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, the procedure for the estimation of the correlation dimension (D(2)) is proposed 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 procedure can detect the presence of multiple scaling regions in the correlation integral function. The connection between the presence of multiple scaling regions and multiple dynamic activities cooperating in a system is investigated through the study of composite time series. In the second part of the paper, the proposed algorithm is applied to the study of cardiac electrical activity through the analysis of electrocardiographic signals (ECG) obtained from the commercially available MIT-BIH ECG arrhythmia database. Three groups of ECG signals have been considered: the ECGs of normal subjects and ECGs of subjects with atrial fibrillation and with premature ventricular contraction. D(2) estimates are computed on single ECG intervals (static analysis) of appropriate duration, striking a balance between stationarity requisites and accurate computation requirements. In addition, D(2) temporal variability is studied by analyzing consecutive intervals of ECG tracings (dynamic analysis). The procedure reveals the presence of multiple scaling regions 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 fibrillation than in normal sinus rhythms. This study points out the importance of considering both the static and dynamic D(2) analysis for a more complete study of the system under analysis. While the static analysis visualizes the underlying heart activity, dynamic D(2) analysis insights the time evolution of the underlying system.