Multiscale multifractality analysis of a 12-lead electrocardiogram

Wang, Jun; Ning, Xinbao; Bian, Chunhua; Xu, Yang; Chen, Ying

doi:10.1103/physreve.71.062902

Cited by 35 publications

(26 citation statements)

References 19 publications

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“…Δα is a measure of the deviation from monofractal, indicating the degree of multifractality. Smaller Δα indicates that the measure tends to be monofractal, and contrarily, larger Δα indicates multifractality [12] .…”

Section: Multifractal Singularity Spectrummentioning

confidence: 99%

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A new measure to characterize multifractality of sleep electroencephalogram

2006

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Traditional methods for nonlinear dynamic 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 formalism reveals more "hidden" information of EEG by using singularity spectrum to characterize its nonlinear dynamics. In this paper, the zero-crossing time intervals of sleep EEG were studied using multifractal analysis. A new multifractal measure Δ as α was proposed to describe the asymmetry of singularity spectrum, and compared with the singularity strength range Δα that was normally used as a degree indicator 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 between sleep and awake, and between sleep stages 3 and 4.The research of nonlinear dynamics in electroencephalogram (EEG) has made much headway in recent years. Nonlinear analysis methods have been successfully applied to the studies of brain functions and pathological changes in EEG [1][2][3] . These studies also proved that EEG exhibited at least partly chaotic characteristics. The detrended fluctuation analysis (DFA) [4] , which has been widely used recently, revealed the longrange power-law correlation in EEG, indicating time scale invariant and fractal structure [5,6] . However, EEG is also rather noisy, displaying short-term decorrelation like white noise, and consequently, the EEG has been traditionally considered as a linear stationary random process. The paradoxical combination of short-term decorrelation and long-range correlation, stochastic and deterministic suggests that a single nonlinear parameter, such as largest Lyapunov exponent, correlation dimension, fractal dimension, scaling exponent, etc., may not be able to fully characterize the "stochastic chaos" (as named by Freeman [7] ) nature of EEG.The long time behavior of chaotic, nonlinear dynamic systems can often be characterized by (mono) fractal or multifractal measures. Monofractals are homogeneous in the sense that they have the same scaling properties, characterized by a single singularity exponent throughout the entire signal. In contrast, multifractals can be decomposed into many (possibly infinite) sub-sets characterized by different exponents. Multifractal signals are intrinsically more complex and inhomogeneous than monofractals. Multifractal models have been used to account for scale invariance properties of various objects in very different domains ranging from the energy dissipation or the velocity field in turbulent flows [8] to underlying hierarchical structure in proteins [9] . Physiologic signals generated by complex self-regulating systems, such as heartbeat interval, electrocardiogram, gait etc. have been proven to be multifractal, and the degree of multifractality often relates to pathological state or natural aging process [10][11][12] ....

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Section: Multifractal Singularity Spectrummentioning

confidence: 99%

“…Physiologic signals generated by complex self-regulating systems, such as heartbeat interval, electrocardiogram, gait etc. have been proven to be multifractal, and the degree of multifractality often relates to pathological state or natural aging process [10][11][12] . The multifractal formalism has been applied to EEG analysis recently [13,14] .…”

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confidence: 99%

A new measure to characterize multifractality of sleep electroencephalogram

2006

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“…and the abnormal lead multifractal singularity spectrum can denote the heart disease region. In 2005, Wang et al [47] proposed an expanded multifractal analysis method, viz. multiscale multifractality (MSMF), for the spatio-temporal analysis of physiologic time series.…”

Section: Chaos and Fractal Analysis In Electrocardiogram Researchmentioning

confidence: 99%

Research progress in nonlinear analysis of heart electric activities

et al. 2006

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Nonlinear science research is a hot point in the world. It has deepened our cognition of determinism and randomicity, simplicity and complexity, noise and order and it will profoundly influence the progress of the study of natural science, including life science.Life is the most complex nonlinear system and heart is the core of lifecycle system. In the late more than 20 years, nonlinear research on heart electric activities has made much headway. The commonly used parameters are based on chaos and fractal theory, such as correlation dimension, Lyapunov exponent, Kolmogorov entropy and multifractal singularity spectrum.This paper summarizes the commonly used methods in the nonlinear study of heart electric signal. Then, considering the shortages of the above traditional nonlinear parameters, we mainly introduce the results on short-term heart rate variability (HRV) signal (500 R-R intervals) and HFECG signal (1-2s). Finally, we point out it is worthwhile to put emphasis on the study of the sensitive nonlinearity parameters of short-term heart electric signal and their dynamic character and clinical effectivity.

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“…In that study, the authors examined the distributions of entropy measures with scale factors from HRV signals in healthy young and healthy elderly subjects, and found that at some scale factor or within a certain range, the nonlinear parameter resulted in better discrimination. Wang et al [20] also proposed the multiscale multifractality (MSMF) method, and examined the distribution of singularity strength range with scale factor from ECG of 65 healthy humans. Our studies [21] pointed out that the essence of multiscale analysis is just to change the sampling frequency of the signals, and then explore them at diversified time levels.…”

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confidence: 98%

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

Yang

Liu

et al. 2011

Sci. China Life Sci.

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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.

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Multiscale multifractality analysis of a 12-lead electrocardiogram

Cited by 35 publications

References 19 publications

A new measure to characterize multifractality of sleep electroencephalogram

A new measure to characterize multifractality of sleep electroencephalogram

Research progress in nonlinear analysis of heart electric activities

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

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