Parametric study designs proved very useful in characterizing the rela
tionship between experimental parameters (e.g., word presentation rate
) and regional cerebral blood flow in positron emission tomography stu
dies. In a previous paper we presented a method that fits nonlinear fu
nctions of stimulus or task parameters to hemodynamic responses, using
second-order polynomial expansions. Here we expand this approach to m
odel nonlinear relationships between BOLD responses and experimental p
arameters, using fMRI. We present a framework that allows this techniq
ue to be implemented in the context of the general linear model employ
ed by statistical parametric mapping (SPM). Statistical inferences, in
this instance, are based on F statistics and in this respect we empha
size the use of corrected P values for F fields (i.e., SPM{F}). The ap
proach is illustrated with a fMRI study that looked at the effect of i
ncreasing auditory word-presentation rate. Our parametric design allow
ed us to characterize different forms of rate-dependent responses in t
hree critical regions: (i) bilateral frontal regions showed a categori
cal 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 assoc
iation cortex exhibited a nonlinear (inverted U) relationship to word
rate. (C) 1998 Academic Press.