Magnetic field distribution in models of trabecular bone

Authors

  • J. Chetley Ford Ph.D.,

    Corresponding author
    1. Department of Radiology, University of Pennsylvania Medical Center, Philadelphia, Pennsylvania
    • Department of Radiology, 1 Silverstein Building, 3400 Spruce Street, Philadelphia, PA 19104-4283
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  • Felix W. Wehrli,

    1. Department of Radiology, University of Pennsylvania Medical Center, Philadelphia, Pennsylvania
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  • Hsiao-Wen Chung

    1. Department of Radiology, University of Pennsylvania Medical Center, Philadelphia, Pennsylvania
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Abstract

A magnetostatic model consisting of a tetragonal lattice of struts of diamagnetic material, mimicking vertebral trabecular bone, was developed. The model allows estimation of the magnetic field histogram within the lattice's unit cell as a function of geometric parameters. The field was computed analytically from the induced magnetic surface charge density on the faces of the struts. The contribution from the induced magnetic field to the effective transverse relaxation rate, R2 was obtained as the mean decay rate of the Fourier transformed histograms, for both fixed and randomly oriented lattices. The model predicts the field distribution to increase with both strut thickness and density, paralleling material density. Finally, significant changes in R2′ are predicted at constant material density, in that the field distribution widens with simultaneously increasing strut number density and decreasing strut thickness.

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