Review of “Universal” Rules Governing Bone Composition, Organization, and Elasticity Across Organizational Hierarchies

Abstract

“Universal” organizational patterns in bone are reviewed and presented, in terms of mathematically expressed rules concerning the composition and elasticity of a large variety of tissues. Firstly, experimental data sets gained from dehydration-demineralization tests, dehydration-deorganification tests, and dehydration-ashing tests are thoroughly analyzed. On this basis, bilinear relations can be identified, between the mass density of the extracellular bone matrix on the one hand, and the apparent mass densities of its basic constituents (water, hydroxyapatite, and organic matter), on the other hand. Secondly, the question as to how hydroxyapatite is distributed in bone tissue is addressed. To that end, mass and volume measurements gained from wet, dehydrated, and demineralized tissue samples, as well as optical densities provided by transmission electron microscopy, are studied, confirming a rule on how the mineral is partitioned between fibrillar and extrafibrillar spaces in the ultrastructure of bone. Thirdly, a swelling rule for hydrating collagen is validated through processing of experimental data from X-ray diffraction, vacuum drying, and mass measurements, quantifying the change of the bone tissue composition upon hydration. And fourthly, application of the mass conservation law to extracellular bone matrix considered as closed thermodynamic system, allows for studying the change of bone tissue composition during mineralization. Finally, these compositional rules, which are shown to be “universally” valid throughout the vertebrate kingdom, enter a micromechanical homogenization scheme for upscaling the experimentally accessible elastic properties of the elementary mechanical building blocks of bone (hydroxyapatite minerals, type I collagen, and water with non-collageneous organics) to the macroscopic scale of cortical and trabecular bone.