achievements and applications
M. Gospodinov, E. Gospodinova. Mathematical Analysis of the Linear and Non-linear Properties of Electrocardiological Data

Key Words: HRV; ECG; linear analysis; non-linear analysis; Poincaré plot.

Abstract. The article is devoted to the mathematical analysis of the linear and nonlinear properties of heart rate variability (HRV) determined by digital electrocardiological data. The advantage of the mathematical methods used is their ability to detect minor cardiovascular abnormalities and a way to evaluate the overall functional capabilities of the body. The quantitative dimensions of the studied parameters when using linear mathematical methods of analysis have significant clinical application because the boundaries of norm-pathology are known. The application of non-linear mathematical methods in data analysis provides additional information on the physiological status of patients. The article presents the results of the linear analysis of the studied data in the frequency domain and the results of the nonlinear analysis by applying the Poincare graphical method, which allows the doctors to see the whole electrocardiological record at a glance and quickly detect cardiovascular disorders if there are some. The analysis of HRV by applying linear and nonlinear methods provides ample opportunity for clinical and research applications.