Quantifying Nonlinear Contributions to Cortical Responses Evoked by Continuous Wrist Manipulation

Cortical responses to continuous stimuli as recorded using either magneto- or electroencephalography (EEG) have shown power at harmonics of the stimulated frequency, indicating nonlinear behavior. Even though the selection of analysis techniques depends on the linearity of the system under study, the importance of nonlinear contributions to cortical responses has not been formally addressed. The goal of this paper is to quantify the nonlinear contributions to the cortical response obtained from continuous sensory stimulation. EEG was used to record the cortical response evoked by continuous movement of the wrist joint of healthy subjects applied with a robotic manipulator. Multisine stimulus signals (i.e., the sum of several sinusoids) elicit a periodic cortical response and allow to assess the nonlinear contributions to the response. Wrist dynamics (relation between joint angle and torque) were successfully linearized, explaining 99% of the response. In contrast, the cortical response revealed a highly nonlinear relation; where most power ( $\sim 80$ %) occurred at non-stimulated frequencies. Moreover, only 10% of the response could be explained using a nonparametric linear model. These results indicate that the recorded evoked cortical responses are governed by nonlinearities and that linear methods do not suffice when describing the relation between mechanical stimulus and cortical response.