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.     

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.     

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 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.     

Correction of eddy current-induced artefacts in diffusion tensor imaging using iterative cross-correlation.

Geometric distortions of echo-planar images produced by the strong eddy currents present in the diffusion tensor imaging experiment are a major confound to the accurate quantification of diffusion coefficients, and measures of diffusion anisotropy based upon them. Here we investigate how the method of iterative cross-correlation (ICC) of baseline and diffusion-weighted images (DWIs) originally proposed by Haselgrove and Moore (Magn. Reson. Med. 36:960-964; 1996) can be extended to correct high b-value DWIs, without the need for extrapolation of distortion parameters determined from low b-value images. Monte Carlo simulations of synthetic brain images show that the maximum value of the trace of the b-matrix, Tr(b), at which distorted DWIs can be accurately corrected by direct comparison with the undistorted baseline image is approximately 300 s mm(-2). Removal of the cerebrospinal fluid signal greatly extends this value of Tr(b) (up to approximately 2000 s mm(-2)), thereby allowing direct comparison of baseline and distorted images. The use of ICC distortion parameters determined from separate calibrations of water phantom images is also investigated, and found to be effective in correcting geometric distortions observed in the DWIs collected as part of a human volunteer diffusion tensor imaging study. This work suggests that distorted DWIs acquired at high values of b may be corrected using the ICC algorithm without collecting additional low b-value images, thus allowing simplified methods of measuring the apparent diffusion tensor D, based on collecting a small number of DWIs, to be implemented in quantitative patient examinations.     

Correction of B0 susceptibility induced distortion in diffusion-weighted images using large-deformation diffeomorphic metric mapping

Geometric distortion caused by B0 inhomogeneity is one of the most important problems for diffusion-weighted images (DWI) using single-shot, echo planar imaging (SS-EPI). In this study, large-deformation, diffeomorphic metric mapping (LDDMM) algorithm has been tested for the correction of geometric distortion in diffusion tensor images (DTI). Based on data from nine normal subjects, the amount of distortion caused by B0 susceptibility in the 3-T magnet was characterized. The distortion quality was validated by manually placing landmarks in the target and DTI images before and after distortion correction. The distortion was found to be up to 15 mm in the population-averaged map and could be more than 20 mm in individual images. Both qualitative demonstration and quantitative statistical results suggest that the highly elastic geometric distortion caused by spatial inhomogeneity of the B0 field in DTI using SS-EPI can be effectively corrected by LDDMM. This postprocessing method is especially useful for correcting existent DTI data without phase maps.     

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.     

Field camera versus phantom-based measurement of the gradient system transfer function (GSTF) with dwell time compensation

PurposeThe gradient system transfer function (GSTF) can be used to describe the dynamic gradient system and applied for trajectory correction in non-Cartesian MRI. This study compares the field camera and the phantom-based methods to measure the GSTF and implements a compensation for the difference in measurement dwell time.MethodsThe self-term GSTFs of a MR system were determined with two approaches: 1) using a dynamic field camera and 2) using a spherical phantom-based measurement with standard MR hardware. The phantom-based GSTF was convolved with a box function to compensate for the dwell time dependence of the measurement. The field camera and phantom-based GSTFs were used for trajectory prediction during retrospective image reconstruction of 3D wave-CAIPI phantom images.ResultsDifferences in the GSTF magnitude response were observed between the two measurement methods. For the wave-CAIPI sequence, this led to deviations in the GSTF predicted trajectories of 4% compared to measured trajectories, and residual distortions in the reconstructed phantom images generated with the phantom-based GSTF. Following dwell-time compensation, deviations in the GSTF magnitudes, GSTF-predicted trajectories, and resulting image artifacts were eliminated (< 0.5% deviation in trajectories).ConclusionWith dwell time compensation, both the field camera and the phantom-based GSTF self-terms show negligible deviations and lead to strong artifact reduction when they are used for trajectory correction in image reconstruction.     

Adaptive-optics ultrahigh-resolution optical coherence tomography

Merging of ultrahigh-resolution optical coherence tomography (UHR OCT) and adaptive optics (AO), resulting in high axial (3 microm) and improved transverse resolution (5-10 microm) is demonstrated for the first time to our knowledge in in vivo retinal imaging. A compact (300 mm x 300 mm) closed-loop AO system, based on a real-time Hartmann-Shack wave-front sensor operating at 30 Hz and a 37-actuator membrane deformable mirror, is interfaced to an UHR OCT system, based on a commercial OCT instrument, employing a compact Ti:sapphire laser with 130-nm bandwidth. Closed-loop correction of both ocular and system aberrations results in a residual uncorrected wave-front rms of 0.1 microm for a 3.68-mm pupil diameter. When this level of correction is achieved, OCT images are obtained under a static mirror configuration. By use of AO, an improvement of the transverse resolution of two to three times, compared with UHR OCT systems used so far, is obtained. A significant signal-to-noise ratio improvement of up to 9 dB in corrected compared with uncorrected OCT tomograms is also achieved.     

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.     

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.     

具有在线形貌矫正能力的组织体光学参数测量系统

针对具有复杂形貌的大面积组织体,基于空间频率域方法,提出并搭建了一种具有在线形貌矫正能力的绝对光学参数测量系统.首先利用相位轮廓术获取组织体三维表面轮廓,用余弦辐射公式法矫正由组织体表面复杂形貌引起的光照度的差异.然后,采用漫反射板代替传统方法中的参考仿体,基于空间频率域测量模式进行绝对光学参数测量,并利用提出的光学参数反演方法实现组织体吸收系数的重建.组织仿体实验结果表明,对于表面高度小于29mm的仿体,经矫正后,吸收系数的测量相对误差从60%下降到13%.     

Deconvolution of vibroacoustic images using a simulation model based on a three dimensional point spread function

Vibro-acoustography (VA) is a medical imaging method based on the difference-frequency generation produced by the mixture of two focused ultrasound beams. VA has been applied to different problems in medical imaging such as imaging bones, microcalcifications in the breast, mass lesions, and calcified arteries. The obtained images may have a resolution of 0.7–0.8 mm. Current VA systems based on confocal or linear array transducers generate C-scan images at the beam focal plane. Images on the axial plane are also possible, however the system resolution along depth worsens when compared to the lateral one. Typical axial resolution is about 1.0 cm. Furthermore, the elevation resolution of linear array systems is larger than that in lateral direction. This asymmetry degrades C-scan images obtained using linear arrays. The purpose of this article is to study VA image restoration based on a 3D point spread function (PSF) using classical deconvolution algorithms: Wiener, constrained least-squares (CLSs), and geometric mean filters. To assess the filters’ performance on the restored images, we use an image quality index that accounts for correlation loss, luminance and contrast distortion. Results for simulated VA images show that the quality index achieved with the Wiener filter is 0.9 (when the index is 1.0 this indicates perfect restoration). This filter yielded the best result in comparison with the other ones. Moreover, the deconvolution algorithms were applied to an experimental VA image of a phantom composed of three stretched 0.5 mm wires. Experiments were performed using transducer driven at two frequencies, 3075 kHz and 3125 kHz, which resulted in the difference-frequency of 50 kHz. Restorations with the theoretical line spread function (LSF) did not recover sufficient information to identify the wires in the images. However, using an estimated LSF the obtained results displayed enough information to spot the wires in the images. It is demonstrated that the phase of the theoretical and the experimental PSFs are dissimilar. This fact prevents VA image restoration with the current theoretical PSF. This study is a preliminary step towards understanding the restoration of VA images through the application of deconvolution filters.     

3D shape measurement of larger complex objects based on fringe cycle correction

The grating fringe on the reference plane is broadened in the intersecting axis system because of oblique-angle projection. In order to solve this problem, we study the theoretical model of the temporal phase unwrapping method based on the fringe cycle correction. We also study the 3D shape measurement theoretical model of the larger complex objects after considering the coordinate deviation and lens distortion. Experimental results demonstrate that the fringe cycle on the reference plane can be corrected to a constant value, the lens distortion can be corrected, and 3D shape of larger complex objects can be accurately measured.     

光子计数位置灵敏探测器畸变多项式校正

采用多项式校正方法对光子计数位置灵敏探测器成像畸变进行校正。介绍光子计数位置灵敏探测器工作原理并分析其畸变产生原因;介绍多项式校正原理,并给出光子计数位置灵敏探测器畸变多项式校正流程;采用该方法对两种不同畸变程度的基于楔条形阳极该类探测器进行了畸变校正,校正后残余误差分别为2.5pixel和1.2pixel。实验结果表明,多项式校正法能够有效校正光子计数位置灵敏探测器成像畸变。     

A quantitative comparison of two methods to correct eddy current-induced distortions in DT-MRI

Eddy current-induced geometric distortions of single-shot, diffusion-weighted, echo-planar (DW-EP) images are a major confounding factor to the accurate determination of water diffusion parameters in diffusion tensor MRI (DT-MRI). Previously, it has been suggested that these geometric distortions can be removed from brain DW-EP images using affine transformations determined from phantom calibration experiments using iterative cross-correlation (ICC). Since this approach was first described, a number of image-based registration methods have become available that can also correct eddy current-induced distortions in DW-EP images. However, as yet no study has investigated whether separate eddy current calibration or image-based registration provides the most accurate way of removing these artefacts from DT-MRI data. Here we compare how ICC phantom calibration and affine FLIRT (http://www.fmrib.ox.ac.uk), a popular image-based multi-modal registration method that can correct both eddy current-induced distortions and bulk subject motion, perform when registering DW-EP images acquired with different slice thicknesses (2.8 and 5 mm) and b-values (1000 and 3000 s/mm(2)). With the use of consistency testing, it was found that ICC was a more robust algorithm for correcting eddy current-induced distortions than affine FLIRT, especially at high b-value and small slice thickness. In addition, principal component analysis demonstrated that the combination of ICC phantom calibration (to remove eddy current-induced distortions) with rigid body FLIRT (to remove bulk subject motion) provided a more accurate registration of DT-MRI data than that achieved by affine FLIRT.     

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.     

On the use of water phantom images to calibrate and correct eddy current induced artefacts in MR diffusion tensor imaging

The accurate determination of absolute measures of diffusion anisotropy in vivo using single-shot, echo-planar imaging techniques requires the acquisition of a set of high signal-to-noise ratio, diffusion-weighted images that are free from eddy current induced image distortions. Such geometric distortions can be characterized and corrected in brain imaging data using magnification (M), translation (T), and shear (S) distortion parameters derived from separate water phantom calibration experiments. Here we examine the practicalities of using separate phantom calibration data to correct high b-value diffusion tensor imaging data by investigating the stability of these distortion parameters, and hence the eddy currents, with time. It is found that M, T, and S vary only slowly with time (i.e., on the order of weeks), so that calibration scans need not be performed after every patient examination. This not only minimises the scan time required to collect the calibration data, but also the computational time needed to characterize these eddy current induced distortions. Examples of how measurements of diffusion anisotropy are improved using this post-processing scheme are also presented.     

Image feature based automatic correction of low-frequency spatial intensity variations in MR images

An automatic method of compensating for low-frequency variations in magnetic resonance images is presented. Small variations within a tissue type are modelled and a correction function is generated. The methods is based completely on image features and does not need a phantom or user interaction to generate the compensation function. This image correction simplifies digital image analysis and may enhance clinical evaluation. As a result, the correction technique reduces inhomogeneity and improves contrast. Our results show that the radiofrequency response variation of coils can be reduced. The segmentation process, even with a simple threshold method, produces more reliable results when corrected images are used. The presented method is most useful for images acquired in the sagital and coronal planes with circular local coils, or using surface coils, e.g., spine coils.     

Reduced distortion artifact whole brain CBF mapping using blip-reversed non-segmented 3D echo planar imaging with pseudo-continuous arterial spin labeling

PurposeTo implement and evaluate interleaved blip-up, blip-down, non-segmented 3D echo planar imaging (EPI) with pseudo-continuous arterial spin labeling (pCASL) and post-processing for reduced susceptibility artifact cerebral blood flow (CBF) maps.Materials and methods3D EPI non-segmented acquisition with a pCASL labeling sequence was modified to include alternating k-space coverage along phase encoding direction (referred to as “blip-reversed”) for alternating dynamic acquisitions of control and label pairs. Eight volunteers were imaged on a 3T scanner. Images were corrected for distortion using spatial shifting transformation of the underlying field map. CBF maps were calculated and compared with maps obtained without blip reversal using matching gray matter (GM) images from a high resolution 3D scan. Additional benefit of using the correction for alternating blip-up and blip-down acquisitions was assessed by comparing to corrected blip-up only and corrected blip-down only CBF maps. Matched Student t-test of overlapping voxels for the eight volunteers was done to ascertain statistical improvement in distortion.ResultsMean CBF value in GM for the eight volunteers from distortion corrected CBF maps was 50.8 ± 9.9 ml/min/100 gm tissue. Corrected CBF maps had 6.3% and 4.1% more voxels in GM when compared with uncorrected blip up (BU) and blip down (BD) images, respectively. Student t-test showed significant reduction in distortion when compared with blip-up images and blip-down images (p < 0.001). When compared with corrected BU and corrected BD only CBF maps, BU and BD corrected maps had 2.3% and 1% more voxels (p = 0.006 and 0.04, respectively).ConclusionPseudo-continuous arterial spin labeling with non-segmented 3D EPI acquisition using alternating blip-reversed k-space traversal and distortion correction provided significantly better matching GM CBF maps. In addition, employing alternating blip-reversed acquisitions during pCASL acquisition resulted in statistically significant improvement over corrected blip-up and blip-down CBF maps.