Timely detection of dynamical complexity changes in natural and man-made systems has deep scientific and practical meanings. We introduce a complexity measure for time series： the base-scale entropy. The definition d...Timely detection of dynamical complexity changes in natural and man-made systems has deep scientific and practical meanings. We introduce a complexity measure for time series： the base-scale entropy. The definition directly applies to arbitrary real-word data. We illustrate our method on a practical speech signal and in a theoretical chaotic system. The results show that the simple and easily calculated measure of base-scale entropy can be effectively used to detect qualitative and quantitative dynamical changes.展开更多
In this paper the decrease in the Hurst exponent of human gait with aging and neurodegenerative diseases was observed by using an improved rescaled range （R/S） analysis method. It indicates that the long-range corre...In this paper the decrease in the Hurst exponent of human gait with aging and neurodegenerative diseases was observed by using an improved rescaled range （R/S） analysis method. It indicates that the long-range correlations of gait rhythm from young healthy people are stronger than those from the healthy elderly and the diseased. The result further implies that fractal dynamics in human gait will be altered due to weakening or impairment of neural control on locomotion resulting from aging and neurodegenerative diseases. Due to analysing short-term data sequences rather than long datasets required by most nonlinear methods, the algorithm has the characteristics of simplicity and sensitivity, most importantly, fast calculation as well as powerful anti-noise capacities. These findings have implications for modelling locomotor control and also for quantifying gait dynamics in varying physiologic and pathologic states.展开更多
In this paper, the ensemble empirical mode decomposition （EEMD） is applied to analyse accelerometer signals collected during normal human walking. First, the self-adaptive feature of EEMD is utilised to decompose th...In this paper, the ensemble empirical mode decomposition （EEMD） is applied to analyse accelerometer signals collected during normal human walking. First, the self-adaptive feature of EEMD is utilised to decompose the ac- celerometer signals, thus sifting out several intrinsic mode functions （IMFs） at disparate scales. Then, gait series can be extracted through peak detection from the eigen IMF that best represents gait rhythmicity. Compared with the method based on the empirical mode decomposition （EMD）, the EEMD-based method has the following advantages： it remarkably improves the detection rate of peak values hidden in the original accelerometer signal, even when the signal is severely contaminated by the intermittent noises; this method effectively prevents the phenomenon of mode mixing found in the process of EMD. And a reasonable selection of parameters for the stop-filtering criteria can improve the calculation speed of the EEMD-based method. Meanwhile, the endpoint effect can be suppressed by using the auto regressive and moving average model to extend a short-time series in dual directions. The results suggest that EEMD is a powerful tool for extraction of gait rhythmicity and it also provides valuable clues for extracting eigen rhythm of other physiological signals.展开更多
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 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.展开更多
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 sophi...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.展开更多
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 impract...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.展开更多
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...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.展开更多
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 mul...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.展开更多
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 elec...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.展开更多
文摘Timely detection of dynamical complexity changes in natural and man-made systems has deep scientific and practical meanings. We introduce a complexity measure for time series： the base-scale entropy. The definition directly applies to arbitrary real-word data. We illustrate our method on a practical speech signal and in a theoretical chaotic system. The results show that the simple and easily calculated measure of base-scale entropy can be effectively used to detect qualitative and quantitative dynamical changes.
基金Project supported by the National Natural Science Foundation of China(Grant No60501003)
文摘In this paper the decrease in the Hurst exponent of human gait with aging and neurodegenerative diseases was observed by using an improved rescaled range （R/S） analysis method. It indicates that the long-range correlations of gait rhythm from young healthy people are stronger than those from the healthy elderly and the diseased. The result further implies that fractal dynamics in human gait will be altered due to weakening or impairment of neural control on locomotion resulting from aging and neurodegenerative diseases. Due to analysing short-term data sequences rather than long datasets required by most nonlinear methods, the algorithm has the characteristics of simplicity and sensitivity, most importantly, fast calculation as well as powerful anti-noise capacities. These findings have implications for modelling locomotor control and also for quantifying gait dynamics in varying physiologic and pathologic states.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 60501003 and 60701002)
文摘In this paper, the ensemble empirical mode decomposition （EEMD） is applied to analyse accelerometer signals collected during normal human walking. First, the self-adaptive feature of EEMD is utilised to decompose the ac- celerometer signals, thus sifting out several intrinsic mode functions （IMFs） at disparate scales. Then, gait series can be extracted through peak detection from the eigen IMF that best represents gait rhythmicity. Compared with the method based on the empirical mode decomposition （EMD）, the EEMD-based method has the following advantages： it remarkably improves the detection rate of peak values hidden in the original accelerometer signal, even when the signal is severely contaminated by the intermittent noises; this method effectively prevents the phenomenon of mode mixing found in the process of EMD. And a reasonable selection of parameters for the stop-filtering criteria can improve the calculation speed of the EEMD-based method. Meanwhile, the endpoint effect can be suppressed by using the auto regressive and moving average model to extend a short-time series in dual directions. The results suggest that EEMD is a powerful tool for extraction of gait rhythmicity and it also provides valuable clues for extracting eigen rhythm of other physiological signals.
基金supported by the National Natural Science Foundation of China (60701002)Ph.D. Programs Foundation of Ministry of Education of China (20090095120013)Technology Funding Project of China University of Mining and Technology (2008C004)
文摘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.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant No. 60501003）.
文摘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.
基金Supported by the National Natural Science Foundation of China (Grant No. 60701002
文摘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.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 60501003, 60701002) Colleges Oriented Provincial Natural Science Research Plan of Jiangsu Province (Grant No. 06KJD510138)
文摘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.
基金supported by the National Natural Science Foundation of China (Grant No. 61003169)the Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 20090095120013)the Technology Funding Project of China University of Mining and Technology (Grant No. 2008C004)
文摘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.
基金supported by the Wellcome Trust and British Heart Foundationsupported by the National Natural Science Foundation of China(Grant No.60501003).
文摘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.
