This work is motivated by a quantitative Magnetic Resonance Imaging study of the relative change in tumor vascular permeability during the course of radiation therapy. The differences in tumor and healthy brain tissue physiology and pathology constitute a notable feature of the image data-spatial heterogeneity with respect to its contrast uptake profile (a surrogate for permeability) and radiation induced changes in this profile. To account for these spatial aspects of the data, we employ a Gaussian hidden Markov random field (MRF) model. The model incorporates a latent set of discrete labels from the MRF governed by a spatial regularization parameter. We estimate the MRF regularization parameter and treat the number of MRF states as a random variable and estimate it via a reversible jump Markov chain Monte Carlo algorithm. We conduct simulation studies to examine the performance of the model and compare it with a recently proposed method using the Expectation-Maximization (EM) algorithm. Simulation results show that the Bayesian algorithm performs as well, if not slightly better than the EM based algorithm. Results on real data suggest that the tumor "core" vascular permeability increases relative to healthy tissue three weeks after starting radiotherapy, which may be an opportune time to initiate chemotherapy and warrants further investigation.