Time-varying analysis methods and models for the respiratory and cardiac system coupling in graded exercise

The analysis of heart period series is a difficult task especially under graded exercise conditions. From all the information present in these series, we are the most interested in the coupling between respiratory and cardiac systems, known as respiratory sinus arrythmia. In this paper, we show that precise patterns concerning the respiratory frequency can be extracted from the heart period series. An evolutive model is introduced in order to achieve tracking of the main respiratory-related frequencies and their time-varying amplitudes. Since respiration acts to modulate the sinus rhythm, we relate the frequencies and amplitudes to this modulation by analyzing in detail its nonlinear transformation giving the heart period signal. This analysis is performed assuming stationary conditions but also in the realistic case where the mean heart period, the amplitude, and the frequency of the respiration are time-varying. Since this paper is devoted to the theoretical and complete presentation of the method used in a physiological study published elsewhere, the capabilities of our method will be illustrated in a realistic simulated case.