On the noise in "augmented T1-weighted steady state magnetic resonance imaging"

Recently, Ye and colleagues proposed a method for "augmented T1-weighted imaging" (aT₁ W). The key operation is a complex division of gradient-echo (GRE) images obtained with different flip angles. Ye and colleagues provide an equation for the standard deviation of the obtained aT₁ W signal. Here, we show that this equation leads to wrong values of the standard deviation of such an aT₁ W signal. This is demonstrated by Monte Carlo simulations. The derivation of the equation provided by Ye and colleagues is shown to be erroneous. The error consists of a wrong handling of random variables and their standard deviations and of the wrong assumption of correlated noise in independently acquired GRE images. Instead, the probability distribution obtained with the aT₁ W-method should have been carefully analyzed, perhaps on the basis of previous literature on ratio distributions and their normal approximations.