Cardiac Time Series Research Articles

Improved cross sample entropy with error-metric based cardiac variability time series evaluation

Improved cross sample entropy with error-metric based cardiac variability time series evaluation

Bradycardia May Decrease Cardiorespiratory Coupling in Preterm Infants.

Bradycardia, frequently observed in preterm infants, presents significant risks due to the immaturity of their autonomic nervous system (ANS) and respiratory systems. These infants may face cardiorespiratory events, leading to severe complications like hypoxemia and neurodevelopmental disorders. Although neonatal care has advanced, the influence of bradycardia on cardiorespiratory coupling (CRC) remains elusive. This exploratory study delves into CRC in preterm infants, emphasizing disparities between events with and without bradycardia. Using the Preterm Infant Cardio-Respiratory Signals (PICS) database, we analyzed interbeat (R-R) and inter-breath intervals (IBI) from 10 preterm infants. The time series were segmented into bradycardic (B) and non-bradycardic (NB) segments. Employing information theory measures, we quantified the irregularity of cardiac and respiratory time series. Notably, B segments had significantly lower entropy values for R-R and IBI than NB segments, while mutual information was higher in NB segments. This could imply a reduction in the complexity of respiratory and cardiac dynamics during bradycardic events, potentially indicating weaker CRC. Building on these insights, this research highlights the distinctive physiological characteristics of preterm infants and underscores the potential of emerging non-invasive diagnostic tools.

Information theory-based direct causality measure to assess cardiac fibrillation dynamics.

Understanding the mechanism sustaining cardiac fibrillation can facilitate the personalization of treatment. Granger causality analysis can be used to determine the existence of a hierarchical fibrillation mechanism that is more amenable to ablation treatment in cardiac time-series data. Conventional Granger causality based on linear predictability may fail if the assumption is not met or given sparsely sampled, high-dimensional data. More recently developed information theory-based causality measures could potentially provide a more accurate estimate of the nonlinear coupling. However, despite their successful application to linear and nonlinear physical systems, their use is not known in the clinical field. Partial mutual information from mixed embedding (PMIME) was implemented to identify the direct coupling of cardiac electrophysiology signals. We show that PMIME requires less data and is more robust to extrinsic confounding factors. The algorithms were then extended for efficient characterization of fibrillation organization and hierarchy using clinical high-dimensional data. We show that PMIME network measures correlate well with the spatio-temporal organization of fibrillation and demonstrated that hierarchical type of fibrillation and drivers could be identified in a subset of ventricular fibrillation patients, such that regions of high hierarchy are associated with high dominant frequency.

Information-Theoretic Analysis of Cardio-Respiratory Interactions in Heart Failure Patients: Effects of Arrhythmias and Cardiac Resynchronization Therapy.

The properties of cardio-respiratory coupling (CRC) are affected by various pathological conditions related to the cardiovascular and/or respiratory systems. In heart failure, one of the most common cardiac pathological conditions, the degree of CRC changes primarily depend on the type of heart-rhythm alterations. In this work, we investigated CRC in heart-failure patients, applying measures from information theory, i.e., Granger Causality (GC), Transfer Entropy (TE) and Cross Entropy (CE), to quantify the directed coupling and causality between cardiac (RR interval) and respiratory (Resp) time series. Patients were divided into three groups depending on their heart rhythm (sinus rhythm and presence of low/high number of ventricular extrasystoles) and were studied also after cardiac resynchronization therapy (CRT), distinguishing responders and non-responders to the therapy. The information-theoretic analysis of bidirectional cardio-respiratory interactions in HF patients revealed the strong effect of nonlinear components in the RR (high number of ventricular extrasystoles) and in the Resp time series (respiratory sinus arrhythmia) as well as in their causal interactions. We showed that GC as a linear model measure is not sensitive to both nonlinear components and only model free measures as TE and CE may quantify them. CRT responders mainly exhibit unchanged asymmetry in the TE values, with statistically significant dominance of the information flow from Resp to RR over the opposite flow from RR to Resp, before and after CRT. In non-responders this asymmetry was statistically significant only after CRT. Our results indicate that the success of CRT is related to corresponding information transfer between the cardiac and respiratory signal quantified at baseline measurements, which could contribute to a better selection of patients for this type of therapy.

Visibility Graph Analysis of Heartbeat Time Series: Comparison of Young vs. Old, Healthy vs. Diseased, Rest vs. Exercise, and Sedentary vs. Active.

Using the visibility graph algorithm (VGA), a complex network can be associated with a time series, such that the properties of the time series can be obtained by studying those of the network. Any value of the time series becomes a node of the network, and the number of other nodes that it is connected to can be quantified. The degree of connectivity of a node is positively correlated with its magnitude. The slope of the regression line is denoted by k-M, and, in this work, this parameter was calculated for the cardiac interbeat time series of different contrasting groups, namely: young vs. elderly; healthy subjects vs. patients with congestive heart failure (CHF); young subjects and adults at rest vs. exercising young subjects and adults; and, finally, sedentary young subjects and adults vs. active young subjects and adults. In addition, other network parameters, including the average degree and the average path length, of these time series networks were also analyzed. Significant differences were observed in the k-M parameter, average degree, and average path length for all analyzed groups. This methodology based on the analysis of the three mentioned parameters of complex networks has the advantage that such parameters are very easy to calculate, and it is useful to classify heartbeat time series of subjects with CHF vs. healthy subjects, and also for young vs. elderly subjects and sedentary vs. active subjects.

Analysis of heartbeat time series via machine learning for detection of illnesses

The heart, a component of the cardiovascular system, is responsible for pumping oxygenated and deoxygenated blood. It does not behave like a metronome and normally there is a variation in the duration of the intervals between each heartbeat, called Heart Rate Variability (HRV). In the presence of diseases or with the progression of aging, there is a reduction in HRV due to dysfunction of the autonomic nervous system. The objective of this work is to show, using machine learning techniques, that these techniques are able to relate directly the variability of the heart with the degree of the disease. Producing, as a practical result, the use of these techniques in the prediction of different types of diseases by only analyzing their time series. One of the first techniques used in our work is the unsupervised learning algorithm (t-Stochastic Neighbor Embedding). We show that this algorithm is able to differentiate the type and degree of the disease just by analyzing time series, we demonstrate that it is possible to design a neural network architecture capable of learning these characteristics, relating cardiac variability and the disease. In a complementary analysis, we check that cardiac variability can be directly related to permutation entropy, proving that the healthier an individual is, the more stochastic his cardiac time series is. We build a classification algorithm, using deep learning, from the confusion matrix and the ROC curve. This algorithm can be used as an entry point in diagnosing patients by measuring their HRV.

A machine-learning approach for long-term prediction of experimental cardiac action potential time series using an autoencoder and echo state networks.

Computational modeling and experimental/clinical prediction of the complex signals during cardiac arrhythmias have the potential to lead to new approaches for prevention and treatment. Machine-learning (ML) and deep-learning approaches can be used for time-series forecasting and have recently been applied to cardiac electrophysiology. While the high spatiotemporal nonlinearity of cardiac electrical dynamics has hindered application of these approaches, the fact that cardiac voltage time series are not random suggests that reliable and efficient ML methods have the potential to predict future action potentials. This work introduces and evaluates an integrated architecture in which a long short-term memory autoencoder (AE) is integrated into the echo state network (ESN) framework. In this approach, the AE learns a compressed representation of the input nonlinear time series. Then, the trained encoder serves as a feature-extraction component, feeding the learned features into the recurrent ESN reservoir. The proposed AE-ESN approach is evaluated using synthetic and experimental voltage time series from cardiac cells, which exhibit nonlinear and chaotic behavior. Compared to the baseline and physics-informed ESN approaches, the AE-ESN yields mean absolute errors in predicted voltage 6-14 times smaller when forecasting approximately 20 future action potentials for the datasets considered. The AE-ESN also demonstrates less sensitivity to algorithmic parameter settings. Furthermore, the representation provided by the feature-extraction component removes the requirement in previous work for explicitly introducing external stimulus currents, which may not be easily extracted from real-world datasets, as additional time series, thereby making the AE-ESN easier to apply to clinical data.

A Super Fast Algorithm for Estimating Sample Entropy.

Sample entropy, an approximation of the Kolmogorov entropy, was proposed to characterize complexity of a time series, which is essentially defined as , where B denotes the number of matched template pairs with length m and A denotes the number of matched template pairs with , for a predetermined positive integer m. It has been widely used to analyze physiological signals. As computing sample entropy is time consuming, the box-assisted, bucket-assisted, x-sort, assisted sliding box, and kd-tree-based algorithms were proposed to accelerate its computation. These algorithms require or computational complexity, where N is the length of the time series analyzed. When N is big, the computational costs of these algorithms are large. We propose a super fast algorithm to estimate sample entropy based on Monte Carlo, with computational costs independent of N (the length of the time series) and the estimation converging to the exact sample entropy as the number of repeating experiments becomes large. The convergence rate of the algorithm is also established. Numerical experiments are performed for electrocardiogram time series, electroencephalogram time series, cardiac inter-beat time series, mechanical vibration signals (MVS), meteorological data (MD), and noise. Numerical results show that the proposed algorithm can gain 100–1000 times speedup compared to the kd-tree and assisted sliding box algorithms while providing satisfactory approximate accuracy.

Long-Time Prediction of Arrhythmic Cardiac Action Potentials Using Recurrent Neural Networks and Reservoir Computing.

The electrical signals triggering the heart's contraction are governed by non-linear processes that can produce complex irregular activity, especially during or preceding the onset of cardiac arrhythmias. Forecasts of cardiac voltage time series in such conditions could allow new opportunities for intervention and control but would require efficient computation of highly accurate predictions. Although machine-learning (ML) approaches hold promise for delivering such results, non-linear time-series forecasting poses significant challenges. In this manuscript, we study the performance of two recurrent neural network (RNN) approaches along with echo state networks (ESNs) from the reservoir computing (RC) paradigm in predicting cardiac voltage data in terms of accuracy, efficiency, and robustness. We show that these ML time-series prediction methods can forecast synthetic and experimental cardiac action potentials for at least 15–20 beats with a high degree of accuracy, with ESNs typically two orders of magnitude faster than RNN approaches for the same network size.

An epoch based methodology to denoise magnetocardiogram (MCG) signals and its application to measurements on subjects with implanted devices

Magnetocardiograms (MCG) provide clinically useful diagnostic information in a variety of cardiac dysfunctions. Low frequency baseline drifts and high frequency noise are inevitably present in routine MCG even for those measured inside magnetically shielded rooms. These interferences sometimes exceed subtle cardiac features in MCG recorded on subjects with implanted devices like cardiac pacemakers; this makes interpretation of cardiac magnetic fields difficult. The present study proposes a correlation-based beat-by-beat approach and principal component analysis to eliminate drifts and high frequency noise respectively; the approach is suitable for denoising both single and multi-channel MCG data. The methodology is critically evaluated on simulated noisy measurements using a 37 channel MCG system, when objects such as implantable permanent pacemaker and stainless-steel wire are sequentially kept externally on the chests of five healthy subjects. By characterizing the noise introduced by each of these objects, the deterioration in the quality of MCG and its subsequent restoration by using the proposed method is assessed. The performance of the proposed method is also compared with other conventional denoising techniques namely, bandpass filters, wavelets and ensemble empirical mode decomposition. The proposed method not only exhibits least distortion, but also preserves the beat-by-beat dynamics of cardiac time series. The method has also been illustrated on actual MCG measurements on two subjects with implanted pacemaker which highlight the ability of the proposed method for denoising MCG in general and during extremely noisy measurement situations.

Combining Convolutional Neural Network and Distance Distribution Matrix for Identification of Congestive Heart Failure

Congestive heart failure (CHF) is a serious pathophysiological condition with high morbidity and mortality, which is hard to predict and diagnose in early age. Artificial intelligence and deep learning combining with cardiac rhythms and physiological time series provide a potential to help in solving it. In this paper, we proposed a novel method that combines a convolutional neural network (CNN) and a distance distribution matrix (DDM) in entropy calculation to classify CHF patients from normal subjects, and demonstrated the effectiveness of this combination. Specifically, three entropy methods were used to generate the distribution matrixes from a 300-point RR interval (i.e., the time interval between the successive cardiac cycles) time series, which are Sample entropy, fuzzy local measure entropy, and fuzzy global measure entropy. Then, three high representative CNN models, i.e., AlexNet, DenseNet, and SE_Inception_v4 were chosen to learn the pattern of the data distributions hidden in the generated distribution matrixes. All data used in our experiments were gathered from the MIT-BIH RR Interval Databases ( http://www.physionet.org ). A total of 29 CHF patients and 54 normal sinus rhythm subjects were included in this paper. The results showed that the combination of FuzzyGMEn-generated DDM and Inception_v4 model yielded the highest accuracy of 81.85% out of all proposed combinations.

Cardiac complexity and emotional dysregulation in children

ObjectiveSample entropy (SampEn) gives an estimate of signal complexity in cardiac time series and can give information beyond linear heart rate variability. Lower cardiac SampEn is associated with psychopathology in adults. Emotional dysregulation is widely present in adult psychopathology and a forerunner to later mental problems in children. Therefore, this study investigated whether SampEn relates to emotional dysregulation in children. MethodsParticipants were 32 children between 9 and 13years with internalizing difficulties and 25 controls. Parents filled out the “Emotional Problems” subscale in the Strengths and Difficulties questionnaire and the “Lability/Negativity” scale in the Emotion Regulation Checklist. SampEn, root mean square of successive differences (RMSSD), normalized power of high frequency (HFnu) components of the cardiac signal and pre-ejection period (PEP) were computed at rest. The study investigated the predictive power of SampEn, RMSSD and HFnu on the measures of emotional dysregulation. It also tested whether RMSSD or PEP were related to SampEn. ResultsSampEn was a significant predictor of both measures of emotional dysregulation, while RMSSD and HFnu were not. RMSSD and PEP were both significant predictors of SampEn. ConclusionsSampEn is a potential marker of dysregulation in the underlying neurovisceral processes vital for emotion regulation, and an important complementary measure to linear cardiac indices, explaining more of the variance in emotional dysregulation than RMSSD and HFnu in this study. Lower SampEn can also be linked to both higher vagal and sympathetic activation via RMSSD and PEP.

Increased sample asymmetry and memory of cardiac time-series following endotoxin administration in cirrhotic rats

Sepsis, and other causes of acute systemic inflammation, can reduce heart rate variability (HRV) and increase cardiac cycle regularity in mammals. Thus, HRV monitoring has been used for early detection of sepsis in adults and neonates. Liver cirrhosis is associated with reduced basal HRV and the development of tolerance to the cardiac chronotropic effects of bacterial endotoxin. This may pose limitations on the use of heart rate monitoring in early detection of sepsis in this patient population. In a study to develop a physiomarker for the detection of sepsis in cirrhosis, we observed that endotoxin administration in adult cirrhotic rats leads to the development of transient heart rate decelerations, a phenomenon which has been reported in neonates with sepsis, and quantified using sample asymmetry analysis. In the present study, cirrhosis was induced by surgical ligation of the bile duct in rats. Cirrhotic rats were given intraperitoneal injections of either saline or endotoxin (1 mg kg−1). Changes in sample asymmetry and memory length of cardiac time-series were studied in conscious rats using implanted telemetric probes. Cirrhotic (but not control) rats exhibited increased sample asymmetry following endotoxin injection, which was consistent with the development of transient heart rate deceleration. Endotoxin administration in cirrhotic rats was associated with prolongation of memory length for observing decelerating perturbations in the cardiac rhythm. These findings may have application in the development of an HRV monitoring system for early detection of sepsis in cirrhosis.

The fractal heart - embracing mathematics in the cardiology clinic.

For clinicians grappling with quantifying the complex spatial and temporal patterns of cardiac structure and function (such as myocardial trabeculae, coronary microvascular anatomy, tissue perfusion, myocyte histology, electrical conduction, heart rate, and blood-pressure variability), fractal analysis is a powerful, but still underused, mathematical tool. In this Perspectives article, we explain some fundamental principles of fractal geometry and place it in a familiar medical setting. We summarize studies in the cardiovascular sciences in which fractal methods have successfully been used to investigate disease mechanisms, and suggest potential future clinical roles in cardiac imaging and time series measurements. We believe that clinical researchers can deploy innovative fractal solutions to common cardiac problems that might ultimately translate into advancements for patient care.

Complexity quantification of cardiac variability time series using improved sample entropy (I-SampEn).

The sample entropy (SampEn) has been widely used to quantify the complexity of RR-interval time series. It is a fact that higher complexity, and hence, entropy is associated with the RR-interval time series of healthy subjects. But, SampEn suffers from the disadvantage that it assigns higher entropy to the randomized surrogate time series as well as to certain pathological time series, which is a misleading observation. This wrong estimation of the complexity of a time series may be due to the fact that the existing SampEn technique updates the threshold value as a function of long-term standard deviation (SD) of a time series. However, time series of certain pathologies exhibits substantial variability in beat-to-beat fluctuations. So the SD of the first order difference (short term SD) of the time series should be considered while updating threshold value, to account for period-to-period variations inherited in a time series. In the present work, improved sample entropy (I-SampEn), a new methodology has been proposed in which threshold value is updated by considering the period-to-period variations of a time series. The I-SampEn technique results in assigning higher entropy value to age-matched healthy subjects than patients suffering atrial fibrillation (AF) and diabetes mellitus (DM). Our results are in agreement with the theory of reduction in complexity of RR-interval time series in patients suffering from chronic cardiovascular and non-cardiovascular diseases.

Measuring heart rate variability by means of information entropies based on Choi-Williams distribution.

The Shannon entropy theory was applied to the Choi-Williams time-frequency distribution (CWD) of cardiac time series (RR series) in order to extract entropy information in both time and frequency domains. From this distribution, four indexes were defined: (1) instantaneous partial entropy; (2) spectral partial entropy; (3) instantaneous complete entropy; (4) spectral complete entropy. These indexes were used for analyzing the heart rate variability of ischemic cardiomyopathy patients (ICM) with different sudden cardiac death risk. The results have shown that the values of these indexes tend to decrease, with different proportion, when the severity of pathological condition increases. Statistical differences (p-value < 0.0005) of these indexes were found comparing low risk and high risk of cardiac death during night and between daytime and nighttime periods of ICM patients. Finally, these indexes have demonstrated to be useful tools to quantify the different complex components of the cardiac time series.

Exploring the autonomic correlates of personality.

The aim of this study was to investigate the relationship between personality and resting heart rate variability (HRV) indices. Healthy volunteers (n=106) completed a 240-item Big Five personality inventory, the state/Trait Anxiety inventory, and a ten minute electrocardiographic recording. Time and frequency domain estimates of HRV were derived from the cardiac time series and related to the Big Five dimensions of personality, to personality types extracted from a cluster analysis, and to Trait Anxiety. Frequency domain measures of HRV (HRV-HF, LF/HF) were associated with specific dimensions of personality, but significance was not noted for the time domain measure (STD-RR). Furthermore, distressed personality types exhibited significantly greater autonomic imbalance (LF/HF) than other personality types. However, significance was not noted for the time domain measure (STD-RR). These results can be explained with reference to a contemporary model of neurovisceral integration.

From the time series to the complex networks: The parametric natural visibility graph

We present the modification of natural visibility graph (NVG) algorithm used for the mapping of the time series to the complex networks (graphs). We propose the parametric natural visibility graph (PNVG) algorithm. The PNVG consists of NVG links, which satisfy an additional constraint determined by a newly introduced continuous parameter—the view angle. The alteration of view angle modifies the PNVG and its properties such as the average node degree, average link length of the graph as well as cluster quantity of built graph, etc. We calculated and analyzed different PNVG properties depending on the view angle for different types of the time series such as the random (uncorrelated, correlated and fractal) and cardiac rhythm time series for healthy and ill patients. Investigation of different PNVG properties shows that the view angle gives a new approach to characterize the structure of the time series that are invisible in the conventional version of the algorithm. It is also shown that the PNVG approach allows us to distinguish, identify and describe in detail various time series.

Use of SSA and MCSSA in the Analysis of Cardiac RR Time Series

A new preprocessing procedure in the analysis of cardiac RR interval time series is described. It uses the singular spectrum analysis (SSA) and the Monte Carlo SSA (MCSSA) test. A novel feature of this preprocessing procedure is the ability to identify the noise component present in the series with a given probability and to separate the time series into a trend, signal, and noise. The MCSSA test involves testing whether the modes obtained from SSA can be generated by a noise process leading to separation of the noise modes from the signal. The procedure described here does not discard or modify any sample in the record but merely separates the time series into a trend, signal, and noise, allowing for further analysis of these components. The procedure is not limited to the length of the record and could be applied to nonstationary data. The basis functions used in SSA are data adaptive in that they are not chosen a priori but instead are dependent on the data set used, increasing flexibility to the analysis. The procedure is illustrated using the RR interval time series of a healthy, congestive heart failure, and atrial fibrillation subject.

Evolution of cardiorespiratory interactions with age

We describe an analysis of cardiac and respiratory time series recorded from 189 subjects of both genders aged 16–90. By application of the synchrosqueezed wavelet transform, we extract the respiratory and cardiac frequencies and phases with better time resolution than is possible with the marked events procedure. By treating the heart and respiration as coupled oscillators, we then apply a method based on Bayesian inference to find the underlying coupling parameters and their time dependence, deriving from them measures such as synchronization, coupling directionality and the relative contributions of different mechanisms. We report a detailed analysis of the reconstructed cardiorespiratory coupling function, its time evolution and age dependence. We show that the direct and indirect respiratory modulations of the heart rate both decrease with age, and that the cardiorespiratory coupling becomes less stable and more time-variable.