A Study On The Mechanical Property And Permeability Of Porous Fractal Bone Scaffold

Objective: Traditional methods of repairing bone injury have many drawbacks,such as,limited resources of autogenous bone transplantation,immune rejection to the material of allogeneic bone graft.Allograft also faces ethical issues.Emerging tissue engineering provides an effective method for bone tissue repair.As one of the important factors in bone tissue engineering(BTE),the design of bone scaffolds is particularly important.An excellent scaffold requires proper geometry(porosity,pore size,etc.),physical properties(mechanics,infiltration,etc.)properties,and biological properties in order to provide porosity,mechanical strength,permeability coefficient and material transport capabilities that matches that of natural bone tissue,and to provide a suitable biological environment for cell proliferation,differentiation,and migration.Natural bone tissue is a complex anisotropic porous structure with a certain degree of self-similarity.This complex bone structure is difficult to describe using traditional Euclidean geometry,but fractal-based non-Euclidean geometry is often used to describe the geometrical characteristics of irregular porous structures.So this paper has constructed a hierarchical scaffold with certain self-similar properties.The fractal dimension of the scaffold was calculated,and the relation of the fractal dimension to the mechanical and permeable properties were studied.Method: Firstly,the one-level(3 groups)and two-level(3 groups)scaffolds with structural transversely isotropy are constructed by controlling the anisotropic coefficient of structure and the pore size of one-level structure,and the fractal dimension of the structure is calculated using the calculation method of the complex porous media.Secondly,using the commercial finite element software,ABAQUS,to numerically study the mechanical properties of the scaffold structure.Based on the knowledge of structural mechanics,the relationship of the structural elastic modulus,yield strength and their anisotropies to the structural fractal dimension were obtained.Finally,the commercial finite element software,FLUENT,was used to numerically study the permeability characteristics of the scaffold.Based on Darcy’s law,the relationship of the structural permeability coefficient and its anisotropy to the fractal dimension were obtained.The effect of wall shear stress of the scaffold effect of was also discussed.Result: When the structural anisotropy coefficient is fixed and the pore size of one-level structure is changed,elastic modulus and yield strength,in axial and transverse directions,of one-level and two-level scaffold are positively correlated with the fractal dimension,while the permeability coefficient is negatively correlated with the fractal dimension.When the pore size of one-level structure is fixed and the structural anisotropy coefficient is changed,the anisotropy of elastic modulus and yield strength of two-level are all greater than that of one-level,while the anisotropy of the permeability coefficient of two-level is smaller.With the increase of the anisotropic coefficient,their anisotropies also increase.In addition,the maximum wall shear stress of all two-level is around 1 mPa,which is beneficial to the growth of osteoblasts(Bancroft et al.,PNAS,2002,99(20): 12600-12605).Conclusion: By increasing the anisotropic coefficient and fractal dimension of the scaffold,a greater anisotropy can be obtained.At the same time,elastic modulus,yield strength,permeability coefficient and wall shear stress can be controlled by adjusting the structure series and the pore size of one-level.Therefore,for bone tissues in different physiological positions,there are certain differences in the mechanical characteristics and permeability characteristics.In the scaffold design,the fractal structure can be constructed according to the damaged bone tissue to meet the needs of bone tissue regeneration.