基于分形理论的人体骨微观结构仿生设计

背景:设计人体骨微观结构需建立一种能有效地描述其中的孔结构和连接体的模型,由于这些孔具有不规则的边界,而这种不规则性很可能就与功能有着密切的关系。分形理论能否有效的找出这些不规则结构中蕴含的规则性?目的:利用分形理论对人体骨微观结构进行了分形特性描述,根据分形维构造符合人体要求的微孔结构,利用快速成型制造技术,从仿生学的角度提出了一种新的人体骨微观结构三维建模设计方法。设计:计算机辅助仿生设计。单位:武汉理工大学生物中心。材料:实验于2005-01/06在武汉理工大学生物中心完成,材料为1名健康中年男性人体髋关节骨灰度图原始图。方法:对人体骨灰度图进行处理,提取其典型微孔结构的边缘轮廓,得到的人体骨边缘轮廓图。利用B样条作图原理将其矢量化。①利用分形理论,分析典型微孔结构的分形维数,结果用维数(D=2s,s为拟和直线的斜率)表示,找出微孔结构之间的内在联系。②在VC 下利用蒙特卡罗撒点法生成具有适当孔隙率的人体骨二维微观结构,利用快速成型分层制造技术生成三维结构模型。主要观察指标:①人体骨微观组织微孔结构的分形维数。②人体骨二维及三维模型建立结果。结果:①对具有代表性的孔进行了分维计算,得出这些维数值介于1.14～1.28之间,这些微孔结构的分维值是非常接近的,证明了人体骨边界轮廓具有自相似性。②得到了人体骨微观结构的二维模型,得到二维模型之后,利用快速成型分层制造技术生成了三维结构模型,在保证二维模型较大孔隙率的情况下,三维模型的孔隙率以及连通性均能达到较高要求,通过计算,该模型的孔隙率达到40%以上,能够实现层与层之间的相互贯通,满足设计要求。结论:从人体骨微观结构仿生型应该满足的基本要求入手,将分形理论应用于人体骨二维仿生模型建立。对人体骨灰度图及其典型微孔的边缘轮廓的分形特性进行了分析。利用VC 开发出适应组织工程的人体骨二维仿生微观结构的软件,同时将二维模型导入到三维软件中生成三维模型,最终生成符合人体骨功能的3维支架结构模型。

Bionic design of human bone microstructure based on fractal theory

BACKGROUND: The design of the microstructure of human bone is in fact to construct a model, which could characterize the connecting-porosity cell frame structure. As the porosity structure is represented as irregular curve, and this irregularity has close relationship with the bone function, does the fractal theory effectively find the irregularity containing in the irregular structure?OBJ ECTIVE: To analyze the microstructure of human bone by applying the fractal property, and construct the 3D model that has structural similarity to the natural bone. With the help of Rapid Prototyping technology, a new bionic technique instead of traditional modeling method is presented to model artificial human bone.DESIGN: Computer aided bionic design.SETTING: Biomaterials and Engineering Center of Wuhan University ofTechnoiogy.MATERIALS: The experiment was carried out in the Biomaterials and Engineering Center of Wuhan University of Technology from January to June 2005. The material is the original gray chart of hip joint of one healthy middle-aged male.METHODS: The contour of the human bone microstructure was obtained by exaltation and extraction of the grey chart.B-spline technique was used for vectorization. ①The fractal theory was adopted to compute the fractal dimension of typical aperture structure and the result was represented by dimensions (D=2s, s is the slope of fitting line) to find the inherent relation among apertures. ② Monte Carlo method was used to generate the two-dimensional model of microstructure of bone with the appropriate porosity. The 3D model was manufactured by rapid prototyping technology.MAIN OUTCOME MEASURES: ①Fractal dimension of porous structure of human bone; ② Results of 2D and 3D model of the microstructure of human bone.RESULTS: ①The fractal dimensions of some representative apertures were between 1.14and 1.28. The fractal dimensions of these micro-apertures are rather close, which testified the self-similarity in the edge contour of the microstructure of human bone. ②3D model was generated by cumulating the plane model layer by layer with the rapid prototyping technology. If the high porosity of plane model was ensured, the porosity and connectivity of 3D model could meet the high requirement. Through the computer simulating, the porosity of the model was greater than 40%, which meets the design requirement.CONCLUSION: Fractal theory is applied in the construction of 2D model of human bone based on the requirements in bionic design of the microstructure model of human bone. The fractal characteristics of the grey chart of human bone and the edge contourof its typical micropore are analyzed. The software suitable for 2D tissue engineered bionic microstructure of human bone is developed with VC++, meanwhile, 3D cell scaffold model is constructed by cumulating the planer model, which meets the human bone functions.