NONLINEAR EVENT-RELATED RESPONSES IN FMRI

This paper presents an approach to characterizing evoked hemodynamic r esponses in fMRI based on nonlinear system identification, in particul ar the use of Volterra series. The approach employed enables one to es timate Volterra kernels that describe the relationship between stimulu s presentation and the hemodynamic responses that ensue. Volterra seri es are essentially high-order extensions of linear convolution or ''sm oothing.'' These kernels, therefore, represent a nonlinear characteriz ation of the hemodynamic response function that can model the response s to stimuli in different contexts (in this work, different rates of w ord presentation) and interactions among stimuli. The nonlinear compon ents of the responses were shown to be statistically significant, and the kernel estimates were validated using an independent event-related fMRI experiment. One important manifestation of these nonlinear effec ts is a modulation of stimulus-specific responses by preceding stimuli that are proximate in time. This means that responses at high-stimulu s presentation rates saturate and, in some instances, show an inverted U behavior. This behavior appears to be specific to BOLD effects (as distinct from evoked changes in cerebral blood flow) and may represent a hemodynamic ''refractoriness.'' The aim of this paper is to describ e the theory and techniques upon which these conclusions were based an d to discuss the implications for experimental design and analysis.