Phase Space Analysis of Cardiac Spectra

Cardiac diseases are one of the main reasons of mortality in modern, industrialized societies, and they cause high expenses in public health systems. Therefore, it is important to develop analytical methods to improve cardiac diagnostics. Electric activity of heart was first modeled by using a set of nonlinear differential equations. Latter, variations of cardiac spectra originated from deterministic dynamics are investigated. Analyzing the power spectra of a normal human heart presents His-Purkinje network, possessing a fractal like structure. Phase space trajectories are extracted from the time series graph of ECG. Lower values of fractal dimension, D indicate dynamics that are more coherent. If D has non-integer values greater than two when the system becomes chaotic or strange attractor. Recently, the development of a fast and robust method, which can be applied to multichannel physiologic signals, was reported. This manuscript investigates two different ECG systems produced from normal and abnormal human hearts to introduce an auxiliary phase space method in conjunction with ECG signals for diagnoses of heart diseases. Here, the data for each person includes two signals based on V_4 and modified lead III (MLIII) respectively. Fractal analysis method is employed on the trajectories constructed in phase space, from which the fractal dimension D is obtained using the box counting method. It is observed that, MLIII signals have larger D values than the first signals (V_4), predicting more randomness yet more information. The lowest value of D (1.708) indicates the perfect oscillation of the normal heart and the highest value of D (1.863) presents the randomness of the abnormal heart. Our significant finding is that the phase space picture presents the distribution of the peak heights from the ECG spectra, giving valuable information about heart activities in conjunction with ECG.