Simulating of human physiological supersystems: integrative function of organs supporting cell life
A quantitative model of fluids’ dynamics (MFD) in the human body is created. Initially, MFD was realized as an autonomous C# software module (SM) functioning under given dynamic input characteristics. Later, SM was incorporated into our special software-modeling tool (SMT) capable of simulating the...
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Problems in programming| _version_ | 1859476979138428928 |
|---|---|
| author | Grygoryan, R.D. Degoda, A.B. Lyudovyk, T.V. Yurchak, O.I. |
| author_facet | Grygoryan, R.D. Degoda, A.B. Lyudovyk, T.V. Yurchak, O.I. |
| author_sort | Grygoryan, R.D. |
| baseUrl_str | https://pp.isofts.kiev.ua/index.php/ojs1/oai |
| collection | OJS |
| datestamp_date | 2025-04-16T13:57:48Z |
| description | A quantitative model of fluids’ dynamics (MFD) in the human body is created. Initially, MFD was realized as an autonomous C# software module (SM) functioning under given dynamic input characteristics. Later, SM was incorporated into our special software-modeling tool (SMT) capable of simulating the main modes of the human physiological super-system (PSS) providing cells' life. MFD describes mechanisms regulating long-term blood, lymph, total cells’, and intercellular volumes. SMT simulates both intracellular and multicellular mechanisms providing cell energy balance despite casual dynamics of energy consumption rate. Multicellular mechanisms include complex systems controlling systemic and regional hemodynamics, interaction of the liver with the pancreas, blood filtration in kidneys, bladder function, and liquid expirations in lungs and skin in the background of a dynamic external environment. The latter is a gas atmosphere with altering pressure, illumination, temperature, humidity, and wind speed. Models have been tested using algorithms that design scenarios, including simulation of either short-time or long-time (hours or days) observations. Input data include different combinations of internal and external parameters including osmotic, and oncotic pressures. Output data include the main parameters characterizing organs and life support systems. Both student-medics and physiologists interested in providing theoretical research can be users of SM. Prombles in programming 2024; 4: 77-88 |
| first_indexed | 2025-07-17T09:47:43Z |
| format | Article |
| fulltext |
Комп’ютерне моделювання
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УДК 517.958:57 +519.711.3 + 612.51.001 http://doi.org/10.15407/pp2024.04.077
R.D. Grygoryan, A.G. Degoda, T.V. Lyudovyk, O.I.Yurchak
SIMULATING OF HUMAN PHYSIOLOGICAL SUPERSYSTEMS:
INTEGRATIVE FUNCTION OF ORGANS
SUPPORTING CELL LIFE
A quantitative model of fluids’ dynamics (MFD) in the human body is created. Initially, MFD was realized
as an autonomous C# software module (SM) functioning under given dynamic input characteristics. Later,
SM was incorporated into our special software-modeling tool (SMT) capable of simulating the main modes
of the human physiological super-system (PSS) providing cells' life. MFD describes mechanisms regulating
long-term blood, lymph, total cells’, and intercellular volumes. SMT simulates both intracellular and multi-
cellular mechanisms providing cell energy balance despite casual dynamics of energy consumption rate. Mul-
ticellular mechanisms include complex systems controlling systemic and regional hemodynamics, interaction
of the liver with the pancreas, blood filtration in kidneys, bladder function, and liquid expirations in lungs and
skin in the background of a dynamic external environment. The latter is a gas atmosphere with altering pres-
sure, illumination, temperature, humidity, and wind speed. Models have been tested using algorithms that
design scenarios, including simulation of either short-time or long-time (hours or days) observations. Input
data include different combinations of internal and external parameters including osmotic, and oncotic pres-
sures. Output data include the main parameters characterizing organs and life support systems. Both student -
medics and physiologists interested in providing theoretical research can be users of SM.
Keywords: physical health, body fluids, physiological control, quantitative model, simulator
Р.Д. Григорян, А.Г. Дегода, Т.В. Людовиk, О.І. Юрчак
СИМУЛЯТОР ФІЗІОЛОГІЧНИХ НАДСИСТЕМ ЛЮДИНИ:
ІНТЕГРАТИВНА ФУНКЦІЯ ОРГАНІВ
ЖИТТЄЗАБЕЗПЕЧЕННЯ КЛІТИНИ
Створено кількісну модель динаміки рідин (РРР) в організмі людини. Спочатку MFD був реалізований
як автономний програмний модуль C# (SM), що функціонує при заданих динамічних вхідних характери-
стиках. Пізніше SM було включено в наш спеціальний інструмент програмного моделювання (SMT),
здатний моделювати основні режими фізіологічної суперсистеми людини (PSS), що забезпечує життєді-
яльність клітин. MFD описує механізми довготривалої регуляції крові, лімфи та загального внутрішньо-
клітинного та міжклітинного об’ємів. SMT моделює як внутрішньоклітинні, так і багатоклітинні механі-
зми, що забезпечують енергетичний баланс клітини, незважаючи на випадкову динаміку швидкості спо-
живання енергії. Багатоклітинні механізми включають складні системи контролю системної та регіона-
льної гемодинаміки, взаємодії печінки з підшлунковою залозою, фільтрації крові в нирках, функції сечо-
вого міхура, виділення рідини в легенях і шкірі на тлі динамічного зовнішнього середовища. Останнє
являє собою газову атмосферу зі змінним тиском, освітленістю, температурою, вологістю та швидкістю
вітру. Моделі були перевірені з використанням алгоритмів, які розробляють сценарії, включаючи симу-
ляцію короткочасних або тривалих (години або дні) спостережень. Вхідні дані включають різні комбіна-
ції внутрішніх і зовнішніх параметрів, включаючи осмотичний і онкотичний тиск. Вихідні дані містять
основні параметри, що характеризують органи та системи життєзабезпечення. Користувачами СМ мо-
жуть бути як студенти-медики, так і фізіологи, зацікавлені у проведенні теоретичних досліджень.
Ключові слова: фізичне здоров’я, рідини організму, фізіологічний контроль, кількісна модель, тренажер
© R.D. Grygoryan, A.G. Degoda, T.V. Lyudovyk, O.I. Yurchak, 2024
ISSN 1727-4907. Проблеми програмування. 2024. №4
Комп’ютерне моделювання
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Introduction
Physiologists and physicians use em-
pirical technologies to measure a limited num-
ber of life parameters that can quantitatively
characterize the level of human physical health
(HPH). Certainly, these parameters were sta-
tistically verified for populations of healthy
and seek people. However, physicians meet a
problem: the parametric landscape of HPH dis-
plays essential and often very complex altera-
tions in time [1-3]. The origin of the observed
instability of life parameters is still unknown.
Moreover, neither physiologists nor medical
scientists have ideas for conceptual overcom-
ing the problem. In our opinion, the concept of
physiological supersystems (PSS) [4-6],
properly realized as a specialized computer
simulator, could essentially assist in finding a
way out of this methodological dead-end. The
simulator must be based on special quantitative
models of organs and anatomical-physiologi-
cal systems that, according to PSS, were saved
in vertebrates due to the essential role of these
organs in evolution. Basic mathematical mod-
els and software components have been al-
ready developed [7-10].
The article proposes our vision of the
final model, which integrates these compo-
nents. Additionally, the article presents several
test simulations demonstrating the potential of
our software for physiologists and physicians.
Mathematical model of PSS
According to the concept of PSS, opti-
mal cell metabolism is a fundamental condi-
tion for the cellular long life and functionality
in unstable external/internal environments. In-
teractions between certain biochemical factors
(also known as adaptation factors [1,11,12]) of
every specialized cell and its nucleus adapt the
expression of genes responsible for the effi-
ciency of many molecular events including the
rate of energy (ATP molecules) synthesis.
However, the efficiency of autonomous intra-
cellular regulators essentially falls in parallel
with an increasing imbalance between biosyn-
thesis and molecular destruction. Therefore,
special adaptation factors, produced in these
problematic cells and penetrated lymph or in-
tercellular space, finally modify the activity of
multiple multi-cellular mechanisms (MM).
Some of MM enhances the basic intracellular
regulators. In particular, a set of MM provides
molecular rebuilding in the problematic cells
with materials (oxygen, water, nutrients). An-
other group of MM purifies the cytoplasm in
these cells. So, the entire organism is chroni-
cally under the influence of adaptation factors.
This is the humoral mechanism capable of
originating HPH's instability. As many chemi-
cals influence target neurons of CNS, the latter
also modifies the parametric landscape of
HPH. It is the understanding that the landscape
depends on the number of problematic cells.
Every cell is a dynamic object adap-
tively compensating for intracellular destruc-
tions. In this context, one of the roles of MM is
providing intracellular adaptive re-buildings
with adequate inflows of primary materials
(nutrients, oxygen, and water). The second role
of MM provided by other organs is in ade-
quately removing metabolic wastes. To pro-
vide such a requirement, PSS must have a ra-
ther complex construction. It was shown [5,6]
that the digestive system, lungs, cardiovascular
system (CVS), liver, pancreas, kidneys, ther-
moregulatory system (TS), as well as special
neural-hormonal mechanisms providing the
fluids’ homeostasis are components of the PSS
to be modeled. The main structural-functional
blocks of PSS and their interrelations are illus-
trated in Fig. 1.
According to Fig.1, body fluids are par-
tially located in four main reservoirs: cellular,
intercellular, cardiovascular, and lymphatic.
The cardiovascular system (CVS) is the pri-
mary space for receiving the fluids absorbed in
the gastrointestinal tract. A part of blood
through capillaries penetrating the interstitial
liquid space is the internal source for cells tak-
ing oxygen and nutrients. The blood, remaining
in capillaries, flows into venous capillaries and
veins finally filling the central vein which is the
reservoir for filling the right heart. So, in statics,
the blood volume that leaves CVS and lym-
phatic return to CVS are equal. However, mul-
tiple factors can violate this equality.
The interstitial reservoir plays a dual
role. It is the second source of lymph and the
space for the liquid exchanging with cells. The
Комп’ютерне моделювання
79
cellular liquid contains both oxygen and nutri-
ents. They are internal sources for the molecular
synthesis of specific biological macromole-
cules. A part of them (molecules of ATP) pro-
vides all forms of intracellular biological work.
Other macromolecules are ultra-structural units
for constructing cellular organelles.
Thanks to liver-pancreas interaction, ex-
cess blood sugars can be transformed and accu-
mulated into the liver as glycogen. Under low
blood concentrations of glucose, this glycogen
is back-transformed to glucose.
The dynamics of boy fluids are associated
with the activities of multiple specialized organs
that are under the influences of nervous and hor-
monal regulators. Models of these mechanisms
have been already published by us [7-10].
Fluids can leave the body in three main
ways – blood filtration in the kidneys, skin
sweating (this is under mechanisms controlling
the thermoregulation), and lung expiration.
Therefore, the total body fluids and their parts
in the four relatively isolated internal spaces
can display complex dynamics depending on
multiple external and internal factors. Our mod-
els were properly advanced: the dynamics of in-
ternal fluids' redistributions are described.
Let us denote the body's total fluid vol-
ume for every time moment as )(tVT . It can be
presented as a sum of four components:
)()()()()( tVtVtVtVtV LyInVСCVST +++= (1)
In (1), CVSV is the total blood volume,
VСV is the total liquid into cells, InV is the volume
of the intercellular space, and LyV is the lym-
phatic volume.
)(tVCVS depends on the velocity of
blood’s inflows and outflows. Let us the water
inflow is )(tqInp , )(tqLE is the outflow
(expiration) in lungs, )(tqSE is the
evaporation through the skin, )(tqU is
the urine outflow, )(tq IVС and )(tqVСС are the
flows of liquid into and out of a virtual cell,
)(tqIn is the inflow into the intercellular space,
)(tqCf is the filtration in capillaries, and )(tqLy
is the lymph flow. Then, the differential equa-
tions (2)-(5) below describe relationships be-
tween volumes and liquid flows:
)()()(
)()()()(
tqtqtq
tqtqtqtq
dt
dV
LyInCf
USELEInp
CVS
+−−
−−−=
(2)
Fig. 1. Interaction of organs and anatomical-functional systems involved in PSS
Комп’ютерне моделювання
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)()()( tqtqtq
dt
dV
LyVССCf
VIn −−= (3)
)()( tqtq
dt
dV
LyCf
VСС −= (4)
)()( tqtq
dt
dV
LyVСС
VLy −= (5)
The next system of equations (6)-(8)
describes relationships between flows, pres-
sures, and resistances in compartments:
)(/))()(()( tRtPtPtq CInCCf −= (6)
)(/))()(()( tRtPtPtq InCCInIn −= (7)
)(/))()(()( tRtPtPtq LyСVLyLy −= (8)
In (6)-(8), )(tPC is capillaries’ pressure,
)(tRC is capillaries’ resistance, )(tP
In
is inter-
stitial liquid’s pressure, )(tRInC is the re-
sistance between interstitial and cell spaces,
)(tPLy is the lymphatic pressure, СVP is the cen-
tral vein pressure, and )(tRLy is the resistance of
lymphatic collector.
So, the equations’ system (1)-(8) is in-
corporated into our algorithms developed for
computer simulations of complex physiologi-
cal mechanisms responsible for physical
health. Calculations of pressures include the
hydrostatic and osmotic (oncotic) components.
Namely, two latter components play a key role
in mechanisms that control the acid-basis and
electrolytic homeostasis.
Brief information about research
software
Simulation algorithms are similar to
those published in [8,9]. Every simulation
starts from the actualization of input data and
simulation scenarios. These procedures are
provided with assistant window forms. The
simulation scenario covers both the simula-
tion duration and combinations of dynamic
tests. Our early software versions provided
the user with simulation graph results only af-
ter the entire scenario was processed. The cal-
culation algorithm was modified to make sim-
ulations more effective without using a more
empowered computer. To construct graphs,
the modified algorithm creates and saves a se-
ries of data only for three neighbor time points
(previous, current, next). This cardinally in-
creased the real-time observation to be simu-
lated. It can be both several seconds and sev-
eral weeks. However, under long-lasting sim-
ulations, the user was not informed about the
simulation dynamics which sometimes can be
wrong. Thus the algorithm is modified to il-
lustrate the calculation dynamics for a repre-
sentative group of biometric characteristics
that can inform the modeler whether the sim-
ulation goes in the planned course.
Main simulation results
The limited space of the article forced
us to consider a limited number of test simula-
tions. At the same time, we tried to illustrate
both the simulation technology that may be in-
teresting for programmers and several biologi-
cal data that could attract physiologists and
medics-researchers who are interested in wid-
ening the research methods.
This article does not provide the reader
with simulation data reflecting the effects of
concrete diseases. All simulations shown be-
low have to demonstrate that our models and
the software technology, despite being an in-
terim product yet, are promising scientific
tools. Perhaps, physiologists and medics-re-
searchers as potential users of our software
will know that after a proper modification, the
proposed software can be used for mining ad-
ditional information concerning functions of
every organ involved in PSS.
Figures 2 and 3 illustrate special graph
forms, providing tuning procedures for appro-
priate model components.
Комп’ютерне моделювання
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Fig. 2. A fragment of the user interface illustrating the window form for actualizing values of
intercellular, cellular, and lymphatic compartments of the model before starting a simulation
Fig. 3. A fragment of the user interface illustrating the window form for actualizing values
of the kidney and bladder models before starting the simulation
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Figures 4-12 illustrate several results of a computer simulation. The simulation scenario includes the
following: 1) the human body position is horizontal; 2) neural and hormonal regulators controlling
the function of CVS are switched on; 3) brain neurons reacting to alterations of liquor’s osmotic
pressure are switched off; 4) concentrations of atmosphere gases are in the norm; 5) within 24 hours
period of observation the light intensity alters with the 12-hour day/night period starting from 6 hours
of the morning; 6) air temperature, humidity, wind speed have the fixed dynamics; 7) serotonin and
melatonin hormones display normal circadian dynamics.
Fig. 4. Seven biological characteristics that can be specially displayed during calculations
(the user arbitrarily sets intervals for every next time point)
Fig. 5. The dynamics of body fluids (total and in four compartments). The simulation scenario
provides a 24-hour experiment under natural dynamics of environmental temperature and lightness
without activating the brain receptors of osmotic pressure
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Fig. 6. Simulated dynamics of air parameters
Fig. 7. Simulated dynamics of body temperatures according to the model of thermoregulation
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Fig. 8. Simulated dynamics of additional characteristics according to the model of thermoregulation
Fig. 9. Simulated dynamics of several cardiovascular characteristics
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Fig. 10. Simulated dynamics of additional cardiovascular characteristics
Fig. 11. Simulated dynamics of the kidney model demonstrating the difference between
the production of the primary urine and its partial reabsorption
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Fig. 12. Simulated dynamics of the kidney-bladder model demonstrating periodical fillings and
emptying of the bladder per day (changes in hormonal activity taken into account)
Discussion
Our models are based on fundamental
physiological knowledge including quantita-
tive data like those presented in [2,3,11,12,16].
It was also critically analyzed the experience
of colleagues [13-17]. Certainly, not every
model constant is strongly verified. At the
same time, such parameters were varied in
some ranges to estimate their potential role in
system-scale incorrectness. Results illustrated
in Fig.4 – Fig.12 are only part of the infor-
mation provided by our current software-mod-
elling tool. It can simulate more thinkable sce-
narios and yield essentially more physiological
output data. However, our current purpose was
mainly to demonstrate the usability of the sim-
ulator. We plan to publish physiological as-
pects in biomedical journals. Before doing it,
we aimed to thoroughly test every component
model and the whole simulator using much
more empirical data. Besides, the final user in-
terface will be advanced to become maximally
friendly for physiologists and physicians. We
think that the fact that such a complex research
tool has already been developed is an essential
step forward.
Conclusion
For the first time, a special software-
modeling tool (simulator) capable of essen-
tially widening and deepening research op-
portunities of modern human physiologists
and medics-researchers was developed. The
main models, software units and the entire
simulator had been mainly tested for the most
well-known test scenarios. In addition to a
big list of standard scenarios, the simulator
provides the user with easy algorithms for
constructing and simulating new scenarios.
The simulator is the lonely research tool for
obtaining novel data concerning the interac-
tion of human organs that optimize cells’ me-
tabolism.
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Одержано: 27.09.2024
Внутрішня рецензія отримана: 01.10.2024
Зовнішня рецензія отримана: 15.10.2024
Комп’ютерне моделювання
88
About authors:
Grygoryan Rafik,
Department chief, PhD, D-r in biology
http://orcid.org/0000-0001-8762-733X.
Degoda Anna,
Senior scientist, PhD.
http://orcid.org/0000-0001-6364-5568.
Lyudovyk Tetyana,
Senior scientist, PhD.
https://orcid.org/0000-0003-0209-2001.
Yurchak Oksana,
Leading software engineer.
https://orcid.org/0000-0003-3941-1555.
Place of work:
Institute of software systems
of Ukraine National Academy of Sciences
03187, Кyїv,
Acad. Glushkov avenue, 40,
Phone.: 066 683 0853.
Е-mail:rgrygoryan@gmail.com,
anna@silverlinecrm.com,
tetyana.lyudovyk@gmail.com,
daravatan@gmail.com,
|
| id | pp_isofts_kiev_ua-article-676 |
| institution | Problems in programming |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2025-07-17T09:47:43Z |
| publishDate | 2025 |
| publisher | PROBLEMS IN PROGRAMMING |
| record_format | ojs |
| resource_txt_mv | ppisoftskievua/2c/169500b29d72af12f1938f2b61a5352c.pdf |
| spelling | pp_isofts_kiev_ua-article-6762025-04-16T13:57:48Z Simulating of human physiological supersystems: integrative function of organs supporting cell life Симулятор фізіологічних надсистем людини: інтегрована функція органів життєзабезпечення клітини Grygoryan, R.D. Degoda, A.B. Lyudovyk, T.V. Yurchak, O.I. physical health; body fluids; physiological control; quantitative model; simulator UDC 517.958:57 +519.711.3 + 612.51.001 фізичне здоров’я; рідини організму; фізіологічний контроль; кількісна модель; тренажер УДК 517.958:57 +519.711.3 + 612.51.001 A quantitative model of fluids’ dynamics (MFD) in the human body is created. Initially, MFD was realized as an autonomous C# software module (SM) functioning under given dynamic input characteristics. Later, SM was incorporated into our special software-modeling tool (SMT) capable of simulating the main modes of the human physiological super-system (PSS) providing cells' life. MFD describes mechanisms regulating long-term blood, lymph, total cells’, and intercellular volumes. SMT simulates both intracellular and multicellular mechanisms providing cell energy balance despite casual dynamics of energy consumption rate. Multicellular mechanisms include complex systems controlling systemic and regional hemodynamics, interaction of the liver with the pancreas, blood filtration in kidneys, bladder function, and liquid expirations in lungs and skin in the background of a dynamic external environment. The latter is a gas atmosphere with altering pressure, illumination, temperature, humidity, and wind speed. Models have been tested using algorithms that design scenarios, including simulation of either short-time or long-time (hours or days) observations. Input data include different combinations of internal and external parameters including osmotic, and oncotic pressures. Output data include the main parameters characterizing organs and life support systems. Both student-medics and physiologists interested in providing theoretical research can be users of SM. Prombles in programming 2024; 4: 77-88 Створено кількісну модель динаміки рідин (РРР) в організмі людини. Спочатку MFD був реалізований як автономний програмний модуль C# (SM), що функціонує при заданих динамічних вхідних характеристиках. Пізніше SM було включено в наш спеціальний інструмент програмного моделювання (SMT), здатний моделювати основні режими фізіологічної суперсистеми людини (PSS), що забезпечує життєдіяльність клітин. MFD описує механізми довготривалої регуляції крові, лімфи та загального внутрішньоклітинного та міжклітинного об’ємів. SMT моделює як внутрішньоклітинні, так і багатоклітинні механізми, що забезпечують енергетичний баланс клітини, незважаючи на випадкову динаміку швидкості споживання енергії. Багатоклітинні механізми включають складні системи контролю системної та регіональної гемодинаміки, взаємодії печінки з підшлунковою залозою, фільтрації крові в нирках, функції сечового міхура, виділення рідини в легенях і шкірі на тлі динамічного зовнішнього середовища. Останнє являє собою газову атмосферу зі змінним тиском, освітленістю, температурою, вологістю та швидкістю вітру. Моделі були перевірені з використанням алгоритмів, які розробляють сценарії, включаючи симуляцію короткочасних або тривалих (години або дні) спостережень. Вхідні дані включають різні комбінації внутрішніх і зовнішніх параметрів, включаючи осмотичний і онкотичний тиск. Вихідні дані містять основні параметри, що характеризують органи та системи життєзабезпечення. Користувачами СМ можуть бути як студенти-медики, так і фізіологи, зацікавлені у проведенні теоретичних досліджень.Prombles in programming 2024; 4: 77-88 PROBLEMS IN PROGRAMMING ПРОБЛЕМЫ ПРОГРАММИРОВАНИЯ ПРОБЛЕМИ ПРОГРАМУВАННЯ 2025-04-16 Article Article application/pdf https://pp.isofts.kiev.ua/index.php/ojs1/article/view/676 10.15407/pp2024.04.077 PROBLEMS IN PROGRAMMING; No 4 (2024); 77-88 ПРОБЛЕМЫ ПРОГРАММИРОВАНИЯ; No 4 (2024); 77-88 ПРОБЛЕМИ ПРОГРАМУВАННЯ; No 4 (2024); 77-88 1727-4907 10.15407/pp2024.04 en https://pp.isofts.kiev.ua/index.php/ojs1/article/view/676/728 Copyright (c) 2025 PROBLEMS IN PROGRAMMING |
| spellingShingle | physical health body fluids physiological control quantitative model simulator UDC 517.958:57 +519.711.3 + 612.51.001 Grygoryan, R.D. Degoda, A.B. Lyudovyk, T.V. Yurchak, O.I. Simulating of human physiological supersystems: integrative function of organs supporting cell life |
| title | Simulating of human physiological supersystems: integrative function of organs supporting cell life |
| title_alt | Симулятор фізіологічних надсистем людини: інтегрована функція органів життєзабезпечення клітини |
| title_full | Simulating of human physiological supersystems: integrative function of organs supporting cell life |
| title_fullStr | Simulating of human physiological supersystems: integrative function of organs supporting cell life |
| title_full_unstemmed | Simulating of human physiological supersystems: integrative function of organs supporting cell life |
| title_short | Simulating of human physiological supersystems: integrative function of organs supporting cell life |
| title_sort | simulating of human physiological supersystems: integrative function of organs supporting cell life |
| topic | physical health body fluids physiological control quantitative model simulator UDC 517.958:57 +519.711.3 + 612.51.001 |
| topic_facet | physical health body fluids physiological control quantitative model simulator UDC 517.958:57 +519.711.3 + 612.51.001 фізичне здоров’я рідини організму фізіологічний контроль кількісна модель тренажер УДК 517.958:57 +519.711.3 + 612.51.001 |
| url | https://pp.isofts.kiev.ua/index.php/ojs1/article/view/676 |
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