Natural Science Forum / Physics / Acoustics / April 2006

May 11 2004 5:44 am, alt.sci.physics.acoustics
Re: Basilar membrane mathematics of place theory
Eckard Blumschein wrote:

Because of the work of Bekesy and others, it is known that the inner
ear responds to different frequencies at different places along the
length of the basilar membrane, by sending electrical impulses along
the aural nerve into the brain.  This principle is at the basis of
'cochlear implant' technology, which is used to help deaf people in
situations where the ear is severely damaged but the aural nerve is
unimpaired.  A cochlear implant is in effect an 'artificial ear', which
replaces the functionality of most of the ear and the cochlea: a
microphone earpiece transforms sounds into electrical signals
corresponding to the frequency bandwidths of the 'formants' of human
speech, and a thin wire inserted into the cochlea stimulates the
basilar membrane at places along its length corresponding to these
frequency bandwidths.

For some reason, the performance of cochlear implants has been
disappointing.  Recipients often report that the implants only help
them distinguish between sounds and silences - if the implants are
're-tuned', sounds seem higher or lower for a while, but the effect
soon wears off.  Although recipients are encouraged to persevere, on
the principle that their brain would gradually learn to make sense of
the input noise, many of them prefer to leave their implants switched
off most of the time because they are too noisy.

One could suggest that these patients were unlucky - perhaps their
aural nerve was too damaged for cochlear implants to work for them.
However, one does not also hear of lucky successes in cochlear implant
operations, where patients who were previously deaf have become able to
hear speech relatively clearly.  The idea behind cochlear implants is
correct (from Bekesy), today's technology is certainly capable of the
speed and precision necessary to transform sounds into the required
electrical signals (a normal cochlea sends only a few thousand signals
per second along the aural nerve), and technicians can tune the
frequency response from different places along the cochlear implant to
a very high accuracy for any particular recipient - sufficient that one
might expect the technology to be not only adequate for human speech
(which is the focus of cochlear implant research these days), but also
for sounds as varied as thunder, Beethoven symphonies, and birdsong.
So why aren't cochlear implants more successful?  The answer must be
that the 'place theory' model of hearing is incomplete - but there is
of course no point in finding faults in the place theory (as many
laymen do) without being able to suggest a better theory.

My interest in the subject came about as a composer of music, with
normal hearing.  I was trying to construct a filter which would
stimulate the inner ear in patterns which are unlikely to occur in
nature, in the hope that interesting and unusual sounds would result,
and I developed a computational model of the ear which takes Bekesy's
observations into account, but is independent of any specific mechanics
of the ear.  Using this model, I was able to theorise about sounds
which would frequently cause unusually large numbers of electrical
impulses to happen at the same time, or which had abnormally large
micro-silences between impulses, or which consisted of rearrangements
of small slices of an input signal, perhaps partially reversed, or out
of phase, or with pre- and post- 'micro-echoes'.  I came to the
conclusion that the effect I was hoping for would be equivalent to
subliminally tricking the ear/brain into hearing something in a sound
that wasn't there to begin with - rather a waste of time from a
composer's point of view.  More importantly, if it were possible to
trick the ear like that, much of the animal kingdom would already have
evolved the ability to psychologically control their prey by producing
various 'unlikely' clicks and buzzing sounds, and hearing would be
worse than useless - the ear must in fact have evolved to make such
subliminal tricks impossible.

So I discarded my computational model of hearing, and continued instead
with another compositional avenue I was exploring.  The idea was to
spectrum analyse speech, transcribe the output for performance on an
acoustic microtonal player-piano, and then 'sculpture' the result by
cutting out the more discordant notes and leaving in the more musical
elements where possible, to produce interesting 'talking piano'
effects.  I was looking for some formant analysis of typical speech,
and discovered that a lot of the necessary work has already been done
by cochlear implant reseachers, but also, that cochlear implants have
fallen a long way short of their theoretical potential.  It naturally
occurred to me that my discarded model of hearing might in fact be
useful, but in the context of curing deafness rather than in composing
music.  I myself have neither the resources nor interest in cochlear
implants to pursue the ideas, but as I haven't been able to find
anything similar on the internet, I am presenting them here in the
expectation that they will find their way to whoever's job it is to
look into such matters.  In the unlikely event that the model has not
already been considered and properly evaluated by researchers, I hope
that it will enable clinical technicians to program cochlear implants
more effectively and improve their success rate with deaf patients, who
will then be able to hear my microtonal piano compositions!

The model is as follows:

Consider the ear/brain connection as a large number of (conceptual)
synapses, equivalent to the cilia inside the cochlea.  The point of the
model is that it doesn't matter precisely where in the ear or the brain
these conceptual synapses are, or even if they have exact physical
counterparts, but because sounds are caused solely by air pressure
varying over a period of time, it is computationally valid to deal with
the problem as though pressure were the only physical variable.
Synapses corresponding to cilia nearer the centre of the cochlea are
less sensitive to variations in air pressure, they have a lower maximum
repeat firing rate and need more energy to fire - those at the other
end of the basilar membrane are more sensitive, they have a higher
maximum repeat firing rate and need less energy to fire.

Conceptual synapses are like miniature batteries, which are charged up
by a combination of continued pressure above an ambient, and increases
in pressure.  When a battery is fully charged, it discharges its
contents (fires) onto the aural nerve, and then starts to recharge
according to the subsequent sound pressure variations.  There might be
a short delay after a synapse fires before it can recharge efficiently,
and the other computational variables are: the capacity of each
battery/synapse; the time it takes to charge a synapse (which is
related to the maximum repeat rate for that synapse); the dependency of
the charging rate on continued pressure and increases in pressure; and
the ambient pressure.  The values of all these variables are likely to
be slightly different for each synapse/cilium, but it is assumed that
the differences increase gradually from one end of the basilar membrane
to the other in some reasonably linear manner which can be discovered
by experiment.

The conceptual synapses behave like thousands of individual primitive
ears, each sending their own coarse interpretation of the sound
pressure variations along the aural nerve and into the brain, and
together they form electrical impulse patterns which the brain attempts
to interpret.  It is important to realise that these patterns contain
temporal information because of the time between firings of different
synapses, so the brain can deduce frequency information from the
distance between the electrical impulses corresponding to these
firings.  Amplitude information is deduced from the quantity of firings
occurring for a particular pattern.  While the impulse patterns are
travelling in the brain, they are matched against patterns from
previously-heard sounds which have been stored in the brain's auditory
memory.  During this process, neural pathways in the memory are
strengthened, resulting in the brain deciding on what the sound 'is'.

I could go into considerably more detail, but I assume that anyone who
is familiar with the problem will understand what I am getting at, and
will be able to adapt or add to the model where required.  Many
clinical trials would be necessary to decide on realistic values for
the computational variables, but once that has been done, the synaptic
firings predicted by the model for an input pressure waveform, should
be spread out along the cochlear implant according to the distribution
of the corresponding cilia, to produce patterns of electric signals
similar to those produced by a normal ear, for all types of sound.  It
should not be necessary to pre-analyse sound into formants to make the
cochlear implant especially responsive to human speech, because the
distribution of the sensitivity of the synapses/cilia along the basilar
membrane already performs that function.