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

Formulas are derived for longitudinal magnetization in multiple-echo inversion recovery (IR), saturation recovery, and progressive saturation pulse sequences with imperfect pulses. The effects of imperfect pulses on the signal intensities and on the calculated T1 relaxation times are discussed. Relaxation data from all three methods can be fitted with an equation of the form: Signal intensity=[a+b exp(−TX/T1)]/[1+c exp(−TX/T1)], where TX is a variable delay time and the values of T1, a, b, and c are adjusted to optimize the fit. Only three parameters need to be fitted for progressive saturation with no echoes because b=−a. For modified fast IR (with constant repetition time TR), 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 method for multiple-slice measurements of T1 in magnetic resonance imaging (MRI) are reviewed. Other applications of these formulas include estimating errors in T1 calculations, finding the flip angles (“Ernst angles”), echo spacing, and TR that maximize the signal-to-noise ratio in multiple-echo sequences, optimizing contrast between tissues in MRI, and determining how quickly a steady state is approached. ©1999 John Wiley & Sons, Inc. Concepts Magn Reson 11: 29–49, 1999