The effective elastic properties of human trabecular bone may be approximated using micro-finite element analyses of embedded volume elements

Abstract

word count: 249 Total word count: 3393Attachments: 5 figures and 2 tables + 1 figure and 4 tables in the appendices 2 Disclosure pageThe authors have no conflict of interest to report. AcknowledgmentsThe script manager Medtool (www.dr-pahr.at) was used to generate the µFE models, start the computations and analyse the results. The authors would like to thank Prof. Bert van Rietbergen for sharing the µCT data. Karol Daszkiewicz is supported by grants from the are also gratefully acknowledged. AbstractBoundary conditions (BCs) and sample size affect the measured elastic properties of cancellous bone. Samples too small to be representative appear stiffer under kinematic uniform BCs (KUBCs) than under periodicity-compatible mixed uniform BCs (PMUBCs). To avoid those effects, we propose to determine the effective properties of trabecular bone using an embedded configuration. Cubic samples of various sizes (2.63, 5.29, 7.96, 10.58 and 15.87 mm) were cropped from µCT scans of femoral heads and vertebral bodies. They were converted into µFE models and their stiffness tensor was established via six uniaxial and shear load cases. PMUBCs-and KUBCs-based tensors were determined for each sample. "In situ" stiffness tensors were also evaluated for the embedded configuration, i.e. when the loads were transmitted to the samples via a layer of trabecular bone. The Zysset-Curnier model accounting for bone volume fraction and fabric anisotropy was fitted to those stiffness tensors and model parameters ν0 (Poisson's ratio), E0 and µ0 (elastic and shear moduli) were compared between sizes. BCs and sample size had little impact on ν0. However, KUBCs-and PMUBCs-based E0 and µ0 respectively decreased and increased with growing size, though convergence was not reached even for our largest samples. Both BCs produced upper and lower bounds for the in situ values that were almost constant across samples dimensions, thus appearing as an approximation of the effective properties. PMUBCs seem also appropriate for mimicking the trabecular core, but they still underestimate its elastic properties (especially in shear) even for nearly orthotropic samples.

Explicit expressions for the estimation of the elastic constants of lamellar bone as a function of the volumetric mineral content using a multi-scale approach

“…In this process, it is necessary to assign material properties to the bone tissue and that is not a trivial issue. Usually, no direct influence of the mineral content is taken into account and typical isotropic elastic constants are considered (Ulrich et al, 1998;Roque et al, 2013;Daszkiewicz et al, 2017).…”

Using Non-linear Homogenization to Improve the Performance of Macroscopic Damage Models of Trabecular Bone

“…Therefore, a study completely based on numerical simulations is the only alternative even though the results cannot be currently validated experimentally. The use of kinematic uniform boundary conditions in the μFE analyses could also be considered a limitation, as they are known for providing an upper bound of the stiffness tensor (Pahr and Zysset, 2008 ; Wang et al, 2009 ) or macroscopic yield (Panyasantisuk et al, 2015 ), and may also affect the damage morphology when compared to the in situ case (Daszkiewicz et al, 2017 ). We also assume that the orthotropic directions do not rotate during loading, which may be a valid assumption for the considered range of strains.…”

An explicit micro‐FE approach to investigate the post‐yield behaviour of trabecular bone under large deformations

“…KUBCs showed a stiffer response especially at lower BV/TV values. Moreover, Daszkiewicz et al and Wili et al showed that apparent elastic and yield properties determined with PMUBCs are close to an embedded configuration of cubic RVEs of trabecular bone. Therefore, in the present study, PMUBCs are applied in the μFE analyses as well.…”