# Optimizing Sample Size and Statistical Methods for Probabilistic Sweet Spot Mapping in Deep Brain Stimulation

Vittoria Bucciarelli, Dorian Vogel, Teresa Nordin, Marc Stawiski, Jérôme Coste, Jean-Jacques Lemaire, Karin Wårdell, Raphael Guzman, Simone Hemm

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Vittoria Bucciarelli, Dorian Vogel, Teresa Nordin, Marc Stawiski, Jérôme Coste, et al., Optimizing Sample Size and Statistical Methods for Probabilistic Sweet Spot Mapping in Deep Brain Stimulation. Conference proceedings: .. Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual Conference, 2025, 47th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), pp.1-4. 10.1109/EMBC58623.2025.11251620. hal-05400468

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# Optimizing Sample Size and Statistical Methods for Probabilistic
Sweet Spot Mapping in Deep Brain Stimulation *

Vittoria Bucciarelli, Member, IEEE, Dorian Vogel, Teresa Nordin, Marc Stawiski, Jérôme Coste, Jean-Jacques Lemaire, Karin Wårdell, Member, IEEE, Raphael Guzman, Simone Hemm, Member, IEEE

**Abstract**— Deep Brain Stimulation (DBS) for movement disorders can greatly benefit from the insights provided by probabilistic mapping. This consists in the application of statistical approaches to stimulation data of multiple patients. Such analysis is influenced by the input data and chosen statistical method, hindering the generalizability of the obtained results. This study aims at determining the minimum sample size yielding stable results, and the statistical approach providing higher results consistency. Intra-operative stimulation test data of 36 patients who underwent DBS surgery for Parkinson's Disease (PD), were used to compute Probabilistic Sweet Spots (PSS). The PSS were calculated with sample sizes ranging from 4 to 36 (steps of 2) using Bayesian t-test, Wilcoxon test with False Discovery Rate correction and Wilcoxon test with nonparametric permutations correction. Calculations were repeated 10 times. Obtained PSS were compared in terms of size and position variability across sample sizes and between statistical methods. Only the PSS computed with the Bayesian t-test reached stability in all the three chosen metrics. Stability in size and centroid location was reached from a sample size of 14 patients, while the covered volume (Dice coefficient) stabilized from a sample size of 18 patients. The Bayesian t-test also provided higher results consistency with respect to the other approaches. The composition of the dataset in cohorts with <20 patients has a greater influence on the extent and location of computed PSS. Moreover, the Bayesian t-test demonstrated the highest suitability to extrapolate results from analyses involving small sample sizes.

**Clinical Relevance**— Determining the minimum number of patients and most suitable method to calculate stable PSS is crucial for ensuring the reliability and clinical applicability of Probabilistic Mapping approaches. This ensures the generalizability of findings, allowing for a more accurate understanding of the underlying pathology. These insights can be used to refine diagnostic approaches and optimize clinical interventions, ultimately improving patient care.

## I. INTRODUCTION

Deep Brain Stimulation is a neurostimulation therapy to alleviate symptoms of movement (e.g., PD, Essential Tremor) and treatment resistant psychiatric disorders [1]. The deep brain structures targeted by the stimulation are disorder- and symptom-specific. However, for most disorders, there is no

universal agreement on the optimal stimulation areas, since the disease mechanisms are still not completely understood [2]. In the last decades, Probabilistic Mapping has gained increasing attention as data-driven approach to determine optimal stimulation areas, also known as Probabilistic Sweet Spots (PSS) [3], [4]. Probabilistic Mapping is, indeed, the core part of DBS group analysis, which aims to extract general information by analyzing stimulation data of a patient cohort. Starting from the patients' brain images, electrode positions, and stimulation parameters, the Electric Field (EF) spread in the tissue can be simulated [5]. This allows the Volume of Tissue Activated (VTA) to be delineated for each combination of stimulation parameters. The transformation of all the patients' VTAs into a normalized anatomical space (anatomical template [6]) allows the joint examination of the VTAs. The effects associated with the stimulation of each voxel in the anatomical space are statistically tested to obtain PSS [3], [7]. PSS comprise, in fact, the voxels significantly associated with high symptom improvement. However, some recent studies based on post-operative stimulation tests data, have shown that the computed PSS depend on the input stimulation data [8], and on the chosen statistical approach [9]. The objective of this study was, therefore, to investigate how many patients are needed to obtain stable PSS results. PSS stability was assessed in terms of volume size and location. The calculations were repeated using three different statistical methods, with the secondary objective of determining which of them would yield the most consistent results.

## II. MATERIALS AND METHODS

### A. Patients' data

Intra-operative stimulation test data of 36 patients with PD were collected at the Department of Neurosurgery of Clermont-Ferrand University Hospital (France) during bilateral subthalamic nucleus DBS surgery. All the patients signed a written informed consent (Ptoleme Electrophysiologie project: IRB 5921, CE-CIC-GREN-18-03) for the retrospective data analysis. The data consisted of stimulation parameters (current amplitude, position of stimulation) and the corresponding symptom improvement score. Stimulation tests (semi-electrode; Alpha-Omega Engineering, Israel; frequency 130 Hz; pulse width 60 µs) was

*Research supported by the Swiss National Science Foundation (Grant No. 205320-207491).

V.B., D.V., M.S. and S.H. Institute for Medical Engineering and Medical Informatics, School of Life Sciences, University of Applied Sciences and Arts Northwestern Switzerland, Muttenz, Switzerland, (corresponding author: vittoria.bucciarelli@fhnw.ch, e-mails: dorian.vogel@fhnw.ch, marc.jermann@fhnw.ch, simone.hemm@fhnw.ch).

T.N., K.W. Department of Biomedical Engineering, Linköping University, Linköping, Sweden (e-mails: teresa.nordin@liu.se, karin.wardell@liu.se).

J.C., J.J.L. Université Clermont Auvergne, Clermont Auvergne INP, CHU Clermont-Ferrand, CNRS, Institut Pascal, F-63000 Clermont-Ferrand, France (e-mails: jerome.coste@uca.fr, jjlemaire@chu-clermontferrand.fr).

R.G. Department of Neurosurgery, University Hospital Basel, Basel, Switzerland (e-mail: Raphael.Guzman@usb.ch).
<figure><img src="image_3.png" /><figcaption>Figure 1. (A) Graphical representation of the Probabilistic Mapping workflow from the generation of a patient-specific brain conductivity model to Electric Field simulations, transformation of Volumes of Tissue Activated (VTAs) to a cohort-specific anatomical atlas and voxel-wise statistical testing. The Probabilistic Sweet Spot (PSS) is obtained at the end of the workflow. The PSS was computed with 3 different statistical approaches and variable sample sizes. The used datasets ranged from 4 patients to 36 in steps of 2. The dataset sampling was repeated 10 times.</figcaption></figure>

(B) The impact of sample size on the PSS was evaluated by computing geometrical variability metrics between one sample size and the next (increased of 2 patients) for each method and each iteration. For each method the results were averaged across iterations, to determine whether the PSS geometrical characteristics stabilize after a certain sample size.

(C) To assess methods consistency, geometrical variability metrics were computed between the 10 PSS of each method and each sample size. The metrics distributions corresponding to each method (considering all the sample sizes together) were statistically compared.

applied in 1-mm steps over 14 mm, increasing the current amplitude between 0.2 and 3 mA (steps of 0.2 mA). Clinical improvement was classified by the neurologist as “no improvement” (0%), “poor” (25%), “fair” (50%), “good” (75%), “excellent” (100%). Intermediate values were also used, if deemed necessary. The lowest current amplitude that yielded the highest improvement (motor threshold) was recorded for each position. Data from the first implanted hemisphere (left) were used.

## B. Probabilistic Mapping workflow

**Fig. 1A** provides a graphical representation of the Probabilistic Mapping workflow. Patient-specific brain tissue conductivity models were generated from T1 brain MR images with the software ELMA<fnref n="1" /> [10], classifying the tissues in cerebrospinal fluid, grey and white matter. Microelectrode models were placed in the patient reference space with 3D Slicer<fnref n="2" /> Stereotaxia plugin [11], and EF volumes were simulated in Comsol Multiphysics 5.5 (COMSOL AB,

Sweden) [12]. Stimulation used the active microelectrode contact as source and the guide tube as ground, with the other contacts left floating. EF meshes of each patient were transferred to a group-specific anatomical template, generated with an optimized anatomical normalization method [6], and resampled on a grid with units (voxels) of 0.5x0.5x0.5 mm³. The meshes were thresholded at 0.2 V mm⁻<fnref n="1" /> (minimum EF value needed to activate neurons with axons of 3–4 µm [5]) to obtain the VTAs. Each VTA was labelled with the corresponding symptom improvement score. Therefore, each voxel encompassed by many VTAs was associated with a distribution of improvement scores. Voxel-wise statistical testing was performed to compute PSS, meaning that each voxel was statistically tested to determine its membership to the PSS. Three statistical approaches were implemented: Wilcoxon test with False Discovery Rate correction (WFDR) as state-of-the-art method, Wilcoxon test with nonparametric permutations correction (WPerm) proposed as alternative

<footnote n="1">¹ https://liu.se/en/article/ne-downloads</footnote>

<footnote n="2">² https://www.slicer.org/</footnote>
correction not affected by false positives inflation [13], and Bayesian t-test (B) given its promising results in fMRI [14]. For the WPerm approach, inspired by [15], the improvement scores were permuted 200 times between patients and stimulation configurations, yielding 200 permuted datasets. A Probabilistic Stimulation Map was obtained from each dataset. The p-values assigned to each voxel across the 200 maps were used to calculate the final corrected p-value associated with the voxel.

Fixed arbitrary improvement thresholds can be very sensitive to use-case scenarios (e.g. specific patient cohort) [9]. To better adapt to the different cohort samples, a flexible improvement threshold was used. Thus, the null and alternative hypotheses for the tests were:

- H₀: improvement≤median(voxel_improvement)

- H₁: improvement>median(voxel_improvement)

Binary PSS were generated by retaining only voxels with p<0.05 (for the Wilcoxon test) or Bayes Factor≥10 (for the Bayesian t-test).

### C. Impact of sample size

To evaluate the impact of the sample size (Fig. 1B), the PSS were computed from datasets with an increasing patient number, ranging from 4 (randomly sampled) to 36, adding 2 patients at each step (randomly sampled). The procedure was repeated 10 times (iterations) for each statistical test, yielding 161 (16x10 with 4 to 34 patients + 1 from the whole cohort) PSS per test. To assess the PSS geometric variability with increasing sample size, for each method and each of the 10 iterations, the following metrics were computed between one

dataset and the next (e.g. between 4Pat and 6Pat, 6Pat and 8Pat):

* Volume differences normalized by the largest volume in the pair [%]

* Dice coefficient [%]

* Centroid distances normalized to the largest diameter in the pair [%]

Results were then averaged between the repeated iterations. A method was deemed to have achieved stability when the variations between successive datasets remained within 10%.

### D. Methods consistency

The consistency of statistical methods across datasets with different compositions was also analyzed (Fig. 1C). For each method and each sample size (4Pat, 6Pat...34Pat) the 10 PSS were used to compute the following metrics:

* Volume coefficient of variation [%]:
  $$ \frac{\text{std}(\text{volumes})}{\text{mean}(\text{volumes})} * 100 $$

* Pairwise Dice coefficients [%]

* Pairwise centroid distances normalized to largest diameter in the pair [%]

The metrics values for all the patients' groups were compared between methods with one-way ANOVA, or Kruskal-Wallis test, and Tukey post-hoc testing.

## III. RESULTS

### A. Impact of sample size

The normalized volume differences, Dice coefficients and normalized centroid distances between one dataset and the

<figure><img src="image_4.png" /><figcaption>Figure 2. Volume differences normalized by largest volume (A), Dice coefficients (B) and centroid distances normalized by largest diameter (C) for B (blue), WFDR (green) and WPerm (pink). The metrics were calculated between one sample size and the next. Points represent the average value between iterations and the filled area represents the standard deviation.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Figure 3. Volume coefficients of variation (A), Dice coefficients (B) and centroid distances normalized by largest diameter (C) for B (blue), WFDR (green) and WPerm (pink). The metrics were first calculated between the 10 PSS of each patient group and then averaged. Bars represent the average value and the error bars the standard deviation (*p<0.05, **p<0.01, ***p<0.001).</figcaption></figure>
next for the three statistical tests are shown in **Fig. 2A, 2B, 2C**, respectively. The PSS computed with the B method showed a stable volume and centroid location from a sample size of 14 patients (~210 stimulations), and a consistent covered volume (overlap, Dice coefficient) from a sample size of 18 patients (~270 stimulations). The WPerm did not reach stability with the chosen threshold of 10%, while the WFDR presented stable centroid locations from 14 patients onwards, but variable covered volumes and volume sizes.

## B. Methods consistency

When comparing the tests in terms of consistency, B showed significantly lower volume coefficients of variation (33.1±20.9%) than WFDR (72.6±41.1%) and WPerm (74.4±15.7%) (**Fig. 3A**, p<0.01). The highest Dice coefficients were observed in B (58.6±26.3%) followed by WFDR (49.8±30.52%) and WPerm (20.9±20.5%) (**Fig. 3B**, p<0.01). The same ranking was observed when assessing the consistency in terms of centroid distances (**Fig. 3C**): B had significantly lower values than (11.2±12.4%), WFDR (16.1±17.5%) and WPerm (25.4±20.8%) (p<0.01).

## IV. DISCUSSION

This study aimed to assess the minimum sample size required to obtain geometrically stable PSS. Moreover, the PSS were calculated with three different statistical approaches to determine the approach that yielded the most consistent results. The PSS calculated with the Bayesian t-test were the most consistent across different datasets and were the only ones to reach a stable point in all three computed metrics. The B PSS results stabilized starting from a sample size of 14 and 18 patients, depending on the metrics considered. This indicates that results obtained with lower sample sizes should be evaluated with care, since the PSS location would be more influenced by the electrode positions of the patients included in the dataset. The resulting minimum sample size is smaller than the one reported by [8] of 30 patients. This could be due to the difference in statistical tests or in the nature of the stimulation data. This study is, in fact, based on intra-operative stimulation tests instead of post-operative monopolar review data. Intra-operative tests allow exploration of more stimulation positions with a smaller spacing between one and the next, yielding a higher number of data points per patient (~15±3 in this study, ~4 in [8]). The higher number of available stimulations per patient may result in the PSS stabilization already at lower sample sizes. Conversely, the minimum number of stimulations reported by [8] (~120) is lower than the one identified in this study (~210), highlighting the interplay between patient number and amount of data points in defining the minimum PSS sample size. A limitation of this study is that it primarily focused on the impact of the number of patients, without accounting for the influence of the number of stimulation points per patient. Future studies should, therefore, investigate the trade-off between sample size and number of stimulations. Determining the minimum number of patients and/or stimulations required to achieve stable PSS is, in fact, crucial for assessing the reliability and generalizability of Probabilistic Mapping results. Moreover, the patient cohort available for this study was of medium size, making it valuable to replicate the analysis with a larger cohort. However, in DBS research, small- to medium-sized

cohorts are most commonly encountered. In agreement with [9], we observed that the chosen method impacts on extent and location of the computed PSS. For this reason, we also examined the consistency of statistical methods as probabilistic mapping workflows should prioritize approaches that ensure robust results even with a limited number of patients. The greater the validity of these findings, the more they contribute to advancing the understanding of pathological mechanisms and optimizing clinical practice.

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