VOLUME 37 | NUMBER 6JUNE 2013

JOU

RN

AL

OF

MA

GN

ET

IC R

ES

ON

AN

CE

IMA

GIN

GV

OL

UM

E 3

7|

NU

MB

ER

6|

JUN

E 2

01

3|

PA

GE

S 1

25

7–

15

04

CME

www.w

ileyhea

lthlearning.com/jmri

EDITOR-IN-CHIEF

C. Leon Partain

CORRECTION OF EDDY CURRENT DISTORTIONS IN HIGH ANGULAR RESOLUTION DIFFUSION IMAGING from the article by Zhuang et al (pp 1460-1467)

Original Research

Correction of Eddy Current Distortions in HighAngular Resolution Diffusion Imaging

Jiancheng Zhuang, PhD,* Zhong-Lin Lu, PhD, Christine Bouteiller Vidal, PhD,

and Hanna Damasio, MD

Purpose: To correct distortions caused by eddy currentsinduced by large diffusion gradients during high angularresolution diffusion imaging without any auxiliary refer-ence scans.

Materials and Methods: Image distortion parameterswere obtained by image coregistration, performed onlybetween diffusion-weighted images with close diffusiongradient orientations. A linear model that describes dis-tortion parameters (translation, scale, and shear) as afunction of diffusion gradient directions was numericallycomputed to allow individualized distortion correction forevery diffusion-weighted image.

Results: The assumptions of the algorithm were success-fully verified in a series of experiments on phantom andhuman scans. Application of the proposed algorithm inhigh angular resolution diffusion images markedlyreduced eddy current distortions when compared toresults obtained with previously published methods.

Conclusion: The method can correct eddy current arti-facts in the high angular resolution diffusion images, andit avoids the problematic procedure of cross-correlatingimages with significantly different contrasts resultingfrom very different gradient orientations or strengths.

Key Words: high angular resolution diffusion imaging;distortions; eddy currents; echo planar imagingJ. Magn. Reson. Imaging 2013;37:1460–1467.VC 2012 Wiley Periodicals, Inc.

DIFFUSION TENSOR IMAGING (DTI) has become apopular tool to provide information about the intrinsicarchitecture of white matter in the human brain (1).However, the DTI technology has significant limita-tions in resolving orientation heterogeneity within sin-gle voxels due to the constraints of tensor models.As an obstacle for efforts to construct white matterpathways from diffusion magnetic resonance imaging(MRI) data, this limitation has prompted the

development of diffusion imaging methods capable ofresolving intravoxel fiber crossings, such as HARDI(high angular resolution diffusion imaging) (2). AmongHARDI techniques, diffusion spectrum imaging (DSI)employs the Fourier relationship between the diffu-sion signal and the function of diffusion wave vector q(3), and q-ball imaging (QBI) uses Funk–Radon trans-form to process the HARDI signal (4).

However, because most of the HARDI techniquesrequire high to ultrahigh diffusion sensitizing gra-dients (b >4000 s/mm2), the capability of HARDI toprovide valid and reliable information about tissuestructures can be affected adversely by eddy currentartifacts. In echo planar images, usually used to ac-quire diffusion-weighted images (DWI), eddy currentsproduce significant distortions in the phase-encodingdirection because of the relatively low bandwidth inthat direction and the large changes in diffusion gra-dients during HARDI scanning. Image distortionsfrom eddy currents blur the interface of gray andwhite matter tissues, cause misregistration betweenindividual diffusion-weighted images, produce errone-ous calculations of diffusion signals, and spoil thedetected high angle-resolution characteristics of diffu-sion at each voxel.

Eddy current distortions can be reduced effectivelyin one of three ways: first, by selecting an appropriatepulse sequence (such as a dual spin-echo sequence)(5,6) or gradient waveforms (such as bipolargradients) (7); second, by correcting k-space data,such as calibration of eddy current artifacts ink-space (8–10); third, by postacquisition image proc-essing that registers DWIs to the reference images.This third approach, based on postprocessing algo-rithms, is appealing because of its relative ease andaccessibility. One widely used postprocessing algo-rithm, iterative cross-correlation (ICC) (11), estimatesdistortions in DW images by cross-correlating themwith an undistorted baseline image in terms of scal-ing, shear, and translation along the phase-encodingdirection. The estimated distortion parameters arethen used to correct all distorted images (11–14).

One serious limitation of the original ICC algorithm(11), however, is its inability to correct image distor-tions at high b-values. The contrasts of cerebrospinalfluid (CSF), gray matter, and white matter in images

Dana and David Dornsife Cognitive Neuroscience Imaging Center,University of Southern California, Los Angeles, California, USA.

*Address reprint requests to: J.Z., 3620 South McClintock Ave., SGM501, Los Angeles, CA 90089. E-mail: jc.zhuang@gmail.com

Received January 31, 2012; Accepted October 1, 2012.

DOI 10.1002/jmri.23929View this article online at wileyonlinelibrary.com.

JOURNAL OF MAGNETIC RESONANCE IMAGING 37:1460–1467 (2013)

CME

VC 2012 Wiley Periodicals, Inc. 1460

acquired with no diffusion weighting differ greatlyfrom the contrasts found in images acquired withhigh (b-value) diffusion weighting. The contrast differ-ences lead to unreliable registration of the two typesof images, which in turn interferes with eddy currentdistortion corrections. This problem is more serious inmost q-space diffusion images for which high or ultra-high b-values are commonly used (2–4).

Various methods have been proposed to more accu-rately estimate effects of eddy current distortions.Some investigators proposed a method of extrapolat-ing distortion parameters from low to high b-valueimages (11). Others employed the ICC algorithm withreference to CSF-suppressed images (such as FLAIR)to minimize the major source of contrast change inimages acquired with different b-values (15). DWIs ofa water phantom have also been used to measure dis-tortion parameters directly, and these parameters canthen be used to calibrate the ICC of brain images (13).Although these procedures extend the possibility touse the ICC algorithm with b-values as high as 2000s�mm�2, they require acquisition of additional imagesthat prolongs scanning times, which is not alwaysdesirable.

Two recent approaches use only DWIs to estimaterelative distortions. One approach, coregistration ofpairs of DW images with exactly the reversed diffusiongradients followed by corrections of the distortionsusing ICC, will double the acquisition time (14); theother, applying the known gradient strength anddirection to model the absolute distortions onlybetween DW images, may involve inaccurate imagecoregistration, especially at ultrahigh diffusion gradi-ent strength, due to image contrast differences result-ing from changes of diffusion gradient directions (16).

Here we describe a new algorithm to detect eddycurrent distortions by modeling the distortion withthe known x, y, and z components of diffusion gra-dients exclusively from DW images with close diffu-sion gradient directions. The algorithm was validatedin experimental data. Finally, we demonstrate its suc-cessful application to correct distortions in DWIs ofthe human brain.

MATERIALS AND METHODS

Theory

Diffusion-sensitizing gradients consist of componentsalong each of the x, y, and z axes. The eddy currentsinduced by a change in a single gradient component,the x gradient, for example, can be distributed alongthe x, y, and z axes. Such eddy currents produce re-sidual gradient fields in the frequency encoding,phase encoding, and slice-selection directions. Theseresidual gradients in turn cause shearing, scaling,and translational distortions, all visible along thephase-encoding direction of echo-planar images (EPIs)(11). Assuming that the interaction between thesethree components of gradient fields is negligible (14),the total eddy current distortion will be equal to thelinear sum of the distortion induced by the x, y, and zgradients (16).

Accordingly, the x, y, and z components of the i-thdiffusion gradient Gi ¼ (Gix, Giy, Giz) will produce acorresponding image translation distortion Gi�T ¼GixTxþGiyTyþGizTz, where T ¼ (Tx, Ty, Tz) is the trans-lation along the phase-encoding direction induced bythe corresponding unit changes in the x, y, and z gra-dients. The resulting distortion in translation Dti fromthe alignment between the images of the i-th diffusiongradient direction and the j-th (reference) gradientdirection can be calculated for i = j as:

Dti ¼ ðGixTx þGiyTy þGizTzÞ � ðGjxTx þGjyTy þGjzTzÞ;

or

G0 � T ¼ Dt;

where the rows of matrix G0 are formed by the differ-ences (Gix�Gjx, Giy�Gjy, Giz-Gjz) for the i-th diffusiongradient, and Dt is the distortion vector of imagetranslation that is measured by the registrationbetween the reference image and the images fromother diffusion gradients. The three unknown ele-ments of vector T can be calculated as:

T ¼ ðG0T �G0Þ�1 �G0T �Dt ; ½1�

where the superscripts ‘‘T’’ and ‘‘–1’’ denote matrixtransposition and inversion, respectively.

Similarly, a vector S of the shear distortion inducedby a unit change of the x, y, and z components ofthe gradient can be calculated using the followingequation:

S ¼ ðG0T �G0Þ�1 �G0T �Ds; ½2�

where Ds is the vector for shearing, which is meas-ured by coregistering the image from the i-th diffusiongradient with that from the j-th diffusion gradient.

Scaling (or magnification) distortion Dmi, measuredby comparing the image from the i-th diffusion gradi-ent and the image from the j-th (reference) diffusiongradient, can also be calculated for i = j as:

Dmi ¼1þGixMx þGiyMy þGizMz1þGjxMx þGjyMy þGjzMz

; ½3�

where Mx, My, and Mz are the unknown componentsof scaling induced by unit changes in the x, y, and zgradient components, respectively.

Therefore the following can be derived:

G00 �M ¼ D0m ; ½4�

where the matrix G00 is formed as (Gix�DmiGjx,Giy�DmiGjy, Giz�DmiGjz) and D0mi ¼ Dmi –1 for i = j. Thevector M ¼ (Mx, My, Mz) can thus be obtained from:

M ¼ ðG00T �G00Þ�1 �G00T �D0m : ½5�

Equations 1, 2, and 5 are basically least-squaresestimates for T, S, and M. Given the model parame-ters for the distortions T, S, and M, we can determinethe total distortions for the i-th diffusion gradient in

Eddy Current Correction in HARDI 1461

relation to the undistorted, non-DW images using thedot products of Gi�T, Gi�S, and Gi�M. Thereafter, imagedistortions can be corrected by reverse application ofthese parameters to the distorted DW images, and theDW images will be automatically registered to thenon-DW images.

As just seen, the accuracy of the estimation of T, S,and M depends on the coregistration between theimages obtained with the i-th and j-th diffusion gradi-ent directions. If the orientations of the i-th and j-thdiffusion gradient vectors are very different, the con-trast difference between the images acquired withthese diffusion gradients will be large (Fig. 1). Thus,the coregistration needed to derive the distortion pa-rameters T, S, and M can be inaccurate. On the otherhand, if the orientations of the diffusion gradient vec-tors are similar, the contrast difference between thecorresponding DW images is small, and the coregis-tration might be good enough to obtain the correctdistortion parameters.

Material

Five young adults with no history of neurological dis-ease (three males and two females) were scanned on aSiemens 3T Trio Tim MRI system (Siemens Health-care, Erlangen, Germany). HARDI data were acquiredusing a single-shot spin-echo echo planar sequencewith the following parameters: relaxation time (TR) ¼10,000 msec, echo time (TE) ¼ 110 msec, 128 diffu-sion gradient directions, 51 axial slices for whole-brain coverage, field of view (FOV) ¼ 240 � 240 mm2,and matrix ¼ 96 � 96, 2.5 mm in-plane resolutionand 2.5 mm slice thickness. Three of the subjectswere scanned with a single 5000 s/mm2 b-value. Thetwo remaining subjects were scanned using a range ofb-values: 1000 s/mm2, 3000 s/mm2, 5000 s/mm2,7000 s/mm2, and 9000 s/mm2. We also scanned aphantom with the exact same parameters and thesame range of b-values used for the latter two sub-jects. All subjects gave written informed consentaccording to national guidelines and those of theInstitutional Review Board at the university.

Algorithm Implementation

The ICC algorithm was used to coregister between DWimages and obtain distortion vectors Dt, Ds, and Dm.It iteratively compared the scaling, shearing, andtranslation of each phase-encoding column (the y-axisin our case) on the distorted image in relation to thereference image (11,14). In each slice we assumed oneparameter for shearing, one for translation, and onefor scaling. The 1D scaling transformation along y isachieved by linear interpolation, and the shearing canbe viewed as a series of progressively larger transla-tions at each phase-encoding column. The normalizedcross-correlation function between the new adjustedimage and reference image can be calculated. Theiterations were performed by varying the parametersof translation in increments of 0.25 pixels, the shear-ing in increments of 0.005 pixel/column, and scalingfactor in increments of 0.005. The fine incrementalstep was selected as described in previous studies(13,14). The position of the maximum index in theiterative cross-correlation array indicated the optimal

Figure 1. DW image signal intensity changes with diffusiongradient directions (at b ¼ 3000 s/mm2). On the x axis, 0–6represents the nondiffusion-weighted and six different diffu-sion gradient directions (displayed as lines on the back-ground). The y axis represents the pixel position at the 55thcolumn highlighted as a white line in the nondiffusion-weighted image on the right side. The z axis represents MRsignal intensity.

Figure 2. Examples of the close (a) and far-away (b) diffusion gradient directions, relative to the direction of diffusion gradi-ent in the reference DW image (represented by the dashed line in the figure).

1462 Zhuang et al.

translation, scaling, and shearing parametersrequired for the registration of two images.

We selected six sets of DW images for coregistrationand model fitting from the 128 DWIs in our study. Ineach set, one image is used as the reference imageand the other 15 used for coregistration have the clos-est spatial directions of diffusion sensitizing gradientswith the reference image (Fig. 2). The criteria forselecting the sets of images were: the diffusion gradi-ent directions of the reference images were randomlyselected with one exclusion criterion, that the angledifference between any pair of the gradient vectors ofthe six reference images had to be between 30� and150� (the maximum possible angle is 180�). Withineach set of DW images, the angle difference of the dif-fusion gradient vectors between the DW images to becoregistered and the reference image had to be alwaysless than 30� or more than 150�.

Therefore, coregistration is only performed withineach set of DW images with close diffusion gradientdirections. The distortion components of shearing,scale, and translation were calculated for each set ofgradient directions using Eqs. [1], [2], and [5]. The pa-rameters T, S, and M calculated from these six setswere averaged into one set of parameters (shearing,scale, and translation), and subsequently used to cor-rect the corresponding distortions for all 128 gradientdirections. Our algorithm was implemented in MatLab7.0 (MathWorks, Natick, MA), requiring about 10minutes to correct one dataset on a 3.0 GHz IntelXeon personal computer. Matrix inversions werecalculated by MatLab’s implementation of LAPACK(Linear Algebra PACKage) (17).

Test of Coregistration Between DW Images andValidation of Model Fitting of Eddy CurrentDistortions

To test the validity of the coregistration algorithmbetween images with large diffusion gradient differen-ces, we performed the ICC calculation on the twohuman datasets with varying diffusion gradientdirections and strengths (b-values as 1000 s/mm2,3000 s/mm2, 5000 s/mm2, 7000 s/mm2, and 9000s/mm2). One reference DW image was randomlyselected on each dataset. The ICC coefficients wereobtained between images without any prior coregistra-tion. The DW images of the human subjects were vis-ually inspected for head movement. If a head motionwas detected or the coregistration between the imageand reference image was too poor, the correspondingimage was discarded.

Another validation of our proposed algorithm wasconducted using both the phantom and human data.Coregistration was only performed between the 16images that had the closest diffusion gradient orienta-tions. The distortion components of shearing, scale,and translation were calculated for each set of these16 gradient directions using Eqs. [1], [2], and [5]. Theparameters obtained from these six sets were com-pared and plotted together. For the purpose of com-parison, six sets of 16 DW images with very differentor far-away diffusion gradients (angle difference of

gradient orientations is between 30� and 150�) wereused to calculate distortion parameters as well (Fig.2). Because the phantom differs minimally in contrastbetween different DW images, the results obtained onthe phantom data serve as a reliable benchmark forthe evaluation of the algorithm.

Correction of Eddy Current Distortions on Q-ballImages From the Human Brain

Q-ball reconstruction was implemented using FRT(Funk–Radon transform) (4) on a pixel-by-pixel basisfrom the DW data obtained in the three subjectsscanned with only a single b-value of 5000 s/mm2.The diffusion ODF (Orientation Distribution Function)was reconstructed for each voxel using the matrixFRT, a linear matrix formulation based on sphericalradial basis function interpolation. Each ODF wasthen smoothed and divided by the (maximum-mini-mum) value for normalization to emphasize the orien-tation structure of the ODF. The Q-ball Imaging (QBI)data were further processed using Trackvis (18) forfiber tracking (19).

We compared the images corrected by our proposedalgorithm with the corrected images using the originalICC method (11) and with uncorrected images. Usingan index from Bastin and Armitage (13), we quantifiedimprovement in the resulting DW images by countingthe number of pixels in which any of the three diffu-sion eigenvalues was negative in all image slices. Alarger value of this index indicates DW images ofpoorer quality. Such calculated index was compared

Figure 3. Correlation coefficients of ICC between DW imagesof human subjects depend on the spatial angle difference ofdiffusion gradients and gradient strength (b-values in unitsof s/mm2). The cross-correlation was performed between onereference DW image (randomly selected as the 51st imagesin the 128 diffusion directions) and other six images with dif-fusion gradient angle difference listed on x axis. The ‘‘0’’ gra-dient direction on the x axis represents the correlation of thereference DW image with a nondiffusion-weighted image.

Eddy Current Correction in HARDI 1463

among the corrected DW images using our algorithm,the corrected images using the original ICC method,and the uncorrected DW images. Furthermore, we

compared the fiber length detected from corrected anduncorrected images. Fiber tracking of poor DWI datacan not resolve fiber-crossing within voxels without

Figure 4. All resulting distortion components (T, S, and M in Eqs. [1–5]) from model fitting on the human data (with whitebackground) and the phantom data (with gray background), using six sets of close (diamond marker) or far-away (trianglemarker) diffusion gradients, as functions of the b-value.

1464 Zhuang et al.

errors, rendering the tracks incomplete. Thus, theresulting fiber lengths from uncorrected images areshorter than those obtained in corrected images. Inother words, a shorter average fiber length may reflectpoorer quality of fiber tracking. We compared the av-erage fiber length obtained in corrected DW imagesusing our algorithm, with those obtained from cor-rected images using the original ICC method anduncorrected DW images.

RESULTS

The ICC algorithm did not give high correlation coeffi-cients in coregistering the same slices with far-awaydiffusion gradient directions when the diffusionweight was higher than 3000 s/mm2 (Fig. 3). Butwhen the diffusion gradient directions were closeenough, the ICC algorithm did provide reliablecoregistration at the same diffusion weight. When dif-fusion weight was lower than 3000 s/mm2, the ICCcalculation provided good coregistration on the sameslices between different gradient directions, independ-ent of gradient orientation differences. A further testindicated that the results of correlation coefficientswere similar to those obtained with a different refer-ence DW image.

We calculated the values of eddy current distor-tions, in the phantom experiment, in relation to theDW images with close diffusion gradient directionsusing our modeling method. The results were com-pared to those of DW images with large differences in

diffusion gradient directions. The results from the twosets of calculations were in close agreement across allgradient directions (Fig. 4). The distortion parametersobtained from six sets of far-away diffusion gradientswere also close to each other under the circumstancethat the contrast of DW images on the phantom dif-fers minimally between these different diffusion gra-dients, further supporting the validity and accuracy ofthe proposed algorithm. On the human data, the dis-tortion components calculated from six sets of imageswith large diffusion gradient differences were not con-sistent. However, the distortion components calcu-lated from six sets of close diffusion gradients wererelatively consistent (Fig. 4). In our results, each T, S,or M was calculated from the normalized gradienttables without considering the absolute b-value.Among different b-values, the resulting parametersmay not be identical even after taking the b-value intoaccount, because different separation times and dura-tions of diffusion gradients were used to achieve thedifferent b-values on the scanner.

In the QBI analysis on human data, tractographyperformed on images corrected by our method showsfiber tracks with smoother contours and higher numberof tracked fibers than the fiber maps constructed with-out correction (Fig. 5a,b). The average length of trackedfibers increased significantly (P < 0.0001) after applyingour correction (Table 1). Bastin and Armitage’s index(13) also decreased significantly (P < 0.0001) afterapplying our correction method (Table 2). In contrast,the correction using the original Haselgrove’s methoddid not result in a statistically significant improvement

Figure 4. (Continued)

Eddy Current Correction in HARDI 1465

(Tables 1, 2). This result also underscores the effective-ness of the proposed algorithm.

Our results show that the contrasts of DW imagesvary with the strength and direction of diffusion gra-dients, especially when high gradient strength isapplied (Figs. 1, 3). When images acquired with simi-larly oriented diffusion gradients are coregistered, thedetected components of translation, shearing, and scal-ing in eddy current distortions depend linearly on thecorresponding diffusion gradient vector. Moreover, thisdependence can be exploited to correct eddy currentdistortions by using the known strength and directionof diffusion gradients applied in DWI acquisition.

DISCUSSION

Our algorithm needs to estimate 3 (distortions) � 3(components of diffusion gradients) ¼ 9 unknown

parameters. Every pair of DW images gives 3 distor-tion parameters of shear, scale, and translation. Tosolve the equations for these 9 unknown variables, weneed 3 images (to be registered) þ 1 image (as refer-ence) ¼ 4 diffusion gradient directions. Thus, for ouralgorithm to be effective each set of DW images to becoregistered requires at least four diffusion gradientdirections, and these four diffusion gradient direc-tions must be spatially close (angle differences lessthan 30� or more than 150�). It is difficult to findsuch close gradient directions if only a small numberof diffusion gradients are applied, such as in conven-tional DTI scans. Fortunately, most conventional DTIscans use b-values lower than 2000 s/mm2, so thatsome of the existing methods (16) are sufficient toappropriately correct eddy current distortions in thosecases. With more gradient directions, as regularlyapplied in HARDI studies, diffusion gradients withcloser orientations are available and higher accuracy

Figure 5. Representative fiber tracking results constructed from the QBI data of a human brain, with and without the eddycurrent correction proposed in this study. The colors of the fibers indicate the major directions of fibers. The proposed algo-rithm increased both the number and average length of the tracked fibers (see Table 1 for details).

Table 1

Mean Fiber Length Obtained From Uncorrected Images, Images

Corrected by Haselgrove’s Algorithm and Images Corrected by Our

Algorithm on Human Brains

Method Mean (mm) SD

Uncorrected 57.4 (17.6)

Haselgrove’s algorithm 59.3 (16.3)

Proposed algorithm 68.9 (22.4)

Comparison t value P-value

Haselgrove’s algorithm vs.

uncorrected

3.3 (>0.001)

Proposed algorithm vs.

uncorrected

18.5 (

can be achieved in solving the nine parameters neces-sary for our method. The b-values used in mostHARDI studies are often higher than 2000 s/mm2,which makes our algorithm more desirable for thecorrection of eddy current distortions in HARDI thanother methods. In this study, selecting the six sets of16 DW images is required to minimize the estimationerror in the algorithm with the maximum possibleclose gradient orientations in each set.

There have been two previous attempts to modelgeometric distortions based on gradient directions.One of them calibrated eddy current distortions ineach of three orthogonal diffusion gradients in aphantom scan, and subsequently applied the resultsto ascertain the distortions in DW images acquiredwith arbitrary gradient amplitudes and directions in ahuman scan (13). However, eddy current distortionscan depend on the detailed experimental conditionsand scan parameters for each scan, such as RF coil,TE, slice orientation, and isocenter offset. This de-pendence is difficult to calibrate in advance, but canbe modeled on a scan-by-scan basis using our pro-posed algorithm. The other approach used a mathe-matical framework to model geometric distortionsbased on slice position and gradient direction (20).Both of these approaches coregister DW images with-out considering whether the orientation of their diffu-sion gradients are close or far away, which in realityis only applicable to some diffusion imaging dataobtained at low diffusion gradient strengths.

In this study we only tested our algorithm for the Q-ball imaging method. The algorithm is also suitablefor other regular HARDI methods, such as DSI, whenthe diffusion gradient strength (b-value) does not varyexcessively. If gradient strength changes dramaticallywith each diffusion gradient vector, such as insome multiple wave-vector diffusion imaging methods,the assumption in our algorithm will need furtherverification.

Another common artifact in HARDI data is due tohead movement. The difficulty to correct head move-ment artifact in HARDI is similar to that for eddy cur-rent correction, especially in terms of coregisteringbetween DW images. The effects of these two artifactscan get mixed together, making postprocessing moredifficult and confounding. It is difficult to separate theeffects from head motion and eddy current in DWimages. But head movements are random and inde-pendent of diffusion gradients. Therefore, the resultsfrom our Eqs. [1–5], which have high correlation withthe diffusion gradients, have already discounted theeffects of head movements. Furthermore, estimationerrors from head motion were reduced by averagingthe results from six subsets of DW images in our algo-rithm. In future work we will continue our effort tocompletely separate the effects of eddy currents andhead motion in HARDI data postprocessing.

The proposed approach implicitly assumes that thetime constants of significant eddy currents are longrelative to the EPI readout to allow simple decomposi-tion of eddy current distortions into translation,shear, and scale. This may not be true if a differentspectrometer or a different sequence is used. The linearity

assumption of the model should therefore be verifiedafter any such change is made, as well as after adjust-ment of the time constants in the eddy current com-pensation circuits.

In conclusion, the proposed method for eddy currentdistortion correction is both accurate and feasible inreal-world settings. The method not only circumventsthe difficulties of prior published correction algorithmsthat are associated with large contrast differencesacross high b-value DW and non-DW images, but alsoeliminates the requirement to acquire additionalimages specifically meant for distortion correction.

REFERENCES

1. Basser PJ, Mattiello J, LeBihan D. Estimation of the effectiveself-diffusion tensor from the NMR spin echo. J Magn Reson B1994;103:247–254.

2. Tuch DS, Reese TG, Wiegell MR, Makris N, Belliveau JW, Wedeen VJ.High angular resolution diffusion imaging reveals intravoxel whitematter fiber heterogeneity. Magn Reson Med 2002;48:577–582.

3. Wedeen VJ, Hagmann P, Tseng WI, Reese TG, Weisskoff RM. Map-ping complex tissue architecture with diffusion spectrum magneticresonance imaging, Magn Reson Med 2005;54:1377–1386.

4. Tuch DS. Q-Ball imaging. Magn Reson Med 2004;52:1358–1372.5. Wider G, Dotsch V, Wuthrich K. Self-compensating pulsed mag-

netic-field. Gradients for short recovery times. J Magn Reson A1994;108:255–258.

6. Reese TG, Heid O, Weisskoff RM, Wedeen VJ. Reduction of eddycurrent-induced distortion in diffusion MRI using a twice-refo-cused spin echo. Magn Reson Med 2003;49:177–182.

7. Alexander AL, Tsuruda JS, Parker DL. Elimination of eddy cur-rent artifacts in diffusion-weighted echo-planar images: the useof bipolar gradients. Magn Reson Med 1997;38:1016–1021.

8. Jezzard P, Barnett AS, Pierpaoli C. Characterization of and cor-rection for eddy current artifacts in echo planar diffusion imag-ing. Magn Reson Med 1998;39:801–812.

9. Calamante F, Porter DA, Gadian DG, Connelly A. Correction foreddy current induced B0 shifts in diffusion-weighted echo-planarimaging. Magn Reson Med 1999;41:95–102.

10. Papadakis NG, Smponias T, Berwick J, Mayhew JEW. K-space cor-rection of eddy-current-induced distortions in diffusion-weightedecho-planar imaging. Magn Reson Med 2005;53:1103–1111.

11. Haselgrove JC, Moore JR. Correction for distortion of echo-planarimages used to calculate the apparent diffusion coefficient. MagnReson Med 1996;36:960–964.

12. Horsfield MA. Mapping eddy current induced fields for the correc-tion of diffusion-weighted echo planar images. Magn Reson Imag-ing 1999;17:1335–1345.

13. Bastin ME, Armitage PA. On the use of water phantom images tocalibrate and correct eddy current induced artefacts in MR diffu-sion tensor imaging. Magn Reson Imaging 2000;18:681–687.

14. Bodammer N, Kaufmann J, Kanowski M, Tempelmann C. Eddycurrent correction in diffusion-weighted imaging using pairs ofimages acquired with opposite diffusion gradient polarity. MagnReson Med 2004;51:188–193.

15. Bastin ME. On the use of the FLAIR technique to improve thecorrection of eddy current induced artefacts in MR diffusion ten-sor imaging. Magn Reson Imaging 2001;19:937–950.

16. Zhuang J, Hrabe J, Kangarlu A, et al. Correction of eddy current dis-tortions in diffusion tensor imaging using the known gradientstrengths and directions. J Magn Reson Imaging 2006;24:1188–1193.

17. Anderson E, Bai Z, Bischof C, et al. LAPACK users’ guide, 3rd ed.Philadelphia: Society for Industrial and Applied Mathematics; 1999.

18. Wang R, Benner T, Sorensen AG, Wedeen VJ. Diffusion toolkit: asoftware package for diffusion imaging data processing and trac-tography. Proc. In: Proc 15th Annual Meeting ISMRM, Berlin;2007. p 3720.

19. Mori S, Crain BJ, Chacko VP, van Zijl PCM. Three dimensionaltracking of axonal projections in the brain by magnetic resonanceimaging. Ann Neurol 1999;45:265–269.

20. Andersson JLR, Skare S. A model-based method for retrospectivecorrection of geometric distortions in diffusion-weighted EPI.NeuroImage 2002;16:177–199.

Eddy Current Correction in HARDI 1467

JC_Zhuang-EddyCurrentInHARDI-CoverJMRI-2013

/ColorImageDict > /JPEG2000ColorACSImageDict > /JPEG2000ColorImageDict > /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 150 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict > /GrayImageDict > /JPEG2000GrayACSImageDict > /JPEG2000GrayImageDict > /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 1200 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict > /AllowPSXObjects false /CheckCompliance [ /PDFX1a:2003 ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError false /PDFXTrimBoxToMediaBoxOffset [ 9.00000 9.00000 9.00000 9.00000 ] /PDFXSetBleedBoxToMediaBox false /PDFXBleedBoxToTrimBoxOffset [ 9.00000 9.00000 9.00000 9.00000 ] /PDFXOutputIntentProfile (None) /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /Unknown

/Description >>> setdistillerparams> setpagedevice