Some cognitive neuroscientific hypotheses might concern neural responses oc
curring during particular periods of time in a behavioral trial. Here, thes
e particular periods of time are referred to as temporal components of the
trial. A difficulty in using BOLD fMRI to test hypotheses about neural resp
onses during temporal components is that some information is irretrievably
lost when neural responses are hemodynamically transformed. As a result, on
e cannot in general use the fMRI signal to unambiguously specify if there w
as a neural response during a given temporal component. However, adoption o
f a linear-time invariant model for the transform from neural signal to fMR
I signal and constraint of the space of underlying neural waveforms might a
llow one to ask such questions. Here, the basic theory relevant to this iss
ue and a corresponding method are discussed. The application of this method
to fMRI time series data collected during the performance of a delayed-res
ponse trial is provided as an illustrative example. (C) 2000 Academic Press
.