Phase Space Analysis of Cardiac Spectra
Onder Pekcan Taner Arsan
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.