Effects of coarse-graining on the scaling behavior of long-range correlated and anti-correlated signals.

We investigate how various coarse-graining (signal quantization) methods affect the scaling properties of long-range power-law correlated and anti-correlated signals, quantified by the detrended fluctuation analysis. Specifically, for coarse-graining in the magnitude of a signal, we consider (i) the Floor, (ii) the Symmetry and (iii) the Centro-Symmetry coarse-graining methods. We find that for anti-correlated signals coarse-graining in the magnitude leads to a crossover to random behavior at large scales, and that with increasing the width of the coarse-graining partition interval Δ, this crossover moves to intermediate and small scales. In contrast, the scaling of positively correlated signals is less affected by the coarse-graining, with no observable changes when Δ < 1, while for Δ > 1 a crossover appears at small scales and moves to intermediate and large scales with increasing Δ. For very rough coarse-graining (Δ > 3) based on the Floor and Symmetry methods, the position of the crossover stabilizes, in contrast to the Centro-Symmetry method where the crossover continuously moves across scales and leads to a random behavior at all scales; thus indicating a much stronger effect of the Centro-Symmetry compared to the Floor and the Symmetry method. For coarse-graining in time, where data points are averaged in non-overlapping time windows, we find that the scaling for both anti-correlated and positively correlated signals is practically preserved. The results of our simulations are useful for the correct interpretation of the correlation and scaling properties of symbolic sequences.

[Multiscale entropy analysis of electrocardiogram].

Using the algorithm proposed by Costa M, et al., we studied the multiscale entropy (MSE) of electrocardiogram. The sample entropy (SampEn) of the healthy subjects was found to be higher than that of the subjects with coronary heart disease or myocardial infarction. The healthy subjects' complexity was found to be the highest. The SampEn of the subjects with coronary heart disease was noted to be only slightly higher than that of the subjects with myocardial infarction. These findings show that the complexity of the subjects with coronary heart disease or myocardial infarction is distinctly lower than the complexity of the healthy ones, and the subjects suffereing from coronary heart disease are liable to the onset of myocardial infarction.

[Singularity spectra analysis of the ST segments of 12-lead electrocardiogram].

By analysing the f(a) singularity spectra of the ST segments of the synchronous 12-lead ECG, we have found that the singularity spectrum is close to monofractality and its area is only half the area of the synchronous 12-lead ECG f(alpha) singularity spectrum. The ST segments of the synchronous 12-lead ECG signal also has f(alpha) singularity spectra distribution and it also has a reasonable varying scope. We have also found that the lead number of the ST segment f (alpha) singularity spectra for adults having coronary heart disease overstep the reasonable scope tends to increase over that of the ECG f(alpha) singularity spectra. These findings show that using the ST segments f(alpha) singularity spectra distribution of the synchronous 12-lead ECG is more effective than using the synchronous 12-lead ECG on the clinical analysis.

[Influence of heart and brain disease on multifractal singularity spectrum of synchronous 12-lead ECG signals].

We analyzed the multifractal singularity spectrum of synchronous 12-lead ECG (electrocardiogram) signals from heart and brain disease patients, and found that multifractal curves of different leads do not overlap each other. After calculating the scope of the singularity strength, we noticed that the averages of scope are not the same in different subjects,and the dispersing degree is also different in someone's different leads. Both the deltaalpha, the average of the deltaalpha, and the dispersing degree deltaalpha (be defined as standard deviation) of the deltaalpha of every one's 12-lead ECG were computed. Then, a comparison was made between the spectrum of the healthy subjects and the heart disease patients. The results showed that their deltaalpha are close, but their deltaalpha are markedly different. Also the healthy subjects and brain disease patients were compared, we found that their deltaalpha are close, but their deltaalpha are markedly different. These indicate that the character of multifractal spectrum is controlled by both the neurosystem of body and the self-syntonic property of cardiac structures. Furthermore, the deltaalpha is related with the neuroautonomic control of people's body on the ECG, and the deltaalpha is related with the anisotropy of the heterogeneous tissue and the electric signal propagation in heart.

Multiscale multifractality analysis of a 12-lead electrocardiogram.

This paper proposes that a multiscale multifractality (MSMF) method be adopted for the spatiotemporal analysis of 12-lead ECG. By using this method, the authors find that, in some frequency range, 12-lead ECG has a more complex fractal structure, and the position of the largest singularity strength range delta alpha is not relying on the data length but on the scale factor. By determining the inflexion, the MSMF proves to be more sensitive in displaying the trend that the singularity strength range delta alpha of human ECG decreases with human aging.

[Research on the application of neural network to diagnosis of cardiopathy].

Neural networks can fit any nonlinear function. After drawing out several characteristic parameters from the three-dimension spectrum for high frequency QRS waves, we input them into the network and trained the network. In this way, we can get a m-dimension curved surface in the m-dimension space which is constructed by those parameters, and this curved surface divides the space into two parts: the unhealthiness and the health. Now, the network can automatically distinguish between the healthiness and the unhealthiness according to their three-dimension spectrum for high frequency QRS waves.