Gain and coherence estimates between respiration and heart-rate: differences between inspiration and expiration

The interaction of respiration and heart-rate variability (HRV), leading to respiratory sinus arrhythmia (RSA) and, in the inverse direction, cardioventilatory coupling has been subject of much study and controversy. A parametric linear feedback model can be used to study these interactions. In order to investigate differences between inspiratory and expiratory periods, we propose that models are estimated separately for each period, by finding least mean square estimates only over the desired signal segments. This approach was tested in simulated data and heart-rate and respiratory air flow signals recorded from 25 young healthy adults (13 men and 12 women), at rest, breathing spontaneously through a face mask for 5 min. The results show significant differences (p<0.05) between the estimates of coherence obtained from the whole recording, and the inspiration and expiration periods. Simple and causal coherence from respiration to HRV was higher during inspiration than expiration. The estimates of gain also differed significantly in the high frequency (HF) band (0.15-0.5Hz) between those obtained from the whole recording, and the inspiratory and expiratory periods. These results indicate that a single linear model fitted to the whole recording neglects potentially important differences between inspiration and expiration, and the current paper shows how such differences can be estimated, without the need to control breathing.