# Efficient Gaussian process-based motor hotspot hunting with concurrent optimization of TMS coil location and orientation

## TL;DR

This paper introduces a faster and more accurate method for finding the best TMS coil position and angle using advanced optimization techniques.

## Contribution

A novel approach that concurrently optimizes TMS coil location and orientation using Gaussian processes and Bayesian optimization.

## Key findings

- Simultaneous optimization of spatial and angular TMS parameters improves hotspot hunting efficacy and precision.
- Thompson sampling performs best among acquisition functions by balancing exploration and exploitation.
- Arbitrary coil rotation constraints reduce effectiveness and should be removed for better results.

## Abstract

Transcranial magnetic stimulation (TMS) is a widely used non-invasive brain stimulation technique in neuroscience research and clinical applications. TMS-based motor hotspot hunting describes the process of identifying the optimal scalp location to elicit robust and reliable motor responses. It is critical to ensure reproducibility of TMS parameters, as well as to determine safe and precise stimulation intensities in both healthy participants and patients. Typically, this process targets motor responses in contralateral short hand muscles. However, hotspot hunting remains challenging due to the vast parameter space and time constraints. To address this, we present an approach that concurrently optimizes both spatial and angular TMS parameters for hotspot hunting using Gaussian processes and Bayesian optimization. We systematically evaluated five state-of-the-art acquisition functions on electromyographic TMS data from eight healthy individuals enhanced by simulated data from generative models. Our results consistently demonstrate that optimizing spatial and angular TMS parameters simultaneously enhances the efficacy and spatial precision of hotspot hunting. Furthermore, we provide mechanistic insights into the acquisition function behavior and the impact of coil rotation constraints, revealing critical limitations in current hotspot-hunting strategies. Specifically, we show that arbitrary constraints on coil rotation angle are suboptimal, as they reduce flexibility and fail to account for individual variability. We further demonstrate that acquisition functions differ in sampling strategies and performance. Functions overly emphasizing exploitation tend to converge prematurely to local optima, whereas those balancing exploration and exploitation—particularly Thompson sampling—achieve superior performance. These findings highlight the importance of acquisition function selection and the necessity of removing restrictive coil rotation constraints for effective hotspot hunting. Our work advances TMS-based hotspot identification, potentially reducing participant burden and improving safety in both research and clinical applications beyond the motor cortex.

Transcranial magnetic stimulation (TMS) is a non-invasive technique used to stimulate the human brain. It is widely applied in both neuroscience research and clinical practice. A key step in many TMS procedures is hotspot hunting, which involves finding the optimal spot on the scalp to produce muscle responses. This process is often slow and relies on manual adjustments of the stimulation settings. In this study, we developed a method that automatically optimizes the position and rotation of the TMS coil using advanced techniques such as Gaussian processes and Bayesian optimization. We tested our approach on data from healthy participants and supported it with realistic computer simulations. Our results show that our method improves both the speed and accuracy of hotspot detection. We also found that certain choices in the optimization process—especially how uncertainty is managed—have a strong effect on performance. In particular, we show that common restrictions on coil rotation can reduce effectiveness and should be reconsidered. This work provides a step toward making TMS faster, safer, and more reliable for both research and clinical use.