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Extra info for Advanced Instrumentation and Measurement Techniques (csni-r1997-33)
1987, The case for stochastic models of digesta flow, J. Theo. , in press. Matis, J. H. and Wehrly, T. , 1979, Stochastic models of compartmental systems, Biometrics, 35:199. Matis, J. H. and Wehrly, T. , 1984, On the use of residence time moments in the statistical analysis of age-dependent stochastic compartmental systems, In: "Mathematics in Biology and Medicine", S. L. PaveriFontana and V. ), New York: Springer-Verlag. Matis, J. H. and Wehrly, T. , 1985, Stochastic compartmental models with gamma retention times: An application and estimation procedure, In: "Mathematics and Computers in Biomedical Applications·, J.
25) is W(t) (26) as before in Eq. (14), however, the eigenvalues in the nontrivial case n 1 + n2 > 2 are not distinct and not necessarily real; hence the Wij(t), and subsequent p .. (t), solutions for this model do not have the sums of exponentials foriJgiven in Eq. (15). Some special cases of the above model which have been investigated in the literature are outlined below. A new model which is potentially useful for NMR da ta is then introduced. 4 Some Particular Models with Erlanq Retention Times One of the early papers to consider generalized compartment models was Matis (1972), which considers a two-compartment irreversible system where the first compartment is Erlang.
It can be seen that these curves are widely different at early times but converge with increasing time until at 45 minutes the differences over the entire range of (k2* + k3*) equal only a small fraction of the value of the integral. These curves demonstrate that at short times enormous errors can occur if the values of the rate constants are not precisely known, but only negligible errors occur at 45 minues, even over a wide range of rate constants of several fold. In fact, it was precisely for this reason that [14C]deoxygluCOSe rather than [14C]gluCose was selected as the tracer for glucose metabolism.