On the variability of motor-evoked potentials: experimental results and mathematical model

Abstract

The purpose of this study was to determine the form of the relation between the mean amplitude and variance of motor-evoked potentials (MEP). To this end, single-pulse transcranial magnetic stimulation (TMS) was applied over the motor cortex of seventeen neurologically normal adult human subjects. The coil was positioned at a locus on the scalp that elicited an MEP in the first dorsal interosseous (FDI) at the lowest stimulus intensity. The subjects were instructed to maintain tonic activity in the FDI of 5 or 10% of the maximum voluntary contraction (MVC). The relation between MEP variance and amplitude was found to have an inverted parabolic shape, with maximal variance occurring near the half-maximal MEP amplitude. The coefficient of variation $\text{CV}$ of MEPs decreased approximately as a rectangular hyperbolic function of MEP amplitude (i.e. ~ 1/MEP). A probabilistic model is proposed to explain the inverted parabolic relation between MEP variance and MEP amplitude, as well as the sigmoid shape of the MEP input–output relation (i.e. stimulus–response curve). The model is based on a description of α-motoneurons as binary threshold units, with unit thresholds distributed according to a positively skewed probability density function. The units are driven by noisy synaptic input currents having a Gaussian distribution. The model predicts an inverse parabolic relation between MEP variance and amplitude and a sigmoid input–output relation, as experimentally observed. Furthermore, increasing model motoneuron excitability by increasing the background synaptic drive increases MEP variability independently of MEP size, a surprising prediction. The model also explains the approximately rectangular hyperbolic relation between $\text{CV}$ and MEP amplitude. The implications of these results for the interpretation of neurophysiological experiments and the statistical analysis of MEPs are discussed.