Motor-evoked potentials (MEPs) are among the few directly observable responses to external brain stimulation and serve a variety of applications, often in the form of input-output (IO) curves. Previous statistical models with two variability sources inherently consider the small MEPs at the low-side plateau as part of the neural recruitment properties. However, recent studies demonstrated that small MEP responses under resting conditions are contaminated and over-shadowed by background noise of mostly technical quality, e.g., caused by the amplifier, and suggested that the neural recruitment curve should continue below this noise level. This work intends to separate physiological variability from background noise and improve the description of recruitment behaviour. We developed a triple-variability-source model around a logarithmic logistic function without a lower plateau and incorporated an additional source for background noise. Compared to models with two or fewer variability sources, our approach better described IO characteristics, evidenced by lower Bayesian Information Criterion scores across all subjects and pulse shapes. The model independently extracted hidden variability information across the stimulated neural system and isolated it from background noise, which led to an accurate estimation of the IO curve parameters. This new model offers a robust tool to analyse brain stimulation IO curves in clinical and experimental neuroscience and reduces the risk of spurious results from inappropriate statistical methods. The presented model together with the corresponding calibration method provides a more accurate representation of MEP responses and variability sources, advances our understanding of cortical excitability, and may improve the assessment of neuromodulation effects.

翻译：运动诱发电位（MEP）是外部脑刺激产生的少数可直接观测的响应之一，常以输入-输出（IO）曲线的形式应用于多种场景。先前包含两种变异源的统计模型本质上将低侧平台区的小幅MEP视为神经募集特性的组成部分。然而，近期研究表明，静息状态下的小幅MEP响应受到主要来自技术性背景噪声（如放大器引起）的污染与掩盖，并指出神经募集曲线应在此噪声水平之下继续延伸。本研究旨在分离生理变异性与背景噪声，并改进对募集行为的描述。我们围绕无下平台区的对数逻辑函数构建了三变异源模型，并额外纳入背景噪声源。与仅含两种或更少变异源的模型相比，我们的方法能更好地描述IO特性，所有受试者和脉冲形态下更低的贝叶斯信息准则分数证明了这一点。该模型独立提取了受刺激神经系统中隐藏的变异性信息，并将其与背景噪声分离，从而实现了对IO曲线参数的精确估计。这一新模型为临床与实验神经科学中分析脑刺激IO曲线提供了稳健工具，并降低了因统计方法不当而产生伪结果的风险。所提出的模型及其配套校准方法能更准确地表征MEP响应与变异源，推进我们对皮层兴奋性的理解，并可能提升神经调控效应的评估效果。