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TECHNICAL PAPERS: Bone/Orthopedics

[+] Author and Article Information
Jenni M. Buckley

Orthopaedic Biomechanics Laboratory, Department of Mechanical Engineering, University of California, Berkeley, CA 94720jbuckley@me.berkeley.edu

Danny C. Leang

Orthopaedic Biomechanics Laboratory, Department of Mechanical Engineering, University of California, Berkeley, CA 94720

Tony M. Keaveny

Orthopaedic Biomechanics Laboratory, Department of Mechanical Engineering, and Department of Bioengineering, University of California, Berkeley, CA 94720tmk@me.berkeley.edu

J Biomech Eng 128(5), 641-646 (Apr 14, 2006) (6 pages) doi:10.1115/1.2241637 History: Received December 21, 2004; Revised April 14, 2006

## Abstract

The sensitivity of vertebral body strength to the distribution of axial forces along the endplate has not been comprehensively evaluated. Using quantitative computed tomography-based finite element models of 13 vertebral bodies, an optimization analysis was performed to determine the endplate force distributions that minimized (lower bound) and maximized (upper bound) vertebral strength for a given set of externally applied axial compressive loads. Vertebral strength was also evaluated for three generic boundary conditions: uniform displacement, uniform force, and a nonuniform force distribution in which the interior of the endplate was loaded with a force that was 1.5 times greater than the periphery. Our results showed that the relative difference between the upper and lower bounds on vertebral strength was $14.2±7.0%$$(mean±SD)$. While there was a weak trend for the magnitude of the strength bounds to be inversely proportional to bone mineral density ($R2=0.32$, $p=0.02$), both upper and lower bound vertebral strength measures were well predicted by the strength response under uniform displacement loading conditions ($R2=0.91$ and $R2=0.99$, respectively). All three generic boundary conditions resulted in vertebral strength values that were statistically indistinguishable from the loading condition that resulted in an upper bound on strength. The results of this study indicate that the uncertainty in strength arising from the unknown condition of the disc is dependent on the condition of the bone (whether it is osteoporotic or normal). Although bone mineral density is not a good predictor of strength sensitivity, vertebral strength under generic boundary conditions, i.e., uniform displacement or force, was strongly correlated with the relative magnitude of the strength bounds. Thus, explicit disc modeling may not be necessary.

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## Figures

Figure 1

A schematic illustrating the strategy used to determine the sensitivity of vertebral strength to endplate force distributions

Figure 2

The QCT-based “voxel” finite element mesh of a representative vertebral body (L2, male, 72 y.o.). Voxel size is 2mm (isotropic), and there are a total of 10,300 linear hexahedral elements.

Figure 3

Whole-bone response of a representative vertebral body subjected to the same net compressive force but using various endplate boundary conditions. For this specimen, the upper bound, uniform force, stepped force, and uniform displacement responses overlapped.

Figure 4

Axial force distributions on the endplate resulting in lower bound vertebral strengths. (a) Central force concentrations, (b) anterior and posterior force concentrations, and (c) lateral force concentrations.

Figure 5

(a) Both the upper and lower bound measures of vertebral compressive strength were well predicted by the strength computed using the uniform displacement boundary condition. (b) Relative difference between upper and lower bound vertebral strengths versus specimen bone mineral density.

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