Figure 2.
Pharmacokinetic models developed to study the hepatobiliary disposition of [11C]erlotinib. (a) Four compartment model developed from the combination of two previously developed models [60,89]. This model includes two main regions of interest (ROIs): the liver and the extrahepatic bile duct and gall bladder (eBD/GB). The liver ROI includes compartments representing the amount of radioactivity in the blood fraction in the liver sinusoids used as the model input function (Xblood, 0.25% of the total liver volume), in the hepatocytes (Xhep) and in the intrahepatic bile (Xih, 0.32% of the total liver volume). The extrahepatic ROI compartment represents the amount of radioactivity in the visible part of the extrahepatic bile duct and the gall bladder. The kinetic parameters define the exchange rate of radioactivity between blood and hepatocytes (k1 and k2), from hepatocytes to the intrahepatic bile duct (k3), or from the intrahepatic bile duct to the extrahepatic bile duct and gall bladder (k5). (b) The three compartment model includes compartments representing the blood in the liver sinusoids (used as the model input function), liver tissue (combination of the hepatocytes and the intrahepatic bile duct from the four compartment model) and excreted bile out of the liver ROI. The kinetic parameters define the exchange rate of radioactivity between the blood and the liver (k1 and k2) or from the liver to the excreted bile (k3). The differential equations depicted under the kinetic models are implemented to fit the amount of radiotracer in each compartment to the obtained PET TACs and obtain the estimates of the kinetic parameters. In the equations, X represents the amount of radiotracer in the compartment and ks are the respective rate constants. Note that k1 represents the basolateral uptake rate and does not discriminate between active or passive uptake mechanisms. According to PET pharmacokinetic modeling, the parameter K1 is perfusion-dependent and can be related to blood flow (Q) as: K1 = E x Q; where E represents the unidirectional first-pass extraction ratio [140]. In the present model, k1 can be expressed by means of K1 as k1 = K1 x (Vliver/Vblood), where Vliver corresponds to the volume of hepatocytes in (a) and the volume of liver tissue in (b), and Vblood corresponds to the volume of blood in the hepatic sinusoids. Therefore, the uptake rate constant k1 can be expressed in terms of perfusion as: k1 = (E x Q x Vliver)/Vblood.