复合载荷条件下运动膝关节软骨的数值分析
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摘要
背景:有报道通过建立软骨两相模型,数值模拟循环压缩载荷下固体基质的应变,在细胞水平上研究了机械刺激对关节炎的影响。但考虑软骨实际运动所受到变化的载荷和运动角度方面的研究较少。目的:揭示膝关节软骨的压缩、滚动、滑动或旋转以及复合载荷下的力学状态。方法:建立考虑钙化层、软骨下骨作用的关节软骨模型,使模型更接近完整的软骨天然生理结构。膝关节运动为胫骨平台与股骨远端的相对运动,简化为一刚化球体作用在平面软骨的几何模型。考虑屈伸、内/外翻及内/外旋转等运动特性,建立人行走时膝关节可实现复合载荷的三维有限元模型。研究膝关节软骨的压缩、滚动、滑动或旋转及复合载荷下的数值分析。结果与结论:(1)模拟步态过程中,关节软骨所受的最大应力区域分布在软骨下骨;(2)随着压缩过程的进行,Mises应力、应变与孔隙压力随压缩量的增大而增大,且增幅呈非线性减小的趋势;(3)结果发现,滚压载荷与总的复合载荷最为接近,可为组织工程体外功能化培养实验和方案的设计提供数据参考。
BACKGROUND: By establishing biphasic cartilage model and simulating solid matrix stress under compressive load, the effect of mechanical stimulation on arthritis is investigated at molecular level. However, the changes of loads and movement angle of cartilage in actual exercise are little reported.OBJECTIVE: To reveal the mechanical characteristics of knee joint cartilage under compression, rolling, sliding or rotation and combined loads. METHODS: An articular cartilage model considering the role of the calcified layer and subchondral bone was established, which was closer to the natural physiological structure of cartilage. The motion of the knee joint was the relative motion between tibial plateau and distal femur, which was simplified as a geometric model of rigid sphere acting on the plane cartilage. Considering the kinematics of flexion, extension, introversion, extroversion, internal rotation and external rotation, the three-dimensional finite element model of knee joint during walking under combined load was established. The mechanical characteristics of knee joint cartilage under compression, rolling, sliding or rotation and combined loads were analyzed. RESULTS AND CONCLUSION:(1) In the gait process, the maximum stress area of articular cartilage was distributed on the subchondral bone.(2) With the progress of the compression, the Mises stress, strain and pore pressure increased with the compressive load increasing, and the increase range showed a trend of nonlinear decrease.(3) These results imply that the rolling load is closest to the total combined loads, which provides reference for the in vitro functional cultivation of tissue-engineered cartilage and protocol design.
BACKGROUND: By establishing biphasic cartilage model and simulating solid matrix stress under compressive load, the effect of mechanical stimulation on arthritis is investigated at molecular level. However, the changes of loads and movement angle of cartilage in actual exercise are little reported.OBJECTIVE: To reveal the mechanical characteristics of knee joint cartilage under compression, rolling, sliding or rotation and combined loads. METHODS: An articular cartilage model considering the role of the calcified layer and subchondral bone was established, which was closer to the natural physiological structure of cartilage. The motion of the knee joint was the relative motion between tibial plateau and distal femur, which was simplified as a geometric model of rigid sphere acting on the plane cartilage. Considering the kinematics of flexion, extension, introversion, extroversion, internal rotation and external rotation, the three-dimensional finite element model of knee joint during walking under combined load was established. The mechanical characteristics of knee joint cartilage under compression, rolling, sliding or rotation and combined loads were analyzed. RESULTS AND CONCLUSION:(1) In the gait process, the maximum stress area of articular cartilage was distributed on the subchondral bone.(2) With the progress of the compression, the Mises stress, strain and pore pressure increased with the compressive load increasing, and the increase range showed a trend of nonlinear decrease.(3) These results imply that the rolling load is closest to the total combined loads, which provides reference for the in vitro functional cultivation of tissue-engineered cartilage and protocol design.
引文
[1]Mow VC, Kuei SC, Lai WM, et al. Biphasic creep and stress relaxation of articular cartilage in compression? Theory and experiments. J Biomech Eng. 1980;102(1):73-84.
[2]Mow V. Structure and function of articular cartilage and meniscus. Basic Orthopaedic Biomechanics.2005.
[3]Guo H, Shah M, Spilker R L. A finite element implementation for biphasic contact of hydrated porous media under finite deformation and sliding. Proc Inst Mech Eng H. 2014;228(3):225-236.
[4]Wang X, Ayati BP, Brouillete MJ, et al. Modeling and simulation of the effects of cyclic loading on articular cartilage lesion formation. Int J Numer Method Biomed Eng. 2014;30(10):927-941.
[5]Gao LL, Zhang CQ, Yang YB, et al. Depth-dependent strain fields of articular cartilage under rolling load by the optimized digital image correlation technique. Mater Sci Eng C Mater Biol Appl. 2013;33(4):2317-2322.
[6]Gao LL, Zhang CQ, Dong LM, et al. Description of depth-dependent nonlinear viscoelastic behavior for articular cartilage in unconfined compression. Materials Science and Engineering C.2012;32(2):119-125.
[7]Zhang CQ, Gao LL, Dong LM, et al. Depth-dependent normal strain of articular cartilage under sliding load by the optimized digital image correlation technique. Materials Science and Engineering C.2012;32(8):2390-2395.
[8]卫小春.关节软骨[M].北京:科学出版社, 2007.
[9]Meng Q, An S, Damion R A, et al. The effect of collagen fibril orientation on the biphasic mechanics of articular cartilage. J Mech Behav Biomed Mater. 2017;65:439-453.
[10]Halonen KS, Mononen ME, Jurvelin JS, et al. Deformation of articular cartilage during static loading of a knee joint-experimental and finite element analysis. J Biomech.2014;47(10):2467-2474.
[11]Joseph A. Buckwalter, Thomas A. Einhorn, Sheldon R. Simon.Orthopaedic basic science:biology and biomechanics of the musculoskeletal system. Second edition. 2000.陈启明,梁国穗,等译.骨科基础科学-骨关节肌肉系统生物学和生物力学[M].北京:人民卫生出版社, 2003:407-420.
[12]李哲,徐镭,倪国新.不同强度跑台运动对大鼠软骨下骨三维结构的影响[J].中华物理医学与康复杂志,2016,38(11):803-806.
[13]Li LP, Buschmann MD, Shirazi-Adl A. A fibril reinforced nonhomogeneous poroelastic model for articular cartilage:inhomogeneous response in unconfined compression. J Biomech. 2000;33(12):1533-1541.
[14]van der Voet A. A comparison of finite element codes for the solution of biphasic poroelastic problems. Proc Inst Mech Eng H, 1996; 210(2):209-211.
[15]孟迪.压缩载荷下软骨缺损修复后力学状态的研究[D].天津:天津理工大学, 2016.
[16]张述卿.软骨缺损修复的有限元模拟及滚压装置的设计[D].天津:天津理工大学, 2011.
[17]郜军霞.培养物袋装滚动加载的生物反应器研制及有限元仿真[D].天津:天津理工大学, 2012.
[18]Wilson W, van Donkelaar CC, Huyghe J M. A comparison between mechano-electrochemical and biphasic swelling theories for soft hydrated tissues.J Biomech Eng.2005;127(1):158-165.
[19]Dabiri Y, Li L P. Altered knee joint mechanics in simple compression associated with early cartilage degeneration.Comput Math Methods Med. 2013;2013:862903
[20]Dabiri Y, Li L P. Influences of the depth-dependent material inhomogeneity of articular cartilage on the fluid pressurization in the human knee. Med Eng Phys. 2013;35(11):1591-1518.
[21]Elhamian SM, Alizadeh M, Shokrieh MM, et al. A depth dependent transversely isotropic micromechanic model of articular cartilage. J Mater Sci Mater Med.2015; 26(2):111.
[22]刘清宇,王富友,刘俊利,等.含有天然钙化软骨层骨软骨支架的研制[J].中华创伤杂志,2014,30(5):467-470.
[23]Madry H, Orth P, Cucchiarini M. Role of the subchondral bone in articular cartilage degeneration and repair. J Am Acad Orthop Surg. 2016;24(4):e45-6.
[24]Yang T, Spilker RL. A Lagrange multiplier mixed finite element formulation for three-dimensional contact of biphasic tissues.J Biomech Eng. 2007;129(3):457-471.
[25]Ateshian GA, Maas S, Weiss JA. Finite element algorithm for frictionless contact of porous permeable media under finite deformation and sliding.J Biomech Eng.2010; 132(6):061006.
[26]郝智秀,冷慧杰,曲传咏,等.骨与膝关节生物力学行为研究[J].固体力学学报, 2010, 31(6):603-612.
[27]孙英彩,崔建岭,李石玲,等. MRI测量正常人膝关节软骨厚度[J].实用放射学杂志,2004,20(11):1007-1010.
[28]晏丹,周广东,曹谊林.关节软骨生化结构及其与力学性能关系研究进展[J].上海交通大学学报(医学版),2009, 29(3):341-345.
[29]Federico S, Grillo A, La Rosa G, et al. A transversely isotropic,transversely homogeneous microstructural-statistical model of articular cartilage. J Biomech. 2005;38(10):2008-2018.
[30]戴尅戎.力学生物学在骨与软骨研究中的应用[J].中华骨科杂志,2006,26(6):429-431.
[31]Guo H, Spilker RL. Biphasic finite element modeling of hydrated soft tissue contact using an augmented Lagrangian method.J Biomech Eng.2011;133(11):111001.
[32]Madry H. The subchondral bone:a new frontier in articular cartilage repair. Knee Surg Sports Traumatol Arthrosc. 2010;18(4):417-418.
[33]Chung C, Burdick JA. Engineering cartilage tissue. Adv Drug Deliv Rev. 2008;60(2):243-262.
[34]Guilak F. Functional tissue engineering. Annals of the New York Academy of Sciences.2002;961(1):193-195.
[35]戴尅戎.骨与关节的力学生物学研究[C]//全国生物力学学术会议,2009:1-1.
[2]Mow V. Structure and function of articular cartilage and meniscus. Basic Orthopaedic Biomechanics.2005.
[3]Guo H, Shah M, Spilker R L. A finite element implementation for biphasic contact of hydrated porous media under finite deformation and sliding. Proc Inst Mech Eng H. 2014;228(3):225-236.
[4]Wang X, Ayati BP, Brouillete MJ, et al. Modeling and simulation of the effects of cyclic loading on articular cartilage lesion formation. Int J Numer Method Biomed Eng. 2014;30(10):927-941.
[5]Gao LL, Zhang CQ, Yang YB, et al. Depth-dependent strain fields of articular cartilage under rolling load by the optimized digital image correlation technique. Mater Sci Eng C Mater Biol Appl. 2013;33(4):2317-2322.
[6]Gao LL, Zhang CQ, Dong LM, et al. Description of depth-dependent nonlinear viscoelastic behavior for articular cartilage in unconfined compression. Materials Science and Engineering C.2012;32(2):119-125.
[7]Zhang CQ, Gao LL, Dong LM, et al. Depth-dependent normal strain of articular cartilage under sliding load by the optimized digital image correlation technique. Materials Science and Engineering C.2012;32(8):2390-2395.
[8]卫小春.关节软骨[M].北京:科学出版社, 2007.
[9]Meng Q, An S, Damion R A, et al. The effect of collagen fibril orientation on the biphasic mechanics of articular cartilage. J Mech Behav Biomed Mater. 2017;65:439-453.
[10]Halonen KS, Mononen ME, Jurvelin JS, et al. Deformation of articular cartilage during static loading of a knee joint-experimental and finite element analysis. J Biomech.2014;47(10):2467-2474.
[11]Joseph A. Buckwalter, Thomas A. Einhorn, Sheldon R. Simon.Orthopaedic basic science:biology and biomechanics of the musculoskeletal system. Second edition. 2000.陈启明,梁国穗,等译.骨科基础科学-骨关节肌肉系统生物学和生物力学[M].北京:人民卫生出版社, 2003:407-420.
[12]李哲,徐镭,倪国新.不同强度跑台运动对大鼠软骨下骨三维结构的影响[J].中华物理医学与康复杂志,2016,38(11):803-806.
[13]Li LP, Buschmann MD, Shirazi-Adl A. A fibril reinforced nonhomogeneous poroelastic model for articular cartilage:inhomogeneous response in unconfined compression. J Biomech. 2000;33(12):1533-1541.
[14]van der Voet A. A comparison of finite element codes for the solution of biphasic poroelastic problems. Proc Inst Mech Eng H, 1996; 210(2):209-211.
[15]孟迪.压缩载荷下软骨缺损修复后力学状态的研究[D].天津:天津理工大学, 2016.
[16]张述卿.软骨缺损修复的有限元模拟及滚压装置的设计[D].天津:天津理工大学, 2011.
[17]郜军霞.培养物袋装滚动加载的生物反应器研制及有限元仿真[D].天津:天津理工大学, 2012.
[18]Wilson W, van Donkelaar CC, Huyghe J M. A comparison between mechano-electrochemical and biphasic swelling theories for soft hydrated tissues.J Biomech Eng.2005;127(1):158-165.
[19]Dabiri Y, Li L P. Altered knee joint mechanics in simple compression associated with early cartilage degeneration.Comput Math Methods Med. 2013;2013:862903
[20]Dabiri Y, Li L P. Influences of the depth-dependent material inhomogeneity of articular cartilage on the fluid pressurization in the human knee. Med Eng Phys. 2013;35(11):1591-1518.
[21]Elhamian SM, Alizadeh M, Shokrieh MM, et al. A depth dependent transversely isotropic micromechanic model of articular cartilage. J Mater Sci Mater Med.2015; 26(2):111.
[22]刘清宇,王富友,刘俊利,等.含有天然钙化软骨层骨软骨支架的研制[J].中华创伤杂志,2014,30(5):467-470.
[23]Madry H, Orth P, Cucchiarini M. Role of the subchondral bone in articular cartilage degeneration and repair. J Am Acad Orthop Surg. 2016;24(4):e45-6.
[24]Yang T, Spilker RL. A Lagrange multiplier mixed finite element formulation for three-dimensional contact of biphasic tissues.J Biomech Eng. 2007;129(3):457-471.
[25]Ateshian GA, Maas S, Weiss JA. Finite element algorithm for frictionless contact of porous permeable media under finite deformation and sliding.J Biomech Eng.2010; 132(6):061006.
[26]郝智秀,冷慧杰,曲传咏,等.骨与膝关节生物力学行为研究[J].固体力学学报, 2010, 31(6):603-612.
[27]孙英彩,崔建岭,李石玲,等. MRI测量正常人膝关节软骨厚度[J].实用放射学杂志,2004,20(11):1007-1010.
[28]晏丹,周广东,曹谊林.关节软骨生化结构及其与力学性能关系研究进展[J].上海交通大学学报(医学版),2009, 29(3):341-345.
[29]Federico S, Grillo A, La Rosa G, et al. A transversely isotropic,transversely homogeneous microstructural-statistical model of articular cartilage. J Biomech. 2005;38(10):2008-2018.
[30]戴尅戎.力学生物学在骨与软骨研究中的应用[J].中华骨科杂志,2006,26(6):429-431.
[31]Guo H, Spilker RL. Biphasic finite element modeling of hydrated soft tissue contact using an augmented Lagrangian method.J Biomech Eng.2011;133(11):111001.
[32]Madry H. The subchondral bone:a new frontier in articular cartilage repair. Knee Surg Sports Traumatol Arthrosc. 2010;18(4):417-418.
[33]Chung C, Burdick JA. Engineering cartilage tissue. Adv Drug Deliv Rev. 2008;60(2):243-262.
[34]Guilak F. Functional tissue engineering. Annals of the New York Academy of Sciences.2002;961(1):193-195.
[35]戴尅戎.骨与关节的力学生物学研究[C]//全国生物力学学术会议,2009:1-1.
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