2.2. Fiducial array

The system phantom contains a 3D fiducial array that can be used to assess geometric distortion, image uniformity and B ₁ homogeneity. The fiducial array was modeled on the ADNI phantom, 4 which has successfully been used to correct geometric distortions and image nonuniformity. The fiducial array spheres all have the same fill solutions with the same T ₁ and T ₂ properties (T ₁ = 407 ms ± 6 ms, T ₂ = 347 ms ± 6 ms at 20.0°C, 3.0 T), which means they can be used to assess image homogeneity and calculate B ₁ variation, both transmit, B1+, and receive, B1‐, fields.

The fiducial array consists of a set of 57 precision‐machined polyvinyl chloride (PVC) 10.0 mm ± 0.1 mm inner‐diameter spheres on a 3D cubic lattice, with a lattice spacing of 40 mm ± 0.1 mm. Figure ​Figure22 shows a coronal MRI with a subset of the fiducial spheres along with 10 mm diameter circular regions of interest (ROIs) at their prescribed positions, before automated sphere location. Figure ​Figure22 shows standard output from the Python‐based analysis package, after sphere location, plotting image uniformity and geometric distortion along the x, y, z axes, respectively. The fiducial spheres are numbered 1 through 57, starting at plate 1, increasing from right to left, then inferior to superior. For data presentation purposes, the 57 fiducial array elements are divided into seven groups: 27 internal spheres on central 3 × 3 × 3 grid, 5 spheres at each of the six outward faces of the phantom. Each set of fiducials is represented by a different color in the plots in Figure ​Figure22.

A, Coronal 3D gradient echo image of the fiducial array along with 10.0 mm circular ROIs located on prescribed 40 mm grid, which allows for visual identification of geometric distortion. S, I, L, R refer to superior, inferior, left, right directions, respectively. The scan is at 3T using a body transmit coil and a head receive coil with 0.97 mm isotropic voxels, TR = 6.3 ms, TE = 1.89 ms. The nonuniform gradient corrections are turned off. B, Normalized integrated intensity of all 57 spheres obtained after the sphere location procedure. C,D,E, Geometric distortion along the x, y, z directions, respectively. Geometric distortion, δR→=R→a‐R→p, is defined as the distance between the apparent position R→a and the prescribed position R→p, of the sphere centers after an affine transformation has accounted for rotation, translation, and overall scale correction.

The spheres are filled with a CuSO₄ solution made by mixing 0.802 g CuSO₄* 5H₂O per liter of deionized water (Supporting Information Sec. 4). The Cu⁺² ion concentration was measured, using an inductively coupled plasma‐optical emission spectroscopy and a NIST traceable Cu standard (such as NIST standard reference material 3114) to be 0.18901 ± 0.00055 mg/g or 2.969 ± 0.008 mM. A small amount of blue dye (erioglaucine disodium salt, 0.12 µg/ml) was added to assist in the visual recognition of the fiducial elements. The fiducial spheres are machined in two parts from PVC stock, glued together and attached to the plates using an M8‐1.25 threaded stub, as shown in Supporting Information Figure S1C. PVC was chosen because it is inexpensive, can be easily glued, and has a low permeability to water. The spheres are sealed with a tapered polyvinylidene difluoride (PVDF) plug. The fiducial solution was chosen to have short T ₁ times to give, for most scans in the protocol, high signal and contrast with respect to the surrounding fill composed of long‐T ₁ deionized water. High contrast is beneficial for automated location of the fiducial sphere positions.