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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
16559…/1655/12/$10.00 © 1998 Am. Assoc. Phys. Med.
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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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1657 Velthuizen et al. : Evaluation of MRI nonuniformity
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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 !
g~r !5s~r !1
n~r !
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
Medical Physics, Vol. 25, No. 9, September 1998
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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!.
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1658 Velthuizen et al. : Evaluation of MRI nonuniformity
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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.
l. 25, No. 9, September 1998
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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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1659 Velthuizen et al. : Evaluation of MRI nonuniformity
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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
Medical Physics, Vol. 25, No. 9, September 1998
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ted
-t-
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sare
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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1660 Velthuizen et al. : Evaluation of MRI nonuniformity
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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
Medical Physics, Vol. 25, No. 9, September 1998
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sse-
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.
-
1661 Velthuizen et al. : Evaluation of MRI nonuniformity
corrections 1661
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.
ethth
ageae-e
e
um
ten
inerk.
s
, oiontedthbinlyw
fie
t
eaipredc
de-hece
tingthee
s,do-
suein
-e toayuc-si--mehaninhasree
c-angebe-
thees
o theffi-n-n
landec-hedav-ces.edert
e-tient
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
Medical Physics, Vol. 25, No. 9, September 1998
ate
es
r
d
rf
l-i-he-
rns
el-t
e
d
he
dh-f-e-e
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
-
s
the
re-
for
1662 Velthuizen et al. : Evaluation of MRI nonuniformity
corrections 1662
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.
al
th
lcopcte
onv
w
bo
ch
T1eanainea-tolilarthecor-thethe
canare
and each follow-up, the response measurements are clated as:
Respi j 5Vi j 2Vi0
Vi0, ~6!
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
Medical Physics, Vol. 25, No. 9, September 1998
cu-
e
u--
hdseol-ill
yst
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.
the
r-
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.
1663 Velthuizen et al. : Evaluation of MRI nonuniformity
corrections 1663
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
acthn
, eelbrrioepet
Thectio
ue
anIII.est
ch
nifi-
hic
cate
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
Medical Physics, Vol. 25, No. 9, September 1998
h-lyx-
a-ye-nob-at
hee-n
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
-
osy
t
asev
the
ion,-n aMRIents.dsm.ali-edbeons.
a-
f tT
nd
me
1664 Velthuizen et al. : Evaluation of MRI nonuniformity
corrections 1664
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!.
Medical Physics, Vol. 25, No. 9, September 1998
rs-he
snoia-
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.
hehe
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
d--
byc
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.
-
tioqubsla
bn-e
ast
nde
ucrua
r-ssf
teththinmit
nnsfai
upthcc
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ldn-od
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y-I
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. J.tasis
. A.n-
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id,don.
,h-
.ch-
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e -
1665 Velthuizen et al. : Evaluation of MRI nonuniformity
corrections 1665
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
Medical Physics, Vol. 25, No. 9, September 1998
niteeices
e
f-
-he
nthct-s
ueorr-ode
-orh
t,ectn
eu-the
mhe
s
sf
individual multispectral MR slices for brain tumor
responmeasurements.
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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