Fig 1.
Phase shift in nested spheres.
(a) Nested sphere as the superposition of two homogeneous spheres. (b) Corresponding phase shift maps.
Fig 2.
(a) Steps for the fabrication of a spherical inclusion phantom. (b) Pictures of each step. 3D-printed, bowl-shaped holder (grey) had a hole in the middle which is visible in Steps 1, 2, 4.
Table 1.
Materials used for the fabrication of a 10 cm-diameter gelatin sphere phantom with three inclusions.
Fig 3.
(a,b) Pictures of the completed spherical phantom. The white blob at the top of the phantom is settled hot glue. (c) Phantom positioned for imaging in a head-neck array coil.
Table 2.
Scan parameters for volumetric phase imaging and single-plane relaxation parameter mapping.
Fig 4.
3-plane gradient echo magnitude images of the spherical inclusion phantom.
Small air bubbles are visible on the gel boundaries (black arrows). Three inclusions with iron concentrations of 0.043, 0.086, 0.129 mM are indicated as 1, 2, 3, respectively.
Fig 5.
(a) Measured phase. Phase variations due to air bubbles (white arrows), phantom stand (yellow arrows), and imperfect shimming (green dotted arrows) are visible. Spherical inclusions (1–3) produce dipolar field patterns consistent with the main field (Bapp) direction (blue arrows). (b) Dipolar model phase for inclusion susceptibilities 0.1, 0.2, 0.3 ppm. (c) Phase difference, showing good agreement between model and measurement. White arrowheads indicate error due to model boundary mismatch.
Table 3.
Relaxation rates and relaxivities of the three inclusion spheres.
Fig 6.
3-plane quantitative susceptibility maps of the phantom processed with algorithm 1 (a) and 2 (b). In (a), streaking artifacts are apparent on the coronal and sagittal planes (orange dashed arrows), giving rise to artificial susceptibility elevation on the axial plane (orange arrow). In both (a) and (b), phase due to the phantom stand produced little susceptibility artifact (white arrows on sagittal planes). The inset of (b) shows the mean susceptibilities of the three inclusions for each processing method. Numerical values and linear fit results are listed in S6 File.
Fig 7.
QSM by MEDI obtained with the same phantom 85 days apart.
(a-b) 3 plane susceptibility maps; (a) is the same as in Fig 6B. Yellow arrows in (b) indicate additional surface defects. (c) Mean and standard deviation of susceptibility in each inclusion. (d) Plot of susceptibility, with error bars according to 1 std from (c).