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Systems Compartmentation in Immunological Modeling

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Part of the book series: Lecture Notes in Biomathematics ((LNBM,volume 32))

Abstract

A nonlinear model of the humoral immune system is studied with blood, bone marrow, spleen, and gut-associated lymph tissue, lymph and lymph nodes represented by four compartments. Bilinear structures appear as the basis of the open-loop processes which include cell division and differentiation followed by chemical binding of molecular antibodies and antigen. A preliminary analysis is made of system identifiability in terms of compartmental accessibility for tracer insertion and tracer measurement.

Research supported by US National Science Foundation Grant No. ENG 74–15503A01.

Formerly at Oregon State University.

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References

  1. S. Merrill, “Mathematical models of humoral immune response”, Technical Report IM76–1, Univ. of Iowa, Dept of Maths., Iowa City, Iowa, 1976

    Google Scholar 

  2. G.I. Bell, A.S. Perelson and G.H. Pimbley, Jr., (eds) Theoretical Immunology, Immunology series, vol. 8, Marcel Dekker, New York, 1978.

    MATH  Google Scholar 

  3. N.K. Jerne, “The immune system — a web of V domains”, The Harvey Lectures 70, 93–110, Academic Press, New York, 1976.

    Google Scholar 

  4. C. DeLisi, “Some mathematical problems in the initiation and regulation of the immune response”, Math, Biosci. 35, 1–26, 1977.

    Article  Google Scholar 

  5. G.I. Bell, “Lymphocyte traffic patterns and dell-cell interactions”, in Theoretical Immunology, chapter 12, 341–375 op. cit., 1978.

    Google Scholar 

  6. J. Sprent, “Circulating T and B lymphocytes of the mouse. I. Migratory properties”, Cell Immunol. 7, 10–39, 1973.

    Article  Google Scholar 

  7. B.J. Hammonds, “A compartmental analysis of circulatory lymphocytes in the spleen”, Cell Tissue Kinet. 8, 153–169, 1975.

    Google Scholar 

  8. W.L. Ford, “Lymphocyte migration and immune responses”, Pro. Allergy19, 1–59, 1975.

    Google Scholar 

  9. G.H. Rannie and W.L. Ford, “Physiology of lymphocyte recirculation in animal models,” Excerpta Med.Int’l Congress Series 423, Transpl. and Clinical Immun., 165–171, 1977.

    Google Scholar 

  10. R.R. Mohler, C.F. Barton, and C.S. Hsu, “T and B cell models in the immune system”, in Theoretical Immunology, op. cit., Chapter 14, 415–435, 1978.

    Google Scholar 

  11. C. Bruni, M.A. Giovenco, G. Koch, and R. Strom, “A dynamical model of humoral immune response”, Math. Bioscience 27, 191–211, 1975.

    Article  MATH  Google Scholar 

  12. F.L. Alder, “Studies on mouse antibodies, I. The response to sheep red cells”, The Journal of Immunology 95, 26–38, 1965.

    Google Scholar 

  13. R.R. Mohler, “Biological Modeling with variable compartmental structures”, IEEE Trans. Auto. Control AC-19, 922–926, 1974

    Article  Google Scholar 

  14. W.D. Smith and R.R. Mohler, “Necessary and sufficient conditions in the tracer determination of compartmental system order”, J. Theoret. Biol. 57, 1–21,1976.

    Article  MathSciNet  Google Scholar 

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© 1979 Springer-Verlag Berlin Heidelberg

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Mohler, R.R., Hsu, C.S. (1979). Systems Compartmentation in Immunological Modeling. In: Bruni, C., Doria, G., Koch, G., Strom, R. (eds) Systems Theory in Immunology. Lecture Notes in Biomathematics, vol 32. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93130-7_14

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  • DOI: https://doi.org/10.1007/978-3-642-93130-7_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09728-0

  • Online ISBN: 978-3-642-93130-7

  • eBook Packages: Springer Book Archive

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