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Two-compartment dispersion model for analysis of organ perfusion system of drugs by fast inverse laplace transform (FILT)

  • Yoshitaka Yano
  • Kiyoshi Yamaoka
  • Yoshihiro Aoyama
  • Hisashi Tanaka
Article

Abstract

A dispersion model developed in Chromatographic theory is applied to the analysis of the elution profile in the liver perfusion system of experimental animals. The equation for the dispersion model with the linear nonequilibrium partition between the perfusate and an organ tissue is derived in the Laplace-transformed form, and the fast inverse Laplace transform (FILT) is introduced to the pharmacokinetic field for the manipulation of the transformed equation. By the analysis of the nonlinear least squares method associated with FILT, this model (two-compartment dispersion model) is compared to the model with equilibrium partition between the perfusate and the liver tissue (one-compartment dispersion model) for the outflow curves of ampicillin and oxacillin from the rat liver. The model estimation by Akaike's information criterion (AIC) suggests that the two-compartment dispersion model is more proper than the one-compartment dispersion model to mathematically describe the local disposition of these drugs in the perfusion system. The blood space in the liver, VB, and the dispersion number DN are estimated at 1.30 ml (±0.23 SD) and 0.051 (±0.023 SD), respectively, both of which are independent of the drugs. The efficiency number, RN, of ampicillin is 0.044 (±0.049 SD) which is significantly smaller than 0.704 (±0.101 SD) of oxacillin. The parameters in the two-compartment dispersion model are correlated to the recovery ratio, FH, mean transit time, ¯tH, and the relative variance, σ2/¯tH2, of the elution profile of drugs from the rat liver.

Key words

AIC rat liver perfusion FILT MULTI (FILT) one-compartment dispersion model two-compartment dispersion model ampicillin oxacillin 

Notation

A

Cross-sectional area of the blood space

C(t, z)

Concentration of drug (one-compartment dispersion model)

∼C(s, z)

Laplace transform of C(t, z)

C1(t, z)

Concentration of drug in blood space (two-compartment dispersion model)

C2(t, z)

Concentration of drug in the liver tissue (two-compartment dispersion model)

∼C1 (s, z)

Laplace transform ofC1(t, z)

D

Axial or longitudinal dispersion coefficient

Dc(=D· A2)

Corrected dispersion coefficient

DN

Dispersion number

fI(t)

Input function with respect tot

fI(z)

Input function with respect toz

FI(s)

Laplace transform of fI(t)

fs(t)

System weight function with respect tot

fs(z)

System weight function with respect to z

FH

Recovery ratio

k′

Partition ratio (distribution ratio)

k12, k21

Forward and backward partition rate constant in the central elimination two-compartment dispersion model

k12p,k21p

Forward and backward partition rate constant in the peripheral elimination two-compartment dispersion model

ke

Elimination (or irreversible transfer) rate constant

kep

Elimination rate constant in peripheral elimination model

KH

Distribution constant

L

Length of blood space in liver

M

Amount of drug injected

m

Coefficient related to the injected amount

ph

Mass transfer coefficient from perfusate to hepatic tissue

Q

Flow rate of perfusate

RN

Efficiency number

s

Laplace variable

t

Time

¯ tH

Mean transit time

υ

Linear flow velocity of the perfusate

VB(= L·A)

Blood volume (sum of the sinusoid volume and the space of Disse)

vh

Apparent volume of distribution

VH

Anatomical volume of liver tissue

z

Axial coordinate in the liver

δ(t)

Delta function

ɛ

Volume ratio of the anatomical liver tissue to the blood space

δ2

Variance of transit time

δ2/¯tH2

Relative dispersion to transit time

Partial derivatives

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Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • Yoshitaka Yano
    • 1
  • Kiyoshi Yamaoka
    • 1
  • Yoshihiro Aoyama
    • 1
  • Hisashi Tanaka
    • 1
  1. 1.Faculty of Pharmaceutical SciencesKyoto UniversityKyotoJapan

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