On the stationary states in gradient echo imaging

Abstract

A formalism is presented that concisely describes the magnetization of a sample subjected to a periodic series of RF pulses. In this formalism, the steady state of the magnetization is shown to be a sum of magnetic substates, each with unique contrast characteristics. When more than one substate contributes to a given image, the substates interfere with each other, producing ghosts and other artifacts. Properly designed gradient protocols can image single substates, producing ghost-free images. The contrast of the image depends largely on the choice of the imaged substate. Analytic solutions for unspoiled, RF spoiled, and gradient spoiled magnetizations are presented.

Moment and direction of the spoiler gradient for effective artifact suppression in RF‐spoiled gradient echo imaging

“….N͒, wherein is the RF-spoiling phase increment. If the phase of the ADC is cycled accordingly, this is equivalent to an additional phase (4) n ϭ n [1] that the magnetization obtains at the end of each sequence cycle. In practice, a range of values can be chosen for to get the image T 1 -weighted according to the Ernst formula (3,9,10).…”

“…With a spoiling moment of 2 in one of the three spatial directions, a steady state of the voxel signal is built up according to Eq. [4], if the voxel is assumed to have uniform spin density.…”

“…[4]. The evolution of the voxel signal s n ͑t͒ (i.e., the signal from a one voxel object) is recorded during the influence of the readout gradient and writes to:…”

“…[5] is equivalent to Eq. [4] only at echo time t ϭ 0 where the magnetization is written as M n echo ͑͒ and obeys the equality M n echo ͑͒ ϭ M n ϩ ͑͒. Eq.…”

“…Obviously a steady state as in Eq. [4] is also built up for a spoiling moment of integer multiples of 2, see the above mentioned first condition. However, literature presumes only that the spoiling moment must be "large enough" to make RFspoiling effective (3,6), which means obtaining T 1 -weighted contrast in images without ghosting artifacts.…”