Stiffness vs damping in the cochlea: A negative conclusion?

Abstract

While the notion of an active mechanism at work in the inner ear giving rise to amplification of low-level stimuli is widely considered to be firmly established, the nature of the underlying mechanisms(s) is however still a topic of significant debate. Disparate arguments have been about the nature of the underlying active term, specifically whether it manifests as a negative stiffness (position-dependent) or a negative damping (velocity-dependent). We analytically describe here that for a for an autonomous second-order resonator, a negative stiffness alone is insufficient to produce a super-critical Hopf bifurcation (a property commonly attributed to argue for amplification) and a negative damping is required. Moreover, an autonomous resonator with a negative stiffness alone cannot exhibit limit cycles (i.e., spontaneous oscillations). These observations are thus consistent with the notion that an active mechanism contributes in a velocity-dependent fashion. While simple second-order models alone are likely too simple to capture essential features of the ear, our results can help guide interpretation of more detailed/complex approaches (e.g., coupled oscillators, stochastic forcing). © 2011 American Institute of Physics.