Reconstruction of time-shifted hemodynamic response

Regression of voxel time course onto expected response is a standard procedure in functional magnetic resonance imaging that relies on exact onset time and shape of superimposed hemodynamic response functions. Elegant capture of time deviation by time derivative regressors appears complicated by shape distortion and limited to ±1 s, and is usually not exploited for reconstructing the true time-shifted response function together with its magnitude. This analysis of the time-derivative approach provides closed-form functional relations between time shift and regression coefficients that allow for hemodynamic shifts of ±5 s and can explain shape distortion and reconstruction behavior. Reliable absolute latencies were no smaller than 0.6 s in a best-case experiment. Confusions of latency are a previously undiscussed shortcoming where current limitation strategy may eliminate correct latencies and protect incorrect ones.