Selection of entropy-measure parameters for knowledge discovery in heart rate variability data

Modified multiscale Renyi distribution entropy for short-term heart rate variability analysis

BACKGROUND

Multiscale sample entropy (MSE) is a prevalent complexity metric to characterize a time series and has been extensively applied to the physiological signal analysis. However, for a short-term time series, the likelihood of identifying comparable subsequences decreases, leading to higher variability in the Sample Entropy (SampEn) calculation. Additionally, as the scale factor increases in the MSE calculation, the coarse-graining process further shortens the time series. Consequently, each newly generated time series at a larger scale consists of fewer data points, potentially resulting in unreliable or undefined entropy values, particularly at higher scales. To overcome the shortcoming, a modified multiscale Renyi distribution entropy (MMRDis) was proposed in our present work.

METHODS

The MMRDis method uses a moving-averaging procedure to acquire a family of time series, each of which quantify the dynamic behaviors of the short-term time series over the multiple temporal scales. Then, MMRDis is constructed for the original and the coarse-grained time series.

RESULTS

The MMRDis method demonstrated superior computational stability on simulated Gaussian white and 1/f noise time series, effectively avoiding undefined measurements in short-term time series. Analysis of short-term heart rate variability (HRV) signals from healthy elderly individuals, healthy young people, and subjects with congestive heart failure and atrial fibrillation revealed that MMRDis complexity measurement values decreased with aging and disease. Additionally, MMRDis exhibited better distinction capability for short-term HRV physiological/pathological signals compared to several recently proposed complexity metrics.

CONCLUSIONS

MMRDis was a promising measurement for screening cardiovascular condition within a short time.

Heart rate variability is not suitable as a surrogate marker for pain intensity in patients with chronic pain

ABSTRACT

The search towards more objective outcome measurements and consequently surrogate markers for pain started decades ago; however, no generally accepted biomarker for pain has qualified yet. The goal is to explore the value of heart rate variability (HRV) as surrogate marker for pain intensity chronic pain setting. Pain intensity scores and HRV were collected in 366 patients with chronic pain, through a cross-sectional multicenter study. Pain intensity was measured with both the visual analogue scale and numeric rating scale, whereas 16 statistical HRV parameters were derived. Canonical correlation analysis was performed to evaluate the correlation between the dependent pain variables and the HRV parameters. Surrogacy was determined for each HRV parameter with point estimates between 0 and 1 whereby values close to 1 indicate a strong association between the surrogate and the true endpoint at the patient level. Weak correlations were revealed between HRV parameters and pain intensity scores. The highest surrogacy point estimate was found for mean heart rate as marker for average pain intensity on the numeric rating scale with point estimates of 0.0961 (95% confidence interval [CI] 0.0384-0.1537) and 0.0209 (95% CI 0-0.05) for patients without medication use and with medication, respectively. This study indicated that HRV parameters as separate entities are no suitable surrogacy candidates for pain intensity, in a population of chronic pain patients. Further potential surrogate candidates and clinical robust true endpoints should be explored, to find a surrogate measure for the highly individual pain experience.

Complex Brain-Heart Mapping in Mental and Physical Stress

OBJECTIVE

The central and autonomic nervous systems are deemed complex dynamic systems, wherein each system as a whole shows features that the individual system sub-components do not. They also continuously interact to maintain body homeostasis and appropriate react to endogenous and exogenous stimuli. Such interactions are comprehensively referred to functional brain-heart interplay (BHI). Nevertheless, it remains uncertain whether this interaction also exhibits complex characteristics, that is, whether the dynamics of the entire nervous system inherently demonstrate complex behavior, or if such complexity is solely a trait of the central and autonomic systems. Here, we performed complexity mapping of the BHI dynamics under mental and physical stress conditions.

METHODS AND PROCEDURES

Electroencephalographic and heart rate variability series were obtained from 56 healthy individuals performing mental arithmetic or cold-pressure tasks, and physiological series were properly combined to derive directional BHI series, whose complexity was quantified through fuzzy entropy.

RESULTS

The experimental results showed that BHI complexity is mainly modulated in the efferent functional direction from the brain to the heart, and mainly targets vagal oscillations during mental stress and sympathovagal oscillations during physical stress.

CONCLUSION

We conclude that the complexity of BHI mapping may provide insightful information on the dynamics of both central and autonomic activity, as well as on their continuous interaction.

CLINICAL IMPACT

This research enhances our comprehension of the reciprocal interactions between central and autonomic systems, potentially paving the way for more accurate diagnoses and targeted treatments of cardiovascular, neurological, and psychiatric disorders.

Evaluation of autonomic nervous system activity in intradialytic hypotension using entropy and skin sympathetic nerve activity

Introduction

The function of the autonomic nervous system (ANS) is crucial in the development of intradialytic hypotension (IDH). This study introduced the entropy of heart rate variability (HRV) and skin sympathetic nerve activity (SKNA) to provide a complementary nonlinear and dynamic perspective for evaluating ANS function concerning IDH.

Methods

93 patients undergoing hemodialysis (HD) were enrolled, and the baseline data, electrocardiogram (ECG), and SKNA were collected. The patients were separated into the IDH and nonIDH groups based on the thresholds, which were characterized as reductions in systolic blood pressure (SBP) of at least 20 mm Hg or mean arterial pressure (MAP) of at least 10 mm Hg. We developed a logistic regression model for IDH after analyzing the changes in the time domain, frequency domain, the entropy of HRV, and SKNA indices during HD.

Results

After 4-h HD, the detected results for heart rate, the ratio of low frequency and high frequency (LF/HF), and average SKNA (aSKNA) all increased in both groups. Nine out of the ten HRV indices and aSKNA in the nonIDH group were higher than those in the IDH group at most moments. aSKNA was positively correlated with heart rate (p = 0.0001) and LF/HF (p = 0.0005) in the nonIDH group, while the correlation disappeared in the IDH group, which indicated a worse ANS response in IDH patients. The logistic regression model exhibited the results of initial SBP [odds ratio (OR) 1.076; p = 0.001], and the difference between the last and first segments (DLF) of heart rate [OR 1.101; p =0.012] and LF/HF [OR 0.209; p =0.034], as well as the extreme value of the difference between other segments and the first segments (EOF) of aSKNA [OR 2.908; p =0.017], which were independent indicators for IDH.

Discussion

The new nonlinear and dynamic assessment perspectives provided by the entropy of HRV and SKNA help to distinguish differences in ANS patterns between IDH patients and nonIDH patients and have the potential to be used in clinical monitoring for HD patients.

Complexity Modulation in functional Brain-Heart Interplay series driven by Emotional Stimuli: an early study using Fuzzy Entropy

Increasing attention has recently been devoted to the multidisciplinary investigation of functional brain-heart interplay (BHI), which has provided meaningful insights in neuroscience and clinical domains including cardiology, neurology, clinical psychology, and psychiatry. While neural (brain) and heartbeat series show high nonlinear and complex dynamics, a complexity analysis on BHI series has not been performed yet. To this end, in this preliminary study, we investigate BHI complexity modulation in 17 healthy subjects undergoing a 3-minute resting state and emotional elicitation through standardized image slideshow. Electroencephalographic and heart rate variability series were the inputs of an adhoc BHI model, which provides directional (from-heart-to-brain and from-brain-to-heart) estimates at different frequency bands. A Fuzzy entropy analysis was performed channel-wise on the model output for the two experimental conditions. Results suggest that BHI complexity increases in the emotional elicitation phase with respect to a resting state, especially in the functional direction from the heart to the brain. We conclude that BHI complexity may be a viable computational tool to characterize neurophysiological and pathological states under different experimental conditions.

Detection of fetal arrhythmias in non-invasive fetal ECG recordings using data-driven entropy profiling

Objective:Fetal arrhythmias are a life-threatening disorder occurring in up to 2% of pregnancies. If identified, many fetal arrhythmias can be effectively treated using anti-arrhythmic therapies. In this paper, we present a novel method of detecting fetal arrhythmias in short length non-invasive fetal electrocardiography (NI-FECG) recordings.Approach:Our method consists of extracting a fetal heart rate (FHR) time series from each NI-FECG recording and computing an entropy profile using a data-driven range of the entropy tolerance parameter r. To validate our approach, we apply our entropy profiling method to a large clinical data set of 318 NI-FECG recordings.Main Results:We demonstrate that our method (TotalSampEn) provides strong performance for classifying arrhythmic fetuses (AUC of 0.83) and outperforms entropy measures such as SampEn (AUC of 0.68) and FuzzyEn (AUC of 0.72). We also find that NI-FECG recordings incorrectly classified using the investigated entropy measures have significantly lower signal quality, and that excluding recordings of low signal quality (13.5% of recordings) increases the classification accuracy of TotalSampEn (AUC of 0.90).Significance:The superior performance of our approach enables automated detection of fetal arrhythmias and warrants further investigation in a prospective clinical trial.

Real-World Data Difficulty Estimation with the Use of Entropy

In the era of the Internet of Things and big data, we are faced with the management of a flood of information. The complexity and amount of data presented to the decision-maker are enormous, and existing methods often fail to derive nonredundant information quickly. Thus, the selection of the most satisfactory set of solutions is often a struggle. This article investigates the possibilities of using the entropy measure as an indicator of data difficulty. To do so, we focus on real-world data covering various fields related to markets (the real estate market and financial markets), sports data, fake news data, and more. The problem is twofold: First, since we deal with unprocessed, inconsistent data, it is necessary to perform additional preprocessing. Therefore, the second step of our research is using the entropy-based measure to capture the nonredundant, noncorrelated core information from the data. Research is conducted using well-known algorithms from the classification domain to investigate the quality of solutions derived based on initial preprocessing and the information indicated by the entropy measure. Eventually, the best 25% (in the sense of entropy measure) attributes are selected to perform the whole classification procedure once again, and the results are compared.

Determination of Parameters for an Entropy-Based Atrial Fibrillation Detector

Entropy algorithm is an important nonlinear method for cardiovascular disease detection due to its power in analyzing short-term time series. In previous a study, we proposed a new entropy-based atrial fibrillation (AF) detector, i.e., Entropy_AF, which showed a high classification accuracy in identifying AF and non-AF rhythms. As a variation of entropy measures, Entropy_AF has two parameters that need to be initialized before the calculation: (1) tolerance threshold r and (2) similarity weight n. In this study, a comprehensive analysis for the two parameters determination was presented, aiming to achieve a high detection accuracy for AF events. Data were from the MIT-BIH AF database. RR interval recordings were segmented using a 30-beat time window. The parameters r and n were initialized from a relatively small value, then gradually increased, and finally the best parameter combination was determined using grid searching. AUC (area under curve) values from the receiver operator characteristic curve (ROC) were compared under different parameter combinations of parameters r and n, and the results demonstrated that the selection of these two parameters plays an important role in AF/non-AF classification. Small values of parameters r and n can lead to a better detection accuracy than other selections. The best AUC value for AF detection was 98.15%, and the corresponding parameter combinations for Entropy_AF were as follows: r = 0.01, n = 0.0625, 0.125, 0.25, or 0.5; r = 0.05 and n = 0.0625, 0.125, or 0.25; and r = 0.10 and n = 0.0625 or 0.125.

Heart Rate Variability in Psychology: A Review of HRV Indices and an Analysis Tutorial

The use of heart rate variability (HRV) in research has been greatly popularized over the past decades due to the ease and affordability of HRV collection, coupled with its clinical relevance and significant relationships with psychophysiological constructs and psychopathological disorders. Despite the wide use of electrocardiograms (ECG) in research and advancements in sensor technology, the analytical approach and steps applied to obtain HRV measures can be seen as complex. Thus, this poses a challenge to users who may not have the adequate background knowledge to obtain the HRV indices reliably. To maximize the impact of HRV-related research and its reproducibility, parallel advances in users' understanding of the indices and the standardization of analysis pipelines in its utility will be crucial. This paper addresses this gap and aims to provide an overview of the most up-to-date and commonly used HRV indices, as well as common research areas in which these indices have proven to be very useful, particularly in psychology. In addition, we also provide a step-by-step guide on how to perform HRV analysis using an integrative neurophysiological toolkit, NeuroKit2.

Short-Term HRV Analysis Using Nonparametric Sample Entropy for Obstructive Sleep Apnea

Obstructive sleep apnea (OSA) is associated with reduced heart rate variability (HRV) and autonomic nervous system dysfunction. Sample entropy (SampEn) is commonly used for regularity analysis. However, it has limitations in processing short-term segments of HRV signals due to the extreme dependence of its functional parameters. We used the nonparametric sample entropy (NPSampEn) as a novel index for short-term HRV analysis in the case of OSA. The manuscript included 60 6-h electrocardiogram recordings (20 healthy, 14 mild-moderate OSA, and 26 severe OSA) from the PhysioNet database. The NPSampEn value was compared with the SampEn value and frequency domain indices. The empirical results showed that NPSampEn could better differentiate the three groups (p < 0.01) than the ratio of low frequency power to high frequency power (LF/HF) and SampEn. Moreover, NPSampEn (83.3%) approached a higher OSA screening accuracy than the LF/HF (73.3%) and SampEn (68.3%). Compared with SampEn (|r| = 0.602, p < 0.05), NPSampEn (|r| = 0.756, p < 0.05) had a significantly stronger association with the apnea-hypopnea index (AHI). Hence, NPSampEn can fully overcome the influence of individual differences that are prevalent in biomedical signal processing, and might be useful in processing short-term segments of HRV signal.

Statistical Features in High-Frequency Bands of Interictal iEEG Work Efficiently in Identifying the Seizure Onset Zone in Patients with Focal Epilepsy

The design of a computer-aided system for identifying the seizure onset zone (SOZ) from interictal and ictal electroencephalograms (EEGs) is desired by epileptologists. This study aims to introduce the statistical features of high-frequency components (HFCs) in interictal intracranial electroencephalograms (iEEGs) to identify the possible seizure onset zone (SOZ) channels. It is known that the activity of HFCs in interictal iEEGs, including ripple and fast ripple bands, is associated with epileptic seizures. This paper proposes to decompose multi-channel interictal iEEG signals into a number of subbands. For every 20 s segment, twelve features are computed from each subband. A mutual information (MI)-based method with grid search was applied to select the most prominent bands and features. A gradient-boosting decision tree-based algorithm called LightGBM was used to score each segment of the channels and these were averaged together to achieve a final score for each channel. The possible SOZ channels were localized based on the higher value channels. The experimental results with eleven epilepsy patients were tested to observe the efficiency of the proposed design compared to the state-of-the-art methods.

Entropy Profiling: A Reduced-Parametric Measure of Kolmogorov-Sinai Entropy from Short-Term HRV Signal

Entropy profiling is a recently introduced approach that reduces parametric dependence in traditional Kolmogorov-Sinai (KS) entropy measurement algorithms. The choice of the threshold parameter r of vector distances in traditional entropy computations is crucial in deciding the accuracy of signal irregularity information retrieved by these methods. In addition to making parametric choices completely data-driven, entropy profiling generates a complete profile of entropy information as against a single entropy estimate (seen in traditional algorithms). The benefits of using "profiling" instead of "estimation" are: (a) precursory methods such as approximate and sample entropy that have had the limitation of handling short-term signals (less than 1000 samples) are now made capable of the same; (b) the entropy measure can capture complexity information from short and long-term signals without multi-scaling; and (c) this new approach facilitates enhanced information retrieval from short-term HRV signals. The novel concept of entropy profiling has greatly equipped traditional algorithms to overcome existing limitations and broaden applicability in the field of short-term signal analysis. In this work, we present a review of KS-entropy methods and their limitations in the context of short-term heart rate variability analysis and elucidate the benefits of using entropy profiling as an alternative for the same.

Modified Distribution Entropy as a Complexity Measure of Heart Rate Variability (HRV) Signal

The complexity of a heart rate variability (HRV) signal is considered an important nonlinear feature to detect cardiac abnormalities. This work aims at explaining the physiological meaning of a recently developed complexity measurement method, namely, distribution entropy (DistEn), in the context of HRV signal analysis. We thereby propose modified distribution entropy (mDistEn) to remove the physiological discrepancy involved in the computation of DistEn. The proposed method generates a distance matrix that is devoid of over-exerted multi-lag signal changes. Restricted element selection in the distance matrix makes "mDistEn" a computationally inexpensive and physiologically more relevant complexity measure in comparison to DistEn.

Suppressing the Influence of Ectopic Beats by Applying a Physical Threshold-Based Sample Entropy

Sample entropy (SampEn) is widely used for electrocardiogram (ECG) signal analysis to quantify the inherent complexity or regularity of RR interval time series (i.e., heart rate variability (HRV)), with the hypothesis that RR interval time series in pathological conditions output lower SampEn values. However, ectopic beats can significantly influence the entropy values, resulting in difficulty in distinguishing the pathological situation from normal situations. Although a theoretical operation is to exclude the ectopic intervals during HRV analysis, it is not easy to identify all of them in practice, especially for the dynamic ECG signal. Thus, it is important to suppress the influence of ectopic beats on entropy results, i.e., to improve the robustness and stability of entropy measurement for ectopic beats-inserted RR interval time series. In this study, we introduced a physical threshold-based SampEn method, and tested its ability to suppress the influence of ectopic beats for HRV analysis. An experiment on the PhysioNet/MIT RR Interval Databases showed that the SampEn use physical meaning threshold has better performance not only for different data types (normal sinus rhythm (NSR) or congestive heart failure (CHF) recordings), but also for different types of ectopic beat (atrial beats, ventricular beats or both), indicating that using a physical meaning threshold makes SampEn become more consistent and stable.

Cross Entropy Profiling to Test Pattern Synchrony in Short-Term Signals

Examining nonlinear bi-variate time series for pattern synchrony has been largely carried out by the cross sample entropy measure, X-SampEn, which is highly bound by parametric restrictions. Threshold parameter r is the one that limits X-SampEn estimations most adversely. An inappropriate r choice leads to erroneous synchrony detection, even for the case of X-SampEn analysis on simple synthetically generated signals like the MIX(P) process. This gives us an intimation of how difficult it would be for such synchrony measures to handle the more complex physiologic data. The recently introduced concept of entropy profiling has been proved to release such measures from the clutches of r dependence. In this study, we demonstrate how entropy profiling with respect to r can be implemented on cross entropy analysis, particularly X-SampEn. We have used different sets of simple MIX(P) processes for the purpose and validated the impact of X-SampEn profiling over X-SampEn estimation, with a special focus on short-term data. From results, we see that X-SampEn profiling alone can accurately classify MIX(P) signals based on pattern synchrony. Here, X-SampEn estimation fails undoubtedly, even at the higher data lengths where traditional SampEn estimation is known to perform with good accuracy.

Entropy Profiling to Detect ST Change in Heart Rate Variability Signals

Elevation or depression in an electrocardiographic ST segment is an important indication of cardiac Ischemia. Computer-aided algorithms have been proposed in the recent past for the detection of ST change in ECG signals. Such algorithms are accompanied by difficulty in locating a functional ST segment from the ECG. Laborious signal processing tasks have to be carried out in order to precisely locate the start and end of an ST segment. In this work, we propose to detect ST change from heart rate variability (HRV) or RR-interval signals, rather than the ECG itself. Since HRV analysis does not require ST segment localization, we hypothesize an easier and more accurate automated ST change detection here. We use the recent concept of entropy profiling to detect ST change from RR interval data, where the estimation corresponds to irregularity information contained in the respective signals. We have compared results of SampEn, FuzzyEn and TotalSampEn (entropy profiling) on 18 normal and 28 ST-changed RR interval signals. SampEn and FuzzyEn give maximum AUCs of 0.64 and 0.62 respectively, at the data length N = 750. T otalSampEn shows a maximum AUC of 0.92 at N = 50, clearly proving its effectiveness on short-term signals and an AUC of 0.88 at N = 750, proving its efficiency over SampEn and F uzzyEn.

Slope Entropy: A New Time Series Complexity Estimator Based on Both Symbolic Patterns and Amplitude Information

The development of new measures and algorithms to quantify the entropy or related concepts of a data series is a continuous effort that has brought many innovations in this regard in recent years. The ultimate goal is usually to find new methods with a higher discriminating power, more efficient, more robust to noise and artifacts, less dependent on parameters or configurations, or any other possibly desirable feature. Among all these methods, Permutation Entropy (PE) is a complexity estimator for a time series that stands out due to its many strengths, with very few weaknesses. One of these weaknesses is the PE’s disregarding of time series amplitude information. Some PE algorithm modifications have been proposed in order to introduce such information into the calculations. We propose in this paper a new method, Slope Entropy (SlopEn), that also addresses this flaw but in a different way, keeping the symbolic representation of subsequences using a novel encoding method based on the slope generated by two consecutive data samples. By means of a thorough and extensive set of comparative experiments with PE and Sample Entropy (SampEn), we demonstrate that SlopEn is a very promising method with clearly a better time series classification performance than those previous methods.

EEG Complexity Maps to Characterise Brain Dynamics during Upper Limb Motor Imagery

The Electroencephalogram (EEG) can be considered as the output of a nonlinear system whose dynamics is significantly affected by motor tasks. Nevertheless, computational approaches derived from the complex system theory has not been fully exploited for characterising motor imagery tasks. To this extent, in this study we investigated EEG complexity changes throughout the following categories of imaginary motor tasks of the upper limb: transitive (actions involving an object), intransitive (meaningful gestures that do not include the use of objects), and tool-mediated (actions using an object to interact with another one). EEG irregularity was quantified following the definition of Fuzzy Entropy, which has been demonstrated to be a reliable quantifier of system complexity with low dependence on data length. Experimental results from paired statistical analyses revealed minor topographical changes between EEG complexity associated with transitive and tool-mediated tasks, whereas major significant differences were shown between the intransitive actions vs. the others. Our results suggest that EEG complexity level during motor imagery tasks of the upper limb are strongly biased by the presence of an object.

Comparison of QT interval variability of coronary patients without myocardial infarction with that of patients with old myocardial infarction

BACKGROUND

The significant association of myocardial ischemia with elevated QT interval variability (QTV) has been reported in myocardial infarction (MI) patients. However, the influence of the time course of MI on QTV has not been investigated systematically.

METHOD

Short-term QT and RR interval time series were constructed from the 5 min electrocardiograms of 49 coronary patients without MI and 26 patients with old MI (OMI). The QTV, heart rate variability (HRV), and QT-RR coupling of the two groups were analyzed using various time series analysis tools in the time- and frequency-domains, as well as nonlinear dynamics.

RESULTS

Nearly all of the tested QTV indices for coronary patients with OMI were higher than those for patients without MI. However, no significant differences were found between the two groups in any of the variables employed to assess the HRV and QT-RR coupling. All of the markers that showed statistical significances in univariate analyses still possessed the capabilities of distinguishing between the two groups even after adjusting for studied baseline characteristics, including the coronary atherosclerotic burden.

CONCLUSIONS

The results suggested that the QTV increased in coronary patients with OMI compared to those without MI, which might reflect the influence of post-MI remodeling on the beat-to-beat temporal variability of ventricular repolarization. The non-significant differences in the HRV and QT-RR couplings could indicate that there were no differences in the modulation of the autonomic nervous system and interaction of QT with the RR intervals between the two groups.

A New Physically Meaningful Threshold of Sample Entropy for Detecting Cardiovascular Diseases

Sample Entropy (SampEn) is a popular method for assessing the regularity of physiological signals. Prior to the entropy calculation, certain common parameters need to be initialized: Embedding dimension m, tolerance threshold r and time series length N. Nevertheless, the determination of these parameters is usually based on expert experience. Improper assignments of these parameters tend to bring invalid values, inconsistency and low statistical significance in entropy calculation. In this study, we proposed a new tolerance threshold with physical meaning (rp), which was based on the sampling resolution of physiological signals. Statistical significance, percentage of invalid entropy values and ROC curve were used to evaluate the proposed rp against the traditional threshold (rt). Normal sinus rhythm (NSR), congestive heart failure (CHF) as well as atrial fibrillation (AF) RR interval recordings from Physionet were used as the test data. The results demonstrated that the proposed rp had better stability than rt, hence more adaptive to detect cardiovascular diseases of CHF and AF.

Effects of spinal cord stimulation on heart rate variability in patients with Failed Back Surgery Syndrome

Background

Building on the recent finding that chronic pain patients with impaired functioning of the descending nociceptive inhibitory system (DNIS) present lower resting heart rate variability (HRV), this study aims to investigate the impact of Spinal Cord Stimulation (SCS) on HRV in patients with Failed Back Surgery Syndrome (FBSS). More precisely, we hypothesize that SCS influences the DNIS, with increased parasympathetic tone as a consequence, as measurable by HRV analysis.

Methods

Twenty-two patients diagnosed with FBSS and treated with SCS participated in this study. HRV was measured with a 2-lead ECG registration tool during on and off states of SCS. HRV analysis for time, frequency, time-frequency and nonlinear domain parameters was based on a 5-minute recording segment.

Results

The mean heart rate and low frequency power were significantly lower when SCS was activated. HRV, absolute and normalized high frequency power significantly increased during SCS compared to without SCS. The ratio of low frequency/high frequency ratios, as parameter for global sympathetic-parasympathetic equilibrium, significantly decreased when SCS was activated.

Conclusions

When SCS is switched off, patients with FBSS present relatively stronger sympathetic tone and weaker parasympathetic activity. Activation of the SCS, possibly via stimulation of the DNIS, restores this disbalance of autonomic activity.

Renyi Distribution Entropy Analysis of Short-Term Heart Rate Variability Signals and Its Application in Coronary Artery Disease Detection

Coronary artery disease (CAD) is a life-threatening condition that, unless treated at an early stage, can lead to congestive heart failure, ischemic heart disease, and myocardial infarction. Early detection of diagnostic features underlying electrocardiography signals is crucial for the identification and treatment of CAD. In the present work, we proposed novel entropy called Renyi Distribution Entropy (RdisEn) for the analysis of short-term heart rate variability (HRV) signals and the detection of CAD. Our simulation experiment with synthetic, physiological, and pathological signals demonstrated that RdisEn could distinguish effectively among different subject groups. Compared to the values of sample entropy or approximation entropy, the RdisEn value was less affected by the parameter choice, and it remained stable even in short-term HRV. We have developed a combined CAD detection scheme with RdisEn and wavelet packet decomposition (WPD): (1) Normal and CAD HRV beats obtained were divided into two equal parts. (2) Feature acquisition: RdisEn and WPD-based statistical features were calculated from one part of HRV beats, and student’s t-test was performed to select clinically significant features. (3) Classification: selected features were computed from the remaining part of HRV beats and fed into K-nearest neighbor and support vector machine, to separate CAD from normal subjects. The proposed scheme automatically detected CAD with 97.5% accuracy, 100% sensitivity and 95% specificity and performed better than most of the existing schemes.

Entropy Measures as Descriptors to Identify Apneas in Rheoencephalographic Signals

Rheoencephalography (REG) is a simple and inexpensive technique that intends to monitor cerebral blood flow (CBF), but its ability to reflect CBF changes has not been extensively proved. Based on the hypothesis that alterations in CBF during apnea should be reflected in REG signals under the form of increased complexity, several entropy metrics were assessed for REG analysis during apnea and resting periods in 16 healthy subjects: approximate entropy (ApEn), sample entropy (SampEn), fuzzy entropy (FuzzyEn), corrected conditional entropy (CCE) and Shannon entropy (SE). To compute these entropy metrics, a set of parameters must be defined a priori, such as, for example, the embedding dimension m, and the tolerance threshold r. A thorough analysis of the effects of parameter selection in the entropy metrics was performed, looking for the values optimizing differences between apnea and baseline signals. All entropy metrics, except SE, provided higher values for apnea periods (p-values < 0.025). FuzzyEn outperformed all other metrics, providing the lowest p-value (p = 0.0001), allowing to conclude that REG signals during apnea have higher complexity than in resting periods. Those findings suggest that REG signals reflect CBF changes provoked by apneas, even though further studies are needed to confirm this hypothesis.

Embedded Dimension and Time Series Length. Practical Influence on Permutation Entropy and Its Applications

Permutation Entropy (PE) is a time series complexity measure commonly used in a variety of contexts, with medicine being the prime example. In its general form, it requires three input parameters for its calculation: time series length N, embedded dimension m, and embedded delay τ. Inappropriate choices of these parameters may potentially lead to incorrect interpretations. However, there are no specific guidelines for an optimal selection of N, m, or τ, only general recommendations such as N>>m!, τ=1, or m=3,…,7. This paper deals specifically with the study of the practical implications of N>>m!, since long time series are often not available, or non-stationary, and other preliminary results suggest that low N values do not necessarily invalidate PE usefulness. Our study analyses the PE variation as a function of the series length N and embedded dimension m in the context of a diverse experimental set, both synthetic (random, spikes, or logistic model time series) and real–world (climatology, seismic, financial, or biomedical time series), and the classification performance achieved with varying N and m. The results seem to indicate that shorter lengths than those suggested by N>>m! are sufficient for a stable PE calculation, and even very short time series can be robustly classified based on PE measurements before the stability point is reached. This may be due to the fact that there are forbidden patterns in chaotic time series, not all the patterns are equally informative, and differences among classes are already apparent at very short lengths.

Magnetotelluric Signal-Noise Identification and Separation Based on ApEn-MSE and StOMP

Natural magnetotelluric signals are extremely weak and susceptible to various types of noise pollution. To obtain more useful magnetotelluric data for further analysis and research, effective signal-noise identification and separation is critical. To this end, we propose a novel method of magnetotelluric signal-noise identification and separation based on ApEn-MSE and Stagewise orthogonal matching pursuit (StOMP). Parameters with good irregularity metrics are introduced: Approximate entropy (ApEn) and multiscale entropy (MSE), in combination with k-means clustering, can be used to accurately identify the data segments that are disturbed by noise. Stagewise orthogonal matching pursuit (StOMP) is used for noise suppression only in data segments identified as containing strong interference. Finally, we reconstructed the signal. The results show that the proposed method can better preserve the low-frequency slow-change information of the magnetotelluric signal compared with just using StOMP, thus avoiding the loss of useful information due to over-processing, while producing a smoother and more continuous apparent resistivity curve. Moreover, the results more accurately reflect the inherent electrical structure information of the measured site itself.

Short-term QT interval variability in patients with coronary artery disease and congestive heart failure: a comparison with healthy control subjects

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. Graphical abstract Fig. The framework of this paper. The arrows show the sequential analysis of the data.

Predicting delayed cerebral ischemia after subarachnoid hemorrhage using physiological time series data

To develop and validate a prediction model for delayed cerebral ischemia (DCI) after subarachnoid hemorrhage (SAH) using a temporal unsupervised feature engineering approach, demonstrating improved precision over standard features. 488 consecutive SAH admissions from 2006 to 2014 to a tertiary care hospital were included. Models were trained on 80%, while 20% were set aside for validation testing. Baseline information and standard grading scales were evaluated: age, sex, Hunt Hess grade, modified Fisher Scale (mFS), and Glasgow Coma Scale (GCS). An unsupervised approach applying random kernels was used to extract features from physiological time series (systolic and diastolic blood pressure, heart rate, respiratory rate, and oxygen saturation). Classifiers (Partial Least Squares, linear and kernel Support Vector Machines) were trained on feature subsets of the derivation dataset. Models were applied to the validation dataset. The performances of the best classifiers on the validation dataset are reported by feature subset. Standard grading scale (mFS): AUC 0.58. Combined demographics and grading scales: AUC 0.60. Random kernel derived physiologic features: AUC 0.74. Combined baseline and physiologic features with redundant feature reduction: AUC 0.77. Current DCI prediction tools rely on admission imaging and are advantageously simple to employ. However, using an agnostic and computationally inexpensive learning approach for high-frequency physiologic time series data, we demonstrated that our models achieve higher classification accuracy.

Incorporating High-Frequency Physiologic Data Using Computational Dictionary Learning Improves Prediction of Delayed Cerebral Ischemia Compared to Existing Methods

Purpose

Accurate prediction of delayed cerebral ischemia (DCI) after subarachnoid hemorrhage (SAH) can be critical for planning interventions to prevent poor neurological outcome. This paper presents a model using convolution dictionary learning to extract features from physiological data available from bedside monitors. We develop and validate a prediction model for DCI after SAH, demonstrating improved precision over standard methods alone.

Methods

488 consecutive SAH admissions from 2006 to 2014 to a tertiary care hospital were included. Models were trained on 80%, while 20% were set aside for validation testing. Modified Fisher Scale was considered the standard grading scale in clinical use; baseline features also analyzed included age, sex, Hunt-Hess, and Glasgow Coma Scales. An unsupervised approach using convolution dictionary learning was used to extract features from physiological time series (systolic blood pressure and diastolic blood pressure, heart rate, respiratory rate, and oxygen saturation). Classifiers (partial least squares and linear and kernel support vector machines) were trained on feature subsets of the derivation dataset. Models were applied to the validation dataset.

Results

The performances of the best classifiers on the validation dataset are reported by feature subset. Standard grading scale (mFS): AUC 0.54. Combined demographics and grading scales (baseline features): AUC 0.63. Kernel derived physiologic features: AUC 0.66. Combined baseline and physiologic features with redundant feature reduction: AUC 0.71 on derivation dataset and 0.78 on validation dataset.

Conclusion

Current DCI prediction tools rely on admission imaging and are advantageously simple to employ. However, using an agnostic and computationally inexpensive learning approach for high-frequency physiologic time series data, we demonstrated that we could incorporate individual physiologic data to achieve higher classification accuracy.

Understanding Irregularity Characteristics of Short-Term HRV Signals Using Sample Entropy Profile

Sample entropy (), a popularly used "regularity analysis" tool, has restrictions in handling short-term segments (largely ) of heart rate variability (HRV) data. For such short signals, the estimate either remains undefined or fails to retrieve "accurate" regularity information. These limitations arise due to the extreme dependence of on its functional parameters, in particular the tolerance . Evaluating at a single random choice of parameter is a major cause of concern in being able to extract reliable and complete regularity information from a given signal. Here, we hypothesize that, finding a complete profile of (in contrast to a single estimate) corresponding to a data specific set of values may facilitate enhanced information retrieval from short-term signals. We introduce a novel and computationally efficient concept of profiling in order to eliminate existing inaccuracies seen in the case of estimation. Using three different HRV datasets from the PhysioNet database-first, real and simulated, second, elderly and young, and third, healthy and arrhythmic; we demonstrate better definiteness and classification performance of profile based estimates ( and ) when compared to conventional and estimates. Our novelty is to identify the importance of reliability in short-term signal regularity analysis, and our proposed approach aims to enhance both quality and quantity of information from any short-term signal.

Stability, Consistency and Performance of Distribution Entropy in Analysing Short Length Heart Rate Variability (HRV) Signal

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 analyzed 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.

Early warnings of heart rate deterioration

Hospitals can experience difficulty in detecting and responding to early signs of patient deterioration leading to late intensive care referrals, excess mortality and morbidity, and increased hospital costs. Our study aims to explore potential indicators of physiological deterioration by the analysis of vital-signs. The dataset used comprises heart rate (HR) measurements from MIMIC II waveform database, taken from six patients admitted to the Intensive Care Unit (ICU) and diagnosed with severe sepsis. Different indicators were considered: 1) generic early warning indicators used in ecosystems analysis (autocorrelation at-1-lag (ACF1), standard deviation (SD), skewness, kurtosis and heteroskedasticity) and 2) entropy analysis (kernel entropy and multi scale entropy). Our preliminary findings suggest that when a critical transition is approaching, the equilibrium state changes what is visible in the ACF1 and SD values, but also by the analysis of the entropy. Entropy allows to characterize the complexity of the time series during the hospital stay and can be used as an indicator of regime shifts in a patient's condition. One of the main problems is its dependency of the scale used. Our results demonstrate that different entropy scales should be used depending of the level of entropy verified.

Influence of embedding dimension on distribution entropy in analyzing heart rate variability

Distribution entropy (DistEn) is a recent measure of complexity that is used to analyze Heart Rate Variability (HRV) data. DistEn which is a function of data length N, number of bins M and embedding dimension m is known to be stable and consistent with respect to parameters N and M respectively. Also, (N, M) are known to have a combined effect in deciding performance of DistEn as a classification feature. But, all such analysis have mostly ignored the influence of the third parameter m on DistEn properties. Though a random fixed choice of m value has so far succeeded in portraying the effect of other parameters on DistEn, it is considered equally important to reveal the influence of a varying m on DistEn and its characteristics. This study examines the impact of m on the stability, consistency and performance of DistEn when the latter is used to analyze HRV data belonging to (i) healthy subjects discerned by age and (ii) subjects discerned by their heart's physiologic condition. Here, data length N of each signal is varied from 50 to 1000, while the number of bins M used varies from 100 to 2000. Information pertaining to m variations is obtained by carrying out experiments at four different values of embedding dimension; m = 2, 3,4 and 5. The study shows that the stability, consistency and classification performance of DistEn is not much influenced by changes in m.

Noisy EEG signals classification based on entropy metrics. Performance assessment using first and second generation statistics

This paper evaluates the performance of first generation entropy metrics, featured by the well known and widely used Approximate Entropy (ApEn) and Sample Entropy (SampEn) metrics, and what can be considered an evolution from these, Fuzzy Entropy (FuzzyEn), in the Electroencephalogram (EEG) signal classification context. The study uses the commonest artifacts found in real EEGs, such as white noise, and muscular, cardiac, and ocular artifacts. Using two different sets of publicly available EEG records, and a realistic range of amplitudes for interfering artifacts, this work optimises and assesses the robustness of these metrics against artifacts in class segmentation terms probability. The results show that the qualitative behaviour of the two datasets is similar, with SampEn and FuzzyEn performing the best, and the noise and muscular artifacts are the most confounding factors. On the contrary, there is a wide variability as regards initialization parameters. The poor performance achieved by ApEn suggests that this metric should not be used in these contexts.

Aging and cardiovascular complexity: effect of the length of RR tachograms

As we age, our hearts undergo changes that result in a reduction in complexity of physiological interactions between different control mechanisms. This results in a potential risk of cardiovascular diseases which are the number one cause of death globally. Since cardiac signals are nonstationary and nonlinear in nature, complexity measures are better suited to handle such data. In this study, three complexity measures are used, namely Lempel-Ziv complexity (LZ), Sample Entropy (SampEn) and Effort-To-Compress (ETC). We determined the minimum length of RR tachogram required for characterizing complexity of healthy young and healthy old hearts. All the three measures indicated significantly lower complexity values for older subjects than younger ones. However, the minimum length of heart-beat interval data needed differs for the three measures, with LZ and ETC needing as low as 10 samples, whereas SampEn requires at least 80 samples. Our study indicates that complexity measures such as LZ and ETC are good candidates for the analysis of cardiovascular dynamics since they are able to work with very short RR tachograms.

Effect of embedding dimension on complexity measures in identifying Arrhythmia

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., m = 2, 3,4 and 5. Normal and Arrhythmic RR intervals taken at data lengths ranging from 50 to 1000 have been used for the purpose. At any choice of m, DistEn and PE are the best measures to classify Arrhythmic data, whose AUC (Area under the ROC curve) values can go as high as 0.94 and 1 respectively. However PE performance becomes unstable with N for m > 3 (highest Δ being 0.3 at m = 5, Δ being the difference between minimum and maximum AUC). Irrespective of the choice of m, DistEn performance remains the most efficient and stable (highest Δ being only 0.03 at m = 4) for Arrhythmia classification. In the case of all other entropy measures, it is recommended that the value of m be chosen with discretion to ensure stability and efficiency in classification performance.

Assessing heart rate variability through wavelet-based statistical measures

Because of its utility in the investigation and diagnosis of clinical abnormalities, heart rate variability (HRV) has been quantified with both time and frequency analysis tools. Recently, time-frequency methods, especially wavelet transforms, have been applied to HRV. In the current study, a complementary computational approach is proposed wherein continuous wavelet transforms are applied directly to ECG signals to quantify time-varying frequency changes in the lower bands. Such variations are compared for resting and lower body negative pressure (LBNP) conditions using statistical and information-theoretic measures, and compared with standard HRV metrics. The latter confirm the expected lower variability in the LBNP condition due to sympathetic nerve activity (e.g. RMSSD: p=0.023; SDSD: p=0.023; LF/HF: p=0.018). Conversely, using the standard Morlet wavelet and a new transform based on windowed complex sinusoids, wavelet analysis of the ECG within the observed range of heart rate (0.5-1.25Hz) exhibits significantly higher variability, as measured by frequency band roughness (Morlet CWT: p=0.041), entropy (Morlet CWT: p=0.001), and approximate entropy (Morlet CWT: p=0.004). Consequently, this paper proposes that, when used with well-established HRV approaches, time-frequency analysis of ECG can provide additional insights into the complex phenomenon of heart rate variability.

Reprint of 'A nonlinear parameterization of multivariate electrohysterographical signals'

Electrohysterography is a technique which measures a bioelectrical activity of a uterus. This paper presents an application of a nonlinear parameterization of multivariate electrohysterographical signals for a uterine activity assessment to improve unsatisfactory a labor prediction accuracy by methods published in literature. A multivariate sample entropy used for differentiated 4-channel electrohysterographical signals, general Spearman's correlation and a combined index being the sum of them, were tested. These nonlinear measures use joint information contained in a multivariate signal. The results confirm that the combined index provides the best assessment of uterine contractions: 87% sensitivity and 50% specificity of labor prediction in the studied data. These results should be verified in a prospective study.

Machine Learning and Decision Support in Critical Care

Clinical data management systems typically provide caregiver teams with useful information, derived from large, sometimes highly heterogeneous, data sources that are often changing dynamically. Over the last decade there has been a significant surge in interest in using these data sources, from simply re-using the standard clinical databases for event prediction or decision support, to including dynamic and patient-specific information into clinical monitoring and prediction problems. However, in most cases, commercial clinical databases have been designed to document clinical activity for reporting, liability and billing reasons, rather than for developing new algorithms. With increasing excitement surrounding "secondary use of medical records" and "Big Data" analytics, it is important to understand the limitations of current databases and what needs to change in order to enter an era of "precision medicine." This review article covers many of the issues involved in the collection and preprocessing of critical care data. The three challenges in critical care are considered: compartmentalization, corruption, and complexity. A range of applications addressing these issues are covered, including the modernization of static acuity scoring; on-line patient tracking; personalized prediction and risk assessment; artifact detection; state estimation; and incorporation of multimodal data sources such as genomic and free text data.

Distribution Entropy (DistEn): A complexity measure to detect arrhythmia from short length RR interval time series

Heart rate complexity analysis is a powerful non-invasive means to diagnose several cardiac ailments. Non-linear tools of complexity measurement are indispensable in order to bring out the complete non-linear behavior of Physiological signals. The most popularly used non-linear tools to measure signal complexity are the entropy measures like Approximate entropy (ApEn) and Sample entropy (SampEn). But, these methods become unreliable and inaccurate at times, in particular, for short length data. Recently, a novel method of complexity measurement called Distribution Entropy (DistEn) was introduced, which showed reliable performance to capture complexity of both short term synthetic and short term physiologic data. This study aims to i) examine the competence of DistEn in discriminating Arrhythmia from Normal sinus rhythm (NSR) subjects, using RR interval time series data; ii) explore the level of consistency of DistEn with data length N; and iii) compare the performance of DistEn with ApEn and SampEn. Sixty six RR interval time series data belonging to two groups of cardiac conditions namely `Arrhythmia' and `NSR' have been used for the analysis. The data length N was varied from 50 to 1000 beats with embedding dimension m = 2 for all entropy measurements. Maximum ROC area obtained using ApEn, SampEn and DistEn were 0.83, 0.86 and 0.94 for data length 1000, 1000 and 500 beats respectively. The results show that DistEn undoubtedly exhibits a consistently high performance as a classification feature in comparison with ApEn and SampEn. Therefore, DistEn shows a promising behavior as bio marker for detecting Arrhythmia from short length RR interval data.

Effect of data length and bin numbers on distribution entropy (DistEn) measurement in analyzing healthy aging

Complexity analysis of a given time series is executed using various measures of irregularity, the most commonly used being Approximate entropy (ApEn), Sample entropy (SampEn) and Fuzzy entropy (FuzzyEn). However, the dependence of these measures on the critical parameter of tolerance `r' leads to precarious results, owing to random selections of r. Attempts to eliminate the use of r in entropy calculations introduced a new measure of entropy namely distribution entropy (DistEn) based on the empirical probability distribution function (ePDF). DistEn completely avoids the use of a variance dependent parameter like r and replaces it by a parameter M, which corresponds to the number of bins used in the histogram to calculate it. When tested for synthetic data, M has been observed to produce a minimal effect on DistEn as compared to the effect of r on other entropy measures. Also, DistEn is said to be relatively stable with data length (N) variations, as far as synthetic data is concerned. However, these claims have not been analyzed for physiological data. Our study evaluates the effect of data length N and bin number M on the performance of DistEn using both synthetic and physiologic time series data. Synthetic logistic data of `Periodic' and `Chaotic' levels of complexity and 40 RR interval time series belonging to two groups of healthy aging population (young and elderly) have been used for the analysis. The stability and consistency of DistEn as a complexity measure as well as a classifier have been studied. Experiments prove that the parameters N and M are more influential in deciding the efficacy of DistEn performance in the case of physiologic data than synthetic data. Therefore, a generalized random selection of M for a given data length N may not always be an appropriate combination to yield good performance of DistEn for physiologic data.

Analysis of short-term heart rate and diastolic period variability using a refined fuzzy entropy method

BACKGROUND

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.

METHODS

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 [Formula: see text] 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.

RESULTS

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).

CONCLUSIONS

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.

Complex nonlinear autonomic nervous system modulation link cardiac autonomic neuropathy and peripheral vascular disease

BACKGROUND

Physiological interactions are abundant within, and between, body systems. These interactions may evolve into discrete states during pathophysiological processes resulting from common mechanisms. An association between arterial stenosis, identified by low ankle-brachial pressure index (ABPI) and cardiovascular disease (CVD) as been reported. Whether an association between vascular calcification-characterized by high ABPI and a different pathophysiology-is similarly associated with CVD, has not been established. The current study aims to investigate the association between ABPI, and cardiac rhythm, as an indicator of cardiovascular health and functionality, utilizing heart rate variability (HRV).

METHODS AND RESULTS

Two hundred and thirty six patients underwent ABPI assessment. Standard time and frequency domain, and non-linear HRV measures were determined from 5-min electrocardiogram. ABPI data were divided into normal (n = 101), low (n = 67) and high (n = 66) and compared to HRV measures.(DFAα1 and SampEn were significantly different between the low ABPI, high ABPI and control groups (p < 0.05).

CONCLUSION

A possible coupling between arterial stenosis and vascular calcification with decreased and increased HRV respectively was observed. Our results suggest a model for interpreting the relationship between vascular pathophysiology and cardiac rhythm. The cardiovascular system may be viewed as a complex system comprising a number of interacting subsystems. These cardiac and vascular subsystems/networks may be coupled and undergo transitions in response to internal or external perturbations. From a clinical perspective, the significantly increased sample entropy compared to the normal ABPI group and the decreased and increased complex correlation properties measured by DFA for the low and high ABPI groups respectively, may be useful indicators that a more holistic treatment approach in line with this more complex clinical picture is required.