Detecting synchronization of self-sustained oscillators by external driving with varying frequency

We propose a method for detecting the presence of synchronization of self-sustained oscillator by external driving with linearly varying frequency. The method is based on a continuous wavelet transform of the signals of self-sustained oscillator and external force and allows one to distinguish the case of true synchronization from the case of spurious synchronization caused by linear mixing of the signals. We apply the method to driven van der Pol oscillator and to experimental data of human heart rate variability and respiration.Comment: 9 pages, 7 figure

Detection of synchronization from univariate data using wavelet transform

A method is proposed for detecting from univariate data the presence of synchronization of a self-sustained oscillator by external driving with varying frequency. The method is based on the analysis of difference between the oscillator instantaneous phases calculated using continuous wavelet transform at time moments shifted by a certain constant value relative to each other. We apply our method to a driven asymmetric van der Pol oscillator, experimental data from a driven electronic oscillator with delayed feedback and human heartbeat time series. In the latest case, the analysis of the heart rate variability data reveals synchronous regimes between the respiration and slow oscillations in blood pressure.Comment: 10 pages, 9 figure

Mandelbrot set in coupled logistic maps and in an electronic experiment

We suggest an approach to constructing physical systems with dynamical characteristics of the complex analytic iterative maps. The idea follows from a simple notion that the complex quadratic map by a variable change may be transformed into a set of two identical real one-dimensional quadratic maps with a particular coupling. Hence, dynamical behavior of similar nature may occur in coupled dissipative nonlinear systems, which relate to the Feigenbaum universality class. To substantiate the feasibility of this concept, we consider an electronic system, which exhibits dynamical phenomena intrinsic to complex analytic maps. Experimental results are presented, providing the Mandelbrot set in the parameter plane of this physical system.Comment: 9 pages, 3 figure

Simulating Dynamics of Circulation in the Awake State and Different Stages of Sleep Using Non-autonomous Mathematical Model With Time Delay

We propose a mathematical model of the human cardiovascular system. The model allows one to simulate the main heart rate, its variability under the influence of the autonomic nervous system, breathing process, and oscillations of blood pressure. For the first time, the model takes into account the activity of the cerebral cortex structures that modulate the autonomic control loops of blood circulation in the awake state and in various stages of sleep. The adequacy of the model is demonstrated by comparing its time series with experimental records of healthy subjects in the SIESTA database. The proposed model can become a useful tool for studying the characteristics of the cardiovascular system dynamics during sleep

Dynamics of 0.1 Hz Oscillations Synchronization in Cardiovascular System during the Treatment of Acute Myocardial Infarction Patients

Aim: The aim was the studying of synchronization between 0.1 Hz oscillations in heart rate (HR) and plethysmographic peripheral microcirculation (PM) in acute myocardial infarction (AMI) patients and in healthy subjects. Material and Method: 12 healthy volunteers aged 26±5 years and 125 patients with AMI aged 65±9 years were involved in the study. Simultaneous registration of electrocardiogram and photoplethysmogram were performed during 10 min. In AMI patients the signals were recorded twice: the first record was done during 3-5 days after AMI, the second record was done during the third week after AMI. Phase differences between HR and PM oscillations were used to measure the degree of synchronization (S). Data are submitted as medians with inter-quartile ranges (25%, 75%). Results: S was 65.8% (50.5%; 79.5%) in healthy subjects whereas in AMI patients at the first week after AMI S was 16.3% (9.4%; 24.6%) (p<0.001). In records made at the third week after AMI index S was 18.4% (11.2%; 28.2%). Two groups of AMI patients were identified on the basis of individual S dynamics. In 100 AMI patients no dynamics of S was observed during the observation period and in 25 AMI patients the increase of S was observed. The group of AMI patients with increase of S had greater HR values during the first week after AMI. Conclusion: The index S of synchronization of 0.1 Hz oscillations in HR and PM appears to be a sensitive indicator of autonomic control dynamic disturbances in AMI patients

Problem of power spectra estimation in application to the analysis of heart rate variability

We investigated how the parameters of the spectral analysis affect standard deviation and error of the estimation of well-known indices for the heart rate variability. We compared the nonparametric Fourier transform to the parametric approach based on autoregressive models. We also investigated how the precision of the indices estimation depends on the choice of the window function, parameterization of the Bartlett’s method, and the lengths of time series. For each set of parameters, we calculated the sensitivity and specificity of the resulting indices when diagnosing arterial hypertension. To isolate and investigate the errors caused by inaccuracy of the spectral analysis itself, we conducted our study using the mathematical models of heart rate variability for healthy subjects and arterial hypertension patients, for which the correct values of the spectral indices are known. The obtained results suggest that the analysis of 20-min signals, comparing to 5-min signals, significantly decreases the standard deviation of the estimations and increases both their sensitivity and specificity. We found no advantages of using the parametric approach over the Fourier transform. We have shown that application of the Hann’s window function and normalization of the spectral indices decreases the sensitivity and specificity of the medical diagnostics

Method of estimation of synchronization strength between low-frequency oscillations in heart rate variability and photoplethysmographic waveform variability

This paper describes in detail a new method proposed by authors for quantitative estimation of the strength of synchronization between the low-frequency oscillations (with the main frequency of about 0.1 Hz) in the heart rate variability (HRV) and photoplethysmogram (PPG). Calculation of index value is followed by statistical significance control. The proposed method is applied for the analysis of 1056 pairs of HRV and PPG signals obtained from patients having different clinical status. Methodological recommendations are developed for method application in clinical studies