脊椎椎體椎籠(Vertebral Body Cage )在治療脊椎病症中，扮演著很重要的角色，臨床上，當脊椎椎體椎籠陷入脊椎椎體時，可能會導致脊椎椎體的塌陷、脊椎後凸症、骨融合失效，造成病人脊椎疼痛、變形、或神經傷害等症狀。
常見的探討下陷的文獻中，都以最大負荷作為脊椎椎體椎籠抵抗下陷的負荷，且假設脊椎椎體椎籠端部的齒狀物已完全埋入骨骼內，但是，在測試過程中不同的脊椎椎體椎籠設計會有不同的位移-負荷變化，若僅以最大的負荷作為脊椎椎體椎籠最佳設計的目標是不適當的，且實際在骨科手術後，脊椎椎體椎籠端部的齒狀物並非完全的埋入骨骼內。因此，本研究的目的為找出在植入不同尖釘高度時的脊椎椎體椎籠最佳化設計。
本研究建立椎籠及椎骨的三維有限元素分析模型，以有限元素法來分析椎籠下陷問題，並以田口法與類神經網路建立椎籠的最佳化目標函數，最後再以遺傳演算法來獲得最佳設計，期望找出有最好抵抗下陷能力的椎籠設計。最佳化目標分成兩部份作探討，一為各別考慮植入1/4尖釘高度、植入2/4尖釘高度、植入3/4尖釘高度、植入4/4尖釘高度這四個階段，另一個為考慮整個下陷過程。結果發現僅看1/4、2/4、3/4植入尖釘高度時，不同的人工椎體椎籠設計的抵抗下陷差異極大，而椎體椎籠的尖釘完全(4/4尖釘高度)植入椎骨時，椎籠抵抗下陷的能力與不同尖釘設計的關係較不明顯。而考慮整個下陷過程的最佳化椎體椎籠設計參數，分別為齒型高度(SH)1mm、齒型寬度(SW)1.72mm、齒形傾斜程度(SO)為1、齒型排數(SR)16排、齒型內徑(ID)10mm。
本研究所得出的椎籠最佳化設計有很好的抵抗下陷能力，而類神經網路搭配遺傳演算法能有效的降低搜尋椎體椎籠的最佳化時間。本研究的結果可提供骨科醫師於臨床應用的選擇依據。

關鍵字：脊椎椎體椎籠、脊椎椎體椎籠下陷、有限元素法、類神經網路、遺傳演算法

The vertebral body cages (VBCs) play an important role in the treatment of spinal disorders. However, the VBCs subsiding into the vertebral body may cause some demerits, such as collapse, progression of kyphosis, or fusion failure. These complications may cause some symptoms including spinal pain, deformity, or nerve damage and so on. Based on the past researches, the maximum load was always used to evaluate the subsidence resistance of VBCs. In addition, the spikes of VBCs were assumed to be fully inserted into the vertebral body. However, different VBC designs may have a different load-deformation curve in mechanical tests, and the spikes of VBCs are not fully implanted into the vertebra in clinical applications. Therefore, the purpose of this study was to search the optimum VBC design under different insertion depths of the VBCs.
To obtain the VBC design with excellent subsidence resistance, three-dimensional finite element models of the VBC with the vertebra were developed and analyzed by using ANSYS Workbench. Then, Taguchi methods and artificial neural networks were used to construct the objective functions of the VBCs. Finally, genetic algorithms were used to find the optimum designs of the VBCs. In this study, two kinds of the optimization problems are discussed including single insertion depth (1/4, 2/4, 3/4, or 4/4 of spike height) and multiple insertion depth (whole subsidence process). The results showed that the subsidence resistance of the VBCs had much difference in the situations with an insertion depth of 1/4, 2/4, and 3/4. However, it had no significant difference in the situation with an insertion depth of 4/4. Moreover, the optimum parameters of the VBCs for multiple insertion depth were the spike height of 1 mm, the spike width of 1.72 mm, the spike oblique of 1, 16 spike rows per 28 mm, and the spike diameter of 10 mm.
In conclusion, the optimum designs of the VBCs revealed excellent subsidence resistance. The artificial neural network based genetic algorithms can effectively reduce the effort and time required for searching the optimum designs of the VBCs. The outcome of this study can directly provide the selection information to orthopedic surgeons.

Keywords：Vertebral Body Cage；Subsidence；Finite element Analysis；Artificial Neural Network；Genetic Algorithms

[1]S. Boriani, S.Bandiera, R. Donthineni, L.Amendola, M. Cappuccio, F. De Iure, and A. Gasbarrini, "Morbidity of en bloc resections in the spine," European Spine Journal, vol. 19, pp. 231-241(2010)
[2]S. Rapan, S. Jovanović, and G. Gulan, "Vertebroplasty for vertebral compression fracture," Collegium Antropologicum, vol. 33, pp. 911-914(2009)
[3]C. Y. Greaves, M. S. Gadala, and T. R. Oxland, "A three-dimensional finite element model of the cervical spine with spinal cord: An investigation of three injury mechanisms," Annals of Biomedical Engineering, vol. 36, pp. 396-405(2008)
[4]F. D. Marcel, "Effectiveness of Titanium Mesh Cylindrical Cages in Anterior Column Reconstruction After Thoracic and Lumbar Vertebral Body Resection," Spine, vol. 28, pp. 902-908(2003)
[5]A. H. Fayazi, S. C. Ludwig, M. Dabbah, R. B. Butler, and D. E. Gelb, "Preliminary results of staged anterior debridement and reconstruction using titanium mesh cages in the treatment of thoracolumbar vertebral osteomyelitis," Spine Journal, vol. 4, pp. 388-395(2004)
[6]R. H. J. Dietl, M. Krammer, A. Kettler, H. J. Wilke, L. Claes, and C. B. Lumenta, "Pullout test with three lumbar interbody fusion cages," Spine, vol. 27, pp. 1029-1036(2002)
[7]I. Thongtrangan, R. S. Balabhadra, H. Le, J. Park, and D. H. Kim, "Vertebral body replacement with an expandable cage for reconstruction after spinal tumor resection," Neurosurgical focus electronic resource, vol. 15(2003)
[8]W. H. Hsu, C. K. Chao, H. C. Hsu, J. Lin, and C. C. Hsu, "Parametric study on the interface pullout strength of the vertebral body replacement cage using FEM-based Taguchi methods," Medical Engineering and Physics, vol. 31, pp. 287-294(2009)
[9]C. Knop, U. Lange, L. Bastian, M. Oeser, and M. Blauth, "Biomechanical compression tests with a new implant for thoracolumbar vertebral body replacement," European Spine Journal, vol. 10, pp. 30-37(2001)
[10]L. Claes, M. Schultheiss, S. Wolf, H. J. Wilke, M. Arand, and L. Kinzl, "A new radiolucent system for vertebral body replacement: Its stability in comparison to other systems," Journal of Biomedical Materials Research, vol. 48, pp. 82-89(1999)
[11]J. S. Tan, C. S. Bailey, M. F. Dvorak, C. G. Fisher, and T. R. Oxland, "Interbody device shape and size are important to strengthen the vertebra-implant interface," Spine, vol. 30, pp. 638-644(2005)
[12]J. M. Elaine N. Marieb, 馮琮涵，陳金山譯著, 2006,人體解剖學:第三(更新)版.
[13]蔡仁祥, 2006,解剖學.
[14]D. Grob, S. Daehn, and A. F. Mannion, "Titanium mesh cages (TMC) in spine surgery," European Spine Journal, vol. 14, pp. 211-221(2005)
[15]A. A. Hussein, E. El-Karef, and M. Hafez, "Reconstructive surgery in spinal tumours," European Journal of Surgical Oncology, vol. 27, pp. 196-199(2001)
[16]T. K. J. P. Giehl, "Distractible vertebral body replacement in patients with malignant vertebral destruction or osteoporotic burst fractures," International Orthopaedics, vol. 28, pp. 106-109(2004)
[17]M. Ruf, D. Stoltze, H. R. Merk, M. Ames, and J. Harms, "Treatment of vertebral osteomyelitis by radical debridement and stabilization using titanium mesh cages," Spine, vol. 32, pp. E275-E280(2007)
[18]R. J. Hacker, "Threaded cages for degenerative cervical disease," Clinical Orthopaedics and Related Research, pp. 39-46(2002)
[19]Y. Chen, D. Chen, Y. Guo, X. Wang, X. Lu, Z. He, and W. Yuan, "Subsidence of titanium mesh cage: a study based on 300 cases," Journal of spinal disorders & techniques, vol. 21, pp. 489-492(2008)
[20]E. Kast, S. Derakhshani, M. Bothmann, and J. Oberle, "Subsidence after anterior cervical inter-body fusion. A randomized prospective clinical trial," Neurosurgical Review, vol. 32, pp. 207-214(2009)
[21]G. L. Thomas, H. Shukor, A. W. Lucas, F. O. Michael, A. S. David, J. D. Molly, and T. Julie, "A Biomechanical Study of Regional Endplate Strength and Cage Morphology as It Relates to Structural Interbody Support," Spine, vol. 29, pp. 2389-2394(2004)
[22]A. Rohlmann, T. Zander, and G. Bergmann, "Effects of fusion-bone stiffness on the mechanical behavior of the lumbar spine after vertebral body replacement," Clinical Biomechanics, vol. 21, pp. 221-227(2006)
[23]Z.-C. Zhong, S.-H. Wei, J.-P. Wang, C.-K. Feng, C.-S. Chen, and C.-h. Yu, "Finite element analysis of the lumbar spine with a new cage using a topology optimization method," Medical Engineering & Physics, vol. 28, pp. 90-98(2006)
[24]W. H. Hsu, C. C. Hsu, C. K. Chao, Y. H. Tsai, and H. C. Hsu, "Analysis of Compressive Strength and Subsidence of the vertebral Body Cage with Taguchi Methods," Journal of Chinese Institute of Engineers(2009 Submitted)
[25]E.-C. T. Kai Yang, Franz Konstantin Fuss, "Application of Taguchi method in optimization of cervical ring cage," Journal of Biomechanics, vol. 40, pp. 3251-3256(2007)
[26]林昇輔、徐永吉, 2009,遺傳演算法及其應用五南圖書出版公司.
[27]M. A. Lee and H. Takagi, "Integrating design stages of fuzzy systems using genetic algorithms," presented at the Second IEEE International Conference on Fuzzy Systems, San Franciscu,CA,USA(1993).
[28]許文賢，"人工椎體支撐器之生物力學分析與機械測試，" 博士論文，國立台灣科技大學, 台北( 2009)