Automatic Ventral Intermediate Nucleus Localization Based on Anterior Commissure and Posterior Commissure

The ventral intermediate nucleus (Vim), as the motor thalamic nuclei section, is a generally used target in brain lesion surgery or stimulation for decreasing tremors in people with Parkinson’s disease. Determining the exact position of Vim is challenging because Vim cannot be visualized clearly in commonly used magnetic resonance imaging (MR). Indirect methods, i.e., Coordinate-based targeting and Guiot’s, utilize anterior commissure and posterior commissure to detect the location of Vim. In practice, neurosurgeons manually implement these methods in existing neurosurgical planning software, so the accuracy of the targeting depends on their memory and foresight. Afterward, Coordinate-based targeting and Guiot’s locate Vim based on anterior commissure (AC) and posterior commissure (PC), so neurosurgeons must correctly determine AC and PC. This paper proposes automatic indirect methods and measures the accuracy of indirect methods in MRIs with correct and incorrect orientations of AC-PC planes. An objective of analyzing indirect methods in MRIs with incorrect orientations of AC-PC planes is to discover the most resilient indirect method with inaccuracy AC-PC planes. To develop automatic indirect methods, the first step is redefining the plane passing through three defined points, i.e., AC, PC, and midline reference, by a quaternion. Secondly, Coordinate-based targeting and Guiot’s are implemented to determine the Vim targeting location automatically. This paper converts the rules of those methods in voxels because the rules use millimeters while the three-dimensional MRIs use voxels. The experiment shows that Vim locations obtained by Guiot’s are more accurate than those by Coordinate-based targeting in MRIs with the correct orientation of AC-PC planes. Guiot’s has 0.05 mm smaller value of average error results than Coordinate-based targeting. In contrast, Vim locations based on Coordinate-based targeting are more accurate in the MRIs with the incorrect orientation of AC-PC planes. Coordinate-based targeting has 0.032 mm smaller value of average error results than Guiot’s. AC-PC plane. The methods are automatically determining the AC-PC plane based on defined an AC point, a PC point, and a midline reference (MR) line. Then, the proposed automatic methods convert the coordinates from millimeters to voxels to determine the Vim location. The conversion is applied because rules of Coordinate-based targeting and Guiot’s uses millimeters while three-dimensional MRIs are measured in voxels. Vim locations based on automatic indirect methods are compared with those based on manual determinations of neurosurgeons, and the results show similar positions between them. The similar positions prove Vim determination accuracy of proposed automatic indirect methods.


INTRODUCTION
Parkinson's disease (PD) has the fastest enhancement worldwide among neurological disorders. The number of affected individuals in 2016 was more than doubled times as high as individuals in 1990 [1]. Southeast Asia contributed six portions of overall affected individuals, and Indonesia is the largest contributor in Southeast Asia. Nevertheless, there is no treatments or medicines which cure PD [2,3]. Current treatments of PD focus on reducing its symptoms; one of them is tremor.
There are some treatments to decrease Parkinson's disease, such as drug administration [4,5], brain lesion [2,6,7], and deep brain stimulation [8][9][10]. A common brain part as the target of deep brain stimulation and brain lesion is ventral intermediate nucleus (Vim) [9]. Vim is a section of Thalamic nuclei, and it has been anatomic target treatments for movement disorders, including PD [11].
Although Vim is designated as a target of PD treatments, determining the exact position of Vim is challenging. Vim locations cannot be visualized clearly in 3 Tesla magnetic resonance imaging (MR) [3,12]. By looking at the difficulty of detecting the location of the Vim, some indirect methods are developed. The widely used indirect methods are Coordinate-based targeting [2,13] and Guiot's [14,15].
Coordinate-based targeting determines the coordinates of the Vim based on the human brain atlas data, i.e. Schatelbrand-Bailey's atlas [16]. Coordinate-based targeting defines Vim location is 15 mm x-coordinate from AC-PC line and around 6 mm y-coordinate from posterior commissure (PC). AC point is a center point in the border of AC and PC point is a center point in the border of PC. Guiot's method [17,18] determines the y-coordinate of the Vim based on the real distance between the anterior commissure (AC) and the posterior commissure (PC) of the patient and the x-coordinate based on the Coordinate-based targeting method. Guiot's defines one-fourth or three-twelfth of AC-PC line as the ycoordinate of the Vim. Successful determination of Vim based on these indirect methods depends on the accuracy of AC and PC.
To facilitate Vim locations determination, neurosurgical planning applications are available, i.e. Leksell Surgiplan [17][18][19] and Inomed Planning Software (IPS) [20]. Both of those applications provide displaying three-dimensional views of an MRI and measuring the distance between brain parts. Except for those capabilities, all neurosurgical planning applications have no feature of automatic indirect methods. Neurosurgeons need their memory and their ability to implement indirect methods in those applications.
Referring Based on those motivations, this paper proposes automatic indirect methods of Vim localizations. It analyzes indirect methods in cases of MRIs with the correct and incorrect orientation of AC-PC planes. There are several steps for developing proposed automatic indirect methods. First, the brain MRIs are aligned automatically based on defined AC point, a PC point, and a midline reference (MR) line. Then, the proposed automatic indirect methods convert the coordinates from millimeters to voxels to determine the Vim location. The conversion is applied because rules of Coordinate-based targeting and Guiot's uses millimeters while three-dimensional MRIs are measured in voxels. The Vim locations obtained by proposed automatic indirect methods are compared with those determined manually by neurosurgeons.
This paper analyzes indirect methods by measuring the accuracy of Coordinate-based targeting and Guiot's based on MRIs with correct and incorrect orientation of AC-PC planes. This paper uses thirty post-operative 3T T2-Flair MRIs in the experiment. In MRIs with the correct orientation of AC-PC planes, Vim locations based on those two methods are compared with ground truth. The ground truth in this paper is a set of centers of Vim brain lesions which are captured in post-operative T2-Flair MRIs. Thereupon, in MRIs with incorrect orientation of AC-PC planes, each Vim location obtained by one of those methods from MRI with incorrect orientation is compared with its obtained by same method from MRI with the correct orientation. MRIs with the incorrect orientation are formed by rotating with specific degrees on x-axis rotation, y-axis rotation, and z-axis rotation. Euclidean distance is used to determine the accuracy, wherein smaller Euclidean distance means higher accuracy of Vim locations determination.
The remainder of this paper is structured as follows: Section 2 explains parts of the brain which are utilized in determining Vim locations, indirect methods, and the measurement methods. Section 3 describes the proposed automatic indirect methods. Section 4 provides the experiment results and analysis related to the obtained results. The last section, Conclusion section, sums up all works of this study.

Ventral Intermediate Nucleus
The ventral intermediate nucleus (Vim) is commonly used in the surgical treatment of Parkinsonian and essential tremors [23]. The Vim is a nuclear part of the thalamus, which delivers signals from sensors, such as motor signals. The location of the Vim cannot be identified with certainty by using commonly magnetic resonance imaging. However, it can be detected by referring to surrounding parts of a brain. The center point of Vim is located approximately 1.5 mm next to the corticospinal tract (CST), which can be observed clearly in MRIs with T2-fluid-attenuated inversion recovery (T2-FLAIR) sequences. Referring to Figure 1

Anterior Commissure, Posterior Commissure and Midline Reference
The anterior commissure (AC), posterior commissure (PC), and midline (mid-sagittal plane) reference (MR) are used to align the brain [24]. The location of the AC is in the anterior wall of the third ventricle at the upper end of the lamina terminals. The area of the PC is in the posterior wall of the third ventricle. The anterior commissureposterior commissure line (AC-PC line), defined by Talairach [25], is a line that connects an AC point (a center point in the border of AC) and a PC point (a center point in the border of PC). AC-PC points can be determined based on the sagittal plane and the axial plane. AC-PC points are symbolized as green signs, and an AC-PC line is visualized as a yellow line of Figure 2.  After determining the points of AC-PC, the midline (mid-sagittal plane) reference (MR) is determined. The mid-sagittal plane divides the left and the right brain. The point of MR is obtained based on a point in a line that is perpendicular to the AC-PC line and splits the brain stem. MR is denoted as M2 (the yellow circle) in Figure 3.

Indirect Methods for Determining Vim Localization
There are two general indirect methods for finding the location of Vim, i.e. Coordinate-based targeting and Guiot's method. Coordinate-based targeting [2,13] is a Vim localization method based on the human brain atlas data, i.e. Schatelbrand-Bailey's atlas. The equations for locating the Vim are given in Theorem 1, whose symbols are explained in Definition 1. Red circles of Figure    Guiot's method [14,15] determines the y-coordinate of the Vim based on the real distance between AC and PC of the patient and the x-coordinate based on the Coordinate-based targeting method. The equations for locating the Vim are given in Theorem 2, whose symbols are explained in Definition 1. The red circles of Figure 5 represent right and left Vim obtained by Guiot's.

Measurements of Accuracy
This paper measures the accuracy of Coordinate-based targeting and Guiot's based on MRIs with the correct and incorrect orientation of AC-PC planes. In MRIs with the correct orientation of AC-PC planes, Vim locations based on those two methods are compared with ground truth. The ground truth in this paper is a set of centers of dark spots in Vim brain lesions which are captured in post-operative T2-Flair MRIs. Thereupon, in MRIs with incorrect orientation of AC-PC planes, each Vim location obtained by one of those methods from MRI with the incorrect orientation is compared with its obtained by same method from MRI with correct orientation. MRIs with the incorrect orientation are formed by rotating with specific degrees on x-axis rotation, y-axis rotation, and z-axis rotation. The illustration of x-axis, yaxis and z-axis is shown in Figure 6. The specific degrees in this experiment are −10°, −5°, 5°, 10° xaxis rotations, −10°, −5°, 5°, 10° y-axis rotations, and −10°, −5°, 5°, 10° z-axis rotations.  (1) and Equation (2).
where: : error result of each patient in a medical image (MRI) with correct orientation of AC-PC planes : number of patients : x-coordinate of Vim location determined by a Vim targeting method : x-coordinate of a center of a dark spot in a Vim brain lesion as ground truth : y-coordinate of Vim location determined by a Vim targeting method : y-coordinate of a center of a dark spot in a Vim brain lesion as ground truth : z-coordinate of Vim location determined by a Vim targeting method : z-coordinate of a center of a dark spot in a Vim brain lesion as ground truth where: : average error results in medical images with a certain degree of a certain axis (x-axis, y-axis, or z-axis) : number of patients : degree of certain axis : x-coordinate of Vim location determined by a Vim targeting method in a medical image with a certain degree of a certain axis 0 : x-coordinate of Vim location determined by a Vim targeting method in a medical image with 0° degree toward x, y, and z planes : y-coordinate of Vim location determined by a Vim targeting method in a medical image with a certain degree of a certain axis 0 : y-coordinate of Vim location determined by a Vim targeting method in a medical image with 0° degree toward x, y, and z planes : z-coordinate of Vim location determined by a Vim targeting method in a medical image with a certain degree of a certain axis 0 : z-coordinate of Vim location determined by a Vim targeting method in a medical image with 0° degree toward x, y, and z planes

Material
This paper used thirty post-operative magnetic resonance imaging 3 Tesla (MRI 3T) of people with PD. These MRI 3T modalities are from T2-fluid-attenuated inversion recovery (T2-FLAIR) sequences. There are some reasons of using post-operative MRI 3T with T2-Flair sequences. First, MRIs with T2-Flair define clearly anatomical landmarks, namely AC and PC, to support Vim determination [22]. Secondly, post-operative MRIs are chosen because they visualized brain lesions. Centers of darker spots in brain lesions are appointed as ground truth in this paper. M5 point of Figure  7 indicates the center and white areas surrounding M5 are a brain lesion. Out of thirty patients, 72% are men with PD. Parkinson's disease affects more men; statistics in 2016 expose a ratio of men and women with PD is 1.7:1.2 [1]. The other information of patients whose data were used in the experiment is shown in Table 1. The length of AC-PC line has an average of 23.766 [1.513] mm. The high standard deviation scores of AC and PC point indicate the high difference in location of AC and PC point. The high difference of location of those points manifests differences in brain morphology of one patient and others.

Methods
This paper develops automatic indirect methods to determine Vim location. There are three steps in developed methods: (1) defining the anterior commissure (AC), posterior commissure (PC) and midline reference (MR) points in 3-vector coordinates; (2) redefining the plane passing through those points using 3 normal vectors which have been rotated by a quaternion; and (3) determining the Vim targeting location based on Coordinate-based targeting and Guiot's method.

Defining Anterior Commissure, Posterior Commissure and Midline Reference
Anterior commissure (AC) point, posterior commissure (PC), and midline (mid-sagittal plane) reference (MR) are used to align the brain [24]. Those points and midline are manually determined by neurosurgeons. The brain alignment based on defined points and midline is performed automatically in our developed methods.
Based on the points of AC, PC, and MR, the plane for determining the Vim location is obtained (denoted as Plane A or Pa). A visualization of Pa is shown in Figure 8. The position of this plane is in the center of the brain. C in Figure 9 is the center point of the plane. Even though Pa has been obtained, the geometric calculation cannot be conducted on the plane; this paper redefines Pa using 3 normal vectors which have been rotated by a quaternion [26,27].

Redefining The plane
The redefinition of the plane is explained step by step in Algorithm 1. The inputs are the points of AC, PC, MR and 3 normal vectors. The result is 3 normal vectors which have been rotated by a quaternion [26].
Algorithm 1: Redefine The Obtained Plane Inputs: AC, PC, MR and 3 normal vectors which are determined by Equation (3) Outputs: 1 Calculate the quaternion between and based on Equations (4) and (5) 2 Project AC and MR to Py based on Equations (6) to (13) [26] 3 Calculate the angle of and , then multiply it by 1 based on Equations (14) and (15) [26] 4 Rotate the normal vector using 1 based on Equations (16) and (18)   : rotated normal vector of z plane

Determining Vim Location
The last step is determining the Vim location. The automatic Vim localization based on Guiot's method is determined by Equations (19) to (21), while that based on Coordinate-based targeting is determined by Equations (22), (23), and (21).
where: : distance of PC point and Vim point in the x-plane : amount of space between voxels in the 3D medical images : point of posterior commissure (PC)

RESULTS AND ANALYSIS
In this section, our proposed automatic indirect methods are evaluated by comparing the Vim locations obtained by our methods with those obtained by manual determination by a neurosurgeon on post-operative MRIs. Subsequently, Vim locations based on Coordinate-based targeting methods and those based on Guiot's are compared based on MRIs with correct orientation of AC-PC planes and MRIs with incorrect orientation of AC-PC planes.

Evaluation of Proposed Automatic Indirect Methods
Vim locations on 3-planes based on our proposed automatic indirect methods and those based on manual determination by a neurosurgeon are shown in Figure 10. The proposed automatic indirect methods were implemented with Node.js [28]. A neurosurgeon determines Vim locations manually by an existing neurosurgical planning application, which is IPS. Based on Figure 10, the positions of Vim by automatic indirect methods and manual indirect methods are similar. It can be concluded that our proposed indirect methods obtain correct locations of Vim. Figure 10. Comparison between the proposed method (above) and the manual determination of a neurosurgeon (below).

Evaluation of Indirect Methods in MRIs with Correct Orientation of AC-PC planes and MRIs with Incorrect Orientation of AC-PC planes
Indirect methods, i.e., Guiot's and Coordinate-based targeting, are compared based on correct and incorrect orientation of AC-PC planes. Correct orientation of AC-PC planes means used MRIs are already aligned based on AC, PC, and MR. Incorrect orientation of AC-PC planes means MRIs with correct orientation are rotated with specific degrees on x-axis, y-axis and z-axis. The specific degrees in this experiment are −10°, −5°, 5°, 10°. Table 2 shows the average error results based on MRIs with the correct orientation of AC-PC planes. The average results of all patients show Coordinate-based targeting has 0.05 mm higher value of average error results of all patients than Guiot's. Briefly, Vim locations obtained by Guiot's is more accurate than those obtained by Coordinate-based targeting.
By analyzing results in Table 2, there are several data with >1.5 mm errors. There are some underlying causes. First, a person with PD, denoted by 6 th patient, has unusual brain morphology because of a cyst that affected corpus callosum. The comparison of a patient with a cyst and a patient without a cyst is shown in Figure 11. Red circles denote two corpus callosum. The corpus callosum that is pressed by the cyst is smaller than a normal corpus callosum. Shrinking corpus callosum causes shrinking of AC-PC line. Shrinking of AC-PC line raises errors in determining Vim locations. Secondly, the experiment of this paper used post-operative MRIs. Post-operative MRIs have differences with preoperative MRIs. However, indirect methods are destined to a planning stage, so implementing those methods in post-operative MRIs reduces the accuracy of those methods. Table 3 shows the average error results based on MRIs with the incorrect orientation of AC-PC planes. The average results of all rotations show Coordinate-based targeting has 0.032 mm smaller value of average error results of all rotations than Guiot's. It can be concluded that Vim locations based on Coordinate-based targeting are more accurate in MRIs with the incorrect orientation of AC-PC planes. Therefore, Coordinate-based targeting is more resilient with inaccuracy AC-PC planes.

CONCLUSION
This paper develops proposed automatic indirect methods of VIM localization and observes Vim locations based on indirect methods in MRIs with the correct orientation of AC-PC planes and MRIs with the incorrect orientation of AC-PC planes. There are several steps of automatic indirect methods. The first step is determining the plane of the anterior commissure (AC) and the posterior commissure (PC) because this paper presents the center of the MRI image as the middle point of the AC-PC plane. The methods are automatically determining the AC-PC plane based on defined an AC point, a PC point, and a midline reference (MR) line. Then, the proposed automatic methods convert the coordinates from millimeters to voxels to determine the Vim location. The conversion is applied because rules of Coordinate-based targeting and Guiot's uses millimeters while three-dimensional MRIs are measured in voxels. Vim locations based on automatic indirect methods are compared with those based on manual determinations of neurosurgeons, and the results show similar positions between them. The similar positions prove Vim determination accuracy of proposed automatic indirect methods.
Left and right Vim locations are determined based on AC-PC planes. AC-PC planes are determined based on AC-PC points. If the AC-PC points are not aligned accurately, then AC-PC planes contain errors. The possibility of the occurrence of these errors is a cause of this paper to observe indirect methods not only in MRIs with the correct orientation of AC-PC planes but also those with the incorrect orientation of AC-PC planes. Based on the experiment conducted in this paper, Vim locations obtained by Guiot's are more accurate than those by Coordinate-based targeting in MRIs with the correct orientation of AC-PC planes. Guiot's has 0.05 mm smaller value of average error results than Coordinate-based targeting. In contrast, Vim locations based on Coordinate-based targeting are more accurate in the MRIs with the incorrect orientation of AC-PC planes. In summary, Guiot's provides more accurate Vim localization in MRIs with the correct orientation of AC-PC planes. Coordinatebased targeting has 0.032 mm smaller value of average error results than Guiot's. Nevertheless, Coordinate-based targeting method is more resilient with inaccuracy AC-PC planes.
The determination of AC-PC points is still manual in this study. Segmentation of AC and PC to automate the location of AC-PC points is the development of the continuation of this study.

Availability of data and materials
The used raw dataset in this research is not publicly available. Readers can contact the author if they want to access the data Competing interest The authors declare that they have no competing interests. Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Authors' contributions RS is the supervision that has the idea for creating automatic Vim localization. KRS composed the manuscript and did the experiment. MAR built the program. AF is neurosurgeon that operated on patients with Parkinson's disease and determine the used methods. AT and AHB are neurosurgeon that evaluates the results that are obtained by KRS. All authors read and approved the final manuscript.