The Impact of Bayesian Penalized Likelihood Reconstruction Algorithm on Quantitative Accuracy of Positron Emission Tomography Volumetric Measurements

Objectives The metabolic tumor volume (MTV) of positron emission tomography/computed tomography (PET/CT) is an important index to evaluate the prognosis and the responses of treatments. The purpose of this study is to assess the impact of Bayesian Penalized Likelihood (BPL) reconstruction algorithm and segmentation methods on the accuracy of MTV via a phantom study. Methods Using the National Electrical Manufactures Association/International Electrotechnical Commission (NEMA/IEC) image quality phantom, six hot spheres and background were lled with 21.56 KBq/ml and 5.39 KBq/ml Na 18 F (a sphere to background ratio of 4: 1). Acquired images were reconstructed using BPL (β = 400) and non-BPL (Ordered subsets expectation maximization + time of ight + point spread function, OSEM+TOF+PSF) algorithms, respectively. MTVs of six spheres were delineated using maximum standardized uptake value (SUV max ) percentage threshold method and iterative adaptive method, respectively. The actual measured volumes of spheres were used as the standard for comparative analysis. Results The MTVs measurement errors in BPL were 4.96%, -3.00%, 6.18%, 5.20%, -10.00% and 18.33%, which was signicantly lower than that in non-BPL ( Z = - 2.562, p = 0.009), and the measurement errors in non-BPL were 16.70%, 10.77%, 26.00%, 30.00%, 61.82% and 113.33%. The optimal percentage SUV max threshold of spheres in BPL algorithm was raged in 40% - 45%, which was not affected by the ball size. And there was no signicant difference of MTVs measurement accuracy between the 42%SUV max and iterative adaptive threshold (Z = -0.48, p = 0.699). However, using the non-BPL algorithm, the measurement errors of 42%SUV max and iterative adaptive delineation methods were 16.70%, 10.77%, 26.00%, 30.00%, 61.82%, 113.33%, and -7.70%, -9.00%, -8.73%, -5.20%, -12.91%, 38.33% respectively. The MTVs measurement accuracy of iterative adaptive was signicantly better than that of the 42%SUV max threshold (Z = -2.24, p = 0.026). The iterative adaptive and 42%SUV max threshold methods had excellent interobserver reliability (ICCs=1.00 for all of six spheres) for MTVs measurement. Conclusion BPL reconstruction algorithm can improve the accuracy of MTVs measurements, especially for small lesions. In the case of using non-BPL methods, the iterative adaptive delineation method should be adopted to improve the accuracy of MTVs measurements.


Introduction
The quantitative parameters of PET/CT have been widely used in tumor clinical practice. In addition to uptake metabolic parameters such as SUV max and SUV mean , volume metabolic parameters MTV and total lesion glycolysis (TLG, de ned as MTV × SUV mean ) are also becoming more and more important.
Studies have shown that MTV and TLG are closely related to tumor burden, treatment response evaluation and prognosis judgment [1][2][3][4][5]. Consequently, accurate MTV measurements of tumor lesions have become a challenge for achieving clinical purposes. In addition, the accuracy of MTV measurement highly depends on the PET/CT image reconstruction method and lesion delineation method.
Bayesian penalized likelihood (BPL) reconstruction is a new PET/CT reconstruction algorithm based on the iterative reconstruction [6]. Compared with conventional reconstruction methods, BPL does not only improve the quantitation accuracy of lesions, but also effectively reduce the noise level of the image, and then improve the general image quality and conspicuity of small lesions [7]. However, the method using for MTV delineation also needs to be careful and precise. At present, most studies use a xed SUV threshold (such as SUV ≥ 2.5 or SUV ≥ 4.0) or a percentage of SUV max (such as 42% SUV max ) to de ne MTV [8][9][10]. Meanwhile, Xu et al. also proposed that using the iterative adaptive method of PET VCAR software (GE Healthcare, Milwaukee) was more accurate than using the SUV max percentage threshold method to determine MTVs [11].
According to literatures, there are few studies on how different image reconstruction methods and MTV delineation methods affects the accuracy of the MTV measurement, and how to effectively combine reconstruction algorithms with delineation methods to further improve the accuracy of MTV measurement. Therefore, this study performed a phantom study to analyze the impact of BPL reconstruction algorithm and delineation methods on the accuracy of the MTV measurement.

Image analysis
The AW workstation (GE Healthcare, Milwaukee) was used for image fusion and processing. The PET VCAR software (GE Healthcare, Milwaukee) was used to reconstruct PET images with BPL and non-BPL methods respectively. The volume of interest (VOI) was delineated on six hot spheres by using three different methods: the SUV max percentage threshold method (range: 30% -70%, with an increasement of 5%); the 42%SUV max threshold method; the iterative adaptive method. The MTV values (cm 3 ) were then calculated automatically. In iterative adaptive method, SUV max and SUV mean were weighted by a weighting factor to determine the delineation threshold of the VOI and background tissue, which was automatically set to 0.5 [12].
By using BPL and non-BPL reconstruction methods, three experienced nuclear medicine physicians used the percentage SUV max threshold method and the iterative adaptive method to delineate VOIs and recorded MTV readings of each hot sphere. For VOIs delineation, a boundary box (i.e. the tool for automatic delineation and segmentation of VOIs) was placed on the PET image at the lesion layer. The cross-sectional, coronal and sagittal sections were repeatedly checked and adjusted to ensure that the whole hot sphere was included and the background was excluded.
Pure water was injected into each sphere manually to determine the actual volumes of spheres, which were then used as the gold standard. The percentage errors between MTVs and actual volumes (%error = (MTV -actual volume) x 100% / actual volume) were then calculated to determine the optimal %SUV max threshold and the best delineation methods under different reconstruction methods. Results with the smallest %error were considered as the best option.

Statistical analysis
All data were analyzed by using the SPSS 22.0 software. Mann-Whitney U test was used to compare the MTVs errors of different reconstruction methods and different delineation methods. The intraclass correlation coe cient (ICC) was used to estimate the measurement reliability of MTVs using the 42% SUV max and the iterative adaptive methods. Results were considered as statistically signi cant when p < 0.05. Figure 1 shows the PET/CT transversal images of the phantom with six hot spheres were clearly displayed without deformation under the BPL reconstruction method, especially the image clarity and edge sharpness of 13 mm and 10 mm spheres were signi cantly better than those of non-BPL images. By using the 42%SUV max threshold as the delineation method, results showed that the measurement errors of MTVs in BPL were 4.96%, -3.00%, 6.18%, 5.20%, -10.00% and 18.33%, which was signi cantly lower than that in non-BPL ( Z = − 2.562, p = 0.009), and the measurement errors in non-BPL were 16.70%, 10.77%, 26.00%, 30.00%, 61.82% and 113.33% (Table 1). The errors of spheres MTVs in BPL were signi cantly lower than non-BPL algorithm (Mann-Whitney U, Z=-2.562, p = 0.009) by 42%SUV max threshold delineation method, and BPL algorithm especially improved the accuracy of the smaller spheres MTV (13 mm and 10 mm).

Discussion
A number of studies have consistently shown that MTV of PET/CT can provide valuable diagnostic and prognostic information for malignant tumors, and can be used to monitor disease progression and evaluate treatment response [3,4]. In addition, PET/CT has been proved to be very important for de ning the target volume of radiotherapy. The precise de nition of MTV is essential for increasing the radiation dose of pancreatic cancer, gynecological tumor and rectal cancer, reducing the risk of organ exposure, and developing personalized in vitro radiotherapy plan [13,14]. PET quantitative accuracy is affected not only by the hardware of equipment, but also by reconstruction algorithms. The BPL reconstruction method is the latest commercial PET/CT reconstruction algorithm which can be used in clinic. In novel PET/CT imaging systems, BPL is allowed to be applied simultaneously with TOF and PSF, results in signi cant improvements in signal-to-noise ratio, contrast and reconstruction resolution while keeping the edge unchanged and better quantitation accuracy compared with conventional reconstruction methods [15].
In this study, the actual volumes of NEMA phantom spheres were used as the reference, and the BPL reconstruction algorithm signi cantly improved the measurement accuracy of MTV compared with the non-BPL reconstruction algorithm. BPL signi cantly reduced the MTV measurement error when using the 42%SUV max threshold delineation method (p = 0.009). Parvizin et al. [16] carried out a study on PET/CT quantitative parameters of 42 liver metastases (mean diameter of 25 mm, range of 6-86 mm). Using 40%SUV max as the threshold, the MTVs of lesions decreased from 21.5 ml (1.5-143.4 ml) of OSEM to 16.3 ml (0.7-110.4 ml) of BPL (p < 0.001). According to Vallot D et al. [6], the MTV of 61.8% tumor lesions in BPL group was lower than that in OSEM group, but the difference was not signi cant (p = 0.069). This result is attributed to the full convergence of BPL reconstruction algorithm. Compared with conventional OSEM methods, BPL can reduce the noise and increase the number of iterations. By regularizing the relative difference between adjacent pixels of β parameter penalized, the image presents the optimal contrast and reconstruction resolution while maintaining the edge of the lesion, so as to ensure the accuracy of MTV. In addition, the accuracy of the 42%SUV max threshold method mostly depends on the accuracy of SUV max . Phantom and clinical case studies have con rmed the role of BPL algorithm in accurate quanti cation of SUV max , and this improvement is mainly focused on small lesions [17]. Results shown in Table 1 are consistent with their ndings, which show that BPL can signi cantly reduce the MTV measurement errors of 13 mm and 10 mm spheres. At the same time, the role of BPL algorithm to keep the lesion edge unchanged also avoids the Gibbs artifact of small lesion edge given from PSF [18,19]. Therefore, compared with the non-BPL algorithm, the BPL algorithm obtains higher reconstruction spatial resolution [20], reduces the impact of partial volume effect on small lesions, and improves the quantitative accuracy of MTV for small lesions.
The latest research of Texte E et al. also proposed that BPL reconstruction method can signi cantly reduce the MTV of lung tumor lesions, and results are also closely related to the delineation method of tumor lesions [21]. In this study, the incremental% SUV max threshold was used to nd the optimal delineation threshold of the BPL and non-BPL methods. The results showed that the optimal segmentation threshold under BPL was fall in a relatively narrower range of 40% − 45%, when compared with the non-BPL group (45% − 60%). Notably, the segmentation threshold of small lesions needed to be adjusted to 60% to achieve acceptable MTV errors when using the non-BPL method. That is to say, under the BPL reconstruction method, the manufacturer's default setting of 42% can meet the acceptable MTV accuracy of any size lesions. This further avoids the error caused by manual adjustment of thresholds and increases the results repeatability.
The results also showed that, by using the BPL method, the MTV error range of the 42%SUV max and the iterative adaptive methods are − 3.00% ~ 18.33% and − 3.22% ~ 15.00% (from 37 mm to 10 mm), respectively, and there was no signi cant difference between them (p = 0.699). It indicates that BPL algorithm can make the measurement less affected by the segmentation method. With the non-BPL reconstruction method, PET/CT quantitative studies on cervical cancer and lung cancer lesions have con rmed that the iterative adaptive method can improve the MTV measurement accuracy [10,11]. The iterative adaptive method is to get the optimal threshold value by weighting SUV max and SUV mean in the targeted lesion [12]. This means that MTV measured by the iterative adaptive method is determined by SUV max and SUV mean at the same time. This is more accurate than that of percentage SUV max threshold method, which is only determined by SUV max . Therefore, in view of the performance advantages of BPL reconstruction algorithm combined with iterative adaptive delineation methods the results of this study have guiding value for clinical practice of quantitative accuracy of PET/CT volumetric measures.
In this study, we did not study the effect of BPL on the accuracy of MTV measurement of actual tumor lesions. The research of NEMA phantom was carried out under the ideal conditions of regular shape and uniform radioactive distribution, the impact of BPL on MTV measurement accuracy of tumor lesions with irregular edge and heterogeneous radioactive uptake may be different. In addition, the sphere-to-background ratio was 4: 1 in this study, the results of different sphere-to-background ratios need to be further investigated by relevant phantom and clinical studies.

Conclusion
The BPL reconstruction algorithm can signi cantly improve the accuracy of MTV measurement, especially for small lesions. With the non-BPL reconstruction algorithm, the accuracy of MTV measurement can also be improved by using the iterative adaptive segmentation method.

Compliance with Ethical Standards
The authors declare that have no con ict of interest. This paper does not contain any studies with human participants performed by any of the authors. For this type of study formal consent is not required.  The impact of PET reconstruction algorithm and six spheres delineation method on MTV measurement accuracy in phantom (sphere-to-background ratio of 4:1)