Fuzzy-based Entropy Methods And Their Application In Analysis Of Cardiovascular Time Series

Cardiovascular disease(CVD)has become the leading cause of death in the world,seriously endangering human health.CVD has significant morbidity and mortality,and it is also irreversible.So early detection and prevention of CVD are crucial.Early signs of CVD are usually reflected in changes of physiological signals.Analysis of cardiovascular physiological signals,especially the non-linear dynamic analysis methods,is an important way for early detection of disease risk since it aims for the non-linear dynamic properties of human body system.Entropy measurement is an important method among the developed non-linear dynamic methods,especially suitable for analyzing short-term(a few minutes)signal and has high clinical application value.This study mainly focuses on the newly developed entropy methods based on fuzzy set.It elaborated on the inevitability of development of entropy algorithms from traditional entropy to fuzzy entropy through in-depth analysis of the principle and correlation of typical entropy algorithms.Influence of typical parameters on traditional entropy algorithm and fuzzy entropy algorithm on heart failure detection was analyzed and verified,and the reasonable parameter selection rules were determined.Fuzzy-based entropy methods for specific CVD abnormalities(heart failure,atrial fibrillation(AF),etc.)was developed to improve the clinical performance of the entropy index by combining entropy algorithm with machine learning methods.Meanwhile,univariate fuzzy measure entropy was extended to multivariate fuzzy measure entropy,which could jointly analyze the coupling/correlation degree between the multiple time series.Recognition ability of the multivariate fuzzy measure entropy for different physiological states were verified.In conclusion,the main works of this study are listed as follows:(1)Typical entropy algorithms applied to physiological signal analysis in recent years were reviewed,including univariate entropy,cross entropy,multivariate entropy,multi-scale entropy etc.Development process of each kind of entropy algorithm,implementation mechanism and advantages/disadvantages were summarized.Based on this,three research directions were proposed for short-term cardiovascular physiological signal analysis:determination of entropy parameters,information mining of distance distribution matrix in entropy calculation,and entropy algorithm design for specific disease abnormalities.This study focuses on these three research directions.(2)Embedding dimension m,tolerance threshold r,and time series length N have great influence on entropy results.For univariate sample entropy(SampEn)and fuzzy measure entropy(FuzzyMEn),RR interval time series from the MIT Normal and MIT congestive heart failure(CHF)group were used for testing the parameter effects.Different parameter value selection schemes were compared,and the combinations of entropy parameters that can be used to distinguish normal/CHF group were determined.The results confirmed that the effective(distinguishable)parameter combinations in FuzzyMEn were more than in SampEn,and the combinations were more regular.Moreover,FuzzyMEn in normal group were always lower than those in CHF group while SampEn not,indicating the former had better relative consistency.In addition,the influence of ectopic beats on entropy result was studied,which confirmed the necessity of excluding the ectopic intervals before entropy analysis.(3)Vector phase space reconstruction is an essential step for entropy calculation.Determination of vector similarity is a key process.Traditionally,entropy value is determined by calculating the information variation in vector phase space when vector dimension change from m to m+1.Herein,the information of two-dimensional vector distance matrix is fused and summarized into a single entropy value output.However,a large amount of sequence pattern information is lost in this process.In this study,a novel normal/heart failure classification method combining distance matrix image and convolutional neural network(CNN)was proposed.RR interval time series from the MIT Normal and CHF databases were still used.Distance matrix images were generated in the calculation process of SampEn,local fuzzy measure entropy(FuzzyLMEn)and global fuzzy measure entropy(FuzzyGMEn)were inputted into the CNN models.A simple CNN model and AlexNet model were constructed under Matlab environment and Tensorflow platform respectively for normal/CHF classification.The results confirmed that using distance matrix images from FuzzyGMEn as CNN input achieved the highest classification performance.(4)A new entropy-based AF detection algorithm,named the normalized fuzzy AF entropy,was proposed.The improvements in the new AF detector were from five aspects:1)vector distance was redefined by range function,which avoided the limitation of traditional Chebyshev distance;2)fuzzy function was used to replace the traditional Heaviside function to enhance the algorithm sensitivity due to the influence of tolerance threshold r;3)density estimation was used to replace the probability estimation when calculating the information variation when vector dimension changed from m to m + 1,to improve the algorithm robustness to extremely short sequences;4)tolerance threshold r was dynamically adjusted according to the minimum average matching number of vectors,which replaced the traditional fixed threshold and improved the algorithm generalization ability;5)AF is usually accompanied by a quick heart rate,thus the influence of heart rate was adjusted by subtracting the natural log value of the mean RR interval during entropy calculation.Both MIT AF database and clinical wearable ECG data were used for testing.The results showed that compared to other three algorithms(SampEn,FuzzyMEn and coefficient of sample entropy(CosEn)),the new algorithm reported better performance in evaluation indexes like sensitivity,specificity,accuracy,positive predictive value,negative predictive value,total error,receiving operator curve(ROC),etc.,which verified the effectiveness of the new algorithm for AF monitoring.(5)Multivariate analysis can make full use of the coupling/correlation information from different components in cardiovascular system,while the use of fuzzy function can improve the statistical stability of entropy algorithm for short time series.Thus,a new multivariate fuzzy measure entropy(MFuzzyMEn)algorithm was proposed by combing multivariate analysis and fuzzy function.It was found that multivariate fuzzy measure entropy on the simulated coupled Gaussian signals presented a strict monotonic change trend with the increase of coupling degree,while the comparable method of multivariate sample entropy(MSampEn)had local fluctuations,confirming the new MFuzzyMEn had better consistency.Analysis of RR time series,first and second heart sound amplitude time series showed that.MFuzzyMEn obtained significant difference results in two physiological states when using any of the three heart sounds acquired in different body locations,while MSampEn did not yield the similar result,verifying the new algorithm had better recognition ability for different physiological states.