Feasibility of Population-Based Input Function for Kinetic Modeling of [C]-DPA-713

Feasibility of Population-Based Input Function for Kinetic Modeling of [C]-DPA-713 Mercy I. Akerele, PhD; Sara A. Zein, PhD; Sneha Pandya, MSc; Anastasia Nikolopoulou, PhD; Susan A. Gauthier, DO, MPH; Ashish Raj, PhD; Claire Henchcliffe, MD, DPhil; P. David Mozley, MD; Nicolas A. Karakatsanis, PhD; Ajay Gupta, MD; John Babich, PhD; Sadek A. Nehmeh, PhD a Department of Radiology, Weill Cornell Medical College, New York, NY 10021 b Department of Neurology, Weill Cornell Medical College, New York, NY 10021 c Feil Family Brain and Mind Institute, Weill Cornell Medical College, New York, NY 10021

In PET, kinetic modeling is often essential for the accurate quantification of tracer uptake and metabolism in the tissue.
This often requires the measurement of the tracer concentration in the arterial blood over time, an invasive and a potentially risky procedure (13), which can also adversely influence subject accrual (14).
An alternative technique such as an image-derived input function (IDIF) (15,16) or population-based input function (PBIF) (17,18) can facilitate the adoption of PET protocols requiring input functions. In brain studies, IDIF is usually deduced from the dynamic images of the carotid arteries, and hence is susceptible to partial volume effect (15)(16)(17).
Previous studies showed the feasibility of PBIF as a robust alternative to IDIF for some radiopharmaceuticals (17,18).
PBIF is generated by averaging the normalized patient-specific arterial input functions (PSAIFs) deduced from a cohort of subjects. Several normalization techniques have been reported in the literature; for example traditional scaling using blood samples by correlating the measured plasma activity with the AUC (17); correlation of the PBIF with PSAIF venous samples (19); scaling by injected dose and weight (20,21); and non-invasive scaling using individual parameters like weight, body surface area (BSA), and lean body mass (LBM) (17). Many studies have assessed the feasibility of PBIF for kinetic analysis using [ 18 F]FDG (18,(22)(23)(24)(25), yet very few studies involved neuroreceptor PET tracers (17,26), including TSPO brain studies (19,21,27). To the best of our knowledge, no PET kinetic modeling study has been performed with [ 11 C]DPA-713 using PBIF.

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A major concern in the kinetic analysis of TSPO brain studies is the effect of genotype on the input functions. Owen et al. (28,29) demonstrated that the second generation TSPO tracers target two binding sites in humans, which leads to three affinity patterns: low-, high-, and mixed-affinity binders (LABs, HABs. and MABs, respectively). Past researches have shown that this variability in binding affinity has a major influence on the kinetic parameters where the values for HABs could be approximately twice that of MABs (29,30). Most studies therefore tend to carry out a genotype-based kinetic analysis for TSPO brain studies, especially when this involves any population-based implementation. However, for [ 11 C]-DPA-713 PET study, Coughlin et al (31) showed that different genotype-and physiological-related factors have varying degrees of influence on the global TSPO changes in the brain, thereby hindering accurate PET analysis, even among individuals with the same genotype. This was also confirmed by other TSPO studies (32)(33)(34). These previous studies also showed that normalization by the gray matter allows compensating for this genotypic dependency and other unknown physiological factors (not related to inflammation) that can affect the distribution of radiotracers binding to TSPO in the PET brain studies.

A. Subjects
In total, twelve subjects (9 males and 3 females; age 56.6 ± 11.9 years) were recruited from a Parkinson's Disease

B. PET Measurements and Reconstruction
PET data were acquired in list-mode format on a 4-ring Siemens Biograph mCT TM for a total of 90 minutes. The PET data were reconstructed into 32 dynamic frames (6×10 s, 4×30 s, 3×60 s, 2×120 s, 5×240 s, 12×300 s) using ordered subset expectation maximization (OSEM) with attenuation, scatter, and randoms corrections. Continuous arterial sampling was performed at 15 second intervals for the first 10 minutes using an automated fraction collector, followed by five additional samples collected at 20, 30, 45, 60, and 90 minutes respectively. Each of the blood samples was weighed and counted using a Wizard ® automatic gamma counter (Perkin Elmer), and then the activity concentration was calculated. Blood samples drawn at 5, 10, 20, 30, 45, 60, and 90 minutes post-injection were also used to estimate metabolite fractions. The blood time activity curves (TACs) were finally corrected for metabolites, yielding a metabolite-corrected, arterial input function.

C. Data Analysis and Kinetic Modeling
Each subject underwent a T1-weighted MRI scan. Inter-frames head motion correction was achieved by rigidly coregistering the individual dynamic PET frames to the last 10 minutes imageset using PMOD (version 3.8; PMOD Technologies Ltd). The resulting dynamic imageset was then rigidly registered to the T1-MR imageset. Brain regions were delineated on the MRI images using FreeSurfer software (35), the corresponding Volumes of Interest (VOIs) were overlaid on the co-registered and motion-corrected dynamic PET images, and finally the corresponding TACs were deduced.
Kinetic modeling was done for each patient using the Logan VT model. Kinetic analysis was performed using the PSAIFs, and then repeated using the PBIFs. For each of the selected brain structures (white matter, cerebellum, thalamus, caudate, putamen, pallidum, brainstem, hippocampus and amygdala), the total volume of distribution (VT) were estimated with the blood volume fixed to 5%. Following the recommendations of past TSPO studies by Coughlin and others (31,33,36), the VT was also normalized by the corresponding gray matter values (referred to as GM normalization in this study) to correct for physiologic factors (unrelated to inflammation) which may affect radioligand brain uptake (31,32,36). The gray matter was recommended for normalization because it is believed to have relatively uniform binding pattern in healthy participants (33).

D. Test-Retest Repeatability and Reliability
Five healthy control subjects underwent a test-retest within the same day to assess the reproducibility of the kinetic parameters in the brain structures. Kinetic analysis was carried out for all the selected brain regions, for both the test and retest datasets, using the Logan VT model and the corresponding PSAIF's. The repeatability of VT was assessed using the Bland-Altman analysis (37): The corresponding confidence interval of the mean bias (CI), 95% limits of agreement (LoA) and the coefficient of repeatability (CR) between test and retest were determined using: where = number of subjects, and = , where 2 is the variance of the relative difference, , between the test and retest estimates. This represents the value below which the relative difference between test and retest is expected to lie with a 95% probability (37,38).

E. Generation of Population-Based Input Functions
The PBIFs were generated from the metabolic-corrected PSAIFs of all the 18 subjects under review. The individual PSAIFs were fitted using the "tri-exponential" function and then corrected for metabolites after fitting the later using AUC scaling was done by tail-fitting the PBIF and the PSAIF using the last 30 minutes time points as this best reproduced the actual subject AUC. The reproducibility of VT using PBIF was assessed using Bland-Altman analysis, with PSAIF values as gold reference. For each structure, the % relative difference (Relative Diff), , between the parameters was estimated using: where and are the kinetic parameters generated by PBIF and PSAIF respectively.

F. Statistical Analysis
Data were analyzed using SPSS (IBM SPSS statistics for windows, version 26.0) and Real statistics (http://www.realstatistics.com/) software. Normality of distribution was tested using the Shapiro-Wilk test. The statistical difference between the three normalization techniques was evaluated using the one-way Analysis of Variance (ANOVA). The pairwise t-test was also performed as a follow-up test to ANOVA in order to reveal which specific pair of the normalization techniques are significantly different, and Bonferroni correction was applied to correct for the potential error due to multiple testing. In all cases, a P-value < 0.05 was considered to suggest statistical significance.

A. Test-Retest Repeatability and Reliability
The repeatability of the VT estimates for all selected brain regions of interest in the test-retest studies are shown in Figure 1, and results are displayed without and with GM Normalization. Without GM normalization, the VT estimates in the retest studies exhibited positive bias (ranging from 20 to 30%) compared to those deduced from the test studies ( Figure 1A), where all the differences lie above the zero line (systematic bias). This systematic bias between test and retest VT estimates was compensated for after normalization by the corresponding values of the GM resulting in a bias within ±5% for all brain regions ( Figure 1B). The LOA also reduced with GM normalization (from ~70% to ~20%).
Normalization by the GM also resulted in reducing both the % bias and CR between the test and retest kinetic parameters. The corresponding results with and without normalization by the GM are summarized in Figure 2 and Table 1. VT values exhibited a large reduction in the mean % bias between test and retest studies after normalization by the corresponding GM values (from ~30% to ~5%). The VT values also showed improved CR after GM normalization (from ~15% to ~5%) ( Figure 2B). Based on the advantage of normalizing the VT by the corresponding GM values to remove systematic bias and improve repeatability as outlined above, all the remaining analysis in this work has been reported with and without GM normalization. Table 1 shows the repeatability of the test-retest for the 5 healthy subjects as estimated by the Bland-Altman analysis (equations (1-5)). With GM normalization, VT exhibited reduced variability between the test and retest studies (95% LOA reduced from ±70% to ±20%) for all the brain regions.

B. Evaluation of the PBIF and the Normalization Criteria
The PBIF was generated using the PSAIF of all eighteen subjects included in this study. Figure 3 shows the overlaid normalized PSAIFs ( Figure 3A) and the resulting PBIF generated after normalizing each PSAIF by Weightsubject×AUC ( Figure 3B).

Figure 3 Overlaid normalized PSAIFs from all 18 patients (A) and the resulting PBIF generated by normalization
with Weightsubject×AUC (B). The zoomed PBIF over the first 5 minutes is also shown. In (b), the blue points are the mean PBIF while the red points are the standard error of the mean (SEM) Figure 4 shows the % difference and the LoAs between the VT estimates generated by the PSAIF and PBIF for selected brain regions. The comparison is made using PSAIF and the PBIF generated by the three normalization techniques.

Figure 4 The % relative difference in VT and the LoAs between PSAIF and PBIF of some specific structures as generated by the three normalization techniques: (A) without GM normalization, (B) with GM normalization
Without GM normalization, the mean % difference is -10% for Weightsubject×DoseInjected; +8% for AUC and +2% for Weightsubject×AUC; while the LoAs lie within ±45% for Weightsubject×DoseInjected; ±50% for AUC and ±35% for Weightsubject×AUC. The ANOVA analysis shows a significant difference between the results generated by the three normalization techniques for all brain structures except the brainstem (P-value = 0.095). Although for the same brainstem, the pairwise test shows a significant difference between Weightsubject×DoseInjected versus AUC (P-value = 0.034). However, with GM normalization, no statistically significant differences (P-value > 0.05) existed in the % difference among the three normalization techniques. The three normalization techniques, however, yielded slight differences for the LoAs measurements: (LoAs lie within ±12% for Weightsubject×DoseInjected; ±13% for AUC and ±10% for Weightsubject×AUC). In all cases, normalizing by Weightsubject×AUC yielded the smallest % bias and variability (% bias = ±2% and ±1.5%; LOA = ±38% and ±10% without and with GM normalization respectively) for all brain regions.
The mean bias (±SD) between the PSAIF and PBIF for the VT generated by normalization with Weightsubject×AUC are shown in Figure 5 and Table 2 (for all brain regions). LoA for all brain regions lies within ±38% and ±10% without and with GM normalization respectively.

DISCUSSION
Several studies have shown the feasibility to image neuroinflammation in multiple sclerosis (MS), Parkinson's disease (PD), and Alzheimer disease (AD) using [ 11 C]DPA-713 PET for quantifying differences between patients and controls (4,(9)(10)(11)(12). Accurate quantification of tracer uptake and metabolism in the tissue through kinetic modeling often requires blood sampling, (13) or some alternative approach such as simplified reference modeling (41,42), cluster analysis (41,43) or image-derived input function (IDIF) techniques. The apparent limitations of these approaches (15)(16)(17)19,21,44) are giving way to the exploration of the population-based input function (PBIF) approach as a more quantitatively reliable and less invasive alternative.
In this study, we have assessed the reproducibility of kinetic analysis of [ 11 C]DPA-713 dynamic PET images using PBIF, compared to PSAIF, in a cohort of subjects with Parkinson Disease. The repeatability of the VT estimate was also assessed in a cohort of healthy subjects that underwent a test-retest [ 11 C]DPA-713 dynamic PET within the same day. Kinetic analysis with PSAIF was determined to be reproducible with PBIF if the corresponding LoA are within those of the test-retest study.
The test-retest repeatability of the [ 11 C]DPA-713 uptake exhibited systematic increase in uptake values between test and retest (Figure 1). Although the cause of this bias is yet to be fully explored because most repeatability studies are done days or even weeks apart (34). Few recent studies that performed same day retest have reported the same systematic bias, and they suggested that the possible explanation to this systematic bias could be due to hormonemediated changes in TSPO expression, tonic changes due to scan-related stress/anxiety, or alteration in blood cholesterol due to food intake between the test and retest scans (45,46). While performing the test and retest studies under similar conditions on different days could eliminate this bias, other parameters such as alteration in TSPO density due to chronic disease as well as non-disease-related factors may be difficult to control (31). Owen et al. (28,29) demonstrated that the second generation TSPO tracers target two binding sites in humans, which leads to three affinity patterns: low-, high-, and mixed-affinity binders (LABs, HABs. and MABs, respectively). Past researches have shown that this variability in binding affinity has a major influence on the kinetic parameters where the values for HABs could be approximately twice that of MABs (29,30). For [ 11 C]-DPA-713 dynamic PET studies, Coughlin et al. (31) argued that those genotype-as well as other unknown physiological factors have varying degrees of influence on the global TSPO changes in the brain, thereby hindering accurate PET analysis, even among individuals with the same genotype. He therefore stated that the dependencies of the kinetic parameters can be compensated for by normalizing them with the corresponding GM parameters kinetic rate constants. This was confirmed in other TSPO studies (32)(33)(34), and adopted in here.
One potential approach to compensate for the bias between the test and retest studies is by normalization by the corresponding kinetic parameters of the GM as suggested by past studies (31,36) and also shown by this study.
Without GM normalization, the % relative difference between test and retest VT values lies significantly above the zero line for all structures, indicating that retest values are always higher than test values. But with GM normalization, the % relative difference is symmetric about the zero line. The mean % Diff and the LOA are also significantly reduced, thereby improving repeatability. The detailed results are presented in Figures 1 and 2 where the average percent biases over all brain regions were reduced from 30% to 5% after normalization. Normalization by the GM also resulted in improving the repeatability of kinetic analysis (the LOA changes from 70% to 20%; and the CR reduced from 15% to 5%).
Ye et al. (47) opined that the bias in kinetic parameter estimation in direct reconstruction with PBIF depends on the normalization and scaling technique used. In this study, we have assessed and compared three normalization approaches: (a) Weightsubject×DoseInjected, (b) AUC, and (c) Weightsubject×AUC. An example of the normalized PSIFs and the resulting PBIF are shown in Figure 3. The performance of these techniques was evaluated using the percent relative difference between the PSAIF-and PBIF-derived VT in selected brain regions ( Figure 4). Without GM normalization, there is a significant difference between the three normalization techniques for all brain structures except the brainstem, but with GM normalization, no statistically significant differences among those three techniques were observed.
Several normalization techniques have been reported in the literature which include: traditional scaling using blood samples by correlating the measured plasma activity at a given time-point with the AUC;(17) correlation of the PBIF with AIF at any time-point using venous samples (19); by accounting for injected dose and weight (20,21); noninvasive scaling using individual parameters like weight, body surface area (BSA), and lean body mass (LBM) (17).
In this study, we have assessed the three aforementioned normalization approaches. Subsequently, a subject IF was deduced by scaling the PBIF by his/her weight and injected dose. In the case of AUC normalization, that was measured after scaling the PBIF by the ratio of the average activity concentration of blood samples acquired over the last 30 minutes of the dynamic scan and that of the tail of the PBIF over the same time frames (this setting was used as this best predicted the original subject AUC; result not shown). Practically, venous blood samples may be used instead for scaling purpose assuming that arterial and venous blood reach equilibrium at about 30-45 minutes post-injection time (17). In this study, normalization by Weightsubject×AUC yielded the smallest % bias (±2%) and variability (LoAs ±38%) between PBIF and PSAIF. Furthermore, the LOA of the VT estimates (either without or with GM normalization) were within those of the repeatability study (determined from the test/retest) (Table 1), thus the corresponding PBIF can be an alternative for PSAIF for kinetic modeling of [ 11 C]DPA-713 dynamic PET images of the brain.
VT measured with PBIF showed good reproducibility (LOA of ±38% and ±10%) but with a positive bias (±2% and ±1.5%) without and with GM normalization respectively ( Figure 5 and Table 2). These were also in agreement with the findings of Lavisse et al. (19) As a final note, the reproducibility of the PBIF-based VT estimates compared with PSAIF-based VT fall well within the test-retest results, either with, or without GM normalization, hence showing the feasibility of [ 11 C]-DPA-713 PET kinetic modelling using PBIF.
A major limitation for this study is the relatively small sample size (n = 18), even though our findings are in agreement with previous results of smaller (n = 9) (19) and larger (n = 42) (20) sample sizes. The common thing is that these studies normalize the individual input functions to remove variabilities in the PBIF. This might suggest that the efficiency of the PBIF in accurately estimating the kinetic parameters depend less on the sample size used, but more on the normalization. This was also consolidated by Ye et al. (47) who opined that the bias in kinetic parameter estimation in direct reconstruction with PBIF was mostly due to inaccuracy in normalization and scaling.

CONCLUSION
This study demonstrated the feasibility of [ 11 C]-DPA-713 PET kinetic modelling using PBIF, thus potentially alleviating the need for arterial blood sampling. Moreover, it was shown that the optimal result in terms of kinetic parameter accuracy was obtained when the PSAIFs were normalized with Weightsubject×AUC. Finally, VT showed more reproducibility after normalizing the targeted kinetic parameter to those estimated in gray matter. However, this does not in any way affect the feasibility of using PBIF as an alternative to PSAIF for [ 11 C]-DPA-713 PET kinetic analysis as reflected in this study.

COMPLIANCE WITH ETHICAL STANDARDS
Funding: This study was funded by the National Center for Advancing Translational Sciences of the National Institutes of Health under Award Numbers UL1TR000457 and RO1 NS104283.