Summary
General equations are derived for the disposition functions of any compartment in a linear mammillary model, when the system input occurs into a peripheral compartment. Laplace transforms and matrix algebra are used to derive these equations. Equations describing the time-course of a drug in any compartment are readily obtainable using disposition and input functions.
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Beckett, A.H., Salmon, J.A.: Pharmacokinetics of absorption, distribution and elimination of fenfluramine and its main metabolite in man. J. Pharm. Pharmacol.24, 108–114 (1972)
Benet, L.Z.: General treatment of linear mammillary models with elimination from any compartment as used in pharmacokinetics. J. pharm. Sci.61, 536–541 (1972)
Bellman, R.: Introduction to Matrix Analysis, p. 304. London: McGraw-Hill Co. Inc. 1960
Doetsch, G.: Guide to the applications of Laplace transforms, p. 193. London: D. Van Nostrand Co. Ltd. 1961
Ewy, G.A., Kapadia, G.G., Yao, L., Lullin, M., Marcus, F.E.: Digoxin metabolism in the elderly. Circulation39, 449–453 (1969)
Garret, E.R., Alway, C.D.: Proc. IIIrd Intern. Congr. Chemother. p. 1666. Stuttgart: Georg Thieme 1963
—— and Lambert, H.J.: Pharmacokinetics of trichloroethanol and metabolites and interconversions among variously referenced pharmacokinetic parameters. J. pharm. Sci.62, 550–572 (1973)
Gibaldi, M., Feldman, S.: Pharmacokinetic basis for the influence of route of administration on the area under the plasma concentration-time curve. J. pharm. Sci.58, 1477–1488 (1969)
Levy, G., Gibaldi, M., Jusko, W.J.: Multi-compartment pharmacokinetic models and pharmacological effects. J. pharm. Sci.58, 422–424 (1969)
Loo, T.L., Tanner, B.B., Housholder, G.E., Shepard B.: Some pharmacokinetic aspects of 5-(dimethyl-triazeno)-imidazole-4-carboxamide in dogs. J. pharm. Sci.57, 2126–2131 (1968)
Nagashima, R., Levy, G., O'Reilly, R.A.: Comparative pharmacokinetics of coumarin anticoagulants IV. J. pharm. Sci.57, 1888–1895 (1968)
Rescigno, A.: On some topological properties of the systems of compartments. Bull. math. Biophys.26, 31–38 (1964)
—— and Segre, G.: Drug and tracer kinetics, Chap. 4. New York: Blaisdell 1966
—— —— On some metric properties of the systems of compartments. Bull. math. Biophys.27, 315–323 (1965)
Riggs, D.S.: Control theory and physiological feedback mechanisms, chap. 3. Baltimore: Williams & Wilkins 1970
Rowland, M., Riegelman, S.: Pharmacokinetics of acetylsalicyclic acid and salicylic acid after intravenous administration in man. J. pharm. Sci.57, 1314–1319 (1968)
Vaughan, D.P., Beckett, A.H.: An analysis of the inter-subject variation in the metabolism of pentazocine. J. Pharm. Pharmacol.26, 789–798 (1974)
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Vaughan, D.P., Mallard, D.J.H., Trainor, A. et al. General pharmacokinetic equations for linear mammillary models with drug absorption into peripheral compartments. Eur J Clin Pharmacol 8, 141–148 (1975). https://doi.org/10.1007/BF00561564
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DOI: https://doi.org/10.1007/BF00561564