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Automatic oculomotor nerve identification based on data‐driven fiber clustering

Abstract The oculomotor nerve (OCN) is the main motor nerve innervating eye muscles and can be involved in multiple flammatory, compressive, or pathologies. The diffusion magnetic resonance imaging (dMRI) tractography is now widely used to describe the trajectory of the OCN. However, the complex cranial structure leads to difficulties in fiber orientation distribution (FOD) modeling, fiber tracking, and region of interest (ROI) selection. Currently, the identification of OCN relies on expert manual operation, resulting in challenges, such as the carries high clinical, time‐consuming, and labor costs. Thus, we propose a method that can automatically identify OCN from dMRI tractography. First, we choose the multi‐shell multi‐tissue constraint spherical deconvolution (MSMT‐CSD) FOD estimation model and deterministic tractography to describe the 3D trajectory of the OCN. Then, we rely on the well‐established computational pipeline and anatomical expertise to create a data‐driven OCN tractography atlas from 40 HCP data. We identify six clusters belonging to the OCN from the atlas, including the structures of three kinds of positional relationships (pass between, pass through, and go around) with the red nuclei and two kinds of positional relationships with medial longitudinal fasciculus. Finally, we apply the proposed OCN atlas to identify the OCN automatically from 40 new HCP subjects and two patients with brainstem cavernous malformation. In terms of spatial overlap and visualization, experiment results show that the automatically and manually identified OCN fibers are consistent. Our proposed OCN atlas provides an effective tool for identifying OCN by avoiding the traditional selection strategy of ROIs.

Tractography based on diffusion magnetic resonance imaging (dMRI) can reveal the trajectory of OCN in three-dimensional, including the intramesencephalic and cisternal segments (Basser, Mattiello, & LeBihan, 1994;Gong et al., 2009;Hodaie, Quan, & Chen, 2010;Yoshino et al., 2016) which has been widely used in OCN identification to obtain the three dimensional (3D) relationship with surrounding structures Li et al., 2018;Muhammad & Niemelä, 2019). Hodaie et al. (2010) used dMRI data with the singleregion of interest (ROI) selection method (cisternal segment of OCN) and diffusion tensor imaging (DTI) to reconstruct OCN. Results showed that the OCN terminates in the ONC or extends down the brainstem. Yoshino et al. (2016) used high-definition fiber tractography and two-ROI selection method (fourth ventricle at the level of upper pons and cisternal segment) to identify OCN fibers in healthy subjects and patients with brain tumors and presented similar results. Previous studies (Hodaie et al., 2010;Yoshino et al., 2016) identified putative OCN fibers through manually placed ROIs. However, common tractography methods have difficulty in tracking the complete OCN pathway because of the elongated structure of the OCN, cerebrospinal fluid (CSF) where the cisternal segment of OCN is infiltrated, and partial volume effect Maier-Hein et al., 2017). Therefore, experts should place the ROI manually to promote OCN tractography and identification. (1) The identification of the OCN is sensitive to the ROI placement, and manual ROI selection methods suffer from imaging artifacts and/or noise and operator bias. Thus, the selection of the best-performing ROIs remains a challenge Zhang et al., 2020). (2) Manually placing ROIs is laborious, time-consuming, and unfriendly to beginners who suffer from lack of knowledge in anatomy (Jacquesson, Yeh, et al., 2019;Xie et al., 2020).
Automatic identification methods are proposed to avoid the pitfalls of traditional ROI selection methods. The automatic identification based on cortical parcellation (Sporns, Tononi, & Kötter, 2005;Wassermann et al., 2016) allows for highly specific identification but leads to the low sensitivity of tract identification and effects from individual anatomical variations (Bonilha et al., 2015). Many methods based on atlas and shape models, which emphasize the use of statistical shape or statistical appearance, have been proposed to identify cranial nerves (Sultana, 2017). However, these methods cannot identify the nerve course of the intramesencephalic segment. Another type of method can identify by registering ROI templates in standard onto individual information for tractography fiber selection (Malinsky et al., 2013). However, such ROI-based methods rely on the accuracy of the registration algorithm. When squeezed by tumors, cranial nerves are displaced. Common ROI templates are no longer applicable, resulting in recognition failure (Chen et al., 2011;Jacquesson, Yeh, F I G U R E 1 Schematic anatomical overview of the oculomotor nerve (OCN). (a) The transverse plane of the T1-weighted MR image at the level of the midbrain. (b) The details of (a). (c) The sagittal plane of the T1-weighted MR image. (d) The details of (c) et al., 2019). Moreover, ROI-based methods are sensitive to tractography methods that require multiple ROIs to be constrained. In contrast to other methods, the dMRI tractography atlas uses a distinct white matter connectivity modeling assumption to group fibers with comparable trajectories into clusters. These studies successfully demonstrated the automated identification of anatomical white matter fiber tracts Zhang et al., 2020) (e.g., trigeminal never and white matter tracts), which achieve in escape from individual differences including objects, time, locations, and experimental conditions (Fischl, 2012;O'Donnell et al., 2017), with several advantages as follows.
(1) Fiber tracts can be automatically identified with high consistency across subjects and augmented with anatomical annotations . (2) The automatic identification method uses only dMRI data, obviating the need for inter-modality registration . (3) Kwon, Kim, Kim, & Jang, 2013;Li et al., 2021;Miller, Mark, Ho, & Haughton, 1997;Vitoševi c et al., 2013). Finally, we have applied the proposed atlas to identify the OCN of the new 40 subjects. Results show that the automatic identification of OCN by our proposed strategy is quantitatively and qualitatively consistent with the findings of ROIs manually placed by an expert. The OCN is dissimilar from the trigeminal never and white matter tracts and is more elongated, resulting in the strict selection of methods and parameters (including tractography parameters, ROI, and similarity) in tractography and atlas generation. After creating the atlas, we have successfully applied the OCN atlas to patients with brainstem cavernous malformation (BSCM). We have accurately identified the OCN, which surrounds the BSCM and the 3D positional relationship between OCN and surrounding tissues.
In the rest of this article, we describe our proposed methods, that is, OCN atlas creation and automatic OCN identification. Then, we demonstrate an application to dMRI datasets from two different acquisition sites, including HCP dataset and two patient data with BSCM. Finally, the OCN identification performance of our proposed method is evaluated quantitatively and qualitatively and compared with the method in which the expert selects the OCN. Medical University has given its permission before testing.

| Data processing
We design a series of processing pipelines, including motion correction, denoising, and eddy current correction. First, we apply denoising and eddy correction on dMRI and denoising on T1w images (Tournier et al., 2019).
Second, the automated reconstruction and labeling of cortical and subcortical regions are performed using the Freesurfer (Fischl, 2012) on T1w images. The seed imaging and regions of avoidance (ROAs) are chosen by automatically extracting the corresponding numbered brain area. We set the whole brainstem as the seed imaging (as shown in Figure 2). In terms of anatomical considerations, the anatomical pathway of the OCN originates from the ONC which is located in the central and dorsal midbrain (Brazis et al., 2012;Condos, 2021). Then OCN crosses the ventral midbrain and enters the cistern from the outer edge of the interpeduncular fossa (Park et al., 2017). And the rest of the brain regions (i.e., the whole brain excepts brainstem) are used as (ROAs. Because the pathway of the cisternal segment of OCN does not enter any other brain areas (Park et al., 2017).

| Comparison of multiple tractography and parameters
Tractography methods are widely used in cranial nerve studies (Behan et al., 2017;Castellaro et al., 2020;He et al., 2021;Hodaie et al., 2010). To find a better method for OCN reconstruction, we  (Hodaie et al., 2010) to reconstruct the 3D trajectory of OCN. In contrast to CSD and DTI, MSMT-CSD is utilized to fit a five-tissue-type segmented tissue image by using multiple b-values for the multi-type tissue fiber orientation distribution (FOD; Castellaro et al., 2020;Jeurissen, Tournier, Dhollander, Connelly, & Sijbers, 2014). To describe the complete OCN pathway, we prepare a careful plan for each method, including the seed imaging, ROAs, and parameters.

| Parameters
We conduct an experiment to determine the best-performing parame- and method has improved performance in OCN reconstruction. We first determine the optimal parameters for each tractography method and perform a cross-method comparison to determine the best combination of method and parameters for OCN tractography performance. Tractography methods and parameters are used as the basis for subsequent atlas and test subjects.

| Reconstruction rate of OCN subdivisions
We assess the ability of each tractography method to reconstruct the two subdivisions of the OCN successfully. Specifically, we consider that the fiber pathway is successfully traced if at least one fiber is retained on both sides and each OCN anatomical subdivision is successfully reconstructed fibers after ROI selection (i.e., OCN and F I G U R E 3 Region of interest (ROI) and region of avoidance (ROA) for OCN and OCNM selection. (a) ROI (cisternal segment of oculomotor nerve [OCN]) and ROA (tegmentum of the pons) for OCN selection. (b) OCNM selection differing from OCN selection only in the tegmentum of the pons used as ROI. Note that, in order to show complete OCN, the location of the slice chose from T1 anatomical image maybe lower (or further back) than the position of OCN OCNM). So, we compute the overall reconstruction rate for the full OCN pathway (i.e., the percentage of subjects where both subdivisions are successfully reconstructed).

| OCN atlas generation
We first determine the optimal parameters for each tractography method and then perform a cross-method comparison to determine the best combination of method and parameters for OCN tractography performance. The tractography methods and parameters are used as the basis for subsequent atlas and test subjects.

| Generation of OCN fiber clustering atlas
We learn a data-driven model of common OCN structure in humans through the following processes:

OCN tractography of atlas subjects
We acquire pre-brainstem fibers from 40 atlas subjects. Each atlas subject tractography is performed with the best-performance tractography strategy (i.e., MSMT-CSD, angle threshold of 45, and FA threshold of 0.05). Then individual brainstem fibers are produced after removing invalid fibers passing through ROAs to reduce memory space and computational cost as illustrated in Figure 2a.

Multi-subject fibers registration
In a multiscale way, we compute an unbiased entropy-based . The registration employs 20,000 fibers from each subject for a total of 800,000 fibers, with a minimum fiber length of 45 mm, and affine then coarse-to-fine b-spline registration with multiscale sigma values from 20 down to 2 mm and a final b-spline grid size of 8 Â 8 Â 8. After registration, an OCN tractography with high density and good spatial correspondence is produced.

Spectral clustering
OCN tractography data are divided into K clusters by spectral clustering to create a high-dimensional fiber clustering atlas (O'Donnell & Westin, 2007), in which K is a user-supplied parameter that defines the parcellation scale. First, many tractography fibers are highly similar to their neighboring fibers on the basis of anatomy (Presseau, Jodoin, Houde, & Descoteaux, 2015). Thus, we perform a random sampling of 20,000 fibers from each subject rather than analyzing all fibers across subjects and ensure that the extracted number of fibers is sufficient to represent the anatomical structure of the OCN in the population. Then, we implement groupwise spectral embedding and clustering to divide OCN tractography fibers. The groupwise spectral embedding creates an independent spectral space that represents similarity information between fibers. In addition, we use a random sampling method called Nystrom (Fowlkes, Belongie, Chung, & Malik, 2004) to represent the space compactly and remarkably reduce the number of fiber distance calculations in the subsequent steps. Four iterations (over two standard deviations from the cluster's mean fiber affinity) are performed to remove improbable fibers for cluster consistency in the atlas (O'Donnell et al., 2017;O'Donnell & Westin, 2007).
We generate multiple OCN atlases (as shown in Figure S1

| Supervision of OCN fiber clusters
Based on the experience of our previous work , the OCN is present in multiple fiber clusters, and the integration of these fiber clusters can represent an anatomical subdivision of the complete OCN. We obtain the fixed atlas by subdividing multi-subject regis-   Figure S2). The OCN is present in six fiber clusters, where we select the 25th, 38th, 148th, and 166th clusters in the subject-specific atlas to form anatomically OCN fibers, and the 71st and 177th clusters to form anatomically OCNM fibers, as illustrated in Figure 4d,e. We perform the following work to evaluate the OCN identification performance of our method.

| OCN identification
We report the average identification rate of different anatomical subdivisions (OCN and OCNM) in 82 subjects (including 80 HCP subjects and 2 BSCM patients). First, two experts (Mengjun Li and Mingchu Li) perform anatomical confirmation of the OCN in each subject and subdivide its anatomy into OCN fibers and OCNM fibers. Specially, we define that if more than an OCN fiber or/and OCNM fiber of the subject is successfully identified, the atlas is valid for the subject. Then, we calculate the average percentage of successfully automatically identified OCN in HCP subjects. For spatial overlap, referring to the traditional segmentation task, we use the Accuracy (ACC), Sensitivity (SE), and Precision (PR) (Taha & Hanbury, 2015) to assess the ability of our method to identify correct OCN fibers of individual HCP subject. ACC, SE, and PR are defined as Then, we quantify the spatial overlap between manually and automatically identified OCN with the weighted Dice (wDice) coefficient (Cousineau et al., 2017;Dice, 1945). On the basis of the traditional Dice calculation method that is designed to calculate the fiber overlap, wDice sets high weights for voxels with high fiber density, which is also scientific and reasonable. We calculate the mean and standard deviation of wDice coefficients for 40 atlas subjects, 40 test subjects, and 2 BSCM patients.
In addition, to demonstrate the robustness of our proposed OCN atlas, we classify the brainstem tractography of the same subject five times based on the fixed atlas by clustering at the same scale. Then we visualize the identification OCN results for each spectral clustering. We use wDice (Cousineau et al., 2017;Dice, 1945) to quantitatively describe the consistency among each result and the similarity of each automatic identification result with the manual identification result.

| OCN visualization
We use the 3D Slicer to visualize the automatic and manual identification

| EXPERIMENTAL RESULTS
In the present study, we create an OCN atlas to identify the OCN automatically from new subjects. We perform the identification rate calculation, spatial overlap calculation, and the OCN visualization to demonstrate the reliability of our proposed automatic identification of the OCN atlas. First, we invite anatomical experts (Mengjun Li and Mingchu Li) to identify the OCN manually from brainstem fibers, which are obtained from 27 combinations with methods and parameters. The results of reconstruction rate (see Table 1) and visualization (see and OCNM identification compared with those of expert manual selection are higher than 90.50%, and the mean wDice of OCN is higher than that of OCNM. Finally, the atlas is successfully used to identify OCN from tumor subjects, and we verify the identified results with the finding in surgery. We find that the automatic identification result is highly consistent with surgery findings.    are an ideal outcome according to Cousineau et al. (2017). OCN fibers and OCNM fibers obtained from the OCN atlas are highly comparable to the manually identified OCN. Furthermore, the wDice coefficient demonstrates the accuracy of our approach.

| OCN spatial overlap
The lowest wDice coefficient among the five clustering results is 0.9846 as illustrated in Figure 6d, which proves that the clustering results based on the fixed atlas from each spectral clustering are consistent. The results are also consistent with the manual identification by experts.  OCN. This patient has adduction dysfunction of the left eye, which could be caused by the displacement of the left OCN resulting from BSCM, the adduction dysfunction of the left eye is relieved after surgery ( Figure 8).

| Case 2
A 42-year-old man presents with a BSCM at the right pons. Displacement is not observed in the right automatically visualized OCN constructed from the OCN atlas. The disruption is not identified when compared to the contralateral automatically visualized OCN.
This patient has no motor dysfunction of the right OCN. However, this patient has ghosting and horizontal nystagmus, which could be caused by the displacement of the MLF resulting from BSCM ( Figure 9).

| DISCUSSION
In this article, we propose an automatic OCN identification method to enable robust anatomical OCN identification from new subjects and investigate the patient whose tumor involves morphological changes in the OCN. We demonstrate the robustness and reliability of our In tractography for individuals, we set the VentralDC and brainstem as ROI for OCN tractography because the OCN passes through the VentralDC into the cistern (Bogousslavsky, Maeder, Regli, & Meuli, 1994;Castro, Johnson, & Mamourian, 1990)  The proposed atlas can identify the different subdivisions of OCN. Unlike the cisternal segment of OCN that has been studied in multiple previous works, the intramesencephalic segment is relatively less studied (Tsutsumi, Miranda, Ono, & Yasumoto, 2017;Uz & Tekdemir, 2006). To our knowledge, Jang and Kwak (2017)   shells and tissues to estimate fiber directions in each voxel (Castellaro et al., 2020). Tissues respond differently with changes in b-value, and different tissues can be effectively distinguished on the basis of their different response functions (i.e., WM, GM, CSF) (Castellaro et al., 2020;Jeurissen et al., 2014). This phenomenon reduces the partial volume effect to obtain accurate fiber orientation models and explains that fibers by MSMT-CSD are clearer and more accurate than those by other two methods in the intramesencephalic segment. In the experiments on OCN reconstruction in this article, the experimental results provide a phenomenon that OCN is easier to be reconstructed than OCNM, so OCNM is equal to the overall rate.
According to Figure  identification (Zolal et al., 2016). For the creation of the OCN atlas, we utilize multi-shell HCP data in the present study, and the HCP dataset has minimal distortion artifacts and the highest quality.  (Castro et al., 1990;Miller et al., 1997;Vitoševi c et al., 2013). Moreover, OCN is close to the medial lemniscus (the outward path around the red nucleus), but all fibers converge below the red nucleus and through the interpeduncular fossa into cistern together (Miller et al., 1997;Vitoševi c et al., 2013). We propose that the OCN atlas In our work, we find that our proposed automatic OCN identification method has several advantages over traditional relied-on ROI methods to identify OCN fibers. First, the template of ROIs, which is used to overcome the variability, and the presence of pathology/ degenerative changes across subjects still have limitations (Hodaie et al., 2010;Wedeen et al., 2008). Second, experts are unable to draw ROIs directly on structural images when the tumor occurs. Complex skull base tissues are displaced by compression and imaging artifacts and/or noise at the skull base region. In contrast to relied-on ROI methods, our method practically eliminates dependence on the manual placement of ROIs and avoids subjectivity. Moreover, the problem of multimodal data registration is avoided, and the OCN atlas identifies OCN fibers from dMRI tractography directly. Therefore, our method provides a robust tool for OCN identification.
The potential limitations of the present study, including suggested future work to address limitations, are as follows. First, we use our method to identify the OCN of subjects with different health statuses, including healthy subjects and patients with tumor.
Further evaluation can include an investigation of patients with diseases that affect OCN, for example, the relationship between the positions of OCN and blood vessel of the patient with posterior communicating aneurysms and differences in OCN between patients with diabetes and healthy subjects. Second, the orbital segment of the OCN cannot be well reconstructed at present, and our proposed method for the automatic identification of OCN does not possess an improved identification of the orbital segment of OCN.
In future work, we will design methods to reconstruct the OCN pathway completely and improve our OCN atlas on the basis of our previous studies (Feng & He, 2020). Third, the proposed method performs poorly in identifying OCN that is affected by big BSCM. The mass effect of large BSCM usually leads to substantial morphological changes in OCN. Given that fiber clusters are subdivided in accordance with fiber shape and position, deformed OCN fibers may not be classified into the same cluster within the OCN atlas. In our future research, BSCM shape and the identifiers of surrounding tissues should be considered as inputs for clustering.

| CONCLUSION
In this study, we propose an automatic OCN identification strategy.
Experimental results show that our selected tractography method and parameters are highly valuable for OCN reconstruction. The results of automatic OCN identification atlas based on dMRI tractography fibers are highly consistent with the manual OCN identification by experts.
Moreover, the automatic method shows advantages over the traditional manual selection method and allows for the robust identification of different anatomical subdivisions of the OCN in the data from the different acquisitions. In the end, we successfully apply the automatic method to the data of patients with BSCM. The study provides an efficient tool for simple post-processing and reduces expert labor costs.