Before phantom fabrication can begin, relaxivities r1 and r2 of soy lecithin and agar have to be determined (see Eqs. 1 and 2). For this purpose, pure aqueous soy lecithin solutions and pure agar gels of different concentrations (0, 1, 2, 3, 4, 5%) were prepared and examined using T1- and T2 mapping techniques.

Furthermore, it has to be ensured that the two substances are compatible and retain their effect even when mixed. A change in relaxivity as a function of the concentration of the other substance would make it impossible to apply simple Eqs. (1, 2) for determination of concentrations and thus produce correct phantoms. At least, the T1 modifier should have stable longitudinal relaxivity r1 and the T2 modifier should have stable transverse relaxivity r2. To verify this, relaxivities of soy-lecithin were measured in the presence of different concentrations of agar (1%, 2%, 3%, 4%), while agar-relaxivities were measured in the presence of different concentrations of soy lecithin (1%, 2%, 3%, 4%).

After the preliminary experiments, test phantoms were designed to match the relaxation times T1/T2 of different tissues: grey matter (1820 ms/99 ms [3]), white matter (1084 ms/69 ms [3]), kidney cortex (1142 ms/76 ms [22]), kidney medulla (1545 ms/81 ms [22]), spleen (1328 ms/61 ms [22]), liver (812 ms/42 ms [3]), and muscle (1295 ms/34 ms [22]). Using the previously determined relaxivities and Eqs. 1 and 2, the appropriate concentrations of soy-lecithin and agar were calculated to achieve the desired T1 and T2 values. For the relaxation rates of pure water, the values R1w = 2950 ms and R2w = 2000 ms were used (determined by several preliminary measurements).

The phantoms were tested for correctness (agreement between measured and target values), reproducibility and temporal stability. For this, all phantoms were prepared three times, independently on different days and examined on the day of preparation and 4 weeks after preparation. Possible mold growth was monitored by visual inspection of the samples during the 4-week study period. In addition, the samples were checked for homogeneity and the absence of air bubbles. Air bubbles are problematic because they cause magnetic field distortions that lead to susceptibility artifacts [15].

Phantoms were prepared as follows (Fig. 1): First, the appropriate amount of soy lecithin (Carl Roth, Karlsruhe, Germany) was dissolved in demineralized water (Carl Roth, Karlsruhe, Germany) under magnetic stirring at 650 rpm for 10 min. Agar (Agar powdered pure, food grade, PanReac-AppliChem-ITW Reagents, Darmstadt, Germany) was then stirred into the soy lecithin solution and the mixture was boiled using a microwave heater until the solution was clear and homogeneous. The solutions were then filled into sterilized polypropylene tubes (50 ml, Greiner Bio-One, Frickenhausen, Germany) and cooled to room temperature for gelation. High viscosity solutions were sonicated with an ultrasonic homogenizer (Hielscher Ultrasonics, Teltow, Germany) to remove air bubbles prior to solid gel formation. Pure aqueous soy lecithin solutions and agar gels of different concentrations (0, 1, 2, 3, 4, 5%) were prepared by the same procedure without addition of the other substance.

Schematic representation of the manufacturing process of the soy-lecithin-agar phantoms. Created with BioRender.com

For the measurements, the samples were fixed in water-filled MR-compatible housings (Fig. 2a–b): The measurements to determine the individual relaxivities of soy lecithin and agar as well as for the final test phantoms were performed using a cylindrical housing that can hold up to 7 tubes. In contrast, due to the large number of samples, the compatibility measurements of soy lecithin and agar were carried out using a larger square housing that can hold up to 16 phantoms.

Photographs of the water-filled sample tube housings: a cylindrical housing with 7 sample tubes b larger square housing with 16 sample tubes. Photographs of the measurement setup on a clinical 3T whole-body MR scanner: c the cylindrical housing with 7 sample tubes was scanned using a 20-channel head coil d the square housing with 16 sample tubes was scanned using an 18-channel body array coil

All phantoms were stored in the scanner room for at least 6 h before measurements to ensure that the temperature of the samples could stabilize and adapt to the ambient temperature. Between measurements, the samples were stored in the dark in a laboratory cabinet at a room temperature of approx. 21 °C.

Measurements were performed on a clinical 3.0 Tesla whole-body MR scanner (MAGNETOM Prismafit, Siemens Healthcare, Erlangen, Germany) with a 20-channel head coil at 21 °C ± 0.5 °C.

Relaxivity measurements of soy lecithin and agar in the mixture (compatibility measurements) were performed using an 18-channel body array coil, as the square housing containing all samples did not fit into the head coil. The corresponding measurement setups are shown in Fig. 2c–d. All data were processed and analyzed offline using in-house developed software (MATLAB, MathWorks, Natick, MA).

T1 and T2 measurements were performed with the following parameters: matrix = 128 × 128, FOV = 200 × 200 mm, slice thickness = 5 mm, number of slices = 1, slice in coronal plane, positioned in the center of the samples.

T1 was measured using a single slice inversion recovery turbo spin echo pulse sequence (IR-TSE) with TR of 10,000 ms and TE of 9.9 ms. Images were acquired for 9 different TIs in the range of 25–6400 ms (logarithmically equally spaced). T1 maps were calculated from the acquisitions with multiple TIs by pixel-wise monoexponential fitting of signal intensities (SI): SI = SI0 (1–a exp(-TI/T1) + exp(-TR/T1)) [23].

T2 was measured in the same slice using a multi-echo CPMG spin echo pulse sequence with a TR of 6000 ms and 32 TEs ranging from 10 to 320 ms (equally spaced). Since soy lecithin has a relatively small effect on T2, the T2 decay for the pure soy lecithin solutions (without agar) was sampled for longer TEs in the range of 50–1600 ms (equally spaced). T2 maps were calculated on a pixelwise basis by monoexponential fitting of the measured SI’s: SI = SI0 exp(-TE/T2) + c [22]. All signal values were noise corrected before fitting.

Relaxation times (T1, T2) and relaxation rates (R1 = 1/T1, R2 = 1/T2) of each sample were determined from circular regions of interest in the calculated parametric maps. Relaxivities were calculated from the linear regression of the relaxation rates on the concentration of the substance: R1,2 = r1,2· [concentration] + c. The slope of the line represents the relaxivity r1,2.

A 3D T1-weighted gradient echo sequence (VIBE) with high spatial resolution was applied to examine the phantoms for homogeneity and the absence of air bubbles. Acquisition parameters include: TR = 6.3 ms, TE = 2.46 ms, FOV = 256 × 256, spatial resolution = 0.5 × 0.5x0.5 mm, number of slices = 10, coronal planes.