Nonlinear regression in parametric activation studies.

Parametric study designs can reveal information about the relationship between a study parameter (e.g., word presentation rate) and regional cerebral blood flow (rCBF) in functional imaging. The brain's responses in relation to study parameters might be nonlinear, therefore the (linear) correlation coefficient as often used in the analysis of parametric studies might not be a proper characterization. We present a noninteractive method, which fits nonlinear functions of stimulus or task parameters to rCBF responses, using second-order polynomial expansions. This technique is implemented in the context of the general linear model and statistical parametric mapping. We also consider the usefulness of statistical inferences, based on F fields, about similarities and differences of these nonlinear responses in different groups. This approach is illustrated with a 12-run H215O PET activation study using an auditory paradigm of increasing word presentation rates. A patient who had recovered from severe aphasia and a normal control were studied. We demonstrate the ability of this new technique to identify brain regions where rCBF is closely related to increasing word presentation rate in both subjects without constraining the nature of this relationship and where these nonlinear responses differ.