# How Sample Size Impacts Probabilistic Stimulation Maps in Deep Brain Stimulation

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Clinical Data

#### 2.2. Electric Field Simulations

_{2}-weighted MRI. The DBS lead was modeled according to manufacturer specification and placed in the tissue volume according to the post-operative CT. A 250 µm thick peri-electrode space surrounding the lead was modeled as white brain matter [20]. The simulations were computed in a box of size 100 × 100 × 100 mm with a physics-controlled mesh (the finest element size closest to the lead).

#### 2.3. Image Normalization

#### 2.4. Probabilistic Stimulation Maps

_{i}less than 10% of all the sampled simulations or 5, whichever was greatest, were excluded from the analysis, i.e., the threshold was dependent on the sample size. To evaluate the effect of the exclusion threshold, complete analyses were also run with fixed thresholds of N

_{i}≤ 5 and N

_{i}≤ 12 corresponding to the minimum threshold and the 10% threshold for 30 patients. The $\widehat{TR}$, weighted with the electric field norm

**E**(V/m) over the stimulation amplitude A (V), was calculated in each voxel i according to

#### 2.5. Evaluation of Sample Size

#### 2.6. Data Analysis

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The overall p-value for the computed p-maps with (

**a**) 200 and (

**b**) 1000 permutations with 10% exclusion threshold and with 200 permutations for fixed exclusion thresholds of (

**c**) 5 simulations and (

**d**) 12 simulations. All data are shown with the median (straight line) and the variation is displayed with the quartiles (dashed line) and max/min (dotted line).

**Figure 2.**Computed cluster volumes for (

**a**–

**c**) high improvement and (

**d**–

**f**) low improvement for the 10% exclusion threshold (top row), and fixed threshold at 5 simulations (second row) and 12 simulations (bottom row).

**Figure 3.**The total volume included in the statistical analysis (

**a**–

**c**), and the mean number of simulations in the analyzed voxels (Ni) (

**d**–

**f**) for the 10% exclusion threshold (top row), and fixed threshold at 5 simulations (second row) and 12 simulations (bottom row).

**Figure 4.**Dice coefficient for the clusters within each sample size for the (

**a**–

**c**) high-improvement clusters and (

**d**–

**f**) low-improvement clusters with the 10% exclusion threshold (top row), and fixed threshold at 5 simulations (second row) and 12 simulations (bottom row).

**Figure 5.**The top row shows on the left an example (n = 60) of a p-map and on the right the same p-map as high- and low-improvement clusters in sagittal views together with outlines from a digital version of Morel’s atlas [22,23]. The bottom row shows sagittal views of the outlines from all high- and low-improvement clusters computed with 5, 30, and 60 patients. The clusters converge with increasing sample size and the location is expanded in the superior direction. All images are from the analysis with the 10% exclusion threshold. CL = central lateral nucleus, CM = centromedian nucleus, MDpc = mediodorsal nucleus (parvocellular division), PuM = medial pulvinar, STN = subthalamic nucleus, VApc = ventral anterior nucleus (parvocellular division), VLpd = ventral lateral posterior nucleus (dorsal division), VLpv = ventral lateral posterior nucleus (ventral division), VM = ventral medial nucleus, VPM = ventral posterior medial nucleus, A = anterior, P = posterior, n = number of included patients.

**Table 1.**Median cluster volumes for 5, 30, and 60 patients and overall variability (mean ± standard deviation) of the IQR over the total range of sample sizes.

10% Threshold | Fixed Threshold of 5 | Fixed Threshold of 12 | |
---|---|---|---|

High improvement | |||

Median volume [mm^{3}] | |||

n = 5 | 54 | 44 | 0.3 |

n = 30 | 277 | 290 | 227 |

n = 60 | 229 | 490 | 373 |

IQR [mm^{3}] | 96 ± 24 | 187 ± 64 | 94 ± 43 |

Low improvement | |||

Median volume [mm^{3}] | |||

n = 5 | 3.9 | 4.1 | 0 |

n = 30 | 89 | 154 | 107 |

n = 60 | 121 | 251 | 177 |

IQR [mm^{3}] | 51 ± 14 | 75 ± 22 | 50 ± 26 |

**Table 2.**The number of patients (n) where the largest median DC values were reached and the overall variability (mean ± standard deviation) of the IQR over the total range of sample sizes.

10% Threshold | Fixed Threshold of 5 | Fixed Threshold of 12 | |
---|---|---|---|

High improvement | |||

DC max | 0.73 (n = 57) | 0.68 (n = 61) | 0.70 (n = 47) |

IQR | 0.16 ± 0.06 | 0.17 ± 0.06 | 0.15 ± 0.06 |

Low improvement | |||

DC max | 0.69 (n = 58) | 0.72 (n = 61) | 0.72 (n = 60) |

IQR | 0.15 ± 0.05 | 0.15 ± 0.06 | 0.13 ± 0.06 |

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**MDPI and ACS Style**

Nordin, T.; Blomstedt, P.; Hemm, S.; Wårdell, K.
How Sample Size Impacts Probabilistic Stimulation Maps in Deep Brain Stimulation. *Brain Sci.* **2023**, *13*, 756.
https://doi.org/10.3390/brainsci13050756

**AMA Style**

Nordin T, Blomstedt P, Hemm S, Wårdell K.
How Sample Size Impacts Probabilistic Stimulation Maps in Deep Brain Stimulation. *Brain Sciences*. 2023; 13(5):756.
https://doi.org/10.3390/brainsci13050756

**Chicago/Turabian Style**

Nordin, Teresa, Patric Blomstedt, Simone Hemm, and Karin Wårdell.
2023. "How Sample Size Impacts Probabilistic Stimulation Maps in Deep Brain Stimulation" *Brain Sciences* 13, no. 5: 756.
https://doi.org/10.3390/brainsci13050756