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Comment
. 2014 Jul;72(1):1-3.
doi: 10.1002/mrm.25021. Epub 2014 Apr 24.

Sphere of Lorentz and demagnetization factors in white matter

Jeff H Duyn  1 , Thomas M Barbara
Affiliations
Comment

Sphere of Lorentz and demagnetization factors in white matter

Jeff H Duyn et al. Magn Reson Med. 2014 Jul.
No abstract available

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Figures

FIGURE
FIGURE
Model of average water environment in optic nerve with both oriented and elongated and isotropic magnetic susceptibility inclusions. Because of correlations between the space occupied by water space and the distribution of elongated inclusions, water hydrogen protons on average sample the field in an elongated space with average magnetic susceptibility χ1, which contains contributions from bulk water magnetic susceptibility of water (χw) and the isotropic inclusions (with nerve-averaged susceptibility χiso). Importantly, because isotropic inclusions are excluded from the space occupied by the elongated ones, their local magnetic susceptibility in the elongated compartment is increased to {χiso/(1−VL)}, with VL the volume fraction of elongated inclusions. The susceptibilities inside and outside the nerve are χ2 and χe respectively. Boundaries S between adjacent regions add shifts to the average frequency characterizing water hydrogen protons inside the nerve, determined from the susceptibility difference between the regions and the demagnetization factors F for each successive boundary [ {13} for spheres and {sin2α2} for cylinders/elongated (prolate) ellipsoids]. FSL indicates the standard SL factor for the field sampled by a proton in a water pocket. Note that in this particular model, the size scale of the anisotropic inclusions is assumed to be larger than that of isotropic inclusions; also, the effect of the nerve on the average frequency of 1H2O outside it was assumed negligible. In this simplified model, susceptibilities were assumed to be isotropic. To deal with magnetic susceptibility anisotropy it is necessary to consider the elements of the susceptibility tensor in deriving shape factors.
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