The electrical activity of the heart (ECG), respiratory function and
electric activity of the brain (EEG) were simultaneously recorded in
conscious, healthy humans. Instantaneous frequencies of the heart
beat, respiration and α-waves were then determined from
30-minutes recordings. The instantaneous cardiac frequency was
defined as the inverse value of the time interval between two
consecutive R-peaks. The instantaneous respiratory frequency was
obtained from recordings of the excursions of thorax by application
of the Hilbert transform. To obtain the instantaneous frequency of
α-waves, the EEG signal recorded from the forehead was first
analysed using the wavelet transform. Then the frequency band
corresponding to α-waves was extracted and the Hilbert
transform applied. Synchronization analysis was performed and the
direction of coupling was ascertained, using pairs of instantaneous
frequencies in each case. It is shown that the systems are weakly
bidirectionally coupled. It was confirmed that, in conscious healthy
humans, respiration drives cardiac activity. We also demonstrate
from these analyses that α-activity drives both respiration
and cardiac activity.
The complexities exhibited by biological systems are highly intriguing. Their activity can span both micro and macroscopic scales simultaneously. Often noise plays an important role. So, the analysis of the dynamical properties of such systems poses a major challenge. In this paper we introduce an approach that is applicable within both the micro and macroscopic worlds, where a large number of oscillators acting on a similar time scale can be represented as an ensemble that, on the macroscopic scale, may be taken as a single oscillator. On the macroscopic scale they interact with other similar type of oscillators, but usually on widely different time scales. We use recently introduced nonlinear dynamics methods and methods derived from information theory, and extend their application to oscillations acting on micro and macroscopic scales at the same time. We demonstrate such interactions using numerical examples and real physiological data related to cardiac, respiratory and brain activities.
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