The Aarhus study was a retrospective evaluation of prospectively collected clinical FDG PET/CT data, approved by the local ethics committee of the Central Denmark Region (1-10-72-188-19). Inclusion into the dynamic whole-body (D-WB) protocol was solely based on whether patients were deemed fit to lie still for nearly 70 min while in the PET/CT scanner; in practice, this excluded patients with cognitive impairments. The study population of 52 (28 F, 24 M) patients had been referred for FDG-PET due to infection/inflammation (n = 11), lymphoma (n = 14), lung cancer (n = 7), and various other oncological indications (n = 30) [25].

Aarhus participants were scanned using a fully automated multiparametric PET acquisition protocol (Multiparametric PET Suite AI, Siemens Healthineers, Knoxville, TN, USA) on a Siemens Biograph Vision 600 PET/CT scanner (Siemens Healthineers, Knoxville, TN, USA) with 26.2 cm axial field of view. First, we performed a low-dose whole body CT (25 Ref mAs, 120 kV, CareDose4D, CarekV, Admire level 3), and then initiated PET recording at the start of a standardized injection of FDG (4 MBq/kg) using an Intego PET Infusion System (MEDRAD, Inc., Warrendale, PA, USA). The 70-min PET protocol consisted of an initial 6-min dynamic scan of the chest region, including the aorta, heart and liver, followed by a 64-min dynamic WB-PET, which consisted of 16 continuous bed motion passes: 7 × 2-min WB passes followed by 9 × 5-min WB passes. PET images were reconstructed using software version VG76A and list-mode data extending to approximately 67 min post-injection (reconstruction parameters: TrueX + TOF, 4 iterations, 5 subsets, 440 matrices, voxel size 1.65 × 1.65 × 1.65 mm3, 2-mm Gaussian filter and relative scatter correction). SUV images were normalized to body weight and injected dose.

After acquisition, the automated scan protocol automatically identifies anatomical structures on the low-dose WB CT scan [26], and places a 1.6 mm3 cylindrical VOI in the proximal descending aorta [15]. The aorta-VOI was inspected for motion, and an IDIF extracted from the full dynamic PET series of the chest region (0–70 min). The aorta IDIF was recorded at intervals of 0.1 min for the first minute post injection, 0.5 min for the next five minutes, two minutes for the next 15 min, and at five minute intervals, with frame truncation at 67 min post injection, for harmonization of scan duration with the Bern data.

We used the SUV head image for GM and WM matter VOI definition in Aarhus. Each subject's skull and brain was manually isolated using a box-shaped VOI, with rigid matching of the isolated head to an FDG PET template included within PMOD. Tissue probability maps of GM, WM, and cerebrospinal fluid of each subject were then generated using PMOD's adaption of the unified segmentation method from the SPM8 or SPM12 toolbox (https://www.fil.ion.ucl.ac.uk/spm/). Although the tool “MRI Probability/Inhomogeneity” was developed for MRI images, it performs reasonably well for FDG PET data in conjunction with carefully chosen cut-off values. Individual VOIs were generated using a cut-off of > 99.5% for GM probability and > 90% for WM, based on pilot evaluation of the first few subjects, with quality control according to visual inspection of the overlay maps.

The Bern data consisted of FDG-PET scans from 24 patients (9 women, 15 men) under investigation for lymphoma (n = 9), breast cancer (n = 6), lung cancer (n = 4) and various other tumor types (n = 5). Details of the analysis of data from these patients are reported elsewhere [21]. The local Institutional Review Board approved the study (KEK 2019–02193), and all patients provided written informed consent. FDG was administered as a single intravenous bolus at a radiochemical dose of 3 MBq/kg. PET data were acquired on a Siemens Biograph Vision Quadra [19]. Acquisition of list-mode PET data started 15 s before the intravenous bolus injection. The emission data were binned into 62 frames of the following durations: 2 × 10 s, 30 × 2 s, 4 × 10 s, 8 × 30 s, 4 × 60 s, 5 × 120 s, and 10× 300 s, with linear truncation of the final frame at 67 min for harmonization with Aarhus data. Frame-wise images were reconstructed using a proprietary software prototype for image reconstruction (e7-tools version VR10, Siemens Healthineers) employing the PSF + TOF algorithm (four iterations and five subsets). The final images were reconstructed in voxels measuring 1.65 × 1.65 × 1.65 mm3, with smoothing using a post-reconstruction Gaussian filter (FWHM 2 mm). Images were reconstructed with the high sensitivity mode, which employs a maximum ring difference of 85. The PET data were corrected for randoms, scatter, attenuation, and radioactive decay, following the methods used as clinical standard. Standard uptake value (SUV) images were generated by normalizing the late frame images to body weight and injected dose. Attenuation correction of PET emission data was by means of co-registered low-dose CT scans (voltage: 120 kV, tube current 25 mA, CareDose4D, CarekV).

Segmentations of the aorta were obtained using a deep-learning based method employing spatial ensemble learning [27]. The automatically-obtained aorta segmentations were manually edited to isolate the descending aorta (10 mm luminal diameter cylinders) in which the IDIF was computed as described previously [21]. The IDIF was recorded at intervals of 0.05 min for the first 1.5 min post injection, every 0.25 min for the next 3.5 min, at one-minute intervals for the next 12.5 min, and every five minutes thereafter until the end of the PET recording. We extracted brain GM and WM VOIs using the FDG healthy brain template in standard-space (available in PMOD v.4.1, PMOD Technologies, Zurich, Switzerland). This processing step entailed cropping and spatial normalization of each subject’s brain SUV image to the template using rigid and non-rigid registration methods [28]. Next, we applied the atlas-defined GM and WM templates to the subject’s native space PET images, with manual inspection of the registration.

In Aarhus and Bern we noted the time to first sign of blood radioactivity and the time to peak radioactivity in each case. We then plotted the natural logarithm of the blood radioactivity as a function of circulation time. Linear regression of the late phase semi-log plots gave the plasma radioactivity concentration as Ce−λ3(t), where C is a constant and λ3 is the fractional rate constant for the renal clearance of plasma FDG. Next, the extrapolate magnitude of Ce−λ3(t) was subtracted from the total measured IDIF concentration series, and the intermediate phase calculated as Be−λ2(t) (Fig. 1A), followed by an additional decomposition of the residuals to isolated the early, rapid phase of FDG distribution, defined as Ae−λ1(t). Thus, the entire IDIF was described using a function similar to the exponential form used previously by Feng et al. [29], namely,

$$}_}} \left( } \right) \, = }^\left( } \right)}} + }^\left( } \right)}} + }^\left( } \right)}}$$

(A) Scatter plot of the natural logarithm of the arterial FDG concentration as a function of circulation time from a representative subject. Here the measured IDIF is decomposed into its late component (λ3 and its ordinate intercept C) and the intermediate component (λ2 and its ordinate intercept, B), obtained by the method of residuals of the Cλ3 phase. The open circles indicate the residuals of the partial decomposition of Cλ3. In this example, the ordinate intercepts of the linear regressions corresponding to B and C are nearly identical. For clarity of presentation; we omit the corresponding decomposition of the fastest phase, Aλ1. (B) Semi-logarithmic plots of the clearance phase from representative slow, intermediate and fast eliminators. (C) The relationship between λ3 and subject age from (n = 52) patients scanned in Aarhus. (D) The corresponding empirical relationship between the total measured AUC(0–67 min) and the mean arterial concentration measured during the final three frames of the PET recording (Ca(52–67 min). The empirical relationships between the normalized arterial integral measured during the final three frames (theta(52–67 min) as functions of (E) the individual late phase FDG clearance rate constant (λ3) and (F) age of the subjects

For each individual, we calculated the mean plasma FDG concentration measured during the final 15 min of the PET recording (Ca(52–67 min)), the measured area under the curve (AUC) or plasma integral to the end of the PET recording, and the corresponding AUCs estimated from one, two, and three exponential terms. The measured area under the curve (AUC) to 67 min (AUC(0–67 min)) was calculated for each case, along with the corresponding AUCs calculated for the mono-, bi, and tri-exponential functions, which were then calculated as percentage recovery of the measured AUC, with evaluation of the exponential components beginning at the time (circa 0.5 min) of the first appearance of radioactivity in the measured IDIF. The final arterial FDG concentration was calculated as the mean of three measurements during the last three frames (52–67 min), and the corresponding normalized arterial input (theta, min) was the ratio of the AUC(0–67 min)) to the measured Ca(52–67 min).

The relationships between the various plasma kinetic parameters and age of the individual were calculated as a correlation matrix, separately for Aarhus (n = 52) and Bern (n = 24) data. An initial exploration of the correlations revealed a number of relationships useful for modeling of the IDIF and calculating the complete AUC from various late phase recordings, including a single frame PET recording corresponding to 52–67 min post injection. The magnitude of the standard net blood–brain clearance (Ki; ml g−1 min−1) in WM and GM was calculated by linear graphic analysis of PET frames in the interval 12–67 min post injection relative to the complete measured IDIFs, using the mean ordinate intercept for GM (VD, K1/k2) as one point in the voxelwise two-point Patlak analysis of the magnitude of FDG-Ki, separately for whole GM and whole WM.

We performed four kinds of single-point Patlak analysis, using pharmacokinetic relationships that emerged from the IDIF analyses, as described below. In Method 1, we defined the limiting slope of the semi-log transformation of the FDG blood concentration during the interval 35–67 min, and calculated λ3 (min−1), the fractional rate constant for the elimination of FDG from arterial blood. We then obtained a population mean correction factor for the AUC of the Ce−λ3(t) term for each individual to estimate the AUC of their complete IDIF, and thereby calculated for each individual the terminal theta(52–67 min) relative to the terminal blood concentration (Ca(52–67 min). We then estimated Ki as a two point Patlak-Gjedde plot defined by the ordinate intercept in the IDIF evaluation for GM (VD; 0.55 ml g−1 at both scanning sites) and the tracer distribution volume calculated from the mean radioactivity concentrations measured in GM, WM, and blood during the final three frames of the PET recording. Method 2: From the site-specific empirical relationships between AUC(0–67) as a function of Ca(52–67 min), we similarly calculated Ki from Ca(55–67 min) as a two point Patlak plot. Method 3: We similarly used the site-specific empirical relationships between theta(52–67 min) and λ3 measured during the interval 35–67 min post injection. Method 4: We similarly used the site-specific empirical relationships between theta(52–67 min) and subject age in the two populations.