Search

14 www.nature.com/bonekey P33 Wolff’s Law and the Interplay between Bone Structure and External Loading Davide Ruffoni1, Patrik Christen2, Heike Scherf3, Richard Weinkamer4 1Department of Aerospace and Mechanical Engineering, University of Liege, Liege, Belgium, 2Institute for Biomechanics, ETH Zurich, Zurich, Switzerland, 3Institute for Archaeological Sciences, University of Tubingen, Tubingen, Germany, 4Department of Biomaterials, Max Planck Institute of Colloids and Interfaces, Potsdam, Germany

Bone is a complex material which exhibits several hierarchical levels of structural organization. At the submicron-scale, the local tissue porosity gives rise to discontinuities in the bone matrix which have been shown to influence damage behavior. Computational tools to model the damage behavior of bone at different length scales are mostly based on finite element (FE) analysis, with a range of algorithms developed for this purpose. Although the local mechanical behavior of bone tissue is influenced by microstructural features such as bone canals and osteocyte lacunae, they are often not considered in FE damage models due to the high computational cost required to simulate across several length scales, i.e., from the loads applied at the organ level down to the stresses and strains around bone canals and osteocyte lacunae. Hence, the aim of the current study was twofold: First, a multilevel FE framework was developed to compute, starting from the loads applied at the whole bone scale, the local mechanical forces acting at the micrometer and submicrometer level. Second, three simple microdamage simulation procedures based on element removal were developed and applied to bone samples at the submicrometer-scale, where cortical microporosity is included. The present microdamage algorithm produced a qualitatively analogous behavior to previous experimental tests based on stepwise mechanical compression combined with in situ synchrotron radiation computed tomography. Our results demonstrate the feasibility of simulating microdamage at a physiologically relevant scale using an image-based meshing technique and multilevel FE analysis; this allows relating microdamage behavior to intracortical bone microstructure.

The determining factors for the fixation of uncemented screws in bone are the bone-implant interface and the peri-implant bone. The goal of this work was to explore the role of the peri-implant bone architecture on the mechanics of the bone-implant system. In particular, the specific aims of the study were to investigate: (i) the impact of the different architectural parameters, (ii) the effects of disorder, and (iii) the deformations in the peri-implant region. A three-dimensional beam lattice model to describe trabecular bone was developed. Various microstructural features of the lattice were varied in a systematic way. Implant pull-out tests were simulated, and the stiffness and strength of the bone-implant system were computed. The results indicated that the strongest decrease in pull-out strength was obtained by trabecular thinning, whereas pull-out stiffness was mostly affected by trabecular removal. These findings could be explained by investigating the peri-implant deformation field. For small implant displacements, a large amount of trabeculae in the peri-implant region were involved in the load transfer from implant to bone. Therefore, trabecular removal in this region had a strong negative effect on pull-out stiffness. Conversely, at higher displacements, deformations mainly localized in the trabeculae in contact with the implant; hence, thinning those trabeculae produced the strongest decrease in the strength of the system. Although idealized, the current approach is helpful for a mechanical understanding of the role played by peri-implant bone.

On a sub-millimeter length scale, bone is a very heterogeneous material with varying mineral content. This heterogeneity can be measured by quantitative backscattered electron imaging (qBEI) and quantified by a probability distribution called the bone mineralization density distribution (BMDD). The stochastic nature of the backscattering of electrons during the measurement makes the results dependent on the acquisition time. In this work the influence of the measurement conditions was quantified and was corrected for using Tikhonov regularization. Deconvolution reduces the width of the BMDD and allows a more precise definition of a reference BMDD for healthy adults. The corrected information was used as input for a mathematical model that predicts the time evolution of the BMDD. Simulations of osteoporosis treatment reveal a double peak in the BMDD that is not observed in experiments due to limited acquisition time. Our method allows determining the necessary acquisition time to resolve such double peaks.