How many classes of Electrical Signs are observed in the brain

 

There exists a quite diffused tendency to identify the mechanisms of  nervous information fluxes and elaborations in   the spiking activity of neurons. This tendency creates, in many cases, the basis for a quite simplistic illusion on the possible mirroring of brain activities by Artificial Neural Networks (ANN). Our knowledge on the importance of chemicals, as serotonine, in primordial brains suggests that electrical activity represents, also in very simple brains, just a part of the mechanism of competence [1 ].

If we restrict however to the electric signals that can be detected in living brains, we must admit that neural spiking represents just a class of the observed phenomena., that we briefly sum up in the following.

 

1)     Single unit spikes (50-100 µm ) of  an active unit is the most known phenomenon. It has to be noticed however that slow potentials are generally contemporarily  observed down to <1 Hz.

 

2)     Localized Multiunit activity is also observed  (100-200 µm). It consists of a fast common spiking  activity of several units (up to some tens).

 

3)      Moreover neurobiologists use the term Hash to define spatially coordinated spiking  activities of small amplitude.

 

(2) and (3) represent local contraction of entropy  that play a major role in the whole dynamics of living beings.

As noticed by Tononi et al. [2 ], this phenomena of  local coordination of spiking activities can be well formally captured making use of statistics. Consider an isolated ensemble of n neurons N that we assume approximately described by a stationary multidimensional process. If we represent the state of each neuron by a binary variable (1 for “spiking” and 0 for “silent”) and assume that their states are totally independent, then the state of the system N is represented by a random binary string of length n. The number of the possible states is 2ⁿ. All of them have, by definition, the same probability. The entropy of the system is therefore:

  

in bits.

One can of course, consider a partition of N into two subsystems K and N-K, made respectively of K and n-k neurons. If the above condition holds, the above sum is divided into two sub-sums, the result remaining the same. More precisely we can write:

If the entropy of the system is lower that its maximum value, one can rewrite the above equation as:

where MI(K/N-K) is the mutual information between the two sets K and N-K. MI=0 implies that the two sets are statistically independent.

Moreover one can introduce, for an arbitrary set X, made of x neurons, an integration measure I defined as follows:

By comparison with the X entropy definition, I is a measure of statistical correlation between the elements of the set-

By combining the above definition, one obtains:

Given N, there exist:

ways of taking k neurons out of n. We can therefore take therefore consider the average values of I(k) on those possibilities. Then we can evaluate a complexity index C_N(N) defined by:

where <> represents the above described average.

Statistical coordination between local ( but also non-local) clusters of neurons is well represented by the above complexity index. As noticed by Tononi et al. in a number of papers [ 2,3 , 4 ], variation in the complexity index can deeply affect the global behaviour of a large set of neurons. This observations suggest a very suggestive global model of the neuronal brain [5 ]. Therefore this kind of neural brain activity can deeply affect our understanding of the brain’s neural mechanisms.

Another kind of observed electrical activity are the so called:

4)     Intracellular potentials. These are signals  one identifies within a single unit , in general in one precise part of the cell. Slow intracellular shifts can be very different in their properties. They represent somehow the complex continuous dynamics of each single neuron. One can refer to the original work by  Gesell [6 ] .  Here we will not discuss the possible implications of varying intracellular potentials.

 

5)     Fast oscillations not associated with spiking. They can be oscillatory in nature (10-100 Hz) or isolated (1-10 ms). Their origin is not well understood, even if they contribute to EEG. They have been observed in different areas of the brain and seem to be characterised by typical frequencies depending on the specific area. They can be interpreted in general as the effect of some form of neural synchronisation due to reverberation in neural circuits. The effects of those signals can be understood somehow making use of the same approach adopted for the spiking activity synchronisation. Unfortunately they completely escape in general any ANN modelling.

 

6)     Slow Potentials (10-10000 ms and 0.1-50 Hz). They are the major responsible of EEG and are the result of synchronized synaptic potential. [7 ].

 

7)     Infraslow potentials.. They are standing potentials with a time persistence T>10 s. They can be larger in amplitude than any of the usual faster and probably affect the firing  tendency of neurons firing, according to their orientation. See [8].

 

We can therefore conclude that ANN can capture just some details of very local mechanisms taking place in the nervous system. In any case they cannot represent in any sense the “explanation” of the brain performances. One is left with the typical problem affecting physics in general. The conceptual legality of reduction is incorrectly used to justify a hypothetical constructivism that should justify the permanence of reductionist researches.

[1] Allman J. (1999) Evolving Brains, Scientific American Library, New York

[2] Tononi G., Sporns O., Edelman G.M., A measure for brain complexity: Relating functional segregation and integration in the nervous system, Proc. Natl. Acad. Sci. USA, Vol. 91, pp. 5033-5037, May 1994, Neurobiology

[3] Tononi G., Sporns O., Edelman G.M., A complexity measure for selective matching of signals by the brain.Proc. Natl. Acad. Sci. USA, Vol.93, pp. 3422-3427, April 1996, Neurobiology

[4] Tononi G., Sporns O., Edelman G.M., Measures of degeneracy and redundancy in biological networks.Proc. Natl. Acad. Sci. USA, Vol.96, pp. 3257-3262, March 1999, Neurobiology

[5] Edelman G. M., Tononi G., (2000), A universe of consciousness, Basic Books, New York

[6] Gesell, R. (1940) Ergebn. Physiol. 43, 476-639 .

 

[7]  Boulton, A. B., Baker, G. B. & Vanderwolf, C. H., eds. (1990) Neurophysiological Techniques:Basic Methods and Concepts, and Applications to Neural Systems, Neuromethods, eds. Boulton, A. B. & Baker, G. B. (Humana, Clifton, NJ), Vols. 14 and 15

 

[8]  Adey, W. R. (1969) Neurosci. Res. Program Bull. 7, 75-180 .