Motor unit number estimation using reversible jump Markov chain Monte Carlo

(2007) Motor unit number estimation using reversible jump Markov chain Monte Carlo methods. Summary. We present an application of reversible jump Markov chain Monte Carlo (RJMCMC) from the field of neurophysiology where we seek to estimate the number of motor units within a single muscle. Such an estimate is needed for monitoring the progression of neuro-muscular diseases such as amyotrophic lateral sclerosis (ALS). Our data consist of action potentials recorded from the surface of a muscle in response to stimuli of different intensities applied to the nerve supplying the muscle. During the gradual increase in stimulus intensity from threshold to supramaximal, all motor units are progressively excited. However, at any given submaximal stimulus intensity, the number of units that are excited is variable, because of random fluctuations in axonal excitability. Furthermore, the individual motor unit action potentials exhibit variability. To account for these biological properties, Ridall et al. (2006) developed a model of motor unit activation capable of describing the response where the number of motor units, N , is fixed. The purpose of this paper is to extend that model so that the possible number of motor units, N , is a stochastic variable. In this paper we illustrate the elements of our model, show that the results are reproducible and show that our model can measure the decline in motor unit numbers during the course of ALS. Our method holds promise of being useful in the study of neurogenic diseases.