Introduction

In recent years, small-animal positron emission tomography (PET) has gained popularity and established its utility in the biomedical research arena owing to its high sensitivity and capability to provide quantitative measurements of biochemical and molecular processes in vivo [1, 2]. For optimal image quality and accurate quantification in PET imaging, object-specific correction of background (randoms) and physical degrading factors such as photon attenuation, Compton scatter, partial volume effects and motion have to be compensated for prior to reconstruction or incorporated within statistical iterative image reconstruction techniques [3, 4]. However, little has been published on the assessment of the quantitative capability of small-animal PET studies [5–7].

Attenuation is the loss of true events due to scatter and absorption which impacts the measured data and results in inaccurate quantification of reconstructed PET images, whereas scatter degrades image contrast and affects both relative and absolute PET quantification. The scatter magnitude and spatial distribution depend mainly on the size and density of the object and scanner-related parameters such as design geometry, detector energy resolution and acquisition energy window [8]. In clinical PET imaging, it is well established that scatter correction is essential for accurate quantification of tracer uptake since the scatter fraction (SF) varies between 30 and 35 % in brain imaging and 50 and 60 % in whole-body imaging in three-dimensional acquisition mode [9, 10]. On the other hand, when imaging small subjects such as rodents, scatter is assumed to be a minor factor due to the small size of the animals. The origin of scatter for small-animal imaging has not been well characterized, but has been proposed to stem mainly from the gantry and environment rather than the animal itself [11]. This opinion is supported by the fact that scatter correction usually does not involve correcting for scatter in the detector crystal. However, annihilation photons are subject to attenuation and scatter even in small animals such as mice and rats [12, 13]. SF estimates ranging from 5 to 21 % for mice and 15 to 30 % for rats have been reported [11, 14–18]. Another 11C-raclopride PET study reported a larger SF (25–45 %) in the rat brain with an increase in the distribution volume ratio of 3.5 % after scatter correction [19].

It has become a common practice nowadays to scan multiple rodents simultaneously at different radial offsets in the scanner's field-of-view (FOV) to increase the throughput in small-animal PET imaging [20–22]. However, this is achieved at the expense of deterioration of image quality and loss of quantitative accuracy due to combined effects of photon attenuation and Compton scatter [23]. The lack of literature reporting on the magnitude, spatial distribution of the scatter component and effect of scatter correction on image quality and quantitative accuracy when imaging multiple rodents simultaneously motivated this study.

The purpose of this work is, first, to characterize the magnitude and spatial distribution of the scatter component in small-animal PET imaging when scanning single and multiple rodents (mice and rats) simultaneously and, second, to assess the relevance and impact of scatter correction on image quality and quantitative accuracy under similar conditions.

Materials and Methods

Small-Animal PET System

The LabPET™-8 is the PET subsystem of the integrated trimodality TriumphTM PET/SPECT/CT pre-clinical imaging system (Gamma Medica, Inc., Northridge, CA). It is a state-of-art avalanche photodiode (APD)-based digital small-animal PET scanner designed with quasi-individual crystal readout along with parallel digital architecture to achieve high performance [24]. The scanner has 7.5-cm axial and 10-cm transaxial FOVs. Scintillators of 2 × 2 × 12/14 mm3 in size are composed of a Lu0.4Gd1.6SiO5 (LGSO) and Lu1.9Y0.1SiO5 (LYSO). These are optically coupled one after the other, forming phoswich pairs of detectors. Four phoswich detectors are enclosed in a hermetic container made of kovar (an alloy of iron–nickel–cobalt having a density of 8.359 g/cm3). The end of the axial FOV shielding is made of tungsten (19.3 g/cm3 density, 15.75 mm thickness and 131 mm internal diameter) to minimize the detection of out-of-FOV activity. The most relevant design features of the LabPET™-8 can be found in [24], whereas the technical specifications and performance assessment of the system used in our laboratory are given elsewhere [17].

Monte Carlo Simulation Studies

Monte Carlo simulations provide the ability to generate data under controlled conditions and to discriminate between scattered and unscattered events [25]. As such, it is considered as a useful tool to assist in the development and evaluation of scatter correction techniques. An experimentally validated Monte Carlo simulation model of the LabPET™-8 scanner was used in this work [8]. The LabPET™-8 scanner is modelled as realistically as possible in terms of geometry, physics of radiation transport and signal processing using the Geant4 Application for Tomographic Emission (GATE) Monte Carlo simulation toolkit [26]. All simulations were run using a coincidence timing window of 10 ns, an energy resolution of 25 % and lower energy thresholds of 250, 350 and 425 keV, while the upper energy threshold was kept constant (650 keV). Back-to-back 511 keV annihilation photons were generated to decrease computational time. A total of 109 events were generated for each simulation study, yielding count rates equivalent to those encountered in typical small-animal PET studies. The GATE output information comprising separate prompt and scattered events was recorded in ASCII format. The SF, estimated as the ratio of scattered to total events, was then calculated. In a second step, coincidence events were binned into sinograms for further characterization of the spatial distribution of Compton scatter. Reconstructions were performed by means of the Software for Tomographic Image Reconstruction (STIR) using the iterative three-dimensional ordered subsets maximum a posteriori using the one-step late (OSMAPOSL) algorithm with four subsets and eight iterations [27].

Various simple digital phantoms and computerized anatomical models of rodents enabling to simulate simple source geometries and more realistic complex patterns of tracer distributions were used to assess the magnitude and spatial distribution of scattered events [28]. Rodent studies were simulated using typical spatial biodistribution of 2-deoxy-2-[18F]fluoro-D-glucose for mice and rats [29, 30] considering the corresponding distribution of attenuation coefficients. The NEMA NU-04 image quality phantom [31] and more realistic digital phantoms such as mouse whole body (MOBY) and rat whole body (ROBY) [32] were used to study the scatter component for single- and multiple-subject scanning configurations. The different arrangements of phantoms adopted in this work are shown in Fig. 1. In the ‘single-subject’ configuration, one subject was located in the centre of the scanner's FOV. In the ‘three-subject’ configuration, two subjects were located on the left and right sides of the centrally located subject, whereas in the ‘five-subject’ configuration, five subjects were located at the left, centre, right, top and bottom positions in the scanner's FOV. The true image obtained by reconstructing the unscattered component from the GATE simulations is used as reference for comparison.

Fig. 1.
figure 1

Illustration of single- and multiple-subject imaging configurations used in this study showing: a single subject located centrally in the FOV, b three subjects in the FOV placed on the left, central and right positions and c five subjects in the FOV placed on the left, central, right, up and down positions.

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Evaluation of the Scatter Component and Out-of-FOV Scatter

The scatter component of the LabPET™-8 scanner was characterized in terms of object and detector/gantry scatter. Object scatter consists of annihilation photons which have undergone Compton scattering only in the object, whereas detector/gantry scatter represents Compton scattering in different components of the scanner other than the object under study. This includes scintillation crystals, scanner gantry, detector covering and end-of-FOV shielding. Compton-scattered events in these different components were also evaluated.

The magnitude of out-of-FOV scatter for the LabPET™-8 scanner was evaluated using both simulated and experimental measurements. This was performed using short (7 cm height and 2.5 cm diameter) and long (14 cm high and 2.5 cm in diameter) solid polyethylene phantoms. The short phantom was placed within the axial FOV of the scanner, while the long phantom was placed within the axial FOV extending outside the axial FOV at both ends. A line source (7 cm long) containing 10 MBq of F-18 was inserted into the short phantom parallel to its long axis, whereas a line source (14 cm long) containing 20 MBq of F-18 was used for the long phantom. The SF was calculated according to the method described in the NEMA NU-04 standards [31]. Scatter from out-of-FOV activity was calculated by subtracting the SF of the short phantom from that of the long phantom.

Scatter Modelling and Correction

Model-based scatter estimation techniques use emission and transmission images to estimate the probability of scattered events along each line of response for selected scatter points in the transmission image by calculating the line integral of the scatter photon trajectories [9]. The scatter distribution is calculated by summation of the probabilities of Compton scattering estimated for each possible scatter point in the transmission image and every detector pair. The single-scatter simulation (SSS) technique used in this work is based on the single-scatter approximation and estimates the scatter distribution using the Klein–Nishina formula [33].

The scatter distribution is calculated using the SSS technique, which is scaled to account for multiple scatter and scatter from out-of-FOV activity. However, the implementation in STIR package is optimized for clinical scanners where coarse sampling is used to speed up the scatter computation, and the full scatter sinogram is constructed by interpolation [34]. The number of detectors is smaller in small-animal PET scanners compared to clinical scanners and, as such, full detector sampling was adopted. The resulting scatter sinogram obtained using two iterations was compared to Monte Carlo simulated scatter sinograms for both single- and simultaneous multiple-subject studies.

The PET data were corrected for attenuation by multiplying the attenuation correction factors obtained by forward projection of the object(s)-specific attenuation map at 511 keV. The scatter sinogram was used as additive terms in the iterative OSMAPOSL algorithm using STIR.

Image Quality and Quantitative Accuracy

The effect of scatter correction on image quality and quantitative accuracy was evaluated for single- and simultaneous multiple-subject PET imaging using various figures of merits including contrast, signal-to-noise ratio (SNR), spill-over ratio (SOR) and recovery coefficients. Regions of interest (ROIs) with diameters approximately equal to half the radius of the two cold cylinders (no radioactivity) were defined and the mean counts/ROI in each region and in the background of the NEMA image quality phantom determined for true, uncorrected, attenuation corrected only and attenuation and scatter-corrected images. SOR was calculated as the ratio of counts in the respective cold cylinder to the counts in the uniformly active region. The contrast recovery (ideal value of 100 %) was calculated according to:

$$ \mathrm{Contrast}=\left(\frac{N_{\mathrm{BG}}-{N}_{\mathrm{cold}}}{N_{\mathrm{BG}}}\right)100\% $$
(1)

where N BG is the count density in the background's ROI, and N cold is the count density in the cold cylinder's (air or water) ROI.

The SNR was defined as the mean number of counts divided by the standard deviation of pixel intensities in a ROI defined within the background region of the NEMA image quality phantom.

$$ \mathrm{SNR}=\left(\frac{\overline{N_{\mathrm{ROI}}}}{\sigma_{\mathrm{ROI}}}\right) $$
(2)

The recovery coefficient, defined as the percentage ratio of counts in an ROI in the corrected image to those in the same ROI in the true images, was calculated according to:

$$ \mathrm{Recovery}\;\mathrm{coefficient}=\left(\frac{N_{\mathrm{ROI}}^{\mathrm{corrected}}}{N_{\mathrm{ROI}}^{\mathrm{true}}}\right)\times 100\% $$
(3)

Results

Modelling the Scatter Component

The magnitude of Compton scattering originating from the various physical materials present in the LabPET™-8 scanner and the amount of out-of-FOV scatter for various energy windows are summarized in Table 1. The maximum amount of scatter observed is due to kovar, which is used as a covering material for the detectors. The scatter contribution due to lead shielding is negligible. Both experimental and simulated out-of-FOV SFs show that out-of-FOV scatter is negligible in small-animal PET imaging using the LabPET™-8 scanner. The effect of increasing the number of objects in scanner's FOV on the magnitude of scatter can be observed in Table 2. In the case of MOBY, the percentage increase in SF for three and five subjects is 36.4 and 63.6 % in comparison to one subject, respectively. Full axial lengths of the NEMA image quality phantom and MOBY model were covered in one acquisition, whereas the ROBY model was scanned at three different axial positions corresponding to brain, thorax and pelvis regions. As expected, object SF decreases with increasing the LET.

Table 1 The scatter fraction due to different materials in the LabPET™-8 scanner for lower energy thresholds of 250, 350 and 400 keV. The experimental out-of-FOV SF values are also shown between brackets
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Table 2 Object scatter fraction estimates for single and simultaneous multiple scanning of the NEMA image quality phantom, MOBY and ROBY for lower energy thresholds of 250, 350 and 400 keV. The percentage increase in SF for three and five subjects with respect to single-subject configuration is shown between brackets
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The good agreement between experimentally measured and Monte Carlo simulated projection data (total events) for a single NEMA image quality phantom is depicted in Fig. 2 for both the uniform region and region-containing active rods. Comparisons between the scatter distributions obtained using model-based scatter estimation and Monte Carlo simulations for single and multiple scanning of the NEMA image quality phantom and ROBY are shown in Figs. 3 and 4, respectively. Overall, a good agreement was observed between model-based and Monte Carlo simulated scatter profiles. A small discrepancy between the tails of the scatter profiles can be observed, which is likely due to the fact that analytical modelling of multiple scattering does not account for the different angular distributions of the rescattered photons.

Fig. 2.
figure 2

Comparison of experimental and Monte Carlo simulated projection data (total events) for the single NEMA image quality phantom through a the uniform region and b the region covering the active rods.

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Fig. 3.
figure 3

Comparison between Monte Carlo simulated and model-based scatter sinogram plane (upper row) and corresponding profiles (lower row) for a single and b multiple five NEMA image quality phantoms.

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Fig. 4.
figure 4

Comparison of Monte Carlo simulated and model-based scatter component sinogram plane (upper row) and corresponding profiles (lower row) for a single ROBY and b two ROBY models.

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Assessment of Image Quality and Quantitative Accuracy

In the uniform compartment of the NEMA phantoms, the SNR for the five subjects is less than that of the three subject arrangement, the latter being also less than that of the single phantom configuration (data not shown). Scatter-corrected images have a poorer SNR, which can be explained by the scatter subtraction process. The SORs measured in the cold compartment of the NEMA phantom are shown in Table 3. The SOR increased in the case of multiple subjects scanning compared to single-subject scanning. Scatter correction decreases the SOR in both air- and water-filled compartments in the configurations adopted in this study. However, the effect of scatter correction was more noticeable in the air compartment than in the water compartment. The effect of attenuation and scatter correction on image contrast is demonstrated in Table 4 for different configurations of the NEMA image quality phantom. The contrast was more degraded in the multiple subjects' arrangement. Attenuation correction had a negligible effect on the contrast. However, scatter correction along with attenuation correction improved the contrast for the cold air compartment in single- and multiple-subject PET studies. The impact of scatter correction was more pronounced in simultaneous multiple subjects.

Table 3 Spill-over ratio (SOR) measured in the cold compartments of the NEMA phantom reconstructed without correction (NC), with attenuation correction only (AC) and with attenuation and scatter corrections (AC + SC) for different scanning configurations. Estimates of the same metric in the actual images are also shown
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Table 4 Contrast measured in the NEMA phantom reconstructed without correction (NC), with attenuation correction only (AC) and with attenuation and scatter correction (AC + SC) for different scanning configurations. Values of the same metric in the true images are also shown
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A representative transaxial slice of the NEMA image quality phantom corresponding to single-, three- and five-subject configurations is shown in Fig. 5. Horizontal profiles through the centre of images corresponding to the true image (unscattered events only) serving as reference, the image reconstructed after attenuation correction only and after applying attenuation and scatter corrections are also shown. It can be seen that scatter correction improves the contrast in the cold cylinders and matches better the true image, especially in the five-subject configuration.

Fig. 5.
figure 5

Reconstructed images of the simulated NEMA image quality phantom (upper row) and their corresponding horizontal profiles (lower row) comparing true, attenuation corrected (AC) and attenuation and scatter-corrected (AC + SC) images for a single, b three and c five phantom configurations. The displayed transverse slices correspond to AC + SC images.

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The recovery coefficients in the lung, liver, left and right kidney regions of the MOBY phantom are summarized in Table 5 for the different scanning configurations. The use of attenuation correction overestimates the recovery coefficients especially in the five-subject configuration, whereas attenuation and scatter correction underestimate the recovery coefficients. Higher recovery coefficients are obtained for single compared to multiple-subject imaging after scatter correction. A transverse slice of the MOBY phantom corresponding to single-, three- and five-subject configurations through the kidney region is shown in Fig. 6. It can be seen that scatter correction has little value especially for the single-subject configuration.

Table 5 Recovery coefficients measured in different body regions of the MOBY phantom reconstructed with attenuation correction only (AC) and with attenuation and scatter corrections (AC + SC) for different scanning configurations
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Fig. 6.
figure 6

Representative slices of the simulated MOBY phantom (upper row) and their corresponding horizontal profiles (lower row) comparing true, uncorrected (NC), attenuation corrected (AC) and attenuation and scatter-corrected (AC + SC) images for a single, b three and c five MOBY model configurations.

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The recovery coefficients in the lung, heart and kidney regions of the ROBY phantom reconstructed with attenuation correction only and with attenuation and scatter corrections for single- and two-subject scanning configurations are represented in Fig. 7. The use of scatter correction compensates for the overestimation of recovery coefficients resulting from attenuation correction alone but induces equivalent underestimation. Transaxial slices and corresponding horizontal profiles of the ROBY thorax region representing the true, uncorrected, attenuation corrected only and attenuation and scatter-corrected images are shown in Fig. 8.

Fig. 7.
figure 7

Recovery coefficients measured in different body regions of the ROBY phantom reconstructed with attenuation correction only (AC) and with attenuation and scatter correction (AC + SC) for a single and b two ROBY models.

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Fig. 8.
figure 8

Representative slices of the simulated ROBY thorax region (upper row) and their corresponding horizontal profiles (lower row) comparing true, uncorrected (NC), attenuation corrected (AC) and attenuation and scatter-corrected (AC + SC) for a single and b two ROBY models.

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Discussion

In this work, we assessed the magnitude and spatial distribution of the scatter component in small-animal PET when imaging single- and multiple-subject simultaneously. The impact of scatter correction on image quality and quantitative accuracy under the same conditions was also evaluated. Monte Carlo calculations are widely used to study the characteristics of Compton scattering in PET [35]. Moreover, the Monte Carlo method offers the unique capability to provide detailed information about unscattered and scattered events and even to distinguish between single- and multiple-scattered events. Recent developments in computationally efficient Monte Carlo simulation packages combined with advances in computational platforms including graphical processing units and cloud computing has made it possible to model the scatter component in small-animal PET imaging using realistic source distributions within complex anatomical models under controlled conditions [25].

In this work, the GATE platform was used to study the scatter characteristics of the LabPET-8 scanner. It was observed that the scatter contribution from kovar covering material was significantly higher in comparison to scatter originating from lead and copper plate serving as end-of-FOV shielding material. This is due to the fact that kovar, being a high-density alloy covering the entire detectors, produces more Compton scattering in the LabPET-8 scanner. Similar observations regarding the behaviour of this material were reported more recently [18]. In particular, when imaging rats, organs presenting with high uptake such as the heart, brain and bladder can be outside the imaging FOV owing to the small axial FOV of the scanner. This might increase detected scatter originating from outside the FOV. Therefore, the contribution of scattered events arising from outside the FOV was evaluated. It was observed that events arising from outside the FOV have a negligible impact (<1 %) for LETs of 350 and 450 keV, whereas the contribution was less than 1.7 % for a LET of 250 keV, thus indicating that the end shields of the LabPET-8 scanner are reasonably effective in rejecting out-of-FOV scatter. This also implies that a scatter correction method that models only scattered events originating within the FOV, such as the single-scatter simulation method used in this study [33], is reasonably adequate is small-animal PET imaging. The object SF was evaluated for single and multiple scanning of the NEMA image quality phantom, MOBY and different body regions of the ROBY anatomical model. The SF increases substantially for simultaneous multiple subjects imaging compared to single-subject imaging, implying that scatter correction is important when imaging simultaneous multiple subjects.

Since APDs are inherently slow, APD-based systems such as the LabPET-8 scanner require a wide coincidence window as well as a wide energy window. Also, different timing windows are used for LGSO-LGSO, LYSO-LYSO and LGSO-LYSO in LabPET-8 scanner. Hence, the SF was evaluated under realistic conditions for a selected coincidence timing window of 10 ns and lower energy threshold of 250, 350 and 425 keV (the upper threshold was set to 650 keV). As expected, the SF decreased with increasing the LET [8].

The estimated scatter distribution using the single-scatter simulation method shows good agreement with Monte Carlo simulations for single- and simultaneous multiple-subject imaging. The SNR for scatter-corrected images deteriorates owing to the scatter subtraction process and the consequent reduction of statistics in the acquired data sets. However, the quantitative accuracy is improved especially for simultaneous multiple-subject imaging. The spill-over ratio increases with increasing the number of subjects in the FOV. Scatter correction improves the SOR for both cold water and air compartments in single- and multiple-subject imaging; however, this effect is much noticeable for the air compartment. Similar observations about the SOR were reported in a related study [21]. The model-based scatter correction technique improves image contrast for both cold compartments of the NEMA image quality phantom compared to the case where no correction is performed. Likewise, the recovery coefficients in different body regions of the MOBY and ROBY phantoms were remarkably improved after scatter correction for simultaneous multiple mice as well as single and multiple rat imaging.

Conclusion

The scatter component originating from different parts of the LabPET-8 scanner including gantry and out-of field-of-view was characterized. The magnitude and spatial distribution of Compton scattering were evaluated for single and simultaneous multiple subjects. Model-based estimation of the scatter component has good agreement with corresponding Monte Carlo simulations. Attenuation and scatter corrections improve contrast and quantification in small-animal PET especially for simultaneous multiple-subject imaging. For accurate PET quantification, attenuation correction is required for single and multiple mice and rat studies, whereas scatter correction is required for single rat and multiple mice and rat studies.