Influence of Sampling Schedules of [¹⁸F]FDG on Individualised Internal Dosimetry in PET/CT Scanning

PET/CT image-based pharmacokinetic data

In this study, a total of twenty unenhanced whole-body [¹⁸F]FDG PET/CT scans were conducted on a cohort of 12 males and 8 females, with an average weight of 65±5 kg and a mean age of 69±13 years. This cohort represents a realistic and typical patient population undergoing clinical PET/CT imaging, particularly in oncologic and metabolic contexts such as [¹⁸F]FDG PET. It is crucial to highlight that all patients included in this study were clinically stable at the time of imaging and were carefully selected to have minimal or no major comorbidities (e.g., diabetes, renal or hepatic dysfunction, inflammatory conditions) that could substantially affect tracer kinetics or organ function, thereby reducing the potential for bias in the results. Each participant received an intravenous administration of 370±10 MBq of the probe, utilising the Philips Ingenuity TF PET/CT scanner. This hybrid device features LYSO crystals and an 18.0 cm axial field of view (FOV), producing 64 image slices per scan and supporting time-of-flight (TOF) capability. The helical CT component supports 128 channels with 4.0 cm axial coverage. Data were collected over 3 to 300 s per bed position (depending on the TP measurement) at four static TPs: 5 (TP5min), 20 (TP20min), 60 (TP60min), the baseline, and 90 min (TP90min) p.i. An ordered subset expectation maximisation (OSEM) algorithm was used for image reconstruction on a 144×144×235 matrix, with PET images corrected for attenuation. The low-dose CT images were reconstructed on a 512×512×320 grid. Having registered PET and CT images, the three organs under investigation (lungs, spleen, and liver) of each patient were manually segmented (under the supervision of an experienced radiologist to reduce inter-observer variability) on all CT slices using the widely recognised 3D Slicer software version 5.6.1. Subsequently, a homemade MATLAB script was developed to generate a segmentation mask for each organ. The mean organ TAC data were calculated by averaging all voxels forming the corresponding organ. Fig 1 shows the baseline (60 min p.i.) PET/CT image along with the segmentation of the lungs, spleen, and liver.

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Fig 1: Three sample slices from the whole-body PET/CT dataset: (a) PET (left), (b) Low-dose CT (middle), and (c) Organ segmentation masks for the liver (top right), lungs (middle right), and spleen (bottom right). PET: Positron emission tomography; CT: Computed tomography; PET/CT: Positron emission tomography/computed tomography

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Organ TAC data fitting

PET/CT scans were employed to determine the TAC from each patient's lungs, spleen, and liver at the four static TPs. In other words, organ TACs were calculated by summing the [¹⁸F]FDG activity within the surrounding voxels. It is well-established that radioactive decay and many physiological processes in the human body exhibit exponential behaviour over time.^{[24, 33-38]} Two scenarios were then evaluated for TAC determination: (1) incorporating both the uptake and clearance phases (Scenario I), and (2) considering only the clearance phase from the injection time (Scenario II). The former is characterised by an initial increase in the TAC from 0 at t = 0 to a peak, followed by a gradual decline. The latter is characterised by a decreasing trend starting from the peak value of the TAC, meaning A(t = 0) ≠ 0. The time t = 0 refers to the injection time. The bi- (Scenario I) and mono-exponential (Scenario II) models are as outlined in Eqs. 1 and 2:

where Abi(t) and Amono(t) denote the activity at time t in the bi- and mono-exponential models, respectively. , , and are positive rate constants of the exponential terms, and A1, A2, and A3 represent coefficients of these exponential terms. Additional constraints include enforcing A(t) ≥ 0 across all models, the requirement that only physical decay occurs following the last TP in empirical modelling, and the condition A(t = 0) = 0 in bi-exponential TAC modelling. The assumption of A(t = 0) = 0 is considered both reasonable and applicable to most organs, with the notable exception of blood. To accurately capture the rapid kinetic profile and reduce potential bias introduced by this assumption, early PET/CT imaging is utilised. It is important to emphasise that fitting bi-exponential and mono-exponential TAC data mandates a minimum of four and two time-point measurements, respectively.

Despite the uptake phase being rapid compared to the clearance phase, its impact on internal dose calculation was studied. Organ TAC data fitting in a least-squares sense was performed using the Curve Fitting Toolbox in MATLAB R2020b software for different [¹⁸F]FDG kinetic models based on the TAC shape: bi-exponential modelling for Scenario I and mono-exponential modelling for Scenario II. Scenario I consisted of five TAC data fittings: (TP0min, TP5min, TP20min, TP60min), (TP0min, TP5min, TP20min, TP90min), (TP0min, TP5min, TP60min, TP90min), and (TP0min, TP5min, TP20min, TP60min, TP90min). It should be noted that there was no PET/CT measurement at the time TP0min, and it was assumed that A(t = 0) = 0. Likewise, (TP5min, TP20min), (TP5min, TP60min), (TP5min, TP90min), (TP20min, TP60min), (TP20min, TP90min), (TP60min, TP90min), (TP5min, TP20min, TP60min), (TP5min, TP60min, TP90min), (TP5min, TP20min, TP90min), (TP20min, TP60min, TP90min), (TP5min, TP20min, TP60min, TP90min) were considered for Scenario II. In fact, each combination results in a distinct sampling schedule for the [¹⁸F]FDG. Fig 2 illustrates a hypothetical bi-exponential TAC modelling for a typical organ of interest, showing PET/CT measurements at four TPs: 5, 20, 60, and 90 min p.i.

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Fig 2: Diagram (not to scale) illustrating a hypothetical bi-exponential time-activity curve (TAC) modelling with PET/CT measurements at four TPs: 5, 20, 60, and 90 min p.i. of [¹⁸F]FDG. The dashed red line delineates the uptake and clearance phases of the TAC for a typical organ of interest. TP: Time point; TAC: Time-activity curve; PET/CT: Positron emission tomograph/computed tomography; FDG: Fluorodeoxyglucose

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For comparison, an empirical model^[24] was also considered [Fig 3], utilising the trapezoidal rule to integrate TPs and accounting for physical decay (T1/2,physical = 110 min) beyond the last TP extending to infinity. Additionally, as denoted in Eqs. 3 and 4, the integration span for each organ TAC was considered from injection time to the last TP (i.e., TIA90min, Case I) and again to infinity (i.e., TIA∞, Case II) to assess the impact of the TAC's tail on radiation dose. The analytical integration method was employed for fitted (analytical) TAC models to calculate the TIA. TAC data fittings' accuracy was assessed through visual inspection and calculation of the adjusted coefficient of determination () to account for the different degrees of freedom of each TAC model.

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Fig 3: Diagram (not to scale) illustrating a hypothetical empirical timeactivity curve (TAC) modelling with PET/CT measurements at four TPs: 5, 20, 60, and 90 min p.i. of [¹⁸F]FDG. The dashed red line delineates the uptake and clearance phases of the TAC for a typical organ of interest. TP: Time point; TAC: Time-activity curve; PET/CT: Positron emission tomography/computed tomography; FDG: Fluorodeoxyglucose

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Here, TIA90min and TIA∞ represent the areas under the TAC up to the last TP (i.e., 90 min p.i.) and up to infinity, respectively. A(t) represents the organ activity ascertained from the PET scans at time t, incorporating both the physical and biological half-lives of [¹⁸F]FDG.

Organ s-value calculation

The MIRD schema necessitates the organ S-value to calculate the internal radiation exposure, as indicated in Eq. 5, where denotes the radiation dose of the voxel in Gy, represents the TIA in Bq•s, and S is the S-value in Gy/Bq•s.^[32] The TIA is essentially the integral of the voxel TAC.

Accurate voxel S-values were calculated using GATE (version 8.2) MC modelling. GATE is based on the well-validated GEANT4 toolkit, dedicated to the simulation of medical imaging scanners^[28-30] and radiation dosimetry, particularly internal dosimetry.^[27,39,40] For accurate MC simulations, the physical half-life of the ¹⁸F tracer (110 min) was taken into account. After motion correction of PET/CT scans, the images were resampled to the same size and subsequently registered by exploiting the B-spline method. The CT images served as a voxelised phantom, while the PET scans were treated as voxelised sources. Due to the high computational cost of GATE MC simulations, only 5.0% of the list-mode PET data were reconstructed. The dose actor was used to score the 3D dose rate maps for each patient. The statistical uncertainties in the GATE-simulated dose rates were kept below 1.0%. The MC simulation was validated against experimental data using a methodology similar to that employed in our previous study.^[6]

The S-value maps were then generated by dividing the dose rate matrices by the administered [¹⁸F]FDG activity of each patient. Then, voxel-level internal doses were estimated by multiplying each voxel S-value by its corresponding voxel TIA. As elaborated earlier, the MATLAB script, in conjunction with CT-based organ segmentation masks, was finally used to compute the average internal dose for each organ precisely. The absorbed doses corresponding to TIA90min and TIA∞ are denoted as D90min and D∞, respectively. The absorbed dose calculated using all considered TPs (4-TP PET/CT measurements plus the assumption A(t = 0) = 0 in Scenario I) was regarded as the reference radiation dose, Dref. The organ doses were presented as the mean ± standard deviation (SD), offering descriptive estimates, with no additional statistical comparisons conducted. Fig 4 presents a flowchart illustrating the primary steps of this research.

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Fig 4: The workflow of this study for calculating organ internal doses using various time-activity curve (TAC) data modelling approaches. PET/CT: Positron emission tomography/computed tomography; TAC: Time-activity curve; MIRD: Medical internal radiation dose; TP: Time point; TIA: Time-integrated activity

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Gate-derived organs’ s-values

Fig 5 shows the average S-values of the liver, lungs, and spleen (measured in mGy/MBq.s) for 20 patients, along with their SD. The spleen exhibits the greatest variability in computed S-values. This is primarily due to the challenges associated with accurately segmenting it from CT imaging data. These difficulties arise from various anatomical and technical factors: its relatively small size, intricate and variable morphological structure, and close anatomical proximity to neighbouring abdominal organs that have similar attenuation. The average S-value for each organ is determined by averaging the S-values of all voxels within that organ. For instance, the S-value for the liver was determined to be 6.45E-05 mGy/MBq.s. The internal doses to each organ can be evaluated using the corresponding TIA by calculating the organs' S-values using GATE MC simulations. The authors have previously studied the impact of the PET/CT image segmentation method (either manual or deep-learning-based) on internal dosimetry.^[41]

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Fig 5: Average organ S-values for the liver, lungs, and spleen, as determined by GATE simulations, including associated standard deviation (SD).

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Internal dosimetry in empirical tac modelling

An easy and rapid method to calculate TIA is by using empirical modelling of the TAC without fitting the data.^[24] Table 1 displays the mean relative doses calculated using empirically modelled organ TACs. Given the rapid uptake of the organs under investigation, which reaches its peak early, and the requirement of realistic bi-exponential TAC modelling to capture this peak, the TP corresponding to early uptake (TP5min) is included in all sampling combinations. However, the time course to reach peak or plateau levels varies depending on the specific organ being studied and its condition, whether malignant, inflammatory, or healthy.^[42] It is important to emphasise that empirical TAC modelling in Scenario II is impractical because it neglects the assumption A(t = 0) = 0, thereby overlooking the intake phase of the TAC. A potential solution involves extrapolating the TAC data back to time t = 0 to determine the TAC value at the time of injection for a specific organ. However, since this process necessitates linear fitting of the TAC data, it cannot be classified as a true empirical model.

Although empirical modelling of TAC data is straightforward, easily implemented, and free from systematic bias, it frequently leads to substantial overestimation of the TIA.^[24] This overestimation primarily arises from neglecting the biological clearance of [¹⁸F]FDG from the target organ beyond the last TP and the limitations imposed by a finite number of TPs in numerical integration. As demonstrated in Table 1, the sampling schedule significantly affects the magnitude of this overestimation, with sparser sampling schedules producing greater inaccuracies. The absence of delayed sampling further exacerbates this issue. Notably, in the first two rows of Table 1, inclusion of a later TP (i.e., TP90min) enhances the accuracy of internal dose estimates across the three organs studied, due to reduced bias from the assumption that activity beyond the final TP declines solely via physical decay, without accounting for biological clearance. Thus, to achieve a more accurate TIA calculation using empirical TAC modelling, it is essential to include delayed measurements. An overestimated TIA can lead to an overestimated internal dose assessment, which poses a greater challenge in therapeutic or theranostic applications, where higher doses of radionuclide are usually administered.^[24,43,44] The ultimate consequence of overestimated internal doses may be suboptimal image quality in diagnostic tasks and undertreatment in therapeutic applications.^[24] Consequently, empirical modelling should not be regarded as the preferred method for internal dosimetry applications requiring high accuracy.

Internal dosimetry in mono-exponential tac modelling

Table 2 lists the estimated mean relative doses from [¹⁸F] FDG for various 2-TP measurements using analytic TAC modeling. Based on the data presented in Table 2, employing exclusively early sampling schedules (e.g., TP5min, TP20min) in the analytical fitting of TAC data results in the systematic underestimation of internal doses across the three examined organs. This underscores the importance of incorporating delayed PET/CT measurements for personalized internal dosimetry. Selecting the (TP60min, TP90min) schedule results in overestimated internal dose values for the three organs and is therefore not recommended for internal dosimetry tasks, despite its significant diagnostic benefits. The optimal choice, (TP5min, TP60min), yields ratios near unity, except for the lungs. As shown in Table 1, for 2-TP internal dosimetry assessments, combining an early PET/CT acquisition with a baseline image at 60 min p.i. yields the most accurate internal dose estimates, as this approach more effectively captures the complete time-TAC profile of [¹⁸F]FDG over time. The discrepancy between D∞/Dref and D90min/Dref indicates the significance of the TAC tail in internal dosimetry. It is clear that omitting an early TP PET/CT measurement substantially affects internal dosimetry, even with a late TP sample taken at 90 min p.i. Specifically, for the liver and 2-TP PET/CT measurements conducted at 60 and 90 min p.i., the calculated internal dose is elevated by 59%.

Like Table 2, Table 3 presents estimated mean relative doses from [¹⁸F]FDG using mono-exponential TAC modelling for 3- and 4-TP PET/CT measurements. As presented in Table 3, the sampling schedule comprising TP5min, TP60min, and TP90min yields the most accurate results among all evaluated 3-TP schedules for [¹⁸F]FDG when applying mono-exponential modelling. In comparison to all 3-TP PET/CT measurements, the 4-TP sampling schedule provides superior TIA estimation and, consequently, more accurate internal dose assessments. Compared to Table 2, the reduced discrepancy between the ratios demonstrates the superiority of denser sampling of [¹⁸F]FDG. For 3-TP samples taken at 5, 60, and 90 min p.i., the internal dose calculation for the spleen increases by 21%. The overestimation is less pronounced for the liver and lungs. Additionally, the influence of the TAC tail on internal dosimetry is diminished in organs with rapid clearance kinetics. In contrast, organs characterized by slow clearance, such as the brain, or those demonstrating high retention, including the bladder, may experience an impact.

The mono-exponential [¹⁸F]FDG kinetic model assumes a continuously decreasing trend for the tracer and does not satisfy the condition A(t = 0) = 0. Instead, it presumes a high initial value for A(t = 0), resulting in an overestimated TIA∞ and subsequently an overestimated internal dose of [¹⁸F]FDG. This means that while the mono-exponential fitting method requires fewer TP measurements, it compromises the accuracy of dose calculation. The level of inaccuracy varies depending on the probe's uptake pattern in the specific organ. Notably, the mono-exponential [¹⁸F]FDG kinetic model can function with as few as two PET/CT measurements, enhancing patient comfort and clinical efficiency. In contrast, the bi-exponential [¹⁸F]FDG kinetic model offers more accurate internal dosimetry, making it better suited for tasks that require high precision, particularly with theranostic probes. However, it may compromise patient comfort and radiation protection.

Internal dosimetry in bi-exponential TAC modelling

By using the S-values [Fig 5] and employing 4-TP bi-exponential TAC modelling [refer to the bottom row of Table 4], we calculated a mean effective dose of 0.016 ± 0.002 mSv/MBq for this study cohort. This result is similar to the 0.02 mSv/MBq reported by Kaushik et al.^[4] and Huang et al.^[5] The main difference in our individualised approach lies in the use of a validated GATE MC simulation ^[6], whereas Kaushik's method relies on the OLINDA/EXM software and dynamic PET/CT scans, and Huang et al. used dose coefficients from ICRP publication 103.^[4,5] Moreover, the ICRP 128^[45] provides a dose coefficient of 0.019 mSv/MBq for [¹⁸F]FDG, showing a variation of about 15%. This discrepancy arises from the approach used to calculate the effective dose. While the ICRP relies on reference phantom models, our method is based on personalised data.

Table 4 presents the estimated relative doses from [¹⁸F]FDG using analytic TAC modelling for 3- and 4-TP PET/CT measurements. Notably, there is no PET/CT measurement at the injection time (TP0min), and we assume A(t = 0) = 0. The 4-TP schedule [bottom row of Table 4], which includes all PET/CT measurements and employs bi-exponential TAC modelling, is considered the reference TAC. Thus, the ratios for this combination are unity when the integration period extends to infinity. Ratios approaching unity observed with the 4-TP sampling schedule underscore the benefits of increased temporal resolution in TAC sampling. According to Table 4, the baseline PET/CT scan plays a crucial role in the sampling schedule, as combinations including this TP measurement yield ratios closer to unity. When 3-TP samples are taken at 5, 60, and 90 min p.i., the internal dose of the spleen is overestimated by approximately 13%, which is about 8% lower than the overestimation from mono-exponential TAC modelling [compare Tables 3 and 4]. These findings indicate that bi-exponential modelling of the TAC provides greater accuracy than mono-exponential modelling for a given set of PET/CT measurements. Furthermore, within each modelling framework, increasing the number of sampling TPs further improves the accuracy of dosimetric estimates.

Fig 6 illustrates mono-exponential kinetic modelling of [¹⁸F] FDG using different 3-TP sampling schedules. Four different schedules, (TP5min, TP20min, TP60min), (TP5min, TP60min, TP90min), (TP5min, TP20min, TP90min), and (TP20min, TP60min, TP90min), are compared. The results indicate that mono-exponential modelling lacks accuracy if either the early TP measurement or the baseline PET/CT images are missing. The administered activity normalises the PET-derived activities (mean 370 MBq), allowing the area under the TAC to represent the TIAC. This normalisation enables comparisons across different PET scans by eliminating variations due to clinic-specific FDG dosages. Fig 7 compares 3-TP mono- and 4-TP bi-exponential TAC data modelling. It is evident that the mono-exponential model overestimates the TIA and, consequently, the internal doses. Beyond 5 min p.i., both models align, predicting the same TIA. All TAC data were fitted with an value exceeding 0.90. it should be noted that our observed trends in TACs align with those reported in^[4] for the organs studied.

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Fig 6: Comparison of normalised liver mono-exponential time-activity curve (TAC) data modelling for different 3-TP sampling schedules of [¹⁸F]FDG. Image-derived activities are normalised to the administered activity.

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Fig 7: Comparison of normalised liver time-activity curve (TAC) using mono- and bi-exponential models for [18F]FDG PET/CT measurements at 5, 20, 60, and 90 min p.i. Image-derived activities are normalised to the administered activity. FDG: Fluorodeoxyglucose; PET/CT: Positron emission tomography/computed tomography

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