# Towards robust probabilistic maps in Deep Brain Stimulation: exploring the impact of patient number, stimulation counts, and statistical approaches

## TL;DR

This paper explores how patient numbers and stimulation counts affect the stability of brain stimulation maps used in Deep Brain Stimulation, aiming to improve their reliability.

## Contribution

The study introduces a stability boundary model for probabilistic maps in DBS and evaluates statistical methods for robustness.

## Key findings

- A non-linear trade-off exists between patient count and stimulation count for stable probabilistic maps.
- Bayesian t-test achieves stability with fewer patients compared to Wilcoxon-based methods.
- Stability boundary defines minimum data requirements for anatomically robust maps.

## Abstract

Probabilistic Stimulation Maps (PSMs) are increasingly employed to identify brain regions associated with optimal therapeutic outcomes in Deep Brain Stimulation (DBS). However, their reliability and generalizability are challenged by the limited size of most patient cohorts and the inherent variability introduced by different statistical methods and input data configurations. This study aimed to investigate the geometrical variability of Probabilistic Sweet Spots (PSS) as a function of both the number of patients (nPat) and the number of stimulations per patient (nStim), and to model a stability boundary defining the minimum data requirements for obtaining geometrically stable PSS.

Three statistical approaches–Bayesian t-test, Wilcoxon test with False Discovery Rate (FDR) correction, and Wilcoxon test with nonparametric permutation correction–were applied to two patient cohorts: a primary cohort of 36 patients undergoing DBS for Parkinson’s Disease (PD), and a secondary cohort of 61 patients treated for Essential Tremor (ET), used to assess generalizability. Stimulation test data was collected intra-operatively for the first cohort and post-operatively for the second one. Geometric stability was evaluated based on variability in PSS volume extent and centroid location.

The analysis revealed a non-linear trade-off between nPat and nStim to yield stable PSS. A stability boundary was defined, representing the minimum combinations of nPat–nStim required for anatomically robust PSS. Among the tested methods, the Bayesian t-test achieved stability with smaller sample sizes (∼15 patients) and demonstrated a consistent performance across both cohorts. In contrast, the Wilcoxon-based methods showed variable behavior between cohorts, which differed in symptom type and testing phase (intra-operative testing vs. post-operative screening).

The proposed PSS stability boundary provides a practical reference for designing DBS studies and stimulation screening protocols aimed at probabilistic mapping. The Bayesian t-test emerged as a reliable method across both cohorts, supporting its potential in studies with limited sample sizes and scenarios where the method needs to be readily generalized to varying symptoms. These findings underscore the importance of considering both cohort size and stimulation count in probabilistic DBS mapping and call for further investigation into method-specific sensitivities to clinical and procedural factors.