骨重建及骨干横截面生长仿真分析
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摘要
骨代谢是一个复杂的过程,从出生到骨发育停止,一直进行着骨的生长和塑建,骨成熟以后又不断进行着骨重建。力学因素参与了整个过程,通过骨吸收与骨形成的相互作用来调整骨的形状、大小及有机组成,使得骨骼结构能够适应不断变化的力学环境。骨形成和骨吸收两者之间的转换紊乱或异常会引起骨疾病,比如骨质疏松症、骨畸形等等,为了对这些疾病的预防和治疗手段有更好的理解和提供一定的理论依据,有限元技术得到了广泛的应用。因此,进行骨重建及横截面生长过程的数值模拟有着重要的学术意义和应用价值。
本课题在骨再造理论的基础上,结合骨生长生理调控机制,选择Wistar鼠股骨近端作为研究对象,进行了骨重建的仿真分析,并根据股骨所承受载荷与时间的关系,模拟出整个生长期中骨干横截面的直径变化。使用Micro-CT扫描股骨近端,获取断层图像数据,利用MIMICS软件进行图像数据处理,构造出均匀的面网格模型,导入有限元软件ANSYS建立出有限元模型,然后利用CT值与骨密度、弹性模量之间的关系式,得到接近真实的材料属性,赋予到有限元模型的每个单元中。使用APDL语言编制程序实现骨重建算法,为了更加接近骨生理机理,考虑了骨细胞与反应细胞之间的相互影响,经过迭代计算得到三维股骨近端表面密度分布。另外,假设骨干横截面的初始外形,根据载荷与时间之间关系图进行有限元分析,计算出一个时间增量后骨横截面中每个单元的力学激励,利用力学激励与骨重建率和吸收率之间的关系,计算出横截面新的外形,循环以上过程,直到预定时间停止迭代,可以模拟出骨干横截面的生长过程。
本文还研究了骨再造率系数、参考激励值等参数对骨再造的影响。结果表明以上参数取得合适的数值后,股骨头受压面的密度比较大,载荷由股骨头传递到内侧的皮质骨,骨干表面区域的骨质较密,表现为皮质骨,在骨干中间区域出现骨髓腔,骨密度趋近于零,与实际生理结构较吻合。对骨外膜与骨内膜的初始直径大小进行设置,最后结果表明在生长期内骨干骨外膜和骨内膜直径明显增大,表现出骨外膜向外扩展和骨内膜扩展后吸收。
Bone metabolism is a complex process which controls bone growth and modeling during development, and bone remodeling after maturation. Mechanical factors involve in the whole process. To make the bone structure to adapt to changing mechanical environment, the interaction between bone resorption and bone formation adjusts the bone shape, size and organic composition. Abnormal conversion between bone resorption and formation can cause bone disease such as osteoporosis, bone deformity and so on. In order to have a better understanding and provide a theoretical basis for preventing and treating diseases, finite element technique has been widely applied. So research on simulation of bone remodeling and the process of cross-section growth has important academic significance and technical value.
This paper carries out numerical simulation of bone remodeling of Wistar rat femur based on bone adaptive remodeling theory, integrated into the physiological regulation of bone growth. According to the relationship between load subject to on the femur and time, we simulate the change in the cross-section diameter of diaphysis during growth. Proximal femur is scanned by Micro-CT to obtain image data. The image data is processed to construct a uniform surface mesh model, and then the model is imported into the finite element software ANSYS to create FEM. The approximately real material property which is obtained using the relation between CT value and bone density is assigned into each element of FEM. Bone remodeling algorithm is performed by writing a program using APDL language. To get close to physiological mechanism of bone, interaction between bone cells and cells is considered into algorithm, apparent density of proximal femur can be obtained after iterative calculation. In addition, assuming the initial cross-section of diaphysis, the finite element analysis is performed to obtained stimulus of each element in cross-section, and then new shape of cross-section can be calculated according to the relation between stimulus and rate of bone remodeling. Repeating above process, the growth process of cross-section of diaphysis can be simulated.
Some parameters such as bone remodeling coefficient, the reference value of stimulus and so on are researched in this paper. It is shown that results are consistent with actual physical structure after setting appropriate parameters above. The load is delivered from the femur head to cortical bone, bone which is dense on the surface of diaphysis represents cortical bone; bone marrow cavity appears in the middle region of diaphysis where bone density gets close to zero. For bone initial geometries, the periosteal and endosteal diameters are set, the results show that the periosteal and endosteal diameters can increased significantly after simulation, it is presented that periosteum expands outward and endosteal resorbs after expansion.
本课题在骨再造理论的基础上,结合骨生长生理调控机制,选择Wistar鼠股骨近端作为研究对象,进行了骨重建的仿真分析,并根据股骨所承受载荷与时间的关系,模拟出整个生长期中骨干横截面的直径变化。使用Micro-CT扫描股骨近端,获取断层图像数据,利用MIMICS软件进行图像数据处理,构造出均匀的面网格模型,导入有限元软件ANSYS建立出有限元模型,然后利用CT值与骨密度、弹性模量之间的关系式,得到接近真实的材料属性,赋予到有限元模型的每个单元中。使用APDL语言编制程序实现骨重建算法,为了更加接近骨生理机理,考虑了骨细胞与反应细胞之间的相互影响,经过迭代计算得到三维股骨近端表面密度分布。另外,假设骨干横截面的初始外形,根据载荷与时间之间关系图进行有限元分析,计算出一个时间增量后骨横截面中每个单元的力学激励,利用力学激励与骨重建率和吸收率之间的关系,计算出横截面新的外形,循环以上过程,直到预定时间停止迭代,可以模拟出骨干横截面的生长过程。
本文还研究了骨再造率系数、参考激励值等参数对骨再造的影响。结果表明以上参数取得合适的数值后,股骨头受压面的密度比较大,载荷由股骨头传递到内侧的皮质骨,骨干表面区域的骨质较密,表现为皮质骨,在骨干中间区域出现骨髓腔,骨密度趋近于零,与实际生理结构较吻合。对骨外膜与骨内膜的初始直径大小进行设置,最后结果表明在生长期内骨干骨外膜和骨内膜直径明显增大,表现出骨外膜向外扩展和骨内膜扩展后吸收。
Bone metabolism is a complex process which controls bone growth and modeling during development, and bone remodeling after maturation. Mechanical factors involve in the whole process. To make the bone structure to adapt to changing mechanical environment, the interaction between bone resorption and bone formation adjusts the bone shape, size and organic composition. Abnormal conversion between bone resorption and formation can cause bone disease such as osteoporosis, bone deformity and so on. In order to have a better understanding and provide a theoretical basis for preventing and treating diseases, finite element technique has been widely applied. So research on simulation of bone remodeling and the process of cross-section growth has important academic significance and technical value.
This paper carries out numerical simulation of bone remodeling of Wistar rat femur based on bone adaptive remodeling theory, integrated into the physiological regulation of bone growth. According to the relationship between load subject to on the femur and time, we simulate the change in the cross-section diameter of diaphysis during growth. Proximal femur is scanned by Micro-CT to obtain image data. The image data is processed to construct a uniform surface mesh model, and then the model is imported into the finite element software ANSYS to create FEM. The approximately real material property which is obtained using the relation between CT value and bone density is assigned into each element of FEM. Bone remodeling algorithm is performed by writing a program using APDL language. To get close to physiological mechanism of bone, interaction between bone cells and cells is considered into algorithm, apparent density of proximal femur can be obtained after iterative calculation. In addition, assuming the initial cross-section of diaphysis, the finite element analysis is performed to obtained stimulus of each element in cross-section, and then new shape of cross-section can be calculated according to the relation between stimulus and rate of bone remodeling. Repeating above process, the growth process of cross-section of diaphysis can be simulated.
Some parameters such as bone remodeling coefficient, the reference value of stimulus and so on are researched in this paper. It is shown that results are consistent with actual physical structure after setting appropriate parameters above. The load is delivered from the femur head to cortical bone, bone which is dense on the surface of diaphysis represents cortical bone; bone marrow cavity appears in the middle region of diaphysis where bone density gets close to zero. For bone initial geometries, the periosteal and endosteal diameters are set, the results show that the periosteal and endosteal diameters can increased significantly after simulation, it is presented that periosteum expands outward and endosteal resorbs after expansion.
引文
1 J.L.Wolff. Das Gesetz der Transformation der Knochen. Hirschwald. 1892:110~157
2杨佳通,吴文周等.骨力学.科学出版社. 1989:76~77
3 G.Pauwels. Kurzen uber die Mechanische Beanspruchung des Knochens und Ihre Bedeutung fur die Funktionelle Anpassung. Z.Orthop., 1973,3,681~705
4 H.M.Forst. Bone Mass and the Mechanostat: A Proposal. The Anatomy Record. 1987,219(1):1~9
5 H.M.Forst. Perspectives: A Proposed General Model of The Mechanostat. The Anat- omy Record. 1996,224(2):139~147
6朱东,马宗民等.带有力学调控系统的各向异性骨再造模型.生物医学工程杂志. 2006,23(3):525~529
7 S.C.Cowin, D.H.Hedgedus. Bone Remodeling I: A Theory of Adaptive Elasticity. J.Elasticity. 1976,6(3):313~326
8 D.P.Fyhire, D.R.Carter. A Unifying Principle Relating Stress to Trabecular Bone Morphology. J.Orthop.Res. 1986,4:304~317
9 R.Huiskes, H.Weinans, et al. Adaptive Bone-remodeling Theory Applied to Prosthetic-design Analysis. J.Biomechanics. 1987,20:1135~1150
10 D.R.Carter. Mechanical Loading History and Skeletal Biology. J.Biomechanics. 1987,20:1095~11009
11 D.R.Carter, M.Wong. The Role of Mechanical Loading Histories in the Development of Diarthrodial Joints. J.Orthop.Res. 1988,6:804~816
12 D.R.Carter, D.P.Fyhrie, R.T.Whalen. Trabecular Bone Density and Loading History: Regulation of Connective Tissue Biology by Mechanical Energy. J.Biomechanics. 1987,20:785~794
13 D.R.Carter, D.P.Fyhire, et al. Influences of Mechanical Stress on Prenatal and Postnatal Skeletal Development. Clin.Orthop. 1987,219:237~250
14 M.Wong. D.R.Carter. A Theoretical Model of Endochondral Ossification and Bone Architectural Construction in Long Bone Ontogeny. Anatomy and Embryology. 1990,181:523~532
15 G.S.Beaupré, T.E.Orr, D.R.Carter. An Approach for Time-dependent Bone Modeling and Remodeling Theoretical Development. J.Orthop.Res. 1990,8:651~661
16 G.S.Beaupré, T.E.Orr, D.R.Carter. An Approach for Time-dependent Bone Modeling and Remodeling Application:A Preliminary Remodeling Simulation. J.Orthop.Res. 1990,8:662~670
17 H.Weinans, R.Huiskes, H.J.Grootenboer. The Behavior of Adaptive Bone Remodeling Simulation Models. J.Biomechanics. 1992,25(12):1425~1441
18 M.G.Mullender, R.Huiskes, H.Weinans. A Physiological Approach to Simulation of Bone Remodeling as a Self-organizational Control Process. J.Biomechanics. 1994,27(11):1389~1394
19 C.R.Jacobs, M.E.Levenston, G.S.Beaupré, et al. Numerical Instabilities in Bone Re- modeling Simulations: The Advantages of a Node-based Finite Element Approach. J.Biomechanics. 1995,28(4):449~459
20 M.A.Stülpner, et al. A Three-dimensional Finite Analysis of Adaptive Remodeling in The Proximal Femur. J.Biomechanics. 1997,30(10):1063~1066
21 C.R.Jacobs, et al. Adaptive Bone Remodeling Incorporation Simulations Density And Anisotropy Considerations. J.Biomechanics. 1997,30(6):603~613
22 M.Doblaré, J.M.García. Anisotropic Bone Remodeling Model Based on A Continuum Damage-repair Theory. J.Biomechanics. 2002,35(1):1~17
23马宗民.各向异性骨再造理论模型及骨质疏松模拟研究.吉林大学博士学位论文. 2005:33~34
24 Zhu.Xinghua, Gong He, Zhu Dong, Gao Bingzhao. A Study of The Effect of Non-linearities in The Equation of Bone Remodeling. J.Biomechanics. 2002,35(7),951~960
25张毅奕,陶祖莱.载荷诱导骨生长的力学细胞生物学机制.力学进展. 2000,30(3):443~445
26 S.K.Slikes. The Natural History of The African Elephant. American Elsevier Publishing Company, Inc., New York. 1971
27 L.E.Lanyon. The Influence of Function on The Development of Bone Curvature. An Experimental Study On The Rat Tibia. J.Zool. 1980,192:457~466
28 M.Rudwick, G.Cuvier. Fossil Bones, and Geological Catastrophes. The University of Chicago Press. Chicago. 1997
29 R.J.Hall, D.H.Watt. Osseous Changes Due to A False Aneurysm of The Proper Digital Artery: A Case Report. J.Hand Surg. 1986,11:440~442
30 Von Bhl M, J.Maltha, et al. Focal Hyalinization During Experimental Tooth Movement In Beagle Dogs. Am J Orthod Dentofacial Orthop. 2004,125:615~623
31 S.C.Cowin, W.C.Van Buskirk. Internal Bone Remodeling Induced by A Medullary Pin. J.Biomechanics. 1978,11:269~275
32 M.C.H.Van der Meulen, G.S.Beaupré, D.R.Carter. Mechnobiologic Influences In Long Bone Cross-Sectional Growth. Bone. 1993,14:635~642
33 R.D.Carpenter, D.R.Carter. The Mechanobiological Effects of Perosteal Surface Loads. Biomecham Model Mechanobiol. 2008,7:227~242
34杨佳通等.生物力学.重庆出版社. 2000:14~18
35程亮.骨应力重建仿真研究.上海交通大学硕士学位论文. 2008:10~11
36 S.Dharmananda. Treatment of Avascular Necrosis of The Femoral Head With Chinese Herbs. Portland. 2000
37陈峥嵘.现代骨科学.复旦大学出版社. 2010:35~42
38 Y.C.Fung. Biomechanics. Springer. 1990
39 D.P.Fyhrie, J.H.Kimura. Cancellous Bone Biomechanics. Journal of Biomechanics. 1999,32:1139~1148
40 S.J.Hollister. Application of Homogenization Theory to The Study of Trabecular Bone Mechanics. Journal of Biomechanics. 1991,24:825~839
41 S.J.Hollister, N.Kikuchi. Homogenization Theory and Digital Imaging: A Basis for Studying the mechanics and Design Principle of Bone Current Tissue. Biotechnology and Bioengineering. 1994,43:586~596
42朱兴华,宫赫,白雪飞,王福荣.弹性模量与表观密度的分段函数关系用于股骨近端的结构模拟.中国生物医学工程学报. 2003,22(3):250~256
43白雪飞,朱东,张春秋.近端股骨的结构模拟.吉林工业大学自然科学学报. 2000,30(4):56~60
44陈闯,周淑秋,黎刚.医学CT三维重建.首都师范大学自然科学学报. 2004,25:30~31
45费王华.基于新鲜骨骼CT图像的有限元分析及实验验证.南京理工大学硕士学位论文. 2008:25~26
46 D.C.Wirtz, N.Schiffers, et al. Critical Evaluation of Known Bone Material Properties to Realize Anisotropic FE-Simulation of The Proximal Femur. Journal of Biomechanics. 2000,33: 1325~1330
47 C.B.Ruff, W.C.Hayes. Subperiosteal Expansion and Cortical Remodeling of The Human Femur and Tibia With Aging. Science. 1982,217:945~948
48 D.R.Carter, G.S.Beaupré. Skeletal Function and Form Mechanobiology of Skeletal Development, Aging, and Regeneration. Cambridge University Press. 2001, 85~86
2杨佳通,吴文周等.骨力学.科学出版社. 1989:76~77
3 G.Pauwels. Kurzen uber die Mechanische Beanspruchung des Knochens und Ihre Bedeutung fur die Funktionelle Anpassung. Z.Orthop., 1973,3,681~705
4 H.M.Forst. Bone Mass and the Mechanostat: A Proposal. The Anatomy Record. 1987,219(1):1~9
5 H.M.Forst. Perspectives: A Proposed General Model of The Mechanostat. The Anat- omy Record. 1996,224(2):139~147
6朱东,马宗民等.带有力学调控系统的各向异性骨再造模型.生物医学工程杂志. 2006,23(3):525~529
7 S.C.Cowin, D.H.Hedgedus. Bone Remodeling I: A Theory of Adaptive Elasticity. J.Elasticity. 1976,6(3):313~326
8 D.P.Fyhire, D.R.Carter. A Unifying Principle Relating Stress to Trabecular Bone Morphology. J.Orthop.Res. 1986,4:304~317
9 R.Huiskes, H.Weinans, et al. Adaptive Bone-remodeling Theory Applied to Prosthetic-design Analysis. J.Biomechanics. 1987,20:1135~1150
10 D.R.Carter. Mechanical Loading History and Skeletal Biology. J.Biomechanics. 1987,20:1095~11009
11 D.R.Carter, M.Wong. The Role of Mechanical Loading Histories in the Development of Diarthrodial Joints. J.Orthop.Res. 1988,6:804~816
12 D.R.Carter, D.P.Fyhrie, R.T.Whalen. Trabecular Bone Density and Loading History: Regulation of Connective Tissue Biology by Mechanical Energy. J.Biomechanics. 1987,20:785~794
13 D.R.Carter, D.P.Fyhire, et al. Influences of Mechanical Stress on Prenatal and Postnatal Skeletal Development. Clin.Orthop. 1987,219:237~250
14 M.Wong. D.R.Carter. A Theoretical Model of Endochondral Ossification and Bone Architectural Construction in Long Bone Ontogeny. Anatomy and Embryology. 1990,181:523~532
15 G.S.Beaupré, T.E.Orr, D.R.Carter. An Approach for Time-dependent Bone Modeling and Remodeling Theoretical Development. J.Orthop.Res. 1990,8:651~661
16 G.S.Beaupré, T.E.Orr, D.R.Carter. An Approach for Time-dependent Bone Modeling and Remodeling Application:A Preliminary Remodeling Simulation. J.Orthop.Res. 1990,8:662~670
17 H.Weinans, R.Huiskes, H.J.Grootenboer. The Behavior of Adaptive Bone Remodeling Simulation Models. J.Biomechanics. 1992,25(12):1425~1441
18 M.G.Mullender, R.Huiskes, H.Weinans. A Physiological Approach to Simulation of Bone Remodeling as a Self-organizational Control Process. J.Biomechanics. 1994,27(11):1389~1394
19 C.R.Jacobs, M.E.Levenston, G.S.Beaupré, et al. Numerical Instabilities in Bone Re- modeling Simulations: The Advantages of a Node-based Finite Element Approach. J.Biomechanics. 1995,28(4):449~459
20 M.A.Stülpner, et al. A Three-dimensional Finite Analysis of Adaptive Remodeling in The Proximal Femur. J.Biomechanics. 1997,30(10):1063~1066
21 C.R.Jacobs, et al. Adaptive Bone Remodeling Incorporation Simulations Density And Anisotropy Considerations. J.Biomechanics. 1997,30(6):603~613
22 M.Doblaré, J.M.García. Anisotropic Bone Remodeling Model Based on A Continuum Damage-repair Theory. J.Biomechanics. 2002,35(1):1~17
23马宗民.各向异性骨再造理论模型及骨质疏松模拟研究.吉林大学博士学位论文. 2005:33~34
24 Zhu.Xinghua, Gong He, Zhu Dong, Gao Bingzhao. A Study of The Effect of Non-linearities in The Equation of Bone Remodeling. J.Biomechanics. 2002,35(7),951~960
25张毅奕,陶祖莱.载荷诱导骨生长的力学细胞生物学机制.力学进展. 2000,30(3):443~445
26 S.K.Slikes. The Natural History of The African Elephant. American Elsevier Publishing Company, Inc., New York. 1971
27 L.E.Lanyon. The Influence of Function on The Development of Bone Curvature. An Experimental Study On The Rat Tibia. J.Zool. 1980,192:457~466
28 M.Rudwick, G.Cuvier. Fossil Bones, and Geological Catastrophes. The University of Chicago Press. Chicago. 1997
29 R.J.Hall, D.H.Watt. Osseous Changes Due to A False Aneurysm of The Proper Digital Artery: A Case Report. J.Hand Surg. 1986,11:440~442
30 Von Bhl M, J.Maltha, et al. Focal Hyalinization During Experimental Tooth Movement In Beagle Dogs. Am J Orthod Dentofacial Orthop. 2004,125:615~623
31 S.C.Cowin, W.C.Van Buskirk. Internal Bone Remodeling Induced by A Medullary Pin. J.Biomechanics. 1978,11:269~275
32 M.C.H.Van der Meulen, G.S.Beaupré, D.R.Carter. Mechnobiologic Influences In Long Bone Cross-Sectional Growth. Bone. 1993,14:635~642
33 R.D.Carpenter, D.R.Carter. The Mechanobiological Effects of Perosteal Surface Loads. Biomecham Model Mechanobiol. 2008,7:227~242
34杨佳通等.生物力学.重庆出版社. 2000:14~18
35程亮.骨应力重建仿真研究.上海交通大学硕士学位论文. 2008:10~11
36 S.Dharmananda. Treatment of Avascular Necrosis of The Femoral Head With Chinese Herbs. Portland. 2000
37陈峥嵘.现代骨科学.复旦大学出版社. 2010:35~42
38 Y.C.Fung. Biomechanics. Springer. 1990
39 D.P.Fyhrie, J.H.Kimura. Cancellous Bone Biomechanics. Journal of Biomechanics. 1999,32:1139~1148
40 S.J.Hollister. Application of Homogenization Theory to The Study of Trabecular Bone Mechanics. Journal of Biomechanics. 1991,24:825~839
41 S.J.Hollister, N.Kikuchi. Homogenization Theory and Digital Imaging: A Basis for Studying the mechanics and Design Principle of Bone Current Tissue. Biotechnology and Bioengineering. 1994,43:586~596
42朱兴华,宫赫,白雪飞,王福荣.弹性模量与表观密度的分段函数关系用于股骨近端的结构模拟.中国生物医学工程学报. 2003,22(3):250~256
43白雪飞,朱东,张春秋.近端股骨的结构模拟.吉林工业大学自然科学学报. 2000,30(4):56~60
44陈闯,周淑秋,黎刚.医学CT三维重建.首都师范大学自然科学学报. 2004,25:30~31
45费王华.基于新鲜骨骼CT图像的有限元分析及实验验证.南京理工大学硕士学位论文. 2008:25~26
46 D.C.Wirtz, N.Schiffers, et al. Critical Evaluation of Known Bone Material Properties to Realize Anisotropic FE-Simulation of The Proximal Femur. Journal of Biomechanics. 2000,33: 1325~1330
47 C.B.Ruff, W.C.Hayes. Subperiosteal Expansion and Cortical Remodeling of The Human Femur and Tibia With Aging. Science. 1982,217:945~948
48 D.R.Carter, G.S.Beaupré. Skeletal Function and Form Mechanobiology of Skeletal Development, Aging, and Regeneration. Cambridge University Press. 2001, 85~86