Solving the problem of concomitant gradients in ultra-low-field MRI

Efficient concomitant and remanence field artifact reduction in ultra‐low‐field MRI using a frequency‐space formulation

“…We first studied the computational complexity of our proposed method compared to conventional 2D fast Fourier transform algorithm and direct time‐domain method . For an image of m ‐by‐ n pixels (thus spatially encoded by n phase‐encoding steps and m frequency‐encoded samples), the fast Fourier transform algorithm with the complexity of O ( m log m ) has to be repeated n times (across n phase encoding steps) in the first “ f ” stage.…”

“…When the concomitant field effect is moderate (ε ≤ 1) , the artifact can be corrected by image post‐processing using the Fourier reconstruction method after respectively correcting the local magnetization phases and frequencies disturbed by the concomitant fields in phase‐ and frequency‐encoding directions. Stronger concomitant field artifacts can be corrected by the TDR method, which directly relates the detected MRI signal to magnetization dynamics under the influence of a stronger concomitant field . However, the signal equation in the TDR can be too large to be solved (see our computational complexity analysis).…”

Rotary scanning acquisition in ultra‐low‐field MRI

“…Note that the magnetization precession frequency xðx; zÞ depends on the spatial distribution of the magnetic field strength b(x, z): xðx; zÞ ¼ g b ðx; zÞ, where c is the gyromagnetic ratio. According to Maxwell's equations, a linear magnetic field in the z direction generated by gradient coils must have nonzero x and y field components (13)(14)(15). In fact, this physical principle causes significant concomitant-field artifacts in low-field and ULF MRI (13)(14)(15).…”

“…This feature also suggests that RSA, like radial-trajectory acquisition, can have better quality using fewer data samples than Cartesian trajectory acquisition (12). Different from the radial-trajectory acquisition, where careful measurement of the concomitant field across rotation angles and complicated postprocessing methods (13)(14)(15) are needed to reduce image blurring and distortion artifacts in ULF MRI, RSA can reduce the image distortion and blurring caused by the concomitant field without tedious calibration measurements, because concomitant fields do not change between rotation angles in RSA. Using empirical data, we demonstrate that RSA can generate a full-FOV image using 33% of the amount of data collected by the conventional Fourier encoding method with only three localized SQUID sensors.…”

SQUID-sensor-based ultra-low-field MRI calibration with phantom images: Towards quantitative imaging

“…In this paper, it is shown that, by making a ULF-MR image of a phantom with known longitudinal and transverse relaxation times, spin density, etc., it is possible to calibrate the measurement setup by a careful consideration of the imaging hardware and the signal processing in the image formation. The presented implementation is based on Fourier image reconstruction, but it may be modified to situations where concomitant gradients are significant and traditional Fourier reconstruction methods are inaccurate [17][18][19]. The method enables stable calibration of not only the reading of the SQUID sensors, but the measurement geometry.…”