**1. Introduction**

Prostate cancer is the most frequent occurring malignancy in men. Global incidence in 2015 was estimated at over 1.6 million with prostate cancer having the highest incidence of all cancers in Western Europe, United States and Canada [1]. Many prostate cancers have a relatively indolent behavior and do not lead to significant medical complaints during the lifetime of a patient. However, patients may eventually progress to metastatic and/or castration-resistant prostate cancer (CRPC), which is considered an incurable and fatal stage of the disease. The optimal treatment for metastatic prostate cancer depends on characteristics of the tumor and of the patient, and may consist of multiple modalities including hormone therapy, chemotherapy, radiation therapy, and radionuclide therapy [2]. Selection and adjustment of a treatment is strongly dependent on treatment response. Therefore, there is a need for a tool that provides quantitative, lesion-specific and observerindependent response evaluation. Functional metabolic imaging with radiolabeled 68Ga prostate-specific membrane antigen (PSMA) and positron emission tomography (PET) is potentially such a tool. Although there is a vast amount of literature on PSMA-PET in

**Citation:** Rijnsdorp, S.; Roef, M.J.; Arends, A.J. Impact of the Noise Penalty Factor on Quantification in Bayesian Penalized Likelihood (Q.Clear) Reconstructions of 68Ga-PSMA PET/CT Scans. *Diagnostics* **2021**, *11*, 847. https:// doi.org/10.3390/diagnostics11050847

Academic Editor: Lioe-Fee de Geus-Oei

Received: 8 April 2021 Accepted: 4 May 2021 Published: 8 May 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

staging and restaging of prostate cancer, response evaluation using PSMA-PET is less well explored and a standardized quantitative approach still needs to be developed.

It is known that uptake measurements of radiolabeled tracers with in vivo PET are affected by many parameters, as demonstrated by experience with 18F-fluor deoxyglucose (FDG), and standardization prior to application as response parameter is required [3]. For 18F-FDG-PET, repeatabilities of around 10% on average and higher are reported [4–7]. Notwithstanding the differences in pharmacodynamics and pharmacokinetics between FDG and PSMA, this probably applies equally to PSMA-PET. Before quantification of PSMA uptake can be used as a biomarker or surrogate endpoint to identify response to treatment, and before we can design sufficiently powered response evaluation studies, a thorough understanding of parameters affecting the quantitative results is required. Uptake of FDG and PSMA differ due to pharmacodynamical differences [8–10]. Therefore, comparison of uptake measurements from scans with different ligands should be approached with caution.

The spatial resolution of PET imaging is limited due to inherent physical characteristics such as positron range and noncollinearity of annihilation photons. Combined with detector characteristics and image sampling effects caused by discretization of the continuous activity distribution by recording it in finite sized voxels, these result in spillover from structures with a high activity concentration to those with a low activity concentration and vice versa, referred to as partial volume effect (PVE) [11,12]. The PVE is particularly of interest when the object is smaller than 2–3 times the spatial resolution expressed by its full width at half maximum (FWHM) [13,14] which is typically around 4–5 mm for stateof-the-art PET/CT systems [15]. As prostate cancer recurrence often involves relatively small metastatic nodal lesions, these effects are of particular importance with respect to PSMA signal evaluation. Resolution recovery techniques such as point spread function (PSF) modelling can be applied in order to partly recover the true shape and uptake of these lesions. In this study, attention is given in particular to image reconstruction using a Bayesian penalized likelihood (BPL) algorithm which may be advantageous for the signal evaluation of such small lesions, due to better signal-to-noise ratios (SNRs) compared to standard reconstruction techniques.

A potentially relevant difference between 18F-FDG-PET and 68Ga-PSMA-PET is the positron energy. Positrons emitted by 68Ga and 18F have a mean energy of 0.88 MeV and 0.25 MeV [16] corresponding to mean ranges in water of 2.9 mm and 0.6 mm, respectively [17]. Higher positron energy negatively affects the spatial resolution, which is well described for high resolution preclinical PET scanners [18–20]. For small nodal lesions, the resulting blurring effect may have an effect on measured uptake values and lesion detectability. In addition, PSMA exhibits high specificity causing a high tumor-to-background (T/B) ratio which increases accuracy of quantification for larger lesions and visual detection of small lesions [21–23].

The BPL algorithm implemented by GE Healthcare (GE Healthcare, Chicago, IL, United States), Q.Clear, is an iterative reconstruction algorithm which enables users to define a noise penalty factor β. In contrast to ordered subset expectation maximization (OSEM [24]) reconstructions, penalized likelihood reconstructions can be run until full convergence leading to higher quantitative accuracy [25], improved lesion visual conspicuity and maximum standardized uptake value (SUVmax) in small nodules for low β [26] and a more consistent signal-to-noise ratio [27,28].

Although preferred image smoothness for visual assessment of PET studies is user dependent, suggestions for optimal β values are described in the literature for various types of PET/CT studies: a β of 400 for 18F-FDG whole body PET/CT scans [29]; a β of 300 for BPL reconstructions of 18F-fluciclovine scans for imaging of recurrent prostate cancer [30] and a β of 4000 for scans after administration of 90Y for selective internal radiotherapy [31].

The aim of this study was to explore the effect of acquisition time and reconstruction parameters by providing recovery coefficients for various T/B ratios and sphere sizes, obtained from phantom studies with 68Ga-PSMA while applying different β values, and

to find an optimal β value for quantification as well as visual assessment of 68Ga-PSMA PET/CT scans.

#### **2. Materials and Methods**

The Micro Hollow Sphere phantom (Data Spectrum Corporation, Durham, NC, United States) and the NEMA IEC Image Quality phantom (PTW, Freiburg, Germany) were used to obtain PET/CT images that could be assessed objectively and reproducibly. Both phantoms consist of a fillable background compartment and multiple hollow and fillable spheres with inner diameters 37, 28, 22, 17, 13 and 10 mm for the NEMA Image Quality phantom and 10, 8, 6, 5 and 4 mm for the Micro Hollow Sphere phantom, see Figure 1.

**Figure 1.** Transverse PET slices of the NEMA IEC Image Quality phantom (**left**) and the Micro Hollow Sphere phantom (**right**). The image of the Micro Hollow Sphere phantom is scaled up by a factor four with respect to that of the NEMA IEC Image Quality phantom to properly show the features. The dimensions of the largest sphere in the Micro Hollow Sphere phantom match with those of the smallest sphere in the NEMA IEC Image Quality phantom. As the voxel dimensions in the transverse plane are 2.73 by 2.73 mm, individual pixels can be clearly distinguished causing a seemingly low image resolution.

Both the background compartments and sets of spheres were filled with solutions of 68Ga in water. To represent a patient scan, the ratio between the activity concentration of both solutions was based on reported T/B ratios for 68Ga-PSMA diagnostic PET/CT scans one hour after administration of the radiopharmaceutical. A concise overview is given in Table 1. Based on these reports, the decision was made to perform two scans of the phantoms, one with a ratio of 20:1 and one with a ratio of 10:1 between the activity concentration in the spheres and the background compartment.


**Table 1.** Overview of T/B ratios in several studies concerning 68Ga-PSMA PET/CT imaging. The T/B ratio was either computed with the tumor uptake and the SUVmean obtained from a region of interest (ROI) drawn in gluteal muscle [22,32,33] or tumor uptake and the SUVmean from adjacent healthy tissue [34].

#### *2.1. Phantom Preparation and Scanning Procedure*

Both phantoms were filled in a way similar to the one described in the 'Standard operating procedures for quality control' described in the EARL Accreditation Manual [35]. A solution with an activity concentration of 40 kBq/mL used to fill the spheres was prepared by adding 20 MBq 68Ga to 500 mL of water (stock solution) and homogenized by extensive shaking. To obtain an activity concentration of 2 kBq/mL in the water-filled background compartments of known volumes, required amounts of 68Ga were directly added to these volumes. The solutions in the background compartments were homogenized by shaking the phantoms extensively.

Subsequently, data were acquired with a GE Discovery 710 PET/CT scanner (GE Healthcare, Chicago, IL, USA). Both phantoms were scanned simultaneously. The long axes of both phantoms were aligned to coincide with the axis of the bore. The system was set to acquire data in list-mode to enable multiple reconstructions with different count statistics for both acquisitions. An acquisition time of 10 min per bed position was chosen, with a total of three bed positions per scan. The axial field of view was 15.7 cm and the overlap between subsequent bed positions was 23%. The bed positions were chosen in such a way that the spheres were not placed in the overlapping part of two bed positions.

Directly after the first scan, the activity concentrations in both background compartments were doubled by adding amounts of activity equal to those in step 1, to obtain a 10:1 ratio between the activity concentration in the spheres and the background compartments, correcting for radioactive decay. Again, the background compartments were homogenized by shaking the phantoms extensively. Exactly 68 min (one half-life of 68Ga) after starting the acquisition of the first scan, a second acquisition with identical phantom placement and scanning parameters as described in step 2 was performed.

Using the acquired list-mode dataset, multiple iterative reconstructions were made for both scans. All data were corrected for attenuation, random events and scatter. Reconstructions were made with Q.Clear with varying β (300, 400, 450, 500, 600, 700, 800, 900 and 1000) including PSF modelling, for multiple simulated scan times (1, 2, 2.5, 5 and 10 min per bed position). As a reference, conventional iterative OSEM reconstructions with 2 iterations and 24 subsets, 6.4 mm Gaussian filter and 1:4:1 filter in axial direction with and without PSF modelling were obtained. All reconstructions used time-of-flight data and consisted of 2.73 × 2.73 × 3.27 mm<sup>3</sup> voxels and a 256 × 256-pixel matrix.
