## 2 Materials and Methods
### Selection of Reconstruction Method Using a Cylindrical Phantom  
Two reconstruction methods were compared using a cylindrical phantom filled with water uniformly mixed with radioactive \({}^{99\text{m}}\)Tc following the procedure reported in [17]. The cylindrical phantom was 17 cm long and 22 cm in diameter for an inner volume of 6862 mL (Figure 2a, Table 1). A total activity of 205.9 MBq was injected in the volume, thereby obtaining a final activity concentration of 0.030 MBq/mL. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Phantom**} & **Nominal Volume** & **Length** & **Outside Diameter** \\  & **(mL)** & **(cm)** & **(cm)** \\ \hline Point-like source & 0.1 & 0.01 & 0.01 \\ Homogeneous & & & \\ cylindrical & 6462 & 17 & 22 \\ NEMA/IEC & 9700 & 18 & 30 \\ Abdo-Man & 1783 & 25.1 & 34.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The main geometrical characteristics of the investigated phantoms/geometries. Figure 2: Data acquisition using the reference phantoms (**a**) homogeneous cylindrical and (**b**) the NEMA/IEC phantom. Raw SPECT data for the reference cylindrical phantom were reconstructed testing two methods (Table 2) using a 256 \(\times\) 256 matrix with 2.39 mm\({}^{3}\) voxel size as described in the following. The first investigated method was the well-known Ordered Subset Expectation Maximization technique (OSEM, 8 iterations, 4 subsets, no filters) that provides images expressed in counts. The second method was the novel xSPECT reconstruction algorithm based on the Ordered Subset Conjugated Gradient method (OSCG, 24 iterations, 2 subsets, 2.5 mm Gaussian filter) that provides images directly expressed in units of Bq/mL without the need a post-reconstruction scaling of voxels values to quantitative values [20]. In xSPECT software, attenuation correction is achieved generating \(\upmu\)-maps from CT data, converting Hounsfield units to \(\upmu\) values using a bi-linear transformation. Scatter correction is performed by using the triple energy window technique [21; 22]. The number of iterations and subsets used for OSEM reconstruction (8 and 4, respectively) was selected based on standard protocols adopted in the clinical practice. Similarly, the number of iterations and subsets used with OSCG in association with post-smoothing (i.e., 24 iterations, 2 subsets, 2.5 mm Gaussian filter) was selected based on a preliminary internal study investigating the best combination in the range of 1-7 subsets and 1-30 iterations. Of note, our results confirmed the manufacturer recommendations. A comparison was performed between profiles generated at a central slice of the phantom reconstructed with the xSPECT software, in order to investigate the relative differences of the activity profiles. At present, there is no general agreement on the best method to outline a given region of interest (ROI) in emission tomography. The size of the selected region may have a significant impact on the final activity recovered in the imaged phantom, especially in the presence of small objects and in areas close to the phantom wall. Consequently, we decided to compare three different ROI delineation methods: a cylindrical ROI representing the cylindrical phantom's physical inner volume (ROI1) was firstly generated, from which a second and a third ROIs were obtained using an automatic contraction to include the 80% of the phantom's volume (ROI2) and a third ROI including the external wall of the phantom (ROI3) using the automatic whole-body tool. For each defined ROI, the recovery coefficient (RC) and the coefficient of variation (\(COV\)) were also determined as follows:  
* Recovery coefficient in a uniform geometry (\(\mathbf{RC_{ug}}\)): \[\mathbf{RC_{ug}}=\frac{\mathbf{c_{bg}}}{\mathbf{C_{bg}}}\] (2) with \(\mathbf{c_{bg}}\) the activity concentration measured in the reconstructed SPECT phantom background and \(\mathbf{C_{bg}}\) the expected activity concentration known from the phantom preparation.