A novel k‐space trajectory measurement technique

Abstract

A new k-space trajectory measurement technique is proposed and demonstrated. This technique measures the k-space trajectory, in seconds, using only a few readout lines, using phase values of acquired MR signals. As a result of the technique's efficiency, k-space trajectory measurement using patient data becomes possible. The utility of this techniques is demonstrated in phantom and human studies at 4.1 T.

Improved k‐space trajectory measurement with signal shifting

“…6. Briefly, signals are acquired from two slices located along the axis of the gradient of interest (e.g., x-axis), at positions x 1 and x 2 (x 1 x 2 ).…”

“…[1] represents a Fourier transform relation between signal S i and the "effective magnetization density" i (x)e -j (t) . In practice, the phase term (t) can be neglected in the following calculations (6). For a sample that is homogeneous over the slice, the effective magnetization density is equivalent to the slice profile.…”

“…[1] can be written as the product of the Fourier transform of the centered slice and a phase term dependent on the slice location x i : S i ͑k x ͑t͒͒ ϭ ˆ͑k x ͑t͒͒e Ϫj2 kx,(t)xi [2] If 1 (t) and 2 (t) are the phases of the complex signals acquired from two slices 1 and 2, the effective k-space coordinate k x (t) can then be obtained, as shown in Ref. 6, using:…”

“…Thus, signal nulling occurs at time points that differ from those observed in the absence of the dephasing gradient. The signal becomes: [6] Note that the temporal evolution of the phase term i (t) ϭ Ϫ2 k x (t)x i is not affected by the dephasing gradient. Provided that the latter has been applied sufficiently smoothly so as to avoid additional eddy currents, the signal presents a global phase offset and a modified amplitude.…”

Fast, simple gradient delay estimation for spiral MRI

“…Beaumont et al (9) recognized that for the methods of Zhang et al (7) and Duyn et al (8), low or zero amplitude values would occur at k-space locations farther from the origin than a distance equal to the inverse of the slice thickness. The slice thickness must therefore be kept very small to obtain accurate estimates of larger k-space values.…”