Abstract : Physiological and biophysical models have been proposed to link neural activity to the Blood Oxygen Level-Dependent (BOLD) signal in functional MRI (fMRI). They rely on a set of parameter values that cannot always be extracted from the literature. Their estimation is challenging because there are more than 10 potentially interesting parameters involved in non-linear equations and whose interactions may result in identifiability issues. However, the availability of statistical prior knowledge on these parameters can greatly simplify the estimation task. In this work we focus on the extended Balloon model and propose the estimation of 15 parameters using an Evolutionary Computation (EC) global search method. To combine both the ability to escape local optima and to incorporate prior knowledge, we derive the EC objective function from Bayesian modeling. This novel method provides promising results on a challenging real fMRI data set involving rats with epileptic activity and compares favorably with the conventional Expectation Maximization Gauss-Newton approach.