Quantitative Computed Tomography-Based Finite Element Models of the Human Lumbar Vertebral Body: Effect of Element Size on Stiffness, Damage, and Fracture Strength Predictions

[+] Author and Article Information
R. Paul Crawford, William S. Rosenberg

Department of Neurological Surgery, University of California, San Francisco, CA 94143

Tony M. Keaveny

Departments of Mechanical Engineering and Bioengineering, University of California, Berkeley, CA 94720-1740

J Biomech Eng 125(4), 434-438 (Aug 01, 2003) (5 pages) doi:10.1115/1.1589772 History: Received April 03, 2002; Revised April 03, 2003; Online August 01, 2003
Copyright © 2003 by ASME
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Comparison of “low” (3×3×3 mm element size) and “high” (1×1×1.5 mm) resolution voxel-based finite element models of the same vertebral body. The low-resolution model contains 2105 nodes and 1524 elements while the high resolution model contains 27,298 nodes and 23,725 elements. Elements of polymethylmethacrylate (PMMA) necessary to establish plano-parallel surfaces on the top and bottom of the vertebral body are identified by the darker colors (solid layers of PMMA not shown).
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Finite element-derived stiffness values for each vertebral body as a function of in-plane resolution (1, 2, 3, or 4 mm) and slice thickness (1.5 mm or 3 mm). Linear regression lines are shown for each vertebral body as a function of in-plane element size for both slice thickness values. An analysis of covariance indicated that stiffness was positively correlated with in-plane resolution (p<0.0001) and negatively correlated with slice thickness (p=0.0036).
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Axial strain (Ezz), axial stress (Szz), maximum principal strain, and minimum principal strain of high resolution model depicted in Fig. 1 under a load corresponding to an overall strain of 0.5% (a, b, c, and d, respectively). A wedge-shaped section was removed to illustrate results in the trabecular centrum. The maximum legend shading in c and minimum legend shading in d represent elements that exceeded the defined failure criterion in tension and compression, respectively.
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Plot of experimentally measured fracture strength (Fmax) as a function of high- (1×1×1.5 mm element size) and low- (3×3×3 mm) resolution model stiffness (K). Regression equation reports slope and intercept (±standard error). The high-resolution model stiffness was 4% greater (p=0.05) than the low-resolution model. The slopes (p<0.001) and intercepts (p<0.007) were significantly different from zero, but the high- and low-resolution slopes were not significantly different from each other (p=0.85). Eliminating the strongest vertebral body resulted in the following changes (n=13): high-resolution model Fmax=0.29±0.039 K–0.35±0.72,r2=0.83; low-resolution model, Fmax=0.28±0.043 K–0.45±0.82,r2=0.80.




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