Accounting for nonlinear BOLD effects in fMRI: parameter estimates and a model for prediction in rapid event-related studies

Nonlinear effects in fMRI BOLD data may substantially influence estimates of task-related activations, particularly in rapid event-related designs. If the BOLD response to each stimulus is assumed to be independent of the stimulation history, nonlinear interactions create a prediction error that may reduce sensitivity. When stimulus density differs among conditions, nonlinear effects can cause artifactual differences in activation. This situation can occur in rapid event-related designs or when comparing blocks of unequal lengths. We present data showing substantial nonlinear history effects for stimuli 1 s apart and use estimates of nonlinearities in response magnitude, onset time, and time to peak to form a low-dimensional parameterization of these nonlinear effects. Our estimates of nonlinearity appear relatively consistent throughout the brain, and these estimates can be used to form adjusted linear predictors for future rapid event-related fMRI studies. Adjusting the linear model for these known nonlinear effects results in a substantially better model fit. The biggest advantages to using predictors adjusted for known nonlinear effects are (1) higher sensitivity at the individual subject level of analysis, (2) better control of confounds related to nonlinear effects, and (3) more accurate estimates of design efficiency in experimental fMRI design.