An elementary method for solving compartmental models with time-dependent coefficients

Several of the biokinetic models used in ICRP Publication 56, Age-dependent Doses to the Public from exposures to Radionuclides, depict the movement of materials among explicitly defined organs and tissues using transfer coefficients that vary continuously with age from infancy to adulthood. Such physiologically and/or biologically based models are appealing because of the identifiability of model components, but their application has been limited by the general perception that such models can only be evaluated using sophisticated mathematical tools. The purpose of this paper is to describe an elementary method for solving complex compartmental models with time-dependent transfer coefficients. The method has practically no limitations on the number of compartments or connections between compartments and thus is applicable to a wide class of models, including those that depict recycling of material. We illustrate the method by applications to the age-specific biokinetic models described in ICRP Publication 56.