Originally inspired by biological neural networks, artificial neural networks (ANN) are powerful mathematical models that can solve complex problems such as filtering, classification, prediction and more. In fact, neural networks (NN) have been used to model complex nonlinear systems, including biomedical time series among other applications to inverse problems. This thesis addresses the application of ANN to the inverse functional magnetic resonance imaging (fMRI) problem. The fMRI response, given by the hemodynamic model, is described using four states related to each other by a system of first order differential equations. The measured fMRI signal, Blood Oxygenation Level Dependent (BOLD), is a nonlinear combination of the model states. A lot of research has been done on the fMRI modeling and data analysis, this work exploits the prediction property of Nonlinear Auto-Regressive with eXogenous input (NARX) NN to estimate the hidden states ) ) )) of the brain hemodynamic model. Synthetic data are used to train the neural network and test its performance. This approach is accurate and robust in presence of signal noise and does not depend on the integration step.