Research Article MEG Connectivity and Power Detections ... - neuro…neuro.hut.fi/~jjkujala/pdfs/hincapie_et_al_CIN_2016.pdf · MEG Connectivity and Power Detections with Minimum

Research ArticleMEG Connectivity and Power Detections with Minimum NormEstimates Require Different Regularization Parameters

Ana-Sofiacutea Hincapieacute1234 Jan Kujala45 Jeacutereacutemie Mattout4 Sebastien Daligault6

Claude Delpuech6 Domingo Mery2 Diego Cosmelli3 and Karim Jerbi14

1Psychology Department University of Montreal Montreal QC Canada H2V 2S92Department of Computer Science Pontificia Universidad Catolica de Chile 7820436 Santiago de Chile Chile3School of Psychology and Interdisciplinary Center for Neurosciences Pontificia Universidad Catolica de Chile7820436 Santiago de Chile Chile4Lyon Neuroscience Research Center DyCog Team Inserm U1028 CNRS UMR5292 69675 Bron Cedex France5Department of Neuroscience and Biomedical Engineering Aalto University 02150 Espoo Finland6MEG Center CERMEP 69675 Bron Cedex France

Correspondence should be addressed to Karim Jerbi karimjerbiumontrealca

Received 15 October 2015 Revised 19 January 2016 Accepted 14 February 2016

Academic Editor Jussi Tohka

Copyright copy 2016 Ana-Sofıa Hincapie et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Minimum Norm Estimation (MNE) is an inverse solution method widely used to reconstruct the source time series that underliemagnetoencephalography (MEG) dataMNE addresses the ill-posed nature ofMEG source estimation through regularization (egTikhonov regularization) Selecting the best regularization parameter is a critical step Generally once set it is common practiceto keep the same coefficient throughout a study However it is yet to be known whether the optimal lambda for spectral poweranalysis of MEG source data coincides with the optimal regularization for source-level oscillatory coupling analysis We addressedthis question via extensive Monte-Carlo simulations of MEG data where we generated 21600 configurations of pairs of coupledsources with varying sizes signal-to-noise ratio (SNR) and coupling strengths Then we searched for the Tikhonov regularizationcoefficients (lambda) that maximize detection performance for (a) power and (b) coherence For coherence the optimal lambdawas two orders of magnitude smaller than the best lambda for power Moreover we found that the spatial extent of the interactingsources and SNR but not the extent of coupling were the main parameters affecting the best choice for lambda Our findingssuggest using less regularization when measuring oscillatory coupling compared to power estimation

1 Introduction

Healthy brain function is largely mediated by coordinatedinteractions between neural assemblies in different corticaland subcortical structures As a result the study of neuronalprocesses requires techniques that can reliably measure thespatiotemporal dynamics of large-scale networks To this endit is important to assess the modulations of local activationsas well as long-range coupling between brain areas Overrecent years the quantification of neuronal interactions in agiven behavioral task or brain state has been the focus of alarge body of research and various techniques are currentlyused to detect and probe the role of functional connectivity

(eg [1 2]) In particular a widely used technique for thedetection of large-scale interactions among neural assembliesis magnetoencephalography (MEG) [3ndash5] This is primarilydue to its high temporal resolution which is in the sameorder of magnitude as the neuronal processes themselves(milliseconds) Unlike electroencephalography (EEG) MEGmeasures magnetic fields that are less affected by the skulland brain tissue and provides whole-head coverage which ismandatory for the assessment of large-scale brain networksThe use of MEG has advanced our comprehension of themechanisms underlying functional brain connectivity [6]involved in sensory motor and higher-order cognitive tasks[3 7ndash11] higher-order cognitive tasks resting state [6 12ndash18]

Hindawi Publishing CorporationComputational Intelligence and NeuroscienceVolume 2016 Article ID 3979547 11 pageshttpdxdoiorg10115520163979547

2 Computational Intelligence and Neuroscience

The ability to measure brain interactions at the sourcelevel rather than between sensor channels is an importantprerequisite if we want to make useful inferences aboutthe anatomical-functional properties of the network Tothis end source reconstruction techniques are applied inorder to estimate the spatiotemporal activity of the corticalgenerators underlying the recorded sensor-level MEG dataSolving this relationship is an ill-posed inverse problem forwhich numerous methods have been developed [4] Thedifferences between the various techniquesmainly stem fromthe assumptions theymake about the properties of the neuralsources and from the way they incorporate various forms ofa priori information if any is available Conceptually solvingthe MEG inverse problem boils down to solving a system ofequations that is underdetermined (ie no unique solution)since we generally have far more sources (thousands) thanmeasurements (hundreds) Identifying a solution to such aproblem can be achieved by imposing constraints on thesources A typical constraint is to minimize the source powerAmong thesemethods theMinimumNormEstimate (MNE)relies on minimizing the L2-norm and is one of the mostwidely used techniques [4 7 8 18ndash37] By contrast estimatesobtained by minimizing the L1-norm are referred to asMinimum-Current Estimates (MCE) [34 38] While the L2-norm assumes a Gaussian a priori current distribution theL1-norm assumes a Laplacian distribution [39]

In principle MNE looks for a distribution of sourceswith the minimum (L2-norm) current that can give the bestaccount of the measured data As the problem is ill-posedMNE generally uses a regularization procedure that sets thebalance between fitting the measured data (minimizing theresidual) and minimizing the contributions of noise [22 4041]The Tikhonov orWiener regularization [42 43] and SVDtruncation are among the most widely used regularizationprocedures Regularization may be considered a necessaryevil it is required to stabilize the solution of the inverseproblem yet too much regularization leads to overly smoothsolutions (spatial smearing) Since we do not have a precisemodel of brain activity and noise the choice of the optimalamount of regularization is a nontrivial step for which nomagical recipe exists [44] The relationship between optimalregularization and the patterns of underlying generators isstill poorly understood In particular the effect of regulariza-tion on the detection accuracy of Minimum Norm Estimatesof source power and interareal source coupling has not beenthoroughly investigated This raises the question of whetherone should use the same regularization coefficient for MNE-based power and connectivity analyses as is generally doneor would one benefit from optimizing the regularizationcoefficients separately for each analysis Furthermore howdoes the optimal regularization coefficient in such configu-rations depend on sensor-level SNR source size or couplingstrength

With these questions in mind we performed exten-sive Monte-Carlo simulations creating over 20000 pairsof coupled oscillatory time series in MEG source spacesand computed the resulting surface MEG recordings Thenwe estimated source power and coherence using the MNEframework with variable degrees of Tikhonov regularization

Moreover we used an approach based on an area under thecurve (AUC) to identify the optimal regularization coefficient(lambda) in the case of power and coherence analyses Wefound a systematic difference between the optimal lambdasin each analysis for source-level coherence analysis theoptimal lambda was two orders of magnitude smaller thanthe best lambda for power detection Lastly our findings arebroken down as a function of SNR cortical patch size andcorticocortical coupling strength

2 Methods and Materials

In this section we first present the MEG inverse problemformulation and the MNE framework Then we describethe simulation reconstruction and performance assessmentprocedures

21TheMEG Inverse Problem The inverse problem looks foran estimation of the active sources S (3119899sources times time points)that generates the measurements M (119899channels times time points)recorded at the sensors The dimension 3119899 of the columnsof S accounts for the three components of the source 119899in the 119909 119910 and 119911 directions According to anatomicalobservations the main generators of MEG are located inthe grey matter and their orientation is perpendicular to thecortical sheet [45] Here we used a constrained orientationapproach (perpendicular to the cortical surface) and hencethe dimensions of S are reduced to 119899sources times time pointsAssuming a linear relationship between the measurementsand the active sources the problem is modeled as

M = LS + N (1)

where L is the lead field matrix (119899channels times 119899sources) and Nis additive noise applied at the MEG channels (119899sources timestime points)The lead fieldmatrix describes how each sourcecontributes to the measurements at each sensor given aspecific head conductivity model and a source space As thenumber of sources is usually much higher than the numberof sensors the lead field matrix is highly underdeterminedand thus not invertible The estimation of the activity of thesources requires the definition of an inverse operatorW

S =W119879M (2)

where S represents the estimated sources (119899sources timestime points) and the superscript 119879 denotes matrix transpose

22 Minimum Norm Estimate (MNE) As the MEG inverseproblem is ill-posed a regularization scheme is needed [22]and one of the most common options is the Tikhonovregularization [42 43] MNE calculates an inverse operatorW by searching for a distribution of sources Swithminimumcurrents (L2-norm) that produces an estimation of themeasurements (LS) most consistent with the measured data(M) The solution is a trade-off between the norm of theestimated regularized sources current 1205822S2 and the normof the quality of the fit they provide to the measurementsM minus LS2 Assuming the noise N and the sources strength

Computational Intelligence and Neuroscience 3

S to be normally distributed with zero mean and covariancematrix Q and R respectively a general form of the MNEinverse solution can thus be given as [35 46 47]

S = argminS10038171003817100381710038171003817Qminus12 (M minus LS)10038171003817100381710038171003817

2

+ 1205822 10038171003817100381710038171003817Rminus12S10038171003817100381710038171003817

2

(3)

where 120582 is the Tikhonov regularization parameter Thus theinverse operatorW is defined as

W = RL119879 (LRL119879 + 1205822Q)minus1

(4)

where the superscript minus1 denotes matrix inverseThe Minimum Norm Estimate embodies the assumption

of independently and identically distributed (IID) sourceswhich corresponds to an identity matrix R in the aboveformula Alternatively R can incorporate more informed(spatial) assumptions yielding a so-called weighted Mini-mum Norm Estimate [28 35 44] Here we use the generaland classical minimum norm solution The noise covariancematrix Q was computed from the actual noise which wasadded to the sensors in each simulation

23 Simulations We simulated 117s of oscillatory activity inpairs of cortical sources with different degrees of coupling inthe alpha band (9ndash14Hz)We computed the resulting sensor-level data through forward modeling based on a 275-channelCTF MEG system configuration Our sources consistedof current dipoles placed at the vertices of a tessellatedMNI-Colin 27 cortical surface which was segmented andtessellated using FreeSurfer [48] and downsampled to 15028vertices Different strengths of coupling were obtained byforcing the time series of the second source to have a certainlevel of coherence with the first source time series Themagnetic fields at the sensors were calculated using a singlesphere head model and constraining the orientations of thesources to be normal to the cortical surface The simulateddatawere generated using a combination of customMATLABcode in addition to functions from Brainstorm [49] andFieldTrip [50] toolboxes The source time courses weresimulated by first setting the base frequency of the oscillator(eg 12Hz) and inducing a small jitter to its instantaneousfrequency across time points The frequency modulated timecourses were then generated using an exponential functionThis procedure causes fluctuations in the phase relationshipbetween two oscillators with the same base frequency allow-ing us to achieve coherence levels below 1 The frequencyjittering was performed randomly in a loop until the desiredcoherence level (eg 04) between the time courses of the twooscillators was reached

We randomly selected two locations (seeds) for each sim-ulated pair of sources (600 pairs) Next for each pair we var-ied three additional parameters in the simulations the spatialextent of the sources the strength of the coupling betweenthe two sources and the signal-to-noise ratio (SNR) at thesensorsThese parameters are described inmore detail below

(i) Patches and Point-Like Sources We simulated point-likesources (ie 1 dipole) and cortical patches (with surface areas2 4 or 8 cm2) The activity of a cortical patch was simulated

by placing identical time series at the vertices that make upthe patch As described above the vertices were obtained viatessellation of the MNI brain (Colin 27)

(ii) Coupling Strength When generating the time series foreach of the two sources of a pair of simulated generators wedefined the coupling by setting the alpha-band coherence toeither 01 02 or 04We simulated time series that were 7000samples long (600Hz sampling frequency) Note here thatby actually simulating true coherence at the source level wecircumvent debates about spurious coupling that arises fromfield spread As such we assess here the ability to recover trulycoherent cortical activity

(iii) Signal-to-Noise Ratio (SNR) White noise was added tothe sensor signals in order to achieve three levels of SNR(0 dB minus20 dB and minus40 dB) calculated as the ratio of theFrobenius normof signal and noise amplitudes at the sensors

In summary we randomly chose 600 different pairs ofcortical location configurations for which we varied sourcesize (4 levels point-like 2 4 or 8 cm2) coupling strength (3levels 01 02 or 04) and SNR (3 levels 0 dB minus20 dB andminus40 dB) This yielded a total of 21600 sets of simulated MEGsensor-level data Next we evaluated the effect of varying theTikhonov regularization parameter 120582 on detection perfor-mance of MNE independently for power and for coherencemapping

24 Power and Coherence Reconstructions The previoussection described the cortical power and coherence config-urations that were generated in the MEG data simulationstep Now in order to assess our ability to reconstructthese simulated (ie known) source configurations we firstreconstruct the source time series by applying MNE to thesimulated sensor data and then we compute spectral powerand coherence from these estimated time series

Most MEG studies that use MNE select a single lambdavalue once and for all to be used throughout the study thesame regularization coefficient is hence used for both powerand coupling estimations (assuming both are performedwithin the study) This is not the case here precisely becauseour objective is to test whether optimal lambda values differbetween power and coherence mapping

Therefore in order to find the regularization coefficientproviding the most accurate reconstruction of (a) powerand (b) interareal coherence across all 21600 simulatedconfigurations we used multiple values for 120582 ranging from1119890 minus 11 to 1119890 minus 5 (7 values) In addition to searching forthe optimal lambda that provides the best results across allsimulations the definition of best lambda was also separatelyexamined as a function of SNR coupling strength and sourceextent Finally for the sake of comparison we also computedthe optimal 120582 value obtained from the standard L-curvemethod [51] The range of possible lambda values examinedin our estimations was selected based on visual inspection ina subset of simulations and chosen to ensure it included thelambda obtained via the L-curve approach

Notably for the coupling analysis we used the recon-structed time series at one of the two simulated dipoles as


reference point and we calculated coherence with all othersource time series across the brain Spectral power (at anylocation 119903) and magnitude squared coherence (between twolocations 119903

1and 1199032) were calculated as follows

119875 (119903 119891) = Cs (119903 119903 119891)

Coh (1199031 1199032 119891) =

1003816100381610038161003816Cs (1199031 1199032 119891)1003816100381610038161003816

2

119875 (1199031 1199031 119891) 119875 (119903

2 1199032 119891)

(5)

where Cs is the cross-spectral density matrix and 119891 is thefrequency bin Power and MS coherence were calculatedvia built-in standard MATLAB (Mathworks Inc MA USA)functions based on Welchrsquos averaged and modified peri-odogram method [52]

25 Receiver Operating Characteristic (ROC) Curves Weevaluated the performance of each method using the areaunder the curve (AUC) from the ROC curves obtained byplotting the True Positive Fraction (TPF) versus the FalsePositive Fraction (FPF) at a given threshold 120572 calculated asfollows

TPF (120572) = TP (120572)Number of simulated dipoles

FPF (120572)

=FP (120572)

Total number of dipoles minusNumber of simulated dipoles

(6)

where TP(120572) represents the true positives (defined as theintersection between simulated sources and active sourcesat threshold 120572) and FP(120572) represents the false positives(defined as all active sources but excluding the true positivesat activation threshold 120572) By computing TPF and FPFrepeatedly for successive values of activation thresholds 120572we obtain a ROC curve from which we derive the AUCThe AUC is taken as a measure of performance that is thebest regularization coefficient would be the one that yieldsthe highest AUC Statistical comparisons were performedusing standard parametric two-tailed 119905-tests Note that forreference-based coherence reconstruction computing truepositives can be ambiguous if we consider the sources withinthe ldquoreference patchrdquo (location 1) to be true positives Toavoid this problem we chose to quantify how well the distantcoherent patch (location 2) was detected In other words weused the time series estimated at location 1 (as a seed) andconsidered only the simulated activity that make up the patchat location 2 to be the vertices we wish to detect Thereforethe vertices within the reference patch were excluded fromthe ROC calculations for coherence evaluations

3 Results

31 Optimal Tikhonov Regularization Coefficient Is Not theSame for Power and Coherence Reconstructions Figure 1(a)shows the effect of lambda selection on quality of powerand coherence detection across all simulated conditions andconfigurations (measured as mean AUC) Importantly wefound that the best mean value of lambda for power (10119890 minus 7)

differs from the best mean lambda for coherence which wastwo orders of magnitude smaller (10119890 minus 9) In comparisonto the optimal value for power the lower optimal value forcoherence implies that a smaller residual should be allowed tohave an optimal coherence reconstruction The observationsin Figure 1(a) also indicate that coherence reconstructions aremore sensitive to the selection of an appropriate lambda valuethan power reconstructions (as AUC for coherence peaks at1119890minus09 and drops again while AUC for power displays a flatterdistribution for values neighboring 1119890 minus 07)

Interestingly Figure 1(b) shows a significant difference(119901 lt 0001 119905-test) between the power reconstructionperformances achieved using the optimal lambda for powercompared to using the lambda determined to be optimalfor coherence Similarly coherence reconstructions were alsosignificantly better when using the coherence optimal ambdacompared to the power optimal lambda Simply put oursimulations demonstrate that on average across 21600 simu-lated pairs of sources tuning lambda selection differently forcoherence and for power analyses significantly impacts theresults In the next section we examine how SNR couplingstrength and source size individually affect these results

32 Effect of SNR Source Size and Coupling StrengthFigure 2 depicts the effect of (a) SNR (b) source size and(c) coupling strength on optimal lambda In each panel theresults are shown independently for power (upper row) andcoherence (lower row)

Figure 2(a) shows that a decrease in SNR leads asexpected to an overall decrease in the performance of MNEas measured by mean AUC For power reconstructions apeak (ie easily identifiable optimal lambda) seems to be lim-ited to the higher SNR As for coherence reconstructions thelower rowof Figure 2(a) indicates that stronger regularizationis needed as SNR drops Next Figure 2(b) suggests thatfor both power and coherence detection point-like sourcesrequire more (an order of magnitude higher) regularizationthan cortical patches Furthermore Figure 2(c) shows thatstronger coupling leads to better detection performances(higher mean AUC) However it also suggests that theoptimal lambda values (1119890 minus 07 for power and 1119890 minus 09for coherence) do not vary with source coupling strength(Figure 2(c))

33 Comparison with the L-Curve Method A common andrather well-established heuristic to optimize 120582 in a data-driven manner is the L-curve The L-curve is a plot of thenorm of the regularization term versus the norm of theresiduals representing the trade-off between these two termsThe lambda with the best compromise between minimizingthe norm of the current and that of the residual is chosenas the optimal lambda [51] As it is a fast and widely usedmethod we decided to compare the optimal lambda givenby the L-curve approach with the two average lambda valueswhich we found to optimize either power or coherence

The mean optimal lambda obtained with the L-curvewas 1119890 minus 10 Application of this Tikhonov coefficient led tosuboptimal reconstructions of both power and coherenceFor both cases the mean AUC obtained was significantly


1

08

06

04

02

01e minus 11 1e minus 10 1e minus 09 1e minus 08 1e minus 07 1e minus 06 1e minus 05

Mea

n AU

C

Power detection performance

Lambda

1

08

06

04

02


Mea

n AU

C

Lambda

Coherence detection performance

(a)

1

09

08

07

06

05

04

03

02

01

0

Mea

n AU

CPower detection Coherence detection

lowast

lowast

Best lambda for coherence (1e minus 09)Best lambda for power (1e minus 07)

(b)

Figure 1The averaged optimal regularization for power reconstruction is different from the one obtained for coherence detection (a) MeanAUC for power and coherence reconstructions (b) Mean AUC achieved with best lambda for power (1119890 minus 07) or best lambda for coherence(1119890 minus 09) when applied in each case both for power and for coherence lowast indicates statistically significant differences at 119901 lt 0001 119905-test

smaller (119901 lt 0001 119905-test) than the mean AUC observedwith the optimal lambda values derived from the data(Figure 3(a)) In fact the L-curve based estimation ofoptimal lambda turned out to be one and three orders ofmagnitude smaller than the optimal values we had found forcoherence and power respectively Figures 3(b)ndash3(d) showan example of a simulated pair of sources (Figure 3(a)) andits reconstructions using the optimal lambdas found withthe data-driven AUC-based optimization (1119890 minus 7 for powerand 1119890 minus 9 for coherence) and with the L-curve optimization(1119890minus10)This configuration illustrates a typical casewhere theregularization coefficient derived from the L-curve approachfails It also illustrates how the application of regularizationthat is suitable for power detection (1119890 minus 07) can lead tovery poor detection in the case of coherence where lessregularization (1119890 minus 09) provides acceptable detection Notethat the case shown here is based on an arbitrary selection ofa source configuration from among 21600 simulations Bothpoorer and nicer single examples can be found of course butwe chose to represent a realistic intermediate case that servesto illustrate the point made by our study

4 Discussion

Overall we have shown using extensive simulations of cou-pled pairs of sources that on average when using MNE thebest results are achieved by selecting separate regularization

coefficients for power and for coupling estimations in sourcespace In particular we found on average that the Tikhonovregularization coefficient that yields best coherence detectionis substantially smaller than the optimal regularization coef-ficient for the detection of oscillatory power This is largelydue to the fact that increased smoothing (which arises fromincreased regularization) blows up the rate of false positivesa problem that appears to be amplified for corticocorticalcoupling

Most MEG studies that apply MNE to estimate thesource-level spatiotemporal dynamics do not fine-tune theregularization as a function of the proposed subsequent spec-tral analyses Our simulations suggest that a regularizationparameter that maximizes the detection of oscillatory sourcepower may impair our ability to reliably reconstruct spectralconnectivity As a rule of thumbwe suggest using 1 to 2 ordersof magnitude lower Tikhonov coefficient when searching forsource coupling Obviously this suggestion stems from thesimulations performed in this study and might not neces-sarily be the best choice if other minimum norm methodsare used or if different source coupling configurations arepresent

The variables that appear to have the strongest effecton the optimal lambda according to our simulations arethe SNR and the spatial extent of the sources In contrastthe strength of source coupling only minimally impactedthe optimal choice for lambda It is also noteworthy that


1

08

06

04

02

0

1

08

06

04

02

0

Effect of SNR on power detection (AUC)

Effect of SNR on coherence detection (AUC)

0dB minus20dB minus40dB


(a)

1

08

06

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02

0

1

08

06

04

02

0

Point-like 2 cm24 cm2

8 cm2


8 cm2

Effect of source size on power detection (AUC)

Effect of source size on coherence detection (AUC)

(b)

1

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02

0

1

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01 02 04

01 02 04

Effect of coupling strength on power detection (AUC)

Effect of coupling strength on coherence detection (AUC)

1e minus 11

1e minus 10

1e minus 09

1e minus 08

1e minus 07

1e minus 06

1e minus 05

Lambda

(c)

Figure 2 Power and coherence detection with MNE as a function of three simulation parameters best lambda for power and coherencedetection as a function of (a) SNR (0 dB minus20 dB and minus40 dB) (b) size of the sources (point-like 2 4 and 8 cm2) and (c) coupling strength(01 02 and 04) Power and coherence performances are depicted in the upper and lower rows of each panel respectively

in general hitting the right lambda seems to be even morecritical for coherence than for power while the performancesfor power appeared to stabilize when sufficient regularizationis applied coherence detection appeared to drop again whenregularization becomes too excessive (see Figure 1(a))

For comparison we also used a standard procedureknown as the L-curve approach to identify an optimalTikhonov regularization from our simulated data Thisresulted in a lambda value that was three orders of magnitudesmaller than the best choice for power analyses and oneorder ofmagnitude smaller than the best choice for coherenceanalysis The fact that the L-curve does not yield the bestresults is not amajor problemThe L-curve approach remainsa useful approach in real data analysis with MNE where theground truth is not known Here because we simulated the

MEG data we were in a position to compare the performanceof the regularization coefficient lambda calculated usingthe L-curve approach to the results achieved by a widerange of lambda values Previous reports have also indicatedsuboptimal results when applying L-curve to simulated data(eg [53]) Other methods for a data-driven selection oflambda (eg [44 47]) and other regularization methods(such as SVD truncation) have been proposed For instancelambda selection can be derived from SNR as lambda =trace(LRL119879)[trace(119876)timesSNR2] [47] whichwith prewhiteningand appropriate selection of source covariancematrix119877 (suchthat trace(LRL119879)trace(119876) = 1) yields lambdasim1SNR whereSNR is (amplitude) signal-to-noise ratio Approaches used todetermine SNR values vary substantially Exploring specificlinks between these formulations and the analyses performed


1

08

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0

1

08

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Mea

n AU

CM

ean

AUC

Power

Coherence

(a)

Lambda

(b)

(c)

(d)

lowast

lowast Power detection

05

10

05

10

1e minus 10 1e minus 07


120582 = 1e minus 10 (L-curve) 120582 = 1e minus 09 120582 = 1e minus 07

Simulated coupled sources

Source 1(seed)

Source 2

Size = 4 cm2

Coherence = 04

SNR = 0dB

Coherence detection


Figure 3 Differences in MNE performance when using the optimal lambda found using the L-curve approach and the best lambda valuesobtained from our simulations (a) Difference in performance using the L-curve and the empirically derived lambda for power (upper row)and coherence (lower row) (lowast indicates statistically significant differences at 119901 lt 0001 119905-test) (b) Illustrative example of a simulated pairof coupled sources (alpha-band coherence = 04 patch size = 4 cm2 and SNR = 0 dB) ((c) and (d)) Power and coherence reconstructionsbased on simulated data shown in panel (b) using three options for the definition of an optimal lambda value 120582 = 1119890 minus 10 (obtained with theL-curve) 120582 = 1119890minus 09 (mean optimal value for coherence detection) and 120582 = 1119890minus 07 (mean optimal value for power detection) Note that thepower and coherence maps are normalized with respect to the maximum on each map and subsequently thresholded at 20 of maximumamplitude

here is of high interest but it goes beyond the scope of thespecific question we address which focuses on differences inoptimal lambda selectionwhen switching between power andconnectivity analysis

Note that we focused here on MNE because it is a widelyapplied source estimation technique that is implemented ina number of toolboxes [49 50 54] Besides the classicalminimum norm solution has been shown to be a valuablemethod whenever no reliable a priori information aboutsource generators is available [30] However many otherapproaches exist (eg spatial filters) and the increased suit-ability of one method over another generally depends on theavailability of a priori information and the validity for thedata at hand of the theoretical assumptions that go into eachmethod

A prominent observation in the current study is thatincreases in the degree of regularization have a strongerimpact on coherence than on power detection While localpower peaks remain fairly stable even with a high degree ofsmoothing higher lambda values yield a drop in sensitivityin coherence analysis driven by an increase in false positivedetections (spurious coupling) Since the smoothing effect islargely specific to MNE assumptions one may ask whethercoherence would be better estimated by using a differentinverse approach based on different assumptions (eg spatialfilters) While this could theoretically be the case one shouldkeep inmind that each inversemethod comeswith its own setof assumptions that are more or less suitable for the detectionof coupled sources For instance from a theoretical point ofview the beamformer approach assumes that the sources are


not correlated In practice beamformers are able to detectinteracting sources if the extent of coupling is sufficientlyweak To fully tackle the question in the context of ourdata we would need to perform the same simulation studyusing other inverse solutions alongside MNE in order todirectly compare performances of the methods using thesame detection metrics This is part of an ongoing study andgoes beyond the specific scope of the current paperwhich is tocompare the effect of regularization on power and coherencedetections using MNE

It is noteworthy that our evaluation of coherence detec-tion was characterized by how accurately the second sourceis detected when using the first as a seed point in a brain-widecoherence analysis In other words we do not use the result ofa source localization procedure to identify the seed Althoughthis comeswith certain limitations it also allows us to addressthe two questions separately In addition corticocorticalcoupling is not exclusively performed on sources that showsignificant activations in the source localization step Aselection of a source or a region of interest (ROI) basedon the literature (or on a specific hypothesis) is also usedas a preliminary step to seed-based source-space couplinganalyses Our results directly apply to such approaches

Although we explored many source configurations vary-ing spatial location source coupling strength SNR andsource size (21600 simulations in total) our simulations areof course not exhaustive For example it could be of interestto extend this framework to EEG data or a combinationof EEG and MEG simulations (here we focused on MEGsince it is more commonly used for source-level connectivityanalysis) In addition exploring more realistic noise signalsand head models could be beneficial Furthermore it couldbe of interest to examine the effect of the presence of a thirdnoninteracting source on our findings Also whether theresults would significantly change if other forms ofmin-normestimators are used is an open question although previousfindings suggest that this is quite unlikely [31]

Standard and modified ROC analyses and the associatedAUC metrics have often been used to assess and comparethe performance of different inverse methods to reconstructEEGMEG with simulated neural sources [47 53 55ndash58] Analternative approach to comparing detection performance isthe use of precision-recall (PR) curve [59] This approach aswell as some of the modified ROCAUC metrics mentionedabove can be particularly useful in the case of a heavily imbal-anced ratio of true positives and true negatives (eg [60ndash62]) It has been shown that when comparing performances acurve that dominates in ROC space will also dominate in PRspace However a method that optimizes the area under theROC curve is not guaranteed to optimize the area under thePR curve [63] In the future it could therefore be of interest toextend the current framework to include other performancemetrics such as the PR curve

Moreover we restricted our coupling simulations to gen-erating magnitude squared coherence between two distanttime series Coherence estimation has known limitationssuch as its sensitivity to field spread effects inMEG [2] Othercoupling measures can be implemented in our frameworkin future studies but it is important to keep in mind that

we actually generated true magnitude squared coherencebetween the sources and we evaluate the effect of reg-ularization on our ability to recover this specific type ofcoupling from sensor recordings (in comparison to localspectral power) Likewise an interesting question for futureresearch is to evaluate to which extent these results hold inthe presence of more than two coupled sources In additionall the results reported here pertain to the robustness ofdetecting absolute coherence and absolute power It could beof interest to explicitly test the implications for condition-based (eg task A versus task B) or baseline-based (eg taskA versus prestimulus period) comparisons This being saidour results readily apply to analysis of ongoing MEG signalssuch as MEG resting-state studies

5 Conclusions

In this study we address a simple question that has generallybeen overlooked in the field of MEG source reconstructionusing MNE should one use a different amount of regular-ization depending on whether one is interested in estimatinglocal activity or in detecting interareal connectivity Ourresults based on Monte-Carlo simulations (21600 sourceconfigurations) suggest that optimal results are obtainedwhen setting separate regularization coefficient to estimatethe source time series with MNE for the analysis of powerand coherence In particular coherence estimation in source-space is enhanced by using less regularization than what isused for spectral power analysis Furthermore we found thatSNR and the spatial extent of the source generally have astronger impact on lambda selection than coupling strengthThese results provide some practical guidelines for MNEusers and suggest in particular that one should regularizeone to two orders of magnitude less when performingconnectivity analysis compared to local spectral power esti-mations Ideally if one plans to run both power and couplinganalysis based onMNE source estimates two distinct inverseoperators should be implementedWhether the phenomenonobserved here may have similar implications or concerns inthe context of other inverse solutions is an interesting topicfor future research

Competing Interests

The authors declare they have no competing interests

Acknowledgments

Ana-Sofıa Hincapie was supported in part by a scholarshipfrom Comision Nacional de Ciencia y Tecnologıca de Chile(CONICYT) Colfuturo Colombia and by the French ANRproject ANR-DEFIS 09-EMER-002 CoAdapt The researchwas performed within the framework of the LABEX COR-TEX (ANR-11-LABX-0042) of Universite de Lyon withinthe program ANR-11-IDEX-0007 The authors would liketo thank the Academy of Finland (personal grant to JanKujala) TES Foundation KAUTE Foundation and OskarOflund Foundation for financial support Diego Cosmelliacknowledges support by FONDECYT Grant no 1130758


This research was also undertaken thanks to funding fromthe Canada Research Chairs program and a Discovery Grant(RGPIN-2015-04854) awarded by the Natural Sciences andEngineering Research Council of Canada to Karim JerbiTheauthors are also thankful to the computing center of theNational Institute for Nuclear Physics and Particle Physics(CC-IN2P3-CNRS Lyon)

References

[1] K Friston R Moran and A K Seth ldquoAnalysing connectivitywith Granger causality and dynamic causal modellingrdquo CurrentOpinion in Neurobiology vol 23 no 2 pp 172ndash178 2013

[2] J-M Schoffelen and J Gross ldquoSource connectivity analysis withMEG and EEGrdquoHuman BrainMapping vol 30 no 6 pp 1857ndash1865 2009

[3] J Gross S Baillet G R Barnes et al ldquoGood practice forconducting and reporting MEG researchrdquo NeuroImage vol 65pp 349ndash363 2013

[4] S Baillet J CMosher and RM Leahy ldquoElectromagnetic brainmappingrdquo IEEE Signal Processing Magazine vol 18 no 6 pp14ndash30 2001

[5] M Hamalainen R Hari R J Ilmoniemi J Knuutila and OV Lounasmaa ldquoMagnetoencephalography theory instrumen-tation and applications to noninvasive studies of the workinghuman brainrdquoReviews ofModern Physics vol 65 no 2 pp 413ndash497 1993

[6] M L Scholvinck D A Leopold M J Brookes and P HKhader ldquoThe contribution of electrophysiology to functionalconnectivity mappingrdquo NeuroImage vol 80 pp 297ndash306 2013

[7] H K M Meeren B de Gelder S P Ahlfors M S Hamalainenand N Hadjikhani ldquoDifferent cortical dynamics in face andbody perception anMEGstudyrdquoPLoSONE vol 8 no 9 ArticleID e71408 2013

[8] I SimanovaMA J vanGerven ROostenveld and PHagoortldquoPredicting the semantic category of internally generated wordsfrom neuromagnetic recordingsrdquo Journal of Cognitive Neuro-science vol 27 no 1 pp 35ndash45 2015

[9] F Lopes da Silva ldquoEEG and MEG relevance to neurosciencerdquoNeuron vol 80 no 5 pp 1112ndash1128 2013

[10] K Jerbi J-P Lachaux K N1015840Diaye et al ldquoCoherent neuralrepresentation of hand speed in humans revealed by MEGimagingrdquo Proceedings of the National Academy of Sciences of theUnited States of America vol 104 no 18 pp 7676ndash7681 2007

[11] A Schnitzler and J Gross ldquoNormal and pathological oscillatorycommunication in the brainrdquoNature Reviews Neuroscience vol6 no 4 pp 285ndash296 2005

[12] G C OrsquoNeill M Bauer M W Woolrich P G Morris G RBarnes and M J Brookes ldquoDynamic recruitment of restingstate sub-networksrdquo NeuroImage vol 115 pp 85ndash95 2015

[13] J Cabral H Luckhoo M Woolrich et al ldquoExploring mech-anisms of spontaneous functional connectivity in MEG howdelayed network interactions lead to structured amplitudeenvelopes of band-pass filtered oscillationsrdquo NeuroImage vol90 pp 423ndash435 2014

[14] L Marzetti S Della Penna A Z Snyder et al ldquoFrequencyspecific interactions of MEG resting state activity within andacross brain networks as revealed by the multivariate interac-tion measurerdquo NeuroImage vol 79 pp 172ndash183 2013

[15] J F Hipp D J Hawellek M Corbetta M Siegel and A KEngel ldquoLarge-scale cortical correlation structure of sponta-neous oscillatory activityrdquo Nature Neuroscience vol 15 no 6pp 884ndash890 2012

[16] F de Pasquale S Della Penna A Z Snyder et al ldquoA cortical corefor dynamic integration of functional networks in the restinghuman brainrdquo Neuron vol 74 no 4 pp 753ndash764 2012

[17] M J BrookesMWoolrichH Luckhoo et al ldquoInvestigating theelectrophysiological basis of resting state networks using mag-netoencephalographyrdquo Proceedings of the National Academy ofSciences of the United States of America vol 108 no 40 pp16783ndash16788 2011

[18] R N Henson J Mattout K D Singh G R Barnes AHillebrand and K Friston ldquoPopulation-level inferences for dis-tributed MEG source localization under multiple constraintsapplication to face-evoked fieldsrdquoNeuroImage vol 38 no 3 pp422ndash438 2007

[19] W-T Chang I P Jaaskelainen J W Belliveau et al ldquoCombinedMEG and EEG show reliable patterns of electromagnetic brainactivity during natural viewingrdquo NeuroImage vol 114 pp 49ndash56 2015

[20] C-H Cheng S Baillet F-J Hsiao and Y-Y Lin ldquoEffects ofaging on the neuromagnetic mismatch detection to speechsoundsrdquo Biological Psychology vol 104 pp 48ndash55 2015

[21] F-J Hsiao H-Y Yu W-T Chen et al ldquoIncreased intrinsicconnectivity of the default mode network in temporal lobeepilepsy evidence from resting-state MEG recordingsrdquo PLoSONE vol 10 no 6 Article ID e0128787 2015

[22] M S Hamalainen and R J Ilmoniemi ldquoInterpreting measuredmagnetic fields of the brain estimates of current distributionsrdquoTech Rep Helsinki University of Technology Department ofTechnical Physics 1984

[23] Y Attal and D Schwartz ldquoAssessment of subcortical sourcelocalization using deep brain activity imaging model withminimum norm operators a MEG studyrdquo PLoS ONE vol 8 no3 Article ID e59856 2013

[24] Y Kanamori H Shigeto N Hironaga et al ldquoMinimum normestimates in MEG can delineate the onset of interictal epilepticdischarges a comparison with ECoG findingsrdquo NeuroImageClinical vol 2 no 1 pp 663ndash669 2013

[25] O Hauk and M Stenroos ldquoA framework for the design offlexible cross-talk functions for spatial filtering of EEGMEGdata DeFleCTrdquoHuman Brain Mapping vol 35 no 4 pp 1642ndash1653 2014

[26] S Palva S Monto and J M Palva ldquoGraph properties ofsynchronized cortical networks during visual working memorymaintenancerdquo NeuroImage vol 49 no 4 pp 3257ndash3268 2010

[27] F-H Lin T Witzel S P Ahlfors S M Stufflebeam J WBelliveau andM S Hamalainen ldquoAssessing and improving thespatial accuracy in MEG source localization by depth-weightedminimum-norm estimatesrdquo NeuroImage vol 31 no 1 pp 160ndash171 2006

[28] J Mattout M Pelegrini-Issac L Garnero and H BenalildquoMultivariate source prelocalization (MSP) use of functionallyinformed basis functions for better conditioning the MEGinverse problemrdquoNeuroImage vol 26 no 2 pp 356ndash373 2005

[29] O David L Garnero D Cosmelli and F J Varela ldquoEstimationof neural dynamics from MEGEEG cortical current densitymaps application to the reconstruction of large-scale cortical


synchronyrdquo IEEE Transactions on Biomedical Engineering vol49 no 9 pp 975ndash987 2002

[30] O Hauk ldquoKeep it simple a case for using classical minimumnorm estimation in the analysis of EEG and MEG datardquoNeuroImage vol 21 no 4 pp 1612ndash1621 2004

[31] O Hauk D G Wakeman and R Henson ldquoComparison ofnoise-normalized minimum norm estimates for MEG analysisusing multiple resolution metricsrdquo NeuroImage vol 54 no 3pp 1966ndash1974 2011

[32] R Grave de Peralta Menendez O Hauk S Gonzalez AndinoH Vogt and C Michel ldquoLinear inverse solutions with optimalresolution kernels applied to electromagnetic tomographyrdquoHuman Brain Mapping vol 5 no 6 pp 454ndash467 1997

[33] A K Liu JW Belliveau andAMDale ldquoSpatiotemporal imag-ing of human brain activity using functional MRI constrainedmagnetoencephalography data Monte Carlo simulationsrdquo Pro-ceedings of the National Academy of Sciences of the United Statesof America vol 95 no 15 pp 8945ndash8950 1998

[34] K Matsuura and Y Okabe ldquoSelective minimum-norm solutionof the biomagnetic inverse problemrdquo IEEE Transactions onBiomedical Engineering vol 42 no 6 pp 608ndash615 1995

[35] A M Dale and M I Sereno ldquoImproved localization of corticalactivity by combining EEG and MEG with MRI corticalsurface reconstruction a linear approachrdquo Journal of CognitiveNeuroscience vol 5 no 2 pp 162ndash176 1993

[36] J-ZWang S J Williamson and L Kaufman ldquoMagnetic sourceimaging based on the minimum-norm least-squares inverserdquoBrain Topography vol 5 no 4 pp 365ndash371 1993

[37] M S Hamalainen and R J Ilmoniemi ldquoInterpreting magneticfields of the brain minimum norm estimatesrdquo Medical ampBiological Engineering amp Computing vol 32 no 1 pp 35ndash421994

[38] K Uutela M Hamalainen and E Somersalo ldquoVisualizationof magnetoencephalographic data using minimum currentestimatesrdquo NeuroImage vol 10 no 2 pp 173ndash180 1999

[39] P HansenM Kringelbach and R SalmelinMEG An Introduc-tion to Methods Oxford University Press New York NY USA2010

[40] J Sarvas ldquoBasic mathematical and electromagnetic conceptsof the biomagnetic inverse problemrdquo Physics in Medicine andBiology vol 32 no 1 pp 11ndash22 1987

[41] A Pascarella and A Sorrentino ldquoStatistical approaches to theinverse problemrdquo inMagnetoencephalography E W Pang EdInTech Rijeka Croatia 2011

[42] A N Tikhonov and V I Arsenin Solutions of Ill-PosedProblems Winston 1977

[43] M Foster ldquoAn application of the Wiener-Kolmogorov smooth-ing theory to matrix inversionrdquo Journal of the Society forIndustrial and Applied Mathematics vol 9 no 3 pp 387ndash3921961

[44] C Phillips J Mattout M D Rugg P Maquet and K J FristonldquoAn empirical Bayesian solution to the source reconstructionproblem in EEGrdquoNeuroImage vol 24 no 4 pp 997ndash1011 2005

[45] P L Nunez and R Srinivasan Electric Fields of the Brain TheNeurophysics of EEG Oxford University Press 2006

[46] A M Dale A K Liu B R Fischl et al ldquoDynamic statisticalparametric mapping combining fMRI and MEG for high-resolution imaging of cortical activityrdquo Neuron vol 26 no 1pp 55ndash67 2000

[47] F-H Lin T Witzel M S Hamalainen A M Dale J WBelliveau and S M Stufflebeam ldquoSpectral spatiotemporalimaging of cortical oscillations and interactions in the humanbrainrdquo NeuroImage vol 23 no 2 pp 582ndash595 2004

[48] B Fischl ldquoFreeSurferrdquo NeuroImage vol 62 no 2 pp 774ndash7812012

[49] F Tadel S Baillet J C Mosher D Pantazis and R MLeahy ldquoBrainstorm a user-friendly application for MEGEEGanalysisrdquoComputational Intelligence andNeuroscience vol 2011Article ID 879716 13 pages 2011

[50] R Oostenveld P Fries E Maris and J-M Schoffelen ldquoField-Trip open source software for advanced analysis of MEGEEG and invasive electrophysiological datardquo ComputationalIntelligence and Neuroscience vol 2011 Article ID 156869 9pages 2011

[51] P C Hansen ldquoAnalysis of discrete ill-posed problems by meansof the L-curverdquo SIAM Review vol 34 no 4 pp 561ndash580 1992

[52] P D Welch ldquoThe use of fast Fourier transform for the estima-tion of power spectra a method based on time averaging overshortmodified periodogramsrdquo IEEETransactions onAudio andElectroacoustics vol 15 no 2 pp 70ndash73 1967

[53] E Kucukaltun-Yildirim D Pantazis and R M Leahy ldquoTask-based comparison of inverse methods in magnetoencephalog-raphyrdquo IEEETransactions on Biomedical Engineering vol 53 no9 pp 1783ndash1793 2006

[54] A Gramfort M Luessi E Larson et al ldquoMNE software forprocessing MEG and EEG datardquo NeuroImage vol 86 pp 446ndash460 2014

[55] FDarvasD Pantazis E Kucukaltun-Yildirim andRM LeahyldquoMapping human brain function with MEG and EEG methodsand validationrdquo NeuroImage vol 23 supplement 1 pp S289ndashS299 2004

[56] C Grova J Daunizeau J-M Lina C G Benar H Benaliand J Gotman ldquoEvaluation of EEG localization methods usingrealistic simulations of interictal spikesrdquo NeuroImage vol 29no 3 pp 734ndash753 2006

[57] J Mattout C Phillips W D Penny M D Rugg and K JFriston ldquoMEG source localization under multiple constraintsan extended Bayesian frameworkrdquo NeuroImage vol 30 no 3pp 753ndash767 2006

[58] R A Chowdhury J M Lina E Kobayashi and C GrovaldquoMEG source localization of spatially extended generators ofepileptic activity comparing entropic and hierarchical bayesianapproachesrdquo PLoS ONE vol 8 no 2 Article ID e55969 2013

[59] T Yu ldquoROCS receiver operating characteristic surface for class-skewed high-throughput datardquo PLoS ONE vol 7 no 7 ArticleID e40598 2012

[60] R Bunescu R Ge R J Kate et al ldquoComparative experimentson learning information extractors for proteins and theirinteractionsrdquoArtificial Intelligence inMedicine vol 33 no 2 pp139ndash155 2005

[61] M Goadrich L Oliphant and J Shavlik ldquoLearning ensemblesof first-order clauses for recall-precision curves a case study inbiomedical information extractionrdquo in Inductive Logic Program-ming R Camacho R King and A Srinivasan Eds vol 3194 ofLecture Notes in Computer Science pp 98ndash115 Springer BerlinGermany 2004

[62] M Craven and J Bockhorst ldquoMarkov networks for detectingoveralpping elements in sequence datardquo in Advances in Neural


Information Processing Systems 17 L K Saul Y Weiss and LBottou Eds pp 193ndash200 MIT Press 2005

[63] J Davis andM Goadrich ldquoThe relationship between Precision-Recall and ROC curvesrdquo in Proceedings of the 23rd InternationalConference on Machine Learning (ICML rsquo06) pp 233ndash240 NewYork NY USA June 2006

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Distributed Sensor Networks


Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014


ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014


Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications


Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia


Biomedical Imaging


ArtificialNeural Systems

Advances in


RoboticsJournal of



Computational Intelligence and Neuroscience

Industrial EngineeringJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in



The ability to measure brain interactions at the sourcelevel rather than between sensor channels is an importantprerequisite if we want to make useful inferences aboutthe anatomical-functional properties of the network Tothis end source reconstruction techniques are applied inorder to estimate the spatiotemporal activity of the corticalgenerators underlying the recorded sensor-level MEG dataSolving this relationship is an ill-posed inverse problem forwhich numerous methods have been developed [4] Thedifferences between the various techniquesmainly stem fromthe assumptions theymake about the properties of the neuralsources and from the way they incorporate various forms ofa priori information if any is available Conceptually solvingthe MEG inverse problem boils down to solving a system ofequations that is underdetermined (ie no unique solution)since we generally have far more sources (thousands) thanmeasurements (hundreds) Identifying a solution to such aproblem can be achieved by imposing constraints on thesources A typical constraint is to minimize the source powerAmong thesemethods theMinimumNormEstimate (MNE)relies on minimizing the L2-norm and is one of the mostwidely used techniques [4 7 8 18ndash37] By contrast estimatesobtained by minimizing the L1-norm are referred to asMinimum-Current Estimates (MCE) [34 38] While the L2-norm assumes a Gaussian a priori current distribution theL1-norm assumes a Laplacian distribution [39]

In principle MNE looks for a distribution of sourceswith the minimum (L2-norm) current that can give the bestaccount of the measured data As the problem is ill-posedMNE generally uses a regularization procedure that sets thebalance between fitting the measured data (minimizing theresidual) and minimizing the contributions of noise [22 4041]The Tikhonov orWiener regularization [42 43] and SVDtruncation are among the most widely used regularizationprocedures Regularization may be considered a necessaryevil it is required to stabilize the solution of the inverseproblem yet too much regularization leads to overly smoothsolutions (spatial smearing) Since we do not have a precisemodel of brain activity and noise the choice of the optimalamount of regularization is a nontrivial step for which nomagical recipe exists [44] The relationship between optimalregularization and the patterns of underlying generators isstill poorly understood In particular the effect of regulariza-tion on the detection accuracy of Minimum Norm Estimatesof source power and interareal source coupling has not beenthoroughly investigated This raises the question of whetherone should use the same regularization coefficient for MNE-based power and connectivity analyses as is generally doneor would one benefit from optimizing the regularizationcoefficients separately for each analysis Furthermore howdoes the optimal regularization coefficient in such configu-rations depend on sensor-level SNR source size or couplingstrength

With these questions in mind we performed exten-sive Monte-Carlo simulations creating over 20000 pairsof coupled oscillatory time series in MEG source spacesand computed the resulting surface MEG recordings Thenwe estimated source power and coherence using the MNEframework with variable degrees of Tikhonov regularization

Moreover we used an approach based on an area under thecurve (AUC) to identify the optimal regularization coefficient(lambda) in the case of power and coherence analyses Wefound a systematic difference between the optimal lambdasin each analysis for source-level coherence analysis theoptimal lambda was two orders of magnitude smaller thanthe best lambda for power detection Lastly our findings arebroken down as a function of SNR cortical patch size andcorticocortical coupling strength

2 Methods and Materials

In this section we first present the MEG inverse problemformulation and the MNE framework Then we describethe simulation reconstruction and performance assessmentprocedures

21TheMEG Inverse Problem The inverse problem looks foran estimation of the active sources S (3119899sources times time points)that generates the measurements M (119899channels times time points)recorded at the sensors The dimension 3119899 of the columnsof S accounts for the three components of the source 119899in the 119909 119910 and 119911 directions According to anatomicalobservations the main generators of MEG are located inthe grey matter and their orientation is perpendicular to thecortical sheet [45] Here we used a constrained orientationapproach (perpendicular to the cortical surface) and hencethe dimensions of S are reduced to 119899sources times time pointsAssuming a linear relationship between the measurementsand the active sources the problem is modeled as

M = LS + N (1)

where L is the lead field matrix (119899channels times 119899sources) and Nis additive noise applied at the MEG channels (119899sources timestime points)The lead fieldmatrix describes how each sourcecontributes to the measurements at each sensor given aspecific head conductivity model and a source space As thenumber of sources is usually much higher than the numberof sensors the lead field matrix is highly underdeterminedand thus not invertible The estimation of the activity of thesources requires the definition of an inverse operatorW

S =W119879M (2)

where S represents the estimated sources (119899sources timestime points) and the superscript 119879 denotes matrix transpose

22 Minimum Norm Estimate (MNE) As the MEG inverseproblem is ill-posed a regularization scheme is needed [22]and one of the most common options is the Tikhonovregularization [42 43] MNE calculates an inverse operatorW by searching for a distribution of sources Swithminimumcurrents (L2-norm) that produces an estimation of themeasurements (LS) most consistent with the measured data(M) The solution is a trade-off between the norm of theestimated regularized sources current 1205822S2 and the normof the quality of the fit they provide to the measurementsM minus LS2 Assuming the noise N and the sources strength




2

+ 1205822 10038171003817100381710038171003817Rminus12S10038171003817100381710038171003817

2

(3)


W = RL119879 (LRL119879 + 1205822Q)minus1

(4)

















119875 (119903 119891) = Cs (119903 119903 119891)

Coh (1199031 1199032 119891) =

1003816100381610038161003816Cs (1199031 1199032 119891)1003816100381610038161003816

2

119875 (1199031 1199031 119891) 119875 (119903

2 1199032 119891)

(5)




FPF (120572)

=FP (120572)


(6)


3 Results









1

08

06

04

02


Mea

n AU

C


Lambda

1

08

06

04

02


Mea

n AU

C

Lambda


(a)

1

09

08

07

06

05

04

03

02

01

0

Mea

n AU


lowast

lowast


(b)



4 Discussion






1

08

06

04

02

0

1

08

06

04

02

0





(a)

1

08

06

04

02

0

1

08

06

04

02

0


8 cm2


8 cm2



(b)

1

08

06

04

02

0

1

08

06

04

02

0

01 02 04

01 02 04



1e minus 11

1e minus 10

1e minus 09

1e minus 08

1e minus 07

1e minus 06

1e minus 05

Lambda

(c)






1

08

06

04

02

0

1

08

06

04

02

0

Mea

n AU

CM

ean

AUC

Power

Coherence

(a)

Lambda

(b)

(c)

(d)

lowast


05

10

05

10





Source 1(seed)

Source 2

Size = 4 cm2

Coherence = 04

SNR = 0dB

Coherence detection













5 Conclusions


Competing Interests


Acknowledgments




References











































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






2

+ 1205822 10038171003817100381710038171003817Rminus12S10038171003817100381710038171003817

2

(3)


W = RL119879 (LRL119879 + 1205822Q)minus1

(4)

















119875 (119903 119891) = Cs (119903 119903 119891)

Coh (1199031 1199032 119891) =

1003816100381610038161003816Cs (1199031 1199032 119891)1003816100381610038161003816

2

119875 (1199031 1199031 119891) 119875 (119903

2 1199032 119891)

(5)




FPF (120572)

=FP (120572)


(6)


3 Results









1

08

06

04

02


Mea

n AU

C


Lambda

1

08

06

04

02


Mea

n AU

C

Lambda


(a)

1

09

08

07

06

05

04

03

02

01

0

Mea

n AU


lowast

lowast


(b)



4 Discussion






1

08

06

04

02

0

1

08

06

04

02

0





(a)

1

08

06

04

02

0

1

08

06

04

02

0


8 cm2


8 cm2



(b)

1

08

06

04

02

0

1

08

06

04

02

0

01 02 04

01 02 04



1e minus 11

1e minus 10

1e minus 09

1e minus 08

1e minus 07

1e minus 06

1e minus 05

Lambda

(c)






1

08

06

04

02

0

1

08

06

04

02

0

Mea

n AU

CM

ean

AUC

Power

Coherence

(a)

Lambda

(b)

(c)

(d)

lowast


05

10

05

10





Source 1(seed)

Source 2

Size = 4 cm2

Coherence = 04

SNR = 0dB

Coherence detection













5 Conclusions


Competing Interests


Acknowledgments




References











































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






119875 (119903 119891) = Cs (119903 119903 119891)

Coh (1199031 1199032 119891) =

1003816100381610038161003816Cs (1199031 1199032 119891)1003816100381610038161003816

2

119875 (1199031 1199031 119891) 119875 (119903

2 1199032 119891)

(5)




FPF (120572)

=FP (120572)


(6)


3 Results









1

08

06

04

02


Mea

n AU

C


Lambda

1

08

06

04

02


Mea

n AU

C

Lambda


(a)

1

09

08

07

06

05

04

03

02

01

0

Mea

n AU


lowast

lowast


(b)



4 Discussion






1

08

06

04

02

0

1

08

06

04

02

0





(a)

1

08

06

04

02

0

1

08

06

04

02

0


8 cm2


8 cm2



(b)

1

08

06

04

02

0

1

08

06

04

02

0

01 02 04

01 02 04



1e minus 11

1e minus 10

1e minus 09

1e minus 08

1e minus 07

1e minus 06

1e minus 05

Lambda

(c)






1

08

06

04

02

0

1

08

06

04

02

0

Mea

n AU

CM

ean

AUC

Power

Coherence

(a)

Lambda

(b)

(c)

(d)

lowast


05

10

05

10





Source 1(seed)

Source 2

Size = 4 cm2

Coherence = 04

SNR = 0dB

Coherence detection













5 Conclusions


Competing Interests


Acknowledgments




References











































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




1

08

06

04

02


Mea

n AU

C


Lambda

1

08

06

04

02


Mea

n AU

C

Lambda


(a)

1

09

08

07

06

05

04

03

02

01

0

Mea

n AU


lowast

lowast


(b)



4 Discussion






1

08

06

04

02

0

1

08

06

04

02

0





(a)

1

08

06

04

02

0

1

08

06

04

02

0


8 cm2


8 cm2



(b)

1

08

06

04

02

0

1

08

06

04

02

0

01 02 04

01 02 04



1e minus 11

1e minus 10

1e minus 09

1e minus 08

1e minus 07

1e minus 06

1e minus 05

Lambda

(c)






1

08

06

04

02

0

1

08

06

04

02

0

Mea

n AU

CM

ean

AUC

Power

Coherence

(a)

Lambda

(b)

(c)

(d)

lowast


05

10

05

10





Source 1(seed)

Source 2

Size = 4 cm2

Coherence = 04

SNR = 0dB

Coherence detection













5 Conclusions


Competing Interests


Acknowledgments




References











































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




1

08

06

04

02

0

1

08

06

04

02

0





(a)

1

08

06

04

02

0

1

08

06

04

02

0


8 cm2


8 cm2



(b)

1

08

06

04

02

0

1

08

06

04

02

0

01 02 04

01 02 04



1e minus 11

1e minus 10

1e minus 09

1e minus 08

1e minus 07

1e minus 06

1e minus 05

Lambda

(c)






1

08

06

04

02

0

1

08

06

04

02

0

Mea

n AU

CM

ean

AUC

Power

Coherence

(a)

Lambda

(b)

(c)

(d)

lowast


05

10

05

10





Source 1(seed)

Source 2

Size = 4 cm2

Coherence = 04

SNR = 0dB

Coherence detection













5 Conclusions


Competing Interests


Acknowledgments




References











































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




1

08

06

04

02

0

1

08

06

04

02

0

Mea

n AU

CM

ean

AUC

Power

Coherence

(a)

Lambda

(b)

(c)

(d)

lowast


05

10

05

10





Source 1(seed)

Source 2

Size = 4 cm2

Coherence = 04

SNR = 0dB

Coherence detection













5 Conclusions


Competing Interests


Acknowledgments




References











































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










5 Conclusions


Competing Interests


Acknowledgments




References











































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





References











































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in













Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



Documents

Research Article MEG Connectivity and Power Detections ... - neuro…neuro.hut.fi/~jjkujala/pdfs/hincapie_et_al_CIN_2016.pdf · MEG Connectivity and Power Detections with Minimum