Advertisement

Modeling of Hepatic Elimination and Organ Distribution Kinetics with the Extended Convection-Dispersion Model

  • Michael S. Roberts
  • Yuri G. Anissimov
Article

Abstract

The conventional convection-dispersion (also called axial dispersion) model is widely used to interrelate hepatic availability (F) and clearance (Cl) with the morphology and physiology of the liver and to predict effects such as changes in liver blood flow on F and Cl. An extended form of the convection-dispersion model has been developed to adequately describe the outflow concentration–time profiles for vascular markers at both short and long times after bolus injections into perfused livers. The model, based on flux concentration and a convolution of catheters and large vessels, assumes that solute elimination in hepatocytes follows either fast distribution into or radial diffusion in hepatocytes. The model includes a secondary vascular compartment, postulated to be interconnecting sinusoids. Analysis of the mean hepatic transit time (MTT) and normalized variance (CV2) of solutes with extraction showed that the discrepancy between the predictions of MTT and CV2for the extended and unweighted conventional convection-dispersion models decreases as hepatic extraction increases. A correspondence of more than 95% in F and Cl exists for all solute extractions. In addition, the analysis showed that the outflow concentration–time profiles for both the extended and conventional models are essentially identical irrespective of the magnitude of rate constants representing permeability, volume, and clearance parameters, providing that there is significant hepatic extraction. In conclusion, the application of a newly developed extended convection-dispersion model has shown that the unweighted conventional convection-dispersion model can be used to describe the disposition of extracted solutes and, in particular, to estimate hepatic availability and clearance in both experimental and clinical situations.

convection-dispersion model hepatic elimination extended convection-dispersion model interconnecting sinusoids inverse Gaussian distribution secondary vascular compartment hepatic disposition 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    M. Rowland, L. Z. Benet, and G. G. Graham. Clearance concepts in pharmacokinetics. J. Pharmacokin. Biopharm. 1:123–136 (1973).CrossRefGoogle Scholar
  2. 2.
    K. Winkler, L. Bass, S. Keiding, and N. Tygstrup. The effect of hepatic perfusion on the assessment of kinetic constants in regulation of hepatic metabolism. In F. Lundquist and N. Tygstrup (eds.), A. Benzon Symposium VI, Munksgaard, Copenhagen, 1974, pp. 797–807.Google Scholar
  3. 3.
    J. Burggraaf, H. C. Schoemaker, and A. F. Cohen. Assessment of changes in liver blood flow after food intake-comparison of ICG clearance and echo-Doppler. Br. J. Clin. Pharmacol. 42:499–502 (1996).PubMedCentralPubMedCrossRefGoogle Scholar
  4. 4.
    J. Burggraaf, R. C. Schoemaker, J. M. Kroon, and A. F. Cohen. The influence of nifedipine and captopril on liver blood flow in healthy subjects. Br. J. Clin. Pharmacol. 45:447–451 (1998).PubMedCentralPubMedCrossRefGoogle Scholar
  5. 5.
    G. R. Wilkinson and D. G. Shand. Commentary: a physiological approach to hepatic drug clearance. Clin. Pharmacol. Ther. 18:377–390 (1975).PubMedGoogle Scholar
  6. 6.
    M. S. Roberts and M. Rowland. Hepatic elimination—dispersion model. J. Pharm. Sci. 74:585–587 (1985).PubMedCrossRefGoogle Scholar
  7. 7.
    M. S. Roberts and M. Rowland. A dispersion model of hepatic elimination: 1. Formulation of the model and bolus considerations. J. Pharmacokin. Biopharm. 14:227–260 (1986).CrossRefGoogle Scholar
  8. 8.
    M. S. Roberts, J. D. Donaldson, and M. Rowland. 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 (1988).CrossRefGoogle Scholar
  9. 9.
    M. S. Roberts and M. Rowland. A dispersion model of hepatic elimination: 2. Steady-state considerations. Influence of blood flow, protein binding and hepatocellular enzymatic activity. J. Pharmacokin. Biopharm. 14:261–288 (1986).CrossRefGoogle Scholar
  10. 10.
    M. S. Roberts and M. Rowland. A dispersion model of hepatic elimination: 3. Application to metabolite formation and elimination kinetics. J. Pharmacokin. Biopharm. 14:289–307 (1986).CrossRefGoogle Scholar
  11. 11.
    M. S. Roberts and M. Rowland. Correlation between in-vitro microsomal enzyme activity and whole organ hepatic elimination kinetics: Analysis with a dispersion model. J. Pharm. Pharmacol. 38:117–181 (1986).CrossRefGoogle Scholar
  12. 12.
    M. S. Roberts, J. D. Donaldson, and D. Jackett. Availability predictions by hepatic elimination models for Michaelis-Menten kinetics. J. Pharmacokin. Biopharm. 17:687–719 (1989).CrossRefGoogle Scholar
  13. 13.
    L. Bass, M. S. Roberts, and P. J. Robinson. On the relation between extended forms of the sinusoidal perfusion and of the convection-dispersion models of hepatic elimination. J. Theoret. Biol. 126:457–482 (1987).CrossRefGoogle Scholar
  14. 14.
    P. J. Robinson, L. Bass, S. M. Pond, M. S. Roberts, and J. G. Wagner. Clinical applicability of current pharmacokinetic models: splanchnic elimination of 5-fluorouracil in cancer patients. J. Pharmacokin. Biopharm. 16:229–249 (1988).CrossRefGoogle Scholar
  15. 15.
    T. Iwatsubo, H. Suzuki, N. Shimada, K. Chiba, T. Ishizaki, C. E. Green, C. A. Tyson, T. Yokoi, T. Kamataki, and Y. Sugiyama. Prediction of in vivo hepatic metabolic clearance of YM796 from in vitro data by use of human liver microsomes and recombinant P-450 isozymes. J. Pharmacol. Exp. Ther. 282:909–919 (1997).PubMedGoogle Scholar
  16. 16.
    Y. Yano, K. Yamaoka, Y. Aoyama, and H. Tanaka. Two-compartment dispersion model for analysis of organ perfusion system of drugs by fast inverse Laplace transform (FILT). J. Pharmacokin. Biopharm. 17:179–202 (1989).CrossRefGoogle Scholar
  17. 17.
    A. M. Evans, Z. Hussein, and M. Rowland. A two-compartment dispersion model describes the hepatic outflow profile of diclofenac in the presence of its binding protein. J. Pharm. Pharmacol. 43:709–714 (1991).PubMedCrossRefGoogle Scholar
  18. 18.
    M. S. Roberts, S. Fraser, A. Wagner, and L. McLeod. 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 (1990).CrossRefGoogle Scholar
  19. 19.
    L. N. Ballinger, S. E. Cross, and M. S. Roberts. Availability and mean transit times of phenol and its metabolites in the isolated perfused rat liver: normal and retrograde studies using tracer concentrations of phenol. J. Pharm. Pharmacol. 47:949–956 (1995).PubMedCrossRefGoogle Scholar
  20. 20.
    B. A. Luxon and R. A. Weisiger. Extending the multiple indicator dilution method to include slow intracellular diffusion. Math. Biosci. 113:211–230 (1993).PubMedCrossRefGoogle Scholar
  21. 21.
    L. P. Rivory, M. S. Roberts, and S. M. Pond. Axial tissue diffusion can account for the disparity between current models of hepatic elimination for lipophilic drugs. J. Pharmacokin. Biopharm. 20:19–61 (1992).CrossRefGoogle Scholar
  22. 22.
    G. D. Mellick, Y. G. Anissimov, A. J. Bracken, and M. S. Roberts. Metabolite mean transit times in the liver as predicted by various models of hepatic elimination. J. Pharmacokin. Biopharm. 25:477–505 (1997).CrossRefGoogle Scholar
  23. 23.
    D. Y. Hung, G. D. Mellick, Y. G. Anissimov, M. Weiss, and M. S. Roberts. Hepatic structure-pharmacokinetic relationships: the hepatic disposition and metabolite kinetics of a homologous series of O-acyl derivatives of salicylic acid. Br. J. Pharmacol. 124:1475–1483 (1998).PubMedCentralPubMedCrossRefGoogle Scholar
  24. 24.
    D. Y. Hung, G. D. Mellick, Y. G. Anissimov, M. Weiss, and M. S. Roberts. Hepatic disposition and metabolite kinetics of a homologous series of diflunisal esters. J. Pharm. Sci. 87:943–951 (1998).PubMedCrossRefGoogle Scholar
  25. 25.
    C. H. Chou and M. Rowland. Effect of altered tissue binding on the disposition of barbital in the isolated perfused rat liver: application of the axial dispersion model. J. Pharm. Sci. 86:1310–1314 (1997).PubMedCrossRefGoogle Scholar
  26. 26.
    M. Weiss, C. Stedtler, and M. S. Roberts. On the validity of the dispersion model of hepatic drug elimination when intravascular transit time densities are long-tailed. Bull. Math. Biol. 59:911–929 (1997).PubMedCrossRefGoogle Scholar
  27. 27.
    M. Weiss and M. S. Roberts. Tissue distribution kinetics as determinant of transit time dispersion of drugs in organs: application of a stochastic model to the rat hindlimb. J. Pharmacokin. Biopharm. 24:173–196 (1996).CrossRefGoogle Scholar
  28. 28.
    R. E. Oliver, A. C. Heatherington, A. F. Jones, and M. Rowland. A physiologically based pharmacokinetic model incorporating dispersion principles to describe solute distribution in the perfused rat hindlimb preparation. J. Pharmacokin. Biopharm. 25:389–412 (1997).CrossRefGoogle Scholar
  29. 29.
    A. J. Schwab, W. Geng, and K. S. Pang. Application of the dispersion model for description of the outflow dilution profiles of noneliminated reference indicators in rat liver perfusion studies. J. Pharmacokin. Biopharm. 26:163–181 (1998).CrossRefGoogle Scholar
  30. 30.
    C. A. Goresky, G. C. Bach, and B. E. Nadeau. On the uptake of materials by the intact liver. The transport and net removal of galactose. J. Clin. Invest. 52:991–1009 (1973).PubMedCentralPubMedCrossRefGoogle Scholar
  31. 31.
    B. A. Luxon, D. C. Holly, M. T. Milliano, and R. A. Weisiger. Sex differences in multiple steps in hepatic transport of palmitate support a balanced uptake mechanism. Am. J. Physiol. 274:G51–61 (1998).Google Scholar
  32. 32.
    A. Kreft and A. Zuber. On the physical meaning of the dispersion equation and its solutions for different initial and boundary conditions. Chem. Eng. Sci. 33:1471–1480 (1978).CrossRefGoogle Scholar
  33. 33.
    G. F. Froment and K. B. Bischoff. Chemical Reactor Analysis and Design, John Wiley, New York, 1989.Google Scholar
  34. 34.
    P. V. Danckwerts. Continuous flow systems: distribution of residence times. Chem. Eng. Sci. 2:1–13 (1953).CrossRefGoogle Scholar
  35. 35.
    Y. S. Choe, I. S. Kang, and K. S. Chang. A study of the dynamic behaviour of the dispersion-type tubular reactor models. Korean J. Chem. Eng. 15:95–98 (1998).CrossRefGoogle Scholar
  36. 36.
    M. T. van Genuchten and J. C. Parker. Boundary conditions for displacement experiments through short laboratory soil columns. Soil Sci. Soc. Am. J. 48:703–708 (1984).CrossRefGoogle Scholar
  37. 37.
    R. D. Purves. Accuracy of numerical inversion of Laplace transforms for pharmacokinetic parameter estimation. J. Pharm. Sci. 84:71–74 (1995).PubMedCrossRefGoogle Scholar
  38. 38.
    A. Koo, I. Y. Liang, and K. K. Cheng. The terminal hepatic microcirculation in the rat. Quart. J. Exp. Physiol. Cogn. Med. Sci. 60:261–266 (1975).Google Scholar
  39. 39.
    W. Geng, A. J. Schwab, T. Horie, C. A. Goresky, and K. S. Pang. Hepatic uptake of bromosulfophthalein-glutathione in perfused Eisai hyperbilirubinemic mutant rat liver: a multiple-indicator dilution study. J. Pharmacol. Exp. Ther. 284:480–492 (1998).PubMedGoogle Scholar
  40. 40.
    A. J. Schwab, F. D. Barker, C. A. Goresky, and K. S. Pang. Transfer of enalaprilat across rat liver cell membranes is barrier limited. Am. J. Physiol. 258:G461–475 (1990).PubMedGoogle Scholar
  41. 41.
    K. S. Pang, and M. Rowland. Hepatic clearance of drugs. I. Theoretical considerations of a “well-stirred” model and a “parallel tube” model. Influence of hepatic blood flow, plasma and blood cell binding, and the hepatocellular enzymatic activity on hepatic drug clearance. J. Pharmacokin. Biopharm. 5:625–653 (1977).CrossRefGoogle Scholar
  42. 42.
    A. W. Wolkoff, C. A. Goresky, J. Sellin, Z. Gatmaitan, and I. M. Arias. Role of ligandin in transfer of bilirubin from plasma into liver. Am. J. Physiol. 236:E638–648 (1979).PubMedGoogle Scholar
  43. 43.
    Z. Hussein, A. J. McLachlan, and M. Rowland. 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 (1994).PubMedCrossRefGoogle Scholar
  44. 44.
    C. H. Chou, A. M. Evans, G. Fornasini, and M. Rowland. Relationship between lipophilicity and hepatic dispersion and distribution for a homologous series of barbiturates in the isolated perfused in situ rat liver. Drug Metab. Dispos. 21:933–938 (1993).PubMedGoogle Scholar
  45. 45.
    A. M. Evans, Z. Hussein, and M. Rowland. 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 (1993).PubMedCrossRefGoogle Scholar
  46. 46.
    J. M. Diaz-Garcia, A. M. Evans, and M. Rowland. Application of the axial dispersion model of hepatic drug elimination to the kinetics of diazepam in the isolated perfused rat liver. J. Pharmacokin. Biopharm. 20:171–193 (1992).CrossRefGoogle Scholar
  47. 47.
    R. G. Tirona, A. J. Schwab, W. Geng, and K. S. Pang. Hepatic clearance models: comparison of the dispersion and Goresky models in outflow profiles from multiple indicator dilution rat liver studies. Drug Metab. Dispos. 26:465–475 (1998).PubMedGoogle Scholar
  48. 48.
    J.-Y. Parlange, J. L. Starr, M. T. van Genuchten, D. A. Barry, and J. C. Parker. Exit condition for miscible displacement experiments. Soil Sci. 153:165–171 (1992).CrossRefGoogle Scholar
  49. 49.
    J. C. Parker. Analysis of solute transport in column tracer studies. Soil Sci. Soc. Am. J. 48:719–724 (1984).CrossRefGoogle Scholar
  50. 50.
    Y. G. Anissimov, A. J. Bracken, and M. S. Roberts. Interconnected-tubes model of hepatic elimination. J. Theoret. Biol. 188:89–101 (1997).CrossRefGoogle Scholar
  51. 51.
    C. A. Goresky. A linear method for determining liver sinusoidal and extravascular volumes. Am. J. Physiol. 204:626–640 (1963).PubMedGoogle Scholar
  52. 52.
    C. A. Goresky. Kinetic interpretation of hepatic multiple-indicator dilution studies. Am. J. Physiol. 245:G1–12 (1983).PubMedGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1999

Authors and Affiliations

  1. 1.Department of MedicineUniversity of Queensland, Princess Alexandra HospitalWoolloongabbaAustralia;

Personalised recommendations