Mineral-collagen interactions in elasticity of bone ultrastructure a continuum micromechanics approach

摘要

The organization of the elementary components within the ultrastructure of mineralized tissues (bone and mineralized tendons) has provoked some controversy; especially with regard to its impact on the mechanical properties of the ultrastructure. Herein, we aim at shedding some light on the issue, by developing and verifying three different continuum-micromechanics representations of the collagen-mineral interaction in the elasticity of mineralized tissues: (ⅰ) mineral foam matrix with collagen inclusions, (ⅱ) interpenetrating network of hydroxyapaptite crystals and collagen molecules, (ⅲ) composite of fibrils (collagen-hydroxyapatite network) embedded in a collagen-free extrafibrillar mineral foam matrix. The validation of the different concepts, based on independent sets of experiments, shows remarkable predictive capabilites of the different micromechanical representations. Still, there are significant differences in the performance of these three different micromechanical concepts, related to the sophistication with which the ultrastructure of bone is modelled. Consideration of the fibrillar organization of bone ultrastructure improves over simpler concepts like an interpenetrating network of mineral crystals and collagen molecules, which in turn is superior to a crystal-foam representation with collagen inclusions. In fact, the most advanced concept treated here integrates the two others to a consistent whole: Each fibril is regarded as an interpenetrating network of collagen molecules and mineral crystals. The fibrils host the minority of the mineral crystals present in the tissues. At a higher observation scale, the fibrils function as templates or reinforcement in an extrafibrillar crystal foam-type matrix, which hosts the majority of the minerals present in the bone ultrastructure. The reinforcement function corresponds to low-mineralized tissues (such as deer antler) where the extrafibrillar mineral foam is softer than the fibrils, whereas the template function corresponds to high-mineralized tissues (such as cow tibia) where the extrafibrillar mineral foam is stiffer than the fibrils. The collagen is clearly represented as the governing element in inducing the anisotropy of the tissues, by (ⅰ) the anisotropy of molecular collagen itself, (ⅱ) the anisotropy of the fibrils, and (ⅲ) the oriented morphology of the cylindrical fibrils in the isotropic extrafibrillar space.