基于无单元伽辽金法的人体骨骼生物力学仿真研究
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摘要
生物力学是一门应用力学与生物学交叉的学科。它的研究对象不仅涉及到医学、体育运动方面,而且已经深入到了交通、宇航、军事等领域。传统的生物力学常用的研究方法主要有临床研究、志愿者实验、人尸体实验、假人实验、动物实验、数值模拟等。其中数值模拟以其成本低、可操作性强、安全性好等优点越来越被广泛的采用。由于生物力学领域涉及的问题往往具有模型复杂、形变量大、载荷速度快、应变率高等特点,常用的有限元方法在进行数值仿真时,往往会面临前处理建模困难、计算时网格畸变等问题。无网格法以其前后处理简单、只需要节点信息、无网格依赖性等特点,便于复杂模型的建立、离散和分析,特别适合用来处理外形复杂的生物力学模型。为了将无单元伽辽金法法应用到人体骨骼冲击问题研究中,本论文研究做了如下几方面工作:
首先,系统的介绍了人体生物力学的研究方向和方法。通过对现有人体骨骼建模方法的研究对比,得到了适合人体骨骼冲击问题模型的建模方法。该建模方法具有应用范围广、精度高、建模方便等优点,并以此建模方法建立了人体股骨和颅骨生物力学模型。
其次,研究探讨了无单元伽辽金法基本理论和其中的几个关键问题,即:权函数的选取原则、影响域半径的确定方法、积分方案的选择以及边界条件的处理。为本论文研究奠定了理论基础。并用泰勒杆冲击实验对EFG法的几个关键参数进行分析,得到了适合本次研究的关键参数。
最后,利用无单元伽辽金法对人体股骨和颅骨的生物力学冲击问题进行了数值模拟,分析探讨了冲击过程中应力峰值的大小、应力集中常发部位以及应力在人体骨骼内的传播过程。并将结果与有限元进行对比,结果表明两者具有很好的一致性。无单元伽辽金法可以作为一种有效的方法应用在人体骨骼生物力学冲击问题分析中。
Biomechanics is an interdisciplinary which contains Mechanics and Biology. The objects it studied include not only Medical and body movement, but also Transportaion, aerospace and military. The traditional research methods are Clinical research method, Volunteer experiment method, Human body experiment method, Dummy experiment method, animal experiments method and numerical simulation method. The numerical simulation is one of the most widely used method among these methods as it's low cost, easy operability and good security. The biomechanics problems often relate some features like complex models, large distortion, high speed load and large strain rate. So when use the Traditional method finite element method to deal with the biomechanics problems, these issues like difficult to build models or element distortion come up. The element free method has many advantages such as more convenient in pre and post processing, need only the information of nodes, element independence et. With these advantages, the element free method is more convenient in building, scattering and analysing complex models. These make this method particularly suitable for dealing with biomechanics models. In order to apply the element free method into biomechanics impacting of skeleton, this paper is focused on the following aspects:
Firstly, The research directions and methods of the biomechanics has been systematically and comprehensive learned. By comparing the currently existing building measures of the skeleton model, a modeling method which is suitable for skeleton has been obtained. This method has some advantages such as can be widely use、high precision and easy to build models et. By this method , the models of the femur and skull have been created.
Secondly, several crucial points in the basic theory of the element free galerkin method (EFG for short) have been studied through the Taylor impact problem. These pionts included: Choice of the Weight Function; Domain Integration method; Choice of the domain radius; Essential boundary condition treatment et. By studying above aspects, the theoretical foundation had been established.
Finally, the EFG method had been implemented to design the femur and skull impact problems based on discussion in the former chapter. The value of the maximum stress during the impact process had been calculated, the places where the stress concentrated had been found and the stress spread process in bones had been analyzed. Compared these results with finite element method, the two method had highly consistent in accuracy. This indicated that the element free galerkin method could be used as an effective method to deal with the biomechanics impact problems of skeleton.
首先,系统的介绍了人体生物力学的研究方向和方法。通过对现有人体骨骼建模方法的研究对比,得到了适合人体骨骼冲击问题模型的建模方法。该建模方法具有应用范围广、精度高、建模方便等优点,并以此建模方法建立了人体股骨和颅骨生物力学模型。
其次,研究探讨了无单元伽辽金法基本理论和其中的几个关键问题,即:权函数的选取原则、影响域半径的确定方法、积分方案的选择以及边界条件的处理。为本论文研究奠定了理论基础。并用泰勒杆冲击实验对EFG法的几个关键参数进行分析,得到了适合本次研究的关键参数。
最后,利用无单元伽辽金法对人体股骨和颅骨的生物力学冲击问题进行了数值模拟,分析探讨了冲击过程中应力峰值的大小、应力集中常发部位以及应力在人体骨骼内的传播过程。并将结果与有限元进行对比,结果表明两者具有很好的一致性。无单元伽辽金法可以作为一种有效的方法应用在人体骨骼生物力学冲击问题分析中。
Biomechanics is an interdisciplinary which contains Mechanics and Biology. The objects it studied include not only Medical and body movement, but also Transportaion, aerospace and military. The traditional research methods are Clinical research method, Volunteer experiment method, Human body experiment method, Dummy experiment method, animal experiments method and numerical simulation method. The numerical simulation is one of the most widely used method among these methods as it's low cost, easy operability and good security. The biomechanics problems often relate some features like complex models, large distortion, high speed load and large strain rate. So when use the Traditional method finite element method to deal with the biomechanics problems, these issues like difficult to build models or element distortion come up. The element free method has many advantages such as more convenient in pre and post processing, need only the information of nodes, element independence et. With these advantages, the element free method is more convenient in building, scattering and analysing complex models. These make this method particularly suitable for dealing with biomechanics models. In order to apply the element free method into biomechanics impacting of skeleton, this paper is focused on the following aspects:
Firstly, The research directions and methods of the biomechanics has been systematically and comprehensive learned. By comparing the currently existing building measures of the skeleton model, a modeling method which is suitable for skeleton has been obtained. This method has some advantages such as can be widely use、high precision and easy to build models et. By this method , the models of the femur and skull have been created.
Secondly, several crucial points in the basic theory of the element free galerkin method (EFG for short) have been studied through the Taylor impact problem. These pionts included: Choice of the Weight Function; Domain Integration method; Choice of the domain radius; Essential boundary condition treatment et. By studying above aspects, the theoretical foundation had been established.
Finally, the EFG method had been implemented to design the femur and skull impact problems based on discussion in the former chapter. The value of the maximum stress during the impact process had been calculated, the places where the stress concentrated had been found and the stress spread process in bones had been analyzed. Compared these results with finite element method, the two method had highly consistent in accuracy. This indicated that the element free galerkin method could be used as an effective method to deal with the biomechanics impact problems of skeleton.
引文
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[4]张海钟,王东胜,阎力津等,颅面骨撞击伤的生物力学研究.中华创伤杂志, 2004, 20(1):26-29
[5] E. Racker, A New Look at Mechanisms in Bioenergetics, Academic Press. New York, 1976
[6] Cowin. S.C, The mechanical properties of bone. Mechanics of Structured Media, 1981, 231:90-107
[7] Carter. D. R., Wong, M. and Orr, T. E. Musculoskeletal ontogeny, phylogeny, and functional adaptation. Biomechanics, 1991, 24: 3-16
[8] Frost HM. On rho, a marrow mediator and estrogen: their roles in bone strength and "mass" in human females, osteopenias and osteoporoses: insights from a new paradigm. J of Bone and Mineral Metabolism, 1998, 16(2): 113-123
[9] M. Doblare, E. Cueto, B.Calvo, et al. On the employ of meshless methods in biomechanics. Comput. Methods Appl. Mech. Engrg, 2002, 194: 801-821
[10] James D. Lee, Youping Chen, Xiaowei Zeng, et al. Modeling and simulation of osteoporosis and fracture of trabecular bone by meshless method. International Journal of Engineering Science, 2007, 45: 329-338
[11] Liew K M, Wu H Y, Ng T Y. Meshless method for modeling of human proximal femur: treatment of nonconvex boundaries and stress analysis. Computational Mechanics, 2002, 28(5): 390-400
[12] Lee J D, Chen Y P, Zeng X W, et al. Modeling and simulation of osteoporosis and fracture of trabecular bone by meshless method. International Journal of Engineering Science, 2007, 45(2-8): 329-338
[13] Li H, Yan G P, et al. Numerical simulation of controlled nifedipine release from chitosan microgels. Journal of Applied Polymer Science, 2004, 93(4): 1928-1937
[14] Guilkey J. E, Hoying J. B, Weiss J. A. Computational modeling of multicellular constructs with the material point method. Journal of Biomechanics, 2006, 39(11): 2074-2086
[15] IonescuI, Guilkey J E, Berzins M, et al. Simulation Of soft tissue failure using the material point method. Journal of Biomechanical Engineering Transactions Of the Asme, 2006, 128(6): 917-924
[16] Liu YL, Liu W K. Rheology of redblood cell aggregation by computer simulation. Journal of Computational Physics, 2006, 220(1): 139-154
[17] Von Ellenrieder N, Muravchik C H, Nehorai A. A meshless method for solving the EEG forward problem. Ieee Transactions on Biomedical Engineering, 2005, 52(2): 249-257
[18]蒋琳.基于MR图像的左心室标记线跟踪算法与应变计算研究:[南京理工大学硕士学位论文].南京理工大学, 2008, 50-59
[19]庄玲.基于三维图像序列的左心室分割与运动联合估计. [浙江大学博士学位论文],杭州, 2008, 52-53
[20]李重视,闫丹丹,朱善安等.无网格法及其在心电正问题中的应用.国际生物医学工程杂志, 2008, 31(6): 347-351
[21] Liu H F, Shi P C. Meshfree representation and computation: Applications to cardiac motion analysis. Information Processing in Medical Imaging, Proceedings, 2003, 2732: 560-572
[22] Kleinberger M. Application of Finite Element Techniques to the Study of Cervical Spine Mechanics. In: Proc of 37th Stapp Car Crash Conference, San Antonio Texas,1993
[23] Dauvilliers F, Bendjellal F, Weiss M, et al. Development of a Finite Element Model of the Neck. In: Proc of the 38th Stapp Car Crash Conference, Florida, 1994
[24] H.W Ng, E.C Teo. Non-Linear Finite Element Analysis of Lower Cervical Spine(C4-C6) under Axial Loading. Journal of Spinal Disorders, 2000, 14(3): 201-210
[25] Stoppie N, Van Oosterwyck H, Jansen J, et al. The influence of Young's modulusof loaded implants on bone remodeling: An experimental and numerical study in the goat knee.J Biomed Mater Res A, 2008, 9: 1552-l565.
[26]马永有.人体几何建模与姿态仿真的关键技术研究: [上海交通大学博士学位论文].上海:上海交通大学机械与动力工程学院, 2004,19-20
[27]中国标准化与信息分类编码研究所.中国成年人人体尺寸GB10000-88, 1988
[28]陈琼.三维有限元建模方法的研究现状.空腔医学, 2006, 26(2): 154-1
[29]张春才,苏佳灿,禹宝庆.人体骨骼数值模型仿真学.上海:第二军医大学出版社, 2004, 111-235
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