Long-term invariant parameters obtained from 24-h Holter recordings: a comparison between different analysis techniques

Exploring the Short-Term Memory of Heart Rate Variability through Model-Free Information Measures

In this work, we perform a comparative analysis of discrete- and continuous-time estimators of information-theoretic measures quantifying the concept of memory utilization in short-term heart rate variability (HRV). Specifically, considering heartbeat intervals in discrete time we compute the measure of information storage (IS) and decompose it into immediate memory utilization (IMU) and longer memory utilization (MU) terms; considering the timings of heartbeats in continuous time we compute the measure of MU rate (MUR). All measures are computed through model-free approaches based on nearest neighbor entropy estimators applied to the HRV series of a group of 15 healthy subjects measured at rest and during postural stress. We find, moving from rest to stress, statistically significant increases of the IS and the IMU, as well as of the MUR. Our results suggest that both discrete-time and continuous-time approaches can detect the higher predictive capacity of HRV occurring with postural stress, and that such increased memory utilization is due to fast mechanisms likely related to sympathetic activation.

Heart rate variability in different sleep stages is associated with metabolic function and glycemic control in type 2 diabetes mellitus

Introduction: Autonomic nervous system (ANS) plays an important role in the exchange of metabolic information between organs and regulation on peripheral metabolism with obvious circadian rhythm in a healthy state. Sleep, a vital brain phenomenon, significantly affects both ANS and metabolic function. Objectives: This study investigated the relationships among sleep, ANS and metabolic function in type 2 diabetes mellitus (T2DM), to support the evaluation of ANS function through heart rate variability (HRV) metrics, and the determination of the correlated underlying autonomic pathways, and help optimize the early prevention, post-diagnosis and management of T2DM and its complications. Materials and methods: A total of 64 volunteered inpatients with T2DM took part in this study. 24-h electrocardiogram (ECG), clinical indicators of metabolic function, sleep quality and sleep staging results of T2DM patients were monitored. Results: The associations between sleep quality, 24-h/awake/sleep/sleep staging HRV and clinical indicators of metabolic function were analyzed. Significant correlations were found between sleep quality and metabolic function (|r| = 0.386 ± 0.062, p < 0.05); HRV derived ANS function showed strengthened correlations with metabolic function during sleep period (|r| = 0.474 ± 0.100, p < 0.05); HRV metrics during sleep stages coupled more tightly with clinical indicators of metabolic function [in unstable sleep: |r| = 0.453 ± 0.095, p < 0.05; in stable sleep: |r| = 0.463 ± 0.100, p < 0.05; in rapid eye movement (REM) sleep: |r| = 0.453 ± 0.082, p < 0.05], and showed significant associations with glycemic control in non-linear analysis [fasting blood glucose within 24 h of admission (admission FBG), |r| = 0.420 ± 0.064, p < 0.05; glycated hemoglobin (HbA1c), |r| = 0.417 ± 0.016, p < 0.05]. Conclusions: HRV metrics during sleep period play more distinct role than during awake period in investigating ANS dysfunction and metabolism in T2DM patients, and sleep rhythm based HRV analysis should perform better in ANS and metabolic function assessment, especially for glycemic control in non-linear analysis among T2DM patients.

Preliminary Comparison of Zero-Gravity Chair With Tilt Table in Relation to Heart Rate Variability Measurements

Heart rate variability (HRV) measurements are performed using a tilt-table (TT) to diagnose dysfunctionality in the autonomic nervous system (ANS) and the cardiovascular system. To maintain homeostasis, the ANS adapts to body position changes through alterations in sympathetic and parasympathetic responses that can be quantified by extracting time-domain and frequency-domain parameters from the heart rate signal. When body position is changed from supine to erect, a healthy subject’s response also shows changes in ANS activity. However, TT can be unsafe or uncomfortable for elderly or overweight subjects. Furthermore, it may induce anxiety which alters the HRV measurements. This study proposes an alternative strategy to replace the TT with a zero-gravity chair (ZGC). The statistical analysis between HRV parameters from the TT and the ZGC shows that ZGC can be a feasible alternative to TT. Therefore, ZGC can be used as a more convenient, secure, stable and safer option to the traditional HRV analysis with TT.

Model-Based Classification of Heart Rate Variability

Several Heart Rate Variability (HRV) based novel methodologies for describing heart rate dynamics have been proposed in the literature with the aim of risk assessment. One such methodology is ARFIMA-EGARCH modeling which allows the quantification of long range dependence and time-varying volatility with the aim of describing non-linear and complex characteristics of HRV. This study applies the ARFIMA-EGARCH modeling of HRV recordings from 30 patients of the Noltisalis database to investigate the discrimination power of a set of features comprising currently used linear HRV features (low and high frequency components) and new measures obtained from the modeling such as, long memory in the mean, and persistence and asymmetry in volatility. A subset of the multidimensional HRV features is selected in a two-step procedure using Principal Components Analysis (PCA). Additionally, supervised classification by quadratic discriminant analysis achieves 93.3% of discrimination accuracy between the groups using the new feature set created by PCA.

Higuchi Fractal Dimension of Heart Rate Variability During Percutaneous Auricular Vagus Nerve Stimulation in Healthy and Diabetic Subjects

Analysis of heart rate variability (HRV) can be applied to assess the autonomic nervous system (ANS) sympathetic and parasympathetic activity. Since living systems are non-linear, evaluation of ANS activity is difficult by means of linear methods. We propose to apply the Higuchi fractal dimension (HFD) method for assessment of ANS activity. HFD measures complexity of the HRV signal. We analyzed 45 RR time series of 84 min duration each from nine healthy and five diabetic subjects with clinically confirmed long-term diabetes mellitus type II and with diabetic foot ulcer lasting more than 6 weeks. Based on HRV time series complexity analysis we have shown that HFD: (1) discriminates healthy subjects from patients with diabetes mellitus type II; (2) assesses the impact of percutaneous auricular vagus nerve stimulation (pVNS) on ANS activity in normal and diabetic conditions. Thus, HFD may be used during pVNS treatment, to provide stimulation feedback for on-line regulation of therapy in a fast and robust way.

Fractal analysis of heart rate variability as a predictor of mortality: A systematic review and meta-analysis

Previous studies have suggested benefits of applying fractal analysis to intervals between R waves in electrocardiography as an additional prognostic marker. The aim of this study was to investigate whether fractal analysis can provide an independent predictor of cardiac mortality or all-cause mortality. Prognostic cohort studies reporting fractal heart rate variability results from 24-h Holter monitor recordings were selected for comparison. Populations were subdivided into four groups-post-myocardial infarction, left ventricular dysfunction, other cardiac, and non-cardiac patients-and analysed using ANOVA, Forest plots (using pooled mean difference), and Funnel plots. The most significant mean differences were recorded in short-term fractal self-similarity (α₁) (-0.17, 95% CI [-0.21, -0.13], p < 0.00001) and the traditional measure called standard deviation of NN intervals (SDNN) (-13.31, 95% CI [-18.89, -7.73], p < 0.00001) between the deceased and survivor groups. Fractal measures of long-term fractal self-similarity (α₂), 1/f scaling (β), and traditional heart rate variability measures of high frequency to low frequency ratio show promise. This review indicated that fractal measure α₁ and traditional measure SDNN could be potential predictors of mortality, but require further assessment to determine appropriate thresholds for clinical significance and additional targeted prognostic studies to properly define their applicability as prognostic markers. Therefore, clinicians should interpret fractal and traditional measures with caution since such measures have yet to be fully described as biomarkers for clinical application.

Sign and magnitude scaling properties of heart rate variability in patients with end-stage renal failure: Are these properties useful to identify pathophysiological adaptations?

The scaling properties of heart rate variability data are reliable dynamical features to predict mortality and for the assessment of cardiovascular risk. The aim of this manuscript was to determine if the scaling properties, as provided by the sign and magnitude analysis, can be used to differentiate between pathological changes and those adaptations basically introduced by modifications of the mean heart rate in distinct manoeuvres (active standing or hemodialysis treatment, HD), as well as clinical conditions (end stage renal disease, ESRD). We found that in response to active standing, the short-term scaling index (α₁) increased in healthy subjects and in ESRD patients only after HD. The sign short-term scaling exponent (α_1sign) increased in healthy subjects and ESRD patients, showing a less anticorrelated behavior in active standing. Both α₁ and α_1sign did show covariance with the mean heart rate in healthy subjects, while in ESRD patients, this covariance was observed only after HD. A reliable estimation of the magnitude short-term scaling exponent (α_1magn) required the analysis of time series with a large number of samples (>3000 data points). This exponent was similar for both groups and conditions and did not show covariance with the mean heart rate. A surrogate analysis confirmed the presence of multifractal properties (α_1magn > 0.5) in the time series of healthy subjects and ESDR patients. In conclusion, α₁ and α_1sign provided insights into the physiological adaptations during active standing, which revealed a transitory impairment before HD in ESRD patients. The presence of multifractal properties indicated that a reduced short-term variability does not necessarily imply a declined regulatory complexity in these patients.

Effects of guided breath exercise on complex behaviour of heart rate dynamics

INTRODUCTION

Cardiac autonomic regulation is influenced by changes in respiratory rate, which has been demonstrated by linear analysis of heart rate variability (HRV). Conversely, the complex behaviour is not well defined for HRV during this physiological state. In this sense, Higuchi Fractal Dimension is applied directly to the time series. It analyses the fractal dimension of discrete time sequences and is simpler and faster than correlation dimension and many other classical measures derived from chaos theory. We investigated chaotic behaviour of heart rate dynamics during guided breath exercises.

METHOD

We investigated 21 healthy male volunteers aged between 18 and 30 years. HRV was analysed 10 min before and 10 min during guided breath exercises. HRV was analysed in the time and frequency domain for linear analysis and through HFD for non-linear analysis.

RESULTS

Linear analysis indicated that SDNN, pNN50, RMSSD, LF, HF and LF/HF increased during guided breath exercises. HFD analysis illustrated that between K_max 20 to K_max 120 intervals, was enhanced during guided breath exercises.

CONCLUSION

Guided breath exercises acutely increased chaotic behaviour of HRV measured by HFD.

Heart rate dynamics distinguish among atrial fibrillation, normal sinus rhythm and sinus rhythm with frequent ectopy

Atrial fibrillation (AF) is usually detected by inspection of the electrocardiogram waveform, a task made difficult when the signal is distorted by noise. The RR interval time series is more frequently available and accurate, yet linear and nonlinear time series analyses that detect highly varying and irregular AF are vulnerable to the common finding of frequent ectopy. We hypothesized that different nonlinear measures might capture characteristic features of AF, normal sinus rhythm (NSR), and sinus rhythm (SR) with frequent ectopy in ways that linear measures might not. To test this, we studied 2722 patients with 24 h ECG recordings in the University of Virginia Holter database. We found dynamical phenotypes for the three rhythm classifications. As expected, AF records had the highest variability and entropy, and NSR the lowest. SR with ectopy could be distinguished from AF, which had higher entropy, and from NSR, which had different fractal scaling, measured as higher detrended fluctuation analysis slope. With these dynamical phenotypes, we developed successful classification strategies, and the nonlinear measures improved on the use of mean and variability alone, even after adjusting for age. Final models using all variables had excellent performance, with positive predictive values for AF, NSR and SR with ectopy as high as 97, 98 and 90%, respectively. Since these classifiers can reliably detect rhythm changes utilizing segments as short as 10 min, we envision their application in noisy settings and in personal monitoring devices where only RR interval time series may be available.

Advances in heart rate variability signal analysis: joint position statement by the e-Cardiology ESC Working Group and the European Heart Rhythm Association co-endorsed by the Asia Pacific Heart Rhythm Society

Following the publication of the Task Force document on heart rate variability (HRV) in 1996, a number of articles have been published to describe new HRV methodologies and their application in different physiological and clinical studies. This document presents a critical review of the new methods. A particular attention has been paid to methodologies that have not been reported in the 1996 standardization document but have been more recently tested in sufficiently sized populations. The following methods were considered: Long-range correlation and fractal analysis; Short-term complexity; Entropy and regularity; and Nonlinear dynamical systems and chaotic behaviour. For each of these methods, technical aspects, clinical achievements, and suggestions for clinical application were reviewed. While the novel approaches have contributed in the technical understanding of the signal character of HRV, their success in developing new clinical tools, such as those for the identification of high-risk patients, has been rather limited. Available results obtained in selected populations of patients by specialized laboratories are nevertheless of interest but new prospective studies are needed. The investigation of new parameters, descriptive of the complex regulation mechanisms of heart rate, has to be encouraged because not all information in the HRV signal is captured by traditional methods. The new technologies thus could provide after proper validation, additional physiological, and clinical meaning. Multidisciplinary dialogue and specialized courses in the combination of clinical cardiology and complex signal processing methods seem warranted for further advances in studies of cardiac oscillations and in the understanding normal and abnormal cardiac control processes.

Non-Linear Heart Rate Variability Indices in the Frequent Hemodialysis Network Trials of Chronic Hemodialysis Patients

BACKGROUND

Non-linear heart rate variability (HRV) indices were hypothesized to correlate with cardiac function, fluid overload and physical performance in hemodialysis patients.

METHODS

Twenty-four-hour Holter electrocardiograms were recorded in patients enrolled in the Frequent Hemodialysis Network (FHN) Daily Dialysis Trial. Correlations between non-linear HRV indices and left ventricular ejection fraction (LVEF), left ventricular end-diastolic volume (LVEDV), extracellular volume (ECV)/total body water (TBW) ratio, the SF-36 Physical Health Composite (PHC) and Physical Functioning (PF) scores were tested.

RESULTS

We studied 210 subjects (average age 49.8 ± 13.5 years, 62% men, 42% diabetics). In non-diabetic patients, multiscale entropy (MSE) slope sample entropy (SampEn) and approximate entropy (ApEn) correlated positively with LVEF, PF and PHC and inversely with LVEDV and ECV/TBW. Spectral power slope correlated positively with ECV/TBW (r = 0.27). Irregularity measures (MSE ApEn and MSE SampEn) correlated positively with LVEDV (r = 0.19 and 0.20).

CONCLUSION

Non-linear HRV indices indicated an association between a deteriorated heart rate regulatory system and impaired cardiac function, fluid accumulation and poor physical condition.

Beyond long memory in heart rate variability: an approach based on fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity

Heart Rate Variability (HRV) series exhibit long memory and time-varying conditional variance. This work considers the Fractionally Integrated AutoRegressive Moving Average (ARFIMA) models with Generalized AutoRegressive Conditional Heteroscedastic (GARCH) errors. ARFIMA-GARCH models may be used to capture and remove long memory and estimate the conditional volatility in 24 h HRV recordings. The ARFIMA-GARCH approach is applied to fifteen long term HRV series available at Physionet, leading to the discrimination among normal individuals, heart failure patients, and patients with atrial fibrillation.

The rise of hemodialysis machines: new technologies in minimizing cardiovascular complications

Hemodialysis (HD) is a life-saving treatment for more than 1,700,000 patients with chronic kidney disease (CKD) stage V. Every year the HD population becomes increasingly older (average age: 75 years) and more ill due to the associated comorbidities such as cardiovascular disease (heart failure, coronary heart disease and peripheral vascular disease), diabetes, hypertension and peripheral vascular disease. Most of the complications associated with HD involve the cardiovascular system. HD machines have been greatly improved over the last 30 years. We have moved from HD machines simply allowing extracorporeal circulation to high technological medical devices capable of very precisely controlling ultrafiltration, dialysis dose, the patient's core temperature, circulating plasma volume, plasma sodium and producing unlimited volumes of ultrapure dialysate. In this article, we will focus on some of the fundamental achievements in HD machine technology, with particular reference to monitoring tools and bioengineering approaches for biosignal analysis. We propose that along these lines of further development, HD machines in the future will enable a better online identification of patients at higher cardiovascular risk, thus allowing clinicians to select more appropriate treatment modalities and parameters.

Biomedical signal and image processing

Generally, physiological modeling and biomedical signal processing constitute two important paradigms of biomedical engineering (BME): their fundamental concepts are taught starting from undergraduate studies and are more completely dealt with in the last years of graduate curricula, as well as in Ph.D. courses. Traditionally, these two cultural aspects were separated, with the first one more oriented to physiological issues and how to model them and the second one more dedicated to the development of processing tools or algorithms to enhance useful information from clinical data. A practical consequence was that those who did models did not do signal processing and vice versa. However, in recent years,the need for closer integration between signal processing and modeling of the relevant biological systems emerged very clearly [1], [2]. This is not only true for training purposes(i.e., to properly prepare the new professional members of BME) but also for the development of newly conceived research projects in which the integration between biomedical signal and image processing (BSIP) and modeling plays a crucial role. Just to give simple examples, topics such as brain–computer machine or interfaces,neuroengineering, nonlinear dynamical analysis of the cardiovascular (CV) system,integration of sensory-motor characteristics aimed at the building of advanced prostheses and rehabilitation tools, and wearable devices for vital sign monitoring and others do require an intelligent fusion of modeling and signal processing competences that are certainly peculiar of our discipline of BME.

Multiparameter analysis of heart rate variability signal for the investigation of high risk fetuses

The purpose of this study is to evaluate the information content provided by the fluximetry information and the analysis of fetal heart rate (FHR) signals, obtained from cardiotocographic recordings, during prenatal monitoring, in a high risk population. The parameters assessed on FHR signals are divided in: (i) time domain parameters (ii) frequency domain parameters, and (iii) the complexity parameters: Approximate Entropy (ApEn), Sample Entropy (SampEn), Multiscale Entropy (MSE), the Lempel Ziv Complexity (LZC) and the Detrended Fluctuation Analysis (DFA). The fetuses were classified as fetal growth restricted (FGR). The results have shown that the FGR fetuses preterm delivered have produced a markedly reduced heart rate variability in respect with those fetuses which were characterized by an alteration in the fluximetric indices. The normal range in cord blood sampling analysis excludes the prolonged hypoxia as a causing factor. Finally, it seems that the residual cardiovascular response in FGR fetuses could be correlated to an alteration in the flow of the main vessels.

Complexity analysis of the fetal heart rate variability: early identification of severe intrauterine growth-restricted fetuses

The main goal of this work is to suggest new indices for a correct identification of the intrauterine growth-restricted (IUGR) fetuses on the basis of fetal heart rate (FHR) variability analysis performed in the antepartum period. To this purpose, we analyzed 59 FHR time series recorded in early periods of gestation through a Hewlett Packard 1351A cardiotocograph. Advanced analysis techniques were adopted including the computation of the Lempel Ziv complexity (LZC) index and the multiscale entropy (MSE), that is, the entropy estimation with a multiscale approach. A multiparametric classifier based on k-mean cluster analysis was also performed to separate pathological and normal fetuses. The results show that the proposed LZC and the MSE could be useful to identify the actual IUGRs and to separate them from the physiological fetuses, providing good values of sensitivity and accuracy (Se = 77.8%, Ac = 82.4%).

A blind method for the estimation of the Hurst exponent in time series: theory and application

Nowadays many methods for the estimation of self-similarity (Hurst coefficient, H) in time series are available. Most of them, even if very effective, need some a priori information to be applied. We analyzed the eight most used methods for H estimation (working both in time and in frequency). We tested these methods on data generated with four kinds of time series models (fBm and fGn generated iteratively with Feder algorithm, 1f(alpha), and the fractional autoregressive integrated moving-average) in the range 0.1<or=H<or=0.9. We evaluated the performances of each method in terms of accuracy (bias) and precision [standard deviation (STD)] of the deviation from the expected value. The paper proposes a procedure useful for a reliable estimation of H, using these existing methods, without any assumptions on the stationarity/nonstationarity of the time series, where for these types of processes the "nonstationarity" is mainly caused by the divergence of the variance with time. This procedure suggests that one performs, as a first step, the detrended fluctuations analysis, which provides an indication about stationarity of the series and is related to the properties of self-similarity and long correlations. The procedure then identifies the best method for the estimation of H, depending on this first estimation. As an example application, we use our procedure to evaluate the Hurst coefficient in microelectrode array neuronal recordings.

Mapping heart dynamics by using nonlinear indicators

A novel approach for the nonlinear characterization of Electrocardiogram (ECG) signals has been developed. The new developed methodology is based on a numerical algorithm that extracts the value of dinfinity (d-infinite) characterizing the asymptotic chaotic behavior of a system. This algorithm also extracts a measure of the maximum Lyapunov exponent and it is applicable to time series where the knowledge of the system structure and laws is not necessary. In order to prove the significance of the extracted parameters, the presented algorithm was applied on a statistically significant number of ECG signals taken from the MIT-BIH database and including normal subjects and subjects affected by arrhythmia and ventricular arrhythmia. A systematic study, analyzing how dinfinity varies with initial condition was performed showing the sensitivity of such parameter to the initial conditions. Furthermore, two maps, one presenting the maximum Lyapunov exponent and the other the dinfinity versus a control parameter II, as a measure of the rate variation, were drawn using the parameters extracted by the experimental data. They clearly show three distinguishable zones where the normal subjects and the subjects affected by the two different pathologies can be mapped and discriminated. Concluding, the newly presented algorithm, thanks to its implementation features and its effectiveness, it lends itself to future real-time implementation for clinical application in the early diagnosis of cardiac pathologies.

Introduction: Cardiovascular physics

The number of patients suffering from cardiovascular diseases increases unproportionally high with the increase of the human population and aging, leading to very high expenses in the public health system. Therefore, the challenge of cardiovascular physics is to develop high-sophisticated methods which are able to, on the one hand, supplement and replace expensive medical devices and, on the other hand, improve the medical diagnostics with decreasing the patient's risk. Cardiovascular physics-which interconnects medicine, physics, biology, engineering, and mathematics-is based on interdisciplinary collaboration of specialists from the above scientific fields and attempts to gain deeper insights into pathophysiology and treatment options. This paper summarizes advances in cardiovascular physics with emphasis on a workshop held in Bad Honnef, Germany, in May 2005. The meeting attracted an interdisciplinary audience and led to a number of papers covering the main research fields of cardiovascular physics, including data analysis, modeling, and medical application. The variety of problems addressed by this issue underlines the complexity of the cardiovascular system. It could be demonstrated in this Focus Issue, that data analyses and modeling methods from cardiovascular physics have the ability to lead to significant improvements in different medical fields. Consequently, this Focus Issue of Chaos is a status report that may invite all interested readers to join the community and find competent discussion and cooperation partners.