A simplified formula for T1 contrast optimization for short-TR steady-state incoherent (spoiled) gradient echo sequences

There are certain instances in practical magnetic resonance imaging where T1 changes by a small amount relative to a neighboring pixel or between scans for a given pixel. The source of these small changes in T1 can be caused either by changes in tissue water content or by the uptake of a contrast agent. For short repetition time (TR) spoiled gradient echo imaging, we show that a robust and a simple, easy to use back-of-the-envelope expression for the flip angle that optimizes contrast under these conditions is given by radical 3theta E in radians or (180/pi) radical6TR/T1 in degrees. We show that for a TR/T1 ratio of up to 0.3 and for a T1 change of up to +/-50%, this approximation to the optimal flip angle produces a contrast to within 6% of the theoretical maximum value and that these predictions are in good agreement with experiment.