Joint maximum likelihood estimation of the fMRI hemodynamic response function and activation

Modeling the hemodynamic response function (HRF) and estimating the activation level are two important aspects in the statistical analysis of the functional Magnetic Resonance Imaging (fMRI). It is known that the HRF varies between experiments, subjects, and brain regions. A good model should be able to capture these variabilities. On one hand, a good HRF model results in a better activation detection; on the other hand, active voxels need to be defined for the estimation of the HRF. It has been shown that in a homogenous Region Of Interest (ROI), neighbor voxels have the same HRF shape with varying magnitude. Therefore, we propose a joint maximum likelihood estimation of the HRF and activation level in a ROI. There is no assumption on the exact shape of the HRF, thus it is possible to capture the HRF variabilities. The proposed method uses the rank one approximation of the data matrix, which is very convenient to calculate using the singular value decomposition (SVD). Results on the simulated data show that the joint estimate of the HRF and activation levels in a ROI are precise estimates, which are obtained without any assumption on the exact shape of the HRF.