膝關節退化為人體老化時常見的現象，可能會造成膝部的疼痛，也可能會引起膝關節炎等症狀。近年來，人工膝關節置換手術成為許多人改善膝關節不適的方法，主要為切除已經損壞的部分並更換人工膝關節的部件以代替切除下來的骨頭、軟骨及半月板等，使人們能夠回歸正常的生活。本研究以有限單元分析為基礎，建立人體膝關節與更換人工部件的膝關節之有限單元模型，並討論兩者在人體靜止站立的情況下，其應力與位移分布的情形。藉由應力分析來探討更換人工部件後，膝關節受力的變化，並關注人體與人工部件的交界處是否有應力集中的現象產生。由於人體材料參數較難獲得，且過往的文獻未明確指出膝關節結構的負載與邊界條件，本文乃參考相關文獻建立有效的人體膝關節結構韌帶及負載的模型進行分析。結果顯示更換人工部件不會對膝關節的應力與位移造成大的影響，因此可以確定單室人工膝關節置換術在手術成功的條件下，可讓長年受到膝關節炎困擾的病人感到明顯的改善。本文分析結果可給予骨科醫師建議，預期能改善患者術後產生不良結果的機率。

Degeneration of knee joint is a common phenomenon in the aging of human body; it may cause pain in the knee and also may cause symptoms such as knee arthritis. In recent years, artificial knee replacement has become a method for people to reduce the discomfort of knee, by removing the damaged part and replacing the parts of artificial knee joint instead of the bones, cartilage and meniscus. This study is to establish finite element models of the knee joint of human body with the replacement of artificial parts, and to discuss the distributions of stress and displacement in the case where the human body stands still. The ligament was included in the analysis model of knee joint and the standing load condition was prescribed for the human knee joint to facilitate subsequent analysis. The overall stresses of knee joint after replacing the artificial parts was investigated, and the stress concentration problem at the junction between the human body and the artificial parts are discussed. The results show that the replacement of artificial parts does not affect significantly on the stress and displacement of knee joint. It is concluded that Unicompartmental Knee Replacement should be beneficial for patients suffering from knee arthritis for many years after successful knee operation. The present results could give valuable suggestion to orthopaedist for reducing the chance of poor outcomes after surgery.

1. American Academy of Orthopaedic Surgeons, Total Knee Replacement: https://orthoinfo.aaos.org/en/treatment/total-knee-replacement/, retrieved on June 20, 2019.
2. MAKOplasty: http://www.makoplasty.com.tw/mobile/, retrieved on October 3, 2018.
3. R. A. Brand, M. A. Mont, M. M. Manring, “Biographical Sketch: Themistocles Gluck.” Clinical Orthopaedics and Related Research, Vol. 469, pp. 1525-1527, 2011.
4. B. Walldius, “Arthroplasty of the Knee Using an Endoprosthesis: 8 Year’s Experience” Acta Orthopaedica Scandinavica, Vol. 30, pp. 137-148, 1960.
5. Nuffield Health: https://www.nuffieldhealth.com/article/40-years-of-the-oxford-knee, retrieved on October 2, 2018.
6. C. S. Ranawat, J. J. Shine, “Duo-Condylar Total Knee Arthroplasty,” Clinical Orthopaedics and Related Research, Vol. 94, pp. 185-195, 1973.
7. E. A. Unkar, Y. Ozturkmen, E. Sukur, E. Carkci, M. Mert, “Posterior cruciate-retaining versus posterior-stabilized total knee arthroplasty for osteoarthritis with severe varus deformity,” Acta Orthopaedica et Traumatologica Turcica, Vol. 51, pp. 95-99, 2017.
8. K. C. N. Kumar, T. Tandon, P. Silori, A. Shaikh, “Biomechanical stress analysis of a Human Femur bone using ANSYS,” Materials Today, Vol. 2, pp. 2115-2120, 2015.
9. G. Li, O. Lopez, H. Rubash, “Variability of a three-dimensional finite element model constructed using magnetic resonance images of a knee for joint contact stress analysis,” Journal of Biomechanical Engineering, Vol. 123, pp. 341-346, 2001.
10. Y. Wang, Y. Fan, M. Zhang, “Comparison of stress on knee cartilage during kneeling and standing using finite element models,” Medical Engineering and Physics, Vol. 36, pp. 439-447, 2014.
11. M. Taylor, K. E. Tanner, M. A. R. Freeman, “Finite element analysis of the implanted proximal tibia: a relationship between the initial cancellous bone stresses and implant migration,” Journal of Biomechanics, Vol. 31, pp. 303-310, 1998.
12. S. M. Darwish, A. A. Samhan, “The effect of cement stiffness and tibia tray material on the stresses developed in artificial knee,” International Journal of Adhesion and Adhesives, Vol. 28, pp. 120-125, 2008.
13. K. Iesaka, H. Tsumura, H. Sonoda, T. Sawatari, M. Takasita, T. Torisu “The effects of tibial component inclination on bone stress after unicompartmental knee arthroplasty,” Journal of Biomechanics, Vol. 35, No. 7, pp. 969-974, 2002.
14. T. Sawatari, H. Tsumura, K. Iesaka, Y. Furushiro, T. Torisu, “Three-dimensional finite element analysis of unicompartmental knee arthroplasty-the influence of tibial component inclination,” Journal of Orthopaedic Research, Vol. 23, pp. 549-554, 2005.
15. T. W. Chang, C. T. Yang, Y. L. Liu, W. C. Chen, K. J. Lin, Y. S. Lai, C. H. Huang, Y. C. Lu, C. K. Cheng, “Biomechanical evaluation of proximal tibial behavior following unicondylar knee arthroplasty: Modified resected surface with corresponding surgical technique,” Medical Engineering and Physics, Vol. 33, pp. 1175-1182, 2011.
16. M. Kubicek, Z. Florian, “Stress strain analysis of knee joint,” Engineering Mechanics, Vol. 16, No. 5, pp. 315-322, 2009.
17. R. L. Arroyo, J. C. S. Jimenez, R. R. Castro, F. B. Lopez, “Biomechanical Behavior of the Knee Joint Using ANSYS,” International ANSYS Conference Proceedings, ANSYS, Pittsburgh, May 24-26, 2004.
18. J. N. Insall, R. E. Windsor, M. A. Kelly, W. N. Scott, and P. A. Aglietti, Surgery of the Knee, 2nd ed, Churchill Livingstone, New York, U.S., 1993.
19. R. L. Larson, W. A. Grana, The Knee Form, Function, Pathology, and Treatment,1st ed, Saunders, Philadelphia, U.S., 1993.
20. M. Marsh, R. B. Souza, B. T. Wyman, M. P. H. L. Graverand, K. Subburaj, T. M. Link, S. Majumdar, “Difference between X-ray and MRI-determined knee cartilage thickness in weight-bearing and non-weight-bearing conditions,” Osteoarthritis and Cartilage, Vol. 21, pp. 1876-1885, 2013.
21. Z. A. Cohen, D. M. McCarthy, S. D. Kwak, P. Legrand, F. Fogarasi, E. J. Ciaccio, G. A. Ateshian, “Knee cartilage topography, thickness, and contact areas from MRI: in-vitro calibration and in-vivo measurements,” Osteoarthritis and Cartilage, Vol. 7, pp. 95-109, 1999.
22. K. Bloecker, M. Englund, W. Wirth, M. Hudelmaier, R. Burgkart, R. B. Frobell, and F. Eckstein, “Revision 1 Size and position of the healthy meniscus, and its Correlation with sex, height, weight, and bone area- a cross-sectional study,” BMC Musculoskeletal Disorders, Vol. 12, pp. 248-256, 2011.
23. A. Wenger, W. Wirth, M. Hudelmaier, I. N. Huhmann, S. Trattning, K. Bloecker, R. B. Frobell, C. K. Kwoh, F. Eckstein, M. Englund, “Meniscus Body Position, Size, and Shape in Persons With and Persons Without Radiographic Knee Osteoarthritis,” Arthritis and Rheumatology, Vol. 65, pp. 1804-1811, 2013.
24. J. Y. Rho, R. B. Ashman, C. H. Turner, “Young’s modulus of trabecular and cortical bone material: ultrasonic and microtensile measurements,” Journal of Biomechanics, Vol. 26, pp. 111-120, 1993.
25. C. Ohman, M. Baleani, C. Pani, F. Taddei, M. Alberghini, M. Viececonti, M. Manfrini, “Compressive behavior of child and adult cortical bone,” Bone, Vol. 49, pp. 769-776, 2011.
26. H. H. Bayraktar, E. F. Morgan, G. L. Niebur, G. E. Morris, E. K. Wong, T. M. Keaveny, “Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue,” Journal of Biomechanics, Vol. 37, pp. 27-35, 2004.
27. T. D. Brown, A. B. Ferguson, “Mechanical Property Distributions in the Cancellous Bone of the Human Proximal Femur,” Acta Orthopaedica Scandinavica, Vol. 51, pp. 429-437, 1980.
28. M. Ding, M. Dalstra, C. C. Danielsen, J. Kabel, I. Hvid, F. Linde, “Age variations in the properties of human tibial trabecular bone,” The Journal of Bone and Joint Surgery, Vol. 79, pp. 995-1002, 1997.
29. V. Vijayakumar, “Quantifying the Regional Variations in the Mechanical Properties of Cancellous Bone of the Tibia using Indentation Testing and CT imaging,” McMaster University, Ontario, Canada, 2013.
30. A. R. Hopkins, A. M. New, F. R. Baena, M. Taylor, “Finite element analysis of unicompartmental knee arthroplasty,” Medical Engineering and Physics, Vol. 32, pp. 14-21, 2010.
31. A. Steinbruck, M. Woiczinski, P. Weber, P. E. Muller, V. Jansson, C. Schroder, “Posterior cruciate ligament balancing in total knee arthroplasty： a numerical study with a dynamic force controlled knee model,” Biomedical Engineering Online, Vol. 13, pp. 1-13, 2014.
32. E. Pena, B. Calvo, M. Martinez, M. Doblare, “A three-dimensional finite element analysis of the combined behavior of ligaments and menisci in the healthy human knee joint,” Journal of Biomechanics, Vol. 39, pp. 1686-1701, 2006.
33. SolidWorks, https://www.solidworks.com/
34. ANSYS, https://www.ansys.com/
35. R. D. Cook, D. S. Malkus, M. E. Plesha and R. J. Witt, Concepts and Application of Finite Element Analysis, 4th ed., Wiley, Hoboken, NJ, 2002.
36. K. Smeets, J. Slane, L. Scheys, S. Claes , J. Bellemans, “Mechanical analysis of extra-articular knee ligaments. Part one: Native knee ligaments,” The Knee, Vol. 24, pp. 949-956, 2017
37. D. L. Butler, M. D. Kay, D. C. Stouffer, “Comparison of material properties in fascicle-bone units from human patellar tendon and knee ligaments,” Journal of Biomechanics, Vol. 19, pp. 425-432, 1986
38. F. Liu, B. Yue, H. R. Gadikota, M. Kozanek, W. Liu, T. J. Gill, H. E. Rubash, G. Li, “Morphology of the medial collateral ligament of the knee,” Journal of Orthopaedic Surgery and Research, Vol. 5, pp. 69-77, 2010
39. N. Otake, H. Chen, X. Yao, S. Shoumura, “Morphology study of the lateral and medial collateral ligaments of the human knee,” Okajimas Folia Anatomica Japonica, Vol. 83, pp. 115-122, 2007
40. J. M. Brinkman, P. J. A. Schwering, L. Blankevoort, J. G. Koolos, J. Luites, A. B. Wymenga, “The insertion geometry of the posterolateral corner of the knee,” The Journal of Bone and Joint Surgery, Vol. 87-B, No. 10, pp. 1364-1368, 2005
41. B. C. Lyson, R. Smigielski, U. Zdanowicz, M. Drwiega, B. Ciszek, “Anatomy of the anterior cruciate ligament /ACL/ in CT with 3D reconstruction, in magnetic resonance imaging and in analysis of anatomical study of fresh-frozen cadaver knees,” European Congress of Radiology, Vienna, March 6-10, 2014
42. S. Kopf, M. W. A. Pombo, M. Szczodry, J. J. Irrgang, F. H. Fu, “Size Variability of the Human Anterior Cruciate Ligament Insertion Sites,” The American Journal of Sports Medicine, Vol. 39, No. 1, pp. 108-113, 2011
43. J. C. Gali, H. C. S. Oliveira, B. C. B. Lisboa, B. D. Dias, F. G. Casimiro, E. B. Caetano, “Tibial Insertions of the Posterior Cruciate Ligament: Topographic Anatomy and Morphometric Study,” Revista Brasileira de Ortopedia, Vol. 48, No. 3, pp. 263-267, 2013
44. J. C. Gali, D. B. Camargo, F. A. M. Oliveira, R. H. N. Pereira, P. A. C. Silva, “Descriptive anatomy of the anterior cruciate ligament femoral insertion,” Revista Brasileira de Ortopedia, Vol. 53, No. 4, pp. 421-426, 2018
45. J. M. Gere, Mechanics of Materials, 6th ed, Thomson Learning, USA, 2004.
46. A. C. Ugural and S. K. Fenster, Advanced Mechanics of Materials and Applied Elasticity, 5th ed, Person Education Taiwan Ltd. Gauli Books, Taipei, 2015.