Martin, thanks for the ref on the rat IC. They
do mention critical bands in one paragraph under
"functional significance", which I reproduce
here for discussion:
Critical band filters have been postulated to
originate at the midbrain level (Ehret and
Merzenich, 1985; Ehret and Merzenich, 1988;
Ehret and Schreiner, 2005) where inhibitory
processing produces level-tolerant neurons
(narrow FRA types, (Hernandez et al., 2005;
LeBeau et al., 2001). Schreiner and Langner
(1997) suggested that the IC consists of a
stack of 30-40 critical bands, each equal in
size to the frequency-band laminae defined by
the changing steps in the tonotopic map. The
number of critical bands in the rat is not
known, but a rough estimate can be based on two
assumptions: 1) The basilar membranes of
mammals are scale models of each other and
critical bands cover equal distances on the
basilar membrane (Greenwood, 1990); 2) one
critical band is thought to cover roughly 1 mm
(0.7 - 1.3 mm) on the basilar membrane. Based
on the 8 mm length of the rat's basilar
membrane, rats have about 8 - 12 critical bands
(Ehret and Schreiner, 2005). Interestingly, our
data in the IC suggest there may be 8-12
laminae, each covering 0.29-0.36 octave. This
separation is similar to critical bands of
0.333-0.375 octave suggested for the mouse
(Egorova et al., 2006). Moreover, this grouping
is also compatible with studies on the
frequency separation needed to activate
independent neuronal populations in the IC
(Oliver, 2005; Yang et al., 2003; Yang et al.,
2004). Two pure tones 0.5 octaves apart
activate two laminae in the IC, while tones
0.25 octaves apart activate a single lamina.
The paper is all about the IC's laminar
organization, with discrete jumps in tuning,
similar to Ehret's and others' findings in other
species. It's fascinating stuff. I'm still
unclear on how it relates to psychophysical
effects, where there is not evidence of
discontinuities in tuning, as far as I'm aware.
Their final statement that "Two pure tones 0.5
octaves apart activate two laminae in the IC,
while tones 0.25 octaves apart activate a single
lamina" is also somewhat puzzling. Can't tones
0.25 octaves apart fall into and activate two
lamina, depending on the tone frequencies
relative to the CF boundaries?
I don't have any problem with the reported
science data, just questioning some of the
interpretations. I'd still like to know what
properties of critical band phenomena they are
saying are not present in the periphery.
I've always been a bit puzzled by the treatment
of critical bandwidth as if there was a filter
channel per critical band, spaced one critical
band apart, which is what seems to be suggested
by counting the number of critical bands, and by
associating that count with the lamina in IC.
I've been trying to get at this via Schreiner
and Langner 1997, which says "We interpret this
layered frequency organization as a potential
structural substrate for the creation of
critical bands by lateral inhibition." It's
again a very interesting paper, with some
assumptions and speculations that I don't
understand or agree with. But they do explain
that the CF varies within a lamina, so they call
them not "iso-frequency", but "frequency band
lamina." and "In a stack of 30-45 frequency-band
laminae (Fig.3b), each exhibits a shallow,
continuous frequency progression orthogonal to
the traditionally deÞned main dorso-ventral
tonotopic axis, and a more than ten-times
steeper, but discontinuous frequency progression
across the laminae." Then the CF distribution is
continuous. Sounds OK. But when I try to trace
their references about CB, and find out why they
assume that CB phenomena need to be level
independent, I can't find a basis for it.
They cite a whole raft of papers in support of
"The lowest auditory station where neurons do
have invariant Þlter properties comparable to
critical bands is the ICC" but many of these
papers don't even mention ICC. It's pretty much
the same set they cite for "...as the Þlter
bandwidths of the cochlea and peripheral neurons
are level-dependent and vary over a wide range."
I think we can agree than many of these do
support the observation that "Þlter bandwidths
of the cochlea and peripheral neurons are
level-dependent", even though most of them don't
really show that, and even though few
characterizations of the periphery get close to
what would make sense as a description of the
"filter bandwidths of the cochlea and peripheral
neurons" (typically, they get to the FTC, which
is always much sharper than a filter bandwidth,
and don't recognize the different; furthermore,
FTC don't show anything that can be interpreted
as level dependence, since there is no level
that corresponds to these curves).
They say "A neuronal theory of critical bands
would have to account for ... level-independent
bandwidth 1,2, where the citations are to a pair
of very old papers:
1. Fletcher, H. Auditory patterns. Rev. Mod. Physiol. 12, 47-65 (1940).
2. Zwicker,E.etal.Critical bandwidth in loudness
summation. J.Acoust.Soc.Am. 29, 548-557 (1957).
As I pointed out before, the recognition of
nonlinear level-dependent bandwidth in hearing
mostly came out in more recent decades, as both
psychophysical and physiological methods
advanced, and the current estimates for
psychological and physiological peripheral
filtering seem to be reasonably consistent with
each other. Are we pinning all this
interpretation of modern studies of ICC on
ancient approximate critical band observations?
It is seeming so. Furthermore, the cited
Zwicker 1957 describes several sorts of
level-dependent phenomena in his loudness
integration experiments, and says "The critical
band width is approximately invariant with
level." Not a bad approximation, given the
relatively crude methods, but still just an
approximation.
Besides these guys who study ICC, are there
others who see the bandwidth of peripheral
filtering as varying too much to represent
critical band behavior? Or is this POV unique
to the ICC guys?
One of things they point to is the good level
independence of things like echo-correlation
processing in the bat ICC. That makes a lot of
sense in terms of how compression in the
periphery makes it easier for time-domain
processing in the ICC to be tuned to certain
time delays with little level effect, and things
like that. But that sort of processing is
several nonlinear neural layers past the part
that can be sensibly characterized in terms of
spectrum and bandwidth, which are linear-system
concepts.
Part of the interpretation problem may stem from
the widespread confusion about how to interpret
a frequency-threshold curve (FTC) of a
compressively nonlinear cochlea relative to the
underlying linear filtering. Due to the
compression (less than 1:1 mechanical response
to input levels), the FTC comes out quite
sharp-tipped. For example, its width at 10 dB
up from the tip is about like the 3 dB bandwidth
of the underlying filter, for typical 3:1 or
steeper compression. You can't really get from
FTC to an estimate of filter bandwidth and its
level dependence without more data. The
alternative, plots of response versus frequency,
at various levels, is a more direct way to get
at filter bandwidths, and these are alway
broader. It doesn't make sense to compare their
level dependence to that of the FTC, as I
mentioned above, since there's no sensible
interpretation of the FTC in terms of
level-dependent bandwidth. It may be that some
people are looking at the width between left and
right edges at different levels as a bandwidth,
but that makes little sense in the usual linear
systems notion of "filter", since those are
"thresholds" at attentuations increasingly far
from the filter peak as the level increases.
This is not at all what a filtering
interpretation of CB is based on. This width
changes a lot with level, much more than the
underlying filter bandwidth changes. If this
is what people look at when they say that
critical bandwidth phenomena are not present in
peripheral filtering, then it should be
straightforward to explain the problem and get
them back onto a sensible track. But hopefully
they haven't falling into that error. I won't
know until I find something where they actually
say what they're thinking...
Dick