BOLD responses to stimuli: dependence on frequency, stimulus form, amplitude, and repetition rate.

A quantitative theory is developed for the relationship between stimulus and the resulting blood oxygen level-dependent (BOLD) functional MRI signal. The relationship of stimuli to neuronal activity during evoked responses is inferred from recent physiology-based quantitative modeling of evoked response potentials (ERPs). A hemodynamic model is then used to calculate the BOLD response to neuronal activity having the form of an impulse, a sinusoid, or an ERP-like damped sinusoid. Using the resulting equations, the BOLD response is analyzed for different forms, frequencies, and amplitudes of stimuli, in contrast with previous research, which has mostly concentrated on sustained stimuli. The BOLD frequency response is found to be closely linear in the parameter ranges of interest, with the form of a low-pass filter with a weak resonance at approximately 0.07 Hz. An improved BOLD impulse response is systematically obtained which includes initial dip and post-stimulus undershoot for some parameter ranges. It is found that the BOLD response depends strongly on the precise temporal course of the evoked neuronal activity, not just its peak value or typical amplitude. Indeed, for short stimuli, the linear BOLD response is closely proportional to the time-integrated activity change evoked by the stimulus, regardless of amplitude. It is concluded that there can be widely differing proportionalities between BOLD and peak activity, that this is the likely reason for the low level of correspondence seen experimentally between ERP sources and BOLD measurements and that non-BOLD measurements, such as ERPs, can be used to correct for this effect to obtain improved activity estimates. Finally, stimulus sequences that optimize the signal-to-noise ratio in event-related BOLD fMRI (efMRI) experiments are derived using the hemodynamic transfer function.