Characterization, prediction, and correction of geometric distortionin 3 T MR images
Lesley N. Baldwina�
Division of Medical Physics, Departments of Physics and Oncology, University of Alberta,Department of Medical Physics, Cross Cancer Institute, 11560 University Avenue, Edmonton,Alberta T6G 1Z2, Canada
Keith WachowiczDivision of Medical Physics, Department of Oncology, University of Alberta, Department of MedicalPhysics, Cross Cancer Institute, 11560 University Avenue, Edmonton, Alberta T6G 1Z2, Canada
Steven D. Thomas, Ryan Rivest, and B. Gino FalloneDivision of Medical Physics, Departments of Physics and Oncology, University of Alberta,Department of Medical Physics, Cross Cancer Institute, 11560 University Avenue, Edmonton,Alberta T6G 1Z2, Canada
�Received 9 July 2006; revised 4 October 2006; accepted for publication 6 November 2006;published 8 January 2007�
Magnetic resonance imaging �MRI� is an extremely powerfuldiagnostic tool because of its excellent soft-tissue character-ization. As such, it is the optimum imaging modality fortarget delineation. However, because of both machine andpatient related geometric distortions, MR-delineated targetscannot directly be used in radiation therapy treatment plan-ning �RTTP�. While much has been written about distortionmeasurement and correction in MR images, there has beenlittle evidence that distortion correction has entered the realmof routine clinical practice. Furthermore, with the increasingavailability of higher field magnets and faster, shorter gradi-ent sets, image distortion is expected to be increasingly prob-lematic. Thus, we are investigating the use of distortion cor-rected 3 T MRI for direct use in the planning of radiationtreatments by TomoTherapy in particular, and intensity
modulated radiation therapy, in general. These treatment mo-
388 Med. Phys. 34 „2…, February 2007 0094-2405/2007/34„
dalities require accurate three-dimensional �3D� spatial posi-tioning of anatomy to which the delivered dose distributionmust be appropriately designed.
While the structure of a tumor can be seen in great detailon MR images, the geometric accuracy of the images is lim-ited by the homogeneity of the background field, the linearityof the applied gradients, the magnetic susceptibility of theimaged tissues, and chemical shift artifacts. Reconstructionof the MR image relies on the assumption that both a per-fectly uniform background field and linearly varying gradientfields are present. It may be difficult to achieve this, how-ever, due to a number of design features. Short, wide-boresystems are often preferred as they improve the patient“friendliness” of the magnet, but such designs inevitablycompromise B0 homogeneity. In addition, fast, high-performance gradients—especially those employing shortcoils—often suffer from increased gradient nonlinearity.1
Differences in the assumed and true magnetic field experi-
389 Baldwin et al.: Characterization of geometric distortion in 3 T MR images 389
enced at each point within the magnet’s bore lead to distor-tions in the images generated. The magnitude and directionof geometric distortion varies for each type of imaging pro-tocol and distortions of up to 25 mm over a 24 cm field ofview have been reported for 1.5 T magnets.1–4 While geo-metric errors of several millimeters may not be problematicfor routine diagnostic purposes, an accuracy of 1 mm or bet-ter is required for most radiation therapy purposes.3,5
Because of their superior spatial accuracy and electrondensity information, computed tomography �CT� images aregenerally used for treatment planning; however, their poorertumor contrast can make tumor delineation difficult. In con-junction with the superior soft-tissue contrast of MRI, theability to acquire nonaxial images greatly improves 3D tu-mor visualization in MRI. Gross target volumes outlined onMR have been shown to be, on average, significantly largerthan those outlined on CT images and to overlap better withcomposite MR/CT volumes.6,7 Reliance on CT volumeswould thus result in significant under dosing to target vol-umes. Moreover, inter-observer differences in MR target vol-umes have been shown to be less than those in CT targetvolumes as a result of improved visualization.7 As sophisti-cated conformal treatments capable of delivering sharp dosegradients around target volumes become more common-place, accurate tumor localization becomes paramount.
To combine the spatial accuracy of CT with the soft-tissuecontrast of MR, image co-registration is a routine step inRTTP. However, reliance on image fusion involves inherenterrors and registration based on the locations of externallandmarks placed on the skin will be particularly prone todistortions.8 Even registration based on the locations of bonylandmarks �which are both more rigid and less prone to dis-tortion errors because of their greater proximity to isocenterthan surface landmarks� may involve significant distortion-related errors when MR images are acquired on magnetswith poor field homogeneity or gradient nonlinearity. Pro-vided adequate distortion correction can be achieved, the re-liability of MR/CT image fusion could be greatly improved.Alternatively, with additional provisions for image intensitycorrection, bulk tissue electron densities may be assigned tosegmented MR images allowing for treatments to be plannedon MR images without fusion to CT data.8,9,22
Currently, there is a push towards using higher field mag-nets for both imaging and spectroscopic purposes. Concern-ing spectroscopy, an increase in the magnetic field strengthincreases the sensitivity and resolution of the spectraproduced.10 As interest in biological target definition in-creases, cancer centers will therefore be more likely to investin 3 T systems for clinical use. With respect to anatomicalimaging, the signal-to-noise ratio �SNR� has been shown toincrease linearly with B0 field strength.11,12 Alternatively, theSNR can be left unaltered in exchange for reduced scanningtime; this may be particularly advantageous for severely illpatients for whom prolonged immobility is difficult to im-possible. However, distortions due to B0 shimming andpatient-related effects are also proportional to B0 fieldstrength and thus comprehensive knowledge of geometric
distortions at higher magnetic fields becomes even more im-
Medical Physics, Vol. 34, No. 2, February 2007
portant. In order to reduce the effects of B0 distortions, it isoften suggested to use the highest read gradient possible;5,8
however, this increases the bandwidth per pixel and reducesthe signal readout time, effectively decreasing the SNR andlessening one of the primary benefits of high field imaging.Clearly, there are both advantages and disadvantages to im-aging at higher field strengths. Provided image distortions at3 T are not too large as to be reliably detected and corrected,such images may find greater use in the radiotherapy treat-ment planning process.
Finally, it is widely acknowledged that distortions due togradient nonlinearities are constant from scan to scan,whereas distortions due to B0 inhomogeneities and suscepti-bility effects vary from scan to scan according to the inverseof the read gradient strength.5,13 Furthermore, while suscep-tibility effects vary from patient to patient, B0 and gradientdistortions are system specific. Provided the susceptibilityeffects of the anatomy are negligible or can be independentlydetermined—modeled or measured14,15—it would be pos-sible to predict distortion for patient images without the needfor detailed distortion measurements for each scan of eachpatient. This would provide considerable time savings andwould greatly improve the clinical applicability of MR dis-tortion correction.
To our knowledge, no publications have yet provided athorough analysis of distortions on a 3 T MRI system. Fur-thermore, the possibility of distortion prediction based on asingle assessment scan has not yet been investigated. Thisprovides an exciting clinical opportunity to correct spatialdistortions in MR images with little to no additional scantime. This paper, therefore, describes the methods and resultsof our full characterization of the machine-related distortionsinherent in our 3.0 T Intera MRI scanner �Philips MedicalSystems, Cleveland, OH�. By individually characterizing thedistortions due to background inhomogeneities, gradientnonlinearities and phantom-related susceptibility artifacts fora base set of data, machine-related distortions at alternategradient strengths and for alternate imaging protocols can bepredicted. Armed with detailed knowledge of spatial distor-tion, MR images can be undistorted and either combined orused individually for new treatment planning methods thatbenefit from the superior soft-tissue information that mag-netic resonance techniques provide.
II. THEORY
In a MR image, the location of a given feature, r�, isshifted from its true position, r, by an amount, dr. That is
r� = r + dr . �1�
Furthermore, the amount of distortion is proportional to theratio of the magnetic field perturbation, dB, to the gradientstrength, G
dr =dB
G. �2�
MR distortion can be determined by comparing the locations
of corresponding features in both MR and CT data sets. Not
390 Baldwin et al.: Characterization of geometric distortion in 3 T MR images 390
only can the total amount of distortion be measured, but alsothe distortions due to different effects can be separated. Dis-tortions due to inhomogeneities in the static magnetic field—caused by imperfect uniformity of the B0 field as well asobject-induced distortions—are manifest only along fre-quency encoded directions while distortions due to gradientnonlinearities are apparent in each of the three cardinaldirections.13 For standard two-dimensional �2D� imagingprotocols, B0 and object-induced distortions appear along theread encode and slice select directions while the phase en-code direction is free from B0-related distortions. For theensuing discussion, we concern ourselves mainly with 3DMR scans where slice selection is done via an additionalphase encoding step and does not, therefore, suffer fromB0-related distortions. Such distortions are limited to the readdirection and to the initial slab-selection process. If the initialslab-excitation pulse has an insufficiently broad frequencyprofile �i.e., one that does not account for the presence of B0
distortions�, the outer extremities of the object may not beexcited, the slab profile will be distorted and will not corre-spond to the object profile. However, if the slab width isselected to be larger than the true width of the object, thefrequency profile of the excitation pulse may account forresonant frequencies beyond the expected range and all spinswithin the volume will be excited. By using a sufficientlybroad slab width and by further defining the slice directionthrough phase encoding, B0-related distortions need only beconsidered along the single frequency encoding direction.For example, if the read encode gradient is aligned with thex axis and phase encodes are performed along each of the yand z axes for a 3D MR scan, the following distortions willbe present:
x� = x + dx = x +dBGx
�x,y,z�
Gx+
dB0�x,y,z�Gx
+dBS�x,y,z�
Gx
y� = y + dy = y +dBGy
�x,y,z�
Gy
�3�
z� = z + dz = z +dBGz
�x,y,z�
Gz,
where dx ,dy ,dz are the total amounts of distortion,Gx ,Gy ,Gz are the gradient strengths and dBGx
,dBGy,dBGz
arethe gradient nonlinearities in each of the three directions; anddBo and dBS are the distortions due to imperfections in the B0
field and to susceptibility effects, respectively. Distortionsdue to dBo and dBs can be separated from x-gradient distor-tions by reversing the polarity of the read encode gradient,Gx, since this will reverse the signs of both
dB0
Gxand
dBS
Gx, but
not that ofdBGx
Gx. This effect is illustrated in Figs. 1 and 2.
Figure 1 shows that due to nonlinearities in the gradient, afeature at position r0 will be mistakenly placed to the right atposition r0� if the nonlinearity is not taken into account; whenthe gradient and its associated nonlinearity are reversed in
polarity, the feature at position r0 is again misplaced to the
Medical Physics, Vol. 34, No. 2, February 2007
right at position r0�. In the case of B0 inhomogeneities, aperfectly uniform background field, B0, is assumed; however,a nonuniform background field B0� exists. When the appliedgradient and background field strengths are superimposed,we see the field profile shown in Fig. 2�B� and a feature atposition r0 is misplaced to the left at r0�. This time when thereversed gradient polarity and the inhomogeneous B0 fieldare superimposed, a feature at position r0 is misplaced to theright at r0�. For example, the x coordinate of a particularfeature will be found at position x+ in a MR image with apositive read encode gradient and at a position x− in an MRimage with a negative read encode gradient. That is
x+ = x +dBGx
�x,y,z�
Gx+
dB0�x,y,z�Gx
+dBS�x,y,z�
Gx,
�4�
x− = x +dBGx
�x,y,z�−
dB0�x,y,z�−
dBS�x,y,z�.
FIG. 1. Illustration of distortions due to gradient nonlinearities for reversedgradient polarities. �A� the applied gradient is assumed to be linear �dottedline�, whereas the realized gradient suffers nonlinearities �solid line�. Thus,a feature at position r0 is misplaced to the right at position r0�. �B� When thegradient polarity is reversed, the polarity of the nonlinearity is also reversed.This means that a feature at position r0 is again misplaced to the right atposition r0�—distortions due to gradient nonlinearities are not sensitive to thegradient polarity.
Gx Gx Gx
391 Baldwin et al.: Characterization of geometric distortion in 3 T MR images 391
The distortion due to main field inhomogeneities and suscep-tibility effects can thus be determined by calculating the dis-placement from the average x position
x+ − x−
2=
dB0�x,y,z�Gx
+dBS�x,y,z�
Gx. �5�
The distortion due to the x gradient nonlinearities can bedetermined by subtracting Eq. �5� from the total amount ofdistortion in the x direction, dx. Finally, the susceptibilityeffects can be simulated and subtracted from Eq. �5� therebyisolating the effects of the background inhomogeneities. Themagnetic field distortions caused by an arbitrary magneticsusceptibility distribution can be simulated using the explicitfinite difference method.16 The 2D algorithm presented byBhagwandien et al.14 is easily extended to three dimensions.Thus, for a known susceptibility distribution—as is the casewith our phantom—susceptibility-induced distortions can benumerically calculated and subtracted from Eq. �5� in orderto isolate shim-related distortions in the B0 field.
Finally, distortions due to main field inhomogeneities andsusceptibility effects will scale inversely according to thestrength of the read gradient while distortions due to gradienterrors have been shown to be independent of gradientstrength.5,13 As such, it should be possible to predict distor-tion in images acquired with alternate imaging parameters.However, Tanner et al. showed that eddy currents generatedby rapidly pulsed gradients caused system distortions in spinecho images to be dependent upon echo times.13 Because thegradient strengths and rise times affect the presence of time-varying eddy currents within the cryogenic and metal casingsof the magnet, the time at which the signal is digitized �i.e.,the echo time� will influence the apparent distortion. ThePhilips Intera 3 T system is equipped with shielded gradientsand eddy currents are compensated using preemphasis cali-bration; the success or failure of image distortion predictiontherefore rests on the success of these hardware measures toadequately reduce remnant eddy currents. For our purposes,distortion measurements were made with a 3D data set withonly one frequency encode in the x direction and no slicewarping since a phase encode was performed in the slicedirection. In a more typical 2D clinical scan, slice warpwould be present due to the additional frequency encode inthe slice direction; however, slice warp �B0 effects� can eas-ily be predicted and accounted for since distortion sourcesare separated in the initial data set. Thus, it may be possibleto predict the amount and type of distortion in 2D images ofour phantom for a variety of different imaging protocols forwhich detailed 3D distortion data are not acquired.
For patient images where susceptibility effects are not aconcern, the gradient distortions acquired from the data pre-sented in this study would be combined with a scaled versionof the B0 distortion data to predict clinical image distortions.In this case, no additional scans would be necessary to cor-rect patient images. In a more realistic situation, susceptibil-ity effects would be a concern; these could be modeled ac-cording to the methods of Bhagwandien et al.,14 or the
combined effects of susceptibility and B0 distortions could be
Medical Physics, Vol. 34, No. 2, February 2007
measured through phase difference maps according to themethods of Jezzard and Balaban.15 The latter method in-volves acquiring two images with slightly different echo
FIG. 2. Illustration of distortions due to inhomogeneities in the B0 field forreversed gradient polarities. �A� the background field, B0 �dotted line�, isassumed to be constant for all r, whereas an inhomogeneous field, B0� �soldline�, is actually present. �B� When the applied gradient and inhomogeneousB0� field are superimposed, the resulting magnetic field is given by the solidline. Thus a feature at position r0 is mistakenly placed to the left at positionr0� if the magnetic field distribution given by the dotted line �G+homogeneous B0� is assumed. �C� When the gradient polarity is reversedand is again superimposed with the inhomogeneous B0� field, a feature atposition r0 is misplaced to the right at position r0�. The direction of B0 relateddistortions is reversed under gradient polarity reversal, whereas gradientnonlinearity distortions are not. It is this difference that permits the separa-tion of distortion effects through the “reversed gradient method.”
times to create a phase difference map. The difference in
392 Baldwin et al.: Characterization of geometric distortion in 3 T MR images 392
phase evolution at each pixel can be used to create a detailedB0/susceptibility map which can be used to correct all sub-sequent images for that patient.
III. METHODS AND MATERIALS
A. The phantom
For this study, a phantom containing a 3D distribution ofpoints was constructed in house; it consists of 17 polystyrenegrid sheets, evenly spaced within a 30 cm�30 cm�30 cmpolymethylmethacrylate case similar to the design proposedand used by Wang, Doddrell, and Cowin.2 Also constructedwas an alignment jig into which the phantom fit; this wasused to reduce alignment errors �particularly in the x and ydirections� between subsequent data sets and to facilitate reg-istration of MR and CT data. The phantom is displayed inFig. 3. Because the dimensions of the phantom are very closeto the resonant rf wavelength of 1H in water–26 cm at3 T16–interference from superimposed rf waves has complexeffects on rf homogeneity.17 The resonant rf wavelength inmineral oil is approximately 160 cm and the American As-sociation of Physicists in Medicine thus recommends oilover water to reduce such artifacts.18
Control points are found where each of the grid intersec-tions is interfaced with the mineral oil. That is, a controlpoint is defined as the intersection of three planes where thefirst two planes are contained by the grid and the third planeis the liquid/grid interface. Each of the 17 sheets contains289 grid points per face for a total of 9826 control points�2�17�289�. Control point spacing is approximately 15.0�15.0�7.6 mm in the x, y, and z dimensions, respectively.In the recent study by Wang, Doddrell, and Cowin using thistype of phantom, no mention was made of how the trueposition of the phantom control points was determined.2 Theauthors quote the grid spacing in each of the three dimen-sions and it is thus assumed that the true control point posi-tions were defined using this perfectly regular spacing. Whilethe grid sheets used in this phantom experiment were also
manufactured and purchased commercially, a small amount
Medical Physics, Vol. 34, No. 2, February 2007
of variability, particularly in the z direction, was noted. Forthis reason, the true grid positions were determined via acorresponding CT scan.
B. Image acquisition
MR images were acquired on a 3.0 T Intera MRI scanner�Philips Medical Systems, Cleveland, OH� using the bodycoil and a standard 3D gradient echo �GE� sequence with TE,TR, and flip angle of 5.1 ms, 11.1 ms and 28°, respectively.The sequence included phase encode spoiling, but no rfspoiling, and a single k-space line was encoded per TR. A370 mm field of view �FOV� was used along with a 512�512 imaging matrix and a total of 440 contiguous sliceswere acquired at a spacing of 0.72 mm. The resulting x ,y ,zvoxel size was thus 0.72�0.72�0.72 mm3. The selectedslab volume extended approximately 6 cm in the z directionbeyond each end of the volume used in our distortion analy-sis. B0 distortions were considered in the read encode direc-tion only. In order to separate gradient and B0/susceptibilitydistortions in the x direction, two 3D scans were performedwith identical imaging parameters save the reversal of theread gradient polarity.
Finally, automatic shims were turned off for all scans toeliminate changes in B0 homogeneity. The auto shimmingfunction was found to moderately increase homogeneity overthe central region of the imaged volume at the slight expenseof the homogeneity at the volume’s extremities. Thus, meandistortions were not significantly increased without the auto-matic shimming function.
In order to define the true, undistorted control point posi-tions, a corresponding CT scan of the phantom was gener-ated. CT images were acquired using a Philips Gemini pos-itron emission tomography �PET�/CT scanner �PhilipsMedical Systems, Philadelphia, PA�. Again, a 370 mm FOVwas used and 600 contiguous slices were acquired with areduced slice thickness of 0.5 mm due to scanner limitations.Voxel dimensions in the CT data set were thus 0.72�0.72�0.5 mm3.
C. Control point detection and data alignment
MATLAB-based software was developed in order to locatethe 3D coordinates of each of the control points in the phan-tom and was based on a previously published algorithm.2 Forclarity, a brief description of the method follows. Controlpoint detection is based on image edge detection using 3DPrewitt Operators followed by first moment calculation ineach of the three orthogonal directions. Initially, the first de-rivative of the data set is evaluated along the z direction�perpendicular to the plane of the grids�, resulting in an in-creased signal at the grid interfaces where the control pointsare located; this provides an initial estimation of each controlpoint’s z coordinate. Next the interfacial slices are convolvedwith a cross-shaped mask to visually enhance the location ofthe grid points. A threshold is applied and regions of interest�ROIs� are automatically generated around each of the en-hanced control points, thus providing additional initial esti-
mates of the x and y coordinates. The final x and y coordi-
393 Baldwin et al.: Characterization of geometric distortion in 3 T MR images 393
nates of the control point are determined by calculating thefirst moment of the magnitude of the derivative evaluatedalong each of the x and y directions over an expanded ROI ofa standard size �typically 9�15 pixels�. The mean x positionof the control point on the interfacial slice is determined as
I�j,k� =�p=1
ny �q=1nx iq
��fx��iq, jp,k���p=1
ny �q=1nx �fx��iq, jp,k��
, �6�
where fx� is the derivative evaluated along the x direction andnx and ny correspond to the x and y dimensions of the ROI.Because the x and y derivative profiles may not be particu-larly well defined at the interfacial slice, this calculation isrepeated on all slices within the grid. A line is fit to the x andy coordinates on each slice and the final x and y coordinatesare obtained by extrapolating to the interfacial slice. Themean y coordinate is found using an analogous equation. Todetermine the final z coordinate, a second ROI is centered onthe final x and y positions of the control point and the firstmoment in the z direction was found using a similar equa-tion. In this way, 3D coordinates can be determined for eachof the 9826 control points in the phantom.
Control points may occasionally be obscured by the pres-ence of bubbles within the phantom and, on average, thepositions of approximately 0.5% of control points were miss-ing. In such an event, the user may view control points planeby plane and missing control points can be interpolatedbased on the positions of four nearest neighbors.
Finally, pixel indices were converted to Cartesian coordi-nates using an origin placed at the isocenter of the MR scan-ner; the information required to perform this transformationis easily obtained from the image’s header file. In a similarfashion, the corresponding Cartesian coordinates of each ofthe control points was determined from both the reversedread gradient MR scan and the CT scan. The control pointsin each of the three data sets were sorted from top left tobottom right and from front to back such that correspondingdistorted and undistorted control point coordinates could becompared because of their identical positions within the datamatrices. By using a setup jig, which was specially designedto fit both within the MR bore and on top of the PET/CTcouch, phantom alignment errors in the x and y directionswere minimized. Alignment errors may still exist in the zdirection and for this reason it was necessary to determine analignment shift which was applied to the CT data set so thatthe positions of control points near isocenter in both MR andCT data sets coincided. This alignment was achieved by firstcorrecting the MR data for B0 and susceptibility distortions�i.e., by taking the mean x ,y ,z coordinates from the positiveand negative read gradient scans for each control point�.Next, 31 control points in CT and the corrected MR datawere manually selected around the isocenter �seven along thex and y axes on each of the front and back faces of thecentral grid and a further seven along the z axis through theisocenter�. It should be noted that if gradient distortions arepresent over the region immediately surrounding the iso-center, this registration procedure would be faulty and would
introduce a constant shift into each of the gradient distortion
Medical Physics, Vol. 34, No. 2, February 2007
calculations. However, since imaged anatomy is alwaysplaced at the isocenter, magnets are designed to have mini-mal distortion over this central region. It is thus reasonablyassumed that gradient distortions around the isocenter arenegligible; other groups have previously used thisassumption.4
D. Simulation of susceptibility distortions
The 3D magnetic field distortions created by the presenceof the phantom were calculated using an explicit finite dif-ference method.14 The magnetic susceptibility of the mineraloil was measured to be �−8.9±0.5� ppm using an EvansMSB-1 magnetic susceptibility balance while the susceptibil-ity values for the polymethylmethacrylate shell and the poly-styrene grids were determined from the literature to be−6.744 and −7.419 ppm, respectively.19 All volume suscep-tibility values are given in international standards �SI� units.
E. Distortion-map creation
Three-dimensional distortion maps of x, y and z gradientnonlinearities were generated by comparing the positions ofeach of the control points from the MR scans �averaged po-sitions� and the CT scan. Distortions due to B0 and suscep-tibility effects were calculated using both MR data sets ac-cording to the reversed gradient method described in Sec. II.
F. Distortion prediction
To our knowledge, distortion measurement and correctionprocedures previously presented have only shown correctionin images acquired using imaging parameters identical tothose used for the measurement step. It would be clinicallyadvantageous, however, to be able to correct image distor-tions for a variety of imaging protocols using a base set ofdistortion characterization data. We use the base set of dis-tortion data acquired using a 3D GE sequence with fre-quency encoding in the x direction to predict distortion in a2D spin echo �SE� image with frequency encoding in the ydirection. Before proceeding with the distortion predictionand correction we first verified that eddy currents did notsignificantly alter expected distortions when different echotimes were used.
G. Distortion correction
Once the 3D distortion map is known, the geometric fi-delity of MR images can be restored using simple distortioncorrection techniques. The distortion correction procedure issimilar to procedures used in automatic nonrigid image reg-istration and was performed using the National Library ofMedicine Insight Segmentation and Registration Toolkit�ITK�. ITK provides various programming modules useful forimage registration purposes. One such module performsinter-modality registration through image warping using anelastic body spline �EBS� kernel.21 The EBS is based on aphysical model of an elastic body; provided with a set ofcorresponding points in two image sets, it results in a smooth
mapping of one image to the other. Identifying a dense array
394 Baldwin et al.: Characterization of geometric distortion in 3 T MR images 394
of corresponding physical points in two image sets can be adifficult problem for standard image registration, but is easilyaccomplished using the abovementioned phantom and con-trol point detection technique. Furthermore, because the dis-tortion data are defined over a 3D volume, distortion can becorrected in any plane—axial or oblique. The distortion cor-rection procedure used in this study corrects individual 2Dimage slices; however, a 3D volume correction schemewould be a feasible extension of the method.
IV. RESULTS
Corresponding axial slices of the MR and CT phantomdata sets are shown in Fig. 4. As can be seen from the MRimage, the amount of distortion over the central region of thephantom is limited while distortion far from the magnet’sisocenter is more severe.
Commercially available plastic grids were used to con-struct our phantom and a small amount of variability in con-trol point spacing was found. It was thus deemed necessaryto calculate the MR distortion by measuring the difference incontrol point positions in MR relative to CT. For example,while warping of the grid planes was observed in the z di-rection in the MR scan, it was also observed �though to alesser degree� in the CT scan; this is illustrated in Fig. 5.
FIG. 4. A representative CT �top� and MR �bottom� slice of the phantom.
Without the baseline CT scan, all of the z warping seen in the
Medical Physics, Vol. 34, No. 2, February 2007
MR scan would be attributed to slice warp and z-gradientnonlinearities. The presence of a small amount of warp in theCT data set indicates the imperfect design of the grids andshould not be mistaken for gradient nonlinearity.
The distortion caused by each of the gradients and byinhomogeneities in the main magnet was measured andmapped according to Eqs. �3�–�5� and the distortion due tosusceptibility effects was modeled. While these distortionmaps are defined over a 3D volume �dimensions 266�266�205 mm3�, a selection is shown in Fig. 6 for a transverseplane through the isocenter. In this plane, the maximum mag-nitude of distortion is 4.5 mm in the top right corner of thephantom at a radial distance of 197 mm from the isocenter.Figure 7 shows the same types of distortion for a transverseplane approximately 8.5 cm from the isocenter. Distortionsdue to nonlinearities in the x, y and z gradients are similarboth in magnitude and in general form at both locations
FIG. 5. CT slice of one of the grid sections showing visible mechanicaldistortion in the z direction. Without determining the true locations of thecontrol points via a CT scan, this warping would be interpreted as z-gradientnonlinearity.
FIG. 6. Distortion in a transverse plane through isocenter. Top row �left toright�: measured magnitude of distortion, measured x gradient and y gradientdistortions. Bottom row �left to right�: measured z gradient distortion, simu-lated susceptibility distortion, and B0 distortion �total measured inhomoge-
neity distortions minus simulated susceptibility distortion�.
395 Baldwin et al.: Characterization of geometric distortion in 3 T MR images 395
while distortions due to main field inhomogeneities are sig-nificantly increased further from the isocenter. In this plane,the maximum magnitude of distortion is 5.4 mm and occursat a radial distance of 215 mm from the isocenter. The maxi-mum distortions in our data set generally occur at the topcorners of the phantom as the phantom was not perfectlycentered in the magnet; the top corners are thus the pointsfurthest from isocenter. It should be noted that while manyvendors apply distortion correction as part of routine post-processing, the Philips 3T Intera magnet does not.
The distortions caused by the susceptibility differencesbetween the polystyrene grids and the surrounding oil weremodeled and were found to be 0.49 ppm at maximum. Forthe gradient strength used in this imaging sequence�4.50 mT/m�, this corresponds to a maximum linear dis-placement of 0.33 mm. At approximately half a pixel width,and on the order of the uncertainty of the method, the effectof the grid susceptibility was deemed negligible. Thus, sus-ceptibility distortions were modeled using only the suscepti-bility distribution of the oil and the polymethylmethacrylatecase. Based on the simulations, susceptibility effects result ina maximum absolute distortion of 1.73 ppm or 1.15 mm inthe x direction.
The manufacturer’s specifications indicate that the peak-to-peak main field homogeneity should be 4.5 ppm for a40�40�30 cm rectangular volume and 1.3 ppm for a20-cm-diam spherical volume. For our approximately 26�26�20 cm rectangular volume, we see maximum peak-to-peak B0 field inhomogeneity distortions of 8.1 mm in the xdirection; this corresponds to 12.2 ppm for the given gradi-ent strength of 4.50 mT/m. For a 20-cm-diam spherical vol-ume, we see a maximum peak-to-peak distortion of 1.8 mmcorresponding to 2.6 ppm. Despite the fact that measured B0
inhomogeneity was larger than that specified by the manu-facturer, gradient nonlinearity appeared to be the main source
FIG. 7. Distortion in a transverse plane 85 mm from the magnet’s isocenter.Top row �left to right�: measured magnitude of distortion, measured x gra-dient and y gradient distortions. Bottom row �left to right�: measured zgradient distortion, simulated susceptibility distortion, and B0 distortion �to-tal measured inhomogeneity distortions minus simulated susceptibilitydistortion�.
of image distortions over the majority of the analyzed vol-
Medical Physics, Vol. 34, No. 2, February 2007
ume. B0 inhomogeneities were only responsible for the ma-jority of image distortion in transverse planes at the extremeends of the phantom.
In order to validate the reproducibility of the results, dis-tortions were measured on three different data sets collectedover several months. The phantom was removed from themagnet between scans and the setup jig was used in order toimprove the setup reproducibility. Acquisition parameterswere identical in each of the three data sets. Unlike the re-producibility study performed by Wang, Doddrell, andCowin,2 this type of study allows testing not only of theperformance of the control point detection software, but alsothe setup and overall distortion reproducibility. As such,slightly higher reproducibility errors are expected. The meanand standard deviation of reproducibility errors betweenpairs of data sets is graphed in Fig. 8. Because the phantomwas removed and replaced between subsequent scans, distor-tion measurements are acquired at slightly different positionsin each of the data sets. Interpolation of one data set in eachof the pairs is thus required in order to compare the repro-ducibility of distortion measurements at the same locations.A trilinear interpolation scheme was used. The mean andstandard deviation of reproducibility errors between data sets1 and 2 was obtained by averaging the reproducibility errorswhen distortion in data set 1 was interpolated at the positionsgiven in data set 2 and vice versa. The same procedure wasfollowed for comparing data sets 1 and 3, and data sets 2and 3.
Clearly distortions in the y and z gradients are very repro-ducible with mean errors �standard deviation� ranging from0.02�0.03� to 0.05�0.11� mm. These errors are less than 1/4of the pixel dimensions. Reproducibility errors in the x gra-dient, B0 inhomogeneity and magnitude distortion are some-what larger and range from 0.02�0.10� to 0.15�0.25� mm.The largest of these errors represents just over 1 /2 a pixel
FIG. 8. Mean reproducibility errors �plus standard deviation� for differenttypes of distortion for three data sets. Gradient distortion measurements aremore reproducible than B0 distortion measurements.
dimension. It should also be noted that interpolation errors
396 Baldwin et al.: Characterization of geometric distortion in 3 T MR images 396
contribute to these quoted reproducibility errors; by compar-ing identical data sets, interpolation was found to contribute0.0�0.2� mm of intrinsic error.
The variation in maximum and mean total image distor-tion versus image volume is shown in Fig. 9. Maximum andmean distortions were calculated over both cubic and spheri-cal volumes of interest �VOIs� with cube side length andsphere diameters ranging from 40 to 300 mm. As expected,the maximum distortions are always greater in the cubic VOIthan in the spherical VOI of corresponding size.
Next, an individual image slice from the 3D data set wascorrected using the EBS kernel. Distorted control point co-ordinates as determined from the MR slice and undistortedcontrol point coordinates as determined from the correspond-ing CT slice were used as paired landmarks in order to un-warp the MR image geometry to match the correct CT imagegeometry. The mean and standard deviation of distortions forthe 289 control points in the slice before image correctionwere found to be 2.53�0.94� mm. The residual distortion inthe corrected image was determined by locating the 2D con-trol point coordinates in the corrected image �in much thesame way that the 3D coordinates were found in the originaldata set� and compared to the known x and y coordinates ofthe CT image. Residual distortions were found to be0.28�0.15� mm; this represents a ninefold reduction in meanimage distortion. The original and corrected images areshown in Figs. 10�A� and 10�B� while the difference map isshown in Fig. 10�C�. The distortion maps before and aftercorrection are shown in Figs. 10�D� and 10�E�, respectively.
Last, a 2D spin echo �SE� image of the phantom withfrequency encoding in the y direction was acquired 85 mmfrom the isocenter along the z direction. Gradient distortionsmeasured from the 3D GE sequence were used as a basisfrom which to predict the distortion in the SE image. The B0
and susceptibility distortions were scaled according to thedifferent frequency encode gradient strengths used in each ofthe images and were applied in the frequency encode �y�
FIG. 9. Maximum and mean �with standard deviation� magnitude of distor-tions �mm� over various cubic and spherical volumes of interest.
direction in order to predict the location of the control points
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in the 2D SE image. If eddy currents are not adequatelycompensated for in the machine hardware, such currentscould alter distortion patterns for different imaging protocolsand could render the prediction scheme invalid. In order toverify the significance of eddy currents in our magnet, wefirst carried out an experiment in which the distortion wasmeasured at the four corners of a series of five identicalgradient echo image acquisitions and compared this to dis-tortion measurements on a series of five gradient echo im-ages where the echo time was increased in each successiveimage. The results of this experiment are shown in Table I.The average uncertainty �standard deviation� in distortionmeasurement was 0.06 mm for the five identical images andwas 0.24 mm for the five images with TEs ranging from 5 to50 ms. A similar experiment was carried out with spin echoimages and the uncertainty was found to increase from 0.05to 0.27 mm. This approximately fourfold increase in the un-certainty in distortion measurements could be attributed todifferences in remnant eddy currents. Despite the increase inuncertainty, distortion was measured at the four corners�where distortions are expected to be greatest� to within halfa pixel of uncertainty and eddy current effects were deemednegligible in such cases. The distortion prediction schemewas thus validated. Figure 11�A� shows a gradient echo �GE�image of the phantom at z=85 mm; the frequency encodedirection is aligned with the x axis and a large amount ofdistortion is thus observed in the horizontal direction. Figure11�B� shows the SE image acquired at the same z location,but with the frequency encoding �and largest amount of dis-tortion� along the y direction. Using the predicted distortionmap created from the image in 11�A�, the distortion in image11�B� was predicted and corrected. This is shown in Fig.11�C� while a difference map is shown in Fig. 11�D�. Fol-lowing the image correction, mean and standard deviationdistortion was reduced from 1.63�1.02� to 0.29�0.22� mm.
In order to verify the accuracy of the distortion prediction,the control point locations for the SE image were also auto-matically measured. The mean and standard deviation valuesfor the difference in predicted and measured control pointlocations were 0.27 and 0.23 mm, respectively; this repre-sents less than 1 pixel of discrepancy. Image correction usingthe automatically measured image distortion yielded a meanand standard deviation residual distortion of 0.14�0.07� mm.This result is slightly better than that achieved by the usingthe predicted distortion; however, the ability to predict dis-tortion to within 1 pixel of accuracy allows a variety of dif-ferent images of the same object to be corrected based onone set of distortion data. That is, distortion maps do notneed to be calculated for each specific imaging sequence.
V. DISCUSSION
In order to make use of the excellent soft tissue imagingcapabilities of MR in the radiation treatment planning proce-dure, inherent image distortions need to be measured andremoved. This is most readily done using some type of phan-tom measurement; the previous literature suggests two main
phantom types. The phantom presented in this study and in
397 Baldwin et al.: Characterization of geometric distortion in 3 T MR images 397
those by Wang, Doddrell, and Cowin2 has both advantagesand disadvantages over the phantom �linearity test object,LTO� used by Doran et al.4 Because the control points in our
FIG. 10. �A� The original MR image obtained 94 mm along the z axis from ishowing image A-image B �Note: distorted grid lines appear black while comean �standard deviation� distortion of 2.53�0.98� mm; �E� the residual dist
TABLE I. Effects of eddy currents on distortion measurements. Distortionwas measured in the four corners �top left, top right, bottom left, bottomright� of the phantom for five identical image acquisitions �to estimate noisecontributions� and for five image acquisitions with increasing echo times �toestimate the effect of time-varying eddy currents on distortion measure-ments�. The mean and standard deviation was calculated at each corner foreach of the two sets of measurements. Measurement uncertainty increasedwhen echo times were varied but remained within the range of half a pixeldimension.
Mean distortion ± standard deviation
Control point Five identical acquisitionsFive different echo times
�5,10,20,30,50 ms�
Top left −0.01±0.05 −0.22±0.30Top right 4.97±0.07 4.91±0.30Bottom left −0.73±0.07 −1.02±0.20Bottom right 1.79±0.04 1.83±0.16
Medical Physics, Vol. 34, No. 2, February 2007
phantom occur at well-specified points and are not the ex-tended rod objects of the LTO, it is possible to accuratelyquantify distortions in all three dimensions; our phantom al-lows straightforward through-plane distortion measurement.Our phantom is, however, quite heavy and cumbersomecompared to the mostly air-filled LTO. It is further acknowl-edged that a larger phantom, more representative of the sizeand shape of a human torso, would need to be constructed inorder to facilitate distortion correction over more clinicallyrelevant volumes. Such design modifications are currentlyunder way. Finally, as compared to the control point detec-tion scheme used by Doran et al.,4 our detection scheme doesnot require manual matching of any control points in MRand CT.
In the recent study by Wang, Doddrell, and Cowin usingthe same type of phantom, it appears distortion measure-ments were made relative to a priori known control pointlocations—it is not, however, mentioned how these controlpoint locations were determined.2 It is thus understood byour group that a perfectly regular spacing of the control
ter; �B� image A corrected using the elastic body spline; �C� difference mapd grid lines appear white�; �D� the original distortion map of image A with
n map of image B. Distortion is reduced to 0.28�0.15� mm.
socenrrecteortio
points was assumed and that distortion was measured rela-
398 Baldwin et al.: Characterization of geometric distortion in 3 T MR images 398
tive to this assumed spacing. This assumption was avoided inour study as control grid locations were directly measuredusing a corresponding CT scan. Figure 5 illustrated the factthat MR grids were slightly warped even in CT images.
The fat/water chemical shift has not expressly been dealtwith in this study and if fat suppression techniques are notused, chemical shift effects will result in misplaced signal inthe readout direction and potentially in the slice select direc-tion as well. This obviously complicates the treatment plan-ning procedure and such distortions need to be corrected for.In the absence of fat suppression techniques, a high readoutgradient can be used to minimize chemical shift artifacts aswell as B0 and susceptibility effects. Alternatively, adiposetissue can be separately contoured as a postprocessing step;the exact fat/water pixel shift can be determined from theimaging parameters �readout bandwidth, FOV, image resolu-tion, slice select gradient� and an appropriate shift could beapplied to such regions.
The results of this study suggest that distortion in 3 T MRimages can be adequately corrected and that images whichmeet the stringent requirements of spatial accuracy for treat-ment planning can be produced. After segmenting MR im-ages and applying bulk electron density information, someliterature suggests RTTP could be carried out with MR im-ages alone—without the need for image registration andwithout the introduction of errors associated with thisprocess.8,9 Other literature suggests that while MRI providessuperior soft-tissue contrast and more complete and more
FIG. 11. �A� A single distorted slice of the 3D GE image from which dis-tortion maps were obtained. The most pronounced distortion is visible in thex direction �horizontal�; �B� a distorted SE image for which distortion waspredicted based on the GE distortion data. The most pronounced distortion isvisible in the y direction �vertical�; �C� the corrected SE image. The distor-tion was reduced from 1.63�1.02� to 0.29�0.22� mm; �D� a difference mapshowing Image B-Image C �Note: the distorted grid lines appear black whilethe corrected grid lines appear white�.
consistent tumor delineation, the tumor volume information
Medical Physics, Vol. 34, No. 2, February 2007
provided by MR is complementary to that provided by CT. Ifthis is the case, it may be prudent to use both MR and CTimages to provide a composite co-registered image.6,7 What-ever the case may be, it can only be beneficial to start withMR images which are free of geometric distortions andwhich are as spatially accurate as possible. The results of thisstudy show that geometrically accurate images are possibleat 3 T despite the linear increase of B0 inhomogeneities andsusceptibility effects.
VI. CONCLUSIONS
The phantom and methods presented in this paper providea means of quantifying the distortion due to gradient nonlin-earities, susceptibility effects and B0 inhomogeneities for a3D phantom image acquired with a particular set of imagingparameters. The distortion maps created from this proceduremay also be used to predict and correct 2D images �bothaxial and nonaxial� obtained using different acquisition pa-rameters.
Gradient nonlinearities were the main proponent of imagedistortion near the center of the magnet; this finding is inagreement with that of Wang et al. for a 1.5 T magnet.1 Assuch, distortions at 3 T will not necessarily be larger than at1.5 T. Indeed, Wang et al. found maximum distortions of10–25 mm over a 240�240�240 mm3 volume while wefound a maximum absolute distortion of less than 7 mm overour 260�260�200 mm3 volume.1 In addition, Doran et al.report a maximum absolute distortion �due to gradient non-linearities only� of 9 mm over a volume of 257�255�257 mm3.4 Although B0 and susceptibility distortions havea larger effect at higher field strengths, we report smallermaximum distortions at 3 T than previous researchers re-ported at 1.5 T. This implies that the Philips 3 T Intera is awell-shimmed system with excellent gradient linearity and,since gradient nonlinearities are the main source of distor-tions, distortions at 3 T are not necessarily greater than thoseat 1.5 T.
Mean distortions in our 3 T MR system were reducedfrom 2.43�0.94� to 0.28�0.15� mm in an image from whichdistortion maps were created. For an alternative imaging se-quence, the base set of distortion maps was used to predictand correct the image distortion. Following the predictionand image correction, distortion was reduced from an initialamount of 1.63�1.02� to 0.29�0.22� mm �less than 1 pixel ofresidual distortion�. This illustrates how an accurate initialcharacterization of magnetic field variations and gradientnonlinearities can lead to the satisfactory correction of im-ages acquired with any number of different imaging proto-cols; individual time-consuming distortion characterizationscans are not required for each image.
In conclusion, we have demonstrated �1� that image dis-tortions at 3 T are not necessarily greater than at 1.5 T; �2�that such images can be reliably corrected resulting in mini-mal residual distortions; and �3� that distortions can be pre-dicted for images acquired with alternate imaging protocolsthereby reducing the amount of time required to carry out
distortion measurements in clinical situations. The use of
399 Baldwin et al.: Characterization of geometric distortion in 3 T MR images 399
MRI in radiotherapy treatment planning therefore appears tobe a feasible clinical option at 3 T due to both the possibilityof distortion prediction and the minimal distortions observedin both original and corrected images.
ACKNOWLEDGMENTS
The authors would like to acknowledge support from thefollowing agencies: the Natural Sciences and EngineeringResearch Council, the Alberta Heritage Foundation forMedical Research, the Canada Foundation for Innovationand the Alberta Science and Research Investment Program.
a�Electronic mail: [email protected]. Wang, W. Strugnell, G. Cowin, D. M. Doddrell, and R. Slaughter,“Geometric distortion in clinical MRI systems Part I: evaluation using a3D phantom,” Magn. Reson. Imaging 22, 1211–1221 �2004�.
2D. Wang, D. M. Doddrell, and G. Cowin, “A novel phantom and methodfor comprehensive 3-dimensional measurement and correction of geomet-ric distortion in magnetic resonance imaging,” Magn. Reson. Imaging 22,529–542 �2004�.
3M. Breeuwer, M. Holden, and W. Zylka, “Detection and correction ofgeometric distortion in 3D MR images,” Proc. SPIE 4332, 1110–1120�2001�.
4S. J. Doran, E. M. Charles-Edwards, S. A. Reinsberg, and M. O. Leach,“A complete distortion correction for MR images: I. Gradient warp cor-rection,” Phys. Med. Biol. 50, 1343–1361 �2005�.
5C. J. G. Bakker, M. A. Moerland, R. Bhagwandien, and R. Beersma,“Analysis of machine-dependent and object-induced geometric distortionin 2DFT MR imaging,” Magn. Reson. Imaging 10, 597–608 �1992�.
6B. Emami, A. Sethi, and G. J. Petruzzelli, “Influence of MRI on targetvolume delineation and IMRT planning in nasopharyngeal carcinoma,”Int. J. Radiat. Oncol., Biol., Phys. 57�2�, 481–488 �2003�.
7R. K. Ten Haken et al., “A quantitative assessment of the addition of MRIto CT-based, 3-D treatment planning of brain tumors,” Radiother. Oncol.25�2�, 121–133 �1992�.
8
A. Fransson, P. Andreo, and R. Potter, “Aspects of MR image distortions
Medical Physics, Vol. 34, No. 2, February 2007
in radiotherapy treatment planning,” Strahlenther. Onkol. 177�2�, 59–73�2001�.
9Y. K. Lee et al., “Radiotherapy treatment planning of prostate cancerusing magnetic resonance imaging alone,” Radiother. Oncol. 66, 203–216 �2003�.
10R. Gruetter et al., “Resolution improvements in in vivo 1H NMR spectrawith increased magnetic field strength,” J. Magn. Reson. 135, 260–264�1998�.
11J. T. Vaughn et al., “7T vs. 4T: RF power, homogeneity, and signal-to-noise comparison in head images,” Magn. Reson. Med. 46, 24–30�2001�.
12B. L. Schmitz, A. J. Aschoff, M. H. K. Hoffmann, and G. Grun, “Advan-tages and pitfalls in 3T MR brain imaging: A pictorial review,” AJNRAm. J. Neuroradiol. 26, 2229–2237 �2005�.
13S. F. Tanner, D. J. Finnigan, V. S. Khoos, P. Mayles, D. P. Dearnaley, andM. O. Leach, “Radiotherapy planning of the pelvis using distortion cor-rected MR images: the removal of system distortions,” Phys. Med. Biol.45, 2117–2132 �2000�.
14R. Bhagwandien, R. van Ee, R. Beersma, and C. J. G. Bakker, “Numeri-cal analysis of the magnetic field for arbitrary magnetic susceptibilitydistributions in 2D,” Magn. Reson. Imaging 10, 299–313 �1992�.
15P. Jezzard and R. S. Balaban, “Correction for geometric distortion in echoplanar images from B0 field variations,” Magn. Reson. Med. 34, 65–73�1995�.
16F. Schick, “Whole-body MRI at high field: Technical limits and clinicalpotential,” Eur. Radiol. 15, 946–959 �2005�.
17D. I. Hoult and D. Phil, “Sensitivity and power deposition in a high-fieldimaging experiment,” J. Magn. Reson. Imaging 12, 46–67 �2000�.
18R. R. Price et al., “Quality assurance methods and phantoms for magneticresonance imaging: Report of AAPM nuclear magnetic resonance TaskGroup 1,” Med. Phys. 17, 287–295 �1990�.
19CRC Handbook of Chemistry and Physics �CRC, Boca Raton, FL, 2002�.20The Insight Segmentation and Registration Toolkit www.itk.org/. In 2006.21M. H. Davis, A. Khotanzad, D. P. Flamig, and S. E. Harms, “A physics-
based coordinate transformation for 3-D image matching,” IEEE Trans.Med. Imaging 16�3�, 317–328 �1997�.
22L. Chen et al., “MRI-based treatment planning for radiotherapy: Dosim-etric verification for prostate IMRT,” Int. J. Radiat. Oncol., Biol., Phys.
