Some Researches In Computational Bone Mechanics

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 isgiven.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...