A Poincaré plot is a return map that geometrically elucidates the progression of a time-series. It has frequently been used in heart rate variability analyses. However, algorithms for dedicatedly dissecting the shape of this geometrical plot are yet to be established. In this study, we proposed a gridded Poincaré plot by coarse-graining the original graph and using the newly proposed one, defined two novel measures, namely gridded distribution rate (GDR) and gridded distribution entropy (GDE). The GDR essentially represents the percentage of grids with points, while the GDE estimates the Shannon entropy of the grid weight; that is, the number of points in each grid. The performances of the two measures were examined using both theoretical data with known dynamics and experimental short-term RR interval time-series, and they were compared with several existing metrics. Simulation tests demonstrated that both the GDR and GDE could distinguish among different dynamics, while all the compared methods failed. The experimental results further indicated the ability of the GDR and GDE to differentiate healthy young people from healthy aged adults as well as distinguish healthy subjects from patients with coronary artery disease. Our results suggest that the proposed GDR and GDE may better characterize the Poincaré plot in terms of differentiating between varying dynamical regimes, and between human physiological or pathological conditions. Further studies are warranted to establish their feasibility in evaluating cardiovascular functions in clinical practice.
Heart rate variability (HRV), systolic period variability (SPV), and diastolic period variability (DPV) have shown potential for assessing cardiac function. It is unknown whether the time delay between the myocardial electrical and mechanical activities (i.e., electromechanical delay, EMD) also possesses variability, and if it does, whether this EMD variability (EMDV) could render additional value for cardiac function assessment. In this paper, we extracted the beat-to-beat EMD from 5-min simultaneously recorded electrocardiogram and phonocardiogram signals in 30 patients with coronary artery disease (CAD) and 30 healthy control subjects, and studied its variability using the same methods as applied for HRV including time-domain measures [mean and standard deviation (SD)], frequency-domain measures [normalized low- and high-frequency (LFn, HFn) and LF/HF)], and nonlinear measures [sample entropy (SampEn), permutation entropy (PE), and dynamical patterns]. In addition, we examined whether the addition of EMDV could offer improved performance for distinguishing between the two groups compared to using the HRV, SPV, and DPV features. Support vector machine with 10-fold cross-validation was used for classification. Results showed increased SD of SPV, increased mean, SD and decreased SampEn of EMDV in CAD patients. Besides, the dynamical pattern analysis showed that CAD patients had significantly increased fluctuated patterns and decreased monotonous patterns in EMDV. In particular, the addition of EMDV indices dramatically increased the classification accuracy from 0.729 based on HRV, SPV, and DPV features to 0.958. Our results suggest promising of the EMDV analysis that could potentially be helpful for detecting CAD noninvasively.
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.
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.
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.
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.
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.
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.
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.
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.
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.
(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.
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.
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.