The paper considers the actual problem of the development of instrumental methods of examination and diagnostics of carotid apnea. These methods don’t require the constant presence of health personnel and the expensive equipment. The authors proposed a method of registering movement of the chest using a micromechanical accelerometer with extremely small dimensions, low weight, power consumption and cost, along with sensor control oro-nasal flow and pulse oximeter, it allows the recognition of the type of apnea. During experimental studies, the accelerometer was placed on the chest, measuring the total vector acceleration due to the movement of the chest and the acceleration of free fall. Mathematical modeling of signal processing has allowed the optimal lowpass filter Butterworth 6th order, ensuring the selection of the useful signal. The article presents the results of measuring the acceleration along the x-axis and z-axis with continuous breathing and temporary stop. The results of measuring acceleration along three axes showed that the most significant for registration are the x-axis and z-axis. The use of proposed method of measuring the motion of the thorax by means of accelerometers allows to detecting the cessation of breathing, the time lag isn’t more than 0.5 seconds. This method can be used in addition to the pulse oximeter sensors and oro-nasal flow, which will provide registration apnea.

The article considers the aim of modeling humax respiratory system structure for predicting the change of physiological parameters at different methods of physical influence such as operated reduction in breathing circuit. The developed complex of mathematical models includes: equations of mass rate and masstransfer rate in lung channels at arborization of auriferous ways according to the rule of right dichotomy; equations of breathing muscles dynamics, based on moving of cylinder wall in radial and axial directions; special functions, providing automatic muscles turning on and turning off when lungs reach minimal and maximal set volume at inhale/exhale. The article shows the results of numerical modeling of functioning of the sophisticated biotechnical complex «Corrective action facilities – humax respiratory system» in the form of pressure charts and volume flow which the lungs generate in different regimes of resistance in breathing circuit. The results acquired qualitatively and quantitatively reflect the biomechanics of the number of processes which accompany breathing. The developed complex of interconnected mathematical models allows to fulfill specific multiparametric modeling of the dynamics of functioning of the complex biotechnical system «Corrective action facilities – humax respiratory system», which allows the realization of optimal controlling algorithms for execution units in different complexes based on prediction of changes in the condition of the respiratory system.

Scientific relevance and purpose. This research looks at the urgent task of modeling the structure of the human respiratory system and processes occurring in it, in order to predict the changes in physiological parameters occurring under different mechanical actions. Results. This paper suggests mathematical model based on the description of equations of the mass flow and mass flow rate in the pulmonary channels in cases, when airways are branched in accordance with the prin-ciple of regular dichotomy with regard to the equations of work dynamics of the respiratory muscles and the ability to model different stresses in the breathing circuit, caused by trainers. The research examined the stresses generated by muscles in the radial and axial direction of the equivalent hollow cylinder, which represented the chest with regard to the elastic stress component in the cylinder wall and variable muscle stress in the circumfe-rential direction. The paper contains the results of mathematical modeling of breathing without stress, the graphs of volume and mass flow in lungs generations and pressure-flow diagram. Conclusions. The developed mathematical models enable more precise multi-parameter modeling of the dynamics of functioning of complex biotech system "respiratory muscles trainer - human", which enables the implementation of the prediction of shifts of physiological and mechanical properties from the values of the normal process and to adjust the control actions on this basis