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DE GRUYTER Current Directions in Biomedical Engineering 2022;8(1): 13-16 Annika Niemann*, Gabor Janiga, Bernhard Preim, Daniel Behme, and Sylvia Saalfeld Centerline and blockstructure for fast structured mesh generation https://doi.org/10.1515/cdbme-2022-0004 Abstract: In contrast to unstructured meshes, structured meshes yield faster simulation results for bio-medical simula- tions, but are very time-consuming to create. A preprocessing step in the generation of structured meshes is the manual con- struction of a blockstructure approximating the vessel. Here, we present an automatic centerline calculation and blockstruc- Fig. 1: Manual generated blockstructure with centerline (red) ture generation to reduce the user effort and time of struc- tured mesh generation. The centerline is detected as points in between opposite faces. Based on the centerline, cross sec- tions are determined and a blockstructure which approximates the vessel is automatically generated. The centerline detection does not require time-consuming user input and meshes with more than 195,000 vertices are processed in less than 160 sec- onds. The results of the presented automatic centerline detec- tion are compared to a centerline with manual input gener- Fig. 2: Structured mesh for a segment of a blood vessel ated by the widely used vmtk tool. The centerlines are similar, small differences occur at bifurcation and at the aneurysm. 2 Related Work 1 Introduction Guo et al.  presented a deep learning centerline detection for coronary arteries. They use a fully convolutional network Research of deformation of vessels in the brain, like aneurysm with a minimal path extractor to generate single-pixel wide or arteriovenous malformation, often requires several mesh centerlines in binary segmentation masks. Yang et al.  also processing steps of the 3D vessel model. For example the cen- presented deep learning centerline detection, using a U-Net to terline and a blockstructure (Fig. 1) are used to generate struc- predict the centerline of roads in aerial images. These deep tured meshes (Fig. 2) for hemodynamic simulations. An im- learning solutions are tailored to specific use cases and can not portant part is the centerline detection. Based on the centerline, be easily transferred to other applications. A none deep learn- further analysis, for example morphological parameter calcu- ing based framework calculating the centerline of 2D or vox- lation, or preparation of structured meshes for hemodynamic elized 3D models was presented by Hassouna and Farag . simulations is carried out [4, 12]. A common tool for center- Antiga et al.  detect the centerline as shortest part be- line calculation is the vessel modelling toolkit (vmtk) [1, 5, 9]. tween two extremal points based on a voronoi diagram. The However, the centerline calculation with vmtk often requires detection requires start and end point of the centerline and is manual input in form of selecting points on the mesh and rep- not suitable for circular structures, such as the Circle of Wilis. etition if the first result is not sufficient, for example if the cen- Wei et al.  presented a centerline calculation for vascular terline of a vessel branch is missing. The presented approach meshes. Their algorithm is based on the assumption that vas- does not require user input. cular structures consists of segments of cylindrical shape. In the first step, the vessel is segmented into several segments using k-means fuzzy clustering. After segmentation and pos- sible interactive refinement of the segmentation, the centerline *Corresponding author: Annika Niemann, Gabor Janiga, is calculated using cut planes for each vertex. Then, the cen- Bernhard Preim, Sylvia Saalfeld, Otto-von-Guericke University terline is smoothed and thinned. Magdeburg, STIMULATE, e-mail: firstname.lastname@example.org Daniel Behme, Universitätsklinikum Magdeburg Open Access. © 2022 The Author(s), published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 International License. 13 A. Niemann et al., Centerline and blockstructure Other approaches detect the centerline in images and are estimation might be outside of the aneurysm mesh. For each restricted to the image modality they were deveopled for [8, initial centerline point, the vector between the centerline point 10]. and the closest face center of the mesh is calculated and nor- The presented approach works on various 3D models of malized. Under the assumption that the facenormales are ori- vessels, for example aneurysms or circular structures like the ented outwards, for points inside the mesh the vector in direc- circle of willis. It does not require user interaction. tion of the closest face center and the corresponding facenor- mal should have a similar orientation. Centerline points not fullfilling this, are removed as outliers. In the last step, close centerline points are merged together. 3 Centerline For each face f of the surface mesh, the center of the face 𝑓 and the face normal 𝑓 are calculated. Based on this and an 4 Block initialization estimated radius 𝑟 of the vessel, search points 𝑃 are calcu- lated as: In order to fasten the structured mesh generation, blocks are created automatically. The first step is the calculation of the 𝑃 =𝑓 − 𝑟 * 𝑓 . (1) 𝑠 𝑐 𝑛 centerline as described in the previous section. Cross sections of the mesh perpendicular to the center- These search points are points, which are near the triangles op- line are determined. If a cross section is roughly circular, four posite to the face center.The radius is approximated by using points with largest distance to each other are determined. Cir- the radius of the nearest outlet. The nearest outlet is selected cularity is determined based on the variance of the distance be- based on the distance between face and outlet along the mesh tween points of the cross section contour and the center. The surface. The outlets are automatically detected by searching cross sections are shown in Figure 4. The points are ordered for edges which only belong to one face. This is the case for into four lines, as shown in Figure 3. In the first cross section, open meshes, where the outlets are not closed. If none of these four points with maximal distance to each other are selected. are found, edges where the adjacent faces build an approxi- In the following sections the points closest to the points in the mately 90 degree angle are searched for. In the next step, the previous section are selected. The points on these lines are ini- vertices of these edges are analyzed. If they lie in one plane tial corner points for the blocks. Each block consists of eight and form a roughly circular shape, they are classified as outlet. points from two cross sections, two points from each of the For each search point the 𝑘 closest face centers 𝑓 respec- four lines. With exception of the points at the start and the end, tive faces are selected. It is then searched for an intersection of each point belongs to exactly two blocks. These initial blocks the line between 𝑓 and corresponding search point 𝑃 and the 𝑐 𝑠 are iterative merged. Two blocks are merged, if the resulting selected faces. The restriction of the faces which are tested for larger block is still inside the mesh. an intersection improves the run time of the algorithm. Empir- ically, 𝑘 was set to 500 for reliable and timely determination of intersections. Next, the midpoint of the line between the face center and the intersection point is added to the initial center- line estimation. Fig. 4: Points of cross-sections: intersections between mesh and plane perpendicular to centerline Fig. 3: Four lines along the mesh surface 5 Results For various meshes from an own database and the aneurisk In the next step, outliers are removed. Especially with dataset  the centerline is calculated. The centerlines pro- close branches, some faces from different vessel branches can duced here are compared to centerlines produced by the vmtk be included in the faces selected with the search points. This toolkit, which is commonly used in research [1, 3]. In the vmtk leads to intersection points not on the opposite vessel but fur- tool the start and end points at the outlets are manually set. If ther away. As a result, some points from the initial centerline 14 A. Niemann et al., Centerline and blockstructure Fig. 5: Example of centerline detection, blue: own centerline, green: vmtk centerline Fig. 7: Detail: centerline in/under aneurysm, blue: own centerline, green: vmtk centerline Fig. 6: Detail: different centerline at bifurcation, blue: own center- line, green: vmtk centerline necessary, for example because not all branches are included, new points are set or the mesh is split up into several meshes Fig. 8: Centerline with non optimal results. Further merging the (for example meshes containing cycles like the whole Circle points would improve the result. blue: own centerline, green: vmtk of Willis) and the centerline calculation is repeated until the centerline result is sufficient. From a qualitative point of view, both cen- terlines were similar (see Fig. 5). Vmtk is better in producing This could not be achieved with vmtk, as the many branches a smooth centerline in bifurcations and the aneurysm (see Fig. are major challenge and require several iterations of manual 7). The parameters of the presented algorithm were set to pro- seed point selection to produce a complete centerline. duce good results for most aneurysms (for example Fig. 5). The proposed algorithm can approximate vessels with However, this leads to sub-optimal results for some, which re- blocks (see Fig. 10). sults in several points around the actual centerline as shown in Fig. 8. The centerline detection also provides a user interface where the user can adjust the number of merging iterations to address this problem. For Table 1 and Figures 5-9 the param- 6 Discussion eters were constant and not adjusted manual. The times for complete centerline detection without user input are shown in The presented centerline does not require user input. There- Table 1. For a complete Circle of Willis with 149,959 vertices fore, the centerline calculation can be easily included in other the centerline calculation needed 124.81 seconds (see Fig. 9). algorithms, for example automatic morphological parameter calculation or structured mesh generation. It is suitable for a wide variety of structures and can also be used for large ob- Tab. 1: Time for centerline calculation and difference between jects with cycle graphs, for example a whole Circle of Willis. points of the presented centerline and the vmtk centerline While for most datasets the quality of the centerline was Dataset number of vertices time in sec mean difference good, for some meshes non optimal results are produced. Es- pecially at bifurcations a sub-optimal centerline may occur. BP 195278 156.56 0.041 C0079 38055 42.87 0.117 The blockstructure could be used to reduce the necessary C0084 25567 27.90 0.108 user input and simplify the generation of structured meshes. C0055 32119 35.16 0.120 C0021 33215 36.30 0.131 C0047 29890 31.84 0.129 KM 45511 52.16 0.074 RNRN 23987 72.6 0.190 KE 88785 88.81 0.0623 SA 62997 132.20 0.100 15 A. Niemann et al., Centerline and blockstructure  Luca Antiga and David Steinman. Robust and objective decomposition and mapping of bifurcating vessels. IEEE transactions on medical imaging, 23:704–713, 07 2004.  Philipp Berg et al. The Computational Fluid Dynamics Rupture Challenge 2013—Phase II: Variability of Hemody- namic Simulations in Two Intracranial Aneurysms. Journal of Biomechanical Engineering, 137(12), 11 2015. 121008.  Mahsa Ghaffari, Kevin Tangen, Ali Alaraj, Xinjian Du, Fady T. Charbel, and Andreas A. Linninger. Large-scale subject- specific cerebral arterial tree modeling using automated parametric mesh generation for blood flow simulation. Com- puters in Biology and Medicine, 91:353–365, 2017.  Zhihui Guo, Junjie Bai, Yi Lu, Xin Wang, Kunlin Cao, Fig. 9: Result of centerline detection for circle of willis Qi Song, Milan Sonka, and Youbing Yin. Deepcenterline: A multi-task fully convolutional network for centerline extrac- tion. In Albert C. S. Chung, James C. Gee, Paul A. Yushke- vich, and Siqi Bao, editors, Information Processing in Medical Imaging, pages 441–453, 2019.  M.S. Hassouna and A.A. Farag. Robust centerline extraction framework using level sets. In 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05), volume 1, pages 458–465 vol. 1, 2005. Fig. 10: Blockstructure for vessel  Jiafa He, Chengwei Pan, Can Yang, Ming Zhang, Yang Wang, Xiaowei Zhou, and Yizhou Yu. Learning hybrid repre- sentations for automatic 3d vessel centerline extraction. In 7 Summary Anne L. Martel, Purang Abolmaesumi, Danail Stoyanov, Di- ana Mateus, Maria A. Zuluaga, S. Kevin Zhou, Daniel Raco- ceanu, and Leo Joskowicz, editors, Medical Image Com- The presented centerline calculation is automatic and produces puting and Computer Assisted Intervention – MICCAI 2020, results comparable to the often used semi-automatic vmtk tool. pages 24–34, Cham, 2020. Springer International Publishing. Based on the centerline detection an automatic blockstructure  Anne Jorstad, Jérôme Blanc, and Graham Knott. Neuro- construction for structured mesh generation was described. morph: A software toolset for 3d analysis of neurite morphol- For future work, the centerline extraction can speed up the ogy and connectivity. Frontiers in Neuroanatomy, 12, 2018. extraction of morphological parameters  or other hemody-  Zhixun Li, Yingtao Zhang, Guangzhong Liu, Haoyang Shao, Weimin Li, and Xianglong Tang. A robust coronary artery namic preprocessing steps for subsequent blood flow simula- identification and centerline extraction method in angiogra- tion like flow splitting  and creation of structured meshes phies. Biomedical Signal Processing and Control, 16:1–8, based on the blockstructure. Author Statement Research funding: This study was  S. Saalfeld, P. Berg, A. Niemann, M. Luz, B. Preim, and funded by the Federal Ministry of Education and Research O. Beuing. Semiautomatic neck curve reconstruction for intracranial aneurysm rupture risk assessment based on within the Forschungscampus STIMULATE (grant number morphological parameters. International Journal of Computer 13GW0473A) and the German Research Foundation (grant Assisted Radiology and Surgery (IJCARS), 13(11):1781– number SA 3461/3-1). Conflict of interest: Authors state no 1793, 2018. conflict of interest. Informed consent: Informed consent has  Sylvia Saalfeld, Samuel Voß, Oliver Beuing, Bernhard Preim, been obtained from all individuals included in this study. Ethi- and Philipp Berg. Flow-splitting-based computation of outlet cal approval: The research related to human use complies with boundary conditions for improved cerebrovascular simulation in multiple intracranial aneurysms. International Journal of all the relevant national regulations, institutional policies and Computer Assisted Radiology and Surgery, 14(10):1805– was performed in accordance with the tenets of the Helsinki 1813, July 2019. Declaration, and has been approved by the authors’ institu-  Mingqiang Wei, Qiong Wang, Yichen Li, Wai-Man Pang, tional review board or equivalent committee. Luming Liang, Jun Wang, Kelvin Kian Loong Wong, Derek Abbott, Jing Qin, and Jianhuang Wu. Centerline extraction of vasculature mesh. IEEE Access, 6:10257–10268, 2018.  Xiaofei Yang, Xutao Li, Yunming Ye, Raymond Y. K. Lau, References Xiaofeng Zhang, and Xiaohui Huang. Road detection and centerline extraction via deep recurrent convolutional neu-  The vascular modelling toolkit. ral network u-net. IEEE Transactions on Geoscience and  Aneurisk-Team. AneuriskWeb project website, Remote Sensing, 57(9):7209–7220, 2019. http://ecm2.mathcs.emory.edu/aneuriskweb. Web Site, 2012.
Current Directions in Biomedical Engineering – de Gruyter
Published: Jul 1, 2022
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