Detection of coupling in short physiological series by a Joint Distribution Entropy Method

Objective: In this study, we developed a joint distribution entropy (JDistEn) method to robustly estimate the coupling in short physiological series. Methods: The JDistEn method is derived from a joint distance matrix which is constructed from a combination of the distance matrix corresponding to each individual data channel using a geometric mean calculation. A coupled Rössler system and a coupled dual-kinetics neural mass model were used to examine how well JDistEn performed, specifically, its sensitivity for detecting weak coupling, its consistency in gauging coupling strength, and its reliability in processing input of decreased data length. Performance of JDistEn in estimating physiological coupling was further examined with bivariate electroencephalography data from rats and RR interval and diastolic time interval series from human beings. Cross-sample entropy (XSampEn), cross-conditional entropy (XCE), and Shannon entropy of diagonal lines in the joint recurrence plots (JENT) were applied for purposes of comparison. Results: Simulation results suggest that JDistEn showed markedly higher sensitivity than XSampEn, XCE, and JENT for dynamics in weak coupling, although as the simulation models were more intensively coupled, JDistEn performance was comparable to the three others. In addition, this improved sensitivity was much more pronounced for short datasets. Experimental results further confirmed that JDistEn outperformed XSampEn, XCE, and JENT for detecting weak coupling, especially for short physiological data. Conclusion: This study suggested that our proposed JDistEn could be useful for continuous and even real-time coupling analysis for physiological signals in clinical practice.