A total of 108 dynamic [¹¹C]PBR28 PET and MR images were shared by KCL. Available data included a dataset of 94 scans (Dataset 1) collected in healthy volunteers and psychiatric patients gathered from KCL historical database (Age: 34 ± 14 years; Sex: 62 male and 32 female; Genotype: 63 HABs and 31 MABs; Clinical population: 65 healthy controls, 14 subjects at ultra-high risk of psychosis, 15 patients with schizophrenia). A second dataset (Dataset 2) was composed of [¹¹C]PBR28 dynamic PET and MR scans on 7 healthy controls (Age: 30 ± 6 years; Sex: 7 male; Genotype: 7 HABs), who each received scans before and 24 h after an immune challenge performed via subcutaneous injection of IFN-α 2a (Roferon-A 3 million IU/0.5 mL solution for injection).

Details on participants and data acquisition for the two datasets can be found in Bloomfield et al. (2016); Dahoun et al. (2019); and Nettis et al. (2020). In brief, all acquisition protocols included an initial low-dose computer tomography (CT) scan, acquired for attenuation and scatter correction, using a Siemens Biograph^™ TruePoint^™ PET·CT scanner (Siemens Medical Systems, Germany; transaxial field of view (FOV): 60.5 cm, axial FOV: 16.2 cm), followed by a 90 min dynamic PET scan after a bolus injection of [¹¹C]PBR28 (Injected Dose: 329.30 ± 27.43 MBq). Dynamic PET data were binned into 26 frames (durations: 8 × 15 s, 3 × 1 min, 5 × 2 min, 5 × 5 min, 5 × 10 min), reconstructed using filtered back projection, with a 5 mm isotropic Gaussian smoothing, and corrected for random noise, attenuation, and scatter effects. Radio-pharmaceutical preparation acquisition protocol was consistent for all the studies. T1w MR brain scan data were collected using a Siemens 3-T MR scanner on either a Siemens Tim Trio or Siemens MAGNETOM Verio.

Arterial blood data were sampled using the combination of an automatic continuous sampling system of the whole blood activity for the first 15 min of each scan, and a series of discrete blood samples, manually taken at 5, 10, 15, 20, 25, 30, 40, 50, 60, 70, 80, and 90 min. Manual samples were centrifuged and used to determine the plasma over blood activity ratio (POB). Samples taken at 5, 10, 20, 30, 50, 70, and 90 min were also analyzed using radio-high performance liquid chromatography (HPLC) to calculate the PPf. The MIAKAT software (MIAKAT™)¹ was adopted for blood data processing: subjects’ C_b were defined by combining and calibrating continuous and discrete whole blood data; a linear and a sigmoid model were, respectively, fitted over POB and PPf discrete samples and applied for the definition of uncorrected plasma activity (C_{p_uncor}) and C_p for each subject.

MGH dataset (Dataset 3) included dynamic [¹¹C]PBR28 PET/MR images from 51 individuals [Age: 55 ± 16 years; Sex: 27 male and 24 female; Genotype: 31 HABs and 20 MABs; Clinical population: 10 Healthy Controls, 41 subjects with chronic musculoskeletal pain (low back pain, N = 26; knee osteoarthritis, N = 15)] simultaneously collected on a Siemens Biograph mMR whole-body PET/MR scanner (transaxial FOV: 59.4 cm; axial FOV: 25.8 cm). Full details on participant inclusion criteria and data acquisition can be found in original references (Weerasekera et al., 2021; Morrissey et al., 2023).

For all these studies dynamic PET data were acquired for a time period of 0–90 min after a bolus injection of [¹¹C]PBR28 (Injected Dose: 523.60 ± 48.66 MBq), binned into 27 frames (duration: 8x10s, 3x20s, 2x30s, 1x1min, 1x2min, 1x3min, 8x5min, 3x10min) and reconstructed using the Ordered Subset Expectation Maximization (OSEM) with four iterations, 21 subsets, and a 3 mm Full Width Half Maximum (FWHM) Gaussian smoothing. Structural T1w images were used for the generation of attenuation correction maps using an in-house developed magnetic resonance-based approach (Izquierdo-Garcia et al., 2014).

Blood samples were collected at 5, 10, 20, 30, 50, 70, and 90 min post radiotracer injection. In 16 subjects, arterial blood processing was performed using a HyperSep C18 solid extraction cartridge for separation of radio-metabolites from parent radiotracer; in 36 subjects, HPLC was used instead. For each scan, C_{p_uncor} was obtained from collected blood samples and corrected for metabolites to compute the C_p. C_b was not available for these participants.

[¹⁸F]DPA714 dynamic PET and MR scans acquired on 10 healthy volunteers at SFHJ, CEA, Orsay, were shared by the ICM center. Details on acquisition protocol are available in García-Lorenzo et al. (2018) and Lavisse et al. (2015).

For all participants, after a transmission scan using a 137Cs point source, a [¹⁸F]DPA714 slow bolus was intravenously injected over 1 min (Injected Dose: 203.05 ± 25.41 MBq) and subjects underwent dynamic PET scans in a high-resolution research tomograph (HRRT, Siemens, Knoxville, TN, United States; transaxial FOV: 31.2 cm, axial FOV: 25.5 cm) at SHFJ-CEA, Orsay. PET images were corrected for attenuation, random and scattered coincidences, reconstructed with the iterative ordered-subset expectation maximization (Ordinary Poisson [OP]-OSEM) 3D method, and binned into 27 time frames (durations: 6 × 1 min, 7 × 2 min, 14 × 5 min). A 3D Gaussian kernel with 2 mm FWHM was used as a point-spread function correction. Each participant underwent T1w MR imaging, performed with either a Philips (Best, The Netherlands) Achieva 1.5 T MR scanner or a Siemens Trio 3 T (Erlangen, Germany) scanner.

Eight of the participants underwent a second [¹⁸F]DPA714 dynamic PET to generate test–retest data (Dataset 4; Age: 44 ± 13 years; Sex: 2 male and 6 female; Genotype: 6 HABs and 2 MABs). For all participants, the second acquisition was performed between 5 and 67 days after the first visit, with a dose difference between the two acquisitions of 21.29 ± 18.95 MBq.

Metabolite-corrected and uncorrected plasma curves were generated only for 9 of the 10 subjects (Dataset 5; Age: 39 ± 13 years; Sex: 4 male and 5 female; Genotype: 5 HABs and 4 MABs). During PET scan acquisition, 21 sequential arterial blood samples were manually sampled and 7 of them (at 5, 10, 20, 40, 60, 70 and 90 min) analyzed as described in Peyronneau et al. (2023) to determine the PPf, C_{p_uncor}, and C_p activity for each subject. As for MGH dataset, C_b was not available for these participants.

As a first step in the validation, the performance of the proposed methodology in the estimation of K₁ parameter was evaluated by comparison to the standard reference 2T4K-C_p estimates. This step was performed on Dataset 1,3,5. K₁ regional estimates were computed for each subject’s ROIs, and bias introduced for each hypothesis of the proposed simplified method (Figure 1) was sequentially tested. Firstly, we tested whether the one irreversible compartment applied to early frames of the PET dynamics gave comparable results to those obtained with the full compartmental model and the true parent plasma adopted as input function (1T1K-C_p K₁). Then, the effect of the assumptions of metabolites production and red blood cells uptake negligibility was tested by computation of the K₁ using the whole blood input function (1T1K-C_b K₁). To note, information on the whole blood TACs was available only in the case of KCL scans. For MGH and ICM datasets the uncorrected plasma tracer concentration was adopted instead. Finally, regional K₁ parameters were computed with IDIF as input to the reduced model (1T1K-IDIF K₁).

In all the cases, the a priori definition of the time window to use for model fitting was necessary. This choice was based on a trade-off between the opposite necessities to limit the model fit to a short time window, such that the model hypotheses were respected, and to include enough data points for model fitting. Ultimately the time window selection had to account for differences in the speed of the kinetics for the two employed tracers and in the frame binning of dynamic PET scans. The time window was selected for each tracer as the interval following tracer administration in which the parent plasma fraction was >90%. ROIs TACs were also visually inspected with the purpose of ensuring the applicability of Hypothesis #1 of our methodological framework. This resulted in a time window of around 4 min for [¹¹C]PBR28 and 8 min for [¹⁸F]DPA714.

Standard 2T4K-Cp K₁ estimates were finally computed by fitting the whole 0-90 min tracer kinetic using a weighted non-linear least-square estimator with weights chosen optimally as

as suggested by Carson et al. (1983), where t_i is the time instant, Δt_i is the length of the scanning interval and C_ROI (t_i) is the ROI average time activity at time t_i. Both C_p or C_b input functions were corrected for delay (i.e., the variable time of appearance of tracer radioactivity in blood depending on the time required for the tracer to travel from the arterial sampling site to the region of interest; Iida et al., 1988).

To complete the corollary on K₁ analysis, assuming the cerebellum gray matter (CER) as a representative pseudo-reference region (Lyoo et al., 2015), the K₁ ratio

was also computed for each method and each cortex ROI. The relative measure R₁ was introduced for completeness and consistency with previous PET studies where the R₁ measure can be used as a proxy of relative perfusion (Chen et al., 2015). However, it is important to highlight that the identification of a proper reference region remains not trivial, especially for TSPO studies, and disease specific (Albrecht et al., 2018).

Results obtained with each of the three simplified approaches (1T1K-C_p, 1T1K-C_b, 1T1K-IDIF), in terms of both ROIs K₁ and R₁ estimates, were compared to the respective standard 2T4K-C_p estimates by computation of bias and relative bias in absolute value (bias and relBias) and both intra- and between-subjects Pearson’s coefficients of correlation (ρIntra, ρBetween).

A multilinear regression model was finally estimated, describing the subjects’ mean relBias (averaged across ROIs) between the 1T1K-IDIF and the 2T4K-C_p K₁ estimates, in terms of subjects’ age, genotype classification, sex, PET center where the acquisition was performed, and the ratio between the area under the curve of IDIF and C_p over the specific time window selected for fitting (AUCratio). Regression analysis was performed using the fitglm function (Matlab2023a, Mathworks). Predictors and response variables were rescaled to the same range [0 1]. In the case of categorical variables (genotype classification, gender, PET center), with L number of categories assumed by the categorical variable, the first category is assumed as the reference level, and the remaining L – 1 are included as indicator variables in the model and treated as a single variable.

1T1K-C_p, 1T1K-C_b, and 1T1K-IDIF model fitting were repeated using different time intervals, ranging from 2 to 5 min in the case of [¹¹C]PBR28 (Dataset 1) and from 3 to 9 min for [¹⁸F]DPA714 (Dataset 5). The sensitivity of model performance to the choice of the fitting window was investigated for each of the reduced models in terms of between-subjects and intra-subject correlation of K₁ and R₁ estimates and bias of K₁ estimates with respect to reference full model (2T4K-C_p), and precision of K₁ estimates.

Additionally, 1T1K K₁ estimation, with each of the three input functions, was repeated for [¹¹C]PBR28 scans (Dataset 1) with the inclusion in the model of the parametrization of the fraction of blood volume (1T1KV_b) and compared with the previous 1T1K-C_p, 1T1K-C_b and 1T1K-IDIF K₁ estimates obtained under the hypothesis of null V_b.

Finally, the reversible one tissue compartment model (1T2K), with and without the V_b parametrization, was tested and results of 1T1K and 1T2K fitting were compared both in terms of goodness of fit and consistency of K₁ estimates to standard 2T4K-C_p K₁ estimates.

For each subject, regional cortex 2T4K-C_p K₁ and 1T1K-IDIF K₁ estimates were computed from both pre and post IFN-α challenge dynamic PET scans (Dataset 2) and averaged across the cortical ROIs. Distribution across subjects of pre and post mean cortex K₁ estimates were compared via a paired t-test following a test for normality (Lilliefors test).

To test the reproducibility of the results, regional 1T1K-IDIF K₁ estimates were computed for both test and retest scans on a pool of 8 healthy subjects (Dataset 4). K₁ estimates were computed for each subject (both test and retest scan) from mean TACs of 4 cortical brain lobes - frontal, temporal, occipital, and parietal -, insula, cerebellum, thalami, and brainstem. Pearson correlation coefficient (ρ) and mean root distance (MRD) were computed to compare K₁ obtained for test and retest scans.

Different blood sampling and analysis procedures were adopted across the three PET centers, thus introducing differences in available blood data for the different datasets under study. Firstly, while in the case of KCL scans, both C_b and C_{p_uncor} curves (in addition to C_p) were provided, thus allowing an investigation of both POB and PPf effects when using the C_b instead of traditional C_p as input function of the reduced model, only the C_{p_uncor} was available for the MGH and ICM datasets. Additionally, tracer fp - (which is very low for TSPO ligands and difficult to measure Turkheimer et al., 2015), thus discouraging several PET imaging centers from its measurement - was solely available for KCL data; for this reason, the impact of plasma proteins on blood tracer activity was not taken into account in this study. Finally, in the case of MGH and ICM data, for which a continuous blood sampling was not performed, temporal resolution of blood and plasma concentration curves was relatively low, potentially affecting the accuracy of model fitting.

Operatively, the main challenge in the application of the method was linked to the extraction of a reliable input function from the tracer dynamic PET images. In our analysis the AUCratio acts as a measure of goodness of performance for IDIF extraction: the AUC approaches 1 as accuracy improves, while worse results are reflected by lower AUCratio values, since the IDIF approach tends generally to underestimate the blood kinetic peak.

An accurate description of the activity peak in the early phase of the tracer blood kinetic was not trivial, due to the relatively low spatial and temporal resolution in PET dynamic data, which caused, respectively, relevant partial volume effects (PVEs), and the impossibility of following the fast rising and descending part of the curve (Volpi et al., 2023), thus introducing variable bias across subjects. In this study no correction for PVEs was applied to computed IDIF. To the best of our knowledge, there is not a current standard in the application of PVEs approaches (Volpi et al., 2023) and effectiveness of these methods strongly depends on image quality, tracer kinetics, and brain anatomy, leading to uncertainty in the corrected IDIF and the risk of over-correcting and thus obtaining artificially inflated or distorted concentration time curves. These effects can ultimately result in biased estimates of kinetic parameters as well. Further analyses and a robust validation would be necessary to select the optimal method of PVEs correction (depending on scanner and imaging protocols), assess the reliability of the corrected IDIF, and evaluate the impact of correction on study outcomes. These two objectives were beyond the aim of this study.

The strong correlation between bias and AUCratio suggests how the use of more sophisticated pipelines for vessel segmentation, blood voxels selection and correction for IDIF extraction could possibly enhance the performance of the proposed method. The introduction of new generation PET scanners, with better sensitivity, improved spatial resolution and temporal resolution, and larger scanner field of view, opens the promise of a high enhancement in the performances of IDIF extraction (Volpi et al., 2023). It should be noted that K₁ bias in the case of MGH PET scans appears less correlated to AUCratio. This could be linked to different reasons. Firstly, it is worth mentioning that the AUCratio, here assumed as a measure of goodness of IDIF approximation of the arterial C_p, simply counts for differences in the area under the two curves, but not for differences in curves shapes. Secondly, IDIF extraction and time resolution are dependent on PET experimental protocol over which we did not have control being the study performed over pre-existing data. Moreover, as previously highlighted, the blood protocols which will affect the gold standard K₁ estimation are different for the sites.

In general, the use of a limited time window after tracer injection has the strong advantage of allowing to reasonably ignore the metabolite production, which, so far, represents the main unresolved issue and one of the main obstacles to a wider application of IDIF approach (Zanotti-Fregonara et al., 2011a). The radio-metabolites activity in the late phase of blood TACs is indeed known to strongly affect the estimation of tracer binding parameters (Volpi et al., 2023). In a pilot study conducted on [¹¹C]PBR28 PET scans from MGH (Dataset3), V_T estimates obtained with the adoption of the IDIF, without any correction for metabolites activity, showed high inconsistency (Pearson’s coefficient ρ = 0.35) with standard V_T estimates obtained with arterial input function (Whitehead et al., 2023).

The time window for 1T1K model fitting was experimentally chosen for each dataset and tracer, considering the kinetic of the tracer, tracer metabolism, and the temporal resolution of the dynamic PET scan that would determine the total number of samples used for model fitting for a fixed time window. To note, the relatively low time resolution of tissue TACs in the early phase following tracer injection represents one of the major limitations in this study, strongly affecting the accuracy of model fit and K₁ estimates. Sensitivity analysis showed robustness of model performances with respect to the adopted fitting-time-window (Supplementary Figures 2, 3), although higher between-subjects correlation for K₁ estimates was obtained with longer time windows. Of note, the longer the window and the higher the number of data samples adopted for model fitting and thus the precision of the K₁ estimates (i.e., lower coefficient of variation). In the case of [¹⁸F]DPA714, the adoption of an excessively short time window (3.5 or 4.5 min) resulted in a strong reduction of between-subjects correlation of 1T1K-IDIF with respect to 2T4K-C_p K₁ estimates.

The analysis of the impact of V_b parametrization on model performance showed modest to no significant difference in K₁ estimates but a slight improvement in the precision of estimates in the case the V_b parametrization was included (Supplementary Figure 4). This assumption should be further confirmed for those tissues with a higher blood volume fraction. Also, the minor effect of setting the V_b to 0 could be the consequence of the poor fit of the V_b parameter, due to the poor timing resolution at the early phase of tissue tracers kinetic (e.g., initial frame length of 15 s in the case of KCL scans). Interestingly, comparisons of results obtained with different modeling choices (different input functions and compartmental models, both reversible and irreversible) showed better data fits, as assessed by the Akaike Information Criterion (Golla et al., 2017), for 1T2K compared to 1T1K model, but at the cost of higher variability, as well as higher bias and less consistency (in terms of both intra- and inter-subjects correlations) to the standard 2T4K-C_p ROIs K₁ estimates (Supplementary Figure 5).

In this study, results obtained for [¹⁸F]DPA714 seemed to demonstrate different performances with respect to [¹¹C]PBR28 in terms of bias and intra- and between-subjects correlation of K₁ and R₁ estimates. The higher AUCratio and lower relative bias between 1T1K-IDIF and 2T4K-C_p K₁ in the ICM cohort may be explained by the higher spatial resolution of dynamic PET images, with the consequent reduction of the partial volume effects, and the relative slow bolus injection causing the arterial peak to be smoother. Of note, a smaller number of [¹⁸F]DPA714 scans, with respect to [¹¹C]PBR28 scans, were included in the study. Additionally, the acquisition of data in different PET centers and scanners introduces relevant batch effects (Joshi et al., 2009), which could result for example in a different level of noise on the image.

Independently from the specific model adopted, differences across sites were also reported in ROIs K₁ estimates derived from the quantification of KCL and MGH [¹¹C]PBR28 scans. Supplementary Figure 6 shows how between-subjects pairwise correlations of ROIs 2T4K-C_p K₁ estimates of healthy controls of Dataset 1 (KCL) and Dataset3 (MGH) are high when comparing subjects from the same dataset and lower when comparing subjects from different datasets, thus revealing differences in terms of K₁ topological patterns across the two sites. However, it is important to note that the same pattern reported for 2T4K-C_p is detected by 1T1K-IDIF K₁ estimates. The investigation of the causes of this disagreement is beyond the purposes of this study and not necessarily uniquely related to scanner differences. It is worth mentioning indeed that a significant difference in healthy controls’ age (Wilcoxon rank-sum test p < 10⁻⁴) was found between the two datasets, which could partially explain differences in K₁ values between the two scanners.

In general, no effort for data harmonization was performed across the three sites, reflecting the aim of the study to test the performance and general applicability of the proposed methodology for the quantification of K₁ on datasets with different characteristics and experimental settings, rather than performing a comparison between sites. However, the specific dependency of the results on tracers, scanners (resolution, sensitivity, noise on data), and acquisition protocols was not systemically investigated. Nonetheless, we managed to provide good preliminary evidence in support of the 1T1K-IDIF K₁ methodology. Further studies including [¹¹C]PK11195 and third-generation TSPO tracers (e.g., [¹⁸F]LW223 (MacAskill et al., 2021) and [¹¹C]ER176; Ikawa et al., 2017) would shed additional light on the relationship between method performance and tracers pharmacokinetic.