lecturer: lushchyk u.b., md [email protected] coauthors i.p. babii v.v. novytskyy modern...

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Lecturer: Lushchyk U.B., MD [email protected] www . lushchyk . org www.istyna.kiev.ua Coauthors I.P. Babii Coauthors I.P. Babii V.V. Novytskyy V.V. Novytskyy Modern Models for the Living Organism’s Functioning at Normal and Pathological Conditions

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Page 1: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

Lecturer: Lushchyk U.B., [email protected]

www.lushchyk.org www.istyna.kiev.ua

Coauthors I.P. BabiiCoauthors I.P. BabiiV.V. NovytskyyV.V. Novytskyy

Modern Models for the Living Organism’s Functioning at Normal and Pathological Conditions

Page 2: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

Modern Models for the Modern Models for the Living Organism’s Living Organism’s

Functioning at Normal Functioning at Normal and Pathological and Pathological

ConditionsConditions

Page 3: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

A human organism as well as any living A human organism as well as any living organism should be considered as a complex organism should be considered as a complex

dynamic system created by nature dynamic system created by nature

Page 4: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

According to the systems’ modeling According to the systems’ modeling we consider the following essential we consider the following essential

components components needed for functioning of the systemneeded for functioning of the system

1. 1. structural elementsstructural elements ( (in the living systemin the living system: : organs and subsystemsorgans and subsystems ( (cardiovascularcardiovascular, , nervousnervous, , musculoskeletalmusculoskeletal, , digestivedigestive, , secretionsecretion, , endocrine etc.endocrine etc.)),,

2. 2. conductors inside a subsystem,conductors inside a subsystem,3. 3. intersystem conductors,intersystem conductors,4. 4. parameters indication system,parameters indication system,5. data processing system5. data processing system,,6. 6. feedback system,feedback system,7. 7. checking, control systems and various checking, control systems and various

types of regulation.types of regulation.

Page 5: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

Clockwork Clockwork

The mechanical and The mechanical and cybernetic models of the cybernetic models of the complex systemscomplex systems could be could be the more similar to the more similar to prototypes prototypes for the living for the living system in mathematical system in mathematical modeling.modeling.

Very these models are Very these models are combined combined by principle of by principle of dynamic nature – dynamic nature – the the system reacts fast system reacts fast both both inside and outsideinside and outside

Page 6: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

Mechanical systemMechanical system

Peculiar features of the Peculiar features of the mechanical system lie in the mechanical system lie in the fact fact that the system that the system functioning is controlled by functioning is controlled by principle of susceptibility to principle of susceptibility to mechanical changes. mechanical changes.

It means that identification It means that identification sensors react to changing of sensors react to changing of pressure, temperature, pressure, temperature, amplitude of movement etc, amplitude of movement etc,

Page 7: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

Mechanical systemMechanical system

The mechanical system The mechanical system

is sensitive to changes of a is sensitive to changes of a certain gradient certain gradient

(differences of a (differences of a

background and an actual background and an actual index) of that or another index) of that or another

parameter parameter (a gradient (a gradient becomes a parameter becomes a parameter

of sensitivity for the of sensitivity for the system). system).

Page 8: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

… … An analogyAn analogy

Water-supply system Water-supply system functions very on this functions very on this principle namely water principle namely water spontaneously flows spontaneously flows from high pressure to from high pressure to low pressure. low pressure.

In the living system In the living system cardiovascular, cardiovascular, partially digestive and partially digestive and secretion subsystems secretion subsystems correspond to this type correspond to this type of functioning.of functioning.

Page 9: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

Cybernetic systemCybernetic system

When we consider the When we consider the model of the cybernetic model of the cybernetic

system, it is more system, it is more sensitive structure with sensitive structure with

numerous indicators and numerous indicators and powerful control system. powerful control system. It is so kind of electronic It is so kind of electronic

system with large system with large superstructures of superstructures of

consecutive and parallel consecutive and parallel conductors’ connection. conductors’ connection.

Page 10: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

Cybernetic systemCybernetic system

Therefore Therefore

in comparison with the in comparison with the mechanical system chances mechanical system chances of emergency breakage of of emergency breakage of the system are quite high, as the system are quite high, as in case of breakage of one in case of breakage of one segment the whole system segment the whole system could be blocked. could be blocked.

Page 11: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

In the living system In the living system • nervous, nervous, • digestive, digestive, • secretion, secretion, • endocrine, endocrine, • partially cardiovascular partially cardiovascular

subsystems subsystems correspond to the correspond to the electronic-cybernetic electronic-cybernetic type.type.

Cybernetic systemCybernetic system

Page 12: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

Mixed mechanic-electronic Mixed mechanic-electronic (hybrid) model(hybrid) model

Very this distribution Very this distribution

of various algorithms in a of various algorithms in a subsystem’s functions inside the subsystem’s functions inside the

human organism enables to human organism enables to consider its functioning consider its functioning

on the whole on the whole

as a as a mixed mechanic-electronic mixed mechanic-electronic (hybrid) model.(hybrid) model.

Page 13: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

At the present level of the science At the present level of the science development development the living organism is the living organism is

simulated in particular as the simulated in particular as the cybernetic system cybernetic system

with numerous constant and variable with numerous constant and variable parameters, which characterize its parameters, which characterize its

dynamics, dynamics, participate actively in the processes participate actively in the processes

of regulation and control.of regulation and control.

Mixed mechanic-electronic Mixed mechanic-electronic (hybrid) model(hybrid) model

Page 14: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

Naturally, that the question arises: Naturally, that the question arises: «What type of the system control «What type of the system control

prevails in functioning of the hybrid prevails in functioning of the hybrid system?» system?»

It is possible that the muscular It is possible that the muscular system in the human organism is as system in the human organism is as

a mediator between the electronic a mediator between the electronic and mechanical systems. and mechanical systems.

Page 15: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

The hierarchy of functioning of The hierarchy of functioning of the living systemthe living system

According to the hierarchy of According to the hierarchy of functioning of the living system we functioning of the living system we consider the organism as an integral consider the organism as an integral system with numerous indicators that system with numerous indicators that function by principle of feed-back and function by principle of feed-back and submit to single center. submit to single center.

Only such hierarchy enables to make a Only such hierarchy enables to make a principle of subordination and precise principle of subordination and precise submission of different control levels.submission of different control levels.

Page 16: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

Therefore we should multisided consider Therefore we should multisided consider complex hierarchy of the living system and complex hierarchy of the living system and

virtually imagine it in many dimensions:virtually imagine it in many dimensions:

1. Macro- and microlevel of 1. Macro- and microlevel of processes’ organization in processes’ organization in the living organism.the living organism.

2. Level of providing vital 2. Level of providing vital activity in the organismactivity in the organism

3. 3. Levels of subsystems’ Levels of subsystems’ functioningfunctioning

4. 4. A level of the intrasystem A level of the intrasystem balance in every balance in every subsystem of living subsystem of living organismorganism

5. 5. Hierarchical level of the Hierarchical level of the balance controlbalance control

Page 17: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

2. Level of providing vital 2. Level of providing vital activity in the organism:activity in the organism:

• minimum for life minimum for life preservation,preservation,

• average (background) - for average (background) - for providing background vital providing background vital activity of the organism,activity of the organism,

• high (reserve) - for high (reserve) - for supporting the organism at supporting the organism at overloads.overloads.

Therefore we should multisided consider Therefore we should multisided consider complex hierarchy of the living system and complex hierarchy of the living system and

virtually imagine it in many dimensions:virtually imagine it in many dimensions:

Page 18: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

3. Levels of subsystems’ 3. Levels of subsystems’ functioning:functioning:

• structural (reverse and structural (reverse and irreversible damages)irreversible damages)

• hydrodynamic levelhydrodynamic level• hemodynamic levelhemodynamic level• energy level.energy level.

Therefore we should multisided consider Therefore we should multisided consider complex hierarchy of the living system and complex hierarchy of the living system and

virtually imagine it in many dimensions:virtually imagine it in many dimensions:

Page 19: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

Therefore we should multisided consider Therefore we should multisided consider complex hierarchy of the living system and complex hierarchy of the living system and

virtually imagine it in many dimensions:virtually imagine it in many dimensions:

4. 4. A level of the intrasystem balance in A level of the intrasystem balance in every subsystem of living organism:every subsystem of living organism:

• structural balancestructural balance• functional balancefunctional balance• conduction balanceconduction balance• energy balanceenergy balance• mechanical balancemechanical balance• electronic balance (cellular, helectronic balance (cellular, humoralumoral

etc)etc)

Page 20: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

5. 5. Hierarchical Hierarchical level of the level of the balance control:balance control:

• autonomous autonomous subsystemicsubsystemic

• central central intersystemicintersystemic

Therefore we should multisided consider Therefore we should multisided consider complex hierarchy of the living system and complex hierarchy of the living system and

virtually imagine it in many dimensions:virtually imagine it in many dimensions:

Page 21: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

ThusThus

the human organism is a complex the human organism is a complex many-sided living system with many-sided living system with numerous changeable numerous changeable parameters of its functioning on parameters of its functioning on different levels of its different levels of its organization with many organization with many indication systems and feedback indication systems and feedback connection.connection.

Page 22: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

The present level of The present level of mathematical mathematical modeling development modeling development enables to investigate enables to investigate profoundly the profoundly the hierarchy of the hierarchy of the models’ functioning of models’ functioning of the hybrid systems the hybrid systems

and study new unexplored algorithms and study new unexplored algorithms

of of autoautoregulation in the living organism.regulation in the living organism.

Page 23: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

Our experience of patients’ Our experience of patients’ treatmenttreatment

Our large experience of treatment patients in coma - Our large experience of treatment patients in coma - apalapalllicic syndrome (AS) and the analysis of restoration of their syndrome (AS) and the analysis of restoration of their functions in the rehabilitation process made us interested functions in the rehabilitation process made us interested in the aspect of estimation of reserve potential of the in the aspect of estimation of reserve potential of the human organism and capacity of self-restoration with human organism and capacity of self-restoration with numerous and deep damages in the brain, multi-injuries. numerous and deep damages in the brain, multi-injuries. Our considerations we tried to present in the next models Our considerations we tried to present in the next models from minimum capability to maximum adaptation. from minimum capability to maximum adaptation.

Page 24: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

A minimal modelA minimal model

The human body could be an initial stage for modeling The human body could be an initial stage for modeling the living system, which is structurally formed, has the living system, which is structurally formed, has all organs but not all are functioning. In most cases all organs but not all are functioning. In most cases very this model could be as a standard for modeling very this model could be as a standard for modeling any comatose states. Our results have shown that any comatose states. Our results have shown that most patients with AS had satisfactory blood, urine most patients with AS had satisfactory blood, urine tests etc. It says that a living organism was statically tests etc. It says that a living organism was statically preserved, however from dynamic positions it was preserved, however from dynamic positions it was not able to function adequately. This means that not able to function adequately. This means that considering the simple model we have a structurally considering the simple model we have a structurally preserved body, but is not capable to function - a preserved body, but is not capable to function - a body in shock (coma with expressed disbalance in body in shock (coma with expressed disbalance in functioning of vitally important organs).functioning of vitally important organs).

Page 25: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

A chaotic modelA chaotic model

Now we will complicate the model - a body Now we will complicate the model - a body start functioning as a chaotic system, organs start functioning as a chaotic system, organs and systems chaotically work in their and systems chaotically work in their autonomous background mode. This model autonomous background mode. This model reminds an orchestra that keeps training reminds an orchestra that keeps training without a bandleader before a concert. without a bandleader before a concert. Chaos of sounds of different instruments Chaos of sounds of different instruments could be heard. Sometimes occasionally they could be heard. Sometimes occasionally they fall together in euphony. The model of initial fall together in euphony. The model of initial resuscitation can be considered by the resuscitation can be considered by the example of an organism which begins to example of an organism which begins to «wake up» from shock. «wake up» from shock.

Page 26: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

A model of the control A model of the control decentralizationdecentralization

The next model is a variant of The next model is a variant of resuscitaresuscitation, tion, there is a start for rhythmic work of the heart there is a start for rhythmic work of the heart and breathing, however there are no and breathing, however there are no minimum signs of the brain functioning, minimum signs of the brain functioning, which clinically are shown by changing of which clinically are shown by changing of phases «sleep-cheerfulness». That is so-phases «sleep-cheerfulness». That is so-called heavy artillery (heart, breathing) called heavy artillery (heart, breathing) started in the automatic mode, however the started in the automatic mode, however the leading organ – the brain is not able to leading organ – the brain is not able to restore its higher hierarchical function. The restore its higher hierarchical function. The model can be associated with the state of model can be associated with the state of apalapalllicic syndrome. syndrome.

Page 27: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

ThusThus

3 models - coma, resuscitation and 3 models - coma, resuscitation and apaapallliclic syndrome can be in the basis syndrome can be in the basis of the process of mathematical of the process of mathematical modeling, as the most primitive, and modeling, as the most primitive, and the next models of «little» and the next models of «little» and «large» consciousness, self-service, «large» consciousness, self-service, social and professional adaptation social and professional adaptation describe more complicated levels of describe more complicated levels of the human organism’s functioning.the human organism’s functioning.

Page 28: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

Parameters of the living Parameters of the living system modelsystem model

Parameters of the living system model Parameters of the living system model could be divided into parameters of could be divided into parameters of external dynamics (visual and clinical) external dynamics (visual and clinical) and internal dynamics (instrumental).and internal dynamics (instrumental).

There are such variants of identification There are such variants of identification of parameters for the living system of parameters for the living system model:model:

• Visual,Visual,• Clinical,Clinical,• Instrumental.Instrumental.

Page 29: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

In our clinical practice the mentioned approach In our clinical practice the mentioned approach gave significant results and enabled to come to gave significant results and enabled to come to

such conclusionssuch conclusions

1. All living organisms function by principle of stable 1. All living organisms function by principle of stable balance of two mutually opposite vectors of balance of two mutually opposite vectors of influence:influence:

• arteriovenous balancearteriovenous balance• harmonic development - disproportionate harmonic development - disproportionate

ontogenesis ontogenesis • excitation-braking and etc.excitation-braking and etc.

2.2. According to laws of mathematical modeling living According to laws of mathematical modeling living organisms exist as integral with precise systemic organisms exist as integral with precise systemic hierarchies. Violation of subordination of one or hierarchies. Violation of subordination of one or another system in the brain could result in re-another system in the brain could result in re-profiling of the size and vector of excitation, profiling of the size and vector of excitation, violation of processes of synchronization of all violation of processes of synchronization of all involved links.involved links.

Page 30: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

In our clinical practice the mentioned approach In our clinical practice the mentioned approach gave significant results and enabled to come to gave significant results and enabled to come to

such conclusionssuch conclusions

3. 3. The living system functions as a hybrid system at combination The living system functions as a hybrid system at combination and simultaneous existence of two subsystems - mechanical and simultaneous existence of two subsystems - mechanical and electronic control with their partial mutual submission. and electronic control with their partial mutual submission. The mechanical system is more lasting in comparison with the The mechanical system is more lasting in comparison with the hybrid one. hybrid one.

4. 4. Therefore lack of pathological Therefore lack of pathological paroparoxysms, diminishing of their xysms, diminishing of their frequency and duration on a background of harmonic frequency and duration on a background of harmonic development of personality of a patient and balancing of development of personality of a patient and balancing of regulator systems of various vectors should be considered as regulator systems of various vectors should be considered as an end goal in treatment of patients of psychoneurological an end goal in treatment of patients of psychoneurological type. Paradoxical reactions could be an exception, they said type. Paradoxical reactions could be an exception, they said about disbalance or failure in the system of reacting and one about disbalance or failure in the system of reacting and one should consider them and foreseen before the treatment. The should consider them and foreseen before the treatment. The paradoxical reactions of a disbalanced organism can result in paradoxical reactions of a disbalanced organism can result in considerable worsening of the patient’s state in comparison considerable worsening of the patient’s state in comparison with the background ill state. with the background ill state.

Page 31: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

In our clinical practice the mentioned approach In our clinical practice the mentioned approach gave significant results and enabled to come to gave significant results and enabled to come to

such conclusionssuch conclusions

5. 5. A concentration of anticonvulsant drugs in an elbow vein can A concentration of anticonvulsant drugs in an elbow vein can considerably differ from the concentration of these drugs in considerably differ from the concentration of these drugs in the brain areas, especially at presence of the phenomenon of the brain areas, especially at presence of the phenomenon of the arteriovenous shunting in cavernous or in other sinuses of the arteriovenous shunting in cavernous or in other sinuses of the brain.the brain.

6. 6. Stress reactions, which are fixed in the brain and were not Stress reactions, which are fixed in the brain and were not neutralized during psychotherapy sessions, can be a neutralized during psychotherapy sessions, can be a trigtrigggerer of of frightful dreams resulting in a nightly convulsive attack.frightful dreams resulting in a nightly convulsive attack.

7. Today the complex objectivization of the state of all systems in 7. Today the complex objectivization of the state of all systems in the brain (exactly the brain!) is urgently required under the brain (exactly the brain!) is urgently required under control of up-to-date diagnostic equipment for adequate and control of up-to-date diagnostic equipment for adequate and correct tactics of treatment patients with convulsive reactions, correct tactics of treatment patients with convulsive reactions, preferably from the phase of the disease debut.preferably from the phase of the disease debut.

Page 32: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

AlexanderAlexander, 33 , 33 years oldyears old

Alexander FAlexander F., ., born in born in 1977 1977

DiagnosisDiagnosis: : vegetative vegetative state state as a result as a result

of CCCI (February 2004), of CCCI (February 2004), severe brain injurysevere brain injury

Coma duration – 1 weekComa duration – 1 weekBeginning of the treatment – Beginning of the treatment –

November 2004November 2004He had 4 scheduled courses He had 4 scheduled courses

of intensive of intensive neurorehabiliitation neurorehabiliitation

for 30 days each up to July for 30 days each up to July 2005.2005.

Page 33: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

AndrewAndrew, 29 , 29 years oldyears old

Andrew YAndrew Y., ., born in born in 1981 1981

DiagnosisDiagnosis: : vegetative status vegetative status as a as a result of CCCI (August 2001), severe result of CCCI (August 2001), severe brain injury,brain injury, subarachnoidal-subarachnoidal-parenchymatous hemorrhage, brain parenchymatous hemorrhage, brain edemaedema..

Coma duration – 3 weeksComa duration – 3 weeks..

The beginning of treatment – February The beginning of treatment – February 20022002 He had 5 scheduled courses of He had 5 scheduled courses of intensive neurorehabilitation for 30 intensive neurorehabilitation for 30 days each up todays each up to November 2005 November 2005..

Page 34: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

ThereforeTherefore

““losing” of consciousness of patients with convulsive losing” of consciousness of patients with convulsive reactions should be considered as pathologically reactions should be considered as pathologically sanogenisanogenic, which means that the organism’s attempts c, which means that the organism’s attempts to find a way out of a non-standard situation or just to to find a way out of a non-standard situation or just to inform about disorders in the living organism. The inform about disorders in the living organism. The hybrid living system in functioning provides with the hybrid living system in functioning provides with the emergency changing to the system of the hard emergency changing to the system of the hard protective re-start of the organism without interference protective re-start of the organism without interference of the patient himself. However it doesn’t mean that it is of the patient himself. However it doesn’t mean that it is able to overcome all breakages in the organism. Not able to overcome all breakages in the organism. Not "harm the brain and help it to control the situation" - "harm the brain and help it to control the situation" - such approach might be in the base of present such approach might be in the base of present tendencies in treatment of patients with convulsive tendencies in treatment of patients with convulsive attacks, unlike the simple blocking of visual convulsive attacks, unlike the simple blocking of visual convulsive reactions by high doses of anticonvulsants.reactions by high doses of anticonvulsants.

Page 35: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

ThusThus

understanding of peculiar features of the living understanding of peculiar features of the living system re-start in a damaged organism system re-start in a damaged organism enables to simulate states, to foresee a enables to simulate states, to foresee a patient’s state, possible rehabilitation and a patient’s state, possible rehabilitation and a level of restoration of the lost functions of level of restoration of the lost functions of the organism. In our clinical practice the the organism. In our clinical practice the mentioned approach allowed to make sure, mentioned approach allowed to make sure, that there are not any incurable states in that there are not any incurable states in medicine, and there is a problem of using medicine, and there is a problem of using mathematical modeling in questions of the mathematical modeling in questions of the health restoration.health restoration.

Page 36: Lecturer: Lushchyk U.B., MD u.lushchyk@gmail.com    Coauthors I.P. Babii V.V. Novytskyy Modern Models

Thank you for Thank you for your your

attention !attention !