Relevance: To enhance our understanding of motor impairments (e.g. post-stroke or due to Parkinson's Disease), objective measures for communication in the nervous system are required. By applying system identification techniques to oscillations in brain and muscle activity, we can objectively quantify the coupling between these areas.

Gap: Unfortunately, none of the existing techniques combine the ability to assess nonlinear behavior and to detect causality in a closed-loop, which is necessary to fully characterize communication in the nervous system.

Methods: In this study, a new connectivity measure, the Nonlinear Directed Transfer Function (NDTF) is introduced. The NDTF is derived by mapping a nonlinear autoregressive model (i.e. NARX model) to the frequency domain, and provides an approximation of the linear and nonlinear causal influences on the output spectrum.

Results: The NDTF was validated using simulated data of a bidirectional, nonlinear system. Additionally, NDTF was applied to simultaneously recorded EEG-EMG of a wrist flexion task. For the experimental data, the NDTF results were dominated by linear interactions.

Conclusions: The NDTF has proven advantages above existing connectivity measures. However, it is sensitive to changes in the sampling frequency and segmentation, making interpretation difficult. The mainly linear interaction found in the EEG-EMG data implies limited sensory feedback, since the ascending pathways are known to act nonlinear.