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.

Monitoring the fetal behavior does not only have implications for acute care but also for identifying developmental disturbances that burden the entire later life. The concept, of ‘fetal programming’, also known as ‘developmental origins of adult disease hypothesis’, e.g. applies for cardiovascular, metabolic, hyperkinetic, cognitive disorders. Since the autonomic nervous system is involved in all of those systems, cardiac autonomic control may provide relevant functional diagnostic and prognostic information. The fetal heart rate patterns (HRP) are one of the few functional signals in the prenatal period that relate to autonomic control and, therefore, is predestinated for its evaluation. The development of sensitive markers of fetal maturation and its disturbances requires the consideration of physiological fundamentals, recording technology and HRP parameters of autonomic control. Based on the ESGCO2016 special session on monitoring the fetal maturation we herein report the most recent results on: (i) functional fetal autonomic brain age score (fABAS), Recurrence Quantitative Analysis and Binary Symbolic Dynamics of complex HRP resolve specific maturation periods, (ii) magnetocardiography (MCG) based fABAS was validated for cardiotocography (CTG), (iii) 30 min recordings are sufficient for obtaining episodes of high variability, important for intrauterine growth restriction (IUGR) detection in handheld Doppler, (iv) novel parameters from PRSA to identify Intra IUGR fetuses, (v) evaluation of fetal electrocardiographic (ECG) recordings, (vi) correlation between maternal and fetal HRV is disturbed in pre-eclampsia. The reported novel developments significantly extend the possibilities for the established CTG methodology. Novel HRP indices improve the accuracy of assessment due to their more appropriate consideration of complex autonomic processes across the recording technologies (CTG, handheld Doppler, MCG, ECG). The ultimate objective is their dissemination into routine practice and studies of fetal developmental disturbances with implications for programming of adult diseases.

One of the common routes to chaos is intermittency. Identification of the intermittency type is usually made using the properties of the probability distribution of laminar phases and of the average length of the laminar phases. Both have a statistical character and to obtain them a long time series has to be examined. Here, we present a recurrence plot method applicable to the analysis of short time series and through which the type of intermittency may be identified. The three types of intermittency introduced by Pomeau and Manneville and a chaos-chaos intermittency induced by interior crisis were examined. The identification of the type of intermittency is equivalent to the identification of the bifurcation associated with it. Our result seems particularly interesting as our method allows the analysis of short time series. The effect of the measurement noise on the effectiveness of the method is also discussed. An application of the method to the detection of type I intermittency in measured heart rate variability data is discussed.

A dedicated nonlinear oscillator model able to reproduce the pulse shape, refractory time, and phase sensitivity of the action potential of a natural pacemaker of the heart is developed. The phase space of the oscillator contains a stable node, a hyperbolic saddle, and an unstable focus. The model reproduces several phenomena well known in cardiology, such as certain properties of the sinus rhythm and heart block. In particular, the model reproduces the decrease of heart rate variability with an increase in sympathetic activity. A sinus pause occurs in the model due to a single, well-timed, external pulse just as it occurs in the heart, for example due to a single supraventricular ectopy. Several ways by which the oscillations cease in the system are obtained (models of the asystole). The model simulates properly the way vagal activity modulates the heart rate and reproduces the vagal paradox. Two such oscillators, coupled unidirectionally and asymmetrically, allow us to reproduce the properties of heart rate variability obtained from patients with different kinds of heart block including sino-atrial blocks of different degree and a complete AV block (third degree). Finally, we demonstrate the possibility of introducing into the model a spatial dimension that creates exciting possibilities of simulating in the future the SA the AV nodes and the atrium including their true anatomical structure.