Article

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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    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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    • "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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