On the calculation and interpretation of signal intensity in echo-shifted sequences

Echo-shifted sequences have been shown to be useful in applications where strong T*2-weighting and short repetition times are wanted, such as BOLD-contrast fMRI, MR thermometry, and perfusion studies. However, a full understanding of signal formation with such methods, which is mandatory to optimize sequence parameters for particular applications, has still not been achieved. Here, two methods are proposed to calculate the steady-state signal intensity in coherent TR-periodic and TR-shifted gradient-echo sequences. The integration method, which consists of averaging the steady-state magnetization over all isochromats in a voxel, is shown to be a particularly efficient way of obtaining the analytical expression of the measurable signal. The partition method, based on a physical decomposition of the steady-state magnetization into a sum of contributions from past excitation pulses, reveals that the net transverse magnetization results from a destructive interference between the wanted component and a series of stimulated echoes. The analysis includes off-resonance effects and is illustrated by phantom measurements. Relationships with previous publications on this subject are discussed.