Fractal Analysis of Cardiac Spectra

Abstract

Cardiac diseases are one of the main reasons for 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. The heart's electric activity was first modeled using a set of nonlinear differential equations. Variations of cardiac spectra originating from deterministic dynamics are investigated. Analyzing the power spectra of a normal human heart presents the His-Purkinje network, which possesses 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, that can be applied to multichannel physiologic signals, was reported. The convolutional Neural Networks (CNNs) method was also applied to patient-specific ECG classification for real-time heart monitoring. 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 diagnosing heart diseases. Here, the data for each person includes two signals based on V(4 )and modified lead III (MLIII), respectively. The 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, the second signals (i.e., MLIII) have larger D values than the first signals (i.e., V-4), predicting more randomness yet more information. The lowest value of D (i.e., 1.708) indicates the perfect oscillation of the normal heart, and the highest value of D (i.e., 1.863) presents the abnormal heart's randomness. 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.