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RESEARCH PAPERS

# Assessment of Factors Influencing Finite Element Vertebral Model Predictions

[+] Author and Article Information
Alison C. Jones

Institute of Medical and Biological Engineering, School of Mechanical Engineering, University of Leeds, Leeds, LS2 9JT, UKa.c.Jones@leeds.ac.uk

Ruth K. Wilcox

Institute of Medical and Biological Engineering, School of Mechanical Engineering, University of Leeds, Leeds, LS2 9JT, UKr.k.Wilcox@leeds.ac.uk

J Biomech Eng 129(6), 898-903 (May 02, 2007) (6 pages) doi:10.1115/1.2800791 History: Received September 21, 2006; Revised May 02, 2007

## Abstract

This study aimed to establish model construction and configuration procedures for future vertebral finite element analysis by studying convergence, sensitivity, and accuracy behaviors of semiautomatically generated models and comparing the results with manually generated models. During a previous study, six porcine vertebral bodies were imaged using a microcomputed tomography scanner and tested in axial compression to establish their stiffness and failure strength. Finite element models were built using a manual meshing method. In this study, the experimental agreement of those models was compared with that of semiautomatically generated models of the same six vertebrae. Both manually and semiautomatically generated models were assigned gray-scale-based, element-specific material properties. The convergence of the semiautomatically generated models was analyzed for the complete models along with material property and architecture control cases. A sensitivity study was also undertaken to test the reaction of the models to changes in material property values, architecture, and boundary conditions. In control cases, the element-specific material properties reduce the convergence of the models in comparison to homogeneous models. However, the full vertebral models showed strong convergence characteristics. The sensitivity study revealed a significant reaction to changes in architecture, boundary conditions, and load position, while the sensitivity to changes in material property values was proportional. The semiautomatically generated models produced stiffness and strength predictions of similar accuracy to the manually generated models with much shorter image segmentation and meshing times. Semiautomatic methods can provide a more rapid alternative to manual mesh generation techniques and produce vertebral models of similar accuracy. The representation of the boundary conditions, load position, and surrounding environment is crucial to the accurate prediction of the vertebral response. At present, an element size of $2×2×2mm3$ appears sufficient since the error at this size is dominated by factors, such as the load position, which will not be improved by increasing the mesh resolution. Higher resolution meshes may be appropriate in the future as models are made more sophisticated and computational processing time is reduced.

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## Figures

Figure 1

Figure 2

Process of automatic modelling. (a) A horizontal slice through an original scan. (b) The corresponding down-sampled images for Auto1, Auto2, and Auto4. (c) Slices through the voxel-based meshes resulting from the three scan resolutions. Here, the shading corresponds to the gray-scale values interpolated from the image. (d) A full smoothed finite element mesh for each of the resolutions.

Figure 3

Three resolutions (Auto1, Auto2, and Auto4) of the same column model after simulated axial compression. The gray scales in the this figure represent the distribution of material properties.

Figure 4

Convergence graph for the automatically generated vertebral models in both the gray-scale-based material properties and a homogeneous model of vertebra 6

Figure 5

Change in model stiffness with change in location of the applied displacement on the upper rigid plate

Figure 6

Relationship between the experimental (a) stiffness and (b) strength and the corresponding finite element predictions from the four model sets. The line of perfect agreement indicates that the v4 models underestimate the specimen stiffness.

Figure 7

The absolute stiffness error is shown here as a percentage of the experimental stiffness for each of the four model types and each of the experimental specimens

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