© Yu.V.Nikonov

**SELF-ORGANIZATION
OF BIOLOGICAL TIME AT ALCOHOLIC DEPENDENCE**

**Yuri
V. Nikonov**

()

The laws of formation to remissions at the alcoholism (alcoholic dependence on ICD-10) matter not only for narcologia, but also for understanding of a nature of biological time of the man. Formation of remissions at the alcoholic dependence it is possible to consider as process of self-organization open biological ethanol-dependendent system of the organism of man in conditions of deprivation of alcohol.

In the given work the
published materials of a number of the researchers on diagnostic and
clinic of chronic alcoholism [10,11,12,13]
are used with the purpose of new interpretation adding interpretation
of the authors. Shakhbazov V.G. with
the other authors is established, that
percent mobile in an electrical field of
nuclei (PMN)
buccal epithelium, having a negative
electrical charge, depends on age of the donors. The meanings "of
age norm" – average statistical
parameters PMN are determined
depending on age of the donor. PMN is
maximal in the age of about 20 years and then is reduced in process
of aging the man. PMN reflects size of
biological age (BA) of the man (so-called
cytobiophysical parameter BA)
- parameter of a condition of system, biological time of
organism. In process of increase PMN,
BA is reduced [13]. At investigated Sosin
I.K. with other
authors [10,11] patients of alcoholism in
the age of from 20 till 60 years in a condition of
remission average level PMN (PMN_{rem.}).
On 30-35 % there is less age norm. The restoration PMN
up to a level of age norm does not occur. It is essential,
that at the persons abusing with alcohol without attributes of
alcoholic dependence, the termination use of the
spirituous liquors can result in restoration of meanings PMN
of age norm. In a condition sharp alcoholic intoxications
PMN at the patients with generated
alcoholic abstention syndrome
(AAS) it is usual on 3-5 % less age norm, and a line of supervision
is equal to it. At the persons without attributes of alcoholic
dependence dynamics PMN opposite.
In a condition AAS PMN (PMN_{abst.}).
Is reduced on 80-90%, in a number of cases - on 100%. That is at
alcoholic dependence in a situation of the use of alcohol - the
alternations of alcoholic intoxication and AAS, can occur
fluctuations PMN in a range from zero up to meaning of age norm
(range of duration of this process - hours, 1-2 day). At exception of
reception of alcohol (in time formation of
remission) the fluctuations of size PMN from zero (PMN_{abst.})
are possible. Up to meanings PMN_{rem.}
(range of duration of process - about 3 months).

The hypothesis [5,6,7] is developed, according to which at the patient of alcoholism in alcoholic intoxication BA decreases, and in a condition of hangover - is sharply increased. In a condition of remissions the proof, irreversible excess BA rather average statistical of parameters of the given age is kept. The gradual increase use of the spirituous liquors during months and years results to structurally steady to pathological condition – the alcoholism also is accompanied, irreversible, proof change BA.

It is important, that the process gradual increase PMN from zero up to greatest possible exists and in norm. It is dynamics PMN and BA in a negentropycs phase of the ontogenesis. However range of duration of this process, on the average, from birth - till 20 years [13].

It is essential, that dynamics of restoration PMN(so and BA) at the formation remissions is various depending on a way of the medical treatment AAS, that is from the entry conditions of process (it is known, that during self-organization the large meaning have the entry conditions - in this case methods of the medical treatment AAS). Especially is fast PMN is restored at application of a method superficial cranio-cerebral hypothermia - controlled reduction of temperature of a head brain. Let's result the data on influence cranio-cerebral hypothermia on PMN at the patients in the age of 26-29 years with most expressed, heavy displays AAS [10].

PMN has made: 13,3±5,9; 15,7±5,5; 13,7±2,3; 22,0±4,1; accordingly, up to hypothermia, in process hypothermia, ambassador to hypothermia, the next day the ambassador to hypothermia. It is important, that the changes PMN in process medical treatment AAS in the given example are not monotonously increasing, and can be interpeted as fluctuation. The next day the ambassador to hypothermia PMN reached half of age norm, while at use medicinal of ways the comparable result was found out only on 15-20 day of treatment.

In an above mentioned example of the attitude PMN the next day the ambassador to hypothermia, to PMN up to hypothermia, PMN in process to hypothermia, PMN is direct the ambassador to hypothermia have the following meanings:

22,0/13,3 ≈ 1,654; 22,0/15,7≈ 1,400;

22,0/13,7
≈ 1,606; 22,0/100 = 0,220 ≈ (1/1,656)^{3}.

It is easy to see,
what in process of medical treatment AAS,
formation to remissions at realization of
cranio-cerebral hypothermia in dynamics PMN(and
BA) the laws of golden
section, affinity describing of the formation
of remission come to light at alcoholic
dependence of the attitudes (1,654), (1,606), (1,656)^{3},
to a golden proportion (1,618) and its(her)
by derivative (1,400; 20,5; 2 – Fibonacci
numbers).

In accord of M.F.Timofeev [12] the periods of risk of a relapse at the patients with alcoholic dependence at early stages of remission, techniques, revealed with use, of study of reaction of vessels of a head brain on a smell of alcohol among the patients of alcoholism of the men in the age of from 30 till 48 years are published. The periods of the maximal sensitivity to a smell of ethanol (they "the periods of risk" of a relapse of alcoholic dependence) have for initial day (zero day of abstention from alcohol) (I periods), 2-3 days (III periods), 7-8 days (V periods), 19-21 days (VII periods) and 45-50 days (IX periods).

The periods of the minimal sensitivity to a smell of alcohol have for 2 days (II periods), 4-5 days (IV periods), 12-13 days (VI periods), 30-32 days (VIII periods) and 62-66 days (X periods) of remission. Pays on itself attention, that terms of change (in days) I-VII of the periods of the formation to remission precisely correspond(meet) to a line of Fibonacci numbers: 1, 2, 3, 5, 8, 13, 21, invariant is a golden proportion: numbe 1,618. Terms of change VIII-X of the periods make accordingly: 32, 50, 66 days against numbers of a Fibonacci numbers - 34, 55, 89 [1].

I 1; 2; 3; 5; 8; 13; 21; 32; 50; 66.

II 1; 2; 3; 5; 8; 13; 21; 34; 55; 89.

I - Terms of change (in days) periods of formation to remission.

II – Fibonacci numbers.

Naturally, given facts it is not enough for any categorical statements. However it is possible to ascertain a role of golden section, Fibonacci numbers increase of discrete meanings PMN(and reduction) BA - "rejuvenation" of organism) in process of formation to remission of the man with alcoholic dependence (in a range of duration about hours, day, months, years).

Conceptual base of consideration of dynamics PMN and BA as parameter of system, biological time of organism, within the framework of the offered hypothesis, can be synergetics, nonlinear thermodynamics of I. Prigogine, representation about of biological time as fractal. [1,2,8,14]. About a role models of difficult open nonlinear, non-stationary developing systems of Prigogine, bifurcations, synergetics to a role of the theory of accidents of R. Thom, synergetics of H. Haken for psychiatry as parts of a modern science convincingly wrote Yu. Savenko in a context of discussion to new paradigms in psychiatry [9]. A measure and way of achievement of stability of system is the golden proportion (Ô = 1,618 …), and on an error approximation to derivative F it is possible to judge a degree of completeness of that or other natural process. A Fibonacci numbers reflects points bifurcation, condition, determining stability - instability, of system, provides revealing a structural optimum of system during self-organization [8]. The application of concept of fractals to biological time, processes of development of biological systems [1,14] has become usual.

With the purpose of
modeling dynamics PMN (and BA)
in time of formation to
remission at the alcoholism is
applicable the elementary model of the limited growth of discrete
dynamic system, in which increase PMN from
zero up to the maximal size PMN_{rem.},
reflects condition of discrete dynamic system - system BA
of the man [4,5,6,7].

That is:

X_{n+1}
= A X_{n} (1 -
X_{n}),
(1)

Where X_{n}
- number of elements of system (PMN), "À"
– coefficient of Maltus
of duplication of elements. In researches of populations "À"
means, that in each following generation will be in "À"
times more elements, than in previous. The processes with
self-saturation limited growth are widely distributed practically in
any systems and, despite of the simplicity the considered dependence
can give the important rough estimations. X_{n}
in a limit aspires to meaning X_{n+1},
that is in our case to PMN_{rem.}.
Means, on meaning PMN_{rem.}. It is
possible to estimate size of coefficient
"À":

Õ → A Õ (1 - Õ),

À = 1 /(1 - Õ),

And at 1 < A < 3
there is a steady decision. If 1 < A < 2, the sequence X_{n}
comes nearer of asimptotics to X_{n+1}
(X_{n+1} = PMN_{rem}.)
on the one hand, and at 2 < A< 3, from two parties
(in this case sequence "oscillation" concerning a
point X_{n+1}). At the further
increase of parameter “A”
the motionless point X_{n+1} loses
stability, and the sequence meanings of bifurcation
A converges in a limit to meaning of number
d = 4,669 …, that is to constant of
Feigenbaum[4,14].

1/d = 1 /(4,669) ≈ 0,214, where number d = 4,669 … Constant of Feigenbaum, which size is connected to golden section [4,14]:

1/d ≈
0,214 = 1 - 0,786 = 1 - (0,618) ^{0,5}

The process of doubling of period in difficult evolutions systems, is connected with universal by the script of transition to chaos (exit from chaos) in nonlinear dynamic systems, with so-called.

By the cascade of doubling of Feigenbaum [1]. The described doubling of the period reminds fractal, based on binary system with parameter of scaling equal to number d [5,14].

Display (1):

X_{n+1}
= A X_{n} (1 -
X_{n}) to model of the limited growth of a population
is equivalent to display:

Z_{n + 1} = (Z
_{n + 1}) ^{2} + α,
(2)

where α
= À/2 - À^{2}/4;

X_{n}
= 1/2 - Z_{n }/A.

On the basis of display (2) are under construction fractals of Julia, Mandelbrot, Fatou. In case of set Julia J: (α, b) - complex value[4].

At
use in modeling BA of display (2) the
application of the concept of two-dimensional**
**of biological time on is possible G.E.
Mikhailovsky [3]. Two-dimensional**
**of time of the given biological system can be presented as
complex value, valid and which imaginary parts the meanings
ontogenetical and physiological times
accordingly will act. That is in complex value
(α, b): α - parameter of ontogenetical
age (on Mikhailovsky), b - parameter of physiological time.
The negative acceleration physiological hours is in essence
equivalent positive increase of the
indications (i.e. course) ontogenetical
hours. Differently, the delay physiological for the given system of
ontogenetical processes expressing in
fraction, where in a denominator there is a negative square of
physiological time, is equivalent to speed it of processes, in which
denominator costs positive increase
ontogenetical of time. The similar
connection has a place between imaginary and real numbers: the
negative square of imaginary number is a positive real number. That
is it is possible to interpete a coordinate plane, which points
correspond to the moments two-dimensional**
**of biological time, as a complex plane, which imaginary
axis is submitted by physiological time, and valid - ontogenetical
of time. The complex representation of biological time allows to
express within the framework of one formalism as cyclic, and
exponential the character of dynamics, to
which is reduced the overwhelming majority of vital displays [3].

Within the framework of the offered hypothesis formation to remissions at alcoholic dependence can be considered as process of dynamics (including chaotic dynamics) biological time in view of transformations of golden section, Fibonacci numbers, representation of biological time as complex value. The problem of formation to remissions at alcoholic (by consideration it at a biological level) appears of the self-organization, connected to laws, of biological time of systems, features of a nature of the man as systems.

LITERATURE

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