Comparison between kinetic modelling and graphical analysis for the quantification of [^{18}F]fluoromethylcholine uptake in mice
 Dominique Slaets^{1}Email author and
 Filip De Vos^{1}
DOI: 10.1186/2191219X366
© Slaets and De Vos; licensee Springer. 2013
Received: 29 May 2013
Accepted: 8 September 2013
Published: 14 September 2013
Abstract
Background
Until now, no kinetic model was described for the oncologic tracer [^{18}F]fluoromethylcholine ([^{18}F]FCho), so it was aimed to validate a proper model, which is easy to implement and allows tracer quantification in tissues.
Methods
Based on the metabolic profile, two types of compartmental models were evaluated. One is a 3C2i model, which contains three tissue compartments and two input functions and corrects for possible [^{18}F]fluorobetaine ([^{18}F]FBet) uptake by the tissues. On the other hand, a twotissuecompartment model (2C1i) was evaluated. Moreover, a comparison, based on intraobserver variability, was made between kinetic modelling and graphical analysis.
Results
Determination of the [^{18}F]FChoto[^{18}F]FBet uptake ratios in tissues and evaluation of the fitting of both kinetic models indicated that corrections for [^{18}F]FBet uptake are not mandatory. In addition, [^{18}F]FCho uptake is well described by the 2C1i model and by graphical analysis by means of the Patlak plot.
Conclusions
The Patlak plot is a reliable, precise, and robust method to quantify [^{18}F]FCho uptake independent of scan time or plasma clearance. In addition, it is easily implemented, even under nonequilibrium conditions and without creating additional errors.
Keywords
PET [^{18}F]Fluoromethylcholine Kinetic modelling Patlak plot Graphical analysis Metabolic trappingBackground
[^{18}F]Fluoromethylcholine ([^{18}F]FCho) and [^{11}C]choline ([^{11}C]Cho) are radiolabelled biomarkers to study the altered phospholipid metabolism in tumours. Several ongoing clinical trials evaluate their use as diagnostic [1] or as therapy response assessment [2, 3] tools. The latter requires quantification of the tracer uptake. Thus far, this is executed in a semiquantitative way using standardized uptake values (SUV) [4], the percent of injected dose per gram of tissue (%ID/g) [3], or by comparing tumourtomuscle ratios [5]. SUV have an advantage in that they are straightforward to estimate, but when applied in a clinical setting, care should be given about standardization [6]. On the other hand, absolute quantification of tracer uptake, by means of kinetic modelling, is more complex since it requires dynamic scanning and arterial sampling. Nevertheless, this technique is more reliable and independent of scan time or plasma clearance, allowing a more accurate quantification of the tracer uptake [7].
Methods
Athymic Swiss Nu/Nu mice (female, 20 g) were obtained from Charles River Laboratories International (Janvier, France). Sulphuric acid, urea, dimethylaminoethanol, chloroform, and methanol were purchased from SigmaAldrich (Steinheim, Germany). Physiological saline was obtained from B.Braun Medical Ltd. (Sheffield, UK). Isoflurane and heparin were obtained from Medini N.V. (Oostkamp, Belgium).
Radiochemistry
[^{18}F]FCho was prepared by nucleophilic substitution of dimethylaminoethanol to [^{18}F]fluoromethylbromide as described by Slaets et al. [8].
Positron emission tomography
All animal experiments were approved by the local ethics committee (ECD 11/30). Mice (n = 6) were harvested 8 h prior to the study and anaesthetized with isoflurane (1.5% + 1.5 L/min O_{2}) during cannulation, animal handling, and acquisition time. Prior to positioning on the heated scanner bed, the mice were venously and arterially cannulated for tracer injection and arterial blood sampling, respectively. Positron emission tomography (PET) was performed using a Flex Triumph II μPet scan (Gamma Medica, Sherbrooke, Quebec, Canada) with a 7.5cm axial field of view and a 1.2mm spatial resolution. After the synchronized start of the arterial blood sampling and the start of the μPET acquisition, the tracer was intravenously injected (±11.1 MBq in 150 μL saline) over a constant infusion interval of 5 s. List mode data were acquired for 40 min.
Arterial input function determination
Blood concentration
In Equation 1, g(t) depicts the original blood curve, $\frac{\mathit{\text{dg}}}{\mathit{\text{dt}}}$ describes the first derivative of the original blood curve, τ _{disp} is a constant calculated as described by [9], and C _{bl} represents the for dispersioncorrected blood curve.
Plasma concentration and metabolites
In Equation 2, the ratio of the plasma to blood concentration is calculated for several time points (vide supra). The plasma concentration (C _{pl}) was determined by dividing the counts in the plasma (CPS_{pl}) to the standardized volume of plasma in blood (%pl, which is expressed as 0.6). In analogy, the tracer blood concentration (C _{bl}) was calculated by taking the ratio of the sum of the counts in the plasma and hematocrit pellet (represented by CPS_{bl}) to the blood volume, which is expressed as 1.
The obtained ratios and metabolite percentages were fitted to a singlephase exponential curve. The goodness of the fit and the equation were calculated using GraphPad Prism 5.00 for Windows (San Diego, CA, USA; http://www.graphpad.com).
Image reconstruction and corrections
Dynamic images were reconstructed using the MLEM 2D algorithm with ten iterations to the following time frames: 12 s × 5 s, 6 s × 10 s, 6 s × 20 s, 6 s × 60 s, 4 s × 120 s, 3 s × 300 s, and 1 s × 360 s. Quantification of the PET scan was performed relative to a ^{22}Na source placed on the base of the scanning bed.
Regional timeactivity curve computation
The last time frame was used to draw a region of interest on two to three adjacent slices on a part of the tissue of interest, namely the brain, kidney, lung, liver, and muscle. The ROIs were then placed over the complete series of time frames to derive tissue timeactivity curves.
Kinetic modelling
The exploit of kinetic modelling to [^{18}F]FCho is based on the following general assumptions [11, 12]:
There is a single source for [^{18}F]FCho, i.e. the plasma. The concentration varies with time, and transfer from the plasma to the first tissue compartment is reversible.
The capillary concentration of [^{18}F]FCho is assumed to be equal to the arterial plasma concentration, so no gradient could be observed across the capillary membranes.
Since tracer amounts were injected (high specific activity), the test solute did not alter the system and firstorder kinetics could be assumed.
[^{18}F]FCho is homogeneously distributed in the tissues.
Metabolism of choline is under steady state, so the concentration of phosphocholine stays constant during imaging.
In addition to the previous assumptions, [^{18}F]FCho is metabolized to (1) [^{18}F]fluorophosphocholine which is suspected to be metabolically trapped and (2) [^{18}F]FBet, an osmolyte, which is able to cross the cell membranes.
Kinetic analysis was performed using a 3C2i as described by Fujita et al. [13] and was weighed against a 2C1i (Figure 1). The models are described by following the microparameters: K _{1}, k _{2}, k _{3}, and k _{4} for the 2C1i model; and the additional parameter K _{1p}/K _{1m} which represents the ratio of [^{18}F]FCho to [^{18}F]FBet uptake in tissues in the 3C2i model. Transfer coefficients K _{1} and k _{2} describe the uptake and washout of the free tracer and its metabolite ([^{18}F]FBet) across cell membranes. Rate constant k _{3} is regarded as the conversion of [^{18}F]FCho into [^{18}F]FPCho, which is assumed to be metabolically trapped in the cell. Microparameter k _{4} represents dephosphorylation and is expected to be very small. The 3C2i model differentiates between [^{18}F]FCho and [^{18}F]FBet uptake or washout by rate constants K _{1p} and K _{1m}, or k _{2p} and k _{2m}, respectively. During the fitting process using the 3C2i model, six parameters were identified. The vascular volume parameter, present in both models, was not accounted for due to the fast clearance of [^{18}F]FCho. Parameters of interest were the ratio of [^{18}F]FCho to [^{18}F]FBet uptake in tissues, represented by K _{1p}/K _{1m} for the 3C2i model, and the [^{18}F]FCho influx across the membranes (K _{i}) calculated as K _{1}*k _{3}/(k _{2} + k _{3}) [14–16] for both models.
Before the selected kinetic models were fitted, the tracer plasma curves were fitted using a threeexponential decay function [17]. Then, model fitting was conducted and optimized by (1) visual inspection of the agreement of timeactivity curve (TAC) and the model output, (2) evaluation of the percent coefficient of variation of the microparameters, and (3) the goodness of fit displayed by the Akaike information criterion (AIC), Schwartz criterion (SC), and model selection criterion (MSC) as determined by the PMOD software (PMOD version 3.0; PMOD group, Zurich, Switzerland). When the fitting was poor, fits were redone by adjusting the initial parameters. Parameter estimation, in kinetic modelling, was performed using the MarquardtLevenberg algorithm, which uses a nonlinear least squares optimization process, included in the PMOD software.
Graphical analysis
Since absolute quantification of [^{11}C]Cho was already established by means of the Patlak plot [12, 17], this graphical analysis was also applied for [^{18}F]FCho. The macroparameter of interest, i.e. the slope, which resembles [^{18}F]FCho influx into the cells, was determined under nonequilibrium and equilibrium conditions. The latter is usually achieved when the graphical plot describing normalized tissue concentration as a function of the normalized time becomes linear [11, 12]. It is worth noting that the Patlak slope corresponds to the macroparameter of interest K _{i}, defined previously during the kinetic modelling process.
Intraobserver variability of macroparameters
A test was performed to evaluate the robustness of the macroparameter estimation of the [^{18}F]FCho influx (i.e. K _{i}) (vide supra) using these three models, i.e. 3C2i, 2C1i, and the Patlak plot. The percent error is calculated as (Cho influx test − Cho influx retest/(mean test and retest).
Statistical analysis
Statistical analysis was performed using Graphpad Prism 5.00. A D'AgostinoPearson test was conducted to test for normality distribution of the data. Since samples were too little, nonparametric statistical tests were used. A BlandAltman plot was determined to evaluate the percent error during the intraobserver variability test. A KruskalWallis test was performed to evaluate statistical differences between (1) the AIC, SC, and MSC fitting factors of the different models evaluated and (2) the determined [^{18}F]FCho influxes across the cell membrane by comparing the macroparameter K _{i}. A Wilcoxon signedrank test was applied to evaluate if the median ratio K _{1p}/K _{1m}, which represents the ratio of [^{18}F]FCho to [^{18}F]FBet uptake in tissues in the 3C2i model, was statistically different from 1. A Spearman correlation test was performed to evaluate the influence of equilibrium conditions on the model's Patlak slope. Differences were regarded as statistically significant for p < 0.05.
Results
Arterial input function determination
Since kinetic modelling requires an arterial plasma input function of the unmetabolized tracer, corrections are forced on the blood curve which was obtained by the microvolumetric blood counter. The corrections applied were dispersion correction, conversion of the blood curve into a plasma curve, and corrections for metabolites.
Dispersion
Plasma concentration
The plasma concentration was achieved by multiplying the obtained ratios for each time point by the dispersioncorrected blood curve as determined previously.
Corrections for metabolites and parent compound
Percentage of lipophilic and hydrophilic [^{18}F]FCho metabolites present in arterial plasma
Time p.i. (min)  Hydrophilic metabolites (%)  Lipophilic metabolites (%) 

2.5  99.60 ± 0.13  0.40 ± 0.13 
10  98.64 ± 0.05  1.36 ± 0.50 
20  99.31 ± 0.07  0.69 ± 0.07 
40  97.09 ± 1.21  2.91 ± 1.21 
The corresponding percentages per time point obtained from Equations 4 and 5 were multiplied by the plasma curves (vide supra) to obtain the input functions for the selected compartmental models, i.e. the 2C1i and 3C2i models. The [^{18}F]FCho plasma concentration was the only input function in the 2C1i model, whereas the [^{18}F]FCho plasma concentration and the [^{18}F]FBet plasma concentrations were both used in the 3C2i model.
Kinetic modelling
Fitting factors per tissue (AIC, SC, and MSC) for 3C2i and 2C1i models
AIC  SC  MSC  

3C2i  2C1i  3C2i  2C1i  3C2i  2C1i  
Brain  90.54 ± 31.56  91.44 ± 21.48  98.72 ± 31.63  97.00 ± 21.68  1.36 ± 0.52  1.341 ± 0.425 
Kidney  24.63 ± 34.18  19.40 ± 30.54  32.81 ± 34.23  25.19 ± 30.58  3.188 ± 0.634  3.292 ± 0.554 
Liver  51.97 ± 50.19  61.03 ± 41.54  60.13 ± 50.16  66.68 ± 41.43  2.708 ± 1.308  2.544 ± 1.099 
Lung  44.92 ± 24.72  47.79 ± 19.50  53.11 ± 24.75  49.06 ± 27.39  2.669 ± 0.616  2.600 ± 0.490 
Muscle  92.96 ± 15.28  90.34 ± 15.73  100.5 ± 15.85  95.90 ± 15.93  1.489 ± 0.431  1.549 ± 0.333 
Graphical analysis
Equilibrium conditions of the tracer were determined and were usually achieved between 1 and 23 min after injection. Then, linear regression was applied to the data with a good fit (Chi square, 0.0054505 ± 0.0049021) allowing estimation of the slope, which resembles the [^{18}F]FCho influx into the cell. When comparing the Cho influxes K _{i} calculated for the 2C1i and 3C2i model with the slope of the Patlak plot, a good agreement was achieved and no statistical differences were observed (KruskalWallis test, p = 0.8270) (Figure 4).
Intraobserver variability of macroparameters
Discussion
Kinetic modelling requires arterial sampling which can be obtained by taking continuous or discrete blood samples. The latter is laborious, requires more animals due to the limited blood volume, and is characterized by complicated sampling intervals within a specific time window. Therefore, we chose to use the validated microvolumetric blood counter [9] to obtain continuous arterial blood samples by cannulation of the carotid artery by a precision operation and a syringe pump. The obtained blood curve was first smoothed in order to derive the first derivative, and then the dispersion constant was applied for dispersion correction, which occurred in the tubing during blood sampling.
Since only unbound tracer in plasma undergoes tissue uptake, a ratio of the plasma to blood concentration (C _{pl}/C _{bl}) was determined to convert the blood curve into a plasma curve. Therefore, standard hematocrit ranges [18] were used since the exact hematocrit and plasma volumes could not be determined after the addition of urea and sulphuric acid. Then, the discrete ratios were plotted and obtained a good fit using a oneexponential curve. It was preferred to use the equation obtained for bloodtoplasma corrections rather than a constant value, which would consequently underestimate plasma concentrations at early time points with perturbation of tracer uptake or unidirectional influx rate value (i.e. K_{1}) as a result. In addition, the distribution of the plasmatoblood concentration ratio indicates that [^{18}F]FCho, as [^{11}C]Cho [19], is accumulated into the red blood cells.
Comparing the blood metabolism of [^{18}F]FCho to [^{11}C]Cho [19], the following accordances were observed: (1) plasma extraction with chloroform proved that the amount of lipophilic [^{18}F]FCho metabolites in the plasma (<5%, Table 1) is negligible, and (2) [^{18}F]FBet was the only metabolite present in the plasma and it appeared almost immediately. Indeed, at 5 and 25 min post injection, 67.47% and 33.43% [^{18}F]FCho could be detected, which correspond respectively to 62% and 18% [^{11}C]Cho in the plasma [19] and to the metabolism pattern as described by Bansal et al. [10]. Therefore, we can conclude that fitting the percentage of the parent compound in the plasma to a oneexponential curve [20] provides a good fit (R^{2} = 0.9435). When using a threeexponential function as described by Roivainen et al. [19], fittings were not altered nor improved. Therefore, the oneexponential function was applied for metabolite corrections.
In general, kinetic models are developed as comprehensible models, which accurately describe the metabolic process or receptor binding, but are usually simplified to yield workable models that are able to quantify a parameter of interest. In oncology, this parameter is usually a specific enzyme or transporter, which can be described by a microparameter of the selected model. However, in a number of cases, the metabolic rate, which is a combination of microparameters, is determined, for example, glucose metabolic rate by [^{18}F]FDG [21] or cell proliferation rate by [^{18}F]FLT [15]. When evaluating the 3C2i model, the [^{18}F]FCho influx across the cell membranes was calculated with corrections for (possible) [^{18}F]FBet uptake, and the ratio of [^{18}F]FCho to [^{18}F]FBet uptake in tissues (K _{1p}/K _{1m}) was determined. The latter designates the magnitude of [^{18}F]FBet uptake in the tissues and indirectly shows if additional corrections for [^{18}F]Bet uptake should be implemented. These experiments showed that despite the explicit metabolic pattern, [^{18}F]FBet uptake in the tissues is still limited, and so adjustments for its uptake should not be accounted for during kinetic modelling. Indeed, the [^{18}F]FCho influx determined by the 3C2i model (which corrects for [^{18}F]FBet uptake) and the sum of the [^{18}F]FCho and [^{18}F]FBet influx as determined by the 2C1i model were regarded as not statistically different (Figure 4). Furthermore, when comparing goodnessoffit factors (i.e. AIC, SC, and MSC), no statistical enhancement (or superior fitting) could be detected by one of the models (i.e. 2C1i and 3C2i). It is worth noting that reducing the number of compartments, or in this case the input functions, consequently decreased the %COV of the microparameter estimates, resulting in reduced uncertainties. This was also observed in the intraobserver variability test. Therefore, we can conclude that the 2C1i is a workable kinetic model to estimate the [^{18}F]FCho influx without creating additional errors.
Since [^{18}F]FCho is a tracer which is assumed to be metabolically trapped in cells, including tumour cells [22], graphical analysis was applied to quantify the [^{18}F]FCho influx across cell membranes. We evaluated if selection of the equilibrium time frame had an influence on the slope of the Patlak model, which is a measure of the [^{18}F]FCho influx constant (i.e. K_{i}). The Spearman correlation plot showed a good agreement for all tissues, except for kidney tissue. This might be due to the fact that the kidneys are responsible for tracer elimination, which affects the tracer accumulation and therefore might influence the fitting of the model. Since other tissues provided good correlations, we might conclude that nonequilibrium conditions do not influence the linear fitting for this radiotracer. These findings corroborate the Spearman correlation test which demonstrates the insensitivity of the [^{18}F]FCho influx constant (i.e. K_{i}) toward the selection of the linear portion. The fitting can thus be performed without selection of the equilibrium conditions which considerably simplifies the modelling process. Hence, graphical analysis, by means of the Patlak plot, is a very suitable way to estimate [^{18}F]FCho influx across the cell membranes, except for kidney tissues. It is worth noting that the influx constant depends on imaging time, the type of tissue, and the type of tracer used, so preceding validation studies should be performed prior to implementation of the nonequilibrium data to the fitting process.
When comparing the [^{18}F]FCho influx calculated by the 2C1i model (K_{i}) with the Patlak slope, no statistical differences were observed (KruskalWallis test), indicating a good agreement between both methods. On the other hand, the intraobserver variability test (Figure 5) favours the Patlak model, seeing that this analysis obtained the smallest percent error. The latter corresponds to the highest robust method for absolute quantification.
Conclusions
Despite the early presence of the metabolite [^{18}F]FBet in the blood, no explicit metabolite uptake was observed in the tissues. Consequently, modelling of the [^{18}F]FBet uptake should not be performed during quantification of [^{18}F]FCho uptake in tissues. [^{18}F]FCho uptake is well described by the 2C1i and the Patlak model. Our preference goes to the latter since it is a reliable, precise, and robust method independent of scan time or plasma clearance. In addition, the Patlak plot could easily be implemented, even under nonequilibrium conditions and without creating additional errors, for the quantification of [^{18}F]FCho uptake as, for example, in a therapy response assessment.
Abbreviations
 [18F]FCho:

[^{18}F]fluoromethylcholine
 [18F]FBet:

[^{18}F]fluorobetaine
 AIC:

Akaike information criterion
 MSC:

Model selection criterion
 SC:

Schwartz criterion
 SUV:

Standardized uptake values.
Declarations
Acknowledgments
The authors wish to thank the Infinity small animal imaging lab and Prof. C. Vanhove for the registration and reconstruction of the μPET scans.
Authors’ Affiliations
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