Signal intensities and T-1 calculations in multiple-echo sequences with imperfect pulses

Formulas are derived for longitudinal magnetization in multiple-echo invers ion recovery (IR), saturation recovery, and progressive saturation pulse se quences with imperfect pulses. The effects of imperfect pulses on the signa l intensities and on the calculated T-1 relaxation times are discussed. Rel axation data from all three method scan be fitted with an equation of the f orm: Signal intensity = \a + b exp(-T-X/T-1)]/[1 + c exp(-T-X/T-1)\, where T-X is a variable delay time and the values of T-1, a, b, and c are adjuste d to optimize the fit. Only three parameters need to be fitted for progress ive saturation with no echoes because b = -a. For modified fast IR (with co nstant repetition time T-R), c = 0 and a three-parameter fit suffices even if several non-steady-state signals are acquired and a range of flip angles is present within the sample. The advantages of the modified fast IR metho d for multiple-slice measurements of T-1 in magnetic resonance imaging (MRI ) are reviewed. Other applications of these formulas include estimating err ors in T-1 calculations, finding the flip angles ("Ernst angles"), echo spa cing, and T-R that maximize the signal-to-noise ratio in multiple-echo sequ ences, optimizing contrast between tissues in MRI, and determining how quic kly a steady state is approached. (C) 1999 John Wiley & Sons, Inc.