Robust Bayesian estimation of the hemodynamic response function in event‐related BOLD fMRI using basic physiological information

In BOLD fMRI data analysis, robust and accurate estimation of the Hemodynamic Response Function (HRF) is still under investigation. Parametric methods assume the shape of the HRF to be known and constant throughout the brain, whereas non‐parametric methods mostly rely on artificially increasing the signal‐to‐noise ratio. We extend and develop a previously proposed method that makes use of basic yet relevant temporal information about the underlying physiological process of the brain BOLD response in order to infer the HRF in a Bayesian framework. A general hypothesis test is also proposed, allowing to take advantage of the knowledge gained regarding the HRF to perform activation detection. The performances of the method are then evaluated by simulation. Great improvement is shown compared to the Maximum‐Likelihood estimate in terms of estimation error, variance, and bias. Robustness of the estimators with regard to the actual noise structure or level, as well as the stimulus sequence, is also proven. Lastly, fMRI data with an event‐related paradigm are analyzed. As suspected, the regions selected from highly discriminating activation maps resulting from the method exhibit a certain inter‐regional homogeneity in term of HRF shape, as well as noticeable inter‐regional differences. Hum. Brain Mapping 19:1–17, 2003. © 2003 Wiley‐Liss, Inc.