Lecture 13 Read: the two Eckhorn papers. (Don t worry about the math part of them).

Transcription

1 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. 1

2 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 2

3 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 3

4 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 resynchronize 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. 4

5 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 5

6 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. 6

7 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. 7

8 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 8

9 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). 9

10 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. 10

11 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 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 11

12 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. 12