This 3D method follows similar ideas described in the 2D case but its mathematical derivations are much more complicated. In this paper, we demonstrate a new method in the quantification of effective magnetic moments of spheres from MR images. This makes the quantification of magnetic moment as important as the quantification of susceptibility for small objects in MRI. This is particularly true if we only use MR phase images to quantify the magnetic property of a spherical object, as phase is proportional to the effective magnetic moment of the object rather than the susceptibility alone. In fact, before one can reliably quantify susceptibility of a small object from MRI, one must first quantify the magnetic moment of the object. Recent quantitative susceptibility mapping (QSM) techniques also cannot accurately measure the magnetic moments or susceptibilities of small objects (e.g., see ). When the magnetic moment of an object is not large enough, even in the 2D case, the least squares fit method becomes inaccurate. As the magnetic field outside an object decreases quickly, the least squares fit method is only useful for an object with a very large magnetic moment. However, a good fit to the magnetic field distribution requires many voxels outside the nanoparticle dephasing region. The least squares fit method is currently the “best” method of quantifying magnetic moments of nanoparticles. Similarly, localized nanoparticles also appear as dark round spots in images (e.g., see ). Currently, except for number counting, there is no effective method of quantifying these objects. They exist in elder populations or patients with dementia (e.g., see ). Cerebral microbleeds and small calcifications appear as small dark round spots in magnetic resonance (MR) magnitude images.
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