Magnetic resonance imaging-guided attenuation correction in whole-body PET/MRI using a sorted atlas approach

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Magnetic resonance imaging-guided attenuation correction in whole-body PET/MRI using a sorted atlas approach

ARABI, Hossein, ZAIDI, Habib

Abstract

Quantitative whole-body PET/MR imaging is challenged by the lack of accurate and robust strategies for attenuation correction. In this work, a new pseudo-CT generation approach, referred to as sorted atlas pseudo-CT (SAP), is proposed for accurate extraction of bones and estimation of lung attenuation properties. This approach improves the Gaussian process regression (GPR) kernel proposed by Hofmann et al. which relies on the information provided by a co-registered atlas (CT and MRI) using a GPR kernel to predict the distribution of attenuation coefficients. Our approach uses two separate GPR kernels for lung and non-lung tissues. For non-lung tissues, the co-registered atlas dataset was sorted on the basis of local normalized cross-correlation similarity to the target MR image to select the most similar image in the atlas for each voxel. For lung tissue, the lung volume was incorporated in the GPR kernel taking advantage of the correlation between lung volume and corresponding attenuation properties to predict the attenuation coefficients of the lung. In the presence of pathological tissues in the lungs, the lesions are [...]

ARABI, Hossein, ZAIDI, Habib. Magnetic resonance imaging-guided attenuation correction in whole-body PET/MRI using a sorted atlas approach. Medical Image Analysis , 2016, vol. 31, p. 1-15

DOI : 10.1016/j.media.2016.02.002 PMID : 26948109

Available at:

http://archive-ouverte.unige.ch/unige:90688

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Medical Image Analysis

journalhomepage:www.elsevier.com/locate/media

Magnetic resonance imaging-guided attenuation correction in whole-body PET/MRI using a sorted atlas approach ^R

Hossein Arabi

^a

, Habib Zaidi

^a,b,c,∗

aDivision of Nuclear Medicine and Molecular Imaging, Department of Medical Imaging, Geneva University Hospital, CH-1211 Geneva 4, Switzerland

bGeneva Neuroscience Center, Geneva University, CH-1205 Geneva, Switzerland

cDepartment of Nuclear Medicine and Molecular Imaging, University of Groningen, University Medical Center Groningen, 9700 RB Groningen, Netherlands

a rt i c l e i n f o

Article history:

Received 23 July 2015 Revised 5 February 2016 Accepted 9 February 2016 Available online 17 February 2016 Keywords:

PET/MRI

Attenuation correction Pseudo-CT generation Atlas

Quantification

a b s t r a c t

Quantitativewhole-bodyPET/MRimagingischallengedbythelackofaccurateandrobuststrategiesfor attenuationcorrection. Inthiswork,anewpseudo-CTgenerationapproach, referredtoassorted atlas pseudo-CT(SAP),isproposedforaccurateextractionofbonesandestimationoflungattenuationprop- erties.Thisapproach improvestheGaussian processregression (GPR)kernel proposed byHofmannet al.whichreliesontheinformationprovidedbyaco-registeredatlas(CT andMRI)usingaGPRkernel topredictthedistributionofattenuationcoefficients.Ourapproachusestwo separateGPR kernelsfor lungand non-lungtissues.Fornon-lungtissues,theco-registeredatlasdatasetwassortedonthebasis oflocalnormalizedcross-correlationsimilaritytothetargetMRimagetoselectthemostsimilarimage intheatlasforeachvoxel.Forlungtissue,thelungvolumewasincorporatedintheGPRkerneltaking advantageofthecorrelationbetweenlungvolumeandcorresponding attenuationpropertiestopredict theattenuationcoefficientsofthelung.Inthepresenceofpathologicaltissuesinthelungs,thelesions aresegmentedonPETimagescorrectedforattenuationusingMRI-derivedthree-classattenuationmap followedbyassignmentofsoft-tissueattenuationcoefficient.Theproposedalgorithmwascomparedto othertechniquesreportedintheliteratureincludingHofmann’sapproachandthethree-classattenuation correctiontechniqueimplementedonthePhilipsIngenuityTFPET/MRwhereCT-basedattenuationcor- rectionservedasreference.FourteenpatientswithheadandneckcancerundergoingPET/CTandPET/MR examinationswereusedforquantitativeanalysis.SUVmeasurementswereperformedon12normalup- takeregionsaswellashighuptakemalignantregions.Moreover,anumberofsimilaritymeasureswere usedtoevaluatetheaccuracyofextractedbones.TheDicesimilaritymetricrevealedthattheextracted boneimprovedfrom0.58±0.09to0.65±0.07whenusingthe SAPtechniquecomparedtoHofmann’s approach.ThisenabledtoreducetheSUVmeanbiasinbonystructuresfortheSAPapproachto-1.7±4.8%

ascomparedto-7.3±6.0%and-27.4±10.1%whenusingHofmann’sapproachandthethree-classatten- uationmap,respectively.Likewise,thethree-classattenuationmapproducesarelativeabsoluteerrorof 21.7±11.8%in thelungs. Thiswas reducedonaverageto 15.8±8.6%and 8.0±3.8% whenusingHof- mann’sandSAPtechniques,respectively.TheSAPtechniqueresultedinbetteroverallPETquantification accuracythanbothHofmann’sandthethree-classapproachesowingtothemoreaccurateextractionof bonesandbetterpredictionoflungattenuationcoefficients.Furtherimprovementofthetechniqueand reductionofthecomputationaltimearestillrequired.

© 2016ElsevierB.V.Allrightsreserved.

1. Introduction

There is growing research and clinical interest in hybrid PET/MRI technology owing to its potential to provide a major

R This paper was recommended for publication by “Nicholas Ayache”.

∗ Corresponding author at: Geneva University Hospital, Division of Nuclear Medicine and Molecular Imaging, CH-1211 Geneva, Switzerland. Tel.: +41 22 372 7258; fax: +41 22 372 7169.

E-mail address: habib.zaidi@hcuge.ch (H. Zaidi).

breakthrough in diagnostic imaging and clinical practice (Disselhorst et al., 2014). The rationale behind the combina- tion of PET and MRI is the higher soft-tissue contrast of MR images compared to CT, the possibility of using various MRI sequences enabling multiparametric imaging and above all the absenceofradiationexposure,acriticalissueparticularlyinserial follow-up studies and pediatric imaging (Torigian et al., 2013;

ZaidiandDelGuerra,2011).

Accuratequantificationoftraceruptakerequirescorrection for attenuationof annihilation photons, which isnot straightforward http://dx.doi.org/10.1016/j.media.2016.02.002

1361-8415/© 2016 Elsevier B.V. All rights reserved.

oncurrentPET/MRIsystemsthatarenotequippedwithx-rayCTor transmissionsources (Bezrukov etal., 2013a;ZaidiandHasegawa, 2003).OwingtothelackofadirectcorrespondencebetweenMRI intensitiesand electron densities,alternative methods are sought forMRI-guided attenuation correction in PET/MRI. The strategies proposed for attenuation correction in PET/MRI can be classified intothreemajorcategories:tissuesegmentation (Martinez-Moller et al., 2009; Schulz et al., 2011; Zaidi et al., 2003), template or atlas-basedmachinelearningapproaches(Burgosetal.,2014;Hof- mannet al., 2011; Hofmann etal., 2008; Izquierdo-Garcia et al., 2014; Johansson et al., 2011), and joint estimation of emission andattenuation(Defriseetal.,2012;MehranianandZaidi,2015c).

Earlyattemptsto estimatetheattenuation mapfromnon-timeof flight (TOF) emission data (Panin et al., 2004) achieved limited success. The advent of TOF PET technology introduced new op- portunitiesforaccuratederivationofattenuationinformationfrom emissiondata. TOF enablesto measurethe detectiontime differ- encesofthecoincidentannihilationphotonswitha temporalun- certaintygoverned by the timing resolutionofthe PET detectors, which narrows the solution space of PET reconstruction. Tissue segmentation methods rely on segmenting an MR image into a numberof tissue classes followedby assignment of uniformlin- earattenuationcoefficients.Atlas-basedmethodsutilizetargetspe- cificdeformeddatasets orananatomicalmodeltoconsiderbones andproducea continuousattenuation map. In addition,machine learningapproachestake advantage ofthe machine learningtask ofinferring a function from labeled trainingdata consisting ofa setoftrainingexamplescontainingvoxel-by-voxelcorrespondence betweenMR and CT images to predict a continuousattenuation map.

Owing to the difficulties associated with bone segmentation, MRI segmentation into three-classes on the Philips Ingenuity TF PET/MR(background air,lung andsoft-tissue)(Schulzetal.,2011;

Zaidi et al., 2011) or 4/5-classes on the Siemens mMR PET/MR (background air, lung, fat, mixture of fat and water, and water) (Bezrukovetal.,2013b;Martinez-Molleretal.,2009)arethemost widely used strategieson commercial PET/MR systems. Although segmentation-based attenuation correction is deemed to provide satisfactory results in whole-body PET/MR, ignoring bone has noticeable impact on the quantification of tracer uptake in the vicinityofbonystructures(Bezrukovetal.,2013b;Hofmannetal., 2011; Schramm etal., 2013; Varoquaux et al., 2014). Recently, a template-based attenuation correction technique which accounts forthepresenceoftheskullinPETbrainimagingwasintroduced on the SIGNA PET/MRI scanner (GE Healthcare, Waukesha, WI) (Wollenweberetal.,2013).The useofultrashortechotime (UTE) (Keereman et al., 2010) or zero time echo (ZTE) (Delso et al., 2015) sequences to distinguish between bony structures and air proved to be capable of addressing this challenge; however, its applications are currently limitedto brainimaging owing to the long acquisition time. Alternatively, it was suggested that the use of a deformed atlas along with patient-specific MR images canovercomethislimitation(Burgosetal., 2014;Hofmannetal., 2008,2011), particularlyforwhole-body imaging wherelong MR sequencesarenotfeasibleyet.

Hofmann et al. proposed a novel approach to merge the in- formation obtained from patient-specific MR images and prior knowledgeprovided by anexisting co-registeredatlasdataset for the purpose of pseudo-CT generation (Hofmann et al., 2011). In thisapproach,aGaussian process regression(GPR) (Ebden, 2008) is utilized to predict the pseudo-CT value for each voxel using intensityinformationofsmallpatchesdefinedonMRimagesand the corresponding CT numbers on the aligned atlasdataset. The performance of Hofmann’s approach in terms of deriving bony structuresdependshighlyontheaccuracyoftheregistrationwith theatlasdataset.Toincreasethe robustnessofatlas-basedmeth-

ods to miss-registration errors, Burgos et al.developed synthetic CTsthrough amulti-atlasinformation propagationschemewhere the MRI-derived patient’s morphology is locally matched to the aligned MRI-CT pairs using a robust local image similarity mea- surebased on localnormalized cross-correlation (LNCC) criterion (Burgos et al., 2014). The local matching through morphological similarityenablesthealgorithmto findlocalmatchesandsimilar anatomy across the atlas dataset. Therefore, poorly matched at- lases are discarded or at least givenlower weights, which leads to a more patient-specific pseudo-CT. This method was mainly developedforbrainPET/MRimagingandwasthereforeevaluated forthisparticular application. One ofourobjectives in thiswork is to modify Hofmann’s pseudo-CT generation approach in order to improvethe accuracy of bone extraction andreduce potential errorsduetothemiss-registrationtypical inwhole-bodyimaging situations.

The bottleneck of atlas-based segmentation and attenuation correctioninwhole-bodyPET/MRIisthelevelofaccuracyachieved by the registration procedure for inter-subject image alignment.

Regardless of the type ofalgorithm, the validation ofimage reg- istration algorithms dependson the geometryofboth target and sourceimages.Introducingathoroughconceptthatguaranteesthe accuracyofthe registrationprocedureinnon-rigid organsproved tobeadifficulttask(Murphyetal.,2011).Inthiswork,werelied on a registration procedure validatedin a previous work by our group(Akbarzadehetal.,2013)usingtheelastixsoftware(Kleinet al., 2009). The alignment wasperformed by combiningrigidand non-rigidregistrationbasedonnormalizedmutualinformationcri- terionusingB-splineinterpolatorwithanadaptivestochastic gra- dientdescentoptimizer.

Another challenging issue in whole-body PET/MR attenuation correction is the prediction ofpatient-specific attenuation coeffi- cientsforthelung. The densityofthe lungsmightvarybetween patients owing to respiratory motion (Rosenblum et al., 1980), smoking habits, age ordisease state (Soejima etal., 2000). As a consequence,large SUVbiasandsubstantial patienttopatientac- tivityrecoveryvariationswerereportedintheliterature(Hofmann etal.,2011).Izquierdo-Garciaetal.reportedmorethan20%under- estimationofSUV inthelung regionandnoticeable lungdensity variation frompatient to patient (even from left to rightlung in the same patient) (Izquierdo-Garcia et al., 2014). To address this issue, Marshall et al. used linear regression to correlate the in- tensity of the lungs in specific MRsequences (T2 weightedand extrapolated proton density images) and corresponding CT val- ues (Marshall et al., 2012). Berker et al. used maximum likeli- hoodreconstructionofattenuationandactivityfortheestimation oflungattenuationcoefficientsfromtime-of-flight(TOF)PETemis- siondata(Berkeretal.,2012).Amorestablesolutionwasachieved byexploitingaregularizedMLAAalgorithmforestimationoflung linearattenuationcoefficientsusingpriorknowledgeontheGaus- sian distribution of lung attenuation coefficients (Mehranian and Zaidi,2015a).

The second major objective of this work is to propose an improved machine learning approach based on GPR for patient- specific predictionof lung attenuationcoefficients. The technique incorporatesthecorrelationbetweenlungvolumeandcorrespond- ing density and advantages of morphological similarity between targetMRIandatlasdatasets.

The quantitative assessment of the proposed algorithm was performedusingpairs ofclinical whole-bodyPET/MR andPET/CT studieswhereCT-basedattenuationcorrectedPETimagesareused asreference.ComparisonwasalsomadewithHofmann’sapproach asa baselineforevaluationofourmethodandthethree-classat- tenuationmaptechniqueimplementedonthePhilipsIngenuityTF PET/MRscannersincesegmentation-basedmethodsarecommonly usedinclinicalPET/MR.

2. Materialsandmethods

2.1. PET/CTandPET/MRIdataacquisition

The study population comprised 14 patients, who underwent whole body¹⁸F-FDGPET/MRandwhole-body ¹⁸F-FDGPET/CT for staging ofhead andneckmalignancies. A singleinjectionof ¹⁸F- FDG (371 ± 23MBq) was used to perform whole-body ¹⁸F-FDG PET/CT studies at free shallow breathing on a Biograph 64 True Pointscanner(SiemensHealthcare,Erlangen,Germany).Afteralo- calization scout scan, an unenhancedlow doseCT scan (120kVp, 60mAs, 24×1.5 collimation) wasperformed for attenuation cor- rection.Thetypicalacquisition timeforwhole-bodyCTscanswas less than 10s (axialFOV of 16.2cm, pitch of 1.2and 1s per ro- tation).PETdataacquisitionstarted146.2±20minpost-injection with3minperbedpositionforatotalof5–6beds,resultingina totalacquisitiontimeof15–18min.

PET/MRI examinations were performed on the Ingenuity TF PET/MR (Philips Healthcare, Cleveland, USA) (Zaidi et al., 2011).

The patients were almost in the same position during both ex- aminations with arms down. The so-called atMR whole-body MRI sequencewasusedforfast(<3min) derivationofthethree- class attenuation map. It consists of a 3D multi-stack spoiled T1-weighted gradient echo sequence with the following parame- ters: flipangle10°,TE 2.3ms, TR4.1ms,smallestwater–fat shift, 600mm transverse FOV witha slab thickness of 120 mm, voxel size 1.9×1.9×6mm³, 12mm overlap between adjacent stacks (Schulzetal., 2011).The PhilipsIngenuityTFPET/MRutilizesthis three-class attenuation map (air: 0cm⁻¹, lung: 0.022cm⁻¹, soft- tissue: 0.098cm⁻¹) forthepurpose ofPETattenuation correction (Schulzetal.,2011;Zaidietal.,2011).

TheproposedMRI-derivedpseudo-CTgenerationapproachuses awhole bodyMRIDixon volumetricinterpolatedT1-weightedse- quence(Dixon,1984)withthefollowingparameters:flipangle10°, TE₁ 1.1ms, TE₂ 2.0ms, TR 3.2ms, 450×354mm² transverseFOV, 0.85×0.85×3mm³voxelsize,andatotalacquisitiontimeof2min 17s. The study protocolwas approvedby the institutional ethics committeeandallpatientsgaveinformedconsent.

2.2. MRdatapre-processing

The acquired MR images contain a relatively high level of noise, corruption due to the low frequency bias field and inter- patientintensityinhomogeneity(Lotjonenetal., 2010;Nyúletal., 2000;Zhugeetal.,2009).Assuch,thepresenceofanyaforemen- tioned source of intensity uncertainty in MR images might bias the pseudo-CT generation result. To overcome these prospective sources of error, in-phase images of all patients underwent the followingpre-processingstepstominimize statisticalnoise inMR images (gradientanisotropic diffusion filtering), cancel out intra- subjectintensityinhomogeneity(N4biasfieldcorrection)andcor- rect inter-subject intensity non-uniformity (histogram matching).

Other techniquesreportedinthe literature(Tong etal.,2015)can alsobeemployedforthispurpose.

• Gradient anisotropic diffusion filtering (Weickert, 1998) us- ing the following parameters: conductance=4, number of iterations=10andtime step=0.01.Thisisan edgepreserving smoothingalgorithmthatadjuststheconductancetermtopro- duce largediffusion insideregions where thegradient magni- tude is relatively small (homogenous regions) and lesser dif- fusion in regions where the gradient magnitude is large (i.e.

edges).

• N4 bias field correction (Tustison et al., 2010): B-spline grid resolution=400, number of iterations=200 (at each grid resolution), convergence threshold=0.001, B-spline order=3,

Fig. 1. (A) Representative slice of in-phase MR Dixon image. (B) Intensity clustered version of the image shown in (A) using K-means Markov random field algorithm in which neighboring voxels with similar intensity are assigned the same cluster level (1–512). (C) In Hofmann’s method, the information extraction from MR images is performed by calculating the weighted average of voxel intensities confined by rectangular sub-volumes (patch). (D) In our SAP approach, the voxel value within the clustered image (dot point) is directly used in the GPR kernel to facilitate the training process and maintain the edge information.

spline distance=400, number of histogram bins=256 and shrinkfactor=3.

• Histogram matching (McAuliffe et al., 2001): Histogram level=512andmatchpoints=64. Inordertogetthe bestre- sultfromhistogrammatching,weexcludedbackgroundairvox- els ofbothreferenceandtargetimagesbefore processing.The meanabsoluteinter-patientMRIintensityvariabilitydecreased from 29% to 10% after application ofthe aforementioned cor- rections(Robitailleetal.,2012).

Theproposedpseudo-CTgenerationprocedureentailssegmen- tationoftheexternalbody contouraswell aslung identification.

To this end, the external body contour was determined by ap- plying a 3D snake active contour algorithm on the in-phase MR images(Kassetal., 1988). Identificationandsegmentation of the lungs was performed through connected-component analysis of the lower intensity inthe inner partof the body usingthe ITK- SNAPimageprocessingsoftware(Yushkevichetal.,2006).Theseg- mentation wasperformedsemi-automatically following initializa- tionbyuser-specifiedseeds.

InHofmann’sapproach,local informationextractionfromMRI is performed by calculating the weighted average of intensities confined to rectangular sub-volumes (patches) (Hofmann et al., 2011). These weighted average values are used to assess the localsimilarityof MRIintensity acrosssubjects asisindicated in Fig.1.Toalleviatethecomputationalburdeninvolvedbycomput- ingweightedaverages foreachpatchandmoreimportantlyavoid informationlossdueto theaveraging process (particularly atthe boundaryoforgansorinregionswithabruptintensityvariations), intensity clustered MR images are utilized in our approach. The clustering process assigns the same cluster label to voxels with similar intensity considering Markov random field regularization fornoiseandintensitynon-homogeneityreduction.Theclustering iscarried out using theK-means Markov randomfield algorithm implemented in the ITK software package (Yoo et al., 2002). A 512 bins clustering with 50 iterations and a tolerance of 0.001

wasperformedto producethe MRcimage (Fig.1). Therefore,our approach uses the proximity cluster values (the cluster value to which voxels under study belong to) instead of comparing local information across subjects on the basis of weighed intensity averaging of surrounding voxels (Fig. 1). This enables to further reducethenoiseandintensitynon-uniformityacrossthesubjects.

2.3.Pseudo-CTgenerationapproach

2.3.1. Hofmann’sapproach

Since the proposed pseudo-CT generation approach builds on thetechniqueproposedby Hofmannetal.(Hofmannetal.,2011), a brief description of this method is provided here. A Gaussian process regression is utilizedto mergethe atlas registration and local patch information in order to predict more accurately the pseudo-CT values for each voxel of interest (Hofmann et al., 2008).Tothisend,anumberofCT/MRIpairsservedasatlasafter undergoingpairwisenon-rigidregistrationtothetargetMRimage (Eq.(1)).In additionto thelocalinformationin theco-registered atlas database and intensity similarity of patches, the five-class segmentation (background air, lung, fat, fat and non-fat mixture andnon-fattissue)ofin-phaseMRimages(Martinez-Molleretal., 2009)andcorrespondingpatchinformationisusedinEq.(1). k

d_i,d_j

=exp

−

^W

(

^PMR,i

)

^{− W}

P_MR,j

²

2

σ

MR² ,patch

×exp

−

^Xi−X_j

²

2

σ

pos²

×exp

−

^W

PSeg,i

−W

PSeg,j

²

2

σ

_Seg,patch²

(1)

whered=(PMR,PSeg,X) andPMR andPSeg are sub-volumepatches fromthein-phaseMRimageandfive-classsegmentedMRimage, respectively.Wisaweighting vectorassigninga higherweightto centralvoxelsthan peripheralonesinthepatch,X isthetraining centerposition.Eq.(1)representsthekernelofGPRwhichyields a covariance matrix. The indices i and j refer to the different patchesdefinedontrainingMRimages.Ineffect,thethree terms intheGPRkernelmeasuretheintensity, positionandtissuetype distanceofdifferentpatcheson trainingdatasets. Theparameters

σ

^pos,

σ

MR,_patch and

σ

Seg,patch determine how the overall kernel valueisinfluenced bysimilarityinposition,patchintensityvalue inMRandfive-class segmentedimage.The trainingisperformed on samples of d_i and d_j=(P_MR,j, P_Seg,j, X_j), i/j=1,2,…,n, drawn fromrandomlocations inthe MRI atlasdatabaseon the basis of knownCTvaluesforthecorrespondingpatches.OncetheGaussian regressionistrainedandthefreeparametersof

σ

^pos,

σ

MR,_patchand

σ

Seg,patch determined, Eq. (2) is used to calculate the pseudo-CT valueforeachvoxelofinterest.

c_l=k_l^TC⁻¹y (2)

where c_l denotes the calculated pseudo-CT value of a voxel of interest l. k_l=k(d_i,d_l)is an (n×1) matrix where d_i=(P_MR,i, P_Seg,i, X_i)is the informationextractedfrom thepatches defined on the MRI atlas dataset and d_l=(P_MR,l, P_Seg,l, X_l) represents the patch defined on the target MRI. C=k(d_i,d_j) is the (n×n) covariance matrix obtained from Eq. (1) using d_i and d_j patches defined on MR atlas data set. y stands for a (n×1) vector of CT values correspondingtothecentralvoxeloftrainingpatchesd_i.

2.3.2. Proposedsortedatlaspseudo-CT(SAP)approach

The proposed pseudo-CT generation approach, referred to as SAP, employs the morphological similarity between the target in-phase MRI and the co-registered atlas database MRIs, which is computed locally using the local normalized cross-correlation (LNCC) metric proposed by Yushkevich et al. (Yushkevich et al., 2010). TheLNCC processprovides a measurebased onwhich the

Fig. 2. A) In-phase Dixon image of the target patient and B) Target patient atlas se- lection matrix where each color stands for one particular image in the atlas dataset.

well-matched atlas images can be selected. The LNCC process is employed to identifythe bestmatch ormostsimilar atlasimage foreachtargetvoxel.LettheMRofthetargetsubjectbedenoted byI_ref andthewarpedMRimagesintheatlasdatabasebyIm.The LNCCbetweenI_ref andImatvoxelviscalculatedby:

LNCC_v=

^{Im, Iref}v

σ (

^Im

)

v .

σ (

^{Ire f}

)

v

(3)

Accordingto(Cachieretal., 2003),themeanandstandard de- viation ateach voxelv arecomputedusinga GaussiankernelK_G, withastandarddeviationofN_std=0.9cm,throughtheconvolution process:

Im_v=KG∗Im

σ (

^Im

)

v=

Im²_v− Im_v²=

(

^KG ∗Im²

)

−

(

^KG∗Im

)

²

^{Im, Iref}v

^{=Im.Ire f}v− Im_v.Ire f_v=

(

^KG ∗ Im.Ire f

)

−

( (

^KG ∗ Im

)

.

(

^KG ∗ Ire f

) )

⁽⁴⁾

The rangeof LNCCvalues variesconsiderablyamong the sub- jects andlocations within a patient. Moreover, since theLNCC is calculatedvoxelwise,theoutputispronetonoiseandlocaluncer- tainty arising from the lackof sufficient local informationin the images(Burgosetal.,2014;Yushkevichetal., 2010).Toovercome theseshortcomingsofLNCCsimilaritymeasure,k-nearestneighbor kernel was employed to pool the information in the nearvicin- ityinorderto choosethemostsimilar imagetothetarget image from the atlas database (Altman, 1992). To this end, in the first step,the LNCCis calculatedforeach voxelof thetarget in-phase image acrossall theco-registeredatlasimagesusingEqs.(4)and (5). Then, foreach voxel,themostsimilar atlastothe target im- ageisselectedonthebasisofitsk-nearestneighbor LNCCvalues.

Tominimize theimpact of noise,a fixed size window isdefined aroundthetargetvoxelandtheatlaswiththehighestscorewithin thewindowisselectedasthemostsimilaratlasforthatvoxel.It shouldbe notedthatnegativeLNCCscores wereconverted toze- ros beforethe k-nearest filtering. The informationabout selected atlases is storedin theASM(x),the atlas selection matrix,whose voxelsindicate IDsofthemostsimilaratlasimagesto thetarget.

Optimization of the k-nearest neighbor (as described in Section 2.4) led toa window size of5cm×5cm (definedin 2D on each slice). Alarge window size guarantees robust similar atlas selec- tioncarriedoutbytheLNCCprocess.AlthoughusingawideGaus- siankernelfortheLNCCstepmayleadtosimilaroutcomeasthe k-nearestfilter,exploitingthek-nearest filterresultedinmorero- bust similarity measure between large image patches. Fig. 2 de- picts a representative sample ofthe ASM withits corresponding

Fig. 3. Schematic diagram of the SAP method’s workflow.

in-phaseimage whereeach colorstandsforone individual image in the atlasdataset that islocally mostsimilar to the target im- age.TheLNCCmetricenablestodetectandeliminatethecausesof errorduetomisalignmentandanatomicaldissimilarityacrossthe alignedatlasdataset.Inthepresenceofmorphologicaldiscrepancy (owingtoregistration errorsoranatomicaldissimilarity) between thetargetandatlasimages,theLNCCanalysisyieldsrelativelylow scores thus triggering the elimination of the corresponding atlas (orsub-volume)fromfurtherprocessing(supplementalFig.1).Af- ter constructing theASM, the GPRalgorithm fornon-lungregion isrun onthemostsimilar atlasimagesonavoxelby voxelbasis usingtheASMdata.

ThismethodemploystheabovedescribedGaussianprocessre- gression but splits the main kernel in Eq. (1) into two separate Gaussian processing kernels fornon-lungandlung tissues. Fig.3 depictsaschematicdiagramoftheSAPapproachsummarizingthe differentstepsrequiredtogenerateapseudo-CTimage.Infact,two distinct Gaussianprocessregressionsaretrainedandutilizedsep- arately forlung andnon-lung body regions. Fornon-lungregion, theGaussiankernelismodifiedasfollows:

K_non−lung

b_i,b_j

=exp

−MRc,i− MRc,j

²

2

σ

MR² ,cluster

× exp

−

^Xi− X_j

²

2

σ

pos²

(5)

where, b_i and b_j=(MR_c,j, X_j)represent the vector of information extractedfromMRItrainingdatasetforvoxelsi/j=1,2,…,nandMRc

andXrepresentthevoxelvalue(clusterlevelbetween1and512) and position in the clustered atlas MR images, respectively. As mentioned earlier, thevoxel value in theclustered MRimagesis usedinourapproachinsteadofweightedaveragesofvoxelswithin patches of the image used by Hofmann et al. (Hofmann et al., 2011).Inthisway,the9mm×9mmpatchesofvoxels(defined in 2Doneachslice)inHofmann’smethodarereplacedbythecluster numberofthetargetvoxel.Assuch,theparameter

σ

MR,_patchinEq.

(1)isreplacedby

σ

MR,_cluster.ComparingEqs.(1)and(3),theterm

dealingwithsimilarityinthe five-classsegmentedMRimage has beenomittedinthemodifiedversionofthealgorithmsinceitwas foundtohavenegligibleinfluenceontheoutput.

Infact,intheSAPmethod,the atlasregistrationiscarriedout ondenoizedMRimagesasdescribedinSection2.2(beforecluster- ing)andthealignedimagesarefurtherprocessedusingtheLNCC algorithm.Afterdeterminingthemostsimilaratlasforeach voxel inthetargetimage,theselectedatlasesintheASMundergoaclus- teringprocessbeforebeingfedtotheGPRkernel.Thetrainingand pseudo-CTgenerationareperformedusingtheGPRkernelrunning overthemostsimilaratlasforeachvoxelaccordingtotheinforma- tionprovidedbytheASM.TheinformationforeachvoxelfromMR atlasimagesisextractedintheformofclustersratherthanpatches ofvoxels as opposedto what is done inthe original method. In otherwords,theLNCCstepisrunovertheoriginalMRimagesand after determining the most similar atlas for each region, an MR

“composite” imageisconstructedusingthecorrespondingregions fromthe clusteredimage. Thereafter,theGPRisrun overtheMR compositeimage(withclusteredintensity)andtheclusteredtarget image.Thus,theclusteringisperformedonestepbeforeconstruct- ingtheMRcompositeimage.Alternatively,theLNCCcouldberun overtheclusteredMRimagesprovideda largenumberofcluster binsisused.Otherwise,itmayskewthesimilaritymeasurement.

Incontrast,inHofmann’smethod,theGPRkernelisbuiltbased onpatchesofvoxels(notclusteredimages)andrunnon-selectively overtheentireregisteredimages.

2.3.3. Lungattenuationcoefficientsestimation

Wepropose a separate Gaussian kernelforestimation oflung attenuationcoefficients.Tothisend,thekernelinEq.(3)ismod- ifiedbuttheterm regardingtheintensitysimilarity betweentar- get and atlas MRimages remained unchanged in Eq. (6) on the groundthat there ispotentially acorrelation between MRinten- sityandCTattenuationcoefficients(KapanenandTenhunen,2013).

Ontheotherhand,thepositionsimilaritytermwasreplacedwith lungvolumeproximity(V_aj andV_ai)wheretheaiandajdenotethe

Fig. 4. Correlation plots between lung attenuation coefficients (HU) vs. lung volume obtained from CT image segmentation of 50 patients.

atlasindexofthecorresponding iandj clusters,respectively(the V_ajandV_airefertothelungvolumesofatlases,whichtheclusters MR_c,iandMR_c,jaretakenfrom).

K_lung

li,lj

=exp

−

^MRc,i− MR_c,j

²

2

σ

_MR,cluster²

×exp

−

^Vai− V_{a j}

²

2

σ

_l²_ungvolume

(6) Itishypothesizedthatthelungintensityiscorrelatedwiththe lung volume (Lonn andWollenweber, 2012). In order toevaluate the degree to which lung attenuation coefficients are correlated withthelungvolume,CTimagesof50patients(31maleand19fe- male;agerangingfrom35to96years)chosenrandomlyfromthe clinicaldatabasewithout anypreferenceacquiredin free shallow breathing were examined. All the 50 patientswere administered whole-body¹⁸F-FDGPET/CTacquiredonaBiograph64TruePoint scanner(SiemensHealthcare,Erlangen,Germany)usingtheproto- coldescribedinSection2.1.ThetechniquedescribedinSection2.2 wasemployed to segment the lungsfrom CT images.Thereafter, the average lung attenuation coefficient vs. volume was plotted (Fig. 4). Taking advantage of the established correlation between lungvolumeanddensity,theadditionalinformationregardingthe lungvolumewasincorporatedinthelungGPRkernel(K_lung)using theweight

σ

lungvolume.Splittinguptheoriginalkernelgivesusthe possibilityto includelung tissue characteristics into lung-specific kernel.The lung volumetermaddedtothe kernel(Eq.(6))tends topredictlungattenuationcoefficientsconsideringthecloserela- tionshipoflungvolumebetweenthetargetandatlasimages.

Inaddition,asimpletechniquewasdevisedtoestimatetheat- tenuationcoefficientsofprospectivemalignantlesionsinthelungs which might have a different density. PET images corrected for attenuationusing the three-class

μ

^-map (PET-MRAC3c) were an- alyzedto detect lung tumors.To thisend, a lung mask obtained fromsegmentationofin-phaseMRimageswasoverlaid(afterres- olutionmatching) onPET-MRAC3c images anda thresholdof 2.5 SUV wasapplied on voxels located within the lung mask (Chen etal.,2013).Voxelswithan SUVhigherthan2.5wereconsidered asbelonging tothelesion andwereassignedsoft-tissue attenua- tioncoefficientinthepseudo-CTattenuationmap.Sincenoisyvox- elsinthe lungswithspurious SUVover2.5mightbe mappedto

soft-tissue,3Dmedianfilteringwithakerneldimensionof3×3×3 wasapplied to PET-MRAC3c images before thresholding followed by connectivityanalysis(RosenfeldandKak,1982) toexclude re- gionshavingamaximumdiameterbelow4mm basedonrecom- mendationsin(Wahletal.,2009).

In thefinal step,an automatic post-processing rule is applied onthegeneratedpseudo-CTimagesto accountforgaspocketsin the abdomen area. First, the bone tissue is segmented using an intensity thresholdof 140 HU. Then a distance map (Danielsson, 1980) iscomputed onthe obtainedbinarybone map. The voxels thathavealowMRIintensityinthetargetin-phaseimageandre- sideatleast10mmfarfromnearestbonystructuresareassumed to belong to massive and mobile air cavities with a pseudo-CT value of −1000 HU.This procedure enablesto detect air cavities (particularlyintheabdomen)evenwhenthereisnosimilarstruc- tureintheatlasdatabase.

2.4. Parameteroptimization

Weemployedaleave-one-outcross-validation(LOOCV)scheme to find the optimum value for all free parameters and settings.

Inthe first step,MRimagesare non-rigidlyalignedto the corre- sponding CT images ensuring appropriate MRI-CT matching. The coregistered imagesare carefully checkedvisually andin caseof misalignment,theregistrationparameters,suchasfinalgridspace andoptimizationparametersaretunedtoachievethebestpossible alignmentbetweenMRandCTimages.Thealignedatlasdatasetis createdusing13outofthe14availableclinicalstudies.Assuch,for each individualpatient, all theremaining 13in-phaseMRimages weredeformablyregisteredtothetargetimage.

Thek-nearestwindowintheLNCCstepplaysakeyroleinthe implementation of our SAP method. Voxelwise searching for the mostsimilaratlasthroughthewindowofk-nearestneighborwas optimized via varying the window size from 1 to 10cm with a step of1cmandthe resulting pseudo-CTimageswere evaluated intermsofboneextractionaccuracyateachstep.Tothisend,the Dicesimilaritymeasurewasemployedtoevaluatetheaccuracyof extracted bone from the resulting pseudo-CT images considering the bone map extracted from CT images as reference. This pro- cedure was repeatedfor thewhole dataset and thehighest Dice metricwasachievedatawindowsizeof5cm×5cm.

Theparameters

σ

^pos,

σ

MR,_patchand

σ

Seg,patcharethemostinflu- entialfactorsintheoriginalkernel.First,theassociatedparameters were roughly determined for each test patient through examina- tionofthevariance ofpatchintensity,positionandsegmentation terms in Eq. (1). The exact parameter setting was empirically achieved through pseudo-CT generation for each of the 14 atlas images. The parameters that maximized the similarity between pseudo-CTandactual CTimageswere selected.Thesimilaritybe- tweentheresultingpseudo-CTandactualCTimageswasassessed basedon theDicemetric forbone volumeasdescribedearlier.A patchsizeof9×9voxelswasusedtofeedtheGPRkernelandfor each target voxel,80 patches of voxels were chosen to train the kernel. A higher sampling density (120 samples) was used near bone regions asthey areof special interest.The same procedure was followed to train the non-lung SAP kernel and setting of the parameters

σ

MR,_cluster and

σ

pos. Since a separate kernel was employed for thelung tissue inthe SAPmethod, all the patches were sampledoutsidethelung volume (insidethebody contour) withthesamesamplingdensitytotrainthekernelinEq.(3).

The training of Eq. (6) was performed in a similar way, ex- cept thatall thepatches werechosen insidethelung volume us- ing 80 patches for each target voxel. The associated parameters forlung-kernel(

σ

lungvolumeand

σ

MR,_cluster)wereoptimizedthrough thesameschemedescribedabove butinstead oftheDicemetric,

the absolute lung attenuation difference between pseudo-CT and actualCTimageswasusedforparametertuning.

2.5. Quantitativeevaluation

Pseudo-CT images were generated for the 14 clinical studies andtheobtainedattenuationmapsusedforattenuationcorrection of corresponding PET data. Calculations were performedon a PC equipped with Intel Xeon CPU (2.3GHz) running Matlab. It took approximately1100minonaveragetocreateonepseudo-CTimage (almost70%fortheatlasregistrationand25%fortheGPRtraining).

PETimageswere reconstructedby meansofthee7tool (Siemens Healthcare, Knoxville, TN)usingordinary Poissonordered subset- expectation maximization (OP-OSEM) iterative reconstruction al- gorithm. Default parameters (four iterations, eight subsets, anda post-processing Gaussian kernelwitha FWHMof5mm)adopted in clinical protocols were applied. Imagereconstruction was per- formed four times for each clinical study: PET images corrected for attenuationusing CT (PET-CTAC) used asreference, using the three-class attenuation map (PET-MRAC3c) obtainedfromthe In- genuityTFPET/MRscanner(Schulzetal.,2011),usingthepseudo- CTgeneratedbyHofmann’sapproach(PET-HofmannAC)(Hofmann et al., 2011) andour proposed SAP approach (PET-SAPAC). A nu- clear medicine physician drew manually the VOIs on regions of normalphysiologicuptake,sixregionsinthelungs(on theupper, middle and lower parts of the right and left lung), liver, spleen, cerebellum, two bony structures (cervical vertebrae 6 anddorsal vertebrae 5),aorta,andmalignantlesions(Arabietal.,2015).The VOIs were carefully drawn at the center of each organ far away from organ boundaries. The differences between the attenuation correction techniques were quantified in terms of change in the standard uptakevalue (SUV). The SUVswere calculated by divid- ing the activity concentration in each VOI by the injected activ- itydividedbybodyweight.Theaccuracyofattenuationcorrection was assessed through the relative mean error(Eq.(7)) and rela- tive meanabsoluteerror(Eq.(8))betweenSUVmeasured onPET attenuationcorrectedusingMR-derivedattenuationmaps(MRAC) andPET attenuationcorrectedusingreferenceCTimage averaged overallpatients.InadditiontotheROI-basedanalysis,anatomical regionscorrespondingtotheliver,cerebellum,cervicalvertebrae6, dorsalvertebrae5andspleenweresegmentedonCTimagesusing the ITK-SNAP software andthe same PET quantitative evaluation wascarriedout.

Relati

v

eerror

(

^%

)

= MRAC

(

^SUV

)

− Re f erence

(

^SUV

)

Re f erence

(

^SUV

)

^×100%

(7)

Relati

v

eabsolute error

(

^%

)

= ABS[MRAC

(

^SUV

)

− Re f erence

(

^SUV

)

^]

Re f erence

(

^SUV

)

^{×100% (8)}

Inadditionto ROI-basedanalysis, voxel-basedcomparisonwas carried out between PET images corrected for attenuation using the two pseudo-CTimages and PET-CTAC used as reference. The voxel-basedrelative meanbias (RMB)andrelativemean absolute bias (RMAB) were computed for bone, lung, fat and soft-tissue class usingEqs.(7)and(8),respectively.The segmentationoftis- sue classes was performed based on CT Hounsfield units (HU) using the following thresholds; bone if HU≥140, soft-tissue if

−20<HU≤140,and fatif−350<HU≤ −20. The lung mask was obtainedasdescribedinthedataprocessingsection.

Theassessmentoftheaccuracyandrobustnessoftheextracted bones using the proposed (SAP) and Hofmann’s approaches was performed through comparison with the bone segmented from the corresponding CT images. Bonesegmentation was performed

by applyinga threshold of140 HUs on thegenerated pseudo-CT and corresponding CT images. The validation of bone segmenta- tionisreportedusingsevenvolume/distance-basedmetrics(Ayet al.,2014):Dicesimilarity(DSC)(Dice,1945),relativevolumediffer- ence(RVD) (Heimannetal., 2009), Jaccard similarity(JC)(Collins and Pruessner, 2010), sensitivity (S) (Xia et al., 2013), mean ab- solutesurfacedistance(MASD)(Gerigetal.,2001),Hausdorff dis- tance(HD)(Crumetal.,2006)anddistanceerror(DE)(Kleinetal., 2009).

DSC

(

^A,M

)

^{= 2}

|

^A∩M

|

|

^A

|

⁺

|

^M

|

RVD

(

^A,M

)

=100×

|

^M

|

⁻

|

^A

|

|

^A

|

JC

(

^A,M

)

⁼

|

^A∩M

|

|

^A∪M

|

S

(

^A,M

)

⁼

|

^A∩M

|

|

^M

|

MASD

(

^A,M

)

^=dave

(

^SA,SM

)

^+dave

(

^SM,SA

)

2

DE

(

^A,M

)

^{= 1}_N

N

p=1

mindist

(

^Ap,Mp

)

HD

(

^A,M

)

^=max_A

minM

{

^d

(

^A,M

) }

(9)

whereAisthebonesegmentedfromthereferenceCTimageandM denotestheextractedbonefromthepseudo-CTattenuationmaps.

dave(S_A,S_M)istheaveragedirectsurfacedistancefromallpointson theCTbonesurfaceS_A andtothepseudo-CTbonesurfaceS_M.The distanceerrorisequaltotheminimumdistancefromeachbound- arypoint of thesource region (Ap) to theentire setof pointsof thetargetregion(Mp)averagedacrosstheNboundarypoints.The Hausdorff distance measures the maximum distance one would need to move the boundaries of the source region (A) to com- pletelycoverthetargetregion(M).

Moreover, the generated pseudo-CTs were compared to the groundtruth CT through metrics measuring the voxel-wise error (in HUs) between bone volumesusing the mean error(ME) and meanabsoluteerror(MAE)definedas:

ME=

v

(

^MCTv−CT_v

)

V ⁽¹⁰⁾

MAE=

v

|

^MCTv−CT_v

|

V ⁽¹¹⁾

whereVisthenumberofvoxelsinthebonevolume,MCTvandCTv

denotevoxelvaluesinthepseudo-CTandgroundtruthCTimages, respectively.

Furthermore,weexpanded ourevaluationby separatingcorti- calbone (>300 HUs)fromspongybone (140–300HU)by thresh- oldingreferenceCTimagesandgeneratedpseudo-CTimages.Then, alltheabovementionedsegmentationaccuracymeasureswereap- plied separately on the segmentedspongy and cortical bones to preciselyquantifytheperformanceoftheproposedmethod.

Theaccuracyofthe predictedlungattenuation coefficientwas evaluatedbycalculatingtheaveragelungattenuationcoefficienton theobtainedpseudo-CTimagesusingalungmaskandcomparing it withthe corresponding CT images for each individual patient.

Pairedt-testanalysiswasusedtoassessifthedifferencesbetween theobtainedresultsarestatisticallysignificant.Athresholdof0.05 wasusedforstatisticalsignificance.

Fig. 5. A) Target patient CT image, B) corresponding in-phase MR image, and attenuation maps generated using C) Hofmann’ technique and D) our proposed SAP approach.

Table 1

Comparison of cortical bone ( > 300 HU) and spongy bone (140–300 HUs) segmen- tation accuracy (mean ±SD) between Hofmann’s and SAP approaches using various evaluation metrics including Dice similarity (DSC), relative volume distance (RVD), Jaccard similarity (JC), sensitivity (S), mean absolute surface distance (MASD), Haus- dorff distance (HD), distance error (DE), mean absolute error (MAE) and mean error (ME).

Hofmann (all bones P -value SAP (all bones P -value cortical spongy) cortical spongy)

DSC 0.58 ±0.09 0 .10 0.65 ± 0.07 < 0 .05 0.53 ±0.09 0 .10 0.60 ± 0.06 < 0 .05 0.57 ±0.08 0 .09 0.64 ± 0.07 < 0 .05 RVD (%) −36.6 ±10.0 0 .23 −30.7 ± 9.10 0 .17

−41.2 ±11.0 0 .25 −34.2 ± 8.90 0 .18

−38.9 ±10.0 0 .24 −32.8 ± 9.20 0 .17

JC 0.35 ±0.06 0 .15 0.41 ± 0.05 0 .10

0.31 ±0.05 0 .16 0.38 ± 0.04 0 .10 0.33 ±0.06 0 .15 0.40 ± 0.05 0 .10

S 0.40 ±0.15 0 .11 0.48 ± 0.12 0 .08

0.37 ±0.14 0 .12 0.43 ± 0.12 0 .08 0.39 ±0.15 0 .11 0.47 ± 0.11 0 .08 MASD (mm) 6.92 ±3.10 0 .08 4.81 ± 2.60 < 0 .05 7.32 ±3.40 0 .08 4.92 ± 2.53 < 0 .05 7.12 ±3.00 0 .08 4.99 ± 2.61 < 0 .05 HD (mm) 15.9 ±4.70 0 .09 10.9 ± 3.80 < 0 .05 16.3 ±4.80 0 .09 11.4 ± 3.79 < 0 .05 16.1 ±4.70 0 .09 11.2 ± 3.83 < 0 .05 DE (mm) 2.6 ±1.70 < 0 .05 1.1 ± 0.90 < 0 .05 2.8 ±1.65 < 0 .05 1.2 ± 0.92 < 0 .05 2.7 ±1.72 < 0 .05 1.1 ± 0.89 < 0 .05 MAE (HU) 127 ±26.0 < 0 .05 89 ± 12.5 < 0 .05 135 ±27.4 < 0 .05 93 ± 12.9 < 0 .05 132 ±26.8 < 0 .05 91 ± 12.4 < 0 .05 ME (HU) −29 ±32.0 0 .06 −11 ± 20.0 < 0 .05

−31 ±32.8 0 .06 −12 ± 23.2 < 0 .05

−30 ±32.3 0 .06 −11 ± 22.8 < 0 .05

3. Results

Fig. 5 depicts a representative sagittal slice of the generated pseudo-CTattenuationmapalongwithcorrespondingin-phaseMR andCT images.The visual inspection ofimages revealedsharper boneedgeswhenusingourSAPapproach.

AccordingtoTable1,considerablebonedetectionenhancement wasachievedusing the SAPattenuation map based on the aver- ageof14patients. However, thedifferenceswere not statistically differentfor all metrics. Fig. 6 illustrates the segmented bone of the clinical study shownin Fig. 5 using Hofmann’s andSAP ap- proaches. Figs. 5DandE depict the corresponding distance error mapscalculated bycomparingsegmentedbonesusingHofmann’s andSAPattenuationmapswiththe CT-basedattenuation map. A relativelysmalleraveragedistanceerrorisachievedbySAP(7mm max)comparedtoHofmann’smethod(12mmmax).

Fig. 7 compares the average lung attenuation coefficient ob- tained using both MRI-derived pseudo-CT approaches compared with the actual coefficient obtained from CT images for each individual patient. The lung attenuation coefficient predicted by Hofmann’s approach is very close to the average attenuation coefficient of the atlas database resulting in an average lung attenuationestimationerrorof7.92±20%(average±SD)overall patientsusingCTasreference, whereastheSAPapproachyielded an errorof-0.25 ±8% (intermsoflinearattenuationcoefficients at 511keV). The errors in HUs were 8.14 ± 35 and −1.71 ± 14, respectively,indicatingalowerSDfortheSAPmethod.

Fig. 8 illustrates a clinical study presenting with non-small cell lung cancer. The lesion was overlooked by the three-class segmentation procedure implemented on the Philips TF PET/MR system(Fig.8D)andconsequentlyassignedthewrongattenuation coefficient of the lung (0.022cm⁻¹). The SUVmean of the lesion is 6.1 for PET-MRAC3c (Fig. 8H) significantly underestimates the SUVmean for PET-CTAC (9.7) serving as reference owing to the assignment of the wrong attenuation coefficient to the lesion.

Fig.8E showsthesame three-class attenuationmap withcorrect identificationof thelung lesion usingthe proposed PETsegmen- tationtechniqueandproper assignmentofsoft-tissueattenuation coefficient. The measured SUVmean of the lesion after correction (PET-CorrectedMRAC3c)is 7.8(Fig.8I). Dueto thelow MRinten- sity of the lung lesion, Hofmann’s approach fails to assign the correctattenuationcoefficient tothelesion(Fig.8F),thus leading to underestimation of SUV_mean of (8.2) (Fig. 8J). Yet, our SAP approach correctlyidentified the lung lesion(Fig.8G), leadingto anSUVmeanof9.5onPET-SAPAC(Fig.8K).

Fig.9showstherelativeerrorsbetweenSUVmeanestimatedus- ingPETimagescorrectedforattenuationusingSAPandHofmann’s approaches and PET-CTAC images taken as reference. Significant improvement in the accuracy of SUV estimates was achieved in bony structures (cervical 6 and dorsal 5) and structures located nearcortical bone(cerebellum andsome malignant lesions). Fur- thermore,the SAP approach decreased considerably the standard deviationoftheestimatedSUV_meaninthelungs.TheSUVunderes- timationusingthethree-classapproachinornearbonystructures suchasthecerebellumandvertebraeislargerwitherrorsof-13.0

±6.2% and−27.4±10.1%, respectively.Incontrast,Hofmannand SAP approaches yield relative errors of −8.8± 3.8% and −7.3 ± 6.0%,and−3.3±4.9%and−1.7±4.8%,respectively(Table2).

The relative mean absolute errors together with min-max intervals are summarized in Table 3 to examine the precision of MRI-guided attenuation correction techniques. The three-class attenuation map assigning a uniform attenuation coefficient of 0.022cm⁻¹ (−770 HU) to the lungs produces a relative absolute error of 21.7 ± 11.8%. This was reduced on average to 15.8 ± 8.6% and 8.0 ± 3.8% when using Hofmann and SAP techniques,

Fig. 6. Representative slice of bone segmentation from MR images showing: A) Binary image of segmented bone from CT images, segmented bone using B) Hofmann’

technique and C) our proposed SAP approach. Distance error map calculated by comparing Hofmann’ technique D) and our SAP approach E) with the reference bone segmented on CT images.

Fig. 7. Predicted average lung attenuation coefficients using Hofmann’s and the proposed SAP approaches compared to actual value obtained from CT images of each individual patient averaged over the whole lung volume.

respectively. Average and standard deviations of voxelwise RMB andRMABbetweenthe groundtruthPET-CTAC andPET-MRAC3c, PET-SAPACandPET-HofmannACcomputedforlung,fat,soft-tissue andboneregionsaresummarizedinTable4.

Fig.10depictsan exampleofmetalartefacts portrayedonthe MR image andits impact on the attenuation maps produced by

the various strategies as well as the resulting PET images. The three-classattenuationmapgeneratedbytheIngenuityTFPET/MR scanner (Fig. 10C) gave rise to body truncation reflected by the presence of a gap correlated with the void signal produced by MRinthepresenceofmetallicobjects.Giventhat metalimplants usually replace bony structures, mostatlas images predict bones