Electromagnetic stimulation probes and modulates the neural systems that control movement. Key to understanding their effects is the muscle recruitment curve, which maps evoked potential size against stimulation intensity. Current methods to estimate curve parameters require large samples; however, obtaining these is often impractical due to experimental constraints. Here, we present a hierarchical Bayesian framework that accounts for small samples, handles outliers, simulates high-fidelity data, and returns a posterior distribution over curve parameters that quantify estimation uncertainty. It uses a rectified-logistic function that estimates motor threshold and outperforms conventionally used sigmoidal alternatives in predictive performance, as demonstrated through cross-validation. In simulations, our method outperforms non-hierarchical models by reducing threshold estimation error on sparse data and requires fewer participants to detect shifts in threshold compared to frequentist testing. We present two common use cases involving electrical and electromagnetic stimulation data and provide an open-source library for Python, called hbMEP, for diverse applications.

翻译：电磁刺激技术能够探测并调控控制运动的神经系统。理解其效应的关键在于肌肉募集曲线，该曲线描绘了诱发电位幅值与刺激强度的映射关系。现有曲线参数估计方法需要大量样本，但由于实验条件限制，获取足量样本往往难以实现。本文提出一种分层贝叶斯框架，该框架能够处理小样本数据、应对异常值、模拟高保真数据，并返回曲线参数的后验分布以量化估计不确定性。该方法采用修正逻辑函数估计运动阈值，交叉验证表明其在预测性能上优于传统使用的S型函数替代方案。在仿真实验中，本方法通过降低稀疏数据上的阈值估计误差而优于非分层模型，且相较于频率学派检验方法，检测阈值偏移所需的受试者数量更少。我们展示了涉及电刺激和电磁刺激数据的两种典型应用场景，并提供了开源Python库hbMEP以支持多样化应用。