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We are pleased by the interest of Drs. Lockwood and Wack in our recent 13N-ammonia PET study on brain ammonia metabolism in patients with cirrhosis and clinically manifest hepatic encephalopathy (HE).1 Since our results apparently differ from results by Lockwood and coworkers,2–4 Drs. Lockwood and Wack expressed concern about our modeling. This gives us the opportunity to clarify the concepts of PET estimation of the permeability-surface area products (PS) for the blood-brain-barrier (PSBBB) and the metabolism (PSmet) (Fig. 1).1, 5

Unfortunately in our article1 there was an arithmetical error in the calculations of PSBBB. A corrected Table 2 is given in a “Corrections” in this issue of the Journal. Mean PSBBB values in the group of patients with cirrhosis and HE were lower than mean values in the group of healthy controls but the difference was not statistically significant. This is in agreement with another recent dynamic 13N-ammonia PET study.6 Thus, the results still indicate that the elevated blood ammonia and not changed brain ammonia kinetics is the more important factor for the increased ammonia uptake in patients with HE.

Calculation of PSBBB requires dynamic PET recording starting at the time of injection since it includes K1 (Fig. 1). The estimation ofK1 is calculated from the initial time-course of tissue radioactivity and is very sensitive to changes hereof. Lockwood's group calculated PS-values from static PET recordings,2–4 which yield no specific information on the initial time-course of tissue radioactivity. Their PS-values are therefore an opaque mixture of PSBBB and PSmetabolism and not comparable with our PSBBB -values.

Figure 1.

K1, unidirectional clearance (mL blood/min/mL tissue); k2, back-flux rate constant (per minute), k3, rate constant of enzymatic trapping (per minute). PSBBB (mL blood/min/mL tissue) is given as −CBF ln(1-K1/CBF). PSBBB is a measure of the capacity of substrate transfer across BBB. Ammonia diffuses freely across the BBB.9, 10PSmetabolism is a measure of the combined transfer of ammonia from blood to cells and the metabolic trapping within the cells. PSmetabolism is given as - CBF ln(1-Kmetabolism/CBF) where Kmetabolism = K1 k3/(k2 + k3).

Duplicate cerebral blood flow (CBF) measurements in our study deviated less than 5% in each subject.1 The CBF in the healthy controls and in the patients with cirrhosis without clinical signs of HE were similar to the CBF in comparable individuals in other studies.4, 6, 7 We therefore see no reason for doubting the validity of our CBF measurements in chronic liver patients with overt HE.

Our philosophy on kinetic modeling is to make the models as physiologically correct as possible while keeping the number of parameters as low as possible. The simple model proposed by Lockwood and coworkers assuming irreversible trapping of ammonia may be justified in view of their study design and data, among which they assumed blood 13N-ammonia to be cleared within 10 minutes. In our study, however, blood 13N-ammonia fraction decreased throughout 30 minutes but never reached zero in any subject, and we furthermore measured specific 13N-metabolites, which all justifies a more complex model.1, 8

The volume of 0.01 used for the ammonia metabolites does not equal the vascular volume of the brain, but is a kinetic distribution volume which is commonly used in PET kinetics.

Contemporary PET technology with high spatial and temporal resolution in conjunction with proper mathematical-physiological models fitted to the data represents to us an excellent method to address the question of ammonia metabolism in patients with overt HE.

Michael Sørensen*, Susanne Keiding*, * Medical Department V (Hepatology) and PET Center, Aarhus University Hospital, Aarhus, Denmark

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