Medidas de caos em sinais de ECG e classificação de ritmos cardíacos por meio de aprendizado de máquina

Abstract

Since the second half of the last century, the theory of nonlinear systems and chaos has been developing rapidly through a multidisciplinary endeavor. As a result, a large number of techniques were developed seeking the correct identification of chaos in empirical systems. In this sense, an important application is to differentiate the random components of a signal from its deterministic components, essential in any area that involves the analysis of experimental data. In particular, physiology seeks to establish relationships between chaos, stochasticity and the health status of the human body, essential to guide medical applications that allow for easy and accurate diagnosis of diseases and other abnormal conditions. Following this line, in this work we seek to identify chaos in the heart through analysis of electrocardiogram signals from patients with different rhythm conditions: normal or arrhythmic, and try to differentiate them through measures of chaos. To do this, we use alternative methods to those commonly used in the literature, one based on the theory of random matrices and the other based on the principle of maximum entropy that allows us to relate the maximum density of a system to its correlation length. Transforming the time series into typical matrices from the Wigner ensemble and the Wishart-Laguerre ensemble, we found that the average spectral density of the eigenvalues of these matrices do not recover the asymptotic shapes expected from random signals, but resemble those of chaotic signals. We were also able to verify that the maximum density converges particularly well to a function of the signal correlation length, typical of chaotic signals, thus implying the presence of chaos in the system without the need to reconstruct the phase space and calculate its chaotic attractor dimension. In particular, we have in the correlation length a quantitative measure associated with the level of chaos in the system. Finally, using these measurements calculated directly and from the maximum density, we were able to classify signals with normal rhythm and signals with arrhythmia using machine learning algorithms.