Abstract
A drug tracer is most commonly applied to get information about the pharmacokinetics (PK) of a drug that is not confounded by an endogenously produced drug or an unknown drug input. An equally important use of tracers that has not been fully recognized is their use in the study of nonlinear PK behavior. In the present study a system analysis is applied to examine the interaction between drug molecules characteristic and intrinsic to any nonlinear process which enables the nonlinearity to be identified and modeled using a drug tracer. The proposed Tracer Interaction Methodology (TIM) forms a general developmental framework for novel methods for examining nonlinear phenomena. Such methods are potentially much more sensitive and accurate than previous methods not exploiting the tracer principle. The methodology proposed is demonstrated in a simulation study and with real data in a specific implementation aimed at determining the Michaelis-Menten (MM) parameters of nonlinear drug elimination while accounting for drug distribution effects. The simulation study establishes that the TIM-based, MM parameter evaluation produces substantially more accurate parameter estimates than a nontracer (NT) conventional method. In test simulations the accuracy of the TIM was in many cases an order of magnitude better than the NT method without evidence of bias. The TIM-based, MM parameter estimation methodology proposed is ideally suitable for dynamic, non-steady-state conditions. Thus, it offers greater applicability and avoids the many problems specific to steady state evaluations previously proposed. TIM is demonstrated in an evaluation of the nonlinear elimination behavior of erythropoietin, a process that likely takes place via receptor-based endocytosis. Due to its high sensitivity, accuracy, and intrinsic nonlinearity the TIM may be suitable for in-vivo studies of receptor binding of the many biotechnology produced peptide drugs and endogenous compounds displaying receptor-mediated elimination.
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REFERENCES
P. Veng-Pedersen. Linear and nonlinear system approaches in pharmacokinetics: how much do they have to offer? I. General considerations. J. Pharmacokin. Biopharm. 16:413–472 (1988).
D. J. Cutler. Linear systems analysis in pharmacokinetics. J. Pharmacokin. Biopharm. 6:265–282 (1978).
C. D. Thron. Linearity and superposition in pharmacokinetics. Pharmacol. Rev. 26:13–21 (1974).
P. Veng-Pedersen. Theorems and implications of a model independent elimination/distribution function decomposition of linear and some nonlinear drug dispositions. I. Derivations and theoretical analysis. J. Pharmacokin. Biopharm. 12:627–648 (1984).
P. Veng-Pedersen. Drug absorption evaluation in the presence of changes in clearance—An algorithm and computer-program for deconvolution with exact clearance correction. Biopharm. Drug Dispos. 8:185–203 (1987).
P. Veng-Pedersen. Curve fitting and modeling in pharmacokinetics and some practical experiences with NONLIN and a new program FUNFIT. J. Pharmacokin. Biopharm. 5:513–531 (1977).
M. F. Hutchinson and F. R. deHoog. Smoothing noise data with spline functions. Numer. Math. 47:99–106 (1985).
P. Craven and G. Wahba. Smoothing noisy data with spline functions. Numer. Math. 31:377–403 (1979).
J. A. Widness, R. L. Schmidt, N. Modi, P. Veng-Pedersen, and S. T. Sawyer. A sensitive and specific erythropoietin immunoprecipitation assay; Application to pharmacokinetic studies, J. Lab. Clin. Med. 119:285–294 (1992).
S. T. Sawyer. Receptors for erythropoietin: Distribution, structure, and role in receptor-mediated endocytosis in erythroid cells. In J. R. Harris (ed.), Blood Cell Biochemistry, Plenum Press, New York, 1990, pp. 365–402.
J. A. Widness, J. F. Garcia, G. K. Clemons, R. L. Cavalieri, J. B. Susa, K. A. Teramo, et al. Temporal response of immunoreactive erythropoietin to acute hypoxemia in the sheep fetus. Pediat. Res. 20:15–19, (1986).
J. C. Egrie, P. M. Cotes, J. Lane, R. E. G. Das, and R. C. Tam. Development of radioimmunoassays for human erythropoietin using recombinant erythropoietin as tracer and immunogen. J. Immunol. Meth. 99:235–241 (1987).
K. K. Flaharty, J. Caro, A. Erslev, J. J. Whatlen, E. M. Morris, T. D. Bjornsson, et al. Pharmacokinetics and erythropoietic response to human recombinant erythropoietin in healthy men. Clin. Pharmacol. Ther. 47:557–564 (1990).
J. Kochling. Pharmacokinetics and Pharmacodynamics of Recombinant Human Erythropoietin in Haemodialysis Patients [Inaugural-Dissertation], The Free University of Berlin, Berlin, Germany, 1993, p. 107.
P. Veng-Pedersen, J. A. Widness, L. M. Pereira, C. Peters, R. L. Schmidt, and L. S. Lowe. Pharmacokinetic disposition decomposition analysis of erythropoietin in newborn lambs and human neonates: Evidence for receptor mediated elimination. Blood (submitted for publication).
J. A. Widness, P. Veng-Pedersen, C. Peters, L. M. Pereira, R. L. Schmidt, and L. S. Lowe. Erythropoietin pharmacokinetics in premature infants: Developmental, nonlinearity, and treatment effects. J. Appl. Physiol. 80:140–148 (1996).
T. M. Ludden. Nonlinear pharmacokinetics: Clinical Implications. Clin. Pharmacokin. 20:429–446 (1991).
F. Lundquist and H. Wolthers. The kinetics of alcohol elimination in man. Acta Pharmacol. Toxicol. 14:265–289 (1958).
J. G. Wagner. Properties of the Michaelis-Menten equation and its integrated form which are useful in pharmacokinetics. J. Pharmacokin. Biopharm. 1:121, 337–338 (1973).
N. Gerber and N. Wagner. Explanation of dose dependent decline of diphenylhydantoin plasma levels by fitting to the integrated form of the Michaelis-Menten equation. Res. Commun. Chem. Pathol. Pharmacol. 3:455–466 (1972).
L. K. Garrettson and W. J. Jusko. Diphenylhydantoin elimination kinetics in overdosed children. Clin. Pharmacol. Ther. 17:481–491 (1975).
P. K. Wilkinson, A. J. Sedman, E. Sakman, R. H. Earhan, D. J. Weidler, et al. Blood ethanol concentrations during and following constant-rate intravenous infusion of alcohol. Clin. Pharmacol. Ther. 19:213–223 (1976).
Y.-J. Lin, J. Weidler, D. C. Garg, and J. G. Wagner. Novel method of estimating volume of distribution of a drug obeying Michaelis-Menten elimination kinetics. J. Pharmacokin. Biopharm. 6:197–207 (1978).
A. Selen, G. L. Amidon, and P. G. Welling. Pharmacokinetics of probenecid following oral doses to human volunteers. J. Pharm. Sci. 71:1238–1242 (1982).
E. R. Garrett and W. Roth. Nonlinear pharmacokinetics of the new positive inotropic agent sulmazole in the dog. J. Pharm. Sci. 72:105–116 (1983).
A. J. Sedman and J. G. Wagner. Importance of the use of the appropriate pharmacokinetic model to analyze in vivo enzyme constants. J. Pharmacokin. Biopharm. 2:161–173 (1974).
D. D. M. Tong and C. M. Metzler. Mathematical properties of compartment models with Michaelis-Menten type elimination. Math. Biosci. 48:293–306 (1980).
C. M. Metzler and D. D. M. Tong. Computational problems of compartment models with Michaelis-Menten type elimination. J. Pharm. Sci. 70:733–737 (1981).
A. Holmberg. On the practical identifiability of microbial growth models incorporating Michaelis-Menten type nonlinearities. Math. Biosci. 62:23–43 (1982).
K. R. Godfrey and W. R. Fitch. The deterministic identifiability of nonlinear pharmacokinetic models. J. Pharmacokin. Biopharm. 12:177–191 (1984).
J. G. Wagner. A modern view of pharmacokinetics. J. Pharmacokin. Biopharm. 1:363–401 (1973).
J. A. Widness, P. Veng-Pedersen, R. L. Schmidt, L. S. Lowe, J. A. Kistard, and C. Peters. In vivo 125I-erythropoietin pharmacokinetics are unchanged following anesthesia, nephrectomy and hepatectomy in sheep. J. Pharmacol. Exp. Ther. 279:1205–1210 (1996).
S. Gammeltoft. Receptor-Mediated Endocytosis and Degradation of Polypeptide Hormones, Growth Factors, and Neuropeptides, CRC Press, Boston, 1991, chap. 5.
F. Stohlman. Observations on the physiology of erythropoietin and its role in the regulation of red cell production. Ann. N.Y. Acad. Sci. 77:710–724 (1959).
W. Jelkmann and Wiedamann. Relationships to blood hemoglobin concentration and erythrocytic activity of the bone marrow. Klin. Wochenschr. 68:403–407 (1990).
R. J. Grace, R. G. Kendall, A. E. Hartley, D. L. Barnard, and D. R. Norfolk. Changes in serum erythropoietin levels during allogeneic bone marrow transplantation. Eur. J. Haem. 47:81–85 (1991).
S. V. Davies, C. D. Fegan, R. Kendall, and I. Cavill. Serum erythropoietin during autologous bone marrow transplantation: relationship to measures of erythroid activity. Clin. Lab. Haem. 17:139–144 (1995).
V. Pavlovic-Kentera, P. Milenkovic, R. Ruvidic, V. Jovanovic, and L. Biljanovic-Paunovic. Erythropoietin in aplastic anemia. Blut 39:345–350 (1979).
R. Alexanian. Erythropoietin excretion in bone marrow failure and hemolytic anemia. J. Lab. Clin. Med. 82:438–445 (1973).
G. deKlerk, P. C. J. Rosengarten, R. J. W. M. Vet, and R. Goudsmit. Serum erythropoietin (ESF) titres in anemia. Blood 58:1164–1170 (1981).
Y. Beguin, G. K. Clemons, P. Pootrakul, and G. Fillet. Quantitative assessment of erythropoiesis and functional classification of anemia based on measurements of serum transferrin receptor and erythroipetin. Blood 81:1067–1076 (1993).
S. H. Embury, J. F. Garcia, N. Mohandas, R. Pannathru-Das, and M. R. Clark. Effects of oxygen inhalation on endogenous erythropoietin kinetics, erythropoiesis, and properties of blood cells in sickle-cell anemia. New Engl. J. Med. 311:291–295 (1984).
K.-U. Eckardt, J. Dittmer, R. Neumann, C. Bauer, and A. Kurtz. Decline of erythropoietin formation at continuous hypoxia is not due to feedback inhibition. Am. J. Physiol. 258:F1432–F1437 (1990).
T. R. Browne, D. J. Greenblatt, J. S. Harmatz, J. E. Evans, G. K. Szabo, B. A. Evans, and G. E. Schumacher. Studies with stable isotopes III: Pharmacokinetics of tracer doses of drug. J. Clin. Pharmacol. 25:59–63 (1985).
G. W. Houghton and A. Richens. Rate of elimination of tracer doses of phenytoin at different steady-state serum phenytoin concentrations in epileptic patients. Br. J. Clin. Pharmacol. 1:155–161 (1974).
E. Snoeck, P. Jacqmin, A. Van Peer, M. Danhof, K. Ver Donck, H. Van Belle, R. Woestenborghs, R. Crabbe, R. van Gool, A. Dupont, and J. Heykants. The implications of nonlinear red blood cell partitioning for the pharmacokinetics and pharmacodynamics of the nucleoside transport inhibitor draflazine. Br. J. Clin. Pharmacol. 42:605–613 (1996).
P. J. Fielder, A. L. Gurney, E. Stefanich, M. Marian, M. W. Moore, K. Carver-Moore, and F. J. DeSauvage. Regulation of thrombopoietin levels by c-mpl mediated binding to platelets. Blood 87:2154–2161 (1996).
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Veng-Pedersen, P., Widness, J.A., Wang, J. et al. A Tracer Interaction Method for Nonlinear Pharmacokinetics Analysis: Application to Evaluation of Nonlinear Elimination. J Pharmacokinet Pharmacodyn 25, 569–593 (1997). https://doi.org/10.1023/A:1025765330455
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DOI: https://doi.org/10.1023/A:1025765330455