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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.

Aim of the study is to apply the analysis of phase dynamics to investigation of the coupling patterns between heart rate variability, respiration and peripheral circulation in healthy subjects at rest and after moderate physical exercises. Material and Methods ― 30-minutes electrocardiogram (ECG), photoplethysmogram (PPG) and respiration records were obtained from healthy subjects aged 22±2 (mean ± standard deviation) before and after active Martine Kushelevsky test (20 squats in 30 seconds). The coherence function was estimated between all the signals from each subject, and the phase dynamics modeling was used to detect the directional coupling in high-frequency (HF; 0.14-0.40 Hz) and low-frequency ranges (LF; 0.04-0.14 Hz). Results ― At rest (before the physical activity) no statistically significant couplings were detected between the HF rhythms of respiration and heart rate (RR intervals). For the HF rhythms in respiration and PPG, the influence respirationPPG was detected. No couplings were detected between the LF rhythms. After the moderate physical exercise, predominant direction of the influence was RR intervals  PPG in the LF range and both RR intervals  respiration and PPG  respiration in the HF range. The influence PPG  respiration was delayed by several seconds. Conclusion ― adaptation to the moderate physical activity has led to the decrease in the overall coherence and changes in patterns of directional coupling between the LF and HF rhythms in respiration, heart rate and peripheral circulation. The obtained results confirm nonlinearity and complexity of the coupling patterns in cardiovascular system.

The aim of study is to investigate effectiveness of cross-recurrence analysis for the detection of coupling between the loops of heart rate and vessel tone sympathetic control. The cross-recurrence analysis is applied to the interbeat intervals and photopletysmographic signals from the mathematical model of cardiovascular system and from adults and newborn children. The model is examined under the conditions of the four experiments: with fully operational autonomic control, autonomic control weakened by 40%, autonomic control weakened by 70% and autonomic blockade. The coupling is most pronounced in adult subjects and the model with fully operational autonomic control, while it is absent under the autonomic blockade. Autonomic control is also not fully developed in newborn children. As the result, smaller coupling strength is expected. The results of cross-recurrence analysis of the model and experimental data are compared with the results of coupling detection based on the analysos of phase synchronization. Synchronization index demonstrates good correlation with the coupling strength in the model and weak coupling in newborn children in relation to adult subjects. In both cases, no correlation is observed between the synchronization index and the results of cross-recurrence analysis.