基于分形理论的骨支架微观形态建模

Applying Fractal Methodology to Establishing Bone Scaffold Microstructure Models

骨支架微观结构数学模型表达式的缺乏,制约着人工骨在数值仿真方面的研究和进展。文章基于分形数学理论和图像处理技术深入研究骨支架的微观形态,建立了骨支架多孔介质分形维数、孔隙率、渗透率和比表面积的数学模型;通过分形软件和图像处理试验计算医用异体骨的分形维数、孔隙率并根据密度法试验证明该方法行之有效,随之得出渗透率和比表面积数值。结果表明,基于分形理论的多孔介质数学模型可以应用于人工骨支架的数值分析研究,能够为人工骨多孔支架设计和多场耦合分析研究提供微观孔结构的理论指导,还可为骨支架多物理场耦合有限元分析提供基础参数解析表达式和广义有效弹性模量计算理论。

Aim.The introduction of the full paper points out that lacking models restricts numerical analysis of bone scaffold microstructure.Section 1 establishes the three mathematical models of porous media in terms of porosity,permeability and specific surface area respectively.Subsection 1.1 uses the fractal geometrical method to explore the self-similarity scale relationships among the specific surface area,volume and quality of a porous fractal sample,thus deriving eq.（7）.Subsection 1.2 uses the fractal dimensions to calculate the permeability of the porous media with eq.（12）.Subsection 1.3 derives eq.（17） to calculate the specific surface area.Section 2 applies the fractal methodology to analyzing the bone scaffold microstructure.Its core consists of：（2） we use the fractal software and the image processing technique to calculate the bone scaffold＇s fractal dimensions,whose calculated results are given in Table 1;（3） we use the mathematical models to calculate the porosity,permeability and specific surface area,whose calculated results are presented in Tables 2,3 and 4 respectively.The calculated results show preliminarily that,compared with other calculation methods,our calculation method is effective.