An Improved Deflection Energy Method to Normalise energy versus deflection for the thorax are of constant slope. The deflection energy is the ... using a deflection energy method and a two

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  • AbstractNormalisationistheprocessofmodifyingasetofpostmortemhumansubject(PMHS)responsedatatobetterrepresentthatofastandardsizedhuman.Thisimprovedmethodisbasedonthefactthatallplotsofdeflectionenergyversusdeflectionforthethoraxareofconstantslope.Thedeflectionenergyistheintegraloftheappliedimpactforceoverthedeflectionmeasuredbyachestbanduptothepointofmaximumdeflection.Standardsizedhumanthoraxdeflectionenergiesandslopesarefoundfrommultivariateanalysesrelatingenergyandslope,separately,totheanthropometricdataforallsubjects.Forceisthespatialderivativeofthelineardeflectionenergycurveandisaconstant.Theresultingrectangularforceversusdeflectioncurveleadstoscalefactorsforforce,deflection,elasticstiffness,theviscousconstant,andtime,assumingatwoelementsolidviscoelasticmodel.Subjecteffectivemassandpostimpactvelocitywerecalculatedfromconservationofenergyandimpulseequalsmomentum,solvedsimultaneously,providingscalefactorsforeffectivemassandsubjectvelocityatmaximumdeflection.Thetimehistoriesandforceversusdeflectionhavebeenplotted,thestandarddeviationtargetsoverplotted,andcoefficientsofvariationcalculated.Resultshavebeenqualitativelyandquantitativelycomparedtopreviousmethods. Keywords biofidelity,datanormalisation,postmortemhumansubject(PMHS),scaling

    I. INTRODUCTIONTheprocessofnormalisingpostmortemhumansubject(PMHS)responsedatafromimpacttestingtoobtain

    a representationof the typical,or average,human responsehasbeen an importantpartof anthropometriccrash dummy design and development for many years. Normalisation is the process of mathematicallymodifyingtheresponsedatafromasetofPMHSsubjectstoastandardhumansize.Thisnormalisedresponse isusedasastandardagainstwhichtheresponseofananthropometricdummy is

    comparedtoassessthedummybiofidelity.Aquantifiedmeasureofbiofidelityisdesirabletoprovidethebasisforanobjectivedecisionastotheabilityofadummytoassessvehiclecrashprotectionforahumanofsimilarsize.In1984amethodfornormalisingPMHSdatabasedontheratioofthewholebodymassofasubjecttothe

    standard totalbodymass (e.g.50thpercentilemale)wasdeveloped [1]. Thismethodologyassumed thatallsubject responseswill be related directly to thewhole bodymass. Clearly force, deflection and kinematicresponses fromwidelyvarying sizesand shapesofhumansarenot likely tobe related solelybywholebodymass. An impulsemomentum and stiffnessbased normalisationmethod [2]was presented in 1984. Scalefactorsweredevelopedfrombothanthropometrymeasuresandratiosofthesolutionforthesingledegreeoffreedom(DOF)differentialequationforalinearelasticsystemwhichrepresentedalargeimpactingmasssuchasasled typeof impact. In1989an improvement to thismethodologywaspresented [3]byexpanding thederivationofscalefactorstothetwoDOFlinearelasticsystemwhichbetterrepresentspendulumtypeimpactswherethestrikingandstruckmassesaremorenearlyequal.Againthescalefactorsweredevelopedfromratiosofthesolutiontothesystemofdifferentialequations.Animprovement[4]wasmadetothetwoDOFmethodusing the integralof the forceversusdeflection curve, thedeflectionenergy, todevelopanelasticeffectivestiffness directly from the force versus deflection response data rather than from characteristic subjectdimensions.Thislatterstudy[4]alsocomparedtheeffectivenessofthevariousnormalisationmethodsinforceversusdeflectionspaceusingthestandarddeviationellipse[5]andamodifiedcoefficientofvariationmeasuretakingonehalfoftheareaoftheellipsedividedbytheproductofforceanddeflectionateachdatapoint.Thisquantitativecomparison indicated thateffectivestiffnesscollapsed the forceversusdeflectioncurves toward BRDonnellyisaPhDatBiomechanicsResearchAssociatesLtd.,USA,(+17406020531/brucedonnellyphd@columbus.rr.com).HHRhuleisaBSandKMMoorhouseandJAStammenarePhDsattheNationalHighwayTrafficSafetyAdministrationVehicleResearchandTestCenter,USA.YSKangisaPhDattheOhioStateUniversityInjuryBiomechanicsResearchCenter,USA.

    AnImprovedDeflectionEnergyMethodtoNormalisePMHSThoracicResponseData

    BruceR.Donnelly,HeatherH.Rhule,KevinM.Moorhouse,YunSeokKang,JasonA.Stammen

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  • eachothermoreeffectivelythantheothermethods.MorerecentlytheauthorsofthiscurrentstudypresentedamethodfornormalisingPMHSthoracicimpactdatabasedonthedeflectionenergyandatwoDOFviscoelasticmodel [6]. Thisapproachwasmathematically cumbersomebutdid improve thequantitative results slightlyover the effective stiffness approach [4] asmeasured using a time based average coefficient of variationmeasureandtheellipsecoefficientofvariationmeasureforforceversusdeflection.Thisstudybuildsuponallof thispriorwork todevelopan improved,andsimpler,mechanisticmethod for

    normalisingthoracicPMHSdataagainusingatwoDOFviscoelasticmodel. PMHSdatafrom19subjectsfromthreestudies[5][7][8]ofthoracicpendulumtestswereanalysedtoillustratethemethodology.Thedeflectionenergyand theslopeof thedeflectionenergyversusdeflectioncurvewereused todevelopscale factors forenergy,slope,force,deflection,elasticstiffness,theviscousconstant,andtime.Scalefactorsforeffectivemassandsubjectvelocitywerederivedfromconservationofenergyandconservationofmomentum.Of thepreviousnormalisationstudies themassbasedmethodusedsubjectanthropometryand theknown

    anthropometryvaluesofstandardsizedhumanstodevelopscalefactorsfornormalisation. Theotherearliermethodsusedchestanthropometryratiosandaveragesoftheresponsesofthesubjectpoolbeinganalysedtoestimate thestandardsizedhumanresponsesused todevelopscale factors. Thecurrentstudymodifies thisapproachbyusing the responsemeasuresofdeflectionenergyand slope fromall19 subjectsasdependentvariablesandthesubjectanthropometrymeasuresasindependentvariablestodevelopstatisticalmultivariaterelationships for energy and slope. The resulting equations can then be used with any standard humananthropometry values to estimate standard human deflection energy and slope values and to calculate thecorrespondingscalefactorsforthestandardforce,deflection,elasticstiffness,viscousconstant,andtime.Results fromnormalisingall19subjectstothe50thpercentilemalearepresented,alongwithmeancurves

    andstandarddeviationbiofidelitytargets, inbothtimehistoryplotsand forceversusdeflectionplots. Theseplots have been compared with results from previous methods both qualitatively and quantitatively todemonstrate the improved grouping and smaller standard deviation targets of the deflection energynormalisationresults.

    II. METHODSResponsedataandanthropometrydatafrom19PMHStested in lateralandobliquependulumtype impact

    tests in three studieswereanalysedusingadeflectionenergymethodanda twoDOFviscoelasticmodel todevelopscalefactorsfornormalisationtothe50thpercentilesizemalehuman. Standardvaluesfordeflectionenergy and the slope of the deflection energy versus deflection curve were estimated using multivariaterelationshipsbetweenanthropometrymeasuresand impactvelocityas independentvariablesanddeflectionenergyandslopeofdeflectionenergyasdependentvariables.Mechanicalvaluesforenergy,force,deflection,stiffness, theviscousconstant,and timewerecalculated from thedatausing the twoDOFmodel. Effectivemassandsubjectvelocityvalueswere foundusing theequations forconservationofenergyandmomentumsolvedsimultaneously.Normalisationscalefactorstaketheform

    1 andareappliedtotherelevantparameterateachpointinthetimehistory.Adescriptionof the subjects and the data analysed, thederivationof the subjectmechanical values, the

    developmentofthemultivariaterelationshipforthestandardhumanmechanicalvalues,andthedevelopmentofscalefactorsispresentedbelow.

    SubjectDataNineteenPMHSfromthreethoracic impactstudieswereanalysed inthisstudy. Reference[6]testedseven

    PMHS innominal2.5m/s lateralandobliquethoracic impactsatthefourth intercostalspaceusinga23.86kgimpactorwitha15.24cmdiametercircularface.Reference[7]tested12PMHSin4.5m/sand5.5m/slateralandoblique thoracic impact testsat thexyphoidusinga23.99kg impactorwitha15.24cmhighx30.48cmwiderectangularface.Reference[8]alsotestedfiveadditionalPMHSin2.5and4.5m/sinlateralandobliquethoracic impact tests at either the fourth intercostal space or the xyphoid using either the circular face or

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  • rectangularfaceimpactors.Ofthese24PMHS,19wereselectedforanalysisinthisstudy.Thefivethatwerenotusedwereeliminated forvarious reasons suchas the impulseandmomentumcalculatedat the timeofmaximum thoracic deflection beingmore than 30% different [5][9]. Many of these subjects were testedmultipletimesbutonlythefirsttestwasusedinthisstudy.The19subjectsincludedwerejudgedtohaveverygoodqualitydataforanalysisandwouldlendconfidencetoademonstrationoftheprocedure.Theappliedforceversustimeandthechestbanddeflectionversustimewerecrossplottedandintegratedup

    tothepointofmaximumdeflectiontoobtainthedeflectionenergy.Forreasonsofconsistencytimezerowassetatthepointoffirstcontinuouspositivechestbanddeflectionforeverysubject. Generallytherewassomeappliedforcebeforethechestbandregistereddeflectionduetocontactwiththethoraxskinandsubcutaneousfat. Asaresult, attimezerothereusuallywasan initialpositiveforce. Thealternativewouldbetosettimezeroattheinitialpositiveforcebutinthatcasetherewouldbenomeasureddeflectionatthattime.Thedataused in thisanalysis included lateralandoblique testsaswellas circularand rectangular impact

    faces.Reference[8]testedameasureofelasticstiffnessandindicatednosignificantdifferenceinlateralversusoblique responseamong thevarious testsexcept for testswith thecircular impact face. Thestandard ttestprobabilityof=0.05wasused inthatanalysistoprotectagainsttype Ierrorandappropriatelyrejectedthenullhypothesisthatthedifferenceinthemeansofthestiffnesswaszero.Inthisstudyitwasdesirabletohavealargesetofsubjectstodemonstratethemethod.Thestandardforassumingthesubjectsarefromthesamepopulationwaslessstringentthaninastudydevelopingbiomechanicalresponsetargets.Thedatawastestedcomparingthedeflectionenergycurveslopesofthelateralteststotheobliquetestsandcircularimpactorfaceteststotherectangular impactorfacetests inallcombinations(seeAppendixA). Thenullhypothesis ineachcasewas that the difference in the slope valueswas zero. The pvalues for slope varied from 0.4 to 0.9indicatingitwasnotpossibletorejectthenullhypothesisoftheslopesbeingthesame.Itwasfeltthatforthepurposeofdemonstrating themethod itwasacceptable to considerallof the testsasbeing from the samepopulation. This isnotacontradictionofthepreviousresultbutratherpresentsadifferentviewofthedata,examiningadifferentvariable,forthepurposeofdemonstratingthenormalizationmethod. Ifthebiofidelityresponseofadummyinaparticulartestconfigurationwasbeingassessedonemightchoosetouseasubsetofthedata.

    TwoDegreeofFreedomViscoelasticModelThemaximumdeflectionenergyistheintegralofappliedforcewithrespecttothoracicdeflection.

    2

    where E=deflectionenergy F=appliedforce t=time S=thoracicdeflectionfromchestband.Thedeflectionenergyversusdeflectioncurvesforallofthethoracicimpactsexaminedinthisstudyarevirtuallystraight linesofconstantslopeupto,and including,themaximumdeflection. Fig.1showsthreeexamplesofthisphenomenonwhicharetypicalofall19subjects.

    (a) (b) (c)

    Fig.1.Plotsofintegrateddeflectionenergyversusdeflectiondemonstratingthestraightlineslope.

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  • In this study the term deflection energy is used indicate the energy absorbed and dissipated during the

    thoracicimpacteventuptothepointofmaximumdeflection.Deflectionenergyisaonedimensionalanalogtostrainenergy[10]wherethespatialderivativeofdeflectionenergyisforceratherthanstress.Ifthedeflectionenergyversusdefelctioncurvehasaconstantslopeandappliedforce isthespatialderivativeofenergy,thenappliedforceisconstant.Theslopeofthecurveis

    .

    andtherefore

    . 3

    Wehavearelationshipamongenergy,constantforce,anddeflectionthatcanbeusedtodevelopscalefactorsfornormalisation.This relationship also leads directly to a twoDOF viscoelasticmodel that can be used to find the elastic

    stiffness,viscousconstant,damped frequencyand theperiod. The forceversusdeflectioncurvewouldhaveconstantforceuptothemaximumdeflectionasseeninFig.2.

    Fig.2.Schematicofaconstantforcevs.deflectioncurve

    withelasticandviscousenergyareaslabeled.Thetotaldeflectionenergyistheareaunderthecurve,E=Fconstant*Smax.Theelasticenergyportion(stored)of

    theenergyisthelowerrighttriangle,*E=*Fconstant*Smax.Theviscousenergyportion(dissipated)istheupperlefttriangleandhasthesamearea.TheequationfortheforceinatwoDOFviscoelasticmodelis

    (4) where =elasticstiffness =viscousconstant =timederivativeofdeflection(velocity).Theelasticenergyis (5)and

    K= (6)

    Theviscousenergyis (7) where =velocityatzerodeflectionor and (8)

    ThedampednaturalfrequencyfromthedifferentialequationforatwoDOFviscoelasticsolidis

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  • (9)

    where =dampednaturalfrequency =(mI+ms)/(mI*ms) (10) mI=impactormass ms=subjecteffectivemassand theperiodis 2 / . (11)Itshouldalsobenotedthatbecausetheviscousenergy is linearlydependentontherateofdeflection,the

    ratemustbeastraight line in equaltothe impactvelocity, ,whendeflection iszeroandequaltozeroatmaximumdeflection, (12) where =rateofdeflection =impactvelocity =maximumdeflection =deflection.Fora constant force thedifferentialequationabove isequivalent to thedifferentialequation for the two

    element viscoelastic solid (Equation 4). Solving the differential equation for deflection, S(t), results in anincreasing exponential function in time [11]. The rate, , is a complementary decreasing exponentialfunction. Whenmultipliedby their respective coefficientsand combined the result isa constant forceas isrequiredbytheconstantslopeofthedeflectionenergyversusdeflectioncurve.Theeffectivemassofthesubjectandthesubjectvelocityatthetimeofmaximumdeflectioncanbefoundby

    solving the equations for conservation of energy, including the deflection energy, and conservation ofmomentumsimultaneouslyfromtimezerotothepointofmaximumdeflection.Theresultingequationsare

    2 11

    and

    2 12

    where effectivemassofthesubject

    impactormass =impactvelocity,V0= deflectionenergy velocityofsubjectatmaximumdeflection.Finally, it shouldbenoted that thisapproach isapplicable toa twodegreeof freedom system (pendulum

    impact)ortoonedegreeoffreedomsystemssuchassledordroptestsbymodifyingthesizeoftheimpactingmass,i.e.,aninfinitemassforadroptestandaverylargemassforasledtest.

    MultivariateRegressiontoEstimate50thPercentileDeflectionEnergyandSlope Wenowhaveamodelthatprovidesvaluesforenergy,slope,force,deflection,stiffness,theviscousconstant,time, effectivemass, and subject velocity for each subject that can be used to develop scaling ratios tonormalise the response to thatofa standardhuman. The standardhuman responsewasestimated fromamultivariaterelationshipdevelopedusingthedeflectionenergyandtheslopeoftheenergycurve,respectively,asdependentvariablesandtheanthropometrymeasuresforallsubjectsasindependentmeasures.TheMatlabfunction stepwiselm [12]wasused todevelop this relationship. The analysisusing the stepwiselm function

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  • considered all of the independent anthropometry variables...

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