Delay analysis of fMRI time

The high temporal resolution of fMRI allows to supplement the spatial analysis of the hemodynamic response to focal neuronal activation with a study of the temporal response in each region. Signal processing and time series analysis provide a number of tools for achieving this goal. This contribution suggests to apply a novel modelling technique to fMRI time series in order to estimate the temporal pattern of each voxel's response. With the assumption that the fMRI activation signal y(t) can be modelled from the stimulus (paradigm) x(t), the proposed technique eeciently extracts the past delays ft ? dg that are relevant in estimating the fMRI behaviour. This provides a unique insight into the temporal relationship between the stimulus and the actual activation. It is then possible to derive e.g. the eeective delay of response in a given voxel, or identify regions with short-term or long-term delays. The method relies on generalisation, i.e. expected error of a model on previously unseen data. Generalisation eeectively measures the performance of a model and suggests a principled method for extracting the set of delays that optimises performance for time-varying processes 1]. This scheme is applied to fMRI time series as follows: 1) consider delays in chronological order; 2) estimate generalisation performance of the model including candidate delay; 3) accept delay ii it yields signiicant decrease in generalisation. Due to temporal structure in the data, we avoid the traditional caveat of stepwise feature selection that inputs corresponding to a combination of relevant features might be ignored.