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. An 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 >3.6-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. For long-term data, SI showed acceptable performance for both tasks, i.e., for task i p < 0.001, Cohen’s d = 0.93, AUC (area under the receiver-operating characteristic curve) = 0.86; for task ii p < 0.001, d = 0.88, AUC = 0.75. AI performed well for task ii (p < 0.001, d = 1.0, AUC = 0.78); for task i, though the difference was statistically significant (p < 0.001, AUC = 0.76), the effect size was small (d = 0.11). PI and GI failed in both tasks (p > 0.05, d < 0.4, AUC < 0.7 for all). However, for short-term segments, AI indicated better distinguishability for both tasks, i.e., for task i, p < 0.001, d = 0.71, AUC = 0.71; for task ii, p < 0.001, d = 0.93, AUC = 0.74. The rest three measures all failed with small effect sizes and AUC values (d < 0.5, AUC < 0.7 for all) although the difference in SI for task i was statistically significant (p < 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. The proposed AI indicated better performance especially for short-term heartbeat interval data, suggesting potential in the ambulatory application of cardiovascular monitoring.

Heart rate variability (HRV) has been widely used in the non-invasive evaluation of cardiovascular function. Recent studies have also attached great importance to the cardiac diastolic period variability (DPV) examination. Short-term variability measurement (e.g., 5 min) has drawn increasing attention in clinical practice, since it is able to provide almost immediate measurement results and enables the real-time monitoring of cardiovascular function. However, it is still a contemporary challenge to robustly estimate the HRV and DPV parameters based on short-term recordings. In this study, a refined fuzzy entropy (rFuzzyEn) was developed by substituting a piecewise fuzzy membership function for the Gaussian function in conventional fuzzy entropy (FuzzyEn) measure. Its stability and robustness against additive noise compared with sample entropy (SampEn) and FuzzyEn, were examined by two well-accepted simulation models—the $$ 1/f^{\alpha } $$ noise and the Logistic attractor. The rFuzzyEn was further applied to evaluate clinical short-term (5 min) HRV and DPV of the patients with coronary artery stenosis and healthy volunteers. Simulation results showed smaller fluctuations in the rFuzzyEn than in SampEn and FuzzyEn values when the data length was decreasing. Besides, rFuzzyEn could distinguish the simulation models with different amount of additive noise even when the percentage of additive noise reached 60%, but neither SampEn nor FuzzyEn showed comparable performance. Clinical HRV analysis did not indicate any significant differences between the patients with coronary artery disease and the healthy volunteers in all the three mentioned entropy measures (all p > 0.20). But clinical DPV analysis showed that the patient group had a significantly higher rFuzzyEn (p < 0.01) than the healthy group. However, no or less significant difference was observed between the two groups in either SampEn (p = 0.14) or FuzzyEn (p = 0.05). Our proposed rFuzzyEn outperformed conventional SampEn and FuzzyEn in terms of both stability and robustness against additive noise, particularly when the data set was relatively short. Analysis of DPV using rFuzzyEn may provide more valuable information to assess the cardiovascular states than the other entropy measures and has a potential for clinical application.

Coronary artery disease (CAD) is the most common cause of death globally. To detect CAD noninvasively at an early stage before clinical symptoms occur is still nowadays challenging. Analysis of the variation of heartbeat interval (RRI) opens a new avenue for evaluating the functional change of cardiovascular system which is accepted to occur at the subclinical stage of CAD. In addition, systolic time interval (STI) and diastolic time interval (DTI) also show potential. There may be coupling in these electromechanical time series due to their physiological connection. However, to the best of our knowledge no publication has systematically investigated how can the coupling be measured and how it changes in CAD patients. In this study, we enrolled 39 CAD patients and 36 healthy subjects and for each subject the electrocardiogram (ECG) and photoplethysmography (PPG) signals were recorded simultaneously for 5 min. The RRI series, STI series, and DTI series were constructed, respectively. We used linear cross correlation (CC), coherence function (CF), as well as nonlinear mutual information (MI), cross conditional entropy (XCE), cross sample entropy (XSampEn), and cross fuzzy entropy (XFuzzyEn) to analyse the bivariate RRI-DTI coupling, RRI-STI coupling, and STI-DTI coupling, respectively. Our results suggest that the linear CC and CF generally have no significant difference between the two groups for all three types of bivariate coupling. The MI only shows weak change in RRI-DTI coupling. By comparison, the three entropy-based coupling measurements show significantly decreased coupling in CAD patients except XSampEn for RRI-DTI coupling (less significant) and XCE for STI-DTI and RRI-STI coupling (not significant). Additionally, the XFuzzyEn performs best as it was still significant if we further applied the Bonferroni correction in our statistical analysis. Our study indicates that the intrinsic electromechanical coupling is most probably nonlinear and can better be measured by nonlinear entropy-based measurements especially the XFuzzyEn. Besides, CAD patients are accompanied by a loss of electromechanical coupling. Our results suggest that cardiac electromechanical coupling may potentially serve as a noninvasive diagnostic tool for CAD.

Heart rate variability (HRV) has been widely used in clinical research to provide an insight into the autonomic control of the cardiovascular system. Measurement of HRV is generally performed under a relaxed resting state. The effects of other conditions on HRV measurement, such as running, mountaineering, head-up tilt, etc, have also been investigated. This study aimed to explore whether an inflation-and-deflation process applied to a unilateral upper arm cuff would influence the HRV measurement. Fifty healthy young volunteers aged between 21 and 30 were enrolled in this study. Electrocardiogram (ECG) signals were recorded for each subject over a five minute resting state followed by a five minute external-cuff-inflation-and-deflation state (ECID state). A one minute gap was scheduled between the two measurements. Consecutive RR intervals in the ECG were extracted automatically to form the HRV data for each of the two states. Time domain (SDNN, RMSSD and PNN50), frequency domain (LFn, HFn and LF/HF) and nonlinear (VLI, VAI and SampEn) HRV indices were analyzed and compared between the two states. In addition, the effects of mean artery pressure (MAP) and heart rate (HR) on the aforementioned HRV indices were assessed for the two states, respectively, by Pearson correlation analysis. The results showed no significant difference in all aforementioned HRV indices between the resting and the ECID states (all p > 0.05). The corresponding HRV indices had significant positive correlation (all p < 0.01) between the two states. None of the indices showed MAP-related change (all p > 0.05) for either state. Besides, none of the indices showed HR-related change (all p > 0.05) for either state except the index of VLI in the resting state. To conclude, this pilot study suggested that the applied ECID process hardly influenced those commonly used HRV indices. It would thus be applicable to simultaneously measure both blood pressure and HRV indices in clinical practice.

Percutaneous coronary intervention (PCI) is a common treatment method for patients with coronary artery disease (CAD), but its effect on synchronously measured heart rate variability (HRV) and pulse transit time variability (PTTV) have not been well established. This study aimed to verify whether PCI for CAD patients affects both HRV and PTTV parameters. Sixteen CAD patients were enrolled. Two five-minute ECG and finger photoplethysmography (PPG) signals were recorded, one within 24 h before PCI and another within 24 h after PCI. The changes of RR and pulse transit time (PTT) intervals due to the PCI procedure were first compared. Then, HRV and PTTV were evaluated by a standard short-term time-domain variability index of standard deviation of time series (SDTS) and our previously developed entropy-based index of fuzzy measure entropy (FuzzyMEn). To test the effect of different time series length on HRV and PTTV results, we segmented the RR and PTT time series using four time windows of 200, 100, 50 and 25 beats respectively. The PCI-induced changes in HRV and PTTV, as well as in RR and PTT intervals, are different. PCI procedure significantly decreased RR intervals (before PCI 973 ± 85 vs. after PCI 907 ± 100 ms, p < 0.05) while significantly increasing PTT intervals (207 ± 18 vs. 214 ± 19 ms, p < 0.01). For HRV, SDTS-only output significant lower values after PCI when time windows are 100 and 25 beats while presenting no significant decreases for other two time windows. By contrast, FuzzyMEn gave significant lower values after PCI for all four time windows (all p < 0.05). For PTTV, SDTS hardly changed after PCI at any time window (all p > 0.90) whereas FuzzyMEn still reported significant lower values (p < 0.05 for 25 beats time window and p < 0.01 for other three time windows). For both HRV and PTTV, with the increase of time window values, SDTS decreased while FuzzyMEn increased. This pilot study demonstrated that the RR interval decreased whereas the PTT interval increased after the PCI procedure and that there were significant reductions in both HRV and PTTV immediately after PCI using the FuzzyMEn method, indicating the changes in underlying mechanisms in cardiovascular system.