A mathematical model is proposed for the autonomic control of cardiovascular system, which takes into account two separated self-exciting sympathetic control loops of heart rate and peripheral vascular tone. The control loops are represented by self-exciting time-delay systems and their tone depends on activity of the aortic, carotid, and lower-body baroreceptors. The model is used to study the dynamics of the adaptive processes that manifest in a healthy cardiovascular system during the passive head-up tilt test. Computer simulation provides continuous observation of the dynamics of the indexes and variables that cannot be measured in the direct experiment, including the noradrenaline concentration in vessel wall and heart muscle, tone of the sympathetic and parasympathetic control, peripheral vascular resistance, and blood pressure. In the supine and upright positions, we estimated the spectral characteristics of the model variables, especially in the low-frequency band, and the original index of total percent of phase synchronization between the low-frequency oscillations in heart rate and blood pressure signals. The model demonstrates good quantitative agreement with the dynamics of the experimentally observed indexes of cardiovascular system that were averaged for 50 healthy subjects.

The origin of complex irregular dynamics in a cardiovascular system is still being actively debated. Some hypotheses suggest the crucial role of stochastic modulation of cardiovascular parameters, while others argue for the importance of cardiac pacemakers' chaotic deterministic dynamics. In the present study, we estimate the largest Lyapunov exponent and the correlation dimension for the 4-h experimental interbeat intervals and the chaotic signals generated by the mathematical model of the cardiovascular system. We study the complexity of the mathematical model for such cases as the autonomic blockade, the exclusion of all the stochastic components, and the absence of variability of respiration. The obtained results suggest that the complexity of the heart rate variability is largely due to the chaotic dynamics in the loops of autonomic control of circulation.

A change in the human psychophysiological state, caused by stress in particular, affects the processes of autonomic control, the activity of which is reflected in infra-slow oscillations of brain potentials with a frequency of less than 0.5 Hz. We studied the infra-slow oscillations in scalp electroencephalogram (EEG) signals in the frequency ranges of 0.05–0.15 Hz and 0.15–0.50 Hz that are associated with the processes of sympathetic and parasympathetic control, respectively, in healthy subjects at rest and during stress-inducing cognitive tasks. The power spectra of EEG signals, the phase coherence coefficients, and indices of directional coupling between the infra-slow oscillations in the signals of different EEG leads were analyzed. We revealed that, compared with the state of rest, the stress state is characterized by a significant decrease in the power of infra-slow oscillations and changes in the structure of couplings between infra-slow oscillations in EEG leads. In particular, under stressful conditions, a decrease in both intrahemispheric and interhemispheric coupling between EEG leads occurred in the range of 0.05–0.15 Hz, while a decrease in intrahemispheric and an increase in interhemispheric couplings was observed in the range of 0.15–0.50 Hz.