Bone fibrillogenesis and mineralization: Quantitative analysis and implications for tissue elasticity

Abstract

Data from bone drying, demineralization, and deorganification tests, collected over a time span of more than eighty years, evidence a myriad of different chemical compositions of different bone materials. However, careful analysis of the data, as to extract the chemical concentrations of hydroxyapatite, of water, and of organic material (mainly collagen) in the extracellular bone matrix, reveals an astonishing fact: it appears that there exists a unique bilinear relationship between organic concentration and mineral concentration, across different species, organs, and age groups, from early childhood to OLD AGE: During organ growth, the mineral concentration increases linearly with the organic concentration (which increases during fibrillogenesis), while from adulthood on, further increase of the mineral concentration is accompanied by a decrease in organic concentration. These relationships imply unique mass density-concentration laws for fibrillogenesis and mineralization, which -in combination with micromechanical models -deliver 'universal' mass density-elasticity relationships in extracellular bone matrix -valid across different species, organs, and ages. They turn out as quantitative reflections of the well-instrumented interplay of osteoblasts, osteoclasts, osteocytes, and their precursors, controlling, in a fine-tuned fashion, the chemical genesis and continuous transformation of the extracellular bone matrix. Considerations of the aformentioned rules may strongly affect the potential success of tissue engineering strategies, in particular when translating, via micromechanics, the aformentioned growth and mineralization characteristics into tissue-specific elastic properties.

Hierarchical analysis and multi-scale modelling of rat cortical and trabecular bone

“…For comparison, bone mineral, organic and water densities and bone volume fractions of the samples are plotted along with the results of other organs and species in the literature [21,79,[91][92][93][94][95][96][97] (figure 9). These plots were first reported by Vuong & Hellmich [97] to verify the universal relation among the bone constituents. As outlined in Vuong & Hellmich [97], The volume fractions of bone constituents (f min , f org and f wn ) versus extracellular bone density are shown in figure 9e.…”

Layered Water in Crystal Interfaces as Source for Bone Viscoelasticity: Arguments from a Multiscale Approach

“…While the answer is potentially 'yes', this was not the purpose of the work described herein. We are interested in the general understanding of the mechanical phenomena occurring in bone micro-and nanostructures; and in the present work, we have tackled the question whether the multiscale scheme for bone as given in Figure 2, which has been successfully validated by means of dehydration/demineralisation tests, diffraction tests, microscopic data and ultrasonic tests at different frequencies, as well as by quasi-static tests for elasticity and strength, see (Hellmich and Ulm 2003;Fritsch et al 2009;Vuong and Hellmich 2011), would also be valid for bone creep, by just introducing tissue independent, 'universal' viscous properties related to sliding along interfaces of layered water. The first results shown here are affirmative.…”

A multiscale analytical approach for bone remodeling simulations: Linking scales from collagen to trabeculae

“…from its mineral, collagen, and water contents. The latter were derived from age-dependent weight fractions of ash per mass of dry bone WF ash dry , as provided by Currey [32], through the following steps: First, the ash fraction was converted into a mineral fraction [33],…”

“…Then, the general compositional rules given in [33] give access to tissue mineral and collagen content at any age, see Table 2 for chosen ages between 6 and 13 years. The corresponding age-dependent volume fractions of mineral, water, and collagen components served as inputs for the 4-step micromechanical homogenization scheme developed in [33], from which the stiffness tensors for the extracellular bone matrix were obtained, see Fig. 3(b) and Table 3.…”

“…3. a) Apparent mass densities of water, hydroxyapatite, and organic matter, as functions of the overall mass density of extracellular bone matrix, according to [33]; b) four-step homogenization scheme after [33]. As far as the osteocyte mechanosensitivity is concerned, by comparing the two models the calculated difference were 11.7% (Figs.…”