Otoacoustic Emissions from Residual Oscillations of the Cochlear Basilar Membrane in a Human Ear Model

Abstract

Sounds originating from within the inner ear, known as otoacoustic emissions (OAEs), are widely exploited in clinical practice but the mechanisms underlying their generation are not entirely clear. Here we present simulation results and theoretical considerations based on a hydrodynamic model of the human inner ear. Simulations show that, if the cochlear amplifier (CA) gain is a smooth function of position within the active cochlea, filtering performed by a middle ear with an irregular, i.e., nonsmooth, forward transfer function suffices to produce irregular and long-lasting residual oscillations of cochlear basilar membrane (BM) at selected frequencies. Feeding back to the middle ear through hydrodynamic coupling afforded by the cochlear fluid, these oscillations are detected as transient evoked OAEs in the ear canal. If, in addition, the CA gain profile is affected by irregularities, residual BM oscillations are even more irregular and tend to evolve towards self-sustaining oscillations at the loci of gain irregularities. Correspondingly, the spectrum of transient evoked OAEs exhibits sharp peaks. If both the CA gain and the middle-ear forward transfer function are smooth, residual BM oscillations have regular waveforms and extinguish rapidly. In this case no emissions are produced. Finally, and paradoxically albeit consistent with observations, simulating localized damage to the CA results in self-sustaining BM oscillations at the characteristic frequencies (CFs) of the sites adjacent to the damage region, accompanied by generation of spontaneous OAEs. Under these conditions, stimulusfrequency OAEs, with typical modulation patterns, are also observed for inputs near hearing threshold. This approach can be exploited to provide novel diagnostic tools and a better understanding of key phenomena relevant for hearing science.

Do Forward- and Backward-Traveling Waves Occur Within the Cochlea? Countering the Critique of Nobili et al.

“…Nature of the fluid coupling Nobili et al (2003a) launch their critique of waveequation formulations of cochlear mechanics by arguing that transmission-line models fundamentally misrepresent the hydrodynamics of the cochlea. In particular, they claim that transmission-line models ''reduce fluid coupling to a sort of local interaction, thus failing to represent adequately its long-range character.''…”

“…As in Figure 6 of Nobili et al (2003a), the solid lines show the amplitude and phase of the response to a sinusoidal stimulus ($2 kHz) applied at the BM location x indicated by the labeled vertical line spanning the top and bottom panels. In this case, the impedance mismatch at the cochlear boundary with the middle ear results in a stapes reflection coefficient with the value R stapes = -0.8.…”

“…The dotted lines show the forward-traveling wave elicited when the stimulus is applied at the stapes. As in Nobili et al (2003a), the amplitudes represented by the solid and dotted lines were normalized to similar peak values and then offset slightly for clarity. BM velocity responses were computed using the model of Zweig (1991) line equations [i.e., the pressure ''basis waves'' (Shera and Zweig 1991a;Talmadge et al 1998)] and the three complex constants a + and b ± are determined by requiring that P(x) satisfy both the basal boundary condition at the stapes and continuity of pressure and conservation of volume velocity at x.…”

“…In recent years, however, Nobili and colleagues have criticized wave-equation formulations of cochlear mechanics on the grounds that they fundamentally misrepresent the hydrodynamics of the cochlea (Nobili 2000;Nobili et al 1998Nobili et al , 2003a. They write, for example, that ''the solutions of the BM [basilarmembrane] motion equation are not of the bi-directional wave-propagation type'' and can ''in no way ... be represented as the superposition of progressive and regressive wave components.…”

“…As a corollary of their critique, Nobili et al (2000Nobili et al ( , 2003aNobili et al ( , 2003b condemn existing models of otoacoustic emissions (OAEs), especially those that incorporate the language of wave propagation and reflection (e.g., Shera and Zweig 1993;Zweig and Shera) 1995;Talmadge et al 1998Talmadge et al , 2000. They write, for example, that although wave-reflection models of OAEs may seem ''conceptually appealing'' on the surface, their underlying tenets are, ''in reality, ... difficult to reconcile ... with the physics of the cochlea.''…”