patient-specific simulations of stenting procedures in coronary bifurcations: two clinical cases

G

J

PT

SJa

b

c

a

ARRA

KFIISC

1

miiiimqIm

S2

1h

ARTICLE IN PRESS Model

JBE-2248; No. of Pages 10

Medical Engineering & Physics xxx (2013) xxx– xxx

Contents lists available at SciVerse ScienceDirect

Medical Engineering & Physics

jou rna l h omepa g e: www.elsev ier .com/ locate /medengphy

atient-specific simulations of stenting procedures in coronary bifurcations:wo clinical cases

tefano Morlacchia,∗, Sebastian George Colleonia, Rubén Cárdenesb, Claudio Chiastraa,ose Luis Diezc, Ignacio Larrabideb, Francesco Migliavaccaa

Laboratory of Biological Structure Mechanics (LaBS), Chemistry, Materials and Chemical Engineering Department “Giulio Natta”, Politecnico di Milano, ItalyCenter for Computational Imaging & Simulation Technologies in Biomedicine (CISTIB), Universitat Pompeu Fabra and CIBER-BBN, Barcelona, SpainCardiology Department, University Hospital Dr. Peset, Valencia, Spain

r t i c l e i n f o

rticle history:eceived 19 July 2012eceived in revised form 3 December 2012ccepted 21 January 2013

eywords:inite element modelmage-based reconstructionnterventional cardiologytentoronary bifurcations

a b s t r a c t

Computational simulations of stenting procedures in idealized geometries can only provide generalguidelines and their use in the patient-specific planning of percutaneous treatments is inadequate. Con-versely, image-based patient-specific tools that are able to realistically simulate different interventionaloptions might facilitate clinical decision-making and provide useful insights on the treatment for eachindividual patient.

The aim of this work is the implementation of a patient-specific model that uses image-based recons-tructions of coronary bifurcations and is able to replicate real stenting procedures following clinicalindications. Two clinical cases are investigated focusing the attention on the open problems of coronarybifurcations and their main treatment, the provisional side branch approach. Image-based reconstruct-ions are created combining the information from conventional coronary angiography and computedtomography angiography while structural finite element models are implemented to replicate the realprocedure performed in the patients.

First, numerical results show the biomechanical influence of stents deployment in the coronary bifurca-
tions during and after the procedures. In particular, the straightening of the arterial wall and the influenceof two overlapping stents on stress fields are investigated here. Results show that a sensible decrease ofthe vessel tortuosity occurs after stent implantation and that overlapping devices result in an increasedstress state of both the artery and the stents. Lastly, the comparison between numerical and image-basedpost-stenting configurations proved the reliability of such models while replicating stent deployment in coronary arteries.
. Introduction

In the last decade, several numerical models have been imple-ented to simulate different stenting procedures and provide new

nformation about their biomechanical influence on the surround-ng vascular environment [1]. The main advantage of these modelss the ability of assessing several quantities hard to measure withn vivo or in vitro tests such as the stresses in the arterial wall or the

echanical deformation of the devices [2,3]. In literature, theseuantities have been associated with poor clinical outcomes [4,5].

Please cite this article in press as: Morlacchi S, et al. Patient-specific simucases. Med Eng Phys (2013), http://dx.doi.org/10.1016/j.medengphy.2013.

n particular, post-stenting adverse events include thrombus for-ation within the stented segment and/or intimal hyperplasia (the

∗ Corresponding author. Laboratory of Biological Structure Mechanics (LaBS),tructural Engineering Department, Politecnico di Milano, Piazza L. da Vinci, 32,0133 Milano, Italy. Tel.: +39 02 2399 4283; fax: +30 02 2399 4286.

E-mail address: [email protected] (S. Morlacchi).

350-4533/$ – see front matter © 2013 IPEM. Published by Elsevier Ltd. All rights reservettp://dx.doi.org/10.1016/j.medengphy.2013.01.007

© 2013 IPEM. Published by Elsevier Ltd. All rights reserved.

rapid proliferation of smooth muscle cells in vessel wall) [6] which,in the extreme, leads to restenosis (re-occlusion of the vessel).

Currently, important limitations still preclude the routine appli-cation of computational models in the clinical field. Among theselimits, the majority of numerical studies until today is still based onhighly idealized geometries and only aims at replicating standardstenting procedures [7–10]. Therefore, such studies can onlyprovide universal guidelines and not patient-specific indicationsfor the planning of each treatment. The possibility to compare dif-ferent procedural options considering the specific anatomical andmechanical properties of each patient before its treatment mighthelp the improvement of the interventional planning and clinicaloutcome. However, recent developments in coronary imaging havepaved the way to new methods that are able to create realisticimage-based reconstructions of vascular districts [11], potentially

lations of stenting procedures in coronary bifurcations: Two clinical01.007

useful for patient-specific simulations of stenting procedures.In this light, the aim of this work is to prove the feasibility

of implementing patient-specific structural models starting fromimage-based reconstructions of atherosclerotic coronary arteries.

d.

dx.doi.org/10.1016/j.medengphy.2013.01.007


http://www.sciencedirect.com/science/journal/13504533

http://www.elsevier.com/locate/medengphy

mailto:[email protected]


ARTICLE IN PRESSG Model

JJBE-2248; No. of Pages 10

2 S. Morlacchi et al. / Medical Engineering & Physics xxx (2013) xxx– xxx

ies inv

Tpinaootal(o[rttmtwoacsagiq

2

2

acciiatm

Fig. 1. Geometrical reconstructions of the two LAD coronary arter

he replicas of two real clinical cases are simulated by following therocedural indications of the physician who actually performed the

nterventions. In particular, the two studied cases involved coro-ary bifurcations of the left anterior descending (LAD) coronaryrtery since such regions are very critical from a biomechanics pointf view [12] and are still affected by lower clinical and proceduralutcomes [13]. Interventions were performed at University Hospi-al Doctor Peset in Valencia (Spain) and patients were treated with

provisional side branch (PSB) stenting without final kissing bal-oon. This strategy consists of deploying a stent in the main branchMB) across the bifurcation followed by the optional treatmentf the side branch (SB) in the case of sub-optimal clinical results14]. Pre-stenting acquisitions with computed tomography angiog-aphy (CTA) and conventional coronary angiography (CCA) are usedo generate image-based models of the atherosclerotic bifurca-ions [15] that are subsequently discretized with fully hexahedral

eshes. Atherosclerotic plaques are included in the model, moni-oring the distance from each node to the centerline of the externalall. Curvature and tortuosity of the coronaries entail the devel-

pment of preliminary structural analyses to accurately crimp anddvance the devices to the correct position. Afterwards, stressedonfigurations of the devices are used within the final structuralimulations, replicating the actual stenting procedures by means of

finite element commercial code [9]. Lastly, for one case, the finaleometrical configuration obtained in silico is compared with themage-based reconstruction of post-stenting geometry providing aualitative validation of the proposed numerical approach.

. Materials and methods

.1. Image-based coronary bifurcation models

Two clinical cases of adult females are investigated in this work,fter informed patient consent and approval of the hospital ethicalommittee for this study. In both cases, the patients underwent per-utaneous coronary stent implantation. In particular, the first casenvestigated (case A) involves the proximal section of the LAD while


n the second case (case B) both the proximal and mid part of LADre included. Pre-treatment CCA and CTA are used to reconstructhe internal surfaces of the pre-stenting geometries following the

ethodology proposed by Cárdenes et al. [15]. The combination

estigated: from medical images (top) to 3D solid models (below).

of these two imaging systems allows a more realistic reconstruc-tion of coronary bifurcations than just using one of them alone. CTAprovides the 3D trajectories followed by the arteries while CCA pro-vides accurate lumen radius estimations. The internal surfaces arethen used to construct 3D solid models of the two coronary bifurca-tions investigated (Fig. 1). First, the open-source software packageVMTK [16] is used to identify the centerline of the internal wallreconstruction. Second, due to the lack of imaging data, externalwall surfaces are created by smoothly connecting circumferentialcross sections perpendicular to the centerlines using the CAD soft-ware Rhinoceros 4.0 Evaluation (McNeel & Associates, Indianapolis,IN, USA). To allow a better description of arteries and correctlylocalize potentially asymmetric atherosclerotic plaques, cross sec-tions are only defined in those regions where, by angiographicinspection, no plaques or symmetric plaques are recognized. Thediameters of the external wall are chosen in order to comply withthe internal diameter and physiological wall thicknesses of healthycoronary branches [17]. Regarding case A, external wall diametersvary from a maximum of 5.2 mm at the inlet of the MB to 1.6 mmat the outlet of the second SB. For case B, external diameters atthe inlet and the outlet of the MB are equal to 5.43 mm and 4 mm,respectively. In this case, the external diameter of the SB resultedin 3.49 mm.

The 3D geometries are discretized using ANSYS ICEM CFD(ANSYS Inc., Canonsburg, PA, USA) with fully hexahedral meshes(Fig. 2a). Mesh density is increased in the bifurcation area and closeto the internal surface of the arterial wall. In this way, the areascharacterized by lower stress gradients such as the external layersof the arterial wall and the regions far from the stented area are lessdensely meshed; mesh-independency of the results is guaranteedwithout excessively increasing the computational cost. Indeed, ourresults are very similar in terms of mesh density to those reportedand verified by Capelli et al. [8] for a similar coronary artery model.A total of 120,344 and 187,326 elements is used to discretize thearterial geometries of case A and B, respectively.

The combination of CCA and CTA cannot provide adequate infor-mation on the typology of biological tissues characterizing thearterial wall and, in particular, it cannot identify the precise loca-


tion of atherosclerotic plaques and its composition. For this reason,a method based on the calculation of the distance between eachnode of the mesh and the centerline of the external wall (Fig. 2b)is implemented. With this approach, if the calculated distance is


ARTICLE ING Model


S. Morlacchi et al. / Medical Engineerin

Fig. 2. (A) Discretization process of an image-based coronary model. On the top, thearterial wall is subdivided in regions topologically equivalent to parallelepipeds thathave been subsequently subdivided in hexahedral elements. Below, in the details,the refinement of the mesh close to the internal surface and the bifurcated regionare depicted. (B) plaque identification process based on the calculation of the dis-tir

lFprcsacpalc

rtherttrr

vps

ance between each mesh node and the centerline of the external wall. Black arrowsndicate some nodes characterized by lower distances than the physiological lumenadius of a healthy LAD.

ower than a reference radius of a healthy artery (black arrows,ig. 2b), that node will be considered part of the atheroscleroticlaque; otherwise (white arrow, Fig. 2b), it will be part of the arte-ial wall. The reference radius linearly decreases along the arteryonsidering the intrinsic diameter reduction occurring in the recon-tructed arteries. Stenosis is measured by dividing the area of thetherosclerotic plaque by the area of the arterial lumen of the sameross-section, obtained removing the elements belonging to thelaque itself. Different sections perpendicular to the centerline aressessed in cases A and B. Following this qualitative method, theocal maximum degrees of stenosis obtained are 84% and 73% forases A and B, respectively.

The material properties used for the arterial wall and the plaqueseplicate the mechanical behavior in the circumferential direc-ion of the media layer and cellular plaques, respectively. Theyperelastic constitutive models implemented [7] are based on thexperimental values described in Holzapfel et al. [18] for the arte-ial wall and in Loree et al. [19] for the atherosclerotic plaques. Inhe plaque model, perfect plasticity is associated to the hyperelas-ic strain energy density function to roughly simulate the plaqueupture at the experimental tensile stress values measured in theeferenced study (about 400 kPa).


For the reconstruction of the post-treatment anatomy of theessel, immediate post-treatment CCA and post-operative CTAerformed after six months are used to reconstruct the internalurfaces of the post-stenting geometries following the previously

PRESSg & Physics xxx (2013) xxx– xxx 3

described methodology [15]. This post-stenting geometry will giveus an insight on the similarity between our numerically simulatedmodel and the one obtained from real images, and it is only avail-able for case A since the patient of case B did not undergo anyfollow-up CTA.

2.2. Stent and balloon angioplasty models

Two different stents are used in the interventions (Fig. 3). TheirCAD geometrical models resemble the Xience Prime (Abbott Lab.,USA) stent for case A and the Endeavor Resolute (Medtronic, USA)device in case B. Considering its un-crimped configuration, theMultilink Vision stent is characterized by an external diameter of1.76 mm, a strut thickness of 81 �m and a length of approximately28 mm. The Endeavor Resolute stent model has a circular sectionwith a diameter of 91 �m and in the un-crimped configuration ischaracterized by an external diameter of 1.6 mm and a length of15 mm. The meshes of the devices are partially shown in Fig. 3 andresult in a total amount of 448,424 and 272,384 reduced integra-tion hexahedral elements for the Xience and the Endeavor stents,respectively. Both stents are constructed of a cobalt–chromiumalloy that is described through a Von Mises-Hill plasticity modelwith isotropic hardening, with the following properties: 233 GPa,0.35, 414 MPa, 933 MPa and 44.5% in terms of Young modulus,Poisson coefficient, yield stress, ultimate stress and deformationat break, respectively [20].

Polymeric angioplasty balloons with different diameters (from2 to 3.5 mm) and lengths (from 15 to 32 mm) are created. In thevirtual implantations, the balloon models are selected to exactlymatch those used by the clinical operators in the actual interven-tions. Similarly to the models previously described in Gastaldi et al.[7], angioplasty balloons are created in the expanded configuration,discretized with quadrilateral membrane elements and deflated toachieve a multi-folded configuration.

2.3. Preliminary simulations: crimping and bending

To precisely position the stents in the complex patient-specificgeometries, preliminary simulations of crimping and bending of thedevices are performed using the implicit finite element commercialcode ABAQUS/Standard (Dassault Systemes Simulia Corp., RI, USA).At the end of each simulation, the stressed configurations of thedevices are passed to the subsequent steps in order to keep trackof the history of stress modifications.

At first, the initial configurations of the devices are crimpedto an external diameter of 1.00 mm by controlling the radialdisplacement of a cylindrical surface in contact with the stents(Fig. 4a). After elastic recoil, crimped configurations of the stentsare imported in the bending simulation (Fig. 4b – Video 1). Sincethe arterial tracts preceding the coronary bifurcations have greaterdiameters and higher curvature radii, stent advancement in theseregions is assumed to be negligible for the stent final positioningand stressed state. Therefore, two cylindrical internal guides arecreated following the centerline of the two patient-specific bifur-cations obtained after the simulation of the angioplasty procedures(see Section 2.4). The guides are discretized with rigid homoge-neous shell elements. At this point, to simulate stent advancementand obtain realistic stress distributions on the bent struts, the stentsare pushed against the guide imposing longitudinal displacementto the nodes positioned close to the links. Such boundary condi-tions are removed once the links approach the first curve in orderto let the stent freely bend along the guide. Contacts are set to


have a friction coefficient equal to 0.3 and the normal behavioris modeled with a “softened” contact relationship in which thecontact pressure is a linear function of the clearance between thesurfaces. In the last step of the bending simulations, even the last





Fig. 3. On the top, geometrical model of a stent resembling the commercial Xience Prime (Abbott Lab., USA) used in case A and characterized by a length of 28 mm anda eavor

c odels.

dosfictco

iiaftav

Fc1b

n external diameter of 1.76 mm. Below, geometrical model resembling the Endross-section. On the right, details of the hexahedral discretization of these stent m

isplacement boundary condition is removed and one stent noden the distal end is constrained to its current position allowing thetent to adapt to the bending guide and reach a minimum-energynal static equilibrium. Simulations of crimping and bending ofases A and B require a simulation time of 38 and 13 h, respec-ively, using two nodes of a high computing cluster, each of themharacterized by a 2 Quad-Core Intel Xeon E5620 processor, 24 GBf RAM.

Lastly, the creation of the curved configurations of the balloonss also required to fit inside the curved geometries that character-ze the stents after the bending and before the implantation. Tochieve this goal, advancement simulations similar to those usedor the stents are implemented in ABAQUS/Explicit (Dassault Sys-


emes Simulia Corp., RI, USA). In this case, however, the balloonsre not pulled by means of displacement boundary conditions butia concentrated forces applied to the distal nodes of the balloon.

ig. 4. Preliminary structural simulations. (A) Crimping of the Endeavor Resolute stent mrimped to an external diameter of 1 mm by controlling the radial displacement of a rigid

.11 mm (below). (B) Bending simulation of case B where a Xience-Prime stent is advancey a 0.8 mm diameter.

Resolute stents (Medtronic, USA) used in case B and characterized by a circular

2.4. Final simulations: replica of two clinical cases

Numerical simulations of the stents deployment are simulatedas quasi-static processes using the explicit dynamics solver imple-mented in ABAQUS/Explicit. To ensure this condition, the ratio ofkinetic to internal energy has to be monitored to avoid that anyinertial effect in the solution influences the dynamic equilibrium,thus guaranteeing the reliability of the structural results obtained.An adequate semi-automatic mass scaling governs the stable timeincrement in order to reduce the computational cost while vis-cous pressure is applied to the external surfaces of the arterialand stent models to dampen dynamic oscillations. More detailson these models can be found in Gastaldi et al. [7] and Morlacchi


et al. [21]. The procedural indications adopted in the two clinicalcases are used to assign specific loading and boundary conditions asfollows:

odel, for clarity only two stent struts are shown. The initial stent geometry (top) iscylindrical surface (middle). After the elastic recoil, the final stent diameter is aboutd onto a cylindrical internal guide following the vessel centerline and characterized




S. Morlacchi et al. / Medical Engineering & Physics xxx (2013) xxx– xxx 5

Table 1Summary and description of the steps implemented for the simulation of case A.

Step Description Loads Contacts Boundary conditions

1 Angioplasty balloon inflation Pressure of 10 atm acting onthe 2 × 20 mm balloon

Balloon – catheter, balloon –artery

Artery: end nodes constrained inthe longitudinal directionCatheter guides: fully constrained

2 Elastic recoil post-angioplasty No loads applied Interactions removed3 Stent expansion Pressure of 14 atm acting on

the 3 × 32 mm balloonBalloon – stent, balloon –artery, balloon – catheter, stent– artery

4 Elastic recoil post expansion No loads applied Stent – artery5 Proximal optimization

techniquePressure of 18 atm acting onthe proximal 3.5 × 20 mmballoon

Balloon – stent, balloon –artery, balloon – catheter, stent– artery

aotpp

bbpwmao

Tbib[

od

3

3

fAsl[tt

TS

6 Elastic recoil post proximalexpansion

No loads applied

– Case A: after pre-dilatation at 10 atm with a 2 × 20 mm longngioplasty balloon, a Xience Prime stent characterized by a lengthf 28 mm is deployed across the bifurcation between the LAD andhe SB by inflating a 3 × 32 mm angioplasty balloon at 14 atm. Therocedure ends with a post-dilatation at 18 atm in the proximalart of the MB using a 3.5 × 20 mm balloon.

– Case B: two Endeavor stents are implanted across the twoifurcations between the LAD and the first and second diagonalranches. After a pre-dilatation at 13 atm with a 2.5 × 15 mm angio-lasty balloon, the distal device is inserted and expanded at 12 atmith a 2.75 × 18 mm angioplasty balloon. Afterwards, the proxi-al stent is implanted across the first bifurcation with a 3 × 18 mm

ngioplasty balloon inflated at 14 atm resulting in a small overlapf about 2.00 mm with the previously implanted device.

The different steps of the simulations are summarized inables 1 and 2 for cases A and B, respectively, reporting the loads,oundary conditions and contact domains implemented. Contacts

nvolving the arterial surface are all modeled using a hard normalehavior and a frictional tangential behavior with a penalty of 0.0622]. All other contacts have a friction coefficient of 0.2 [23].

Final simulations of cases A and B require a computational timef 60 and 56 h, respectively, using two nodes of the previouslyescribed high computing cluster.

. Results and discussion

.1. Choice of the solution scheme

The ABAQUS finite element commercial code includes two dif-erent tools to solve structural problems: ABAQUS/Standard andBAQUS/Explicit. For several analyses, it is clear which solverhould be used but in some cases, such as the quasi-static non-


inear problems investigated in this study, the choice is not trivial24]. Each strategy has its own advantages and modeling difficul-ies and several studies have been recently published to comparehe two approaches [25–28].

able 2ummary and description of the steps implemented for the simulation of case B.

Step Description Loads

1 Angioplasty balloon inflation Pressure of 13 atm acting on the2.5 × 15 mm balloon

2 Elastic recoil post-angioplasty No loads applied

3 Distal stent expansion Pressure of 12 atm acting on the2.75 × 18 mm distal balloon

4 Elastic recoil post distal expansion No loads applied

5 Proximal stent expansion Pressure of 14 atm acting on the3 × 18 mm proximal balloon

6 Elastic recoil post proximalexpansion

No loads applied

Stent – artery

In this work, three kinds of simulation are implemented: stentcrimping, stent advancement and stent deployment in coronaryarteries. The first two analyses have been efficiently solved usingABAQUS/Standard mainly due to the relatively low number ofelements in the model (stent and cylindrical surfaces) and unso-phisticated contact conditions. Conversely, the simulation of stentdeployment in coronary arteries is characterized by a very largenumber of degrees of freedom since several parts (one or twostents, angioplasty balloons, catheter guides, coronary arteries)with highly non-linear mechanical behaviors are involved. More-over, multiple self-contact and contact conditions among theparts are included in the model, enhancing the complexities ofthe system. Hence, ABAQUS/Explicit is adopted to take advan-tage of its robust contact functionality. However, while usingABAQUS/Explicit to solve quasi-static problems, kinetic energiesthat are associated to nodal velocities and element density mustbe maintained negligible with respect to the internal energy ofthe system (sum of the elastic and artificial strain energies, theenergies dissipated through plasticity, viscoelasticity, damage anddistortion control and the fluid cavity energy) to ensure that iner-tial effects do not influence dynamic equilibrium and to guaranteethe reliability of the mechanical results. As a consequence, beforeanalyzing any mechanical result, the quasi-staticity condition isverified for each deployment simulation by checking that the ratiobetween kinetic and internal energy of the stents is maintainednegligible (below 2% in this study).

3.2. Procedural outcomes and straightening of the arterial wall

Figs. 5 and 6 show the sequential steps of the two clinicalcases simulated while in Video 2 is observable the animated rep-resentation of case B. In agreement with the post-stenting clinical


evidence, in both cases virtual stenting implantations succeed inre-opening the arterial lumen by providing an adequate structuralsupport to the arterial wall and restoring the vessel patency at theend of the procedures. In particular, the degree of stenosis in the

Contacts Boundary conditions

Balloon – catheter, balloon – artery

Artery: end nodes constrained inthe longitudinal directionCatheter guides: fully constrained

No interactionsBalloon – stent, balloon – artery,balloon – catheter, stent – arteryStent – arteryBalloon – stents, balloon – artery,balloon – catheter, stents – artery,MB stent – SB stentStents – artery, MB stent – SB stent





Fig. 5. Clinical case A. Steps of the final numerical simulation: (A) angioplasty procedure with a 2.0 mm balloon expanded at 10 atm; (B) deployment of the Xience Primes 3.5 mc

mael6p

fatFtfswlas

Fa1

tent with a 3.0 mm balloon at 14 atm; (C) proximal optimization technique with aonfiguration at the end of the stenting procedure.

ost critical section of case A changes from 84% to 76% after thengioplasty procedure, enlarging the free lumen and allowing anasier advancement of the device. Concerning case B, the simu-ated angioplasty results in a reduction of the stenosis from 73% to4%. In both cases, no stenosis is present at the end of the stentingrocedures.

In Fig. 7, a visualization of the post-treatment CCA is presentedor both the models. The position of the 3D models is manuallydjusted to match the viewpoint of the angiography. The visualiza-ion of the stent on the angiography is poor due to its low opacity.or this reason, the position of the stent is obtained by visual inspec-ion of the complete image sequence and highlighted in the secondrame of Fig. 7. In the third frame an overlay of the 3D model of thetent and the angiography with matching viewpoints is reportedhile the 3D numerical outcomes of the stent inside the vessel


umen model is presented in the last frame. For case A we observe good matching between the stent implanted in the patient and theimulation. In case B, where two stents are implanted, we observe

ig. 6. Clinical case B. Steps of the final numerical simulation: (A) angioplasty procedurcross the distal bifurcation with a 2.75 mm balloon inflated at 12 atm; (C) deployment o4 atm; (D) final geometrical configuration at the end of the stenting procedure.

m balloon deployed in the proximal part of the MB at 18 atm; (D) final geometrical

that the distal side of the stent implanted distally is slightly dislo-cated with respect to the real one. This should be mainly attributedto the motion of the coronaries (heart pulsation and respiration)and the fact that the reconstructed model does not account for thismotion. Still, the mismatch is limited to the final portion of thestent showing a good resemblance in the remaining locations andfor case A.

In both cases, post-stenting straightening of the arterial walloccurs. In literature, this phenomenon is frequently reported inin vivo studies [29,30]. This occurrence is clinically relevant sinceit is also identified as a valid predictor for major adverse cardiacevents such as death, acute myocardial infarction, or target lesionrevascularization [31]. Since then, flexibility of coronary stents hasbecome a key point during the design of coronary stents and sev-eral numerical models have been implemented to investigate this


issue [32,33].Fig. 8 provides a qualitative representation of the influence of

stent implantation on the arterial geometries. In order to more

e with a 2.5 mm balloon expanded at 13 atm; (B) expansion of an Endeavor stentf a second Endeavor stent across the proximal bifurcation with a 3.0 mm balloon at





F d B (bo phy wv with

qi

T

wiavf0

riirm

Ffir

ig. 7. Visualization of the post-treatment coronary angiography for cases A (top) anf the angiography. From left to right: the post-treatment CCA alone, the angiograisualization of the stents from the FEM simulation, and the result of the simulation

uantitatively assess the post-stenting straightening, a tortuosityndex (TI) [34] is evaluated for each of the cases and defined as

I = L

L′ − 1

here L is the length of the centerline of the coronary arteries and L′

s the distance between the extremes of the region of interest. TI has value of zero for a straight vessels and increases with vessel cur-ature. Regarding case A, after the stenting procedure, TI changesrom 0.119 to 0.085 (−28.6%) while for case B TI decreases from.054 to 0.044 (−18.5%).

For case A only, an image-based post-stenting geometry iseconstructed combining the information of 6 months post-


ntervention CTA and CCA acquired immediately after thentervention (Fig. 9). This geometrical model can be considered aealistic model of the patient because it is based on actual measure-ents on image patient data, and because no in-stent restenosis is

ig. 8. Comparison of the pre-stenting (red) and post-stenting (blue) configurationsor case A (top) and case B (below). The straightening of the arterial wall is visiblen both cases. (For interpretation of the references to color in this figure legend, theeader is referred to the web version of the article.)

ottom). The position of the 3D models is manually adjusted to match the viewpointith the position of the stent highlighted, the angiography with the superimposed

the stent inside the deformed vessel model.

clinically observed after 6 months. Thus, it is fairly acceptable thatthe diameters of the artery did not greatly change in this period.Therefore, similarities of this reconstruction with respect to ournumerical model (Fig. 9) obtained by replicating the intervention,provide a first evidence of the success of our methodology. To quan-titatively measure the straightening effect, the TI is computed ineach case resulting in values of 0.085 and 0.089 for the numericaland image-based geometries, respectively.

In conclusion, it is shown quantitatively and qualitativelyhow the straightening of the vessel is properly simulated, prov-ing the reliability of finite element simulations in predictingpatient-specific stenting intervention geometrical outcomes. Cer-tain regions of the numerically simulated model differ more clearlyfrom the image-based model, such as a narrowing at the beginningof the SB, and in the MB at the proximal part of the stent. This can


be explained by plaque shift in these regions, a phenomenon thatis actually expected looking at CCA images, and that is not includedin our current numerical modeling capabilities.

Fig. 9. Post-stenting geometrical configuration: comparison between the numericaloutcome (blue) and the reconstruction from medical images (green). (For interpre-tation of the references to color in this figure legend, the reader is referred to theweb version of the article.)





F stentt

3

tbodlcds

cp

F(it

ig. 10. Contour maps of the Von Mises stresses in the two stents at the end of thehe overlapping region and in the strut with the highest stress.

.3. Effect of overlapping stents

In case B, the clinical procedure performed consists of a sequen-ial implantation of two devices across the first and second diagonalranches of the LAD. At first, the distal stent is expanded by meansf deployment of a 2.5 mm angioplasty balloon. Then, a secondevice is implanted with a 2.75 mm balloon allowing a small over-

ap between the devices. This occurrence is not uncommon in thease of long atherosclerotic lesions even if it has been associated toelayed healing [35] and emerging structural issues like coronary


tent fracture [36].The biomechanical results obtained in this study highlight the

riticisms provoked by two overlapping stents. For instance, theeak values of the von Mises stresses both at the maximum

ig. 11. (A) Contour maps of the PEEQ in the two stents at the end of the stenting procedB) Plot of the average PEEQ calculated in every ring of struts for the proximal (blue) andn those located at the bifurcations and in the overlapping struts of the distal stent. (For io the web version of the article.)

ing procedure of case B. In the magnification areas below, details of the stresses in

expansion of the second device (917 MPa) and at the end of theprocedure (904 MPa) can be found in the overlapping region of thedistal stent (Fig. 10). These values are very close to the ultimatestress at break (933 MPa) showing the potential risk of ruptureat these locations. The same region is proven to be mechanicallyrisky considering the plastic equivalent strains (PEEQ) as well. Thisquantity is a scalar representation of the amount of plastic strainsthat stent struts undergo during expansion while providing struc-tural support to the arterial wall and preventing its immediate fullrecoil. The PEEQ peak value at the end of the procedure is located


in the first ring of the proximal stent (Fig. 11a) and equals 0.454. Atotal of two stent struts, both located in the first ring of the prox-imal stent, exceed the ultimate tensile strain limit of the materialmodel implemented (0.445). Fig. 11b reports the values of the mean

ure of case B. In the magnification area below, details of the most deformed strut. distal (red) stent. Peak values are obtained in the first struts of the proximal stent,nterpretation of the references to color in this figure legend, the reader is referred





F of thH

Pwfisfitoidhom[stwtmo

sa[rtdFaw

3

mshctFeopli

rii

both in the device and the arterial wall and a higher metal-to-artery

ig. 12. Contour maps of the maximum principal stresses in the artery at the endigher values are obtained in the overlapping region.

EEQ calculated averaging the maximum values obtained along thehole ring of the struts. Besides the overlapping region where therstly implanted device is over expanded by the deployment of theecond device, high values of averaged PEEQ can be found in therst struts of the proximal stent and in the struts located level withhe bifurcations (black lines) as well. In these areas, the absencef plaques and the origin of the SB decrease the radial forces act-ng on the expanded stent and allow the device to expand andeform more. Besides structural integrity of the metallic devices,igh deformation areas are also critical for the potential damager delamination of the polymer coating and consequent impair-ent of drug supply to the arterial wall, as shown by Guerin et al.

37]. Lastly, the overlapping region also results in an increase oftresses in the arterial wall. Fig. 12 depicts the contour maps ofhe maximum principal stresses in different sections of the arterialall at the end of the procedure. The maximum value is found in

he central section of the overlapping area reaching 525 kPa at theaximum expansion of the second device and 374 kPa at the end

f the procedure.In conclusion, the major biomechanical influence of overlapping

tents has been proven in several clinical studies in terms of delayedrterial healing [38], risk of stent fracture due to fatigue failure36] and more frequent target lesion revascularization [35]. Theesults of our models seem to match these considerations provinghe criticism of overlapping stent in terms of higher stresses andeformation occurring both in the devices and the arterial wall.urthermore, an increased metal-to-artery ratio of the overlappingrea will likely result in a widely modified hemodynamic field asell.

.4. Model limitations and further developments

Some limitations are present in the implemented numericalodels. Firstly, the image-based reconstructions still present some

implifications such as, for instance, the circular cross-sectionypothesized along the whole geometry and the assumed smoothonfiguration of the external wall. This study lacks information onhe biological tissues composition of the two patient-specific cases.urthermore, the artery is considered isotropic and homogeneous,ven though the vessel wall is anisotropic due to the collagen fibersrientation and is characterized by different layers. Also, plaqueositioning is only hypothesized and entirely modeled as soft cellu-

ar plaque. Moreover, arterial blood pressure (averaged 100 mmHg)nside the vessels and wall movement are neglected.


The mechanical behavior of the exact Co–Cr alloys used to fab-icate the commercial devices is not available due to manufacturerndustrial policies. Hence, a standard Co–Cr medical alloy mechan-cal behavior is used. This limitation has to be considered while

e stenting procedure of case B. For clarity of view, only some sections are shown.

discussing the presented results and stress values may only be usedin a qualitative way.

In light of these considerations, further developments of thepresented model could surely provide more accurate results andadditional information for both the clinical and the industrial pointof view. First, the use of anisotropic arterial wall modeling, takinginto consideration the collagen fibers orientation, could improvethe biological tissues material models; secondly, a more detailedreconstruction of arterial geometry could be possible using morerecent vascular imaging techniques, such as IVUS and OCT. Further-more, the combination of structural analyses with computationalfluid dynamics [21,39] or drug eluting models [40,41] could behelpful in completing the picture and better understanding thebiomechanical influence of stenting procedure in patient-specificcases.

Lastly, since the main limitations that currently restrict theadoption of finite element models in clinical practice are theircomplex implementation and their high computational cost,automatic methods of image-based geometrical reconstructionand discretization should be matched with less computationallydemanding modeling techniques such as the use of beam ele-ments for the stents or shell elements for the arteries. In such away, quicker simulations and comparisons of different optionaltreatments might be implemented fostering the use of these mod-els during the interventional planning. In this light, the complexnumerical methods here presented might be used to validate thesemore rapid but less accurate modeling tools.

4. Conclusion

This work shows the feasibility of implementing a patient-specific virtual model replicating two actual clinical cases. This stepmay be considered a step forward toward the routine applicationof such models in the clinical field that, however, is still limitedby some restrictions such as the computational cost and complexpreparation of the models itself. In both simulations, the straight-ening of the arterial wall due to stent implantation is obtained,in agreement with previous experimental studies and with theimage-based post-stenting configuration of the second case stud-ied, reconstructed after the 6 months follow-up. Then, the presenceof overlapping stents proved to be a critical occurrence from abiomechanical point of view because of higher mechanical stresses


ratio due to the double metallic layer. These findings are in agree-ment with in vivo studies that recognized overlapping stents as anindependent factor of coronary stent fractures [36] and delayedarterial healing [35].


ING Model

J

1 neerin

E

ot

A

pfmatgfS

A

i2

C

t

R

[

[

[

[

[

[

[[

[

[

[

[

[

[[[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

ARTICLEJBE-2248; No. of Pages 10

0 S. Morlacchi et al. / Medical Engi

thical approval

“Dr. Peset” Hospital Ethical Committee approval was obtainedn 30/06/2010. Local Code: 19/10. Patients gave informed consento the work on their anonymous image data.

cknowledgements

Authors affiliated to Politecnico di Milano are supported by therojects “RT3S-Real Time Simulation for Safer vascular Stenting”unded by the European Commission and “Development of hybrid

agnesium degradable stents with polymeric coating for medicalpplication” funded by the Fondazione CARITRO. Authors affiliatedo UPF and Dr. Peset are partially funded by a CDTI CENIT-cvREMODrant of the Spanish Ministry of Science and Innovation. R.C. is alsounded by a Beatriu de Pinòs post-doctoral program, from AGAUR,pain.

ppendix A. Supplementary data

Supplementary data associated with this article can be found,n the online version, at http://dx.doi.org/10.1016/j.medengphy.013.01.007.

onflict of interest

The authors declare that they have no competing interests inhis study.

eferences

[1] Morlacchi S, Migliavacca F. Modeling stented coronary arteries: where we are,where to go. Ann Biomed Eng; 1–17, in press

[2] Martin D, Boyle FJ. Computational structural modeling of coronarystent deployment: a review. Comput Methods Biomech Biomed Eng2011;14(4):331–48.

[3] Murphy J, Boyle FJ. Predicting neointimal hyperplasia in stented arteries usingtime-dependant computational fluid dynamics: a review. Comput Biol Med2010;40:408–18.

[4] Edelman ER, Rogers C. Pathobiologic responses to stenting. Am J Cardiol1998;81(7A):4E–6E.

[5] Siow RC, Mallawaarachchi CM, Weissberg PL. Migration of adventitial myofib-roblasts following vascular balloon injury: insights from in vivo gene transferto rat carotid arteries. Cardiovasc Res 2003;59(1):212–21.

[6] Mudra H, Regar E, Klauss V, Werner F, Henneke KH, Sbarouni E, Theisen K. Serialfollow-up after optimized ultrasound-guided deployment of Palmaz–Schatzstents in-stent neointimal proliferation without significant reference segmentresponse. Circulation 1997;95:363–70.

[7] Gastaldi D, Morlacchi S, Nichetti R, Capelli C, Dubini G, Petrini L, Migliavacca F.Modeling of the provisional side-branch stenting approach for the treatmentof atherosclerotic coronary bifurcations: effects of stent positioning. BiomechModel Mechanobiol 2010;9:551–61.

[8] Capelli C, Gervaso F, Petrini L, Dubini G, Migliavacca F. Assessment of tissueprolapse after balloon-expandable stenting: influence of stent cell geometry.Med Eng Phys 2009;31:441–7.

[9] Mortier P, De Beule M, Van Loo D, Verhegghe B, Verdonck P. Finite elementanalysis of side branch access during bifurcation stenting. Med Eng Phys2009;31:434–40.

10] Williams AR, Koo BK, Gundert TJ, Fitzgerald PJ, LaDisa JF. Local hemodynamicchanges caused by main branch stent implantation and subsequent virtualside branch balloon angioplasty in a representative coronary bifurcation. J ApplPhysiol 2010;109(2):532–40.

11] Steinman DA. Image-based computational fluid dynamics modeling in realisticarterial geometries. Ann Biomed Eng 2002;30:483–97.


12] Moore JE, Timmins LH, Ladisa JF. Coronary artery bifurcation biomechan-ics and implications for interventional strategies. Catheter Cardiovasc Interv2010;76(6):836–43.

13] Routledge H, Lefevre T, Colombo A, Oldroyd K, Hamm C, Guagliumi G, et al.Three-year clinical outcome of percutaneous treatment of bifurcation lesions

[

PRESSg & Physics xxx (2013) xxx– xxx

in multivessel coronary artery disease with the sirolimus-eluting stent: insightsfrom the arterial revascularisation therapies study, part ii (arts ii). Eurointer-vention 2009;5:190–6.

14] Lefevre T, Darremont O, Albiero R. Provisional side branch stenting for thetreatment of bifurcation lesions. Eurointervention 2010;6(Suppl. J):J65–71.

15] Cárdenes R, Díez JL, Larrabide I, Bogunovic H, Frangi AF. 3D modeling of coro-nary artery bifurcations from CTA and conventional coronary angiography. MedImage Comput Comput Assist Interv 2011;14(Pt. 3):395–402.

16] Vascular Modeling Toolkit. http://www.vmtk.org/ [accessed 10.12.11].17] Gradus-Pizlo I, Bigelow B, Mahomed Y, Sawada SG, Rieger K, Feigenbaum H.

Left anterior descending coronary artery wall thickness measured by high-frequency transthoracic and epicardial echocardiography includes adventitia.Am J Cardiol 2003;91(1):27–32.

18] Holzapfel GA, Sommer G, Gasser CT, Regitnig P. Determination of layer-specificmechanical properties of human coronary arteries with non-atheroscleroticintimal thickening and related constitutive modeling. Am J Physiol Heart CircPhysiol 2005;289:H2048–58.

19] Loree HM, Grodzinsky AJ, Park SY, Gibson LJ, Lee RT. Static circum-ferential tangential modulus of human atherosclerotic tissue. J Biomech1994;27(2):195–204.

20] Poncin P, Proft J. Stent tubing: understanding the desired attributes. In:Proceedings of the Materials & Processes for Medical Devices Conference. 2003.

21] Morlacchi S, Chiastra C, Gastaldi D, Pennati G, Dubini G, Migliavacca F. Sequen-tial structural and fluid dynamic numerical simulations of a stented bifurcatedcoronary artery. J Biomech Eng 2011;133(12):121010.

22] Dunn AC, Zaveri TD, Keselowsky BG. Macroscopic friction coefficient measure-ments on living endothelial cells. Tribol Lett 2007;27:233–8.

23] http://engineershandbook.com [accessed 20.09.11].24] Hibbitt, Karlsson, Sorensen. ABAQUS theory manual. RI, USA: Pawtucket; 1997.25] Harewood FJ, McHugh PE. Comparison of the implicit and explicit finite element

methods using crystal plasticity. Comput Mater Sci 2007;39:481–94.26] Rebelo N, Nagtegaal JC, Taylor LM, Passmann R. Industrial application of implicit

and explicit finite element methods to forming processes. American Society ofMechanical Engineers, Computer Engineering Division, CED. 1992;5:67–76.

27] Sun JS, Lee KH, Lee HP. Comparison of implicit and explicit finite elementmethods for dynamic problems. J Mater Proc Technol 2000;105:110–8.

28] Kim J, Kang SJ, Kang BS. A comparative study of implicit and explicit FEM forthe wrinkling prediction in the hydroforming process. Int J Adv Manuf Technol2003;22(7–8):547–52.

29] Wentzel JJ, Whelan DM, van der Giessen WJ, van Beusekom HM, Andhyiswara I,Serruys PW, Slager CJ, Krams R. Coronary stent implantation changes 3-D vesselgeometry and 3-D shear stress distribution. J Biomech 2000;33:1287–95.

30] Liao R, Green NE, Chen SY, Messenger JC, Hansgen AR, Groves BM, Carroll JD.Three-dimensional analysis of in vivo coronary stent–coronary artery interac-tions. Int J Cardiovasc Imaging 2004;20:305–13.

31] Gyongyosi M, Yang P, Khorsand A, Glogar D. Longitudinal straightening effectof stents is an additional predictor for major adverse cardiac events AustrianWiktor Stent Study Group and European Paragon Stent Investigators. J Am CollCardiol 2000;35:1580–9.

32] Petrini L, Migliavacca F, Auricchio F, Dubini G. Numerical investigation of theintravascular coronary stent flexibility. J Biomech 2004;37(4):495–501.

33] Mortier P, Holzapfel GA, De Beule M, Van Loo D, Taeymans Y, Segers P, VerdonckP, Verhegghe B. A novel simulation strategy for stent insertion and deploymentin curved coronary bifurcations: comparison of three drug-eluting stents. AnnBiomed Eng 2010;38(1):88–99.

34] Piccinelli M, Veneziani A, Steinman Da, Remuzzi A, Antiga L. A framework forgeometric analysis of vascular structures: application to cerebral aneurysms.IEEE Trans Med Imaging 2009;28(8):1141–55.

35] Räber L, JüniP, Löffel L, Wandel S, Cook S, Wenaweser P, et al. Impact of stentoverlap on angiographic and long-term clinical outcome in patients undergoingdrug-eluting stent implantation. J Am Coll Cardiol 2010;55:1178–88.

36] Nakazawa G, Finn AV, Vorpahl M, Ladich E, Kutys R, Balazs I, et al. Incidence andpredictors of drug-eluting stent fracture in human coronary artery a pathologicanalysis. J Am Coll Cardiol 2009;54(21):1924–31.

37] Guerin P, Pilet P, Finet G, Goueffic Y, N’Guyen J, Crochet D, et al. Drug-elutingstents in bifurcations: bench study of strut deformation and coating lesions.Circ Cardiovasc Interv 2010;3:120–6.

38] Finn AV, Kolodgie FD, Harnek J, et al. Differential response of delayed healingand persistent inflammation at sites of overlapping sirolimus- or paclitaxel-eluting stents. Circulation 2005;112:270–8.

39] Chiastra C, Morlacchi S, Pereira S, Dubini G, Migliavacca F. Computational fluiddynamics of stented coronary bifurcations studied with a hybrid discretizationmethod. Eur J Mech B: Fluids 2012;35:76–84.

40] D’Angelo C, Zunino P, Porpora A, Morlacchi S, Migliavacca F. Model reduc-


tion strategies enable computational analysis of controlled drug release fromcardiovascular stents. SIAM J Appl Math 2012;71(6):2312–33.

41] Cutrì E, Zunino P, Morlacchi S, Chiastra C, Migliavacca F. Drug delivery pat-terns for different stenting techniques in coronary bifurcations: a comparativecomputational study. Biomech Model Mechanobiol; in press


http://dx.doi.org/10.1016/j.medengphy.2013.01.007

http://dx.doi.org/10.1016/j.medengphy.2013.01.007

http://dx.doi.org/10.1007/s10439-012-0681-6

http://www.vmtk.org/

http://engineershandbook.com/

http://dx.doi.org/10.1007/s10237-012-0432-5

patient-specific simulations of stenting procedures in coronary bifurcations: two clinical cases

Documents