Causal Squared Coherence Analysis to Estimate Cardiorespiratory Coupling in Athletes.

Cardiorespiratory coupling (CRC) accounts for the interactions between the heart period (HP) and respiration (RESP) and can be computed through the bivariate analysis of the HP and RESP time series. The study of CRC is useful to understand the chronic effects of different modalities of training on CRC regulation in athletes. Increases in CRC values have been associated with a raise of oxygen consumption. Several methods have been proposed to estimate the CRC, such as the squared coherence ( $K_{2}$ ). However, one of the main disadvantages of this approach is its inability to impose a directionality, thus limiting its ability in elucidating physiological mechanisms involved in chronic adaptation to exercise. We propose a tool able to account for causality, namely the causal $K^{2}$ , to estimate the CRC. Analysis was performed in 42 male healthy subjects (i.e., athletes and sedentary individuals), aged between 20 to 40 years old. Causal $K^{2}$ was applied by considering the action of RESP on $HP\ (K^{2}RESP\rightarrow HP)$ , as well as of HP on RESP ( $K^{2}HP\rightarrow RESP$ ). Athletes showed higher resting CRC, and this increase is attributed to the temporal direction from RESP to HP. We conclude that computing directional indexes is of value when estimating CRC, especially in athletes.