A Method to measure arbitrary k‐space trajectories for rapid MR imaging

Abstract

A method to measure arbitrary k-space trajectories was developed to compensate for nonideal gradient performance during rapid magnetic resonance (MR) imaging with actively or nonactively shielded gradients at a magnetic field strength of 4.1 T. Accurate MR image reconstruction requires knowledge of the k-trajectory produced by the gradient waveforms during k-space sampling. Even with shielded gradients, residual eddy currents and imperfections in gradient amplifier performance can cause the true k-space trajectory to deviate from the ideal trajectory. The k-space determination was used for spiral gradient-echo imaging fo the human brain. While individual calibrations are needed for new pulse sequences, the method of k-space determination can be used for any sequence of preparation pulses and readout gradient waveforms and should prove useful for other trajectories, including the rastered lines of echo-planar imaging.

NMR probes for measuring magnetic fields and field dynamics in MR systems

“…It can then be modeled as ͑t͒ ϭ 0 ϩ ␥Bt, where the parameters B and 0 are obtained by linear regression. Assembling the discrete set of sampled phase values in the column vector ⌽, the phase model can be written in matrix-vector form as: [7] where the matrix T consists of one column filled with ones and one column containing the sampling instants at which the phases were measured, multiplied by ␥. Using weighted least-squares theory (37) the best estimates of 0 and B are obtained by:…”

“…The correspondence of the underlying physics also ensures that NMR probes offer sufficient temporal resolution. When used in a pulsed mode, their resonance signal can be sampled at very high frequency, with the signal phase reflecting the time integral of the magnetic field magnitude (5)(6)(7). NMR experiments with test samples have previously been used for studying eddy current behavior in MR systems (8).…”

Modified block uniform resampling (BURS) algorithm using truncated singular value decomposition: Fast accurate gridding with noise and artifact reduction

“…In the computer simulations, was set to 3 for all Cartesian grid points. This truncation scheme was determined by inspecting the plots of g noisy TSVD ( ) at the grid points [2,3], [20,4], and [20,20].…”

“…where is a constant determined by inspecting the plots of g noisy SRSVD ( ) of the same grid points [2,3], [20,4], and [20, 20]. was adjusted so that g noisy SRSVD ( ) stabilized for large .…”

Fast, simple gradient delay estimation for spiral MRI

“…Mason et al (6) measured k-space coordinates through the accurate placement, and scanning with the sequence of interest, of a small spherical phantom. The signal phase at each scan point is proportional to the k-space value scaled by the known phantom location.…”