A microvascular compartment model validated using 11C-methylglucose liver PET in pigs.

The standard compartment model (CM) is widely used to analyse dynamic PET data. The CM is fitted to time-activity curves to estimate rate constants that describe the transport of a tracer between well-mixed compartments. The aim of this study was to develop and validate a more realistic microvascular compartment model (MCM) that includes capillary tracer concentration gradients, backflux from cells into the perfused capillaries and multiple re-uptakes during the passage through a capillary. The MCM incorporates only parameters with clear physiological meaning, it is easy to implement, and it does not require numerical solution. We compared the MCM and CM for the analysis of 3 min dynamic PET data of pig livers (N = 5) following injection of 11C-methylglucose. During PET scans, the tracer concentrations in blood were measured in the abdominal aorta, portal vein and liver vein by manual sampling. We found that the MCM outperformed the CM and that dynamic PET data include information which cannot be extracted using standard CM. The MCM fitted dynamic PET data better than the CM (Akaike values were 46 ± 4 for best MCM fits, and 82 ± 8 for best CM fits; mean ± standard deviation) and extracted physiologically reasonable parameter estimates such as blood perfusion that were in agreement with independent measurements. The difference between model-independent perfusion estimates and the best MCM perfusion estimates was -0.01 ± 0.05 ml/ml/min, whereas the difference was 0.30 ± 0.13 ml/ml/min using the CM. In addition, the MCM predicted the time course of concentrations in the liver vein, a prediction fundamentally unobtainable using the CM as it does not return tracer backflux from cells to capillary blood. The results demonstrate the benefit of using models that include more physiology and that models including concentration gradients should be preferred when analysing the blood-cell exchange of any tracer in any capillary bed.

Hepatic galactose metabolism quantified in humans using 2-18F-fluoro-2-deoxy-D-galactose PET/CT.

UNLABELLED: Accurate quantification of regional liver function is needed, and PET of specific hepatic metabolic pathways offers a unique method for this purpose. Here, we quantify hepatic galactose elimination in humans using PET and the galactose analog 2-(18)F-fluoro-2-deoxy-d-galactose ((18)F-FDGal) as the PET tracer. METHODS: Eight healthy human subjects underwent (18)F-FDGal PET/CT of the liver with and without a simultaneous infusion of galactose. Hepatic systemic clearance of (18)F-FDGal was determined from linear representation of the PET data. Hepatic galactose removal kinetics were determined using measurements of hepatic blood flow and arterial and liver vein galactose concentrations at increasing galactose infusions. The hepatic removal kinetics of (18)F-FDGal and galactose and the lumped constant (LC) were determined. RESULTS: The mean hepatic systemic clearance of (18)F-FDGal was significantly higher in the absence than in the presence of galactose (0.274 ± 0.001 vs. 0.019 ± 0.001 L blood/min/L liver tissue; P < 0.01), showing competitive substrate inhibition of galactokinase. The LC was 0.13 ± 0.01, and the (18)F-FDGal PET with galactose infusion provided an accurate measure of the local maximum removal rate of galactose (V(max)) in liver tissue compared with the V(max) estimated from arterio-liver venous (A-V) differences (1.41 ± 0.24 vs. 1.76 ± 0.08 mmol/min/L liver tissue; P = 0.60). The first-order hepatic systemic clearance of (18)F-FDGal was enzyme-determined and can thus be used as an indirect estimate of galactokinase capacity without the need for galactose infusion or knowledge of the LC. CONCLUSION: (18)F-FDGal PET/CT provides an accurate in vivo measurement of human galactose metabolism, which enables the quantification of regional hepatic metabolic function.

Analogue tracers and lumped constant in capillary beds.

The lumped constant is a proportionality factor for converting a tracer analogue's metabolic rate to that of its mother substance. In a uniform system, it is expressed as the ratio of the tracer analogue's extraction fraction (E*) to the extraction fraction of its mother substance (E). Here we show that, in capillary beds perfused by unidirectional blood flow, unequal concentration gradients of the tracer analogue and of the mother substance influence extraction fractions both locally and across the organ and that the direct proportionality of E* and E must be replaced by ln(1-E*)/ln(1-E) to yield Λ, i.e. the lumped constant derived from first principles of bi-substrate enzyme and membrane kinetics. In other words, at a given capillary blood flow (F), the ratio of systemic clearances (FE*/FE), often used in compartmental kinetic analysis, must be replaced by the ratio of the intrinsic clearances, [-F ln(1-E*)]/[-F ln(1-E)]. The conclusion is supported by 2-[(18)F]fluoro-2-deoxy-D-galactose removal kinetics in pig liver in vivo from previous publications by the dependence of E*/E and the independence of Λ, on blood galactose concentration. Moreover, our corrections to the results of compartmental kinetics are quantified for comparing extraction fractions in different regions of interest (e.g. by positron emission tomography) and for calculating Λ using whole-organ E* and E measured by arteriovenous concentration differences.

Benefits and risks of transforming data from dynamic positron emission tomography, with an application to hepatic encephalopathy.

Transforming data sets to bring out expected model features can be valuable within limits and misleading outside them. Here we establish such limits for the widely used Gjedde-Patlak representation of dynamic PET data, with an application to hepatic encephalopathy.

A method to estimate dispersion in sampling catheters and to calculate dispersion-free blood time-activity curves.

The authors developed a transmission-dispersion model to estimate dispersion in blood sampling systems and to calculate dispersion-free input functions needed for kinetic analysis. Transport of molecules through catheters was considered in two parts: a central part with convective transmission of molecules and a stagnant layer that molecules may enter and leave. The authors measured dispersion caused by automatic and manual blood sampling using three PET tracers that distribute differently in blood (C15O, H2(15)O, and 11C-methylglucose). For manual sampling, dispersion was negligible. For the automated sampling procedure, characteristic parameters were calibrated for each tracer, and subsequently used in calculating dispersion-free input functions following real bolus injections. This led to shapes of dispersion-free input functions C(i)(t) that had sharper peaks than the measured C(o)(t), and the authors quantified the effect of correcting for dispersion before kinetic modeling. The transmission-dispersion model quantitatively takes apart effects of transmission and dispersion, it has transparent noise properties associated with each component, and it does not require deconvolution to calculate dispersion-free input functions. Once characteristic parameters are estimated, input functions can be corrected before applying kinetic models. This allows bias-free estimation of kinetic parameters such as blood flow.

Hepatic uptake and metabolism of galactose can be quantified in vivo by 2-[18F]fluoro-2-deoxygalactose positron emission tomography.

Metabolism of galactose is a specialized liver function. The purpose of this PET study was to use the galactose analog 2-[(18)F]fluoro-2-deoxygalactose (FDGal) to investigate hepatic uptake and metabolism of galactose in vivo. FDGal kinetics was studied in 10 anesthetized pigs at blood concentrations of nonradioactive galactose yielding approximately first-order kinetics (tracer only; n = 4), intermediate kinetics (0.5-0.6 mmol galactose/l blood; n = 2), and near-saturation kinetics (>3 mmol galactose/l blood; n = 4). All animals underwent liver C15O PET (blood volume) and FDGal PET (galactose kinetics) with arterial and portal venous blood sampling. Flow rates in the hepatic artery and the portal vein were measured by ultrasound transit-time flowmeters. The hepatic uptake and net metabolic clearance of FDGal were quantified by nonlinear and linear regression analyses. The initial extraction fraction of FDGal from blood-to-hepatocyte was unity in all pigs. Hepatic net metabolic clearance of FDGal, K(FDGal), was 332-481 ml blood.min(-1).l(-1) tissue in experiments with approximately first-order kinetics and 15.2-21.8 ml blood.min(-1).l(-1) tissue in experiments with near-saturation kinetics. Maximal hepatic removal rates of galactose were on average 600 micromol.min(-1).l(-1) tissue (range 412-702), which was in agreement with other studies. There was no significant difference between K(FDGal) calculated with use of the dual tracer input (Kdual(FDGal)) or the single arterial input (Karterial(FDGal)). In conclusion, hepatic galactose kinetics can be quantified with the galactose analog FDGal. At near-saturated kinetics, the maximal hepatic removal rate of galactose can be calculated from the net metabolic clearance of FDGal and the blood concentration of galactose.

Hepatic microcirculation assessed by positron emission tomography of first-pass ammonia metabolism in porcine liver.

AIMS/BACKGROUND: Intrahepatic branching of the hepatic artery (HA) to liver microcirculatory units, the acini, is more heterogeneous than that of the portal vein (PV). Furthermore, part of HA blood enters the sinusoid partially downstream between the in- and outlets. We examined the effects of these vascular variations on porcine hepatic first-pass ammonia metabolism, which is characterised by high uptake and separate periportal urea and perivenous glutamine formations. METHODS: (13)NH(3) was given via the PV, HA or caval vein, followed by 22 min dynamic liver positron emission tomography (PET) recordings in six pigs. Heterogeneity of liver (13)N-metabolism was quantified by the coefficient of variation of tissue (13)N-radioactivity measured 10 min after tracer infusion. Sinusoidal zonal clearances of (13)NH(3) into (13)N-urea and (13)N-glutamine were calculated by kinetic PET modelling. RESULTS: Liver metabolic heterogeneity was 0.65+/-0.20 (mean+/-SD, n=6) following (13)NH(3)-infusion into HA, 0.34+/-0.17 into PV and 0.10+/-0.02 into the caval vein. Clearance of (13)NH(3) to (13)N-urea was of similar magnitude following (13)NH(3) administration into HA and PV: 0.27+/-0.11 ml/min/g (mean+/-SD) and 0.29+/-0.09 ml/min/g, respectively. Clearances of (13)NH(3) to (13)N-glutamine when (13)NH(3) was given into HA and PV were also similar: 0.47+/-0.18 and 0.50+/-0.13 ml/min/g, respectively. CONCLUSIONS: The present measurements of the hepatic metabolism of (13)NH(3) showed metabolic heterogeneity compatible with variation of the HA supply of the acini. Second, results of PET modelling of the sinusoidal zonation metabolism of (13)NH(3) to (13)N-urea and to (13)N-glutamine did not indicate metabolically important partial downstream arterial entry into the sinusoids.

Determination of regional flow by use of intravascular PET tracers: microvascular theory and experimental validation for pig livers.

UNLABELLED: Today, the standard approach for the kinetic analysis of dynamic PET studies is compartment models, in which the tracer and its metabolites are confined to a few well-mixed compartments. We examine whether the standard model is suitable for modern PET data or whether theories including more physiologic realism can advance the interpretation of dynamic PET data. A more detailed microvascular theory is developed for intravascular tracers in single-capillary and multiple-capillary systems. The microvascular models, which account for concentration gradients in capillaries, are validated and compared with the standard model in a pig liver study. METHODS: Eight pigs underwent a 5-min dynamic PET study after (15)O-carbon monoxide inhalation. Throughout each experiment, hepatic arterial blood and portal venous blood were sampled, and flow was measured with transit-time flow meters. The hepatic dual-inlet concentration was calculated as the flow-weighted inlet concentration. Dynamic PET data were analyzed with a traditional single-compartment model and 2 microvascular models. RESULTS: Microvascular models provided a better fit of the tissue activity of an intravascular tracer than did the compartment model. In particular, the early dynamic phase after a tracer bolus injection was much improved. The regional hepatic blood flow estimates provided by the microvascular models (1.3 +/- 0.3 mL min(-1) mL(-1) for the single-capillary model and 1.14 +/- 0.14 min(-1) mL(-1) for the multiple-capillary model) (mean +/- SEM mL of blood min(-1) mL of liver tissue(-1)) were in agreement with the total blood flow measured by flow meters and normalized to liver weight (1.03 +/- 0.12 mL min(-1) mL(-1)). CONCLUSION: Compared with the standard compartment model, the 2 microvascular models provide a superior description of tissue activity after an intravascular tracer bolus injection. The microvascular models include only parameters with a clear-cut physiologic interpretation and are applicable to capillary beds in any organ. In this study, the microvascular models were validated for the liver and provided quantitative regional flow estimates in agreement with flow measurements.

Capillaries within compartments: microvascular interpretation of dynamic positron emission tomography data.

Measurement of exchange of substances between blood and tissue has been a long-lasting challenge to physiologists, and considerable theoretical and experimental accomplishments were achieved before the development of the positron emission tomography (PET). Today, when modeling data from modern PET scanners, little use is made of earlier microvascular research in the compartmental models, which have become the standard model by which the vast majority of dynamic PET data are analysed. However, modern PET scanners provide data with a sufficient temporal resolution and good counting statistics to allow estimation of parameters in models with more physiological realism. We explore the standard compartmental model and find that incorporation of blood flow leads to paradoxes, such as kinetic rate constants being time-dependent, and tracers being cleared from a capillary faster than they can be supplied by blood flow. The inability of the standard model to incorporate blood flow consequently raises a need for models that include more physiology, and we develop microvascular models which remove the inconsistencies. The microvascular models can be regarded as a revision of the input function. Whereas the standard model uses the organ inlet concentration as the concentration throughout the vascular compartment, we consider models that make use of spatial averaging of the concentrations in the capillary volume, which is what the PET scanner actually registers. The microvascular models are developed for both single- and multi-capillary systems and include effects of non-exchanging vessels. They are suitable for analysing dynamic PET data from any capillary bed using either intravascular or diffusible tracers, in terms of physiological parameters which include regional blood flow.

Impulse-response function of splanchnic circulation with model-independent constraints: theory and experimental validation.

Modeling physiological processes using tracer kinetic methods requires knowledge of the time course of the tracer concentration in blood supplying the organ. For liver studies, however, inaccessibility of the portal vein makes direct measurement of the hepatic dual-input function impossible in humans. We want to develop a method to predict the portal venous time-activity curve from measurements of an arterial time-activity curve. An impulse-response function based on a continuous distribution of washout constants is developed and validated for the gut. Experiments with simultaneous blood sampling in aorta and portal vein were made in 13 anesthetized pigs following inhalation of intravascular [15O]CO or injections of diffusible 3-O-[11C]methylglucose (MG). The parameters of the impulse-response function have a physiological interpretation in terms of the distribution of washout constants and are mathematically equivalent to the mean transit time (T) and standard deviation of transit times. The results include estimates of mean transit times from the aorta to the portal vein in pigs: T = 0.35 +/- 0.05 min for CO and 1.7 +/- 0.1 min for MG. The prediction of the portal venous time-activity curve benefits from constraining the regression fits by parameters estimated independently. This is strong evidence for the physiological relevance of the impulse-response function, which includes asymptotically, and thereby justifies kinetically, a useful and simple power law. Similarity between our parameter estimates in pigs and parameter estimates in normal humans suggests that the proposed model can be adapted for use in humans.