Bogatushin I.J.

Russia, St.-Petersburg, St.-Petersburg institute for information and automation RAS,



In the report the known and new kinds of mathematical models of an organism of the person, his organs and systems are systems up, which one provide a capability of intellectual control of telemedical objects. The miscellaneous ways of obtaining of formal mathematical models of telemedical objects in the algebraic and differential intellectual are indicated.



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The intellectual control of telemedical objects can implement in real-time mode with usage of mathematical models of separate organs both systems and all organism of the person as a whole, and also models of different processes of operation of an organism of the person and his systems. These models can be applied also for organization of educational processes of the students and during improvement of professional skill of the doctors of the professionals from different areas of medicine.

For maintenance of effective telemedical diagnostic, the controls of modern medical and telemedical complexes and medical processes are necessary for plotting different mathematical models of objects of an organism of the person, using them experimental and idealized data. These models are expedient for creating by the way of systems of linear and non-linear ordinary differential equations, systems of functional, algebraic and transcendental equations keeping arbitrary constants, systems function differential equations, systems of integral, function - integral, integro-differential, function - integro-differential equations, systems of equationss in partial derivatives (including equations with deviating arguments), and also systems of equationss of a blended type, that is enumerated equations, consisting of different kinds. The systems of function - integral and function - integro-differential equations for the first time are entered in consideration by the writer. They should contain required functions both with deviating arguments, and with argument t. The selection of this or that kind of model is determined by nature of object of simulation, capability of affiliation of several models of different telemedical objects in one common model and other yardsticks of quality. In telemedicine the simulation of all organism of the person both his separate organs and systems implements.

The simulation of separate organs of the person (heart, liver, mild, lien and other organs) is made with the purpose of application of the obtained models in telemedical diagnostic and at implementation of medical effects. As medical effects we shall call telemedical acoustic, voice, electromagnetic, thermal, laser and other effects on a person, located on deleting in the open field or in some closed workstation (in a cabin of an airplane or automobile), and also therapeutic and physiotherapeutic, medicamental, surgical and other effects.

With same purpose the simulation of separate systems of an organism of the fibres, departments head and spinal cord, blood, lymph, cornea of an eye and other biological objects (with the purpose of fulfilment of effective medical effects at recovery of injured organs of the person);

- processes of operation of an organism of the person after obtaining by him(it) of different venenatings, combustions, atomic irradiation discovered and closed mechanical traumas, electrical combustions and other lesions of an organism (with the purpose of statement of the telemedical diagnosis and well-timed acceptance of effective protective measures and medical effects).

The models of the different people can be obtained on the basis of experimental data or as a result of usage of idealized models. The simulation of the whole organism of the concrete person under his auricular data and data obtained different by other by methods, and also on the basis of the biological analyses, electrocardiograms and with application of other experimental data is executed for implementation of monitoring behind a condition of his health, telemedical diagnostic and implementation of medical effects. The simulation of all organism of the concrete person can be made by systems-up of parameters of idealized models of his separate organs both systems and affiliation of these models in one. Probably also usage of many models for the description of the separate person from the miscellaneous points of view.

In telemedicine the relevant value has simulation of control procedures a brain of the concrete person, and also his separate organs, systems and all organism on the basis of models of person (central and vegetative nervous systems, circulatory, lymphatic, respiratory, genitourinary and other systems) implements. Large value have the models of neuronic cages, their systems, different departments head both spinal cord and circumferential nervous endings.

Alongside with simulation of organisms of the able-bodied people, their organs and systems the simulation of organs, systems and organisms of the different people having widespread diseases (of disease of vegetative and central nervous systems, hepatitis and other diseases) is executed.

In telemedicine the simulation relevant for maintenance of operation of an organism of the person of processes implements:

- digestion, breathing, allocation;

- recovery and adhesion of muscle tissues, skin, tendons, cartilaginous and osteal tissues, nervous organs, systems and all organism constructed earlier, when the person was young and is able-bodied. The obtained models can be utilised with the purpose of updating current incorrect control of an organism or his any part by a brain of this person. For this purpose the creation of bases of idealized models of the people miscellaneous ages and bases of models of the concrete people adjusted or updated during life of these people as required is necessary. The updating of models implements every time, when the new experimental data act.

Described the models high can enter as the constituents in multimedia of a systems cloning operation of separate organs and systems of an organism of the person and imaging them on screens of displays. Multimedia of a system can be utilised in educational process as for analysis of processes of operation of organs, systems and whole organism of the person, and for fulfilment of different medical effects on these organs (fulfilment of operations, medicamental and other effects). It is possible to call it as educational telemedicine.

The mining of computer systems of control of all processes of telemedical medical effects by the way of workstations of the doctors being the specialists in miscellaneous areas of medicine is an actual problem. These management systems should provide research of a condition of the able-bodied or ill person. They should give the reliable information about his condition or about necessity of padding examination. If necessary of implementation of medical effects these management systems should supply mining of the best policy of treatment with allowance for of available resources. Including doctor they should make implementation of this policy by control of available resources and medical equipment, and also allowing capabilities of this doctor.

Scientific activity on mining models of the person and different objects of his organism, and also workstations of the doctors and telemedical telecommunication systems are indispensable at creation of polyclinical, hospital, district, urban, regional, sanatorium, departmental, regional and all-Russian telemedical systems of service of all inhabitants of Russia. If there is these means the implementation with indispensable frequency of constant day-night overseeing by a condition of health of the people is possible. Thus the control behind dangerous deviations of major parameters of an organism of the person can be made with the purpose of an avoidance of distresses. For example, it is possible in time to define a beginning of process of a cardiac standstill of the operator of nuclear station, pilot, engineman of an electric locomotive or driver of the automobile. The data of constant supervision can be utilised also for warning the people about approach of other crisis situations in their organisms. If the sharp aggravation of symptoms of health of the person can result in his incapability, in this case it is possible provide transition to emergency automatic control of object controlled this person, and also to take measures on recovery of his health.

The formal mathematical models of telemedical objects can be obtained with usage of so-called model general integrals (MGI), model general functional equations (GFE), model differential equations (DE), of model function - differential equations (FDE) [1] and other model objects.

Definition 1. The model general integral of some class of model ordinary differential equations of order n concerning a function y (t) calls expression

F1(gi(t), j j(y(t)) = F2(fk(t), cl), (1)

where (i=1, , I; j=1, , J; k=1, , K; l=1, , n), keeping functions, continuous and differentiated on all arguments, F1 and F2, continuous and differentiable functions fk (t), gi (t), y (t), j j(y(t)) on arguments t and y accordingly and arbitrary constants cl.

The remark. Hereinafter items of information on ranges of indexes i, j, k, l and other we shall record by the way (i,j,k,lN), where N set of natural numbers.

Definition 2. A MGDE of order n of some class ODE the equation receiving by derivation MGI (1), exception n of arbitrary constants cl and collecting terms of the members is called.

Definition 3. The model general functional equation of some class MFDE of order n concerning a function y (t) calls expression

1(gi1(t), = 2 (fi5(t), ci6) (i1,,i6N), (2)

consisting from continuous and differentiable functions of the arguments, independent variable t and n of arbitrary constants ci6.

Definition 4. The model functionally differential equation of some class FDE calls an equation receiving by derivation MGFE (2), exception n of arbitrary constants and collecting terms of the members.

Let's consider different ways of obtaining new MGI and GFE with using already available. The most simple and effective way of transition from one MGI and GFE to other is the way of a change of variables. Thus in initial MGI and GFE can be exchanged some functions or all functions. Any single function is in that specific case changed only. Let, for example, in MGI [1] of a ordinary linear inhomogeneous differential equation of the maiden order

f1 (t) y (t) + f2 (t) = c (3)

the change of variables as follows is made:

y (t) = [h1 (t) u (t) + h2 (t)] / [h3 (t) u (t) + h4 (t)]].

Then we shall receive MGI equations [1]:

[ (f1h1 + f2h3) u + (f1h2 + f2h)] / [h3u + h4] = c. (4)

If is present a little bit MGI of a different kind, for example,

I1 = c1, I2 = c2, , In = cn, (Ij = Ij (y (t), f1 (t), f2 (t), , fmj (t)), (5)

that with application of arithmetic, algebraic operations and operations of a superposition of functions is possible to construct infinite systems new MGI. As an example we shall indicate a general view such MINE:

F (I1, I2, , In, h1 (t), h2 (t), , hr (t)) = c. (6)

Differentiating MGI (3), we shall receive a MGDE

U1 = 0, U2 = 0, , Un = 0, (7)

with usage which one are possible are to constructed by infinite systems, generally speaking, not allowed concerning a high derivative a MGDE of a kind

H (U1, U2, , Un, h1 (t), h2 (t), , hk (t)) = 0.

The obtaining new systems function differential equations, systems of function - integro-differential equations and other formal model objects on the basis of available is made similarly. Any formal mathematical model transforms to actual model with application of the data about modelled object. Besides the mathematical models of telemedical objects having the differential operators, can be exchanged with equivalent models not keeping these operators. They should contain only arbitrary constants and some functions, which one enter in MGI or in GFU.

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