Automatic estimation of the correlation dimension for the analysis of electrocardiograms

The main purpose of the present work is the definition of a fully automatic procedure for correlation dimension (D-2) estimation. In the first part, t he procedure for the estimation of the correlation dimension (D-2) is propo sed and tested on various types of mathematical models: chaotic (Lorenz and Henon models), periodical (sinusoidal waves) and stochastic (Gaussian and uniform noise). In all cases, accurate D-2 estimates were obtained. The pro cedure can detect the presence of multiple scaling regions in the correlati on integral function. The connection between the presence of multiple scali ng regions and multiple dynamic activities cooperating in a system is inves tigated through the study of composite time series. In the second part of t he paper, the proposed algorithm is applied to the study of cardiac electri cal activity through the analysis of electrocardiographic signals (ECG) obt ained from the commercially available MIT-BIH ECG arrhythmia database. Thre e groups of ECG signals have been considered: the ECGs of normal subjects a nd ECGs of subjects with atrial fibrillation and with premature ventricular contraction. D-2 estimates are computed on single ECG intervals (static an alysis) of appropriate duration, striking a balance between stationarity re quisites and accurate computation requirements. In addition, D-2 temporal v ariability is studied by analyzing consecutive intervals of ECG tracings (d ynamic analysis). The procedure reveals the presence of multiple scaling re gions in many ECG signals, and the D-2 temporal variability differs in the three ECG groups considered; it is greater in the case of atrial fibrillati on than in normal sinus rhythms. This study points out the importance of co nsidering both the static and dynamic D-2 analysis for a more complete stud y of the system under analysis. While the static analysis visualizes the un derlying heart activity, dynamic D-2 analysis insights the time evolution o f the underlying system.