One of the advantages of event-related functional MRI (fMRI) is that it permits estimation of the shape of the hemodynamic response function (HRF) elicited by cognitive events. Although studies to date have focused almost exclusively on the magnitude of evoked HRFs across different tasks, there is growing interest in testing other statistics, such as the time-to-peak and duration of activation as well. Although there are many ways to estimate such parameters, we suggest three criteria for optimal estimation: 1) the relationship between parameter estimates and neural activity must be as transparent as possible; 2) parameter estimates should be independent of one another, so that true differences among conditions in one parameter (e.g., hemodynamic response delay) are not confused for apparent differences in other parameters (e.g., magnitude); and 3) statistical power should be maximized. In this work, we introduce a new modeling technique, based on the superposition of three inverse logit functions (IL), designed to achieve these criteria. In simulations based on real fMRI data, we compare the IL model with several other popular methods, including smooth finite impulse response (FIR) models, the canonical HRF with derivatives, nonlinear fits using a canonical HRF, and a standard canonical model. The IL model achieves the best overall balance between parameter interpretability and power. The FIR model was the next-best choice, with gains in power at some cost to parameter independence. We provide software implementing the IL model.

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