Three-dimensional reconstruction of femur based on Laplace operator and statistical shape model_Journal of Biomedical Engineering

Authors：

ZHANG Zupei ¹ ,  ZHANG Xiaogang ¹ , ZHANG Yali ¹ , JIN Zhongmin ^1,2

1. School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, P. R. China;
2. School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, P. R. China;

Corresponding author：

ZHANG Xiaogang, Email: xg@swjtu.edu.cn

Keywords：

Three-dimensional reconstruction; Statistical shape model; Laplace operator; Bone geometry

DOI：

10.7507/1001-5515.202303024

Video：

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Reconstructing three-dimensional (3D) models from two-dimensional (2D) images is necessary for preoperative planning and the customization of joint prostheses. However, the traditional statistical modeling reconstruction shows a low accuracy due to limited 3D characteristics and information loss. In this study, we proposed a new method to reconstruct the 3D models of femoral images by combining a statistical shape model with Laplacian surface deformation, which greatly improved the accuracy of the reconstruction. In this method, a Laplace operator was introduced to represent the 3D model derived from the statistical shape model. By coordinate transformations in the Laplacian system, novel skeletal features were established and the model was accurately aligned with its 2D image. Finally, 50 femoral models were utilized to verify the effectiveness of this method. The results indicated that the precision of the method was improved by 16.8%–25.9% compared with the traditional statistical shape model reconstruction. Therefore, the method we proposed allows a more accurate 3D bone reconstruction, which facilitates the development of personalized prosthesis design, precise positioning, and quick biomechanical analysis.

Citation： ZHANG Zupei, ZHANG Xiaogang, ZHANG Yali, JIN Zhongmin. Three-dimensional reconstruction of femur based on Laplace operator and statistical shape model. Journal of Biomedical Engineering, 2023, 40(6): 1168-1174. doi: 10.7507/1001-5515.202303024 Copy

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24.	Fernández A V, Manandhar S, Hétroy W F, et al. A 3D+t Laplace operator for temporal mesh sequences. Comput Graph, 2016, 58: 12-22.
25.	Fisher M, Springborn B, Schröder P, et al. An algorithm for the construction of intrinsic delaunay triangulations with applications to digital geometry processing. Computing, 2007, 81(2-3): 199-213.
26.	Li J, Zhang Y, Xu P, et al. Adaptive 3D facial deformation based on personal characteristics// Proceedings of the 12th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD). Zhangjiajie: IEEE, 2015: 1258-1262.
27.	Tejera M, Hilton A. Learning part-based models for animation from surface motion capture// 2013 International Conference on 3D Vision. Seattle: IEEE, 2013: 159-166.
28.	Steinbrecher T, Gerth M. Dental inlay and onlay construction by iterative Laplacian Surface Editing. Comput Graph Forum, 2008, 27(5): 1441-1447.
29.	Karade V, Ravi B. 3D femur model reconstruction from biplane X-ray images: a novel method based on Laplacian surface deformation. Int J Comput Assist Radiol Surg, 2015, 10(4): 473-485.
30.	Chen D, Yao J. Improved livewire method for segmentation on low contrast and noisy images// Pluim J P W, Reinhardt J M. Medical Imaging 2007: Image Processing. Washington: SPIE, 2007, 6512: 65122Z.
31.	Besl P J, Mckay N D. A method for registration of 3-d shapes. IEEE Trans Pattern Anal Mach Intell, 1992, 14(2): 239-256.
32.	Cootes T F, Taylor C J, Cooper D H, et al. Active shape models-their training and application. Comput Vis Image Underst, 1995, 61(1): 38-59.
33.	Zhang S, Huang J, Metaxas D N. Robust mesh editing using Laplacian coordinate. Graph Models, 2011, 73(1): 10-19.
34.	Zheng G, Schumann S. 3D reconstruction of a patient-specific surface model of the proximal femur from calibrated X-ray radiographs: a validation study. Med Phys, 2009, 36(4): 1155-1166.
35.	Zheng G. Statistical shape model-based reconstruction of a scaled, patient-specific surface model of the pelvis from a single standard AP X-ray radiograph. Med Phys, 2010, 37(4): 1424-1439.
36.	Gay B V, Perriollat M, Bartoli A, et al. Image registration by combining thin-plate splines with a 3D morphable model// Proceedings of the IEEE International Conference on Image Processing (ICIP). Atlanta: IEEE, 2006: 1069.

1. Tian Z, Mao X, Gao Z, et al. A simple method for restoring the femoral head center in hip arthroplasty: a 3-dimensional analysis in the Chinese population. BMC Musculoskelet Disord, 2022, 23(1): 986.
2. 彭鳒侨, 张占磊, 钟世镇, 等. 基于全膝关节置换的三维术前规划实践. 中国数字医学, 2013, 8(12): 45-49, 57.
3. Kilian D, Sembdner P, Bretschneider H, et al. 3D printing of patient-specific implants for osteochondral defects: workflow for an MRI-guided zonal design. Bio-des Manuf, 2021, 4(4): 818-832.
4. Peng M J, Ju X Y, Ma L M, et al. Dynamics analysis for flexion and extension of elbow joint motion based on musculoskeletal model of Anybody. Int J Med Robot, 2021, 17(6): e2321.
5. 魏明杰, 徐永清, 罗浩天, 等. 应用Mimics软件构建钩骨3D可视化解剖学研究. 中国临床解剖学杂志, 2020, 38(6): 652-656.
6. Sodhi N, Jacofsky D J, Chee A, et al. Benefits of CT scanning for the management of knee arthritis and arthroplasty. J Knee Surg, 2021, 34(12): 1296-1303.
7. Wang Yueguang, Zuo Yuming, Zhou Hongyan, et al. The application of three-dimensional reconstruction of CT on the diagnosis and treatment of the adolescence distal tibial triplane fracture. Chin J Mod Med, 2011, 21(25): 3184.
8. Lee M K, Lee S H, Kim A, et al. The study of femoral 3D reconstruction process based on anatomical parameters using a numerical method. J Biomech Sci Eng, 2008, 3(3): 443-451.
9. Laporte S, Skalli W, De Guise J A, et al. A biplanar reconstruction method based on 2D and 3D contours: application to the distal femur. Comput Methods Biomech Biomed Engin, 2003, 6(1): 1-6.
10. Chaibi Y, Cresson T, Aubert B, et al. Fast 3D reconstruction of the lower limb using a parametric model and statistical inferences and clinical measurements calculation from biplanar X-rays. Comput Methods Biomech Biomed Engin, 2012, 15(5): 457-466.
11. Wang Y, Wang Y, Nie S. Research progress in medical diagnostic X-ray sources. Chin J Med Phys, 2018, 35(10): 1214-1216.
12. Cootes T F, Taylor C J, Cooper D H, et al. Training models of shape from sets of examples// Hogg D, Boyle R. BMVC92. London: Springer, 1992: 9-18.
13. Lorenz C, Krahnstöver N. Generation of point-based 3D statistical shape models for anatomical objects. Comput Vis Image Underst, 2000, 77(2): 175-191.
14. 张志伟, 陈瑱贤, 张志峰, 等. 基于统计形状模型的股骨快速建模方法. 生物医学工程学杂志, 2022, 39(5): 862-869.
15. He J, Guo Z, Zhou Y, et al. Statistical shape model of the calcaneus bone for comprehensive assessment of three-dimensional morphology. Int J Biomed Sci Eng, 2023, 11(2): 27-32.
16. Ding A S, Lu A, Li Z S, et al. Statistical shape model of the temporal bone using segmentation propagation. Otol Neurotol, 2022, 43(6): 679-687.
17. Pontiki A A, De A, Dibblin C, et al. Development and evaluation of a rib statistical shape model for thoracic surgery// 2022 44th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC). Glasgow: IEEE, 2022: 3758-3763.
18. Fang L, Wang Z, Chen Z, et al. 3D shape reconstruction of lumbar vertebra from two X-ray images and a CT model. IEEE/CAA J Autom Sinica, 2020, 7(4): 1124-1133.
19. Tsai T Y, Li J S, Wang S, et al. Principal component analysis in construction of 3D human knee joint models using a statistical shape model method. Comput Methods Biomech Biomed Engin, 2015, 18(7): 721-729.
20. Zheng G, Gollmer S, Schumann S, et al. A 2D/3D correspondence building method for reconstruction of a patient-specific 3D bone surface model using point distribution models and calibrated X-ray images. Med Image Anal, 2009, 13(6): 883-899.
21. Rajamani K T, Styner M A, Talib H, et al. Statistical deformable bone models for robust 3D surface extrapolation from sparse data. Med Image Anal, 2007, 11(2): 99-109.
22. Smoger L M, Shelburne K B, Cyr A J, et al. Statistical shape modeling predicts patellar bone geometry to enable stereo-radiographic kinematic trackin. J Biomech, 2017, 58: 187-194.
23. Vanden B P, Demol J, Gelaude F, et al. Virtual anatomical reconstruction of large acetabular bone defects using a statistical shape mode. Comput Methods Biomech Biomed Engin, 2017, 20(6): 577-586.
24. Fernández A V, Manandhar S, Hétroy W F, et al. A 3D+t Laplace operator for temporal mesh sequences. Comput Graph, 2016, 58: 12-22.
25. Fisher M, Springborn B, Schröder P, et al. An algorithm for the construction of intrinsic delaunay triangulations with applications to digital geometry processing. Computing, 2007, 81(2-3): 199-213.
26. Li J, Zhang Y, Xu P, et al. Adaptive 3D facial deformation based on personal characteristics// Proceedings of the 12th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD). Zhangjiajie: IEEE, 2015: 1258-1262.
27. Tejera M, Hilton A. Learning part-based models for animation from surface motion capture// 2013 International Conference on 3D Vision. Seattle: IEEE, 2013: 159-166.
28. Steinbrecher T, Gerth M. Dental inlay and onlay construction by iterative Laplacian Surface Editing. Comput Graph Forum, 2008, 27(5): 1441-1447.
29. Karade V, Ravi B. 3D femur model reconstruction from biplane X-ray images: a novel method based on Laplacian surface deformation. Int J Comput Assist Radiol Surg, 2015, 10(4): 473-485.
30. Chen D, Yao J. Improved livewire method for segmentation on low contrast and noisy images// Pluim J P W, Reinhardt J M. Medical Imaging 2007: Image Processing. Washington: SPIE, 2007, 6512: 65122Z.
31. Besl P J, Mckay N D. A method for registration of 3-d shapes. IEEE Trans Pattern Anal Mach Intell, 1992, 14(2): 239-256.
32. Cootes T F, Taylor C J, Cooper D H, et al. Active shape models-their training and application. Comput Vis Image Underst, 1995, 61(1): 38-59.
33. Zhang S, Huang J, Metaxas D N. Robust mesh editing using Laplacian coordinate. Graph Models, 2011, 73(1): 10-19.
34. Zheng G, Schumann S. 3D reconstruction of a patient-specific surface model of the proximal femur from calibrated X-ray radiographs: a validation study. Med Phys, 2009, 36(4): 1155-1166.
35. Zheng G. Statistical shape model-based reconstruction of a scaled, patient-specific surface model of the pelvis from a single standard AP X-ray radiograph. Med Phys, 2010, 37(4): 1424-1439.
36. Gay B V, Perriollat M, Bartoli A, et al. Image registration by combining thin-plate splines with a 3D morphable model// Proceedings of the IEEE International Conference on Image Processing (ICIP). Atlanta: IEEE, 2006: 1069.

Journal of Biomedical Engineering

Three-dimensional reconstruction of femur based on Laplace operator and statistical shape model

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