Bivariate assessment of directionality based on High Resolution Joint Symbolic Dynamics

The detection and quantification of the coupling strength and direction are important aspects for a more detailed understanding of physiological regulatory processes in the field of Network Physiology. Here, we introduced a new directionality index ($D_{\text {HRJsd }}$) derived from the pattern family density matrix from the High Resolution Joint Symbolic Dynamics approach (HRJSD) to determine the coupling direction and driver-response relationships. For the validation of this index different linear and non-linear multivariate coupled systems (Gaussian autoregressive models) with different mutual influences were generated. The simulation results revealed that $D_{\text {HRJSd }}$ was able to correctly detect the dominating coupling direction in linear bivariate coupled systems, but is only partly able to detect the dominating coupling direction in non-linear bivariate coupled systems.