MRI geometric distortion: A simple approach to correcting the effects of non‐linear gradient fields

Langlois, Serge; Desvignes, Michel; Constans, Jean-Marc; Revenu, Marinette

doi:10.1002/(sici)1522-2586(199906)9:6<821::aid-jmri9>3.3.co;2-u

Cited by 34 publications

(47 citation statements)

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“…[13] is required as per Langlois et al (9). This method can be readily applied irrespective of the particular pulse sequence and/or k-space trajectory.…”

Section: Theorymentioning

confidence: 99%

Use of spherical harmonic deconvolution methods to compensate for nonlinear gradient effects on MRI images

Janke

Zhao

Cowin

et al. 2004

Magnetic Resonance in Med

140

191

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Spatial encoding in MR techniques is achieved by sampling the signal as a function of time in the presence of a magnetic field gradient. The gradients are assumed to generate a linear magnetic field gradient, and typical image reconstruction relies upon this approximation. However, high-speed gradients in the current generation of MRI scanners often sacrifice linearity for improvements in speed. Such nonlinearity results in distorted images. The problem is presented in terms of first principles, and a correction method based on a gradient field spherical harmonic expansion is proposed. In our case, the amount of distortion measured within a typical field of view (FOV) required for head imaging is sufficiently large that without the use of some distortion correction technique, the images would be of The quality of an MR image is dependent upon the accuracy with which the physical position is spatially encoded. Since MRI data are now used routinely for stereotaxy, longitudinal studies of atrophy, and functional studies, it is critical to ensure that images have no distortion or inhomogeneity. The principal machine-dependent sources of this inhomogeneity are eddy currents, gradient nonlinearity, and B 0 and B 1 inhomogeneity (14). In this study we present an analytical approach to calculating and removing the effects of nonlinear gradients only. We chose to focus on a gradient-only solution because of the recent interest in short-bore, high-speed gradients. Although peripheral nerve stimulation is a limiting feature of short rise times, such gradients have been found to be useful in high-speed echo-planar imaging (EPI) of the heart and diffusion tensor imaging (DTI) of the brain. To achieve short rise times and avoid peripheral nerve stimulation, designers have restricted the length of gradients and limited the number of turns in those gradients. Although these constraints are suitable for the implementation of pulse sequences with the desired speed, they have the undesired consequence of increased nonlinearity.Nonlinear pulsed field gradients induce image distortions due to incorrect spatial encoding of the signal. If we assume that the field gradients are linear, it follows that k-space is sampled linearly, and thus the fast Fourier transform (FFT) is suitable for reconstruction. However, any deviation from linearity in the gradients results in nonlinear data sampling and subsequent errors in image spatial encoding. A nonlinear FT would allow these data to be correctly transformed to an image. Unfortunately, nonlinear FT greatly increases computation time by N/log 2 N, relative to an FFT, which makes real-time image generation computationally prohibitive. Here we present a general analytical solution to correct image distortions induced by gradient nonlinearity. The method is applicable to any gradient configuration. It is robust and, more importantly, is based upon an approach whereby the FFT is maintained for image reconstruction.The notion of mapping and correcting such MRI distortions is not new. Two early pa...

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“…[13] is required as per Langlois et al (9). This method can be readily applied irrespective of the particular pulse sequence and/or k-space trajectory.…”

Section: Theorymentioning

confidence: 99%

Use of spherical harmonic deconvolution methods to compensate for nonlinear gradient effects on MRI images

Janke

Zhao

Cowin

et al. 2004

Magnetic Resonance in Med

140

191

View full text Add to dashboard Cite

show abstract

“…In this case, the coils generate curvilinear yet time-invariant field patterns and standard Fourier imaging still applies in the resulting curved coordinate system. The corresponding image distortions can be removed by unwarping (1) and, in the extreme case of non-bijective gradient fields, by unfolding based on array detection (2,3). Magnetic fields of higher than first order in space also arise from imperfection of the main magnet and susceptibility effects.…”

Section: Introductionmentioning

confidence: 99%

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

Wilm

Barmet

Pavan

et al. 2011

Magnetic Resonance in Med

149

246

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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. Magn Reson Med 65:1690-1701, 2011.

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“…The distortion model, describing the spatial dependence of the three gradient fields, was based on a finite sum of sum of spherical harmonics (when expressed in spherical coordinates) [2], or a sum of homogeneous polynomials (when expressed in Cartesian coordinates) [4]. Using the ideal planes obtained previously, theoretical "undistorted" data points were calculated using the ideal plane equations and acquired data points.…”

Section: Distortion Modelingmentioning

confidence: 99%

“…Further, letx i ,ȳ i , andz i be the undistorted coordinates that correspond to x i , y i , and z i , that is, (x i ,ȳ i ,z i ) is the point on the ideal plane that produced the point (x i , y i , z i ) in the image. Including spherical harmonics up to second order, the distortion model, expressed in Cartesian coordinates, becomes [4]:…”

Section: Distortion Modelingmentioning

confidence: 99%

“…Although current methods are successful in handling gradient nonlinearity distortion [1], [2], [3], none of them have been proven to provide the high level of geometric accuracy required to confidently perform highprecision functional radiosurgery on brain targets. We have developed a software package for a phantom-based distortion method originally suggested by Langlois, et al [4]. This report describes the structure and implementation of the code, as well as first results of its performance in stereotactic localization.…”

Section: Introductionmentioning

confidence: 99%

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Software-Based Algorithm for Modeling and Correction of Gradient Nonlinearity Distortions in Magnetic Resonance Imaging

Lee

Schubert

Schulte

2008

Advances in Electrical and Electronics Engineering - IAENG Special Edition of the World Congress on Engineering and Computer Sc

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Abstract-Functional radiosurgery is a noninvasive stereotactic technique that requires magnetic resonance image (MRI) sets with high spatial resolution. Gradient nonlinearities introduce geometric distortions that compromise the accuracy of MRI-based stereotactic localization. We present a gradient nonlinearity correction method based on a cubic phantom MRI data set. The approach utilizes a sum of spherical harmonics to model the geometrically warped planes of the cube and applies the model to correct arbitrary image sets acquired with the same scanner. In this paper, we give a detailed description of the Matlab distortion correction program, report on its performance in stereotactic localization of phantom markers, and discuss the possibility to accelerate the code using General-Purpose Computing on Graphics Processing Units (GPGPU) techniques.

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MRI geometric distortion: A simple approach to correcting the effects of non‐linear gradient fields

Cited by 34 publications

References 0 publications

Use of spherical harmonic deconvolution methods to compensate for nonlinear gradient effects on MRI images

Use of spherical harmonic deconvolution methods to compensate for nonlinear gradient effects on MRI images

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

Software-Based Algorithm for Modeling and Correction of Gradient Nonlinearity Distortions in Magnetic Resonance Imaging

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