Lina Zhao

Analysis of heart rate variability using fuzzy measure entropy

This paper proposed a new entropy measure, Fuzzy Measure Entropy (FuzzyMEn), for the analysis of heart rate variability (HRV) signals. FuzzyMEn was calculated based on the fuzzy set theory and improved the poor statistical stability in the approximate entropy (ApEn) and sample entropy (SampEn). The simulation results also demonstrated that the FuzzyMEn had better algorithm discrimination ability when compared with the recently published fuzzy entropy (FuzzyEn), The validity of FuzzyMEn was tested for clinical HRV analysis on 120 subjects (60 heart failure and 60 healthy control subjects). It is concluded that FuzzyMEn could be considered as a valid and reliable method for a clinical HRV application.

Determination of Sample Entropy and Fuzzy Measure Entropy Parameters for Distinguishing Congestive Heart Failure from Normal Sinus Rhythm Subjects

Entropy provides a valuable tool for quantifying the regularity of physiological time series and provides important insights for understanding the underlying mechanisms of the cardiovascular system. Before any entropy calculation, certain common parameters need to be initialized: embedding dimension m, tolerance threshold r and time series length N. However, no specific guideline exists on how to determine the appropriate parameter values for distinguishing congestive heart failure (CHF) from normal sinus rhythm (NSR) subjects in clinical application. In the present study, a thorough analysis on the selection of appropriate values of m, r and N for sample entropy (SampEn) and recently proposed fuzzy measure entropy (FuzzyMEn) is presented for distinguishing two group subjects. 44 long-term NRS and 29 long-term CHF RR interval recordings from http://www.physionet.org were used as the non-pathological and pathological data respectively. Extreme (>2 s) and abnormal heartbeat RR intervals were firstly removed from each RR recording and then the recording was segmented with a non-overlapping segment length N of 300 and 1000, respectively. SampEn and FuzzyMEn were performed for each RR segment under different parameter combinations: m of 1, 2, 3 and 4, and r of 0.10, 0.15, 0.20 and 0.25 respectively. The statistical significance between NSR and CHF groups under each combination of m, r and N was observed. The results demonstrated that the selection of m, r and N plays a critical role in determining the SampEn and FuzzyMEn outputs. Compared with SampEn, FuzzyMEn shows a better regularity when selecting the parameters m and r. In addition, FuzzyMEn shows a better relative consistency for distinguishing the two groups, that is, the results of FuzzyMEn in the NSR group were consistently lower than those in the CHF group while SampEn were not. The selections of m of 2 and 3 and r of 0.10 and 0.15 for SampEn and the selections of m of 1 and 2 whenever r (herein, rL = rG = r) are for FuzzyMEn (in addition to setting nL = 3 and nG = 2) were recommended to yield the fine classification results for the NSR and CHF groups.

Gaussian fitting for carotid and radial artery pressure waveforms: comparison between normal subjects and heart failure patients

It has been reported that Gaussian functions could accurately and reliably model both carotid and radial artery pressure waveforms (CAPW and RAPW). However, the physiological relevance of the characteristic features from the modeled Gaussian functions has been little investigated. This study thus aimed to determine characteristic features from the Gaussian functions and to make comparisons of them between normal subjects and heart failure patients. Fifty-six normal subjects and 51 patients with heart failure were studied with the CAPW and RAPW signals recorded simultaneously. The two signals were normalized first and then modeled by three positive Gaussian functions, with their peak amplitude, peak time, and half-width determined. Comparisons of these features were finally made between the two groups. Results indicated that the peak amplitude of the first Gaussian curve was significantly decreased in heart failure patients compared with normal subjects (P<0.001). Significantly increased peak amplitude of the second Gaussian curves (P<0.001) and significantly shortened peak times of the second and third Gaussian curves (both P<0.001) were also presented in heart failure patients. These results were true for both CAPW and RAPW signals, indicating the clinical significance of the Gaussian modeling, which should provide essential tools for further understanding the underlying physiological mechanisms of the artery pressure waveform.

Reduction of False Alarms in Intensive Care Unit using Multi-feature Fusion Method

In thist study, we proposed a multi-feature fusion method for accurately classifying the true or false alarms for five life-threatening arrhythmias: asystole, extreme bradycardia (EB), extreme tachycardia (ET), ventricular flutter/fibrillation (VF) and ventricular tachycardia (VT). The proposed method consisted of four steps: 1) signal pre-processing, 2) detection validation and feature calculation, 3) real-time determining and 4) retrospectively determining. Up to four signal channels, that is, two ECGs, one arterial blood pressure (ABP) and/or one photoplethysmogram (PPG) signals were analyzed to obtain the classification features. Multi-features from those signals were merged to reduce the maximum number of false alarms, while avoiding the suppression of true alarms. Two events existed: Event 1 for “real-time” and Event 2 for “retrospectively”. The optimal results of true positive ratio (TPR) for the training set were: 100% for asystole, EB, ET and VF types and 94% for VT type. The corresponding results of true negative ratio (TNR) were 93%, 81%, 78%, 85% and 50% respectively, resulting in the corresponding scores of 96.50, 90.70, 88.89, 92.31 and 64.90, as well as with score 80.57 for Event 1 and 79.12 for Event 2. The results of the our open source entries for the Challenge obtained the optimal scores of 88.73 for asystole, 77.78 for EB, 89.92 for ET, 67.74 for VF and 61.04 for VT types, with the final scores 71.68 for Event 1 and 75.91 for Event 2.

Measuring synchronization in coupled simulation and coupled cardiovascular time series: A comparison of different cross entropy measures

Synchronization provides an insight into underlying the interaction mechanisms among the bivariate time series and has recently become an increasing focus of interest. In this study, we proposed a new cross entropy measure, named cross fuzzy measure entropy (C-FuzzyMEn), to detect the synchronization of the bivariate time series. The performances of C-FuzzyMEn, as well as two existing cross entropy measures, i.e., cross sample entropy (C-SampEn) and cross fuzzy entropy (C-FuzzyEn), were first tested and compared using three coupled simulation models (i.e., coupled Gaussian noise, coupled MIX(p) and coupled Henon model) by changing the time series length, the threshold value for entropy and the coupling degree. The results from the simulation models showed that compared with C-SampEn, C-FuzzyEn and C-FuzzyMEn had better statistical stability and compared with C-FuzzyEn, C-FuzzyMEn had better discrimination ability. These three measures were then applied to a cardiovascular coupling problem, synchronization analysis for RR and pulse transit time (PTT) series in both the normal subjects and heart failure patients. The results showed that the heart failure group had lower cross entropy values than the normal group for all three cross entropy measures, indicating that the synchronization between RR and PTT time series increases in the heart failure group. Further analysis showed that there was no significant difference between the normal and heart failure groups for C-SampEn (normal 2.13 ± 0.37 vs. heart failure 2.07 ± 0.16, P = 0.36). However, C-FuzzyEn had significant difference between two groups (normal 1.42 ± 0.25 vs. heart failure 1.31 ± 0.12, P < 0.05). The statistical difference was larger for two groups when performing C-FuzzyMEn analysis (normal 2.40 ± 0.26 vs. heart failure 2.15 ± 0.13, P < 0.01).

Modelling Arterial Pressure Waveforms Using Gaussian Functions and Two-Stage Particle Swarm Optimizer

Changes of arterial pressure waveform characteristics have been accepted as risk indicators of cardiovascular diseases. Waveform modelling using Gaussian functions has been used to decompose arterial pressure pulses into different numbers of subwaves and hence quantify waveform characteristics. However, the fitting accuracy and computation efficiency of current modelling approaches need to be improved. This study aimed to develop a novel two-stage particle swarm optimizer (TSPSO) to determine optimal parameters of Gaussian functions. The evaluation was performed on carotid and radial artery pressure waveforms (CAPW and RAPW) which were simultaneously recorded from twenty normal volunteers. The fitting accuracy and calculation efficiency of our TSPSO were compared with three published optimization methods: the Nelder-Mead, the modified PSO (MPSO), and the dynamic multiswarm particle swarm optimizer (DMS-PSO). The results showed that TSPSO achieved the best fitting accuracy with a mean absolute error (MAE) of 1.1% for CAPW and 1.0% for RAPW, in comparison with 4.2% and 4.1% for Nelder-Mead, 2.0% and 1.9% for MPSO, and 1.2% and 1.1% for DMS-PSO. In addition, to achieve target MAE of 2.0%, the computation time of TSPSO was only 1.5 s, which was only 20% and 30% of that for MPSO and DMS-PSO, respectively.

Effects of Blood Pressure and Sex on the Change of Wave Reflection: Evidence from Gaussian Fitting Method for Radial Artery Pressure Waveform

An early return of the reflected component in the arterial pulse has been recognized as an important indicator of cardiovascular risk. This study aimed to determine the effects of blood pressure and sex factor on the change of wave reflection using Gaussian fitting method. One hundred and ninety subjects were enrolled. They were classified into four blood pressure categories based on the systolic blood pressures (i.e., ≤110, 111–120, 121–130 and ≥131 mmHg). Each blood pressure category was also stratified for sex factor. Electrocardiogram (ECG) and radial artery pressure waveforms (RAPW) signals were recorded for each subject. Ten consecutive pulse episodes from the RAPW signal were extracted and normalized. Each normalized pulse episode was fitted by three Gaussian functions. Both the peak position and peak height of the first and second Gaussian functions, as well as the peak position interval and peak height ratio, were used as the evaluation indices of wave reflection. Two-way ANOVA results showed that with the increased blood pressure, the peak position of the second Gaussian significantly shorten (P<0.01), the peak height of the first Gaussian significantly decreased (P<0.01) and the peak height of the second Gaussian significantly increased (P<0.01), inducing the significantly decreased peak position interval and significantly increased peak height ratio (both P<0.01). Sex factor had no significant effect on all evaluation indices (all P>0.05). Moreover, the interaction between sex and blood pressure factors also had no significant effect on all evaluation indices (all P>0.05). These results showed that blood pressure has significant effect on the change of wave reflection when using the recently developed Gaussian fitting method, whereas sex has no significant effect. The results also suggested that the Gaussian fitting method could be used as a new approach for assessing the arterial wave reflection.

Multivariable Fuzzy Measure Entropy Analysis for Heart Rate Variability and Heart Sound Amplitude Variability

Simultaneously analyzing multivariate time series provides an insight into underlying interaction mechanisms of cardiovascular system and has recently become an increasing focus of interest. In this study, we proposed a new multivariate entropy measure, named multivariate fuzzy measure entropy (mvFME), for the analysis of multivariate cardiovascular time series. The performances of mvFME, and its two sub-components: the local multivariate fuzzy entropy (mvFEL) and global multivariate fuzzy entropy (mvFEG), as well as the commonly used multivariate sample entropy (mvSE), were tested on both simulation and cardiovascular multivariate time series. Simulation results on multivariate coupled Gaussian signals showed that the statistical stability of mvFME is better than mvSE, but its computation time is higher than mvSE. Then, mvSE and mvFME were applied to the multivariate cardiovascular signal analysis of R wave peak (RR) interval, and first (S1) and second (S2) heart sound amplitude series from three positions of heart sound signal collections, under two different physiological states: rest state and after stair climbing state. The results showed that, compared with rest state, for univariate time series analysis, after stair climbing state has significantly lower mvSE and mvFME values for both RR interval and S1 amplitude series, whereas not for S2 amplitude series. For bivariate time series analysis, all mvSE and mvFME report significantly lower values for after stair climbing. For trivariate time series analysis, only mvFME has the discrimination ability for the two physiological states, whereas mvSE does not. In summary, the new proposed mvFME method shows better statistical stability and better discrimination ability for multivariate time series analysis than the traditional mvSE method.

A novel encoding Lempel-Ziv complexity algorithm for quantifying the irregularity of physiological time series

BACKGROUND AND OBJECTIVE The Lempel-Ziv (LZ) complexity and its variants have been extensively used to analyze the irregularity of physiological time series. To date, these measures cannot explicitly discern between the irregularity and the chaotic characteristics of physiological time series. Our study compared the performance of an encoding LZ (ELZ) complexity algorithm, a novel variant of the LZ complexity algorithm, with those of the classic LZ (CLZ) and multistate LZ (MLZ) complexity algorithms. METHODS AND RESULTS Simulation experiments on Gaussian noise, logistic chaotic, and periodic time series showed that only the ELZ algorithm monotonically declined with the reduction in irregularity in time series, whereas the CLZ and MLZ approaches yielded overlapped values for chaotic time series and time series mixed with Gaussian noise, demonstrating the accuracy of the proposed ELZ algorithm in capturing the irregularity, rather than the complexity, of physiological time series. In addition, the effect of sequence length on the ELZ algorithm was more stable compared with those on CLZ and MLZ, especially when the sequence length was longer than 300. A sensitivity analysis for all three LZ algorithms revealed that both the MLZ and the ELZ algorithms could respond to the change in time sequences, whereas the CLZ approach could not. Cardiac interbeat (RR) interval time series from the MIT-BIH database were also evaluated, and the results showed that the ELZ algorithm could accurately measure the inherent irregularity of the RR interval time series, as indicated by lower LZ values yielded from a congestive heart failure group versus those yielded from a normal sinus rhythm group (p < 0.01).

Comparison of time-domain, frequency-domain and non-linear analysis for distinguishing congestive heart failure patients from normal sinus rhythm subjects

Abstract It is known that patients with congestive heart failure have reduced ability to modulate heart rate in comparison with normal subjects. However, the characteristics of these changes is not well understood. This study therefore investigated the characteristic features of heart rate changes to assess how they differed between both groups. Fifty-two normal sinus rhythm subjects and 18 congestive heart failure patients from the PhysioNet database were studied. Nine common heart rate indices were studied: three time-domain indices (MEAN RR interval, standard deviation of successive RR SDNN, and square root of mean squared differences of successive RR RMSSD), three frequency-domain indices (normalized low-frequency power LFn, normalized high-frequency power HFn, and their ratio LF/HF), and three non-linear indices (vector length index VLI, vector angle index VAI and sample entropy SampEn). Two 5-min segments from every subject, neither of which had any ectopic beat, were analyzed. The statistical differences between the two clinical groups for the first and second segments, and their average were determined for all nine indices. Results showed that there was no significant difference between the two 5-min RR interval segments for any technique. All frequency-domain and non-linear indices, but only one time-domain index (SDNN), were significantly different between subject groups. However, some indices were much more sensitive to the clinical differences than others; with the best performing techniques, one non-linear index VLI and one time domain index SDNN, followed by all three frequency indices of LFn, HFn and LF/HF, and finally two of the other non-linear indices VAI and SampEn. A simple RBF SVM-based classification algorithm gave a good performance for classifying the CHF and NSR subjects. And the mean Se, Sp and Acc of SVM classifier from 10 folds were 91.31%, 90.04% and 90.95% respectively. We have shown that there are characteristic differences in heart rate changes between congestive heart failure and normal sinus rhythm, suggesting characteristic rhythm differences.