P. G. Ridall

The relationship between Bayesian motor unit number estimation and histological measurements of motor neurons in wild-type and SOD1G93A mice

OBJECTIVE To assess the relationship between Bayesian MUNE and histological motor neuron counts in wild-type mice and in an animal model of ALS. METHODS We performed Bayesian MUNE paired with histological counts of motor neurons in the lumbar spinal cord of wild-type mice and transgenic SOD1(G93A) mice that show progressive weakness over time. We evaluated the number of acetylcholine endplates that were innervated by a presynaptic nerve. RESULTS In wild-type mice, the motor unit number in the gastrocnemius muscle estimated by Bayesian MUNE was approximately half the number of motor neurons in the region of the spinal cord that contains the cell bodies of the motor neurons supplying the hindlimb crural flexor muscles. In SOD1(G93A) mice, motor neuron numbers declined over time. This was associated with motor endplate denervation at the end-stage of disease. CONCLUSION The number of motor neurons in the spinal cord of wild-type mice is proportional to the number of motor units estimated by Bayesian MUNE. In SOD1(G93A) mice, there is a lower number of estimated motor units compared to the number of spinal cord motor neurons at the end-stage of disease, and this is associated with disruption of the neuromuscular junction. SIGNIFICANCE Our finding that the Bayesian MUNE method gives estimates of motor unit numbers that are proportional to the numbers of motor neurons in the spinal cord supports the clinical use of Bayesian MUNE in monitoring motor unit loss in ALS patients.

Biological basis for motor unit number estimation through Bayesian statistical analysis of the stimulus-response curve.

Publisher Summary This chapter discusses that a method is developed on a Bayesian statistical analysis of the data obtained from the stimulus–response curve. The stimulus–response curve is the graph of the compound muscle action potential (CMAP), obtained from repeated stimulation of a nerve at stimulus intensities from the threshold to supramaximal, and has been found to differ between normal subjects and patients with amyotrophic lateral sclerosis (ALS). The chapter reviews that in Bayesian statistical analysis of any situation, unknown quantities or parameters are considered to be random variables. Data that are relevant to the situation are then collected and used to reduce the uncertainty of the unknowns. It also discusses that the information from the data about the unknowns is summarised by the “likelihood function”. The likelihood function relates how the observed data are likely to have been obtained in terms of the unknowns. A mathematical model of motor unit activation after electrical stimulation was formulated to provide the likelihood function. The chapter provides the biological basis of this mathematical model and the assumptions that have been made. The assumptions cover the development of an action potential after electrical stimulation of a motor nerve, the motor unit action potentials (MUAPs), and the summation of individual MUAPs to form a CMAP.

Results of Bayesian statistical analysis in normal and ALS subjects

Publisher Summary This chapter reviews the need for a broadly applicable motor unit number estimation (MUNE) method to allow research into possible therapies for amyotrophic lateral sclerosis (ALS). An ideal MUNE method needs to be applicable to all stages of ALS, to avoid the problems associated with sampling motor units, to allow for motor unit variability, and to have simple data collection methods so that it can be widely applied in different centers. The chapter explores that the knowledge obtained from the study of the stimulus–response curve, and from existing MUNE methods and their limitations led to the development of a Bayesian statistical approach to MUNE. The biological background and statistical methods for Bayesian MUNE method based on the whole stimulus–response curve have been presented. The results of studies in normal subjects and patients with ALS are also discussed in the chapter.

Bayesian analysis of the stimulus-response curve

In this paper we present our Bayesian method for carrying out motor unit number estimation (MUNE) using stimulus–response data collected from surface electrophysiological recordings. We formulate and justify our assumptions in Ridall et al. (2006) and base these on available scientific evidence, as outlined in the previous paper. The object of our methodology is to express the uncertainty about the number of motor units in a muscle in terms of a posterior distribution. From studies taken over time, these posterior distributions can be used to estimate the rate of loss of motor units. A by-product of this method of MUNE is that it provides a means of tracking a given population of motor units over time. Examples of the parameters that can be tracked over time include the distribution of the excitability parameters, the single motor unit action potentials and the between and within motor unit variability.