**4. Discussion**

The quantitative capabilities of PET are confounded by a number of degrading factors, whereas the most prominent factors are low signal-to-noise ratio and intrinsically limited spatial resolution [20]. Tumor-targeted theranostic approaches have high lesion-tobackground ratio. For example, PET imaging with Ga-68 labeled somatostatin analogues shows high affinity for tumors expressing somatostatin receptors [7,8]. However, the image blurring caused by the positron range effect of Ga-68 may impact the accuracy of treatment planning based on Ga-68 PET imaging. Fourier devolution techniques have been applied to compensate the positron range effects in PET imaging [21], which inspired us to investigate the possibility of using CNN methods for positron range correction. According to Herraiz et al. [22], their study published in 2021 was the first work to successfully combine deep learning and positron range correction in a coherent framework. In our opinion, more studies are needed in this field. Hence, we investigated the feasibility of positron range correction based on three different CNN models in preclinical PET imaging of Ga-68.

Song et al. have presented a work to recover high-resolution PET image from its lowresolution version by using CNN-based approaches for F-18 FDG exams [23]. A 3-layer CNN model proposed by Dong et al. [15], i.e., CNN1, and a 20-layer CNN model proposed by Kim et al. [24] were adapted in their work. The low-resolution images used as the CNN inputs were acquired with Siemens HR+ scanner, while the high-resolution images used as the CNN labels were acquired with Siemens HRRT scanner, a high-resolution dedicated brain PET scanner. Two simulation studies using the BrainWeb digital phantom and a clinical patient study were conducted. They concluded that adding additional channels that extract anatomical features from MRI could improve the performance of CNN-based resolution recovery methods, whereas deep CNNs outperform shallow CNNs. Since the positron range effect would result in image blurring, it is intuitively reasonable to expect that CNN models designed for resolution recovery may be potential candidate for positron range correction in Ga-68 PET imaging. Hence, CNN1 was adapted in our study.

Herraiz et al. have presented a work which adapts the U-Net network to correct positron range effects of Ga-68 in preclinical PET imaging [22]. In their work, the input data to CNN were Ga-68 images, while the label data were the F-18 images. The PET images for CNN training and testing were generated by using the Monte Carlo simulator MCGPU-PET to model data acquisition in an Inveon PET/CT scanner. Their results demonstrated that their proposed method was able to restore the PET images going from 60% up to 95% while maintain low noise levels. They concluded that it is sufficient to use PET images without the corresponding CT as input for the neural network, and including not only the reference slice but also some additional neighbor slices could improve the CNN-based positron range correction method. In our opinion, Herraiz et al. demonstrated that CNN models suitable for positron range correction were not only limited to those designed for resolution recovery, because the U-Net network was originally designed for image segmentation [25]. Positron range correction is inherently an ill-posed problem, because there are multiple Ga-68 activity distributions that may correspond to the same blurred image. Pseudo CT synthesis from MRI is also proposed to solve ill-posed problem, because there are multiple MRI values that may correspond to the same CT value. It was hypothesized that CNN models designed for pseudo CT synthesis from MRI may be potential candidate for positron range correction, so CNN2 and CNN3 were adapted in our study.

In Reference [22], it was assumed that the reconstruction method already incorporated positron range correction for F-18, and their image data for CNN training, testing, and validation were generated from numerical models of mice from a repository. In this work, the CNN output images were back-to-back 511-keV gamma rays, which were not affected by the positron range effects. Hence, our method can be used in PET scanners without F-18 positron range correction. NEMA performance measurements have been well accepted by the manufacturers, and most major companies now specify their product performance in terms of these standardized and traceable specifications. This approach to performance documentation facilitates quantitative comparison of cameras by the user with the assurance that all reported values are measured in the same way and, therefore, are directly comparable [26,27]. Hence, a modified NEMA protocol was used in this study to evaluate the performance of CNN-based positron range correction in terms of resolution recovery and spill-over. Our results demonstrated that the image quality of Ga-68 images was improved after positron range correction based on the 3 CNN models investigated in this work, while CNN3 outperformed CNN1 and CNN2 qualitatively and quantitatively. With regard to qualitative observation, it was found that boundaries in Ga-68 images became sharper after correction (see Figures 3, 4 and 8). As for quantitative analysis, the RC and SOR were increased after correction, while no substantial increase in CVRC or CVSOR was observed. Overall, CNN3 should be a good candidate architecture for positron range correction in Ga-68 preclinical PET imaging.

Several limitations to this study need to be acknowledged. First, the data acquisition, processing and reconstruction approaches can influence the study results. The protocol parameters used in this study were suggested by the manufacturers and are currently employed in a real scanner installed in our institution. Second, all images were generated from Monte Carlo simulations. Since it is difficult to obtain PET images without positron range effect from real experiments, Monte Carlo simulation was used to generate Ga-68 images and corresponding gamma source images for CNN training and testing. Third, the impact of image blurring caused by positron range effect on the accuracy of treatment planning based on Ga-68 was not investigated. Assessments of the proposed methods in real Ga-68 images and the resulting impact on treatment planning for Lu-177 radionuclide therapy need to be further investigated.
