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# Statistical Multiscore Functional Atlas Creation for Image-guided Deep Brain Stimulation

Xiongbiao Luo, Zhuo Zeng, Song Zheng, Jianhui Chen, Pierre Jannin

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Xiongbiao Luo, Zhuo Zeng, Song Zheng, Jianhui Chen, Pierre Jannin. Statistical Multiscore Functional Atlas Creation for Image-guided Deep Brain Stimulation. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 2025, 33, pp.818-828. 10.1109/tnsre.2025.3542395. hal-04981949

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# Statistical Multiscore Functional Atlas Creation for Image-Guided Deep Brain Stimulation

Xiongbiao Luo<sup>D</sup>, Senior Member, IEEE, Zhuo Zeng, Song Zheng, Jianhui Chen, and Pierre Jannin, Senior Member, IEEE

**Abstract**— Deep brain stimulation is increasingly performed for patients who suffer from drug-resistant movement disorders. It still remains challenging to determine the optimal electrode contact location to obtain the optimal surgical outcome and simultaneously minimize adverse effects. This paper proposes to construct a new statistical functional atlas to guide electrode contact targeting during deep brain stimulation. The construction of the atlas consists of four main steps: 1) multimodal image segmentation and registration, 2) activation volume modeling, 3) computing and combining multiple functional scores, and 4) generation of multiscore functional atlas. Based on these steps, the statistical functional atlas is created by integrating anatomical information analysis with multiple clinical scores that postoperatively characterize stimulation efficacy (e.g., motor symptom) and adverse effect. We evaluated the created atlas on 40 subthalamic nucleus stimulated parkinsonian patient datasets. The experimental results show that the reproducibility of the created statistical functional atlas was more than 75% in the cross validation. In addition, the motor, neuropsychological, and health scores can be reproduced up to 77%, 82%, and 78%. Compared to the actually implanted electrode position,

the atlas predicted and the manually planned electrode position errors were 2.89 mm and 2.38 mm, respectively. The constructed multiscore atlas provides an automatic and accurate electrode targeting strategy that potentially outperforms manually planned approaches.

**Index Terms**— Deep brain stimulation, Parkinson's disease, probabilistic atlas, volume of tissue activated.

## I. INTRODUCTION

DEEP brain stimulation (DBS) is a surgical procedure that can treat movement disorders, e.g., Parkinson's disease (PD), essential tremor, dystonia, chronic pain, major depression and obsessive-compulsive disorder [1]. Electrodes are placed at deep brain structures such as the subthalamic nucleus (STN) or the globus pallidus internus (GPi) in the brain. The performance of the DBS procedure depends critically on accurate electrode contact targeting.

Conventionally, the electrode contact targeting in DBS consists of two steps: (1) preoperative planning to manually determine the electrode target position and (2) intraoperative adjustment to obtain the finally placed electrode contact location. The first step is to manually select initial electrode entry and target locations by neurosurgeons in terms of preoperative magnetic resonance (MR) images. The second step is to adjust the electrode target position around the manually planned target location and simultaneously fine-tune stimulation parameters to obtain the optimal neurosurgical outcome. The intraoperative adjustment is usually performed in accordance with microelectrode recordings (e.g., the electrode stimulated voltage and its pulse variables) and stimulation response (on-site subjective judgment from the neurosurgeon) at each electrode depth. The electrode contact targeting procedure aims to find the optimal location where the optimal neurosurgical outcome or performance can be achieved simultaneously with minimal adverse effects at a low stimulation voltage.

Many publications have discussed various methods on probabilistic atlases to guide the electrode contact targeting in the literature. Baumgarten et al. [2] discussed a probabilistic atlas that can preoperatively estimate pyramidal tract side effect. More recently, Horn et al. [3] studied the structural and functional connectivity to evaluate the surgical outcome of DBS, while Akram et al. [4] used such a connectivity to guide thalamic segmentation. Seo et al. [5] introduced a multiscale atlas

Received 25 June 2024; revised 11 January 2025; accepted 6 February 2025. Date of publication 14 February 2025; date of current version 20 February 2025. This work was supported in part by the National Natural Science Foundation of China under Grant 82272133, in part by the High-Quality Development Science and Technology Major Project of Xiamen Health Commission under Grant 2024GZL-ZD03, and in part by Ningbo 2035 Key Research and Development Program under Grant 2024Z127. The work of Xiongbiao Luo was supported by the Institut des Neurosciences Clinique de Rennes (INCR), France. (Xiongbiao Luo and Zhuo Zeng contributed equally to this work.) (Corresponding author: Xiongbiao Luo.)

This work involved human subjects or animals in its research. Approval of all ethical and experimental procedures and protocols was granted by the Ethical Committee of Centre Hospitalier Universitaire de Rennes under Protocol No. B110464-80.

Xiongbiao Luo was with the Equipe Inserm MediCIS, LTSI, Inserm UMR 1099, Université de Rennes, 35043 Rennes, France. He is now with the Department of Computer Science and Engineering, National Institute for Data Science in Health and Medicine, Xiamen University, Xiamen 361102, China, and also with Xiamen University Affiliated Zhongshan Hospital, Xiamen 361004, China (e-mail: xiongbiao.luo@gmail.com).

Zhuo Zeng is with the Tan Kah Kee College, Xiamen University, Zhangzhou 363105, China.

Song Zheng and Jianhui Chen are with Fujian Medical University Union Hospital, Fuzhou 350001, China.

Pierre Jannin is with the Equipe Inserm MediCIS, LTSI, Faculté de Médecine Rennes, Inserm UMR 1099, Université de Rennes, 35043 Rennes, France (e-mail: pierre.jannin@univ-rennes.fr).

Digital Object Identifier 10.1109/TNSRE.2025.3542395
<figure><img src="image_3.png" /><figcaption>Fig. 1. Our developed neurostimulation surgical planning system with structural-functional atlases predicting surgical outcomes.</figcaption></figure>

to characterize the correlation between the stimulus-induced electric field and neuronal responses. Nguyen et al. [6] characterized the relationship between the electrode location and the volume of tissue activated (VTA) model and created a probabilistic map by voxel-wise statistical analysis to predict clinical efficacy of directional DBS. Treu et al. [7] introduced a new tool to analyze DBS images at group-level. While Boon et al. [8] evaluated the subthalamic DBS-induced apathy on the basis of a structural and functional correlation atlas in PD patients, Wei et al. [9] built a biological-faithful computational network model of basal ganglia for the DBS guidance. Rusheen et al. [10] used 7T magnetic resonance images to guide surgical neuromodulation. Rodriguez-Rojas et al. [11] employed diffusion-weighted imaging to evaluate STN connectivity patterns associated with motor outcomes, while van Wijk et al. [12] found that functional connectivity maps are coherent within the STN region. Basile et al. [13] generated an in vivo probabilistic functional atlas in accordance with track density imaging and optimized diffusion tractography. Oxenford et al. [14] reported a multimodal platform with stereotactic planning, neuroimaging, and microelectrode recordings for DBS surgery. While Melo et al. [15] compared direct MRI guided and atlas-based targeting for STN and GPI stimulation, Neudorfer et al. [16] introduced new preprocessing tools include WarpDrive and algorithms for electrode localization during DBS. More recently, Meng et al. [17] tested a noninvasive neurostimulation tool of ultrasound DBS to deal with the problem of obesity, while Liu et al. [18] explored structural brain connectivity guided STN contact targeting.

Although these methods discussed above work well, it still remains challenging to automatically and precisely localize the electrode at specific brain structures to obtain the optimal neurosurgical outcome, i.e., the connectivity between the stimulation site (structure) and the surgical outcome (function) is still unclear. Most current electrode targeting approaches generally use preoperative images, intraoperative electrophysiological information, postoperative CT data and single motor-related functional score to create probabilistic atlases. While multiple functional scores are commonly used to evaluate the surgical outcome, these single score based atlases probably limit themselves to accurately find the optimal electrode contact position and obtain the optimal clinical outcome with minimal adverse effects. On the other hand, using multiple functional scores to quantitatively assess symptom reduction (efficacy) and adverse effects potentially provides an accurate mean to understand the stimulation performance and optimize the electrode contact targeting.

This work aims to address the limitation mentioned above by creating accurate functional atlases on the basis of the postoperative multiple assessment information and develop a fully automatic and accurate surgical planning approach for DBS. Several highlights of this work are clarified as follows. We develop a DBS surgical planning system with a statistical multiscore functional atlas to predict surgical outcomes. Fig. 1 illustrates our developed surgical planning system that would be publicly available at GitHub after approved by our collaborators. Technically, we propose a new concept of constructing a statistical multiscore functional atlas (MFA) that integrates anatomical information analysis with a large group of pre- and
<figure><img src="image_4.png" /><figcaption>Fig. 2. Flowchart of constructing the statistical multiscore functional atlas with four main steps.</figcaption></figure>

post-operative clinical scores. In particular, we create MFA by four motor scores, two neuropsychological scores, and two quality of life scores from pre- and post-operative quantitative assessment of PD patients. From the clinical impact of view, the MFA map provides neurosurgeons with a promising way to precisely implant the electrode at a proper deep brain structure in DBS, achieving maximal surgical outcomes while minimizing adverse effects.

## II. MATERIALS AND METHODS

This section presents technical details of the construction of statistical multiscore functional atlas. Such a new atlas construction method consists of three main steps (1) anatomical information analysis including pre- and post-operative image segmentation and registration, (2) modeling the volume of tissue activated, (3) calculation of multiple clinical scores, and (4) creating a statistical multiscore functional atlas. Fig. 2 illustrates the process flowchart of constructing the statistical multiscore functional atlas. Before discussing pre-, intra-, and post-operative CT/MR segmentation and registration, we briefly introduce our database used in this work.

### A. Data Collection

A total of 40 advanced PD patients (22 males and 18 females, a mean age of 56 years old) were bilaterally implanted in the STN DBS surgery at the university hospital. As for these retrospective datasets, 20 activated contacts (electrodes) were bilaterally located in 10 patients, while 30 activated contacts were located at in the brain left or right side since either stimulation parameters or clinical scores were missed in these cases. In these electrode contacts, we found

that 36 out of 50 contacts were actually implanted inside or around the STN after manually inspected postoperative CT images with implanted leads. Each dataset includes preoperative CT, T1-MR, T2-MR, and postoperative CT images. Typical CT volumes was collected at using 120 kVp, 350 mAs, 512 × 512 × 213 voxels, with resolution 0.574 × 0.574 × 0.625 mm³. MR images usually contain 256 × 256 × 182 voxels, with resolution 1.0 × 1.0 × 1.0 mm³. A Medtronic DBS Therapy system was used to perform electrode implantation. The used electrodes were Medtronic 3387 and 3389 with typical parameters of 4-contacts per electrode, 1.27-mm diameter, and 1.5-mm length. In all of cases, only one contact on the electrode was activated. Additionally, pulse width in these datasets was about 60 µs or below it, while most commonly used frequencies were below 60Hz. These stimulation parameters were essentially determined in accordance with the response of patients and neurophysiological microelectrode recordings with spikes during DBS surgery.

### B. Segmentation and Registration

Several segmentation and registration procedures have been performed during the preoperative planning stage.

1) *MR Deep Structure Segmentation:* During preoperative planning, some brain structures, e.g., white matter, gray matter, and cortical sulci, are segmented and reconstructed to visually guide electrodes that should not pass through those structures during implantation. This segmentation and reconstruction was performed by BrainVISA [19].

The stimulation structures (i.e., DBS targets) such as STN and GPi are also necessarily extracted from MR images. To this end, we created an anatomical atlas called Park-Mix by 57 MR volumes of patients with parkinsonism
<figure><img src="image_5.png" /><figcaption>Fig. 3. Preoperative MR image segmentation results.</figcaption></figure>

symptom [20]. By ParkMix, an atlas-based segmentation framework was exploited to extract those stimulation structures.

Note that an approximate electrode target point is manually selected or preoperatively planned position around anatomical structures STN or GPi in MR images by the neurosurgeon. This selection depends on the surgical experience and knowledge of neurosurgeons who comprehensively evaluate PD patients before DBS surgery and also think that this point will be stimulated with most effective outcomes. Particularly, the target point is different from the finally implanted position that is confirmed and adjusted by intraoperative microelectrode recordings during DBS surgery. Fig. 3 shows some examples of the preoperative segmentation results.

2) Preoperative and Postoperative Registration: After attaching a stereotactic frame on the patient's head and taking a CT scan, a rigid or linear registration must be performed to align preoperative CT and MR images. After the intraoperative electrode implantation, the stimulated patient has another CT scan done with the implanted electrode to evaluate its contact location and neurosurgical outcomes. Again, preoperative MR images and postoperative CT slices must be registered linearly. In our implementation, a boundary-based registration (BBR) method [21] to align preoperative CT, preoperative MR, and postoperative CT spaces is employed to estimate 3D affine transformation with 12 degrees of freedom (DOF) including translation, rotation, scaling, and shearing:

$$ \begin{pmatrix} \hat{x} \\ \hat{y} \\ \hat{z} \end{pmatrix} = \underbrace{\begin{pmatrix} a_1 & a_2 & a_3 \\ a_4 & a_5 & a_6 \\ a_7 & a_8 & a_9 \end{pmatrix}}_{\mathbf{A}} \begin{pmatrix} x \\ y \\ z \end{pmatrix} + \begin{pmatrix} t_x \\ t_y \\ t_z \end{pmatrix} \quad (1) $$

where matrix A contains the aggregated rotation, scaling and shearing in 9 DOF, (x, y, z) indicates a voxel's coordinates, and (t_x, t_y, t_z) denotes the 3-DOF translation. Note that the BBR method was used in this work because it was demonstrated more accurate than correlation ratio or normalized mutual information and is considerably more robust to even strong voxel intensity inhomogeneities [21]. Moreover, BBR

is a coarse-to-fine approach with global-local hybrid optimization to find the optimal parameters using Powell's method [22]. Additionally, BBR is also employed to be a pre-alignment step for deformable registration described below.

Deformable registration must be performed to register each patient's data to a MR atlas (here refers to as ParkMix), which is a repository of information from a population of PD patients. In this work, the pairwise volumetric deformable registration is implemented using symmetric normalization-based nonrigid registration (SNNR) [23], which involves an elastic transformation but not affine transformation to calculate a mapping from patient image I(v) to atlas image J(v) through deformable field D(v), where v = (x, y, z) is a voxel. The symmetric normalization algorithm iteratively implements the following three steps to optimize the elastic transformation parameters:

$$ \nabla \mathbf{E}_f(v) = \frac{\partial \Psi(\mathbf{I}(v), \mathbf{J}(v + \mathbf{D}(v)))}{\partial \mathbf{D}_f(v)}, \quad f \in \{x, y, z\}, \quad (2) $$

$$ \mathbf{D}(v) \leftarrow \mathbf{D}(v) + \delta \nabla \mathbf{E}(v), \quad (3) $$

$$ \mathbf{D}(v) \leftarrow G(v) * \mathbf{D}(v), \quad (4) $$

where Ψ(·) is the similarity measure, δ is a gradient step length, and G(·) denotes Gaussian smoothing. While Eq. 2 calculates the similarity gradient, Eqs. 3 and 4 update and regularize the deformable field D(v), respectively. Fig. 4 displays some examples of various registration results.

We must clarify that both BBR and SNNR methods are available in a public library of Advanced Normalization Tools (http://stnava.github.io/ANTs/). The average registration error was about 0.7 mm of BBR that aligns preoperative MR and postoperative CT images, while the average registration error of using SNNR to align each patient MR scan to ParkMix was 1.6 mm. Both BBR and SNNR generated registration errors were acceptable for DBS planning. Please also refer to [21] and [23] for more details of BBR and SNNR approaches.

3) Postoperative CT Electrode Segmentation: Segmenting contact regions and axis of the electrode from postoperative CT images is significant for accurate location assessment and direct 3D visualization of electrodes. In this paper, a new and simple mask-driven hypersignal artifact thresholding (MHAT) approach was proposed to extract electrode contact areas. MHAT consists of several steps discussed below.

Skull and electrode contact regions have very similar intensity in the postoperative CT images. We use image registration to separate skull and electrode regions before thresholding. First, a mask volume (Fig. 5 (a)) was created to remove the skull region by registering preoperative CT and MR images using the neuroimaging data processing tool [19]. The second step is to linearly align the postoperative CT volume to the preoperative CT volume. This implies that the preoperative MR images are aligned to the postoperative CT volume. Then, the masked postoperative CT volume is generated by registering the mask volume to the result of the second step. After that, the masked postoperative CT volume only contains the electrode contact region but excludes the skull region. Finally, thresholding was performed to extract all hypersignal artifact pixels on masked or registered postoperative CT (Fig. 5(b)).
<figure><img src="image_6.png" /><figcaption>Fig. 4. Examples of various registration results (coronal view).</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 5. Postoperative electrode contact segmentation and volume of tissue activated.</figcaption></figure>

After extracting all electrode contact (hypersignal) regions from postoperative CT images, the centers of these regions can be easily determined obtained. To obtain the electrode axis or shape (Fig. 5(c)) from the hypersignal region center cloud, a polynomial regression model is employed to fit these points:

$$ \underbrace{\begin{pmatrix} q_1 \\ q_2 \\ \vdots \\ q_c \end{pmatrix}}_{\mathbf{Q}} = \underbrace{\begin{pmatrix} 1 & \mathbf{p}_1 & \cdots & \mathbf{p}_1^d \\ 1 & \mathbf{p}_2 & \cdots & \mathbf{p}_2^d \\ \vdots & \vdots & \ddots & \vdots \\ 1 & \mathbf{p}_c & \cdots & \mathbf{p}_c^d \end{pmatrix}}_{\mathbf{P}} \underbrace{\begin{pmatrix} b_1 \\ b_2 \\ \vdots \\ b_c \end{pmatrix}}_{\mathbf{B}} + \underbrace{\begin{pmatrix} e_1 \\ e_2 \\ \vdots \\ e_c \end{pmatrix}}_{\mathbf{E}} \quad (5) $$

where **P** is the Vandermonde matrix including c center points, **Q** is a fitted point cloud, and **E** is an unobserved random error set. Symbol *d* is called the degree of the polynomial. The estimated polynomial regression coefficients **B** is

$$ \mathbf{B} = (\mathbf{P}^T \mathbf{P})^{-1} \mathbf{P}^T \mathbf{Q}, \quad (6) $$

which is the unique least-squares solution. Note that the optimal degree *d* of the polynomial is determined on the basis of manual segmented electrodes within 20 PD patients.

### C. Activation Volume

Neural response to DBS is generally complex. It depends on various factors such as electrode geometry, electrode and tissue

electrical properties, stimulation parameters, and biophysical properties of the electrode contact's surroundings. These factors lead to the complexity of stimulation response modeling.

Guo et al. [24] reported a 3D Gaussian-based activation volume model to approximate the electric field, which has been further improved by replacing a Gaussian kernel with an annulus kernel [25]. Based on their previous work of diffusion tensor based finite element modeling [26], Butson et al. [27] introduced an evolutionary addition to the concept of a probabilistic brain atlas and further probabilistically analyzed activated tissue volumes generated during DBS. However, these methods often suffer from low computational efficiency. Kuncel et al. [28] discussed an activated tissue volume estimation method, which correlates adverse effects with various stimulation voltages and different distances between activated electrode contacts and anatomical structures. Alternatively, Malder et al. [29] estimated the activation volume by a simplified target-specific model commonly used in the scientific community. Dembek et al. [30] established a formulation that can approximate either Kuncel's or Madler's model to compute the activation radius for different pulse widths.

We employ Kuncel's model to calculate the activation volume. The pulse width of our stimulation data was set at 90μs that was decreased down to 60μs. Clinically relevant stimulation voltage magnitudes in our database generally range from 1.0 to 3.5 voltages, which correspond to an activated volume radius between 2.0 and 3.9 mm that is consistent to Kuncel's work [28]. On the other hand, Kuncel's activation volume modeling algorithm is simple and easily implemented and provides an effective and relatively accurate estimate. Additionally, our PyDBS software platform (Fig. 1) has been integrated with Kuncel's model for surgical planning. This paper follows Kuncel's method to calculate an activated volume $V(x, y, z)$ as a sphere centered at an electrode contact:

$$ V(x, y, z) = \int_{-r}^{r} \int_{-v}^{v} \int_{-u}^{u} dz dy dx, \quad (7) $$

$$ v = \sqrt{r^2 - (x - x_c)^2}, \quad u = \sqrt{v^2 - (y - y_c)^2}, \quad (8) $$

$$ (x - x_c)^2 + (y - y_c)^2 + (z - z_c)^2 \leq r^2 \quad (9) $$

where $(x_c, y_c, z_c)$ is an electrode contact center obtained from the segmentation step and sphere radius *r* is computed:

$$ r = r_{min} + \frac{(w - w_{min})(r_{max} - r_{min})}{w_{max} - w_{min}}, \quad (10) $$

where *w* denotes clinically relevant stimulation voltage magnitudes running from $w_{min} = 1.0$ *v* to $w_{max} = 3.5$ *v*, which
<table><caption>TABLE I
MULTIPLE CLINICAL SCORES AND THEIR DEFINITIONS USED IN THIS WORK [31]</caption><thead><tr><td>Scores</td><td>Definition</td></tr></thead><tbody><tr><td>UPDRS II</td><td>Unified Parkinson's disease rating scale (UPDRS) II to characterize a PD patient's activities of daily life</td></tr><tr><td>UPDRS III</td><td>Unified Parkinson's disease rating scale III to parametrize a PD patient's motion examination</td></tr><tr><td>Hoehn-Yahr</td><td>Hoehn and Yahr scale commonly used to describe how symptoms of Parkinson's disease progress</td></tr><tr><td>Schwab-E</td><td>Schwab and England scale to evaluate a PD patient's activities of daily living</td></tr><tr><td>STROOP</td><td>Stroop testing score to compute a parkinsonian's mental vitality and flexibility</td></tr><tr><td>VERBAL</td><td>Verbal-fluency assessment of producing the number of correct words as many as possible</td></tr><tr><td>PDQ39</td><td>Parkinson's disease questionnaire with 39 questions (PDQ39) to assess a PD patient's quality of life</td></tr><tr><td>SF36</td><td>Short form 36-item (SF36) health survey to determine the cost-effectiveness of a health treatment</td></tr></tbody></table>

correspond to activated volume radii ranging from $r_{min} = 2.0$ mm to $r_{max} = 3.9$ mm. The minimal and maximal voltage and radius are determined by statistical analysis of clinical outcomes from a set of PD patients [28]. Fig. 5(d) illustrates an activation volume created by the method described above.

As one of computational models, VTA is widely used to estimate surgical outcomes and adverse effects of DBS in neural tissues. It is yielded as a function of stimulation contacts and parameters, electrode shape and location, and tissue impedance in the brain. Its roles consist of dynamic visualization and comparing differences in stimulation, evaluating ideal stimulation locations, assisting in selecting post-operative stimulation parameters, and conducting preoperative planning of electrode implantation. Duffley et al. [32] evaluated various functions for calculating VAT in neurostimulation. Currently, neural pathways driven activation volume models are discussed for clinical neurostimulation. While Gunalan et al. [33] built a pathway-activated volume model to estimate the response of the hyperdirect pathway, Pena et al. [34] used a multi-objective particle swarm optimization method to create such a model by preoperative 7T MR images and postoperative CT scans. More recently, Bingham et al. [35] created an anatomically detailed model to find the motor hyperdirect pathway response after subthalamic neurostimulation. Generally speaking, computation of pathway activation volumes or patterns is a promising model to investigate certain links between multiple neural pathways and clinical symptom modulation.

## D. Multiple Clinical Scores Computing

This section defines and computes multiple clinical scores or scales used in this work.

To evaluate the neurosurgical outcome after DBS, multiple clinical scores are defined pre- and post-operatively for each PD patient. Here, we introduce four motor scores (UPDRS II, UPDRS III, Hoehn-Yahr, and Schwab-E), two neuropsychological scores (STROOP and VERBAL), and two health-survey scores (PDQ39 and SF36) to assess the DBS outcome. These clinical scores are commonly used in assessment of parkinsonism symptom before and after neurostimulation. All these scores are defined in Table I.

Various clinical scores are initially obtained by neurologists who test PD patients before neurostimulation with medication OFF and three months after neurostimulation with stimulation ON and medication OFF. Also, note that some clinical scores,

e.g., UPDRS II, Hoehn-Yahr, Schwab-E, PDQ39, and SF36, cannot be evaluated in an ON versus OFF mode. Accordingly, we compute a relative score $P_i$ of improvement or deterioration for each clinical score $S_i$ defined above:

$$P_i = \begin{cases} \frac{(S_i^{\text{post}} - S_i^{\text{pre}})}{S_i^{\text{max}}} & i = 1, 2, 3 \\ \frac{(S_i^{\text{post}} - S_i^{\text{pre}})}{S_i^{\text{max}}} & \text{Otherwise} \end{cases}, \quad i \in \{1, 2, \dots, 8\} \tag{11}$$

where $S_i^{pre}$ and $S_i^{post}$ are the pre- and post-operative clinical scores determined by neurologists testing patients without medication, and each maximal clinical score $S_i^{max}$ is constant. Additionally, note that the high clinical scores of UPDRS II, UPDRS III, and Hoehn-Yahr indicate the bad DBS outcome.

## E. Multiscore Functional Atlas Generation

Current statistical functional atlases are commonly created using probabilistic approaches in accordance with prior of inclusion criteria relevant to clinical testing by neurologists. These atlases colorize preoperative image voxels to represent a meaningful signification, i.e., colorized voxels illustrate different probabilistic values of electrode placements or positions. In our study, the colorized voxels in our created atlas directly indicate the surgical outcome (scores) related to the predicted electrode positions. This is the main difference between our created atlas and other atlases showing the statistical probability of the most implanted positions.

Generally speaking, MFA is constructed by taking into consideration various information including a number of PD patients, activation volumes, and multiple clinical scores.

Based on Eqs. 7 and 11, the average functional atlas $A_n$ generated from the n-th patient is computed with respect to weighted clinical score $P_i^n$

$$A_n = \sum_{i=1}^{M} \omega_n P_i^n, \tag{12}$$

where $M$ (here $M = 8$) is the number of clinical scores used in MFA and weight $\omega_n$ follows

$$\sum_{i=1}^{M} \omega_n = 1, \tag{13}$$
<figure><img src="image_8.png" /><figcaption>Fig. 6. Statistical analysis of weights assigned to different clinical scores for the MFA construction.</figcaption></figure>

Eventually, our functional MFA map is formulated by

$$MFA(x, y, z) = \sum_{n=1}^{N} \lambda_n A_n, \qquad (14)$$

where N is the number of patients and the normalized gain $\lambda_n$ is calculated using all activation volume estimates

$$\lambda_n = \frac{\mathcal{V}_n(x, y, z)}{\sum_{n=1}^{N} \mathcal{V}_n(x, y, z)}, \qquad (15)$$

where $\mathcal{V}_n(x, y, z)$ is the activation volume from patient n.

The weight $\omega_n$ plays an important role in creating the multiscore functional atlas. Unfortunately, there are no standard methods to properly assign a weight to each relative score $P_i^n$. In this study, we determine the weight $\omega_n$ for each score $P_i^n$ in accordance with experience and knowledge of four experts including two DBS surgeons and two neurologists. These experts independently determined these eight weights from 36 PD cases. Fig. 6 shows the statistical analysis of these weights from the four experts. Based on the statistical analysis, these weights were averagely computed to 0.0905±0.0054 of UPDRS II, 0.2049±0.0029 of UPDRS III, 0.0911±0.0098 of Hoehn-Yahr, 0.0914±0.0052 of Schwab-E, 0.1994±0.0052, 0.1501±0.0179 of STROOP, 0.0917±0.0113 of VERBAL, 0.0917±0.0113 of PDQ39, and 0.0916±0.0173 of SF36. The experts generally recognized that the surgical outcome indicated by the clinical scores of UPDRS III and STROOP are usually significantly improved for most PD patients after the DBS procedure, while the next is VERBAL. Eventually, we determined the weights for UPDRS III, STROOP and VERBAL to 0.2, 0.2, and 0.15, respectively, and the weight for the remained five clinical scores is equally set to 0.09.

After creating the MFA map, neurosurgeons can use it to automatically estimate the electrode contact positions. MFA is a functional map that consists of various colorized voxels indicating bad and good surgical outcome from blue to red. The position of the most red voxel on the MFA map is automatically selected as the optimal estimate since it provides the optimal surgical outcome.

<table><caption>TABLE II
REPRODUCIBILITY OF DIFFERENT CLINICAL SCORE ATLASES</caption><thead><tr><td>Clinical scores</td><td>Patient numbers</td><td>Reproducibility</td></tr></thead><tbody><tr><td>UPDRS II</td><td>38</td><td>72±8%</td></tr><tr><td>UPDRS III</td><td>44</td><td>77±6%</td></tr><tr><td>Hoehn-Yahr</td><td>45</td><td>70±7%</td></tr><tr><td>Schwab-E</td><td>45</td><td>74±5%</td></tr><tr><td>STROOP</td><td>38</td><td>72±8%</td></tr><tr><td>VERBAL</td><td>48</td><td>82±9%</td></tr><tr><td>PDQ39</td><td>36</td><td>78±8%</td></tr><tr><td>SF36</td><td>36</td><td>75±6%</td></tr><tr><td>Average</td><td>—</td><td>75±7%</td></tr></tbody></table>

In general, MFA created in this work has several technical highlights when comparing to currently existing electrophysiological maps or atlases. First, it is certainly unnecessary to define inclusion criteria by neurologists when using our MFA strategy to create a functional map. Next, MFA created by multiple clinical scores and a population of PD patients is an anatomical and functional atlas to benefit comprehensive analysis of neurosurgical outcomes after DBS. In addition, the colorized voxels in our created atlas represent general efficacy (symptom reduction) scores but not probabilities of electrode positions, which are more intuitive to predict the neurosurgical outcome. Hence, these highlights of MFA are also mainly different from currently available probabilistic atlases discussed in the literature.

### III. VALIDATION

Several strategies are used to evaluate the constructed multiscore atlas. First, visual inspection of the colorized MFA map is performed by neurosurgeons with their knowledge and experiences. The colorized MFA map indicating symptom reduction is also intuitive and meaningful for neurosurgeons to adjust the electrode contact position in subthalamic DBS.

Next, the confidence of MFA is evaluated by computing reproducibility (i.e., reliability) between two volumetric atlases. Based on the fuzzy set theory for the intersection and union of fuzzy sets, the reproducibility is defined as

$$\mathcal{R} = \frac{\sum_{x,y,z} \mathcal{C}(x, y, z)}{\sum_{x,y,z} \mathcal{A}(x, y, z) + \mathcal{B}(x, y, z) - \mathcal{C}(x, y, z)}, \qquad (16)$$

where intersection set $\mathcal{C}(x, y, z) = \mathcal{A}(x, y, z) \cap \mathcal{B}(x, y, z)$, $\mathcal{A}(x, y, z)$, and $\mathcal{B}(x, y, z)$ are two atlases.

By a k-fold cross-validation approach, the reproducibility is computed for all patients and then averaged, with k running from 0 to 10. This evaluation aims to show the reproducibility of MFA which converges to near-optimal atlases.

Additionally, manually planned, atlas estimated, and finally or actually implanted electrode contact positions are compared by calculating Euclidean distance among them:

$$\chi_m = \| \mathbf{p}_m - \mathbf{p}_a \|, \quad \chi_e = \| \mathbf{p}_e - \mathbf{p}_a \|, \qquad (17)$$

where $\mathbf{p}_m$, $\mathbf{p}_e$, and $\mathbf{p}_a$ are manually planned, atlas estimated, and actually implanted electrode contact positions.

### IV. RESULTS

This section details and compares the experimental results of using different methods to create atlases.
<figure><img src="image_9.png" /><figcaption>**Fig. 7.** Constructed statistical functional atlases with four continuous axial views. Rows 1~9 correspond to UPDRS II, UPDRS III, Hoehn-Yahr, Schwab-E, STROOP, VERBAL, PDQ39, SF36, and MFA (ours). Colorized voxels from *blue* to *red* indicate from low to high efficacy scores.</figcaption></figure>

**Fig. 7** displays the different functional efficacy atlases that were constructed by anatomical or structural information processing and multiple clinical functional scores. All the atlases from the *first* row to the *ninth* row correspond to UPDRS II, UPDRS III, Hoehn-Yahr, Schwab-E, STROOP, VERBAL, PDQ39, SF36, and our proposed MFA, respectively. These atlases were normalized in the ParkMix space with various brain deep structures: Brain ventricles (*blue*), caudate (*cyan*), putamen (*magenta*), GPi (*gray*), STN (*dark orange*), and red nucleus (*red*). Note that the registration procedures introduce errors to shift the position of the structures but these errors are acceptable to neurosurgeons who use our DBS

<figure><img src="image_10.png" /><figcaption>**Fig. 8.** Plotted 50 electrode contact positions that were collected from the STN stimulation: P1 ~ P6 correspond to manually planned, three typical atlases (UPDRS III, STROOP, and VERBAL) predicted, MFA-automatically predicted, and actually implanted positions.</figcaption></figure>

planning system (Fig. 1) to estimate the simulation position. Furthermore, these atlases in Fig. 7 show that the optimal estimated lead positions are either outside of the STN or in the middle/dorsal portion of the STN. This is because that our atlases learn from the actually stimulated positions in our postoperative CT images with implanted leads inside or around the STN. Actually patient-specific implanted positions depend on not only image-guided computational models or atlases and comprehensive assessment (various functional scores) of patients before DBS, but also neurophysiological microelectrode signals with spikes and the on-site response of patients during DBS lead implanting. So, atlas-estimated lead positions are possibly different from actually implanted locations.

Table II summarizes the reproducibility (Eq. 16) of various clinical scores related to MFA. The average reproducibility of all the clinical scores was 75%. In particular, the motor, neuropsychological, and health scores can reproduce the overlapping percentages up to 77%, 82%, and 78%, respectively.

**Fig. 8** plots the positions estimated by these methods on 50 activated contacts from 40 implanted patients. These positions in the anterior and posterior commissure (AC-PC) coordinate system were the center the activation volume (sphere). Note that while the position difference of using these methods is relatively small in the 3D space, they commonly provide totally different surgical outcomes after DBS. **Fig. 9** illustrates the position errors and their regression curves from the different atlas-based approaches. By computed against the actually implanted electrode positions (Eq. 17), the average errors of manually planned, UPDRS III, STROOP, VERBAL, and MFA estimated electrode contact positions were 2.89±1.29, 3.66±1.57, 3.36±1.52, 3.19±1.76, and 2.38±1.25 mm, respectively. The manually planned and automatically MFA-estimated positions produce the comparable or similar errors.

**Fig. 10** demonstrates the different created atlases used for predicting the electrode position. The MFA-guided prediction provides a promising way to accurately plan the electrode location. Note that **Fig. 10** gives an example of the electrode actually placed position close to the dorsal of STN. However, this example never implies that all the electrodes were actually placed at the dorsal of STN. There are two reasons behind this deviation. On one hand, the registration procedures introduce errors to shift the location of STN, possibly resulting in the lead implanted around the STN. On the other hand, our generated atlases learn from 40 postoperative CT scans with actually implanted leads that were slightly deviated from STN.
<figure><img src="image_11.png" /><figcaption>Fig. 9. Position errors of using different approaches evaluated on 50 electrode contacts collected from the STN stimulation.</figcaption></figure>

<table><caption>TABLE III
COMPARISON OF AVERAGE ELECTRODE CONTACT POSITIONS ESTIMATED FROM THE METHODS ON 50 IMPLANTED CONTACTS</caption><thead><tr><th rowspan="2">Methods</th><th colspan="3">Average positions (mm)</th></tr><tr><th>X</th><th>Y</th><th>Z</th></tr></thead><tbody><tr><td>Planned</td><td>114.7±15.9</td><td>108.7±10.4</td><td>84.4±17.4</td></tr><tr><td>UPDRS III</td><td>113.6±15.8</td><td>110.9±10.3</td><td>85.0±17.6</td></tr><tr><td>STROOP</td><td>114.7±16.4</td><td>109.0±10.0</td><td>85.6±17.5</td></tr><tr><td>VERBAL</td><td>114.2±15.7</td><td>108.7±10.6</td><td>84.5±17.3</td></tr><tr><td>Our MFA</td><td>114.4±16.1</td><td>108.6±10.0</td><td>85.0±17.5</td></tr><tr><td>Implanted</td><td>114.3±16.1</td><td>108.6±10.0</td><td>84.6±17.4</td></tr></tbody></table>

Table III compares the average activated electrode contact positions obtained by the manually planned and the actually implanted procedures, three clinical score atlases that are typically used by neurologists to evaluate the parkinsonism symptom, and our created MFA-based method.

V. DISCUSSION

Several interesting aspects of MFA are clarified as follows. First, combining different neurosurgical scores into a statistical atlas potentially provides a better interpretation of the currently poorly understood mechanisms involved in the DBS surgery. A single clinical score characterizes only a typical symptom of parkinsonism, which is insufficient to interpret the neurosurgical outcome. Hence, the single clinical score-based atlas possibly limits the understanding of the DBS outcome. Various scores or scales discussed above are used to assess different neurosurgical outcomes and various aspects of motor, verbal fluency, mental vitality and, quality of life of PD patients in clinical applications, while they also are employed to evaluate whether the electrode location is accurate to reduce PD signs and symptoms. In this respect, a combination of various clinical scores is meaningful to create a statistical functional atlas for better understanding and accurate assessment. MFA is created to exactly meet with clinical requirement. This study combines eight clinical scores to create the MFA map since these scores are exactly used by the neurosurgeon and available in our database. Next, the intensity of colorized voxels on the MFA directly presents a general efficacy score that is more intuitive to predict the electrode location and neurosurgical outcome in the preoperative planning stage. In addition, the

concept of constructing the statistical multiscore functional atlas would be possibly extended to create atlases of adverse effects that may occur after the DBS surgery.

Although our method of creating a multiscore atlas works well, it still has concertina limitations. First, the reproducibility of our multiscore atlas was relatively low because of inter-subject anatomical variability and complex deep brain structure inter-connections. Stimulating the same region or deep structures from different patients possibly generates different motor and cognitive effects. Second, our DBS planning method still limits itself to the performance of the registration procedures. Good registration algorithms certainly improve the position-estimation accuracy of our generated atlases. This work used BBR and SNNR alignment methods are conventional to solve an optimization model carefully designed on image pairs with their exceptionally high computational costs. Recently, deep learning-based deformable registration approaches are increasingly discussed in the scientific community since they can provide fast deformation estimation. One of our future work is to develop a transformer driven unsupervised learning-based diffeomorphic deformable registration method to boost the alignment of for patient MR scans and ParkMix. Next, potential biases may be occurred among surgical procedures performed by various neurosurgeons under different surgical protocols. Our method did not take this into consideration since all the DBS procedures with the datasets used in this paper were performed by the same neurosurgeon under the same surgical protocol. A future work is interesting in investigating the reproducibility of inter-protocol statistical multiscore functional atlases. On the other hand, it should more accurately characterize the effectiveness of various clinical scores contributing to MFA. We need to further investigate the contribution of each clinical score and introduce some other clinical scores and information (e.g., age and sex) to create a more accurate and robust statistical multiscore efficacy atlas for preoperative planning and postoperative assessment. Additionally, MFA-predicted electrode contact locations generally correspond to predicted surgical outcomes (mixed scores) but not to actual PD symptoms. Accurate connectivity between predicted electrode locations and actual PD symptoms is a challenging problem, which requires to further research.

More simulation parameters can be optimized to improve our created functional atlases, such as pulse width, frequency, and microelectrode recordings (MER) with spikes. Specifically, deep learning-based intraoperative MER signals driven VAT models can more precisely estimate stimulation parameters and electrode locations. MER can detect and magnify the neural activity of neurons from the awake patient, assisting in correctly placing the electrode, as well as understanding the anatomical context of intraoperative recording sites and final implantation locations. Hence, automatic mapping of MER to STN) and GPi in MR images can improve clinical outcomes of DBS. On the other hand, neural pathways related activation volume models can further characterize possible correlations between multiple pathways and DBS responses [35]. While this work uses voltage steering with traditional (non-directional) leads for DBS programming, current steering
<figure><img src="image_12.png" /><figcaption>Fig. 10. A comparison of manually planned, various atlas predicted, actually implanted electrode positions (sagittal view). Also note that our method automatically selects the redder position inside the STN as a priority.</figcaption></figure>

through directional leads is a promising way to assist in precisely guiding neurostimulation [36]. Additionally, beyond MER to refine targeting, recent intraoperative imaging guidance (IIG) is increasingly used as an alternative way to verify the electrode implant and clinical efficacy during DBS surgery for Parkinson's disease. Particularly, intraoperative computed tomography (iCT) extrapolation is currently introduced to predetermine and adjust the trajectory of the electrode. Deep learning-based mapping of iCT to MR images is another promising way to enhance the accuracy of MFA.

## VI. CONCLUSION

This paper presents a new concept of creating a statistical multiscore functional atlas to accurately guide the electrode placement and simultaneously obtain the maximal clinical outcome and the minimal adverse effect during the STN stimulation. By evaluating on 40 subthalamic nuclei implanted PD patients, the experimental results demonstrated the new concept's effectiveness. Moreover, the statistical multiscore

functional atlas provides a promising way to strongly understand the DBS working mechanism and precisely predict the electrode location and neurosurgical outcome. Future work includes the improvement of the multiscore atlas's reliability and the creation patient-specific atlases for clinical applications.

## REFERENCES

[1] C. de Hemptinne et al., "Therapeutic deep brain stimulation reduces cortical phase-amplitude coupling in Parkinson's disease," *Nature Neurosci.*, vol. 18, no. 5, pp. 779-786, May 2015.

[2] C. Baumgarten, Y. Zhao, P. Sauleau, C. Malrain, P. Jannin, and C. Haegelen, "Image-guided preoperative prediction of pyramidal tract side effect in deep brain stimulation: Proof of concept and application to the pyramidal tract side effect induced by pallidal stimulation," *J. Med. Imag.*, vol. 3, no. 2, Jun. 2016, Art. no. 025001.

[3] A. Horn et al., "Connectivity predicts deep brain stimulation outcome in Parkinson disease," *Ann. Neurol.*, vol. 82, pp. 67-78, Jul. 2017.

[4] H. Akram et al., "Subthalamic deep brain stimulation sweet spots and hyperdirect cortical connectivity in Parkinson's disease," *NeuroImage*, vol. 158, pp. 332-345, Sep. 2017.
[5] H. Seo and S. C. Jun, "Relation between the electric field and activation of cortical neurons in transcranial electrical stimulation," *Brain Stimulation*, vol. 12, no. 2, pp. 275-289, Mar. 2019.

[6] T. A. K. Nguyen et al., "Directional stimulation of subthalamic nucleus sweet spot predicts clinical efficacy: Proof of concept," *Brain Stimulation*, vol. 12, no. 5, pp. 1127-1134, Sep. 2019.

[7] S. Treu et al., "Deep brain stimulation: Imaging on a group level," *NeuroImage*, vol. 219, Oct. 2020, Art. no. 117018.

[8] L. I. Boon et al., "Structural and functional correlates of subthalamic deep brain stimulation-induced apathy in Parkinson's disease," *Brain Stimulation*, vol. 14, no. 1, pp. 192-201, Jan. 2021.

[9] X. Wei et al., "An embedded multi-core real-time simulation platform of basal ganglia for deep brain stimulation," *IEEE Trans. Neural Syst. Rehabil. Eng.*, vol. 29, pp. 1328-1340, 2021.

[10] A. E. Rusheen et al., "The development of ultra-high field MRI guidance technology for neuronavigation," *J. Neurosurgery*, vol. 137, no. 5, pp. 1265-1277, Nov. 2022.

[11] R. Rodriguez-Rojas et al., "Functional topography of the human subthalamic nucleus: Relevance for subthalamotomy in Parkinson's disease," *Movement Disorders*, vol. 37, no. 2, pp. 279-290, Feb. 2022.

[12] B. C. M. van Wijk et al., "Functional connectivity maps of theta/alpha and beta coherence within the subthalamic nucleus region," *NeuroImage*, vol. 257, Aug. 2022, Art. no. 119320.

[13] G. A. Basile et al., "In vivo probabilistic atlas of white matter tracts of the human subthalamic area combining track density imaging and optimized diffusion tractography," *Brain Struct. Function*, vol. 227, no. 8, pp. 2647-2665, Nov. 2022.

[14] S. Oxenford et al., "Lead-OR: A multimodal platform for deep brain stimulation surgery," *eLife*, vol. 11, p. 72929, May 2022.

[15] M. Melo, L. Furlanetti, H. Hasegawa, N. Mundil, and K. Ashkan, "Comparison of direct MRI guided versus atlas-based targeting for subthalamic nucleus and Globus pallidus deep brain stimulation," *Brit. J. Neurosurgery*, vol. 37, no. 5, pp. 1040-1045, Sep. 2023.

[16] C. Neudorfer et al., "Lead-DBS v3.0: Mapping deep brain stimulation effects to local anatomy and global networks," *NeuroImage*, vol. 268, Mar. 2023, Art. no. 119862.

[17] W. Meng et al., "Ultrasound deep brain stimulation regulates food intake and body weight in mice," *IEEE Trans. Neural Syst. Rehabil. Eng.*, vol. 32, pp. 366-377, 2024.

[18] J. Liu et al., "Structural brain connectivity guided optimal contact selection for deep brain stimulation of the subthalamic nucleus," *World Neurosurgery*, vol. 188, pp. e546-e554, Aug. 2024.

[19] Y. Cointepas et al., "The BrainVISA project: A shared software development infrastructure for biomedical imaging research," in *Proc. 16th AMOHBM*, 2010.

[20] C. Haegelen et al., "Automated segmentation of basal ganglia and deep brain structures in MRI of Parkinson's disease," *Int. J. Comput. Assist. Radiol. Surg.*, vol. 8, no. 1, pp. 99-110, Jan. 2013.

[21] D. N. Greve and B. Fischl, "Accurate and robust brain image alignment using boundary-based registration," *NeuroImage*, vol. 48, no. 1, pp. 63-72, Oct. 2009.

[22] G. Pillo and M. Roma, *Large-Scale Nonlinear Optimization*. Cham, Switzerland: Springer, 2006.

[23] B. B. Avants et al., "Symmetric diffeomorphic image registration with cross-correlation: Evaluating automated labeling of elderly and neuredegenerative brain," *Med. Imag. Anal.*, vol. 12, no. 1, pp. 26-41, 2008.

[24] T. Guo, K. Finnis, A. Parrent, and T. Peters, "Visualization and navigation system development and application for stereotactic deep-brain neurosurgeries," *Comput. Aided Surg.*, vol. 11, no. 5, pp. 231-239, Sep. 2006.

[25] S. Pallavaram et al., "A new method for creating electrophysiological maps for DBS surgery and their application to surgical guidance," in *Proc. MICCAI*, Jan. 2008, pp. 670-677.

[26] C. R. Butson and C. C. McIntyre, "Current steering to control the volume of tissue activated during deep brain stimulation," *Brain Stimulation*, vol. 1, no. 1, pp. 7-15, Jan. 2008.

[27] C. R. Butson, S. E. Cooper, J. M. Henderson, B. Wolgamuth, and C. C. McIntyre, "Probabilistic analysis of activation volumes generated during deep brain stimulation," *NeuroImage*, vol. 54, no. 3, pp. 2096-2104, Feb. 2011.

[28] A. M. Kuncel, S. E. Cooper, and W. M. Grill, "A method to estimate the spatial extent of activation in thalamic deep brain stimulation," *Clin. Neurophysiol.*, vol. 119, no. 9, pp. 2148-2158, Sep. 2008.

[29] B. Mädler and V. A. Coenen, "Explaining clinical effects of deep brain stimulation through simplified target-specific modeling of the volume of activated tissue," *Amer. J. Neuroradiol.*, vol. 33, no. 6, pp. 1072-1080, Jun. 2012.

[30] T. A. Dembek et al., "Probabilistic mapping of deep brain stimulation effects in essential tremor," *NeuroImage*, *Clin.*, vol. 13, pp. 164-173, Jul. 2017.

[31] C. Sampaio, C. G. Goetz, and A. Schrag, *Rating Scales in Parkinson's Disease: Clinical Practice and Research*. Oxford, U.K.: Oxford Univ. Press, 2012.

[32] G. Duffley, D. N. Anderson, J. Vorwerk, A. D. Dorval, and C. R. Butson, "Evaluation of methodologies for computing the deep brain stimulation volume of tissue activated," *J. Neural Eng.*, vol. 16, no. 6, Dec. 2019, Art. no. 066024.

[33] K. Gunalan et al., "Creating and parameterizing patient-specific deep brain stimulation pathway-activation models using the hyperdirect pathway as an example," *PLoS ONE*, vol. 12, no. 4, Apr. 2017, Art. no. e0176132.

[34] E. Peña et al., "Multi-objective particle swarm optimization for postoperative deep brain stimulation targeting of subthalamic nucleus pathways," *J. Neural Eng.*, vol. 15, no. 6, Dec. 2018, Art. no. 066020.

[35] C. S. Bingham and C. C. McIntyre, "Subthalamic deep brain stimulation of an anatomically detailed model of the human hyperdirect pathway," *J. Neurophysiol.*, vol. 127, no. 5, pp. 1209-1220, May 2022.

[36] M. Paff, A. Loh, C. Sarica, A. M. Lozano, and A. Fasano, "Update on current technologies for deep brain stimulation in Parkinson's disease," *J. Movement Disorders*, vol. 13, no. 3, pp. 185-198, 2020.