Hierarchical Bayesian estimation of motor-evoked potential recruitment curves yields accurate and robust estimates

TL;DR

This paper introduces a hierarchical Bayesian method for estimating muscle recruitment curves from small samples, improving accuracy, robustness, and uncertainty quantification over traditional approaches, with practical applications and open-source tools.

Contribution

A novel hierarchical Bayesian framework that accurately estimates recruitment curves from limited data, outperforming existing models and providing uncertainty measures.

Findings

Outperforms non-hierarchical models in threshold estimation accuracy.

Requires fewer participants to detect threshold shifts.

Provides a flexible, open-source Python library for diverse applications.

Abstract

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.