Optimization of signal‐to‐noise ratio in calculated T 1 images derived from two spin‐echo images

A simplified model relating signal intensity in an MR image to spin‐lattice relaxation time ( T 1 ), repetition time ( T R ), number of signal averages and the average tip angle ( α ) of the protons within the slice has been developed. This model has been used to select the optimal repetition times of two spin‐echo images for a fixed total imaging time to maximize signal to noise in calculated T 1 images. Theoretical predictions of T 1 are virtually identical to spectroscopically measured values, and the relative noise (δ T 1 ) in T 1 images calculated from two measured spin‐echo images is in good agreement with the theoretically predicted values of δ T 1 / T 1 . This model predicts that: (a) for a T 1 of approximately 500 ms, the least T 1 image noise is obtained with one of the spin‐echo images collected with a T R of 400–500 ms. The longer the T R of the other spin‐echo image, the lower the T 1 image noise, but past a T R of approximately 1400 ms, T 1 image signal/noise is optimized for the same total imaging time by increasing the number of averages in the shorter T R spin‐echo image rather than increasing the T R of the second spin‐echo image. (b) The error is reduced and the optimum T R1 is reduced as α is increased from 63 to 90°. (c) For a range of T 1 , optimal selection of T R1 and T R2 based on an intermediate value of T 1 , results in relatively little increase over optimal values in δ T 1 / T 1 for the entire T 1 range. © 1986 Academic Press, Inc.