Wiener-Granger Causality in Network Physiology With Applications to Cardiovascular Control and Neuroscience

Since the operative definition given by C. W. J. Granger of an idea expressed by N. Wiener, the Wiener-Granger causality (WGC) has been one of the most relevant concepts exploited by modern time series analysis. Indeed, in networks formed by multiple components, working according to the notion of segregation and interacting with each other according to the principle of integration, inferring causality has opened a window on the effective connectivity of the network and has linked experimental evidences to functions and mechanisms. This tutorial reviews predictability improvement, information-based and frequency domain methods for inferring WGC among physiological processes from multivariate realizations and quantifying the strength of the cause-effect relations in network physiology. Studies relevant to cardiovascular control and neuroscience are listed as examples of applications in prominent biomedical fields in which WGC analysis led to remarkable advancements in our knowledge. The review pays special attention to procedures for checking the reliability of the WGC approaches according to the statistical framework of hypothesis testing.