Human heart rate variability, in the form of time series of intervals between heart beats, shows complex, fractal properties. Recently, it was demonstrated many times that the fractal properties vary from point to point along the series, leading to multifractality. In this paper, we concentrate not only on the fact that the human heart rate has multifractal properties but also that these properties depend on the time scale in which the multifractality is measured. This time scale is related to the frequency band of the signal. We find that human heart rate variability appears to be far more complex than hitherto reported in the studies using a fixed time scale. We introduce a method called multiscale multifractal analysis (MMA), which allows us to extend the description of heart rate variability to include the dependence on the magnitude of the variability and time scale (or frequency band). MMA is relatively immune to additive noise and nonstationarity, including the nonstationarity due to inclusions into the time series of events of a different dynamics (e.g., arrhythmic events in sinus rhythm). The MMA method may provide new ways of measuring the nonlinearity of a signal, and it may help to develop new methods of medical diagnostics.

Current gold-standard algorithms for heart beat detection do not work properly in the case of high noise levels and do not make use of multichannel data collected by modern patient monitors. The main idea behind the method presented in this paper is to detect the most prominent part of the QRS complex, i.e. the RS slope. We localize the RS slope based on the consistency of its characteristics, i.e. adequate, automatically determined amplitude and duration. It is a very simple and non-standard, yet very effective, solution. Minor data pre-processing and parameter adaptations make our algorithm fast and noise-resistant. As one of a few algorithms in the PhysioNet/Computing in Cardiology Challenge 2014, our algorithm uses more than two channels (i.e. ECG, BP, EEG, EOG and EMG). Simple fundamental working rules make the algorithm universal: it is able to work on all of these channels with no or only little changes. The final result of our algorithm in phase III of the Challenge was 86.38 (88.07 for a 200 record test set), which gave us fourth place. Our algorithm shows that current standards for heart beat detection could be improved significantly by taking a multichannel approach. This is an open-source algorithm available through the PhysioNet library.

Abstract

No abstract

We propose a model for heart rate variability (HRV) of a healthy individual during sleep with the assumption that the heart rate variability is predominantly a random process. Autonomic nervous system activity has different properties during different sleep stages, and this affects many physiological systems including the cardiovascular system. Different properties of HRV can be observed during each particular sleep stage. We believe that taking into account the sleep architecture is crucial for modeling the human nighttime HRV. The stochastic model of HRV introduced by Kantelhardt et al. was used as the initial starting point. We studied the statistical properties of sleep in healthy adults, analyzing 30 polysomnographic recordings, which provided realistic information about sleep architecture. Next, we generated synthetic hypnograms and included them in the modeling of nighttime RR interval series. The results of standard HRV linear analysis and of nonlinear analysis (Shannon entropy, Poincaré plots, and multiscale multifractal analysis) show that-in comparison with real data-the HRV signals obtained from our model have very similar properties, in particular including the multifractal characteristics at different time scales. The model described in this paper is discussed in the context of normal sleep. However, its construction is such that it should allow to model heart rate variability in sleep disorders. This possibility is briefly discussed.

Objective: Both the central nervous system and the autonomic nervous system are complex physiological networks which modulate the heart rate. They are spatially extended, have built-in delays and work on many time scales simultaneously—nonhomogeneous networks with multifractal dynamics. The object of our research was the analysis of human heart rate variability (HRV) using the nonlinear multiscale multifractal analysis (MMA) method for several cardiovascular diseases. The analysis of HRV (night-time recordings) involved six groups of patients: 61 healthy persons, 104 cases with aortic valve stenosis, 42 with hypertrophic cardiomyopathy, 36 with atrial fibrillation, 70 patients with coronary artery disease and 19 with congestive heart failure. 85% of patients formed a training data set (282 subjects) and 15% formed a test data set (50 subjects). Approach: Multiscale multifractal analysis allows one to analyze the complexity of HRV and find the scaling properties of its fluctuations. The main result of MMA is the Hurst surface, the shape of which changes depending on the medical case analyzed. We prepared six criteria to distinguish a multifractal pattern for healthy subjects. We also prepared additional criteria, enabling one to recognize atrial fibrillation. Main results: For the training data set, we obtained the following accuracy statistics in distinguishing the patients from the healthy: 68% for coronary artery disease, 67% for hypertrophic cardiomyopathy, 88% for atrial fibrillation, 74% for aortic valve stenosis and 83% for congestive heart failure. For the complete training data set we obtained an accuracy of 73%, and 80% for the test data set (mean for ten random selections of the test data set). Significance: The results of MMA presented here provide an additional input into the diagnostic process and may help to create a paradigm for future studies on medical screening methods, especially in that MMA focuses on very low frequencies of HRV not easily accessible by standard medical techniques. Satisfactory statistics for screening using both MMA and the unfiltered version of LF/HF indicate that the nature of the complete network moderating heart rhythm needs to be studied and that sinus rhythm in clinical patients may not always be separated from arrhythmia when its incidence is large.

Objective: U-shaped patterns, characteristic periods of time observed in tachograms, are a specific subgroup among very low frequency components characterized by relatively short periods of smooth accelerations followed by decelerations of heart rhythm. In this study, we characterize this phenomenon and its effect on heart rate variability (HRV) parameters. Approach: We calculated linear (the mean and standard deviation of RR intervals, RMSSD, pNN50 and the power of the frequency components) and nonlinear (V0, V1 and V2 Porta’s symbolic analysis, Shannon and Sample entropy, Guzik’s and Porta’s asymmetry indexes, the exponents α1 and α2 of detrended fluctuation analysis and the Hurst surface h(q,s) of multiscale multifractal analysis (MMA)) HRV parameters for 65 RR interval night-time series (39 females, 37.5(11.3) years old and 26 males, 41.7(16.5) years old; all without organic heart diseases). All parameters were calculated for original data and for the three kinds of test data in which the following parts of the time series were replaced by 1/f noise: (A) the U-shape patterns annotated in a given data set, (B) randomly chosen windows of similar size as the U-shaped patterns, (C) acceleration-deceleration events shorter than U-shaped patterns. Main results: We found that the U-shaped patterns, as the most persistent structures in RR night-time intervals series, affect the long-range correlation properties (measured by α2). We also found that the U-shaped patterns importantly strictly affect the shape of h(q,s) surface at different scales s. Removing the U-shaped patterns results in the shape of the h(q,s) surface losing the properties characteristic for healthy heart rhythm. The largest quantitative effect of U-shaped patterns was obtained for the power of the VLF component. The mean percentage difference of the VLF component between the original data and the A to C type test data were 19.4%, −4.3% and 5.3%, respectively. Significance: Although percentage contribution of U-shaped patterns is small compared to the whole night-time series (on the average 3.1%(1.7%) with a standard deviation of 1.7%), these patterns have a considerable impact on the HRV parameters describing the VLF, persistency, nonlinear correlations and multifractal properties.

An observational error of heart rate variability (HRV) may arise from many factors, such as a limited sampling frequency, QRS complexes detection process, preprocessing procedures and others. In our study, we focused on the first two origins of measurement error. We introduced a model of observational error and suggested universal descriptors for the assessment of its resultant magnitude in terms of time, frequency as well as nonlinear parameters. For this purpose, we applied Monte Carlo simulations which showed that the most sensitive to observational error are: pNN50 (the proportion of pairs of successive RR intervals that differ by more than 50 ms) and markers obtained from frequency analysis. On the other hand, the most resistant are other time domain parameters as well as the short and long-term slopes of Detrended Fluctuation Analysis (DFA). We postulate that the observational error should be considered in population studies, when different recorders are used in the research centres. Additionally, in the case of patients with similar etiology of disease but with different heart rhythms abnormalities the scatter of HRV parameters will also be observed due to the subject's the time series variability.