The strength of positron emission tomography (PET) lies in its ability to detect metabolic changes in vivo. However, the emission measurements are inherently noisy owing to the limitations of the detection system and the physics behind PET imaging [1–3]. Hence, PET image quality and quantitative accuracy is a function of image correction, reconstruction, and quantification techniques. A well-controlled and calibrated imaging condition is necessary to improve efficacy of these techniques. Therefore, our aim is to establish an unbiased evaluation platform for quantitative imaging using the eXplore VISTA small animal PET system (GE Healthcare, Waukesha, Wisconsin, USA) based on Monte Carlo (MC) simulation. MC simulation can realistically reproduce actual acquisition and is widely accepted as the least biased method [4–6]. For PET imaging, several MC simulation codes, designed and suited for different applications, are publicly available [4–6]. The Geant4 Application for Tomographic Emission (GATE)  is one of the codes by the openGATE collaboration, based on the Geant4 libraries. One important feature of GATE compared with other publicly available codes is its ability to model time-dependent processes, such as count rate, random coincidences, multiple coincidences, and detector dead-time using virtual clock synchronization [7,8].
The modeled scanner is a commercial small animal PET system that uses dual layer phoswich detector modules. The determination of the layer in which interaction occurs is accomplished using differences in light decay time of the scintillator materials . Thus, the eXplore VISTA system can suppress the degradation of radial resolution (the so-called parallax error) compared with an imaging system with identical geometry but without the depth-of-interaction (DOI) capability. Although GATE has been successfully applied to simulate several clinical and preclinical systems [10–13], this is the first time that a model of this DOI-capable small animal PET scanner has been developed. In the proposed detection model, the physics underlying PET, the scanner configuration, various scattering elements and the data collecting system of the eXplore VISTA system are explicitly described using GATE simulation. For verification purposes, the simulated sensitivity, scatter fraction, spatial resolution, and count rate performance are compared with the performance of a real system. After validation tests, we performed a preliminary investigation of the effects of photon attenuation, photon scatter, and random coincidences on the accuracy of quantitative analysis using a small animal PET scanner.
Materials and methods
Monte Carlo model
A MC model based on GATE version 2.2.0 (Geant4 7.0.p01, CLHEP 220.127.116.11, ROOT 4.03, ecat7, LMF 2.0, GATE 2.2.0) was established to simulate the physical processes involved in PET data acquisition, such as positron range, annihilation photon noncollinearity, photoelectric absorption, Compton, and coherent scattering. The PET instrumentation techniques employed in the modeled scanner, including the scanner geometry configuration and the signal processing chain, were also accurately modeled using GATE simulation.
The eXplore VISTA system is a DOI capable small animal PET scanner. The system consists of two rings of 18 detector blocks, and each detector block consists of a 13×13 array of phoswich elements. The 15 mm deep phoswich detector module is made of cerium-doped lutetium–yttrium orthosilicate (LYSO)/cerium-doped gadolinium orthosilicate (GSO) pairs. The length of the front LYSO layer is 7 mm and the rear GSO layer is 8 mm. The LYSO/GSO pair has a sensitive area measuring 1.45×1.45 mm and a 1.55 mm pitch. The detectors cover an axial field-of-view (FOV) of 48 mm and an effective transaxial (FOV) of 67 mm. As shown in Fig. 1, the proximal end shield, the bed and the Delrin cover were also modeled in the simulation.
A sequence of signal processing modules, as shown in Fig. 2, was proposed to simulate the signal flow of the components of data acquisition in eXplore VISTA system. First, the photon interactions within each crystal were summed by the adder and then regrouped by the readout into pulses per detector block. Next, the energy spectrum was blurred by Gaussian functions with full width at half maximum (FWHM) of 26% for LYSO and 33% for GSO, referenced at 511 keV. Then, a low trigger threshold of 100 keV and a paralyzable dead-time of 220 ns, mainly because of the signal integration time, were applied to the simulated events. Next, a coincidence time window of ±10 ns was applied to determine coincidence events. Then, a nonparalyzable dead-time of 1.4 μs, mostly because of the analog-to-digital converter busy time, and a signal flow effect, which is because of the computing capability of processing signals recorded by all 36 detector blocks, were introduced into the chain. Finally, signal selection criteria, including energy window, coincidence window, treatment policy of multiple coincidences and minimum sector difference were applied to those nonrejected events to sort valid coincidence events. Unless otherwise stated, the energy window used in this study was 250–700 keV.
The coincidence output from the simulator was in list-mode format, storing time (eight bytes), energy (one byte), identification (ID) of crystal (one bytes), ID of run (four bytes), ID of event (four bytes) and number of Compton interactions (one byte) in hexadecimal notation for each event. To reconstruct the list-mode output, the detected line of responses were sorted into histograms and organized into three-dimensional (3D) sinograms. The 3D sinograms were then rebinned into two-dimensional (2D) sinograms by Fourier rebinning with a maximum ring difference of 16 and a span of 3. Each sinogram had matrix size of 175×128. Following rebinning, the resultant 2D sinograms were reconstructed using 2D filtered backprojection. The reconstructed images contained 61 planes of matrix size 175×175, with voxel size of 0.3875×0.3875×0.775 mm3.
The protocols used in this study for small animal PET performance evaluation were adapted from the evaluation protocols for clinical whole-body PET systems . Four features of our simulation model were evaluated, including system sensitivity, spatial resolution, scatter fraction and count rate performance.
The 18F solution, contained in a capillary tube that was 1.1 mm in diameter and 2.0 mm in length, was used to create a point source for the sensitivity test. The point source was stepped along the scanner axial axis using a step size of 1 mm. At each point source position, data were acquired for 30 s. Sensitivity was determined as the ratio of true coincidence rate to the point source activity in decays per second. The true coincidences were obtained by correcting the prompt coincidences for radioactive decay, dead-time effects, and random and background coincidences.
In the spatial resolution test, an 18F point source with a diameter of 0.5 mm was stepped along the vertical direction at two fixed axial positions, one at the center of axial FOV and the other 10 mm away from the center of the axial FOV. At each point source location, data were acquired for 30 s. Spatial resolution was defined as the FWHM of the point spread function obtained by interpolating the radial and tangential profiles of the point source images.
In the scatter fraction test, two solid plastic cylinders containing parallel holes for line source were used to simulate mouse and rat imaging conditions. The mouse-sized phantom was 3.2 cm in diameter and 7.5 cm in length and had two 1.5-mm-diameter holes, one along the central axis of the phantom and the other 11 mm away from the cylinder axis. The rat-sized phantom was 5.7 cm in diameter and 15 cm in length. The distance between the on-center and the off-center holes (1.5 mm in diameter) was 20 mm. A 18F line source (1.1 mm in diameter and 7 mm in length) was inserted into the on-center hole. The phantom was then placed at the center of the transaxial and axial FOVs. Data acquisition was performed for 20 min and repeated after moving the line source to the other hole. The scatter fraction was calculated as following:
where T and S are the true and scatter coincidence counts, SF is the scatter fraction, and A is the average activity of the line source. K is the weighting factor determined as the area ratio of the outside annulus to the inside circle of the cylindrical phantom, where the radius of the circle and the annulus thickness are both equal to one-half of the phantom radius. The subscripts ‘center’ and ‘offcenter’ represent the position of the line source. To determine Tcenter, Toffcenter, Scenter and Soffcenter from rebinned sinograms, the peak of the line source in each slice was first aligned with the center of the FOV. The rearranged sinograms were then summed in the angular and axial directions. Finally, the resultant count profile along the transaxial direction was fitted by Gaussian distributions to determine the true and the scatter coincidence counts. In experimental measurements, photon interactions within the phantom might not be the only contribution to the scatter events. Therefore, simulations for computing scatter fraction were also repeated on the detection models including either none or one of these scattering elements under each simulation run to determine the contributions from the scattering photons outside the phantom.
Count rate performance
Validation of count rate simulation was performed using hollow cylinders filled with 18F solution with progressively larger amounts of activity to compare the count rate behavior of our detection model as a function of activity with a real system. A cylinder that was 3.2 cm in diameter, 7.5 cm in length and 55 ml in volume was used to simulate the mouse imaging condition. For the rat imaging condition, a cylinder that was 5 cm in diameter, 15 cm in length and 290 ml in volume was used. Data acquisition was performed for the count rate phantom centered axially and transversally in the FOV. The noise equivalent count rate was calculated using the following equation:
where T, S, R and P are the true, scatter, random and prompt coincidence rate, noise equivalent count rate, NECR, SF is the scatter fraction described in Scatter fraction section and k is the weighing factor defined as the ratio of the diameter of the phantom to the transverse FOV. In eXplore VISTA system, the estimates of the random coincidence count rates were derived from the singles count rates .
Preliminary investigation on quantification loss associated with physical effects
To evaluate the impacts of photon attenuation, photon scatter and random coincidences on quantification accuracy of the modeled imaging system, simulation studies were performed using the proposed detection model. A cylindrical phantom with a spherical source insert was used to represent the mouse xenograft study, and the cylinder was the same mouse-sized phantom described in count rate performance section. To model tumor metabolism over time, the spherical source insert was filled with 18F solutions of 13.11, 26.22, and 52.43 kBq/ml to give target-to-background ratios (TBRs) of 4, 8, and 16, respectively. Three sphere sizes with diameter of 6, 8, and 10 mm were used. To assess the effect of physical factors on quantitative accuracy, the resultant loss in quantification was measured using the following equation:
where AT is the true activity in the sphere insert, and AM is the reconstructed source activity that was obtained by converting the mean sphere intensity within a volume of interest (having the same size and location as the sphere insert) into the reconstructed activity using calibration factor. AM was obtained from the nonattenuation corrected images storing only true events (scatter-corrected, random-corrected, nonattenuation-corrected) to evaluate the quantification loss associated with photon attenuation. Attenuation corrected images storing true and random events (scatter-corrected, nonrandom-corrected, attenuation-corrected) and storing true and scatter events (nonscatter-corrected, random-corrected, attenuation-corrected) were used to measure AM to assess the quantification loss associated with photon scatter and random coincidences, respectively. Data corrections, including scatter, random, normalization, attenuation, decay and dead-time, were performed before Fourier rebinning +2D filtered backprojection reconstruction. For correction of scatter and random events, the simulated prompt coincidences were sorted into the true, random and scatter coincidences according to the information provided by the list-mode output. In attenuation correction, the attenuation map was the attenuation coefficient distribution set in simulation.
Using an energy window of 250–700 keV, the central sensitivity of a real scanner was 4.0%, while the result obtained by simulation was 4.35%. This discrepancy could be a result of several factors, including photomultiplier optical coupling efficiency and light spreading or leakage. Therefore, an efficiency factor of 92% was applied to the simulated data, which was determined as the ratio of the central sensitivity obtained from experimental measurements to the simulated results. A comparison of measured and simulated axial sensitivity profiles is shown in Fig. 3. From Fig. 3, the axial sensitivity profile of the modeled scanner is not a typical triangular function for a 3D PET system, which may be due to the axial gap between two rings of detector blocks .
The simulated and measured spatial resolution results, expressed as tangential and radial FWHM, are depicted in Fig. 4. Experimental measurements were found to be slightly higher than the simulated results, primarily because the light spreading in detector crystal and photomultiplier was not modeled in GATE simulation. At the center of axial FOV, the differences between measured and simulated spatial resolution were within 17% in the radial direction and 14% in the tangential direction (Fig. 4a). For a point source located 10 mm away from the center of axial FOV, the differences were less than 18 and 10% in the radial and tangential directions, respectively (Fig. 4b).
The comparison between scatter fractions of the proposed detection model and a real scanner are presented in Table 1. Simulated results for those detection models including various scattering elements are also listed. It shows that the experimental measurements and the simulation results for the Delrin cover, the proximal end shield and bed differed by 4.3% for the mouse-sized phantom and 5.2% for the rat-sized phantom. On the contrary, the differences were increased to 28.5 and 16.85% for the physical mouse and rat phantoms, respectively, when performing simulations without modeling any scattering element.
Count rate performance
The coincidence count rates in this study covered a range from 1 to 760 kBq/ml for the mouse-sized cylinder and 1 to 200 kBq/ml for the rat-sized cylinder. With an energy window of 250–700 keV, the count rate saturation of the eXplore VISTA system occurred at an activity concentration of 455 kBq/ml for the mouse-sized phantom and 141 kBq/ml for the rat-sized phantom. Figure 5 compares measured and simulated results for the prompt coincidence rate, true coincidence rate, random coincidence rate, and noise equivalent count rate. The differences between simulation results and experimental measurements were within 10% for the mouse-sized phantom and 5% for the rat-sized phantom, up to peak activity. Pulse pile-up was not modeled in GATE simulation, which may explain the increased discrepancy beyond the peak activity.
Preliminary investigation on quantification loss associated with physical effects
Figure 6 provides visual impressions of the mouse-sized phantom with spherical source insert of diameters 6, 8, and 10 mm and their reconstructed images. If no attenuation correction was applied, the quantitative accuracy was underestimated to a level of 13.4, 15.2, and 16.0% for 6, 8 and 10-mm diameter spherical sources, respectively, while the results were not affected by spherical source activity. The quantification biases resulting from photon scatter for a 6-mm diameter spherical source with TBR of 4, 8, and 16 were 2.3, 1.7, and 1.4%, respectively. The results under TBR of 4, 8, and 16 were 2.6, 2.0, and 1.7%, respectively, for an 8-mm diameter spherical source, and were 2.7, 2.1, and 1.8%, respectively, for a 10-mm diameter spherical source. With regard to random coincidences, they contributed least to the prompt coincidences (Fig. 5) and had relatively little influence. For the amount of source activity applied in simulation, the introduced bias was less than 0.01%.
In this study, an MC simulation model of an eXplore VISTA system was developed based on GATE to achieve quantitative PET data analysis. Validation of the proposed detection model focused specifically on system sensitivity, spatial resolution, scatter fraction, and count rate performance. In terms of sensitivity, the simulated results were made to match the measured results by introducing a detection efficiency factor. As shown in Fig. 1, good agreement was obtained for various point source positions. In contrast, the light spreading in the photon detection process was not included in the GATE simulation. This made the simulated spatial resolution results appear to perform better than the experimental measurements. However, the discrepancy was within 10–18% and could be compensated by applying an analytical blurring function on the detected line of responses. With regard to the scatter fraction, scattered photons originating from outside the phantom were found to be important. As shown in Table 1, high accuracy was obtained in calculating scatter fractions for both the mouse-sized and the rat-sized phantoms when scattering elements in the modeled system were properly simulated. Our results show that scattered photon contributions outside the phantoms were mainly from the lead shield. Considering the count rate performance, the differences between simulated results and experimental measurements agreed well for both the mouse-sized and the rat-sized phantoms up to the peak activity. These results indicate that our model is sufficiently accurate for simulating PET imaging in common situations for both mouse (5–10 MBq) and rat models (20–40 MBq). A dead-time model at both singles and coincidence levels (Fig. 2)  was developed to reproduce the count rate behavior of the modeled scanner. Further improvements in modeling of saturation processes occurring at high-count rates are needed.
After the validation tests were completed, we evaluated the effects of photon attenuation, photon scatter and random coincidences on the accuracy of quantitative analysis using the proposed detection model. As mentioned before, the data output from simulation contained information that could not be obtained from experimental measurements, including the true attenuation map and the real distribution of scatter and random coincidences. Based on these measurements, we were able to investigate the cause and extent of quantification loss in reconstructed emission images to further improve the compensation methods. In this study, several simple physical phantoms were used for system performance evaluation. When realistic digital phantoms, such as the MOBY phantom , are employed as input, the proposed detection model can generate data offering realistic complexity.
We present a MC simulation model of the GE eXplore VISTA small animal PET system based on GATE. The developed detection system realistically describes the physics underlying PET, the scanner configuration and the data collecting system of this dual layer phoswich system. Results show good agreement between simulation and experiments, suggesting that our proposed detection model is able to provide physically realistic data, thus facilitating the evaluation and improvement of quantitative imaging techniques for small animal PET studies.
The authors thank Dr Jurgen Seidel (Johns Hopkins Medical Institutions) for helpful discussions and sharing the reconstruction source code. This study is supported in part by the Taiwan Merit Scholarship Program and the NIH grant EB1558 and CA92781.