Journal of Biomechanics ] (]]]]) ]]]–]]]

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Journal of Biomechanics

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Computer modeling of deployment and mechanical expansionof neurovascular flow diverter in patient-specific intracranial aneurysms

Ding Ma a,b, Gary F. Dargush b, Sabareesh K. Natarajan a,c, Elad I. Levy a,c, Adnan H. Siddiqui a,c,d,Hui Meng a,b,c,n

a Toshiba Stroke Research Center, University at Buffalo, State University of New York, Buffalo, NY 14214, USAb Department of Mechanical and Aerospace Engineering, University at Buffalo, State University of New York, Buffalo, NY 14214, USAc Department of Neurosurgery, University at Buffalo, State University of New York, Buffalo, NY 14214, USAd Department of Radiology, University at Buffalo, State University of New York, Buffalo, NY 14214, USA

a r t i c l e i n f o

Article history:

Accepted 8 June 2012Flow diverter (FD) is an emerging neurovascular device based on self-expandable braided stent for treating

intracranial aneurysms. Variability in FD outcome has underscored a need for investigating the hemodynamic

Keywords:

Braided self-expandable stent

Braided stent

Flow-diverting stent

Pipeline embolization device

Finite element analysis

90/$ - see front matter Published by Elsevier

x.doi.org/10.1016/j.jbiomech.2012.06.013

viations: CFD, computational fluid dynamics;

t analysis.

esponding author at: University at Buffalo, S

ents of Mechanical & Aerospace Engineerin

esearch Center, Buffalo, NY 14214, USA. Tel.

716 829 2212.

ail address: huimeng@buffalo.edu (H. Meng).

e cite this article as: Ma, D., et al., Ctient-specific intracranial aneurysm

a b s t r a c t

effect of fully deployed FD in patient-specific aneurysms. Image-based computational fluid dynamics, which

can provide important hemodynamic insight, requires accurate representation of FD in deployed states.

We developed a finite element analysis (FEA) based workflow for simulating mechanical deployment of FD in

patient-specific aneurysms. We constructed FD models of interlaced wires emulating the Pipeline Emboliza-

tion Device, using 3D finite beam elements to account for interactions between stent strands, and between

the stent and other components. The FEA analysis encompasses all steps that affect the final deployed

configuration including stent crimping, delivery and expansion. Besides the stent, modeling also includes key

components of the FD delivery system such as microcatheter, pusher, and distal coil. Coordinated maneuver

of these components allowed the workflow to mimic clinical operation of FD deployment and to explore

clinical strategies. The workflow was applied to two patient-specific aneurysms. Parametric study indicated

consistency of the deployment result against different friction conditions, but excessive intra-stent friction

should be avoided. This study demonstrates for the first time mechanical modeling of braided FD stent

deployment in cerebral vasculature to produce realistic deployed configuration, thus paving the way for

accurate CFD analysis of flow diverters for reliable prediction and optimization of treatment outcome.

Published by Elsevier Ltd.

1. Introduction

Neurovascular flow diverter (FD) is an emerging paradigm fortreating traditionally difficult intracranial aneurysm such as wide-necked or fusiform aneurysms (Nelson et al., 2011). It is a self-expandable, tube-shaped metallic stent with fine braided meshdelivered via a catheter. Owing to its low porosity and high poredensity, FD is effective at reducing blood inflow to the aneurysm sac,promoting intra-aneurysm thrombosis while keeping the adjacentarterial perforators unblocked. Endothelialization on the stent innersurface forms a new blood flow conduit within months that bypassesthe obliterated aneurysm (Szikora et al., 2010).

While this novel intervention has achieved clinical success in anincreasing number of challenging aneurysm cases, serious

Ltd.

FD, flow diverter; FEA, finite

tate University of New York,

g and Neurosurgery, Toshiba

: þ1 716 829 3595;

omputer modeling of deplos. Journal of Biomechanics

complications such as delayed post-treatment hemorrhage havealso been reported (Byrne et al., 2010; Siddiqui et al., 2012). Severalcontributing factors have been hypothesized including extendedaneurysm occlusion time leading to thrombosis-related aneurysmwall weakening (Kulcsar et al., 2011) and post-treatment pressureincrease inside the aneurysm dome (Cebral et al., 2011). Thesehypotheses essentially attribute the variability of clinical outcomesto the patient-specific modification of hemodynamics, which sig-nificantly influences endothelialization, thrombosis and wall remo-deling. Therefore, knowledge of detailed hemodynamics modifiedby FD placement is critical to the prediction of treatment outcome.

Image-based computational fluid dynamics (CFD) analysiscan potentially provide important insight for this purpose butrequires realistic representations of FD in deployed states. Thispresents challenges to the numerical simulation of stent implan-tation, since previous methods do not capture clinically realisticFD deployment processes and cannot reproduce the highly vari-able deployed configurations.

In light of the increasing clinical need for accurate CFD analysisof FD treatment and the inability of current numerical methods toproduce realistically expanded FD geometries, we have developeda virtual FD deployment method using finite element analysis

yment and mechanical expansion of neurovascular flow diverter(2012), http://dx.doi.org/10.1016/j.jbiomech.2012.06.013

D. Ma et al. / Journal of Biomechanics ] (]]]]) ]]]–]]]2

(FEA). In this approach we model the main steps involved in FDstent deployment in patient-specific aneurysm geometry toobtain realistic final FD configuration. Aside from being a pre-requisite in accurate CFD analysis, this method can investigate FDdeployment strategies employed by operating clinicians, as wellas evaluate the mechanical characteristics of FD stents.

Fig. 2. Schema of key components of the simulated FD deployment system

mimicking the Pipeline Embolization Device (Covidien, Irvine, CA).

2. Methods

Our FD deployment modeling workflow (Fig. 1) uses thesestrategies:

(1).

Fig.patie

curre

the r

Plein

FD stent is modeled by 3D finite beam element because of theslender shape of its helical component strands.

(2).

The entire deployment process is modeled from stent crimp-ing (packaging), fitting into a microcatheter, maneuver anddelivery of the stent-microcatheter system, to stent releasefrom the microcatherter.

(3).

Several key components of the FD delivery system are alsomodeled (Fig. 2). They are found essential to the final

1. Modeling workflow for flow diverter (braided stent) deployment in

nt-specific aneurysms. *The final step of CFD analysis is not included in the

nt report. (For interpretation of the references to color in this figure legend,

eader is referred to the web version of this article.)

Fig. 3. Braided-stent model emulating the Pipeline Embolization Device. Top:

design variables (R, outer radius; d, strand thickness; L, stent axial length; j,

braiding angle) and braiding details (Red, left-handed helical strands; Blue, right-

handed helical strands). Bottom left: photograph of a Pipeline FD sample. Bottom

right: generated 3D solid model. (For interpretation of the references to color in

this figure legend, the reader is referred to the web version of this article.)

ase cite this article as: Ma, D., et al., Computer modeling of deploymepatient-specific intracranial aneurysms. Journal of Biomechanics (201

deployed configuration clinically. The crimper is modeled tocrimp the stent radially; the microcatheter is simplified as athin-walled cylindrical tube to deploy the stent; the distalcoil constraining the stent distal end is modeled by a master-point kinetically coupled with the stent’s distal end; thepusher at the proximal end of the stent is simplified as acylinder with rigid element mesh.

(4).

During stent release, operations on the distal coil, micro-catheter, and pusher are coordinated to reproduce desireddeployment results (Section 2.6).

(5).

The deployed FD stent geometry is swept into a 3D solidmodel for conformity assessment and future CFD analysis.

2.1. Braided stent geometry generation

We generated the braided stent wire pattern based on thePipeline Embolization Device (Covidien, Irvine, CA), currently theonly commercial FD approved by FDA. It is a self-expandable,cylindrically-shaped stent with braided structure principallycomposed of Cobalt–Chromium–Nickel (Co–Cr–Ni) alloy strands.

In building the stent geometry (Fig. 3, top), component helicalstrands were wound in clockwise and counter-clockwise direc-tions following a mathematical description (Kim et al., 2008a)(Supplement Part 1). Two FD models (F1 and S1) as specified inTable 1 were created emulating the Pipeline Embolization Deviceof different sizes, with F1 replicating an actual FD sample shownin Fig. 3 (bottom). Their dimensions were checked using CADprograms to ensure geometric accuracy.

nt and mechanical expansion of neurovascular flow diverter2), http://dx.doi.org/10.1016/j.jbiomech.2012.06.013

Table 1Flow diverter model parameters.

Flow divertermodel

F1 S1

Target

aneurysm

model

Wide-necked, nearly

fusiform (F) aneurysm

Wide-necked, giant sidewall (S)

aneurysm

FD outer

diameter (mm)

4.25 3.5

FD unloaded

axial length

(mm)

13 14

FD braiding

angle (degree)

75 71.5

FD strand

diameter (mm)

0.026 0.026

Dimension

determination

Measured from an actual

flow diverter sample

Scaled from F1 to

vessel diameter of the sidewall

aneurysm while maintaining

the same metal coverage as F1

Contactproperties

Friction-coefficient/Abaqus contact algorithm

Intra-strand 0.2 (Variations: 0.1, 0.4, 1.0)/general contact

Stand-catheter 0.05 (Variations: 0.01, 0.025, 0.1)/contact pair

Strand-vessel 0.08 (Variations: 0.04, 0.2, 0.4)/contact pair

Catheter-vessel 0.1/contact pair

Fig. 4. Stages of mechanical packaging of FD, with corresponding dimensions of

components (based on F1 model. ID: inner diameter; OD: outer diameter). The

cylindrical crimper (ID¼4.5 mm for F1; ID¼3.7 mm for S1) is modeled by

membrane element, while the thin-walled cylindrical microcatheter is modeled

by shell element (inner diameter¼0.667 mm, wall thickness¼0.08 mm for both

F1 and S1 model). (A) Stent and crimper at initial state. Crimping happens when

the crimper reduces diameter and compresses the stent in radial direction.

(B) Stent and crimper after crimping. The outer diameter of both F1 and S1 stents

were reduced to 0.5 mm by the crimper. (C) Stent is fit into a microcatheter and

then released inside the microcatheter while virtually removing the crimper.

(D) Stent-microcatheter assembly after packaging.

D. Ma et al. / Journal of Biomechanics ] (]]]]) ]]]–]]] 3

2.2. Stent FEA modeling and validation

The stent geometry was imported into a commercial FEAprogram Abaqus/Explicit 6.9 (SIMULIA, Providence, RI) to gener-ate a beam-element mesh. To determine the required elementsize for solution convergence, we subjected the S1 stent model atdifferent mesh sizes to a radial compression test using Abaqus/Explicit (Supplement Part 2). The adequate beam element sizedetermined from this mesh sensitivity test was then applied toF1 and S1 model for deployment simulations.

We first validated the modeling by comparing mechanicalperformance of a modeled braided stent against published experi-mental data. Due to an absence of mechanical testing data on FD, weresorted to the published in vitro mechanical testing data (Jedwaband Clerc, 1993) of the Wallstent (Boston Scientific, Natick, MA). TheWallstent is a peripheral vascular stent sharing a similar braidingstructure and material property to the Pipeline Embolization Devicealbeit at a higher porosity (80% vs. 70%) and a lower pore density(0.2 pore/mm2 vs. 15 pore/mm2). Using our braided-stent modelingmethod we generated a Wallstent model, subjected it to axialstretching and radial crimping, and plotted its mechanical perfor-mance with the aforementioned experimental data. In the samesetup we also tested solution sensitivity to the intra-strand frictioncoefficient (described in detail in Supplement Part 3).

The modeling method was further validated by a simple in vitrostudy, wherein an actual Pipeline FD device (F1) was unsheathed infree space, and the process was captured by x-ray imaging. Thisunsheathing process was then simulated using the modelingworkflow and results were compared with the experiment.

2.3. Stent packaging

Our FEA workflow of FD deployment in aneurysms starts withstent packaging (Fig. 4). The original unloaded stent is crimped,i.e., compressed in radial direction by the crimper (Fig. 4A and B).The crimped FD is fit into a microcatheter (Fig. 4C) and let expandto the inside of the microcatheter (Fig. 4D), while the crimper isremoved.

Please cite this article as: Ma, D., et al., Computer modeling of deploin patient-specific intracranial aneurysms. Journal of Biomechanics

2.4. Aneurysm models

Two representative patient-specific aneurysm models wereused for FD virtual deployment: a wide-necked, nearly fusiformbasilar artery aneurysm (Tremmel et al., 2010) and a sidewallanterior cerebral artery aneurysm featuring a jet into the aneur-ysm sac (Kim et al., 2008b). Both aneurysms were difficult to treatand would be excellent candidates for FD. Fig. 5A and B shows thefusiform and sidewall aneurysm models, in which the F1 and S1FD models were implanted, respectively.

2.5. Stent delivery in aneurysm

The packaged stent-microcatheter assembly is then numericallyinserted to the aneurysm model, advancing along a prescribeddelivery pathway to the intended location (Fig. 5C and D) fortreating the aneurysm. The pathway represents an establishedguide wire along the lumen. It is represented by a series ofreference points and associated normal directions extracted fromthe center of a sequence of lumen cross-sections.

2.6. Stent release and expansion—Simulation of the bulging strategy

The release of an FD stent from its microcatheter is delicate bothclinically and numerically due to the dramatic foreshortening effect,

yment and mechanical expansion of neurovascular flow diverter(2012), http://dx.doi.org/10.1016/j.jbiomech.2012.06.013

Fig. 5. Two patient-specific aneurysm models for virtual deployment of simulated

FDs and delivery pathways. (A) Wide-necked, nearly fusiform aneurysm (max-

imum vessel diameter 3.9 mm) in which the F1 stent (labeled dimension:

4 mm�20 mm) was implanted; (B) Sidewall aneurysm (maximum vessel dia-

meter 3 mm) in which the S1 stent (labeled dimension: 3.25 mm�20 mm) was

implanted. (C) and (D) Pathways for advancing stent-catheter assembly. Boundary

conditions are assigned to the distal end of the assembly, which passes through

consecutive reference points on the cutting-planes by displacement and rotation

following the normal directions of the cutting planes (arrows). The 3D Eulerian

angular velocity of this motion is calculated from rotational matrices using a

Matlab code (Fuller, 2009). Pusher advancement only involves 1D translation since

it mainly travels along the extended straight lumen on the proximal side during

the entire deployment.

D. Ma et al. / Journal of Biomechanics ] (]]]]) ]]]–]]]4

which makes it difficult to control the stent position (Hauck et al.,2010). Furthermore, it is generally desirable to densely pack thestent filaments across the aneurysm orifice to minimize inflowwhile keeping perforators open in parent vessels.

Our clinical team has developed an effective deploymentstrategy to overcome foreshortening and facilitate local packingby bulging the stent before releasing the distal constraint. Thisstrategy is numerically implemented in our modeling: Upondelivery of the stent-microcatheter assembly to the pathologicalsite, the microcatheter is first pulled back while the distal coilholds the stent in place, exposing the distal 1/3 of the stent. Thecatheter is then advanced forward while the stent’s distal end isstill fastened, causing the stent to bulge to the vessel wall to gaingreater friction. Then the distal coil constraint is released to allowthe stent to open distally. Friction between the bulged stent andthe wall helps to resist stent slippage. The microcatheter is thenretracted again, while the pusher drives the sheathed stentforward until its full release from the microcatheter.

2.7. FEA implementation of FD deployment

Each FD model was discretized by approximately 28,000 3DEuler–Bernoulli beam elements according to our grid sensitivitystudy. We treat the deployment as a large-deformation nonlinearproblem in FEA modeling. Intra-strand interactions were modeledby the ‘‘general contact’’ algorithm in Abaqus/Explicit, whichautomatically detects and computes all interactions within thedomain. Other interactions involved in the deployment weremodeled by the ‘‘contact pair’’ algorithm in Abaqus/Explicit, wheremaster and slave surfaces were specified. The intra-strand, cathe-ter-vessel and strand-vessel friction coefficients were estimatedfrom literature (Stannard et al., 1986; Black and Hastings, 1998;Takashima et al., 2007). Intra-strand friction coefficient value was

Please cite this article as: Ma, D., et al., Computer modeling of deploin patient-specific intracranial aneurysms. Journal of Biomechanics

further checked in the validation study (Supplement Part 3). Thestrand-catheter friction coefficient was estimated approximatelyfrom the strand-vessel friction coefficient. The values are given inTable 1.

Available Co–Cr–Ni material properties were applied to allcomponent strands: elastic modulus E¼206 GPa, 0.2% yieldstress¼2.8 GPa, isotropic hardening slope¼8.8 GPa, Poisson’sratio¼0.26, and density¼8 g/cm3 (De Beule et al., 2009). Thecrimper was modeled by 3200 membrane elements with nomaterial properties assigned. The microcatheter was representedby approximately 8000 reduced-integration shell elements. Itsstiffness was strategically increased (Young’s modulus E¼30 GPa,Poisson’s ratio¼0.3, density¼7 g/cm3) to prevent the simplifiedmodel from buckling and kinking in simulations.

Translational and rotational boundary conditions were imposedonto the simulated components to perform the concerted maneu-vers. The deployment process was treated as quasi-static byneglecting the pulsatile blood flow effect and assuming slowexpansion for minimal impact on the wall. Simulations wereimplemented with much lower kinetic energy compared to strainenergy. Each stent deployment simulation took about 100 h on aDell Precision 490 workstation with two Intel Xeon 5150 processors.This should be greatly accelerated with increased computing power.

2.8. Contact friction evaluation

Since friction coefficients used in the current study were esti-mated from the literature (referred to as the base values), it wasnecessary to evaluate their effects on simulation results. Threefriction coefficients (intra-strand, strand-vessel, strand-catheter)directly associated with stent behavior were varied (Table 1) forre-runs of the F1 stent deployment simulations in the fusiformaneurysm. With each variation of a particular friction coefficient, theother two coefficients were kept at the base values. The obtainednew stent configurations were compared using box plots plottedagainst the friction coefficients.

2.9. Conformity evaluation

Good wall apposition is an important consideration in FDdesign and clinical deployment. Incomplete apposition couldcontribute to in-stent thrombosis (Cook et al., 2007). Therefore,FD stent conformity to parent vessel was evaluated in thedeployed configurations.

Stent conformity was first quantified by a 2D dehiscence ratio(l2D) previously defined as the total area of gaps between stentand parent vessel wall normalized by the total area of stentedlumen in x-ray image (Tanaka et al., 2004). A lower dehiscenceratio value indicates better conformity. We also defined a 3Dvolumetric dehiscence ratio (l3D) as the volume of the 3D gapbetween stent and vessel lumen relative to the volume of animaginary tube wrapping the stent in the vessel segments.To wrap the sent, the FD model was swept into a 3D solid geometry,which would then be covered by a virtual surface (ANSYS ICEM CFD,Canonsburg, PA) to form the stent-occupied volume.

3. Results

3.1. Model validation

First, the grid sensitivity test shows that a beam element sizeof 0.09 mm was sufficient to accurately capture FD stent’sbehavior (Supplement Part 2). Second, experimental validationusing a modeled Wallstent (Fig. 6) shows excellent agreement ofsimulation experiment data. Third, modeling result of an F1 flow

yment and mechanical expansion of neurovascular flow diverter(2012), http://dx.doi.org/10.1016/j.jbiomech.2012.06.013

Fig. 6. Experimental validation result of the stent modeling approach with contact

algorithm using published in vitro experiment data Jedwab and Clerc 1993. (A)

Numerical model of Wallstent subjected to axial loading. (B) The Wallstent model

in crimping test. Radial crimping was imposed by a cylindrical thin-walled

crimper with inward radial displacement. (C) & (D) Axial loading test results of

simulation (open symbols) compared to experimental data and analytical predic-

tions. (C) Stent length vs. diameter curves (1% difference). (D) Axial load vs. length

curves (o5% difference) with intra-strand friction coefficient varied between

0.1 and 0.4 in the simulations, showing insensitivity of the axial mechanical

response to friction coefficient in the given value range. (E) Crimping test results

(radial pressure vs. diameter) of simulation (solid curve) compared to experi-

mental data and analytical prediction (difference o27%).

Fig. 7. Experimental validation of the modeling method by using Pipeline

Embolization Device (F1) unsheathing in unrestrained space. Left ((A) and (C)):

X-ray images of the FD released from catheter. Right ((B) and (D)): snapshots of

simulated unsheathing process. Top ((A) and (B)): The stent has come out of the

catheter while being constraint by the distal coil. Bottom ((C) and (D)): The distal

constraint has been removed, and the stent pops back instantly, demonstrating

the foreshortening effect.

D. Ma et al. / Journal of Biomechanics ] (]]]]) ]]]–]]] 5

diverter in a simple scenario – free release from a sheath inunstrained space – recapitulated time-resolved x-ray imaging ofan actual FD coming out of its microcatheter (Fig. 7). Bothsimulation and experiment demonstrated the unique foreshor-tening effect of the FD upon release.

3.2. Dynamic simulation of FD deployment in patient-specific

aneurysms

We simulated the deployment of F1 and S1 in the respectiveaneurysm models via the bulging strategy used clinically. Thedynamic process was recorded in movies, which are accessiblefrom links provided in Appendix and described in SupplementPart 5. The stepwise deployment is also demonstrated in snap-shots (Fig. 8) at important steps. By simulating FD’s mechanicalresponse, the deployment procedure overcame the foreshorteningeffect and generated desirable dense mesh across aneurysmorifice, as demonstrated in successful clinical operations.

3.3. Key elements in FD delivery system

Multiple trials of simulations have revealed that several factorswere critical for FD deployment result: The delivery wire repre-sented by a pathway was needed to properly bend the crimpedFD. The microcatheter was needed not only to contain thecrimped stent, maneuver it along the pathway and release it,but also to bulge the released stent portion to anchor the stent.The distal coil led the stent through the established pathway andassisted in bulging by holding the stent distal end together duringmicrocatheter advancement. The pusher was needed to holdthe stent in place during microcatheter retraction and topush the stent forward in order to partially pack the stent

Please cite this article as: Ma, D., et al., Computer modeling of deploin patient-specific intracranial aneurysms. Journal of Biomechanics

filaments densely across the aneurysm orifice for maximal flowdiversion.

3.4. Effects of friction coefficient

To compare the deployment results under different frictioncoefficient values, the final stent configuration was quantified bythe displacements of all nodes from their pre-crimping positions.The magnitude of displacements were presented by box plots andplotted against the varied friction coefficient (Fig. 9). Results werenot sensitive to the strand-vessel and strand-catheter frictioncoefficients and, at lower values, insensitive to intra-strandcoefficient. However, simulations at two higher intra-strandcoefficient values (0.4, 1.0) failed due to the excessive intra-strand friction at these values, which prevented the stent fromopening fully and causing it to hit the vessel bifurcation.

3.5. FD conformity to the vessel wall

The conformity of deployed FD to the parent vessel wall and itsquantifications (2D and 3D dehiscence ratios) are illustrated inFig. 10. The 3D dehiscence ratio values (0.111 and 0.176) arehigher than their 2D counterparts (0.037 and 0.036), indicatingless conformity evaluated in 3D than in 2D. Based on comparisonof the calculated 2D dehiscence ratio of these FD models againstpublished data, these FDs conform better than the Wallstent(0.09)—but worse than laser-cut stents (mostly far less than0.01) (Tanaka et al., 2004).

yment and mechanical expansion of neurovascular flow diverter(2012), http://dx.doi.org/10.1016/j.jbiomech.2012.06.013

D. Ma et al. / Journal of Biomechanics ] (]]]]) ]]]–]]]6

4. Discussion

Initial clinical reports of FD treatment showed high successrates in aneurysm occlusions in six months to one year (Lylyk

Please cite this article as: Ma, D., et al., Computer modeling of deploin patient-specific intracranial aneurysms. Journal of Biomechanics

et al., 2009). However, several complications such as inadequatedevice apposition, periprocedural distal thrombo-embolizationand prolonged occlusion time have been reported to causemorbidity and mortality (D’Urso et al., 2011). At Millard FillmoreGates Hospital, applications of FD to aneurysms of the posteriorfossa also encountered mortality and morbidity despite extensiveexperience with FD of our clinicians (Siddiqui et al., 2012). Tounderstand the variability of outcomes, patient-specific hemody-namic flow after FD implantation potentially provides valuableinformation due to the flow-modification nature of FD. Themethod developed in this study accurately simulates FD geometryat deployed states for accurate CFD analysis.

According to literature survey of virtual stent deploymentmethods, no past method is capable of producing mechanicallyrealistically deformed stent geometry in realistic vessel lumens.A 3D stent model might be geometrically bent and fitted into theparent vessel of an aneurysm (Kim et al., 2008a; Fu et al., 2010), thestent is unrealistically hanging in the lumen without expansion orapposition at the vessel wall. A step-up method (Appanaboyinaet al., 2008; Larrabide et al., 2010) produces more appealingdeployed geometry with wall apposition by accounting for stentexpansion—either by geometrically inflating a cylindrical surfacemesh, or by expanding a simplified mesh under artificial externalforces towards the vessel wall and then mapping stent pattern ontothe deformed surface. Such techniques do not model the stentmechanics and do not reflect mechanical responses involved in stentdeformation such as the self-contact within the device and stentposition control exerted by the deployment system. These effectsare particularly important for FD.

Available solid-mechanics methods are primarily for laser-cutstents, which, owing to their repeated zigzag cell-segment design,exhibit negligible longitudinal change, compared to 200–300%elongation of an FD during packaging (Lylyk et al., 2009). A straightcrimped laser-cut stent is directly inserted into the vessel modelwithout bending (Rebelo et al., 2009) wherein the vessel isrelatively straight such as the carotid or femoral artery. To adaptthese FEA methods for FD deployment in tortuous cerebral arteries,we tried a virtual deployment method where the stent was pushedinto a curved cylindrical thin-wall sheath mimicking the vessel(Wu et al., 2007). Our trial simulation showed immediate bucklingof stent strands under the push due to the delicacy and slimness ofthe strands; thus we abandoned this method.

Given that neither the geometry-based stent deformationmethods nor the existing FEA-based methods could model FDdeployment reliably, we developed our novel FEA-based work-flow specifically for FD and other braided stent deployment. OurFEA model initially included only the stent and the aneurysm, butsoon we found it necessary to add the microcatheter to containand bend the crimped stent for delivery, just like in clinicalpractice. The necessity of including the distal coil and pushermodels was a hard-learned lesson for us from repeated simula-tion trials that failed to properly anchor the stent under theuncontrolled free expansion. Similar learning curves have alsoresulted in the implementation of concerted movement of thedistal coil, microcatheter and pusher to overcome the foreshor-tening effect, which mirrors clinical experience. A recent in vitro

Fig. 8. Stepwise deployment of flow diverter models F1 and S1 into the fusiform

(Left column) and sidewall aneurysm (Right column), respectively. Arrow indi-

cates moving direction of the microcatheter. (A) The stent-microcatheter assembly

passes aneurysm orifice. (B) After reaching target location, microcatheter is

retracted, with the stent distal end being secured by the distal coil. (C) Micro-

catheter is pushed forward to bulge the stent. (D) Stent’s distal end is released by

the distal coil. (E) Microcatheter is further retracted while the pusher is pushed

forward to minimize stent slippage on the vessel. (F) Stent is completely detached

from microcatheter and fully expanded to its final deployed configuration.

yment and mechanical expansion of neurovascular flow diverter(2012), http://dx.doi.org/10.1016/j.jbiomech.2012.06.013

Fig. 9. Effect of friction coefficients on stent positioning. The absolute displace-

ments of all nodes in the final deployed configurations compared to pre-crimping

positions are represented by box plot and plotted against: (A) strand-vessel

friction coefficient; (B) strand-catheter friction coefficient; (C) intra-strand friction

coefficient. The darker box plots represent base coefficient values chosen for

this study.

Fig. 10. Conformity of deployed FD stent to parent vessel. ((A) and (B)) Planar

view mimicking angiography images for 2D dehiscence ratio calculation. The

malapposed areas are marked yellow. Their total area is divided by the total area

of stent segment inside the parent vessels (dark red) to yield the 2D dehiscence

ratio. ((C) and (D)) Volumetric view for 3D dehiscence ratio calculation. Surfaces

covering the stent segments inside parent vessels are generated (yellow) for

calculation of total volume occupied by the segment within parent vessels (VFD).

The total volume enclosed by the parent vessel aligned with the same stent

segments (VPV) is also obtained to give 3D dehiscence ratio l3D¼(VPV �VFD)/VFD.

(For interpretation of the references to color in this figure legend, the reader is

referred to the web version of this article.)

D. Ma et al. / Journal of Biomechanics ] (]]]]) ]]]–]]] 7

study made similar findings about the Enterprise stent, wherebycoordinated microcatheter and delivery wire movements stronglyinfluence the deployed stent configuration (Heller and Malek,2011).

Our approach of incorporating the main components andsteps in FD deployment from clinical practice into stentmodeling has eventually led to satisfactory FD positioning withthe least possible artifacts. It was through frequent clinicalconsultation and examination of the real FD device design thatwe have overcome multiple challenges in simulations and devel-oped a comprehensive simulation method with clinical relevance.

The parametric study on friction coefficients demonstratesoverall consistency of the deployment simulation result. How-ever, intra-stent friction coefficient value must be kept at areasonable level (o0.4), since excessive friction could renderstent unable to properly open. This is probably because with

Please cite this article as: Ma, D., et al., Computer modeling of deploin patient-specific intracranial aneurysms. Journal of Biomechanics

excessive intra-strand friction decreases the braided stent’s radialand longitudinal flexibility significantly, resulting in a tendency ofrigid-body motion when subjected to the same microcatheter-pusher motion.

A deployed FD should ideally conform to the vessel with a zerodehiscence ratio. Previous 2D image studies indicate that braidedconstructs tend to have less conformity than laser-cut stents(Tanaka et al., 2004), as shown by the larger dehiscence ratios ofFD in the current study than laser-cut stents. This is because a laser-cut stents consists of longitudinal segments with minimal attach-ment in between, while a braided stent is made of end-to-endhelical strands prohibiting full conformation to the local luminaldiameter. Compared to the Wallstent, which is also braided, thePipeline Embolization Device offers better conformity because of itshigher longitudinal flexibility owing to such design advantages as alarger braiding angle (751 vs. 601), thinner strands (26 mm vs.220 mm) and a smaller stress-free diameter (about 4 mm vs.17.15 mm), even at double the strand number (48 vs. 24).

This study has several limitations. First, there are severalmodeling assumptions such as rigid vessel wall and values ofintra-component friction coefficients adopted from the literature.Although rigid wall is a reasonable simplification for cerebralarteries due to their lack of medial elastin fibers and externalelastic lamina (Hayashi et al., 1980), the effect of stent implanta-tion on vessel morphology should be evaluated, and frictioncoefficients should be measured experimentally in the future.

Second, the simulations were still at the demonstration stage.The target position of the deployed stent F1 was not ideal from aclinical point of view; its distal end should haven been securelyanchored in a branch. Future simulations of actual FD interven-tion cases should be conducted and validated.

Despite these limitations, the current study demonstrates theunprecedented ability to simulate reliable deployed configura-tions of braided FD stents in tortuous cerebral vessels, accountingfor stent mechanical responses to important forces in the packa-ging and delivery system, as well as during operation. Althoughthe current computation takes too long to be practically used

yment and mechanical expansion of neurovascular flow diverter(2012), http://dx.doi.org/10.1016/j.jbiomech.2012.06.013

D. Ma et al. / Journal of Biomechanics ] (]]]]) ]]]–]]]8

in clinical decision-making routine, with increasing computerpower and computation efficiency, this goal should be closer inthe future. Meanwhile, our modeling tool allows us to performfundamental studies of FD treatment to better understand FDmechanism and to optimize treatment result. The demonstratedFD modeling capability paves the way for accurate CFD analysisthat aims at reliable prediction and optimization of FD treatmentoutcome as well as FD design improvement.

5. Conclusion

The variability of FD treatment outcome requires knowledge ofhemodynamic modifications by deployment-specific FD configura-tions in patient-specific aneurysm geometries. A FEA-basedmethod of simulating mechanical deployment of FD has beendeveloped and tested against available experimental data. The 3Dfinite beam element model, accounting for interactions betweenstent strands and between stent and other deployment compo-nents, is shown to capture the mechanical responses of braidedstents including the foreshortening effect of FDs. It is necessary forthe simulation workflow to include elements in the deploymentsystem such as pusher and distal coil, as these components arecritical for the proper implantation of FD in simulation as in clinicalpractice. Coordinated movements of these components can simu-late effective deployment strategies in clinical practice such asstent bulging against foreshortening and partial dense packing ofstent filaments. New strategies can be explored using this simula-tion tool. This study demonstrates for first time the capability ofmechanical modeling of braided FD stent deployment in cerebro-vasculature producing realistic deployed configuration, paving theway for accurate CFD analysis of FD for treatment optimization.

Acknowledgments

This study is partially supported by Toshiba Medical Systems.We thank Corvidien for Pipeline Embolization Device samples forthis study and Debra Zimmer for editorial assistance.

Appendix A. Supporting information

Supplementary data associated with this article can be foundin the online version at http://dx.doi.org/10.1016/j.jbiomech.2012.06.013.

Supplementary data associated with this article includesmovies of the deployment process corresponding to Fig. 8.

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