Interconnected-tubes model of hepatic elimination

Journal of Theoretical Biology

Volumn 188, Issue 1, 1997, Pages 89-101

  Anissimov, Yuri G ^a   Bracken, Anthony J ^a   Roberts, Michael S ^a  

^a UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; DISPERSION; FLOW; LIVER CLEARANCE; LIVER PERFUSION; LIVER SINUSOID; MODEL; PRIORITY JOURNAL; TUBE;

EID: 0031558477     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1006/jtbi.1997.0455     Document Type: Article

References (31)

1. ABRAMOWITZ, M. & STEGUN, I. A. (1965). Handbook of Mathematical Functions, New York: Dover Publications.
2. BASS, L. (1980). Flow dependence of first-order uptake of substances by heterogeneous perfused organs. J. theor. Biol. 86, 365-376.
3. BASS, L., BRACKEN, A. J. & BURDEN, C. J. (1983). Tracer kinetics and physiological modelling. In: Lecture Notes in Biomathematics, Vol. 48 (Lambrecht, R. M. & Rescigno, A., eds) pp. 120-201. Berlin: Springer-Verlag.
4. BASS, L., ROBINSON, P. J. & BRACKEN, A. J. (1978). Hepatic elimination of flowing substrates: The distributed model. J. theor. Biol. 72, 161-187.
5. BASS, L., ROBERTS, M. S. & ROBINSON, P. J. (1987). On the relation between extended forms of the sinusoidal perfusion and of the convection-dispersion models of hepatic elimination. J. theor. Biol. 12, 457-482.
6. CHOU, C. H., EVANS A. M., FORNASINI, G. & ROWLAND, M. (1993). Relationship between lipophilicity and hepatic dispersion and distribution for a homologous series of barbiturates in the isolated perfused in situ rat liver. Drug Metab. Disp. 21, 933-938.
7. ERDELYI, A. ET AL. (1954). Tables of Integral Transforms, Vols I. & II, New York: McGraw Hill.
8. EVANS, A. M., HUSSEIN, Z. & ROWLAND, M. (1993). Influence of albumin on the distribution and elimination kinetics of diclofenac in the isolated perfused rat liver: analysis by the impulse-response technique and the dispersion model. J. Pharm. Sci. 82, 421-428.
9. GORESKY, C. A., BACH, G. G. & NADEAU, B. E. (1973). On the uptake of materials by the intact liver: The transport and net removal of galactose. J. Clin. Invest. 52, 991-1009.
10. GORESKY, C. A., PANG, K. S., SCHWAB, A. J., BARKER III, F., CHERRY, W. F. & BACH, G. G. (1992). Uptake of a protein-bound polar compound, acetaminophen sulfate, by perfused rat liver. Hepatology 16, 173-190.
11. GRAY, M. R. & TAM, Y. K. (1987). The series-compartment model for hepatic elimination. Drug Metab. Dispos. 15, 27-31.
12. HILL, J. M. (1981). On the solution of reaction-diffusion equations. IMA J. Appl. Math. 27, 177-199.
13. HUSSEIN, Z., MCLACHLAN, A. J. & ROWLAND, M. (1994). The distribution kinetics of salicylic acid in the isolated perfused rat liver assessed using moment analysis and the two-compartment axial dispersion model. Pharm. Res. 11, 1337-1345.
14. KOO, A., LIANG, I. Y. S. & CHENG, K. K. (1975). The terminal hepatic microcirculation in the rat. Quart. J. Exp. Physiol. 60, 261-266.
15. LEVENSPIEL, O. (1976). Chemical Reaction Engineering, pp. 253-315. New York: John Wiley and Sons.
16. LUXON, B. A. & WEISIGER, R. A. (1993). Extending the multiple indicator dilution method to include slow intracellular diffusion. Math. Biosci. 113, 211-230.
17. MCNABB, A. (1985). An uncoupling procedure for a class of coupled linear partial differential equations. J. Austral. Math. Soc. Ser. B 26, 503-516.
18. MELLICK, G. D., ANISSIMOV, Y. G., ROBERTS, M. S. & BRACKEN, A. J. (1997). Metabolite mean transit times in the liver as predicted by various models of hepatic elimination. J. Pharmacokin. Biopharm. (in press).
19. MELLICK, G. D. & ROBERTS, M. S. (1996). The disposition of aspirin and salicylic acid in the isolated perfused rat liver: the effect of normal and retrograde flow on availability and mean transit time. J. Pharm. Pharmacol. 48, 738-743.
20. ROBERTS, M. S. & ROWLAND, M. (1985). Hepatic elimination -dispersion model. J. Pharm. Sci. 74, 585-587.
21. ROBERTS, M. S. & ROWLAND, M. (1986a). A dispersion model of hepatic elimination: 1. Formulation of the model and bolus considerations. J. Pharmacokin. Biopharm. 14, 227-260.
22. ROBERTS, M. S. & ROWLAND, M. (1986b). Correlation between in-vitro microsomal enzyme activity and whole organ hepatic elimination kinetics: Analysis with a dispersion model. J. Pharm. Pharmacol. 38, 177-181.
23. ROBERTS, M. S., DONALDSON, J. D. & ROWLAND, M. (1988). Models of hepatic elimination: comparison of stochastic models to describe residence time distributions and to predict the influence of drug distribution, enzyme heterogeneity and systemic recycling on hepatic elimination. J. Pharmacokin. Biopharm. 16, 41-83.
24. ROBERTS, M. S., DONALDSON, J. D. & JACKETT, D. (1989). Availability predictions by hepatic elimination models for Michaelis - Menten kinetics. J. Pharmacokin. Biopharm. 17, 687-719.
25. ROBERTS, M. S., FRASER, S., WAGNER, A. & MCLEOD, L. (1990). Residence time distributions of solutes in the perfused rat liver using a dispersion model of hepatic elimination: 1. Effect of changes in perfusate flow and albumin concentration on sucrose and taurocholate. J. Pharmacokin. Biopharm. 18, 209-234.
26. ROWLAND, M., BENET, L. Z. & GRAHAM, G. G. (1973). Clearance concepts in pharmacokinetics. J. Pharmacokin. Biopharm. 1, 123-136.
27. SCHWAB, A. J., BARKER III, F., GORESKY, C. A. & PANG, K. S. (1990) Transfer of enalaprilat across rat liver cell membranes is barrier limited. Am. J. Physiol. 258, G461-G475.
28. TAYLOR, G. I. (1953). Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. Roy. Soc. Lond. A 219, 186-203.
29. WEISIGER, R. A., MENDEL, C. M. & CAVALIERI, R. R. (1986). The hepatic sinusoid is not well-stirred: Estimation of the degree of axial mixing by analysis of lobular concentration gradients formed during uptake of thyroxine by the perfused rat liver. J. Pharm. Sci. 75, 233-237.
30. WINKLER, K., BASS, L., KEIDING, S. & TYGSTRUP, N. (1974). The effect of hepatic perfusion on the assessment of kinetic constants in regulation of hepatic metabolism. In: A. Benzon Symposium VI. (Lundquist, F. & Tygstrup, N., eds) pp. 797-807. Copenhagen: Munksgaard.
31. YANO, Y., YAMAOKA, K., AOYAMA, Y. & TANAKA, H. (1989). Two-compartment dispersion model for analysis of organ perfusion system of drugs by fast inverse Laplace transform (FILT). J. Pharmacokin. Biopharm. 17, 179-202.