An ARX model-based approach to trial by trial identification of fMRI-BOLD responses

Being able to estimate the fMRI-BOLD response following a single task or stimulus is certainly of value, since it allows to characterize its relationship to different aspects either of the stimulus, or of the subject's performance. In order to detect and characterize BOLD responses in single trials, we developed and validated a procedure based on an AutoRegressive model with eXogenous Input (ARX). The use of an individual exogenous input for each voxel makes the modeling sensitive enough to reveal differences across regions, avoiding any a priori assumption about the reference signal. The detection of variability across trials is ensured by a suitable choice, for each voxel, of the order of the moving average, which in our implementation determines the relative delay between the recorded and the reference signal. This is a quality useful in finding different time profiles of activation from high temporal resolution fMRI data. The results obtained from simulated fMRI data resulting from synthetic activations in actual noise indicate that such approach allows to evaluate important features of the response, such as the time to onset, and time to peak. Moreover, the results obtained from real high temporal resolution fMRI data acquired at l.5 T during a motor task are consistent with previous knowledge about the responses of different cortical areas in motor programming and execution. The proposed procedure should also prove useful as a pre-processing step in different approaches to the analysis of fMRI data.