Abstracts

Cybernetics and Phisiology

Biology and medicine are new fields of mathematics application, especially mathematical theory of control systems. There are medical-biologic problems, for solving which known mathematical methods are used. These are direct problem of description of physiological system behavior at time, indirect problem of definition of systems parameters, etc.

Mathematical methods application at physiology is founded on using of mathematical models.

Mathematical model of arterial pressure control with insulin dependent diabetes is differential equations system with delay argument; system control is impulse function.

Non-linear differential equations system with delay at the terminal period of time is

, , (1)

, (2)

with initial conditions:

(3)

when - persistent matrixes, - persistent matrix, - vector of system non-linearity, - vector - function of state, - impulse function of control:

,

,

- impulse moment.

It is necessary to find control , transferring system (1)-(3) from arbitrary state in to terminal state in .

Mathematical model of arterial pressure control with insulin dependent diabetes is totality of two known medical models. These are arterial pressure control model and glucose level control model. These models were united, taking into consideration two factors: vascular complications type of diabetes, glucose level lowering degree.

(4)

,

with initial conditions

(5)

when - average arterial pressure, - average venous pressure, - glucose concentration in the blood, - glucose concentration changing velocity in the blood, - regression coefficients, и - initial values of arterial and venous pressure, - initial glucose concentration in the blood, - vascular complications type coefficient, .

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