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Four-urn catenary model for excretion. (English) Zbl 0536.92015

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 placed \(w_ 0\) white balls and r black balls while in the 2nd (small intestines) and 3rd (large intestines) urn, only r blacks are put in, with no whites. A sample of size r 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.

MSC:

92Cxx Physiological, cellular and medical topics
60C05 Combinatorial probability
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References:

[1] Bernard, S. R. 1977. ”An Urn Model Study of Variability Within a Compartment.”Bull. math. Biol. 39, 463–470. · Zbl 0381.60070
[2] Bernard, S. R. and R. L. Hayes. 1970. ”Dose to Various Segments of the Gastrointestinal Tract.”Medical Radionuclides: Radiation Dose and Effects. Ed. R. J. Cloutier, C. L. Edwards and W. S. Snyder, AEC Symposium Series 20, pp. 295–314.
[3] Bernard, S. R., M. Sobel and V. R. R. Uppuluri 1981. ”On a Two-urn Model of Polyatype.”Bull. math. Biol. 43, 33–45. · Zbl 0445.60011
[4] Hayes, R. L., J. E. Carlton and W. R. Butler. 1963. ”Radiation Dose to the Human Intestinal Tract from Internal Emitter.”Health Phys. 9, 915–920.
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