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

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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 drag 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 meloprolol 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 singlepass 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.

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Area under the concentration time curve

C b :

Blood concentration

C p :

Plasma concentration

CL i :

Local intrinsic clearance

E i :

Local extraction ratio (= 1−Fi)

f t(t):

Input function

f p(s):

Transfer function through the pulmonary circulation

f p(t):

Weight function through the pulmonary circulation

f s(s):

Transfer function through the systemic circulation

f s(t):

Weight function through the systemic circulation

f r(s):

Recirculatory transfer function

F 1 :

Local recovery ratio

H t :


k b :

Partition ratio of the drug between erythrocyte and plasma


Mean residence time

Q b :

Blood flow rate

Q p :

Plasma flow rate

Q p :

Effective plasma flow rate

R(= M/T) :

Infusion rate (mass/time)

s :

Laplace variable

¯t i :

Mean transit time


Infusion period

V ss, i :

Local steady-state volume of distrubution

a, v:

Arterial and venous sampling

i.a., i.v.:

Intraarterial and intravenous injectionM


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Correspondence to Kiyoshi Yamaoka.

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Yano, Y., Yamaoka, K., Yasui, H. et al. Analysis of arterial–venous blood concentration difference of drugs based on recirculatory theory with fast inverse laplace transform (FILT). Journal of Pharmacokinetics and Biopharmaceutics 19, 71–85 (1991). https://doi.org/10.1007/BF01062193

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Key words

  • recirculatory
  • FILT
  • arterial-venous concentration difference
  • metoprolol
  • cephalexin
  • local disposition
  • Laplace transform
  • pulmonary elimination