Hurst Methods for Fractal Analysis of Electrocardiographical Signals

Abstract

This article is devoted to the fractal analysis of the intervals between heart beats (RR intervals) obtained from electrocardiographical signals. The following methods are used to determine the fractal behavior of the studied signals by the Hurst exponent: Rescaled range, wavelet method, Detrended Fluctuation Analysis. The Hurst exponent value determined by the proposed methods depends on a number of factors: the estimation method, the size of the data, the type of wavelet function, etc. To solve the problem associated with finding the optimal Hurst method, fractal Gaussian noise (FGN) was simulated with different inputs of the Hurst exponent (0.6, 0.7, 0.8, 0.9) and with different data lengths (1000, 10000, 100000). The testing results of the accuracy of the Hurst exponent when applying those three methods is that at a data length of 100000 points, the relative error of the Hurst exponent is the smallest. The Detrended Fluctuation Analysis and wavelet method for estimating the Hurst exponents with respect to the precision parameter have a relative error of less than 1.4%. These two methods have been applied to examine the Holter recordings of two groups of people: healthy and unhealthy subjects. The results show that the Hurst values in healthy and diseased individuals differ. Another marker used to distinguish between the two groups is the generalized Hurst exponent, with diseased subjects having monofractal behavior and healthy subjects-multifractal. In the conclusion, based on the obtained results, it follows that fractal analysis is appropriate for estimating the fuction state of the human body.