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Research Papers

The Role of Cortical Shell and Trabecular Fabric in Finite Element Analysis of the Human Vertebral Body

[+] Author and Article Information
Yan Chevalier1

Institute of Lightweight Design and Structural Biomechanics, Vienna University of Technology, Gusshausstrasse 27-29, 1040 Vienna, Austriayan@ilsb.tuwien.ac.at

Dieter Pahr, Philippe K. Zysset

Institute of Lightweight Design and Structural Biomechanics, Vienna University of Technology, Gusshausstrasse 27-29, 1040 Vienna, Austria

1

Corresponding author.

J Biomech Eng 131(11), 111003 (Oct 16, 2009) (12 pages) doi:10.1115/1.3212097 History: Received September 03, 2008; Revised May 20, 2009; Published October 16, 2009

Classical finite element (FE) models can estimate vertebral stiffness and strength with much lower computational costs than μFE analyses, but the accuracy of these models rely on calibrated material properties that are not necessarily consistent with experimental results. In general, trabecular bone material properties are scaled with computer tomography (CT) density alone, without accounting for local variations in anisotropy or micro-architecture. Moreover, the cortex is often omitted or assigned with a constant thickness. In this work, voxel FE models, as well as surface-based homogenized FE models with topologically-conformed geometry and assigned with experimentally validated properties for bone, were developed from a series of 12 specimens tested up to failure. The effects of changing from a digital mesh to a smooth mesh, including a cortex of variable thickness and/or including heterogeneous trabecular fabric, were investigated. In each case, FE predictions of vertebral stiffness and strength were compared with the experimental gold-standard, and changes in elastic strain energy density and damage distributions were reported. The results showed that a smooth mesh effectively removed zones of artificial damage locations occurring in the ragged edges of the digital mesh. Adding an explicit cortex stiffened and strengthened the models, unloading the trabecular centrum while increasing the correlations to experimental stiffness and strength. Further addition of heterogeneous fabric improved the correlations to stiffness (R2=0.72) and strength (R2=0.89) and moved the damage locations closer to the vertebral endplates, following the local trabecular orientations. It was furthermore demonstrated that predictions of vertebral stiffness and strength of homogenized FE models with topologically-conformed cortical shell and heterogeneous trabecular fabric correlated well with experimental measurements, after assigning purely experimental data for bone without further calibration of material laws at the macroscale of bone. This study successfully demonstrated the limitations of current classical FE methods and provided valuable insights into the damage mechanisms of vertebral bodies.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Setup used for uniaxial compression testing of vertebral bodies embedded with disks of polymethylmethacrylate

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Figure 2

High-resolution peripheral CT scan images at 82 μm of vertebral bodies (a) were used to create two types of finite element models: (1) surface-based homogenized models (in (b)) including a topologically-conformed cortical shell and HRpQCT-based heterogeneous fabric that was used along with density to define the cancellous core properties; (2) voxel models (in (c)) generated from a previously described methodology (14) with density-based properties and fabric assumed to be constant in the superior-inferior direction

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Figure 3

For the corresponding 82 μm HRpQCT image of selected specimens, the map of main principal directions of the trabecular centrum calculated with the MIL method for the surface-based model SMF+C, as well as the BV/TV maps for the voxel method and smooth methods. The principal orientations are displayed in the midsagittal section, with the additional color scale of the vectors referring to the magnitude of the elastic modulus in the principal direction.

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Figure 4

(a) Example of predicted response of one model and the corresponding experimental measurement of a typical vertebral body (A-L4) in uniaxial compression. (b) Predicted force-displacement curves for the four types of models for the same typical vertebral body.

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Figure 5

Correlations between FE and in vitro vertebral stiffness for (a) voxel FE models and surface-based FE models with (b) constant fabric and no explicit cortex; (c) constant fabric and explicit cortex; and (d) HRpQCT-based heterogeneous fabric and explicit cortex

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Figure 6

Correlations between FE and in vitro vertebral strength for (a) voxel FE models and surface-based FE models with (b) constant fabric and no explicit cortex; (c) constant fabric and explicit cortex; and (d) HRpQCT-based heterogeneous fabric and explicit cortex

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Figure 7

Elastic strain energy density distributions at maximum force for selected vertebral bodies in uniaxial compression, modeled with voxel method (VMTI) and constant TI fabric, surface-based method with constant TI fabric (SMTI), surface-based method with constant TI fabric and explicit cortex (SMTI+C), and surface-based method with heterogeneous fabric and cortical shell (SMF+C)

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Figure 8

Damage distributions at maximum force for selected vertebral bodies in uniaxial compression, modeled with voxel method (VMTI) and constant TI fabric, surface-based method with constant TI fabric (SMTI), surface-based method with constant TI fabric and explicit cortex (SMTI+C), and surface-based method with heterogeneous fabric and cortical shell (SMF+C)

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