Complex-number representation of informed basis functions in general linear modeling of Functional Magnetic Resonance Imaging

Detecting the subtle shape differences in hemodynamic responses at the group level

The nature of the hemodynamic response (HDR) is still not fully understood due to the multifaceted processes involved. Aside from the overall amplitude, the response may vary across cognitive states, tasks, brain regions, and subjects with respect to characteristics such as rise and fall speed, peak duration, undershoot shape, and overall duration. Here we demonstrate that the fixed-shape (FSM) or adjusted-shape (ASM) methods may fail to detect some shape subtleties (e.g., speed of rise or recovery, or undershoot). In contrast, the estimated-shape method (ESM) through multiple basis functions can provide the opportunity to identify some subtle shape differences and achieve higher statistical power at both individual and group levels. Previously, some dimension reduction approaches focused on the peak magnitude, or made inferences based on the area under the curve (AUC) or interaction, which can lead to potential misidentifications. By adopting a generic framework of multivariate modeling (MVM), we showcase a hybrid approach that is validated by simulations and real data. With the whole HDR shape integrity maintained as input at the group level, the approach allows the investigator to substantiate these more nuanced effects through the unique HDR shape features. Unlike the few analyses that were limited to main effect, two- or three-way interactions, we extend the modeling approach to an inclusive platform that is more adaptable than the conventional GLM. With multiple effect estimates from ESM for each condition, linear mixed-effects (LME) modeling should be used at the group level when there is only one group of subjects without any other explanatory variables. Under other situations, an approximate approach through dimension reduction within the MVM framework can be adopted to achieve a practical equipoise among representation, false positive control, statistical power, and modeling flexibility. The associated program 3dMVM is publicly available as part of the AFNI suite.