Recycling retention functions

Beginning with the concept of any number of physiologically meaningful compartments that recycle material with a central extracellular fluid compartment and considering various excretion pathways, we solve the differential equations describing the kinetics by the method of Laplace to obtain concise algebraic expressions for the retentions. These expressions contain both fundamental and eigenvalue rate constants; the eigenvalue rate constants are obtained from the solution of a polynomial incorporating the fundamental rate constants. Mathematically exact expressions that predict the biodistribution resulting from continuous uptakes are used to obtain very simple mathematically exact steady state expressions as well as approximate expressions applicable to any time. These steady state and approximate expressions contain only the fundamental rate constants; also, they include a recycling factor that describes the increase in the biodistributions because of recycling. To obtain the values of the fundamental rate constants, short term kinetics studies along with data on the long term distributions are suggested. Retention functions obtained in this way predict both the short term and long term distributions; they therefore are useful in the interpretation of bioassay data and in the estimation of internal doses