Segmentation of EMG time series using a variational Bayesian approach for the robust estimation of cortical silent periods

A variational Bayesian formulation for a manifold-constrained Hidden Markov Model is used in this paper to segment a set of multivari- ate time series of electromyographic recordings corresponding to stroke patients and control subjects. An index of variability associated to this model is defined and applied to the robust detection of the silent period interval of the signal. The accuracy in the estimation of the duration of this interval is paramount to assess the rehabilitation of stroke patients. The Transcranial Magnetic Stimulation (TMS) of the cerebral motor cortex can evoke waves in the electromyographic (EMG) recording of muscle activity. Cor- tical stimulation can elicit excitatory as well as inhibitory effects. One of the latter is called the cortical silent period (CSP). When TMS is delivered over the motor cortex while the subjects maintain voluntary muscle contraction, the CSP is a pause in ongoing EMG activities that follows the motor-evoked potential. The duration of the CSP is an important parameter to gauge the recovery of stroke patients and to provide them with a prognosis. It is known (1) that the shortening of the SP in the affected side is related to an increase of its excitability, indicating an improvement of the motor function of the patients. The measurement of the CSP is sometimes troublesome due to the nature of the signal. The existing measurement methods are yet imprecise and are known to yield a significant error due to the sensitivity to noise of this kind of data (2). The main purpose of this study is to provide an accurate technique for CSP estimation based on a multivariate time series (MTS) segmentation process that behaves robustly in the presence of noise. For this, we resort to a manifold- constrained Hidden Markov Model (HMM). The formulation of this model within a variational Bayesian framework imbues it with regularization properties that minimize the negative effect of the presence of noise in the EMG MTS. A novel index of variability (IV ) is defined for this model. It is capable of providing reli- able estimates of the CSP duration by pinpointing its offset time with precision. ∗ This research is partially funded by Spanish MICINN project TIN2009-13895-C02-01.