A hybrid strategy for correcting geometric distortion in echo-planar images

A hybrid strategy for geometric distortion correction of echo-planar images is demonstrated. This procedure utilizes standard field mapping for signal displacement correction and the so-called reverse gradient acquisition for signal intensity correction. (The term reverse gradient refers to an acquisition of two sets of echo-planar images with phase encoding gradients of opposite polarity.) The hybrid strategy is applied to human brain echo-planar images acquired with and without diffusion-weighting. A comparison of the hybrid distortion corrected images to those corrected with standard field mapping only demonstrates much better performance of the hybrid method. A variant of the hybrid method is also demonstrated which requires the acquisition of only one pair of opposite polarity images within a set of images.     

Magnetic resonance spectroscopic imaging for visualization and correction of distortions in MRI: high precision applications in neurosurgery

We present a method for the quantification and correction of geometrical/intensity distortions of magnetic resonance images predominantly caused by bulk magnetic susceptibility shifts due to susceptibility heterogeneities of measured biologic tissues and shape of the object under investigation. The method includes precise and fast measurements of the static magnetic-field distribution inside the measured object and automated data processing. Magnetic-field deviations in the range −2.4; 2.6 ppm were found in the human brain at B₀ = 1.5 T. For routinely used imaging parameters, with a read gradient strength of about 1 mT/m, the magnetic-field perturbations in the human brain can cause geometrical distortions up to ±4 mm and intensity changes up to ±50%. MR images corrected by the described method are suitable for planning high precision applications in neurosurgery.     

Geometric distortion in clinical MRI systems Part I: evaluation using a 3D phantom

Recently, a 3D phantom that can provide a comprehensive and accurate measurement of the geometric distortion in MRI has been developed. Using this phantom, a full assessment of the geometric distortion in a number of clinical MRI systems (GE and Siemens) has been carried out and detailed results are presented in this paper. As expected, the main source of geometric distortion in modern superconducting MRI systems arises from the gradient field nonlinearity. Significantly large distortions with maximum absolute geometric errors ranged between 10 and 25 mm within a volume of 240 x 240 x 240 mm(3) were observed when imaging with the new generation of gradient systems that employs shorter coils. By comparison, the geometric distortion was much less in the older-generation gradient systems. With the vendor's correction method, the geometric distortion measured was significantly reduced but only within the plane in which these 2D correction methods were applied. Distortion along the axis normal to the plane was, as expected, virtually unchanged. Two-dimensional correction methods are a convenient approach and in principle they are the only methods that can be applied to correct geometric distortion in a single slice or in multiple noncontiguous slices. However, these methods only provide an incomplete solution to the problem and their value can be significantly reduced if the distortion along the normal of the correction plane is not small.     

Concurrent correction of geometric distortion and motion using the map-slice-to-volume method in echo-planar imaging

The accuracy of measuring voxel intensity changes between stimulus and rest images in fMRI echo-planar imaging (EPI) data is severely degraded in the presence of head motion. In addition, EPI is sensitive to susceptibility-induced geometric distortions. Head motion causes image shifts and associated field map changes that induce different geometric distortion at different time points. Conventionally, geometric distortion is "corrected" with a static field map independently of image registration. That approach ignores all field map changes induced by head motion. This work evaluates the improved motion correction capability of mapping slice to volume with concurrent iterative field corrected reconstruction using updated field maps derived from an initial static field map that has been spatially transformed and resampled. It accounts for motion-induced field map changes for translational and in-plane rotation motion. The results from simulated EPI time series data, in which motion, image intensity and activation ground truths are available, show improved accuracy in image registration, field corrected image reconstruction and activation detection.     

Correction of spatial distortion in magnetic resonance angiography for radiosurgical treatment planning of cerebral arteriovenous malformations.

A treatment planning system based on magnetic resonance (MR) angiographic imaging data for the radiosurgery of inoperable cerebral arteriovenous malformations is reported. MR angiography was performed using a three-dimensional (3D) velocity-compensated fast imaging with steady-state precession (FISP) sequence. Depending on the individual MR system, inhomogeneities and nonlinearities induced by eddy currents during the pulse sequence can distort the images and produce spurious displacements of the stereotactic coordinates in both the x-y plane and the z axis. If necessary, these errors in position can be assessed by means of two phantoms placed within the stereotactic guidance system--a "2D-phantom" displaying "pincushion" distortion in the image, and a "3D-phantom" displaying displacement, warp, and tilt of the image plane itself. The pincushion distortion can be "corrected" (reducing displacements from 2-3 mm to 1 mm) by calculations based on modeling the distortion as a fourth order 2D polynomial. Displacement, warp, and tilt of the image plane may be corrected by adjustment of the gradient shimming currents. After correction, the accuracy of the geometric information is limited only by the pixel resolution of the image (= 1 mm). Precise definition of the target volume could be performed by the therapist either directly in the MR images or in calculated projection MR angiograms obtained by a maximum intensity projection algorithm. MR angiography provides a sensitive, noninvasive 3D method for defining target volume and critical structures, and for calculating precise dose distributions for radiosurgery of cerebral arteriovenous malformations.     

Field-map correction in read-out segmented echo planar imaging for reduced spatial distortion in prostate DWI for MRI-guided radiotherapy applications

Diffusion-weighted echo planar imaging (DW-EPI) suffers from geometric distortion due to low phase-encoding bandwidth. Read-out segmented echo planar imaging (RS-EPI) reduces distortion but residual distortion remains in extreme cases. Additional corrections need to be applied, especially for radiotherapy applications where a high degree of accuracy is needed. In this study the use of magnetic field map corrections are assessed in DW-EPI and RS-EPI, to reduce geometric uncertainty for MRI-guided radiotherapy applications. Magnetic field maps were calculated from gradient echo images and distortion corrections were applied to RS-EPI images. Distortions were assessed in a prostate phantom by comparing to the known geometry, and in vivo using a modified Hausdorff distance metric using a T2-weighted spin echo as ground truth. Across 10 patients, field map-corrected RS-EPI reduced maximum distortion by 5 mm on average compared to DW-EPI (σ = 1.9 mm). Geometric distortions were also reduced significantly using field mapping with RS-EPI, compared to RS-EPI alone (p ≤ 0.05). The increased geometric accuracy of these techniques can potentially allow diffusion-weighted images to be fused with other MR or CT images for radiotherapy treatment purposes.     

Correction of concomitant gradient artifacts in experimental microtesla MRI

Magnetic resonance imaging (MRI) suffers from artifacts caused by concomitant gradients when the product of the magnetic field gradient and the dimension of the sample becomes comparable to the static magnetic field. To investigate and correct for these artifacts at very low magnetic fields, we have acquired MR images of a 165-mm phantom in a 66-microT field using gradients up to 350 microT/m. We prepolarize the protons in a field of about 100 mT, apply a spin-echo pulse sequence, and detect the precessing spins using a superconducting gradiometer coupled to a superconducting quantum interference device (SQUID). Distortion and blurring are readily apparent at the edges of the images; by comparing the experimental images to computer simulations, we show that concomitant gradients cause these artifacts. We develop a non-perturbative, post-acquisition phase correction algorithm that eliminates the effects of concomitant gradients in both the simulated and the experimental images. This algorithm assumes that the switching time of the phase-encoding gradient is long compared to the spin precession period. In a second technique, we demonstrate that raising the precession field during phase encoding can also eliminate blurring caused by concomitant phase-encoding gradients; this technique enables one to correct concomitant gradient artifacts even when the detector has a restricted bandwidth that sets an upper limit on the precession frequency. In particular, the combination of phase correction and precession field cycling should allow one to add MRI capabilities to existing 300-channel SQUID systems used to detect neuronal currents in the brain because frequency encoding could be performed within the 1-2 kHz bandwidth of the readout system.     

基于折射率梯度门限的气动光学窗口光传输研究

基于流场界面厚度（Interfacial—Fluid—Thickness,IFT）理论,建立了高折射率梯度门限模型来研究气动光学窗口光传输畸变。首先在光学窗口折射率梯度场基础上,提出高折射率梯度门限,忽略绝对值低于该门限的折射率梯度值,重构折射率场,并对其气动光学传输效应进行仿真。结果表明,当58．37％的梯度值被忽略时,得到的重构折射率场与原折射率场仿真光程差（OPD）最大相对误差不超过1．5％,验证了气动光学窗口高折射率梯度区域是产生光传输畸变的主要原因,也证实了该门限模型对气动光学窗口光传输效应进行仿真的可行性,对气动光学失真的机理、预测及校正有一定的指导意义。     

Characteristics of geometric distortion correction with increasing field-of-view in open-configuration MRI

Open-configuration magnetic resonance imaging (MRI) systems are becoming increasingly desirable for musculoskeletal imaging and image-guided radiotherapy because of their non-claustrophobic configuration. However, geometric image distortion in large fields-of-view (FOV) due to field inhomogeneity and gradient nonlinearity hinders the practical applications of open-type MRI. We demonstrated the use of geometric distortion correction for increasing FOV in open MRI. Geometric distortion was modeled and corrected as a global polynomial function. The appropriate polynomial order was identified as the minimum difference between the coordinates of control points in the distorted MR image space and those predicted by polynomial modeling. The sixth order polynomial function was found to give the optimal value for geometric distortion correction. The area of maximum distortion was < 1 pixel with an FOV of 285 mm. The correction performance error was increased at most 1.2% and 2.9% for FOVs of 340 mm and ~ 400 mm compared with the FOV of 285 mm. In particular, unresolved distortion was generated by local deformation near the gradient coil center.     

Mapping eddy current induced fields for the correction of diffusion-weighted echo planar images

Diffusion-weighted echo-planar magnetic resonance imaging is potentially of great importance as a diagnostic imaging tool; however, the technique currently suffers a number of limitations, including the image distortion caused by the eddy current induced fields when the diffusion-weighting magnetic field gradient pulses are applied. The distortions cause mis-registration between images with different diffusion-weighting, that then results in artifacts in quantitative diffusion images. A method is presented to measure the magnetic fields generated from the eddy currents for each of three orthogonal gradient pulse vectors, and then to use these to ascertain the image distortion that occurs in subsequent diffusion-weighted images with arbitrary gradient pulse vector amplitude and direction, and image plane orientation. The image distortion can then be reversed. Both temporal and spatial dependence of the residual eddy current induced fields are included in the analysis. Image distortion was substantially reduced by the correction scheme, for arbitrary slice position and angulation. This method of correction is unaffected by the changes in image contrast that occur due to diffusion weighting, and does not need any additional scanning time during the patient scan. It is particularly suitable for use with single-shot echo planar imaging.     

An anisotropic images segmentation and bias correction method

Intensity inhomogeneities cause considerable difficulty in the quantitative analysis of magnetic resonance (MR) images. Thus, bias field correction is a necessary step before quantitative analysis of MR data can be undertaken. This paper presents an anisotropic approach to bias correction and segmentation for images with intensity inhomogeneities and noise. Intensity-based methods are usually applied to estimate the bias field; however, most of them only concern the intensity information. When the images have noise or slender topological objects, these methods cannot obtain accurate results or bias fields. We use structure information to construct an anisotropic Gibbs field and combine the anisotropic Gibbs field with the Bayesian framework to segment images while estimating the bias fields. Our method is able to capture bias of quite general profiles. Moreover, it is robust to noise and slender topological objects. The proposed method has been used for images of various modalities with promising results.     

A post-processing method for correction and enhancement of chemical shift images

Chemical shift imaging (CSI) relies on a strong and homogeneous main field. Field homogeneity ensures adequate coherence between the precessions of individual spins within each voxel. Variation of field strength between different voxels causes geometric distortion and intensity variation in chemical shift images, resulting in errors when analyzing the spatial distribution of specific chemical compounds. A post-processing method, based on detection of the spectral peak of water and baseline subtraction with Lorentzian functions, was developed in this study to automatically correct spectra offsets caused by field inhomogeneity, thus enhancing the contrast of the chemical shift images. Because this method does not require prior field plot information, it offers advantages over existing correction methods. Furthermore, the method significantly reduces geometric distortion and enhances signals of chemical compounds even when the water suppression protocol was applied during the CSI data acquisition. The experimental results of the water and glucose phantoms showed a considerable reduction of artifacts in the spectroscopic images when this post-processing method was employed. The significance of this method was also demonstrated by an analysis of the spatial distributions of sugar and water contents in ripe and unripe bananas.     

Double-spin-echo diffusion weighting with a modified eddy current adjustment

Magnetic field inhomogeneities like eddy current-related gradient fields cause geometric distortions in echo-planar imaging (EPI). This in particular affects diffusion-weighted imaging where these distortions vary with the direction of the diffusion weighting and hamper the accurate determination of diffusion parameters. The double-spin-echo preparation often used aims to reduce the cumulative eddy current effect by adjusting the diffusion-weighting gradient pulse durations to the time constant of the dominant eddy current contribution. However, eddy currents with a variety of time constants may be present and cause residual distortions. Here, a modification is proposed where the two bipolar gradient pairs of the preparation are adjusted independently to different time constants. At the expense of a slightly prolonged echo time, residual geometric distortions and correspondingly increased values of the diffusion anisotropy can be reduced as is demonstrated in phantoms and the human brain. Thus, it may help to improve the reliability of diffusion-weighted EPI.     

A novel phantom and method for comprehensive 3-dimensional measurement and correction of geometric distortion in magnetic resonance imaging

A phantom that can be used for mapping geometric distortion in magnetic resonance imaging (MRI) is described. This phantom provides an array of densely distributed control points in three-dimensional (3D) space. These points form the basis of a comprehensive measurement method to correct for geometric distortion in MR images arising principally from gradient field non-linearity and magnet field inhomogeneity. The phantom was designed based on the concept that a point in space can be defined using three orthogonal planes. This novel design approach allows for as many control points as desired. Employing this novel design, a highly accurate method has been developed that enables the positions of the control points to be measured to sub-voxel accuracy. The phantom described in this paper was constructed to fit into a body coil of a MRI scanner, (external dimensions of the phantom were: 310 mm x 310 mm x 310 mm), and it contained 10,830 control points. With this phantom, the mean errors in the measured coordinates of the control points were on the order of 0.1 mm or less, which were less than one tenth of the voxel's dimensions of the phantom image. The calculated three-dimensional distortion map, i.e., the differences between the image positions and true positions of the control points, can then be used to compensate for geometric distortion for a full image restoration. It is anticipated that this novel method will have an impact on the applicability of MRI in both clinical and research settings, especially in areas where geometric accuracy is highly required, such as in MR neuro-imaging.     

A dual image approach for bias field correction in magnetic resonance imaging

In this paper, we propose a dual image approach to correcting intensity inhomogeneities for MR images acquired using surface coils. Previous methods are usually not satisfactory due to restricted application domains, considerable human interactions, or some undesirable artifacts. The proposed algorithm provides nice correction results for a variety of surface-coil MR images. It is accomplished by using an additional body-coil MR image of a smaller size captured at the same position as that of the surface-coil image to facilitate the estimation of the bias field function. The correction algorithm consists of aligning the surface-coil image with the body-coil image and fitting a spline surface from a sparse set of data points for the associated bias field function. Experiments on some real images show satisfactory correction results by using the proposed algorithm.     

Water–fat separation with parallel imaging based on BLADE

Uniform suppression of fat signal is desired in clinical applications. Based on phase differences introduced by different chemical shift frequencies, Dixon method and its variations are used as alternatives of fat saturation methods, which are sensitive to B0 inhomogeneities. Iterative Decomposition of water and fat with Echo Asymmetry and Least squares estimation (IDEAL) separates water and fat images with flexible echo shifting. Periodically Rotated Overlapping ParallEL Lines with Enhanced Reconstruction (PROPELLER, alternatively termed as BLADE), in conjunction with IDEAL, yields Turboprop IDEAL (TP-IDEAL) and allows for decomposition of water and fat signal with motion correction. However, the flexibility of its parameter setting is limited, and the related phase correction is complicated. To address these problems, a novel method, BLADE-Dixon, is proposed in this study. This method used the same polarity readout gradients (fly-back gradients) to acquire in-phase and opposed-phases images, which led to less complicated phase correction and more flexible parameter setting compared to TP-IDEAL. Parallel imaging and undersampling were integrated to reduce scan time. Phantom, orbit, neck and knee images were acquired with BLADE-Dixon. Water–fat separation results were compared to those measured with conventional turbo spin echo (TSE) Dixon and TSE with fat saturation, respectively, to demonstrate the performance of BLADE-Dixon.     

Short planar gradient coils for MR microscopy using concentric return paths

The aim of this work is to design a set of gradient coils with an optimal geometry for magnetic resonance microscopy studies. Designs for a three-axis gradient coil system particularly suited for studies with small radiofrequency coils are presented. The novel geometry involves a planar section with concentric return paths to keep the coil short. Reduction of the external field has been attempted by varying the positions of the return paths using a simulated annealing algorithm. A biplanar version of x- and z-directed prototype gradients was built and tested. A 2D-MR image of a grid phantom has been obtained on a 7-T MR instrument to demonstrate the theory. A three-axis set used as a surface gradient set has also been built and used to obtain high-resolution MR images.     

Distortions of videofiberoscopy imaging: Reconsideration and correction

An analysis was made of the optical distortion of a lens system of a fiberscope and the distortion related to lens-object angles and lens-object distances used in laryngeal flexible endoscopic examinations. The optical distortion was systematic and, therefore, could be corrected through computer processing once the calibration was made. Similarly, the distortion related to the lens-object angle and distance varied systematically depending on distance and angle and, therefore, could be predicted if those parameters were measured simultaneously. The correction of those distortions of videofiberoscopic image is demonstrated, and a procedure for recording and measuring laryngeal images that minimizes measurement error due to those distortions is suggested.     

Geometric distortion in clinical MRI systems Part II: correction using a 3D phantom

In this paper, we present the correction of the geometric distortion measured in the clinical magnetic resonance imaging (MRI) systems reported in the preceding paper (Part I) using a 3D method based on the phantom-mapped geometric distortion data. This method allows the correction to be made on phantom images acquired without or with the vendor correction applied. With the vendor's 2D correction applied, the method corrects for both the "residual" geometric distortion still present in the plane in which the correction method was applied (the axial plane) and the uncorrected geometric distortion along the axis normal to the plane. The evaluation of the effectiveness of the correction using this new method was carried out through analyzing the residual geometric distortion in the corrected phantom images. The results show that the new method can restore the distorted images in 3D nearly to perfection. For all the MRI systems investigated, the mean absolute deviations in the positions of the control points (along x-, y- and z-axes) measured on the corrected phantom images were all less than 0.2 mm. The maximum absolute deviations were all below approximately 0.8 mm. As expected, the correction of the phantom images acquired with the vendor's correction applied in the axial plane performed equally well. Both the geometric distortion still present in the axial plane after applying the vendor's correction and the uncorrected distortion along the z-axis have all been "restored."