Multiscale multivariate transfer entropy and application to functional corticocortical coupling

Objective. Complex biological systems consist of multi-level mechanism in terms of within- and cross-subsystems correlations, and they are primarily manifested in terms of connectivity, multiscale properties, and nonlinearity. Existing studies have each only explored one aspect of the functional corticocortical coupling (FCCC), which has some limitations in portraying the complexity of multivariable systems. The present study investigated the direct interactions of brain networks at multiple time scales.Approach. We extended the multivariate transfer entropy (MuTE) method and proposed a novel method, named multiscale multivariate transfer entropy (MSMVTE), to explore the direct interactions of brain networks across multiple time scale. To verify this aim, we introduced three simulation models and compared them with multiscale transfer entropy (MSTE) and MuTE methods. We then applied MSMVTE method to analyze FCCC during a unilateral right-hand steady-state force task.Main results. Simulation results showed that the MSMVTE method, compared with MSTE and MuTE methods, better detected direct interactions and avoid the spurious effects of indirect relationships. Further analysis of experimental data showed that the connectivity from left premotor/sensorimotor cortex to right premotor/sensorimotor cortex was significantly higher than that of opposite directionality. Furthermore, the connectivities from central motor areas to both sides of premotor/sensorimotor areas were higher than those of opposite directionalities. Additionally, the maximum coupling strength was found to occur at a specific scale (3-10).Significance. Simulation results confirmed the effectiveness of the MSMVTE method to describe direct relationships and multiscale characteristics in complex systems. The enhancement of FCCC reflects the interaction of more extended activation in cortical motor regions. Additionally, the neurodynamic process of brain depends not only on emergent behavior at small scales, but also on the constraining effects of the activity at large scales. Taken together, our findings provide a basis for better understanding dynamics in brain networks.