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Four-urn catenary model for excretion

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Abstract

A chain-like arrangement of four urns (a catenary system) into which different color balls (white, corresponding to radio atoms, and black, corresponding to stable atoms) are being transferred is used to simulate the transport of atoms down the GI tract of man and animals. Into the first urn (stomach) are placedw o white balls andr black balls while in the 2nd (small intestines) and 3rd (large intestines) urn, onlyr blacks are put in, with no whites. A sample of sizer is transferred from the 1st, 2nd and 3rd urns to the 2nd, 3rd and 4th (infinite universe) urns. From the random variable difference equations the first and second moments for the distribution of the number of radio atoms present in each urn are obtained. The variance of the contents of radioatoms in the excretion urn is

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Literature

  • Bernard, S. R. 1977. “An Urn Model Study of Variability Within a Compartment.”Bull. math. Biol. 39, 463–470.

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Authors and Affiliations

  1. University of California, 93105, Santa Barbara, CA, USA

    M. Sobel (Consultant)

  2. Health and Safety Research Division, Oak Ridge National Laboratory, 37830, Oak Ridge, TN, USA

    S. R. Bernard

  3. Computer Sciences Division, Oak Ridge National Laboratory, 37830, Oak Ridge, TN, USA

    V. R. R. Uppuluri & C. W. Nestor Jr.

Authors
  1. M. Sobel
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  2. S. R. Bernard
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  3. V. R. R. Uppuluri
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  4. C. W. Nestor Jr.
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Additional information

Research sponsored by the Office of Health and Environmental Research, U.S. Department of Energy under contract W-7405-eng-26 with the Union Carbide Corporation.

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Sobel, M., Bernard, S.R., Uppuluri, V.R.R. et al. Four-urn catenary model for excretion. Bltn Mathcal Biology 46, 219–227 (1984). https://doi.org/10.1007/BF02460070

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  • DOI: https://doi.org/10.1007/BF02460070

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