Are active elements necessary in the basilar membrane impedance?

This article is motivated by the current hypothesis [Kim et al., Psychological, Physiological and Behavioural Studies in Hearing (Delft U. P., The Netherlands, 1980); Neely, Doctoral dissertation, Washington University, St. Louis, MO (1981); de Boer, J. Acoust. Soc. Am. 73, 567-573 (1983a) and 73, 574-576 (1983b)] that it is necessary to include active elements in the basilar membrane (BM) impedance in order to explain recent data on the vibration of the BM [Khanna and Leonard, Science 215, 305-306 (1982); Sellick et al., J. Acoust. Soc. Am. 72, 131-141 (1982); Robles et al., Peripheral Auditory Mechanisms (Springer, New York, 1986)]. In order to test this hypothesis, first, a method which is an inversion of the customary description of cochlear mechanics is described. Instead of computing the BM velocity for a given point impedance of the membrane, we show how to compute the impedance function from a given BM velocity pattern in response to a sinusoidal input at the stapes. This method is then used to study the sensitivity of the recovered impedance to perturbations in the velocity pattern. The simulations used show that the real part of the impedance is extremely sensitive to such perturbations. Therefore, measured velocity patterns are unlikely to resolve the issue of whether active elements should be included. Frequency responses measured at a few points on the membrane are even less likely to do so.