Analyses of fMRI brain data are often based on statistical tests applied to each voxel or use summary statistics within a region of interest (such as mean or peak activation). These approaches do not explicitly take into account spatial patterns in the activation signal. In this paper, we develop a response surface model with parameters that directly describe the spatial shapes of activation patterns. We present a stochastic search algorithm for parameter estimation. We apply our method to data from a multi-site fMRI study, and show how the estimated parameters can be used to analyze different sources of variability in image generation, both qualitatively and quantitatively, based on spatial activation patterns.