A novel approach for modeling neural responses to joint perturbations using the NARMAX method and a hierarchical neural network

Runfeng Tian, Yuan Yang*, Frans C.T. van der Helm, Julius P.A. Dewald

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


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.

Original languageEnglish (US)
Article number96
JournalFrontiers in Computational Neuroscience
StatePublished - Dec 6 2018


  • EEG
  • Neural modeling
  • Neural network
  • Non-linear system identification

ASJC Scopus subject areas

  • Cellular and Molecular Neuroscience
  • Neuroscience (miscellaneous)


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