## 2 Materials and Methods
### Image Analysis  
A comprehensive image quality evaluation was performed by analyzing a set of physical image quality descriptors to assess and compare the performance of different _MPI systems_. The contrast was evaluated through the contrast between the _LV_ wall and the _LV_ inner chamber, the contrast of the _PD_ with respect to the _LV_ wall, the intrinsic contrast, and the net contrast. The Fiji edition of ImageJ open-source software, (National Institutes of Health, Bethesda, MD, USA) for processing and analyzing image data, version 2.14.0/1.54 f, was used. In ImageJ, the short-axis images were opened as a 32-bit file. The regions of interest were drawn using the freehand option. The mean number of counts in the regions of interest were used in the calculation of the descriptors. In ImageJ, when displaying short-axis images, the lookup table (LUT) \"cool\" was applied. The contrast between the _LV_ wall and the _LV_ inner chamber (_LVIC_) was defined as the percentage of the ratio between the contrast measured on the reconstructed images (\(C_{LV/LVIC,means}\)) and the contrast defined by the preparation of the phantom (\(C_{LV/LVIC,phantom}\)):  
\[C_{LV/LVIC}(\%)=\frac{C_{LV/LVIC,meas}}{C_{LV/LVIC,phantom}}\times 100 \tag{1}\]  
\(C_{LV/LVIC,meas}\) was determined as:  
\[C_{LV/LVIC,meas}=\frac{\overline{\eta_{LV}}-\overline{\eta_{LVIC}}}{\overline {\eta_{LV}}+\overline{\eta_{LVIC}}} \tag{2}\]  
where \(\overline{\eta_{LV}}\) and \(\overline{\eta_{LVIC}}\) are the mean number of counts per voxel in the _LV_ wall and _LV_ inner chamber, respectively, on the short-axis images of the normal heart [1] obtained through image analysis. \(C_{LV/LVIC,phantom}\) is a function of the activity concentrations in the _LV_ wall and _LV_ inner chamber, \(AC_{LV}\) and \(AC_{LVIC}\), respectively. \(C_{LV/LVIC,phantom}\) was defined as:  
\[C_{LV/LVIC,phantom}=\frac{AC_{LV}-AC_{LVIC}}{AC_{LV}+\ AC_{LVIC}} \tag{3}\]  
The contrast of the _PD_ with respect to the _LV_ wall defined by the preparation of the phantom is:  
\[C_{PD,phantom}(100\%)=\frac{AC_{LV}-AC_{PD}}{AC_{LV}+AC_{PD}}\times 100 \tag{4}\]  
where \(AC_{LV}\) and \(AC_{PD}\) are the activity concentrations in the _LV_ wall and in the _PD_, respectively [21]. In the simulation of a pathological heart, the perfusion defect is filled with water and the \(C_{PD,phantom}\) = 100%. Thus, the contrast between the _PD_ and the _LV_ wall was determined as:  
\[C_{PD}(\%)=\frac{\overline{\eta_{LV}}-\overline{\eta_{PD}}}{\overline{\eta_{ LV}}+\overline{\eta_{PD}}}\times 100 \tag{5}\]  
where \(\overline{\eta_{LV}}\) and \(\overline{\eta_{PD}}\) are the mean number of counts per voxel in the _LV_ wall and perfusion defect of the pathological heart, respectively [21]. The contrast between the _PD_ and the \(LV\) wall was evaluated on the short-axis slices of the pathological heart where the \(PD\) was visible. To estimate the intrinsic contrast of the _MPI system_ due to self-attenuation, the contrast of the areas where the \(PD\) was positioned with respect to the \(LV\) wall was evaluated on the corresponding short-axis slices of the normal heart using the regions of interest (ROIs) used for \(C_{PD}\)(%) evaluation:  
\[IC(\%)=\frac{\overline{\eta_{LV,norm}-\overline{\eta_{PD,norm}}}}{\overline{ \eta_{LV,norm}+\overline{\eta_{PD,norm}}}}\times 100 \tag{6}\]  
where \(\overline{\eta_{LV,\ norm}}\) and \(\overline{\eta_{PD,norm}}\) are the mean counts per voxel in the \(LV\) wall of the normal heart and in the position corresponding to the perfusion defect, respectively [21]. Finally, for each type of _MPI system_ and each \(PD\) position, the net contrast was determined as:  
\[NC=C_{PD}-IC \tag{7}\]  
\(NC\) is an image quality descriptor related to the perfusion detection capability of the _MPI system_. \(NC\) values should be used as reference values of the maximum contrast between the \(PD\) and the \(LV\) wall for each _MPI system_ and different \(PD\) positions [21].