以往研究中提到非骨質疏鬆症與骨質疏鬆症的病患上，在接受脊椎融合術後，會有不同之螺釘鬆脫的風險，所以透過生物力學測試與有限元素分析，評估椎弓根螺釘與骨骼之間的拔出強度，但實驗與有限元素分析的拔出強度有段差異，此外，有或無考慮骨擠壓條件，也會影響不同螺釘設計之模擬的拔出負荷，因此，本研究的目的是於人造骨骼上使用非線性的材料模型，模擬骨骼與椎弓根螺釘之間的拔出負荷，並考慮骨擠壓條件對拔出負荷的影響，最後與實驗相互比較相關性。
在SolidWorks 2019創建十種椎弓根螺釘與實心立方體骨骼的三維模型，再透過ANSYS LS-DYNA對於多段線性 (Piecewise Linear Plasticity) 之非線性材料模型的定義以及材料力學的觀念，運用文獻的實驗應力應變曲線，獲得在進入模擬前的重要材料參數，而骨擠壓條件則是依序從SolidWorks 2019劃分骨擠壓層，一路到定義各骨擠壓層的所有材料性質，最後即可在ANSYS Workbench 2022 R1 / LS DYNA分析有限元素模型。
模擬結果在軸向拉伸模型上，高密度骨骼的拔出負荷，不論螺釘設計或有無考慮骨擠壓條件，都遠大於低密度骨骼的拔出負荷，另外，在無骨擠壓的條件下，圓柱形螺釘的拔出強度會大於圓錐形螺釘，原因為螺釘與骨骼之接觸面積的大小，而在骨擠壓的狀況時，圓錐形螺釘的拔出強度會大於圓柱形螺釘，原因為骨擠壓層的機械性能提升以及數量的多寡，此研究可以提供外科醫生在不同的病患上，椎弓根螺釘之鬆脫風險性，和不同的螺釘設計對於骨咬合力的影響程度，以及降低開發新型椎弓根螺釘的實驗成本。

Previous research has indicated varying levels of screw loosening risk in patients with non-osteoporotic and osteoporotic conditions after spinal fusion surgery. Therefore, biomechanical tests and finite element analyses were used to evaluate the pullout strength of pedicle screws in these patients. However, there have significant discrepancies between the experimental and numerical results. Additionally, considering bone compaction conditions can affect the pullout loads of different screw designs. Thus, this study aims to simulate pullout loads of various pedicle screw designs using a nonlinear finite element model with the effect of bone compaction.
Ten different pedicle screws and solid cubic bone structures were created using SolidWorks 2019. The nonlinear material model was defined using a piecewise linear plasticity concept in ANSYS LS-DYNA. Material parameters were obtained from the experimental stress-strain curves of the previous study. Bone compaction conditions were set in SolidWorks 2019 by partitioning bone compaction layers and defining material properties for each layer. Finally, the finite element models can be analyzed using ANSYS Workbench 2022 R1/LS-DYNA.
In the axial tensile model, the simulation results showed that the pullout load of high-density bone was significantly higher than that of low-density bone, regardless of the screw design or consideration of bone compaction conditions. Furthermore, in the absence of bone compaction, cylindrical screws exhibited a more significant pullout load than conical screws due to the difference in contact area between the screw and bone. However, conical screws demonstrated a higher pullout load under bone compaction than cylindrical screws, attributed to the improved mechanical properties and quantity of the bone compaction layer. This study provides valuable insights for surgeons regarding the risk of screw loosening in different patients, the impact of varying screw designs on the fixation between bone and pedicle screws, and reducing the experimental costs associated with developing new pedicle screw designs.

[1] M. P. Jeremiah, B. K. Unwin, M. H. Greenawald, and V. E. Casiano, "Diagnosis and management of osteoporosis," American Family Physician, Article vol. 92, no. 4, pp. 261-268, 2015. [Online]. Available: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84940521964&partnerID=40&md5=6cb6d0801cd94811ca477bffc4b11227.
[2] J. L. Pao. "iSpineCare." https://www.ispinecare.com/index.html (accessed.
[3] F. Galbusera, D. Volkheimer, S. Reitmaier, N. Berger-Roscher, A. Kienle, and H. J. Wilke, "Pedicle screw loosening: a clinically relevant complication?," European Spine Journal, Review vol. 24, no. 5, pp. 1005-1016, 2015, doi: 10.1007/s00586-015-3768-6.
[4] "脊椎-維基百科." https://zh.wikipedia.org/zh-tw/%E8%84%8A%E6%9F%B1 (accessed.
[5] "脊椎構造." https://a8034a8034.pixnet.net/blog/post/27625338-%E8%84%8A%E6%A4%8E%E7%9A%84%E6%A7%8B%E9%80%A0%E4%BB%8B%E7%B4%B9 (accessed.
[6] "腰椎構造." https://compspinecare.com/blogs/laminotomy-vs-laminectomy-whats-the-difference/ (accessed.
[7] K. Alexey. "Osteoporosis stage." https://cn.dreamstime.com/%E5%BA%93%E5%AD%98%E4%BE%8B%E8%AF%81-%E9%AA%A8-%E7%96%8F%E6%9D%BE%E7%97%87%E9%98%B6%E6%AE%B5-image88728637 (accessed.
[8] "Care of Patient with Spine Vertebral Compression Fractures." Taipei Veterans General Hospital. https://ihealth.vghtpe.gov.tw/media/1242 (accessed.
[9] "Anterior Lumbar Interbody Fusion (ALIF)." Betsy Grunch MD. https://www.drgrunch.com/procedure-info/2017/8/14/anterior-lumbar-interbody-fusion-alif (accessed.
[10] X. Han, X. Chen, K. Li, Z. Li, and S. Li, "Finite analysis of stability between modified articular fusion technique, posterior lumbar interbody fusion and posteriorlateral lumbar fusion," BMC Musculoskelet Disord, vol. 22, no. 1, p. 1015, Dec 4 2021, doi: 10.1186/s12891-021-04899-x.
[11] A. Bokov, A. Bulkin, A. Aleynik, M. Kutlaeva, and S. Mlyavykh, "Pedicle Screws Loosening in Patients With Degenerative Diseases of the Lumbar Spine: Potential Risk Factors and Relative Contribution," Global Spine J, vol. 9, no. 1, pp. 55-61, Feb 2019, doi: 10.1177/2192568218772302.
[12] Y. Tokuhashi, H. Matsuzaki, H. Oda, and H. Uei, "Clinical course and significance of the clear zone around the pedicle screws in the lumbar degenerative disease," Spine, Article vol. 33, no. 8, pp. 903-908, 2008, doi: 10.1097/BRS.0b013e31816b1eff.
[13] L. Yuan, X. Zhang, Y. Zeng, Z. Chen, and W. Li, "Incidence, Risk, and Outcome of Pedicle Screw Loosening in Degenerative Lumbar Scoliosis Patients Undergoing Long-Segment Fusion," Global Spine J, vol. 13, no. 4, pp. 1064-1071, May 2023, doi: 10.1177/21925682211017477.
[14] B. Sandén, C. Olerud, M. Petrén-Mallmin, C. Johansson, and S. Larsson, "The significance of radiolucent zones surrounding pedicle screws. Definition of screw loosening in spinal instrumentation," Journal of Bone and Joint Surgery - Series B, Article vol. 86, no. 3, pp. 457-461, 2004, doi: 10.1302/0301-620X.86B3.14323.
[15] S. Tanioka, M. Fujimoto, H. Nishikawa, K. Tanaka, F. Ishida, A. Yamamoto, M. Ikezawa, Y. Kamei, H. Suzuki, and M. Mizuno, "Radiolucent Zone around Screws is Associated with Position Change of Screw-rod Constructs," Clin Neuroradiol, vol. 32, no. 3, pp. 717-724, Sep 2022, doi: 10.1007/s00062-021-01132-z.
[16] S. Tanioka, F. Ishida, K. Kuraishi, K. Tanaka, S. Shimosaka, H. Suzuki, and M. Mizuno, "A Novel Radiologic Assessment of Screw Loosening Focusing on Spatial Position Change of Screws Using an Iterative Closest Point Algorithm with Stereolithography Data: Technical Note," World Neurosurg, vol. 124, pp. 171-177, Apr 2019, doi: 10.1016/j.wneu.2018.12.209.
[17] Z. Chen, F. Lei, F. Ye, H. Zhang, H. Yuan, S. Li, and D. Feng, "Prediction of Pedicle Screw Loosening Using an MRI-Based Vertebral Bone Quality Score in Patients with Lumbar Degenerative Disease," World Neurosurg, vol. 171, pp. e760-e767, Mar 2023, doi: 10.1016/j.wneu.2022.12.098.
[18] J. Li, Z. Zhang, T. Xie, Z. Song, Y. Song, and J. Zeng, "The preoperative Hounsfield unit value at the position of the future screw insertion is a better predictor of screw loosening than other methods," Eur Radiol, vol. 33, no. 3, pp. 1526-1536, Mar 2023, doi: 10.1007/s00330-022-09157-9.
[19] Y. Li, S. Wang, Z. Zhu, L. Chen, Z. Shi, X. Ye, W. Xu, and Z. Li, "Biomechanical Analysis of Cortical Bone Trajectory Screw Versus Bone Cement Screw for Fixation in Porcine Spinal Low Bone Mass Model," Clinical Spine Surgery, Article vol. 36, no. 4, pp. E145-E152, 2023, doi: 10.1097/BSD.0000000000001395.
[20] P. Egenolf, A. Harland, M. Weber, A. Prescher, G. Bratke, P. Eysel, M. J. Scheyerer, and M. Lenz, "Is human bone matrix a sufficient augmentation method revising loosened pedicle screws in osteoporotic bone? – A biomechanical evaluation of primary stability," Clinical Biomechanics, Article vol. 103, 2023, Art no. 105925, doi: 10.1016/j.clinbiomech.2023.105925.
[21] P. S. Patel, D. E. Shepherd, and D. W. Hukins, "The effect of screw insertion angle and thread type on the pullout strength of bone screws in normal and osteoporotic cancellous bone models," Med Eng Phys, vol. 32, no. 8, pp. 822-8, Oct 2010, doi: 10.1016/j.medengphy.2010.05.005.
[22] F. Song, W. Feng, D. Yang, G. Li, K. Iqbal, Y. Liu, and H. Yang, "A Novel Screw Modeling Approach to Study the Effects of Screw Parameters on Pullout Strength," J Biomech Eng, vol. 145, no. 1, Jan 1 2023, doi: 10.1115/1.4055035.
[23] K. Matsukawa, Y. Yato, and H. Imabayashi, "Impact of Screw Diameter and Length on Pedicle Screw Fixation Strength in Osteoporotic Vertebrae: A Finite Element Analysis," Asian Spine J, vol. 15, no. 5, pp. 566-574, Oct 2021, doi: 10.31616/asj.2020.0353.
[24] K. Jendoubi, Y. Khadri, M. Bendjaballah, and N. Slimane, "Effects of the Insertion Type and Depth on the Pedicle Screw Pullout Strength: A Finite Element Study," Appl Bionics Biomech, vol. 2018, p. 1460195, 2018, doi: 10.1155/2018/1460195.
[25] C. K. Chao, C. C. Hsu, J. L. Wang, and J. Lin, "Increasing bending strength and pullout strength in conical pedicle screws: Biomechanical tests and finite element analyses," Journal of Spinal Disorders and Techniques, Article vol. 21, no. 2, pp. 130-138, 2008, doi: 10.1097/BSD.0b013e318073cc4b.
[26] V. Varghese, G. Saravana Kumar, and K. Venkatesh, "A finite element analysis based sensitivity studies on pull out strength of pedicle screw in synthetic osteoporotic bone models," in IECBES 2016 - IEEE-EMBS Conference on Biomedical Engineering and Sciences, 2016, pp. 382-387, doi: 10.1109/IECBES.2016.7843478. [Online]. Available: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85015649729&doi=10.1109%2fIECBES.2016.7843478&partnerID=40&md5=94d3617b2401bf0cba0dd1bff0b7bd89
[27] M. Van den Abbeele, J. M. Valiadis, L. V. P. C. Lima, P. Khalifé, P. Rouch, and W. Skalli, "Contribution to FE modeling for intraoperative pedicle screw strength prediction," Computer Methods in Biomechanics and Biomedical Engineering, Article vol. 21, no. 1, pp. 13-21, 2018, doi: 10.1080/10255842.2017.1414200.
[28] C. C. Hsu, C. K. Chao, J. L. Wang, S. M. Hou, Y. T. Tsai, and J. Lin, "Increase of pullout strength of spinal pedicle screws with conical core: Biomechanical tests and finite element analyses," Journal of Orthopaedic Research, Article vol. 23, no. 4, pp. 788-794, 2005, doi: 10.1016/j.orthres.2004.11.002.
[29] Y. Y. Chen, C. Y. Hsu, K. S. Shih, and C. C. Hsu, "Biomechanical Analysis of Pullout Strength of Spinal Pedicle Screws with Full Insertion and Back-Out Using Finite Element Method," in IFMBE Proceedings, 2020, vol. 74, pp. 86-90, doi: 10.1007/978-3-030-30636-6_12. [Online]. Available: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075809526&doi=10.1007%2f978-3-030-30636-6_12&partnerID=40&md5=7fde34876bf69fa537d50dcbf549ed3e
[30] W. C. Tsai, P. Q. Chen, T. W. Lu, S. S. Wu, K. S. Shih, and S. C. Lin, "Comparison and prediction of pullout strength of conical and cylindrical pedicle screws within synthetic bone," BMC Musculoskeletal Disorders, Article vol. 10, no. 1, 2009, Art no. 44, doi: 10.1186/1471-2474-10-44.
[31] 徐慶琪, "骨螺絲之結構設計與生物力學分析," 博士, 機械工程系, 國立臺灣科技大學, 台北市, 2005. [Online]. Available: https://hdl.handle.net/11296/8avvfv
[32] A. Rohatgi. "WebPlotDigitizer." https://automeris.io/WebPlotDigitizer (accessed.
[33] M. S. Thompson, I. D. McCarthy, L. Lidgren, and L. Ryd, "Compressive and shear properties of commercially available polyurethane foams," J Biomech Eng, vol. 125, no. 5, pp. 732-4, Oct 2003, doi: 10.1115/1.1614820.
[34] B. J. Goodno and J. M. Gere, Mechanics of Materials, Ninth Edition, SI. Cengage Learning, 2018.
[35] F. Andrade and T. Erhart, "Good old *MAT_024 : A review of LS DYNA’s most popular material model," ed: DYNAmore GmbH, 2020.
[36] "Cellular Rigid Polyurethane Foam." Sawbones. https://www.sawbones.com/biomechanical-product-info (accessed.
[37] "ASTM D1621 壓縮測試." https://youtu.be/9U6oL8Ki6_c (accessed.
[38] F. Shen, H. J. Kim, K. T. Kang, and J. S. Yeom, "Comparison of the pullout strength of pedicle screws according to the thread design for various degrees of bone quality," Applied Sciences (Switzerland), Article vol. 9, no. 8, 2019, Art no. 1525, doi: 10.3390/app9081525.
[39] V. Varghese, G. Saravana Kumar, and V. Krishnan, "Effect of various factors on pull out strength of pedicle screw in normal and osteoporotic cancellous bone models," Med Eng Phys, vol. 40, pp. 28-38, Feb 2017, doi: 10.1016/j.medengphy.2016.11.012.
[40] S. Liu, W. Qi, Y. Zhang, Z. X. Wu, Y. B. Yan, and W. Lei, "Effect of bone material properties on effective region in screw-bone model: An experimental and finite element study," BioMedical Engineering Online, Article vol. 13, no. 1, 2014, Art no. 83, doi: 10.1186/1475-925X-13-83.
[41] V. Varghese, V. Krishnan, and G. S. Kumar, "Comparison of pullout strength of pedicle screws following revision using larger diameter screws," Med Eng Phys, vol. 74, pp. 180-185, Dec 2019, doi: 10.1016/j.medengphy.2019.09.008.
[42] D. M. Lai, Y. T. Shih, Y. H. Chen, A. Chien, and J. L. Wang, "Effect of pedicle screw diameter on screw fixation efficacy in human osteoporotic thoracic vertebrae," J Biomech, vol. 70, pp. 196-203, Mar 21 2018, doi: 10.1016/j.jbiomech.2017.10.009.
[43] S. LIVERMORE, TECHNOLOGY, CORPORATION, (LSTC). (2014). LS-DYNA® Theory Manual.
[44] I. Zheng, "LS DYNA 研究生專班 day2-3," ed: SIMWARE Inc, 2017.