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Re: Rationale for Critical Bands

Malmierca et al's paper shows a discontinuous distribution of BFs along electrode penetrations in ICC, suggesting that neighboring parts of neural tissue share the same frequency selectivity. The same group earlier found a tesselation in cat VNLL (without the overall laminar tonotopic organization).

This has nothing to do with the concept of critical band as used in psychophysics.

A critical band is understood as a spectral window over which energy is integrated for certain tasks. This window can be centered anywhere along the frequency axis: there is no implication that center frequencies should be distributed at CB-spaced intervals.

The parallel between BF distributions along electrode paths and the critical band seems to be based on 2 observations: - discontinuity of BF over neural tissue, supposedly analogous to a discontinuity of behavioral measures at the CB boundary,
 - similarity between BF step size in rat and CB size in humans.

"Discontinuity" of behavior at the CB boundary is more an artifact of thresholding than a real step. The authors point out that CB estimates in humans (0.14 - 0.23 octaves) are narrower than BF step sizes (0.29 - 0.36 in rat ICC, 0.333-0.375 in mouse, ~0.28 octaves in cat ICC, 1 octave in rabbit thalamus). Even if the match were more accurate the similarity could be fortuitious, so this argument is weak. A stronger argument would be if behavioral CBs were non-overlapping.

If psychophysical CBs were stacked side by side, as the parallel with rat BFs would imply, we'd expect to observe a granularity in CB-related response measures along the frequency axis. As Dick points out, tones separated by 0.25 octave would interact if they fell in the same fixed band, and not if they straddled a boundary between bands. To the best of my knowledge this has not been observed.

The distributions of BF shown in Figs 6AB are intruiging as they suggest, in addition to discontinuities along electrode paths, that some BFs were more common within the population (604 observations in 125 animals) than others. This might lead us to predict non-uniformities in behavioral measures in rat, as suggested by Malmierca et al in their final paragraph. Supposing they are found, interpreting them in terms of rat "critical bands" would still require some work. Large amounts of ICC data have been gathered by many groups, it would be interesting to know if similar BF clustering is found in other species.

This issue is distinct from that of the shape, width, or level-dependence of tuning which the authors don't report in detail. As Dick pointed out, due to nonlinearity we cannot directly relate the frequency threshold curve (FTC, lower boundary of the FRA) to filter selectivity at any given level. These new data do not contribute to the ongoing discussion as I read it so far.


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...