Multi-scale transitions of fuzzy sample entropy of RR-intervals and their phase-randomized surrogates: A possibility to diagnose congestive heart failure

Influence of the Fuzzy Function on the Estimation of the Fuzzy Sample Entropy with Fixed Tolerance Values for the Evaluation of Surface EMG Muscle Activity

Fixed sample entropy (fSampEn) is a technique that has demonstrated superior performance to other amplitude estimators for assessing respiratory muscle electromyographic activity. This technique is based on the calculation of sample entropy (SampEn) using fixed tolerance thresholds. Fuzzy entropy (FuzzyEn) introduces an improvement to the SampEn algorithm based on the use of a fuzzy measure to evaluate the similarity between vectors. However, several fuzzy functions have been used to calculate the FuzzyEn, and not all of them allow an effective comparison with the SampEn calculation parameters. In the present work, an analysis of the different fuzzy functions previously used has been carried out and a new sigmoid fuzzy function for the calculation of FuzzyEn with fixed tolerance thresholds (fFuzzyEn) has been proposed. The results show that the proposed fuzzy function outperformed both fSampEn and previously proposed FuzzyEn-based algorithms. These results suggest that fFuzzyEn could improve the assessment of muscle activity providing potentially useful diagnostic information.Clinical Relevance- This sets out the appropriate use of the fuzzy function for the estimation of the fuzzy sample entropy with fixed tolerance thresholds (fFuzzyEn). The use of fFuzzyEn could improve methods for detecting the onset and offset of respiratory electromyographic (EMG) signals, as well as the assessment of EMG activation level.

Heart rate variability predicts decline in sensorimotor rhythm control

Objective.Voluntary control of sensorimotor rhythms (SMRs, 8-12 Hz) can be used for brain-computer interface (BCI)-based operation of an assistive hand exoskeleton, e.g. in finger paralysis after stroke. To gain SMR control, stroke survivors are usually instructed to engage in motor imagery (MI) or to attempt moving the paralyzed fingers resulting in task- or event-related desynchronization (ERD) of SMR (SMR-ERD). However, as these tasks are cognitively demanding, especially for stroke survivors suffering from cognitive impairments, BCI control performance can deteriorate considerably over time. Therefore, it would be important to identify biomarkers that predict decline in BCI control performance within an ongoing session in order to optimize the man-machine interaction scheme.Approach.Here we determine the link between BCI control performance over time and heart rate variability (HRV). Specifically, we investigated whether HRV can be used as a biomarker to predict decline of SMR-ERD control across 17 healthy participants using Granger causality. SMR-ERD was visually displayed on a screen. Participants were instructed to engage in MI-based SMR-ERD control over two consecutive runs of 8.5 min each. During the 2nd run, task difficulty was gradually increased.Main results.While control performance (p= .18) and HRV (p= .16) remained unchanged across participants during the 1st run, during the 2nd run, both measures declined over time at high correlation (performance: -0.61%/10 s,p= 0; HRV: -0.007 ms/10 s,p< .001). We found that HRV exhibited predictive characteristics with regard to within-session BCI control performance on an individual participant level (p< .001).Significance.These results suggest that HRV can predict decline in BCI performance paving the way for adaptive BCI control paradigms, e.g. to individualize and optimize assistive BCI systems in stroke.

Application of Multiscale Entropy in Assessing Plantar Skin Blood Flow Dynamics in Diabetics with Peripheral Neuropathy

Diabetic foot ulcer (DFU) is a common complication of diabetes mellitus, while tissue ischemia caused by impaired vasodilatory response to plantar pressure is thought to be a major factor of the development of DFUs, which has been assessed using various measures of skin blood flow (SBF) in the time or frequency domain. These measures, however, are incapable of characterizing nonlinear dynamics of SBF, which is an indicator of pathologic alterations of microcirculation in the diabetic foot. This study recruited 18 type 2 diabetics with peripheral neuropathy and eight healthy controls. SBF at the first metatarsal head in response to locally applied pressure and heating was measured using laser Doppler flowmetry. A multiscale entropy algorithm was utilized to quantify the regularity degree of the SBF responses. The results showed that during reactive hyperemia and thermally induced biphasic response, the regularity degree of SBF in diabetics underwent only small changes compared to baseline and significantly differed from that in controls at multiple scales (p < 0.05). On the other hand, the transition of regularity degree of SBF in diabetics distinctively differed from that in controls (p < 0.05). These findings indicated that multiscale entropy could provide a more comprehensive assessment of impaired microvascular reactivity in the diabetic foot compared to other entropy measures based on only a single scale, which strengthens the use of plantar SBF dynamics to assess the risk for DFU.

Assessing multiscale complexity of short heart rate variability series through a model-based linear approach

We propose a multiscale complexity (MSC) method assessing irregularity in assigned frequency bands and being appropriate for analyzing the short time series. It is grounded on the identification of the coefficients of an autoregressive model, on the computation of the mean position of the poles generating the components of the power spectral density in an assigned frequency band, and on the assessment of its distance from the unit circle in the complex plane. The MSC method was tested on simulations and applied to the short heart period (HP) variability series recorded during graded head-up tilt in 17 subjects (age from 21 to 54 years, median = 28 years, 7 females) and during paced breathing protocols in 19 subjects (age from 27 to 35 years, median = 31 years, 11 females) to assess the contribution of time scales typical of the cardiac autonomic control, namely in low frequency (LF, from 0.04 to 0.15 Hz) and high frequency (HF, from 0.15 to 0.5 Hz) bands to the complexity of the cardiac regulation. The proposed MSC technique was compared to a traditional model-free multiscale method grounded on information theory, i.e., multiscale entropy (MSE). The approach suggests that the reduction of HP variability complexity observed during graded head-up tilt is due to a regularization of the HP fluctuations in LF band via a possible intervention of sympathetic control and the decrement of HP variability complexity observed during slow breathing is the result of the regularization of the HP variations in both LF and HF bands, thus implying the action of physiological mechanisms working at time scales even different from that of respiration. MSE did not distinguish experimental conditions at time scales larger than 1. Over a short time series MSC allows a more insightful association between cardiac control complexity and physiological mechanisms modulating cardiac rhythm compared to a more traditional tool such as MSE.

Multiscale Entropy Analysis of the Differential RR Interval Time Series Signal and Its Application in Detecting Congestive Heart Failure

Cardiovascular systems essentially have multiscale control mechanisms. Multiscale entropy (MSE) analysis permits the dynamic characterization of the cardiovascular time series for both short-term and long-term processes, and thus can be more illuminating. The traditional MSE analysis for heart rate variability (HRV) is performed on the original RR interval time series (named as MSE_RR). In this study, we proposed an MSE analysis for the differential RR interval time series signal, named as MSE_dRR. The motivation of using the differential RR interval time series signal is that this signal has a direct link with the inherent non-linear property of electrical rhythm of the heart. The effectiveness of the MSE_RR and MSE_dRR were tested and compared on the long-term MIT-Boston’s Beth Israel Hospital (MIT-BIH) 54 normal sinus rhythm (NSR) and 29 congestive heart failure (CHF) RR interval recordings, aiming to explore which one is better for distinguishing the CHF patients from the NSR subjects. Four RR interval length for analysis were used ( N = 500 , N = 1000 , N = 2000 and N = 5000 ). The results showed that MSE_RR did not report significant differences between the NSR and CHF groups at several scales for each RR segment length type (Scales 7, 8 and 10 for N = 500 , Scales 3 and 10 for N = 1000 , Scales 2 and 3 for both N = 2000 and N = 5000 ). However, the new MSE_dRR gave significant separation for the two groups for all RR segment length types except N = 500 at Scales 9 and 10. The area under curve (AUC) values from the receiver operating characteristic (ROC) curve were used to further quantify the performances. The mean AUC of the new MSE_dRR from Scales 1–10 are 79.5%, 83.1%, 83.5% and 83.1% for N = 500 , N = 1000 , N = 2000 and N = 5000 , respectively, whereas the mean AUC of MSE_RR are only 68.6%, 69.8%, 69.6% and 67.1%, respectively. The five-fold cross validation support vector machine (SVM) classifier reports the classification Accuracy ( A c c ) of MSE_RR as 73.5%, 75.9% and 74.6% for N = 1000 , N = 2000 and N = 5000 , respectively, while for the new MSE_dRR analysis accuracy was 85.5%, 85.6% and 85.6%. Different biosignal editing methods (direct deletion and interpolation) did not change the analytical results. In summary, this study demonstrated that compared with MSE_RR, MSE_dRR reports better statistical stability and better discrimination ability for the NSR and CHF groups.