An investigation of the impulse functions for the nonlinear BOLD response in functional MRI

Functional MRI (fMRI) based on blood oxygenation level dependent (BOLD) contrast can be used to detect hemodynamic responses to a broad range of stimuli. It however remains unclear in what fashion the BOLD response is a linear system, and how the impulse function differs with stimulation of varying duration. To address this question, fMRI using visual stimulation with a wide range of duration (0.5-12 s) was performed in six human volunteers. A strong linear correlation was shown on the full width at half maximum (r = 0.998) of the BOLD response curves and the area under the curves (r = 0.999) to the duration of stimulation. However, comparing the errors of the measured and predicted response curves, our results showed a poorer linearity at stimuli of shorter duration. By examining the impulse functions derived from different stimuli, based on the assumption that a linear convolution relationship existed, a higher differentiation was shown in the experiments with shorter stimuli (<3 s). Compared to the area under the impulse function derived from 12 s stimulation, with that obtained from 0.5, 1, 2, 3, 4, 8 s stimuli resulted in differences of 66.2, 33.5, 15.1, 5.4, 0.9, 7.9%, respectively. This study suggests a higher degree of nonlinearity in the BOLD signal changes due to stimuli of shorter duration, in agreement with earlier work.