Cochlear travelling wave. An epiphenomenon?

[Antony Locke <A.Locke@xxxxxxxxxxx>]

Dear 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