Pharmacokinetic model equations for the one- and two-compartment models with first-order processes in which the absorption and exponential elimination or distribution rate constants are equal

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Abstract
In fitting the one-compartment open model with first-order processes to empirical data, it has frequently been found for single-dose administration that the absorption and elimination rate constants approach each other. If these rate constants tend to be equal, such combinations are impossible to solve with the general model equation. In 1968, Dost (1) published a special model function by which the problems associated with the general model function can be circumvented. No solution, however, has been published for multiple-dose functions with the one-compartment model in which the absorption and elimination rate constants are equal. For a two-compartment open model with first-order processes, similar problems arise if the absorption and exponential distribution rate constants approach each other. Although this type of problems is often encountered in pharmacokinetic curve-fitting to empirical data, no exact solution has been published. Equations are given for multiple-dose administration with the one-compartment open model in which the absorption and elimination rate constants are equal, and for single-dose and multiple-dose administration with the two-compartment open model in which the absorption and exponential distribution rate constants are equal. Included are criteria to decide whether the new or the classical model functions should be applied in the case of a two-compartment open model.