Reconstruction from NMR data acquired with imaging gradients having arbitrary time dependence

Eddy current-induced artifact correction in high b-value ex vivo human brain diffusion MRI with dynamic field monitoring

PURPOSE

To investigate whether spatiotemporal magnetic field monitoring can correct pronounced eddy current-induced artifacts incurred by strong diffusion-sensitizing gradients up to 300 mT/m used in high b-value diffusion-weighted (DW) EPI.

METHODS

A dynamic field camera equipped with 16 1 H NMR field probes was first used to characterize field perturbations caused by residual eddy currents from diffusion gradients waveforms in a 3D multi-shot EPI sequence on a 3T Connectom scanner for different gradient strengths (up to 300 mT/m), diffusion directions, and shots. The efficacy of dynamic field monitoring-based image reconstruction was demonstrated on high-gradient strength, submillimeter resolution whole-brain ex vivo diffusion MRI. A 3D multi-shot image reconstruction framework was developed that incorporated the nonlinear phase evolution measured with the dynamic field camera.

RESULTS

Phase perturbations in the readout induced by residual eddy currents from strong diffusion gradients are highly nonlinear in space and time, vary among diffusion directions, and interfere significantly with the image encoding gradients, changing the k-space trajectory. During the readout, phase modulations between odd and even EPI echoes become non-static and diffusion encoding direction-dependent. Superior reduction of ghosting and geometric distortion was achieved with dynamic field monitoring compared to ghosting reduction approaches such as navigator- and structured low-rank-based methods or MUSE followed by image-based distortion correction with the FSL tool "eddy."

CONCLUSION

Strong eddy current artifacts characteristic of high-gradient strength DW-EPI can be well corrected with dynamic field monitoring-based image reconstruction.

Eddy current-induced artifacts correction in high gradient strength diffusion MRI with dynamic field monitoring: demonstration in ex vivo human brain imaging

Purpose

To demonstrate the advantages of spatiotemporal magnetic field monitoring to correct eddy current-induced artifacts (ghosting and geometric distortions) in high gradient strength diffusion MRI (dMRI).

Methods

A dynamic field camera with 16 NMR field probes was used to characterize eddy current fields induced from diffusion gradients for different gradients strengths (up to 300 mT/m), diffusion directions, and shots in a 3D multi-shot EPI sequence on a 3T Connectom scanner. The efficacy of dynamic field monitoring-based image reconstruction was demonstrated on high-resolution whole brain ex vivo dMRI. A 3D multi-shot image reconstruction framework was informed with the actual nonlinear phase evolution measured with the dynamic field camera, thereby accounting for high-order eddy currents fields on top of the image encoding gradients in the image formation model.

Results

Eddy current fields from diffusion gradients at high gradient strength in a 3T Connectom scanner are highly nonlinear in space and time, inducing high-order spatial phase modulations between odd/even echoes and shots that are not static during the readout. Superior reduction of ghosting and geometric distortion was achieved with dynamic field monitoring compared to ghosting approaches such as navigator- and structured low-rank-based methods or MUSE, followed by image-based distortion correction with eddy. Improved dMRI analysis is demonstrated with diffusion tensor imaging and high-angular resolution diffusion imaging.

Conclusion

Strong eddy current artifacts characteristic of high gradient strength dMRI can be well corrected with dynamic field monitoring-based image reconstruction, unlike the two-step approach consisting of ghosting correction followed by geometric distortion reduction with eddy.

Higher order reconstruction for MRI in the presence of spatiotemporal field perturbations

Despite continuous hardware advances, MRI is frequently subject to field perturbations that are of higher than first order in space and thus violate the traditional k-space picture of spatial encoding. Sources of higher order perturbations include eddy currents, concomitant fields, thermal drifts, and imperfections of higher order shim systems. In conventional MRI with Fourier reconstruction, they give rise to geometric distortions, blurring, artifacts, and error in quantitative data. This work describes an alternative approach in which the entire field evolution, including higher order effects, is accounted for by viewing image reconstruction as a generic inverse problem. The relevant field evolutions are measured with a third-order NMR field camera. Algebraic reconstruction is then formulated such as to jointly minimize artifacts and noise in the resulting image. It is solved by an iterative conjugate-gradient algorithm that uses explicit matrix-vector multiplication to accommodate arbitrary net encoding. The feasibility and benefits of this approach are demonstrated by examples of diffusion imaging. In a phantom study, it is shown that higher order reconstruction largely overcomes variable image distortions that diffusion gradients induce in EPI data. In vivo experiments then demonstrate that the resulting geometric consistency permits straightforward tensor analysis without coregistration.

Spatially encoded NMR and the acquisition of 2D magnetic resonance images within a single scan

An approach that enables the acquisition of multidimensional NMR spectra within a single scan has been recently proposed and demonstrated. The present paper explores the applicability of such ultrafast acquisition schemes toward the collection of two-dimensional magnetic resonance imaging (2D MRI) data. It is shown that ideas enabling the application of these spatially encoded schemes within a spectroscopic setting, can be extended in a straightforward manner to pure imaging. Furthermore, the reliance of the original scheme on a spatial encoding and subsequent decoding of the evolution frequencies endows imaging applications with a greater simplicity and flexibility than their spectroscopic counterparts. The new methodology also offers the possibility of implementing the single-scan acquisition of 2D MRI images using sinusoidal gradients, without having to resort to subsequent interpolation procedures or non-linear sampling of the data. Theoretical derivations on the operational principles and imaging characteristics of a number of sequences based on these ideas are derived, and experimentally validated with a series of 2D MRI results collected on a variety of model phantom samples.

Single-shot MR imaging using trapezoidal-gradient-based Lissajous trajectories

A novel single-shot trapezoidal-gradient-based Lissajous trajectory is described and implemented on a 3-tesla magnetic resonance (MR) scanner. A feature of this trajectory is that its sampling points are located on a nonequidistant rectangular grid, which permits the usage of one-dimensional optimal algorithms to increase the robustness and speed of image reconstruction. Another advantage of the trajectory is that two images with different effective echo times can be obtained within a single excitation, which might be used for fast T2* mapping, in functional MR imaging scanning of brain activity associated with mental processes. Potential artifacts in reconstructed images were investigated and methods for suppressing these artifacts were developed. Experiments on normal subjects at rest and during brain activation were performed to demonstrate the feasibility of the new sequence.

On the optimality of the gridding reconstruction algorithm

Gridding reconstruction is a method to reconstruct data onto a Cartesian grid from a set of nonuniformly sampled measurements. This method is appreciated for being robust and computationally fast. However, it lacks solid analysis and design tools to quantify or minimize the reconstruction error. Least squares reconstruction (LSR), on the other hand, is another method which is optimal in the sense that it minimizes the reconstruction error. This method is computationally intensive and, in many cases, sensitive to measurement noise. Hence, it is rarely used in practice. Despite their seemingly different approaches, the gridding and LSR methods are shown to be closely related. The similarity between these two methods is accentuated when they are properly expressed in a common matrix form. It is shown that the gridding algorithm can be considered an approximation to the least squares method. The optimal gridding parameters are defined as the ones which yield the minimum approximation error. These parameters are calculated by minimizing the norm of an approximation error matrix. This problem is studied and solved in the general form of approximation using linearly structured matrices. This method not only supports more general forms of the gridding algorithm, it can also be used to accelerate the reconstruction techniques from incomplete data. The application of this method to a case of two-dimensional (2-D) spiral magnetic resonance imaging shows a reduction of more than 4 dB in the average reconstruction error.

Iterative reconstruction of single-shot spiral MRI with off resonance

A variety of applications and research directions in magnetic resonance imaging which require fast scan times have recently become popular. In order to satisfy many of the requirements of these applications, snapshot imaging methods, which acquire an entire image in one excitation, are often used. These snapshot techniques are relatively insensitive to motion and can allow rapidly occurring processes to be imaged. However, snapshot imaging techniques acquire data over a relatively long period, during which off-resonance phase can accumulate, leading to image degradation. This degradation often limits the usefulness of the images. Presented here is a method to iteratively reconstruct an image acquired by a spiral snapshot technique and to remove image degradation due to off resonance. This iterative method does not assume that the inhomogeneity is slowly varying within the image, allowing better results than with deblurring techniques which do not take abrupt changes into account. Although presented here with a spiral imaging technique, the iterative algorithm is general enough to be applied to a variety of snapshot imaging techniques.

An optimal and efficient new gridding algorithm using singular value decomposition

The problem of handling data that falls on a nonequally spaced grid occurs in numerous fields of science, ranging from radio-astronomy to medical imaging. In MRI, this condition arises when sampling under time-varying gradients in sequences such as echo-planar imaging (EPI), spiral scans, or radial scans. The technique currently being used to interpolate the nonuniform samples onto a Cartesian grid is called the gridding algorithm. In this paper, a new method for uniform resampling is presented that is both optimal and efficient. It is first shown that the resampling problem can be formulated as a problem of solving a set of linear equations Ax = b, where x and b are vectors of the uniform and nonuniform samples, respectively, and A is a matrix of the sinc interpolation coefficients. In a procedure called Uniform Re-Sampling (URS), this set of equations is given an optimal solution using the pseudoinverse matrix which is computed using singular value decomposition (SVD). In large problems, this solution is neither practical nor computationally efficient. Another method is presented, called the Block Uniform Re-Sampling (BURS) algorithm, which decomposes the problem into solving a small set of linear equations for each uniform grid point. These equations are a subset of the original equations Ax = b and are once again solved using SVD. The final result is both optimal and computationally efficient. The results of the new method are compared with those obtained using the conventional gridding algorithm via simulations.

Analytical resolution and noise characteristics of linearly reconstructed magnetic resonance data with arbitrary k-space sampling

The effects of time-varying readout gradients and data sampling with variable dwell times in magnetic resonance imaging are examined. General reconstruction formulas are given for linear reconstruction with even k-space weighting. Closed analytic expressions for estimator variance are given for data sampling during arbitrary gradient waveforms with both uniform kx step size and nonuniform kx step size. It is shown that estimator variance increases (the signal-to-noise ratio decreases) for nonconstant gradient waveforms. It is also shown that estimator variance is greater for constant k-space sampling strategies than for constant time sampling at the Nyquist rate. Data collected during a triangular readout gradient waveform, with either constant time or constant k-space sampling, versus conventional (constant gradient) collection confirms theoretical predictions for estimator variance. The benefits of collecting data while the readout gradient is ramping up from and down to zero are discussed.

Reconstruction by weighted correlation for MRI with time-varying gradients

A general reconstruction algorithm for magnetic resonance imaging (MRI) with gradients having arbitrary time dependence is presented. This method estimates spin density by calculating the weighted correlation of the observed free induction decay signal and the phase modulation function at each point. A theorem which states that this method can be derived from the conditions of linearity and shift invariance is presented. Since these conditions are general, most of the MRI reconstruction algorithms proposed so far are equivalent to the weighted correlation method. An explicit representation of the point spread function (PSF) in the weighted correlation method is given. By using this representation, a method to control the PSF and the static field inhomogeneity effects is studied. A correction method for the inhomogeneity is proposed, and a limitation is clarified. Some simulation results are presented.