Spreading Codes Enables the Blind Estimation of the Hemodynamic Response with Short-Events Sequences

Finite impulse response (FIR) filters are considered the least constrained option for the blind estimation of the hemodynamic response function (HRF). However, they have a tendency to yield unstable solutions in the case of short-events sequences. There are solutions based on regularization, e.g. smooth FIR (sFIR), but at the cost of a regularization penalty and prior knowledge, thus breaking the blind principle. In this study, we show that spreading codes (scFIR) outperforms FIR and sFIR in short-events sequences, thus enabling the blind and dynamic estimation of the HRF without numerical instabilities and the regularization penalty. The scFIR approach was applied in short-events sequences of simulated and experimental functional magnetic resonance imaging (fMRI) data. In general terms, scFIR performed the best with both simulated and experimental data. While FIR was unable to compute the blind estimation of two simulated target HRFs for the shortest sequences (15 and 31 events) and sFIR yielded shapes barely correlated with the targets, scFIR achieved a normalized correlation coefficient above 0.9. Furthermore, scFIR was able to estimate in a responsive way dynamic changes of the amplitude of a simulated target HRF more accurately than FIR and sFIR. With experimental fMRI data, the ability of scFIR to estimate the real HRF obtained from a training data set was superior in terms of correlation and mean-square error. The use of short-events sequences for the blind estimation of the HRF could benefit patients in terms of scanning time or intensity of magnetic field in clinical tests. Furthermore, short-events sequences could be used, for instance, on the online detection of rapid shifts of visual attention that, according to literature, entails rapid changes in the amplitude of the HRF.