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Joint manipulation elicits a response from the sensors in the periphery which, via the spinal cord, arrives in the cortex. The average evoked cortical response recorded using electroencephalography was shown to be highly nonlinear; a linear model can only explain 10% of the variance of the evoked response, and over 80% of the response is generated by nonlinear behavior. The goal of this paper is to obtain a nonparametric nonlinear dynamic model, which can consistently explain the recorded cortical response requiring little a priori assumptions about model structure. Wrist joint manipulation was applied in ten healthy participants during which their cortical activity was recorded and modeled using a truncated Volterra series. The obtained models could explain 46% of the variance of the evoked cortical response, thereby demonstrating the relevance of nonlinear modeling. The high similarity of the obtained models across participants indicates that the models reveal common characteristics of the underlying system. The models show predominantly high-pass behavior, which suggests that velocity-related information originating from the muscle spindles governs the cortical response. In conclusion, the nonlinear modeling approach using a truncated Volterra series with regularization, provides a quantitative way of investigating the sensorimotor system, offering insight into the underlying physiology.

Cortical responses to continuous stimuli as recorded using either magneto- or electroencephalography (EEG) have shown power at harmonics of the stimulatedfrequency, 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 formallyaddressed.The goal of this paper is to quantify the nonlinear contributions to the cortical response obtained fromcontinuous sensory stimulation. EEG was used to record the cortical response evoked by continuousmovement 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 allowto assessthe 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 ( ∼ 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 responsesare governed by nonlinearities and that linear methods do not suffice when describing the relation between mechanical stimulus and cortical response.

System identification is an important tool to investigate human motion control. The goal of this study was to identify and address issues in system identification for human motor control and to investigate if linear time invariant system identification techniques are applicable to recorded mechanical and physiological data. During a posture maintenance experiment subjects had to minimize the deviations of the wrist, while a manipulator applied disturbances through a handle. We estimated frequency response functions and categorized and quantified the errors influencing the estimates. The relation between the position and force of the wrist was found to be highly linear and variations over time were the dominant source of error. The relation between the position changes at the wrist and the recorded signals from the brain was highly nonlinear. System identification techniques based on periodic multisine perturbation signals are a promising approach to investigate human motion control, even in the presence of inherent noise and nonlinearities.

A continuous somatosensory stimulation evokes a steady state response in the cortex, which can be measured using electroencephalography. We applied mechanical multisine stimulation of the wrist to investigate the properties of the steady state response in the frequency domain. Our results show a response in the contralateral sensorimotor cortex at the stimulated frequencies yet with more power at their even harmonics, indicating substantial nonlinear behavior. The observed cortical response to a mechanical somatosensory stimulation is time invariant and nonlinear, however shows no subharmonics, allowing for the application of a broad range of (non)linear system identification tools.

Electrical vestibular stimulation is often used to assess vestibulo-motor and postural responses in both clinical and research settings. Stochastic vestibular stimulation (SVS) is a recently established technique with many advantages over its square-wave counterpart; however, the evoked muscle responses remain relatively small. Although the vestibular-evoked responses can be enhanced by increasing the stimulus amplitude, subjects often perceive these higher intensity electrical stimuli as noxious or painful. Here, we developed multisine vestibular stimulation (MVS) signals that include precise frequency contributions to increase signal-to-noise ratios (SNR) of stimulus-evoked muscle and motor responses. Subjects were exposed to three different MVS stimuli to establish that: 1) MVS signals evoke equivalent vestibulo-motor responses compared to SVS while improving subject comfort and reducing experimentation time, 2) stimulus-evoked vestibulo-motor responses are reliably estimated as a linear system and 3) specific components of the cumulant density time domain vestibulo-motor responses can be targeted by controlling the frequency content of the input stimulus. Our results revealed that in comparison to SVS, MVS signals increased the SNR 3–6 times, reduced the minimum experimentation time by 85% and improved subjective measures of comfort by 20–80%. Vestibulo-motor responses measured using both EMG and force were not substantially affected by nonlinear distortions. In addition, by limiting the contribution of high frequencies within the MVS input stimulus, the magnitude of the medium latency time domain motor output response was increased by 58%. These results demonstrate that MVS stimuli can be designed to target and enhance vestibulo-motor output responses while simultaneously improving subject comfort, which should prove beneficial for both research and clinical applications.