REPLY:

We appreciate the comments of Munk et al. regarding our article (1), which give us the opportunity (a) to discuss central aspects of our investigation in more detail, and (b) to relate our results to those reported by Munk et al. (2). Please note that our manuscript had been accepted for publication about 1 month before the paper of Munk and coworkers appeared in The Journal of Nuclear Medicine.

The main challenge in the quantification of ¹⁸F-FDG uptake in the normal liver using dynamic PET is the determination of the dual hepatic blood supply. It was therefore the aim of our experimental study to assess in foxhounds the effect of different input models on the rate constants of the standard 3-compartment FDG model. Each experiment comprised a dynamic PET scan together with the continuous detection of counting rates in arterial and venous blood feeding the liver using 2 independent coincidence-based detector systems. These measurements yielded 3 different blood curves (SUV_aorta^PET, SUV_arterial^detector, and SUV_venous^detector), which were used to define 5 different hepatic input functions, as described in our paper.

For quantification of rate constants characterizing FDG transport and metabolization in the liver, we used the conventional 3-compartment FDG model with a “vascular volume” characterized by a volume fraction f_B and a lag time to correct for the time delay of ¹⁸F-FDG activity arrival in the liver. Although we started the nonlinear least-squares fitting procedure with an initial value for the “vascular volume” fraction of f_B = 0.28 mL/mL (mL blood/mL liver tissue) derived from the literature (3), this parameter was fitted to zero in the majority of the liver curves examined. In 3 cases, the analysis yielded a nonzero but very low value of f_B <0.057 mL/mL. The reason for this observation is that, in accordance with the results reported in Munk et al., the sharp initial peak of the arterial input functions SUV_arterial^detector and SUV_aorta^PET was not reflected in the PET activity–time curves observed in the liver. Therefore, Munk et al. “raise the question of whether our blood sampling system dispersed the arterial (and portal) blood time–activity curves so much that the dual input curve did not resemble the true input to the liver”. The relevance of dispersion effects on the estimation of the “vascular volume” of liver tissue and on the rate constants can, however, be ruled out due to 3 reasons:

1. The arterial blood curve SUV_aorta^PET was determined from a region of interest (ROI) defined over the central part of the aorta visualized on the PET scans of the foxhounds, and thus a substantial dispersion of this input on its way from the aorta to the liver can be neglected. As mentioned above, the fast initial increase of this arterial curve—which also contributes to the dual hepatic input function (see below)—is not compatible with the identification of a large vascular blood compartment in liver tissue.

2. Since tubing and flow rate were identical for both extracorporeal loops, it is reasonable to assume that the dispersion of the inputs SUV_arterial^detector and SUV_venous^detector caused by the monitor systems is nearly identical, and thus a notional system function S can be estimated based on the equation S_venous^detector = S ⊗ SUV_arterial^detector, which describes only the “physiological” dispersion of the arterial input on its way through the GI tract. Using this function, a dual hepatic input was approximated from the arterial input SUV_aorta^PET determined from the PET scans according to Eq. 1 where the factors w_arterial and w_venous determine the relative weights of the arterial and portal venous blood supply, respectively. It is important to note that the dual hepatic input function defined by Eq. 1 is not considerably affected by disturbing dispersion effects, since both SUV_aorta^PET and S are nearly free of them. Nevertheless, this dual input function also resulted in a very low “vascular volume” fraction.

3. Differences in the rate constants estimated for the “nondispersed” hepatic input function defined by Eq. 1 and those computed for the potentially “dispersed” input function

   Eq. 2 were statistically not significant (1; Fig. 7).

The relative weights w_arterial and w_venous were determined from perfusion measurements performed in the same animals by dynamic PET scanning using ¹⁵O-water as well as by a standard microsphere technique as described in a previous paper (4). Since the correlation between the perfusion values determined by both techniques was poor, we used mean values of w_arterial = 0.35 and w_venous = 0.65 averaged over 5 foxhounds for the computation of the input functions according to Eqs. 1 and 2 instead of the individual values. Munk and colleagues, on the other hand, measured the total organ blood flows in the hepatic artery and the portal vein continuously throughout the PET procedure by means of 2 sonographic transit-time flowmeter probes. Therefore, Munk et al. maintain in their letter that their procedure is more accurate since individual perfusion values are used instead of mean values. It should be noted, however, that they also use spatially averaged values, since regional perfusion in an ROI defined on the PET scans to evaluate FDG uptake in liver tissue is by no means identical with the average liver perfusion estimated from the total blood flows measured in the hepatic artery and the portal vein.

In consequence, the estimates obtained in our study for the “vascular volume” of liver tissue for different hepatic input models are fully based on the measured data and are caused neither by uncontrolled dispersion effects nor by the use of inaccurate weighting factors describing the relative fraction of the arterial and portal venous blood supply to the liver. Moreover, a small “vascular volume” does not result in an “unphysiological” model configuration, as stated by Munk et al. It is well known that the “vascular volume” in the standard 3-compartment FDG model does not represent a true physical volume, which can be identified with tissue blood (or plasma) volume. The reason is that the tracer in the capillaries has 2 states, 1 equal to the input concentration in a virtual “vascular volume” characterized by f_B, and 1 present at a “plasma equivalent” tissue concentration (5). In tissues with very high endothelial permeability, the “vascular volume” can approach zero (5). Therefore, the results of our study are not only based on reliable activity–time curves but are also in accordance with basic principles of compartmental analysis and tissue physiology.

We agree with the conclusion of Munk et al. (2) that dual-input models are superior to single-input models with respect to both the approximation of the acquired liver data and the estimation of physiologically reasonable rate constants. In relation to our foxhound PET data, however, differences between the rate constants estimated for different input models are smaller than the parameter variations among the animals. This is strongly supported by a comparison of our data with the results reported by Munk et al. for 6 pigs. Please note that the authors computed an unphysiologically high “vascular volume” of f_B = 0.40 mL/mL, in strong contrast to their own experimental result of f_B = 0.25 mL/mL obtained via the ¹⁵O-carbon monoxide steady-state PET technique. However, their value of 1.07 ± 0.19 mL/min/g (mean ± SEM) obtained for the rate constant K₁ (FDG transport into the liver cells) fits very well into the range of the individual values (0.5 < K₁ < 1.5 mL/min/g) determined in our study for the dual-input models defined by Eqs. 1 and 2. Unfortunately, Munk et al. presented neither a plot of the individual rate constants estimated for the 6 pigs nor an appropriate (nonparametric) statistical test to prove that the reported differences in the mean values obtained for the examined single and dual hepatic input model are significant. On the basis of the data reported (mean ± SEM), it is not possible for the reader to assess whether the differences in the rate constants introduced by differences in the input models exceed the range of the interindividual variations.

Finally, we cannot agree with Munk et al. concerning the application of the Gjedde-Patlak technique in the quantitative analysis of dynamic FDG liver data. This graphical (in other circumstances very useful) approach simply neglects the dephosphorylation of FDG-6-phosphate via the enzyme glucose-6-phosphatase, which is present at a high level in normal liver cells. A Gjedde-Patlak analysis even “perhaps with a correction for k₄,” as suggested by Munk et al., is not applicable since k₃ (the FDG phosphorylation rate constant) and k₄ (the dephosphorylation rate constant) are of the same order of magnitude, as is clearly seen in their data (2; Table 1). This observation is further substantiated when the interested reader recalculates the Patlak parameters K (forward clearance of FDG) and V (virtual volume) directly from the compartmental parameters K₁, k₂, k₃, and V₀ using Eq. 7 in Munk et al. (2). The reanalysis of the data reveals that the FDG forward clearance K is underestimated in the Gjedde-Patlak approach by a factor of 2 to 3.

This discrepancy may also be a consequence of the fact that “data from the first few minutes were not included in the analysis,” as stated in the paper of Munk and coworkers. So it is by no means astonishing that the “robust” Gjedde-Patlak analysis produces the same parameter estimates for the arterial input and the dual-input function, since the 2 input functions are virtually identical 1–2 min after tracer injection (2; Fig. 1). Moreover, the conclusion of Munk et al. that the use of the dual-input function is supported by better statistical scores is only valid for their compartmental analysis (2; Table 1). To the contrary, the single arterial input is clearly favored by the statistical criteria in their Gjedde-Patlak modeling approach (2; Table 2).

At the end of this controversial but stimulating discussion on a complex topic, we would like to emphasize that consensus exists between our groups that the dual hepatic input cannot be measured directly in humans and that it is thus necessary to evaluate alternative procedures for future noninvasive patient studies of liver metabolism. This very fact prompted us to initiate our PET investigation—namely, to provide the clinician with a practicable yet physiologically appropriate modeling approach. For normal liver tissue, the only practical alternative is to approximate the dual hepatic input by using the arterial input function and to estimate the blood supply through the portal vein by a notional system function that describes the dispersion of the arterial input in the GI tract. For humans, this function may be estimated from dynamic MRI studies using a suitable paramagnetic contrast agent. This approach is supported by our observation that the estimation of rate constants as defined by the standard 3-compartment FDG model is a relatively robust procedure in relation to uncertainties in the hepatic input function. With regard to FDG PET examinations of patients with liver diseases, there is a large body of evidence that both malignant and benign lesions of the liver are mainly supplied with blood by the hepatic artery. Taking this fact into account, it seems to be a valid approach for clinical FDG PET studies on patients with liver lesions to approximate the hepatic input by using the arterial input function.