ORIGINAL ARTICLE The effect of angulation in abdominal aortic aneurysms

16 Pages·2010·0.93 MB·English

MedBiolEngComput
DOI10.1007/s11517-010-0714-y
ORIGINAL ARTICLE
The effect of angulation in abdominal aortic aneurysms:
fluid–structure interaction simulations of idealized geometries
Michalis Xenos • Yared Alemu • Dan Zamfir •
Shmuel Einav • John J. Ricotta • Nicos Labropoulos •
Apostolos Tassiopoulos • Danny Bluestein
Received:15April2010/Accepted:3November2010
(cid:2)InternationalFederationforMedicalandBiologicalEngineering2010
Abstract Abdominal aortic aneurysm (AAA) represents disease progression and its possible effects on the AAA
a degenerative disease process of the abdominal aorta that risk of rupture. This dependence on geometric parameters
resultsindilationandpermanentremodelingofthearterial oftheAAAcanbeusedasanadditionaldiagnostictoolto
wall. A fluid structure interaction (FSI) parametric study help clinicians reach informed decisions in establishing
was conducted to evaluate the progression of aneurysmal whether a risky surgical intervention is warranted.
disease and its possible implications on risk of rupture.
Two parametric studies were conducted using (i) the iliac Keywords Aneurysm (cid:2) FSI (cid:2) Risk of rupture (cid:2)
bifurcation angle and (ii) the AAA neck angulation. Ide- Iliac angle (cid:2) Neck aneurysmal angle
alized streamlined AAA geometries were employed. The
simulations were carried out using both isotropic and
anisotropic wall material models. The parameters were 1 Introduction
based on CT scans measurements obtained from a popu-
lation of patients. The results indicate that the peak wall Abdominalaorticaneurysm(AAA)ruptureiscurrentlythe
stresses increased with increasing iliac and neck inlet 13th leading cause of death in the United States claiming
angles. Wall shear stress (WSS) and fluid pressure were the lives of approximately 15,000 patients each year [23].
analyzedandcorrelatedwiththewallstressesforbothsets Aneurysmal dilation of the aorta occurs in 2–4% of males
ofstudies.Anadaptationresponseofatemporaryreduction overtheageof65inthewesternworld.Thediseaseriskis
of the peak wall stresses seem to correlate to a certain increased in patients who have evidence of coronary, car-
extentwithincreasingiliacangles.Fortheneckangulation otid,orperipheralvasculardisease,hypertension,ahistory
studies it appears that a breakdown from symmetric vor- of smoking,or a family history ofaneurysmal disease [20,
tices at the AAA inlet into a single larger vortex signifi- 36, 52, 56]. Its physiological and biomechanical manifes-
cantly increases the wall stress. Our parametric FSI study tation is increased wall stiffness due to loss of elastin,
demonstrates the adaptation response during aneurysmal increasedwallstress,drasticdifferencesinwallshearstress
(WSS) in different regions of the aneurysm, all of which
weakens the aneurysmal region of the aorta, resulting in
M.Xenos(cid:2)Y.Alemu(cid:2)D.Zamfir(cid:2)S.Einav(cid:2)D.Bluestein(&) rupture.
DepartmentofBiomedicalEngineering,StonyBrookUniversity, Forpatientsathighriskofrupture,surgicalintervention
StonyBrook,NY,USA in the form of open surgery or endovascular repair is rec-
e-mail:[email protected]
ommended if the aneurysmal diameter is greater than or
equal to 5 cm and has a growth rate of 0.8 cm/year
J.J.Ricotta(cid:2)N.Labropoulos(cid:2)A.Tassiopoulos
DepartmentofSurgery,StonyBrookUniversityHospital,Stony [23, 26], based on patient follow-ups every 6 months or
Brook,NY,USA every year. However, this diameter based criterion fails to
identifysmallaneurysmsthatmayrupture[31].Attempting
J.J.Ricotta
to refine predictions of AAA rupture in order to help sur-
DepartmentofSurgery,WashingtonHospitalCenter,
Washington,DC,USA geons determine the need for a risky surgical procedure,
123
MedBiolEngComput
several researchers developed models for predicting AAA accounted for on the assessment of rupture risk [47].
rupture, based on relevant biomechanical and medical Geometric features of the aneurysm also play a role in the
parameters.Kleinstreueretal.hasdevelopedamodelwhich stresses developing within the AAA wall, with AAA
takes into account eight different indices [23, 26]. This asymmetryplayinganimportantroleontheincreaseofthe
modeloutputsananeurysmalseverityparameterbetween0 wall stresses [13]. Excessive bulging of one surface of the
and1whichcanbeusedbysurgeonsintheirdecisionwhe- aneurysmalwallresultsinelevationofwallstressesonthe
ther to operate the AAA. Watton et al. [53] developed an opposite surface.
advanced mathematical model combining mechanical and Recently, several researchers have performed FSI sim-
biologicalpropertiesthattakesintoaccountthevesselwall ulations in realistic geometries of the abdominal aorta.
propertiesduringthedevelopmentoftheaneurysm.Antiga Scotti and Finol [40] showed that the FSI transient fluid
et al. [2] have developed a modeling framework (Vascular andwalldynamicsresultedinamaximumwallstress21%
Modeling Toolkit) for patient-specific computational higher than the SS simulations. Additionally, they have
hemodynamics. Breeuwer et al. investigated the feasibility demonstrated that the asymmetry and non-uniform wall
of a patient-based hemodynamic modeling of AAA. This thickness of the pathological aorta plays an important role
methodologyisanefficient(improvedtherapeuticdecision) intheassessmentoftherupturerisk[41].DiMartinoetal.
andarobust(insensitivetovariationinthequalityofinput [11]demonstratedthattheILTcansignificantlyreducethe
data)approachtoriskassessmentofAAA[8]. stress on the wall. Papaharilaou et al. [29] presented a
Accurate estimation of the rupture potential of individ- decoupled approach for estimating the wall stresses on
ual AAA requires that the wall strength distribution be AAA. Our group studied the role of ILT by applying FSI
taken into account. A statistical model of noninvasive methodology with patient-specific reconstructed geome-
parameters for in vivo calculation of the wall strength tries [5]. Recently our group also studied the effect of ILT
distribution was recently developed by the Vorp group and calcifications, combined with anisotropic fiber orien-
[46]. It lumps together significant predictors of local AAA tationcharacterizationofthewallwithpatient-basedAAA
strength,bothclinicalandgeometric,toyieldalocalvalue geometries [36, 37].
ofthewallstrength.Thismodelcanbeusedtogenerate3D Individual patient risk factors that were mostly over-
mapping of the wall strength that can be compared to the looked in the past, may contribute significantly to AAA
local stress distribution, to generate a rupture potential risk of rupture. Those include anatomical geometric char-
index, RPI, which is defined as the locally acting wall acteristicssuchastheAAAneckangleandtheiliacarteries
stress divided by the local wall strength. bifurcation angulation that affect the AAA hemodynamics
Currently,thestateoftheartapproachformodelingthe andundoubtedlycontributetothewallstresses.Therewere
biomechanical behavior of the AAA wall is the fluid several studies that took into account the contribution of
structureinteraction(FSI)approach,inwhichthecoupling such factors to aneurysmal disease. Some of these studies
of the aortic wall with the blood flow depicts a dynamic focusonconsiderationsforendovascularrepairwithaortic
behavior of the AAA during the cardiac cycle. Previously, grafts[3,35,50].Othersanalyzeanatomicalcharacteristics
researches have focused their attention on static structural of AAA patients like the diameter, length, and volume of
(SS) simulations as a less computationally demanding the aneurysmal area and iliacs, for determining the poten-
approach for modeling the biomechanical behavior of tial of elevated risk of rupture [14, 22, 44]. Few studies
AAA, justified on the basis of small differences between report the iliac bifurcation and aortic neck angles [3, 35].
SS and FSI results for particular cases [25]. Substantial Thepaucityofresearchinthisdirectionhighlightstheneed
work has been done in AAA on SS simulations and for a parametric study of the effect that iliac and neck
mechanical tissue behavior by Vorp and collaborators [32, angulationmayhaveinAAAdiseaseprogressionandAAA
33, 45, 49]. Helderman et al. [21] showed, with the use of riskofrupture.Thiswillfacilitateprovidingclinicianswith
finite element method (FEM), exponential expansion of better predictive capabilities as to a specific patient AAA
aneurysmandrevealedthatthelocationofpeakwallstress progression and risk of rupture.
drifts over time. The roles of intraluminal thrombus (ILT) In this study a three-dimensional FSI methodology is
and wall calcifications in patient-specific wall stress of introduced. The methodology takes into consideration the
AAA were studied showing the importance of these walltissueanisotropyandtheinteractionofbloodwiththe
structures in the evaluation of risk of rupture [10, 42, 51]. aneurysmal wall. The effects of iliac bifurcation and the
Anisotropy of the aortic wall, owing to the collagen fibers AAA neck inlet angulations were studied parametrically,
orientation within the vessel wall may have a significant based on a range of geometric parameters that were mea-
impact on wall stress distribution, which needs to be sured in patients.
123
MedBiolEngComput
2 Methods axialinferiorview,iliacanglesabovethereferencelinewere
consideredpositiveandthosebelowthereferencelinewere
2.1 Parametric studies in patients’ AAA considerednegative,toaccountfortheaorticorientation.To
obtain the final anterior–posterior bifurcation angle, the
To establish the range of angles that were applied to the absolutevaluesoftherightandleftangleswereadded.
numericalmodels,thegeometricparametersweremeasured Thebendingangleoftheaortawasalsocalculatedusing
inacohortofAAApatients.CTscanswereacquiredin26 the MMS software. Three points were marked on the
patients with AAAs and reconstructed in three dimensions centerline. One point was chosen at the maximum aortic
usingMMSsoftware(MMS,MedicalMetrxSolutionsInc., bending and the other two are located approximately
WestLebanon,NH).Severalmeasurementswereperformed equidistant above and below on the centerline where the
in the reconstructed geometries. These included the iliac aortic morphology returns to normal, as shown in Fig. 1b.
bifurcation angles, aneurysmal bending angle, tortuosity, The final aortic bending angle was calculated by subtract-
diameters,andAAAlengths.Informedconsentwasobtained ing the obtained angle from 180(cid:3).
retrospectively.TheprotocolwasapprovedbyStonyBrook
University Institutional Review Boards (IRB) Committees 2.1.2 Tortuosity measurements
onResearchInvolvingHumanSubjects.
Fortheevaluationoftortuosityoftheiliacsandtheaortaa
script (MATLAB, The MathWorks Inc., Natick, MA) was
2.1.1 Iliac bifurcation and aortic bending angles
developedbasedonEq. 1.ThisformulasumstheEuclidian
distances between the centerline points defined by the
Two types of iliac bifurcation angles were measured: the
MMSsoftwareanddividesitbythedistanceofthestraight
lateral bifurcation angle and the anterior–posterior bifur-
line formed by the maximum and minimum points on the
cationanglewithrespecttothesagittalplaneofview.The
centerline.
lateralbifurcationanglewasmeasuredusingthecenterline
to mark two points on each of the iliacs and a third point T ¼PNi Si whereS ¼qðffiffixffiffiffiffiffi(cid:3)ffiffiffiffiffixffiffiffiffiffiffiffiÞffiffi2ffiffiþffiffiffiffiðffiyffiffiffiffiffi(cid:3)ffiffiffiffiffiyffiffiffiffiffiffiffiÞffiffi2ffiffiþffiffiffiffiðffizffiffiffiffiffi(cid:3)ffiffiffiffizffiffiffiffiffiffiffiffiÞffiffi2ffi
immediatelybeforethebifurcation,thusformingatriangle, L i i i(cid:3)1 i i(cid:3)1 i i(cid:3)1
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
as depicted in Fig. 1a (used by permission from MMS). andL¼ ðx (cid:3)x Þ2þðy (cid:3)y Þ2þðz (cid:3)z Þ2
max min max min max min
For the anterior–posterior bifurcation angle, an axial
ð1Þ
inferiorviewwasobtainedandtwopointsweremarkedon
eachoftheiliaccenterlinesandanotherpointontheaortic 2.1.3 Aneurysm length and diameter
centerline.Twoanglesweremeasuredfortheleftandright
iliacs,respectively,usingthesagittalplanepassingthrough Maximum aneurysm diameter was measured in the region
the aortic centerline mark as the reference line. Using the of maximal extent of orthogonal dilation for 25 patients.
Fig.1 Angulation
measurements:aLateral
bifurcationangleasmeasured
fromMMSsoftware.bBending
angleoftheaortawascalculated
usingtheMMSsoftware
123
MedBiolEngComput
The aneurysm length was measured axially from the W(cid:2) ¼C ðI (cid:3)3ÞþC ðI (cid:3)3Þ2þD (cid:3)eD2ðI1(cid:3)3Þ(cid:3)1(cid:4);
iso 1 1 2 1 1
beginningtotheendoftheaorticdilation(theregionwhere
(cid:5) (cid:6)
the aneurysm is located). The smaller aneurysmal length I1 ¼tr Cij :
identifies a saccular aneurysm where a large aneurysmal ð2Þ
length identifies a fusiform one.
where I ,isthefirst invariant ofthe Cauchy–Greentensor.
1
The isochoric elastic response for the orthotropic material
2.2 Parametric studies in numerical models
model formulation, W(cid:2) , is given in Eq. 3.
aniso
BAaAsAedgoenomtheetrimeseadseusrcermibeendtsabionvteh,eapraantigeentosf’trheecopnesrttaruincitnedg W(cid:2)aniso ¼W(cid:2)isoþ2kk1 Xhek2ðJi(cid:3)1Þ2 (cid:3)1i;
2i¼4;6
geometric parameters was established for the streamlined
AAA geometries used in the numerical simulations, and a J4 ¼J(cid:3)1=3I4; I4 ¼CijðnaÞiðnaÞj; J6 ¼J(cid:3)1=3I6;
(cid:5) (cid:6)
series of parametric studies was conducted. Streamlined I ¼C ðn Þðn Þ; J ¼det C :
6 ij b i b j ij
ideal AAA geometries with 5 cm (4.8 inner, 5.2 outer)
ð3Þ
maximumdiameterwereconstructed.Theidealizedgeom-
etriesapproachwaschosenoverthepatient-specificones,in where J, is the third invariant of the Cauchy–Green tensor
ordertohaveabettercontroloverthisparametricstudyand C ,n andn arethedirectionsofthefibersdefinedbytwo
ij a b
the interpretations of its results. The AAA geometries angles, a and a , which are offset from the material axes.
a b
includediliacbifurcationanglesthatrangefromu = 30(cid:3)to Inthisphenomenologicalhigherordermodelformulationit
u = 150(cid:3). All the geometries have a constant length, l, of is important to guarantee that the constants chosen must
12.5 cm from the neck to the base of the bifurcation. To result in realistic and stable constitutive responses in all
reduce the number of variables under consideration, the deformation states [7]. Stability (Drucker stability) was
vessel wall was considered as a material with uniform achieved by calculating the tangential stiffness matrix
thickness of 2 mm. We chose to concentrate on the lateral (Hessian) and establishing that it is positive. A nonlinear
plane iliac angulation effects, because such angulation is least-squares estimate was used by our group to fit the
morecommoninhumananatomyduringaneurysmaldisease strain energy curves to previously published AAA patient
progression,andbecauseitdemonstratesbettertheeffectit specimens experimental data [37].
hasonthewallstressdistribution.Inaddition,anglevaria-
tions of the AAA neck were considered based on our 2.2.2 Governing equations
experimental measurements. These angles range from the
vertical, h = 0(cid:3), to h = 40(cid:3). The neck diameter remained ThefluiddomainisgovernedbytheNavier–Stokesandthe
constant and similar to the inlet aortic diameter (approx. continuity equations. The Arbitrary Lagrangian–Eulerian
2.0 cm)forallneckcases(0(cid:3)–40(cid:3))andtheiliacdiameterwas (ALE) moving mesh approach was utilized for re-meshing
1.0 cmforallcases.TheidealAAAgeometryandthevar- the fluid domain at each time step. The momentum and
ious angles for the iliacbifurcation, u, andthe neck of the continuity equations for the fluid domain are shown in
aorta,h,aredepictedinFig. 2a. Eqs. 4 and 5 for a moving reference frame.
r~(cid:2)~q¼0; continuity; ð4Þ
2.2.1 Material models for the AAA wall
(cid:7) (cid:8)
o~q (cid:3) (cid:4)
q þ ~q(cid:3)~q (cid:2)r~~q ¼(cid:3)r~p
Inthisstudyweemployhigherordertermsintheisotropic ot g
Mooney–Rivlin (M–R) strain energy function to account þlr~2~q; fluidmomentum:
for the departure from neo-Hookean/Gaussian behavior at
ð5Þ
large stretches [9], combined with the Holzapfel orthotro-
picmaterialformulations[39].TheHolzapfelstrainenergy where ~q is the fluid velocity vector and ~q is the local
g
function models the vessel wall as fiber-reinforced com- coordinate velocity vector, p is the static pressure, q the
posite material with the fibers corresponding to the col- blood density, and l is the dynamic viscosity. The
lagenous component of the material. Similar models that numerical simulations utilized direct coupling between
combine higher order isotropic terms with Fung type the fluid (blood) and solid (vessel wall) domains. Large
exponential terms have been used recently to describe the strains and large deformations were considered. The
properties of atherosclerotic coronary arteries [55]. The dynamics of the flexible wall were calculated using the
isochoric elastic response for our isotropic material model linear dynamics response of the system shown in Eq. 6
formulation, W(cid:2)iso, is given in Eq. 2. [38].
123
MedBiolEngComput
Fig.2 aIdealAAAgeometry
andtheanglesfortheiliac
bifurcation,u,andtheneckof
theaorta,h.bTheboundary
velocitywaveformusedatthe
inletoftheAAAandthe
pressurewaveformattheoutlet
oftheiliacs.cvonMisesstress
averagedoveracross-sectionat
thecenteroftheisotropic
aneurysmalsolidwall(shownat
theinset)forthreedifferent
computationalmeshesandfor
thecaseof100(cid:3)iliacangle.The
differencebetweenfineand
finercomputationalmeshesis
smallerthan6%
MU€ þCU_ þKU¼R; solidmomentum, ð6Þ entire cardiac cycle with velocity range from 0.3 to -
0.05 m/s, and outlet pressure boundary condition with
M, C, and K, represent mass, damping, and stiffness range between 123 and 83 mmHg, as shown in Fig. 2b.
matrices,respectively.Risthevectorofexternallyapplied BloodwasmodeledasaNewtonianfluid,withadensityof
loads.U€,U_,andUarethevectorsofacceleration,velocity, 1,050 kg/m3 and a viscosity of 3.5 cP [37]. The flow and
and displacement of the structural domain. A first order pressure waveforms applied were extracted from Olufsen
finite-element scheme was used to solve the set of motion et al. [28]. A no-slip condition was applied at the wall
and fluid equations using the commercial software Adina boundaries. Due to the complexity of the geometries,
(ADINA, ADINA R&D Inc, Watertown, MA). residual stress field in the unloaded configurations was not
considered.Instead,allmodelswereassumedtobeinitially
2.2.3 Boundary conditions at zero stress state, followed by initial stress loading that
wasachievedbypressurizingtheAAAfrom0to90 mmHg
For the fluid domain, the pressure and velocity waveforms with zero flow for 1 s, before the FSI waveforms were
were prescribed at the outlet and inlet of the AAA geom- applied at the inlet and outlet. While this may lead to a
etry,respectively.Attheinlet,velocitywaveformspansthe minor degree of geometric exaggeration, it is an effective
123
MedBiolEngComput
way to impose physiological fluid pressure boundary con- more appropriate for FSI simulations since it fully couples
ditions. There are several groups who apply specific tech- the solid and fluid matrices. However, there are differing
niques to prevent geometric inflation [18]. In our future views in the literature for using coupled versus uncoupled
studies we will consider such approaches. For the solid numerical solvers [25, 29, 37,43].
domain, all degrees of freedom were fixed at the inlet and
outlets.
3 Results
2.2.4 Grid independence study
3.1 Measurements in patients’ AAA
Threedifferentmeshdensitieswereusedinordertoensure
grid independency of the results. The computational grids Severalmeasurementswereperformedinthereconstructed
are composed of tetrahedral four node finite elements for geometries. These included the iliac bifurcation angles,
both fluid and solid domain. Table 1 summarizes the three aneurysmalbendingangle,tortuosity,diameters,andAAA
different computational grids composed of fluid and solid lengths. These results are summarized below.
structures. Figure 2c shows the von Mises stress averaged
overacross-sectionofthesolidwallforthethreedifferent 3.1.1 Iliac bifurcation and aortic bending angles
computational meshes and for the case where the iliac
angleis100(cid:3).A19.0%differencewasobservedatthepeak Two types of iliac bifurcation angles were measured: the
systole between the coarse and the fine grids, and only a lateral bifurcation angle (mean: 41.7(cid:3) ± 9.7(cid:3)) and the
5.9% difference at the peak systole between the fine and anterior–posterior bifurcation angle (mean: 42.5(cid:3) ± 21.8(cid:3))
finer computational meshes. Duringthe diastolicphase the withrespecttothesagittalplaneofview.Additionally,the
differences between the three grids were very small. Since aorticbendinganglewasmeasured(mean:40.1(cid:3) ± 16.3(cid:3)).
the difference between fine and finer meshes was small Table 2 represents the mean value and standard deviation
enough,wehaveperformedthelargenumberofparametric forthethreeanglesaswellasthemaximumandminimum
simulations using the fine mesh. This mesh provides values measured from the studied AAA (n = 26). In sev-
accurate replicable results, without the need for further eral patients it was difficult to estimate the length, diame-
refinementthatwouldbecomecomputationallyprohibitive. ter, and tortuosity of the aneurysmal structure and these
The time step size used in the simulations was patients were not selected for the specific measurements.
dt = 0.005 s. We used an automatic time stepping (ATS)
method that controls thetime step sizeinorder toobtain a 3.1.2 Tortuosity measurements
converged solution. If there is no convergence with the
user-specified time step, the program automatically subdi- Tortuosity calculations were divided into three categories.
vides the time step until it reaches convergence [1]. In20patients,thetortuosityfortherightiliac,TRIL,hada
mean of 1.137 with a standard deviation of ±0.051.
2.2.5 Parallel computing Likewise, tortuosity for the left iliac, TLIL, had a mean of
1.144 with a standard deviation of ±0.0518. The aortic
AllFSIsimulationswereperformedonahighperformance tortuosity, TAO, had a mean of 1.030 with a standard
computingclustercomposedoffourquadcoreXeonCPUs deviationof±0.027.Theseresultsindicateamoretortuous
with a shared memory of 64 GB RAM. The CPU time for iliacnaturewithrespecttotheaortictortuosityandtheleft
each simulation was approximately 1.6 days for the fine iliac has a larger mean tortuosity than the right iliac by
computationalgrid,increasedto4.1 daysforthefinermesh. 0.6%, Table 2.
The coarse grid required only 4.0 h of CPU time. A direct
numerical approach was used for the integration of the 3.1.3 Aneurysm length and diameter
highly non-linear coupled system of equations. This
approachincreasesthecomputationaltimebutisconsidered Maximum aneurysm diameter was measured in the region
of maximal extent of orthogonal dilation for 25 patients.
Table1 Number of tetrahedral elements for grid sizes tested to The mean luminal diameter of the reconstructed aneurys-
ensuregridindependence
mal geometries was 38.37 ± 7.99 mm, and 53.97 ±
Numberofelements Coarsemesh Finemesh Finermesh 12.09 mm with the wall and ILT included. The aneurysm
lengthwasmeasuredaxiallyfromthebeginningtotheend
Fluiddomain 17,827 123,579 232,209
oftheaneurysmaldilation.Themeanlengthwas80.74 mm
Solidwall 52,641 311,167 566,437
with a standard deviation of ±24.43 mm. The smaller
Total 70,468 434,746 798,646
aneurysmal length identifies a saccular aneurysm where a
123
MedBiolEngComput
3 large aneurysmal length identifies a fusiform one. Our
4
mm) 24. measurements indicate a maximum measured lateral
( ± bifurcation angle of 65.2(cid:3) and the maximum measured
AAAlength 80.74 128.3 35.4 awnittehriporre–vpiooustselryioprubbilfiushrceadtiroensualntsg[l2e7o]f.8H4o.w8(cid:3)e,vienra,cacdodridtiaonncael
studies report larger iliac bifurcation angles. Resch et al.
diam. ±7.99 a[3n5g]lersep(oLrItAri)g:h8t1i(cid:3)lia±ca3n6g(cid:3)l,ews(iRthIAa)m:7e4a(cid:3)n±va3lu9e(cid:3)afonrdtlheefttiolitaacl
n
mem) 37 9 1 iliac angle at 155(cid:3). Beebe et al. [3] report a maximum
um 8. 8. 8.
L( 3 5 2 bifurcation angle of 127(cid:3). We have extended the range of
the iliac bifurcation angles in our parametric study
9
0 accordingly to 30(cid:3)–150(cid:3), corresponding to the pathophys-
diam. ±12. iological range reported in the literature.
AAA(mm) 53.97 85.2 40.5 meBtraicsedstuodnietshewaebroevecomnedauscuteredmfeonrtsetxwaomsineirniegs opfospsaibrale-
critical indicatorsfor AAA vulnerability. In the first group
7 of parametric studies the effects of the iliac angle on the
2
0.0 AAAlumen hemodynamics and the resulting wall stresses
± wereinvestigated.InthesecondseriestheroleoftheAAA
1
O 30 65 03 inlet neck angle and the effect of the aneurysm angulation
A 0 0 0
T 1. 1. 1. were studied.
8
1 3.2 Iliac bifurcation angle
5
0
0.
± 3 1 In this parametric study, the contribution of AAA iliac
L 4 8 0
LI 14 26 03 bifurcation angle on the wall stresses was explored. The
T 1. 1. 1.
velocity field and the WSS during the cardiac cycle were
analyzed; the pressure distribution within the aneurysm
1
MS 05 wasexaminedduringthecardiaccycle.Thisisaparameter
M 0. that was not accounted for in many previous studies.
±
h 4 8
wit RIL 137 303 051
ns T 1. 1. 1. 3.2.1 Velocity field
o
cti
u
nsionalreconstr Aorticbendingangle()(cid:3) 40.1±16.3 66.5 6.7 ToF0(4f.ih3g)e3t.lhav3este),e.l(co2dTac)irhiadetesyiatafrofiocllyeuecl,rddy0itaici.mss9letpeosrlf.feeorT,sare0hmn.te5wete5vsodeasliri,onle(ic:3afi)(cot1ymu)arfiinaddegfiltdlfdeeifrsaesstrwhte(o6enel0rtepe(cid:3)t,ei0samai.kmn7ed8sifylrsas1a,rt2moaf0nleoe(cid:3)dsr,,
e
m bothanglesatpeaksystole.However,themaximumvelocity
omthethree-di Anterioriliacangle()(cid:3) 42.5±21.8 84.8 5.0 Admthusaergimtnnhgiaetxudcidmaiearusdftmiooarlcevthecielynoct1col2iet0ysp(cid:3)emrvaoeangrggranellesitsrugeedecdoei,rmcftohuereltartyflthieoowwnaanszfigo3uen%lldaetsli.dooewnAvetoerlfeot6aph0real(cid:3)dyn.
fr diastole two counter-rotating vortices were observed near
d
cte ac 7 the inlet influencing the inlet jet of the blood entering the
mentsextra Lateraliliangle()(cid:3) 41.7±9. 65.2 21.1 adwniiaetshutrotylhisecmpf.oerTrwihoaedrsdebuflvtoolwrotsirtceeessntoewrregedyr.etAorwsetatahridensecdtahretdhieraoacurlgcyyhcoslyuesttwotlhaees,
e
ur progressing, this flow reversal was reduced and became
Table2Meas Measurementsn(=26) MeanandSD Max.value Min.value aptlualrmrdogenoe)osrfutoonznrecesresomd(dae(ulb.lgreyi.rn,1gi1l92ila.a05ct(cid:3)e%)ad.nifgaolsretostlh(eee..Tgm.h,ai6sx0ipm(cid:3)h)eu,nmaosmcvoeemlnoopcniatrwyeadmstamogotnhriee-
123
MedBiolEngComput
Fig.3 Velocityfieldinthe
aneurysmalareafortwo
differentangulationsandatfour
differenttimeframesofthe
cardiaccycle(units:m/s).The
fourlocationsforeachiliac
anglearemarkedontheinflow
velocityduringthecardiaccycle
Fig.4 PeakWSSforfive
differentiliacangulationsand
theWSSdistributionnearthe
iliacbifurcationsforthese
anglesduringpeaksystole
(units:Pa).HighestWSSwas
observedontheiliacwallsand
themaximumpeakWSS
occurredat60(cid:3)angle(blue-
darkdots,R2=1).Locallyat
theaneurysmalareathetrendis
oppositewithlowestlocalWSS
at60(cid:3)angle(red-lightdots,
R2=1)
3.2.2 WSS stagnation area in the iliac bifurcation where rupture is
unlikelytooccur,wasalsoplottedforthesefiveanglesand
Abnormally high or low WSS, especially patterns of high compared to the peak WSS of the whole structure. The
followed by low WSS, is a known causative factor of maximum peak WSS occurred at 60(cid:3) iliac angle for the
vasoconstriction, coagulation, andplatelet aggregation and whole structure (aneurysm, iliacs, and stagnation area),
deposition, and is likely to promote ILT formation [4–6, with the peak WSS decreasing for larger iliac angulation,
30, 34]. The peak WSS was analyzed for several iliac reaching the lowest value at 150(cid:3). The peak WSS also
angulations and the WSS distribution near the iliac bran- affectedtheWSSdistributionatthebranchesforthesefive
chesispresentedforseveralanglesof40(cid:3),60(cid:3),100(cid:3),120(cid:3), angles, and with increasing iliac angles larger segments of
and 150(cid:3), correspondingly (Fig. 4, blue dots). The peak the iliac branches were exposed to higher WSS levels. On
WSS of the aneurysm—excluding the iliacs and the the other hand the WSS of the aneurysm excluding the
123
MedBiolEngComput
iliacsandthestagnationareawasreducedat60(cid:3)iliacangle dropped to 0.5 mmHg for 120(cid:3) and above. Pressure dis-
compared with the other four angles (Fig. 4, red dots). As tribution remained almost constant throughout the aneu-
discussed earlier, the flow reversal due to recirculation rysmal area and dropped drastically in the iliacs at peak
zones during early diastole increased the WSS as well. systole and for a 60(cid:3) iliac angle.
3.2.3 Pressure distribution 3.2.4 von Mises stress within the solid wall
The pressure distribution generated by the dynamic blood Analysis was performed for the peak and mean von Mises
flow patterns during the cardiac cycle within the AAA stresswithintheaneurysmalwallfortheisotropicmaterial
lumen is yet another significant mechanism for increasing model formulation—shown for four representative iliac
the wall stresses and exacerbating the risk of rupture. The angles (Fig. 5, ranging from 40(cid:3) to 140(cid:3)). The orthotropic
results indicate highest pressure, p, and highest pressure model formulation for three iliac angles (40(cid:3), 60(cid:3), and
drop,Dp,duringpeaksystole.Astheiliacangleincreased, 100(cid:3)) was also analyzed and the principal axis stresses
the pressure inside the lumen changed significantly. The werereported.Theanisotropicmaterialmodelformulation
pressure reached its peak value during peak systole at two predicted higher principal axis stresses than the isotropic
distinct bifurcation angles of 40(cid:3) and 100(cid:3), respectively formulation. The von Mises stress distribution for these
(it was approx. 149 mmHg, 1 cm above the iliacs). It was four representative iliac angles indicate that as the angle
slightly lower for the 60(cid:3) and 80(cid:3) angles. As the angle increasedtherewasanoverallreductionofthestressinthe
increasedthepeakpressuredecreased(e.g.,for120(cid:3),140(cid:3), aneurysmal wall.
and 150(cid:3) peak pressure was approx. 133 mmHg). The The peak value of the von Mises stress increased as the
pressure drop Dp, defined as the pressure difference iliac angle increased (Fig. 5, red dots). At low iliac angu-
betweentheinletpressureandtheiliacbifurcationpressure lation the peak stress remained less than 1.0 MPa with the
at peak systole, decreased as the iliac angle increased. lowestvalueobservedat60(cid:3)angulation(0.57 MPa).Asthe
It remained around 1.0 mmHg at peak systole for small angle increased the peak von Mises stress increased,
iliac angles through 100(cid:3) (Dp = approx. 1.0 mmHg), and reaching maxima of 1.38 MPa at 100(cid:3) and 150(cid:3),
Fig.5 vonMisesstress
distributioninsidetheAAA
wallandiliacsforfour
representativeiliacangles,40(cid:3),
60(cid:3),100(cid:3),and140(cid:3)forthe
isotropicmaterialmodel
formulation(top).Thepeak
stressversustheiliacanglefor
thewholewalldomain(red-
upperdots,R2=0.5),andfor
theaneurysmalareaonly(green
-lowerdots,R2=0.84)forthe
isotropicmaterialmodel
formulationareshownatthe
bottomleftgraph.The
anisotropicmaterialmodel
showedasimilartrend.Mean
vonMisesstressforthe
isotropicmaterialmodel
formulationversustheiliac
angleareshownatthebottom
rightgraph(R2=0.58).The
meanstressdecreasedasthe
angleoftheiliacsincreased
123
MedBiolEngComput
correspondingly. However, exclusion of the high stress angle is that while for the 0(cid:3) inlet angle a pair of counter-
values characterizing the iliac arteries bifurcation stagna- rotating vortices is formed (Fig. 3, top), the neck angula-
tion points (where rupture is unlikely to occur) revealed a tionbreaksthissymmetricstructureandthevorticesmerge
differentpatternofpeakstressdistributionasafunctionof into a stronger single vortex. The flow field for 40(cid:3) inlet
the iliac angulation (Fig. 5, green dots), with two minima angle was accordingly substantially different from that of
at 60(cid:3) and 120(cid:3). The peak stresses at 50(cid:3), 100(cid:3), and 120(cid:3) 20(cid:3) and 0(cid:3). During systole a stronger jet was observed
angle decreased, but the trend of increasing peak stress enteringthestructureforbothneckangles(Fig. 6).Thisjet
withincreasingangulationremained.Themeanwallstress wasstrongeranditsmaximumvelocitywas7%higherthan
inthewholedomaindemonstratedadifferentpattern,with that of the 0(cid:3). During diastole the inlet recirculation zone
anoveralldecreaseinthemeanstresswithincreasingiliac became more pronounced and dominant. The vortex was
angleasdepictedinFig. 5(bluedots).Thisdecreaseinthe retained throughout diastole, but lost its energy towards
mean stress can be attributed to the changing hemody- early systole (Fig. 6). The recirculation zone was smaller
namicswithinthe AAAlumen astheiliacangleincreases. for the 20(cid:3) neck angle. During early and mid diastole an
Thischangeleadstoaformationofanextensivestagnation additionalsmallerrecirculationzonewasobserveddistalto
area and different WSSs distribution in the iliac branches. the inlet for the 20(cid:3) neck angle.
3.2.5 Anisotropic material model formulation for iliac 3.3.2 WSS
angulation
The WSS distribution of four different inlet angle config-
Additional orthotropic simulations were performed for urations,0(cid:3),20(cid:3),30(cid:3),and40(cid:3)atpeaksystoleofthecardiac
three different iliac angles, 40(cid:3), 60(cid:3), and 100(cid:3) and com- cycle is depicted in Fig. 7. The iliac angle was kept con-
pared with the isotropic simulations. Due to tissue anisot- stant for all inlet angle simulations—at 60(cid:3). A peak WSS
ropyprincipal axis stresseswere used inlieu ofvon Mises level was observed at 0(cid:3) inlet angle (2.66 Pa during peak
stresses (valid only for isotropic material formulation). In systole). The peak WSS decreased for 20(cid:3) inlet angle
all anisotropic simulations the peak stress was higher (1.74 Pa), and increased again for larger inlet angles,
compared to the isotropic simulations, as reported in our (1.82 Pa for 30(cid:3) and 1.95 Pa for 40(cid:3) during peak systole).
previous studies [37]. In 40(cid:3) iliac angle the principal axis
peak stress, p , increased for the orthotropic material 3.3.3 Pressure distribution
1
(32.5% increase). For 60(cid:3) iliac angle the principal axis
peak stress, p , slightly decreased for the orthotropic As the inlet angle increased, the pressure at peak systole
1
material (1.3% decrease) but all other principal axis inside the lumen (1 cm above the iliac bifurcation)
stresses,p andp increasedby1.4and2.3%,respectively. decreased. It was highest for the zero neck angle (it was
2 3
For 100(cid:3) iliac angle the principal axis peak stress, p , approx. 147 mmHg) and decreased to approx. 133 mmHg
1
increased for the orthotropic material model (25.5% for 20(cid:3) and 30(cid:3) neck angulation, reaching a minimum for
increase). Hemodynamic differences between the two 40(cid:3) (approx. 132.7 mmHg). The pressure drop, Dp (the
materialmodelformulationsweremarginal(lessthan5%). pressuredifferencebetween theinletpressureandtheiliac
bifurcation pressure at peak systole), also decreased as the
3.3 Aneurysmal neck angle inlet angle increased. Itwas the highestat peak systole for
zeroinletangle(approx.1.0 mmHg)anddecreasedfor20(cid:3)
The contribution of AAA inlet angle on the stresses and30(cid:3)inletangles(to0.84 mmHg),reachingaminimum
developing within the AAA wall was studied. The FSI for40(cid:3)inletangle(0.76 mmHg).Thepressuredistribution
simulationspredictastrongcorrelationbetweeninletangle remained almost constant throughout the aneurysmal area
and peak stress on the aneurysmal wall indicating an for all inlet angles and dropped drastically in the iliacs, as
increase in wall stresses as the neck angle increased. also reported in the iliac angulation parametric study.
Velocity field, WSS, and fluid pressure during the cardiac
cycle were also analyzed. 3.3.4 von Mises stress on the aneurysmal wall
3.3.1 Velocity field Analysis was performed for the peak and the mean von
Mises stresses of the whole wall domain for three inlet
Thevelocityfieldispresentedatfourdifferenttimeframes angles, ranging from 20(cid:3) until 40(cid:3), Fig. 8. The peak von
ofthecardiaccycleforinletanglesof20(cid:3)and40(cid:3),withan Mises stress increased astheinlet angleincreased.Atzero
iliacbifurcationangleof60(cid:3)(correspondingtothe0(cid:3)inlet inlet angle the peak stress was 0.57 MPa, increasing to a
angle in Fig. 3, top). The major effect of the inlet neck maximum of 0.93 MPa at 20(cid:3). After that a slight decrease
123