Lecture 13 Read: the two Eckhorn papers. (Don’t worry ... Notes/Lecture 13.pdfEckhorn’s SDM idea...

Biological Signal Processing Lecture 13

Lecture 13 Read: the two Eckhorn papers. (Don’t worry about the math part of them).

Last lecture we talked about the large and growing amount of interest in

wave generation and propagation phenomena in the neocortex and elsewhere

in the brain. Today’s lecture is on that topic.

The first paper in your handouts (Gabriel and Eckhorn, 2003) contains a

nice summary of some of the experimental work in this area as well as some

of their more theoretical work relating to making measurements of signaling

correlation and synchronicity in awake monkeys. The mathematics in this

paper is not of any particular importance for purposes of this class (although

if you find yourself in the business of conducting these sorts of experiments

you’ll find it useful). What I want you to pay close attention to is their text

discussion of the problem and their discussion of the results.

The first and main point is this: Neural firing patterns resembling wave

propagation is commonly observed in neocortex. Gabriel & Eckhorn figure 1

illustrates a typical measurement taken with a one-dimension array of

sensors. We can clearly see the arousal of what appears to be “waves” of

firing activity crossing the line defined by the sensors. Note the

characteristic peaks and valleys in activity, reminiscent of wave phenomena

in physics.

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Cortical oscillations are observed in four frequency bands (originally

defined to correspond to EEG frequency bands). They are: (1) LF band,

below 3.5 Hz; (2) α-band, 7 to 14 Hz; (3) β-band, 14 to 28 Hz; and (4) γ-

band, 28 Hz to 70, 80, or 90 Hz (depending on whose paper you’re reading).

The α- and β-band frequencies are apparently very localized. By this I mean

that these bands do not appear to play an obvious role in inter-cortical

signaling over large distances in the brain. The γ-band signals, on the other

hand, have been observed to project over greater distance (including across

brain hemispheres via the corpus callosum). This has sparked the hypothesis

that γ-band signals are the “carriers” of information in the brain. There is a

further hypothesis that it is synchronized firing patterns which are

responsible for the long-distance transmission of information in the cortex.

Here we run into an interesting issue, however. γ-band signals do seem to

travel great distances in the cortex, but they remain synchronized only over a

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range of a few millimeters. After that they become unsynchronized. A

question that particularly seems to concern Eckhorn and his colleagues is:

how can wave-propagation of information be maintained in the face of this

loss of synchronicity?

Synchronicity loss is illustrated in the measurements reported by Bruns

and Eckhorn (2004). Go through and explain this figure. Note low r values

This figure demonstrates a pronounced lack of correlation between the

source (area A) and destination (area B) areas. Area A is in the early visual

association cortex (roughly area V3 and perhaps V2; area B is also in the

visual association cortex. Bruns & Eckhorn assume that area A makes

feedforward projections to area B, although that is not known for sure.

One idea proposed by Eckhorn is that perhaps some small cell group

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networks act to counter the loss of synchronicity through what he calls a

“spike density modulation” mechanism. The reasoning here is that by

chopping up firing activities in neuronal cell groups the ability to re-

synchronize these cells is enhanced. His simulations do bear out that this is

so to some extent, although the synchronization is not as “tight” as with the

linking field connection. His basic idea looks like so:

This network has the same linking field connections among the excitatory

neurons but it also adds an inhibitory neuron that feeds back to an

inhibitory feeding field input to the excitatory neurons. The effect is to

“chop” their outputs into packets of firing activity. How exactly this might

cure the problem is a bit unclear, but his “SDM” would at least tend to cut

down on badly synchronized action potentials arriving at the destination.

One could then increase the synaptic weights at the destination, making it

easier for the “pulse packets” to fire them synchronously.

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Eckhorn’s SDM idea is shown in more detail in the next figure.

While Bruns & Eckhorn did not find much correlation between γ-waves in

areas A and B, they did not an interesting correlation between γ-waves and

LF signals. Eckhorn’s model for this is given in his 2004 IEEE Tr NNets

paper and shown in the next figure.

Explain this figure.

This figure implicitly illustrates a common presupposition used by many

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researchers. I call this presupposition the “relay model” of cortical

interconnection. The idea is basically this: That each “link” in a chain of

neural assemblies projecting forward one to another merely “repeats” or

“relays” the information it has received (possibly with some additional local

reaction that generates signals to be sent off elsewhere). It is an old idea,

found implicit in many models such as Moshe Abeles’ “synfire” model and,

of course, in the old “grandmother cell” paradigm of cerebral signal

processing. Judging from a rough estimate of the locations of areas A and B

in the Bruns-Eckhorn data, assuming a typical axon diameter of about 1

micron (propagation velocity about 6 mm/msec) and comparing this velocity

with Bruns & Eckhorns measured time lag to best correlation, it seems clear

that the signal propagation from A to B does pass through other neuron

assemblies en route. (The lag time is too large to be accounted for by direct

axonal propagation of the signal without intermediate synaptic connections).

Is the relay model a realistic depiction of cerebral signal processing? Last

summer we set out to study this question. We constructed model cell groups

and so-called “functional column” cell assemblies based on what is known

of the anatomical organization of the neocortex (Douglas and Martin, 2004),

(see also TRAP chapter 4). Our basic cell group was as follows.

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Explain the kernel organization; each kernel is an Eckhorn SDM. L-IV excitatory neurons have different parameters from the others (they are spiny stellate cells) and operate in HPF mode. The ENs in other kernels all have the same parameters (they are pyramidal cells) and operate in APF mode when their source kernel fires synchronously. Each kernel has 4 ENs and 1 IN, which is approximately the correct biological ratio.

We constructed frequency-selective networks designed to respond to β-band

synchronous inputs with a “relay” function. One great advantage of the

Eckhorn neuron was that we were able to derive an exact theory to describe

the cortical dynamics of this network. Our “bandpass” functional column

network is shown in the following figure.

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Explain this figure. The second cell group is HP-tuned to pass γ-band frequencies and it feeds back an inhibitory signal to the first cell group. The first cell group is HP-tuned to pass β-band and γ-band frequencies. The γ-band frequencies excite the second (inhibitory) cell group. We then constructed chains of these functional columns as shown in the

next figure.

Explain this figure. Each column has 60 neurons. Cell group 1 layer VI is the output signal to the next column and projects to cell group 1 layer IV there. Our simulations of 180-neuron networks took 46 seconds for 1 second of data at a ∆t of 1 msec. per step.

Here is what we found. The network rejects α-band stimuli (does not

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respond in this frequency range). It does pass synchronous β-band signals

but not as a traveling wave. Each link in the chain “swallows” the first pulse

it receives before passing on the others. Therefore a finite duration tetanus

will not continuously propagate; it will die out after a number of links in the

chain equal to the number of pulses in the tetanus. We call this evanescent

mode propagation.

By far our most interesting results were obtained from input signals that

were NOT synchronous. The next figure shows the response of the first link

in a chain of simple HPF columns (tuned to pass 28 Hz and above; 30

neurons per column, one column = 1 cell group). The input consisted of one

28 Hz input (within the passband) and 3 27 Hz inputs (below the passband).

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The most interesting feature of this response is the packeting of the neuron

responses. point out the packeting. The next two figures illustrate the

evanescent mode; they are the responses of the second and third links in the

chain.

As you can see, this signal isn’t going to travel very far.

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But the most interesting response of all comes from our BPF functional

column when it is driven by asynchronous inputs. The following figure

shows the response of the first link in the chain (60 neurons/column) driven

by asynchronous inputs in the β-band (19 Hz, 20 Hz, 20.4 Hz, and 21.3 Hz).

Here the thing to bear in mind is that the OUTPUT is from neurons 26-29.

Note the DIPULSES that form. This is caused by the re-triggering of L-IV

by L-VI (note the tripulses in L-IV). THESE DIPULSES PROPAGATE as a

traveling wave. They are actually above the γ-band (and the stimuli were all

in the β-band). We called this the “rate multiplier mode”; the output signals

stimulate tripulses in the next link’s L-IV response.

Put another way, this column generated its own signal from the

stimulus and passed this signal on. It is NOT simply relaying a signal from

one point to the next. This action could explain the poor correlation results

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coming out of the laboratories (which we saw earlier).

Finally, another encouraging result was that our networks generated

frequencies in all 4 bands: LF- , α- , β-, and γ-bands. This is shown in the

last figure.

The moral of the story is: (1) Anatomically-plausible neural networks do

generate the various experimentally observed frequencies; (2) the functional

columns are NOT simple relay networks. They generate their own signals;

(3) the signals that do propagate as waves are high-frequency signals; I think

we only have to do some minor parameter adjustments and we’ll get good,

solid γ-band wave propagation. BUT (4) the next link in the chain doesn’t

just pass this on; it generates its own signal.

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Lecture 13 Read: the two Eckhorn papers. (Don’t worry ... Notes/Lecture 13.pdfEckhorn’s SDM idea...

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