo we developed an optical method based on polarization microscopy. The thickness of the preparation prevents the use of transmitted light microscopy. The results of the investigation show that under conditions of polarized incident light illumination, visualization of the cell surface and of the hair bundles of the sensory hair cells can be realized. The image of the hair cells and bundles is formed by the light reflected back by the nerves underlying the low reflective sensory epithelium in the macula. Although at a magnification of 800 × the image of the sensory epithelium is contrast limited, under the most favourable conditions of illumination the individual stereocilia and the kinocilium of the hair bundle can be distinguished. The cupula, a jelly-like structure in which the hair bundles are embedded, does not noticeably disturb the image of the hair cells and its integrity assures physiological conditions for the apical surface of the hair cells.

Based on the experimental observations of the mechano-electrical transduction in hair cells, we formulate a model of the receptor potential utilizing a simple model circuit and ideas of stretch activation. The stereociliary displacement-response relation is developed based on the cilia crosslinking, thus incorporating notions of bidirectional sensitivity, asymmetry, saturation, and adaptation naturally into the model. We then give some simulation results involving periodic stimuli to the hair bundle as well as current stimuli to study latency behavior and other qualitative properties of the model.