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.

翻译：心脏病是现代工业化社会人群死亡的主要原因之一，并给公共卫生系统带来高昂的支出。因此，开发改善心脏诊断的分析方法至关重要。心脏的电活动最初通过一组非线性微分方程建模，随后研究了由确定性动力学引发的心脏光谱变化。对正常人类心脏的功率谱进行分析，揭示了具有分形样结构的希氏-浦肯野网络。从心电图时间序列图中提取相空间轨迹。分形维数 D 的较低值表明动力学更为有序；若 D 出现大于 2 的非整数值，则系统进入混沌或奇异吸引子状态。近期，有研究报道了一种可应用于多通道生理信号的快速稳健方法。本文通过分析正常与异常人类心脏的两种不同心电图系统，提出了一种结合心电图信号的辅助相空间方法以诊断心脏疾病。每例受试者的数据包含分别基于 V4 导联和改良 III 导联（MLIII）的双信号。对相空间中构建的轨迹执行分形分析，采用盒计数法计算分形维数 D。结果表明，MLIII 信号的 D 值高于 V4 信号，预示着更高的随机性但同时包含更多信息。D 的最小值（1.708）对应正常心脏的完美振荡，而 D 的最大值（1.863）则呈现异常心脏的随机性。本研究的显著发现是：相空间图像可呈现心电图光谱中峰值高度的分布特征，结合心电图能为心脏活动提供有价值的评估依据。