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All muscle contractions are dependent on the functioning of motor units. In diseases such as amyotrophic lateral sclerosis (ALS), progressive loss of motor units leads to gradual paralysis. A major difficulty in the search for a treatment for these diseases has been the lack of a reliable measure of disease progression. One possible measure would be an estimate of the number of surviving motor units. Despite over 30 years of motor unit number estimation (MUNE), all proposed methods have been met with practical and theoretical objections. Our aim is to develop a method of MUNE that overcomes these objections. We record the compound muscle action potential (CMAP) from a selected muscle in response to a graded electrical stimulation applied to the nerve. As the stimulus increases, the threshold of each motor unit is exceeded, and the size of the CMAP increases until a maximum response is obtained. However, the threshold potential required to excite an axon is not a precise value but fluctuates over a small range leading to probabilistic activation of motor units in response to a given stimulus. When the threshold ranges of motor units overlap, there may be alternation where the number of motor units that fire in response to the stimulus is variable. This means that increments in the value of the CMAP correspond to the firing of different combinations of motor units. At a fixed stimulus, variability in the CMAP, measured as variance, can be used to conduct MUNE using the "statistical" or the "Poisson" method. However, this method relies on the assumptions that the numbers of motor units that are firing probabilistically have the Poisson distribution and that all single motor unit action potentials (MUAP) have a fixed and identical size. These assumptions are not necessarily correct. We propose to develop a Bayesian statistical methodology to analyze electrophysiological data to provide an estimate of motor unit numbers. Our method of MUNE incorporates the variability of the threshold, the variability between and within single MUAPs, and baseline variability. Our model not only gives the most probable number of motor units but also provides information about both the population of units and individual units. We use Markov chain Monte Carlo to obtain information about the characteristics of individual motor units and about the population of motor units and the Bayesian information criterion for MUNE. We test our method of MUNE on three subjects. Our method provides a reproducible estimate for a patient with stable but severe ALS. In a serial study, we demonstrate a decline in the number of motor unit numbers with a patient with rapidly advancing disease. Finally, with our last patient, we show that our method has the capacity to estimate a larger number of motor units.

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We have developed a new method of motor unit number estimation (MUNE) for assessing diseases such as amyotrophic lateral sclerosis (ALS). We used data from the whole stimulus-response curve and then performed a Bayesian statistical analysis. The Bayesian method uses mathematical equations that express the basic elements of motor unit activation after electrical stimulation and allows for the sources of variability and uncertainty in this formulation. The Bayesian MUNE method was used to determine the most probable number of motor units in 8 normal subjects, 49 ALS subjects, and 3 subjects with progressive lower motor neuron (LMN) weakness. In normals the number of motor units was calculated to be 75-85 in hand and 40-58 in foot muscles. In ALS subjects the number of motor units per muscle was less than in normal subjects. In 17 ALS subjects and 3 subjects with LMN weakness the median, ulnar, or peroneal nerve was studied on repeated occasions over an average of 189 days (range 63-1,071) and the number of motor units progressively declined, with a half-life ranging from 62-834 days. The results of our MUNE technique were reproducible on replicate studies. A Bayesian statistical MUNE method is a new approach that can be used to study ALS patients serially for assessment and treatment trials.

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