Investigation of delay time in interaction between the regulatory circuits in the cardiovascular system of healthy humans using modeling of phase dynamics

Background and Objectives: Low-frequency oscillations with a basic frequency of about 0.1 Hz are observed in the human heart rate and peripheral microcirculation. It is found out that these processes are self-oscillatory and interact between themselves. However, the details and characteristics of this interaction including the direction of coupling and delays in coupling functions are not well studied yet. Thus, the estimation of delay times in the coupling between the low-frequency rhythms of cardiovascular system is an important task for revealing the physiological mechanisms of the cardiovascular regulation. Materials and Methods: The method of coupling detection based on constructing the models of instantaneous phase dynamics is applied for the estimation of delay time in the interaction between the cardiovascular regulatory systems from their experimental time series. The signals of electrocardiogram and photoplethysmogram were recordedusing the device EEGA-21/26 Entsefalan-131-03 (Medikom-MTD, Russia) with a set of standard sensors. The signals were recorded with a frequency of 250 Hz and a resolution of 12 bit. Results: The estimated value of delay time in the interaction between the systems of regulation of cardiovascular low-frequency oscillations is 2.13$\pm$0.14 s for the direction «heart – peripheral microcirculation» and 2.12$\pm$0.17 s for the direction «peripheral microcirculation – heart». Conclusion: The analysis of two-hour experimental time series of healthy subjects revealed that the regulatory systems of low-frequency oscillations in heart rate and peripheral microcirculation demonstrate bidirectional interaction with delay times of about several seconds.