Abstract
Pertubations of the human granulocytopoiesis for which many different reasons can be named have been described with the aid of a biomathematical model by Fliedner & Steinbach [1]. Their model consists of a set of coupled nonlinear differential equations describing the time evolution of the cell content of 7 different cell compartments. The most fundamental of these compartments is the stem cell pool because in case of a pertubation the number of remaining stem cells influences the whole process of recovery. According to Fliedner & Steinbach only a small amount of surviving stem cells is sufficient for complete restauration. Thus, it is a very important issue to estimate the stem cell pool size in order to predict the future behaviour of the granulocytopoiesis. Work towards this direction has already been done by Fliedner, Steinbach and Szepesi [2].
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References
Fliedner, T.M. and Steinbach, K.-H.: Simulationsmodelle von Perturbationen des gran-ulozytaren Zellerneuerungssystems; in Doerr, W. and Schipperges, H. (Ed.); Modelle der Pathologischen Physiologies Springer; Berlin; 1987.
Fliedner, T.M., Steinbach, K.-H. and Szepesi, T.: Hematological Indicators in the Determination of Clinical Management Strategies in Radiation Accidents; International Conference on Biological Effects of Large Dose Ionizing and Non-Ionizing Radiation; Hangzhou; Society of Radiation Medicine and Protection; Chinese Medical Association; Beijing; 1988.
Steinbach, K.-H.: private communication.
Mohler, R.R.: Bilinear control processes’, Academic Press; New York, London; 1973.
Isidori, A.: Nonlinear Control Systems: An Introduction; Springer; Berlin, Heidelberg; 1985.
Hofer, E.P. and Tibken, B.: An Iterative Method for the Finite-Time Bilinear-Quadratic Control Problem; Journal of Optimization Theory and Applications; (1988)57; pp. 411–427.
Tibken, B. and Hofer, E.P.: Systematic Observer Design for Bilinear Systems; Proceedings of the International Symposium on Circuits and Systems; Portland; 1989.
Tibken, B. and Hofer, E.P.: A novel computer approach to optimal feedback control of bilinear systems; Proceedings of the IFAC Symposium on Nonlinear Control Systems Design; Capri; 1989.
Mohler, R.R. and Kolodziej, W.J.: An overview of bilinear System Theory and applications; IEEE Transactions on Systems, Man and Cybernetics; SMC-10(1980) 10; pp. 683–688.
Krener, A.J.: Linearization and Bilinearization of Control Systems; Proceedings of the 1974 Allerton Conference on Circuit and Systems Theory; Urbana 111; 1974.
Bellman, R. and Bekenbach, F.: Inequalities; Springer; New York; 1977.
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© 1991 Springer-Verlag Berlin Heidelberg
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Hofer, E.P., Tibken, B., Fliedner, T.M. (1991). Modern Control Theory as a Tool to Describe the Biomathematical Model of Granulocytopoiesis. In: Möller, D.P.F., Richter, O. (eds) Analyse dynamischer Systeme in Medizin, Biologie und Ökologie. Informatik-Fachberichte, vol 275. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77020-3_4
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DOI: https://doi.org/10.1007/978-3-642-77020-3_4
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