George Zweig

The origin of periodicity in the spectrum of evoked otoacoustic emissions

Current models of evoked otoacoustic emissions explain the striking periodicity in their frequency spectra by suggesting that it originates through the reflection of forward-traveling waves by a corresponding spatial corrugation in the mechanics of the cochlea. Although measurements of primate cochlear anatomy find no such corrugation, they do indicate a considerable irregularity in the arrangement of outer hair cells. It is suggested that evoked emissions originate through a novel reflection mechanism, representing an analogue of Bragg scattering in nonuniform, disordered media. Forward-traveling waves reflect off random irregularities in the micromechanics of the organ of Corti. The tall, broad peak of the traveling wave defines a localized region of coherent reflection that sweeps along the organ of Corti as the frequency is varied monotonically. Coherent scattering occurs off irregularities within the peak with spatial period equal to half the wavelength of the traveling wave. The phase of the net reflected wave rotates uniformly with frequency at a rate determined by the wavelength of the traveling wave in the region of its peak. Interference between the backward-traveling wave and the stimulus tone creates the observed spectral periodicity. Ear-canal measurements are related to cochlear mechanics by assuming that the transfer characteristics of the middle ear vary slowly with frequency compared to oscillations in the emission spectrum. The relationship between cochlear mechanics at low sound levels and the frequency dependence of evoked emissions is made precise for one-dimensional models of cochlear mechanics. Measurements of basilar-membrane motion in the squirrel monkey are used to predict the spectral characteristics of their emissions. And conversely, noninvasive measurements of evoked otoacoustic emissions are used to predict the width and wavelength of the peak of the traveling wave in humans.

Finding the impedance of the organ of Corti

Measurements of the nonlinear response of the basilar membrane to a pure tone are shown to have a simple form for moderate membrane velocities: V(x,f;Vu)/Vu approximately [V(x,f)/Vu]v(x,f), f less than or equal to fc(x), where the response V is the velocity of the membrane at measurement position x, Vu is the umbo velocity, f is the frequency of the stimulus, and fc(x) is the local characteristic frequency. The frequency dependence of the functions v(x,f) and V(x,f) is determined from the data, and v(x,f) and ln V(x,f) are shown to be analytic functions in the lower half of the complex frequency plane, with Re [v(x,f)] a monotonically increasing function of f at fixed x. The linear limit of basilar membrane motion is characterized by a transfer function T(x,f) = (V/V1)v/(1-v), estimated by extrapolating V(x,f;Vu)/Vu to a small membrane velocity V1.T(x,f) and ln T(x,f) are shown to be analytic functions in the lower half of the complex frequency plane. The inverse of the amplitude of the transfer function, which has both a deep dip at f approximately fc(x) and a broad shoulder at lower frequencies, bears a striking resemblance to the neural threshold tuning curve. The functional form of T(x,f) is used to deduce the equation governing the motion of a section of the organ of Corti. Each section acts like a negatively damped harmonic oscillator stabilized at time t by a feedback force proportional to the velocity at the previous time t-tau. The time delay tau is proportional to the oscillator period [tau approximately 1.75/fc(x)]. Like a laser, the organ of Corti pumps energy into harmonic traveling waves. Unlike the laser, the direction of energy flow abruptly reverses as the traveling wave approaches the point of maximum membrane velocity [fc(x) approximately f]. All accumulated wave energy is then pumped back into a small section of the organ of Corti where transduction presumably occurs. Outer hair cells are conjectured to be active elements contributing to the negative damping and feedback of the cochlear amplifier.

The cochlear compromise

It is conjectured that the design of the cochlea is influenced by two conflicting requirements: (1) the cochlea should act as a precise frequency analyzer and (2) waves propagating along the basilar membrane should be transmitted without reflections. Accurate frequency analysis is possible only if the mechanical properties of the cochlea change rapidly with distance along the basilar membrane. Reflections of waves traveling on the basilar membrane will be negligible, however, only if these same mechanical properties change slowly. A compromise between these two requirements is possible if a loss constant δ related to the sharpness of response of the basilar membrane to a pure tone is related to the number N of wavelengths of the wave on the basilar membrane [N/(δ)1/2?1]. Furthermore, if sizable changes in the displacement occur only over distances larger than the width of a hair cell, then δ must be larger than the ratio of the width w of a hair cell to the distance d along the basilar membrane over which...

Reflection of retrograde waves within the cochlea and at the stapes

A number of authors [de Boer and Viergever, Hear. Res. 13, 101-112 (1984); de Boer et al., in Peripheral Auditory Mechanisms (Springer-Verlag, Berlin, 1986); Hear. Res. 23, 1-7 (1986); Viergever, in Auditory Frequency Selectivity (Plenum, New York, 1986), pp. 31-38; Kaernbach et al., J. Acoust. Soc. Am. 81, 408-411 (1987)] have argued that backward-traveling waves, in striking contrast to waves traveling forward towards the helicotrema, suffer appreciable reflection as they move through the basal turns of the cochlea. Such reflection, if present, would have important consequences for understanding the nature and strength of otoacoustic emissions. The apparent asymmetry in reflection of cochlear waves is shown, however, to be an artifact of the boundary condition those authors impose at the stapes: conventional cochlear models are found not to generate reflections of waves traveling in either direction even when the wavelength changes rapidly and the WKB approximation breaks down. Although backward-traveling waves are not reflected by the secular variation of the geometrical and mechanical characteristics of the cochlea, they are reflected when they reach the stapes. The magnitude of that boundary reflection is computed for the cat and shown to be a large, rapidly varying function of frequency.

Middle‐ear phenomenology: The view from the three windows

To provide a common ground for the comparison between theory and experiment, this paper presents a framework for the phenomenological description of middle-ear mechanics. The framework defines those measurements sufficient to characterize the transduction properties of the middle ear and its components. Phenomenological equations are represented in the form of an equivalent electrical circuit that can be used to deduce testable relations among measurable quantities. Two applications are then discussed. First, the classical concept of the middle-ear transformer ratio is generalized to include any effects of eardrum flexion or nonrotational ossicular motion. Middle-ear models predict that the resulting transformer ratios vary considerably with frequency. Second, the conditions under which the topology of existing circuit analogs satisfactorily approximates middle-ear mechanics are given. Most middle-ear models cannot be used to correctly predict the absolute pressures in the cochlea.

Phenomenological characterization of eardrum transduction

A phenomenological description of the transduction effected by the eardrum is presented. That description is provided by a transfer matrix, whose elements define those measurements sufficient to characterize eardrum transduction. Causality provides constraints on the matrix elements. In addition, measurements of the matrix elements can determine whether they satisfy constraints imposed by minimum-phase behavior and the principle of reciprocity. Those constraints may be used either to reduce the number of measurements necessary to characterize the eardrum or to check the consistency of measurements that overdetermine the system. Within its region of validity, the transfer matrix of the eardrum provides a common ground for the comparison between theory and experiment. As an example, a simple model for the transduction characteristics of the eardrum, defined completely in terms of measurable quantities, is presented.

Quark Catalysis of Exothermal Nuclear Reactions

This article discusses circumstances under which free quarks catalyze exothermal nuclear reactions. It also presents possible methods for removing quarks sequestered by nuclear reaction products. Stable quarks that are negatively charged and significantly heavier than electrons attract positively charged nuclei to form new states of matter. The nuclei and quarks are closely bound, and presumably interact through both electromagnetic and nuclear forces. Nuclear fusion and fission are possible, as well as a new class of plural reactions in which either a quark isobar, isotope, or isotone is created in each individual reaction, with catalysis resulting in the overall system because the net transfer of charge, neutrons, or protons to the quarks is zero. The quark with quantum numbers of �� is a promising catalytic candidate. A satisfactory understanding of which reactions are or are not possible awaits the isolation of free quarks and a description of their strong interactions with matter. Finally, other kinds of stable negatively charged particles (such as heavy leptons), if discovered, can catalyze deuterium fusion reactions if thermal neutrons are used to liberate He3-bound catalytic particles.

The Impedance of the Organ of Corti

In previous papers (Zweig 1987, 1988) the impedance of the organ of Corti was deduced from measurements of basilar membrane motion. That impedance is the starting point for this paper. The power transfer between the organ of Corti and its harmonic traveling waves is calculated. The time delays of forces presumed to originate in outer hair cells are estimated.

Linear cochlear mechanics.

An active, three-dimensional, short-wavelength model of cochlear mechanics is derived from an older, one-dimensional, long-wavelength model containing time-delay forces. Remarkably, the long-wavelength model with nonlocal temporal interactions behaves like a short-wavelength model with instantaneous interactions. The cochlear oscillators are driven both by the pressure and its time derivative, the latter presumably a proxy for forces contributed by outer hair cells. The admittance in the short-wavelength region is used to find an integral representation of the transfer function valid for all wavelengths. There are only two free parameters: the pole position in the complex frequency plane of the admittance, and the slope of the transfer-function phase at low frequencies. The new model predicts a dip in amplitude and a corresponding rapid drop in phase, past the peak of the traveling wave. Linear models may be compared by their wavelengths, and if they have the same dimension, by the singularity structure of their admittances.

Determination of the stochasticity of the excitation function of speech

The frequency above which the excitation function of a voiced vowel becomes essentially stochastic is determined. It varies with speaker and stress. Knowledge of this transition frequency can be used to develop better spectral subtraction denoising algorithms, where different methods of spectral estimation are used above and below this frequency. In addition, whenever speech is (1) unvoiced, or voiced with constant pitch, and (2) the convolution of an excitation function with another function, a normalized variance of the spectral estimate of speech can be defined which equals the normalized variance of the spectral estimate of the excitation function. This normalized variance measures the frequency dependence of the relative strengths of the stochastic and deterministic components present in the excitation function. As expected, for voiced vowels the normalized variance is small at low frequencies, confirming that the excitation function is largely deterministic. At high frequencies the normalized varian...