Abstract
In this paper concepts for mathematic models in pharmacokinetics and pharmacodynamics are discussed. As far as kinetic reactions of the first or zero order are considered, a complete linear theory can be introduced for pharmacokinetics.
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References
ARIENS, E.J. (ed.): Molecular Pharmacology. Vol. I. New York 1964.
BARTHOLOMAY, A.F.: Stochastic models for chemical reactions. I.: Theory of the unimolecular reaction process. Bull. Math. Biophys. 20, 175–190 (1958).
BARTHOLOMAY, A.F.: Stochastic models for chemical reactions. II: The unimolecular rate constant. Bull. Math. Biophys. 21, 363–373 (1959).
BARTHOLOMAY, A.F.: The general catalytic queue process. In: Stochastic Models in Medicine and Biology (ed. J. Gurland). Madison 1964.
BERMAN, M., AND SCHOENFELD, R.: Invariants in experimental data and linear kinetics and the formulation of models. Journ. Appl. Physics 27, No. 11, 1161–1370 (1956).
BLISS, C.J.: The method of probits. Science 79, 38–39 and 409–410 (1934).
DELBRÜCK, M.: Statistical fluctuations in autocalatytic reactions. Journ. of Chem. Phys. 8, 120–124 (1940).
DOST, F.H.: Grundlagen der Pharmakokinetic. Stuttgarts. Thieme 1968.
DRUCKREY, H., AND KUPFMULLER, K.: Dosis und Wirkung. Aulendorf 1934.
FELLER, W.: An introduction to probability theory and its application. 2nd ed. New York: J. Wiley 1957.
GLADTKE, E., AND HATTINGBERG, H.M.: Pharmakokinetik. Berlin-Heidelberg, New York: Springer 1973.
HARRIS, T.E.: The theory of branching processes. Berlin-Göttingen-Heidelberg: Springer 1963.
HERRMANN, H.: Stochastische Modelle zum Reiz-Antwort-Prozeß der Pharmakon-Receptor-Theorie. Thesis, Abteilung für Biometrie der Medizinischen Hochschule Hannover, Hannover (1976).
HERRMANN, H.: Treffer- und Besetzungstheorie und ihre Anwendung in der Biologie. (In preparation) (1976a).
ISHIDA, K.: The probability approach in absorption processes. Nippon Kagadu Zasshi 81, 524–529 (1960).
JACQUEZ, J.A.: Compartmental analysis in biology and medicine. Amsterdam: Elsevier 1973.
KRAMERS, H.A.: Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7, 284–304 (1940).
MCQUARRIE, D. A.: Stochastic approach to chemical kinetics. Journ. Appl. Prob. 4, 413–478 (1967).
MICHAELIS, L., AND MENTEN, M.: Biochemische Zeitschrift 49, 333 (1913).
PHARMA-KODEX. Bundesverband der Pharmazeutischen Industrie e.V., Frankfurt/Main.
PREKOPA, A.: Statistical treatment of the degradation process of long chain polymers. Magyar Tud. Akad. Alkalm. Mat. Int. Közl. 2, 103–123 (1954).
RENYI, A.: Treatment of chemical reactions by means of the theory of stochastic processes. Magyar Tud. Akad. Alkalm. Mat. Int. Közl. 2, 93–101 (1954).
RESCIGNO, A., AND SEGRE, G.: Drug and Tracer Kinetics. Massachusetts: Blaisdell 1966.
ROSSUM VAN, J.M.: Die Pharmakon-Rezeptor-Theorie als Grundlage der Wirkung von Arzneimitteln. Arzneimittel-Forschung 16, 1412–1426 (1966).
SHEPPARD, C.W., AND HOUSEHOLDER, A.S.: The mathematical basis of the interpretation of tracer experiments in closed steady-state systems. Appl. Physics 22, No. 4, 510–520 (1951).
TAUTU, P.: Probability models in pharmacodynamics; a prospect. Mimeographed paper by Deutsches Krebsforschungszentrum, Heidelberg (1973).
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Feldmann, U., Schneider, B. (1976). A General Approach to Multicompartment Analysis and Models for the Pharmacodynamics. In: Berger, J., Bühler, W.J., Repges, R., Tautu, P. (eds) Mathematical Models in Medicine. Lecture Notes in Biomathematics, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93048-5_14
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DOI: https://doi.org/10.1007/978-3-642-93048-5_14
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