Comparison of Tracer Kinetic Models for 68Ga-PSMA-11 PET in Intermediate Risk Primary Prostate Cancer Patients

BACKGROUND: 68Ga-PSMA-11 positron emission tomography enables the detection of primary, recurrent, and metastatic prostate cancer. Regional radiopharmaceutical uptake is generally evaluated in static images and quantified as standard uptake values (SUV) for clinical decision-making. However, analysis of dynamic images characterizing both tracer uptake and pharmacokinetics may offer added insights into the underlying tissue pathophysiology. This study was undertaken to evaluate the suitability of various kinetic models for 68Ga-PSMA-11 PET analysis. Twenty-three lesions in 18 patients were included in a retrospective kinetic evaluation of 55-minute dynamic 68Ga-PSMA-11 pre-prostatectomy PET scans from patients with biopsy-demonstrated intermediate to high-risk prostate cancer. A reversible one-tissue compartment model, irreversible two-tissue compartment model, and a reversible two-tissue compartment model were evaluated for their goodness-of-fit to lesion and normal reference prostate time-activity curves. Kinetic parameters obtained through graphical analysis and tracer kinetic modeling techniques were compared for reference prostate tissue and lesion regions of interest. RESULTS: Supported by goodness-of-fit and information loss criteria, the irreversible two-tissue compartment model was selected as optimally fitting the time-activity curves. Lesions exhibited significant differences in kinetic rate constants (K1, k2, k3, Ki) and semiquantitative measures (SUV) when compared with reference prostatic tissue. The two-tissue irreversible tracer kinetic model was consistently appropriate across prostatic zones. CONCLUSIONS: An irreversible tracer kinetic model is appropriate for dynamic analysis of 68Ga-PSMA-11 PET images. Kinetic parameters estimated by Patlak graphical analysis or full compartmental analysis can distinguish tumor from normal prostate tissue.


Background
Prostate cancer has an estimated lifetime incidence of 1 in every 9 men, but it is estimated that between 20% and 40% of prostate cancer diagnoses are unnecessary and attributable to widespread serum prostate-speci c antigen testing [1,2].Surgery and radiotherapy signi cantly reduce the prevalence of metastatic disease progression, but may also cause erectile dysfunction and/or urinary incontinence [3].Appropriately speci c diagnostics can reduce the incidence of overtreatment and improve patient-speci c outcomes.Positron emission tomography (PET) imaging with the urea-based prostate-speci c membrane antigen (PSMA) targeted 68 Ga-Glu-NH-CO-Lys-(Ahx)-HBED-CC ( 68 Ga-PSMA-11) has greatly improved the diagnosis and treatment planning for prostate cancer, as upregulated PSMA expression has been linked with aggressive or advanced disease [4,5].
The 68 Ga-PSMA-11 tracer standardized uptake value (SUV) correlates with pathological Gleason grade and can support surgical planning as well as detect nodal metastases and biochemical recurrence [6,7].
SUVs are commonly favored for their ease of clinical implementation, but SUVs depend on accurate dose and scanner cross-calibration, the time between injection and imaging, image acquisition characteristics (scanner, scatter/attenuation correction, reconstruction, frame duration), patient weight and radiopharmaceutical distribution characteristics, and may be affected by patient motion or partial volume effects.Therefore, differences in acquisition can make the comparison of SUVs across different patients and acquisition timepoints error-prone, especially when numerical cutoffs are used [8].
Kinetic modeling of tracer binding interactions reduces the impact of errors associated with patient weight, uptake timing, and dose calibration [9].Unlike SUV-centered analysis and simple static images, dynamic PET imaging with 68 Ga-PSMA-11 may be used to distinguish physiologic differences in receptorligand a nity, receptor availability, and ligand delivery and extraction, which are considered in aggregate with SUV analysis [10].These physiologic parameters provide additional information which can improve tissue characterization [11,12].However, few studies have compared compartmental models for 68 Ga-PSMA-11, and there is not a clear consensus for whether a reversible or irreversible two-tissue compartmental model optimally suits 68 Ga-PSMA-11 PET data [13,14]. 68Ga-PSMA-11 is rapidly cleared from the blood, and blood metabolite components may be assumed negligible for the compartmental model [15].This study aimed to verify the ndings by Ringheim et al., and con rm the use of an irreversible two-tissue compartment model for 68 Ga-PSMA-11 PET analysis [14].

Patients
Eighteen men with a total of 23 lesions were included in this retrospective evaluation (NCT04936334), after two patients were removed from the study cohort due to excessive motion during imaging.This study was approved by the institutional review board, and informed consent was obtained for all individuals prior to imaging.Men with histologically-proven prostate cancer before scheduled prostatectomy were eligible for this study if they were over the age of 18 and had at least NCCN intermediate risk disease or 3 cores of at least Gleason 3 + 4 disease.Patients needed to be able to lay still for the entire 60-minute PET/CT scan, and were excluded if they had received treatments with ionizing radiation within the past 30 days.The study patients had elevated PSA values (median 6.8, range 4.1-20.6)and enlarged prostates (median 40.4mL, range 27.3-89.4mL),and were primarily white (17/18).The median patient age was 65 (range: 52-75) and the median patient body weight was 90.7kg (range: 63.5-132.0kg).A more complete charting of patient demographics is contained in Table 1.Computed tomography (CT) images were acquired sequentially with the PET scan (120 kV peak, 330ms exposure time, 658 mA tube current, 0.98 x 0.98 x 1.00mm voxels, 500mm eld of view) using a soft tissue kernel (Br38).

Image Analysis
The reconstructed PET/CT images were analyzed by a board-certi ed nuclear medicine physician and a board-certi ed urologist using in-house software (Q-Image) built using IDL (L3Harris Geospatial, Boulder, CO, USA).Forty cubic millimeter (~ 50 voxel) spherical reference regions of interest (ROIs) were sampled in the central, peripheral, and transitional prostatic zones in the left and right hemispheres.Separate ROIs were also contoured under physician guidance for the index lesion, contralateral reference region, and secondary lesions when present.Time-activity curves (TACs) were extracted in Bq/mL units.SUVs were calculated using the nal 15 minutes of the scan, and mean SUV was calculated for each ROI.

Image-derived Input Function
The image-derived input function (IDIF) was calculated using in-house software built in IDL.A spherical ROI (10.0 mm diameter) was placed on a linear segment of the iliac artery on a bolus phase PET image (approximately the rst 60 seconds of data acquisition).Pro les across the vessel were generated at each location along the length of the vessel that fell within the boundaries of the localization spherical ROI.Each pro le was t with a vessel pro le model (vessel width step function convolved with scanner resolution kernel) to estimate the vessel diameters.Vessel diameter estimates were then used to generate a 3D vessel model with a uniform background region that was large enough to capture all signal spillover into the vessel region.Simulated PET images generated by convolving the 3D vessel and background model were generated to estimate resolution distortion correction factors.Resolution distortion corrected time-activity curves for the vessel region were then generated using the distortion correction factors and original time-activity curves for the vessel and background regions.The distribution of 68 Ga-PSMA-11 was assumed to be uniformly distributed between plasma and red blood cells.

Statistical Analysis
Statistical tests were performed with GraphPad Prism 9.5.0 (GraphPad, San Diego, California, USA).
Signi cance was set at 5%, and all variables are reported with median and range or mean and standard deviation.The distributions of all numerical variables were tested for normality.Kinetic and semiquantitative parameters were compared for lesion and reference tissue regions using a patient-wise paired Šídák's test for multiple comparisons.Linear models and Pearson correlations were calculated to assess the association between compartmental parameters, Patlak graphical parameters, and SUVs.The kinetic models were compared for goodness-of-t across the central, transitional, and peripheral prostate, and kinetic parameters were compared for consistency across the three prostate zones.

Model Selection
An example VOI placement for artery, reference prostate, and lesion is shown in Fig. 1.Model results for the 1T2K, 2T3K, and 2T4K compartmental models are shown in Fig. 2. All three models performed similarly for prostate and reference tissue regions, with a of 2.0 for the 2T3K model and a of 4.0 for the 2T4K model, in reference to the 1T2K exchange model.Therefore, the AIC criteria suggests consistent information loss from the 1T2K and 2T3K model, but disfavors the use of the 2T4K model for 68 Ga-PSMA-11 according to rules established by Burnham and Anderson [19].Relative goodness-of-t criteria support the use of the 2T3K and 2T4K models, as is signi cantly reduced for the 2T3K ( , , ) and 2T4K ( , , ) models relative to the 1T2K model, but not relative to each other ( , , ).Therefore, the combination of AIC and goodness-of-t criteria favor the use of the 2T3K model for 68 Ga-PSMA-11.

Parametric Evaluation
An assessment of lesion and reference prostate parameter correlations is shown in Fig. 3. Strong correlations were observed between and for reference prostate tissue (1.00) and in identi ed lesions (0.98).Additionally, the net in ux rate, , demonstrated a strong correlation with SUV in reference prostate and lesions, whether it was calculated by full compartmental analysis or Patlak graphical analysis.Accordingly, the Pearson correlation between the compartmental model and Patlak graphical model was 0.91.However, there was a weak positive correlation between the full compartmental model and the Patlak model intercept terms, especially within lesions.Linear regressions between SUV, , Patlak , , and Patlak intercept are shown in Fig. 4 and Supplemental Fig. 1, demonstrating large coe cients of determination between SUV, K i , and Patlak K i .However, differential uptake patterns can be observed between SUV and Patlak K i images, as shown in Fig. 5.
Median, rst, and third quartile parameter values are charted for reference prostate tissue and lesions in Table 2. Matched lesion and reference prostate parameter values are included in Supplemental Fig. 2. Signi cant differences between parameter values for lesion and reference prostate are noted for K 1 , k 2 , k 3 , K i , and SUV in Table 3.Additionally, temporal variations in normal prostate and lesion SUV are compared in Fig. 6.Despite parametric differences between lesion and reference prostate, no signi cant differences in zone-speci c kinetic rate constants or model goodness-of-t were observed (Supplemental Fig. 3 and Supplemental Fig. 4).

Discussion
The results of this study support a two-tissue, three-parameter kinetic model for characterizing the pharmacokinetics of the 68 Ga-PSMA-11 radiopharmaceutical. 68 Ga-PSMA-11 exhibits free binding to the extracellular domain of PSMA and slow cellular internalization [20,21], thus providing a physiological basis for the irreversible two-tissue compartment model and Patlak analysis.In comparison with other primary evaluations of 68 Ga-PSMA-11 kinetics, the median PSA of patients reported in this study is reduced (6.8ng/mL)versus Sachpekidis et al. (24.1ng/mL) and Ringheim et al (8.64ng/mL).Additionally, 11/18 patients possessed favorable intermediate grade disease, in comparison with the greater proportion of high risk disease in other kinetics studies [14,22].
Although the Akaike information criterion suggested that maximal information was preserved by the 1T2k model, chi-square goodness-of-t criteria suggested that the 1T2k model did not appropriately t 68 Ga-PSMA-11 time-activity curves.Therefore, the 2T3k model is optimal based on dual consideration of the Akaike information criterion and chi-square goodness-of-t criteria.Previous kinetic evaluations of 68 Ga-PSMA-11 for primary prostate cancer have supported the 2T3k or the 2T4k kinetic models, but the ndings of this study are consistent with the analysis in high-risk patients established by Ringheim, et al. [13,14,22].

Kinetic parameters (
) exhibited signi cant differences between lesion and reference prostate tissue, as demonstrated by patient-wise comparison (Fig. 4, Supplemental Fig. 2) and statistical comparisons (Table 3).The sampled compartmental model rate constants were also consistent with those reported by Ringheim, et al. [14].Parameter differences between lesion and reference prostate remained signi cant, regardless of whether estimates were obtained by full compartmental models or Patlak graphical analysis.
values obtained through compartmental modeling and Patlak analysis were substantially correlated for reference prostate tissue and lesions (Pearson r = 0.91).
The current EANM/SNMMI 68 Ga-PSMA-11 image acquisition guidelines recommend an acquisition timeframe between 50 and 100 minutes post-injection, primarily due to increasing time-activity curves and SUVs in late time-windows relative to normal prostate [23][24][25][26].However, it has also been reported that tumor visibility is improved in the 30-45 minute window, where bladder accumulation is reduced and statistical count rates remain high [14,27].Here, we nd that kinetic and semiquantitative parameters can discriminate lesion from reference prostate using earlier acquisition protocols, even as early as 30 minutes post-injection as shown by Fig. 6.Additionally, although previous reports have also favored the lean body mass SUV over body-weight SUV, we show a strong concordance (r 2 = 0.9281, Supplemental Fig. 1) between the percentage of the injected dose per gram and body-weight SUV semiquantitative analysis metrics [28].

Consistent with other reports, lesion
values correlated strongly with SUV for compartmental (Pearson r = 0.94) and Patlak (Pearson r = 0.85) models, indicating that 40-55 minute post-injection SUV metrics provide substantially similar information as values [14,22].Maximal SUVs have also been found to correlate with immunohistochemical PSMA expression and histopathology in patients with prostate cancer [29,30].Therefore, it is unlikely that provides additional information beyond that of either the percentage of the injected dose per gram or the measured SUV, a simpler method which is already commonplace in many clinical work ows.Instead, K i -based images may have utility in imaging of cancers with lower levels of PSMA expression, where improvements in lesion-to-normal tissue contrast from blood pool signal reduction may be more impactful towards differentiating lesions from the image background.

Although
(Patlak and full compartmental analysis) correlated strongly with SUV, individual compartment rate constants (K 1 , k 2 , k 3 ) demonstrated minimal to slightly negative correlation with SUV.Table 2 and Table 3 demonstrate that K 1 and k 3 are signi cantly elevated in lesions, while k 2 is signi cantly decreased.These ndings are consistent with increased PSMA expression and PSMA-11 internalization on the prostatic epithelium.In contrast to , the low correlation of kinetic parameters with SUV indicates that they provide additional independent information of tissue physiology.Therefore, kinetic analysis with the Patlak method is not expected to provide additional diagnostic utility, and the 2T3k compartmental model is the preferred method of dynamic analysis for 68 Ga-PSMA-11 PET.

While
and were uncorrelated parameters in the 2T3k compartmental model (Pearson r 0.2 for reference prostate and lesion), Patlak and were correlated (Pearson r = 0.77) in lesions and moderately anti-correlated (Pearson r=-0.28) in prostate reference tissue.Through a preliminary investigation, the Patlak product was at least three times the value in lesions when compared to reference prostate tissue for all 18 patients.Further investigation is necessary to determine if parameter combinations are diagnostically relevant.
As noted in Supplemental Fig. 3 and Supplemental Fig. 4, there were no statistically signi cant differences between compartmental rate constants, compartmental model , or between normal prostatic tissue in the central, transitional, and peripheral prostatic zone.Additionally, the chi-square goodness-of-t criterion was consistent across all prostatic zones, indicating that the model is likely appropriate regardless of prostatic location.This observation is in contrast to previously reported ndings by Pizzuto, et al, who reported that 68 Ga-PSMA-11 accumulation is higher in the central zone than in the transition or peripheral zone [31].However, the nding was reported during the staging for high-risk disease, and thus could be attributable as a feature of aggressive disease.In our study, 11% (2/18) patients met or exceeded the average SUV mean reported by Pizzuto, et al. in the central zone.
This study, although consistent with other literature reports in its ndings, has several limitations which should inform its interpretation.First, the small sample size limits statistical power and result generalizability.Additionally, the scope of patients included in this study is primarily limited to intermediate-risk disease, as only patients who were candidates for prostatectomy received 68 Ga-PSMA-11 PET/CT scans.The study included no low-risk patients, and only a single high-risk patient.Additionally, the demographics of patients meeting the study risk criteria were highly racially homogeneous.The present study was performed on presurgical research scans, and did not acquire listmode data past 55 minutes.Thus, the kinetics and late time-frame SUV images are temporally constrained and do not fully utilize the timeframes recommended by EANM and SNMMI [23].

Conclusion
The two-tissue irreversible compartment model is appropriate for kinetic analysis in 68 Ga-PSMA-11 imaging.The two-tissue irreversible compartment model is applicable to central, transitional, and peripheral prostate, regardless of tumor involvement.Kinetic parameters (K 1 , k 2 , k 3 ) are useful towards distinguishing prostate cancer lesions from normal prostatic tissue, and kinetic parameters provide information about tissue physiology that is independent from SUV-based metrics and Patlak (K i ) net in ux rate.

Abbreviations
PET positron emission tomography PSMA prostate-speci c membrane antigen 68 Ga-PSMA-11 This study was approved by the Indiana University institutional review board (IORG0000134).The study was performed in accordance with the ethical standards as described in the 1964 Declaration of Helsinki and its later amendments.

Consent to Participate
Written informed consent was obtained for all individuals prior to imaging.

Figure 2 Model
Figure 2

Figure 5 Comparison
Figure 5

Table 1
Patient characteristics, injected doses, and summary pathology classi cation.
Three different kinetic models were evaluated in this analysis: a reversible one-tissue compartment model with two rate constants (1T2k), an irreversible two-tissue compartment model with three rate constants (2T3k), and a reversible two-tissue compartment model with four rate constants (2T4k).Additionally, the fractional blood volume component was estimated for each model.Model optimality was evaluated based on chi-square goodness of t criteria and the Aikake information criterion (AIC), consistent with other studies[8].The 2T3k model net in ux rate and distribution volume were evaluated from the full compartmental model as well as the Patlak graphical method[18].

Table 2
Median parameter values from 23 lesions in 18 patients.Shown are comparative median, mean, standard deviation, rst, and third quartile parameter values in lesions and reference prostate tissue.
Shown are median [mean, standard deviation, rst quartile -third quartile] value comparisons for lesion and normal prostate.Semiquantitative values include the standard uptake value (SUV) and percent injected dose per gram (%ID/g).Quantitative parameters include the kinetic two-tissue, three rate constant model parameters, net in ux rate ( ), distribution volume ( ), and Patlak model net in ux rate(Patlak  ).

Table 3
Comparison of semiquantitative and quantitative parameter values between reference prostate and lesion.
Signi cance level is set at 0.05, and is corrected for multiple comparisons with the Šídák correction.