Nonlinear causal influences assessed by mutual compression entropy

Autonomic control of the heart rate was demonstrated to be complex and nonlinear. Respiratory sinus arrhythima plays a crucial role in heart rate vagal modulation. Here we present an approach of assessing nonlinear causal relationships in bivariate time series, called mutual compression entropy (MCE). We applied MCE to cardiorespiratory data of 29 patients with acute schizophrenia and 29 matched controls. The method is based on data compression and estimates to which extend a (target) time series can be compressed regarding another time series (driver). In schizophrenia an elevated sympathetic and reduced parasympathetic heart rate modulation was found. The nonlinear influence of respiration on heart rate variability was demonstrated by a highly significant reduction of MCE (0.816 vs. 0.808, p<0.01). In healthy subjects MCE was mainly related to sympathovagal balance. We conclude, that this index has the potential to uncover physiological information beyond linear measures.