脊椎畸形是一種影響脊椎發育的疾病，可能在出生時或日後的生長過程中形成。常見的脊椎畸形包括脊椎側彎、脊椎前彎(前凸)和脊椎後彎(後凸)，其治療方法取決於畸形的嚴重程度和患者的症狀，輕度的畸形可以通過定期追蹤和物理治療避免其進一步惡化，而較嚴重的畸形可能需要使用矯正器械或以手術矯正脊椎的彎曲。
S2AI矯正手術為治療脊椎畸形常用的手術，本研究旨在利用有限元素分析模擬該手術過程及術後於腰椎至骨盆段之力學現象。本研究所使用之骨架幾何來自脊椎畸形病人之CT掃描，使用CAD軟體建置包含腰椎、骨盆以及矯正器械(包括骨釘及矯正桿)之數位幾何模型，匯入有限元素軟體Abaqus建立網格模型，建置骨盆周邊的韌帶，並設定邊界條件、負載、接觸關係以及脊椎隨附負載後，再設置S2AI矯正手術過程所需之椎節移動、螺釘及矯正桿接觸以及矯正桿回彈等分析步驟，以模擬經矯正手術後，病患的腰椎、骨盆以及矯正器械間所產生的力學關係。
分析結果顯示，矯正桿回彈量最大可達矯正量的30%，且回彈方向並不完全依循矯正方向。而不同椎節上的固定螺釘有著推與拉兩種不同方向的的軸向總力，其中僅第四節腰椎螺釘為拉力，顯示該椎節上的螺釘鬆脫風險較高；此外由於第三節腰椎與骨盆螺釘皆為推力，故該處螺釘鬆脫風險較低。在應力分析方面，皮質骨上之主應力未超過其破壞強度，顯示皮質骨產生骨折或骨裂的機率較低，而鬆質骨上之主應力則有少部分區域超過抗壓強度，需注意該處之骨折風險。

Spinal deformity is one of the diseases that can affect the development of spine. The treatment of spinal deformity including scoliosis, lordosis and kyphosis depends on the severity of the deformity and symptom of the patient.
The S2AI surgery is one of the surgeries for spinal deformity. In this study, the spine geometries were established according to the CT scan data from a patient with spine deformity by using CAD software, the mesh of these geometries were created by finite element software ABAQUS. The process during the S2AI surgery including the movement of the spine vertebral body, contacts between screws and rods, and spring back of the rods were also simulated by ABAQUS.
The analysis results reveal that the maximum spring back of the rods can be 30%. and the total resultant of axial force of the two screws in the L4 vertebral body are the only ones with pull force. It indicates a higher risk of the screw loosening in the L4 vertebral body. The risk of screw loosening at L3 vertebral body and pelvis is lower since the resultants of which are push forces. For stress analysis results, it is observed that the principal stresses on the cortical bones are lower It indicates low risk of fracture in cortical bones. For cancellous bones, it is found that there exists principal stresses higher than compressive strength on some regions, in which the fracture risk should be noticed.

1. Winter, R.B., Spine deformity in children: Current concepts of diagnosis and treatment. Pediatr Ann, 1976. 5(4): p. 95-112.
2. Divya, V. and M. Anburajan, Finite element analysis of human lumbar spine, in 2011 3rd International Conference on Electronics Computer Technology. 2011. p. 350-354.
3. Casaroli, G., et al., Evaluation of iliac screw, S2 alar-iliac screw and laterally placed triangular titanium implants for sacropelvic fixation in combination with posterior lumbar instrumentation: a finite element study. Eur Spine J, 2019. 28(7): p. 1724-1732.
4. philadelphia, c.s.h.o. Early-onset Scoliosis. Available from: https://www.chop.edu/conditions-diseases/early-onset-scoliosis.
5. Todd, C., Managing the Spino-Pelvic-Hip Complex. An Integrated Approach. 2022: Handspring Publishing.
6. Aaron G. Filler, M., Do You Really Need Back Surgery?: A Surgeon’s Guide to Neck and Back Pain and How to Choose Your Treatment. 2004: Oxford University Press.
7. Bijendra, D., et al., Adjacent Level Vertebral Fractures in Patients Operated with Percutaneous Vertebroplasty. Open Journal of Orthopedics, 2018. 08(03): p. 116-126.
8. Smith, L.J., et al., Degeneration and regeneration of the intervertebral disc: lessons from development. Dis Model Mech, 2011. 4(1): p. 31-41.
9. BruceBlaus., The bones of the pelvis., B. Pelvis, Editor. 2013: Wikimedia Commons. p. Pelvis. See a full animation of this medical topic.
10. Ligaments of the pelvis. Available from: https://doctorlib.info/medical/anatomy/12.html.
11. Suneja, M., et al., DeGowin’s Diagnostic Examination, 11e. Chapter 13: The Spine, Pelvis, and Extremities. 2020: McGraw Hill / Medical.
12. Gao, Z., et al., Comparative radiological outcomes and complications of sacral- 2-alar iliac screw versus iliac screw for sacropelvic fixation. Eur Spine J, 2021. 30(8): p. 2257-2270.
13. Sohn, S., et al., Modified iliac screw fixation: technique and clinical application. Acta Neurochirurgica, 2016. 158(5): p. 975-80.
14. Shin, J.K., et al., Effect of the screw type (S2-alar-iliac and iliac), screw length, and screw head angle on the risk of screw and adjacent bone failures after a spinopelvic fixation technique: A finite element analysis. PLoS One, 2018. 13(8): p. e0201801.
15. Zhang, H. and W. Zhu, The Path to Deliver the Most Realistic Follower Load for a Lumbar Spine in Standing Posture: A Finite Element Study. J Biomech Eng, 2019. 141(3).
16. Sterba, M., et al., Biomechanical analysis of spino-pelvic postural configurations in spondylolysis subjected to various sport-related dynamic loading conditions. Eur Spine J, 2018. 27(8): p. 2044-2052.
17. Schmidt, H., et al., Intradiscal pressure, shear strain, and fiber strain in the intervertebral disc under combined loading. Spine, 2007. 32(7): p. 748-55.
18. Epomedicine. Ligaments of Pelvis. Sacrum to Pelvis 2020; Available from: https://epomedicine.com/medical-students/ligaments-of-pelvis/.
19. Zhao, Y., et al., Comparison of stability of two kinds of sacro-iliac screws in the fixation of bilateral sacral fractures in a finite element model. Injury, 2012. 43(4): p. 490-4.
20. Ambati, D.V., et al., Bilateral pedicle screw fixation provides superior biomechanical stability in transforaminal lumbar interbody fusion: a finite element study. Spine J, 2015. 15(8): p. 1812-22.
21. Sairyo, K., et al., Three dimensional finite element analysis of the pediatric lumbar spine. Part II: biomechanical change as the initiating factor for pediatric isthmic spondylolisthesis at the growth plate. Eur Spine J, 2006. 15(6): p. 930-5.
22. Ali Hamadi Dicko, N.T.-Y., Benjamin Gilles, François Faure, and O. Palombi, Construction and Validation of a Hybrid Lumbar Spine Model For the Fast Evaluation of Intradiscal Pressure and Mobility. International Science Index, Medical and Health Science,, 2015. 9(2): p. 134-145.
23. 謝采軒, 以有限元素法探討高位脛骨截骨手術中骨塊設計及脛骨矯正角度之生物力學 研究, in 機械工程學系. 2022, 國立成功大學. p. 100.
24. Zhao, Y., et al., Mechanical comparison between lengthened and short sacroiliac screws in sacral fracture fixation: a finite element analysis. Orthop Traumatol Surg Res, 2013. 99(5): p. 601-6.
25. Eichenseer, P.H., D.R. Sybert, and J.R. Cotton, A finite element analysis of sacroiliac joint ligaments in response to different loading conditions. Spine, 2011. 36(22): p. E1446-52.
26. Wong, C., et al., Nonlinear finite-element analysis and biomechanical evaluation of the lumbar spine. IEEE Trans Med Imaging, 2003. 22(6): p. 742-6.
27. 30.1.2 Contact pressure-overclosure relationships. Available from: https://classes.engineering.wustl.edu/2009/spring/mase5513/abaqus/docs/v6.6/books/usb/default.htm?startat=pt09ch30s01aus139.html.
28. globusmedical, CREO_Threaded_CoCr_65x35mm_Polyaxial_Screw_CoCr_Head_Ti_Shank, Editor., globusmedical.
29. Lieberman, I.H., R. Khazim, and T. Woodside, Anterior vertebral body screw pullout testing. A comparison of Zeilke, Kaneda, Universal Spine System, and Universal Spine System with pullout-resistant nut. Spine, 1998. 23(8): p. 908-10.
30. Hack, J., et al., Is cement-augmented sacroiliac screw fixation with partially threaded screws superior to that with fully threaded screws concerning compression and pull-out force in fragility fractures of the sacrum? - a biomechanical analysis. BMC Musculoskelet Disord, 2021. 22(1): p. 1034.
31. Gerhardt, L.C. and A.R. Boccaccini, Bioactive Glass and Glass-Ceramic Scaffolds for Bone Tissue Engineering. Materials, 2010. 3(7): p. 3867-3910.
32. Rezwan, K., et al., Biodegradable and bioactive porous polymer/inorganic composite scaffolds for bone tissue engineering. Biomaterials, 2006. 27(18): p. 3413-31.
33. Hernandez, C.J., et al., The influence of bone volume fraction and ash fraction on bone strength and modulus. Bone, 2001. 29(1): p. 74-8.
34. Keaveny, T.M., et al., Biomechanics of trabecular bone. Annu Rev Biomed Eng, 2001. 3: p. 307-33.