An algorithm for eddy currents symmetrization and compensation

Eddy currents, which are induced in the magnet cryostat by pulsed magnetic field gradients in MRI, generate undesired eddy fields within the imaging volume. In this work, an automated and computerized algorithm to compensate these eddy currents is presented. The compensation is done in two steps: (i) Eddy fields are symmetrized electronically with an R-C filter, (ii) The symmetric eddy fields are compensated by another R-C filter. The compensation algorithm is iterative; therefore, errors that remain from one iteration are eliminated in the next iteration. Hence, the compensation process is very robust and accurate. It is shown that all the even harmonics of the eddy fields are eliminated by the symmetrization process, but the odd field harmonics remain. The amplitude of these odd harmonics can be significantly reduced if the gradient coils are designed so that the field they generate is spatially similar to the eddy fields.     

Characterization and reduction of gradient-induced eddy currents in the RF shield of a TEM resonator.

Radiofrequency (RF) shields that surround MRI transmit/receive coils should provide effective RF screening, without introducing unwanted eddy currents induced by gradient switching. Results are presented from a detailed examination of an effective RF shield design for a prototype transverse electromagnetic (TEM) resonator suitable for use at 3 Tesla. It was found that effective RF shielding and low eddy current sensitivity could be achieved by axial segmentation (gap width = 2.4 mm) of a relatively thick (35 microm) copper shield, etched on a kapton polyimide substrate. This design has two main advantages: first, it makes the TEM less sensitive to the external environment and RF interference; and second, it makes the RF shield mechanically robust and easy to handle and assemble.     

Analysis and compensation of eddy currents in balanced SSFP.

Balanced steady-state free precession (SSFP) completely compensates for all gradients within each repetition time (TR), and is thus very sensitive to any magnetic field imperfection that disturbs the perfectly balanced acquisition scheme. It is demonstrated that balanced SSFP is especially sensitive to changing eddy currents that are induced by stepwise changing phase-encoding (PE) gradients. In contrast to the linear k-space trajectory, which has small variations between consecutive encoding steps, other encoding schemes (e.g., centric, random, or segmented orderings) exhibit significant jumps in k-space between adjacent PE steps, and consequently induce rapidly changing eddy currents. The resulting disturbances induce significant image artifacts, such that compensation strategies are essential when nonlinear PE schemes are applied. Although direct annihilation of the induced eddy currents by additional, opposing magnetic fields has been investigated, it is limited by uncertainty regarding the time evolution of induced eddy currents. A generic (and thus system-unrelated) compensation strategy is proposed that consists of "pairing" of consecutive PE steps. Another approach is based on partial dephasing along the slice direction that annihilates eddy-current-induced signal oscillations. Both pairing of the PE steps and "through-slice equilibration" are easy to implement and allow the use of arbitrary k-space trajectories for balanced SSFP.     

Characterization and correction of system delays and eddy currents for MR imaging with ultrashort echo‐time and time‐varying gradients

Reconstruction of high‐quality MR images requires precise knowledge of the dynamic gradient magnetic fields used to perform spatial encoding. System delays and eddy currents can perturb the gradient fields in both time and space and significantly degrade the image quality for acquisitions with an ultrashort echo time or with rapidly varying readout gradient waveforms. A technique for simultaneously characterizing and correcting the system delay and linear‐ and zero‐order eddy currents of an MR system is proposed. A single set of calibration scans were used to compute a set of system constants that describe the effects of system delays and eddy currents to enable accurate reconstruction of data collected before uncorrected eddy currents have decayed. The ability of the proposed technique to reproducibly characterize small fixed delays (<50 μs) and short‐time constant (<1 ms) eddy currents is demonstrated. Magn Reson Med, 2009. © 2009 Wiley‐Liss, Inc.     

Effects of gradient anisotropy in MRI

A gradient system is anisotropic if the impulse responses of at least two of the gradient channels, x, y, or z, differ from each other. Such an undesired condition may arise, for example, from differences between the gradient channels with respect to eddy currents or from unbalanced time delays in the electronic components. Depending on the degree of anisotropy, the actual gradient then deviates from the nominal, desired gradient under certain oblique orientations during the transient periods of gradient switching. The adverse consequence is degradation of image quality, such as distortion, ghosting, and blurring. In this paper, a theoretical analysis is given of the basic effects. Furthermore, the implications for the MRI process and possible correction methods are described. The effects of anisotropy are shown experimentally for echo-planar imaging and two-dimensional selective RF excitation with spiral gradient pulses.     

Self-correction of proton spectroscopic images for gradient eddy current distortions and static field inhomogeneities

A postprocessing method of correcting for gradient eddy current distortions and inter-voxel static field inhomogeneities in spectroscopic imaging is presented. Data is acquired normally and all spatial processing is performed. The FID k each voxel is then digitally filtered to extract the signal from a signal reference line. Phase multiplying the original FID by the phase of this reference signal corrects for gradient eddy currents and static field offsets. Computer simulations show that the method is robust with respect to noise, filter bandwidth and the presence of small lines close to the reference line. The method is demonstrated on proton spectroscopic images of phantoms.     

Momentum-weighted conjugate gradient descent algorithm for gradient coil optimization.

MRI gradient coil design is a type of nonlinear constrained optimization. A practical problem in transverse gradient coil design using the conjugate gradient descent (CGD) method is that wire elements move at different rates along orthogonal directions (r, phi, z), and tend to cross, breaking the constraints. A momentum-weighted conjugate gradient descent (MW-CGD) method is presented to overcome this problem. This method takes advantage of the efficiency of the CGD method combined with momentum weighting, which is also an intrinsic property of the Levenberg-Marquardt algorithm, to adjust step sizes along the three orthogonal directions. A water-cooled, 12.8 cm inner diameter, three axis torque-balanced gradient coil for rat imaging was developed based on this method, with an efficiency of 2.13, 2.08, and 4.12 mT.m(-1).A(-1) along X, Y, and Z, respectively. Experimental data demonstrate that this method can improve efficiency by 40% and field uniformity by 27%. This method has also been applied to the design of a gradient coil for the human brain, employing remote current return paths. The benefits of this design include improved gradient field uniformity and efficiency, with a shorter length than gradient coil designs using coaxial return paths.     

High speed diffusion imaging in the presence of eddy currents

This paper describes two schemes for fast diffusion imaging on a 1.5-T MRI unit with unshielded gradients and 10-mT/m gradient system. The prepared longitudinal magnetization is sampled by a turbo fast low-angle shot (FLASH) sequence. The first scheme involves modifications to a diffusion-weighted driven-equilibrium preparation sequence that yields quantitative diffusion imaging. The second scheme consists of four 90° pulses that form the preparatory period with diffusion gradients applied between the first and last two 90° pulses. Sufficient time is allowed between the diffusion gradients and the beginning of the echo readout to allow eddy currents to decay to an acceptable level. Phantom studies show agreement between diffusion coefficients in the literature with those determined using the above schemes. The potential application of these sequences in monitoring temperature is demonstrated in phantoms. Artifact-free quantitative diffusion-weighted images of the brain using the second scheme are presented.     

A novel eddy current compensation scheme for pulsed gradient systems

We describe a modified pre-emphasis network that uses a number of fixed time constants, only whose amplitudes are adjustable. In comparison with variable time constant pre-emphasis networks we have used, the fixed time constant network is more effective and easier to set on the fly. We have further developed a method to set the fixed time constant network mathematically using a linear least squares technique.     

Quadrupole gradient coil design and optimization: A printed circuit board approach

Three different dual-axis quadrupole gradient coils for quantitative high resolution MR imaging of small animals, phantoms and specimens were designed and built using printed circuit board technology. Numerical optimization of the conductor positions was used to increase the volume of 0.4% gradient uniformity by up to a factor of four. In one coil, the volume of 5% gradient uniformity occupied 88% and 83% of the overall diameter and length of the coil, respectively. A systematic error of 0.5% in the wire placement was shown to cause a reduction in the volume of 0.4% gradient uniformity by a factor of two, though the region of 5% gradient uniformity was not significantly affected. Heat transfer calculations were used to determine maximum peak and root-mean-squared currents that could safely be applied to the coils.     

Asymmetrical gradient coil for head imaging.

This work presents a novel approach to develop dedicated transverse gradient coils for head imaging. The proposed coil design is based on the stochastic optimization of an asymmetrical stream function and improves the matching between the region-of-interest and the homogeneous gradient volume. Additionally, the electric field produced by these asymmetrical coils is 30% lower than that produced by standard symmetrical designs, which minimizes the risk of magnetostimulation of nerves in fast imaging techniques. A prototype of the asymmetrical gradient coil was built to test the method and magnetic field produced by the prototype was measured. Magnetic field measurements and electrical parameters of coils are in good agreement with theoretical calculations.     

Characterization of and correction for eddy current artifacts in echo planar diffusion imaging

Magnetic resonance diffusion imaging is potentially an important tool for the noninvasive characterization of normal and pathological tissue. The technique, however, is prone to a number of artifacts that can severely affect its ability to provide clinically useful information. In this study, the problem of eddy current-induced geometric distortions that occur in diffusion images acquired with echo planar sequences was addressed. These geometric distortions produce artifacts in computed maps of diffusion parameters and are caused by misalignments in the individual diffusion-weighted images that comprise the diffusion data set. A new approach is presented to characterize and calibrate the eddy current effects, enabling the eddy current distortions to be corrected in sets of Interleaved (or snapshot) echo planar diffusion images. Correction is achieved by acquiring one-dimensional field maps in the read and phase encode direction for each slice and each diffusion step. The method is then demonstrated through the correction of distortions in diffusion images of the human brain. It is shown that by using the eddy current correction scheme outlined, the eddy current-induced artifacts in the diffusion-weighted images are almost completely eliminated. In addition, there is a significant improvement in the quality of the resulting diffusion tensor maps.     

Temperature mapping of frozen tissue using eddy current compensated half excitation RF pulses.

Cryosurgery has been shown to be an effective therapy for prostate cancer. Temperature monitoring throughout the cryosurgical iceball could dramatically improve efficacy, since end temperatures of at least -40 degrees C are required. The results of this study indicate that MR thermometry based on tissue R(*)(2) has the potential to provide this information. Frozen tissue appears as a complete signal void on conventional MRI. Ultrashort echo times (TEs), achievable with half pulse excitation and a short spiral readout, allow frozen tissue to be imaged and MR characteristics to be measured. However, half pulse excitation is highly sensitive to eddy current distortions of the slice-select gradient. In this work, the effects of eddy currents on the half pulse technique are characterized and methods to overcome these effects are developed. The methods include: 1) eddy current compensated slice-select gradients, and 2) a correction for the phase shift between the first and second half excitations at the center of the slice. The effectiveness of these methods is demonstrated in R(*)(2) maps calculated within the frozen region during cryoablation.