| Summary: | This paper considers the use of semi-Markov process models with gamma transit times for the description of compartmental systems. The semi-Markov models seem particularly useful for systems with nonhomogeneous, "poorly-stirred" compartments. The paper reviews the Markov process models with exponential transit times, and illustrates the application of such models with a data set from Wise et al. (1968, Math. Biosc.) describing the clearance of calcium in man. The semi-Markov model with gamma transit times is then developed, and the solutions for its concentration-time curves and residence time moments are given. The use of semi-Markov models is illustrated with the same calcium data, and the results from the two models are compared. The example demonstrates that these semi-Markov models are physiologically more realistic than standard models and may befitted to pharmacokinetic data using readily available software.
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