Linear systems analysis of the fMRI signal

In 1995 when we began our investigations of the human visual system using fMRI, little was known about the temporal properties of the fMRI signal. Before we felt comfortable making quantitative estimates of neuronal responses with this new technique, we decided to first conduct a basic study of how the time-course of the fMRI response varied with stimulus timing and strength. The results ended up showing strong evidence that to a first approximation the hemodynamic transformation was linear in time. This was both important and remarkable: important because nearly all fMRI data analysis techniques assume or require linearity, and remarkable because the physiological basis of the hemodynamic transformation is so complex that we still have a far from complete understanding of it. In this paper, we provide highlights of the results of our original paper supporting the linear transform hypothesis. A reanalysis of the original data provides some interesting new insights into the published results. We also provide a detailed appendix describing of the properties and predictions of a linear system in time in the context of the transformation between neuronal responses and the BOLD signal.