Time-Varying Analysis Methods and Models for the Respiratory and Cardiac System Coupling in Graded Exercise

Abstract

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.

Influences of breathing patterns on respiratory sinus arrhythmia in humans during exercise

“…As we mentioned in a previous study (25), when the signal demonstrates spectral lines, it can be approximately modeled as an autoregressive (AR) process. When the signal is nonstationary, the classical AR model no longer applies and must be replaced by:…”

“…In our application, we used the Fourier basis with an order chosen using the Akaike criterion, and we selected the order of the AR model equal to 12, i.e., p ϭ 12 (25).…”

“…Because root computing is a difficult task to ensure a correct tracking of the frequencies fi(k), we used the solution provided by Meste et al (25). Time-varying amplitude estimate.…”

“…, where STFT Ϫ1 stands for the inverse STFT (25). A filtered signal was calculated for each fi(k) (i ϭ 1. .…”

Automatic Cycle Identification in Speaker’s Speech Breathing Signals

“…Although some algorithms are available to isolate specific frequencies of interest in a given waveform [2,3], in the case of physiological behavior, rate measurements are often used as summary statistics of the waveforms. Unfortunately, cycle-averaging techniques are often inadequate when it comes to describing complex behaviors, particularly when that behavior changes over time, e.g., breaching behaviors during speech [4].…”