Large-scale microstructural simulation of load-adaptive bone remodeling in whole human vertebrae.

Identification of individuals at risk of bone fractures remains challenging despite recent advances in bone strength assessment. In particular, the future degradation of the microstructure and load adaptation has been disregarded. Bone remodeling simulations have so far been restricted to small-volume samples. Here, we present a large-scale framework for predicting microstructural adaptation in whole human vertebrae. The load-adaptive bone remodeling simulations include estimations of appropriate bone loading of three load cases as boundary conditions with microfinite element analysis. Homeostatic adaptation of whole human vertebrae over a simulated period of 10 years is achieved with changes in bone volume fraction (BV/TV) of less than 5%. Evaluation on subvolumes shows that simplifying boundary conditions reduces the ability of the system to maintain trabecular structures when keeping remodeling parameters unchanged. By rotating the loading direction, adaptation toward new loading conditions could be induced. This framework shows the possibility of using large-scale bone remodeling simulations toward a more accurate prediction of microstructural changes in whole human bones.

Modeling microdamage behavior of cortical bone.

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 Clinical Biomechanics Award 2012 - presented by the European Society of Biomechanics: large scale simulations of trabecular bone adaptation to loading and treatment.

BACKGROUND: Microstructural simulations of bone remodeling are particularly relevant in the clinical management of osteoporosis. Before a model can be applied in the clinics, a validation against controlled in vivo data is crucial. Here we present a strain-adaptive feedback algorithm for the simulation of trabecular bone remodeling in response to loading and pharmaceutical treatment and report on the results of the large-scale validation against in vivo data. METHODS: The algorithm follows the mechanostat principle and incorporates mechanical feedback, based on the local strain-energy density. For the validation, simulations of bone remodeling and adaptation in 180 osteopenic mice were performed. Permutations of the conditions for early (20th week) and late (26th week) loading of 8N or 0N, and treatments with bisphosphonates, or parathyroid hormone were simulated. Static and dynamic morphometry and local remodeling sites from in vivo and in silico studies were compared. FINDINGS: For each study an individual set of model parameters was selected. Trabecular bone volume fraction was chosen as an indicator of the accuracy of the simulations. Overall errors for this parameter were 0.1-4.5%. Other morphometric indices were simulated with errors of less than 19%. Dynamic morphometry was more difficult to predict, which resulted in significant differences from the experimental data. INTERPRETATION: We validated a new algorithm for the simulation of bone remodeling in trabecular bone. The results indicate that the simulations accurately reflect the effects of treatment and loading seen in respective experimental data, and, following adaptation to human data, could be transferred into clinics.

Deformable image registration and 3D strain mapping for the quantitative assessment of cortical bone microdamage.

The resistance to forming microcracks is a key factor for bone to withstand critical loads without fracturing. In this study, we investigated the initiation and propagation of microcracks in murine cortical bone by combining three-dimensional images from synchrotron radiation-based computed tomography and time-lapsed biomechanical testing to observe microdamage accumulation over time. Furthermore, a novel deformable image registration procedure utilizing digital volume correlation and demons image registration was introduced to compute 3D strain maps allowing characterization of the mechanical environment of the microcracks. The displacement and strain maps were validated in a priori tests. At an image resolution of 740 nm the spatial resolution of the strain maps was 10 µm (MTF), while the errors of the displacements and strains were 130 nm and 0.013, respectively. The strain maps revealed a complex interaction of the propagating microcracks with the bone microstructure. In particular, we could show that osteocyte lacunae play a dual role as stress concentrating features reducing bone strength, while at the same time contributing to the bone toughness by blunting the crack tip. We conclude that time-lapsed biomechanical imaging in combination with three-dimensional strain mapping is suitable for the investigation of crack initiation and propagation in many porous materials under various loading scenarios.