Impact of total variation regularized expectation maximization reconstruction on the image quality of ⁶⁸Ga-PSMA PET: a phantom and patient study

Abstract

Objectives:

To investigate the impact of total variation regularized expectation maximization (TVREM) reconstruction on the image quality of ⁶⁸Ga-PSMA-11 PET/CT using phantom and patient data.

Methods:

Images of a phantom with small hot sphere inserts and 20 prostate cancer patients were acquired with a digital PET/CT using list-mode and reconstructed with ordered subset expectation maximization (OSEM) and TVREM with seven penalisation factors between 0.01 and 0.42 for 2 and 3 minutes-per-bed (m/b) acquisition. The contrast recovery (CR) and background variability (BV) of the phantom, image noise of the liver, and SUV_max of the lesions were measured. Qualitative image quality was scored by two radiologists using a 5-point scale (1-poor, 5-excellent).

Results:

The performance of CR, BV, and image noise, and the gain of SUV_max was higher for TVREM 2 m/b groups with the penalization of 0.07 to 0.28 compared to OSEM 3 m/b group (all p < 0.05). The image noise of OSEM 3 m/b group was equivalent to TVREM 2 and 3 m/b groups with a penalization of 0.14 and 0.07, while lesions’ SUV_max increased 15 and 20%. The highest qualitative score was attained at the penalization of 0.21 (3.30 ± 0.66) for TVREM 2 m/b groups and the penalization 0.14 (3.80 ± 0.41) for 3 m/b group that equal to or greater than OSEM 3 m/b group (2.90 ± 0.45, p = 0.2 and p < 0.001).

Conclusions:

TVREM improves lesion contrast and reduces image noise, which allows shorter acquisition with preserved image quality for PSMA PET/CT.

Advances in knowledge:

TVREM reconstruction with optimized penalization factors can generate higher quality PSMA-PET images for prostate cancer diagnosis.

Introduction

Prostate-specific membrane antigen (PSMA) positron emission tomography (PET) is increasingly used in prostate cancer imaging,¹ for its high accuracy in the detection of the primary tumor or metastasis^2–4 and recurrence.^3–5 Bayesian penalised likelihood reconstruction (BPL) can reduce image noise and increase lesion contrast for PSMA PET compared to ordered subset expectation maximization (OSEM) reconstruction.^6–8 Hence, BPL has the potential to further improve the sensitivity for lesion detection on delayed-time-point PSMA PET,⁹ shorten acquisition time,⁶ or reduce administrated dose.¹⁰

Total variation regularized expectation maximization (TVREM), a new BPL algorithm, was introduced recently (HYPER Iterative, United Imaging Healthcare). TVREM incorporated the pixel-to-pixel total variation, global noise equivalent counts, and local sensitivity profile into the penalisation term^11,12 (Supplementary Material 1 provided more details). A preliminary study demonstrated the potential application of TVREM for PSMA PET.¹³ However, a detailed analysis had not been performed yet. Therefore, the purpose of this study was to investigate the effects of TVREM on the image quality of ⁶⁸Ga-PSMA-11 PET/CT with different penalisation factors and acquisition durations using phantom and clinical data.

Methods and materials

Phantom data acquisition

A National Electrical Manufacturers Association (NEMA) quality phantom (Supplementary Material 1) was scanned with a digital time-of-flight PET/CT scanner (uMI780, United Imaging Healthcare). The phantom background was filled with 14.0 kBq/mL of ⁶⁸Ga solution, and four small spheres (diameter = 10, 13, 17, and 22 mm) were filled with 4:1 sphere-to-background activity ratio of the solution. The list-mode data were acquired after 120 min of waiting time.

All images were reconstructed with FOV 600 mm, matrix 192 × 192, and slice thickness 3.0 mm with time-of-flight and point-spread-function model, attenuation, scatter, and the other necessary corrections. The reconstruction of OSEM (two iterations, 20 subsets, and 3 mm Gaussian post-filtering) and TVREM (seven penalization factors: 0.01, 0.07, 0.14, 0.21, 0.28, 0.35 and 0.42) were applied with 37- and 55-s duration of list-mode data whose counts were comparable to our clinical protocols using 2 and 3 minute-per-bed (m/b) acquisition. A total of 16 groups of PET images were reconstructed for the final analysis. For simplicity, we named these groups as O2 and O3 for OSEM with simulated 2 and 3 m/b data; R2.01, R2.07, R2.14, R2.21, R2.28, R2.35, and R2.42 for TVREM with the acquisition of 2 m/b and penalization factors of 0.01, 0.07, …, and 0.42; and R3.01 to R3.42 for TVREM with the acquisition of 3 m/b and penalization factors of 0.01 to 0.42, respectively.

Phantom data evaluation

The measurement of percent contrast recovery (CR) and background variability (BV) was in accord with NEMA NU2-2012 image quality evaluation protocol. The counts of four hot spheres and standard deviation (SD) of phantom background were measured by placing a region of interest (ROI) on the spheres and the peripheral area in the images of the phantom. The details of ROI placement and the equation for calculating CR and BV can be found in Supplementary Material 1. The normalized activity of a hot sphere was calculated by dividing the mean activity concentrations of TVREM by that of O3. The ROI measurements were performed in the phantom images for the reconstruction groups of O2, O3, R2.01 to R2.42, and R3.01 to R3.42. Since those reconstruction groups attained from the same acquisition in which the injected activity was identical, the comparisons of CR and BV between the reconstruction groups enable the performance evaluation of different reconstruction algorithms and/or settings. In contrast to the CR, the normalized activity of the hot spheres was only based on the measurement from PET images. It showed the relative change attributed to the different reconstructions using O3 as the reference, which made it comparable to the clinical study.

Patients

Twenty patients undergoing PSMA PET/CT for primary staging (n = 12) or follow-up (n = 8) were enrolled retrospectively. The patient characteristics and treatments were listed in Table 1. The patient was included, if met all of the following criteria: the prostate cancer was confirmed with surgery history or biopsy result; serum prostate-specific antigen (PSA) test was available; PSMA avid lesions were found on PET images. The patient was excluded if list-mode raw data were not available for additional PET reconstructions. The study was approved by the Ethics Committee of our hospital and the informed consent was wavered due to the retrospective nature of this study.

Table 1.

Patient characteristics

Characteristics	Value
Agea	72.4 ± 6.2 [53,82] years
Heighta	1.66 ± 0.05 [1.57,1.80] m
Weighta	63.3 ± 6.5 [50.2,75.0] kg
Body mass indexa	22.9 ± 2.3 [17.0,26.4] kg/m2
Uptake timea	75 ± 16 [48,99] minutes
Injected dosea	125.1 ± 12.9 [96.7,156.4] MBq
Injected dose per kga	2.0 ± 0.1 [1.8, 2.2] MBq/kg
Serum PSAa	22.2 ± 24.6 [0.01, 81.3] ng/mL
Treatment-naive patientsb	12
Patients treated with therapiesb	Radical prostatectomy+hormone therapy (n = 4) Hormone therapy (n = 2) Radical prostatectomy (n = 1) Prostate brachytherapy seed implants +hormone+chemotherapy (n = 1)

^aThe values were presented as mean ± SD [range].

^bThe values were the counts of the patients.

Clinical image acquisition

All patients underwent PSMA PET/CT with the same scanner as the phantom study. The ⁶⁸Ga-PSMA-11 was administrated according to patient weight (2.0 MBq/kg) 75 min before the scanning. Data were acquired from skull base to mid-thigh in 3D list mode with 3 m/b of acquisition time. The PET images were reconstructed with the same settings and image reconstruction group naming rules as those described in the phantom study.

Quantitative evaluation of clinical images

The quantitative image evaluation was performed by a nuclear radiologist with open-source software (3D Slicer R4.10.2). A 3-cm-diameter sphere volume of interest (VOI) was carefully placed on homogeneous healthy liver tissue in the right upper lobe. This VOI was first placed on O3 and copied-and-pasted to the other groups. The mean of standard uptake value (SUV_mean) and SD was measured. The image noise was calculated by SD over SUV_mean and presented in percentage.

The lesion was segmented with a semi-automatic 3D segmentation tool.¹⁴ The segmentation mask was outlined on O3 and subsequentially applied to the other groups. The lesions were categorised: the prostate (including seminal vesicle), lymph node, bone, and other organs. One lesion per category if existed was picked from each patient for the segmentation. If a patient had multiple lesions in one category, the smallest one was selected. The maximum of SUV (SUV_max) and the volume of the lesion were measured. The normalised SUV_max was defined by the ratio of SUV_max for TVREM to that for O3. The equivalent diameter (D_e) of the lesion was calculated by:

$$D_e=2\times \sqrt[3]{3\times Volume/4\pi }$$

where D_e equaled the diameter of a sphere that had the same volume of the lesion.

Qualitative assessment of clinical images

Two nuclear radiologists with 3 and 10 years’ experience in oncological PET/CT independently evaluated the image quality of PSMA PET on a commercial workstation (uWS-MI R004, United Imaging Healthcare) using a 5-point scale. A score of 5 was given to the case with excellent image quality, almost free of noise, and ideal contrast and sharp border for the lesion or organ delineation. A score of 4 was given to good quality images with optimal noise, and satisfactory lesion delineation resulting in full diagnostic confidence. A score of 3 was given to adequate image quality with appropriate noise, natural image texture, and sufficient lesion delineation to make a diagnosis. A score of 2 was given to acceptable image quality with sub optimal noise or unnatural texture, and acceptable lesion contrast or delineation but with reduced confidence. A score of 1 was given to the case with poor image quality, excessive noise, or insufficient lesion depiction.

The nuclear radiologists rated the images in a blind manner without knowing the score by the other rater and reconstruction settings. All images were anonymized and the reading sequence was randomized to reduce the bias. The raters assessed the image using the transverse view, maximum intensity projection, and fusion views of PET and CT images. If there was a discrepancy in the scores between two raters, a third senior nuclear radiologist was consulted to settle the difference. The third rater first independently reviewed the images and then gave consent to one of the scores by the first two raters. This score was marked as the unified score and was used in the final analysis.

Statistical analysis

The data were presented as mean ± SD. The SUV of O3 was served as the reference for the comparison between different reconstruction groups because the true value of SUV was unknown in the patient study. To untangle the inter-patient or inter-lesion variance of SUV, paired t-test was used to examine the difference of liver SUV_mean, SD, and lesion SUV_max between O3 and the other groups. The image quality scores of different reconstruction groups were compared with Fisher’s exact test, for the observations of many scores were less than 10. Bonferroni-Holm correction was used to adjust p-value, which controlled the familywise error rate imposed by multiple comparisons. The inter-rater agreement was measured by Cohen’s κ. A p-value of <0.05 was considered statistically significant. R statistical package (R3.4.2) and Microsoft Excel 2016 (v16.0) were used for all statistical analyses.

Results

Phantom study

The CRs were higher for TVREM groups with smaller penalization factors compared to OSEM and TVREM groups with larger penalization (Figure 1, Supplementary Material 1). Most TVREM groups had higher CRs than OSEM when the sphere diameter and acquisition time were the same, except R2.21 to R2.42, and R3.35 to R3.42 for the 10-mm-diameter sphere. The mean of normalized activity was higher than 1.0 in the groups of R2.01 to R2.21 and R3.01 to R3.42 (Figure 2a). All BVs decreased along with the increase of the penalization factors (Figure 1, Supplementary Material 1). The BVs of R2.01, R2.07, and R3.01 were higher than those of O3 at the same diameters. R2.14 and R3.07 had comparable BV to O3, for the difference was limited to −0.3 to 0.2%. The BVs of the other TVREM groups were lower than O3. Moreover, all TVREM groups had better BV performance compared to O2 except for R2.01 (Supplementary Material 1).

Figure 1.

The plot of contrast recovery and background variance for 10 (circle), 13 (square), 17 (diamond), and 22 mm (triangle) spheres with different reconstruction settings in the phantom study. The marks connected with dot-lines and solid-lines were for 2 and 3 m/b groups, respectively. Both CR and BV increased with smaller penalization factors, i.e., the marks at the end-points on the top-right of each dot or solid line had a factor of 0.01 and those on the bottom-left had a factor of 0.42. The TVREM groups were considered to have superior performance to the O3 groups if they fell in the lower right quadrant of the corresponding O3 marks of the hot spheres with the same diameter.

Figure 2.

The relationship between normalized SUV_max, diameters, and reconstruction settings. (a) The mean and SD (circle and error bars) of the normalized activity change for the spheres of 10, 13, 17, and 22 mm (filled circle, triangle, square, and cross) in the phantom study. (b) The mean and SD of normalized SUV_max for the lesions with a diameter of ≤20 and>20 mm in the clinical study. The mean of normalized activity and SUV_max decreased along with the increase of penalization factor for the hot spheres and the lesions ≤20 mm. The mean of normalized SUV_max was higher than 1.1 (range 1.11–1.13) for the lesions >20 mm in all TVREM groups.

Patients

The patients (74.2 ± 6.2 years, 63.3 ± 6.5 kg) had a mean serum PSA level of 22.2 ± 24.6 ng ml⁻¹. The details of patient characteristics were listed in Table 1. A total of 99 PSMA avid lesions were identified: 22 lesions in the prostate, four in the seminal vesicle, 32 in the lymph node, 35 in the bone, one in the rectal wall, and four in the lung. Furthermore, 31 lesions were segmented for quantitative analysis: fourteen in the prostate, one in the seminal vesicle, eight in the lymph node, six in the bone, one in the rectal wall, and one in the lung.

Quantitative analysis of clinical images

The liver SUV_mean increased from 3.706 for O3 to 3.735–3.742 for TVREM groups (Table 2), but these increases were not statistically significant (all p > 0.78). The image noise was 15.0±3.5% and 12.5±2.9% for O2 and O3, respectively. The image noise decreased along with the increase of penalization factors (Table 2). The R2.14 and R3.07 group were considered noise equivalent groups to O3, because their noises did not differ significantly (p = 0.275 and 0.052), and the noise of R2.07 and R3.01 was equivalent to O2 (p = 0.11 and 0.41). The image noise of R2.01, R2.07, and R3.01 group was higher than that of O3 (all p < 0.001) and the image noise of R2.21-R2.42 and R3.14-R3.42 was lower (all p < 0.001). Nevertheless, all TVREM groups had less than 15% image noise except for R2.01 (17.2±3.8%).

Table 2.

SUV_mean, image noise, and normalized SUV_max of the clinical study

Group	SUVmean of the liver	Image noise (%) of the liver	Normalized SUVmax of the lesions
O2	3.712 ± 1.040	15.0 ± 3.5	1.01 ± 0.08
R2.01	3.742 ± 1.033	17.2 ± 3.8	1.19 ± 0.14
R2.07	3.741 ± 1.034	14.5 ± 3.0	1.17 ± 0.14
R2.14	3.741 ± 1.035	11.8 ± 2.3	1.15 ± 0.16
R2.21	3.741 ± 1.036	9.8 ± 2.0	1.11 ± 0.18
R2.28	3.741 ± 1.037	8.4 ± 1.8	1.07 ± 0.22
R2.35	3.741 ± 1.038	7.4 ± 1.7	1.04 ± 0.26
R2.42	3.742 ± 1.038	6.7 ± 1.7	1.00 ± 0.29
O3	3.706 ± 1.037	12.5 ± 2.9	1.00 ± 0.00
R3.01	3.737 ± 1.031	14.5 ± 3.2	1.22 ± 0.15
R3.07	3.736 ± 1.032	12.9 ± 2.7	1.20 ± 0.15
R3.14	3.736 ± 1.031	11.2 ± 2.2	1.18 ± 0.16
R3.21	3.737 ± 1.031	9.7 ± 1.9	1.16 ± 0.17
R3.28	3.736 ± 1.032	8.5 ± 1.7	1.14 ± 0.19
R3.35	3.735 ± 1.032	7.6 ± 1.5	1.11 ± 0.22
R3.42	3.735 ± 1.033	6.9 ± 1.4	1.09 ± 0.24

^aData were presented as the mean ± SD.

The normalized SUV_max decreased with the increase of the penalization factors (Table 2). The SUV_max increased 19% for R2.01, 0% for R2.42, 22% for R3.01, and 9% for R3.42 compared to O3, respectively. The lesions attained higher SUV_max than O3 in most TVREM groups (all p < 0.05) except for R2.35 and R2.42 (p = 0.11 and 0.29).

The lesions were further classified into small and large categories according to their equivalent diameters (D_e ≤ 20 and>20 mm). There were 21 small lesions (range 14.1–18.9 mm) and 10 large lesions (range 24.2–46.9 mm). The mean of normalized SUV_max for the small lesions decreased along with the increased penalization factor, but this decrease was minor for large lesions (Figure 1b). The mean of normalized SUV_max for small lesions was higher than 1.0 in most TVREM groups except R2.35 and R2.42. The mean of normalized SUV_max was higher than 1.1 (range1.11–1.13) for the large lesions in all TVREM groups.

Qualitative image quality of clinical study

R3.07, R3.14, and R3.21 had higher image quality scores compared to O3 (all p < 0.05), and the image quality scores of R2.07, R2.14, R2.28, and R2.35 did not differ from O3 (all p > 0.09) Figure 3, Supplementary Material 1. The highest score was assigned to R2.14 (3.30 ± 0.47) and R3.14 (3.80 ± 0.41) for 2 and 3 m/b groups, respectively. The lowest score was given to R2.01 (2.25 ± 0.44) due to suboptimal image noise (Figure 4) and to R2.42 (1.95 ± 0.39) because of reduced contrast for small lesions (Figure 5). The inter-rater agreement was substantial (k = 0.65).

Figure 3.

The qualitative image quality of the clinical images with different reconstruction groups. The mean (filled circle) and standard deviation (error bar) of the image quality scores were plotted for each reconstruction group. The highest mean score was given to R2.14/R2.21 and R3.14 for 2 and 3 m/b groups, respectively.

Figure 4.

A 76-year-old patient underwent PSMA PET/CT for elevated PSA level (21.1 ng ml⁻¹) who received hormone therapy after radical prostatectomy. The images reveal a small lymph node in front of the sacrum with a diameter of 4.5 mm measured on CT (the image was not shown) and elevated PSMA uptake (SUV_max = 4.81). The lesion is well defined in all TVREM groups. The image quality was considered suboptimal but acceptable for R2.01 due to the noise, adequate for R2.07 to R2.14, and good for R2.21 to R2.42.

Figure 5.

PET images of a 69-year-old patient treated with hormone therapy after radical prostatectomy with elevated PSA level (8.6 ng ml⁻¹). The images depict two lung nodules with moderate PSMA uptake (SUV_max = 3.02 and 7.31). The diameters were 4.8 and 6.2 mm on the CT image (not shown). Both nodules were considered identifiable in all groups by the raters, although the contrast of the nodule on the right side (patient’s right) decreased with higher penalization factors.

Discussion

We investigated the impact of TVREM on the image quality of ⁶⁸Ga-PSMA-11 PET/CT using the phantom and patient data. TVREM with a penalization factor in the range of 0.07 to 0.28 could deliver 7–17% higher lesion contrast and 0–32% lower image noise compared to OSEM 3 m/b group while saving 33% acquisition time. Moreover, our results suggested that a penalization factor between 0.14 and 0.21 might provide the optimal image quality for ⁶⁸Ga-PSMA PSMA PET with lower noise and higher contrast for small and large lesions.

The choice of the optimal penalization factor depends on several factors: the acquisition settings, BPL algorithm tuning, radiologists’ preference, and measures of image quality. Therefore, the optimal factor is often given as a range. A previous study⁶ suggested a factor between 400 and 800 could be used with block sequential regularized expectation maximization (BSREM) for PSMA PET/CT scans, while a pelvic PET/MR study⁷ recommended 400 to 550. However, another PET/MR study¹⁵ pointed out a penalization factor within 250 to 300 generated higher SUV_max but comparable noise to OSEM, while choosing from 500 to 700 had much lower noise. In line with those studies, our results suggested a factor between 0.07 and 0.28 for TVREM reconstruction that provided higher contrast and lower noise compared to OSEM. Moreover, a penalization factor of around 0.07 could attain equivalent image noise to OSEM 3 m/b acquisition, and it should be increased to 0.14 when the acquisition time was shortened to 2 m/b. Therefore, the recommendation of penalization factors should always be accompanied by the acquisition settings and the criteria for the optimal image quality, for they may change the choice of the penalization factor.

The phantom and clinical studies^16,17 showed that BPL improved the lesion quantification accuracy of ¹⁸F-FDG PET/CT compared to OSEM due to its advantage of full iterative convergence without excessive noise amplification. Our phantom study further illustrated the improvement of contrast convergence by TVREM on ⁶⁸Ga-PSMA-11 PET/CT. The CR increased 0.3 to 7.2% for 10- to 22-mm-diameter hot spheres with a penalization factor of 0.14 in 2 m/b group compared to OSEM 3 m/b group, while the change of BV was minor (range −0.3 to 0.2%). The gain of the lesion SUV_max reached 15% in our patient study. This higher gain might be explained by the different size compositions of the hot spheres and lesions in the phantom and patient study.

Our data showed the contrast of the large lesions (>20 mm) increased more than 10% in all TVREM groups compared to OSEM 3 m/b group, while the contrast for the small lesions (<20 mm) increased 22 and 19% in TVREM 3 and 2 m/b groups with 0.01 penalization, and remained higher until the penalization increased to 0.28 and 0.14 for 3 and 2 m/b groups, respectively. Those results were partly consistent with the findings of a previous study using ¹⁸F-PSMA-1007 PET/CT⁸ in which a significant increase of lesion SUV_max between BSREM with a penalization factor of 350 and OSEM was not found on the large lesions. However, a decreased gain of SUV_max was observed regardless of the size of the lesions in a ⁶⁸Ga-PSMA-11 PET/MR study when the BSREM penalization factor increased from 150 to 1200.⁷ Nevertheless, our results and the others^7,8,17 supported BPL could improve the small lesion contrast.

The result of qualitative image quality assessment by nuclear radiologists was affected by the clinical task, personal experience, and image texture. In our study, the mindset of the raters was to detect all malignancies with sufficient confidence, which was relevant to their routine clinical task - the intention to diagnose. Our results showed the highest mean quality score was given when the penalization factor was between 0.14 and 0.21 for 2 m/b acquisition and at 0.14 in 3 m/b acquisition. Those selections had higher penalization than the noise equivalent groups, i.e. R2.14 and R3.07, and hence had lower noise. Although 15% was recommended as the maximal tolerance for the coefficient of variation,¹⁸ a lower background noise level was preferred by the raters, because it increased the confidence to identify small lesions. Our results showed the images with higher image quality score at a penalization of 0.14 had a noise level of 11%. Therefore, a noise level of <11% should be considered the target noise setting for high-quality imaging practice. Further increasing penalization factor might remove more noise, but with less contrast enhancement, which was reflected in the relative lower image quality scores for higher penalization groups. This phenomenon was also reported previously using BSREM on PSMA PET with high penalization.^10,15

Since the clinical practice demand a fixed penalisation factor to maintain the consistency of SUV, our study suggested a penalisation factor of 0.14 to 0.21 as the appropriate choice, which was a balance of visual assessment and quantitative evaluation. This approach had been taken in a study of ¹⁸F-fluciclovine PET.¹⁹ We could suggest 0.14 and 0.07 for 2 and 3 m/b groups, respectively, if we would choose the noise equivalent group as the previous studies.^6,10 Since the radiologists remain the center task-force in practice, it may be appropriate to weigh the raters’ preference on the optimisation of the penalisation factors. Therefore, further studies are needed to develop a task-based lesion detectability indice for the phantom test, which might play a critical role in the quality assurance procedure for the PET scanners with BPL reconstruction algorithms.

Shorter acquisition time is in the interest of patient comfort and throughput. The capability of BPL on shortening acquisition time was demonstrated for ¹⁸F-FDG PET.^18,20 Our result illustrated that TVREM could reduce 33% acquisition time of ⁶⁸Ga-PSMA PET while maintaining the image quality. On the other hand, the ability of noise reduction by BPL could be applied to lower the injected dose or boosting the image quality of late-phase imaging. One PSMA PET/MR study showed 90% injected dose could be saved on a 15 min pelvic scan.¹⁰ And 2 h late-phase PSMA PET scan with BPL detected a lesion that unable to see after 1 h uptake time [9]. However, more studies were needed to explore the potential of BPL on whole body PSMA PET.

Our study has limitations. Our study cohort is small. A larger population of biochemical recurrence prostate cancer patients with lower PSA level should be involved in future studies. The biopsy of metastatic lesions was not available for our study. Further studies with biopsy results are needed to investigate whether increased CR of TVREM can be translated to early detection of prostate tumor or metastatic lesions.

Conclusions

TVREM reconstruction can improve lesion contrast and lower image noise of ⁶⁸Ga-PSMA-11 PET/CT compared to OSEM and hence enable a faster acquisition with preserved image quality.