Zozulia A. Modeling and methods of statistical processing rhythmic cardio signals with increased resolution

The thesis is devoted to the solving of an actual scientific problem, such as development of a new mathematical model and methods in statistical processing of a rhythmic cardiac signal with the increased resolution, which, due to the reflection of its time stochastic dynamics and the addition of new diagnostic features, allow to increase the level of informativeness of heart rate analysis in computer systems of functional diagnostics cardiovascular system and adaptive-regulatory mechanisms of the human body as a whole. It was developed a mathematical model of rhythmocardiosignal with increased resolution in the form of a vector of stationary and stationary-related random sequences that in comparison with the known mathematical models of the classical rhythmocardiosignal, , allows to increase the level of informativeness of heart rate analysis, and in comparison with the vector of random variables as a known mathematical model of the rhythmocardiosignal with increased resolution, allows to take into account the stochastic time dynamics of heart rate. The structure of probabilistic characteristics of the rhythmocardiosignal with increased resolution, which follow from the properties of invariance of the corresponding probabilistic characteristics of the vector of stationary and stationary-related random sequences, is researched. Automatic formation method of the rhythmocardiosignal with increased resolution, by segmentation and characteristic zones detection of the electrocardiogram is developed. Statistical methods for processing rhythmocardiosignals with increased resolution have been developed, namely, it was written expressions for calculating the statistical estimates realizations of distribution functions, mixed initial moment functions, mixed central moment functions, matrix of autocorrelation and intercorrelation functions, matrix of autocovariance and intercovariance functions, vector of initial moment functions of the first order (vector of mathematical expectations) stationary related components of the vector rhythmocardiosignal. the known diagnostic features of the vector rhythmocardiosignal are supplemented by such new diagnostic features as the matrix of correlation functions and the matrix of power spectral power densities of stationary components of the rhythmocardiosignal with increased resolution, which is the basis for increasing the level of heart rate analysis informativeness in modern cardiodiagnostic systems with simultaneous reducing the dimensionality of the diagnostic space by using not the whole set of values of power spectral density functions of the vector rhythmcardiogram components, but only a certain subset of them, which contribute to the total energy of correlation functions estimation not less than 95%. I was developed system of computer programs for heart rate analysis with increased informativeness.