Uncertainty in T1 mapping using the variable flip angle method with two flip angles

Propagation of errors, in conjunction with the theoretical signal equation for spoiled gradient echo pulse sequences, is used to derive a theoretical expression for uncertainty in quantitative variable flip angle T-1 mapping using two flip angles. This expression is then minimized to derive a rigorous expression for optimal flip angles that elucidates a commonly used empirical result. The theoretical expressions for uncertainty and optimal flip angles are combined to derive a lower bound on the achievable uncertainty for a given set of pulse sequence parameters and signal-to-noise ratio (SNR). These results provide a means of quantitatively determining the effect of changing acquisition parameters on T-1 uncertainty.