The Effect of Body Size on Adult Human Rib Structural Properties

Abstract

Rib fractures sustained during motor vehicle crashes are a common cause of increased mortality, and their causes within and between individuals is not fully understood. This study aimed to identify the effect of body height, body weight, and body mass index (BMI) on measured structural properties of human ribs. Two‐ hundred sixty one ribs from one‐hundred forty seven individuals were impacted in a dynamic (2.0 m/s) bending scenario representing a frontal thoracic impact. Linear regression revealed body height and weight each had a significant positive relationship with peak force and stiffness (p<0.001 for all), and weaker relationships with total energy (p=0.003 and 0.015, respectively), although explanatory power remained low for all relationships (R 2 =10‐12%). The introduction of age as an additional variable in multiple regressions increased the ability to predict structural properties: R 2 =33%, 17%, and 41% for peak force, stiffness and total energy, respectively. Body size parameters have a measurable effect on rib properties, but should be used with caution to understand variance in dynamic whole rib response because the source of the majority of variation remains unaccounted for in all models explored here. Future work will incorporate rib‐specific variables and explore the utility of these relationships on scaling and normalization techniques.

Full text

Abstract
Ribfracturessustainedduringmotorvehiclecrashesareacommoncauseofincreasedmortality,andtheir
causeswithinandbetweenindividualsisnotfullyunderstood.Thisstudyaimedtoidentifytheeffectofbody
height,bodyweight,andbodymassindex(BMI)onmeasuredstructuralpropertiesofhumanribs.Two‐
hundredsixtyoneribsfromone‐hundredfortysevenindividualswereimpactedinadynamic(2.0m/s)bending
scenariorepresentingafrontalthoracicimpact.Linearregressionrevealedbodyheightandweighteachhada
significantpositiverelationshipwithpeakforceandstiffness(p<0.001forall),andweakerrelationshipswith
totalenergy(p=0.003and0.015,respectively),althoughexplanatorypowerremainedlowforallrelationships
(R2=10‐12%).Theintroductionofageasanadditionalvariableinmultipleregressionsincreasedtheabilityto
predictstructuralproperties:R2=33%,17%,and41%forpeakforce,stiffnessandtotalenergy,respectively.
Bodysizeparametershaveameasurableeffectonribproperties,butshouldbeusedwithcautionto
understandvarianceindynamicwholeribresponsebecausethesourceofthemajorityofvariationremains
unaccountedforinallmodelsexploredhere.Futureworkwillincorporaterib‐specificvariablesandexplorethe
utilityoftheserelationshipsonscalingandnormalizationtechniques.
KeywordsEnergy,Force,Fracture,Stiffness,Thoraxinjury
I. INTRODUCTION
Thethorax,andespeciallyribs,arecommonlyinjuredinmotorvehiclecrashes(MVC)andthistrauma
representsasignificantthreattolife[1].Understandingribresponseiscrucialtoelucidatespecificmechanisms
offractureanddevelopaccuratetools(e.g.,anthropomorphictestdevicesandcomputationalmodels)designed
toassistinmeasuringthoracicresponseinanMVCandultimatelytomitigatefracturerisk.
Humanribstructuralpropertieshavepreviouslybeenreportedastohowtheyrelatetoindividual
characteristicssuchaschronologicalageandsexwithlimitedsuccess[2].However,theinfluenceofbodysize
onstructuralpropertiesisrelativelyunexplored,andtheseparametershavepotentialtoexplainadditional
variationinpropertiesthatageandsexalonedonot.Therehavebeenonlyafewstudiesexploringhumanbody
sizeanditseffectsondynamicribpropertiesrepresentativeofloadinginacarcrashscenario[2,3].
Furthermore, many researchers rely on scaling techniques which utilize height and weight to normalize
impactresponsedataobtainedfromexperimentaltesting[4‐6]. Severalnormalizationtechniquesutilizeother
morecomplexanthropometricvariablesbeyondheightandweightbutstilloperateundertheassumptionthat
the human body behaves as a simple mechanical system and therefore the relationship between impact
responseandbodysizeparameterscanbeobtainedthroughlinearscalefactorratios[7‐10].However,whereas
thesenormalizationtechniquesareeffectivewhenappliedtoresponsedatafromtestsubjectsthathavesmall
variationsinsize/weightaboutacentralpopulation(i.e.,approximate50thmaletestsubjectsnormalizedtoa
precise50thmaleanthropometry),thetechniquestendtoperformworsewhenadjustingonepopulationtoa
vastly different one (e.g., 50th male to child), likely due to anatomical variation and differences in skeletal
geometricormaterialproperties(tissuequality)thataretoocomplextobeaccountedforusinglinearscaling
ratios.Forexample,[11]exploredvariationinbothribcross‐sectionalgeometryandthecombinationofcross‐
sectional and gross geometry and found these parameters could successfully predict impact response.
Furthermore,theauthorsnotedtheserelationshipswereindependentofbodysize(definedsimplyasweight
multiplied by bone length), indicating there is potential for using specific bone geometry to improve existing
scalingtechniques.
Nonetheless,itisimportanttofirstunderstandtheeffectsofsubject‐levelvariables,suchasbodyheightand
TheEffectofBodySizeonAdultHumanRibStructuralProperties
A.M.Agnew,M.M.Murach,E.Misicka,K.Moorhouse,J.H.BolteIV,Y.S.Kang
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weight,ontheresponseandfractureriskofcomponentsofthehumanbodywhichareatahighriskofinjury
duringmotorvehicleaccidentssuchasthehumanthorax.Forexample,[12]conductedafiniteelement(FE)
studyinwhichbodyweightandheightaswellasareamomentsofinertiaoftheribcageandribsalonewere
variedtoinvestigatetheireffectsontheresponseofthethorax.Althoughtheauthorsconcludedthatthearea
momentsofinertiawerethemostimportantparameters,theyalsofoundthatweightandheightwere
significantpredictorsofthemaximumforceandmaximumchestdeflection,respectively.
AstheseFEmodelsbecomeincreasinglyutilizedinthefieldofinjurybiomechanics,itisimportantthatthe
load‐bearingcomponentofthehumanthorax,theribs,bescaledandmodeledappropriately.Severalstudies
havefocusedontherelationshipbetweenbodysizeandgrossribgeometryandfoundingeneralthatincreases
inbodysizeresultedinincreasesinribgeometry[1,3,13].However,theinfluenceofbodysizeonthestructural
responseofindividualribstodynamicloadingthatisrepresentativeofacarcrashscenariohasyettobe
investigated.Identifyingparametersthatcanbereadilyquantifiedsuchasbodysizethatareimportantfor
understandingfractureriskwillallowforimprovementstoscalingtechniquesandinjurycountermeasures.
Therefore,theobjectiveofthisstudyistoidentifytheeffectoftotalbodyheight,bodyweight,andbodymass
index(BMI)onribstructuralstiffness,peakforce,andtotalenergy.
II. METHODS
Sample
Two‐hundredsixty‐onemid‐levelribs(4‐7)from147adultpost‐mortemhumansubjects(PMHS)were
analyzedinthissample,including67femalesand194males.RibswereacquiredethicallyviatheOhioState
University’sBodyDonationProgramandLifelineofOhio.Totalbodyheightandbodyweightwererecordedat
thetimeofdeath,andbodymassindex(BMI)wascalculatedas:[weight(kg)/height(m)2].BMIwasfurther
categorizedaccordingtotheWorldHealthOrganization(WHO)standards:<18.5=underweight,18.5‐
24.9=normalweight,25.0‐29.9=overweight,and30.0+=obese[14].Heightwasnotrecordedforoneindividual
forwhichoneribwastested,sothetotalsamplesizeisreducedbyoneforheightandBMI.Table1includes
descriptivestatisticsforthesample.


TABLEI
SAMPLE
HeightWeightBMIAge
(cm)(kg)(kg/cm2)UnderweightNormalOverweightObese(yrs)
n(ribs)260261260231137945261
Mean174.776.625.116.621.827.034.556.6
SD9.518.65.81.61.731.44.6423.3
Min142.232.212.5‐
*18.5*25.0*>30.0*15
Max199.4136.048.4<18.5*24.9*29.9*‐
*108
*
WHOdefinedcorridors


ExperimentalTesting
Completeribsfromcostovertebraltocostochondraljunctionwereexcisedfromindividualsimmediatelynear
thetimeofdeath,wrappedinnormalsaline‐soakedgauze,andstoredat‐20°C.Topreparefortesting,ribs
werethawedandcleanedofallexternalsofttissue,andtheendswerepottedin4x4x3cm3blocksofBondo®
BodyFiller(BondoCorporation,Atlanta,GA)insingle‐planeorientation.Twostraingauges(CEA‐06‐062UW‐350,
VishayMicro‐Measurement,Shelton,CT,)eachwereappliedtothepleuralandcutaneoussurfacesat30%and
60%ofthetotalcurvelength(Cv.Le)oftheribfromvertebraltosternalend.Spanlength(Sp.Le),alinear
measurementbetweenribends,wasalsodocumented.Ribswerekeptwell‐hydratedwithnormalsaline
throughoutpreparationandtesting.
Allribswereimpactedinadynamic(average2.0m/sand0.5strain/s)bendingscenariorepresentingafrontal
thoracicimpactwiththesternalribendtranslatedtowardsthevertebralend.Thiswasaccomplishedina
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custompendulum(54kg)fixture.Theexperimentalcoordinatesystemwasconstructedsuchthattheprimary
loadingaxiswasdefinedastheX‐axis,withtheY‐axisextendingverticallyaccordingtotheSAEJ211standard
(Fig.1).Inthisconfiguration,bendingwasrestrictedtotheX‐Yplanealmostentirely.Displacementofthe
sternalribendwasmeasuredbyalinearstringpotentiometer(RayelcoP‐20A,AMETEK,Inc.Berwyn,PA)fixed
tothemovingplateofthefixture.Forcesandmomentswererecordedbya6‐axisloadcell(CRABIneckload
cell,IF‐954,Humanetics,Plymouth,MI)behindthefixedplate.


Fig.1.Bending
experimentshowinga
ribinthetestfixture



DataAnalysis
ForceanddisplacementdatawerefilteredusingaCFC180filter[15].Utilizingtheforce‐displacement(F‐D)
curvefromeachimpact,structuralstiffnesswascalculatedastheslopeof20‐80%ofthelinearelasticportion
[16],peakforcewasdefinedasthemaximumforceintheX(primary)loadingdirectionpriortofracture,and
totalenergywascalculatedastheareabeneaththeF‐Dcurvefromtimezerototimeoffailure.Thestructural
propertiesoflinearstructuralstiffness(K),peakforce(Fpeak),andtotalenergy(Utot)aretreatedasdependent
variablesinthisstudy.Height,weight,andBMIweretreatedasindependentvariablesandwereallassessedas
continuousdatapointstoinvestigatepredictiverelationshipswithstructuralproperties.Thiswasaccomplished
usingbothunivariateandmultipleregressionmodels.Additionally,differencesinmeansofBMIclassifications
werecomparedusinganalysisofvariance(ANOVA)forallstructuralproperties.Anα
valueof<0.05was
consideredsignificantforallstatisticaltests.

III. RESULTS
DescriptivestatisticsforeachstructuralpropertyfortheentiresampleandwhendividedbyBMIcategory
canbefoundinTableII.UnivariateregressionresultsarepresentedinTableIIIandFigure2.Bodyheighthada
significantpositiverelationshipwithpeakforce(p<0.001),stiffness(p<0.001),andtotalenergy(p=0.003).Body
weighthadasignificantpositiverelationshipwithpeakforce(p<0.0001)andstiffness(p<0.0001),andaslightly
weakerrelationshipwithtotalenergy(p=0.015).Bodymassindex(BMI)assessedasdiscretevalueshada
significantpositiverelationshipwithpeakforce(p=0.005)andstiffness(p=0.003),butnottotalenergy
(p=0.200).Heightandweightpredictedpeakforceandstiffnessbest,explainingapproximately10‐12%of
varianceinthedata.
Sincepreviousanalysisonasubsamplehasshownagetohaveastatisticallysignificantinfluenceonthe
structuralpropertiespresentedhere[2],agewasincludedalongwithheightandweightasapredictorvariable
inmultipleregressionanalysis.Thesedatawerestandardizedandcenteredpriortoapplicationinthemodels,
andtheresultscanbefoundinTableIV.Inshort,age,heightandweighttogetherexplainedaround33%of
varianceinpeakforce,17%instiffness,and41%intotalenergy(p<0.0001forallthreemodels),butage
contributestoexplainingthemajorityofvarianceineachcase.
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TableII
DESCRIPTIVESTATISTICS
TotalSampleBMIClassification
UnderweightNormalOverweightObese
PeakForce(N)110.7
(±49.3)
86.2
(±35.6)
100.4
(±46.2)
130.5
(±53.0)
114.3
(±44.1)
Stiffness(N/mm)3.33
(±1.69)
2.48
(±1.25)
3.01
(±1.58)
3.85
(±1.60)
3.66
(±1.95)
TotalEnergy(N*mm)3714
(±2934)
2710
(±2551)
3535
(±2989)
4329
(±3169)
3598
(±2360)




TableIII
UNIVARIATEREGRESSIONRESULTS
PeakForceStiffnessTotalEnergy
R2(%)P‐valueR2(%)P‐valueR2(%)P‐value
Age19.3<0.00017.4<0.000136.9<0.0001
Height12.9<0.00019.8<0.00013.40.003
Weight10.3<0.000110.5<0.00012.30.015
BMI3.00.0053.50.0030.60.200
Note:boldedvaluesarestatisticallysignificant




TableIV
MULTIPLEREGRESSIONRESULTS
PeakForceStiffnessTotalEnergy
Contribution
(%)p‐valueContribution
(%)p‐valueContribution
(%)p‐value
Age18.4<0.00016.49<0.000137.19<0.0001
Height7.55<0.00013.900.0242.140.002
Weight6.070.0045.200.0020.230.972
Age*Height0.060.5400.190.2990.650.099
Age*Weight1.230.0441.070.1840.100.092
Height*Weight0.060.6540.040.8540.370.153
Age*Height*Weight0.000.9920.440.2560.550.133
Total R2=33.36<0.0001R2=17.33<0.0001R2=41.22<0.0001
Note:boldedvaluesarestatisticallysignificant








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Fig.2.Scatterplotsshowingindependentrelationshipsofpeakforce(left),stiffness(center),andtotalenergy(right)withheight
(top),weight(middle),andBMI(bottom)
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
WhenBMIwasassessedcategorically,acleartrendforallstructuralpropertiesemergedofincreasingwith
meanBMIfromtheunderweighttonormaltooverweightcategoriesandthendecreasingfromtheoverweight
toobesecategories(Fig.3).ANOVAresultsrevealsignificantdifferencesinBMIgroups(p<0.0001)forpeak
forceandstiffness,whilenostatisticallysignificantdifferenceswerefoundbetweengroupsfortotalenergy
(p=0.083)despitethesamedistincttrend.Toidentifywherethedifferencesliebetweengroups,posthocTukey
testswereperformed.Nosignificantdifferenceswerefoundbetweenunderweightandnormalgroupsor
betweenoverweightandobesegroups,butadifferencewasfoundbetweennormalandoverweightgroupsfor
peakforceandstiffness.
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ObeseOverweightNormalUnderweight
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Fig.3.Intervalplotsshowingmeanand95%confidenceintervalsofeachBMIclassificationforPeakForce(left)
andTotalEnergy(right).Stiffnessresultsarenotshown,butthetrendappearssimilarwithanincreasein
structuralpropertiesaccompanyinganincreaseinBMI,exceptforintheobesecategory.


IV. DISCUSSION
Thisresearchfoundthatbodysizeparametersplayaroleinthedeterminationofindividualdynamicrib
responseinafrontalloadingscenario.Fewotherstudieshaveexploredtheeffectsofbodysizeonribor
thoracicproperties,althoughtherehasbeenresearchconductedtoexploretherangesofvariationseeninrib
orthoraxgeometryrelatedtosizeparameters.Forexample,[13]usedComputedTomography(CT)datato
developastatisticalribcagegeometrymodelandfoundasignificantinfluenceofheight,BMI,andsex,in
additiontoaweakereffectofage.Similarly,[1]foundalargereffectofBMIthanageonribangle.Despite
thesefindings,therehavebeenfewattemptstolinkthoracicgeometrychangeswithskeletalmechanical
properties.
Kalraetal[17]performed3‐pointbendingonadultribsegmentsataquasi‐staticrateandfoundnoheightor
weighteffectonequivalentmeasuresofmomentandstiffness.Sincethisexperimentwaspointloadingona
smallsectionofribanddidnottaketheoverallsizeoftheboneintoaccount,itisreasonabletoconcludethat
theribcross‐section(presumablyprovidingthemostresistancetobendinginthistest)wouldbelessinfluenced
bytotalbodysize.Althoughinasimilarquasi‐static3‐pointbendingribtestas[17],asignificantrelationship
betweenmomentandheightinchildrenwasfound[18].Tofurtherexploretheeffectoftotalribsizeon
properties,aposthocanalysisonthesampleinthecurrentstudywasconductedutilizingthefollowing
measuresofribsize:totallengthalongthecurvatureoftherib(Cv.Le)andminimumlinearlengthbetweenthe
vertebralandsternalribends(Sp.Le).Asignificant(p<0.0001)correlationwasfoundbetweentotalribsize,
curvelength(Cv.Le)andspanlength(Sp.Le),withbodyheight(Pearson’sr=0.447and0.319,respectively),but
notwithbodyweight(p=0.624and0.185,respectively).Thisisconsistentwithpreviousstudieswhichfoundrib
curvelengthtobeassociatedwithtotalbodyheight[3,19].However,inourstudyanadditionalposthoc
analysisutilizingalinearregressionrevealsnorelationshipbetweenCv.LeorSp.Leandanyofthestructural
properties,suggestingmoreworkneedstobedoneinthisarea.Itisanticipatedthatribcross‐sectional
geometryormicrostructuralvariableswillhelpprovideadditionalunderstanding.Forinstance,inasimulation
study,[12]foundbodyheightandweighttoinfluencethoracicinjuries,butthatrib‐specificmeasurements(e.g.,
areamomentofinertia)couldbetteraccountforoverallthoracicresponsesandinjuries.
Interestingly,[11]foundthatribcross‐sectionalgeometry(totalcross‐sectionalarea,corticalbonearea,and
sectionmodulus)aswellthecombinationofcross‐sectionalandgrossgeometry(robusticityandwholebone
strengthindex)wereallsignificantpredictorsofmeasuredpeakforceandstiffnessandcanaccountforasmuch
as75%ofthevariationseeninthesestructuralproperties.Althoughskeletalmorphology(i.e.grossgeometry)
isrelatedtobodysize,thecross‐sectionalgeometryisdependentonavarietyoffactorssuchasspecificloading
environmentandgenetics[20],andthereforemayprovideawaytoaccountforthesedifferencesbetween
individuals.Thisworkprovidespreliminaryevidencethatinclusionofskeletalgeometrymayimproveexisting
scalingtechniquesandallowforpredictableadjustmentstovariouspopulations(pediatricorelderly),however
moreresearchneedstobedoneinthisarea.
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ThetrendinstructuralpropertiesacrossdiscreteBMIclassificationswhereeachpropertyincreasesfrom
underweighttonormalweight,continuestoincreaseandpeaksintheoverweightcategory,butthenisreduced
inobesity,presentsaninterestingdiscussiontopic.Thedescribedpattern,whichisobservableforallthree
structuralproperties,suggestsafunctionaladvantageintheformofhigherresistancetobendingasmorebody
sizeisgained(tallerandheavier),untilathresholdwherethesebenefitsarethenoutweighedbythedeleterious
effectsofobesity.Theeffectofobesity(i.e.,excessiveadiposetissue)onfractureriskiswidelydebatedinthe
literature[21].However,thereisevidencethatthetrendobservedinthecurrentstudyisrepresentativeof
fractureriskvariationsacrossBMIclassificationsseenintheclinicalenvironment[22]suggestingthatadvanced
obesityhasnegativeimpactsonbonequality[23].Theseresultsshouldbeapproachedwithcautionasthereis
greatvariationintheBMIdataasseeninFigure2,andthereareunequalnumbersofsubjectsineachBMI
category.
Displacementwasnotincludedasadependentvariableinthisstudy,becausepotentialrelationshipswith
bodysizemaybeconfoundedbyitstypicalpresentationasavariablenormalizedbyribspanlength[2,16].This
complicatedinteractionwillbeexploredinfutureworkinconjunctionwiththoracicanthropometry(e.g.,chest
depth)tobetterunderstandhowthesizeandshapeofthethorax,isinfluencedbyindividualribresponse.
Additionally,itwillbecrucialtolearnthespecificrolethatindividualribresponseplaysinoverallthoracic
response.Thisaddedlayerofcomplexitywillaidourunderstandingofthoracicinjuryrisk,asthisisbasedmostly
onchestcompression.
Sexwasnotincludedinthemodelspresentedhere.Pastworkonasubsetofthissamplefoundsexto
influencepeakforce,stiffness,andtotalenergy[2].However,thesedifferencesmayhavebeenduetosexual
dimorphism,inwhichcaseincludingsexhereinwouldconfoundthemodelusingbodysizeparameters.Infact,a
posthocanalysisrevealedsignificantdifferencesinheightandweightbetweenmalesandfemales(studentt‐
test,p<0.0001forboth),supportingtheuseofapooledsampleforthispreliminarywork.Futureresearchaims
toutilizeamorecomplexstatisticalmodelabletoteaseoutsex‐differentiatedstructuralpropertieswhile
controllingforbodysize.Furthermore,apossiblesamplingbiascouldbeinfluencingresultsasnotallagesor
bodysizesareequallyrepresentedinthesample.
Itwasassumedherethatlinearregressionmodelswereappropriateforanalysisofthisdataset.While
previousribdataanalysishasutilizeddifferentandmorecomplexmodelingtechniques[2,16],thoseresultsare
veryconsistentwithsimpleregressionmodelsasprovidedhere,andthereforetheanalysiswassimplifiedfor
thispreliminarywork.Futurestudiescanfurtherexploremorecomplicatedmodelsandpossiblynon‐linearfits.

V. CONCLUSIONS
Bodysizeparametershaveaneffectonstructuralpropertiesofhumanribs,butevenwhenincludedwithage,
predictivemodelsstilldonotexplainthemajorityofvariationinpeakforce,stiffness,ortotalenergy.Future
workwillinvestigatetherelationshipbetweenthoracicanthropometryandribsizeandproperties.Additionally,
morebiologically‐relevantvariablesrelatedtothespecificgeometry,cross‐sectionalgeometry,and
microstructureofribswillbeexploredaspredictorsofribstructuralresponsetoloading.Thesedatacan
ultimatelybeadvantageoustoaidinimprovingsize‐basedscalingtechniques.

VI. ACKNOWLEDGEMENT

ThankyoutotheNationalHighwayTrafficSafetyAdministration(NHTSA)forfundingthiswork.Allopinions
expressedwithinthismanuscriptaresolelythoseoftheauthorsanddonotrepresenttheviewsofthesponsor.
WeareindebtedtotheanatomicaldonorswhomadethisresearchpossibleviaTheOhioStateUniversity’sBody
DonorProgramandLifelineofOhio.ThankyoualsotostudentsandstaffoftheInjuryBiomechanicsResearch
CenterincludingArriannaWillis,JulieBing,RakshitRamachandra,DavidStark,JonBlank,RandeeHunter,and
AksharaSreedhar.



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