Review and evaluation of MRI nonuniformity corrections for...

Review and evaluation of MRI nonuniformity corrections for brain tumorresponse measurements

Robert P. Velthuizena) and John J. HeineDigital Medical Imaging Program of the H. Lee Moffitt Cancer Center and Research Institute,and the Department of Radiology, University of South Florida, Tampa, Florida 33612

Alan B. CantorBiostatistics Core, Cancer Control, H. Lee Moffitt Cancer Center and Research Institute,University of South Florida, Tampa, Florida 33612

Hongbo LinDigital Medical Imaging Program of the H. Lee Moffitt Cancer Center and Research Institute,and the Department of Radiology, University of South Florida, Tampa, Florida 33612

Lynn M. FletcherDepartment of Computer Science and Engineering, University of South Florida, Tampa, Florida 33612

Laurence P. ClarkeDigital Medical Imaging Program of the H. Lee Moffitt Cancer Center and Research Institute,and the Department of Radiology, University of South Florida, Tampa, Florida 33612

~Received 23 June 1997; accepted for publication 1 July 1998!

Current MRI nonuniformity correction techniques are reviewed and investigated. Many approachesare used to remedy this artifact, but it is not clear which method is the most appropriate in a givensituation, as the applications have been with different MRI coils and different clinical applications.In this work four widely used nonuniformity correction techniques are investigated in order toassess the effect on tumor response measurements~change in tumor volume over time!: a phantomcorrection method, an image smoothing technique, homomorphic filtering, and surface fitting ap-proach. Six brain tumor cases with baseline and follow-up MRIs after treatment with varyingdegrees of difficulty of segmentation were analyzed without and with each of the nonuniformitycorrections. Different methods give significantly different correction images, indicating that rfnonuniformity correction is not yet well understood. No improvement in tumor segmentation or intumor growth/shrinkage assessment was achieved using any of the evaluated corrections. ©1998American Association of Physicists in Medicine.@S0094-2405~98!02409-2#

Key words: MRI, image segmentation, nonuniformity, image correction, tumor response, MRIphantom, homomorphic filter, thin-plate splines

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I. INTRODUCTION

Magnetic resonance imaging~MRI! is the modality of choicefor brain visualization. MR images are often segmentedquantification of normal tissues or pathology.1 Segmentationof brain tumors can assist in the identification of target vume for 2-D or 3-D radiation treatment planning,2 the assessment of tumor response to therapy,3 and visualization of le-sions for surgery planning.4 Efforts at our institution arefocused on identifying changes in tumor volume betweenbaseline and follow-up MRIs, after treatment. Accurate msurements of relative tumor volume change over timeprovide: ~1! a basis for determining therapy~clinical man-agement!; ~2! general treatment efficacy evaluation; and~3!the development of new treatment protocols.3,5,6 MR imagesof brain tumor patients are extremely difficult to segmeLimiting the application to the measurement oftumor vol-ume changeavoids the need for absolute measurementsare difficult to validate, as required for RTP or surgeplanning.1

We have developed, implemented, and evaluated a nber of segmentation techniques for assessing serial tuvolume response measurements. These methods includ

1655 Med. Phys. 25 „9…, September 1998 0094-2405/98/25 „

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pervised~operator dependent! techniques such ask nearestneighbors,7 semi-supervised fuzzy c-means~ssFCM!,8,9 andfully unsupervised methods.10,11 The supervised techniqueallow accurate monitoring of brain tumor response, butoperator intensive and not cost effective. Therefore, our crent efforts are directed at developing fully unsupervistechniques, using a novel combination of pattern recognitand expert systems. This hybrid method allows succesrefinements of fuzzy clustering guided by a knowledge bcomprised of anatomical rules and intensrelationships.12,13

Many researchers have claimed that image nonuniformis an obstacle for accurate segmentation.1 Since many seg-mentation methods are based on the assumption that simimage intensity represents the same tissue, shadingspreads out the intensity distributions will interfere with tisue classification~Fig. 1!. The literature on nonuniformitycorrections provides descriptions of methods, but few resuWe have done extensive analysis directed at understanthe MRI nonuniformity problem and found that:~1! the non-uniformity is often inseparable from true signal; and~2! thenonuniformity is rf coil and imaging plane dependent. F

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1656 Velthuizen et al. : Evaluation of MRI nonuniformity corrections 1656

example, most multi-element head coils have reasonableformity in the axial plane,1,14 while surface coils suffer fromsevere fall off in all planes. Recently, the analysis of normvolunteers was used to estimate serial volume measurereproducibility using a multi-element head coil.8 The experi-ment was intended to provide the variability due to MR scner drift, patient positioning, image nonuniformity, and oerator variability for the segmentation method. The stuwas aimed at finding the detectable lower limit of serial vume change and associated confidence level. The resuthe ssFCM method indicates that the reproducibility is tisdependent, and that measurements by independent segtation are within a maximum variation of62.8%, for whitematter volume. These results suggest that nonuniformity mnot be a problem for serial measurements using a melement head coil.

The aim of this work is to evaluate the efficacy of currenonuniformity compensation methods. Due to the pluraof techniques currently used, there are ambiguities connewith the theoretical basis, implementation, and applicationthese methods. Described applications include improvedsual contrast as needed for surface coil images, globalmentation of an MRI volume, for example to locate the brasurface, and localized segmentation of small tissue regsuch as brain tumors. Problems of assessing current tniques are compounded by the lack of common data baIn an effort to address these questions, comparisons of vous nonuniformity correction methods are given in thstudy.15–18 The methods are evaluated on common setsimages acquired over time, that serve as a standard forlyzing each approach and its influence on local tumor vume measurements and the measurement of changesmor volume over time.

II. REVIEW

A. Introduction

The accurate quantitative analysis of MR images caninfluenced by many sources of signal uncertainty,15,19,20such

FIG. 1. The effect of nonuniformity on classification. Top row: a syntheimage without nonuniformity~left! and the histogram of each of the class~right!. Bottom row: after introduction of nonuniformity in the image. Thwell separated classes of the top image cannot be separated without cerable~Bayes! error.

Medical Physics, Vol. 25, No. 9, September 1998

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as: noncoherent system image noise; partial volume effewhere the signal at some voxel site is derived from mixtissue types within the voxel; Fourier imaging artifacts, icluding Gibb’s phenomenon that manifests as ringingsharp boundaries;21 and pixel averaging due to the spatiextent of the spatial response function,22 where the resultingsignal at some arbitrary pixel is influenced by the surrouing volume in the local neighborhood~this could be consid-ered as another type of partial volume effect!. Similarly, im-age degradation may be induced by: different coil loadindue to biological~dielectric! effects; motion artifacts that cacause blurring and ghosting;23 magnetic susceptibilitychanges associated with different tissue types; machinependent magnetic perturbations including both receiver stial response; and rf transmitter inhomogeneities that mcause signal intensity variations across the image. In ation, the main magnetic field inhomogeneities, althousmall in the isocenter, may cause image warping. Nonlingradients can cause image warping and imperfect slicefiles referred to as a potato chip effect,24 where the slice isnot a plane but warped, are factors that can contributeimage degradation. All of the above uncertainties can pobly lead to tissue volume determination errors with intensbased segmentation methods.

The degree of interference due to any particular sourcdependent on the imaging hardware, such as analog sifiltering or coil design, where some designs produce mhomogeneous fields.25 The degree of degradation is alssomewhat dependent on the pulse sequence and imaginrameters. A theoretical development of the MR image infmation content and related SNR resolution compromisegiven by Fuderer.26 Multispectral data acquisition permitthe analysis of two or three sets of nearly independent dand may provide better tissue separation at the expensmore imaging time. Specifically, three spectral componeprovide for superior tissue separation.1,27 Signal variationsdue to magnetic nonuniformities are often dependent on sorientation.14,20,28 As discussed by Condonet al., the mainsource of signal nonuniformity in the transverse plane is dto analog bandwidth filtering of the raw data; the problemthe sagittal or coronal planes is mainly due to rf inhomogneity. The bandwidth anomaly is not applicable to MRI sytems, where the filtering cutoff is sharp~private communica-tion with GE!. Although the total magnitude of the error mabe appreciable, it has been shown that the noise and rf inmogeneities are stable over time.29

In addition to reviewing compensation methods relatedhead images, methods related to surface coils30–35and breastcoils35,36 are referenced due to similar methodologies. Tnoise in a magnitude MR image is often misunderstoThorough treatments of the MR image noise and posscorrection mechanisms can be found in a varietysources.37–40Power losses due to eddy currents are discusby Harpen.41 Motion artifact suppression is discussedHeadly and Yan.42 Geometric distortions due to the mastatic field, gradient inhomogeneities, and sample suscebility differences are discussed by these researchers.24,43–45

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B. Nonuniformity: The problem

All imaging sequences start with exciting the equilibriumagnetization. If the magnitude of the rf excitation field vaies across the sample, the signal amplitudes of like tissuevary accordingly. The accepted model for the signal macscopic nonuniformity perturbation at some arbitrary imalocation r is given by

s0~r !5g~r !s~r !1n~r !, ~1!

wheres0(r ) is the observed corrupted signal,s(r ) is the truesignal,g(r ) is a slow varying gain field responsible for thnonuniformity artifact, andn(r ) is additive noise. This equation applies to both 3-D and 2-D data sets and accountsall sources of nonuniformity and is normally applied to manitude images, but should also apply separately to theand imaginary components of a complex image. In genethe nonuniformity artifact is more severe inter-plane thin-plane. Note that the additive noise condition, as appliedmagnitude images, is only an approximation valid whensignal-to-noise ratio is appreciable;40,46,47 this point is oftenoverlooked or misunderstood. As discussed previously,model assumes that the interference term and true signamultiplicative and independent which may not be universacorrect.14 The separability approximation may be valid fhomogeneous objects such as phantoms, where the magsusceptibility is uniform, but may not be true for heteroenous objects, where the susceptibility varies. This probis accentuated at tissue boundaries. Similar reasoning apto image regions where partial volume effects are predonant and magnet field susceptibilities are mixed.

C. Correction techniques: General approach

Generally, empirical methods are used to estimategain field and correct Eq.~1!. Theoretically, the correctedsignal is given by

sc~r !5s0~r !

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g~r !. ~2!

The resulting noise power acquires spatial dependence wthe theoretical SNR is preserved. A variant of this methuses the logarithm of the image data. The correspondmodel takes the form

log@s0~r !#5 log@g~r !s~r !1n~r !#. ~3!

If the signal term is much greater than the noise, this reduto

log@s0~r !#' log@g~r !#1 log@s~r !#. ~4!

In this form, the correction results in simple subtraction flowed by exponentiation. Usually, the gain field is foundlow-pass filtering of the signal. The corrected image canexpressed as

sc~r !5exp$ log@s0~r !#2 lpf~ log@s0~r !# !%, ~5!

where lpf implies a low-pass filtering operation. This tecnique is often referred to as homomorphic filtering. Thmethod is commonly used to separate inhomogeneities inillumination of a scene and the reflection properties of


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objects in the scene,48 and is based on the idea that the illmination and scene occupy different parts in the frequespectrum. The prospects of finding some approximate mroscopic correction function obtained empirically can besessed by taking the Fourier transform of the above expsion. If the two functions have disjoint~nonoverlapping!frequency spectrums, the separation may be possible. Owise, the correction may interfere with the true signal.

D. Correction techniques: Current applications

Although the particular imaging protocol has a direct ifluence on the resulting image quality, the reported compsation methods reviewed here are not use restricted to aticular imaging sequence. Therefore, just the methodsoutcomes are discussed. The compensation methods fnonuniformity can be classified into two general categorrelating to the gain field characterization:~1! internal meth-ods, derived from the individual imagdata;14,16–18,31,32,34,35,49–57and ~2! external methods, including magnetic field calculations33,58 and phantom basedtechniques.14,15,27,28,36,59With the exceptions of the methodimplemented by Rajapakseet al.,56 Meyer et al.,35 Wellset al.,55 and Guillemaudet al.,57 the data driven methods cabe further divided into two subcategories:~1! filtering meth-ods; and~2! surface fitting techniques. The segmentatimethod presented by Rajapakseet al.56 incorporates a simi-lar idea and assumes that the mean value of a given ticlass is a slowly varying function of position; the rf corretion is not a modular function but incorporated into the geeral tissue segmentation routine. Similarly, Meyeret al.35

use an iterative polynomial volume modeling approach tis robust with respect to inhomogeneity as a preliminary smentation step. Wellset al.55 apply an iterative approachbased on expectation maximization~EM! to estimate andcorrect the gain field; the technique is a data driven adapform of Eqs. ~4!–~5!. A brief generic description of eachtechnique is given. Guillemaudet al.57 present a modifica-tion of the Wellset al.55 EM technique. The reader shoulrefer to the appropriate references for exact detailsimplementation procedures.

1. Phantom based methods

Uniform phantoms are used to map the macroscopicintensity variation. Tip angle variations induce a correspoing signal variation. Using the initial condition that the uperturbed signal is uniform, a correction can be derived aimplemented with Eq.~2!.

2. Surface fitting methods

A surface fitting procedure is used to model the gain fieThe procedure requires some initialization, where it issumed that ‘‘good image regions’’ of like tissue can be idetified a priori. These regions are used as sample pointsthe nonuniformity characteristic. A surface is generated,all points within the field of view are extrapolated from thsurface. The technique is equivalently implemented usEq. ~2! or Eq. ~4!.


Medical Physics, Vo

TABLE I. MRI patient cases. XRT5x-ray radiation therapy; chemo5chemo-therapy.

Patientcase

Sex/Age Tumor type History

MRI days.baseline Operators

1 M/56 Glioblastoma multiforme Biopsy and XRT 2 years prior tobaseline; chemo during MRIperiod

0, 52, 97,117, 140

MV ~3x!RV ~2x!

2 M/37 Anaplastic astrocytoma/glioblastoma multiforme

Partial resection and XRT 2 yearsprior to baseline; chemo duringMRI period

0, 46, 91 MV ~3x!RV ~2x!

3 M/27 Recurrent and malignantmeningioma

Biopsy and two resections 2 yearsprior; biopsy 3 months prior;XRT during the period 6 to 2weeks prior to baseline; chemoduring MRI period

0, 75 MV ~2x!CH ~2x!

4 M/47 Small cell lungmetastasis

Fractionated XRT first 3 weeksafter baseline; chemo during MRIperiod

0, 81 MV ~2x!KG ~2x!

5 M/64 Glioblastoma multiforme XRT just before baseline MRI;chemo during MRI period

0, 49, 116 MV~2x!CH ~2x!

6 F/57 Glioblastoma multiforme Near total resection 2 weeks priorto baseline; XRT and chemoduring MRI period.

0, 32, 89,159, 180

MV ~2x!CH ~2x!

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3. Filtering methods

There are two general approaches taken to estimategain field: filtering the image domain data and using E~1!–~2! to make the correction; or filtering with Fouriemethods and using Eqs.~3!–~5! to make the correction.

The image domain approach often requires a homogenimage assumption, implying that other than the domintissue class must be removed first. For example, in bimages, brain parenchyma is considered as the homogeclass, and the ventricles are removed. The gain field is emated by comparing local estimates of the expected sigvalue with the global expectation. Often the local estimateacquired with order statistical methods,59 such as median fil-tering, or simple averaging techniques applied locally. Tapproach can be extended to include the possibility of mtiple tissue classes, where the anomaly is estimated by cparing the global parameter for some given tissue type wthe locally measured parameter.

The Fourier approach for estimating the gain field is buon the assumption that the gain field is a slowly varyifunction compared to the true signal and that the two speare separable. Using Eqs.~3!–~5!, a low-pass filter is ap-plied; this is often referred to as homomorphic filtering. Tlow-pass filtered image and the observed image can betracted to obtain the correction and the result exponentiaBoth approaches can be applied automatically without invention or initialization.

4. Field calculations

The gain field is derived theoretically for a given cogeometry. Complicated geometries are difficult to modand do not include a model of the susceptibilities of tbiological subject that is imaged.

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E. Assessment of current approaches

The impact of rf nonuniformity correction techniques otissue classification is given in two parts:~a! single imageacquisition analysis and~b! multispectral analysis.

1. Single image acquisition analysis

The results presented by Condonet al. show increasedwhite/gray matter contrast without segmentatidemonstrations.28 Similarly, Wicks et al. demonstrate thathe nonuniformity can be reduced without segmentatanalysis.15 Other analysis53 with segmentation results illustrates that the nonuniformity can be reduced, although,results show significant changes between the correcteduncorrected mean tissue values. Similarly, Meyeret al.showthat the coefficient of variation can be reduced but the mtissue values change significantly after correction.35 DeCarliet al. illustrate that the total volume standard deviation cbe reduced while maintaining the central total volume;54 thisis not significant for particular tissue volume reproducibilitThe modified EM algorithm60 produced very modest improved segmentation of white/gray matter on a very limitdata set. The results presented by Rajapaskeet al. are givenwithout quantitative analysis pertaining to per-scan tissvolume classification.56 In general, these methods are ntested for serial volume reproducibility. Intensity correctioare also used in association with 3-D brain contodetection59 and illustrate some benefit.

2. Multispectral acquisition image analysis

Lim et al.using a global thresholding supervised segmtation method demonstrate moderate agreement betweenraters using the correction technique;50 no control study isgiven for comparison. Kamberet al. show that MS lesionscan be separated.52 Similarly, no control study is given

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FIG. 2. Phantom correction method.~a!Image of a transaxial slice through thphantom does not show a stronger rooff in the frequency-encode direction~b! Average pixel intensity and standard deviations in transaxial slices asfunction of their position along thebore of the magnet~Z-axis!: no effectof interleaved acquisition sequenceseen.~c!–~f! Correction of the coronalphantom images based on the trasaxial data set.~c! Mean pixel intensityand standard deviation in the coronaslices as a function of the position othe slice before~thin line! and after~thick line! correction: better unifor-mity was achieved~smaller error bars!as well as slice-to-slice uniformity.~d!Original coronal image;~e! correctionmatrix found by inverting the tri-linearinterpolation of the transaxial data seand ~f! corrected coronal image.

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Glennon illustrates that the corrections had little effectsegmentation performance.14 Johnstonet al. show that auto-mated segmentation with the correction compares wmanual segmentation and performs better than sesupervised classification methods.18 Dawantet al. show thatcorrection methods reduce the tissue volume coefficienvariation, but before and after correction tissue averagesnot presented.16 These methods were not tested for effectlongitudinal volume reproduction.

Longitudinal studies show that scan to scan and inobserver variability can be reduced in normal brain tissvolume analysis,17 but no conclusion concerning the reprducibility of particular tissue volume of a particular slicover time can be made due to the way the data are presewith total volume averages. Wellset al. use an adaptive approach for segmentation and gain field estimation that copares favorably with manual segmentation and performster than some supervised methods.55 The study does noprovide serial volume measurements; therefore, no assment of relative volume reproducibility can be made. It hbeen demonstrated that the growth of MS lesions cantracked over time which is consistent with a worsenicondition.27 In addition to the nonuniformity correction, thdata were smoothed with a diffusion filtering technique;control study is presented without separating the effect oftwo data correction methods.

III. MATERIALS AND METHODS

A. Serial MRI data

MRI data for six patients having cerebral tumors arevestigated~Table I!. The same cases were analyzed in preous studies.9 The tumor types studied include gliomas~glio-blastoma multiforme, grade III, or higher gradastrocytoma!, metastasis, and meningioma. Meningiomand metastases tend to have well defined boundaries an


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easier to segment; gliomas tend to have diffuse boundaIn this work, we do not differentiate the analysis by tumtype because of the small number of patients. Some patipreviously received a combination of surgery and radiattherapy. During the 32 week monitoring period, each patireceived chemotherapy, radiation therapy, or a combinaof both. The patients were imaged on multiple occasioranging from 2 to 5 scans, depending on the patient cTraining data for the classifier were selected multiple timby various operators with comparable experience, allowthe measurement of operator variability.

B. Imaging scheme

The trans-axial multispectral MR images were acquirusing a 1.5 Tesla GE Signa Advantage MRI scanner witmulti-element head coil~General Electric Company, Mil-waukee, WI!. Contiguous 5 mm slice images were acquirwith a field of view of either 240 mm~for Patients 1–5! or220 mm~for Patient 6! with a 2563192 acquisition matrixand were reconstructed to a 2563256 pixel image. The mul-tispectral data set consisted of a 5 mmthick anatomical sliceT1 weighted, proton-density~PD! weighted, and a T2weighted images. The T1-weighted images were acquusing a standard spin-echo~SE! sequence with aTR/TE5650/11 ms. The PD and T2 images were acquiusing a fast spin-echo~FSE! sequence with a TR/TEeff54000/17 ms for the PD image and a TR/TEeff54000/102 ms for the T2 image. All image sets, includithe FSE images, were acquired after administration of GDTPA contrast enhancement.

C. Segmentation method

The k nearest neighbors (kNN) segmentation method iused for evaluation. Although the ideal method would becompletely unsupervised technique, we have not comple

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the hybrid clustering/expert system approach.13 Thek nearestneighbors method is a standard approach and has beenextensively at this institution and by other researchers,1 andis therefore suitable for the evaluation. Descriptions ofkNNcan be found elsewhere.5,7,9 Training data for the classifiefor the analyzed patients are available from previous wo9

Because of the magnitude of the data handling requiredthis study, the results were processed automatically, i.e.further supervision was done for the selection of the tumlocation in the segmentation result. As a result, some fapositive areas that were discarded~disarticulated! in previousstudies9 are now included in the volume measurements.some cases, this leads to poor correlation with a pixel-pixel expert assessment. It should be emphasized that madisarticulation of false-positives~i.e., selection of the tumolocation! is important for tumor volume accuracy, which wasubject of a previous paper.9 However, in this study we assess the effect of nonuniformity corrections on the segmtation results.

ThekNN segmentation method is applied to multispectdata. Nonuniformity corrections are applied to each specimage individually, before thekNN algorithm is applied. Wecompare fivekNN segmentations of each data set: uncrected data, and after application of each of four correctmethods.

D. Phantom correction method

The phantom correction method proposed by Wicet al.15 is implemented with phantom measurements usthe same MR imaging sequences as used for the patients~seeSec. III B!. The voxel locations in each patient data set wmatched to the phantom intensities using tri-linear interpotion. All patient images were acquired within 15 monthsthe phantom data. During the patient data acquisition peno changes in imaging protocol, scanner software, or hware were performed. Analysis of the daily quality assuraphantom images implemented over a three year period icates some variability exists, but no long term systemdrift was observed in the uniformity measurements~see Ref.25!. Therefore, the phantom image set is appropriate fordata. Wickset al. apply a receiver filter correction to thphantom to compensate for the analog filtering roll-off. Thproblem can be identified by measuring the standard detions of profiles in both phase-encode and frequency-encdirections and proves not to be a problem@Fig. 2~a!#. Theeddy current correction performed by Wickset al. was notperformed, since no effect of interleaved acquisitions wobserved@Fig. 2~b!#. The phantom images were smoothwith a 737 median filter for noise removal as in the studyWicks et al.15

To illustrate the method, show that phantom images wacquired correctly and demonstrate that the coded progracorrect, the experiment described by Wickset al., @see Figs.2~c!–2~f!# was repeated using images of a homogenephantom data acquired on our MRI system. Following Wicet al., the phantom images acquired in the coronal plawere compensated with a correction matrix derived from


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ages acquired in the axial plane with the same pulsequence: a T2 weighted fast spin-echo~FSE! acquisition. Themethod indicates that images acquired in one orientationbe used to develop corrections for images acquired in oorientations. The method is very effective in removing imanonuniformities; see Figs. 2~c! and 2~f!. Wicks et al. definetwo measures of uniformity: in-slice uniformity is the ratof the standard deviation of the image intensities to thmean after noise removal; slice-to-slice uniformity is tstandard deviation of the individual slice means to their ovall mean over all slices.15 In our experiment, the slice-toslice uniformity in the coronal image set is reduced fro6.3% to 1.2% after correction, and the average in-slice uformity is reduced from 8.161.7 to 2.863.7 ~mean6standard deviation!. These figures are similar to thosfound by Wickset al.

E. Image smoothing method

The method proposed by Narayana and Borthakurimplemented. In the previous investigation,17 dual-echo datawere analyzed. Here, this method is applied to the T1, Pand T2 spectral component images. The intracranial masobtained by editing the previouskNN segmentation result.9

No smoothing prior to the correction is applied. Narayaand Borthakur replace some bright areas in the image wthe average value of the remaining pixels, which are psumed to be brain parenchyma. The specific details ofthreshold selection are not given in the study.17 We use a‘‘pre-segmentation’’ based on thresholds. The imagechanged into an image of a relatively uniform object, simito a phantom. The purpose of this step is to remove imfeatures~bright areas!. The rf nonuniformity is subsequentlseparated from the true signal by removing high frequedetails using smoothing. If the image used for correctiononly one tissue type with assumed uniform image intensthe same ideas used for the phantom correction can beplied. If the area outside the brain mask is set to zero,17 thesmoothing would result in a significant fall-off at the edgethe brain. Therefore, the area outside the brain mask musset to a mean value as well. To apply the method tomultispectral brain tumor images, the mean value and sdard deviation~s.d.! of the data within the brain mask arcalculated, and everything outside the interval@mean—2s.d.,mean1s.d.# is set to the mean. This asymmetric interval wdetermined empirically, and was found to replace the baground as well as the ‘‘bright areas’’ in each of the mulspectral images, including the enhancement in theweighted image and the ventricles, vessels, and edema inPD/T2 weighted images. Note that if the intensity intervalmade smaller, the number of pixels that contribute informtion for the calculation of the gain field is reduced. The rsulting image is smoothed with a 25325 median filter, re-sulting in the correction image~the gain field!. The originaldata are then divided by this correction image; see Eq.~2!.Instead of normalizing the corrected images on the mamum pixel intensity, we restore the mean value within tbrain mask. Figure 3 shows an example of the applicationthe correction method.


FIG. 3. Image smoothing technique:~a! original T1weighted image;~b! gain field as found by smoothingimage ~a! using Narayana’s technique; and~c! imagewithin the brain mask after correction.

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F. Homomorphic filtering

This correction method investigated by Johnstonet al. isimplemented.18 This approach is essentially identical to thsmoothing method described above, with the exceptionthe smoothing and correction operations are applied tologarithm of the image; see Eqs.~4! and ~5!. Johnstonet al.set the background in the image to the mean of the imwithin the brain mask and do not consider the bright arwithin the brain mask, which was a concern for othresearchers.17 It was asserted18 that the low-pass image contains the rf nonuniformities. We found that the smoothimages are extremely blurred~bright and dark patterns! ver-sions of the original, and did not necessarily represent thnonuniformity, as illustrated in Fig. 3.18 This is particularly aproblem with large bright areas observed in each of the mtispectral images of the brain tumor patients. This was elinated by using the same approach as described forsmoothing method above, by replacing dark and bright intsities outside the@mean—2s.d. mean1s.d.# interval with themean intensity of the brain region. This point is illustratedFig. 4. Johnstonet al. do not characterize the low-pass filtprocedure, and it is not described in referenced wor30

Since30 states that a linear filter was used, a low-pass 32332boxcar averaging filter is used for this study.

G. Surface fitting

Dawantet al. implement two similar correction methodbased on surface fitting.16 Thin-plate splines are fit to~1! afew manually selected control points, termed the direct fit~2! fitting points returned by a neural network segmentatstep, termed the indirect fit. In our implementation, 32 poiobtained from thekNN white matter segmentation are usfor initialization. The points are spread evenly acrossimage and picked from the regions with the highest probaity of belonging to the white matter tissue class. Dawaimplemented the high probability criterion by selecting onpoints with a neural network output above a threshold;required that allk nearest neighbors (k57) in the trainingset were labeled white matter. If less than 32 points satisthese conditions, the points withk21 white matter neigh-bors were added; this was needed in less than 1% ofcases~10 times out of 1022 sets of training data!. We foundthat the reference points obtained this way were sprevenly over the intracranial mask, and included some pereral reference points. There was no need for additionalerence points on the perimeter of the mask, as Dawantscribes. A thin-plate spline is then fit to the 32 referen


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points. This approach can be considered as a compositerived from both of Dawant’s methods. Figure 5 shows tapplication of the method to one image. A correction surfais generated for each training set. Therefore, the resulvariabilities in the tumor volume measurements includevariability in the nonuniformity correction introduced by threference point selection.

H. Expert assessment of tumor volume

Although MR contrast enhancement has its limitationT1 weighted images acquired after administration of galinium DTPA to improve delineation of tumor margins4 areused as a practical representation of active brain tumor tisand for estimations of relative changes in tumor volumeresponse to therapy.1,4,6,61 Pixel-by-pixel expert hand segmentation is established using a custom design interfacdisplay full multispectral MRI images. A transparent overlof the physician determined segmentation allows reprodible hand drawing of tumor tissue for each 2-D slice. Phycian experts~neuro-radiologists! generate manually tumor labels on each slice through the tumor volumes, a very ticonsuming task. The variation using this method is less t5%,62 with the source of variation being the uncertaintythe image rather than labeling precision. This methodbeen successfully used in our laboratory for the last thyears.9,10,61,62

I. Statistical methods

We are interested in the effect of nonuniformity corretions on the measurement of tumor response, i.e., the chin tumor volume relative to a baseline volume measuredfore treatment started. We compare segmented results toexpert labeling. As a first evaluation, the measured volumthemselves, rather than the responses, can be related texpert labeling. Intuitively, the Pearson correlation coecient Rp should provide insight in the ability of the segmetation method in conjunction with a nonuniformity correctioto reproduce the expert hand segmentation. However, Band Altman have pointed out that correlation does not nessarily provide insight in the clinical adequacy of tmethod under evaluation.63 As an alternative, they proposeto plot the difference of two measurements against theirerage, and calculate the standard deviation of the differenOur analysis of the nonuniformity corrections will be bason the standard deviations of the differences with the explabeling.

In addition to comparing the tumor volumes, the rsponses must be evaluated. For each method, for each pa

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FIG. 4. Homomorphic filtering. Top row: correction aproposed by Johnston~Ref. 18!. Bottom row: modifiedmethod.~a! Original T1 weighted image.~b! Gain fieldfound using Johnston’s method~the ratio of the originalimage a and the Johnston corrected image c, notlow-pass filtered logarithm of the image!. ~c! Correctedimage with original method.~d! ‘‘Featureless image’’where areas outside the range around the mean areplaced with the mean;~e! gain field found using modi-fied method with the same display parameters as~b!; ~f!corrected image. Center and width were the same~a!, ~c!, ~d!, and~f!, and were also the same for~b! and~e!. Note that ~b! and ~e! are very different, but theresulting corrected images are very similar.

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and each follow-up, the response measurements are clated as:

Respi j 5Vi j 2Vi0

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where Respi j is the response measurement obtained forj th follow-up of the i th patient, and theV’s represent thevolumes obtained for this follow-up and the baselineVi0 ,respectively. Moreover, the response measurement is calated for each set of training data as obtained from theerators~see Table I!. The response measurements for eapatient, follow-up, and training data set are then evaluaseparately for each correction method against the respmeasurements obtained using the manually segmentedumes. Again, the standard deviations of the differencesprovide insight in the effect of the correction methods.

IV. RESULTS

Figure 6 shows estimates of the gain fields generatedeach correction method for a representative slice. It is m


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important to note that the gain field is very different for eatechnique~columns 2–5! and each MR image~rows a–c!.The gain fields calculated by the smoothing technique~col-umn 3! and by homomorphic filtering~column 4! can beconsidered blurred versions of the raw image~column 1!,obviously with the exception of the enhancement in theand PD weighted images, which was replaced with the mof the image before calculating the correction. The gfields in Fig. 6 represent significant modifications to the msured data, with multiplication factors ranging from 0.451.45 ~see legend in row d!. It should be noted that pixeintensities between different classes in MRI data have simvariations: the class means vary from 0.50 to 1.70 timesimage means in the uncorrected data. Despite the largerection factors, and the significant differences betweengain fields as calculated by the four correction methods,tumor segmentation results~row e! do not show much varia-tion at all. The main differences in segmentation resultsbe found at the edge of the intracranial region, whichfalse-positives.

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FIG. 5. Surface fitting.~a! Original image.~b! Segmen-tation result before correction.~c! Location of the 32reference points chosen by systematic sampling ofwhite matter pixels with high probabilities.~d! The gainfield as found by fitting thin-plate splines to the refeence points.~e! Corrected image.

resp. forion,meninges.


FIG. 6. Gain fields and segmentation results for a representative slice. The uncorrected MRI slice data~T1, PD, and T2 weighted images! is depicted ina1,b1, andc1, respectively. Columns 2–5 show the gain fields according to the phantom correction, smoothing, homomorphic filtering and surface fitthe corresponding MR images in the row.~d! Legend for the gain fields ina22c5. Row~e!: tumor segmentation results for uncorrected, phantom correctsmoothing, homomorphic filtering and the surface fit resp. The main difference in the segmentation result can be seen in the false positives at the

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Figure 7 shows the measured tumor volumes for epatient and each follow-up, for each of the correction meods. As was also seen in representative slice in Fig. 6, osmall differences between correction methods are seencept for the surface fit. Table II shows the Pearson corrtion coefficients for the correction methods, measuredplotting each of the segmented volumes against the cosponding expert labeled volume. Note that the correlatcoefficients are biased estimates, since the numbers wertained with repeat studies of the same patient and retraining data selection by the same operators. However,bias is the same for each of the correction methods.differences in correlation coefficients confirm that the corrtion techniques have very little impact on the segmenta


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results, with the exception of the surface fitting techniqwhere a weaker correlation is found.

Application of the method proposed by Bland and Altmresults in the graphs in Fig. 8 and the summary in TableThe values of the numbers in Table III are of less interhere than the comparison between the methods. Pairedt-testson the differences obtained without correction and with eaof the corrections methods each showp.0.3, except for thesurface fit data (p,0.01). Application of theF-variance teston the differences in volume measurements shows no sigcant differences in the variances of the distributions~p.0.5 for phantom correction, smoothing and homomorpfilter, p50.16 for the surface fit!. In Fig. 7, the data areseparated by patient. For the surface fit, the results indi

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that thekNN segmentation strongly overestimates the tumvolume compared to manual segmentation. However, notematic differences between the patients can be seen ingraphs.

Table IV lists the results of the Bland and Altman testapplied to the response measurements. Again, there istatistical difference between the means and standard d

FIG. 7. Tumor volumes measured for each of the patients and each ofollow-ups. The expert labels were obtained by manual segmentation.other volumes were obtained usingk nearest neighbors segmentation, awere then averaged over the training sets~operators!.


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tions of the differences in response measurements, withexception of theF-variance test for the surface fit (p50.04).

V. DISCUSSION AND CONCLUSIONS

Many researchers have claimed that in MRI segmentatrf nonuniformity is of critical importance. In this work, various nonuniformity correction approaches were tested osingle database of six patient cases encompassing 20volumes to assess the effect on tumor response assessm

In general the proposed nonuniformity correction methoinvolve removing the lower part of the frequency spectruSimilar techniques are often used in other imaging modties to induce level contrast to irregular highly correlatrandom fields, while maintaining detail. This method maysuperior to standard intensity based contrast manipulatiReduced operator variability is consistent with this data mnipulation.

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TABLE II. Pearson’s correlation coefficient for segmented tumor voluagainst manually labeled volume.

Correction method Rp

No correction 0.90Phantom correction 0.88Smoothing 0.88Homomorphic filter 0.89Surface fit 0.73

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FIG. 8. Analysis of tumor volume mea-surements using the method by Blanand Altman. Each volume measurement is compared to the expert segmentation. The data are separatedpatient. The unit on both axes is cubicentimeters.

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The phantom correction method applies a small correcto the data since the phantom images themselves areuniform in the area of the brain parenchyma. It shouldnoted that our approach to segmentation has been on aby slice basis rather than segmentation of the full volumeis proposed by Wickset al. and Wellset al.13,55 For volumesegmentations, the profile along theZ-axis obviously needscorrection, for which phantom correction techniques mayapplicable.20 For segmentation of localized tumors in trasaxial images our results do not indicate any beneficialfect.

The smoothing and homomorphic filtering techniquessume that there is a separation of spatial frequencies ofgain field and the signal. However, the gain fields fouthrough either filtering technique reflect the tissue dependbrightness patterns in the MR image, indicating that no sseparation is achieved. This is also true even when consting a ‘‘featureless image’’ by replacing bright and dark arewith the mean value in the brain mask.

Surface fitting is in principle equivalent to low-pass filteing. The approach assumes that the correction for one titype is applicable to another; this may not be the caseabnormal image regions that consists of a tumor bed inspersed with necrosis and surrounded by edema. The memay be useful for images of a less complex nature, butdistorted geometric distribution of white matter and thetensity changes due to pathological changes in brain tupatients resulted in this study in a reduced correlation wthe manually labeled tumor size.

Although the corrections themselves are quite significathe application of the correction methods on tumor respomeasurements is very small. This can be attributed to thethat tumors are localized regions, which are positionedapproximately the same way in the MR imager in follow-studies. The true nonuniformity is much smaller thanimage-based gain fields indicate, and does not prohibit arate tumor response measurements. Comparisons ofinter-slice or corresponding intra-slice gain fields indicalittle consistency with each approach except for the phanbased method. This variation may be caused by some oeffects discussed in Sec. II A, the validity of Eq.~1! forobjects other than homogeneous, or both.

In conclusion, the differences in the calculated gain fieshow that rf nonuniformity corrections are not yet well uderstood. Moreover, the implemented correction methhave not shown beneficial effects for tumor segmentation

TABLE III. Result of the Bland and Altman test comparing differences btween manually labeled and segmented tumor volume estimates.d̄ is theaverage difference,s is the standard deviation of the differences.

Correction method d̄ s

No correction 11.7 34.2Phantom correction 3.6 37.0Smoothing 14.9 38.3Homomorphic filter 8.3 37.1Surface fit 232.9 54.0


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ACKNOWLEDGMENTS

This work was funded in part by a grant from NIH R01CA59425. We would like to thank Dr. Mohan VaidyanathaCindy Heidtman, and Karen Gosche for the training datathe patient data sets, and Dr. Murtagh, Dr. Arrington, andSilbiger for the very time consuming manual segmentatof the brain tumors. We would also like to thank the anonmous reviewers for their helpful suggestions.

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- TABLE IV. Same as Table III, but forresponseestimates rather than volumes.

Correction method d̄ s

No correction 0.08 0.22Phantom correction 0.10 0.23Smoothing 0.06 0.21Homomorphic filter 0.09 0.20Surface fit 0.13 0.35

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