Summary
The use of mathematical models in haematology is shown by some examples concerning stem cell kinetics, erythropoiesis and thrombopoiesis. At first, model assumptions are formulated which include the biological knowledge and some regulatory hypotheses. Then, the reaction of the model on stimulation and suppression is calculated. Finally, by comparison with experimental or clincal data one can evaluate how far the model assumptions are sufficient to understand the measurements. Thus one can exclude wrong hypotheses and identify the important regulatory influences.
Similar content being viewed by others
Literatur
Hirschfeld WJ (1970) Models of erythropoiesis. In: Gordon AS (ed) Regulation of hematopoiesis, Vol 1: Red cell production. Appleton-Century-Crofts, New York, pp 297–316
Linker H, Schaefer HE, Ruping B, Waidhas W, Gloeckner W, Borberg H, Wichmann HE, Reuter HD (1981) Thrombopoese, Thrombozytenzahl und Thrombozytenfunktion vor und nach Zellseparation. Verh dtsch Ges inn Med 87:798–802
Loeffler M (1983) Überlegungen zu einem umfassenden kybernetischen Modell der hämopoetischen Stammzellen und Progenitorzellen. Dissertation Universität Köln S 1–149
Loeffler M, Herkenrath P, Wichmann HE (1981) Do erythropoiesis and granulopoiesis interact at the stem cell level? — A first mathematical model calculation. Exp Hematol 9:[Suppl 9] 53
Loeffler M, Wichmann HE (1980) A comprehensive mathematical model of stem cell proliferation which reproduces most of the published experimental results. Cell Tissue Kinet 13:543–561
Monot C, Najean Y, Dresch C, Martin J (1975) Models of erythropoiesis and clinical diagnosis. Math Biosc 27:145–154
Rubinow SI, Lebowitz JL (1975) A mathematical model of neutrophil production and control in normal man. J Math Biol 1:187–225
Steinbach KH, Raffler H, Pabst G, Fliedner TM (1980) A mathematical model of canine granulocytopoiesis. J Math Biol 10:1–12
Wichmann HE (1976) Untersuchung eines nichtlinearen differential-Gleichungssystems und seine Anwendung auf den Regelkreis der Bildung roter Blutzellen (Erythropoese) beim Menschen. Dissertation Universität Köln 1–106
Wichmann HE (1983) Computer modeling of erythropoiesis. In: Dunn CDR: Current concepts in erythropoiesis. Wiley, Chichester pp 99–141
Wichmann HE, Gerhardts MD (1981) Platelet survival curves in man considering the splenic pool. J Theor Biol 88:83–101
Wichmann HE, Gerhardts MD, Spechtmeyer H, Gross R (1979) A mathematical model of thrombopoiesis in rats. Cell Tissue Kinet 12:551–567
Wichmann HE, Gross R (1981) How mathematical models can interpret and predict experimental results in haematology. Klin Wochenschr 59:1–4
Wichmann HE, Loeffler M (1984) Mathematical modeling of cell proliferation. Vol I. Stem cell regulation in hemopoiesis. CRC press Boca Raton, Florida (in press)
Wichmann HE, Spechtmeyer H, Gerecke D, Gross R (1976) A mathematical model of erythropoiesis in man. In: Berger J, Buehler W, Repges R, Tautu P: Mathematical models in medicine. Lecture Notes in Biomathematics, 11. Springer Berlin Heidelberg New York, pp 159–179
Wulff H (1983) Ein mathematisches Modell des erythropoetischen Systems von Ratte und Maus. Dissertation Universität Köln, S 1–249
Author information
Authors and Affiliations
Additional information
Herrn Prof. Dr. R. Gross zum 1.10. 1983 gewidmet
Mit Unterstützung der Deutschen Forschungsgemeinschaft
und der Stiftung Volkswagenwerk
Rights and permissions
About this article
Cite this article
Wichmann, H.E., Loeffler, M., Herkenrath, P. et al. Mathematische Modelle in der Hämatologie. Klin Wochenschr 61, 935–940 (1983). https://doi.org/10.1007/BF01550265
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01550265