Network structure of the human musculoskeletal system ... · 08.01.2018 · The human body is a...

Networkstructureofthehumanmusculoskeletalsystem

shapesneuralinteractionsonmultipletimescales

JenniferN.Kerkmana,AndreasDaffertshofera,LeonardoL.Gollob,Michael

Breakspearb,c,TjeerdW.Boonstrab,d,1

aDepartmentofHumanMovementSciences,FacultyofBehaviouralandMovement

Sciences,VrijeUniversiteitAmsterdam,AmsterdamMovementSciences&InstituteforBrainandBehaviorAmsterdam,Amsterdam,theNetherlands

bQIMRBerghoferMedicalResearchInstitute,Brisbane,AustraliacMetroNorthMentalHealthService,Brisbane,QLD,Australia

dBlackDogInstitute,UniversityofNewSouthWales,Sydney,Australia

1Correspondingauthor

TjeerdBoonstra,BlackDogInstitute,HospitalRd,SydneyNSW2031,Australia.

Email:[email protected]

not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprint (which wasthis version posted January 8, 2018. ; https://doi.org/10.1101/181818doi: bioRxiv preprint

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Abstract

Humanmotorcontrolrequiresthecoordinationofmuscleactivityunderthe

anatomicalconstraintsimposedbythemusculoskeletalsystem.Interactions

withinthecentralnervoussystemarefundamentaltomotorcoordination,butthe

principlesgoverningfunctionalintegrationremainpoorlyunderstood.Weused

networkanalysistoinvestigatetherelationshipbetweenanatomicaland

functionalconnectivityamongst36muscles.Anatomicalnetworksweredefinedby

thephysicalconnectionsbetweenmusclesandfunctionalnetworkswerebasedon

intermuscularcoherenceassessedduringposturaltasks.Wefoundamodular

structureoffunctionalnetworksthatwasstronglyshapedbytheanatomical

constraintsofthemusculoskeletalsystem.Musclenetworksexhibitedamultilayer

architecturewithfunctionalinteractionsatdistincttimescales.Changesinpostural

taskswereassociatedwithafrequency-dependentreconfigurationofthecoupling

betweenfunctionalmodules.Combined,thesefindingssuggestthesespectral

modesmaysignifyacoordinativestructureforflexiblyorganisingmuscleactivity

duringposturalcontrol.Morebroadly,ourmulti-levelnetworkapproachtothe

motorsystemoffersauniquewindowintothecoordinatedneuralcircuitrythat

generatessynergisticinputtomusclesindifferentbehaviours.


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Introduction

Thehumanbodyisacomplexsystemconsistingofmanysubsystemsand

regulatorypathways.Themusculoskeletalsystemgivesthebodystructureand

createstheabilitytomove.Itismadeupofmorethan200skeletalbones,

connectivetissueandover600skeletalmuscles[1].Musclesareattachedtobones

throughtendinoustissueandcangeneratemovementaroundajointwhenthey

contract.Thecentralnervoussystemcontrolsthesemovementsthroughthespinal

motorneurons,whichserveasthefinalcommonpathwaytothemuscles[2].

Whiletheanatomicalandphysiologicalcomponentsofthemusculoskeletalsystem

arewellcharacterized[3,4],theorganisationalprinciplesofneuralcontrolremain

poorlyunderstood.Hereweelucidatetheinterplaybetweentheanatomical

structureofthemusculoskeletalsystemandthefunctionalorganisationof

distributedneuralcircuitryfromwhichmotorbehavioursemerge.

Thetraditionalideathatthecortexcontrolsmusclesinaone-to-onefashionhas

beenchallengedbyseverallinesofevidence[5,6].Forexample,itiswidely

recognizedthatthemanydegrees-of-freedom(DOFs)ofthemusculoskeletal

systemprohibitasimpleone-to-onecorrespondencebetweenamotortaskanda

particularmotorsolution;rathermusclesarecoupledandcontrolledin

conjunction[7].Acouplingbetweenmuscles–whethermechanicalorneural–

reducesthenumberofeffectiveDOFsandhencethenumberofpotential

movementpatterns.Thiscouplingtherebyreducesthecomplexityofmotor

control[8,9].

Thereiscontinuingdebateaboutthenatureofthecouplingbetweenmuscles.The

mechanicalcouplinginthemusculoskeletalsystemconstrainsthemovement

patternsthatcanbegenerated[10,11].Forexample,thebiomechanicsofthelimb

constrainrelativechangesinmusculotendonlengthtoalowdimensional

subspace,resultingincorrelatedafferentinputstospinalmotorneurons[12].The

couplingbetweenmusclescouldalsoresultfromredundanciesintheneural

circuitrythatdrivesspinalmotorneurons[13].Electrophysiologicalstudiesreveal

thatacombinationofonlyafewcoherentmuscleactivationpatterns–ormuscle

synergies–cangenerateawidevarietyofnaturalmovements[14,15].Someof


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thesepatternsarealreadypresentfrombirthanddonotchangeduring

development,whereasotherpatternsarelearned[16].Thissupportsthenotion

thattheneuromuscularsystemhasamodularorganisationthatsimplifiesthe

controlproblem[17,18].Spinalcircuitryconsistingofanetworkofpremotor

interneuronsandmotorneuronsmaygeneratebasicmovementpatternsby

mediatingthesynergisticdrivetomultiplemuscles[19,20].Stimulationof

interneuronalregionsinthespinalcordshowsthatthesemicrocircuitsare

organisedintodiscretemodules,eachgeneratingaspecificpatternofmuscular

forces[21,22].Thesespinalnetworksmayencodecoordinatedmotoroutput

programs[23],whichcanbeusedtotranslatedescendingcommandsformulti-

jointmovementsintotheappropriatecoordinatedmusclesynergiesthatunderpin

thosemovements[4].

Networktheorycanprovideanalternativeperspectiveonthemodular

organisationofthemusculoskeletalsystem.Oneofthemostrelevantfeaturesof

complexnetworksarecommunityormodularstructures,whichrefertodensely

connectedgroupsofnodeswithonlysparserconnectionsbetweenthesegroups

[24,25].Theinvestigationofcommunitystructureshasbeenwidelyusedin

differentdomainssuchasmetabolic[26]andbrainnetworks[27].Ithasrecently

beenappliedtoinvestigatethestructureandfunctionofthemusculoskeletal

system:Theanatomicalnetworkcanbeconstructedbymappingtheoriginand

insertionofmuscles[28,29].Previously,wehaveshownhowfunctionalmuscle

networkscanbeconstructedbyassessingintermuscularcoherencefromsurface

electromyography(EMG)recordedfromdifferentmuscles[30].Thesefunctional

networksrevealfunctionalconnectivitybetweengroupsofmusclesatmultiple

frequencybands.CoherencebetweenEMGsindicatescorrelatedorcommoninputs

tospinalmotorneuronsthataregeneratedbysharedstructuralconnectionsor

synchronisationwithinthemotorsystem[13,31-33].Functionalconnectivity

patternshenceallowtoassessstructuralpathwaysinthemotorsystemusingnon-

invasiverecordings[34].

Hereweinvestigatetheorganisationalprinciplesgoverninghumanmotorcontrol

bycomparingthecommunitystructureofanatomicalandfunctionalnetworks.We


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usemultiplexmodularityanalysis[35]toassessthecommunitystructureof

functionalmusclenetworksacrossfrequenciesandposturaltasks.As

biomechanicalpropertiesofthemusculoskeletalsystemconstrainthemovement

patternsthatcanbegenerated,weexpectasimilarcommunitystructurefor

anatomicalandfunctionalmusclesnetworks.Deviationsincommunitystructure

indicateadditionalconstraintsimposedbythecentralnervoussystem.Wealso

comparefunctionalconnectivitybetweenmodulesduringdifferenttasks

conditionstoinvestigatechangesinfunctionalorganisationduringbehaviour.

Whileaveragefunctionalconnectivityisconstrainedbyanatomicalconstraints,we

expectthatfunctionalmusclenetworksreconfiguretoenabletask-dependent

coordinationpatternsbetweenmuscles.Suchtaskmodulationswouldindicate

thatfunctionalinteractionsbetweenmusclesarenothard-wired,butareinstead

governedbydynamicconnectivityinthecentralnervoussystemthatisshapedby

theanatomicaltopologyofthemusculoskeletalsystem.

Results

Anatomicalmusclenetwork

Weassessedtherelationshipbetweenanatomicalandfunctionalconnectivityof

keymusclesinvolvedintheposturalcontroltasks(36musclesdistributed

throughoutthebody).Weinvestigatedamuscle-centricnetworkinwhichthe

nodesrepresentthemusclesandtheedgesofthenetworkareanatomical

connectionsorfunctionalrelationsbetweenmuscles.Anatomicalmusclenetworks

weredefinedbymappingthephysicalconnectionsbetweenmusclesandbones

[28],whichformabipartitenetwork[29].Theanatomicalnetworkconstituteda

denselyconnected,symmetricalnetwork(Fig.1;networkdensityis0.27).

Modularityanalysisrevealedfivemodulesthatdividedtheanatomicalmuscle

networkintothemainbodysegments(rightarm,leftarm,torso,rightlegandleft

leg)withamodularityof0.38.


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Figure1.Communitystructureoftheanatomicalmusclenetwork.A)Topological

representationoftheanatomicalnetwork.Thenodesofthenetworkrepresentthemusclesandedgesrepresentanatomicalconnectionsbetweenmusclesthatareattachedtothesamebonesorcartilages.Thefivemodulesarecolour-coded.B)Spatialrepresentationofanatomicalmusclenetworkdisplayedonthehumanbody[36].Thesize

ofeachnoderepresentsthenumberofothernodesitisconnectedto.

Functionalmusclenetwork

Functionalmusclenetworksweredefinedbymappingcorrelatedinputsbetween

muscles.Tomapfunctionalnetworks,wemeasuredsurfaceEMGfromthesame36

muscleswhilehealthyparticipantsperformeddifferentposturaltasks.Afull

factorialdesignwasusedinwhichwevariedposturalcontrol(normalstanding,

instabilityinanterior-posteriorormedial-lateraldirection)andpointing

behaviour(nopointing,pointingwiththedominanthandorwithbothhands;see

Methodsfordetails).Weassessedfunctionalconnectivitybymeansof

intermuscularcoherencebetweenallmusclecombinationsandusednon-negative

matrixfactorisation(NNMF)todecomposethesecoherencespectraintofrequency

componentsandcorrespondingedgeweights.Thisyieldedasetofweighted

networkswiththeircorrespondingspectralfingerprints(frequencycomponents).


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Weobservedfourseparatefrequencycomponents(component1:0-3Hz,

component2:3-11Hz,component3:11-21Hz,component4:21-60Hz;Fig.2A),

whichserveasseparatelayersofamultiplexnetworkandexplainedmostofthe

varianceofthecoherencespectra(R2=0.90).Weightswerethresholdedtoobtain

aminimallyconnectedbinarynetworkacrosslayersandtokeepthenumberof

edgesconstantacrosslayers(relativethresholdof0.035).Usingmultiplex

modularityanalysis,weobtainedafixedcommunitystructureacrossallfour

frequenciesandnineconditions,whichrevealedsixmodules:rightupperarm

(rUA),bilateralforearms(FA),torso(T),rightupperleg(rUL),leftupperleg(lUL)

andbilaterallowerlegs(LL)(Fig.2B).Figure2Cdepictshowthesemodulesare

distributedacrossthebody.Distinctnetworktopologieswereobservedacross

layerswithamorewidelyconnectednetworkatlowerfrequenciesandmore

partitionednetworkathigherfrequencies:networkdensitywas0.10,0.09,0.08,

and0.06forcomponents1to4,respectively(Fig.2D).

Figure2.Communitystructureofmultiplexfunctionalmusclenetworks.A)ThefrequencyspectraofthefourcomponentsobtainedusingNNMF.B)Multiplexcommunitystructureoffunctionalmusclenetworkacrosslayersandconditions.Thedominanthand

ofallparticipantsisdisplayedontherightsideofthehumanbody.C)Spatialrepresentationoftheaveragemusclenetworkdisplayedonthehumanbody[36].Thesizeofthenodesrepresentsthenumberofothernodesitisconnectedtoandthewidthoftheedgestheaverageweight.D)Thebinarymusclenetworksforeachlayer.


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Comparisonbetweenanatomicalandfunctionalnetworks

Thecommunitystructuresoftheanatomicalandfunctionalmusclenetworkswere

verysimilar(Randindex=0.80,adjustedRandindex=0.36,P<0.001).Amarked

differencebetweenanatomicalandfunctionalnetworksisthebilateral

connectionsbetweenhomologousforearmandlowerlegmusclesinthefunctional

networks,whichwereabsentintheanatomicalnetwork.Thisisreflectedinthe

communitystructureofthefunctionalnetworks,wherebilaterallowerlegmuscles

andbilateralforearmmusclesweregroupedinmodules.

Figure3.Relationshipbetweenfunctionalconnectivityandanatomicaldistance.A)Adjacencyanddistancematrixoftheanatomicalmusclenetwork.Maximumanatomicaldistance(pathlength)is4.B)Percentageoffunctionaledgesofthresholdednetworksacrossexperimentalconditionsasafunctionofanatomicaldistance.C)Distributionof

edgeweightsoffunctionalnetworksasafunctionofanatomicaldistanceforeachlayer.Weightswereaveragedacrossexperimentalconditions.Edgesconnectingmuscleswithinthesamemodulearecolour-coded(rUA:rightupperarm,FA:bilateralforearms,T:torso,rUL:rightupperleg,lUL:leftupperleg,andLL:bilaterallowerlegs)andgreydots

representedgesbetweenmodules.


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Thecomparisonbetweenanatomicaldistance(pathlength)andfunctional

connectivityrevealedthatanatomicallynearbynodesaremorelikelytoreceive

commoninput(Fig.3A).Wefirstexaminedthepercentageofallpossibleedges,i.e.

thenumberofedgesabovethreshold,whichdecreasedasafunctionofanatomical

distance:11.3%,0.9%,0.6%and0.0%foranatomicaldistance1to4,respectively.

Thisdeclinewithdistancewasevenmorepronouncedforthehigherfrequency

components(Fig.3B).Next,weexaminedthedistributionoffunctionalweightsas

afunctionofanatomicaldistance.Thehighestweightswereobservedforedges

connectingmuscleswithinthesamemodule.Theedgeswithinmostmoduleshad

ananatomicaldistanceof1.Onlyafewedgeshadananatomicaldistanceof2or3

andalloftheseedgeswerecontainedintheFAandLLmodules.Inparticular,

edgesconnectingbilaterallowerlegmuscles(LL)showedrelativelargeweightsat

ananatomicaldistanceof3(Fig.3C).

Task-dependentmodulations

Wenextsoughttostudytheinfluenceoftaskonthisstructure-function

relationship.Thiswasachievedbyemployingclusteredgraphstocompare

functionalmusclenetworksacrosstaskconditions.Thefunctionalmodules

identifiedusingtheprecedingmultiplexmodularityanalysisformthenodesof

theseclusteredgraphs.Figure4Ashowstheclusteredgraphsinthenine

experimentalconditionsandforthefourlayers.Theclusteredgraphswerevery

sparse,asmoduleshavedensewithinmoduleconnectionsbutsparseconnections

betweennodesinothermodules.Mostedgeswereobservedbetweenlegmuscles

modules(LL,rULandlUL)atthelowestfrequencycomponents(0-3and3-11Hz),

inparticularwhenposturalstabilitywaschallengedbyinstabilityinanterior-

posteriorormedial-lateraldirection.Edgesbetweenthearmmusclemodules(rUA

andFA)andthetorso(T)weremainlyobservedatthehigherfrequency

components(11-21and21-60Hz)duringpointing(unimanualandbimanual).


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Figure4.Clusteredgraphsoffunctionalmusclenetworksacrossconditions.A)Theclusteredgraphsinthenineexperimentalconditions(columns)andforeverylayer

(rows).Thenodesarethemodulesidentifiedusingmultiplexmodularityanalysis.Nodesizerepresentsthenetworkdensitywithinandthewidthoftheedgestheconnectiondensitybetweenmodules.B)Spatialrepresentationofthefunctionalmodulesonthehumanbody:rightupperarm(rUA),bilateralforearms(FA),torso(T),rightupperleg(rUL),leftupperleg(lUL)andbilaterallowerlegs(LL).Weusedtoolboxesforgeometry

processingtogeneratethecolouredmeshes[37]anddisplayitonthehumanbody[36].C)Significantdifferencesinclusteredgraphsbetweenthestabilityconditions.Twocontrastswereassessed:normalstability–anterior-posteriorinstabilityandnormalstability–medial-lateralinstability.Apermutationtestwasusedwithasignificancethreshold

correctedformultiplecomparisons(P<0.0033).Significantdifferencesarecolour-coded:Reddepictsanincreaseandblueadecreaseintheaverageweights.D)Significantdifferencesinclusteredgraphsbetweenthepointingconditions.Twocontrastswereassessed:nopointing–unimanualpointingandnopointing–bimanualpointing.


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Theeffectsofthestabilitytaskswerelargelyconfinedtothelegmodules(Fig.4C).Increasedconnectivitywasobservedduringposturalinstability(anterior-posteriorandmedial-lateral)comparedtonormalstandingwithinmostfrequencycomponents.Atthelowestfrequencycomponent(0-3Hz),connectivityincreasedwithinandbetweenmostlegmodules(pcorrected<0.01).Onlysmalldifferenceswereobservedat3-11Hz:increasedconnectivitybetweenthetorso(T)andlowerleg(LL)modulesduringanterior-posteriorinstability(+25%,range[-9,46%],pcorrected=0.01)anddecreasedconnectivitywithinthetorsomoduleduringmedial-lateralinstability(-21%,range[-50,0.3%],pcorrected=0.01).Connectivityincreasedagainatthehighestfrequencycomponents(11-21and21-60Hz)withinandbetweenthetorsoandlegmodules(rUL,lUL,andLL,pcorrected<0.02).

Thepointingtasksshowedadifferentpatterncomparedtotheposturaltasks,but

theeffectsofunimanualandbimanualpointingwereverysimilar(Fig.4D).During

pointing,connectivitydecreasedwithinthetorso(T)moduleatthelowest

frequencycomponents(0-3Hz,-61%,range[-90,-1%],pcorrected<0.005;3-11Hz,-

59%,range[-86,2%],pcorrected<0.02)andbetweenthetorsoandtherightupper

arm(rUA)moduleonlyatthelowestfrequencycomponent(0-3Hz,-67%,range[-

93,-9%],pcorrected<0.005).Incontrast,asignificantincreaseinconnectivitywithin

therUAmodulewasobservedduringunimanualpointcomparedtonopointingat

thehighestfrequencycomponents(11-21Hz,+64%,range[-4,95%],pcorrected=

0.005;21-60Hz,+66%,range[-12,93%],pcorrected=0.015).Inaddition,therewas

increasedconnectivitybetweenthetorsoandtheforearm(FA)modules(+41%,

range[-8,82%],pcorrected<0.01)andbetweenrUAandFA(+44%,range[0,82%],

pcorrected<0.005)duringpointing(unimanualandbimanual)comparedtono

pointingatfrequencycomponent3(11-21Hz).

Discussion

Weusedanetworkapproachtostudythestructure-functionrelationshipofthe

humanmusculoskeletalsystem.Severalprinciplesofthefunctionalrelationship

betweenmuscleswereuncovered:(i)Functionalconnectivitypatternsbetween

musclesarestronglyshapedbytheanatomicalconstraintsofthemusculoskeletal

system,withfunctionalconnectivitystrongestwithinanatomicalmodulesand

decreasedasafunctionofanatomicaldistance;(ii)Bilateralconnectivitybetween


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thehomologousupperandlowerextremitiesisakeycharacteristicofthe

functionalmusclenetworks;(iii)Thefunctionalrelationshipsaretask-dependent

withposturaltasksdifferentiallyimpactinguponfunctionalconnectivityat

differentfrequencyranges.Theuseofamultiplexapproachallowstheintegration

offunctionalmusclenetworksacrossfrequenciesandprovidesaunifyingwindow

intothedistributedcircuitryofthehumancentralnervoussystemthatcontrols

movementsbyinnervatingthespinalmotorneurons.

Identifyingrelationshipsbetweenanatomicalandfunctionalmusclenetworksis

crucialforunderstandinghowmovementiscoordinated.Previousstudieseither

investigatedhowbiomechanicalpropertiesofthemusculoskeletalsystem

constrainthemovementpatternsthatcanbegenerated[11,12],orhowmuscle

activationpatternscanbeexplainedbyacombinationofonlyafewcoherent

muscleactivationpatterns[14,15].Ourcombinedanalysesofanatomicaland

functionalmusclenetworksrevealastrongrelationshipbetweentheanatomical

connectionsinthemusculoskeletalsystemsandcorrelatedinputstospinalmotor

neurons.Thisbuildsonpreviousresearchshowingthatcommoninputisstrongest

tospinalmotorneuronsthatinnervatemusclespairsthatareanatomicallyand

functionallycloselyrelated[13,31].Thesimilaritybetweenstructuraland

functionalnetworkshasbeenasignatureofthestudyofbrainnetworks[38]and

thetopologyofbrainnetworksdependsonthebrain'sspatialembedding[39,40].

Thepresentfindingssuggestthattheprinciplesgoverningembodiedstructural

andfunctionalnetworksalsoappliestotheneuralcircuitrythatcontrols

movementsandmayhencereflectageneralprincipleofthecentralnervous

system.

Thesimilaritiesbetweenanatomicalandfunctionalconnectivitymayindicatethat

theanatomicalstructureconstrainsthefunctionalinteractionsbetweenmuscles.

Theanatomicalconnectionsbetweenmusclesremainlargelyunchangedoverthe

lifespan[41]anditismorelikelythatthefast-changingfunctionalnetworksare

constrainedbythemuchslowerchanginganatomicalnetworksthanviceversa.

Theseconstraintsmaybeimposedthroughafferentactivity.Themusculoskeletal

propertiesofthehumanbodyrestricttheposturaldynamics[12]andthese


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mechanicalcouplingsresultincorrelatedproprioceptivefeedbacktospinalmotor

neurons.Theinfluenceofbiomechanicsonfunctionalmusclenetworksisexpected

tobemostpronouncedatthelowerfrequencycomponents:Musclesactasalow

passfilterofneuronalinputs[43]andkinematicsofthemusculoskeletalsystem

unfoldonaslowtimescale.Thisgeneratescorrelatedactivityatlowfrequencies

thatarefedbacktospinalmotorneuronsviasensoryafferents.Thespatial

distributionofcommoninputwouldarguablymirrorthetopologyofthe

musculoskeletalsystem.

Anatomicalconstraintsmayalsobeimposedduringneuraldevelopment.During

earlydevelopment,changesinthetopographicaldistributionofaxonterminalsof

descendingprojectsaredependentonpatternsofmotoractivityandanatomical

connectivitybetweenmuscles[44].Likewise,largechangesinfunctionalcoupling

isobservedininfantsbetween9and25weeks,whichmayreflectasensitive

periodwherefunctionalconnectionsbetweencorticospinaltractfibresandspinal

motorneuronsundergoactivity-dependentreorganization[45].Theanatomyof

themusculoskeletalsystemwilllimitthemotoractivitypatternsthatcanbe

performed.

Anatomicalandfunctionalconnectivitybetweenmusclesmayalsobothbe

influencedbyexternalfactors.Forexample,theconnectivitypatternsof

descendingpathwaysisinpartgeneticallydetermined[46].Asomatotopic

organisationisobservedacrosstheneuralmotorsystemandthecommunity

structureoftheanatomicalmusclenetworkmirrorstheorganisationofprimary

motorcortexcontrolmodules[29].Likewise,thespatialorganisationofmotor

neuronsofthespinalcordisalsorelatedtotheanatomicalorganisationofmuscles

[47].Thetopographicorganisationofspinalmotorneuronsissimilaracross

species[48]andmayhencebearesultofevolutionaryconservation[49].

Musculoskeletalanatomyandneuronalpathwaysarehencebothsubjecttosome

sortofgeneticcontrol.

Functionalconnectivitywasnotentirelydeterminedbyanatomyandweobserved

severalkeydifferencesbetweenanatomicalandfunctionalmusclenetworks.


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Bilateralmodulesconsistingoftheupperandlowerextremitieswereakey

characteristicofthefunctionalmusclenetworkthatwasabsentintheanatomical

network.Thetwobilateralforearmmuscles(FDSandED)showedcoherent

activityat3-11Hz,consistentwithpreviousstudiesshowingbimanualcouplingat

~10Hzbetweenhomologoushandandforearmmuscles[50,51].Theobserved

bimanualcouplingat3-11Hzmaybegeneratedbytheolivocerebellarsystem,

whichisknowntoproduceoscillationsinthisfrequencyrangeandforits

involvementintheformationoffunctionalmusclecollectives[51,52].The

bilateralforearmmuscleswereonlyweaklycoupledtoothermuscles(Fig.2),

whichmayreflecttherelativelyhighproportionofdirectcorticospinalprojections

–andthusarelativelowproportionofdivergingprojections–tomotorneurons

innervatinghandandforearmmuscles[53].

Incontrast,thebilateralmoduleoflowerlegmusclesrevealedstrongcouplingat

multiplefrequencybands,consistentwithpreviousanalysesonfunctionalmuscle

networks[30],andshowedthestrongestlong-rangeconnectionsobservedinthe

presentstudy(Fig.3C).Bilateralconnectivitybetweenhomologousmusclesduring

balancingcouldbegeneratedbythevestibulospinaltract,whichisknowntobe

involvedinposturalstabilityandinnervatethespinalgreymatterbilaterally[31].

Bilateralconnectivityhasbeenobservedatalllevelsofthecorticospinalaxis[54]

andisparamountforfunctionalbrainnetworks,particularlybetweenhomologous

left-rightcorticalregions[55,56].Thepresentfindingssuggestthatbilateral

couplingisalsoadefiningfeatureoffunctionalmusclenetworks.

Functionalconnectivitydisplayeddistincttask-dependentmodulationsthatwere

linkedtothetaskthesubjectsperformed:functionalconnectivitywasincreased

withinandbetweenthelegmodulesduringposturalinstability,andincreased

withinandbetweenarmandupperbodymodulesinthepointingconditions.

Functionalconnectivitybetweenmusclesisthustaskdependent[31,50],which

maysuggestthepresenceofmultifunctionalcircuitsinwhichagivenanatomical

connectivitypatterncangeneratedifferentfunctionalactivitypatternsunder

variousconditions[42].Suchadistributedcircuitrycreatesthesubstrateto

supportmanybehavioursthataredrivenbytheconcertedactionsofalarge


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distributednetworkasopposedtosimple,dedicatedpathways.Theunderlying

networkconnectivityhenceconstrainsthepossiblepatternsofpopulationactivity

toalow-dimensionalmanifoldspannedbyafewindependentpatterns–neural

modes–thatprovidethebasicbuildingblocksofneuraldynamicsandmotor

control[57].Again,thisfindssimilaritieswithrecentinvestigationsofthe

functionalprinciplesofcognitivenetworksinthebrain[58,59].

Task-dependentchangesoccurredatdifferentfrequencies,whichindicatethe

functioningofamultiplexnetworkorganisation,wherebythefourfrequency

componentsreflectdifferenttypesofinteractionsbetweenmuscles.Fourdistinct

frequencycomponents(0-3,3-11,11-21,and21-60Hz)wereextractedusing

NNMF.Thesefrequencybandscloselymatchthosefoundpreviously[30],

demonstratingtherobustnessofthisfinding.Aninterestingpossibilityisthat

thesefrequencycomponentsreflectthespectralfingerprintsofdifferentpathways

thatprojectontothespinalmotorneurons.Ithasbeensuggestedthatthese

differentfrequenciesmayhavespecificrolesincodingmotorsignals[60].

Functionalconnectivityatthelowestfrequencycomponentsmayresultfrom

afferentpathways,whilefunctionalconnectivityathigherfrequenciesmayreflect

correlatedinputfromdescendingpathways.Forexample,functionalconnectivity

inthebetaband(15-30Hz)mostlikelyreflectscorticospinalprojections[13,50].

Thehighestfrequencycomponentsobservedinthisstudy(21-60Hz)showedthe

mostlocalconnectivitypatterns.Theselocalconnectivitypatternsmayreflect

propriospinalpathways[4,23].Thesefunctionalconnectivitypatternsmaybe

usedtouncoverthecontributionofstructuralpathwaysintheformationof

coordinatedactivitypatternsinthemotorsystem[34].

Insummary,ournetworkanalysisrevealedwidespreadfunctionalconnectivity

betweenmuscles,indicativeofcorrelatedinputstospinalmotorneuronsat

multiplefrequencies.Correlatedinputsindicatedivergentprojectionsorlateral

connectionsintheneuralpathwaysthatinnervatespinalmotorneurons.These

findingsareconsistentwithamany-to-manyratherthananone-to-onemapping

betweenbrainandmuscle[5],inwhichcomplexmovementsarisethrough

relativelysubtlechangesintheco-activationofdifferentdistributedfunctional


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modes.Wepresentanovelapproachthatalignsmovementneurosciencewith

currentresearchonbrainandphysiologicalnetworksbyshowinghowthecentral

nervoussysteminteractswiththemusculoskeletalsystemofthehumanbody.

Fromasystemsbiologyperspective,thebrainandspinalcordareinterwovenwith

thebody:theyare‘embodied’[10].Usingnetworkanalysisasacommon

framework,futureworkcouldintegratefunctionalinteractionsbetweensupra-

spinal,spinalandperipheralregionssimultaneously.Suchanintegrated

frameworkalignswiththebroaderapproachofnetworkmedicine,whichmay

providenewinsightsandinterventionsforneurologicaldisorders[61-63].

Methods

Dataacquisition

Fourteenhealthyparticipants(sevenmalesandsevenfemales,meanage25±8

years,tenrightandfourlefthanded)withoutanyneurological,motordisorderor

diabetesmellitusandwithaBMIbelow25wereincludedinthisstudy.The

experimentswereapprovedbytheEthicsCommitteeHumanMovementSciences

oftheVrijeUniversiteitAmsterdam(referenceECB2014-78)andperformedinfull

compliancewiththeDeclarationofHelsinki.Allparticipantswerewrittenand

verballyinformedabouttheprocedureandsignedaninformedconsentpriorto

participation.

Participantswereinstructedtoperformninedifferentposturaltasks.Afull

factorialdesignwasusedinwhichposturalstability(normalstanding,instability

inanterior-posteriordirectionandinstabilityinmedial-lateraldirection)and

pointingbehaviour(nopointing,pointingwithdominanthand,pointingwithboth

hands)werevaried.Posturalstabilitywasmanipulatedusingabalanceboardwith

onedegreeoffreedom,whichallowsmovementeitherintheanterior-posterioror

medial-lateraldirection.Inthepointingtask,participantsheldalaserpointerwith

theirdominanthand(unimanual)orwithbothhands(bimanual)andpointediton

awhitetarget(25cm2)locatedatadistanceof2.25meter,paralleltothe

transversalaxisofthebodyattheheightoftheacromionoftheparticipant.The

experimenthenceconsistedofnine(3´3)experimentalconditions.Thedurationof

atrialwas30secondsandeachconditionwasrepeatedsixtimes.


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BipolarsurfaceEMGwasrecordedfrom36musclesdistributedacrossthebody,

i.e.18bilateralmuscles(Table1).Thesemusclesaretheprimarymusclesinvolved

inthestabilityandpointingtasksthatcanbeproperlymeasuredwithsurface

EMG.EMGwasacquiredusingthree16-channelPortisystems(TMSi,Enschede,

TheNetherlands),onlinehigh-passfilteredat5Hzandsampledat2kHz.

Table1.Listofmuscles

Muscle Abbreviationtibialisanterior TAgastrocnemiusmedialis GMsoleus SOLrectusfemoris RFbicepsfemoris BFvastuslateralis VLadductorlongus ALexternaloblique EOpectoralismajor PMAsternocleidomastoideus SMAlongissimus LOlatissimusdorsi LDtrapezius TZdeltoid Dbicepsbrachii BBtricepsbrachii TRBextensordigitorum EDflexordigitorumsuperficialis FDS

Anatomicalmusclenetwork

Theanatomicalmusclenetworkwasdefinedbymappingthephysicalconnections

betweenmuscles[28].Thenodesrepresentthe36muscles(18leftand18right)

andtheedgesofthenetworkrepresentthetendinousattachmentsofmusclesonto

bonesandcartilages.Thestructuralconnectionsweredefinedbasedontheorigin

andinsertionofthemuscles[3].Bonesthatshownooralmostnomotioninthe

jointbetweenthemwereconsideredasonerigidbonystructure,i.e.thepelvis,

skeletonthoracisorossacranii.Theconnectionsbetweenmusclesandbones

listedinTable2denoteabipartitenetwork𝐶withmusclesasonegroupand

bonesasthesecondgroup.Wethencreatedamuscle-centricnetworkastheone-

modeprojectionsof𝐶:𝐵 = 𝐶𝐶% [29].Thisgaveaweightedadjacencymatrix

wheretheweightsreflectthenumberofattachmentsbywhichtwomusclesare


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18

connected.Weconvertedthistoabinarynetworkbysettingallnone-zeroweights

to1.

Table2.OriginandinsertionofmusclesMuscle Origin1 Origin2 Origin3 Insertion1 Insertion2TA tibia oscuneiformemediale ossa

metatarsiGM femur calcaneus SOL fibula tibia calcaneus RF oscoxae1,* osilium1,* tibia BF femur osischii1,* fibula tibiaVL femur tibia AL ospubis1,* femur EO costae2,* lineaalba osilium1,*PMA clavicula costae2,* sternum2,* humerus SMA clavicula sternum2,* ostemporale3,* LO ligamentum

sacrospinale1,*vertebra* costae2,* vertebra*

LD costae2,* fasciathoracolumbalis*

vertebra* humerus

TZ ligamentumnuchae* osoccipitale3,* vertebra* clavicula scapulaD clavicula scapula humerus BB scapula radius TRB humerus scapula ulna ED humerus ossadigitorum FDS humerus radius ulna ossadigitorum 1Partofthepelvis;2Partoftheskeletonthoracis;3Partoftheossacranii;*Connectivestructureonthemidlineofthebodyconnectingbilateralmuscles

Functionalmusclenetwork

EMGwasfilteredofflinewithaband-passfilter(1-400Hz)beforeindependent

componentanalysiswasusedforelectrocardiographyremoval[64].Foreach

participant,oneortwoindependentcomponentswereremoved.EMGdatawas

thenhigh-passfiltered(20Hz)andEMGenvelopeswereextractedbymeansofthe

Hilbertamplitude[33].

WefollowedtheproceduredescribedinBoonstraetal.[30]toextractfunctional

musclenetworksfromsurfaceEMG.First,complex-valuedcoherencywas

estimatedandaveragedovertrialswithineachconditionforeachparticipant.The

absolutevalueofcoherencywassquaredtoobtainmagnitude-squaredcoherence.

Intermuscularcoherencewasassessedbetweenall630musclepairs.Next,non-

negativematrixfactorisation(NNMF)[65]wasusedtodecomposethese

coherencespectraacrossallmusclecombinations,conditionsandparticipantsinto

fourdistinctfrequencycomponentsandthecorrespondingweights.Thisyieldeda


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setofweightsforeachfrequencycomponent,whichdefinedanundirected

weightednetworkforeachconditionandparticipant.

Thesefunctionalnetworkswereconvertedtobinarynetworkstofacilitate

comparisontotheanatomicalnetwork.Weightswerethresholdedtoobtaina

minimallyconnectednetworkacrossconditionsandfrequencycomponents.This

thresholdingprocedureyieldsasingle,uniquethresholdvalue,whichcorresponds

tothepercolationthreshold[66].Thisresultedinsparsenetworksinwhicheach

nodewasconnectedtoatleastoneothernodebyanedgeatoneofthelayersof

themultiplexnetwork.

Communitystructure

ThestandardLouvainalgorithmwasusedtoextractthemodulesfromthe

anatomicalnetworks[67].AstheLouvainalgorithmisstochastic,weused

consensusclusteringtoobtainastablepartitionacross1000iterations[68].

Multiplexmodularityanalysis[35]wasusedtoidentifythemodulesoffunctional

musclenetworkacrosstheconditionsandfrequencycomponents.WeusedMolTi,

astandalonegraphicalsoftware,todetectcommunitiesfrommultiplexnetworks

byoptimisingthemultiplex-modularitywiththeadaptedLouvainalgorithm

(https://github.com/gilles-didier/MolTi).Moduleswereextractedacrossthe36

(9´4)binarynetworks,asmulti-graphapproachescanimproveclustering

accuracy[69].WeusedtheRandindexandtheadjustedRandindextocompare

themodulesoftheanatomicalandfunctionalmusclenetworks[25].

Comparisonoffunctionalnetworksacrossconditions

Tofacilitatethecomparisonoffunctionalnetworksacrosstaskconditions,we

coarse-grainedthenetworks[70].Weusedthesetoffunctionalmodulesestimated

acrossconditionsandfrequencycomponentsasaframeofreferencetocoarse-

grainthe36binarynetworksandthencomparedthestrengthoftheinter-and

intra-moduleconnectionsacrossnetworksusingthesemoduleboundaries.Inthe

clusterednetworksthenodesrepresentthemodules(groupsofmuscles,identified

above)andtheedgesrepresenttheconnectionsbetweenmodules.Thenon-

diagonalelementsoftheresultingweightedadjacencymatrixrepresentthe


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20

averageedgeweightsbetweentwomodulesanddiagonalelementstheaverage

edgeweightswithinamodule.

Tocomparetheclusterednetworksacrossconditions,weusedsimplecontrasts

betweentaskconditionsandquantifieddifferencesinthenumbersofconnections

betweenandwithinmodules.Wetestedfourcontrasts:(i)unimanualand(ii)

bimanualpointingcomparedtonopointingand(iii)anterior-posteriorand(iv)

medial-lateralinstabilitycomparedtonormalstanding.Totestthestatistical

significanceofthesecontrasts,weperformedpairedpermutationtestsseparately

oneachofthematrixelements[70].Theclusterednetworkshadamuch-reduced

dimensionalitycomparedtotheoriginalfunctionalmusclenetworks(21insteadof

630edges).Family-wiseerrorcontrolwasmaintainedusingBonferronicorrection

tocorrectformultiplecomparisons(4´21=84comparisons).

Dataavailabilitystatement

Thedatathatsupportthefindingsofthisstudyareavailablefromthe

correspondingauthoruponreasonablerequest.

Acknowledgment

WethankDanieleMarinazzo,SimonFarmer,SjoerdBruijn,HenkSchutte,and

NadiaDominicifortheirinsightfulcomments.Thisworkwassupportedbythe

NetherlandsOrganizationforScientificResearch(NWO45110-030and

016.156.346),theARCCentreofExcellenceinIntegrativeBrainFunction,andthe

AustralianNationalHealthandMedicalResearchCouncil(APP1037196,

APP1110975).

Authorcontributions

J.K.,A.D.andT.B.conceivedthestudy;allauthorsdesignedtheexperiments;J.K.

acquiredtheEMGdata;J.K.andT.B.performedtheevaluationoftheanatomical

network;J.K.,L.G.andT.B.performedtheevaluationofthefunctionalnetwork;T.B.

performedthestatisticalanalyses;J.K.andT.B.wrotethemanuscript;andallthe

authorseditedthemanuscript.


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