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Rate Constants and the Variation of Random Concentration Curves in a 2-Compartment System
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Random concentration curves; Shot noise; 2-compartment model; Mathematica
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In biology and medicine many substances and drugs enter the system not at regular time intervals but rather according to a random process. In the present article a situation is investigated where input enters a 2-compartment system according to a Poisson process. The arising two random concentration curves y(t), one for the central and one for the peripheral compartment are discussed (shot noise). The equations for E[y(t)] and Var[y(t)] are derived. The dependence of E[y(t)] and Var[y(t)] and of the index of dispersion ID[y(t)] on the rate parameters is analysed and discussed in both compartments. The arising calculations were considerably simplified by means of Mathematica, a computer program which allows us to perform symbolic calculations.
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