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Re: Rationale for Critical Bands
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 rat¹s 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 3045 frequency-band laminae
(Fig.3b), each exhibits a shallow, continuous
frequency progression orthogonal to the
traditionally deÞned main dorsoventral 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, 4765 (1940).
2. Zwicker,E.etal.Critical bandwidth in loudness
summation. J.Acoust.Soc.Am. 29, 548557 (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