计算骨力学若干问题研究
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摘要
生物力学是力学与生物学、生理学、医学等多种学科相互结合、相互渗透而形成的一门边缘交叉学科。它是解释生命及其活动的力学,它从生物个体、组织、器官到细胞和分子不同层次研究应力与运动、变形、流动及生长的关系。生物力学帮助我们了解生命,启发我们观察自然、设计和制造各种设备以改善我们的生活质量。近二十年来,生物力学的研究已经从无到有生长起来。目前,生物力学已成为各国学者研究的热点,已深入于医学,生物医学等工程的多个领域,尤其是一些新生的前沿领域,如组织工程、生物功能材料等。骨骼-肌肉力学是生物力学中最被临床医学所接受、认可的一个子领域。骨力学的研究在美欧已经进入骨科临床,而这恰恰是我国生物力学中比较零散、薄弱的一个方面。本文的工作是对计算骨力学的一个探索与尝试。论文以人体骨骼为研究目标,研究骨材料力学性能的计算方法、骨骼重建机理,并与临床医学相结合,对骨科内固定手术的固定件和连接部位进行力学分析,从力学的角度分析手术的质量,研究固定件形状、尺寸等参数对手术效果的影响。
本文分上、中、下三篇。上篇建立了骨微观结构的单胞模型,用均匀化方法分别对密质骨和松质骨的材料力学性能进行预测,并研究探讨了反映骨微观结构的参数与骨力学性能之间的关系。中篇以基于参考应变能和参考应变理论、自适应优化的骨重建理论,以及基于感受细胞的自适应优化模型为基础建立了骨骼重建数值模拟方法,以骨骼材料在外界力学环境下得到的应变能和应变值作为刺激,研究了骨骼重建的规律。应用基于上述重建理论的数值计算模型,对二维和三维股骨头模型、二维整体长骨模型进行了重建数值模拟;对简化为平面模型的第三腰椎冠状面,模拟了年青期椎体和老年期椎体的外部几何形状和内部组织结构;模拟了四种类型的骨折愈合塑形行为。下篇则是生物力学与临床手术的结合,用计算力学的方法对骨折内固定手术及常见的内固定失效问题进行定性和定量的分析,为内固定临床手术提供必要的理论和计算依据。
上中下篇及其各章节的内容安排如下:
上篇的第一章首先简单介绍和回顾了测定骨骼弹性常数的实验方法,给出了各种实验方法下的骨组织弹性模量的值。接着回顾了松质骨和密质骨微观结构模型描述的发展历程,总结了前人在骨骼微观结构模型上的工作。进一步介绍了密质骨材料性质、松质骨材料性质与其相关参数之间的关系。最后概述了本篇的研究工作。
第二章详细描述了骨的结构和性质。骨的结构与性质是本篇研究的一个着手点,这里从骨的最基础的知识出发,阐述了骨的基本结构与性质。骨的结构涉及到骨的宏观结构-密质骨和松质骨,编织骨、板状骨和哈弗氏骨结构以及分子水平的骨。骨的性质包括哈弗氏系统、密质骨和松质骨的力学性质。本章的内容是对上篇以至整个论文的补充和完善。
第三章详细介绍了复合材料宏观弹性常数计算的均匀化方法。均匀化理论是一种具
Biomechanics is mechanics applied to biology. Biomechanics is a marginal and crossed discipline, which is formed as a result of combination and convergence of mechanics, biology, physiology and other discipline. Biomechanics seeks to understand the mechanics of living systems. From the view of life individual, tissue, organ, cell and the different hiberarchy of molecule, it studies the relations between stress and motion, distortion, flow, and growth. Biomechanics helps us to realize the life, to observe the nature, to design and make many kinds of equipments to improve our life qualities. In the recent twenty years, research of biomechanics has been developed quickly. Up to date, the study of biomechanics has been in the climax, which is touched deeply in many fields of iatrology and biology medical engineering, especially in several new fields, such as tissue engineering, biological functional material and etc. Skeleton-muscle mechanics is one sub-field of the most being accepted by clinical medicine. The studies of bone mechanics have entered in the clinic operation in the America and Europe, but it is fragmentary and week in China. The research in the dissertation is one exploration and attempt of computational bone mechanics. We take human bone as object, are to study the computational methods of bone material mechanical properties, are to study the bone remodeling mechanism, are to process the mechanical analysis of steel plate internal fixation.The research in the dissertation consists of three parts. In the first part, the cell models of bone microstructure are based and the homogenization method is used to predict the mechanical properties of compact and cancellous bone. The relationship between the bone mechanical properties and the parameters of the bone microstructure is discussed here. In the second part, based on the reference strain energy theory, the reference strain theory, the adaptive elastic theory and the sensor cell adaptive theory, the numerical simulation methods of bone remodeling have been formed. The strain energy and strain value which can be gotten in FEM are taken as the stimulus then the rule of bone remodeling is applied. The numerical computational models based on the above remodeling theory are applies to process the remodeling numerical simulation of the two dimensional and three dimensional femur models. For the simple plate model of Lumbar vertebrae coronal surface, the outer geometrical shape and inner material distribution in the oldness and in the youngth are simulated. In the mean while, the four types of bone fracture plastic healing are simulated. In the third part, biomechanics is been combined with clinical operation. The method of mechanics is used to analyze bone fracture internal fixation operation qualitatively and quantificationally, which is the guard for internal fixation operation.The contents of the first, second, third part and every chapter are arranged in the following in detail.In chapter 1 of the first part, the experiment methods to test bone elastic constant are introduced and reviewed and the value of bone elastic modulus is given. Then the developing course of describing the microstructure of compact and cancellous bone is reviewed. And then,
the relationship between compact bone, cancellous bone and its relative parameters is introduced respectively. In the last, the works of this part are summarized.In chapter 2, the structure and property of the bone are described in details. The bone structure and property is the onset of the study of this part. From the basic knowledge of bone, the structure and property of bone are set forth. The structure of bone involves the macro structure-compact and cancellous bone, weave bone, lamellar bone Haversian bone and molecule level bone. The properties of bone include the mechanical properties of the haversian system, compact bone and cancellous bone. The content in this chapter is the complement of this part and the entire paper.In chapter 3, the homogenization method of predicting composite material macro elastic modulus is introduced in detail. The homogenization is one mathematic method with strict theory base, which is based on perturbation theory. Using the homogenization method, the reliant relationship between the microstructure and the composite macro properties can be formed. Using homogenization theory to predict mechanical properties of bone is a worth job, which is only in its beginning.In chapter 4, Six cell models are proposed to simulate the microstructures of trabecular bones, and the homogenization theory and finite element method are employed to calculate the macro-equivalent Young's modulus of trabecular bone. The macro-equivalent Young's modulus of different trabecular bones simulated by six cell models and their relations to the volume fraction ratio (VFR) of bone materials are computed and compared to the experimental data given in literatures. It is also discussed how to apply the cell models in different trabecular bones. The results show that the methods and six cell models proposed in this paper can simulate microstructures of trabecular bones and compute material properties effectively.In chapter 5, based on the four hierarchical model of compact bone proposed by Park (1979), the homogenization theory is applied and the first three levels are simulated. The knowledge of various bones, collagen and hydroxyapatite properties are considered during the numerical simulation of compact bone. The macroscopic material properties of compact bone can be computed from the above descending method of the models of hierarchical structure. The results are compared to the experiment data and it can be concluded from the numerical simulation of compact bone: effect of collagen Poission's ratio, effect of model describing a single lamella, effect of the lamellae structure and effect of the mineral content of osteon.In the second part, the bone remodeling mechanism is discussed and corresponding arithmetic is proposed, which is the key work in this dissertation.In chapter 1, the evolving of bone remodeling is treated detailedly. At first, the great meaning to study bone remodeling mechanism is given. Then several basic concepts of bone remodeling is introduced, which include the classify of bone remodeling, the type and function of cell. In the meanwhile, the existing bone remodeling theory is introduced. And then, the history of bone remodeling is reviewed, which includes the developing course of bone remodeling experiments, the discussion of bone remodeling stimulus and the developing course of bone remodeling theory and simulation. At last, the study content in this part is
given.In chapter 2, Combined with the finite element method, an optimization algorithm based on strain energy density criterion and strain criterion are proposed here for the numerical simulation of the internal remodeling of trabecular bones. The strain energy density is taken as the mechanical stimulus, and the bone remodeling is described with the change of material density distribution, which can represent the internal remodeling of trabecular bones. The numerical results of the remodeling simulation for a two-dimensional proximal femur, a three-dimensional proximal femur, and the plastic processing of bone fracture healing have been presented. The numerical results demonstrate that the method proposed here can effectively simulate the material density distribution and some effects of bone remodeling, and illuminate the mechanism of plastic processing of bone fracture healing well. In section 7, the case of existing dead zone is considered. In section 8, the effect of the value of reference strain and strain energy on bone remodeling is discussed. In chapter 9, the effect of bone remodeling coefficient on bone remodeling is discussed. All the results show the model and algorithm are both efficient.chapter 3 is the bone remodeling simulation based on the bone adaptive theory. The skeleton system of human is one most perfect functional adaptive system and it can be always in its optimal structure to adapt to mechanical environments. From this point of view, we study how bone material distribution is formed to satisfy the bone adaptive theory in the condition of limit of volume. The structural optimization method is applied to solve the reserve problem of material distribution and the bone remodeling rules and processes are simulated. SQL and criterion method are used. The numerical results show, the two algorithms both can simulate bone material distribution. More meaningful, for the simple plate model of Lumbar vertebrae coronal surface, the outer geometrical shape and inner material distribution in the oldness and in the youngth are simulated, which accord with the actual situation. In section 7, the time dependency of bone remodeling damping coefficient is considered.In chapter 4, the bone remodeling simulation considering bone cell is processed. In the clinic or medicine, all the bone is through cell to feel external stimulus. When tissue cell which is connected with bone cell senses the stimulus from the pressure, the bone remodeling will take place. Every cell is taken as one receipt, and the concept of "the influencing scope of sensor" is utilized, the bone remodeling mechanism is studied. The simulation results show the theory and method are in effect. The rule of wolff is also validated.In the third part, biomechanics is combined with clinic operations.In chapter 1, the bone fracture and internal fixation basic are summarized first, which include bone fracture, the type of bone fracture, developing process of bone fracture internal fixation and several relative theory of internal fixation. Then the application of FEM to internal fixation is summed up. At last, the engineering background here is combined to explain the meaning of this part.In chapter2, It studies the effects of plate position to bending stiffness and stresses of plate-bone system in the internal fixation of bone surgery by means of the composite beam
本文分上、中、下三篇。上篇建立了骨微观结构的单胞模型,用均匀化方法分别对密质骨和松质骨的材料力学性能进行预测,并研究探讨了反映骨微观结构的参数与骨力学性能之间的关系。中篇以基于参考应变能和参考应变理论、自适应优化的骨重建理论,以及基于感受细胞的自适应优化模型为基础建立了骨骼重建数值模拟方法,以骨骼材料在外界力学环境下得到的应变能和应变值作为刺激,研究了骨骼重建的规律。应用基于上述重建理论的数值计算模型,对二维和三维股骨头模型、二维整体长骨模型进行了重建数值模拟;对简化为平面模型的第三腰椎冠状面,模拟了年青期椎体和老年期椎体的外部几何形状和内部组织结构;模拟了四种类型的骨折愈合塑形行为。下篇则是生物力学与临床手术的结合,用计算力学的方法对骨折内固定手术及常见的内固定失效问题进行定性和定量的分析,为内固定临床手术提供必要的理论和计算依据。
上中下篇及其各章节的内容安排如下:
上篇的第一章首先简单介绍和回顾了测定骨骼弹性常数的实验方法,给出了各种实验方法下的骨组织弹性模量的值。接着回顾了松质骨和密质骨微观结构模型描述的发展历程,总结了前人在骨骼微观结构模型上的工作。进一步介绍了密质骨材料性质、松质骨材料性质与其相关参数之间的关系。最后概述了本篇的研究工作。
第二章详细描述了骨的结构和性质。骨的结构与性质是本篇研究的一个着手点,这里从骨的最基础的知识出发,阐述了骨的基本结构与性质。骨的结构涉及到骨的宏观结构-密质骨和松质骨,编织骨、板状骨和哈弗氏骨结构以及分子水平的骨。骨的性质包括哈弗氏系统、密质骨和松质骨的力学性质。本章的内容是对上篇以至整个论文的补充和完善。
第三章详细介绍了复合材料宏观弹性常数计算的均匀化方法。均匀化理论是一种具
Biomechanics is mechanics applied to biology. Biomechanics is a marginal and crossed discipline, which is formed as a result of combination and convergence of mechanics, biology, physiology and other discipline. Biomechanics seeks to understand the mechanics of living systems. From the view of life individual, tissue, organ, cell and the different hiberarchy of molecule, it studies the relations between stress and motion, distortion, flow, and growth. Biomechanics helps us to realize the life, to observe the nature, to design and make many kinds of equipments to improve our life qualities. In the recent twenty years, research of biomechanics has been developed quickly. Up to date, the study of biomechanics has been in the climax, which is touched deeply in many fields of iatrology and biology medical engineering, especially in several new fields, such as tissue engineering, biological functional material and etc. Skeleton-muscle mechanics is one sub-field of the most being accepted by clinical medicine. The studies of bone mechanics have entered in the clinic operation in the America and Europe, but it is fragmentary and week in China. The research in the dissertation is one exploration and attempt of computational bone mechanics. We take human bone as object, are to study the computational methods of bone material mechanical properties, are to study the bone remodeling mechanism, are to process the mechanical analysis of steel plate internal fixation.The research in the dissertation consists of three parts. In the first part, the cell models of bone microstructure are based and the homogenization method is used to predict the mechanical properties of compact and cancellous bone. The relationship between the bone mechanical properties and the parameters of the bone microstructure is discussed here. In the second part, based on the reference strain energy theory, the reference strain theory, the adaptive elastic theory and the sensor cell adaptive theory, the numerical simulation methods of bone remodeling have been formed. The strain energy and strain value which can be gotten in FEM are taken as the stimulus then the rule of bone remodeling is applied. The numerical computational models based on the above remodeling theory are applies to process the remodeling numerical simulation of the two dimensional and three dimensional femur models. For the simple plate model of Lumbar vertebrae coronal surface, the outer geometrical shape and inner material distribution in the oldness and in the youngth are simulated. In the mean while, the four types of bone fracture plastic healing are simulated. In the third part, biomechanics is been combined with clinical operation. The method of mechanics is used to analyze bone fracture internal fixation operation qualitatively and quantificationally, which is the guard for internal fixation operation.The contents of the first, second, third part and every chapter are arranged in the following in detail.In chapter 1 of the first part, the experiment methods to test bone elastic constant are introduced and reviewed and the value of bone elastic modulus is given. Then the developing course of describing the microstructure of compact and cancellous bone is reviewed. And then,
the relationship between compact bone, cancellous bone and its relative parameters is introduced respectively. In the last, the works of this part are summarized.In chapter 2, the structure and property of the bone are described in details. The bone structure and property is the onset of the study of this part. From the basic knowledge of bone, the structure and property of bone are set forth. The structure of bone involves the macro structure-compact and cancellous bone, weave bone, lamellar bone Haversian bone and molecule level bone. The properties of bone include the mechanical properties of the haversian system, compact bone and cancellous bone. The content in this chapter is the complement of this part and the entire paper.In chapter 3, the homogenization method of predicting composite material macro elastic modulus is introduced in detail. The homogenization is one mathematic method with strict theory base, which is based on perturbation theory. Using the homogenization method, the reliant relationship between the microstructure and the composite macro properties can be formed. Using homogenization theory to predict mechanical properties of bone is a worth job, which is only in its beginning.In chapter 4, Six cell models are proposed to simulate the microstructures of trabecular bones, and the homogenization theory and finite element method are employed to calculate the macro-equivalent Young's modulus of trabecular bone. The macro-equivalent Young's modulus of different trabecular bones simulated by six cell models and their relations to the volume fraction ratio (VFR) of bone materials are computed and compared to the experimental data given in literatures. It is also discussed how to apply the cell models in different trabecular bones. The results show that the methods and six cell models proposed in this paper can simulate microstructures of trabecular bones and compute material properties effectively.In chapter 5, based on the four hierarchical model of compact bone proposed by Park (1979), the homogenization theory is applied and the first three levels are simulated. The knowledge of various bones, collagen and hydroxyapatite properties are considered during the numerical simulation of compact bone. The macroscopic material properties of compact bone can be computed from the above descending method of the models of hierarchical structure. The results are compared to the experiment data and it can be concluded from the numerical simulation of compact bone: effect of collagen Poission's ratio, effect of model describing a single lamella, effect of the lamellae structure and effect of the mineral content of osteon.In the second part, the bone remodeling mechanism is discussed and corresponding arithmetic is proposed, which is the key work in this dissertation.In chapter 1, the evolving of bone remodeling is treated detailedly. At first, the great meaning to study bone remodeling mechanism is given. Then several basic concepts of bone remodeling is introduced, which include the classify of bone remodeling, the type and function of cell. In the meanwhile, the existing bone remodeling theory is introduced. And then, the history of bone remodeling is reviewed, which includes the developing course of bone remodeling experiments, the discussion of bone remodeling stimulus and the developing course of bone remodeling theory and simulation. At last, the study content in this part is
given.In chapter 2, Combined with the finite element method, an optimization algorithm based on strain energy density criterion and strain criterion are proposed here for the numerical simulation of the internal remodeling of trabecular bones. The strain energy density is taken as the mechanical stimulus, and the bone remodeling is described with the change of material density distribution, which can represent the internal remodeling of trabecular bones. The numerical results of the remodeling simulation for a two-dimensional proximal femur, a three-dimensional proximal femur, and the plastic processing of bone fracture healing have been presented. The numerical results demonstrate that the method proposed here can effectively simulate the material density distribution and some effects of bone remodeling, and illuminate the mechanism of plastic processing of bone fracture healing well. In section 7, the case of existing dead zone is considered. In section 8, the effect of the value of reference strain and strain energy on bone remodeling is discussed. In chapter 9, the effect of bone remodeling coefficient on bone remodeling is discussed. All the results show the model and algorithm are both efficient.chapter 3 is the bone remodeling simulation based on the bone adaptive theory. The skeleton system of human is one most perfect functional adaptive system and it can be always in its optimal structure to adapt to mechanical environments. From this point of view, we study how bone material distribution is formed to satisfy the bone adaptive theory in the condition of limit of volume. The structural optimization method is applied to solve the reserve problem of material distribution and the bone remodeling rules and processes are simulated. SQL and criterion method are used. The numerical results show, the two algorithms both can simulate bone material distribution. More meaningful, for the simple plate model of Lumbar vertebrae coronal surface, the outer geometrical shape and inner material distribution in the oldness and in the youngth are simulated, which accord with the actual situation. In section 7, the time dependency of bone remodeling damping coefficient is considered.In chapter 4, the bone remodeling simulation considering bone cell is processed. In the clinic or medicine, all the bone is through cell to feel external stimulus. When tissue cell which is connected with bone cell senses the stimulus from the pressure, the bone remodeling will take place. Every cell is taken as one receipt, and the concept of "the influencing scope of sensor" is utilized, the bone remodeling mechanism is studied. The simulation results show the theory and method are in effect. The rule of wolff is also validated.In the third part, biomechanics is combined with clinic operations.In chapter 1, the bone fracture and internal fixation basic are summarized first, which include bone fracture, the type of bone fracture, developing process of bone fracture internal fixation and several relative theory of internal fixation. Then the application of FEM to internal fixation is summed up. At last, the engineering background here is combined to explain the meaning of this part.In chapter2, It studies the effects of plate position to bending stiffness and stresses of plate-bone system in the internal fixation of bone surgery by means of the composite beam
引文
1 Y. C Fung. Biomechanics, The basic equication of biomechanics. University of California, San Diego, USA. 1990.
2 Y. C. Fung. Biomechanics, motion, flow, stress, and growth. University of California, San Diego, USA. 1990.
3 陶祖莱.生物力学导论.天津科技翻译出版社公司,1992.
4 冯元桢.固体力学研究的趋向和良机.俞稼磐译自:Appl. Mech. Rev. 1985, 10: 1251-1255.
5 曾其蕴等.生物复合材料的特征及仿生的探讨.复合材料学报,1993(3),10(1).
6 郑秀瑗等.运动生物力学进展,国防工业出版社,1998.
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2 Y. C. Fung. Biomechanics, motion, flow, stress, and growth. University of California, San Diego, USA. 1990.
3 陶祖莱.生物力学导论.天津科技翻译出版社公司,1992.
4 冯元桢.固体力学研究的趋向和良机.俞稼磐译自:Appl. Mech. Rev. 1985, 10: 1251-1255.
5 曾其蕴等.生物复合材料的特征及仿生的探讨.复合材料学报,1993(3),10(1).
6 郑秀瑗等.运动生物力学进展,国防工业出版社,1998.
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