Modeling the Nonlinear Cortical Response in EEG Evoked by Wrist Joint Manipulation

Abstract

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.

A Novel Approach for Modeling Neural Responses to Joint Perturbations Using the NARMAX Method and a Hierarchical Neural Network

“…This biologically inspired innovation significantly improves the long-term prediction of NARMAX modeling, showing better performance than the polynomial NARMAX in the estimation of 12 ms ahead EEG oscillation. Furthermore, our results are also better than the previous modeling study on the same datasets using the Volterra model (Vlaar et al, 2018) as demonstrated in Table 1. Finally, our proposed method has lower model complexity with a smaller number of parameters than the polynomial NARMAX and Volterra models.…”

“…In line with the previous modeling study on the same datasets (Vlaar et al, 2018), only one ICA component with the highest SNR was selected as the output of the nervous system for each dataset for modeling. All selected components have their sources located in the primary sensorimotor areas in the contralateral hemisphere (i.e., left hemisphere as all participants are right-hand dominant), indicating that the ICA results are neurophysiological plausible.…”

“…A dipole fitting algorithm implemented in the Fieldtrip toolbox (Oostenveld et al, 2011) was used to estimate the source locations of selected ICA components. The procedure is the same as the previous modeling study using Volterra model in the same datasets (Vlaar et al, 2018).…”

“…The obtained results were compared with those from using the polynomial NARMAX (Chen and Billings, 1989) and Volterra (Vlaar et al, 2018) models. In the Volterra model, the output depends only on the history of the input to the non-linear system:…”

“…Previous studies tried to use a simplified approach based on Volterra series to model the brain response to joint perturbations. This only explained around 40% of the measured EEG signal (Vlaar et al, 2018). Volterra series is a polynomial functional expansion similar to a Taylor series that provides an approximation of input-output relation in a non-linear system (Brockett, 1976).…”