All human images were acquired after informed consent. Ankle images were acquired in sagittal view on a GE 3T Signa EXCITE HDx scanner (GE Healthcare, Waukesha, WI) with a single-channel coil, using a 3D spoiled-gradient-echo sequence with three echo times (2.184, 2.978, and 3.772 ms), one echo per repetition time, a 125 kHz bandwidth, a flip angle of 5°, a 256 × 256 × 8 matrix, an in-plane field of view of 18 cm, and a voxel size of 5 mm along the z direction. Wrist and phantom data were acquired on a Siemens Magnetom Espree 1.5T (Siemens AG Medical Solutions, Erlangen, Germany). Wrist images were acquired with a four-channel wrist coil, using a 3D spoiled-gradient-echo sequence, two separate acquisitions with either uniformly spaced echo times (1.81, 4.26, 6.71, 9.16, 11.61, and 14.06 ms) or nonuniformly spaced echo times (1.81, 4.3, 7, 9.5, and 14.5 ms), a 128 kHz bandwidth, a flip angle of 10°, a 128 × 128 × 8 matrix, an in-plane field of view of 17 cm, and a voxel size of 3 mm along the z direction. Images of a phantom consisting of water, oil, and silicone (GE Silicone I (GE012A); Momentive, Huntersville, NC) were acquired using a 2D spoiled-gradient echo sequence with a four-channel head coil, six echo times with one echo per repetition (initial echo time of 2.1 ms, and echo spacing 2.3 ms), a 128 kHz bandwidth, a flip angle of 20°, a 256 × 256 matrix, and an in-plane field of view of 20 cm. The chemical shifts of water, canola oil, and silicone peaks were 4.7 ppm, 1.3 ppm, and 0.1 ppm, respectively. Data acquired with phased-array coil were first coil-combined in complex value before hierarchical IDEAL.
Hierarchical IDEAL can be applied directly to 3D images. However, to speed up computation, it was applied on a slice-by-slice basis, with the phase map of one slice used as the initial value for the next slice. To improve robustness against strong B0 variations along the z direction, hierarchical IDEAL was applied in low resolution (with three hierarchical levels for speed) first through all the slices as a preprocessing step, followed by applying hierarchical IDEAL with seven hierarchical levels.
A multipeak fat spectrum (16) was used in the in vivo signal model, with spectral peaks at 0.9, 1.3, 2.1, 2.76, 4.31, and 5.3 ppm (water peak at 4.7 ppm), and relative amplitudes of 0.087, 0.694, 0.128, 0.004, 0.039, and 0.048, respectively.