964
B. F. Dibrov et al.
6. CHOU, C. K. and GUY, A. W., Biological Effects of Electromagnetic Waves (Eds. C. Johnson
and M. Shore) pp. 89-103, USNC/URSI Meeting, Boulder, Colorado, 1971
7. BYELYAKOV, Ye. V. et al., Summaries Reports Sixth All-Union Seminar: Use of Low Intensity
MM Radiation in Biology and Medicine (in Russian) p. 94, IRE Akad. Nauk SSSR, Moscow.
1986
8. RYAKOVSKAYA, M. L. el at., Dep. VINITI No. 801, 15 February 1983
X
XH
Biophysic* Vol. 33 No. 3, pp. 964-973, 1988
Printed in Poland
0006-3309/88 S10.00+.00
<0 1989 Pergamon Press fk
I
POPULATION DYNAMICS OF PROLIFERATING CELLS
ON PERIODIC PHASE-SPECIFIC EXPOSURE*
B.
F. Dibrov, Ye.
V. Gel’fand, A. M. Zhabotinskii,
Yu. A. Neifakh and M.
P. Orlova
All-Union Research Institute of the Technology and Safety of Medicinals,
Kupavna (Moscow Region)
{Received A June 1987)
The dynamics of the population size of proliferating cells on periodic exposure to phase-
specific
cytotoxic
agents with a blocking and non-blocking action has been
investigated
theoretically. It is shown that for real values of the parameters of the model soon after the start
of exposure
the
population
size
exponentially
depends on
time. The dependence of the
dynamics of the population size on the integral parameters of the cell cycle and the regime
of exposure has been studied. It Is shown that in certain periods a resonance fall in the damage
to the cells of the population must be observed.
It has been established that the values of
the periods corresponding to the resonance fall in damage are essentially determined by the
mean duration of the cell cycle and the duration of the blocking action, for a short duration
they are approximately a multiple of the mean duration of the cell cycle. Experimental study
of the dependence of damage to the epithelium of the small intestine and the survival rate
of mice on the period of repeated periodic injections of a S-phase specific cytotoxic agent-
hydroxyurea— revealed a resonance increase in the survival of the mice and reduced damage
to the epithelium on injections of this substance with periods close to the mean and double
the mean duration of the cell cycle of the enterocytes of the crypts.
In antitumour chemotherapy and also in various experimental studies phase-specific prepar
*“^J
are widely used, i.e. preparations the action of which extends only to cells in a certain phase o
cell cycle. Earlier when investigating mathematical models we were able to show that on
introduction of high doses of phase-specific cytotoxics there may be resonance dependence °
survival of the proliferating cells on the interval between administrations with resonance m
^
of survival at intervals close to (or a multiple of) the mean duration of the cell cycle
[1 3-
*n
it was shown that this effect may be used to optimize the phase-specific cytotoxic actions in the
m
and, in particular, in tumour chemotherapy.
* Biofizika 33: No. 5, 895-904, 1988.
Approved For Release 2000/08/08
: CIA-RDP96-00789R003100
'
' &
ft-:
•.
&«*
IS”
...
-
•-•/a
• jt.,
•
-
’
•;V
ftvft!
.
'V,
Approved For Release 2000/08/08
: CIA-RDP96-00789R0031 00280001 -7
TAB
Approved For Release 2000/08/08
: CIA-RDP96-00789R0031 00280001 -7
0006-3309/89 $10.00+ .00
O 1991 Pergamon Press pie
g'jisi Vol. 34, No. J, pp. 97S-978, 1989
IKte Poland
DISSIPATIVE FUNCTIONS OF THE PROCESSES OF
Interaction of electromagnetic radiation with
f
BIOLOGICAL OBJECTS*
Yu.
P. Chukova
_ Otklik” Time Scientific Collective
(
(.Received 23 July 1987)
aothors have determined the rate of generation of entropy in biological systems as a
^sult ot the irreversibility of the processes of the interaction with electromagnetic radiation
whlch °ne aC
f
C°.mpan ‘ed by r,se in free “ergy. The characteristics of the irreversibility of
^ process ot plant photosynthesis, human vision, etc. are presented. It is shown that in the
processes considered,
irreversibility may greatly
differ (up to
10s fold)
r
reversibility, as
is known,
is an
integral property of all real processes. After the
wrk of Pngogine [1]
it is characterized by the magnitude S„ called the rate of genera-
10a of entropy, the specific value of which
<7 is called a dissipative function. Among
* vanety f
irreversible processes of the real world we would mention but a few
processes of heat and electrical conductivities, diffusion, thermal chemical
reactions,
at.) for which methods of calculating this magnitude have been devised. As for biolo-
pai objects for them as for more complex systems the question has hardly ever been
iied.
Yet, the achievements of the thermodynamics of irreversible processes in the
ast few years and, m particular, the successful application of the Landau-Vainshtcin
aethoci tor explaining the processes of energy transformation in quantum systems have
ji e possi
e evaluation of the magnitude S, for a large range of processes of interac-
m ot electromagnetic radiation of any spectra] composition with matter.
rhe method of determining S t for endoergic processes occurring under the influence
u electromagnetic radiation
is outlined in
[2].
It
is applicable to open systems in the
y state. While in these conditions electromagnetic radiation with the energy
Ll
m
/r
roCeSSeS aCC°mpanied by rise in the free enerSy (endoergic processes) of the
: r rocif
“ COmpared With the free ener8y of the reactants (FJ the efficiency of
^ =
( 1 )
the points above the magnitudes denote time derivatives. From the laws of ther-
; dynamics for
rjt we have the relation
1'=l-T(St +Sd/Wt ,
‘ Biofizika 34: No. 5, 898-900, 1989.
(2)
[975]
>roved For Release 2000/08/08
: CIA-RDP96-00789R0031 00280001 -7
Yu.
P. Chukova
74 logv[Hz]
Position of zero boundary of endoergic processes on the plane log v-log E, in the appr0
mation of the thermodynamic reversibility of the process.
Approved For Release 2000/08/08
: CIA-RDP96-00789R003100;
wa
where Sa
is the flux of entropy of electromagnetic radiation with the power
W',, whit*
is absorbed by the system.
Usually relation (2)
is analyzed in the approximation of the thermodynamic lime
when S,= 0 [3]. The limiting value of the efficiency of the system (tjt) may in this cm
be calculated for any system
if the main characteristics of the process are known.
S,
may be evaluated from the difference of the real efficiency of the process
(i/ e) from ik
limiting.
The
effects appearing in biological objects as a result of interaction with
electro,
magnetic radiation and those magnitudes from which they are judged with rare exccf
tions cannot be interpreted as efficiency. But in threshold conditions when the biorev
ponse vanishes one may state that the efficiency of the endoergic process
is equal u
zero. This aspect is considered in detail in
[2]. In threshold conditions of real efficicncj
we have
.
.
St=W?jTSa -l.
W
For the red boundary of all bio-effects with a wide frequency action band and (a
bioresonance
effects
the
position of
the
zero
efficiency boundary of the
endoerpt
process in the approximation of the thermodynamic reversibility of the process is gnci
by the relation
c
2Ey = 2nkT v,2 [(l + Po) In (I + Po) — Po ln Po]
>
where v
is frequency; E°
is the spectral density of the radiation at this frequency: 7^
the temperature of the system; e is the speed of light; k and h are Boltzman and “ a
constants; p0 = c2Ey/27:hv3
.
The Figure
illustrates
this dependence for a wide frequency interval,
in
of electromagnetic radiation the characteristics of which (frequency and spectral densw
enter the region A cannot be transformed to the free energy of the system even
«
approximation of the thermodynamic
limit (thermodynamic
reversibility). The
Ev° is always higher than the spectral density ev , r of the radiation of an absolute
W
;>i
•! a?
|the tempers
(hv^kT): El
position of the
dissipative pr
' from the
e:
human vision
v-
Par algae
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