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Research Papers

A Patient-Specific Computer Tomography-Based Finite Element Methodology to Calculate the Six Dimensional Stiffness Matrix of Human Vertebral Bodies

[+] Author and Article Information
Yan Chevalier1

Orthopedics Department, University Hospital Grosshadern, Laboratory for Biomechanics and Experimental Orthopedics, Marchioninistrasse 23, D- 81377 Munich, Germany;  Institute of Lightweight Design and Structural Biomechanics, Gußhausstraße, 27-29, A-1040 Vienna, Austriayan.chevalier@med.uni-muenchen.de

Philippe K. Zysset

Institute of Surgical Technology and Biomechanics,  University of Bern, Stauffacherstrasse 78, CH-3014 Bern, Switzerland; Institute of Lightweight Design and Structural Biomechanics, Gußhausstraße, 27-29 A-1040 Vienna, Austriaphilippe.zysset@itsb.unibe.ch

1

Corresponding author.

J Biomech Eng 134(5), 051006 (Jun 05, 2012) (6 pages) doi:10.1115/1.4006688 History: Received February 01, 2012; Revised March 05, 2012; Posted May 01, 2012; Published June 05, 2012

In most finite element (FE) studies of vertebral bodies, axial compression is the loading mode of choice to investigate structural properties, but this might not adequately reflect the various loads to which the spine is subjected during daily activities or the increased fracture risk associated with shearing or bending loads. This work aims at proposing a patient-specific computer tomography (CT)-based methodology, using the currently most advanced, clinically applicable finite element approach to perform a structural investigation of the vertebral body by calculation of its full six dimensional (6D) stiffness matrix. FE models were created from voxel images after smoothing of the peripheral voxels and extrusion of a cortical shell, with material laws describing heterogeneous, anisotropic elasticity for trabecular bone, isotropic elasticity for the cortex based on experimental data. Validated against experimental axial stiffness, these models were loaded in the six canonical modes and their 6D stiffness matrix calculated. Results show that, on average, the major vertebral rigidities correlated well or excellently with the axial rigidity but that weaker correlations were observed for the minor coupling rigidities and for the image-based density measurements. This suggests that axial rigidity is representative of the overall stiffness of the vertebral body and that finite element analysis brings more insight in vertebral fragility than densitometric approaches. Finally, this extended patient-specific FE methodology provides a more complete quantification of structural properties for clinical studies at the spine.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Creation of the smoothed voxel models (SVM) from the HR-pQCT images, after recoarsening, smoothing of peripheral elements, and addition of a cortical shell of constant thickness

Grahic Jump Location
Figure 2

The three translations and three rotations individually applied on the smooth voxel-based finite element models of vertebral bodies to investigate their stiffness properties along the main anatomical axes

Grahic Jump Location
Figure 3

Reaction forces and moments resulting from an applied load case of lateral shear (applied displacement δ1): (a) Lateral force; (b) anterior force; (c) axial force; (d) anterior bending moment; (e) lateral bending moment; (f) axial moment. The related stiffness components are computed as the initial slope of each curve, shown by the red lines in these graphs.

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