Spinal lordosis optimizes the requirements for a stable erect posture

Wagner Heiko, Liebetrau Anne, Schinowski David, Wulf Thomas, De

Description

Lordosis is the bending of the lumbar spine that gives the vertebral column of humans its characteristic ventrally convex curvature. Infants develop lordosis around the time when they acquire bipedal locomotion. Even macaques develop a lordosis when they are trained to walk bipedally. The aim of this study was to investigate why humans and some animals develop a lumbar lordosis while learning to walk bipedally. Results We developed a musculoskeletal model of the lumbar spine, that includes an asymmetric, dorsally shifted location of the spinal column in the body, realistic moment arms, and physiological cross-sectional areas (PCSA) of the muscles as well as realistic force-length and force-velocity relationships. The model was used to analyze the stability of an upright body posture. According to our results, lordosis reduces the local joint torques necessary for an equilibrium of the vertebral column during an erect posture. At the same time lordosis increases the demands on the global muscles to provide stability. Conclusions We conclude that the development of a spinal lordosis is a compromise between the stability requirements of an erect posture and the necessity of torque equilibria at each spinal segment.

Sujets

• Lordosis
• Évolution
• Spine
• Stability
• Biomechanics

Informations

• Publié par: biomed
• Publié le: 01 janvier 2012
• Nombre de lectures: 12
• Langue: English
• Poids de l'ouvrage: 2 Mo

Extrait

Wagner
etal
.
TheoreticalBiologyandMedicalModelling
2012,
9
:13
http://www.tbiomed.com/content/9/1/13

RESEARCH

OpenAccess

Spinallordosisoptimizestherequirementsfora
stableerectposture
HeikoWagner
1,3,4*
,AnneLiebetrau
1,4
,DavidSchinowski
1
,ThomasWulf
1,3
andMarcHEdeLussanet
2

*Correspondence:heiko.
[e-mail]
1
MotionScience,Westf.Wilhelms-
UniversitätMünster,Horstmarer
Landweg62b,48149Münster
Fulllistofauthorinformationis
availableattheendofthearticle

Abstract
Background:
Lordosisisthebendingofthelumbarspinethatgivesthevertebral
columnofhumansitscharacteristicventrallyconvexcurvature.Infantsdevelop
lordosisaroundthetimewhentheyacquirebipedallocomotion.Evenmacaques
developalordosiswhentheyaretrainedtowalkbipedally.Theaimofthisstudy
wastoinvestigatewhyhumansandsomeanimalsdevelopalumbarlordosiswhile
learningtowalkbipedally.
Results:
Wedevelopedamusculoskeletalmodelofthelumbarspine,thatincludes
anasymmetric,dorsallyshiftedlocationofthespinalcolumninthebody,realistic
momentarms,andphysiologicalcross-sectionalareas(PCSA)ofthemusclesaswell
asrealisticforce-lengthandforce-velocityrelationships.Themodelwasusedto
analyzethestabilityofanuprightbodyposture.Accordingtoourresults,lordosis
reducesthelocaljointtorquesnecessaryforanequilibriumofthevertebralcolumn
duringanerectposture.Atthesametimelordosisincreasesthedemandsonthe
globalmusclestoprovidestability.
Conclusions:
Weconcludethatthedevelopmentofaspinallordosisisa
compromisebetweenthestabilityrequirementsofanerectpostureandthe
necessityoftorqueequilibriaateachspinalsegment.
Keywords:
musclephysiology,lordosis,evolution,spine,stability,biomechanics,
motorcontrolSubmittedto:TheoreticalBiologyandMedicalModelling

Background
Lordosisisthetypicalconvexbendingofthehumanlumbarspine,andisthoughtto
beanadaptationtobipedalism[1-3].Theuprightbodyposturedistinguisheshumans
frommostmammals.Despitelordosisandthesubstantialevolutionarymodifications
ofthehumanlowerspineandhip,thetopographyofbackmusclesinhumansis
remarkablysimilartothatfoundinotherprimates[3].Thedevelopmentofalumbar
lordosisinhumansisapparentlynotgeneticallydetermined.Childrendevelopalordo-
sisastheyadoptbipedalstandingandwalking.EvenJapanesemacaquesgradually
acquireapronouncedlordosisofthelumbarspinewhentheyaretrainedtowalk
bipedally[1].Inwomen,lordosisproliferatessubstantiallyduringpregnancy[4].Thus,
whydohumansandsomeanimalsdevelopalumbarlordosiswhilelearningtowalk
bipedally?Whyisthisapparentlyasolutionthatisspontaneouslyarrivedatbythe
motorsystem?Whenregardingthecoronalplane,thespineismedialinthebody,so
thespinal-muscularsystemissymmetric(Figure1A,B).Normallythespinedoesnot

©2012Wagneretal;licenseeBioMedCentralLtd.ThisisanOpenAccessarticledistributedunderthetermsoftheCreativeCommons
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anymedium,providedtheoriginalworkisproperlycited.

Wagner
etal
.
TheoreticalBiologyandMedicalModelling
2012,
9
:13
http://www.tbiomed.com/content/9/1/13

symmetrical arrangement
A B

asymmetrical arrangement, with eccentricity
D C

asymmetrical arrangement, with eccentricity and spinal curvature
F E

Figure1
Generalizedschemaofthemusculoskeletalarrangement
.Differentgeometricarrangements
ofthespinalcolumn(bluedots)andglobalmuscles(red).Firstrow(A,B):symmetricalarrangementofthe
spinalsegments(asforexampleinthecoronalplane).Secondrow(C,D):asymmetricalarrangementwith
aneccentricspinalcolumn(e.g.themid-sagittalplane).Thirdrow(E,F):asymmetricalarrangementwithan
eccentricspinalcolumnandaspinalcurvature(e.g.alumbarlordosis).Leftcolumn(A,C,E):globalmuscles
actinginparalleltothespine(e.g.m.rectusabdominis,m.erectorspinae).Rightcolumn(B,D,F):global
obliquemuscles(e.g.m.obliquusexternusabdominis,m.obliquusinternusabdominis,m.multifidus).A,B,
C:Amuscularactivitypatternexistsinwhichallsegmentsareinequilibrium.D,E,F:Localcountertorques
arenecessarywhichmaybeminimizedbyaspinalcurvature(E,F).

developacurvatureinthecoronalplane(knownasscoliosis).Ontheotherhand,the
spinedoeshaveaneccentric,dorsalpositioninthebody,inthesagittalplane(Figure
1C,D).Inthisplane,thelumbarspinenormallydevelopsalordosis(Figure1E,F).
Thelumbarregionofthebackissupportedbyshortdeepmuscles,thatconnectthe
vertebrae,andlongsuperficialmuscles,thatconnectthethoraciccageandthepelvis.
Thefirstareusuallyreferredtoaslocalmuscles.Accordingtooneview,thelocalmus-
clesprovidethestabilityofthevertebralcolumn,whereasthesuperficialones,theglo-
balmuscles,wouldbethemobilizers[5-8].Thisviewhasbeenchallengedbecauseit
hasbeenshownthatglobalmusclesalsocontributetospinalstability[9-11].Moreover,
thelocalmusclesare,incontrasttotheglobalmuscles,characterizedbysmalllever
armsandsmallcross-sectionalareas,sothatthesemusclescannotgeneratelargetor-
ques.Thiswouldbeanundesirablepropertyifthestabilityofthespinewoulddepend
onlyonthelocalmuscles.
Ithasbeenshownthatthespinalcolumnofastandinghumanstoreselasticenergy
[12,13],butthiselasticitycannotexplaintheefficiencyofwalking[14].Also,ithas

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Wagner
etal
.
TheoreticalBiologyandMedicalModelling
2012,
9
:13
http://www.tbiomed.com/content/9/1/13

beensuggestedthatlordosisinthelowerbackregionmightminimizetheexternal
momentofthecentreofmassoftheupperbody,whileretainingastablehipjoint
position[12].
Inthepresentworkwestartfromthepremisethatstabilitycontroliscentraltothe
lumbarspine[9].Sincethehumanlumbarspineisaloadedchainofjoints(theinter-
vertebraldiscsbetweenthevertebrae),controllingitsstabilityisinherentlycomplex.
Whereastheglobalmuscleswiththeirlargemomentarmsarepowerfulenough,they
canonlycontrolthechain,butnottheindividualjoints.Thelocalmusclesmight
potentiallystabilizeeachjointiftheyhadthestrength.
Wethushypothesizethatthemotorsystemselectsaconfigurationinwhichthe
requiredlocalstabilizingtorquesoneachofthelumbarjointsisminimal.
Wechosetheconceptofself-stability[15]totestthishypothesis.Self-stabilityisthe
stableperformanceofamusculoskeletalsystemwithoutneuronalfeedback.Therea-
soningunderlyingthisapproachisthatneuronalcontrolistime-delayed,andthus,if
themusculoskeletalsystemismechanicallystablealready,thisenormouslyreducesthe
problemofstablecontrol.Theconceptofself-stabilityreliesfundamentallyonthe
non-linearmechanicalpropertiesofmuscles,asexplainedinthemethods.Forthe
model,weassumethateverydegreeoffreedomofeachofthejointsmustbeself-
stableatanytime,inordertomaintainreliablephysiologicalfunctioningofthespine.
Methods
Themusculoskeletalmodel
Themodelconsistedoffivelumbarvertebraeinaplane(Figure2),andbetweenthe
vertebraeitincludedfivecentersofrotation(CoR),representingthejointsoftheinter-
vertebraldiscs,eachwithonedegreeoffreedomrespectively.Sincetorsionaldegrees
offreedomareirrelevantinthelightofspinalcurvatures(lordosisandscoliosis),the
modelonlydescribedasingleplane(i.e.,eithercoronalorsagittal).Thepositionofthe
pelviswasfixedduringsimulations,andapointmass
m
[kg]representedtheupper
partofthebody(Figure2).Sinceweregardeduprightstanding,thepointmasswasat
horizontalposition0.Theverticalpositionof
m
wasat326mm.Theverticalpositions
oftheCoRsweretakenfrom[16]as:
L
1
L
2
=145mm,
L
2
L
3
=106mm,
L
3
L
4
=72
mm,
L
4
L
5
=35mm,
L
5
S
1
=5mm.
Thespinalcolumnhadahorizontaleccentricity
E
[m](Figure2).Theeccentricity
E
isdefinedasthedistanceofthespinalcolumntothesymmetricalaxis.Forexample,
inthesagittalplane,theeccentricityisequivalenttothedorsallocationofthespinein
thebody.Thespinalcurvaturewasimplementedasacubicsplinethrough
P
1,
P
3,and
P
2.
P
3waslocatedhalfwaybetween
P
1and
P
2,whereas
P
1waslocated176mmabove
P
2[16].AsdisplayedinFigure2,thespinalcurvatureparameter
Λ
[m]wasdefinedas
thehorizontalpositionof
P
3,withrespecttothemidlinebetween
P
1and
P
2.Both
parameterswerevariedfrom0to8cmin100equidistantsteps.
Threeantagonisticpairsofglobalmuscleswereincluded,i.e.straightmusclesacting
inparalleltothespineandtwoobliquearrangements(Figure2).Eachglobalmuscle
consistedoffiveparallelmusclefibers,tosimulatephysiologicallyrealisticsurfacesof
attachmentofthemuscles.
Muscularforcesdependonthelengthofthemuscles
l
andthecontractionvelocity
v
.Theforce-lengthrelationshipwasmodeledas[17,18]:

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Wagner
etal
.
TheoreticalBiologyandMedicalModelling
2012,
9
:13
http://www.tbiomed.com/content/9/1/13

A

B

r M iαM
ext
CT

LL23

0.2
E
Px 10.15
L
1
L
2
LL0.1
23
Λx


P
3
LL 430.05 LL5 4P
2
x

L
5
S
1
0 -0.15 0 0.15
horizontal position [m]
Figure2
A.Thespinemodel.Bluedotsindicatethejointsbetweenthelumbarvertebrae(
L
1
-
L
5
)
andthesacrum(
S
1
)
.Blueandredlinesindicatethelocationsofthestraightandobliqueglobalmuscle
fiber