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Wachstumskinetik

Part of the book series: Medizinische Informatik und Statistik ((MEDINFO,volume 11))

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Literaturhinweise

  1. Anderson, R.M. (1976): Some simple models of the population dynamics of euraryotic parasites. Lecture Notes Biomathematics, Springer, 11, 16–57.

    Google Scholar 

  2. Andreef, M. (1977): Zellkinetik des Tumorwachstums. Thieme Copythek, Stuttgart.

    Google Scholar 

  3. Ashihara, T. (1973): Computer optimization of the fraction of labeled mitoses analysis using the fast Fourier Transformation. Cell. Tissue Kinet. 6, 447–453.

    Google Scholar 

  4. Bailey, N.T.J. (1975): The mathematical theory of infections diseases and its applications. Griffin, London, 2nd ed.

    Google Scholar 

  5. Barrett, J.C. (1966): A mathematical model for the mitotic cycle and its application to the interpretation of percentage labeled mitoses data. J. Nat. Cancer Inst. 37, 443–450.

    Google Scholar 

  6. Barrett, J.C. (1974): Parity models of cell proliferation. J. theory. Biol. 44, 319–336.

    Google Scholar 

  7. Bartlett, M.S. and Hiorus, R.W. (Ed.) (1973): The mathematical theory of the dynamics of biological populations. Academic Press, London.

    Google Scholar 

  8. Bellman, R. and Harris, Th. (1948): On the theory of age-dependent stochastic branching processes. PNAS 34, 601–604.

    Article  Google Scholar 

  9. Bellman, R. and Cooke, K.L. (1963): Differential-difference equations. Academic Press, New York.

    MATH  Google Scholar 

  10. Berkson, J. (1944): Application of the logistic function to bioassay. J. Amer. Stat. Ass. 39, 357–365.

    Google Scholar 

  11. Bharucha-Reid, A.T. (1960): Elements of the theory of Markov Processes and their applications. McGraw Hill, New York.

    MATH  Google Scholar 

  12. Brockwell, P.J.; Trucco, E. and Frey, R.J.M. (1972): The determination of cell cycle parameters from measurements of the fraction of labeled mitoses. Bull. Math. Biophys. 34, 1–12.

    Google Scholar 

  13. Bundesministerium für Gesundheit (1968): Das Gesundheitswesen der Bundesrepublik Deutschland. Kohlhammer, Stuttgart, Bd. I-III.

    Google Scholar 

  14. Chiang, C.L. (1968): Introduction to stochastic processes in Biostatistics. Wiley, New York.

    MATH  Google Scholar 

  15. Cox, D.R. (1970): The analysis of binary data. Methuen, London.

    MATH  Google Scholar 

  16. Deakin, A.S. (1975): Model for the growth of a solid in vitro tumor. Growth 39, 159–165.

    Google Scholar 

  17. Dietz, K. (1976): The transmission dynamics of some helmintic diseases. Proc. 9th Int. Biometric Conf. Boston, 2, 175–188.

    Google Scholar 

  18. Dietz, K. (1976): The influence of infections diseases under the influence of seasonal fluctuations. Lecture Notes Biomathematics, 11, 1–15.

    Article  Google Scholar 

  19. Dombernowsky, P.; Bichez, P. and Hartmann, N.R. (1973): Cytokinetic analysis of the JB-1 ascites tumor at different stages of growth. Cell Tissue Kinet. 6, 347–357.

    Google Scholar 

  20. Dost, F.H. (1968): Grundlagen der Pharmakokinetik. Georg Thieme, Stuttgart, 2. Auflage (1. Aufl. 1953 ).

    Google Scholar 

  21. Doyle, J.T.; Wilson, J.S. and Lépine, Ch. (1953): An evaluation of the measurement of the cardiac output and of the so called pulmonary blood volume by the dye-dilution method. J.Labor. Clin. Medicine, St. Louis, vol. 41, 1, 29–39.

    Google Scholar 

  22. Dubin, N. (1976): A stochastic model for immunological feedback in carcinogenesis. Lecture Notes Biomathematics, Springer, No. 9.

    Book  Google Scholar 

  23. Feichtinger, G. (1971): Stochastische Modelle demographischer Prozesse. Lecture Notes in Operations Research and Mathematical Systems, Springer.

    Google Scholar 

  24. Feichtinger, G. und DeistZer, M. (1973): Bemerkungen über lineare Modelle der Populationsdynamik. Methods of Operations Research, Hain, Meisenheim, 15, 40–62.

    Google Scholar 

  25. Feldmann, U. (1973): Nichtlineare diskrete Approximation mit Lösungen von Operatorgleichungen und ihre Anwendung auf pharmakokinetische Modelle. Dissertation, TU Hannover.

    Google Scholar 

  26. Feldmann, U. und Schneider, B. (1976): A general approach to multicompartment analysis and models for the pharmacodynamics. Lecture Notes Biomathematics, Springer, No. 11, 243–281.

    Google Scholar 

  27. Feldmann, U.; Hagemann, G. und Renner, H. (1976): Zellpopulationskinetik in Experiment und Klinik. Vorlesung Nr. 335, gehalten an der Medizinischen Hochschule Hannover WS 76 /77.

    Google Scholar 

  28. Feller, W. (1939): Die Grundlagen der Volterraschen Theorie des Kampfes ums Dasein in wahrscheinlichkeitstheoretischer Behandlung. Acta Biotheoretica 5, 11–40.

    Article  MathSciNet  Google Scholar 

  29. Feller, W. (1941): On the integral equation of renewal theory. Ann. Math. Statist., 12, 243–267.

    Google Scholar 

  30. Feller, W. (1957): An introduction to the probability theory and its applications. Wiley, New York, Vol. I/II.

    Google Scholar 

  31. Fisz, M. (1971): Wahrscheinlichkeitsrechnung und mathematische Statistik. VEB Deutscher Verlag der Wissenschaften, Berlin.

    MATH  Google Scholar 

  32. Foerster, H. v. (1959): Some remarks on changing populations. In The Kinetics of Cellular Proliferation“. Editor: Stohlmann, T. Grune and Stratton, 382–402.

    Google Scholar 

  33. Galton, F. and Watson, H.W. (1875): On the probability of the extinction of families. J. Anthropol. Soc. London, 4, 138–144.

    Google Scholar 

  34. Gilbert, C.W. (1972): The labeled mitoses curve and the estimation of the parameters of the cell cycle. Cell Tissue Kinet., 5, 53–63.

    Google Scholar 

  35. Hagemann, G. (1973): Reproduktiv-Tod, Interphasen-Tod und Populationskinetik überlebender Hamsterzellen in vitro während 48 Stunden nach Röntgenstrahlendosen bis 800 Rad. Strahlentherapie 145, 4, 456–473.

    Google Scholar 

  36. Hagemann, G. (1974): Persönliche Mitteilung. Medizinische Hochschule Hannover, Department Radiologie.

    Google Scholar 

  37. Hagemann, G. (1976): Reproduktivtod und Populationskinetik überlebender Hamsterzellen in vitro während 48 Stunden nach Röntgenstrahlendosen bis 800 Rad (II. Mitteilung). Strahlentherapie 151, 2, 118–131.

    Google Scholar 

  38. Hahn, G.M. (1967): Cellular kinetics, cell cycles and cell killing. Bull. Math. Biophysics 4, 1–14.

    Google Scholar 

  39. Hahn, G.M. (1970): A formalism describing the kinetics of some mammalian cell populations. Math. Biosciences 6, 295–304.

    Google Scholar 

  40. Harris, Th. (1963): The theory of branching processes. Springer, Prentiss-Hall.

    Book  MATH  Google Scholar 

  41. Hartwich, G. (ed) (1976): Synchronisationsbehandlung maligner Tumore. Perimed. Verlag, Dr.med. Straube, Erlangen.

    Google Scholar 

  42. Heiden, U. An der (1977): Differentialgleichungen mit Verzögerungen in der Biologie. Vortrags-Manuskript, 23. Biometrisches Kolloquium, Nürnberg 1977 (erscheint demnächst).

    Google Scholar 

  43. Hirsch, H.R. and EngeZberg, J. (1966): Decay of cell synchronization: solutions of the cell-growth equation. Bull. Math. Biophysics 28, 391–409.

    Google Scholar 

  44. Howard, A. and Pelc, S.R. (1953): Synthesis of desoxyribonucleic acid in normal and irradiated cells and its relation to chromosome breakage. Herredity 6, Suppl. 261–273.

    Google Scholar 

  45. Hughes, W.H. (1955): The inheritance of differences in growth rate in Escherichia coli. J. Gen. Microbiol. 12, 265–272.

    Google Scholar 

  46. Itô, K. (1951): On stochastic differential equations. Mem. Amer. Math. Soc. No. 4.

    Google Scholar 

  47. Jagers, P. (1975): Branching processes with biological applications. Wiley, New York.

    MATH  Google Scholar 

  48. Josifescu, M. and Tautu, P. (1973): Stochastic processes and applications in Biology and Medicine. Springer, Heidelberg.

    Google Scholar 

  49. Keiding, N. (1976): Population growth and branching processes in random invironments. Proc. 9th Int. Biometric Conf. Boston, 2, 149–165.

    Google Scholar 

  50. Keyfitz, N. (1968): Introduction to the mathematics of population. Addison-Wesley, Reading Mass.

    Google Scholar 

  51. Killander, D. and Zetterberg, A. (1965): The quantitative cytochemical investigation of the relationship between cell mass and initiation of DNA synthesis in mouse fibroblast in vitro. Exp. Cell Res. 40, 12–20.

    Google Scholar 

  52. Kretschmann, H.J. und Wingert, F. (1971): Computeranwendungen bei Wachstumsproblemen in Biologie und Medizin. Springer, Heidelberg.

    Book  Google Scholar 

  53. Kubitschek, H.E. (1962): Normal distribution of cell generation rate. Exp. Cell Res. 26, 439.

    Google Scholar 

  54. Kubitschek, H.E. (1967): Cell generation times; ancestral and internal controls. Proc. 5th Berkeley Symp. Math. Statist. Prob. 4, 549–572.

    Google Scholar 

  55. Kubitschek, H.E. (1971): The distribution of cell generation times. Cell Tissue Kinet. 4, 113–122.

    Google Scholar 

  56. LaZa, P.K. and Patt, H.M. (1966): Cytokinetic analysis of tumor growth. Proc. Nat. Acad. Sci. USA, 1735–1741.

    Google Scholar 

  57. Lang, W.; Herrmann, H. and Georgii, A. (1975): Analysis of continuous labeling data by a simple stochastic method. In “Mathematical models in cell kinetics”. European. Press Medikon, Ghent Belgium, 37–39.

    Google Scholar 

  58. Lang, W.; Zobl, H. und Georgii, A. (1978): The effect of neonatal thymectomy on the growth kinetics of a virus-induced renal sarcoma of the rat. Europ. J. Cancer, 14, 431–437.

    Google Scholar 

  59. Lang, W. (1976): Persönliche Mitteilung. Medizinische Hochschule Hannover, Department für Pathologie.

    Google Scholar 

  60. Lebowitz, J.L. and Rubinow, S.I. (1974): The theory of the age and generation time distribution of a microbial population. J. Math. Biology 1, 17–36.

    Google Scholar 

  61. Lefkovitch, L.P. (1965): An extension of the use of matrices in population mathematics. Biometrics 21, 1–18.

    Article  Google Scholar 

  62. Lefkovitch, L.P. (1966): A population growth model incorporation delayed responses. Bull. Math. Biophysics 28, 219–233.

    Google Scholar 

  63. Leslie, P.H. (1945): On the use of matrices in certain population mathematics. Biometrika 33, 183–212.

    Article  MathSciNet  MATH  Google Scholar 

  64. Lotka, A.J. (1925): Elements of physical biology. Williams and Wilkins Comp., Baltimore.

    MATH  Google Scholar 

  65. Lotka, A.J. (1956): Elements of mathematical biology. Wiley, New York.

    MATH  Google Scholar 

  66. Macdonald, P.D.M. (1970): Statistical influence from the fraction labeled mitoses curve.Biometrika 57, 489–503.

    MathSciNet  MATH  Google Scholar 

  67. Malthus, T.R. (1798): An essay on the principle of population,as it affects the future improvements of society, with remarks on the speculations of Mr. Godwin, Mr. Condorcet and other writers. John Murray, London 1st. ed. 1798 (5th.ed. 1817).

    Google Scholar 

  68. Mardia, K.V. (1970): Families of bivariate distributions.Griffin Statist. Mon. No. 27.

    Google Scholar 

  69. Martinez, H.M. (1966): On the derivation of a mean growth equation for cell cultures. Bull. Math. Biophysics 28, 411–416.

    Google Scholar 

  70. Mellmann, J.R.; Hagemann, G. and Stender, H.St. (1974): Reproductive letal damage of DNA-synthesis outset and its influence on colony population kinetics. Lecture Note 5th Int.Congress of Radiation Research, Seattle.

    Google Scholar 

  71. Mendelsohn, M.L. (1960): The growth fraction: A new concept applied to tumors. Science 132, 1496–1499.

    Google Scholar 

  72. Mendelsohn, M.L. and Takahashi, M. (1971): A critical evalution of the fraction of labeled mitoses method as applied to the analysis of tumor and other cell cycles. The Cell Cycle and Cancer, Dekker, New York, 58–95.

    Google Scholar 

  73. Heyman, J. and Scott, E.L. (1967): Statistical aspect of the problem of carcinogenesis. Proc. 5th Berkeley Symp. Math. Statist. Prob. 4, 745–776.

    Google Scholar 

  74. Norrby, K.; Johanisson, G. and Mellgreen, J. (1967): Proliferation in an established cell line. An analysis of birth,death, and growth rates. Exp. Cell Res. 48, 582–594.

    Google Scholar 

  75. Oldfield, D.G. (1966): A continuity equation for the cell population. Bull. Math. Biophysics 28, 545–554.

    Google Scholar 

  76. Painter, P.R. and Marr, A.G. (1968): Mathematics of microbial populations. Ann. Rev. Microbiol. 22, 519.

    Google Scholar 

  77. Pearl, R. and Reed, L.J. (1920): On the rate of growth of the population of the United States since 1790 and its mathematical representation. Proc. Nat. Acad. Sci. USA, 6, 273–288.

    Google Scholar 

  78. Powell, E.O. (1958): An outline of the pattern of bacterial generation times. J. gen. Microbiol. 18, 382–396.

    Google Scholar 

  79. Powell, E.O. (1969): Generation times of bacteria: Real and artifical distributions. J. gen. Microbiol. 58, 141.

    Google Scholar 

  80. Pujara, C.M. and Whitmore, G.F. (1970): An experimental investigation of the division probability model for cell growth. Cell Tissue Kinet. 3, 99–118.

    Google Scholar 

  81. Quastler, H. and Sherman, E.G. (1959): Cellpopulation kinetics in intestinal epithelium of mice. Exp. Cell. Res. 17, 420–438.

    Google Scholar 

  82. Rescigno, A. and Segre, G. (1966): Drug and tracer kinetics. Blaisdell, Mass.

    Google Scholar 

  83. Rittgen, W. and Tautu, P. (1976): Branching models for the cell cycle. Lecture Notes Biomathematics, Springer, 11, 109–126.

    Google Scholar 

  84. Romahn, H.B. (1974): Unveröffentlichte Daten. Medizinische Hochschule Hannover, Department Radiologie.

    Google Scholar 

  85. Romahn, H.B. (1978): Populationskinetik proliferierender CHO-Fibroblasten nach Pseudopodien - Partialbestrahlung mit ArgonIonen-Laser. Dissertation, Medizinische Hochschule Hannover.

    Google Scholar 

  86. Roti Roti, J.L. and Okada, S. (1973): A mathematical model of the cell cycle of L5178Y. Cell Tissue Kinet. 6, 111–124.

    Google Scholar 

  87. Rubinow, S.L. (1968): A maturity-time representation for cell populations. Biophys. J., 8, 1055.

    Google Scholar 

  88. Schneider, B. (1964): Probitmodell and Logitmodell in ihrer Bedeutung für die experimentelle Prüfung von Arzneimitteln. Antibiotica et Chemotherapia, Karger Basel, 12, 271–286.

    Google Scholar 

  89. Schneider, B. (1966): Versuch einer medizinischen Kybernetik. Method. Inform. Med., Vol. 5, 3, 128–135.

    Google Scholar 

  90. Schneider, B. (1974): Das Wachstum von Populationen. Unveröffentlichtes Manuskript, Medizinische Hochschule Hannover.

    Google Scholar 

  91. Steel, G.G. and Hanes, S. (1971): The technique of labeled mitosis: Analysis by automatic curve fitting. Cell Tissue Kinet. 4, 93–105.

    Google Scholar 

  92. Steel, G.G. (1972): The cell cycle in tumors: An examination of data gained by the technique of labeled mitoses. Cell Tissue Kinet. 5, 87–100.

    Google Scholar 

  93. Takahashi, M. (1968): Theoretical basis of cell cycle analysis II. Further studies on labeled mitosis ware method. J. theor.Biol. 18, 195–209.

    Google Scholar 

  94. Toellner, D.; Hagemann, G. und Stender, H.St. (1973): Der Einfluß ionisierender Strahlen auf die Koloniegrößenverteilung von CHO-Fibroblasten. Strahlentherapie 145, 604–611.

    Google Scholar 

  95. Toellner, D. (1974): Unveröffentlichte Daten. Medizinische Hochschule Hannover, Department Radiologie.

    Google Scholar 

  96. Toellner, D.; Nachtegal, H.; Hagemann, G. und Deinhardt, H. (1975) Koloniegrößenspektren von 60Co-Camma-bestrahlten CHO-Fibroblasten nach Einfrier-Auftauzyklen. Strahlentherapie 149, 5, 520–527.

    Google Scholar 

  97. Toellner, D. (1977): Verteilungsmessungen von Koloniegrößen zum Nachweis cytogenetischer Schäden durch Röntgenstrahlen und Cytostatica. Habilitationsschrift, Medizinische Hochschule Hannover.

    Google Scholar 

  98. Trucco, E. (1965): Mathematical models for cellular systems.Part I: The von Foerster equation. Bull. Math. Biophysics 27, 285–304.

    Google Scholar 

  99. Trucco, E. and Brockwell, P.J. (1968): Percentage labeled mitosis curves in exponentially growing cell populations. J.Theor. Biol. 20, 321–337.

    Google Scholar 

  100. Tuckwell, H.C. (1974): A study of some diffusion models of population growth. Theor. Pop. Biol., 5, 345–357.

    Google Scholar 

  101. Verhulst, P.F. (1838): Notice sur la loi que la population suit dans son accroissement. Correspondance mathématique et physique, publiée par A. Quetelet (Tome X, 113–121 ).

    Google Scholar 

  102. Volterra, V. (1931): Lecons sur la théorie mathématique de la lutte pour la vie. Gauthier-Villars, Paris.

    Google Scholar 

  103. Yule, G.U. (1925): The growth of population and the factors which control it. J. Roy. Statist. Soc. 88, 1–58.

    Google Scholar 

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  1. Department für Biometrie und Medizinische Informatik, Medizinische Hochschule, Karl-Wiechert-Allee 9, 3000, Hannover 61, Deutschland

    Uwe Feldmann

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Feldmann, U. (1979). Literaturhinweise. In: Wachstumskinetik. Medizinische Informatik und Statistik, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-13404-7_5

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  • DOI: https://doi.org/10.1007/978-3-662-13404-7_5

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