Background
Image reconstruction in positron emission tomography (PET) is the process of forming an image data set that represents the spatial distribution of activity in the patient by using the detected coincidence events. The basic algorithm used since the mid-1970s to reconstruct the PET images is filtered back-projection (FBP) [
1]. Along with developments in computing power, new maximum likelihood (ML)-based reconstruction methods were developed that included accurate statistical Poisson-based noise models and physical modeling [
2]. These ML-based models were later combined with expectation–maximization (EM) algorithms [
3]. Compared to FBP, iterative reconstructions led, in most situations, to an improvement in (streaking) artifacts, noise, and resolution as it allowed accurate noise and physics/system models to be included [
4‐
7]. Although the ML-EM reconstructions are accurate, the total reconstruction time is long due to the substantial computing power required per iteration and the many iterations required before convergence is reached. To accelerate the reconstruction process, new methods like ordered subset expectation maximization (OSEM) were developed [
8]. In OSEM, the measured data is divided into subsets (or blocks) and the EM algorithm is applied to each of these subsets [
9]. When all subsets are processed, the next iteration starts. The OSEM method is fast and currently one of the most applied in PET reconstructions. OSEM is, in contrast to ML-EM, not a true ML estimator; it does not converge to a maximum likelihood image [
10]. Moreover, since image noise increases with iterations, ML-EM and OSEM algorithms are usually stopped before the image becomes unacceptably noisy. Typically, some post-filtering is applied to enhance the images [
11].
Several studies reported quantitative differences comparing FBP to OSEM reconstructions [
12,
13]. Most of these could be explained by other effects then the reconstruction process, like differences in attenuation correction, reconstruction filters, higher noise levels in FBP, or ROI selection [
14]. Higher uptake values are sometimes reported for OSEM, but this is almost completely reversible by equalizing the image resolution [
5,
15].
In most cases, OSEM provides accurate quantitative results within 3%; however, larger biases (up to 50%) can be expected in regions with a 5- to 10-fold hotter background [
5]. This can partially be explained by differences in convergence rate in different regions. Cold regions within a hotter background converge at a different rate than hot regions within a colder background [
5]. Stopping early with iterating could therefore result in non-uniform recovery of activity [
16]. This means that, although the resulting images are visually appealing, e.g., hotspot detection in oncology, there could be inaccuracies in a quantitative assessment as the reconstruction algorithm did not reach full “convergence” in all image parts. Moreover, considering the high activity in the urinary bladder and kidneys, and the low background activity and higher tumor to background ratios with
68Ga-PSMA, the quantitative performance of OSEM may be reduced.
In addition to the previously mentioned reconstruction methods, there are also regularized iterative reconstruction methods. The penalized likelihood image reconstruction methods, like block sequential regularized expectation maximization (BSREM), add to the likelihood function a penalty function that controls image quality [
9,
17‐
20]. Due to this penalty function, which provides activity-dependent noise control and edge preservation while iterating, BSREM can run until full convergence is reached [
21]. This means that all image parts are fully converged, thereby increasing the accuracy in a quantitative assessment. Until recently, the penalized likelihood image reconstruction methods were not commonly used. Apart from the longer reconstruction times compared to OSEM, the resulting images of the edge-preserving penalized likelihood methods showed patchy background textures and other undesirable features [
22]. However, new developments show promising results.
In a study by Asma et al. [
23], lesions were inserted into multiple clinical whole-body PET/CT datasets in representative locations. These ‘hybrid’ datasets combine clinically realistic image backgrounds with known lesion activity. They found superior quantitation over early stopped and post-filtered OSEM, while maintaining clinically acceptable image quality. Ahn et al. [
21] extended this study with more clinical datasets from multiple clinical sites and included phantom measurements. Their results also demonstrated improvements in lesion quantitation accuracy compared to OSEM, especially in cold background regions such as lungs. Teoh et al. [
24] performed a phantom and clinical study. They found that the BSREM reconstructions were preferred over OSEM. A clinical evaluation study by Sah et al. [
25] indicated that time-of-flight (TOF) BSREM reconstructions showed the best results in all categories, independent of body compartments, compared to TOF OSEM. Due to recent improvements and these promising results, the BSREM algorithms are also becoming commercially available (e.g., Q.Clear, GE Healthcare, Waukesha, WI, USA).
Although the abovementioned studies show promising results with 2-deoxy-2-[
18F]-fluoro-D-glucose (
18F-FDG) on PET, the situation could be different for the
68Gallium-labeled tracer targeting the prostate-specific membrane antigen (
68Ga-PSMA) as it has a clearly different uptake pattern compared to the
18F-FDG tracer used in most studies. The low background activity, higher tumor to background ratios, higher positron energy, and larger positron range could, e.g., have an effect on the performance [
20,
26]. Moreover, previous studies were performed on PET/computed tomography (CT) whereas in this study, a PET/magnetic resonance (MR) is applied. This could also lead to differences as the current clinical PET/MR scanners have no attenuation coefficients for the bone in the MR-based attenuation map, except for the skull.
As BSREM runs until full convergence, the number of iterations and subsets are no controlling parameters in BSREM. BSREM does, however, have a regularization parameter β. It controls the global strength of the regularization, the relative difference penalty function.
Therefore, in this study, we investigate the optimal regularization parameter β for clinical 68Ga-PSMA PET/MR reconstructions in the pelvic region applying TOF BSREM in comparison to TOF OSEM.
Discussion
We investigated the effect of the regularization parameter β in TOF BSREM reconstructions of clinical 68Ga-PSMA PET acquisitions in the pelvic area. Our quantitative results indicate that the best β value for pelvic 68Ga-PSMA PET with TOF BSREM reconstructions is in the range between 400 and 550 for 2-min emission data and a median-injected dose of 128 MBq.
A β value near 400 will result in images having a similar background noise level and higher SUVmax values compared to reference TOF OSEM with 2 iterations and 28 subsets. These images could be used for clinical evaluations where accurate SUV values are required, like treatment evaluations and follow-up cases. A β value near 550 will result in images having a lower background noise level and similar SUVmax values. The low background noise could make tumor detection easier, but this has to be proven in future studies. Lower β values will result in higher SUVmax and more background noise, and higher β values will result in lower SUVmax and less background noise. The lower the β value, the lower the effect of the regularization function and the more the penalized likelihood function behaves like a normal likelihood function without noise control.
One clinical study performed with
18F-FDG on PET/CT found optimal
β values in the range 350–400 for an injected mean dose of 297 MBq, 60 min uptake time, and 2 min per bed scans [
25]. A phantom/clinical study with
18F-FDG on PET/CT, with an injected dose of 288 MBq, 90 min uptake time, and 4 min per bed scans, found an optimal
β value of 400 [
24]. These findings are slightly below the findings in our study. A higher injected dose and/or longer scan time could be a possible explanation for the lower
β values in their study. Both
18F-FDG studies also noted that higher
β values resulted in lower SUVmax.
Despite the fact that the penalized likelihood algorithms already exist for many years [
17,
19], and the fact that the relative difference penalty by Nuyts et al. [
33,
34], the BSREM by De Pierro et al. [
37], and the combination by Ahn et al. [
10], were already introduced some 15 years ago, these type of reconstruction methods were not used commonly in clinical routine. With todays improved computing power and after recent quantitative evaluations by, e.g., Asma et al. [
23,
38] and Ahn et al. [
21] and clinical evaluations by, e.g., Ma et al. [
39], Passalaqua et al. [
40], Teoh et al. [
24], and Sah et al. [
25], which showed promising results, the TOF BSREM reconstruction method is now attracting more attention and is considered a possibly better alternative to OSEM.
Although OSEM reconstructions are fast, the early termination of the iteration process required to limit the noise, results in different convergence rates in different image regions. The TOF BSREM-penalized likelihood method applied in this study on the other hand achieves effectively full convergence, thereby improving the quantitative accuracy [
21]. The more accurate higher SUVmax values can play a crucial role in detecting small lesions, especially in regions with high background uptake like the liver or brain in
18F-FDG PET. Due to the slow convergence rates of OSEM in cold regions, like the lungs in
18F-FDG, or in regions near hot spots, like the kidneys or urinary bladder, BSREM’s full convergence results in more accurate measurements in these areas [
21,
24]. Besides the improved quantitative accuracy, the increase in SUVmax and the lower background noise with BSREM could possibly also be applied to further reduce the injected tracer dose, but this has to be proven in future studies.
Simulated phantom measurements are an optimal way to investigate certain aspects under specific circumstances, as parameters, like the ground truth, are known. Previous studies included “hybrid” phantom measurements in which lesions with a known activity were inserted in real patient datasets at interesting locations, near hotspots and in cold backgrounds [
21]. In this study, we used clinical patient data which has the advantage of a diverse patient population with lesions in commonly occurring locations. The disadvantage is that the ground truth is not available. We, however, used the same datasets for OSEM and BSREM, meaning that all parameters are the same, except for the reconstruction methods. This means that differences were only due to the differences in reconstruction methods.
The definition of SUVmax, as well as the ROI size and resolution can have a significant impact on measurements [
14,
41]. In our study, we defined SUVmax as the average of the 5 hottest voxels, as the variability of this metric was found to be the lowest, compared to several other measures like the hottest voxel in a lesion [
36,
42]. As all datasets in our study were obtained with the same scanner, and used for both the OSEM and BSREM reconstructions, it should not affect our results. Care has to be taken when comparing our results with other scanners or definitions.
In this study, for each dataset, the variable
β was systematically increased in small steps and the resulting BRSEM reconstructions were compared with one OSEM reconstruction. The probability values (in Table
1) were, however, not corrected for multiple comparisons. As adding more tests by “subsampling” the
β value range will normally not result in accidental positive findings, we believe that it is better not to apply a correction.
This study has some limitations. The current study was, for example, performed on a relatively new TOF PET/MR system. Although we would expect comparable results on similar PET/MR or PET/CT systems, results may vary.
Significant halo artifacts have been reported to occur on many PET/CT and PET/MR systems with the use of 68Ga-PSMA-11. This is mainly due to high organ-to-background activity ratios between the bladder/kidneys and surrounding soft tissue, and due to incorrect scatter correction algorithms [
43,
44]. In those cases, the administration of furosemide is recommended to substantially reduce bladder activity [
27]. The scanners in our institution have a second generation scatter correction algorithm installed, and, as a result, halo artifacts are rarely seen [
45,
46]. Our patient cohort was reconstructed with the latest versions, and no halo artifacts were visible (Additional file
1: Figure S1 in Pizzuto et al. [
47] shows comparable scans).
Tissues surrounding high-activity areas, like the urinary bladder, could suffer from SUV overestimation as activity could spill into this region from the high-activity area [
48]. Proposed solutions range from bladder voiding by urinary catheterization to new segmentation and reconstruction methods [
49]. In our study, the administration of furosemide lowered the urinary bladder activity to a SUVmean of 7.7 g/ml (range 2.5–20.9 g/ml, interquartile range 8.9 g/ml, decay corrected). Three cases with the highest urinary bladder SUV showed similar surrounding SUV values as 3 cases with the lowest urinary bladder uptake. Therefore, the spill-in effect was considered minimal in our study.
Although we included a wide range of patients with different BMI values, the presented results are also expected to be related to the acquisition conditions (dose, uptake time, acquisition time, resolution, etc.) as specified in the materials section.
The pelvis region contains a large percentage of the bone, and MR-based attenuation correction (MR-AC) does generally not incorporate bone attenuation (except for the head). As a result, the average SUVmean of normal tissue in the pelvis region was found to have a bias of − 18.7% for non-TOF and − 10.8% for TOF, and lesions near the bone were reported to have a bias of − 5.2% for non-TOF and − 4.6% for TOF, compared to PET/CT using
18F-FDG and
18F-choline [
50]. Leynes et al. [
51] performed zero echo time (ZTE) scans in the pelvis region, which allows the imaging of the bones with MR. They segmented the data and combined it with the normal Dixon-based MR-AC map to include bone attenuation in their
18F-FGD TOF OSEM reconstructions. For bone lesions in the pelvis region, they found a SUVmax bias of − 10.8% comparing normal MR-AC to CT-AC, which was reduced to − 3.17% when applying their new hybrid ZTE method. For soft tissue lesions in the pelvis region, they found a SUVmax bias of − 7.67% which was further reduced to − 3.54%. In our study, the MR-based AC maps were the same for OSEM and BSREM and had no bone attenuation incorporated. When bone tissue would be included in the AC map, it would improve both the OSEM as well as the BSREM results. We did not investigate the effect of the bone in the attenuation map in the comparison between OSEM and BSREM, but we expect that BSREM will be superior to OSEM, considering the results obtained in other studies applying
18F-FDG PET/CT, which include the bone [
21]. It would be an interesting subject for future studies.
In this study, we did not perform a visual evaluation of the clinical image quality or the clinical significance. Therefore, it is unknown if TOF BSREM would lead to different diagnoses in 68Ga-PSMA PET of the pelvic area. However, the complex effects of the different β values on the behavior of absolute values, as well as on contrast and background, warranted a solid preliminary analysis of a wide range of β values. The current results give more insight and can be used to limit the amount of reconstructed PET images and thus evaluations to only those that are the most promising for further clinical investigations, which need to be performed in larger cohorts.