Nonlinear modeling of FES-supported standing-up in paraplegia for selection of feedback sensors

Tracking ankle joint movements during gait cycle via control of functional electrical stimulation

Functional electrical stimulation (FES) is an effective method to induce muscle contraction and to improve movements in individuals with injured central nervous system. In order to develop the FES systems for an individual with gait impairment, an appropriate control strategy must be designed to accurate tracking performance. The goal of this study is to present a method for designing proportional-derivative (PD) and sliding mode controllers (SMC) for the FES applied to the musculoskeletal model of an ankle joint to track the desired movements obtained by experiments on two healthy individuals during the gait cycle. Simulation results of the developed controller on musculoskeletal model of the ankle joint illustrated that the SMC is able to track the desired movements more accurately than the PD controller and prevents oscillating patterns around the experimentally measured data. Therefore, the sliding mode as the nonlinear method is more robust in face to unmodeled dynamics and model errors and track the desired path smoothly. Also, the required control effort is smoother in SMC with respect to the PD controller because of the nonlinearity.

A Two-Layer Mixture Model of Gaussian Process Functional Regressions and Its MCMC EM Algorithm

The mixture of Gaussian processes (GPs) is capable of learning any general stochastic process based on a given set of (sample) curves for the regression and prediction problems. However, it is ineffective for curve clustering and prediction, when the sample curves are derived from different stochastic processes as independent sources linearly mixed together. In this paper, we propose a two-layer mixture model of GP functional regressions (GPFRs) to describe such a mixture of general stochastic processes or independent sources, especially for curve clustering and prediction. Specifically, in the lower layer, the mixture of GPFRs (MGPFRs) is developed for a cluster (or class) of curves within the input space. In the higher layer, the mixture of MGPFRs is further established to divide the curves into clusters according to its components in the output space. For the parameter estimation of the two-layer mixture of GPFRs, we develop a Monte Carlo EM algorithm based on a Monte Carlo Markov chain (MCMC) method, in short, the MCMC EM algorithm. We validate the hierarchical mixture of GPFRs and MCMC EM algorithm using synthetic and real-world data sets. Our results show that our new model outperforms the conventional mixture models in curve clustering and prediction.

Penalized gaussian process regression and classification for high-dimensional nonlinear data

The model based on Gaussian process (GP) prior and a kernel covariance function can be used to fit nonlinear data with multidimensional covariates. It has been used as a flexible nonparametric approach for curve fitting, classification, clustering, and other statistical problems, and has been widely applied to deal with complex nonlinear systems in many different areas particularly in machine learning. However, it is a challenging problem when the model is used for the large-scale data sets and high-dimensional data, for example, for the meat data discussed in this article that have 100 highly correlated covariates. For such data, it suffers from large variance of parameter estimation and high predictive errors, and numerically, it suffers from unstable computation. In this article, penalized likelihood framework will be applied to the model based on GPs. Different penalties will be investigated, and their ability in application given to suit the characteristics of GP models will be discussed. The asymptotic properties will also be discussed with the relevant proofs. Several applications to real biomechanical and bioinformatics data sets will be reported.

Limb-state feedback from ensembles of simultaneously recorded dorsal root ganglion neurons

Functional electrical stimulation (FES) holds great potential for restoring motor functions after brain and spinal cord injury. Currently, most FES systems are under simple finite state control, using external sensors which tend to be bulky, uncomfortable and prone to failure. Sensory nerve signals offer an interesting alternative, with the possibility of continuous feedback control. To test feasibility, we recorded from ensembles of sensory neurons with microelectrode arrays implanted in the dorsal root ganglion (DRG) of walking cats. Limb position and velocity variables were estimated accurately (average R2 values >0.5) over a range of walking speeds (0.1-0.5 m s(-1)) using a linear combination of firing rates from 10 or more neurons. We tested the feasibility of sensory control of intraspinal FES by recording from DRG neurons during hindlimb movements evoked by intraspinal microstimulation of the lumbar spinal cord in an anesthetized cat. Although electrical stimulation generated artifacts, this problem was overcome by detecting and eliminating events that occurred synchronously across the array of microelectrodes. The sensory responses to limb movement could then be measured and decoded to generate an accurate estimate of the limb state. Multichannel afferent recordings may thus provide FES systems with the feedback needed for adaptive control and perturbation compensation, though long-term stability remains a challenge.

Gaussian Process Functional Regression Modeling for Batch Data

A Gaussian process functional regression model is proposed for the analysis of batch data. Covariance structure and mean structure are considered simultaneously, with the covariance structure modeled by a Gaussian process regression model and the mean structure modeled by a functional regression model. The model allows the inclusion of covariates in both the covariance structure and the mean structure. It models the nonlinear relationship between a functional output variable and a set of functional and nonfunctional covariates. Several applications and simulation studies are reported and show that the method provides very good results for curve fitting and prediction.