Predicting trabecular bone elastic properties from measures of bone volume fraction and fabric on the basis of micromagnetic resonance images

Authors

  • Michael J. Wald,

    1. Department of Radiology, Laboratory for Structural NMR Imaging, University of Pennsylvania Medical Center, Philadelphia, Pennsylvania, United States of America
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  • Jeremy F. Magland,

    1. Department of Radiology, Laboratory for Structural NMR Imaging, University of Pennsylvania Medical Center, Philadelphia, Pennsylvania, United States of America
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  • Chamith S. Rajapakse,

    1. Department of Radiology, Laboratory for Structural NMR Imaging, University of Pennsylvania Medical Center, Philadelphia, Pennsylvania, United States of America
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  • Yusuf A. Bhagat,

    1. Department of Radiology, Laboratory for Structural NMR Imaging, University of Pennsylvania Medical Center, Philadelphia, Pennsylvania, United States of America
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  • Felix W. Wehrli

    Corresponding author
    1. Department of Radiology, Laboratory for Structural NMR Imaging, University of Pennsylvania Medical Center, Philadelphia, Pennsylvania, United States of America
    • MRI Learning Center, Hospital of the University of Pennsylvania, 3400 Spruce St., Philadelphia, PA 19104
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Abstract

The relationship between fabric (a measure of structural anisotropy) and elastic properties of trabecular bone was examined by invoking morphology and homogenization theory on the basis of micromagnetic resonance images from the distal tibia in specimens (N = 30) and human subjects (N = 16) acquired at a 160 × 160 × 160 μm3 voxel size. The fabric tensor was mapped in 7.5 × 7.5 × 7.5 mm3 cubic subvolumes by a three-dimensional mean-intercept-length method. Elastic constants (three Young's and three shear moduli) were derived from linear microfinite element simulations of three-dimensional grayscale bone volume fraction-mapped images. In the specimen data, moduli fit power laws of bone volume fraction (bone volume/total volume) for all three test directions and subvolumes (R2 = 0.92–0.98) with exponents ranging from 1.3 to 1.8. Weaker linear relationships were found for the in vivo data because of a narrower range in bone volume/total volume. When pooling the data for all test directions and subvolumes, bone volume/total volume predicted elastic moduli less well in the specimens (mean R2 = 0.74) and not at all in vivo. A model of bone volume/total volume and fabric was highly predictive of microfinite element-derived Young's moduli: mean R2s of 0.98 and 0.82 (in vivo). The results show that fabric, an important predictor of bone mechanical properties, can be assessed in the limited resolution and signal-to-noise ratio regime of micromagnetic resonance images. Magn Reson Med, 2012. © 2011 Wiley Periodicals, Inc.

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