The treatment of chronic renal diseases usually involves the estimation of the glomerular filtration rate (GFR). The GFR can be estimated in vivo without blood samples by pharmacokinetic methods. These models employ non-linear curve fitting techniques to obtain model parameters fitting the model to concentration curves extracted from 4D DCE-MRI data. However, currently proposed optimization strategies rely on the choice of the initial values. In this paper, we propose an improved optimization algorithm based on the analytical elimination of half of the parameters of the Sourbron model. This reduction vastly reduces the runtime of a parameter fit and essentially allows to eliminate the need to adjust the initialization to the input data using multiple fits on a uniform search space. With this approach, we are able to estimate the GFR in three of four clinical cases within 10% of the clinically measured GFR.