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Research Papers

A New Material Mapping Procedure for Quantitative Computed Tomography-Based, Continuum Finite Element Analyses of the Vertebra

[+] Author and Article Information
Ginu U. Unnikrishnan, Elise F. Morgan

Orthopaedic and Developmental Biomechanics Laboratory, Department of Mechanical Engineering,  Boston University, Boston, MA 02215

J Biomech Eng 133(7), 071001 (Jul 13, 2011) (8 pages) doi:10.1115/1.4004190 History: Received July 22, 2010; Accepted March 27, 2011; Posted May 09, 2011; Published July 13, 2011; Online July 13, 2011

Inaccuracies in the estimation of material properties and errors in the assignment of these properties into finite element models limit the reliability, accuracy, and precision of quantitative computed tomography (QCT)-based finite element analyses of the vertebra. In this work, a new mesh-independent, material mapping procedure was developed to improve the quality of predictions of vertebral mechanical behavior from QCT-based finite element models. In this procedure, an intermediate step, called the material block model, was introduced to determine the distribution of material properties based on bone mineral density, and these properties were then mapped onto the finite element mesh. A sensitivity study was first conducted on a calibration phantom to understand the influence of the size of the material blocks on the computed bone mineral density. It was observed that varying the material block size produced only marginal changes in the predictions of mineral density. Finite element (FE) analyses were then conducted on a square column-shaped region of the vertebra and also on the entire vertebra in order to study the effect of material block size on the FE-derived outcomes. The predicted values of stiffness for the column and the vertebra decreased with decreasing block size. When these results were compared to those of a mesh convergence analysis, it was found that the influence of element size on vertebral stiffness was less than that of the material block size. This mapping procedure allows the material properties in a finite element study to be determined based on the block size required for an accurate representation of the material field, while the size of the finite elements can be selected independently and based on the required numerical accuracy of the finite element solution. The mesh-independent, material mapping procedure developed in this study could be particularly helpful in improving the accuracy of finite element analyses of vertebroplasty and spine metastases, as these analyses typically require mesh refinement at the interfaces between distinct materials. Moreover, the mapping procedure is not specific to the vertebra and could thus be applied to many other anatomic sites.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Development of solid geometry from QCT images

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Figure 10

Distribution of minimum principal strain for different FEA mesh sizes with a material block size of 4.0 mm. The elements having minimum principal strain less than –0.77% are shaded in black.

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Figure 11

Distribution of minimum principal strain on the vertebral half-section for nonuniform compression applied to the vertebral superior surface

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Figure 2

Finite element geometry of (a) column model derived from the vertebra and (b) nonuniform axial compressive loading of vertebral superior surface with an elliptical rigid body

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Figure 3

(a) Density distribution in the calibration phantom block for 5.0 mm material block size; (b) density (mg/cc) at discrete points in the material block for different material block sizes

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Figure 4

(a) Vertebral column stiffness and (b) distribution of minimum principal strain in the column model for different material block sizes

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Figure 5

(a) Vertebral column stiffness and (b) distribution of minimum principal strain in the column model for different sizes of the finite element mesh. All models used a material block size of 4.00 mm.

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Figure 6

Influence of material block size on vertebral stiffness for the models with HU-derived material properties and with homogeneous material properties

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Figure 7

Influence of material block size on the distribution of SI elastic modulus in the vertebra

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Figure 8

Effect of hexahedral and tetrahedral mesh density on the distribution of SI elastic modulus for the material block size of 4.0 mm

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Figure 9

Vertebral stiffness for different mesh densities for both hexahedral and tetrahedral elements. All models used a material block size of 4.0 mm.

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