Fundamental Properties of Spin Echoes

Spin echoes have been known since 1950. Although their formal description by use of the Bloch equations is straightforward, it does not lead to an intuitive understanding of their behavior except for the special cases of 180" or 90" pulses, especially when many pulses are applied before the magnetization has returned into thermal equilibrium. The extended-phasegraph algorithm, which takes into account that the total magnetization in spin-echo sequences is a superposition of many isochromats, allows the recognition of all possible echo signals in arbitrary pulse sequences. Its application to multi-echo sequences leads to a number of surprising results. It can be demonstrated that refocusing pulses with flip angles much lower than 180" generate an unexpectedly high signal intensity after a few echo periods. Apart from leading to a simple algorithm for the exact calculation of echo intensities in arbitrary multi-pulse sequences, the phase-graph algorithm leads to a simple understanding of the contrast behavior of different gradient echo sequences and gives a rational means for the design of MR-imaging sequences that are free from spurious echoes.