

Re: Wasn't v. Helmholtz right?

-----Original Message-----
From: Ben Hornsby [mailto:ben.hornsby@vanderbilt.edu]
Sent: Friday, 16 June 2000 12:17
To: Andrew Bell
Subject: Re: Re: Wasn't v. Helmholtz right?


to some degree. One comment you made caught my eye:

 damping excessive motion."

I noticed that other respondents to the discussion either agreed with this

Ben Hornsby


Dear Ben:

Thankyou for your interest and your perceptive question.

this level, there is insufficient differential pressure developed across the
sufficient common-mode pressure, a factor usually neglected in mathematical
that the acoustic impedance of the helicotrema is much lower than usually
assumed, so that this hole effectively short-circuits the pressure
pressure built up uniformly throughout the cochlea by the inward movement of
speaker enclosure).

Both the low- and high-level processes involve the tectorial membrane, and
only incidentally the basilar membrane (where doppler velocimeter
measurements are made with reflective beads).

Thus, at low SPLs, the OHCs are creating ripples on the underside of the
tectorial membrane. There is effectively no movement of the top layer, which
is covered with a net (indeed, the covering net is designed to damp
movement). The OHC resonant cavity is a regenerative receiver of oscillating
sound pressure (it's like a radio receiver in the cochlea picking up a
broadcast from the transmitter at the oval window). It amplifies the signal
and sends the output to the IHC via ripples on the underside of the TM.
Accompanying this activity, some energy will be communicated to the BM;
however, because the wavelength is small (the distance between OHC1 and
OHC3, about 30 um), and because the reflective beads dropped on the BM are
about that size, the measured movement is much less than the movement
experienced by the IHCs when they sense the radially propagating wave on the
TM. Hence, the measurements are sensing only a residual fraction of what is
really going on. The result is that we end up with unimaginably small
figures for the threshold of detection: figures claiming that at 0 dB the
IHC can detect BM movements of hundredths of nanometres and stereocilia
deflections of hundredths of a degree (see Dallos, in The Cochlea, ed. P.
Dallos et al, Springer, 1996). Of course, the IHC is detecting far bigger
movements because it is closer to the output of the regenerative receiver.

Above about 60 dB, however, the regenerative receiver saturates, and a
second process begins. (Saturation occurs when the membrane potential of all
three OHCs falls to the same resting level: there is now no amplification
because there is no difference in the response of OHC2 compared to its
neighbouring OHC1 and 3.) The cochlear partition begins to move because the
differential pressure across it finally becomes sufficient to exert enough
force. That is, there is some acoustic impedance at the helicotrema to allow
a degree of differential pressure build-up. Now the traveling wave picture
can be introduced, but with a difference - the pressure difference is across
the tectorial membrane, not the basilar membrane.

This is because acoustic pressure builds up across a material only when the
acoustic resistance of that material is appreciable. Think of a thin rubber
sheet immersed in a swimming pool: that sheet is invisible to passing
acoustic waves and the waves pass straight through. By contrast, a sheet of
metal suspended in a pool is detectable because waves bounce off it. The
difference in the two cases is that the speed of sound in the water differs
substantially from that in steel, but not the speed in rubber. In the same
way, the speed of sound in the basilar membrane differs little from that in
water. However, the tectorial membrane is a gel with tensile properties (and
corresponding compressional wave speed) appreciably different to those in
water. The result is that acoustic pressure builds up across the TM, not the
BM. What this means in practice is that the TM is vibrated backwards and
forwards against the vestibular lip, once more generating ripples which are
launched from the lip (that's what it's there for), and propagate along the
underside of the TM towards the IHC. In this respect, we can understand why
the lip is so remarkably sharp and well defined; the lip launches ripples
simultaneously along its length, and because of graded ripple speed along
the partition (based on TM surface tension and thickness), we get a graded
delay of response at the IHCs - otherwise interpreted as a 'traveling wave'

In summary, there are two ripple-generating processes going on: one in the
OHC cavity at low SPLs, and the other from the vestibular lip (at high
SPLs). Note that such an arrangment leads to cancelation of the IHC response
at some intermediate sound level (observed as 'peak splitting' in cochlear
nerve studies); it also leads to dynamic range compression. Compression
occurs because the amplitude of the ripples is a non-linear function of SPL.
It also happens because the OHC detectors saturate, and can become active
absorbers at higher SPLs (simply by changing relative membrane potential
between OHC2 and OHC1&3).

Movement of the basilar membrane, which is usually thought of as the result
of resonant mass/compliance elements in the partition, is simply spreading
of agitation from OHC activity. It is also a process which tends to absorb
energy (Martin Braun [Hearing Research, 97 (1996), 1-10] suggested that this
is what the BM is for). While this is happening, remember that the tuning of
the OHC cavity is about half an octave higher than the mass/compliance
tuning of the TM (and probably an octave or more higher than the strongly
damped movement of the whole partition). Here is an explanation for the
curious half-octave shift of McFadden (In: Basic and Applied Aspects of
Noise-Induced Hearing Loss, Salvi et al (eds), Plenum, 295-312).

Clearly, dropping reflective beads on the BM, or even the top of the TM, is
not going to give us a clear picture of what's going on in the OHC cavities,
particularly at low SPLs. Another misleading result from invasive
experimentation is that drilling a hole in the cochlea is going to disrupt
the pressure response of the OHCs.

Andrew Bell.