Using mutual information to measure coupling in the cardiorespiratory system

Mutual information (MI) analysis represents a general method to detect linear and nonlinear statistical dependencies between time series, and it can be considered as an alternative to the well-known correlation analysis. This article shows how the concept of MI can be used to quantify the coupling between two systems, X and Y. We consider systems as coupled if there are two signals, x(t) and y(t), representing successive measurements of the systems, X and Y, respectively, such that x(t) and y(t) are statistically dependent. Roughly speaking, this means that we can learn anything on x from observations of y, and vice versa. MI represents a measure for the strength of statistical dependencies, hence it could also be used as a measure of coupling. We apply our method to the cardiorespiratory system of a newborn. Here, we find significant changes in the strength of coupling with some characteristic time scales. Typical linear and nonlinear dependencies were found to undergo changes with the sleep states of human newborns. Those changes and scales are also reflected by a correlation analysis. However, we argue that there might be simultaneously rather large correlations, and weak dependencies, quantified by the MI. This can occur because correlation is rather different from M1; correlation describes only linear dependencies, where MI takes into account both linear and nonlinear dependencies.