Applying fractal methodology to establishing bone scaffold microstructure models

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.