Built on top of the Geant4 toolkit, GATE is collaboratively developed for more than 15 years to design Monte Carlo simulations of nuclear-based imaging systems. It is, in particular, used by researchers and industrials to design, optimize, understand and create innovative emission tomography systems. In this paper, we reviewed the recent developments that have been proposed to simulate modern detectors and provide a comprehensive report on imaging systems that have been simulated and evaluated in GATE. Additionally, some methodological developments that are not specific for imaging but that can improve detector modeling and provide computation time gains, such as Variance Reduction Techniques and Artificial Intelligence integration, are described and discussed.

Accurately modeling the light transport in scintillation detectors is essential to design new detectors for nuclear medicine or high energy physics. Optical models implemented in software such as Geant4 and GATE suffer from important limitations that we addressed by implementing a new approach in which the crystal reflectance was computed from 3D surface measurements. The reflectance was saved in a look-up-table (LUT) then used in Monte Carlo simulation to determine the fate of optical photons. Our previous work using this approach demonstrated excellent agreement with experimental characterization of crystal light output in a limited configuration, i.e. when using no reflector. As scintillators are generally encapsulated in a reflector, it is essential to include the crystal-reflector interface in the LUT. Here we develop a new LUT computation and apply it to several reflector types. A second LUT that contains transmittance data is also saved to enable modeling of optical crosstalk. LUTs have been computed for rough and polished crystals coupled to a Lambertian (e.g. Teflon tape) or a specular reflector (e.g. ESR) using air or optical grease, and the light output was computed using custom Monte Carlo code. 3 × 3 × 20 mm3 lutetium oxyorthosilicate crystals were prepared using these combinations, and the light output was measured experimentally at different irradiation depths. For all reflector and surface finish combinations, the measured and simulated light output showed very good agreement. The behavior of optical photons at the interface crystal-reflector was studied using these simulations, and results highlighted the large difference in optical properties between rough and polished crystals, and Lambertian and specular reflectors. These simulations also showed how the travel path of individual scintillation photons was affected by the reflector and surface finish. The ultimate goal of this work is to implement this model in Geant4 and GATE, and provide a database of scintillators combined with a variety of reflectors.

The intrinsic spatial resolution of clinical positron emission tomography (PET) detectors is ~3–4 mm. A further improvement of the resolution using pixelated detectors will not only result in a prohibitive cost, but is also inevitably accompanied by a strong degradation of important performance parameters like timing, energy resolution and sensitivity. Therefore, it is likely that future generation high resolution PET detectors will be based on continuous monolithic scintillation detectors. Monolithic detectors have attractive properties to reach superior 3D spatial resolution while outperforming pixelated detectors in timing, energy resolution and sensitivity. In this work, optical simulations including an advanced surface reflection model, allow us to investigate the influence of three parameters on the spatial resolution: silicon photomultiplier (SiPM) pixel size, photon detection efficiency (PDE) and the number of channels used to read out the SiPM array. A lutetium-yttrium oxyorthosilicate (LYSO) crystal with dimensions 50  ×  50  ×  16 mm3 coupled to an SiPM array is calibrated and a nearest neighbor (NN) algorithm is used to position events. Findings show that the tested parameters affect the spatial resolution resulting in 0.40–0.66 mm full width at half maximum (FWHM). Best resolution could be obtained with smaller SiPM pixels, higher PDE, and an individual channel readout. However, it was shown that combining channels by adding their signals can significantly reduce the amount of readout channels while having small or no significant impact on the resolution. The mean depth of interaction (DOI) estimation error is 1.6 mm. This study demonstrates the ultimate spatial resolution that can be obtained with this detector without being constrained by practical limitations of experimental setups. In the future these optical simulations may be used as a more precise and fast method to obtain calibration data for real monolithic detectors.

Typical PET detectors are composed of a scintillator coupled to a photodetector that detects scintillation photons produced when high energy gamma photons interact with the crystal. A critical performance factor is the collection efficiency of these scintillation photons, which can be optimized through simulation. Accurate modelling of photon interactions with crystal surfaces is essential in optical simulations, but the existing UNIFIED model in GATE is often inaccurate, especially for rough surfaces. Previously a new approach for modelling surface reflections based on measured surfaces was validated using custom Monte Carlo code. In this work, the LUT Davis model is implemented and validated in GATE and GEANT4, and is made accessible for all users in the nuclear imaging research community. Look-up-tables (LUTs) from various crystal surfaces are calculated based on measured surfaces obtained by atomic force microscopy. The LUTs include photon reflection probabilities and directions depending on incidence angle. We provide LUTs for rough and polished surfaces with different reflectors and coupling media. Validation parameters include light output measured at different depths of interaction in the crystal and photon track lengths, as both parameters are strongly dependent on reflector characteristics and distinguish between models. Results from the GATE/GEANT4 beta version are compared to those from our custom code and experimental data, as well as the UNIFIED model. GATE simulations with the LUT Davis model show average variations in light output of <2% from the custom code and excellent agreement for track lengths with R > 0.99. Experimental data agree within 9% for relative light output. The new model also simplifies surface definition, as no complex input parameters are needed. The LUT Davis model makes optical simulations for nuclear imaging detectors much more precise, especially for studies with rough crystal surfaces. It will be available in GATE V8.0.

To detect gamma rays with good spatial, timing and energy resolution while maintaining high sensitivity we need accurate and efficient algorithms to estimate the first gamma interaction position from the measured light distribution. Furthermore, monolithic detectors are investigated as an alternative to pixelated detectors due to increased sensitivity, resolution and intrinsic DOI encoding. Monolithic detectors, however, are challenging because of complicated calibration setups and edge effects. In this work, we evaluate the use of neural networks to estimate the 3D first (Compton or photoelectric) interaction position. Using optical simulation data of a 50 × 50 × 16 mm3 LYSO crystal, performance is evaluated as a function of network complexity (two to five hidden layers with 64 to 1024 neurons) and amount of training data (1000−8000 training events per calibration position). We identify and address the potential pitfall of overfitting on the training grid through evaluation on intermediate positions that are not in the training set. Additionally, the performance of neural networks is directly compared with nearest neighbour positioning. Optimal performance was achieved with a network containing three hidden layers of 256 neurons trained on 1000 events/position. For more complex networks, the performance degrades at intermediate positions and overfitting starts to occur. A median 3D positioning error of 0.77 mm and a 2D FWHM of 0.46 mm is obtained. This is a 17% improvement in terms of FWHM compared to the nearest neighbour algorithm. Evaluation only on events that are not Compton scattered results in a 3D positioning error of 0.40 mm and 2D FWHM of 0.42 mm. This reveals that Compton scatter results in a considerable increase of 93% in positioning error. This study demonstrates that very good spatial resolutions can be achieved with neural networks, superior to nearest neighbour positioning. However, potential overfitting on the training grid should be carefully evaluated.