**1. Introduction**

Positron emission tomography (PET) is widely recognized as a powerful imaging technique for in vivo quantification and localization of physiological and pathophysiological functions. Furthermore, PET imaging allows to follow the progression of human diseases in transgenic and knockout mice noninvasively, so it has been used to study the effectiveness of new drugs or treatments [1–3]. Due to the small size of experimental animals, high spatial resolution is mandatory in preclinical PET system, which is associated with positron physics, scanner design, data correction, and the reconstruction algorithm [4,5]. Among various positron emission radioisotopes, F-18 is by far the most widely used radionuclide. Nevertheless, with the increasing interest in theranostic approaches for cancer treatment, radioisotopes other than F-18 are also considered in PET imaging, such as Ga-68 [6–8]. Using Ga-68 labeled tracers for diagnostics can be effectively followed by targeted radionuclide therapy performed using the same tracer labeled with Lu-177. Since Ga-68 PET imaging is used to determine the therapeutic protocols with Lu-177, the dose delivered to targets and organs at risk through Lu-177 radionuclide therapy is affected by the imaging performance of Ga-68 PET [9–11]. The mean positron energy of Ga-68 is 0.83 MeV, which results in a mean positron range of 3.5 mm. Hence, the spatial resolution of PET imaging is inferior with Ga-68 compared to F-18 [12]. Improving spatial resolution through positron range correction would increase the accuracy of Ga-68 PET-based treatment planning.

**Citation:** Yang, C.-C. Compensating Positron Range Effects of Ga-68 in Preclinical PET Imaging by Using Convolutional Neural Network: A Monte Carlo Simulation Study. *Diagnostics* **2021**, *11*, 2275. https:// doi.org/10.3390/diagnostics11122275

Academic Editors: Lioe-Fee de Geus-Oei and Alessio Imperiale

Received: 29 September 2021 Accepted: 1 December 2021 Published: 4 December 2021

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Convolutional neural network (CNN) has been applied in several medical imaging areas, and various architectures have been developed for different tasks [13]. This study aimed to investigate the feasibility of positron range correction based on three different CNN models in preclinical PET imaging of Ga-68. The first CNN model (CNN1) used in this study was originally designed to recover high resolution image from low resolution input image, while the second CNN model (CNN2) and the third CNN model (CNN3) were originally designed to convert MRI into pseudo CT. The image data for CNN training and testing were generated by Monte Carlo simulation to prevent experimental errors while realistically modeling the positron range effects.

## **2. Materials and Methods**

#### *2.1. Monte Carlo Simulation Toolkit*

Monte Carlo simulation was performed by using GATE (GEANT4 Application for Tomographic Emission) version 6.0.0 [14]. GATE comprises four layers of codes, which is GEANT4 in the innermost layer, followed by the core layer, application layer, and user layer. GEANT4, a toolkit for the simulation of the passage of particles through matter based on Monte Carlo method, has been proven to be a proper tool for simulation of positron transportation. In GATE, the scanner geometry, particle type, position, energy, physical interactions of particles with matter and run process were defined by using a scripted language at the user layer to output descriptive data in the form of random number for running simulation using GEANT4.

## *2.2. Preclinical PET System*

A FLEX Triumph PET/CT scanner (Gamma Medica-Ideas, Nortridge, CA, USA) was modeled by using the cylindrical PET system in GATE, which was comprised of 5 hierarchic levels: world cylindrical PET, r sector, module, crystal, layer, to produce and store the hit information that generates the singles and the coincidences of the simulation. The preclinical PET scanner investigated in this study includes 180 detector blocks that are arranged into 48 rings, and each block contains an 8 × 8 array of BGO crystals of 2.3 × 2.3 × 10 mm3. This configuration covers a transaxial field-of-view (FOV) of 10 cm and an axial FOV of 11.6 cm. PET data were simulated with a 250- to 750-keV energy window and 12-ns timing window in listmode format, which were consequently assigned into 3D sinograms. The sinograms were Fourier rebinned first and then reconstructed using 2D ordered subsets expectation maximization with 4 iterations and 10 subsets. The voxel size used for PET reconstruction was 0.4 × 0.4 × 0.4 mm3.
