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.
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.
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