Blood ﬂow and structure interactions in a stented...

Medical Engineering & Physics 27 (2005) 369–382

Blood flow and structure interactions in a stented abdominalaortic aneurysm model

Zhonghua Lia, Clement Kleinstreuerb, ∗a Department of Mechanical and Aerospace Engineering, North Carolina State University, Campus Box 7910,

3198 Broughton Hall, Raleigh, NC 27695-7910, USAb Department of Mechanical and Aerospace Engineering and Department of Biomedical Engineering, North Carolina State University,

Campus Box 7910, 3198 Broughton Hall, Raleigh, NC 27695-7910, USA

Received 10 September 2004; received in revised form 7 December 2004; accepted 12 December 2004

Abstract

Since the introduction of endovascular techniques in the early 1990s for the treatment of abdominal aortic aneurysms (AAAs), the insertion ofan endovascular graft (EVG) into the affected artery segment has been greatly successful for a certain group of AAA patients and is continuouslyevolving. However, although minimally invasive endovascular aneurysm repair (EVAR) is very attractive, post-operative complications mayo ring a 3Ds ., pulsatileb n the EVGa tile bloodp re is reduceds EVG wall,s ble, wheref©

K tion

1

sttoweri

U(

sel,Thesh

hasortedayvity,pture.therce,lood

havessesrAA

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ccur. Typically, they are the result of excessive fluid–structure interaction dynamics, possibly leading to EVG migration. Considetented AAA, a coupled fluid flow and solid mechanics solver was employed to simulate and analyze the interactive dynamics, i.elood flow in the EVG lumen, pressure levels in the stagnant blood filling the AAA cavity, as well as stresses and displacements ind AAA walls. The validated numerical results show that a securely placed EVG shields the diseased AAA wall from the pulsaressure and hence keeps the maximum wall stress 20 times below the wall stress value in the non-stented AAA. The sac pressuignificantly but remains non-zero and transient, caused by the complex fluid–structure interactions between luminal blood flow,tagnant sac blood, and aneurysm wall. The time-varying drag force on the EVG exerted by physiological blood flow is unavoidaor patients with severe hypertension the risk of EVG migration is very high.

2005 IPEM. Published by Elsevier Ltd. All rights reserved.

eywords:Fluid–structure interaction; Stented abdominal aortic aneurysm; Endovascular graft; Sac pressure; Wall stress; Drag force; EVG migra

. Introduction

Aneurysms, an irreversible ballooning of weakened arteryegments, occur most frequently in the abdominal aorta. Ashe aneurysm expands, it may eventually rupture, making ithe 13th leading cause of mortality in the US. Alternative topen surgery, where the diseased aorta segment is replacedith a synthetic graft, a minimally invasive technique hasvolved over the last decade called endovascular aneurysmepair (EVAR). In EVAR, an endovascular graft (EVG)s guided from the iliac to the affected area where the

∗ Corresponding author. Tel.: +1 919 515 5261; fax: +1 919 515 7968.E-mail address:[email protected] (C. Kleinstreuer).

RL: http://www.mae.ncsu.edu/research/ckCFPDlab/index.htmlC. Kleinstreuer).

EVG expands and forms a new artificial blood vesshielding the aneurysm from the pulsatile blood flow.EVG or stent-graft is basically a cylindrical wire meembedded in synthetic graft material. While EVARshown outstanding success, especially for non-distabdominal aortic aneurysms (AAAs), EVG failure moccur due to blood leakage into the aneurysm cawhich elevates the sac pressure and may cause ruThis may also be caused by EVG migration whendrag force exerted on the EVG exceeds the fixation foexposing the aneurysm sac again to the pulsatile bflow.

So far, experimental studies and computational workfocused on the analysis of blood flow induced wall streof either the AAA or the EVG[1–12]. For example, Fillingeet al.[1,2] computed the peak wall stresses in realistic A

350-4533/$ – see front matter © 2005 IPEM. Published by Elsevier Ltd. All rights reserved.oi:10.1016/j.medengphy.2004.12.003

370 Z. Li, C. Kleinstreuer / Medical Engineering & Physics 27 (2005) 369–382

configurations and declared the maximum stress to be themost important indicator of AAA rupture. Di Martino et al.[3,4] and Finol et al.[9] simulated the interactions betweenblood flow and aneurysm wall to analyze system parameterswhich are of concern in AAA-rupture risk assessment.Raghavan et al.[5] and Thubrikar et al.[7] investigatedwall stress distribution on three-dimensionally reconstructedmodels of human abdominal aortic aneurysms. Chong andHow [11] measured the flow patterns in an endovascularEVG for abdominal aortic aneurysm repair. Liffman et al.[12], Morris et al.[13], and Mohan et al.[14] investigatednumerically or clinically the forces on a bifurcated EVG,assuming a rigid EVG wall.

Typically, the EVG is anchored to the aortic neck due tofrictional forces, where arterial ingrowth and/or stent barbsand hooks may play supportive roles. Clearly, a long cylindri-cal AAA neck with healthy tissue is most desirable for secureEVG placement[15,16]. Nevertheless, Resch et al.[17] re-ported that 45% of patients after EVAR showed migrationof their EVGs. Other than problematic AAA necks, Volodoset al. [18] added systemic hypertension as a major factor inEVG migration.

So far, most publications focused on AAA-wall stress orEVG-lumen flow separately. However, a stented AAA is acomplex and strongly coupled system between blood flowand EVG/AAA wall. Thus, in order to evaluate blood flowp dragf o bec pledF perw pacto sacp tatives

2

2

el iss i-n ndA ur-c teryw lledw ssurea Thed netm ly re-a

2

uidfl tion,

following Einstein’s repeated index convention, are:

continuity : ui,i = 0 (1)

momentum : ρ∂ui

∂t+ρ(uj − uj)ui,j = −pi,j + τij,j + ρfi

in FΩ(t) (2a)

stress tensor : τij = ηγij (2b)

non-Newtonian fluid model :

η = ηp[1 − 1

2

(k0+k∞γ

1/2r

1+γ1/2r

)Ht

]2(2c)

whereui is the velocity vector,pi the pressure scalar,ρ thefluid density,fi the body force at timet per unit mass, ˆui

the wall displacement velocity at timet, FΩ(t) the movingspatial domain upon which the fluid is described,γij theshear rate tensor,ηp the plasma viscosity,γr = γ/γc arelative shear rate,γc is defined by a “phenomenologicalkinetic model” [19], k0 the lower limit Quemada viscosityconstant,k∞ the upper limit Quemada viscosity constant,and Ht is the hemotocrit. The parameter values for the blooda

2

micsa

m

a

w

e

a

c

Hpt red ne

rysmw erioni

σ

w

atterns, wall stress distributions, sac pressure and EVGorces, fluid–structure interaction (FSI) dynamics have tonsidered. Presently, no publication dealt with fully couSI dynamics of stented AAAs. The purpose of this paas to analyze the pulsatile 3D hemodynamics and its imn EVG placement, EVG/AAA wall stress distributions,ressure generation, and EVG drag force in a representented AAA.

. Methods

.1. System geometry

The representative 3D asymmetric stented AAA modhown inFig. 1. The interacting materials include the lumal blood, EVG wall, stagnant blood in the AAA cavity, aAA wall. The EVG is assumed to be a uniform 3D bifating shell attached to the proximal neck and iliac arall. The cavity between EVG and aneurysm wall is fiith stagnant blood, experiencing a time-dependent pres a result of the dynamic fluid–structure interactions.rag force exerted on the EVG, due to fluid friction andomentum change, was computed under physiologicallistic conditions to assess incipient EVG migration.

.2. Flow equations

For transient three-dimensional incompressible flow, the governing equations in tensor (or comma) nota

nd the structures are given in Section2.4.

.3. Structure equations

The general governing equations for structure dynare:

omentum : ρai = σij,j + ρfi in SΩ(t) (3a)

i = dui

dt(3b)

here

quilibrium of condition : σijni = Ti onSΓ (t) (4)

nd

onstitutive : σij = Dijklεkl in SΩ(t) (5)

ere,SΩ(t) is the structure domain at timet, ni the outwardointing normal on the wall surfaceSΓ (t), Ti the surface

raction vector at timet, SΓ (t) the boundary of the structuomain,σij the mechanical stress tensor,Dijkl the Lagrangialasticity tensor, andεkl is the strain tensor.

In order to analyze the stress distributions in the aneuall, the Von Mises stress, used as a material fracture crit

n complicated geometries, is employed. Especially,

Von Mises=√

2

2

√(σ1 − σ2)2 + (σ2 − σ3)2 + (σ3 − σ1)2

(6)

hereσ1, σ2, andσ3 are the three principal stresses.

Z. Li, C. Kleinstreuer / Medical Engineering & Physics 27 (2005) 369–382 371

Fig. 1. (a) Representative AAA with EVG, (b) system inlet and outlet profiles, and (c) actual EVG photograph (Zenith, Cook Incorporated 2003C).


Table 1Assumptions for blood flow and structure characteristics

Blood flow Structure characteristics (artery wall, aneurysm wall, and EVG)

Incompressible Isotropic and elasticNon-Newtonian fluid (Quemada model) IncompressibleLaminar blood flow Non-linear (large deformations)No slip at the wall No tissue growth on wallsBlood particle effects not considered No residual stressesNo endoleaks in stented aneurysm models EVG consists of equivalently uniform materialStagnant blood in cavity No EVG migration

2.4. Numerical method

The underlying assumptions for simulating the coupledfluid–structure interactions are listed inTable 1.

The blood parameter values in Eq.(2c) areρ = 1.050 g/cm3, k0 = 4.58619, k∞ = 1.29173, Ht = 40%,andηp = 0.014 dyn/cm2 [19]. Table 2lists the structure pa-rameter values used in the present simulations. With respectto Young’s moduli for the arterial wall and aneurysm, exper-imental data indicate that Young’s modulus of an aneurysmis much higher than for a normal artery[7]. In this paper, theYoung’s modulus is assumed to be 4.66 MPa. The healthyartery section (neck) is incompressible with a Poisson ratio of0.49, and the aneurysm wall is nearly incompressible with aPoisson ratio of 0.45[3]. For a bifurcated NiTi-stent interwo-ven with graft material (EVG), no direct experimental dataare available; thus, an equivalent Young’s modulus for theuniform EVG configuration was assumed to be10 MPa[20].

The physiologically representative inflow velocity wave-form is shown inFig. 1 with a maximum Reynolds number(Remax) of 1950 and average Reynolds number (Reaverage) of330. For the outlet pressure (seeFig. 1), the peak and averagepressures are 122 and 98.7 mmHg, respectively[21]. Thepulse period is chosen asT= 1.2 s. The inlet velocity profileis assumed to be parabolic. For the composite structures, theboundary conditions are a fixed degrees-of-freedom (DOF)a Thefl eenl c’ss

forl ary

Fig. 2. Flow chart of fluid–structure interaction solution algorithm.

Lagrangian–Eulerian (ALE) formulation has been employedto solve this fluid–structure interaction problem. Specifically,it uses separately ANSYS FLOTRAN for the fluid domainand ANSYS structural solver for the solid parts. It transfersfluid forces, solid displacements, and velocities across thefluid–solid interface (seeFig. 2). A total of 76,730 8-nodefluid elements were needed for meshing the luminal bloodflow region, 66,820 structure elements for the EVG and AAA

TP

P Aneurysm EVG

W 1.0 mm Equivalent: 0.2 mm

D 60 mm Main body diameter: 17 mmIliac leg: 11 mm

L 80 mm Main body: 60 mmIliac leg: 70 mm

Y 4.66 MPa Equivalent: 10 MPaP 0.45 Equivalent: 0.27D 1.12 g/cm3 Equivalent: 6.0 g/cm3

t the inlet and the exit, and a free DOF on the wall.uid–structure interactions occur on the interfaces betwuminal blood flow and EVG wall, as well as the satagnant blood and aneurysm/EVG wall.

The finite element software package (ANSYS7.1)inear and non-linear multi-physics analysis in Arbitr

able 2arameters required in the simulation

arameters Normal artery

all thickness 1.5 mm

iameter Neck aorta (inner): 17 mmIliac artery (inner): 11 mm

ength Neck aorta:30 mmIliac artery:30 mm

oung’s modulus 1.2 MPaoisson ratio 0.49ensity 1.12 g/cm3


Table 3aComparison of results between simulations and theoretical analyses

ANSYS FSI simulation results Theoretical results[22] Error (%)

Straight arteryRadial deformation (internal wall) 0.0195 cm 0.0203 cm 4.1Circumferential stress (internal wall) 0.121 MPa 0.115 MPa 5.0Radial strain (internal wall) 0.0212 0.0203 4.2Radial strain (external wall) 0.0162 0.0155 4.3

AneurysmMaximum circumferential stress 0.175 MPa 0.16 MPa (Laplace’s equation) 8.6%

wall, and 19,250 non-net-flow fluid elements for the stag-nant cavity. The number of elements on the FSI interface was7168.

The algorithm continues to loop through the solid andfluid analyses until convergence is reached for each time step(seeFig. 2). Convergence in the stagger loop is based onthe quantities being transferred at the fluid–solid interface.A variable time step was employed, wheretmin = 0.005 swith 60 total time steps per cycle. Six cycles were required toachieve convergence for the transient analysis. Using a singleprocessor, the total CPU time was about 50 h on an IBM p690workstation.

2.5. Model validations

2.5.1. Comparison to theoretical results and clinicalobservations

In order to test the accuracy of the ANSYS-ALE-FSIsolver for simulating interacting flow and wall phenomena,several computer model validation studies were performed.The comparison between our present simulations and theo-retical analyses as well as clinical observations is listed inTables 3a and 3b.

2.5.2. Comparison with Womersley’s wave propagationtheory

w ina

c

w de-p rties;F ns,a s-t g’sm tion

Table 3cExperimental parameters for stented aneurysm

Aneurysm model type Latex fusiformEVG type Knitted polyethylenePerfusate Saline solutionAneurysm length 50 mmMaximum aneurysm diameter 60 mmAneurysm volume 80 mlNeck diameter 18 mmWall compliance (%/100 mmHg) 6 coats: 3.45± 0.5; 12

coats: 1.4± 0.2Pressure 50–120 mmHgFlow rate 1.0–2.5 l/min

value of c* = 831.0 cm/s from Eq.(7) for a longitudinallytethered elastic tube, ANSYS-ALE-FSI simulation resultsyieldedc* = 880 cm/s, i.e., the error is 5.9%.

2.5.3. Comparison with experimental dataGawenda et al.[26] measured the sac pressure with in

vitro stented aneurysm models consisting of 6 or 12 layers oflatex. The model parameters are listed inTable 3c.

Now, the sac pressures were computed for similarstented aneurysm models and flow conditions employing theANSYS-ALE-FSI-solver.Fig. 3presents the comparison be-tween the experimental and numerical results. It can be seenthat the simulation results are in good agreement with theexperimental data.

3. Results

The results are divided into three groups, i.e., the bene-ficial impact of EVG insertion (Figs. 4 and 5), the luminalblood velocity fields, wall stress distributions and sac pres-sure levels at three selected time levels during the cardiaccycle (Figs. 6–8), and the effect of blood pressure waveformson the transient EVG drag force, calculated from the wall

TC

results

VDM ed ane

eurysmmm

The wave propagation equation for viscous blood flolongitudinally tethered elastic vessel is

∗ = c0

√1 − F10

1 − σ2(7)

herec0 is the Moens–Korteweg wave speed, whichends on the system’s geometric and material prope10 a function of the Womersley number, Bessel functiond Young’s modulus; andσ is Poisson’s ratio of the ela

ic tube. Using a Womersley number of 10 and Younodulus of 1.0 MPa, compared with the wave propaga

able 3bomparison of results between simulations and clinical observations

ANSYS FSI simulation

on Mises stress drop 82%iameter decrease 12.0%aximum wall displacement 1.52 mm in non-stent

0.179 mm in stented an

Clinical observations

75%[25]10%[23]

urysm;.

1.0 mm in non-stented aneurysm and 0.2in stented aneurysm[24]


Fig. 3. Comparison between simulation results and experimental data.

shear stress distribution and the net momentum change (seeFig. 9).

3.1. EVG impact

A securely placed EVG forms a new smooth conduitfor blood flow (Fig. 1) and hence protects the weakenedaneurysm wall from high pressure and stress levels (Fig. 4).In fact, in case of zero leakage into the cavity, the sac pres-sure is reduced by a factor of 10 and the maximum wallstress decreases by a factor of 20 throughout the cardiac cy-cle when an EVG is inserted (seeFig. 4a and b). As a result,the largest change in maximum AAA diameter drops duringsystole from 2 to 0.17 mm (Fig. 4c). Indeed, as reported byMalina et al.[24], EVG placement can reduce the maximumwall deformation to 0.2 mm.

Clearly, these dynamic system parameter variations due tocyclic fluid–structure interactions are powered by the givenblood pressure waveform (cf.Figs. 1 and 4, keeping in mindthat the inlet pressure differs only by 5% from the outletpressure).

A snapshot during the critical deceleration phase(t/T= 0.27, peak blood pressure) shows the velocity fieldsas well as the pressure and wall stress distributions in boththe open AAA and the stented AAA (Fig. 5). Referring toF ods ongv st im-p ectedn wellb igh-e walls igh-e walls urca-t urso inp ceptf d il-i re

interactions between lumen blood, EVG wall, stagnant sac,and AAA wall, the sac pressure still remains at 14.38 mmHg,i.e., 11.8% of the lumen pressure. Triggered by the EVG wallshear stress and net momentum change, the drag force actingon the EVG is at that moment almost 2 N. While the stress inthe AAA wall and the pressure in the cavity are very low, theEVG carries the blood flow impact as numerically indicatedwith a peak EVG wall stress of 1.7 MPa at the stagnation (orbifurcation) point (seeFig. 5b and c).

3.2. Transient fluid–structure interactions

In order to illustrate the dynamics of pulsatile blood flowinfluencing the stented AAA parameters (seeFigs. 6–8), threerepresentative time levels were selected, i.e., reverse flow att/T= 0.1 (Re=−70), peak systole att/T= 0.2 (Re= 1950), andflow deceleration att/T= 0.27 (Re= 1200). In general, thesac pressure stays very low throughout the cycle; however,it increases slightly as the flow input waveform progresses(and time elapses) because of the blood pressure transmissionfrom the EVG lumen via the distensible EVG wall into theaneurysm cavity. The same can be observed for the peakσmax in the AAA wall, occurring always in the same location,which is basically an inflection point in the geometric mid-plane wall function. Naturally, the stress in the (healthy) neckt ing tok dersf llyf VGd mumE on-l thep thefl i.e.,t

lst s int -fl ow( flow

ig. 5a, the angulated AAA neck guides the jet-like blotream into the large cavity, forming immediately two strortices due to the sudden area expansion. The greateact of the angled blood stream occurs, as can be expot where the an eurysm has its maximum diameter, butelow near the iliac bifurcation, i.e., the impact area of hst net momentum change. Interestingly, the maximumtress and wall deflection in non-stented AAA have their hst magnitudes in different locations, i.e., the maximumtress (0.59 MPa) occurs on the right side above the bifion; while the maximum wall deformation (2.3 mm) occn the left side near the angled neck. Now, with an EVGlace, the blood flow is tubular and rather uniform, ex

or a few areas of secondary flows caused by neck anac angles (Fig. 5b). As a result of complex fluid–structu

,

issue is the highest because of the necessary oversizeep the EVG anchored. The luminal blood flow meanrom the AAA neck part through the aneurysm with typicaour small recirculation zones until it bifurcates into the Eaughter tubes, i.e., the iliac legs. As expected, the maxiVG wall stress can be found at the EVG bifurcation, n

inearly increasing during the observation time. Althoughresent AAA geometry is anterior–posterior symmetric,ow field and wall stress distributions are asymmetric,he results are fully three-dimensional (seeFigs. 6–8).

Comparing slices C–C inFigs. 6–8more closely, reveahat the location of the maximum EVG stress switchehe daughter tubes between up-flow (Fig. 6) and peak downow (Fig. 7), and back again during decelerating down-flFig. 8). Strong secondary flows appear before the EVG


Fig. 4. EVG impacts on AAA: (a) EVG impact on sac pressure, (b) EVG impact on maximum wall stress, and (c) EVG impact ondAAA,max changes.

division (see slices B–B inFigs. 6–8), an area which alsoexperiences a relatively high wall stress.

3.3. EVG migration

If the actual EVG drag force starts to exceed the fixa-tion force, the EVG will migrate or dislodge. As mentioned,

the drag force is composed of the integral over the surfaceshear plus the net pressure, where the shear stress contribu-tion is typically only 3% of the total. The fixation force foran EVG without barbs and hooks is the friction between theproximal EVG segment and the AAA neck which is usuallyoversized to supply, at least initially, solid anchoring. In ad-dition, the EVG ends may be secured via frictional effects


Fig. 5. Comparison between non-stented AAA and stented AAA (t/T= 0.27): (a) non-stented AAA, (b) stented AAA, and (c) wall stress distribution in EVG.


Fig. 6. Fluid–structure interactions of stented AAA (t/T= 0.1).


Fig. 9. Effect of blood pressure waveform on EVG drag force.

to the iliac lumen. In case the EVG migrates, blood can leakinto the AAA cavity, leading to a dangerous pressure buildupand subsequently aneurysm rupture. As alluded to in Section1, ideally the AAA neck should be long, cylindrical, and ofhealthy tissue. Obviously, AAA patients with severe hyper-tension (see waveform IV inFig. 9) are especially at risk forEVG failure because in that case the drag force has a maxi-mum and the relatively large pressure difference during thecardiac cycle may reduce the EVG fixation to a calcified, i.e.,hardened, neck tissue. Specifically, the pressure descriptionsof waveforms I–IV range from “normal” to “severe”, wherepmax,normal= 40 mmHg andpmax,severe= 70 mmHg. Forexample, Mohan et al.[14] declared that high blood pressureis one important factor to cause EVG migration, while Morriset al.[13] found that the drag force may vary over the cardiaccycle between 3.9 and 5.5 N. Thus, for an EVAR patient withsevere hypertension, extra fixation should be considered.

Because of the incompressible-fluid condition, the tran-sient drag force exhibits, with a very small time lag, basi-cally the same trend as the given inlet pressure waveform(seeFig. 9).

4. Discussion

re-p oc-c ter-a for ar VGh flu-e nantb the

beneficial impact of an EVG, the blood velocity field, thehighest pressure level in the aneurysm sac, the stress distri-butions, and displacements of both of the EVG wall and theAAA wall, as well as the maximum drag force exerted onthe EVG. It was readily demonstrated that a securely placedEVG shields the diseased AAA wall from the pulsatile bloodpressure and hence keeps the maximum wall stress 20 timesbelow the wall stress value in the non-stented AAA.

An interesting finding is that the sac pressure is reducedsignificantly but is not zero after the sac is completely ex-cluded by the EVG, i.e., no blood leakage exists. Thus, oursimulation shows that even in the absence of endoleaks, thesac pressure can be generated by the complex fluid–structureinteractions between luminal blood flow, EVG wall, stagnantsac blood, and aneurysm wall. The EVG/AAA wall compli-ance plays an important role in sac pressure generation.

As indicated in Section2.5, our simulation results are ingood agreement with the experimental data of Gawenda et al.[26]. As shown inFigs. 7–9, the intra-sac pressure varies from9.8 to 14.4 mmHg (4.6 mmHg pulsatility) during one cycle,while the average EVG lumen blood pressure (plumen) rangesfrom 82.3 to 120.3 mmHg (38 mmHg pulsatility). Sonessonet al.[25] found that the sac pressure pulsatility varied from0 to 6 mmHg clinically. Dias et al.[27] indicated that themean sac pressure pulsatility ranged from 2 to 10 mmHg fortheir 30 patients. Compared to the lumen pressure pulse, thep theA R,a vateds large-m

theh the

Although minimally invasive endovascular aneurysmair is very attractive, post-operative complications mayur, which are the result of excessive fluid–structure inction dynamics. Thus, the fluid–structure interactionsepresentative AAA model with and without a realistic Eave been investigated in terms of pulsatile blood flow inncing EVG movement, which is transmitted via the staglood in the cavity to the aneurysm wall. Of interest are

ressure pulsatility in the sac is not substantial. WhileAA volume should typically shrink after successful EVAneurysm enlargement might still occur because an eleac pressure could cause a delayed aortic aneurysm enent, even after successful EVAR[28].EVG wall deformations are insignificant due to

igh material stiffness; indeed, our results show that


maximum graft deformation is less than 1 mm. However,EVG wall deformation is a main factor when determiningthe sac pressure[26,32]. Furthermore, even relatively small,repetitive EVG-wall deformations may result in interactionsbetween the metallic wire and the interwoven graft material,leading to fabric abrasion and holes[30]. In addition,transient solid–fluid interactions can lead to material fatigueand hence device failure. Clinically, that includes metallicfracture (metal wire fracture, stent-strut, and barb/hookbreakage), graft fabric holes and suture breakage, and/orseparation. Additionally, device corrosion has also beenobserved clinically. So far, there is no model which canpredict such device deteriorations[33]. The reason is theserious lack of time-dependent clinical data due to shortfollow-ups, especially for the second generation of stent-grafts. Another reason is that most of the patients have beenasymptomatic and have not as of yet needed interventionsfor device fatigue[34]. In this study, we did not considerdevice failure cases. However, it is possible to simulatedevice fatigue employing a fluid–structure interaction solverfor a realistic stented AAA model in order to assess suchproblems.

Endoleaks were not considered in this paper. However,in cases of a loose neck attachment, graft defect and/orminor branch backflows, blood may leak into the AAAsac after EVAR. For example, Zarins et al.[37] indicatedt 38%o n sacp riouse then oundt me,t e by6

thes a dragf ther per-t mft pa-t ionc nceE rcei small( atedt rgen iliacE on-e d thep e thee akeni liter-a tt rtedt gle

[14]. Sternbergh et al.[35] declared that the migration rateincreases by 30% for AAAs with neck angles greater than40.

Interestingly, compared with open surgery, the mortalityof EVAR is almost the same. However, the key advantagesof EVAR are reduced morbidity, shorter hospitalisation, andquicker recovery; but, these benefits may be offset by the costof the device, the need for continuous control measurements,and eventually the need for late intervention or conversion toopen repair[31].

It should be noted that in this study the AAA wall wasassumed to be smooth. Intraluminal thrombus and smallbranches were not considered. In patient-specific stentedAAAs, intraluminal thrombi and small braches may affectthe fluid–structure interactions, sac pressure and hence pos-sible EVG migration. In the range of pressure loads from80 to 120 mmHg, linearly elastic property values are gener-ally used[3,6,7]. However, non-linear wall properties mayprovide even more realistic results[5,9,36]. Considering thedifficulty to model an actual EVG, i.e., a NiTi-wire mesh in-terwoven with synthetic graft material, presently the EVG isassumed to be a uniform shell made of an equivalent com-posite material. Furthermore, the blood particle effects on thewall were not considered. In a future study, patient-specificCT scan models, non-linear material properties, impact of anintraluminal thrombus, blood particle effects, and additionalE

fullyc ct ofE ssurev hys-i thea tudyo ngo ude,p eda

R

E.ortic

oftress

R,ee-assess–55.In:ionalrys-g, in

g. 3rd1. p.

hat endoleaks were diagnosed with CT scans inf 398 patients. Endoleaks may cause an increase iressure and hence higher stresses in the AAA wall. Sendoleaks can result in EVR failure, AAA rupture, andeed for second procedures. In a preliminary study, we f

hat if an endoleak volume of 3% is added to the sac voluhe sac pressure and AAA wall stress can increas0%[32].

Even though EVG placement may reduce significantlyac pressure and wall stress, the hemodynamics incursorce which may trigger EVG migration. It is shown thatisk of migration can be high for patients with severe hyension (seeFig. 9). EVG migration is a common probleor EVAR patients. For example, Zarins et al.[29] reportedhat the migration rate was up to 8.4% for their 1119ients within 12 months after EVAR. Serious EVG migratan cause endoleaks, EVG twisting or kinking and heVG failure. In this paper, the maximum EVG drag fo

s about 2 N because the selected EVG size is relative17 mm). However, our preliminary research results indichat the EVG drag force can exceed 5 N for AAAs with a laeck angle, iliac angle, large EVG size, and aorto-uni-VG [32]. Thus, the fixation of self-expandable or balloxpandable EVG contact may be inadequate to withstanulling forces caused by net momentum changes insidndovascular graft. Means of extra fixation should be t

nto account when possible. Concerning the supportiveture, Liffman et al.[12] and Morris et al.[13] confirmed tha

he drag force increases with EVG size. Mohan et al. repohat the drag force is non-linearly increasing with iliac an

VG configurations will be considered.In summary, this study provides a new technique, i.e.,

oupled fluid–structure interaction, to evaluate the impaVG placement, determine wall stresses and sac prealues, calculate EVG migration forces, and provide pcal insight into the biomechanics of stented AAAs. Touthors’ knowledge, this is the first computational FSI sf a stented AAA. Additional clinical applications, includiptimal EVG designs, minimizing sac pressure magnitreventing endoleaks, and EVG migration, will be performs future work.

eferences

[1] Fillinger MF, Raghavan ML, Marra P, Cronenwett L, KennedyIn vivo analysis of mechanical wall stress and abdominal aaneurysm rupture risk. J Vasc Surg 2002;36:589–96.

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