Testing for neural responses during temporal components of trials with BOLD fMRI

Some cognitive neuroscientific hypotheses might concern neural responses occurring during particular periods of time in a behavioral trial. Here, these particular periods of time are referred to as temporal components of the trial. A difficulty in using BOLD fMRI to test hypotheses about neural responses during temporal components is that some information is irretrievably lost when neural responses are hemodynamically transformed. As a result, one cannot in general use the fMRI signal to unambiguously specify if there was a neural response during a given temporal component. However, adoption of a linear-time invariant model for the transform from neural signal to fMRI signal and constraint of the space of underlying neural waveforms might allow one to ask such questions. Here, the basic theory relevant to this issue and a corresponding method are discussed. The application of this method to fMRI time series data collected during the performance of a delayed-response trial is provided as an illustrative example.