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

Abstract

The human nervous system is an ensemble of connected neuronal networks. Modeling and system identification of the human nervous system helps us understand how the brain processes sensory input and controls responses at the systems level. This study aims to propose an advanced approach based on a hierarchical neural network and non-linear system identification method to model neural activity in the nervous system in response to an external somatosensory input. The proposed approach incorporates basic concepts of Non-linear AutoRegressive Moving Average Model with eXogenous input (NARMAX) and neural network to acknowledge non-linear closed-loop neural interactions. Different from the commonly used polynomial NARMAX method, the proposed approach replaced the polynomial non-linear terms with a hierarchical neural network. The hierarchical neural network is built based on known neuroanatomical connections and corresponding transmission delays in neural pathways. The proposed method is applied to an experimental dataset, where cortical activities from ten young able-bodied individuals are extracted from electroencephalographic signals while applying mechanical perturbations to their wrist joint. The results yielded by the proposed method were compared with those obtained by the polynomial NARMAX and Volterra methods, evaluated by the variance accounted for (VAF). Both the proposed and polynomial NARMAX methods yielded much better modeling results than the Volterra model. Furthermore, the proposed method modeled cortical responded with a mean VAF of 69.35% for a three-step ahead prediction, which is significantly better than the VAF from a polynomial NARMAX model (mean VAF 47.09%). This study provides a novel approach for precise modeling of cortical responses to sensory input. The results indicate that the incorporation of knowledge of neuroanatomical connections in building a realistic model greatly improves the performance of system identification of the human nervous system.

Cross-Frequency Coupling in Descending Motor Pathways: Theory and Simulation

“…Neuronal processing of synaptic inputs can lead to the modulation of inter-spike intervals which produces cross-frequency coupling, i.e., synchronization across different frequencies between input and output (Koch and Segev, 2000;Markram, 2003;Yang et al, 2018). Our previous work on multisynaptic ascending sensory pathways (Yang et al, 2016b;Tian et al, 2018), as well as a recent opinion article (Yang et al, 2018), argued that multi-synaptic interaction in a neural pathway can lead to a substantial expression of cross-frequency coupling. However, insights into possible mechanisms underlying neural coupling in the multi-synaptic descending motor pathways are currently lacking.…”

Quantifying the Nonlinear Interaction in the Nervous System Based on Phase-Locked Amplitude Relationship

“…The experimental procedure was approved by the Human Research Ethics Committee of the Delft University of Technology. The multi-sine signal contained nine sinusoids with frequencies of 5,7,9,11,13,16,17,23,29 Hz and randomly chosen phases. Previous studies have indicated the importance of the second-order nonlinearity in the human proprioceptive system [3,23,24].…”

“…Previous studies have indicated the importance of the second-order nonlinearity in the human proprioceptive system [3,23,24]. The designed multi-sine signal allows generation of nonlinear cortical response in different EEG frequency bands, including alpha (10-15 Hz), beta (15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30) and gamma bands (> 30 Hz)., which allows to check whether the amplitude transfer in the human proprioceptive system is mediated by the dynamics of any specific brain rhythms. The period of the multisine signal was 1 s and the peak-to-peak value was 0.06 radians.…”

“…To confirm the dominance of the second-order nonlinearity in the EEG response, we also computed the FFT amplitude spectrum of the EEG component phase-locked to the 1-s perturbation signal, which was obtained by averaging the EEG over segments before computing its amplitude spectrum [3]. The results are presented as the spectrum of the EEG frequency, i.e., the response frequency, to check whether the amplitude transfer in the proprioceptive system is mediated by the dynamics of specific brain rhythms, such as alpha (10-15 Hz), beta (15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30) and gamma bands (> 30 Hz). Considering the individual difference, the CATF was normalized by the maximum value of CATF for each subject to get the spectra bounded by 0 and 1 for computing the grant averaging CATF over all subjects.…”

“…Several studies used sophisticated nonlinear system identification approaches such as Volterra-Wiener Model [15] and NARMAX (nonlinear autoregressive moving average model with exogenous inputs) [16,17] to investigate nonlinear transfer in biological systems [12,18,19]. Unlike the linear system identification approach (e.g., autoregressive with exogenous input) where the parameters can be relatively easily estimated, the parameter estimation in nonlinear system identification approaches requires a sophisticated procedure where an iterative method such as generalized least square algorithm is usually needed [16].…”