Point spread functions of the T₂ decay in k-space trajectories with long echo train

T₂ decay during long echo trains of magnetic resonance (MR) imaging pulse sequences is known to cause a blurring effect, due to the peak broadening of the point spread function (PSF). In contrast, the simultaneous amplitude-loss effect, led by the peak reduction of the PSF, has gained much less attention. In this report, we analyzed the PSFs of both the truncation and T₂ decay for Cartesian (linear profile ordering and low-high ordering) and spiral trajectories, respectively. Then, we derived simple formulas to characterize both the blurring and amplitude-loss effects, which are functions of the ratios of the echo train duration (T_k) over T₂ (T_k/T₂). Signal-to-noise ratio (SNR) per unit time was thus analyzed considering both the amplitude-loss effect induced by the T₂ decay and the SNR gain from the long acquisition duration based on MR sampling theory. Optimum T_k/T₂ ratios to achieve maximum SNR per unit time were 1.2 for the Cartesian trajectory and 0.8 for the spiral trajectory.