On the relationship between the microstructure of bone and its mechanical stiffness

Abstract

A recent study of bone structure shows that the plate-shaped carbonate apatite crystals in individual lamellae are arranged in layers across the lamellae, and that the orientation of these layers are different in alternate lamellae. Based on these findings, a new micromechanical model for the Young's modulus of bone is proposed, which accounts for the anisotropy and geometrical characteristics of the material. The model incorporates the platelet-like geometry of the basic reinforcing unit, the presence of alternating thin and thick lamellae, and the orientations of the crystal platelets in the lamellae. The thin and thick lamellae are modeled as orthotropic composite layers made up of thin rectangular apatite platelets within a collagen matrix, and classical orthotropic elasticity theory is used to calculate the Young's modulus of the lamellae. Bone is viewed as an assembly of such orthotropic lamellae bent into cylindrical structures, and having a constant, alternating angle between successive lamellae. The micromechanical model employs a modified rule-of-mixtures to account for the two types of lamellae. The model provides a curve similar to the published experimental data on the angular dependence of Young's modulus, including a local maximum at an angle between 0 and 90°. A rigorous testing of the model awaits additional experimental data.