A Simple Mathematical Model of the Human Liver


The parameter estimation problem for a continuous dynamical system is a difficult one. In this paper we study a simple mathematical model of the liver. For the parameter identification we use the observed clinical data obtained by the BSP test. Bellman's quasilinearization method and its modifications are applied.

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  1. [1]

    R. Bellman, R. Roth: Quasilinearization and the Identification Problem. World Scientific, Singapore, 1983.

    Google Scholar 

  2. [2]

    P. Hartman: Ordinary Difierential Equations. S. M. Hartman, Baltimore, 1973.

    Google Scholar 

  3. [3]

    E. Hrnčíř: Personal notes. Unpublished.

  4. [4]

    R. Kalaba, K. Spingarn: Control, Identification, and Input Optimization. Mathematical Concepts and Methods in Science and Engineering, Vol. 25. Plenum Press, New York-London, 1982.

    Google Scholar 

  5. [5]

    J. M. Watt, A. Young: An attempt to simulate the liver on a computer. Comput. J. 5 (1962), 221-227.

    Google Scholar 

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Čelechovská, L. A Simple Mathematical Model of the Human Liver. Applications of Mathematics 49, 227–246 (2004). https://doi.org/10.1023/B:APOM.0000042364.85016.7d

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  • identification of parameters
  • quasilinearization method