Linear and nonlinear information flow based on time-delayed mutual information method and its application to corticomuscular interaction.

OBJECTIVE: To propose a model-free method to show linear and nonlinear information flow based on time-delayed mutual information (TDMI) by employing uni- and bi-variate surrogate tests and to investigate whether there are contributions of the nonlinear information flow in corticomuscular (CM) interaction. METHODS: Using simulated data, we tested whether our method would successfully detect the direction of information flow and identify a relationship between two simulated time series. As an experimental data application, we applied this method to investigate CM interaction during a right wrist extension task. RESULTS: Results of simulation tests show that we can correctly detect the direction of information flow and the relationship between two time series without a prior knowledge of the dynamics of their generating systems. As experimental results, we found both linear and nonlinear information flow from contralateral sensorimotor cortex to muscle. CONCLUSIONS: Our method is a viable model-free measure of temporally varying causal interactions that is capable of distinguishing linear and nonlinear information flow. With respect to experimental application, there are both linear and nonlinear information flows in CM interaction from contralateral sensorimotor cortex to muscle, which may reflect the motor command from brain to muscle. SIGNIFICANCE: This is the first study to show separate linear and nonlinear information flow in CM interaction.