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 (Tk) over T2 (Tk/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 Tk/T2 ratios to achieve maximum SNR per unit time were 1.2 for the Cartesian trajectory and 0.8 for the spiral trajectory.