Specimen-specific beam models for fast and accurate prediction of human trabecular bone mechanical properties

Institute for Biomedical Engineering, University and ETH Zürich, Moussonstrasse 18, 8044 Zürich, Switzerland.
Bone (Impact Factor: 4.46). 01/2007; 39(6):1182-9. DOI: 10.1016/j.bone.2006.06.033
Source: PubMed

ABSTRACT Direct assessment of bone competence in vivo is not possible, hence, it is inevitable to predict it using appropriate simulation techniques. Although accurate estimates of bone competence can be obtained from micro-finite element models (muFE), it is at the expense of large computer efforts. In this study, we investigated the application of structural idealizations to represent individual trabeculae by single elements. The objective was to implement and validate this technique. We scanned 42 human vertebral bone samples (10 mm height, 8 mm diameter) with micro-computed tomography using a 20 microm resolution. After scanning, direct mechanical testing was performed. Topological classification and dilation-based algorithms were used to identify individual rods and plates. Two FE models were created for each specimen. In the first one, each rod-like trabecula was modeled with one thickness-matched beam; each plate-like trabecula was modeled with several beams. From a simulated compression test, assuming one isotropic tissue modulus for all elements, the apparent stiffness was calculated. After reducing the voxel size to 40 microm, a second FE model was created using a standard voxel conversion technique. Again, one tissue modulus was assumed for all elements in all models, and a compression test was simulated. Bone volume fraction ranged from 3.7% to 19.5%; Young's moduli from 43 MPa to 649 MPa. Both models predicted measured apparent moduli equally well (R2 = 0.85), and were in excellent agreement with each other (R2 = 0.97). Tissue modulus was estimated at 9.0 GPa and 10.7 GPa for the beam FE and voxel FE models, respectively. On average, the beam models were solved in 219 s, reducing CPU usage up to 1150-fold as compared to 40 microm voxel FE models. Relative to 20 microm voxel models 10,000-fold reductions can be expected. The presented beam FE model is an abstraction of the intricate real trabecular structure using simple cylindrical beam elements. Nevertheless, it enabled an accurate prediction of global mechanical properties of microstructural bone. The strong reduction in CPU time provides the means to increase throughput, to analyze multiple loading configuration and to increase sample size, without increasing computational costs. With upcoming in vivo high-resolution imaging systems, this model has the potential to become a standard for mechanical characterization of bone.

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Available from: Harry Van Lenthe, Jul 30, 2015
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    • "Both phenomenological and mechanistic formulations of mechanical adaptation of bone have been developed for further understanding this adaptive response (Doblare and Garcia, 2002; Ruimerman et al., 2005; Vahdati and Rouhi, 2009; Jacobs et al., 1997; Tsubota et al., 2009; Beaupre et al., 1990). The mathematical descriptions of mechanically-induced bone adaptation when combined with subject-specific modeling have the potential for being important predictive tools, providing insight into bone remodeling around implants, fracture risk, pre-surgical planning, and mechanical causes of bone pathologies such as osteoporosis (Lenaerts and van Lenthe, 2009; van Lenthe et al., 2006). Particularly in recent years, there has been a paradigm shift from evaluation of medical interventions in the average patient to personalized medicine and tailored therapeutics. "
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    ABSTRACT: The typical bone density patterns in the proximal femur can be explained using bone remodeling simulations incorporating a load-adaptive response. Yet, subject-specific variations in bone density have not received much attention. Therefore, the objective of this study was to quantify to what extent subject-specific bone geometry and subject-specific musculoskeletal loading affect the predicted bone density distribution. To accomplish this goal, a computational bone remodeling scheme was combined with gait analysis and a subject-specific musculoskeletal model. Finite element models incorporating the subject-specific geometry as well as the subject-specific hip contact forces and associated muscle forces were used to predict the density distribution in the proximal femur of three individuals. Next, the subject-specific musculoskeletal loads were interchanged between the subjects and the resulting changes in bone remodeling of the proximal femur were analyzed. Simulations results were compared to computed tomography (CT) image-based density profiles. The results confirm that the predicted bone density distribution in the proximal femur is drastically influenced by the inclusion of subject-specific loading, i.e. hip contact forces and muscle forces calculated based on gait analysis data and musculoskeletal modeling. This factor dominated the effect of individualized geometry. We conclude that when predicting femoral density distribution in patients, the effect of subject-specific differences in loading conditions of the hip joint and the associated difference in muscle forces needs to be accounted for.
    12/2013; 30C:244-252. DOI:10.1016/j.jmbbm.2013.11.015
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    • "Nonlinear FE analysis for a 5.6 Â 5.6 Â 5.6 mm 3 trabecular bone cube can be done within 14 s by a PC using the HR-pQCT-based PR model, which requires 5 h using the HRpQCT-based voxel model and 246 h using lCT-based voxel model (unpublished work). There have been other groups trying to assess the mechanical properties of trabecular bone using beam-shell or beam FE models [9] [10]. They have demonstrated the excellent predictive power of the beam-shell model in estimating the elastic modulus by linear FE analysis with an average 33- fold reduction in CPU time. "
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    ABSTRACT: Currently, specimen-specific micro finite element (μFE) analysis based micro computed tomography (μCT) images have become a major computational tool for the assessment of the mechanical properties of human trabecular bone. Despite the fine characterization of the three-dimensional (3D) trabecular microstructure based on high-resolution μCT images, conventional μFE models with each voxel converted to an element are not efficient in predicting the nonlinear failure behavior of bone due to a prohibitive computational cost. Recently, a highly efficient individual trabecula segmentation (ITS)-based plate and rod (PR) modeling technique has been developed by substituting individual plates and rods with shell and beam elements, respectively. In this technical brief, the accuracy of novel PR μFE models was examined in idealized microstructure models over a broad range of trabecular thicknesses. The Young's modulus and yield strength predicted by simplified PR models strongly correlated with those of voxel models at various voxel sizes. The conversion from voxel models to PR models resulted in an ∼762-fold reduction in the largest model size and significantly accelerated the nonlinear FE analysis. The excellent predictive power of the PR μFE models, demonstrated in an idealized trabecular microstructure, provided a quantitative mechanical basis for this promising tool for an accurate and efficient assessment of trabecular bone mechanics and fracture risk.
    Journal of Biomechanical Engineering 04/2013; 135(4):44502. DOI:10.1115/1.4023983 · 1.75 Impact Factor
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    • "The simple rod-like geometry of the samples and the presented local strain analysis allowed us to correlate whitening (micro-damage), with tensile strains and to quantitatively determine the tensile strain needed for damage initiation. Our experiments complements efforts in FEA of trabecular bone structures (Williams and Lewis, 1982; Dagan et al., 2004; Nagaraja et al., 2005; Shefelbine et al., 2005; van Lenthe et al., 2006) by providing important data for formulation of a future damage model with solid experimental foundation. From our results we propose that damage in trabecular bone tissue forms asymmetric with microdamage originating at tensile strains of 0.7%–2.5%. "
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    ABSTRACT: The use of bone mineral density as a surrogate to diagnose bone fracture risk in individuals is of limited value. However, there is growing evidence that information on trabecular microarchitecture can improve the assessment of fracture risk. One current strategy is to exploit finite element analysis (FEA) applied to 3D image data of several mm-sized trabecular bone structures obtained from non-invasive imaging modalities for the prediction of apparent mechanical properties. However, there is a lack of FE damage models, based on solid experimental facts, which are needed to validate such approaches and to provide criteria marking elastic-plastic deformation transitions as well as microdamage initiation and accumulation. In this communication, we present a strategy that could elegantly lead to future damage models for FEA: direct measurements of local strains involved in microdamage initiation and plastic deformation in single trabeculae. We use digital image correlation to link stress whitening in bone, reported to be correlated to microdamage, to quantitative local strain values. Our results show that the whitening zones, i.e. damage formation, in the presented loading case of a three-point bending test correlate best with areas of elevated tensile strains oriented parallel to the long axis of the samples. The average local strains along this axis were determined to be (1.6±0.9)% at whitening onset and (12±4)% just prior to failure. Overall, our data suggest that damage initiation in trabecular bone is asymmetric in tension and compression, with failure originating and propagating over a large range of tensile strains.
    05/2011; 4(4):523-34. DOI:10.1016/j.jmbbm.2010.12.009
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