The advent of modern MRI scanners and computer equipment permits the rapid sequential collection of images of gadolinium chelate (Gd) transit through the kidney. The excellent spatial and temporal (0.9 s) resolution permits analyzing the shape of the recovered curves with a sophisticated model that includes both space and time. The purpose of this manuscript is to present such a mathematical model. By building into the model significant physical processes that contribute to the shape of the measured curve, quantitative values can be assigned to important parameters. In this work, quantitative values are determined for blood dispersion through the cardio-pulmonary system, systemic clearance rate of Gd, blood flow into each kidney, blood transit time in each kidney, the extraction rate of Gd across the capillary membrane, interstitial distribution volume, and the GFR for each kidney.