Modeling Pulmonary Kinetics of 2-Deoxy-2-[18 F ] fluoro- d -glucose During Acute Lung Injury

Rationale and Objectives

Dynamic positron emission tomographic imaging of the radiotracer 2-deoxy-2-[ 18 F]fluoro- d -glucose ( 18 F-FDG) is increasingly used to assess metabolic activity of lung inflammatory cells. To analyze the kinetics of 18 F-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 18 F-FDG distribution in edematous injured tissue could require a modified model to properly describe 18 F-FDG kinetics.

Materials and Methods

We developed and validated a new model of lung 18 F-FDG kinetics that includes an extravascular/noncellular compartment in addition to blood and 18 F-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 18 F-FDG net uptake and distribution volume in the precursor pool for phosphorylation correlated between the two models ( R 2 = 0.98, 0.78), but were overestimated with the Sokoloff model by 17% ( P < .05) and 16% ( P < .0005) compared to the new one. The range of the extravascular/noncellular 18 F-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 18 F-FDG kinetics during acute lung injury more accurately than the Sokoloff model and may provide new insights in the pathophysiology of lung injury.

In basic science and clinical investigation of lung pathology, there is a growing interest in new pulmonary imaging techniques ( ). Recently, positron emission tomographic (PET) imaging of the glucose analog 2-deoxy-2-[ 18 F]fluoro- d -glucose ( 18 F-FDG), a standard tool in oncology, is increasingly used to assess metabolic activity of pulmonary inflammatory cells ( ). Such measurement is based on the fact that 18 F-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 18 F-FDG kinetics in the inflamed lung. Some investigators ( ) calculated a lung net uptake rate of 18 F-FDG ( K i ) using the Patlak method ( ) and normalized K i by the initial tracer distribution volume ( ) or by the tissue fraction ( ) to account for regional differences in lung density. Other investigators ( ) considered tracer kinetic modeling with Sokoloff’s three-compartment model ( ) as the gold standard for analyzing lung 18 F-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 18 F-FDG kinetics in solid tissues such as brain, tumors, and myocardium ( ). An assumption of this model is that all extravascular 18 F-FDG in the region of interest is the precursor pool for hexokinase-catalyzed phosphorylation to 18 F-FDG-6-phosphate ( 18 F-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 18 F-FDG. In these conditions, it could be necessary to model pulmonary tracer kinetics by a compartment model specifically designed to reflect lung 18 F-FDG kinetics during acute lung injury (ALI). Also, previous investigators ( ) have used iterative nonlinear curve fitting to determine the individual rate constants of the Sokoloff model. This technique entails initialization of the parameter vector ( ), which may lead to incorrect solutions when the initial guess is not appropriate ( ). This may be problematic for modeling pulmonary 18 F-FDG, because little is known about typical values of the model parameters.

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

Methods

Model of Lung 18 F-FDG Kinetics During Acute Lung Injury: Two Equilibrating Compartment (TEC) Model

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CROI(t)=FBCp(t)+Ce(t)+Cee(t)+Cm(t) C

ROI

(

)

(

)

(

)

(

)

(

)

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C…ROI(t)=a1C¨ROI(t)+a2C˙ROI(t)+a3C…p(t)+…………a4C¨p(t)+a5C˙p(t)+a6Cp(t) C

⃛

ROI

(

)

ROI

(

)

ROI

(

)

⃛

(

)

…

(

)

(

)

(

)

with the coefficients a 1 = −( k 2 + k 3 + k 5 + k 6 ), a 2 = − k 6 ( k 2 + k 3 ), a 3 = F B , a 4 = ( k 2 + k 3 + k 5 + k 6 ) F B + k 1 , a 5 = k 1 ( k 3 + k 5 + k 6 ) + F B k 6 ( k 2 + k 3 ), and a 6 = k 1 k 3 k 6 . Once these coefficients were identified by GLSQ, the parameters of the lung-specific model were computed according to:

FB=a3,k1=a4+a1a3, F

k2=−a5+a2a3a4+a1a3−a1, k

−

k3=−k2a6a6+k1a2, k

−

k6=−a6+k1a2k1k2, k

−

and k5=−(k2+k3+k6+a1) k

−

(

) . Under the assumption of steady-state conditions, the 18 F-FDG distribution volume of the precursor compartment as a fraction of lung volume ( F e ), can be derived as

Fe=k1k2+k3 F

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

Fee=k5k6k1k2+k3. F

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Ki=Fek3=k1k3k2+k3 K

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

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Sokoloff Model

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Model Selection

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AIC=N1n(Σi=1Ne2(ti))+2n AIC

(

)

where N was the number of PET image frames, and 2 n 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 ( ).

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Experimental Data

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Statistical Analysis

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Results

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Table 1

Number of Exposed and Contralateral (Protected) Lungs With TEC-Type 18 F-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 k 5 and k 6

k 5 (1/min)k 6 (1/min) Mean ± Standard Deviation Range Mean ± Standard Deviation Range ALI-type tracer kinetics 0.0444 ± 0.0221 ⁎ 0.0219 to 0.0917 ± 0.0757 ± 0.0452 ⁎ 0.0079 to 0.1595 Sokoloff-type tracer kinetics −0.2080 ± 0.9521 −3.4685 to 0.4087 −0.4968 ± 1.3378 −4.4665 to 1.4575

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Table 3

Percentile Values of ANOVA Test of Exposure and Type of Exposure Effects on Model-Derived Parameters

Source_K_ i F e Uncorrected_F_ ee K i F e Bonferroni Correction_F_ ee 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 x type of exposure 0.1282 0.1293 0.5516 0.3847 0.3880 1.6547

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Discussion

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Conclusion

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Appendix

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q˙p⇒e(t)=k1VROICp(t) q

⇒

(

)

ROI

(

)

where V ROI is the volume of the region of interest (ROI), and the constant k 1 describes the rate of facilitated 18 F-FDG transport from blood to tissue per unit of organ volume ( ). Alternatively, in the lung, V ROI can contain significant amounts of blood and alveolar gas, and a parenchyma-specific 18 F-FDG blood-to-tissue transfer rate ( k 1 *) can be computed as k 1 \* = k 1 /(1 − F B − F gas ), where F B and F gas are the fractional volumes of blood and alveolar gas. With the rate constants k 2 , k 3 , k 5 , and k 6 describing, respectively, the rate of 18 F-FDG diffusion from tissue to blood, the rate of hexokinase-catalyzed phosphorylation to 18 F-FDG-6-P, and the transport rates of 18 F-FDG from the precursor compartment into the extravascular/noncellular compartment and back, we obtain for tracer dynamics of the precursor compartment

q˙e(t)=k1VROICp(t)−(k2+k3)qe(t)−k5qe(t)+k6qee(t)=k1VROICp(t)−(k2+k3+k5)qe(t)+k6qee(t) q

(

)

ROI

(

)

−

(

)

(

)

−

(

)

(

)

ROI

(

)

−

(

)

(

)

(

)

where q e ( t ) and q ee ( t ) are the decay-corrected quantities of tracer in the precursor and the extravascular/noncellular compartments. The transfer of 18 F-FDG between the precursor compartment and the extravascular/noncellular 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/noncellular 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/noncellular compartment

q˙ee(t)=pVeqe(t)−pVeeqee(t)=k5qe(t)−k6qee(t) q

(

)

(

)

−

(

)

(

)

−

(

)

where V e and V ee are the absolute distribution volumes of the precursor compartment and extravascular/noncellular compartment. Finally, for the tracer quantity in the metabolite compartment ( q m ( t )) we obtain

q˙m(t)=k3qe(t). q

(

)

(

)

Normalizing Equations A2, A3, and A4 by V ROI to reflect changes in ROI activity concentration gives

C˙e(t)=k1Cp(t)−(k2+k3+k5)Ce(t)+k6Cee(t) C

(

)

(

)

−

(

)

(

)

(

)

C˙ee(t)=k5Ce(t)−k6Cee(t) C

(

)

(

)

−

(

)

C˙m(t)=k3Ce(t). C

(

)

(

)

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sCe(s)=k1Cp(s)−(k2+k3+k5)Ce(s)+k6Cee(s) s

(

)

(

)

−

(

)

(

)

(

)

sCee(s)=k5Ce(s)−k6Cee(s) s

(

)

(

)

−

(

)

sCm(s)=k3Ce(s). s

(

)

(

)

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s3CROI(s)=a1s2CROI(s)+a2sCROI(s)+a3s3Cp(s)+…………a4s2Cp(s)+a5sCp(s)+a6Cp(s) s

ROI

(

)

ROI

(

)

ROI

(

)

(

)

…

(

)

(

)

(

)

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

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Modeling Pulmonary Kinetics of 2-Deoxy-2-[18 F ] fluoro- d -glucose During Acute Lung Injury

Rationale and Objectives

Materials and Methods

Results

Conclusion

Methods

Model of Lung 18 F-FDG Kinetics During Acute Lung Injury: Two Equilibrating Compartment (TEC) Model

Sokoloff Model

Model Selection

Experimental Data

Statistical Analysis

Results

Discussion

Conclusion

Appendix

References

Further Reading

A Robust Method for Estimating Regional Pulmonary Parameters in Presence of Noise

Abstracts of Funded National Institutes of Health Grants

Advances in Physiologic, Metabolic, and Molecular Lung Imaging