Modeling pulmonary kinetics of 2-deoxy-2-[18F]fluoro-D-glucose during acute lung injury

Abstract

Rationale and objectives

Dynamic positron-emission tomography (PET) imaging of the radiotracer 2-deoxy-2-[18F]fluoro-D-glucose (¹⁸F-FDG) is increasingly used to assess metabolic activity of lung inflammatory cells. To analyze the kinetics of ¹⁸F-FDG in brain and tumor tissues the ‘Sokoloff’ model has been typically used. In the lungs, however, a high blood-to-parenchymal volume ratio and ¹⁸F-FDG distribution in edematous injured tissue could require a modified model to properly describe ¹⁸F-FDG kinetics.

Material and Methods

We developed and validated a new model of lung ¹⁸F-FDG kinetics that includes an extravascular/non-cellular compartment in addition to blood and ¹⁸F-FDG precursor pools for phosphorylation. Parameters obtained from this model were compared with those obtained using the Sokoloff model. We analyzed dynamic PET data from 15 sheep with smoke or ventilator-induced lung injury.

Results

In the majority of injured lungs, the new model provided better fit to the data than the Sokoloff model. Rate of pulmonary ¹⁸F-FDG net uptake and distribution volume in the precursor pool for phosphorylation correlated between the two models (R² = 0.98, 0.78), but were overestimated with the Sokoloff model by 17% (p < 0.05) and 16% (p < 0.0005) as compared to the new one. The range of the extravascular/non-cellular ¹⁸F-FDG distribution volumes was up to 13% and 49% of lung tissue volume in smoke and ventilator-induced lung injury, respectively.

Conclusion

The lung-specific model predicted ¹⁸F-FDG kinetics during acute lung injury more accurately than the Sokoloff model and may provide new insights in the pathophysiology of lung injury.

Introduction

In basic science and clinical investigation of lung pathology, there is a growing interest in new pulmonary imaging techniques (1–3). Recently, PET imaging of the glucose analog 2-deoxy-2-[¹⁸F]fluoro-D-glucose (¹⁸F-FDG), a standard tool in oncology, is increasingly used to assess metabolic activity of pulmonary inflammatory cells (4–11). Such measurement is based on the fact that ¹⁸F-FDG is phosphorylated and trapped in activated pulmonary neutrophils in proportion to the cells’ glucose uptake, which is much higher than that of lung parenchyma. There is, however, no consensus about a standard method to quantitatively analyze ¹⁸F-FDG kinetics in the inflamed lung. Some investigators (4,6,8,12) calculated a lung net uptake rate of ¹⁸F-FDG (K_i) using the Patlak method (13,14) and normalized K_i by the initial tracer distribution volume (8,12) or by the tissue fraction (4,6) to account for regional differences in lung density. Other investigators (10) considered tracer kinetic modeling with Sokoloff’s three-compartment model (15) as the gold standard for analyzing lung ¹⁸F-FDG kinetics. Compared to the Patlak method, compartmental modeling has the advantage that it provides rate constants for tracer transfer among the model compartments, quantifying individual steps in the glucose metabolic pathway. However, the Sokoloff model was developed and validated for ¹⁸F-FDG kinetics in solid tissues such as brain, tumors, and myocardium (16–18). An assumption of this model is that all extravascular ¹⁸F-FDG in the region of interest is the precursor pool for hexokinase-catalyzed phosphorylation to ¹⁸F-FDG-6-phosphate (¹⁸F-FDG-6-P). This assumption, however, could be inaccurate for acutely injured lungs where large pools of edematous tissue may be functionally far away from neutrophils that trap ¹⁸F-FDG. In these conditions, it could be necessary to model pulmonary tracer kinetics by a compartment model specifically designed to reflect lung ¹⁸F-FDG kinetics during acute lung injury (ALI). Also, previous investigators (10) have used iterative nonlinear curve fitting to determine the individual rate constants of the Sokoloff model. This technique entails initialization of the parameter vector (19), which may lead to incorrect solutions when the initial guess is not appropriate (20). This may be problematic for modeling pulmonary ¹⁸F-FDG, since little is known about typical values of the model parameters.

In this paper, we formulate a model of lung ¹⁸F-FDG kinetics that includes an extravascular/non-cellular compartment in addition to blood and parenchyma, representing a pool of ¹⁸F-FDG that is not a direct precursor for phosphorylation. We analyze previously obtained experimental PET imaging data from sheep with smoke inhalation (6) or ventilator-induced ALI (4) and compare the Sokoloff model against the new lung-specific model in their ability to characterize the pulmonary ¹⁸F-FDG kinetics. Also, we utilize a generalized linear least squares (GLSQ) method (21) to identify the models’ parameters instead of the iterative non-linear curve fitting typically used for this purpose.

Methods

Model of lung ¹⁸F-FDG kinetics during acute lung injury: two equilibrating compartment (TEC) model

Lung ¹⁸F-FDG kinetics is modeled with the time-activity curve in pulmonary arterial plasma as input function (C_p(t)) and the lung tissue time-activity curve obtained from dynamic PET imaging as output function. The tracer activity in a lung region of interest (ROI) is considered as the sum of tracer activity in four functional compartments (Fig. 1A): 1) A blood compartment accounting for the amount of ¹⁸F-FDG that is confined to the pulmonary vessels (C_p(t)F_B), where F_B is the fractional volume of pulmonary blood; 2) an extravascular compartment representing the concentration of ¹⁸F-FDG in the ROI that constitutes the precursor pool for phosphorylation to ¹⁸F-FDG-6-P (C_e(t)); 3) an extravascular/non-cellular compartment, which accounts for the concentration of ¹⁸F-FDG in the ROI that is not an immediate precursor for phosphorylation (C_ee(t)); and 4) a metabolite compartment accounting for the ROI concentration of ¹⁸F-FDG-6-P (C_m(t)). The activity concentration in the region of interest (C_ROI(t)) is given as

$$C_{\text{ROI}}(t)=F_{\mathrm{B}}{C}_{\mathrm{p}}(t)+C_{\mathrm{e}}(t)+C_{\mathrm{e}\mathrm{e}}(t)+C_{\mathrm{m}}(t)$$ (1)

Figure 1.

Compartment model diagrams. A: Lung-specific model for ¹⁸F-FDG kinetics during acute lung injury, including two equilibrating compartments (TEC model). C_p(t) = blood plasma concentration of ¹⁸F-FDG; C_e(t) = concentration of ¹⁸F-FDG in the region of interest (ROI) that constitutes the precursor pool for hexokinase-catalyzed phosphorylation; C_ee(t) = ROI concentration of ¹⁸F-FDG in extravascular/non-cellular compartment; C_m(t) = ROI concentration of phosphorylated ¹⁸F-FDG. Rate constants k₁ and k₂ account for forward and backward transport of ¹⁸F-FDG between blood and tissue; k₃ = rate of ¹⁸F-FDG phosphorylation; k₅ and k₆ = forward and backward rate constants of tracer transfer between substrate and non-substrate compartments. B: Sokoloff model for ¹⁸F-FDG tissue kinetics.

According to Figure 1A, facilitated ¹⁸F-FDG transport from blood into the tissue, per unit of lung volume, is quantified by the rate constant k₁ (see Appendix). The rate constant k₂ quantifies tracer transport from tissue back into the blood, and k₃ is the rate of ¹⁸F-FDG phosphorylation to ¹⁸F-FDG-P, which is proportional to hexokinase activity. Dephosphorylation of ¹⁸F-FDG-P was assumed to be negligible for the duration of the imaging (75 min). As derived in the Appendix, the rate constants k₅ and k₆ describe the changes in ROI activity concentration due to forward and backward ¹⁸F-FDG transfer between the precursor compartment and the extravascular/non-cellular compartment.

To directly estimate the model parameters we used GLSQ, a least squares, integral-based method that does not require initial parameter values, and can produce unbiased estimates (21,22). This method requires a linear differential equation describing the system’s input-output dynamics according to (see Appendix)

$$\begin{array}{cc}{\stackrel{•••}{C}}_{\text{ROI}}(t)=\hfill & a_1{\stackrel{••}{C}}_{\text{ROI}}(t)+a_2{\stackrel{•}{C}}_{\text{ROI}}(t)+a_3{\stackrel{•••}{C}}_{\mathrm{p}}(t)+\hfill \\ \hfill & a_4{\stackrel{••}{C}}_{\mathrm{p}}(t)+a_5{\stackrel{•}{C}}_{\mathrm{p}}(t)+a_6{C}_{\mathrm{p}}(t)\hfill \end{array}$$ (2)

with the coefficients a₁ = − (k₂ + k₃ + k₅ + k₆), a₂ = − k₆(k₂ + k₃), a₃ = F_B, a₄ = (k₂ + k₃ + k₅ + k₆)F_B + k₁, a₅ = k₁(k₃ + k₅ + k₆) + F_Bk₆(k₂ + k₃), and a₆ = k₁k₃k₆. Once these coefficients were identified by GLSQ, the parameters of the lung-specific model were computed according to: $F_{\mathrm{B}}=a_3,k_1=a_4+a_1{a}_3,k_2=-\frac{a_5+a_2{a}_3}{a_4+a_1{a}_3}-a_1,k_3=-\frac{k_2{a}_6}{a_6+k_1{a}_2},k_6=-\frac{a_6+k_1{a}_2}{k_1{k}_2}$, and k₅ = − (k₂ + k₃ + k₆ + a₁). Under the assumption of steady state conditions, the ¹⁸F-FDG distribution volume of the precursor compartment as a fraction of lung volume (F_e), can be derived as

$$F_{\mathrm{e}}=\frac{k_1}{k_2+k_3}$$ (3)

which is effectively the same equation as the one used to derive F_e from the rate constants of the Sokoloff model (14). The corresponding fractional ¹⁸F-FDG distribution volume of the extravascular/non-cellular compartment (F_ee) is given by

$$F_{\text{ee}}=\frac{k_5}{k_6}\frac{k_1}{k_2+k_3}$$ (4)

The net uptake rate K_i was derived from the estimates of the individual rate constants as

$$K_{\mathrm{i}}=F_{\mathrm{e}}{k}_3=\frac{k_1{k}_3}{k_2+k_3}$$ (5)

where right side is identical to the corresponding equation used for the Sokoloff model (14).

Sokoloff model

For comparison against the two equilibrating compartment (TEC) model, the Sokoloff model of ¹⁸F-FDG kinetics was used (Fig. 1B), which encompasses a blood and two tissue compartments and has been previously used to model lung ¹⁸F-FDG kinetics (10). The parameters k₁, k₂, k₃, and F_B of the Sokoloff model are the forward rate constant between blood and tissue, the rate constant for tracer transfer from the tissue into the blood, the rate constant representing trapping of ¹⁸F-FDG intracellularly after phosphorylation by hexokinase, and the fractional volume of blood. For GLSQ parameter estimation, the linear differential equation of the Sokoloff model can be derived from Eq. (2) with k₅ = k₆ = 0. The net uptake rate, K_i, and the fractional distribution volume of the precursor compartment, F_e, were calculated according to Eqn. (3) and Eqn. (5).

Model selection

To determine the model that best describes ¹⁸F-FDG kinetics the Sokoloff and TEC models were applied to each lung, and the respective results were compared in terms of 1) the value of estimated parameters and 2) the residuals of the curve fit (Fig. 2) as follows. First, the TEC model was rejected if k₆≤0 or k₅≤0, and the lung’s tracer kinetics was classified as Sokoloff-type. Second, we determined the model that fitted the imaging data with the fewest possible number of parameters, i.e. the most parsimonious model, by computing Akaike’s information criterion (AIC) from the residuals of the curve fits (e(t)) according to (19)

$$\text{AIC}=N\ln \left({\displaystyle \sum _{i=1}^N{e}^2(t_i)}\right)+2n$$ (6)

where N was the number of PET image frames, and 2n a penalty factor accounting for the number of model parameters, n (i.e. n = 4 for the Sokoloff model, and n = 6 for the TEC model). The model with the smallest AIC was considered best to fit the data (19).

Figure 2.

Strategy of model selection for ¹⁸F-FDG analysis of a particular lung. The TEC model of ¹⁸F-FDG kinetics was used when estimates of k₅ and k₆ were physiologically plausible (k₅ and k₆ > 0), and if Akaike’s information criterion (AIC) computed from the curve fits was smaller with the TEC (AIC_TEC) than with the Sokoloff model (AIC_Sok).

Depending on which model was best to describe the time-activity data of a particular lung, K_i and F_e were computed from the rate constants of either the Sokoloff model (for Sokoloff-type tracer kinetics) or the TEC model (for TEC-type tracer kinetics). F_ee was set to zero for tracer kinetics classified as Sokoloff-type (Fig. 2).

Experimental data

We re-analyzed ¹⁸F-FDG PET imaging and pulmonary arterial blood sampling data from previous studies on lung inflammation in sheep (4,6). These studies included 5 sheep exposed to unilateral cigarette smoke inhalation (smoke group) (6) and 10 sheep exposed to unilateral injurious ventilation (4), 6 of which with negative end-expiratory pressure of −10 cm H₂O (NEEP group), and 4 of which with positive end-expiratory pressure of 10 cm H₂O (PEEP group). In each study, the lungs were separated with a double lumen tube, and the left lung was exposed to the injurious insult, while the right lung was ventilated with a protective pattern. Detailed information about animal preparation and experimental procedures were described previously (4,6).

PET imaging of ¹⁸F-FDG started two hours after smoke exposure and one hour after the end of injurious ventilation. The sheep was positioned prone in the PET camera (Scanditronix PC4096, General Electric, Milwaukee, WI, USA) with the most caudal slice adjacent to the diaphragm dome to maximize imaged lung volume (23). The camera collected 15 transverse cross sectional slices of 6.5 mm thickness over a 9.7 cm long axial field. A transmission scan was obtained to correct for tissue attenuation of the emitted photons and to define regions of interest corresponding to lung fields. 370 MBq of ¹⁸F-FDG were injected at a constant rate over one minute. The acquisition protocol for ¹⁸F-FDG consisted of 32 consecutive images for a total of 75 minutes (6×30s, 7×1min, 15×2min, 1×5min, and 3×10min). PET images were reconstructed in an interpolated matrix of 128 × 128 × 15 voxels, each with a size of 2 × 2 × 6.5 mm. The effective in-plane resolution of the PET device was approximately 7 mm full width at half maximum for a point source.

Volumetric masks of the imaged lung field were generated with an interactive software tool that allowed combining data from different PET scans, as described previously (6). In brief, masks generated by thresholding voxels of aerated lung (gas fraction > 0.28 ml gas/ml lung) derived from a transmission scan, were combined with masks generated by thresholding voxels of perfused lung, assessed by the nitrogen-13 bolus injection technique (6). In this way, not only aerated regions but also collapsed, or flooded and perfused regions were included in the analysis. One mask was defined covering the exposed lung and another covering the protected lung, with pulmonary vessels and airways larger than second generation were excluded manually. Thus, two volumetric regions of interest were defined per animal, each involving the entirety of the imaged right or left lungs.

¹⁸F-FDG activity in blood plasma as a function of time C_p(t) was assessed from a blood pool region of interest in the PET images using two calibration samples of pulmonary arterial blood, as described previously (5).

Statistics

For statistical analysis, parameter estimates were classified according to 1) type of exposure (smoke, NEEP, or PEEP) and 2) whether or not the lung was exposed to an injurious insult, and were analyzed with a two-way ANOVA test. The level of significance was p< 0.05 for single comparisons, and p < 0.05/n for multiple (n) comparisons The coefficient of determination (R²) was computed to quantify the linear correlation of parameter estimates obtained with the Sokoloff model and those obtained with the TEC model.

Results

The number of lungs for which the TEC model best described the time-activity data is summarized in Table 1. In lungs where tracer kinetics was classified as Sokoloff-type, estimates of k₅ and k₆ were not significantly greater than zero (Table 2). For positive k₆, AIC obtained with the TEC model (AIC_TEC) tended to be smaller than that obtained with the Sokoloff model (AIC_Sok), and the AIC difference between the two models (AIC_Sok – AIC_TEC) correlated with k₆ (Fig. 3). For negative values of k₆, the AIC of the TEC model tended to be larger than that of the Sokoloff model, classifying these tracer kinetics’ as “Sokoloff-type”. In one exposed lung initially classified as “TEC-type”, F_ee was larger than unity and the corresponding tracer kinetics was retrospectively classified as Sokoloff-type.

Table 1.

Number of exposed and contralateral (protected) lungs with TEC-type ¹⁸F-FDG kinetics.

	Exposed lung	protected lung
Smoke	4/5	0/5
NEEP	5/6	4/6
PEEP	1/4	0/4

NEEP: negative end-expiratory pressure

PEEP: positive end-expiratory pressure

Table 2.

Mean, standard deviation, and range of model parameters k₅ and k₆.

	k5(1/min)		k6(1/min)
	Mean ± standard deviation	range	Mean ± standard deviation	range
ALI-type tracer kinetics	0.0444 ± 0.0221*	[0.0219 0.0917]	0.0757 ± 0.0452*	[0.0079 0.1595]
Sokoloff-type tracer kinetics	−0.2080 ± 0.9521	[−3.4685 0.4087]	−0.4968 ± 1.3378	[−4.4665 1.4575]

^*p<0.0001

Figure 3.

Difference in Akaike’s information criterion (AIC) between Sokoloff and TEC model of ¹⁸F-FDG kinetics (AIC_Sok – AIC_TEC) plotted against estimates of the rate constant k₆, for protected (○) and exposed lungs (●). Tracer kinetics with data points in the upper right quadrant were analyzed with the TEC model. One of these lungs was retrospectively classified as Sokoloff-type, since F_ee was > 1. Data points of seven of the protected lungs and four of the exposed lungs were all out of range with values of AIC_Sok ≪ AIC_TEC or with a non-numeric result for AIC_TEC (n = 2) and thus classified as Sokoloff-type.

For tracer kinetics classified as Sokoloff-type, the Sokoloff model provided excellent curve fits (Fig. 4A). For some of these specific cases, the TEC model could provide good curve fits to the data, but the time-activity curve associated with the extravascular/non-cellular compartment (C_ee(t)), and the values of k₅ and/or k₆ adopted negative, and thus unrealistic values (k₅ = −0.17 10⁻³ min⁻¹ and k₆ = −0.0665 min⁻¹ for the example of Fig. 4B). In contrast, when the Sokoloff model was applied to tracer kinetics classified as TEC-type, it generated a systematic error in the curve fit, particularly during the early phase (t < 20 min) (Fig. 4C), while the TEC model resulted in a virtually unbiased fit of the experimental data (Fig. 4D). Typically, for TEC-type tracer kinetics, the PET signal component associated with the precursor compartment peaked earlier and higher than that of the extravascular/non-cellular compartment (Fig. 4D). Similar characteristics of the tracer kinetics could be observed when smaller ROI’s were analyzed, as exemplified in Figure 5 for a lung area of decreased aeration and increased ¹⁸F-FDG uptake following smoke inhalation exposure.

Figure 4.

Comparison of curve fits achieved with the two different models for Sokoloff-type (A and B) and acute lung injury-type (C and D) lung ¹⁸F-FDG kinetics. A: Curve fit obtained with the Sokoloff model for Sokoloff-type lung ¹⁸F-FDG kinetics. The heavy line is the PET-acquired tissue time-activity curve (C_ROI(t)). C_model is calculated as the sum of model-derived time-activity curves from the individual model compartments. B: Curve fit obtained with the TEC model applied to the same ¹⁸F-FDG kinetics as in A. C and D: Curve fits obtained for lung ¹⁸F-FDG kinetics exhibiting TEC-type behavior in a lung with smoke inhalation exposure. C: Curve fit obtained with Sokoloff model. D: Curve fit obtained with TEC model applied to the same lung ¹⁸F-FDG kinetics as in C.

Figure 5.

Analysis of a localized region of interest (white outlines) in a lung with unilateral smoke inhalation exposure (exposed lung on the right side of each image). Top left: transmission scan, illustrating decreased lung aeration in the region of interest. Top right: PET image acquired 70 min after ¹⁸F-FDG injection. Bottom: time-activity curves in the individual compartments of the TEC model of ¹⁸F-FDG kinetics. The parameter estimates for this ROI are: F_B = 0.05 mL blood/mL lung; K_i = 26.61 · 10⁻³ mL blood/mL lung/min; F_e = 0.54 mL blood/mL lung; F_ee = 0.35 mL blood/mL lung.

Looking only at tracer kinetics classified as TEC-type, the Sokoloff model significantly under estimated k₁ and k₂ by 29 % (p < 0.005) and 43 % (p < 0.001), respectively, and overestimated F_e, and K_i by 17 % (p < 0.05) and 16 % (p < 0.0005), compared with the parameters obtained using the TEC model (Fig. 6). There was, however, a high correlation between the estimates by the two models for K_i and F_B (Fig. 6).

Figure 6.

Parameter estimates of the Sokoloff model (y-axis) plotted against those of the TEC model (x-axis). The graphs show (clockwise from top left) results for k₁, k₂, K_i, F_B, F_e, and k₃, for lung tracer kinetics classified as TEC-type. ● = smoke, exposed lungs; ▼ = PEEP, exposed lungs; ▲ = NEEP, exposed lungs; △= NEEP, protected lungs. R = correlation coefficient.

Analyzing all data according to their classification (Fig. 2), both K_i and F_e were greater in smoke-and NEEP-exposed compared to respective protected lungs (Fig. 7), but this difference was not statistically significant when the level of significance was adjusted to account for multiple comparisons. ANOVA indicated that whether or not a lung was exposed to an injurious insult had more of an effect on K_i and F_e than the type of insult (Table 3). Conversely, the magnitude of F_ee was dependent on the type of exposure, and was between 0 and 0.13 mL blood/mL lung in the smoke exposed lungs, and between 0 and 0.49 mL blood/mL lung in the exposed lungs of the NEEP group (Fig. 7, F_ee was set to 0 for Sokoloff-type tracer kinetics).

Figure 7.

Summary of parameters derived from the compartment models for sheep with unilateral exposure to smoke inhalation (SMOKE), injurious ventilation with negative (NEEP) and positive (PEEP) end-expiratory airway pressure. ○ = protected lungs; ● = exposed lungs; * = p<0.05, exposed vs. protected lungs as determined by paired t-test.

Table 3.

Percentile values of ANOVA test of exposure and type of exposure effects on model-derived parameters.

Source	Ki	Fe	Fee	Ki	Fe	Fee
	uncorrected			Bonferroni correction
Exposure to injurious stimulus	0.0031	0.0284	0.0818	0.0094	0.0852	0.2454
Type of exposure	0.1642	0.0429	0.0261	0.4925	0.1288	0.0783
Exposure × type of exposure	0.1282	0.1293	0.5516	0.3847	0.3880	1.6547

In the sheep exposed to unilateral smoke, k₃ was similar in both lungs (average exposed-to-protected k₃ ratio = 1), but F_e and K_i were in average twice as high in the exposed lung compared to the protected one (p<0.1 and p<0.05, respectively, Fig. 8). In the sheep exposed to unilateral ALI with NEEP, values for k₃, F_e, and K_i were in average about 1.5, 2, and 2.7 times higher in the injury exposed lung as compared to the respective values in the protected side (p<0.05, 0.025, and 0.025, respectively). Finally, in the sheep exposed to unilateral ALI with PEEP, average F_e was 84% lower in the exposed lung (p<0.025), while k₃ was in average 30% higher in the exposed lung than in the protected one (p=non significant) K_i, however, was similar in both lungs (average exposed-to-protected K_i ratio = 1.1)

Figure 8.

Comparison of exposed lung-to-protected lung ratios for k₃, F_e, and K_i. NEEP = negative end-expiratory pressure; PEEP = positive end-expiratory pressure. Error bars reflect ± 1 × standard error.

Discussion

The main finding of this analysis is that in the majority of the acutely injured lungs with smoke and ALI with NEEP the Sokoloff model was not adequate to describe ¹⁸F-FDG kinetics, while a refined model, including an extravascular/non-cellular compartment, provided excellent fit to the measured ¹⁸F-FDG kinetics.

We used only one region of interest per lung, delineating the entire imaged lung field. Thus, we did not account for the fact that some degree of intra-regional heterogeneity was present in some lungs, particularly in those exposed to smoke as shown in Figure 3 of our recent publication (6). Although the regional analysis falls beyond the scope of this paper, our methodology is also suitable for smaller regions of interest, as shown in Figure 5.

Remarkably, direct exposure of lung tissue to a specific injurious stimulus, or protection from it, did not necessarily determine whether the tissue presented TEC or Sokoloff-type tracer kinetics. This observation could be explained by the fact that there was a marked variability in the response to the injurious insults among the sheep and experimental protocols. This explanation is in line with our previous finding of a substantial variability of the pathophysiological response to smoke inhalation in the sheep studied (6), and the fact that VILI with NEEP but not with PEEP led to measurable ventilation-perfusion mismatch (4). Also, a substantial fraction of the protected lungs in the NEEP sheep presented TEC-type ¹⁸F-FDG kinetics. We specultate that this observation could be related to a systemic release of inflammatory mediators that could have not only affected the magnitude of ALI in the exposed lungs, but also led to indirect injury of the protected lungs, a process termed ‘biotrauma’ (24). Because the severity of lung injury was quite variable among the sheep studied, the TEC model may have caused ‘over-fitting’ in lungs with minor levels of injury. It was therefore important for the analysis to classify tracer kinetics as Sokoloff or TEC-type. Clearly, the Sokoloff model is a specific case of the TEC model in which the volume of distribution of the extravascular/non-cellular compartment is negligible (Fig 9). Although it would have been in most cases sufficient to do this classification by visual inspection of the model-generated curve fits – the Sokoloff model produced curve fits with clear and systematic biases when applied to severely injured lungs (Fig. 4) – we chose the AIC method as an objective measure to account for both curve fit error and increased number of model parameters. This approach was confirmed by comparing parameter estimates associated with the extravascular/non-cellular compartment against the AIC difference between the two models (Fig. 3). The results further indicated that, in borderline cases such as the one presented in Figure 4A and 4B, the two models converged to similar K_i, F_e, and F_B parameters, with F_ee≈ 0 for the TEC model. Given that computation of AIC involves a penalty factor for the number of model parameters, in these cases, AIC_Sok was lower than AIC_TEC, and the Sokoloff model was preferred over the TEC model. This approach is consistent with the general rule that the model with the minimum number of parameters that adequately fits the data is the best choice (25), while models that contain more than this minimum number of parameters result in parameter estimates of higher statistical uncertainty.

Figure 9.

Paradigm of ¹⁸F-FDG compartmentation in non-edematous (left) and edematous (right) inflamed lung tissue.

How reasonable is it to assume kinetically separated extravascular/non-cellular compartments for ¹⁸F-FDG, as it is implemented in the TEC model? In various types of acute lung injury, activated pulmonary neutrophils have been identified as the major determinant of pulmonary ¹⁸F-FDG uptake (9,26,27). Neutrophils have been shown to contribute to lung injury, increased pulmonary vascular permeability, and pulmonary edema after smoke inhalation injury in sheep (28). In ventilator-induced lung injury, disruption of the alveolar-capillary barrier is an important mechanism in the formation of alveolar edema (29), and there is increasing evidence that lung injury due to injurious ventilation strategies is enhanced by neutrophils (30). Furthermore, there is some experimental evidence for sequestration of activated neutrophils during the acute response to lung injury without significant alveolar neutrophilia (9). Thus, particularly during the early phase of acute lung injury, it seems reasonable to assume that interstitial and alveolar edema could constitute a compartment functionally far enough from activated pulmonary inflammatory cells and acting kinetically separate from the ¹⁸F-FDG precursor pool for phosphorylation. Other investigators (10) found that the Sokoloff model produced ‘excellent’ curve fits to ¹⁸F-FDG kinetics measured from acutely injured dog lungs exposed to endotoxin and oleic acid-induced pulmonary edema. Unfortunately, comparing those results against ours is difficult, since quantitative data about the quality of the curve fits was not provided in that report. It therefore remains to be shown, if the TEC model can improve the analysis of ¹⁸F-FDG kinetics in the setting of endotoxin and oleic acid-induced pulmonary edema.

An important finding of our study was that estimates of K_i correlated highly between the two compartment models (R = 0.99), even though the Sokoloff model produced a pronounced bias mostly during the early-phase curve fits. We, therefore, argue that the major determinant of K_i is the net ¹⁸F-FDG uptake by cells in the lung region of interest, and that K_i remains unaffected by the presence of more than one extravascular compartment for un-phosphorylated ¹⁸F-FDG. In another report of ¹⁸F-FDG uptake in dog lungs exposed to oleic acid (9), the investigators interpreted the absence of substantial increases in K_i as an indicator that the imaged signal was not primarily the result of vascular leak of ¹⁸F-FDG during ALI. Conversely, our modeling study suggests that a significant component of the lung ¹⁸F-FDG PET signal may originate from tracer in distribution volumes, which are not a precursor pool for phosphorylation, without significantly affecting estimates of the net uptake rate K_i.

In earlier publications we already reported on the changes in K_i in our sheep (4,6). The modeling analyses of this study allow a more detailed insight into the components that might have contributed to the K_i increases in the injury exposed lungs. A common interpretation of K_i is to consider it as the product of two terms: k₁, the rate of tracer transport from blood into tissue, and k₃/(k₂+k₃), the steady state fraction of the tracer in the tissue that reaches the metabolite compartment (20). Given the high sensitivity of ¹⁸F-FDG-PET for activated inflammatory cells in the lungs (9,26,27,31), an alternative interpretation seems possible. During acute lung inflammation, the rate of ¹⁸F-FDG phosphorylation, k₃, is associated with the activation status of inflammatory cells, and the ¹⁸F-FDG distribution volume in the precursor compartment, F_e, is linked to the total number of activated inflammatory cells per volume of lung tissue. Since F_e = k₁/(k₂+k₃), K_i can be thought of as the product of k₃ and a term that is associated with the number of neutrophils per volume of lung tissue. Applying this concept to the data of Figure 8 allows for a compelling hypothesis about the nature of ¹⁸F-FDG uptake in our different experimental protocols. For sheep of the smoke group, k₃ was similar for the protected and the smoke exposed lungs, suggesting that the higher ¹⁸F-FDG uptake in the smoke exposed lung was mostly caused by recruitment of a larger number of activated inflammatory cells per unit volume of lung tissue. Conversely, in the sheep of the NEEP group, the difference in K_i between protected and injury exposed lungs was the result of both increased activation and number of inflammatory cells in the injury exposed lung. Interestingly, in the PEEP group, k₃ of the injury-exposed lung was elevated compared to the protected lung, but this effect was compensated for by a lower F_e value.

Values of F_e reported for solid tissues have been substantially higher than those found in this study. For instance, in human gray and white brain matter, Phelps et al. (16) reported ¹⁸F-FDG distribution volumes of 0.59 mL/g and 0.38 mL/g. Knowing the fractional volume of pulmonary blood, F_B, and the fractional volume of alveolar gas (F_gas) (6), the ratio F_e/(1-F_B-F_gas) can be taken as an estimate of a parenchyma-specific distribution volume (see Appendix). For protected and exposed lungs of the smoke group F_e/(1-F_B-F_gas) was (mean±SE) 0.29±0.03 mL blood/mL lung and 0.34±0.03 mL blood/mL lung. Thus, for smoke exposed lungs, the parenchyma-specific F_e was below that of human white brain matter (assuming a brain tissue density of ~1 g/mL). However, for localized consolidated lung regions like the one analyzed in Figure 5, F_e approached values found in human gray matter.

Values of F_B in protected lungs were within the expected physiological range of pulmonary blood volume in sheep, which can be estimated as follows. Assuming a lung volume of 1200 mL, and taking the total pulmonary blood volume in sheep of about 108 mL (32) gives a fractional blood volume of approximately 0.13 mL blood/mL lung, which is similar to the average F_B of 0.14±0.04 mL blood/mL lung found in the protected lungs of our sheep. However, we also found high F_B variability among exposed lungs. A potential explanation for this variability could be that capillary perfusion was affected by various mechanisms that control local blood flow in pulmonary inflammation, such as hypoxic vasoconstriction and thromboxane synthesis (33). An assumption of the Sokoloff model is that the tracer transfer from blood into tissue is not flow limited (15). In acutely injured lungs with increased vascular permeability, this assumption might have to be reconsidered. Future studies will have to elucidate the effect of regional perfusion on pulmonary ¹⁸F-FDG uptake in these conditions.

Computed tomography is frequently used to study inflammatory lung diseases like ARDS, where a main goal has been to find clinical and easily measurable signs that could identify the primary pathologic characteristics of this disease, i.e., the high-permeability inflammatory noncardiogenic lung edema (34). Although PET does not provide comparable structural information, ¹⁸F-FDG PET in combination with the modeling approach proposed here could provide clinically relevant functional parameters to assess both inflammation and extravascular distribution volumes, which—we hypothesize—are the result of pulmonary edema.

In conclusion, for characterizing lung ¹⁸F-FDG kinetics during ALI, a new lung-specific tracer kinetic model is more accurate than the Sokoloff model and, if prospectively confirmed by corroborating data, may provide new insights in the pathophysiology of lung injury. This seems particularly relevant given that ¹⁸F-FDG is a widely available and easily applicable tracer—in contrast to short-lived tracers previously used to assess regional lung edema, such as oxygen-15-labeled water (35).

Appendix

The tracer influx from blood into the precursor compartment $({\stackrel{•}{q}}_{\mathrm{p}\Rightarrow \mathrm{e}}(t))$ is given as

$${\stackrel{•}{q}}_{\mathrm{p}\Rightarrow \mathrm{e}}(t)=k_1{V}_{\text{ROI}}{C}_{\mathrm{p}}(t)$$ (A1)

where V_ROI is the volume of the ROI, and the constant k₁ describes the rate of facilitated ¹⁸F-FDG transport from blood to tissue per unit of organ volume (36). Alternatively, in the lung, V_ROI can contain significant amounts of blood and alveolar gas, and a parenchyma-specific ¹⁸F-FDG blood-to-tissue transfer rate (k₁^*) can be computed as k₁^* = k₁/(1-F_B-F_gas), where F_B and F_gas are the fractional volumes of blood and alveolar gas. With the rate constants k₂, k₃, k₅, and k₆ describing, respectively, the rate of ¹⁸F-FDG diffusion from tissue to blood, the rate of hexokinase-catalyzed phosphorylation to ¹⁸F-FDG-6-P, and the transport rates of ¹⁸F-FDG from the precursor compartment into the extravascular/non-cellular compartment and back, we obtain for tracer dynamics of the precursor compartment

$$\begin{array}{cc}{\stackrel{•}{q}}_{\mathrm{e}}(t)=\hfill & k_1{V}_{\text{ROI}}{C}_{\mathrm{p}}(t)-(k_2+k_3)q_{\mathrm{e}}(t)-k_5{q}_{\mathrm{e}}(t)+k_6{q}_{\text{ee}}(t)\hfill \\ \hfill & =k_1{V}_{\text{ROI}}{C}_{\mathrm{p}}(t)-(k_2+k_3+k_5)q_{\mathrm{e}}(t)+k_6{q}_{\text{ee}}(t)\hfill \end{array}$$ (A2)

where q_e(t) and q_ee(t) are the decay-corrected quantities of tracer in the precursor and the extravascular/non-cellular compartments. The transfer of ¹⁸F-FDG between the precursor compartment and the extravascular/non-cellular compartment is modeled as passive diffusion, where the gradient in tracer concentrations is the driving force of mass transfer. The permeability (p) of the barrier between the precursor and extravascular/non-cellular compartment is given as the product of diffusion surface area and permeability coefficient. Assuming the initial conditions q_e(t) = 0, t<0, one obtains the following differential equation for tracer dynamics in the extravascular/non-cellular compartment

$${\stackrel{•}{q}}_{\text{ee}}(t)=\frac{p}{V_{\mathrm{e}}}{q}_{\mathrm{e}}(t)-\frac{p}{V_{\text{ee}}}{q}_{\text{ee}}(t)=k_5{q}_{\mathrm{e}}(t)-k_6{q}_{\text{ee}}(t)$$ (A3)

where V_e and V_ee are the absolute distribution volumes of the precursor compartment and extravascular/non-cellular compartment. Finally, for the tracer quantity in the metabolite compartment (q_m(t)) we obtain

$${\stackrel{•}{q}}_{\mathrm{m}}(t)=k_3{q}_{\mathrm{e}}(t)$$ (A4)

Normalizing Eqn. (A2), Eqn. (A3), and Eqn. (A4) by V_ROI to reflect changes in ROI activity concentration gives

$${\stackrel{•}{C}}_{\mathrm{e}}(t)=k_1{C}_{\mathrm{p}}(t)-(k_2+k_3+k_5)C_{\mathrm{e}}(t)+k_6{C}_{\text{ee}}(t)$$ (A5)

$${\stackrel{•}{C}}_{\text{ee}}(t)=k_5{C}_{\mathrm{e}}(t)-k_6{C}_{\text{ee}}(t)$$ (A6)

$${\stackrel{•}{C}}_{\mathrm{m}}(t)=k_3{C}_{\mathrm{e}}(t)$$ (A7)

GLSQ parameter identification requires a single differential equation that is linear in its parameters. This equation is found by applying the Laplace transform to Eqn. (A5), Eqn. (A6), and Eqn. (A7), yielding

$$s{C}_{\mathrm{e}}(s)=k_1{C}_{\mathrm{p}}(s)-(k_2+k_3+k_5)C_{\mathrm{e}}(s)+k_6{C}_{\text{ee}}(s)$$ (A8)

$$s{C}_{\text{ee}}(s)=k_5{C}_{\mathrm{e}}(s)-k_6{C}_{\text{ee}}(s)$$ (A9)

$$s{C}_{\mathrm{m}}(s)=k_3{C}_{\mathrm{e}}(s)$$ (A10)

The solution of this equation system is

$$\begin{array}{cc}{s}^3{C}_{\text{ROI}}(s)=\hfill & a_1{s}^2{C}_{\text{ROI}}(s)+a_2\mathrm{s}{C}_{\text{ROI}}(s)+a_3{s}^3{C}_{\mathrm{p}}(s)+\hfill \\ \hfill & \hfill a_4{\mathrm{s}}^2{C}_{\mathrm{p}}(s)+a_{5}s{C}_{\mathrm{p}}(s)+a_6{C}_{\mathrm{p}}(s)\hfill \end{array}$$ (A11)

the inverse Laplace transform of which gives the differential equation of the system (Eq. (2)).