JointSENSEReconstructionforFasterMulti-ContrastWaveEncoding

BerkinBilgic1,StephenFCauley1,LawrenceLWald1,andKawinSetsompop1

1MartinosCenterforBiomedicalImaging,Charlestown,MA,UnitedStates,

PrimaryReviewTopic:900Acquisition,Reconstruction&Analysis

Primary Review Category:902 Acquisition, Reconstruction & Analysis: Novel Acquisition - EncodingMethods,Trajectories&Reconstructions

SecondaryReviewTopic:900Acquisition,Reconstruction&Analysis

SecondaryReviewCategory:905Acquisition,Reconstruction&Analysis:ParallelImagingReconstruction(in-planeandsimultaneousmulti-slice)Synopsis

We introduce Joint SENSE acquisition/reconstruction to provide higher acceleration in multi-contrastacquisitionswith improved imagequality.Weemployacomplementarysampling strategy across the contrast by shifting the k-space samplingpatterns across the contrasts,which inducesphase ramps inimage space. By harnessing these ramps as additional coil sensitivity variations, we improvereconstruction error and g-factor performance by >2x compared to standard SENSE reconstruction.Further,wecombineJointSENSEwithWaveencodingtoexploit4-dimensionalsensitivityencoding,3Dacrossspace+1Dacrosscontrasts,toproviderapidmulti-contrastacquisitionwithhighquality.

Introduction

Multi-echoacquisitions areubiquitous in clinical and research applications,with applications in T2/T2*parametermapping,water-fatseparation[1],BOLDsensitivityenhancement[2,3]andB0fieldestimation[4].Theimageinformationintheseechoesfeaturesubstantialsimilarities,whichcanbeleveragedusingmodel-basedreconstruction[5],joint-sparseand/orlow-rankregularization[6,7].In this work, we propose Joint SENSE, a complementary approach that exploits similarities betweencontrasts at the sensitivity encoding level. To this end,we shift the k-space sampling patterns of eachecho,whichcreatesphaserampsinimagespace.Wethensolveforeachindividualcontrastusingk-spacedata fromallechoes,usingnewandadditional coil sensitivities that include the incurredphase ramps.ThesehelpsynthesizehigherorderFourierharmonics,therebysubstantiallyimprovingpRxcapability.Wedemonstrate the application of joint reconstruction in Wave encoding [8], which now exploits 4-dimensionalsensitivityencoding:3Dspace+1Dcontrastdimension.

Data/code:LINKTheory

Asshownin[Fig1,left],weincurk-spaceshiftsbetweenechoesduringthemulti-contrastacquisition.DuetoFouriershifttheorem,shiftedsamplingcreatesaphaserampinimageρ:

whereFdenotesFourierTransformandej⋅ramprepresentsthephaseramp.Weemploytheserampsforextraspatialencoding.Bystackingdatafromallcontrasts inthecoilaxis,wecreateadditionalchannelsandobtaintheJointSENSEforwardmodel[Fig1,right]:

Hereρ1andρ2areimageswithdifferentcontrasts,andρ2hasbeenshiftedink-spacetoincurej⋅ramp.Caretheactualcoilsensitivities(asinconventionalSENSE[9])andC1andC2aretheunknownsensitivitiesthatwillbeemployedinJointSENSE.SensitivitiesconsistentwiththeforwardmodelareC1=CandC2=C⋅ej⋅ramp⋅ρ2/ρ1.Thisindicatesthattheincurred phase ramps are transferred to the additional coil sensitivities C2, along with an undesiredcontrast-dependent term ρ2/ρ1. To mitigate its effect, we downweight the contribution from othercontrastswithλtoobtainthefinalJointSENSEmodel:

where FΩ is sub-sampled Fourier transform and kspacei are the acquired data from contrast i. Weiterativelysolveforρ1usingLSQR.DataAcquisitionandReconstructionData acquisitions were performed at 3T. Figs 2&3 employed conventional readout (withoutWave)and16SVDcompressedcoils [10,11].WeexploredWaveencoding inFig4with24SVDcoils. λ=5⋅10−3 was used in all Joint SENSE/Wave reconstructions. Joint sensitivities Ci wereestimatedautomaticallyusingESPIRiT[12,13]afterconcatenatingallechoes inthecoilaxis.G-factorswerecomputedusing300Monte-Carloiterations[14].Multi-Echo MPRAGE [15,16] [Fig2]: 1mm isotropic resolution, matrix=256x240x192, TEs={1.7,3.6, 5.4, 7.3} ms, TR/TI=2500/1100 ms, BW=650 Hz/pixel. A slice along readout axis was

undersampledbyR=5x3-fold.K-spaceshifts foreachecho in JointSENSEwere (Δky,Δkz)=(0,0);(1,1);(2,2);(3,3).Multi-EchoSpin-Echo [Fig3]: 0.9mm in-plane resolution,matrix=256x216, TEs={30,50,60,75,90}ms,TR=800ms,BW=130Hz/pixel,R=5-foldacceleration.ForJointSENSE,thefiveechoeswereshiftedbyΔky={0,1,2,3,4}samples.Multi-Echo Wave MPRAGE [Fig4]: Using the same dataset in Fig2, multi-echo Wave wassimulated using 3 sinusoidal cycles, Slewmax=180mT/m/s, Gradientmax=14.6mT/m. JointSENSE/WavereconstructionswereperformedwithΔky={0,1,2,3}shiftsatR=4x3acceleration.Results[Fig2]:JointSENSEimprovedRMSEby>2-fold,andsuccessfullymitigatednoiseamplificationwithaverageg-factor Gavg=1 compared to Gavg=2.8 in SENSE. Such improvement was possible thanks to additionalsensitivityencodinganddataaveragingacrossechoes.[Fig3]: JointSENSEalleviatedstructuredaliasingartifactsandnoiseamplificationpresent inSENSE,with>2xreductioninRMSEand>4ximprovementinGavg.[Fig4]: Joint SENSE partially mitigated noise and artifacts present in SENSE reconstruction, with 1.4xreductioninRMSE.CombiningJointreconstructionandWaveencodinginJointWaveprovided>2xerrorreductionwithfurtherqualityimprovement.DiscussionandConclusion

Joint SENSE acquisition/reconstruction provides >2x improvement in RMSE and g-factor compared tostandard SENSE. It can further be enhanced with low-rank and/or joint-sparse priors, and is flexiblyextended to includeWave encoding. JointWave is particularly helpful in high-bandwidthME-MPRAGEacquisitions,wherethereadoutperiod istooshorttoplaya largeWavecorkscrew, limitingthebenefitfromWaveencodingalone.

Adrawbackisthecontrastweightingintheextracoilsensitivities,whichwasmitigatedbydownweightingtheir contribution. This complicates Joint SENSE reconstruction ofME-GRE datawith large ΔTE,wherelargedifferencesbetweenphaseof theechoescounteract theeffectof theaddedphaseramps.Phasenavigator/ACSinformationcouldhelpaddressthisdrawback.

(1),(2,3)(4).(5)(6)(7).(8)

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Figures

Fig1.Inmulti-contrastacquisition,weperformshiftedsamplingink-spaceacrossdifferentechoes,whichincursphaserampsinimagespace.DuringJointSENSEreconstruction,coildatafromallcontrastsandallchannelsarestackedtogether,sothatallimages contribute to the reconstruction of a particular contrast. Concatenating the coil data from all images allow us toautomatically transfer the incurred phase ramps to the ESPIRiT sensitivitymaps. Added phase variations thus provide extraspatialencoding,andsubstantiallyimprovepRxcapability.

Fig2.[Left]StandardSENSEreconstructionformulti-echoMPRAGEacquisitionatR=15-foldacceleration.BothindividualechoesandtheRSoScombinedimagesufferfromseverenoiseamplificationandartifacts,asquantifiedbytheg-factoranalysisandRMSE(Gavg=2.8,15.4%error).[Right]JointSENSEprovides>2ximprovementing-factorandRMSE,withsubstantiallyimprovedimagequality.WenotethatdespiteachievingGavg=1.0thankstonoiseaveragingacrossechoes,theintrinsicsqrt(R)penaltyonSNRduetoundersamplingstillimpactsthereconstruction.

Fig3.[Left]IndividualandRSoScombinedechoesin5-foldaccelerated2Dmulti-echoSEacquisitionusingstandardSENSEreconstruction.Suchhighaccelerationintheright-leftdirectionwithtightFOVresultedinstructuredaliasingartifactsandhighg-factornoiseamplification.[Right]JointSENSEreconstructionprovided>2ximprovementinbothRMSEandg-factorperformance,yieldinghighSNRimageswithlowartifactlevels.

Fig4.a)Multi-echoMPRAGEwithstandardSENSEreconstructionatR=4x3(AsinFig2,RyandRzarealonganterior-posteriorandleft-rightdirections,withreadoutlyingalonghead-foot).SENSEsufferedlargeRMSE,inpartduetolowreceiversensitivityandlowsignalinthenasalcavity/mouthregionsinthissagittalview.b)Wave-CAIPIspreadsthealiasingin3DtoimproveRMSEandSNRretention.c)JointSENSEutilizestheadditionalsensitivityencodingthroughshiftedsampling,yetyieldsworseperformancethanWaveencodingalone.d)CombinationofWaveandJointSENSEispowerful,providing>2xRMSEimprovementandcleanerreconstruction.