In this paper, we propose a compartment model with two interstitial space compartments for the quantitative description of the contrast medium kinetics in dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). The model accounts for heterogeneity of contrast medium uptake behavior within voxels and thus more appropriately describes the uptake behavior in malignant tissue, especially at tumor margins. The posterior distribution obtained with a Bayesian approach provides valuable information on model fit and complexity as well as criteria for model selection. We propose a model selection technique to choose between the proposed two compartment model and the standard one compartment model per voxel. Results are evaluated for simulated and in vivo data.