In the quantitative analysis of dynamic contrast-enhanced magnetic resonance imaging compartment models allow the uptake of contrast medium to be described with biologically meaningful kinetic parameters. As simple models often fail to describe adequately the observed uptake behaviour, more complex compartment models have been proposed. However, the non-linear regression problem arising from more complex compartment models often suffers from parameter redundancy. We incorporate spatial smoothness on the kinetic parameters of a two-tissue compartment model by imposing Gaussian Markov random-field priors on them. We analyse to what extent this spatial regularization helps to avoid parameter redundancy and to obtain stable parameter point estimates per voxel. Choosing a full Bayesian approach, we obtain posteriors and point estimates by running Markov chain Monte Carlo simulations. The approach proposed is evaluated for simulated concentration time curves as well as for in vivo data from a breast cancer study.