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FindSources3D - Source Localization Using Rational Approximation on Plane Sections
Todor Jordanov, Jean-Paul Marmorat, Maureen Clerc, Juliette Leblond, Andre Waelkens, Théodore Papadopoulo
To cite this version:
Todor Jordanov, Jean-Paul Marmorat, Maureen Clerc, Juliette Leblond, Andre Waelkens, et al.. Find-Sources3D - Source Localization Using Rational Approximation on Plane Sections. Organization Hu-man Brain Mapping, Annual Meeting, Jun 2014, Hamburg, GerHu-many. Poster listings. �hal-01098108�
FindSourceOj1ä1Source1Localization1Using1
Rational1/pproximation1on1Plane1Sections
Todor1JordanovNH1JeanäPaul1Marmorat:H1Maureen1'lercOH1Juliette1LeblondOH1/ndre1WaelkensNH1
Theodore1PapadopouloO @cole1des1Mines1ParisTechH1Sophia1/ntipolisH1France : (@S/1GmbHH1GräfelfingH1Germany N INRI/H1Sophia1/ntipolisH1France O 'orresponding1authorK
I
INTROjU'TION
II
M/T@RI/LS1and1M@THOjS
III R@SULTS
IV 'ON'LUSION
Cortical. mapping Planar. singularities. detectionjeep1source Superficial1source Two1sources
Three1sources R R L L A.new.method.for.EEG.source.localization.based.on.rational.approximation.techniques.in.the.complex.plane.[H].was.suggestedI.The.method.is. used.in.the.context.of.a.nested.sphere.head.model3.in.combination.with.a.cortical.mapping.procedureI.This.method.was.shown.to.perform. perfectly.for.numerical.simulations.without.noise.but.its.performance.with.respect.to.different.signalDtoDnoise.ratios.RSNRs)3.to.different.number. of.sources.and.to.real.EEG.data..was.not.investigated.until.nowI.The.method3.formally.called.FindSource4D.RFS4D)[4]3.is.evaluated.here.with. data.simulations.and.a.real.EEG.data.setI FS4D.was.able.to.reconstruct.perfectly.the.simulated.brain.activity.without.noise.up.to.two.sourcesI.In.the.case.of.three.sources.the.estimated. dipoles. did. not. match. the. simulated. exactly. but. the. results. could. still. be. considered. reliableI. The. performance. of. FS4D. decreases. with. increasing. of. the. noise. level. as. expected3. however3. the. estimated. localizations. remain. adjacent. to. the. simulated. even. for. the. lowest. SNRI. Finally3.FS4D.was.able.to.reconstruct.correctly.the.auditory.evoked.responses.in.real.EEG.dataI
FS4D.makes.use.of.a.spherical.head.model.made.of.consecutive.layers.Rscalp3.skull3.brain).of. constant.conductivityI
The. algorithm. of. FS4D. consists. of. two. main. steps. D. data. transmission. and. source. recovery. RFigure.1)I
1I.Data.transmission.from.the.scalp.to.the.cortex.involves.the.followingI
1I1I. Cortical. mapping. D. The. data. are. transmitted. from. the. surface. of. the. scalp. where. it. is. measured.onto.the.surface.of.the.brain.[1]I
1IHI.Harmonic.projection.D.Filtering.out.possible.outer.sources.by.keeping.only.the.information. related.to.the.effective.inner.sources.in.the.brainI
HI.Source.recovery.in.the.brain.from.data.on.the.cortical.surface.involves.the.followingI
HI1I.Plane.sections.D.The.sphere.modeling.the.cortical.surface.is.sliced.along.families.of.parallel. planes. yielding. disks. inside. which. the. singularities. will. be. soughtI. The. HD. singularities. form. within.the.sphere.a.family.of.lines.intersecting.at.the.position.of.the.4D.sourcesI
HIHI. Planar. singularity. detection. D. HD. approximation. techniques. are. used. to. find. the. planar. singularities.on.the.plane.sections.of.the.brain3.approximated.by.poles.of.rational.functionsI
HI4I.4D.source.localization.D.For.a.putative.number.of.sources3.the.sources.are.localized.in.4D. by.analyzing.the.sets.of.planar.singularitiesI.
HI:I. In. order. to. fineDtune. the. resulting. source. estimation. an. additional. dipole. fit. algorithm. with. constrained.source.movement.range.was.appliedI
FindSource3D
Simulations without noise
The. reconstruction. with. FS4D. for. the. simulated. data. without. noise. yielded.the.following.results9.for.the. dipole. in. the. right. amygdala. the. distance.between.the.simulated.and. the. estimated. source. was. kI6. mm3. for. the. left. primary. motor. cortex. D. 4I:. mm3. for. the. bilateral. temporal. case. D. kI4. mm. right. and. kI0. mm. left3. for. the. three. sources. case. D. 1kI5. mm. left3. 10IH. mm. right. and. 1HI:.mm.frontal.source.RFigure.H)I
Fig. 11Typical1workflow1of1FSOjK1iE1scalp1potential1mapH1iiE1
cortical1 mappingH1 iiiE1 planar1 singularity1 detectionH1 ivE1 clustering1of1the1planar1singularities1and1vE1dipole1fittingf
In.order.to.investigate.the.performance.of.FS4D.various.EEG.data.with.71.standard.electrodes. were. simulated9. R1). single. deep. source3. RH). single. superficial. source3. R4). bilateral. temporal. sources3. R:). three. sources. D. in. the. medial. frontal. gyrus3. left. and. right. insulaI. Additionally3. the. bilateral. temporal. activity. was. altered. by. adding. different. noise. levels. to. the. sensors3. thus. yielding.data.with.18.different.SNRs.between.H.and.HkI
Simulations
Real EEG Data
Tones.of.0.intensities.R6k3.5k3.7k3.8k3.1kk.dB.sound.pressure.level).were.presented.binaurally.in.pseudorandomized.formI.Evoked.potentials. were.recorded.with.4H.electrodes.referenced.to.Cz.and.sampling.rate.H0k.HzI.For.the.source.reconstruction.with.FS4D.the.6k.dB.condition3. latency.'.77.ms3.was.usedI.After.artifact.rejection.6:.trials.were.accepted.for.averagingI [N]1'lercH1MfH1KybicH1JfH1:II.f1'ortical1mapping1by1Laplace–'auchy1transmission1using1a1boundary1element1methodf1Inverse1Problf1:OH1:w[]f [:]1'lercH1MfH1LeblondH1JfH1MarmoratH1JfäPfH1PapadopouloH1TfH1:IN:f1Source1localization1using1rational1approximation1on1plane1sectionsf1Inverse1Problf1:[H1IwwIN[f1 [O]1httpKyywwwäsopfinriaffryapicsyFindSourcesOjyeny Scalp. potential Clustering Dipole. fitting
Simulations with different SNRs
The.simulations.with.different.SNRs. revealed. a. negative. linear. trend. in. the. relation. between. SNR. and. distance. to. the. simulated. sources. RFigure.4)I
Real EEG data
In. the. case. of. real. EEG. data. the. sources. estimated. by. FS4D. are. located.bilateral.in.the.medial.end.of. the. left. and. right. HeschlNs. gyrus. RFigure.:)I
Fig. 21 Performance1 of1 FSOj1 for1 simulations1 without1 noisef1 (lue1
dipoles1 mark1 the1 simulated1 sourcesH1 red1 dipoles1 ä1 sources1 reconstructed1by1FSOjf1
Fig. 31Results1for1simulations1with1two1sources1and1different1SNRsf1
The1 solid1 curves1 show1 the1 distance1 hmmE1 between1 the1 simulated1 and1 the1 estimate1 sourcesf1 The1 dashed1 lines1 show1 the1 corresponding1linear1trendsf1
Fig. 41The1sources1estimated1by1FSOj1in1the1case1of1real1@@G1data1
are1located1bilateral1in1the1medial1end1of1the1Heschlks1gyrusf1
Todor1Jordanov1htodorfjordanov9besafdeE GräfelfingH1Germany
