Characterizing Stimulus–Response Functions Using Nonlinear Regressors in Parametric fMRI Experiments

Parametric study designs proved very useful in characterizing the relationship between experimental parameters (e.g., word presentation rate) and regional cerebral blood flow in positron emission tomography studies. In a previous paper we presented a method that fits nonlinear functions of stimulus or task parameters to hemodynamic responses, using second-order polynomial expansions. Here we expand this approach to model nonlinear relationships between BOLD responses and experimental parameters, using fMRI. We present a framework that allows this technique to be implemented in the context of the general linear model employed by statistical parametric mapping (SPM). Statistical inferences, in this instance, are based on F statistics and in this respect we emphasize the use of corrected P values for F fields (i.e., SPM¿F¿). The approach is illustrated with a fMRI study that looked at the effect of increasing auditory word-presentation rate. Our parametric design allowed us to characterize different forms of rate-dependent responses in three critical regions: (i) bilateral frontal regions showed a categorical response to the presence of words irrespective of rate, suggesting a role for this region in establishing cognitive (e.g., attentional) set; (ii) in bilateral occipitotemporal regions activations increased linearly with increasing word rate; and (iii) posterior auditory association cortex exhibited a nonlinear (inverted U) relationship to word rate.