Simulation of transcatheter aortic valve implantation throughpatient-specific finite element analysis: Two clinical cases

S. Morganti a,n, M. Conti b, M. Aiello c, A. Valentini d, A. Mazzola c, A. Reali b, F. Auricchio b

a University of Pavia, Dept. of Industrial Eng. and Informatics, Via Ferrata 3, 27100 Pavia, Italyb University of Pavia, Dept. of Civil Eng. and Architecture, Via Ferrata 3, 27100 Pavia, Italyc IRCCS Policlinico San Matteo, Dept. of Cardiothoracic Surgery, Viale Golgi 19, 27100 Pavia, Italyd IRCCS Policlinico San Matteo, Institute of Radiology, Viale Golgi 19, 27100 Pavia, Italy

a r t i c l e i n f o

Article history:Accepted 4 June 2014

Keywords:Aortic valvePatient-specific modelingTAVIStructural finite element

a b s t r a c t

Transcatheter aortic valve implantation (TAVI) is a minimally invasive procedure introduced to treataortic valve stenosis in elder patients. Its clinical outcomes are strictly related to patient selection,operator skills, and dedicated pre-procedural planning based on accurate medical imaging analysis. Thegoal of this work is to define a finite element framework to realistically reproduce TAVI and evaluate theimpact of aortic root anatomy on procedure outcomes starting from two real patient datasets. Patient-specific aortic root models including native leaflets, calcific plaques extracted from medical images, andan accurate stent geometry based on micro-tomography reconstruction are key aspects included in thepresent study. Through the proposed simulation strategy we observe that, in both patients, stentapposition significantly induces anatomical configuration changes, while it leads to different stressdistributions on the aortic wall. Moreover, for one patient, a possible risk of paravalvular leakage hasbeen found while an asymmetric coaptation occurs in both investigated cases. Post-operative clinicaldata, that have been analyzed to prove reliability of the performed simulations, show a good agreementwith analysis results. The proposed work thus represents a further step towards the use of realisticcomputer-based simulations of TAVI procedures, aiming at improving the efficacy of the operationtechnique and supporting device optimization.

& 2014 Elsevier Ltd. All rights reserved.

1. Introduction

The first percutaneous transcatheter implantation of an aorticvalve prosthesis in humans was described more than 10 years ago,in 2002, by Cribier et al. (2002). Since then, such a minimallyinvasive procedure to restore valve functionality in case of calcificstenosis has become a routine approach for high-risk or eveninoperable patients (Smith et al., 2011).

Many papers collecting the results of transcatheter aortic valveimplantation (TAVI) demonstrate that, with respect to standardtherapy, rates of death from any cause are reduced (Leon et al.,2010). Mid-term follow-up has shown no evidence of restenosis orprosthesis dysfunction (Zajarias and Cribier, 2013). Moreover,recent registers report satisfactory outcomes of TAVI in terms offeasibility, short-term hemodynamics, and functional improve-ment (Thomas et al., 2011; Eltchaninoff et al., 2011; Vahanianet al., 2008).

However, a high percentage of treated patients have shownmoderate to severe perivalvular aortic regurgitation (Zajarias andCribier, 2013), that is one of the most frequent complicationsassociated with TAVI, which correlates with an increased rate ofmortality (Generaux et al., 2013). Incomplete prosthesis appositiondue to calcifications or annular eccentricity (Blanke et al., 2010),undersizing of the device, and malpositioning of the valve (Détaintet al., 2009) are the most common determinants of paravalvularleakage. As a direct consequence, an appropriate annular measure-ment, a correct evaluation of calcifications, and an appropriatesizing of the prosthetic valve are “of utmost importance” (Gurvitchet al., 2011; Delgado et al., 2010; Détaint et al., 2009).

Given such considerations, advanced computational tools inte-grating patient-specific information and accurate device modelingcan be used to support pre-operative planning. In the litera-ture, several studies addressing computer-based simulations ofTAVI through finite element analysis (FEA) are already available.Specifically, Smuts et al. (2011) have developed new concepts fordifferent percutaneous aortic leaflet geometries while Wang et al.(2012) and Sun et al. (2010) have investigated the post-opera-tive TAVI mechanics and hemodynamics, respectively. Moreover,Capelli et al. (2012) have virtually evaluated the feasibility of TAVI

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Journal of Biomechanics

http://dx.doi.org/10.1016/j.jbiomech.2014.06.0070021-9290/& 2014 Elsevier Ltd. All rights reserved.

n Corresponding author.E-mail address: simone.morganti@unipv.it (S. Morganti).

Journal of Biomechanics 47 (2014) 2547–2555

in morphologies which are currently borderline cases for apercutaneous approach (e.g., failed bioprosthetic aortic valves).More recently, Auricchio et al. (2012a) have proposed a patient-specific FEA-based simulation accounting for all the proceduralsteps able to reproduce the prosthesis post-operative performancethrough the inclusion in the analysis of the biological valve sewninto the metallic frame. However, to the authors’ knowledge,a comparison with postoperative medical data has not beenaddressed yet.

In this context, the present work proposes a systematicapproach to realistically simulate TAVI, tailored to the clinicalpractice; in particular, we propose a study, based on the analysis ofpre-operative medical images of two real patients who underwentTAVI, with the final ambitious goal of predicting the post-operativeperformance of the prosthesis with respect to the specific anato-mical features. The present work includes different issues whichmake it an original contribution, presenting the capabilities of anadvanced tool for clinical support and, in particular: (i) the aorticvalve model is complete of both the aortic sinuses and the nativevalve leaflets and the considered material model is calibrated onhuman data, (ii) the calcific plaque is included within the modelon the basis of imaging records, (iii) the geometry of the prostheticstent is very accurate, being obtained from micro-tomography(micro-CT) reconstruction.

Last but not least, post-operative data collected by physicians forpatients’ follow-up are used for comparison with numerical resultswith the aim of assessing the capabilities of the proposed simulationsto predict the procedural outcomes. Validation of TAVI simulation is acritical issue since it is usually difficult to obtain good quality post-operative data and images from standard post-operative procedures.Additionally, postoperative CT is not included in the routine protocolof transcatheter aortic valve implantation either to not overload renalactivity of often already critical patients with the use of a contrastdie, or to avoid high radiation doses for the patient. Instead, theoperation outcome is generally evaluated by intraoperative angio-graphy as well as by follow-up ultrasound. In the present paper, onthe basis of such routinely obtained data, we try to address acomparison between the real procedure outcomes and the simula-tion results.

2. Materials and methods

Two patients that underwent TAVI have been included in the present study,both with severe symptomatic aortic stenosis: Patient-1 is a 83 year-old malesubject, while Patient-2 is a 84 year-old male subject; both patients underwentTAVI through transapical access.1 In both cases, the preoperative planning startedfrom a CT examination, which, at present, represents the standard methodology fordevice selection based on the measurement of the virtual ring proposed by Piazzaet al. (2008).

For both patients, the Edwards SAPIEN XT size 26 was selected by physicians asthe optimal device for implantation. In both cases, the implantation was performedsuccessfully, that is, without procedural mortality as well as without embolization(i.e., migration of the implanted valve either into the left ventricle or into the aorta).

The adopted computational framework to simulate transcatheter aortic valveimplantation can be roughly divided into four main steps:

� Step 1: Processing of medical images.� Step 2: Creation of analysis-suitable models.� Step 3: Performance of all the required analyses to reproduce the entire clinical

procedure.� Step 4: Post-processing of the simulation results and comparison with follow-

up data.

As described in Table 1, the four main stages of the developed workflowaccount for different sub-steps, which are detailed in the following.

2.1. Medical image processing

Preoperative CT examinations were performed at IRCCS Policlinico San Matteo(Pavia, Italy) using a dual-source computed tomography scanner (Somatom Definition,Siemens Healthcare, Forchheim, Germany). To obtain contrast-enhanced images aiodinated contrast agent was injected. Scan main parameters for cardiac CT were asfollows: scan direction, cranio-caudal; slice thickness, 0.6 mm; spiral pitch factor, 0.2;tube voltage, 120 kV.

The CT data sets are processed using ITK-Snap v2.4 (Yushkevich et al., 2006). Inparticular, a confined region of interest (i.e., the aortic root from the left ventricularoutflow to the sinotubular junction) is extracted from the whole reconstructedbody exploiting the contrast enhancement, cropping, and segmentation capabilitiesof the software.

Using different Hounsfield unit thresholds, it is possible to discern the calcificcomponent from the surrounding healthy tissue and evaluate it in terms of bothlocation and dimension. Once the segmented region is extracted, we export theaortic lumen as well as the calcium deposits as stereolithographic (STL) files,represented in Fig. 1.

2D echocardiography is routinely performed and almost all patients affected byaortic pathologies undergo ultrasound examination since it does neither needradiation doses exposition nor contrast injection. In particular, with 2D ultrasoundtechnique aortic valve leaflets result visible and, for this reason, preoperativeechographic images obtained using a Prosound Alpha 10 machine (ALOKA, Tokyo,Japan) have been used to measure specific leaflet dimensions and, in particular, theleaflet free margin length.

2.2. Analysis-suitable models

In this section, we describe the procedure to obtain analysis-suitable models ofboth the native aortic valve including calcifications and prosthetic device.

Native aortic valve model: The obtained STL file of the aortic root is processedimplementing in Matlab (The Mathworks Inc., Natick, MA, USA) a procedure able todefine a set of splines, resembling the cross sectional contours of the aortic lumen.These curves are used to automatically generate a volume model of the aortic rootwall, which is finally imported in Abaqus CAE software (Simulia, Dassáult Systems,Providence, RI, USA) for the finite element analysis set-up.

The geometrical model of the aortic root obtained by processing the STL file thusrepresents the starting point of the finite element analysis of TAVI. It is worth notingthat we generate not only the aortic wall but also the native valve leaflets in order toget a complete and realistic model for the simulations. In particular, to include thenative leaflets geometry, the first step consists in the identification of nine reference

Table 1The four blocks of the developed modeling strategy.

Step-1 Step-2 Step-3 Step-4Medical images Analysis-suitable Analysis Post-processing

models

Ct data Aortic sinuses Stent crimping Simulation output2D echo data native leaflets stent expansion follow-up data

calcifications valve mappingprosthetic device valve closure

Lumen Calcium

View 2

View 2View 1

RC

LC

LC

RC

NC

Fig. 1. Through image processing procedures the aortic lumen (red) and thecalcium deposits (yellow) can be isolated and extracted from CT data of the wholebody. (For interpretation of the references to color in this figure caption, the readeris referred to the web version of this article.)

1 For technical details refer to Lichtenstein et al. (2006).

S. Morganti et al. / Journal of Biomechanics 47 (2014) 2547–25552548

points: six of them refer to the commissural extremes (A, A0 , B, B0, C, C0 in Fig. 2a) whilethe others correspond to the center of the basal leaflet attachment (N1,N2,N3 in Fig. 2a).

Such reference points are used for the definition of proper planes which drivethe partition of the whole aortic root model aimed at extracting the leafletcommissures and attachment lines (light blue lines in Fig. 2). The free margin issimply defined as a circular arc whose length can be measured by ultrasound. Oncethe perimeter of all the leaflets is identified, it is possible to reconstruct the leafletsurface in the open configuration.

The aortic wall model of Patient-1 is meshed using 265,976 tetrahedralelements for the healthy region and 2936 for the calcific part while the leafletsare discretized using 3212 shell elements with reduced integration for the healthytissue and 427 for the calcific region.

The aortic wall model of Patient-2 is completely calcium-free because all thecalcifications are localized in the leaflets. The model is meshed using 235,558tetrahedral elements; the healthy tissue of the leaflets is discretized using 3258shell elements with reduced integration while for the plaque 342 elementsare used.

Fig. 3 shows the resulting aortic root model in the case of Patient-1; the modelis composed of the vessel wall, the native leaflets and calcific plaque. Thesuperimposition of the model on the 3D reconstructions derived from medicalimages shows a good correspondence; in particular, in Fig. 3b,c the closed model ofthe native aortic valve, obtained through a simulation of valve closure, highlights agood agreement between the real patient's plaques and the position of calcific shellelements.

Prosthesis model: Although several devices for TAVI have been proposed overthe last decade (Padala et al., 2010), only two of them are very frequently used inclinical practice: the Medtronic CoreValve and the Edwards Lifesciences SAPIEN.While the CoreValve is self-expandable, the Edwards SAPIEN valve is basicallycomposed of three flexible biological leaflets sutured into a balloon-expandablestent. In the present study, we focus on the SAPIEN XT prosthesis moving frommedical images regarding two real patients who underwent TAVI as discussed inthe following.

Both patients were treated with an Edwards Lifesciences SAPIEN XT size 26. Afaithful geometrical model of such a device is based on a high-resolution micro-CTscan (Skyscan 1172 with a resolution of 0.17 micron) of a real device sample. Theobtained stent model is meshed using 84,435 solid elements with reduced integration.

Material models: For the sake of simplicity, the material for the native aortictissues is assumed to be isotropic and homogenous, as already assumed inGnyaneshwar et al. (2002) and Capelli et al. (2012). In particular, the nearlyincompressible reduced polynomial form is used to reproduce material behavior(Selvadurai, 2006; Yeoh, 1993). The form of the reduced polynomial strain energypotential is

Ψ ¼ ∑N

i ¼ 1Ci0ðI1�3Þi ; ð1Þ

where N and Ci 0 are material parameters, I1 is the first deviatoric strain invariantdefined as

I1 ¼ λ21þλ

22þλ

23 ; ð2Þ

where the deviatoric stretches λk ¼ J�1=3λk , being J the total volume ratio and λk theprincipal stretches. After choosing a sixth-order polynomial form (N¼6), we findthe unknown material constants Ci 0 by fitting experimental data obtained fromhuman samples for each single lealfet and sinus (Martin et al., 2011; Stradins et al.,2004). In particular, in Table 2 we report the constant values resulting from theimplemented fitting procedure described in Auricchio et al. (2012c):

In Fig. 4, the results of the fitting procedure are shown for the Left-Coronary sinus.Both circumferential and axial behavior are well-captured by the considered model.

AB

A’

B’

C

C’

N3

N1

N2

N1

A

A’

commissure

basal leafletattachment

leafletfree margin

Fig. 2. From 3D reconstructions of the aortic lumen it is possible to identifyreference points for modeling native valve leaflet: (a) the commissures and basalleaflet attachment lines are highlighted on a rendering of the aortic lumen;(b) reference points extracted from the aortic root reconstruction are used togenerate leaflet surface. (For interpretation of the references to color in this figurecaption, the reader is referred to the web version of this article.)

Lumen (Real)Calcium (Real)

View 1

View 1

Wall (Model)Leaflets (Model)Calcium (Model)

Fig. 3. Rendering of the STL file vs aortic model created for simulations: (a) the real aortic root lumen (red) and calcifications (yellow) are overlapped to the aortic wall model(gray); (b) the closed native leaflets (blue mesh) of our model are perfectly matching with real calcifications obtained by processing CT images; (c) top view is shown.(For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)

Table 2Yeoh parameters [kPa] obtained from model calibration on human aortic data.

Anatomical region C10 C20 C30 C40 C50 C60

SinusLeft-coronary 23.29 624.4 1.98e3 201.5 22.15 29.11Non-coronary 18.35 190.9 1.22e3 1.04e3 629.7 1.58e3Right-coronary 22.44 959.9 2.58e3 1.19e3 1.36e3 205.3

LeafletLeft-coronary 23.46 1.01e3 2.11e3 607.8 674.3 679.9Non-coronary 18.01 1.69e3 1.95e3 994.1 1.49e3 301.5Right-coronary 0.11 758.2 941 895.7 1.04e3 752.8

S. Morganti et al. / Journal of Biomechanics 47 (2014) 2547–2555 2549

Aortic wall and native valve leaflets are assumed to have a uniform thickness of2.5 and 0.5 mm, respectively (Auricchio et al., 2012a). Following Capelli et al.(2012), calcified tissue is assumed to be characterized by an elastic modulus of10 MPa, a Poisson ratio of 0.35, a density of 2000 kg/m3, while the thickness ofcalcific shell elements is chosen equal to 1.4 mm.

A Von Mises plasticity model with an isotropic hardening is adopted for thestent which is made of a cobalt–chromium alloy. In particular the followingparameters are used: 233 GPa, 0.35, 414 MPa, 933 MPa and 44.5% in terms ofYoung modulus, Poisson coefficient, yield stress, ultimate stress and deformation atbreak, respectively (Morlacchi et al., 2013).

Finally, regarding the prosthetic valve leaflets, there are different beliefsconcerning the constitutive characteristics of bovine pericardium after the fixationprocess. In the present work, we model the leaflets as an isotropic material (Hanlonet al., 1999; Lee et al., 1989; Trowbridge et al., 2011) and, in particular, an elasticmodulus of 8 MPa, a Poisson coefficient of 0.45, and a density of 1100 kg/m3 areused following Xiong et al. (2010). The prosthetic valve is meshed with 6000quadrilateral shell elements, while a uniform thickness of 0.4 mm is considered.

2.3. Finite-element analyses

The TAVI procedure is a complex intervention composed by several steps; torealistically reproduce the whole procedure, we set-up a simulation strategyconsisting in the following two main stages:

a. Stent crimping and deployment: In this step, the prosthesis stent model iscrimped to achieve the catheter diameter which, for a transapical approach, isusually 24 French (8 mm); then, the prosthetic stent is expanded within thepatient-specific aortic root to reproduce the implantation due to balloonexpansion.

b. Valve mapping and closure: The prosthetic leaflets are mapped onto theimplanted stent and a physiological pressure is applied to virtually recreatethe diastolic behavior of the SAPIEN device.

All the numerical analyses are non-linear problems involving large deformationand contact. For this reason, Abaqus Explicit solver v6.10 is used to perform largedeformation analyses; in particular, quasi-static procedures are used again assum-ing that inertia forces do not change the solution. Kinetic energy is monitored toensure that the ratio of kinetic energy to internal energy remains less than 10%.

a. Stent crimping and deployment: A cylindrical surface is gradually crimpedfrom an initial diameter of 28 mm to a final diameter of 8 mm. The cylinder ismeshed using 2250 4-node surface elements with reduced integration and it ismodeled as a rigid material with a density equal to 7000 kg/m3. A frictionlesscontact is defined between the crimping surface and the stent. For the set-up ofstent apposition simulation (see Fig. 5a), the deformed configuration of the stent isthen reimported in Abaqus CAE, taking into account as initial state the tensionalstate resulting from the crimping analysis.

To reproduce stent expansion, a pure and uniform radial displacement isgradually applied to the nodes of a rigid cylindrical surface, which is assumed torepresent the wall of the expanding balloon. The rigid cylinder is widened from aninitial diameter of 6 mm to a final diameter of 26 mm. During stent expansion theballoon axis remains always fixed. This assumption can be accepted as observedthrough intraoperative angiography which shows negligible axis rotation andtranslation. For both stent expansion and prosthetic valve closure, the nodes ofthe aortic model extremities (i.e., the left ventricular outflow tract and the distalsection of the ascending aorta) are free to move radially but they are confined tothe plane of their original configuration.

Frictionless contact is enabled between the stent and the cylindrical surface, aswell as between the stent and the aortic root model (see Fig. 5b). However, to avoidvalve embolization, the nodes at the top of the three supporting hollow bars of thestent are constrained such that their vertical displacement is prevented.

b. Valve mapping and closure: Following the procedure presented in Auricchioet al. (2012a), to reproduce the realistic behavior of the prosthetic device andevaluate the post-operative prosthesis performance, the prosthetic leaflets aremapped onto the implanted stent: precomputed displacements are assigned to thebase of the valve and to the nodes of the leaflet commissures, which allows toachieve a complete configuration of the implanted prosthetic device, as shown inFig. 5c.

Consequently, it results possible to reproduce the post-operative diastolicbehavior of the SAPIEN XT expanded within the patient-specific model of theaortic root. To simulate valve behavior at the end of the diastolic phase, a uniformphysiologic pressure of 0.01 MPa is applied to the prosthetic leaflets (Wiggers,1952) and a frictionless self-contact is defined for the prosthetic valve.

2.4. Measured parameters

In addition to stress/strain patterns, we evaluate the post-operative configurationand, consequently, the performance of the implanted device in terms of stenteccentricity, risk of paravalvular leakage, and leaflet coaptation. Stent eccentricityhas been measured to get an indication of the deformation affecting the stent afterimplantation, which may have important implications also on valve closure. Since theimplanted configuration has the approximate shape of an elliptic cylinder, the measureof the eccentricity can be made at any level of the prosthesis. We choose to measureeccentrity of the stent taking as reference points the prosthesis commissures (i.e., thepoints at the top of the three supporting bars).

The risk of paravalvular leakage is assumed to be proportional to the dimensionof the paravalvular holes generated in case of non-perfect adhesion of the stent tothe inner wall of the native aortic root. The malapposition of the stent is evaluatedin two different ways: (i) measuring the distance between the inner wall of theaortic root and the outer surface of the stent at the annulus level (i.e., at the planepassing through the three nadir of the three sinuses); (ii) measuring the area of the

0 0.01 0.02 0.03 0.04 0.05 0.06 0.070

10

20

30

40

50

60

70

strain [−]

Cau

chy

stre

ss [k

Pa]

circumferentialaxialmodel

Fig. 4. Fitting results on the experimental data (dots) of the human aortic left-coronary sinus (Martin et al., 2010) by using a reduced-polynomial form of the strainenergy function.

Prosthetic(leaflets)

Calcium

AorticRoot

Nativeleaflet

PhrostheticStent

Fig. 5. Procedural steps of TAVI reproduced through a computer-based simulation strategy: (a) the crimped stent is properly placed inside the aortic root model; (b) the stentis expanded within the patient-specific aortic root; (c) prosthetic leaflet closure is reproduced to evaluate postoperative performance.

S. Morganti et al. / Journal of Biomechanics 47 (2014) 2547–25552550

obtained holes, again at the annulus level. Finally, the coaptation area is defined asthe total area of the prosthetic leaflet elements in contact with each other at theend of diastole.

3. Results

The obtained results can be classified into two main groups:(i) from the simulation of stent expansion we can evaluate theimpact of the metallic frame of the stent on the native calcifiedaortic root wall; (ii) from the simulation of valve closure, we canpredict the post-operative device performance.

In Fig. 6a von Mises aortic wall stresses induced by stent expan-sion are shown from two different views for the two consideredpatients.

Such a distribution should be ideally uniform, resembling anhomogeneous interaction of the stent prosthesis with the aorticroot base. Our results suggest instead that the stresses are notuniformly distributed. In particular, in both cases, spots of con-centrated stresses are visible in correspondence with the adhesionbetween the inner aortic wall and the metallic frame of the stent.

In Fig. 7a, a contour map representing the point-wise distancebetween the basal stent crown of the expanded stent and theinner aortic wall is shown.

Higher values (up to 2 mm) are obtained for Patient-2 while agood and uniform degree of adherence is achieved after stentexpansion in Patient-1. Such results are also confirmed by Fig. 7bwhere two proximal cross-sections of the implanted device arerepresented. Greater holes (for a total area of 36.9 mm2) betweenthe stent and the aortic root wall are found for Patient-2 than forPatient-1 whose area associated to paravalvular leakage is negli-gible being equal to 4.1 mm2.

The native morphology of the aortic root and, in particular, thequantity and position of calcifications may induce a non-circularshape to the implanted device. In both cases, an elliptical shape ofthe device is obtained, as highlighted in Fig. 8a. Regarding stenteccentricity, the sides of the obtained post-implant triangle (reddotted lines in Fig. 8a) measure: a¼22.2 mm, b¼23.1 mm, c¼21.8for Patient-1; a¼23.4 mm, b¼23.3 mm, c¼21.3 for Patient-2.

The ratio between the minor and major elliptical axes (blue dottedlines in Fig. 8a) is: e¼0.91 for Patient-1 and e¼0.75 for Patient-2.

Finally, simulation of valve closure (see valve top-view ofFig. 8b) allows the quantification of coaptation area which resultsequal to 207.3 mm2 for Patient-1 and 164.8 mm2 for Patient-2.

Table 3 summarizes all the obtained results for the two specificpatients.

4. Discussion

It is well-known and extensively reported in the literature thatthe selection of prosthetic device size and type is very importantto avoid (or, at least, reduce) aortic regurgitation and/or other TAVIcomplications (Generaux et al., 2013; Delgado et al., 2010; Détaintet al., 2009). Such a critical choice not only depends on annulardimensions but also on the complex native aortic root morphologyas well as on position and dimensions of calcifications (Feuchtneret al., 2013).

Computational analyses, which take into account both thepatient-specific structure of the native aortic valve and an accurateevaluation of calcifications, can be used to predict several para-meters which, being of clinical interest, can support and guidedevice selection. In the present work, a complete framework toreproduce transcatheter aortic valve implantation has been devel-oped and applied to two real clinical cases.

Stress distribution is characterized by concentrated spots ofhigher stress values induced by the contact between the stent andthe aortic wall (see Fig. 6). Additionally, in agreement with Wanget al. (2012), high values of the maximum principal stress areobtained in the aortic regions closed to calcifications. On one side,higher stress values can be related to higher force of adherencebetween stent and aortic wall; on the other side, high stress patternsconcentrated in the annular region can indicate a major risk of aorticrupture (Eker et al., 2012) which is a possible TAVI complicationleading to cardiac tamponade and subsequent fatal events.

Y

Patient-1 Patient-2

Vie

w 1

Z

X

X Y

Z

2V

iew

(Avg: 75%)S, Mises

+0.000e+00+1.250e-01+2.500e-01+3.750e-01+5.000e-01+6.250e-01+7.500e-01+8.750e-01+1.000e+00+1.125e+00+1.250e+00+1.375e+00+3.408e+00

(Avg: 75%)S, Mises

+0.000e+00+1.250e-01+2.500e-01+3.750e-01+5.000e-01+6.250e-01+7.500e-01+8.750e-01+1.000e+00+1.125e+00+1.250e+00+1.375e+00+3.408e+00

(Avg: 75%)S, Mises

+0.000e+00+4.167e-01+8.333e-01+1.250e+00+1.667e+00+2.083e+00+2.500e+00+2.917e+00+3.333e+00+3.750e+00+4.167e+00+4.583e+00+1.222e+01

(Avg: 75%)S, Mises

+0.000e+00+4.167e-01+8.333e-01+1.250e+00+1.667e+00+2.083e+00+2.500e+00+2.917e+00+3.333e+00+3.750e+00+4.167e+00+4.583e+00+1.222e+01

Fig. 6. Impact of the prosthesis implant on the aortic root: von Mises stress [MPa] distribution along the vessel is reported to evaluate the interaction between the prostheticstent and the aortic root wall; a huge difference in terms of maximum stress values is observable. This is attributable to the position and extension of calcifications of theaortic root as well as to the preoperative configuration of the aortic annulus: for Patient-2 a very irregular and elliptic shape has been extracted from CT images.

S. Morganti et al. / Journal of Biomechanics 47 (2014) 2547–2555 2551

If aortic rupture is quite unusual, paravalvular leak is one of themost frequent complications which may occur after TAVI due toincomplete adherence of the prosthetic stent to the aortic wall. Forboth considered patients, we can quantitatively evaluate the area ofthe perivalvular holes, which can be assumed to be proportional tothe amount of retrograde perivalvular blood flow (i.e., perivalvularleakage). Interestingly, the obtained results are in agreement withpostoperative medical data.

Indeed, as reported in Fig. 9, quantitative postoperativeDoppler Echocardiography has recorded a significantly higherregurgitant flow for Patient-2, whose maximum retrograde jet velo-city was measured equal to 3.86 m/s, while the maximum velocity forPatient-1 was 1.70 m/s. Also angiographic movies (attached as sup-plementary material) are in agreement with our results since thepostoperative retrograde flow, highlighted by a contrast agent, isqualitatively much more visible in Patient-2 than in Patient-1.

Finally, the measured eccentricity of the implanted stent showsthat for both patients the positioned stent assumes a non-circularshape. For Patient-2 a slightly worst scenario has been predicted byour analyses (see Fig. 8a). Eccentricity of the implanted stent direct

influences valve closure and, in particular, coaptation. In fact, thenon-symmetric closure highlighted in Fig. 8b is attributed to theelliptical stent configuration, in agreement with results by Auricchioet al. (2011) and Auricchio et al. (2011) showing that one leafletcloses below the other two producing a small central gap responsibleof a regurgitant flow. Even though we think that the geometricalasymmetry of the stent is the main determinant of the central gapobtained during diastole, it is worth highlighting that the choice ofthe leaflet material model, which has been proven to have a strongimpact on coaptation values (Auricchio et al., 2012b), may alter theobtained results. However, the resulting intravalvular gap is inagreement with follow-up evaluations which, in both patients, havehighlighted a central “mild intra-prothesic leak” (extraction frompostoperative medical records of both Patient-1 and Patient-2).

5. Limitations

Even though the present work represents a clear improvementwith respect to the current state of the art due to the previously

Fig. 7. Evaluation of the degree of apposition between the prosthesis stent and the patient-specific root anatomy: (a) the reconstructed model of the aortic root isrepresented in light-gray, while the stent is shown in dark-gray; on the basal crown of the stent, which, at the end of implantation, should completely adhere with the aorticannulus, a contour-map of the radial distance [mm] between the inner aortic wall and the outer surface of the implanted stent is represented; (b) for both patients a cross-section at the proximal side of the implanted device allows to highlight the holes between the stent and the aortic root wall, responsible of paravalvular leakage.

S. Morganti et al. / Journal of Biomechanics 47 (2014) 2547–25552552

a

b

c

a

b

c

Patient-1 Patient-2

Patient-1 Patient-2

Fig. 8. Prosthesis configuration after implantation: (a) An evaluation of the non-circularity of the implanted stent is proposed as the measure of the three distances betweenthe points at the top of the three supporting bars; minor and major axes of the originated ellipse are also highlighted for Patient-1 and Patient-2. (b) Due to stent non-circularity, the top-view of the closed prosthetic valves shows a non-physiological closure in both cases. Even though no insufficiency is evident from this view, a central gapdue to asymmetric closure may occur.(For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)

Table 3Analysis results from simulation of TAVI in the two considered patients. VMS stands for Von Mises Stress; MPS stands for Maximum PrincipalStress.

Anatomical region Peak VMS Peak MPS Distance stent-wall Perivalvular holes Eccentricity Coaptation area(MPa) (MPa) (mm) (mm2) (–) (mm2)

Patient-1 3.41 7.09 0.71 4.1 0.91 207.3Patient-2 12.2 20.1 2.01 36.9 0.75 164.8

Fig. 9. Postoperative Doppler Echocardiography records show a lower retrograde blood flow for Patient-1 (a) than for Patient-2 (b).

S. Morganti et al. / Journal of Biomechanics 47 (2014) 2547–2555 2553

highlighted key aspects, it still presents some limitations. Materialmodeling has been simplified: homogeneous isotropic propertieshave been assigned to all the involved materials, even thoughcalibrated on human experimental data. Our findings indicate adifferent level of post-implant solicitation of the root tissue. Suchresults call for further developments in two directions: investiga-tion of the constitutive modeling influence on the simulationoutcomes, i.e., stress of the root wall after the implant; studyextension to a higher number of cases in order to evaluate thestatistical relevance of the simulation findings. Further develop-ments of the study will be also devoted to the evaluation of theinfluence of ecographic resolution of the performed leaflet mea-surements and on the final simulation outcomes. In dealing withthe simulation strategy, we expand the metallic frame of theprosthesis using a cylindrical surface while in the real procedure aballoon is used. Future developments of the work will enhance therealism of the proposed approach.

Finally, postoperative CT data can be used to perform a detailedcomparison between the resulting configuration of the implanteddevice, outcome of the analysis, and the real scenario. However,postoperative CT is not usually included within the TAVI protocol,and we believe that also a comparison with commonly performedexaminations (angiography and ultrasound) represents an inter-esting added value of the present work.

6. Conclusions

Two clinical cases of transcatheter aortic valve implantationhave been investigated through structural finite element analysis.In particular, the impact of patient-specific anatomical features ofthe native aortic valve on the postoperative performance of theballoon-expandable Edwards Sapien XT device has been analyzed.Stress distributions, geometrical changes, coaptation values, andrisk of paravalvular leakage have been computed and evaluated forboth patients. Comparison between the obtained numerical resultsand in-vivo postoperative measurements shows a good agree-ment, demonstrating that the proposed simulation strategy canoffer a reliable and useful tool to evaluate several clinicallyrelevant aspects of TAVI. Although limited to only two patients,this study represents a further step towards the use of realisticcomputer-based simulations for virtual planning of TAVI proce-dures, aiming at improving the efficacy of the operation techniqueand supporting device optimization.

Conflict of interest

The authors report no conflicts of interest.

Acknowledgments

This work is partially funded by the European Research Councilthrough the Project no. 259229 entitled ‘ISOBIO: IsogeometricMethods for Biomechanics’, partially by MIUR through the PRINProject no. 2010BFXRHS., and partially by Cariplo Foundationthrough the Project iCardioCloud no. 2013-1179 and by RegioneLombardia through the Project no. E18F13000030007. We wouldalso like to thank Dr Anna Ferrara, Dept. of Civil Engineering andArchitecture, University of Pavia, Italy, for providing the calibrationdata of the aortic tissues, and Dr E. Raviola of IRCCS Policlinico SanMatteo, Pavia, Italy, for providing postoperative medical images.

Appendix A. Supplementary material

Supplementary data associated with this article can be found in theonline version at http://dx.doi.org/10.1016/j.jbiomech.2014.06.007.

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