Recursive Decomposition of Electromyographic Signals With a Varying Number of Active Sources: Bayesian Modeling and Filtering

Abstract

This paper describes a sequential decomposition algorithm for single channel intramuscular electromyography (iEMG) generated by a varying number of active motor neurons. As in previous work, we establish a Hidden Markov Model of iEMG, in which each motor neuron spike train is modeled as a renewal process with inter-spike intervals following a discrete Weibull law and motor unit action potentials are modeled as impulse responses of linear time-invariant systems with known prior. We then expand this model by introducing an activation vector associated to the state vector of the Hidden Markov Model. This activation vector represents recruitment/derecruitment of motor units and is estimated together with the state vector using Bayesian filtering. Non-stationarity of the model parameters is addressed by means of a sliding window approach, thus making the algorithm adaptive to variations in contraction force and motor unit action potential waveforms. The algorithm was validated using simulated and experimental iEMG signals with varying number of active motor units. The experimental signals were acquired from the tibialis anterior and abductor digiti minimi muscles by fine wire and needle electrodes. The decomposition accuracy in both simulated and experimental signals exceeded 90% and the recruitment/derecruitment was successfully tracked by the algorithm. Because of its parallel structure, this algorithm can be efficiently accelerated, which lays the basis for its future real-time applications in human-machine interfaces, e.g. for prosthetic control.

On-Line Recursive Decomposition of Intramuscular EMG Signals Using GPU-Implemented Bayesian Filtering

“…Based on the linear model presented in subsection II-A, a Hidden Markov Model (HMM) is proposed in [15], [16]. In the following part of this section, we will review the HMM.…”

“…As presented in our previous work on the algorithm [16], to estimate the inter-spike law parameters (discrete Weibull parameters), a recursive maximum likelihood (RML) estimator was implemented. The likelihood is optimized iteratively by the quasi-Newton method.…”

“…As proposed in our previous work [16], the posterior probability recursion was derived by means of an update-prediction scheme. As follows from the Bayes' theorem, for all possible realizations s n of S n , the update step is: ) is a zero-mean and variance v Gaussian PDF.…”

“…In order to characterise the complexity of the decomposition task, we use the superposition percentage as in our previous work [16]:…”

“…Recently we proposed a Bayesian filtering approach for single-channel iEMG decomposition [15], as well as its version adapted to a case of varying number of active MUs [16]. The proposed algorithm achieves full sequential decomposition of iEMG signals.…”