Overall methology for Perfusion SPECT/CT simulations
In order to test the various delineation methods, we simulated a large spectrum of PE, with various size and location (44 clinical scenarios), on lung perfusion SPECT/CT. Three different sizes of lungs were simulated in order to assess the impact of the statistical maps’ deformable registrations. As the variability of the intensity of the anterior to posterior gradient is a key issue for the delineation of lung perfusion volumes, we also simulated three different anterior to posterior intensity gradients. Overall, 44 × 3 × 3 = 396 perfusion SPECT/CT scans were therefore simulated. As PVOI is a quantification of lung perfusion, ventilation delineation was not assessed in this work, but it was integrated in the model to improve the realism of simulations in terms of Compton scattering.
PE models definition
To define a catalog of PE, CT examinations of real patients were delineated. A senior nuclear medicine physician with experience in reading V/Q scan delineated the lobes following the fissures and the lung segments based on the bronchial tree. The segments were then divided to obtain two half segments. We defined 44 models of PE, selecting the lobes, segments, and sub-segments to be turned off for simulations. We defined 8 sub-segmental PE (one or multiple sub-segments), 10 single segmental PE, 19 multi segmental PE (from 2 to 14 segments), 5 lobar PE, and 2 multi lobar PE. The exact definition of the models can be found in the supplementary material.
Lung SPECT simulations and reconstructions
All simulations were run with Simind software [16]. Realistic dual isotopes lung V/Q SPECT scans were simulated using a methodology described in a previous work [15]. Briefly, we used CT data from real SPECT-CT examinations acquired on a Symbia T6 system (Siemens, Erlangen) equipped with a medium energy low penetration (MELP) collimator. The camera modeling parameters were set in order to correspond to this system as it is used for dual isotopes V/Q SPECT-CT [17]. CT data (low-dose free breathing CT) were used to define three simulation digital phantoms corresponding to small (1915 mL), regular (2730 mL), and large (3515 mL) lungs. These scans were selected so that the lung volume fit the mean, the mean plus one, and mean minus one standard deviation volume, measured on the database of 73 normal cases [14]. Simulation geometries were Zubal-like phantoms [18, 19], built from the CT. CT data were segmented according to hounsfield units using MiM software (7.0, Cleveland). Six representative tissues were delineated, including outside air, bones, fat, soft tissues, lungs, bronchi, and the PE area. A code was assigned to each area. Images bit depth was set to 8 bits, and a unique value was attributed to each segmented area using ImageJ sofware [20]. Those values were used in Simind to set the desired value of density and radioactivity concentration in the defined areas. Digital phantom was sub-sampled in a 1282 matrix to accelerate the simulation calculation, and the simulation grid was 128 × 128 × 108 matrix, corresponding to 3.92 × 3.92 × 3.59 mm voxels. With regard to ventilation, the simulated radioactivity was evenly set to 55 kBq.mL− 1 in the lungs and the airways. With regard to perfusion, in order to model the anterior to posterior gradient, lungs were divided into sixteen coronal planes. For each coronal plane, a relative to maximum radioactivity concentration value was assigned. Three different sets of values were defined to model a weak, regular, and a strong gradient. The gradients were defined to fit the mean, the mean plus one, and mean minus one standard deviation anterior to posterior intensity gradient measured on the database of 73 normal cases [14]. Radioactivity concentrations rose from the first to the last coronal plane to define weak, regular, and strong gradients (64 to 85 kB.mL− 1, 49 to 98 kB.mL− 1 and 29 to 116 kB.mL− 1) for the small phantom, 52 to 67 kB.mL− 1, 42 to 78 kB.mL− 1 and 27 to 95 kB.mL− 1 for the regular phantom, and 44 to 56 kB.mL− 1, 36 to 67 kB.mL− 1, and 24 to 85 kB.mL− 1 for the large phantom. As the source map is different when simulating ventilation and perfusion, simulations were not run simultaneously. Photons emitted from 99mTc decay were simulated with a 140 keV energy and 88.5% abundance. As Krypton gas is continuously inspired and expired and has a very fast decay (half-life is 13 s), it was simulated as a stationary gas without significant decay, with homogeneous concentration, with a 190 keV energy and 100% abundance. Scatter data was stored at each energy window, and 81mKr scatter was added to 99mTc lower scatter and primary energy windows. All SPECT reconstructions were performed on Siemens MI-Apps software , with FLASH3D, 4 iterations, 8 subsets, and 8.4 mm gaussian post filtering, scatter correction (double energy windows method), with attenuation correction. Overall, we defined 44 models of PE, simulated on three different geometries (small, regular, and large lungs) with three different radioactivity source maps (weak, regular, and strong anterior to posterior intensity gradient). Three hundred ninety-six datasets were therefore reconstructed.
Segmentation methods
We evaluated three segmentation methods of lung volumes with normal perfusion. First, we tested a fixed intensity threshold for all pixels, expressed as a percentage of the maximal pixel value (MaxTh), with six different thresholds (10%, 15%, 20%, 25%, 30%, 35%), applied on both lungs. Then, we tested two original methods, based on the quantification of abnormality, inspired by the SPM method used for brain imaging: a Z-score map threshold method (ZTh), and a relative difference map threshold (RelDiffTh) method. These methods were applied using mean (NMmap) and a standard deviation (NSDmap) maps built in a previous study from 73 normal V/Q SPECT/CT cases [14]. For each simulation dataset, we performed a free-form registration, based on CT data, of the NMmap and NSDmap up to the simulated SPECT-CT. Then, we normalized the simulated SPECT to the mean intenity value, and we computed two parametric maps, a Z-score map (Zmap) and a relative difference map (RelDiffmap) as follows:
$$ {Zmap}_{simulated\ SPECT}\left(x,y,z\right)=\frac{\left[ normSPECTPixelvalue\left(x,y,z\right)- NMmapValue\left(x,y,z\right)\right]}{NSDmapValue\left(x,y,z\right)}; $$
$$ {RelDiffmap}_{simulated\ SPECT}\left(x,y,z\right)=\frac{\left[ normSPECTPixelvalue\left(x,y,z\right)- NMmapValue\left(x,y,z\right)\right]}{NMmapValue\left(x,y,z\right)}; $$
An example of the different datasets of one case is shown in Fig. 1. Finally, we tested several thresholds on Zmap (− 0.6, − 0.8, − 1, − 1.2, − 1.4, − 1.6) and RelDiffmap (− 30%, − 40%, − 50%, − 60%).
As the threshold tool delineated pixels whose intensities were higher than the threshold values, only the functional lung volumes where segmented for the three methods.
Quantitative measurements
The whole lung volume (WLv) was the volume computed from CT data. From the phantom data, the ground truth volumes were computed, including the functional lungs volume (FLvph) and the PE volume (PEvph). Ground truth PVOI was calculated as follows : PVOIph = PEvph/WLv. For each simulation, segmentation method and threshold value, the segmented functional lungs (FLvs) were stored and the PE volume (PEvs) and simulation PVOI were calculated as follows: PEvs = WLv-FLvs, PVOIs = PEvs/WLv. To measure the efficiency of the segmentation, DICE indices (DICEPE) of segmented PE volumes (PEvs) and phantom PE volumes (PEvph) were calculated as follows DICEPE = (2xPEvs∩PEvph)/( PEvs + PEvph).
Statistical analysis
All measurements were separated in two batches. 10 models of PE (90 simulations) were randomly selected to define the best threshold for each segmentation method. The best threshold was defined as the threshod which provided the highest mean DICEPE index for each method. Thirty-four models (306 simulations) were available for the complete analysis. DICEPE were expressed graphically as [min;Q1;median;mean;Q3;max] and quantitatively as mean (± SD). DICE PE indexes distributions were compared using a Wilcoxon signed rank test. A p value < 0.05 was considered statistically significant. The correlations between PVOIph and PVOIs were tested using Pearson’s r correlation coefficient, and a Bland and Altman visual analysis was performed in terms of absolute difference and relative difference.