Li P. EZ Entropy: a software application for the entropy analysis of physiological time-series. BioMedical Engineering OnLine. 2019;18 (1) :30. Publisher's VersionAbstract
Entropy analysis has been attracting increasing attentions in the recent two or three decades. It assesses complexity, or irregularity, of time-series which is extraordinarily relevant to physiology and diseases as demonstrated by tremendous studies. However, the complexity can hardly be appreciated by traditional methods including time-, frequency-domain analysis, and time-frequency analysis that are the common built-in options in commercialized measurement and statistical software. To facilitate the entropy analysis of physiological time-series, a new software application, namely EZ Entropy, was developed and introduced in this article.
Yan C, Li P, Yao L, Karmakar C, Liu C. Impacts of reference points and reference lines on the slope- and area-based heart rate asymmetry analysis. Measurement. 2019;137 :515–526. Publisher's VersionAbstract
Heart rate asymmetry (HRA) could capture valuable dynamical properties from the electrocardiographic RR interval time-series that are helpful for evaluating the cardiovascular functioning. Several metrics derived from the Poincaré plot have been established for assessing HRA such as the slope index (SI) and the area index (AI). In the current study, we aimed to examine how different reference points and reference lines affect the calculations of SI and AI. To understand their performance, two case studies that were to classify subjects with (1) arrhythmias and (2) congestive heart failure, respectively, from normal controls were performed. To examine whether these effects depend on data lengths, the case studies were performed on both long-term heartbeat interval time-series and short-term segments. Our results showed that different reference points or reference lines could strongly affect the performance of both SI and AI, especially when short-term data were being analyzed. Using the minimum of data as the reference point might be a conservative solution in application but a spectrum of SI or AI measurements with multiple reference points and reference lines are highly recommended.
Li Y, Li P, Wang X, et al. Short-term QT interval variability in patients with coronary artery disease and congestive heart failure: a comparison with healthy control subjects. Medical & Biological Engineering & Computing. 2019;57 (2) :389–400. Publisher's VersionAbstract
This study aimed to test how different QT interval variability (QTV) indices change in patients with coronary artery disease (CAD) and congestive heart failure (CHF). Twenty-nine healthy volunteers, 29 age-matched CAD patients, and 20 age-matched CHF patients were studied. QT time series were derived from 5-min resting lead-II electrocardiogram (ECG). Time domain indices [mean, SD, and QT variability index (QTVI)], frequency-domain indices (LF and HF), and nonlinear indices [sample entropy (SampEn), permutation entropy (PE), and dynamical patterns] were calculated. In order to account for possible influence of heart rate (HR) on QTV, all the calculations except QTVI were repeated on HR-corrected QT time series (QTc) using three correction methods (i.e., Bazett, Fridericia, and Framingham method). Results showed that CHF patients exhibited increased mean, increased SD, increased LF and HF, decreased T-wave amplitude, increased QTVI, and decreased PE, while showed no significant changes in SampEn. Interestingly, CHF patients also showed significantly changed distribution of the dynamical patterns with less monotonously changing patterns while more fluctuated patterns. In CAD group, only QTVI was found significantly increased as compared with healthy controls. Results after HR correction were in common with those before HR correction except for QTc based on Bazett correction. Open image in new window Graphical abstract Fig. The framework of this paper. The arrows show the sequential analysis of the data.
Zheng D, Chen F, Li P, Peng S-Y. Advanced Signal Processing for Cardiovascular and Neurological Diseases. Computational and Mathematical Methods in Medicine. 2018. Publisher's Version
Li P, Yu L, Lim ASP, et al. Fractal regulation and incident Alzheimer's disease in elderly individuals. Alzheimer's & Dementia. 2018;14 (9) :1114–1125. Publisher's VersionAbstract
Introduction Healthy physiological systems exhibit fractal regulation (FR), generating similar fluctuation patterns in physiological outputs across different time scales. FR in motor activity is degraded in dementia, and the degradation correlates to cognitive decline. We tested whether degraded FR predicts Alzheimer's dementia. Methods FR in motor activity was assessed in 1097 nondemented older adults at baseline. Cognition was assessed annually for up to 11 years. Results Participants with an FR metric at the 10th percentile in this cohort had a 1.8-fold Alzheimer's disease risk (equivalent to the effect of being ∼5.2 years older) and 1.3-fold risk for mild cognitive impairment (equivalent to the effect of being ∼3.0 years older) than those at the 90th percentile. Consistently, degraded FR predicted faster cognitive decline. These associations were independent of physical activity, sleep fragmentation, and stability of daily activity rhythms. Discussion FR may be a useful tool for predicting Alzheimer's dementia.
Jiang X, Wei S, Ji J, et al. Modeling radial artery pressure waveforms using curve fitting: Comparison of four types of fitting functions. Artery Research. 2018;23 :56–62. Publisher's VersionAbstract
Background Curve fitting has been intensively used to model artery pressure waveform (APW). The modelling accuracy can greatly influence the calculation of APWs parameters that serve as quantitative measures for assessing the morphological characteristics of APWs. However, it is unclear which fitting function is more suitable for APW. In this paper, we compared the fitting accuracies of four types of fitting functions, including Raleigh function, double-exponential function, Gaussian function, and logarithmic normal function, in modeling radial artery pressure waveform (RAPW). Methods RAPWs were recorded from 24 healthy subjects in resting supine position. To perform curve fitting, 10 consecutive stable RAPWs for each subject were randomly selected and each waveform was fitted using three instances of the same fitting function. Results The mean absolute percentage errors (MAPE) of the fitting results were 5.89% ± 0.46% (standard deviation), 3.31% ± 0.22%, 2.25% ± 0.31%, and 1.49% ± 0.28% for Raleigh function, double-exponential function, Gaussian function, and logarithmic normal function, respectively. Their corresponding mean maximum residual errors were 23.71%, 17.83%, 6.11%, and 5.49%. Conclusions The performance of using Gaussian function and logarithmic normal function to model RAPW is comparable, and is better than that of using Raleigh function and double-exponential function.
Wang X, Yan C, Shi B, et al. Does the Temporal Asymmetry of Short-Term Heart Rate Variability Change during Regular Walking? A Pilot Study of Healthy Young Subjects. Computational and Mathematical Methods in Medicine. 2018;2018 :1–9. Publisher's Version
Li P, Karmakar C, Yearwood J, et al. Detection of epileptic seizure based on entropy analysis of short-term EEG. PLOS ONE. 2018;13 (3) :1-17. Publisher's VersionAbstract
Entropy measures that assess signals’ complexity have drawn increasing attention recently in biomedical field, as they have shown the ability of capturing unique features that are intrinsic and physiologically meaningful. In this study, we applied entropy analysis to electroencephalogram (EEG) data to examine its performance in epilepsy detection based on short-term EEG, aiming at establishing a short-term analysis protocol with optimal seizure detection performance. Two classification problems were considered, i.e., 1) classifying interictal and ictal EEGs (epileptic group) from normal EEGs; and 2) classifying ictal from interictal EEGs. For each problem, we explored two protocols to analyze the entropy of EEG: i) using a single analytical window with different window lengths, and ii) using an average of multiple windows for each window length. Two entropy methods—fuzzy entropy (FuzzyEn) and distribution entropy (DistEn)–were used that have valid outputs for any given data lengths. We performed feature selection and trained classifiers based on a cross-validation process. The results show that performance of FuzzyEn and DistEn may complement each other and the best performance can be achieved by combining: 1) FuzzyEn of one 5-s window and the averaged DistEn of five 1-s windows for classifying normal from epileptic group (accuracy: 0.93, sensitivity: 0.91, specificity: 0.96); and 2) the averaged FuzzyEn of five 1-s windows and DistEn of one 5-s window for classifying ictal from interictal EEGs (accuracy: 0.91, sensitivity: 0.93, specificity: 0.90). Further studies are warranted to examine whether this proposed short-term analysis procedure can help track the epileptic activities in real time and provide prompt feedback for clinical practices.
Ji L, Liu C, Li P, et al. Increased pulse wave transit time after percutaneous coronary intervention procedure in CAD patients. Scientific Reports. 2018;8 (1) :115.Abstract
Pulse wave transit time (PWTT) has been widely used as an index in assessing arterial stiffness. Percutaneous coronary intervention (PCI) is usually applied to the treatment of coronary artery disease (CAD). Research on the changes in PWTT caused by PCI is helpful for understanding the impact of the PCI procedure. In addition, effects of stent sites and access sites on the changes in PWTT have not been explored. Consequently, this study aimed to provide this information. The results showed that PWTT significantly increased after PCI (p \textless 0.01) while the standard deviation (SD) of PWTT time series had no statistically significant changes (p = 0.60) between before and after PCI. Significantly increased PWTT was found in the radial access group (p \textless 0.01), while there were no significant changes in the femoral access group (p \textgreater 0.4). Additionally, PWTT in the left anterior descending (LAD) group significantly increased after PCI (p \textless 0.01), but the increase that was found in the right coronary artery (RCA) group was not significant (p \textgreater 0.1). Our study indicates that arterial elasticity and left ventricular functions can benefit from a successful PCI procedure, and the increase of peripheral PWTT after PCI can help to better understand the effectiveness of the procedure.
Li P, Yu L, Li Y, C K, Liu C. Increased beat-to-beat variation in diastolic phase percentages in patients with congestive heart failure. Conf Proc IEEE Eng Med Biol Soc. 2017;2017 :1328–1331.Abstract
Diastolic time (DT) may reflect the functioning status of cardiac relaxation/diastolic filling. Previous studies shown that beat-to-beat variation in RR interval (i.e., HRV) is preferentially expressed in the variation in DT series, raising up a question that whether DT possesses intrinsic variation, or whether the DT variation is simply a surrogate of HRV without additional information. In this study, we defined the diastolic phase percentages (DP) by correcting DT by the corresponding RR interval and proposed to analyze DP variation (DPV) in order to eliminate the masking effect of HRV. We studied DPV of 60 patients with congestive heart failure (CHF) and 60 healthy control subjects. Radial artery pressure (RAP) was monitored in synchrony with electrocardiography (ECG) for 5 min in order to extract the proposed DPV. Additionally, DPV was corrected by the individual mean DP level which resulted in the coefficient of DPV (cDPV). The differences in DPV and cDPV between the two groups were determined by linear regression models controlled for age and sex. Results showed that both DPV and cDPV increased significantly in CHF patients compared with healthy control subjects (both p \textless; 0.05). Those results, highly endorsing the existence of intrinsic physiological variation in DT, may suggest that CHF patients have less stable cardiac relaxation (that is not due to HRV) or/and less stable contractility (since the diastolic and systolic phases are mutually complementary). This study may provide helpful reference for the noninvasive evaluation of cardiac functionality and for the further understanding of multiple physiological variabilities.
Yan C, Li P, Ji L, et al. Area asymmetry of heart rate variability signal. Biomedical Engineering Online. 2017;16 :112.Abstract
Heart rate fluctuates beat-by-beat asymmetrically which is known as heart rate asymmetry (HRA). It is challenging to assess HRA robustly based on short-term heartbeat interval series.\textbarAn area index (AI) was developed that combines the distance and phase angle information of points in the Poincaré plot. To test its performance, the AI was used to classify subjects with: (i) arrhythmia, and (ii) congestive heart failure, from the corresponding healthy controls. For comparison, the existing Porta's index (PI), Guzik's index (GI), and slope index (SI) were calculated. To test the effect of data length, we performed the analyses separately using long-term heartbeat interval series (derived from \textgreater3.6-h ECG) and short-term segments (with length of 500 intervals). A second short-term analysis was further carried out on series extracted from 5-min ECG.\textbarFor long-term data, SI showed acceptable performance for both tasks, i.e., for task i p \textless 0.001, Cohen's d = 0.93, AUC (area under the receiver-operating characteristic curve) = 0.86; for task ii p \textless 0.001, d = 0.88, AUC = 0.75. AI performed well for task ii (p \textless 0.001, d = 1.0, AUC = 0.78); for task i, though the difference was statistically significant (p \textless 0.001, AUC = 0.76), the effect size was small (d = 0.11). PI and GI failed in both tasks (p \textgreater 0.05, d \textless 0.4, AUC \textless 0.7 for all). However, for short-term segments, AI indicated better distinguishability for both tasks, i.e., for task i, p \textless 0.001, d = 0.71, AUC = 0.71; for task ii, p \textless 0.001, d = 0.93, AUC = 0.74. The rest three measures all failed with small effect sizes and AUC values (d \textless 0.5, AUC \textless 0.7 for all) although the difference in SI for task i was statistically significant (p \textless 0.001). Besides, AI displayed smaller variations across different short-term segments, indicating more robust performance. Results from the second short-term analysis were in keeping with those findings.\textbarThe proposed AI indicated better performance especially for short-term heartbeat interval data, suggesting potential in the ambulatory application of cardiovascular monitoring.
Shi B, Zhang Y, Yuan C, Wang S, Li P. Entropy Analysis of Short-Term Heartbeat Interval Time Series during Regular Walking. Entropy. 2017;19 :568.
Li P, To T, Chiang W-Y, et al. Fractal regulation in temporal activity fluctuations: A biomarker for circadian control and beyond. JSM Biomarkers. 2017;3 :1008.
Wang S, Li P, Chen P, et al. Pathological brain detection via wavelet packet tsallis entropy and real-coded biogeography-based optimization. Fundamenta Informaticae. 2017;151 :275–291.Abstract
(Aim) In order to detect pathological brains in a more efficient way, (Method) we proposed a novel system of pathological brain detection (PBD) that combined wavelet packet Tsallis entropy (WPTE), feedforward neural network (FNN), and real-coded biogeography-based optimization (RCBBO). (Results) The experiments showed the proposed WPTE + FNN + RCBBO approach yielded an average accuracy of 99.49% over a 255-image dataset. (Conclusions) The WPTE + FNN + RCBBO performed better than 10 state-of-the-art approaches.
Li P, Morris CJ, Patxot M, et al. Reduced Tolerance to Night Shift in Chronic Shift Workers: Insight From Fractal Regulation. Sleep. 2017;40 :zsx092.Abstract
Study Objectives: Healthy physiology is characterized by fractal regulation (FR) that generates similar structures in the fluctuations of physiological outputs at different time scales. Perturbed FR is associated with aging and age-related pathological conditions. Shift work, involving repeated and chronic exposure to misaligned environmental and behavioral cycles, disrupts circadian coordination. We tested whether night shifts perturb FR in motor activity and whether night shifts affect FR in chronic shift workers and non-shift workers differently. Methods: We studied 13 chronic shift workers and 14 non-shift workers as controls using both field and in-laboratory experiments. In the in-laboratory study, simulated night shifts were used to induce a misalignment between the endogenous circadian pacemaker and the sleep-wake cycles (ie, circadian misalignment) while environmental conditions and food intake were controlled. Results: In the field study, we found that FR was robust in controls but broke down in shift workers during night shifts, leading to more random activity fluctuations as observed in patients with dementia. The night shift effect was present even 2 days after ending night shifts. The in-laboratory study confirmed that night shifts perturbed FR in chronic shift workers and showed that FR in controls was more resilience to the circadian misalignment. Moreover, FR during real and simulated night shifts was more perturbed in those who started shift work at older ages. Conclusions: Chronic shift work causes night shift intolerance, which is probably linked to the degraded plasticity of the circadian control system.
Karmakar C, Udhayakumar RK, Li P, Venkatesh S, Palaniswami M. Stability, Consistency and Performance of Distribution Entropy in Analysing Short Length Heart Rate Variability (HRV) Signal. Frontiers in Physiology. 2017;8.Abstract
Distribution entropy (\$DistEn\$) is a recently developed measure of complexity that is used to analyse heart rate variability (HRV) data. Its calculation requires two input parameters - the embedding dimension \$m\$, and the number of bins \$M\$ which replaces the tolerance parameter \$r\$ that is used by the existing approximation entropy (\$ApEn\$) and sample entropy (\$SampEn\$) measures. The performance of \$DistEn\$ can also be affected by the data length \$N\$. In our previous studies, we have analysed stability and performance of \$DistEn\$ with respect to one parameter (\$m\$ or \$M\$) or combination of two parameters (\$N\$ and \$M\$). However, impact of varying all the three input parameters on \$DistEn\$ is not yet studied. Since DistEn is predominantly aimed at analysing short length heart rate variability (HRV) signal, it is important to comprehensively study the stability, consistency and performance of the measure using multiple case studies. In this study, we examined the impact of changing input parameters on \$DistEn\$ for synthetic and physiological signals. We also compared the variations of \$DistEn\$ and performance in distinguishing physiological (Elderly from Young) and pathological (Healthy from Arrhythmia) conditions with \$ApEn\$ and \$SampEn\$. The results showed that \$DistEn\$ values are minimally affected by the variations of input parameters compared to \$ApEn\$ and \$SampEn\$. \$DistEn\$ also showed the most consistent and the best performance in differentiating physiological and pathological conditions with various of input parameters among reported complexity measures. In conclusion, DistEn is found to be the best measure for analysing short length HRV time series.
Ji L, Li P, Li L, et al. Analysis of cardiac electro-mechanical time-series in patients with coronary artery disease based on entropy. Computer Engineering and Applications. 2016;52 :265–270.
Li P, Karmakar C, Yan C, Palaniswami M, Liu C. Classification of five-second epileptic EEG recordings using distribution entropy and sample entropy. Frontiers in Physiology. 2016;7 :136.Abstract
Epilepsy is an electrophysiological disorder of the brain, the hallmark of which is recurrent and unprovoked seizures. Electroencephalogram (EEG) measures electrical activity of the brain that is commonly applied as a non-invasive technique for seizure detection. Although a vast number of publications have been published on intelligent algorithms to classify interictal and ictal EEG, it remains an open question whether they can be detected using short-length EEG recordings. In this study, we proposed three protocols to select 5 s EEG segment for classifying interictal and ictal EEG from normal. We used the publicly-accessible Bonn database, which consists of normal, interical, and ictal EEG signals with a length of 4097 sampling points (23.6 s) per record. In this study, we selected three segments of 868 points (5 s) length from each recordings and evaluated results for each of them separately. The well-studied irregularity measure—sample entropy (SampEn)—and a more recently proposed complexity measure—distribution entropy (DistEn)—were used as classification features. A total of 20 combinations of input parameters m and τ for the calculation of SampEn and DistEn were selected for compatibility. Results showed that SampEn was undefined for half of the used combinations of input parameters and indicated a large intra-class variance. Moreover, DistEn performed robustly for short-length EEG data indicating relative independence from input parameters and small intra-class fluctuations. In addition, it showed acceptable performance for all three classification problems (interictal EEG from normal, ictal EEG from normal, and ictal EEG from interictal) compared to SampEn, which showed better results only for distinguishing normal EEG from interictal and ictal. Both SampEn and DistEn showed good reproducibility and consistency, as evidenced by the independence of results on analysing protocol.
Li P, Li K, Liu C, et al. Detection of coupling in short physiological series by a joint distribution entropy method. IEEE Transactions on Biomedical Engineering. 2016;63 :2231–2242.Abstract
OBJECTIVE: In this study we developed a joint distribution entropy (JDistEn) method to robustly estimate the coupling in short physiological series. METHODS: The JDistEn method is derived from a joint distance matrix which is constructed from a combination of the distance matrix corresponding to each individual data channel using a geometric mean calculation. A coupled Rossler system and a coupled dual-kinetics neural mass model were used to examine how well JDistEn performed, specifically, its sensitivity for detecting weak coupling, its consistency in gauging coupling strength, and its reliability in processing input of decreased data length. Performance of JDistEn in estimating physiological coupling was further examined with bivariate electroencephalography (EEG) data from rats and RR interval and diastolic time interval (RRI-DTI) series from human beings. Cross-sample entropy (XSampEn), cross-conditional entropy (XCE), and Shannon entropy of diagonal lines in the joint recurrence plots (JENT) were applied for purposes of comparison. RESULTS: Simulation results suggest that JDistEn showed markedly higher sensitivity than XSampEn, XCE, and JENT for dynamics in weak coupling, although as the simulation models were more intensively coupled, JDistEn performance was comparable to the three others. In addition, this improved sensitivity was much more pronounced for short data sets. Experimental results further confirmed that JDistEn outperformed XSampEn, XCE, and JENT for detecting weak coupling, especially for short physiological data. CONCLUSION: this study suggested that our proposed JDistEn could be useful for continuous and even real-time coupling analysis for physiological signals in clinical practice.
Udhayakumar RK, Karmakar C, Li P, Palaniswami M. Effect of embedding dimension on complexity measures in identifying Arrhythmia. In: ; 2016 :6230–6233.Abstract
{Entropy measures like Approximate entropy (ApEn) and Sample entropy (SampEn) are well established tools to analyze Heart Rate Variability (HRV) data. Critical parameters involved in these computations namely embedding dimension m and tolerance r are in most cases assumed to be 2 and 0.2*signal SD (standard devaition) respectively. Such assumptions do not work fairly across data sets and thus create misleading results in many cases. Problems with r have been addressed with the advent of newer entropy measures like Permutation entropy (PE), Fuzzy entropy (FuzzyEn) and Distribution entropy (DistEn) that simply eliminate, modify or replace r from calculations. On the other hand, the disadvantage of using a fixed assumed choice of m when such measures are used for data classification is yet to be investigated. The smallest variation in m may effect the extent of information retrieval from HRV data and hence it is extremely important to analyze different possibilities and outcomes of the same. In this study, we scrutinize the behavior of different entropy measures with regard to their classification performance at four different values of embedding dimension i.e.