Consequence of equal absorption, distribution and/or elimination rate constants

When fitting experimental data to an open one- or two-compartment model, with first order kinetics, it may happen that no optimized value is obtained for model parameters. Several authors pointed out that this case is especially encountered when absorption and elimination coefficients approach each other in a one-compartment model or when absorption and exponential elimination or distribution rate constants are equal in a two-compartment model. We analyze these situations of equal coefficients here. Firstly, dealing with a one-compartment model, we get the concentration in the central compartment after a single oral dose and after successive various doses at various times (first order kinetics). Secondly, dealing with a two-compartment model, also for single or successive various doses, the concentration is expressed when absorption and exponential elimination or distribution rate constants are equal. In all cases, the areas under concentration curves and the mean residence time of the drug are calculated even when cancellation of one exponential term occurs. Furthermore, the concentration at steady-state is taken into account.