Application of a non-linear dispersion model to analysis of the renal handling of p-aminohippurate in isolated perfused rat kidney

To analyze the renal handling of therapeutic compounds observed as a non-linear process with a diffusion phenomenon, we employed a non-linear dispersion model described with a partial differential equation and solved it by using the finite difference method with an implicit scheme in a model dependent analysis. In this study, the renal handling of p-aminohippurate (PAH) was investigated in isolated perfused rat kidney, in which a 50 μl bolus of injection solution containing [³]PAH and [¹⁴C]inulin was administered rapidly into the renal artery. The venous outflows were then collected for 15 min with a fraction collector. The renal extraction ratio of PAH was decreased from 65% to 18% as the PAH concentration in the injection solution was increased from 2 μM to 10 mM. The PAH outflow profile changed as the extraction process became saturated. With the non-linear dispersion model, the Miehaelis-Menten parameters for the PAH extraction process were estimated by a model fitting calculation. The calculated values were 0.83 μmol/min/kidney for V(max) and 89 μM for K(m). It was demonstrated that the model dependent analysis with a non-linear dispersion model is a useful approach to characterize renal drug handling, and is probably applicable for examining other non-linear processes which involve a diffusion phenomenon.