Locally Periodic Kernel-Based Regression to Identify Time-Varying Ankle Impedance During Locomotion: a Simulation Study.

Human joint impedance is a fundamental property of the neuromuscular system and describes the mechanical behavior of a joint. The identification of the lower limbs' joints impedance during locomotion is a key element to improve the design and control of active prostheses, orthoses, and exoskeletons. Joint impedance changes during locomotion and can be described by a linear time-varying (LTV) model. Several system identification techniques have been developed to retrieve LTV joint impedance, but these methods often require joint impedance to be consistent over multiple gait cycles. Given the inherent variability of neuromuscular control actions, this requirement is not realistic for the identification of human data. Here we propose the kernel-based regression (KBR) method with a locally periodic kernel for the identification of LTV ankle joint impedance. The proposed method considers joint impedance to be periodic yet allows for variability over the gait cycles. The method is evaluated on a simulation of joint impedance during locomotion. The simulation lasts for 10 gait cycles of 1.4 s each and has an output SNR of 15 dB. Two conditions were simulated: one in which the profile of joint impedance is periodic, and one in which the amplitude and the shape of the profile slightly vary over the periods. A Monte Carlo analysis is performed and, for both conditions, the proposed method can reconstruct the noiseless simulation output signal and the profiles of the time-varying joint impedance parameters with high accuracy (mean VAF ~ 99.9% and mean normalized RMSE of the parameters 1.33-4.06%).The proposed KBR method with a locally periodic kernel allows for the identification of periodic time-varying joint impedance with cycle-to-cycle variability.

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

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.