Analysis of arterial–venous blood concentration difference of drugs based on recirculatory theory with fast inverse laplace transform (FILT)

Abstract

An arterial and venous blood (or plasma) concentration difference of drugs across the lung of rats was evaluated based on the recirculatory concept. The recirculatory system is given by the combination of the transfer functions for the pulmonary and the systemic circulations and is described by a Laplace-transformed equation, i.e., an image equation. For the manipulation of the image equations, the fast inverse Laplace transform (FILT) was adopted and MULTI(FILT) was used for the simultaneous curve fitting to estimate the pharmacokinetic parameters in the recirculatory model. Metoprolol as a test drug and cephalexin as a control drug were infused respectively into the femoral vein for 30 min, and arterial and venous blood samples were collected simultaneously through the cannula at the femoral artery and at right atrium during and after the infusion. Exponential functions were assumed for the weight functions through both the pulmonary and systemic circulations. Results of the curve fitting showed that the single-pass extraction ratio through the pulmonary circulation (Ep) of metoprolol was about 0.2, whereas that of cephalexin was negligible. The mean transit times through the pulmonary circulation (tp) of metoprolol and cephalexin were both about 0.5 min, which is small. The single-pass extraction ratios through the systemic circulation (Es) of metoprolol and cephalexin were both about 0.1, and the mean transit times through the systemic circulation (ts) were 11.5 min and 8.2 min, respectively.