Decoding the cortical responses to mechanical wrist perturbations: A two-step shared structure NARX method

Shared structure nonlinear autoregressive with exogenous input (NARX) model is a promising tool for exploring cortical responses mechanism to external stimuli, essential for advancing our understanding of brain function and developing methods for direct brain information encoding. In this paper, we proposed a two-step method to overcome limitations in existing method, which neglect data relationships and rely on a greedy search for regression terms, leading to less accurate models. In our approach, data from multiple trials are concatenated, and then the orthogonal forward regression (OFR) algorithm identifies model terms in first step, enhancing inter-trial connections and establishing a preliminary model for each subject. Shared model terms across subjects are then used to construct a general target model. Next, non-shared regression terms that best represent population-level information are identified, using adaptive multi-population genetic algorithms, and use to enhance the target models' descriptive power. Simulations results show significant competitiveness in terms of accuracy as compared to other state-of-the-art methods. When applied to real electroencephalography signals under mechanical disturbance, structural and parameter analysis revealed consistent neural response patterns across subjects, with subject-specific responses likely stemming from muscle feedback. Frequency response analysis further suggests that the brain may generate motor inhibition signals based on sensory inputs to maintain a pre-disturbance resting state. These findings provide valuable insights into cortical response mechanisms and have potential implications for future brain information encoding research.