Deformation and dynamic response of abdominal aortic aneurysm sealing

17 Pages·2017·9.42 MB·English

Abdominalaorticaneurysmsandendovascularsealing: deformationanddynamicresponse
Abdominal aortic aneurysms and endovascular
sealing: deformation and dynamic response
L.P. ARGANI1, F. TORELLA2, R.K. FISHER2, R.G. MCWILLIAMS3, M.L.
WALL4, AND A.B. MOVCHAN1
7 1DepartmentofMathematicalSciences,UniversityofLiverpool,UK
1
2LiverpoolVascular&EndovascularService,Liverpool,UK
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3RoyalLiverpool&BroadgreenUniversityHospitalsNationalHealthServiceTrust,Liverpool,UK
2
4RussellsHallHospital,TheDudleyGroupNHSFoundationTrust,Dudley,UK
t
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O

3
Abstract
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Endovascularsealingisanewtechniquefortherepairofabdominalaorticaneurysms.

]
Commercially available in Europe since 2013, it takes a revolutionary approach to
h
p aneurysm repair through minimally invasive techniques. Although aneurysm seal-
- ingmaybethoughtasmorestablethanconventionalendovascularstentgraftrepairs,
d
post-implantationmovementoftheendoprosthesishasbeendescribed,potentiallylead-
e
m ingtolatecomplications.Thepaperpresentsforthefirsttimeamodel,whichexplains
thenatureofforces,instaticanddynamicregimes,actingonsealedabdominalaortic
.
s aneurysms,withreferencestorealcasestudies.Itisshownthatelasticdeformationof
c
theaortaandoftheendoprosthesisinducedbystaticforcesandvibrationsduringdaily
i
s activitiescanpotentiallypromoteundesiredmovementsoftheendovascularsealing
y
structure.
h
p
[
1 Introduction

2
v
Thefirstattemptofanabdominalaorticaneurysmligationwasmadebackin1817bySir
4
AstleyCooper,andthefirstsuccessfulaneurysmrepairwasperformedin1951byCharles
1
6 Dubost. Theoperationremainedagreatchallengeformanyyears,andAlbertEinsteinwas
7 amongthosewhodiedasaresultofanabdominalaneurysmrupturein1955.
0
Aneurysmsoftheaortaarecommon,theymostofteninvolvetheinfra-renalsegment,as
.
0 showninFig.1,and,inmanycases,aretreatedbyendovascularaneurysmrepair(EVAR),
1
whichislessinvasivethanconventionalsurgery[1,2]. Traditionalaorticendograftsare
7
1 composedoftubesofthinsurgicalfabricreinforcedwithametallicskeletonandareinserted
: throughsmallgroinincisionsviathefemoralarteries;endograftsexcludeabdominalaortic
v
aneurysmsfromthecirculationbyanchoringthemselvesontosectionsofnormalartery
i
X
proximalanddistaltothedilatedsegment(the‘landingzones’)bymeansofbarbsorhooks,
r andbyexertingradialforceonthearterialwall. Despitetheirproveneffectiveness,ina
a
proportionofpatientstheseendograftsfailbyallowingbloodtore-entertheaneurysm.
Thisphenomenoniscalled‘endoleak’,whichisclassifieddependingonthecausesofthis
bloodflow; inparticular, themaintypesofendoleaksareillustratedinFig.1c. TypeIa
andIbcorrespond,respectively,toaleakaroundtheproximalandthedistallandingzones
oftheendoprosthesis;typeIIcorrespondstoapersistingcommunicationbetweenoneor
moreaorticside-branchesandtheaneurysm;typeIIIcorrespondstoaleakduetoholesin
thefabriccoverortodisconnectionbetweentheendograftmodules.[3]TheEVAR1trial
suggestedthattheneedforreinterventionforendoleakswasapproximately25%inthelife
1
Abdominalaorticaneurysmsandendovascularsealing: deformationanddynamicresponse
Figure1: ComparisonbetweenEVARandEVASsytems.a,SchematicrepresentationofthegeometryofanAAA
withanEVARendograft;athree-dimensionalreferencesystem(Oxyz)isintroduced(thex-axisis
perpendiculartotheplaneofthepage),whereascircledlettersLandRdenoterespectivelytheleftand
therightofthepatient. b,ReferenceschemeofthesameAAAwiththeEVASsystem. c,Schematic
representationofpossiblefailuretypesofEVAR.
ofthestudy;reinterventioniscostlyandtimeconsumingforthehealthcareprofessionals
andforthepatientsandgreatbenefitwouldbegainedifitcouldbeavoided[4,5].
Endovascularsealing(EVAS)isanewtechniquetotreatabdominalaorticaneurysms
(AAA).TheconceptunderlyingEVASisoriginal: thelumenoftheAAAiscompletelyfilled
byabio-compatiblepolymercontainedinendobagstraversedbycoveredstents,which
maintainperfusionoftheiliacarteries. Unliketraditionalaorticendografts,theNellix®
(©EndologixInc. Irvine,Ca,USA)endoprosthesis,presentlytheonlyendograftavailable
forEVAS,remainsinplacebyvirtueofthefactthat,followingitsdeployment,thereisno
roomfordisplacement,thuseliminatinganypotentialspaceforendoleaks. EVASmaybea
simpler,quickerprocedurethanEVAR,thusmayreducecostandbesafertothepatient,
andmayresultinlesserradiationusethanEVAR,thuspotentiallylessharmfulforpatient
andtheoperatingteam[6].Fig.1aandFig.1bshowthestructuraldifferencebetweenEVAR
andEVAS.
TheEVASconceptassumesthatthelandingzonesdonotdilateintime,thatthede-
pressurisedAAAdoesnotchangeinsizeorshape,andthatthethrombusoftencontained
withinAAAsremainsunalteredinvolumeanddistributionpost-implantation,asanyof
theseprocessescouldresultinendoleakorendograftdisplacement(‘migration’). Clinical
experienceislimitedbutresultsofEVAShavebeenpromisingthusfar[7–9],althoughmi-
grationoftheNellix®endoprosthesishasbeendescribed[10],suggestingthatoneormore
oftheaboveassumptionsmaynotholdtrueineverycase. Itisunclear,however,whyor
howpost-EVASmigrationoccurs: intuitively,themechanismsleadingtothiscomplication
willbeverydifferentthanthoseobservedfollowingimplantationofstandardendografts,
becausetheNellix®endoprosthesisisradicallydifferentfromconventionalvascularstent
grafts. AsignificantdifferencefromEVARisthatithasagreatermassdependentonthe
volumeoftheendobagspolymerfiller. Astheeffectsofstaticanddynamicloadsonan
objectarehighlydependentonitsmass,itislikelythatinvivoforcesmayhavearadically
differenteffectonpatientstreatedwithEVAS,ascomparedtothosetreatedwithstandard
endografts. Theaimofthisresearchwastoproducemathematicalmodelstodescribeand
quantifytheeffectoftheseforcesonEVASinvivo.
ThenewmodeloftheEVASsystemsincorporatesfluid-solidinteractionandcontact
interfaces. Thepatient’simmediatepost-operativeCTscanwasusedtobuildthegeometry
inthecomputationalmodel,basedonthenovelmathematicalapproach. Thefindingsof
themodelwereobtainedbeforetheclinicalinformationabouttheevolutionoftheEVAS
andsubsequentobservationsinthesecasestudiesbecameavailable.
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Abdominalaorticaneurysmsandendovascularsealing: deformationanddynamicresponse
Figure2: Mathematicalmodelgeometryofpost-EVASAAA.a,Solidcut-viewoftheidealisedgeometryofa
sealedAAAwithhelical-likeshapestents.b,Transparentviewoftheidealisedgeometryofasealed
AAAshowingthesurfaceseparatingthetwopolymerfilledendobags.c,Transparentviewofthesealed
AAAforPatient1.d,TransparentviewofthesealedAAAforPatient2.
2 Practical challenge and modelling
Athree-dimensionalmathematicalmodelofanAAAtreatedwithEVASwasdeveloped.
Inparticular,themodelwasfocussedonthezoneoftheabdominalaortabetweentherenal
arteriesandthecommoniliacbifurcations,assketchedinFig.1b;thesetwobranchpoints
havebeentreatedasthegeometricallimitofthesystem,whichincludestheaorticwall,the
thrombuslayer,andtwoendograftsenclosedintopolymer-filledendobags. Theendografts
haveasufficientlengthtocovertheinfrarenalaortaandmostofthecommoniliacartery
length.
Severalmathematicalmodelsbasedonidealisedandrealisticgeometriesareprovidedin
literature,whichshowtheeffectsoftheaorticbulgingontheredistributionofthepressure
and velocity of the blood and the subsequent stresses in the aortic wall, compared to a
healthyartery[11–16];theeffectsofstent-graftEVARontheinteractionbetweentheaorta
andthebloodflowhavealsobeeninvestigatedinidealisedandrealcasestudies[17–26].
Theaimofthisworkwastoanalyseelasticdisplacementsandstrainsinamodelofa
sealedAAA,whosegeometrywasextrapolatedfromrealisticmedicalmeasurements. wo
casesofpatientstreatedbyEVAS.Theendoprosthesishadbeenplacedinaccordancewith
theindicationsforuseprescribedbythemanufacturer. ThedrawingspresentedinFigs.2c
and2drepresenttheanatomyonthebasisofthepost-operativeCTscans.Theobjectivewas
toprovideapredictiveanalysisofmechanisms,whichmayberesponsibleformigration
and separation of components of the AAA sealing system in the postoperative period.
Furthermore,anidealisedgeometrywasalsoconsideredinthisworkwiththeaimtoshow
theroleofboundaryconstraints,supportingclinicalobservationsofEVARreportedinthe
literature[27–29]andconnectingthisconcepttoEVAS.Inparticular,thepapers[27,28]
haveaddressedtheroleofdistalfixationsforEVARsystems,andtheclinicalresults[29]
areconcernedwiththeimportanceoftheproximalfixationinEVARinstallations. This
idealisedsystemisdepictedinFigs.2aand2b,wheretheaortaandthethrombushavea
circularcross-sectiononlywithintheproximalanddistalneckzones,whereasinthecentral
part(theaneurysmsac)theyhaveanellipticalcross-section.
Themodelincludestwoparts,whichcomplementeachotherinthepredictiveanalysis
oftheAAArepairedwithEVAS:(1)the‘modalanalysis’, whichidentifiesthedynamic
responseofthesysteminabsenceofdrivingordampingforcesintermsofnatural(resonant)
frequenciesandtheirrelativevibrationmodes,whereallthecomponentsofthesystem
areoscillatingatthesamefrequencyinabsenceofanydrivingordampingforce;(2)the
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Abdominalaorticaneurysmsandendovascularsealing: deformationanddynamicresponse
Table1: Resonantfrequenciesfortheidealisedmodelwithdifferentboundaryconditionsandforthepatient
specificmodels.
Idealisedmodel
Patientspecificmodel
Mode
Endograftedgesconstrained
None(free) Bottom Topandbottom Patient1 Patient2
1 4.32Hz 8.58Hz 10.86Hz 11.55Hz 8.03Hz
2 10.15Hz 11.82Hz 15.91Hz 16.59Hz 14.49Hz
3 10.22Hz 12.17Hz 16.37Hz 17.12Hz 19.46Hz
4 16.37Hz 17.20Hz 17.32Hz 18.75Hz 21.76Hz
5 17.09Hz 26.46Hz 33.81Hz 26.37Hz 28.97Hz
6 18.07Hz 28.94Hz 34.62Hz >32Hz 29.75Hz
7 21.15Hz 35.85Hz 42.83Hz >32Hz >30Hz
‘staticanalysis’,whichaccountsformeanstaticbloodpressureandgravityforceactingin
differentregimes,includingthecaseswhenapatientstandsvertically,orislyingproneor
sidewaysafterthesurgery.
Themodalanalysisillustratestherelativemovementsofthesystemthatcanbeactivated
whenapatientissubjectedtovibrations. Becausethisanalysistakesintoaccounttheinertia
oftheentiresystem,specialattentionisgiventothepresenceofthepolymerfillercontained
in the endobags. It can be noted that an additional mass associated with the polymer
filler (2000kgm−3 density) may reach up to 500-700g, which would significantly lower
thefirstnaturalfrequencyofthesealedAAAsystem,comparedtotheAAAwithoutan
additionalmass. Thestaticanalysisallowsfortheevaluationofthetotaldisplacementof
theendoprosthesisduringtheimmediatepost-operativeperiod;differentconfigurationsof
thegravityforcearerepresentativeofthepositionsassumedbyapatientduringdailylife.
Oneofthemostchallengingfeaturesofthemodellingproposedinthiswork,which
differentiatesitfromthecurrentliteratureoncomputationalvascularbiomechanics[11–26],
isrepresentedbytheinteractionbetweenthecomponentsoftheEVASsystem. Inparticular,
theso-calledcontactinteraction(namely,theanalysisofthebehaviourofsolidstouching
each other at one or more points or zones) was implemented, taking into account the
possibilityofslipping(withandwithoutfriction)andseparationoftheEVAScomponents,
thusallowingforthedetectionofpossiblerelativedisplacementand/ortheseparation
betweentheendobagsaswellasbetweentheendobagsandthethrombus/aorta. Another
important feature implemented was the mutual interaction between the blood and the
structurewithintheanalysisoftheresonantfrequenciesofthesystem.
Thepurposeofthepresentpaperistointroducethenewmethodologyofthestudy
basedontheanalysisofpartialdifferentialequationsdescribingadynamicresponseofthe
EVASsystem,whichistypicallyneglected,ratherthanstatisticalanalysisofalargedataset.
ThefrictionalcontactstaticproblemsolvedinthecontextofEVAS,hasbeenpresentedfor
thefirsttimeheretodemonstratepossibleslippageandseparationoftheEVAScomponents,
whichhasbeenobservedbutnotaddressedinthepastinanymodellingwork.
3 Modal analysis
Everyfiniteelasticsystempossessesresonantfrequencies,whichcanbeobtainedby
meansofthemodalanalysis(eigenfrequencies). Ifsuchfrequenciesareinitiatedbyexternal
means,thendisplacementsassociatedwithresonantvibrationsmayoccur. Thenatureof
externalforces,actingonahumanbody,maybelinkedtofactorslikewalking,running,
horseriding,usingdifferentmeansoftransportation,usingmachinerywhichmayproduce
4
Abdominalaorticaneurysmsandendovascularsealing: deformationanddynamicresponse
Figure3: Firstthreevibrationmodesforthesealedaneurysmoftwopatients.Deformedandundeformedshapes
ofthesystemaresuperimposedforeachoscillatorymotion(highlightedwitharrows)foreachvibration
mode.Thehigherthemode(anditsrelativefrequency)themorecomplexistheshape;itcanbenoted
thattorsional-likemovementaffectsthevibrationmodesforbothpatientsalreadyforthefirstthree
vibrationmodes.Therepresentedamplitudeofvibrationisintentionallymagnifiedforclaritypurposes.
vibrations. Ifthefirsteigenfrequencyissufficientlyhigh,thiswouldimplythatthepatient
islesslikelytobeaffectedbythelowfrequencydynamicinput,whichmayresultfrom
everydayactivities. Forinstance,itshallbenotedthatthefrequencythatcanbeinduced
byrunningisapproximately3Hz,whereaspublictransportation(includingthecasesof
roughstreetsurfaceorspeedhumps)caneasilyinducevibrationsinarangebetween1Hz
and20Hzorwider,andhencefallingwithinarangeofinterestforhealthandsafetythatis
investigatedbynormsandotherworksaboutwhole-bodyvibrationexposure[30–32].
Weshallusetheterm‘frictionalclamping’toidentifyconstraintsatthelandingzones
of the EVAS components. This term is not conventional in medical practice, but it is
importanttoacknowledgeaconstraint,whichpreventstheEVAScomponentsfromfree
verticalmovement. ThenumericalimplementationisdiscussedintheMethodssection.
The results of the modal analysis for the idealised model are summarised in Table 1,
showing clearly that a stronger (longer sealing zone) graft frictional clamping leads to
higherresonantfrequenciesfortheAAArepairsystem. Inparticular,itcanbenotedthat
the first eigenfrequency can be relatively low (4.32Hz) in the case of a ‘weak’ frictional
clamping (i.e. when the endografts or the landing zones are too short). In contrast, a
‘strong’distalfrictionalclamping(whichispresentifthebottomedgesoftheendograftsare
constrained)providesahigherfirstnaturalfrequency(8.58Hz),whichbecomesevenhigher
(10.86Hz) when strong proximal and distal frictional clampings (both top and bottom
edgesoftheendograftsareconstrained)areimplemented,sothatinthesecasesresonant
phenomenainducedbyvibrationsarelesslikelytohappenduringadailyliferoutine.
TheresonantfrequenciesobtainedforthetwopatientsaresummarisedinTable1,where
itcanbenotedthatthefirstresonantfrequency(correspondingtoaswingingsidewaysmo-
tionoftheaneurysmsac)forPatient1(11.55Hz)isgreaterthanthefirstresonantfrequency
forPatient2(8.03Hz),whichmakesthesecondpatientpotentiallymorevulnerabletothe
externaldynamicforces. Nevertheless,asinpatientsfourresonantfrequencieswereinthe
5
Abdominalaorticaneurysmsandendovascularsealing: deformationanddynamicresponse
Figure4: ColourmapofthedisplacementfieldmagnitudeUfordifferentstaticloadcases.Discontinuities(jumps)
inthedisplacementfieldmayoccuronlyacrossthecomponentsinterfaces(contactsurfaces)anddenote
relativemovementsbetweenthecomponentsofthesystem;theendobagscanslidetogether(bottomleft)
withrespecttotheaorticwallorseparately(topleftandbottomright).Themapsofthedisplacement
magnitudearereferredtothetopandtothemiddlecross-sectionsoftheaneurysmsacforbothpatients.
rangebetween0Hzand20Hz,bothcouldstillbesubjectedtoundesiredvibrationinduced
movementsoftheendoprosthesis(migrationand/orseparationoftheendobags)during
routineactivities. Thefirstthreevibrationmodesandtheircorrespondingfrequenciesfor
eachofthetwopatientsaredepictedinFig.3.
4 Static forces and deformations
Threeconfigurationsofstaticloadingwereinvestigatedintheframeworkofthestatic
analysis,correspondingtodifferentdirectionsofgravity(inparticularthethreeprincipal
directionsofthethree-dimensionalreferencesystem)withconstantmeanbloodpressure.
Numericalsimulationsproducedforbothpatientsforaforementionedloadingsidentified
displacement jumps across the interfaces of the EVAS components, as summarised in
Fig.4. Theseincludetheinterfacebetweentheendobags,aswellastheinterfacebetween
individualendobagsandthethrombus/aorta;thesejumpsindisplacementfielddenote
relativemovementbetweentheEVAScomponents,thusdemonstratingthepossibilityof
migration.
Staticanalysisalsodemonstratesthatopeningofsmallvoidsbetweentheendobagsmay
alreadyoccurintheimmediatepostoperativeperiod. Furthermore,smallvoidopeningcan
alsooccursimultaneouslyatmanypointsbetweentheendobagsandthethrombus/aorta
withintheaneurysmsacand/oratthetopofthelandingzone,asdepictedinFig.7. Itcan
benotedthatpartialdetachmentoftheendoprosthesisfromthethrombusandaorticwalls
leadstolocalisedcontactpressure,whichincreasesthestressesontheaortaand,potentially,
canpromotethrombusdisplacement.
Itisshownthatgravityyieldsdisplacementofdifferentmagnitudedependingonthe
directionoftheforceandthatrelativemovementsoftheendoprosthesisaredecreasingin
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Abdominalaorticaneurysmsandendovascularsealing: deformationanddynamicresponse
Figure5: Colour map of the displacement field magnitude U for Patient 1. Discontinuities (jumps) in the
displacementfieldmayoccuronlyacrossthecomponentsinterfaces(contactsurfaces)anddenote
relativemovementsbetweenthecomponentsofthesystem.
7
Abdominalaorticaneurysmsandendovascularsealing: deformationanddynamicresponse
Figure6: Colour map of the displacement field magnitude U for Patient 2. Discontinuities (jumps) in the
displacementfieldmayoccuronlyacrossthecomponentsinterfaces(contactsurfaces)anddenote
relativemovementsbetweenthecomponentsofthesystem.
8
Abdominalaorticaneurysmsandendovascularsealing: deformationanddynamicresponse
Figure7: Partialdetachmentoftheendoprosthesisfromthesurroundingaorticandthrombusinnerwallsfor
differentpositionsofapatient(gisgravity).Partialseparationcanoccursimultaneouslyininterface
zoneswithinthesealedaneurysm. a,Smallvoidopeningbetweenthetwoendobagsandtheaorta
(Patient1).b,Partialseparationoftheendoprosthesisfromtheintraluminalthrombusininterfacezones
withintheaneurysmsac(Patient1).c,Smallvoidopeningatthetopleftinterfacezone(Patient2).d,
Verticalcut-viewofthepartialdetachmentoftheendoprosthesisfromtheupperaorticwall(Patient2).
thedistalneck. DetailedresultsareprovidedinFigs5and6.
ThetheoreticalanalysissuggeststhepossibilityofseparationoftheendobagsforPa-
tient 2, where the first eigenfrequency was low. The vibration modes as well as static
deformations(foreachforcedirection)showedspaceopeningbetweentheendobags,as
wellasbetweentheendobagsandtheaortaintheproximalpartofthesealedaneurysm
(maximumdepthandwidthdetectedequalto6.71mmand1.02mmrespectively,seeFig.7).
Onthecontrary,inPatient1thesealedAAAhasahigherfirsteigenfrequencyandrelative
displacementsofendobagsindicatingapossiblerelativeslippageratherthanseparation.
Thenumericalmodellingpresentedhereisdeterministicanddoesnottakeintoaccount
thewholetransienthistoryofdynamicforcing. Itisusedtopredictthetendencytomigra-
tion/separationofEVAScomponentsratherthanresultsofalong-timeevolution.
Thestaticanalysisfortheidealisedmodelconfirmedthatgraftclampingisimportant
alsoforEVASbecausethejumpsindisplacementfielddetectedinthewholeAAArepair
systemwereconsiderableinthecaseofweakfrictionalclampingandalmostnegligible
whendouble(topandbottomconstraints)‘strong’frictionalclampingwasprovided.
Theprobleminhandhasbeensolveddirectlythroughthepartialdifferentialequations
analysisofboundaryvalueproblemsandspectralproblems. Thenumericalresultsand
theoreticalconceptspresentedherearedeterministicanddonotinvolveatransientloading.
Althoughthecomputationalmodeldoesnotallowforavarietyofprobabilisticscenarios
of possibledynamic transientloads, itprovidesa valuableinsight on EVASlinking the
strengthofproximalfrictionalclampingandmigrationoftheendoprosthesisunderstatic
anddynamicforces. Itisalsonotedthatthedimensionsoftheendobagsdependonthe
longitudinalandlateralsizesoftheaneurysmandideallytheendobagsfillingoccupiesthe
entireaneurysmsac–otherwiserelativemovementofEVAScomponentsmayoccur. EVAS
techniqueisdesignedinsuchawaythatitdoesnotexertradialforcesonthelandingzones
9
Abdominalaorticaneurysmsandendovascularsealing: deformationanddynamicresponse
duringitsdeployment. However, itisshowninthenumericalsimulationsthatcontact
pressure acting on proximal and distal necks, arising from static and dynamic loading,
provideselasticdeformation(andsubsequentinducedstresses)oftheselandingzones.
5 From EVAR to dynamic EVAS
Despiteitsinnovativedesign,theNellix®endoprosthesismaybemorevulnerableto
certainforcesbecauseofitsmass.Thepresentstudydemonstratesthatresonancemayoccur
whentheendograftisexposedtofrequenciesencounteredduringday-to-dayactivities,
causingpendularmovementswhich,intime,maycontributetoendograftinstabilityand
migration. Interestingly,fixationoftheproximalanddistalendoftheendograftreduces
therangeofthesefrequencies,pushingthelowesttowardsthehigherendofthespectrum
experiencedduringdailyactivities. Evengravity,modelledasastaticload,may,potentially,
resultindisplacementoftheendobagsthatcouldallowbloodtoseepbetweenthem,or
betweentheendobagsandtheaorticwall. Thismay,inturn,createawedgethatintime
couldfosterendobagseparationandre-pressurizationoftheaneurysm.
Themodellingandnumericalsimulationswereperformedforaccuratelyreproduced
geometry and physical conditions describing the sealed AAA. The combination of the
modalandstaticanalysissuggeststhatthefirstpatientmaybepronetomigration,and
that,inthesecondcase,separationoftheendobagsmayoccur. Actualobservations,three
yearsafterEVAS,haveshownthat,inthefirstpatient,therehasbeenprogressivemigration
of1cmoftheendobags,togetherwithasmallincreaseofAAAvolume(maximumdiameter
increased2mm)withoutendoleak;inthesecondpatienttherehasnotbeenanymigration
nor endoleak but a relative separation (of 6mm) of the EVAS components and a small
increaseofAAAvolumehavebeendetected(maximumdiameterincreased3mm).
The results of this theoretical study can be used in three ways. First, they help to
elucidatepotentialmechanismsoffailureoftheNellix®endograftand, moregenerally,
oftheaneurysmsealingconcept. Second, astheeffectsofgravityandvibrationappear
dependent on the physical property of individual AAAs, these studies may be used in
selectionofpatientswhoseaorticanatomymakesthemmoreorlesssusceptibletotheeffect
oftheseforcespost-implant,ultimatelyenablingclinicianstorecommendmorepersonalised
treatment strategies. Third, they may inform future product designs, as manufacturers
strivetoproducenewgenerationsofendograftsthatarelesssusceptibletotheeffectsof
forcesexperiencedbypatientsduringtheirdailyactivities.
6 Methods
Ethics statement. The work did not involve any experiments on humans; the work is
purelytheoreticalanddidnotinvolveanyexperimentonhumantissues.Thepaperdoesnot
includeanyphotographs,X-raysorCTscansofhumanorgans. TheEVASendoprosthesis,
discussedinthepaper,hadbeenplacedinaccordancewiththeindicationsforuseprescribed
bythemanufacturer.
Geometry for real patients. The geometry was imported from two sets of data for
anonymisedpatientstreatedwithEVASin2013atRoyalLiverpoolandBroadgreenUni-
versity Hospital. For Patient 1 the AAA length and its maximal diameter are 107.3mm
and 67.4mm respectively, whereas for Patient 2 the length and the maximal diameter
are110.7mmand61.4mmrespectively. TheproximalnecklengthandangulationforPa-
tient1areequalto20mmand0°respectively,whileforPatient2theyareequalto45mm
and5°respectively. Inparticular,thediameterofthetopandofthebottomcross-sectionsof
10