Deriving main rhythms of the human cardiovascular system from the heartbeat time series and detecting their synchronization

We demonstrate a possibility of determining the instantaneous phases and instantaneous frequencies of the main rhythmic processes governing the cardiovascular dynamics in humans from heart rate variability data with the methods using bandpass filtration, empirical mode decomposition and wavelet transform. For the cases of spontaneous respiration and paced respiration with a fixed frequency we investigate synchronization between the rhythms of the cardiovascular system analyzing univariate data in the form of the heartbeat time series. It is shown that the main heart rhythm and the rhythm of slow regulation of blood pressure with fundamental frequency close to 0.1 Hz can be synchronized with respiration.