图像分形法研究多孔骨支架微观形态

Study on Bone Scaffolds Microstructure Based on Fractal Methodology

为了研究多孔材料微观形态特征:孔隙率、渗透率的数学模型,为进一步研究数值仿真提供基础数学模型.采用分形数学和图形图像处理技术深入开展多孔材料分形维数研究.通过分形维数推导出多孔材料孔隙率φ,渗透率K的数学表达式;通过对6种羟基磷灰石骨支架微观形态的研究,得到6种骨支架的孔隙率、渗透率.通过与密度法得出的孔隙率对比研究,表明图形图像法得到的孔隙率数学模型行之有效,同时能从理论上计算出孔隙率和渗透率,简化了测量实验方法以及为多孔材料的数值分析奠定数学模型基础.

Bone scaffolds microstructure including the mathematical model expressions of porosity and permeability is studied to provide mathematical models for numerical analysis. Based on the fractal mathematical theory and the image processing technology, the authors have deeply investigated bone scaffolds microstrueture and have established the bone scaffolds porous medium fraetal dimension, porosity, permeability mathematical models. The bone＇s fractal dimension, porosity and permeability of the 6 bone scaffolds models have been computed through the fractal software and image process technique. Through comparing the porosity results based on the demonstrated mathematical model to the porosity on density method experiment, this method is proved effective. The computation results indicate that this theory methodology may apply artificial bone scaffolds numerical analysis research. It can not only provide the microstructure for the artificial bone scaffolds design, instruction, but may also provide the foundation of important parameters formulae for porosity, permeability analytic expression in multi-physics coupling seepage analytical theory.