Bone Ultrastructure as Composite of Aligned Mineralized Collagen Fibrils Embedded Into a Porous Polycrystalline Matrix: Confirmation by Computational Electrodynamics

Abstract

Micromechanical representation of bone ultrastructure as a composite of aligned mineralized collagen fibrils embedded in a porous polycrystalline matrix has allowed for successfully predicting the (poro/visco-)elastic and strength properties of bone tissues throughout the entire vertebrate animal kingdom, based on the “universal” mechanical properties of the material's elementary components: molecular collagen, hydroxyapatite, and water-type fluids. We here check whether the explanatory power of this schematic representation might extend beyond the realm of mechanics; namely, toward electrodynamics and X-ray physics. This requires knowledge about the electron density distribution across the bone ultrastructure, reflecting the organization of collagen molecules, hydroxyapatite (mineral) crystals, and water with non-collageneous organics. The latter follow three principal, mathematically formulated, “universal” rules, namely (i) a unique bilinear relationship between mineral and collagen concentrations found in bone tissues throughout the vertebrate animal kingdom, (ii) the precipitation of mineral from a ionic solution under closed thermodynamic conditions, governing mass density-dependent lateral distances between the long collagen molecules, and (iii) the identity of the extracollageneous mineral concentration in the fibrillar and extrafibrillar, as well as in the gap and the overlap compartments of bone ultrastructure. The corresponding electron density distributions are then inserted into Fourier transform-type solutions of the Maxwell equations specified for a Small Angle X-ray Scattering setting. The aforementioned mineral distribution, as well as random fluctuations of fibrils, both within their transverse plane around a hexagonal lattice and in form of axial shifts, turn out to be the key for successfully predicting experimentally observed X-ray diffraction patterns. This marks a new level of quantitative, “mathematized” understanding of the organization of bone ultrastructure. In particular, earlier interpretations of SAXS data, leading to the idea of bone being a soft organic matrix with stiff mineral inclusions, may have been overcome, in favor of a more complex, but also more realistic modeling concept concerning the ultrastructural organization of bone.