Renal function is often characterized by the activity/time curves obtained by imaging the aorta and kidney. Non-parametric deconvolution of the activity/time curves is clinically useful as a diagnostic tool in determining renal transit times. Typically non-parametric deconvolution is performed using a technique that does not require a priori information, e.g. matrix-based and Fourier-transform methods. Using data filtering and conservation of mass constraints, non-parametric deconvolution continues to exhibit noise in the deconvolved curves. This noise hampers the identification of renal transit times. Given the shortcomings of non-parametric deconvolution, a parametric model of the renal response has been developed. Our model is shown to be anatomically and physiologically plausible. In this paper, the parametric model structure is used, in conjunction with experimental data, to estimate renal physiological parameters. These parameters include the filtration fraction, renal blood transit time and urine transit times. The model parameters are then related to the minimum transit time (MinTT), mean transit time (MTT), glomerular filtration rate (GFR) and parenchymal transit time index (PTTI). As deconvolution techniques often produce negative artifacts, Fine et al developed a technique to determine an aorta background to minimize this effect. In this paper this work is extended to determine a reasonable renal background from aorta activity/time curves. Non-parametric deconvolution is used to provide initial estimates of model parameters. The model is then fitted to twelve healthy background-corrected kidneys by an iterative parameter-estimation technique. The normal values correspond to those reported in the literature. These normal values are then used to identify renal arterial stenosis in two renal hypertensive patients. The results suggest that parametric identification, based on a renal-retention-function model, may provide additional anatomical and physiological information that is not provided by conventional non-parametric methods.