Khvostivska L. Mathematical model and methods of pulse signal analysis to increase the informativeness of photoplethysmographic systems

In the dissertation the actual scientific problem of a pulse signal mathematical model substantiation and development methods of its analysis of photoplethysmographic systems informativeness increasing is solved. The mathematical model of the pulse signal in the form of a periodically correlated random process is substantiated, which made it possible to take into account randomness, periodicity and correlation between different pulse waves (cycles) of one implementation to solve the problem of studying the dynamics of changes in the phase-time parameters of the signal as a sensitive indicator of the state of vascular rigidity. A computational method and algorithm for estimating the pulse signal period based on finding the minimum of the centered signal mean value variation function have been developed to increase the accuracy of its analysis by reducing the blurring of the calculated estimates of informative features in photoplethysmographic systems. A model of photoplethysmographic system for registration and analysis of pulse signal is developed. The results of metrological verification confirmed the authenticity of the layout. On the basis of a pulse signal substantiated model methods and algorithms of its analysis for calculation of averaged correlation components as informative (diagnostic) signs of a condition of human vessels rigidity are developed. The computational complexity of pulse signal analysis algorithms in relation to their software implementation is estimated. Specialized software as a component of photoplethysmographic systems for a pulse signal computer analysis by in-phase and component methods in MATLAB environment has been developed. A method and algorithm for analysis methods verification based on simulation of a pulse signal as periodically extended in time space sums of two time-shifted functions of normal distribution taking into account randomness of amplitude and phase-time indicators were developed. A software with a graphical user interface in the MATLAB environment to simulate high-probability implementations of test pulse signals by input parameters (wave amplitude, their time durations and moments, number of cycles, randomness, phase changes, etc.) was developed. According to the verification results using a pulse signal simulation model the interrelation between phase shifts of direct and reflected pulse waves in the structure of simulated signals with averaged correlation components as informative features is revealed which confirmed the fact of their informativeness and truth about the efficiency of the methods of analysis of the pulse signal at detection of the human vessels rigidity manifestations. The validation procedure to establish the truth of the efficiency of the pulse signal in-phase and component analysis methods and algorithms by comparing the analysis results of the simulated pulse signals with experimental data is carried out. Based on Fisher's parametric criterion, the similarity of the analysis results (averaged correlation components) of the simulated and experimental pulse signal with the reliability of the decision 0.95 (0.99) and the error of the decision 0.05 (0.01), was confirmed.