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

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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 T1 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 T1 uncertainty.