Subject: Cochlear travelling wave. An epiphenomenon? From: Antony Locke <A.Locke(at)SOTON.AC.UK> Date: Tue, 27 Jun 2000 12:34:25 +0100Dear Andrew Bell, Eckard Blumschein and list The list has seen a number of observations stated, models proposed and opinions aired regarding cochlear mechanics. Andrew's model invokes a novel mechanism to explain energy transfer within the cochlear, but at the same time disregards two established, and fundamental, observations of cochlear mechanics. (In Jont's notation...) In my opinion (IMO), the utility of the discussion can be increased with reference to the notion of 'level of description'. At the most basic level of description, i.e. within a linear one dimensional (macroscopic) approximation (corresponding to a high stimulus level), the following two observations have been made (for a fuller and more elegant explanation see Lighthill, 1991 Trans ASME Vol 113):- 1) The mechanical property of the cochlear partition (CP) is highly graded; the stiffness changes by approx. 4 orders of magnitude. Here the CP is taken to encompass those structures that respond to sound; i.e. basilar membrane, IHC, OHC, supporting cells, TM). This statement refers to a macroscopic description. The stiffness is primarily governed by the basilar membrane and is shown to be anisotropic. 2) The cochlea can support two modes of wave motion; one mode initiates a fast wave the other launches a slow wave. The fast wave is a compressional wave that propagates within the scalae from the base to apex at roughly 1500 m/s. There is no net pressure across the cochlear partition. On the other hand, the slow wave is a hydromechanical wave that is dependent upon the interaction of the CP and fluid within the scalae; it is referred to as the travelling wave. The energy within the travelling wave is shared between the kinetic energy of the fluid and potential energy of the CP. Consider driving the ear under sinusoidal excitation. At positions basal to the characteristic place the propagation speed is of the order of 100 m/s. At positions closer to the characteristic place the travelling wave slows down, energy plies up. At the characteristic place the travelling wave ceases propagating. At a higher driving frequency the characteristic place, by virtue of the highly graded CP, shifts towards the base. The cochlea leads to dispersion. The cochlea acts as an acoustic prism. The finding of a highly graded CP, in my opinion, indicates that the travelling wave is the mode of energy transfer from base to characteristic place; the highly graded CP and travelling wave are intimately linked. Andrew and Eckard state that the travelling wave is an epiphenomenon. I interpret that to mean that in your model the mode of energy transfer from base to characteristic place is independent of the travelling wave. Question 1: Is there any functional relevance of the highly graded CP? If so, why is the travelling wave not the obvious candidate for energy transfer at the most basic level of description? Question 2: How is the dispersion (i.e. tonotopic: mapping frequency to space) property of energy propagation within the cochlea explained by your model without invoking the travelling wave? Kind regards Antony Locke