NEW APPROACH TO THE ANALYSIS OF ELECTROENCEPHALOGRAMS

A transcription of the National Technical Information Service's English translation of the1970 paper by S. K. Lisitsyn.

This epic paper lists the frequencies and control codes used by the human brain.

We would appreciate assistance from any mathematicians or engineers in finalizing the exact transcription of some of the formulae, which are presented as scanned from an indistinct photocopy. These will also clarify a couple of cells in Table 22, which also need cross-checking. (contact)

Up to recently data on the biopotentials of the brain have been utilized weakly in psychophysical research. To a considerable degree this is explained by the difficulty of exposing on an electroencephelogram (EEG) the functional statistical and semantic regularities; by the absence of information on the role of EEG- signals in the work of the brain; by inadequate knowledge of the nature of EEG-waves.

It is possible to isolate the purely informational side of the question and to consider that EEG-signals will carry definite and varied information from one section of the brain to another according to the principle "to all! to all!". The advantage of such a hypothetical circuit of information is the reliability of the connection under conditions of the absence of many relays over cellular paths, but the difficulties appear in the coding and decoding of independent signals on a number of channels.

The statistical structure of EEG-signals has been traced by us during research on the time parameters of an EEG of a man normally and at rest on a modernized analyzer of the type AI-100-1 [1]. In this work it has been shown that clipped EEG-signals in their statistical structure are sharply distinguished from all known random processes and are in all probability a complex information function. The density of distribution of the amplitude of a nonclipped EEG is

extremely close to the Gaussian while the densities of the time intervals of a clipped signal are clearly and orderly determined. The average length "of a period" of rhythm is a function of its ordinal number. These and other discovered regularities in the structure of EEG rhythms make it possible to assume that the spectrum of zeros of an EEG appears earlier than the spectrum of amplitudes and the latter are shaped according to any simple principle, for example a optimum band of frequencies.

It is possible evidently to base a further analysis of the EEG signals on the following natural premises. Let there be a certain autonomous system of signals, the role of which, in particular consists of the following:

a) to give the possibility to a correspondent to discover a previously unknown frequency of the source of information;

b) to synchronize in the known meaning the work of the separate subsytems and the organs of the system;

c) to continuously transmit on many channels information in all direction (similar to broadcasting) with the aid of a certain code.

The problem of detecting the source of information, the statistical and semantic characteristics of which previously nothing was known, is examined in work [2]. The system of signals proposed by Von Horner, which serve this purpose is wonderfully similar to the system of clipped EEG signals although there is also a number of substantial differences. Nevertheless one must not pass this surprising analogy.

The second question which refers to synchronizing the work of the subsystems and organs of the system, is associated, apparently, directly with problem of the so-called biological clock. In recent years we became witnesses to how fruitful the idea was of condensing the channels of communications, for example, in radio relay lines. It falls completely into this representation and the presence of many EEG rhythms, which form a parallel, and at the same time in every

removal, a series of data transmission system. It is natural to assume that condensation of the channels and functions in such a system reaches a high level. We are only concerned with the most primitive of them.

Finally the third question which concerns the code structure, i.e., the semantic irregularities of the EEG in the broad sense, has been studied less than anything. Any conceived disturbances in the activity of any one of the indicated sides of functioning of the system can be represented as pathology. Thus, a insufficiently precise detection and tracking of the source of information causes for the correspondent possibly, the same deep disorder, as does the absence of proper synchronizing or short duration failures in coding and decoding. Thus far questions connected only with rhythmics and synchronizing have been studied.

Let us suppose there is an infinite system of signals, the average frequencies of which are constant and are determined by the set

0, . . . , f₋_t, . . . , f₋_n−1, f₋_n, f₀, f_n−1, f_n, . . . , f_k, . . . , ∞.

We accept the fact that the function f(n) is monotone, and furthermore, it possesses the following property:

If the bands of frequencies ∆ f_nare symmetric with respect to average frequencies f_n and they are in contact with the bands of frequencies ∆ f_n−1 and ∆ f_n+1, but nowhere do they cut each other in the interval of frequencies (0, ∞), that corresponds to the interval of the ordinal numbers of the signals (−∞, +∞), then the width of the band ∆ f_ncan be expressed by the formula

From geometric considerations it follow that the limit of the relationship of the band of frequencies to the average frequency of rhythm, with the leaning of the rhythm to infinity, is equal to two, i.e.,

To detect the source of information at frequency f (0), the content and statistical nature of which was previously unknown, it is necessary that search be conducted at least on two sliding frequencies f (−n) and f (n). The relationship between these frequencies is determined by equation (6).

where A_n and A_−n — the same type information taken in frequencies (−n) and f (n).

The concept of the uniformity in this case is spread both to the semantics, and to the statistics, or to this or another together. Separation with time can or cannot be absent. The information content at frequency f (0), naturally, can not depend upon the information transmitted at frequencies f (−n) and f (n). This is explained by the specific place of the central source in system, and also by the symmetry of the system with respect to the central frequency f (0).
????lilon (5) can serve as on of the simple conditions for fulfilling conjunction (9). Von Horner concentrated his attention on it in the above mentioned work. It is true that he spoke about an absolute band of frequencies, and expression (2) determines the equality of the relative frequencies, which substantially facilitates the detection of the frequency f (0).

Subsequently after establishing frequencies f (n) and f (−n) tracking can be accomplished on frequency f (0) according to (2).

It is possible to consider the EEG rhythms as rhythms in the system of counting time. To calculate the approximate values of all possible periods (or frequencies) of EEG-rhythms it is possible to use the following empirical formula (1):

The table gives the values of frequencies f (n), f (−n) and, where this is convenient, the value of the corresponding periods. If we limit the life of a man to 200 years, then the maximum length of the half-cycle should also be equal to 400 years. Hence we get that the rhythms, which lie beyond the limits of a given frequency are not of a physiological meaning. Thus, the entire set of EEG rhythms should not exceed 22 (± 11 rhythms). The alpha-rhythm is in this case 23rd in counting and zero in order.

The relative width of the band of the 11th rhythm, according to (7) is close to two octaves. The shortest subrhythms of this

rhythm refer to the yearly rhythms, the longest go beyond the limits of the necessary. That fact, that in this case in organism all components can be utilized, should not astonish us. Experimental observations over EEG rhythms (minute and hourly) show that separate rhythms are split, show themselves partially, or are temporarily completely absent. The picture drawn above of rhythms is steady only in the statistical plan.

With frequency interpretation of biological rhythms functional restraints are not applied to the amplitudes of separate rhythms or to their average values.

It is another matter if the discussion concerns the length of clipped signals. In this case the amplitude of the rhythms should monotonically and very definitely grow with the increase in the period. Otherwise the length of the time intervals of a clipped signal will become constant under some conditions.

There is experimental confirmation of the fact that the square of the average amplitude of an alpha-rhythm is equal to the product of the squares of the amplitudes of equidistant rhythms [3]. Considering the results of work [4], one can assume, that the average values of the amplitudes of EEG rhythms change depending on the ordinal number of rhythm according to the law

It is known that variable voltages of an EEG are observed in the background of constant voltages, the size of which can exceed the amplitude of EEG-waves by 10 thousand times. Assuming the average value of the amplitude of an alpha-rhythm equal to 10 μV we find that at k = 1 the value of the amplitude of the 11th rhythm will be equal to 50 μV. This result will not contradict the observations.

Table. Average frequencies and periods of rhythms.
(The frequency of the alpha-rhythms has been accepted as equal to 10 Hertz)

Number	1	2	3	4	5	6	7	8	9	10	11	12	Average frequency, Hertz
Note	12.5	16.3	23.4	39.6	87	250	1840	31700	2.5x10⁴	4.75x10⁸	7.85x10¹²	8.1x10²⁰	Growing frequencies
Infrasonic range								Ultra-sonic	Short waves	Deci- metric waves	Milli- metric range	Light
	Experimentally discovered						Experiment is required

Number	-1	-2	-3	-4	-5	-6	-7	-8	-9	-10	-11	-12
Average period, sec.	0.125	0.163	0.234	0.396	0.87	2.51	18.4	317	2.5x10⁴	4.75x10⁷	7.85x10¹¹	8.1x10¹⁹	Growing periods
	Fractions of a second					Second range		Minute rhythm	8-hour rhythm	1.713 years	2500 years	Without physi- ological meaning
Experimentally discovered										Experiment is required

The longest periods of physiological rhythms can be formed from shorter periods with the aid of simple circuits similar to a trigger and composed of neurons. This assumption will contradict, however, the fact, that at least, 11 EEG rhythms of a man have nonmultiple frequencies and appear as statistically independent oscillating processes. However it is not possible to deny the possibility of deviations from this rule for the lowest periods.

It is known that the electrical rhythms of the brain are synchronized with external light and sound signals, and are also under the influence of electrical and magnetic fields. In work [5] it has been shown that the EEG and EKG of a man to a known degree are synchronized with sounding music. This synchronization is especially distinct in lovers of jazz music. It is possible that our love for music is associated with the mechanisms for synchronizing the biological processes. It is possible that "good music" - that music at which the brain is maximally unloaded from cares with regard to the synchronization of a complex system. In another work it has been said [6] that under the influence on both eyes by discontinuous light with nonmultiple frequencies heavy disturbances in the nervous system occur.

It is natural to propose in this case the disturbance of synchronizing on a number of rhythms, disorder of the biological clock, short duration failures in the code, large errors in the system for tracking the alpha-rhythm frequency. All this on the whole also leads to the death of experimental animals. Apparently, the organism compensates for noise, if it is alone. But if through each eye individually two independent interferences penetrate into the brain, then compensation does not occur.

In conclusion it follows to recall the words of the known scientist A. S. Zalmanov [7]: "there occur cases - and they are frequent - when the death of a patient cannot be explained either by the development of an unhealthy phenomena, or by insufficiency in the most important forms of activity of the organism (breathing, blood circulation, excretion), or by serious premortal complications. There remains a probable hypothesis: this breakdown of the synchronous enrhythmia? (i.e., of normal rhythmics. - S. L.).

But not only synchronization of the frequencies (in the statistical plan) is the necessary condition for normal activity in the organism. The shift in the phases of the biological rhythms can also substantial. Thus, the shift in the phase with respect to time which ?????? on a flight from Europe to America, requires a greater adjustment than a flight along a meridian. It is considered, for example, that agreement with time of the amplified activity of the stomach and liver leads to the gastritis and stomach ulcer. All this indicates the need for research on the phase relationships even for and electroencephalaogram. Considering the complexity of the organism, it is possible to comprehedn that for synchronization and control of a large number of organs and functions a considerable number of different frequencies is required. Many of these rhythms, up to radio-frequencies, are already registered. To deny the possibilty of detecting rhythms on other frequencies is not possible. Carefully conducted experiments and special equipment are necessary.

The polymodal character of the density of distribution of "half-cycles" "periods" and more of the long chains of a clipped EEG signal of a man with open eyes indicates the possibility of a reference of each of the modes of distribution to the appropriate digit of the positional code.

The characteristic criterion which finds that the observed combinations of digits of the code reflect not a random wandering, but are subordinated to a certain restricted number of rules, is the series change in the curves of distribution of increasingly longer chains(?) from the time intervals. The discrete and slender character of the distribution for the very long chains serves as convincing proof of the existence of the code in the statistical meaning.

The calculation of the probabilities of transition from one digit to another showed that the greatest probability for the observed 11 (?) digits is the zero digit (alpha-rhythm). The probability of transition to the zero digit after any of the given digits, is greatest (?) when the delay does not exceed several units. Already now

it can be said that blocks with a length on the order of seconds exists. These blocks slip relative to each other. There is no doubt, that before us is an extremely complex code which can be described as nonsystematic, i.e., with a different number of signs in the block; block type because there exist strictly constant in duration long groupings; uneven because the number of signs in the group is varied; recurrent because blocks are of different duration and slip relative to each other; incomplete (great excessiveness in comparison with language); conditionally binary for each of the positions.

In a healthy organism the number of digits of the code does not exceed it seems 44. Utilizing the code relationships of the EEG-signal, it is possible to considerably extend the sensitivity of the EEG method of research.

	_−n−1
∆ f_n−1 = 2 f (−n) − 4	∑	(−1)