Separating three variability and noise sources in the response fluctuation of brain stimulation

Motor-evoked potentials (MEPs) are among the few directly observable responses to suprathreshold brain stimulation and serve a variety of applications. If the MEP size is graphed over the stimulation strength, they form an input-output (IO), recruitment, or dose-response curve. Previous statistical models with two variability sources inherently consider the small MEPs at the low plateau as part of the neural recruitment properties. However, recent studies demonstrated that small MEP responses are contaminated and over-shadowed by background noise of mostly technical quality and suggested that the 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 model with three variability sources and a logarithmic logistic function without a lower plateau. Compared to previous models, we incorporated an additional source for background noise from amplifiers, electrode impedance, and remote bioelectric activity, which form the obesrved low-side plateau. Compared to the dual-variability source modes, 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, reducing the risk of spurious results from inappropriate statistical methods. By providing a more accurate representation of MEP responses and variability sources, this approach advances our understanding of cortical excitability and may improve the assessment of neuromodulation effects.