Symbolization And Nonlinearity Analysis Of Physiological Time Series

The human organism is an integration of nonlinear physiological systems,each including interactive organs,tissues,etc.and interacting with each other differently.The fundamental question in nonlinear analysis of physiological systems is to identify and quantify the nonlinearity of and the dynamical interactions among physiological systems to characterize different physiological or pathological conditions.Taking contribution of the symbolic time series analysis,the nonlinearity of individual signal is identified by symbolic entropy and time irreversibility,and the coupling causality of double systems and networked behaviors of multiple signals are quantified by transfer entropy.Firstly,to analyze the effects of symbolization on nonlinearity detection,systematic researches,taking contributions of the Logistic series and heartbeats,are conducted on static and dynamic symbolic entropy.The fact that the nonlinearity extraction based on symbolization is parameter-dependent and symbolic methods should be selected accordingly due to the different structural or dynamical information is verified.Equal values are proved to widely exist in heartbeats and have significant effects on the permutation-based methods,and the distribution of equal heartbeat intervals has important information about cardiac conditions.To combine different symbolic sequences,several approaches are summarized from the ways of symbolization,coding and analytical methods,and the double symbolic joint entropy that has reliable nonlinearity detection is proposed and it contributes to the findings that symbolic dynamics extracted by static and dynamic symbolizations are different.Symbolic entropy methods contribute to our understandings to the nonlinear complexity of and the complexity-losing theory about diseased and aging heart activities.Secondly,to simplify the quantification of time irreversibility for EEG(Electroencephalogram)and heartbeats,the order patterns instead of raw vectors are employed based on the mathematical similarity between the calculation of joint probability and the construction of phase space.Forward-backward probabilistic difference is proved to be equivalent to that of symmetric vectors,and a subtraction-based parameter Ys is proposed considering the forbidden permutation.The inherent nonlinearity of EEG and the abnormally high time irreversibility in seizure EEG are highlighted,and a hypothesis of periodic nonlinearity in epileptic EEG is proposed.The consideration of equal values that might generate self-symmetric permutation contributes to reliable time irreversibility analysis in heartbeats,and the effects of multi-scale theory on equal heartbeats are testified.The relationship of the Shannon entropy and time irreversibility are discussed,and the time irreversibility analysis provides valuable information about nonequilibrium features in heartbeats and EEG.Thirdly,to characterize the brain-heart interactions under different sleep states,statistical information flows between them are quantified by static and dynamic symbolic transfer entropy that measures dynamical statistical correlation or informational influence between two(sub)systems.Information exchanges between ECG(Electrocardiogram)and EEG of full and of individual frequency bands decrease with the increase of sleep depth while increase with the increase of EEG band frequency.The information transfer from ECG to EEG more effectively reflects the changes of sleep states and is higher than the reverse information flow,suggesting the ECG is the driving factor while the EEG is the responding one.The connections among symbolic coding,permutation,phase space and sampling frequency are discussed,and the quantified informational interactions contribute to novel understanding to the brain-heart causal relationship and provide valuable information for the analysis of classification of sleep stages.Finally,permutation transfer entropy is applied to facilitate directed and weighted physiological networks whose statistical characteristics under different conditions are analyzed.Epileptic brain networks have evidently lower informational exchanges among brain regions and in all individual and the whole brain areas and have lower Shannon entropy than the healthy,suggesting the epilepsy reduces brain informational exchanges and the complexity of brain interactive activities.Information flows among organs and in the whole physiological networks as well as the informational complexity decrease with the increase of sleep stages,indicating the networked informational coherence decrease with the deepening sleep.Characteristics of physiological networks are discussed,and the networked analysis of brain and organs play important roles in elucidating the complex physiological interactions and in understanding epileptic and sleeping physiological or pathological features.In this contribution,the double symbolic joint entropy and permutation-based time irreversibility are proposed,the nonlinearity in and statistical interactions between physiological systems are characterized,the effects of symbolization and equal heartbeats on time series analysis are verified,and the hypothesis of periodic nonlinearity in epileptic brain activities is proposed.Some novel findings are achieved while there are more related issues needing further researches.