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limb-specific muscle parameters during bipedal walking for humans, apes and early hominids with the implications for the evolution of body proportion

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limb-specific muscle parameters during bipedal walking for humans, apes and early hominids with the implications for the evolution of body proportionlimb-s

    limb-specific muscle parameters during bipedal walking for humans, apes and early

    hominids with the implications for the

    evolution of body proportion

    28卷第8

    20078

    仪器仪表

    ChineseJournalofScientificInstrument

    V0I.28No.8

    Aug.2007

    Estimateofthelower--limb--specificmuscleparameters

    duringbipedalwalkingforhumans.apesandearlyhominidswiththe

    implicationsfortheevolutionofbodyproportion

    WangWeijie'

    (JInstituteofMotionMandResearch,DepartmentofOrthopedicandTraumaSurgery,NinewellsMedicalSchool,

    DundeeUniversity,Dundee,DD19SY,UK;

    2CollageofPhysicalEducationandSportScience,SuzhouUniversity,Suzhou215006,China)

    Abstract:Modemhumanhasdifferentbodyproportionfromearlyhominidsandgreatapes.Comparingwithothers,

    ingeneral,modemhumanadultshaverelativelylonglowerlimbandheavierbodyweight.Sincethelowerlimbspro.

    videsupporttothewholebodyandplayanimportantroleinwalking,itisproposedthattheratioofthelowerlimbto

    thewholebodyformodemhumancouldbebeneficialtobipedalwalking.Thisstudytriedtoest

imatethemusclepa.

    rametersofthelowerlimbinwalkingforthesubjectswithvariousbodyproportions.Usingasimplifiedmusculoskele-

    talmodel,somemuscleparametersofthelowerlimb,e.g.muscleforce,stress,workandpower,wereestimated

    formodemhumanadult,child,AL288-1(thefossilspecimensofAustralopithecusafarensis,3.18millionyears

    old)andapes.Theresultsshowthatwiththebodyproportionmodemhumanadultspendslessmuscleworkand

    powerinwalkingthanothersubjects.Theresultsimplythatusingthecostoftransport(i.e.themuscleworkofthe

    lowerlimbperunitofdisplacement)asthecriteria,theearlyhominids,iftheirbodyproportionswerestructurally

    similartoAL288-1,couldevolvetowardswhatmodemhumanadultlookslike,inordertosaveenergyduringbi-

    pedalwalking.

    Keywords:ratiooflowerlimbtowholebody;bipedalwalking;musclework;stress 1Introduction

    Itisknownthathuman,apesandearlyhominidshaveva-

    rioussizesandbodyproportions,especiallytheratioofthe

    lowerlimbtothewholebody.Ingenera1.modemhumana.

    duhshaverelativelylonglowerlimbthangreatapes.Ac-

    cordingto,underthesametrunkheight,thelowerlimb

    lengthsforhumanadultsare143%longerthanthatforgoril-

    la,136%thanchimpanzee(Pan),150%thanPongo,and

    120%thanHylobates.Consequently,theratioofthelower

    limbmasstothewholebodymass(RLW)ishigherinhu-

    mansthanthatingreatapes.TheRLWforhumanadultsis

    about30%,butforpygmychimpanzees(Panpaniscus)is

    about24%,andforPantroglodytes,PongoandSymphalan-

    gusisonlyabout18%.Inearlyhominids.thefossilspec- imens,AL288-1(Australopithecusafarensis,knownas 'Lucy',3.18millionsyearold)hasaRLWabout28%, whichismidwaybetweenthoseofmodemhumanadultsand greatapes[.Lucyisestimatedtohavethestatureof 1.05mandthebodymassof30kg,butmodemhuman

    childrenwithherstaturemayhavetheirbodymassesaround only1520kg.ortheywithherbodymassmayhavethe

    statureashighasabout1.31.4m.Whatbodyproportions

    arebeneficialtobipedalwalking?Sincemodemhumantakes bipedalwalkingasanormallocomotivepatternindailylife, itwashypothesizedinthisstudythatthebodyproportionsof modemhumanadultsshouldbesuitableforbipedalwalking. Thoughbodyproportioncouldincludesomeimplications forunderstandingofhumanevolution[']andthebodys1'ze isrelatedtotheworkandenergyinmotion.fewauthors havefocusedontherelationshipsamongRLW,musclepa- rametersandbipedalwalking.Sincethelowerlimbssupport andcarrythewholebodymassduringwalking,itisimpor- ReceivedDate:2007-01收稿日期:2007-01

    }Foundationitem:SupportedinpartbythegrantsfromtheBiotechnologyandBiologicalScie

    ncesResearchCouncil,theLeverhulmeTrust,andtheNat. uralEnvironmentResearchCouncil,U.K.

8WangWeijie:Estimatesofthelowerlimb

    s~cfficmuscleparan~tersduringbipedalwalkingforhumans, apesandearlyhominidswiththeimplicationsfortheevolutionofbodyproportion1359

    tantt0estimatethemusclep~ametemofthelowerlimbin termsofRLWandbipedalwalking.

    Theoretically.theabilityofthelowerlimbstodrivethe

wholebodyduringwalkingcouldbereflectedbysomebio

    mechanicalparameters,suchasmuscleforce,stress,work andpower.Theseparameterswilldeterminewhetherornota subjectwalksproperly,suchasspendingmoreorlessenergy inwalking.Therefore,itwasproposedinthisstudythatthe lowerlimbspecific(LLS)biomechanicalparametersin walkingcanbeusedasthecriterionfortheevaIuationand comparisonofthesubjectswithdifferentbodyproportions. Tocalculatesocalledlowerlimbspecificparameters,all

    muscleparameterswillbenormalizedbythemassofthelow

    erlimb.Wherevernecessary,thelengthofthelowerlimb willalsobeconsideredintheexpressionsofparameters. 2Methodsandmaterials

    2.1Assumptions

    Sincebiologicalsubjectsarestructurallycomplex,this studydidnotintendtogiveacompletedescriptiononthe musculoskeletalfunctionofthelowerlimb,butattemptedto findpossiblecluesforunderstandingofRLW.Tosimplify modelingprocedure,severalassumptionsweregivenasfol

    lows:(1)Thebiomaterialinvariousbiosubjectsisuni

    form;(2)Differentsubjectswalkatasimilarway,nomat

    teroftheirsizes;(3)Bothpositiveandnegativemuscle workconsumechemicalenergyofthebody.

    2.2Subjects

    Sometypicalsubjectswithvariousbodyproportionswere usedforvalidatingthemodel(table1).Theweightsandleg lengthsformodemhumanadultandchildweretakenfrom generalpeople,whilethosedataforAL2881areestimated

    bvtheliterature[]:forthechimpanzeereferredto[19]; fortheorangutanmeasureddirectlyfromalivingoneinthe

    ChesterZoo,U.K;andforthegorillaobtainedfromthe previousstudy[2o_.

    Thebodyproportionsforthevarioussub

    iectswerecitedfromtheliterature[.

    Table1comparisonsofthebodyillass,

    thelengthsoflowerlimbfromsometypicalsubjects Note:(1)RLW:theratioofthelowerlimbmasstothe wholebodymass.(2)AL-2881hasrelativelyshortstature, andthushasshortlowerlimbandrelativelyheavybodyin comparisonwithmodemhumanandgreatapes.

    2.3Simplifiedmodel

    Themodelconsistsofthreeparts,theHAT(head,armsand trunk)andthetwolegs(.1(a)).Themusclesinthejoints aleusedtodrivethelowerlimbs,andthusdrivethewhole body.Infig.1(a),Listhelowerlimblength,Lsisthestep length,andthus2Lsisthestridelength,orthedisplacementof thecenterofmassoveracycleofwalking;RFistherightfoot instancephase,andLFistheleftfootinstancephase. Thegeometricandmechanicalrelationshipsofthelower limbareshowning.1(b),wherethegeometricparameters inthelowerlimbarechanged:Asisasmalldisplacementof thecentreofhip,thusroughlythatofthecentreofmass,r isthecharacteristicradiusoftheleg,Listhecharacteristic lengthoftheleg,A0isasmallchangeinthejointangle, ALisasmallchangeinmusclelengthwhichisproportional tothechangeintherotationangleandthelegradius. RFLFRFiIi

    r.一一一一一一一一一一一一一一一一一一一'

    (a)Threepartsofthemodel

    iI

TnlkTmnk1.———

    (b)Themuscoluskeletalpartofthesupposingleg

    Fig.1Asimplemodel

l360仪器仪表第28

    (1)Proportionalrelationships

    Whenasubjectwalksontheground,theresultantground reactionforce(GRF)shouldbeproportionaltothebody weight.Consideringthesupportingleg,thetorqueinthehip shouldbeproducedbytheGRF,thelegitself,andthean- gularaccelerationandmomentofinertia.Sincethetorque shouldbebalancedbythemomentsproducedbythemuscles ofthelowerlimb,thusitisproportionaltotheproductofthe muscleforceandthemomentalTllofmuscleinthejoint(e. g.,thehip).Therefore,therearesomebasicproportional relationshipsforthesupportinglegexistedasbelow. Theresultanttorqueinthehipshouldbe:

    1

    K?GRF?L+,ng?sin0+,0(1)

    

    whereisthetorqueinthejoint(hip);Kisthesinevalue oftheanglebetweenthevectorsoftheGRFandtheleg;Lis thecharacteristiclengthofthelowerlimb;misthelower limbmass;0istherotatinganglebetweenthelegandthe verticaldirection(seefig.1(b)),and'Gc'meaning'be proportionalto'.IntherightsideofEq.(1),thefirstitem isproducedbytheGRF,thesecondbythelegitselfandthe thirdbytheangularacceleration.

    Further,theGRFisproportionaltothemassandgravita- tionalconstant,thus:

GRFM.g(2)

    whereMisthewholebodymassandgthegravitationalac

    celeration,takenas9.8m/s.

    Accordingtoanumberofreportsontheanalysisofvarious gaits,thejointtorqueinswingphaseislessincomparison withthatinstancephase.Besides,theswinglegislikeapen

    dulum,whichisabletoexchangethekineticandpotentialen- ergiesefficiently,thatistosay,thebodyconsumeslittlechi

    mericalenergyinswingphase.Therefore,thejointtorquein swingphaseisneglected.Additionally,fromtheexperimentson humannormalwalking,itwasobservedthat:(1)inthe sagittalplane,thevectorofGRFrelatedtotheverticaldirection changesfromtheminimumdegree16?2.6tomt~mLlln-31?

    5(60walkingtrialsfrom6adultsaged2040yearsold,walk

    ingatself-determinedspeeds);(2)inthesinglestance(i.e. alegsupportingontheground),therelativeangularvelocityin thehipisnearlykeptinaconstant,andinthedoublestance (i.e.bothlegssupportingontheground)theangularvelocity changesalitter.Basedontheobservations,tosimplifythe model,theKineq.(2),orthedirectionofGRF,isconserva- tivelygiventobesin30.,or1/2;andtheangularacceleration ineq.(2)issettobezero.

    Ontheotherhand.theintemalmomentproducedbythe musclesinthejointshouldbeproportionaltotheextemal torque,thusthemuscletorqueshouldbe:

    F.r+?.sinM+?

    sin0(3)

    andmuscleforce:

    F::+:

    rr

(4)

    whereFisthemuscleforceinthelowerlimb:andrthe characteristicradiusofthelowerlimb.

    (2)Geometricrelationship

    Referringtothesimplifiedthreebodymodel(seefig.1

    (a)),ifmaximumrangeofjointangleisfrom——to

    forthesupportingleg(seefig.1(a)and(b)),thegeomet- ricrelationshipsbetweentheangularmaximumandthestep lengthcanbeexpressedasfollowing:

    .

    sin

    L

    (5)

    whereListhesteplength,i.e.2L,isthedisplacementofthe centerof?lass(CM)inacycleofwalking(seefig.1(a)). Anincrementinmusclelengthisproportionaltotheprod- uctofthelowerlimbradiusandthesmallchangeinjointan- gle,thusforthesupportingleg:

    dlr?d0(6)

    whered/istheincrementinmusclelength;andd0theincre- mentinjointangleforthesupportingleg(seefig.1(b)). Intheeqs(16),theshapeoftheleghasbeenassumed

    tobeanidealcylinder.Asthebio-materialofallsubjectsis uniform,themassofthelowerlimbshouldbe:

    m=P?1T?r?(7)

    wherePisthedensityofthematerials,roughly1000kg/m; 1Tistheconstant.3.14.

    2.4lower-limb-specific(LLS)muscleforce

    Fromeq.(4),themaximumofmuscleforceshouldbe: Fmax+

    SinceaLI_Sparameterisdefinedtobetheparameterdi- videdbythemassofthelowerlimb.thustlleUmuscle forceshouldbe:

    g+卫等

    Or,puttingeq.(7)intoeq.(9)togetanexpressionwith M,LandRLW:

    t

    ,

8WangWeijie:Estimatesofthelowerlimb

    spec~cmuscleparametersduringbipedalwalkingforhumans, apesandearlyhominidswiththeimplicationsfortheevolutionofbodyproportion1361

    g+1

    (1O)

    wherePistIIeratioofthelowerlimbmasstothewholebody mass,orRLW.

    (3)LLSmusclestress

    Undertheassumptionthatthephysiological?cross?-section?- areas(PCSA)ofmusclesareproportionaltothesquareof thelowerlimbradius,andwitheq.(10),theLLsmuscle stressshouldbe:

    +(11O'asg)了一+)

    .c+c3/2Lsg('rrp)+(叩寿

    (12)

    whereismusclestress.

    2.5LLSmuscleworkdone

    Accordingtothedefinitionofwork,muscleworkisthe productofthemuscleforceandthechangeinmusclelength. Thuswitheqs(4)and(6),themuscleworkis:

dW:F.df.Cdf+d(13)

    Puttingeq.(6)intoeq.(13),themuscleworkdone shouldbe:

    dWo5M?g?L?dO+Lmg?sin0?d0(14)

    Thus,duringacycleofwalking,theworkdoneshouldbe proportionalto:

    .cd+sin(15)

    Undertheassumptionthatbothpositiveandnegativemus

    cleworkconsumechemicalenergy,thus:

    Wo52MgLO+2Lmg?[1COS0](16)

    Puttingtheeq.(5)intoeq.(16),theworkdoneduring bipedalwalkingis:

    .c2L"arcsin(2~)+2L,?[1,

    (17)

    NotethatthedisplacementofCMoveracycleofwalking is2L,therefore,theLLsworkperunitdistanceis: =

    .cgarcsinc

    (18)

    whereisthelowerlimbspecificanddistancespecific

    muscleworkdone,whichexpressesthemuscleworkdoneby themassofthelowerlimbsperunitdisplacementofCM,or thecostoftransport.

    2.6LLSmusclepower

    Similarly,accordingtothedefinitionofpowerandwith eq.(14),themusclepoweristheworkdoneperunittime: P=.cML?+L.sid0(19)

    Providingthattheinstantangularvelocityis"proportional totherangeofjointangleandinverselyproportionaltothe durationtimeoveracycleofwalking:

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