1
xLXRX4 xlassical LOR/TX Xnalysis Recursively Xpplied Todor Vordanov ] G Karsten @oechstetter ]. G Patrick 9erg ]F G )sabella PaulmVordanov ] G Michael Scherg ] Munich University of Xpplied SciencesG MunichG (ermany . 9/SX (mb@G (räfelfingG (ermany ] University of KonstanzG KonstanzG (ermany F []] XndersonG VäSäG _ergusonG MäXäG LopezmLarsonG MäG YurgelunmToddG qäG .[]]ä Reproducibility of SinglemSubject _unctional xonnectivity Measurementsä Xmä Vä Neuroradiolä F.G DYN–DDDä [.] LinG _äm@äG WitzelG TäG XhlforsG SäPäG StufflebeamG SäMäG 9elliveauG VäWäG @ämäläinenG MäSäG .[[0ä Xssessing and improving the spatial accuracy in M/( source localization by depthmweighted minimummnorm estimatesä Neuro)mage F]G ]0[–]j]ä [F] LiuG @äG (aoG XäG SchimpfG Pä@äG YangG _äG (aoG SäG .[[Yä X recursive algorithm for the threemdimensional imaging of brain electric activity4 Shrinking LOR/TXm_OxUSSä )/// Transä 9iomedä /ngä D]G ]j5Y–]N[.ä [Y] MaddockG RäVäG (arrettG XäSäG 9uonocoreG Mä@äG .[[]ä Remembering familiar people4 the posterior cingulate cortex and autobiographical memory retrievalä Neuroscience ][YG 00j–0j0ä [D] PascualmMarquiG RäqäG MichelG xäMäG LehmannG qäG ]55Yä Low resolution electromagnetic tomography4 a new method for localizing electrical activity in the brainä )ntä Vä Psychophysiolä Offä Vä )ntä Organä Psychophysiolä ]NG Y5–0Dä [0] SkrandiesG WäG ]55Dä Source localization4 xontinuing qiscussion of the )nverse Problemä )S9/T Newslä 0ä [j] http4zzwwwäbesaädezupdateszbesa_simulatorz xorresponding author4 Todor Vordanov Mtodoräjordanov7besaädeS (räfelfingG (ermany ) )NTROqUxT)ON )) MXT/R)XLS and M/T@OqS ))) R/SULTS )V xONxLUS)ONS Real EEG data Data were acquired in an auditory oddball experiment with -AA Hz standard tones f‘%P repetitions4 and -%A Hz deviant tones f1G‘ repetitions4O presented to the subject through the right earE For the method comparisonO localization was performed at ‘P ms post stimulus in the averaged response to the standard stimuli f-k- trials after artifact rejection4E CLARA In an initialization stepO a LORET' image is calculatedE Then the following steps are performed per iterationS :E The resulting image is spatially smoothed with a GD Gaussian kernel fthis step is omitted in the first iteration4E 1E 'll grid points with amplitudes below a threshold of :g of the maximum activity are set to zeroO thus being effectively eliminated from the source space in the subsequent stepE GE The resulting image defines a spatial weighting term ffor each voxel the corresponding image amplitude4E kE ' LORET' image is computed with an additional spatial weighting term for each voxel as computed in step GE The procedure can be repeated one or more times depending on the data and the research objectivesE Comparison procedure Parameters used for comparing the iterative methods were the distance to the simulated sourcesO and the number of the estimated sources fnumber of maxima in the volume distribution4E The three methods that were compared were f:4 7L'R' R applying depth weighting and Laplace weighting for each iterationO f14 ‘SLF’ R a modified algorithm with depth weighting but without Laplace weighting during the iterations fcomparable with Shrinking LORET'RFO7USS [G]4 and fG4 ‘Laplace only fLO4’ R another modification without depth weighting but with Laplace weighting during the iterationsE The comparison was performed for regularization values AEAAA:O AEA:O AE:O AE% fg of the largest singular value for the MooreRPenrose pseudoinverse calculation4 and number of iterations 1O %O :AE Data with different SNRs The best results for the data with different SNRs wereS 7L'R' R % iterationsO AEA: regularizationO the same for the iterations weighted only with Laplace and SLF R % iterationsO AE% regularization fFigure G4E Fig. 2 xomparison between LOR/TX and xLXRX for closemby deep sourcesä The dipoles mark the simulated sources MleftSG the estimation with LOR/TX is shown in the middleG the estimation with xLXRX on the rightä Fig. 3 Results for the different iterative methodsä The blue and green lines show the distance to the simulated sources in mmä The red and purple lines denote the number of estimated sourcesä Application to real EEG data 'pplication of 7L'R' to real EEG data revealed the expected activity in both auditory cortices fFigure k4E Fig. 4 Source reconstruction with xLXRX MleftSG LO MmiddleS and SL_ MrightSä Results are comparable for all three methodsä Results calculated with SL_ shift the left source further superior than the other two methodsä Simulation LOR/TX xLXRX xLXRX Laplace only SL_ Fig. 1 Simulations with different levels of noise No noise Only noise SNR . SNR 5 SNR .[ R L R L Low resolution electromagnetic tomography fLORET'4 [%][P] is a well known method for source reconstruction based on the weighted minimum 1 Rnorm algorithm [1] with the inverse Laplace operator as an additional weighting termE Even though it was shown that the method localizes deep sources correctlyO it appears to produce a very smooth and widespread source distributionO and fails to resolve closely neighboring cortical sourcesE In order to overcome these difficultiesO a new iterative application of LORET' with a reduced source space per iteration is suggestedE This method is called 7lassical LORET' 'nalysis Recursively 'pplied f7L'R'4E Results demonstrate that 7L'R'S EEE is able to localize deep sources correctlyO EEE is able to resolve closely neighboring sourcesO EEE yields focal localizationsO EEE performs reliably over a wide range of noise levels and EEE reliably estimates the activity in real EEG data acquired under the condition of an auditory oddball experimentE In order to investigate 7L'R'’s and LORET'’s ability to resolve sources that are close togetherO two closely neighboring dipoles fFigure 14 without noise were simulated in the left and right dorsal posterior cingulate area G: [:][k]E To compare 7L'R' with other iterative methodsO brain activity was simulated in the left and right HeschlFs gyrusE Real EEG noise was added to the simulated evoked responses resulting in :1 different signalRtoRnoise ratios fSNRs4 between 1 and 1A fFigure :4E Data were generated with the free tool BES' Simulator [C]E Simulations CLARA vs. LORETA The simulation with neighboring sources showed that LORET' was not able to resolve the sources even with the minimum regularization possibleE 7L'R' localized both sources correctly with a regularization of AEAAA: and :A iterations fFigure 14E Future developmentsS 7ortical 7L'R'S Restraining the solution to the cortical surface and applying a 1D instead of GD Laplacian would improve the method with respect to the following two aspectsE :E The GD Laplacian smooths in all three directions without accounting for the cortical topologyE 1E The GD Laplacian is unstable on the brain boundaryE

xXX4PxP/XPXP RecursiPXied - BESA€¦ · xXX4PxP/XPXP RecursiPXied TodorPVv]GPP@chstetter].GPP9g]FGP)PmVdanov]GPPcherg] MunichPPPXPGPGP(y] 9/XP(@GP(GP(F UniverPPGPGP(]PXGPVääGP_GPäXäGPmGPäGPmGPqäGP

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Page 1: xXX4PxP/XPXP RecursiPXied - BESA€¦ · xXX4PxP/XPXP RecursiPXied TodorPVv]GPP@chstetter].GPP9g]FGP)PmVdanov]GPPcherg] MunichPPPXPGPGP(y] 9/XP(@GP(GP(F UniverPPGPGP(]PXGPVääGP_GPäXäGPmGPäGPmGPqäGP

xLXRX4PxlassicalPLOR/TXPXnalysisPRecursivelyPXppliedTodorPVordanov]GPKarstenP@oechstetter].GPPatrickP9erg]FGP)sabellaPPaulmVordanov]GPMichaelPScherg]

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Real EEG dataDatavwerevacquiredvinvanvauditoryvoddballvexperimentvwithv-AAvHzvstandardvtonesvf‘%Pvrepetitions4vandv-%AvHzvdeviantvtonesvf1G‘vrepetitions4OvpresentedvtovthevsubjectvthroughvthevrightvearEvForvthevmethodvcomparisonOvlocalizationvwasvperformedvatv‘Pvmsvpostvstimulusvinvthevaveragedvresponsevtovthevstandardvstimulivf-k-vtrialsvaftervartifactvrejection4ECLARAInvanvinitializationvstepOvavLORET'vimagevisvcalculatedEvThenvthevfollowingvstepsvarevperformedvperviterationSvvvvvvvv:EvThevresultingvimagevisvspatiallyvsmoothedvwithvavGDvGaussianvkernelvfthisvstepvisvvvvvvvvvvvvvomittedvinvthevfirstviteration4Evvvvvvvv1Ev'llvgridvpointsvwithvamplitudesvbelowvavthresholdvofv:gvofvthevmaximumvactivityvarevvvvvvvvvvvvvsetvtovzeroOvthusvbeingveffectivelyveliminatedvfromvthevsourcevspacevinvthevsubsequentvstepEvvvvvvvvGEvThevresultingvimagevdefinesvavspatialvweightingvtermvfforveachvvoxelvthevcorrespondingvimagevamplitude4EvvvvvvvvkEv'vLORET'vimagevisvcomputedvwithvanvadditionalvspatialvweightingvtermvforveachvvoxelvasvcomputedvinvstepvGEThevprocedurevcanvbevrepeatedvonevorvmorevtimesvdependingvonvthevdatavandvthevresearchvobjectivesEComparison procedureParametersvusedvforvcomparingvthev iterativevmethodsvwerevthevdistancevtovthevsimulatedvsourcesOvandvthevnumbervofv thevestimatedvsourcesvfnumberv ofv maximav inv thev volumev distribution4Ev Thev threev methodsv thatv werev comparedv werev f:4v 7L'R'v Rv applyingv depthv weightingv andvLaplacevweightingvforveachviterationOvf14v‘SLF’vRvavmodifiedvalgorithmvwithvdepthvweightingvbutvwithoutvLaplacevweightingvduringvtheviterationsvfcomparablevwithvShrinkingvLORET'RFO7USSv[G]4vandvfG4v‘LaplacevonlyvfLO4’vRvanothervmodificationvwithoutvdepthvweightingvbutvwithvLaplacevweightingvduringvtheviterationsEvThevcomparisonvwasvperformedvforvregularizationvvaluesvAEAAA:OvAEA:OvAE:OvAE%vfgvofvthevlargestvsingularvvaluevforvthevMooreRPenrosevpseudoinversevcalculation4vandvnumbervofviterationsv1Ov%Ov:AE

Data with different SNRsThev bestv resultsv forv thev datav withv differentvSNRsv wereSv 7L'R'v Rv %v iterationsOv AEA:vregularizationOv thev samev forv thev iterationsvweightedv onlyv withv Laplacev andv SLFv Rv %viterationsOvAE%vregularizationvfFigurevG4E

Fig. 2P xomparisonP betweenP LOR/TXP andP xLXRXP forPclosembyP deepP sourcesäP TheP dipolesP markP theP simulatedPsourcesPMleftSGPthePestimationPwithPLOR/TXPisPshownPinPthePmiddleGPthePestimationPwithPxLXRXPonPthePrightäP

Fig. 3PResultsP forP thePdifferentP iterativePmethodsäPThePbluePandPgreenPlinesPshowPthePdistancePtoPthePsimulatedPsourcesPinP mmäP TheP redP andP purpleP linesP denoteP theP numberP ofPestimatedPsourcesä

Application to real EEG data'pplicationv ofv 7L'R'v tov realv EEGv datavrevealedv thev expectedv activityv inv bothvauditoryvcorticesvfFigurevk4E

Fig. 4P SourceP reconstructionP withP xLXRXP MleftSGP LOPMmiddleSP andP SL_P MrightSäP ResultsP areP comparableP forP allPthreeP methodsäP ResultsP calculatedP withP SL_P shiftP theP leftPsourcePfurtherPsuperiorPthanPthePotherPtwoPmethodsä

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Lowv resolutionv electromagneticv tomographyv fLORET'4v [%][P]v isv av wellv knownv methodv forv sourcev reconstructionv basedv onv thev weightedvminimumvℓ1Rnormvalgorithmv[1]vwithvthevinversevLaplacevoperatorvasvanvadditionalvweightingvtermEvEvenvthoughvitvwasvshownvthatvthevmethodvlocalizesv deepv sourcesv correctlyOv itv appearsv tov producev av veryv smoothv andv widespreadv sourcev distributionOv andv failsv tov resolvev closelyvneighboringvcorticalvsourcesEvInvordervtovovercomevthesevdifficultiesOvavnewviterativevapplicationvofvLORET'vwithvavreducedvsourcevspacevperviterationvisvsuggestedEvThisvmethodvisvcalledv7lassicalvLORET'v'nalysisvRecursivelyv'ppliedvf7L'R'4E

Resultsvdemonstratevthatv7L'R'S➤vEEEvisvablevtovlocalizevdeepvsourcesvcorrectlyO➤vEEEvisvablevtovresolvevcloselyvneighboringvsourcesO➤vEEEvyieldsvfocalvlocalizationsO➤vEEEvperformsvreliablyvovervavwidevrangevofvnoisevlevelsvand➤vEEEvreliablyvestimatesvthevactivityvinvrealvEEGvdatavacquiredvvvvvundervthevconditionvofvanvauditoryvoddballvexperimentEv

➤v Inv orderv tov investigatev 7L'R'’sv andv LORET'’sv abilityv tov resolvev sourcesv thatv arev closevtogetherOv twovcloselyvneighboringvdipolesv fFigurev14vwithoutvnoisevwerevsimulatedv inv thev leftvandvrightvdorsalvposteriorvcingulatevareavG:v[:][k]E➤v Tov comparev 7L'R'v withv otherv iterativevmethodsOv brainv activityv wasv simulatedv inv thev leftv andvrightvHeschlFsvgyrusEvRealvEEGvnoisevwasvaddedvtovthevsimulatedvevokedvresponsesvresultingvinv:1vdifferentvsignalRtoRnoisevratiosvfSNRs4vbetweenv1vandv1AvfFigurev:4E➤vDatavwerevgeneratedvwithvthevfreevtoolvBES'vSimulatorv[C]E

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CLARA vs. LORETAThev simulationv withv neighboringv sourcesvshowedv thatv LORET'v wasv notv ablev tovresolvev thev sourcesv evenv withv thev minimumvregularizationv possibleEv 7L'R'v localizedvbothvsourcesvcorrectlyvwithvavregularizationvofvAEAAA:vandv:AviterationsvfFigurev14E

FuturevdevelopmentsS➤v 7orticalv 7L'R'Sv Restrainingv thev solutionv tov thev corticalv surfacev andvapplyingv av 1Dv insteadv ofv GDv Laplacianv wouldv improvev thev methodv withvrespectvtovthevfollowingvtwovaspectsE:EvThevGDvLaplacianvsmoothsvinvallvthreevdirectionsvwithoutvaccountingvforvthevcorticalvtopologyE1EvThevGDvLaplacianvisvunstablevonvthevbrainvboundaryE