A Theoretical Study on the Mechanical Significance of Mineralized Collagen Fibril Orientation in Osteonal Lamellar Bone

Abstract

In this study, the effect of orientation of mineralized collagen fibrils on bone mechanical properties relating to bone anisotropy was studied using data obtained from rehydrated lamellar bone samples. The dehydration-rehydration based and experimentally determined contraction, observed in orientations parallel and perpendicular to the osteonal axis was used to calculate bone anisotropy. The sublamellar bone model, with the layered mineralized collagen fibrils rotating at 5° was used. Following this model, the mineralized collagen layers were transformed at 5° relative to the orthogonal axes using a transform matrix. With dehydration, fibril diameter was reduced towards the mineral, forming contraction vectors. The x, y and z intercepts for these vectors were then calculated to give the u, v and w displacements, which gave anisotropy ratios ranging from 0.15266 to 6.55054. Compared with the experimental nanoindentation findings in the literature, there may be an indication of a correlation with the results of sublamellar arrangement at 20° angles. As the lateral indentation used in the anisotropy experiments may involve varying amounts of u and v displacements, the aspect angle of lateral indentation was evaluated in relation to the structural features of the model. This evaluation indicated the larger contribution of v displacement and thus relatively much smaller contribution of u displacement to lateral contraction. These findings indicate the significant effect of the mineralized collagen fibril arrangement on bone anisotropy.

Keywords

• contraction
• mineralized collagen fibril orientation
• anisotropy ratio
• transformation matrix
• anizotropi oranları
• transformasyon matrisi
• büzülme vektörü
• mineralize kolajen fibrili yönlenmesi