In order to infer neural activity from fMRI, the neurovascular relationship is most frequently modeled as a linear convolution system. It means that the BOLD signal surrounding the activated neural tissue results from the local neural activity convoluted with a time-invariant HRF, which describes the hemodynamic consequence of an impulse neural response. The linear HRF serves as an approximation for the complex interactions between neuronal activity, metabolic demand and blood flow and oxygenation [47]. With approximations made at various degrees, the HRF may be simply a Gauss, gamma [115] or double-gamma function [116]. While all these functions capture the key features of hemodynamics (e.g. the sluggishness and long duration), the double-gamma HRF entails the most detailed features, including a delayed onset time, initial dip, overshoot, undershoot, etc.
