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.

本研究的目的是确定运动诱发电位 (MEP) 的平均振幅和方差之间的关系形式。为此，单脉冲经颅磁刺激 (TMS) 应用于 17 名神经系统正常成人受试者的运动皮层。线圈位于头皮上的一个位置，在最低刺激强度下在第一背侧骨间 (FDI) 中引发 MEP。指示受试者在 FDI 中保持最大自主收缩 (MVC) 的 5% 或 10% 的强直活动。发现 MEP 方差和幅度之间的关系具有倒抛物线形状，最大方差发生在半最大 MEP 幅度附近。变异系数\(\text{CV}\)MEPs 的下降近似为 MEP 振幅的矩形双曲线函数（即~1/MEP）。提出了一个概率模型来解释 MEP 方差和 MEP 幅度之间的倒抛物线关系，以及 MEP 输入 - 输出关系（即刺激 - 响应曲线）的 sigmoid 形状。该模型基于将 α-运动神经元描述为二元阈值单元，单元阈值根据正偏态概率密度函数分布。这些单元由具有高斯分布的嘈杂突触输入电流驱动。正如实验所观察到的，该模型预测 MEP 方差和幅度之间的反抛物线关系以及 sigmoid 输入-输出关系。此外，通过增加背景突触驱动来增加模型运动神经元的兴奋性，增加了独立于 MEP 大小的 MEP 变异性，这是一个令人惊讶的预测。该模型还解释了之间的近似矩形双曲线关系\(\text{CV}\)和 MEP 幅度。讨论了这些结果对神经生理学实验解释和 MEP 统计分析的影响。