Specimen-specific multi-scale model for the anisotropic elastic constants of human cortical bone

Abstract

The anisotropic elastic constants of human cortical bone were predicted using a specimen-specific micromechanical model that accounted for structural parameters across multiple length scales. At the nano-scale, the elastic constants of the mineralized collagen fibril were estimated from measured volume fractions of the constituent phases, namely apatite crystals and Type I collagen. The elastic constants of the extracellular matrix (ECM) were predicted using the measured orientation distribution function (ODF) for the apatite crystals to average the contribution of misoriented mineralized collagen fibrils. Finally, the elastic constants of cortical bone tissue were determined by accounting for the measured volume fraction of Haversian porosity within the ECM. Model predictions using the measured apatite crystal ODF were not statistically different from experimental measurements for both the magnitude and anisotropy of elastic constants. In contrast, model predictions using common idealized assumptions of perfectly aligned or randomly oriented apatite crystals were significantly different from the experimental measurements. A sensitivity analysis indicated that the apatite crystal volume fraction and ODF were the most influential structural parameters affecting model predictions of the magnitude and anisotropy, respectively, of elastic constants.

Elasticity–density and viscoelasticity–density relationships at the tibia mid-diaphysis assessed from resonant ultrasound spectroscopy measurements

“…Many multiscale cortical bone models have been proposed to derive mesoscale elastic properties based on a more or less large number of parameters (e.g., Crolet et al 1993;Hellmich and Ulm 2004;Dong and Guo 2006;Deuerling et al 2009;. These parameters describe the composition and the microstructure (collagen or mineral orientation, osteon size, relative volumes of osteonal and interstitial tissues, types of porosities, etc.)…”

Effect of porosity and mineral content on the elastic constants of cortical bone: a multiscale approach

“…Many researchers have recently addressed this problem by developing models, either analytical or numerical, of the elastic behavior of cortical bone (Deuerling et al 2009;Dong and Guo 2006;Ghanbari and Naghdabadi 2009;Kotha and Guzelsu 2007;Porter 2004;Sevostianov and Kachanov 2000). These models use homogenization techniques, some of them with a multiscale approach, but none gives a complete description of the hierarchical organization of cortical bone.…”

Stochastic multiscale modelling of cortical bone elasticity based on high-resolution imaging

“…2) and collagen orientation changes from one lamella to another (Reisinger et al 2011;Spiesz et al 2011;Granke et al 2013). Moreover, mineral particles (at the mineral foam scale) were assumed to be spherical whereas they are actually platelets with thickness of a few nanometres and length and width of a few to several tens of nanometres (Rho et al 1998;Deuerling et al 2009). While on the one hand our hypothesis of cylindrical pores at the tissue scale seems reasonable (Granke et al 2015), our assumptions at the lower scales (aligned collagen fibres and spherical mineral particles) may lead to inaccurate predictions (Deuerling et al 2009).…”

“…Moreover, mineral particles (at the mineral foam scale) were assumed to be spherical whereas they are actually platelets with thickness of a few nanometres and length and width of a few to several tens of nanometres (Rho et al 1998;Deuerling et al 2009). While on the one hand our hypothesis of cylindrical pores at the tissue scale seems reasonable (Granke et al 2015), our assumptions at the lower scales (aligned collagen fibres and spherical mineral particles) may lead to inaccurate predictions (Deuerling et al 2009). Other micro-and nanoscale features such as the morphology of the lacuno-canalicular network and the mineralisation at the nanoscale can affect bone elasticity, strength, and failure (Tai et al 2008;Langer et al 2012;Schrof et al 2014).…”