Distribution of correlation dimensions of synchronous 12-lead ECG signals

Correlation dimensions D2 of the synchronous 12-lead ECG signals have been investigated for the first time by distributed multi-sensor (multi-electrode) technique. The results show that correlation dimension of heart has the distributed characteristics. D2 calculated from different lead ECG signals is not a constant regardless of a healthy person or a coronary heart disease (CHD) patient with sinus rhythm. But with the same lead signal, D2 of CHD patients is evidently smaller than that of a healthy person except I, II, III leads. A healthy person and CHD patient can be identified by D2 statistically and D2 shows the potential application in the diagnosis of the CHD patients.

Multifractal mass exponent spectrum of complex physiological time series

Physiological signal belongs to the kind of nonstationary and time-variant ones.Thus,the nonlinear analysis methods may be better to disclose its characteristics and mechanisms.There have been plenty of evidences that physiological signal generated by complex self-regulated system may have a fractal structure.In this work,we introduce a new measure to characterize multifractality,the mass exponent spectrum curvature,which can disclose the complexity of fractal structure from total bending degree of the spectrum.This parameter represents the nonlinear superpositions of the discrepancies of fractal dimension from all adjacent points in the curve and therefore solves the problem of original parameters for not fully reflecting the information of entire subsets in the fractal structure.The evaluations of deterministic fractal system Cantor measure validate that it is completely effective in exploring the complexity of chaotic series,and is also not affected by nonstability of the signal as well as disturbances of the noises.We then apply it to the analysis of human heart rate variability(HRV) signals and sleep electroencephalogram(EEG) signals.The experimental results show that this method can be better to discriminate cohorts under different physiological and pathological conditions.Compared with the indicator of singularity spectrum width,there are some improvements both on the computing efficiency and accuracy.Such conclusion may provide some valuable information for clinical diagnoses.

Lyapunov exponents for synchronous 12-lead ECG signals

The Lyapunov exponents of synchronous 12-lead ECG signals have been investigated for the first time using a multi-sensor (electrode) technique. The results show that the Lyapunov exponents computed from different locations on the body surface are not the same, but have a distribution characteristic for the ECG signals recorded from coronary artery disease (CAD) patients with sinus rhythms and for signals from healthy older people. The maximum Lyapunov exponent L1 of all signals is positive. While all the others are negative, so the ECG signal has chaotic characteristics. With the same leads, L1 of CAD patients is less than that of healthy people, so the CAD patients and healthy people can be classified by L1, L1 therefore has potential values in the diagnosis of heart disease.

A new measure to characterize multifractality of sleep electroencephalogram

Traditional methods for nonlinear dy-namic analysis,such as correlation dimension,Lyapunov exponent,approximate entropy,detrended fluctuation analysis,using a single parameter,cannot fully describe the extremely sophisticated behavior of electroencephalogram (EEG). The multifractal for-malism reveals more “hidden” information of EEG by using singularity spectrum to characterize its nonlin-ear dynamics. In this paper,the zero-crossing time intervals of sleep EEG were studied using multifractal analysis. A new multifractal measure Δasα was pro-posed to describe the asymmetry of singularity spec-trum,and compared with the singularity strength range Δα that was normally used as a degree indi-cator of multifractality. One-way analysis of variance and multiple comparison tests showed that the new measure we proposed gave better discrimination of sleep stages,especially in the discrimination be-tween sleep and awake,and between sleep stages 3 and 4.

Multiscale analysis of heart beat interval increment series and its clinical significance

Analysis of multiscale entropy(MSE) and multiscale standard deviation(MSD) are performed for both the heart rate interval series and the interval increment series.For the interval series,it is found that,it is impractical to discriminate the diseases of atrial fibrillation(AF) and congestive heart failure(CHF) unambiguously from the healthy.A clear discrimination from the healthy,both young and old,however,can be made in the MSE analysis of the increment series where we find that both CHF and AF sufferers have significantly low MSE values in the whole range of time scales investigated,which reveals that there are common dynamic characteristics underlying these two different diseases.In addition,we propose the sample entropy(SE) corresponding to time scale factor 4 of increment series as a diag-nosis index of both AF and CHF,and the reference threshold is recommended.Further indication that this index can help discriminate sensitively the mild heart failure(cardiac function classes 1 and 2) from the healthy gives a clue to early clinic diagnosis of CHF.

Sign series entropy analysis of short-term heart rate variability

Complexity and nonlinearity approaches can be used to study the temporal and structural order in heart rate variability (HRV) signal, which is helpful for understanding the underlying rule and physiological essence of cardiovascular regulation. For clinical applications, methods suitable for short-term HRV analysis are more valuable. In this paper, sign series entropy analysis (SSEA) is proposed to characterize the feature of direction variation of HRV. The results show that SSEA method can detect sensitively physiological and pathological changes from short-term HRV signals, and the method also shows its robustness to nonstationarity and noise. Thus, it is suggested as an efficient way for the analysis of clinical HRV and other complex physiological signals.

Nonlinear short-term heart rate variability prediction of spontaneous ventricular tachyarrhythmia

As malign ventricular tachyarrhythmias triggering sudden cardiac death (SCD), both ventricular tachycardia (VT) and ventricular fibrillation (VF) are major causes of mortality. The most efficient ther- apy for SCD prevention is implantable cardioverter defibrillators (ICD). The ICD can accurately and ef- fectively identify the forthcoming of fatal ventricular tachyarrhythmias and deliver a shock in order to restore patients’ normal sinus rhythm. In this study, two nonlinear complexity measures based on en- tropy: approximate entropy (ApEn) and sample entropy (SampEn) as well as two time linear indices: the mean RR interval (the average of time intervals between consecutive R-waves) and the standard devia- tion of RR intervals were used for short-term forecasting of VT-VF occurrence. The last small sections of interbeat intervals preceding 135 VT-VF episodes from 78 patients stored by the ICD were analyzed and compared with individually acquired control time series (CON series) from the same patients, which are normally intrinsic sinus rhythms. The results demonstrate that in addition to an obvious in- crease in heart rates of the patients, the values of two entropy measures are significantly smaller for VT-VF episodes than those for CON series. Conclusions can be drawn that when a ventricular tach- yarrhythmia approaches, the sympathetic tone of the patients is increased, and the complexity of their RR intervals immediately before the onset of VT-VF events is obviously lower than that of RR intervals recorded during sinus rhythms. For a better separation, the optimal range of threshold r is determined for two algorithms. ApEn and SampEn measures might be the suitable nonlinear parameters for short- term prediction of life-threatening ventricular tachyarrhythmias in the application of the cardioversion and defibrillation.

The SARD variety of multi-fractality of ventricular epicardial mapping during ischemia

We have analyzed cardiac ische- mia-reperfusion in an animal model using epicardial electropotential mapping. We investigated the rela- tionship between ischemia and variability of multi- fractality in epicardial electrograms. We present a new parameter called the singularity spectrum area reference dispersion (SARD) that clearly demon- strates the change in multifractility with the extent of myocardiaischemia. By contrasting the 3D ventricular epicardial SARD map with the activation map, we conclude that myocardial ischemia significantly in- fluences the variety of multifractality of ventricular epicardium electrograms and the SARD parameter is useful in correlating multifractality of epicardial elec- trograms with location of ischemia closely.

Complexity and characteristic frequency studies in ECG signals of mice based on multiple scale factors

Existing methods of physiological signal analysis based on nonlinear dynamic theories only examine the complexity difference of the signals under a single sampling frequency.We developed a technique to measure the multifractal characteristic parameter intimately associated with physiological activities through a frequency scale factor.This parameter is highly sensitive to physiological and pathological status.Mice received various drugs to imitate different physiological and pathological conditions,and the distributions of mass exponent spectrum curvature with scale factors from the electrocardiogram (ECG) signals of healthy and drug injected mice were determined.Next,we determined the characteristic frequency scope in which the signal was of the highest complexity and most sensitive to impaired cardiac function,and examined the relationships between heart rate,heartbeat dynamic complexity,and sensitive frequency scope of the ECG signal.We found that all animals exhibited a scale factor range in which the absolute magnitudes of ECG mass exponent spectrum curvature achieve the maximum,and this range (or frequency scope) is not changed with calculated data points or maximal coarse-grained scale factor.Further,the heart rate of mice was not necessarily associated with the nonlinear complexity of cardiac dynamics,but closely related to the most sensitive ECG frequency scope determined by characterization of this complex dynamic features for certain heartbeat conditions.Finally,we found that the health status of the hearts of mice was directly related to the heartbeat dynamic complexity,both of which were positively correlated within the scale factor around the extremum region of the multifractal parameter.With increasing heart rate,the sensitive frequency scope increased to a relatively high location.In conclusion,these data provide important theoretical and practical data for the early diagnosis of cardiac disorders.