Marzio Di Giuseppe

Solmaz Farzaneh

Massimiliano Zingales

Salvatore Pasta

Stéphane Avril
email: avril@emse.fr

Marzio Di

Patient-Specific Computational Evaluation of Stiffness Distribution in Ascending Thoracic Aortic Aneurysm

Keywords: Ascending Thoracic Aortic Aneurysm, Bicuspid Aortic Valve, Extensional Stiffness, Noninvasive Inverse Method, Shear Stress

Introduction

Ascending thoracic aortic aneurysm (ATAA) is a life-threatening cardiovascular disease, leading to weakening of the aortic wall and permanent dilation. ATAA affects approximately 10 out of 100,000 persons per year in the general population [START_REF] Coady | Natural history, pathogenesis and etiology of thoracic aortic aneurysms and dissections[END_REF], and this disease is associated with a high risk of mortality and morbidity [START_REF] Elefteriades | Thoracic aortic aneurysm: clinically pertinent controversies and uncertainties[END_REF]. Bicuspid aortic valve (BAV) is a predisposing risk factor to ATAA formation and development with patients having associated aortopathy on approximately 40% of whole bicuspid population [START_REF] Verma | Aortic dilatation in patients with bicuspid aortic valve[END_REF] and higher rate of aortic dissection compared to patients with the tricuspid aortic valve (TAV) [START_REF] Januzzi | Characterizing the young patient with aortic dissection: results from the international registry of aortic dissection (IRAD)[END_REF].

To avoid aortic complications (i.e. rupture or dissection), the current clinical management of ATAA is based on strict monitoring of the aneurysm size and elective repair is recommended when aortic diameter reaches a critical size [START_REF] Borger | The american association for thoracic surgery consensus guidelines on bicuspid aortic valve-related aortopathy: full online-only version[END_REF]. However, aortic size is not a sufficient predictor of the risk of ATAA failure [START_REF] Pape | Aortic diameter >or = 5.5 cm is not a good predictor of type A aortic dissection: observations from the International Registry of Acute Aortic Dissection (IRAD)[END_REF]. Aortic stiffness is associated with progressive aortic dilatation and aneurysm formation as shown by imaging modalities [START_REF] Longobardo | Impairment of elastic properties of the aorta in bicuspid aortic valve: relationship between biomolecular and aortic strain patterns[END_REF][START_REF] Teixeira | Circumferential ascending aortic strain and aortic stenosis[END_REF], computational analyses (Farzaneh et al., 2019a;Martin et al., 2013a;Pasta et al., 2017a) and biomechanical studies [START_REF] Selvin | A comprehensive histopathological evaluation of vascular medial fibrosis: Insights into the pathophysiology of arterial stiffening[END_REF][START_REF] Smoljkic | Biomechanical characterization of ascending aortic aneurysms[END_REF]. High aortic stiffness was associated with high rates of surgical aortic replacement and aortic root dilation in children and adults with connective tissue disorders [START_REF] Prakash | Segmental aortic stiffness in children and young adults with connective tissue disorders: relationships with age, aortic size, rate of dilation, and surgical root replacement[END_REF]. In Marfan patients, aortic stiffness proved to be important in predicting progressive aortic dilatation [START_REF] Guala | Influence of aortic dilation on the regional aortic stiffness of bicuspid aortic valve assessed by 4-dimensional flow cardiac magnetic resonance: comparison with Marfan syndrome and degenerative aortic aneurysm[END_REF][START_REF] Sulejmani | Biomechanical properties of the thoracic aorta in Marfan patients[END_REF]. A recent study of abdominal aortic aneurysms found that segmental stiffening of the aorta preceded aneurysm growth and introduced the concept that stiffening may act as an early mechanism triggering elastin breakdown and aneurysm growth [START_REF] Raaz | Segmental aortic stiffening contributes to experimental abdominal aortic aneurysm development[END_REF].

Imaging based on 4D Flow MRI [START_REF] Mahadevia | Bicuspid aortic cusp fusion morphology alters aortic three-dimensional outflow patterns, wall shear stress, and expression of aortopathy[END_REF], in silico computational modeling [START_REF] Mendez | Comparison of hemodynamic and structural indices of ascending thoracic aortic aneurysm as predicted by 2-way FSI, CFD rigid wall simulation and patientspecific displacement-based FEA[END_REF]Pasta et al., 2017b) or combination of them [START_REF] Youssefi | Patient-specific computational fluid dynamics-assessment of aortic hemodynamics in a spectrum of aortic valve pathologies[END_REF] have confirmed an altered hemodynamic environment in BAV ATAAs with well-functioning or stenotic aortic valve leaflets [START_REF] Van Ooij | Aortic valve stenosis alters expression of regional aortic wall shear stress: New insights from a 4-dimensional flow magnetic resonance imaging study of 571 subjects[END_REF]. The underlying hypothesis is that flow disturbances induce local wall shear stress (WSS) forces on the dilated aorta, portending to adverse vascular remodeling by mechanotransduction. This can further lead to changes in the biomechanical properties of ATAA wall as reflected by an increased stiffness for the dilated aorta.

Risk assessment based on the aortic stiffness of the ATAA wall are being developed [START_REF] Duprey | Biaxial rupture properties of ascending thoracic aortic aneurysms[END_REF]Farzaneh et al., 2019b;Martin et al., 2013a). In this way, the quantification of local elastic properties of the ATAA wall from in vivo data is crucial to establish a reliable method for estimating the severity of an ATAA [START_REF] Mousavi | Patient-specific stress analyses in the ascending thoracic aorta using a finite-element implementation of the constrained mixture theory[END_REF][START_REF] Rooprai | Thoracic aortic aneurysm growth in bicuspid aortic valve patients: role of aortic stiffness and pulsatile hemodynamics[END_REF]. Most importantly, new strategies of risk assessment should be accurate and compatible with clinical time framework. For that purpose, the in vivo non-invasive identification of aortic stiffness would be essential for clinicians to improve the clinical decision making process. Recently, Farzaneh et al. (Farzaneh et al., 2019a)

Methods

Study Population

After internal review board approval and informed consent, 30 patients (12 BAV and 18 TAV) referred for aortic size evaluation by electrocardiographic-gated computed tomography (ECG-gated CT) were enrolled. Table 1 shows demographic data of the patient population as well as aortic diameter. For all patients, ECG-gated CT scans were performed after intravenous injection of contrast agent to improve image quality. Imaging was carried out on a GE VCT 64-channel scanner (GE Medical Systems, Milwaukee, Wisconsin), with gantry rotation velocity of 0.5 m/s and spiral pitch of 0.984. Retrospective reconstruction of images was performed to obtain images at cardiac phases corresponding to both end-diastole and end-systole at the resolution of 512 x 512 and slice thickness of 0.625 mm. Prior to imaging, diastolic and systolic blood pressures were measured by brachial sphygmomanometer for each patient.

Images Analysis

For each patient, segmentation of ECG-gated CT images was performed at both diastolic and systolic phases using Mimics v20 (Materialise, Leuven, BE). Specifically, semi-automatic threshold-based segmentation of the aortic lumen was performed to obtain a point cloud of ATAA geometries. The same smoothing factor was applied to all phases. The threedimensional (3D) surface of the aorta was generated for each phase and exported as STL file. Then, 3D aortic surfaces reconstructed at both cardiac phases were cut by identical cross-sectional planes in Rhinoceros (Robert McNeel & Associates, Seattle, USA) to define a domain of the aorta larger than the final segment of interest. A set of nodes was defined across each reconstructed aortic geometry, with the requirement that a node represented the position of the same material point at each phase of the cardiac cycle. For this, it was essential to reconstruct a structural mesh for all phases with an identical number of elements and nodes. The Vascular Modeling Toolkit (VMTK, Orobix, Bergamo, Italy; www.vmtk.org) [START_REF] Antiga | Robust and objective decomposition and mapping of bifurcating vessels[END_REF] was employed to generate the structural mesh from STL files.

The extracted data from VMTK were postprocessed in MATLAB to extract an accurate mesh using the longitudinal and circumferential metrics obtained from VMTK. A structural mesh composed of 3871 quadrilateral shell elements, 49 along the circumferential direction and 79 along the longitudinal direction, was defined on the template geometry. Each node of the structural mesh was related to assumedly the same material points for systole and diastole phases.

The LESI methodology for calculating the extensional stiffness was described by Farzaneh et al. (Farzaneh et al., 2019a). In brief, local principal strain components (𝜀 1 and 𝜀 2 ) were deduced by computing the spatial gradients of displacements between diastolic and systolic configurations. Although the aortic tissue is globally anisotropic and nonlinear, its mechanical behavior was linearized in the range of strains induced by pressure variations between diastole and systole, and anisotropic effects were neglected in this range. The local principal stress components (τ 1 0 and τ 2 0 ) were derived by finite-element analysis (FEA) performed on the ATAA diastolic geometry using average blood pressure evaluated over the cardiac cycle [START_REF] Joldes | A simple, effective and clinically applicable method to compute abdominal aortic aneurysm wall stress[END_REF]. To obtain radii of curvature (𝑟 1 0 and 𝑟 2 0 ) and their variations (𝛥𝑟 2 and 𝛥𝑟 1 )

fast and efficiently, a method based on the principle of virtual work was developed, as previously introduced in Bersi et al. [START_REF] Bersi | Novel methodology for characterizing regional variations in the material properties of murine aortas[END_REF].

Finally it was possible, for each element, to relate the extensional stiffness to the pulsed pressure 𝛥𝑃 such as:

𝑄 = 𝛥𝑃 + τ 1 0 𝛥𝑟 1 (𝑟 1 0 ) 2 + τ 2 0 𝛥𝑟 2 (𝑟 2 0 ) 2 𝜀 1 + 𝜈𝜀 2 𝑟 1 0 + 𝜈𝜀 1 + 𝜀 2 𝑟 2 0
In the current study we used the concept of "extensional stiffness" (intensive property) which equals the material stiffness times the thickness and whose dimension is MPa.mm.

The aortic thickness could not be measured accurately due to the limited spatial resolution of CT.

Once LESI results were obtained for each patient, the average extensional stiffness was evaluated in each of the four quadrants, including the major, minor, anterior and posterior regions (Fig. 1).

Computational Flow Analysis

Computational flow modeling was applied to study ATAA hemodynamics at systolic peak when the aortic valve is supposedly fully open [START_REF] D'ancona | Haemodynamic predictors of a penetrating atherosclerotic ulcer rupture using fluid-structure interaction analysis[END_REF]. For each patient, the fluid domain of ATAA geometry at end-systole was meshed with unstructured tetrahedral elements with size of 0.1 mm. The blood was assumed as a non-Newtonian incompressible fluid (density of 1060 kg/m3 and viscosity of 0.00371 Pa*s) adopting the Carreau model [START_REF] Khanafer | Modeling pulsatile flow in aortic aneurysms: effect of non-Newtonian properties of blood[END_REF]Leuprecht and Perktold, 2001). The solution was obtained with FLUENT v18 (ANSYS Inc., Canonsburg, PA) using the SIMPLE algorithm for the pressurevelocity coupling and second order accurate discretization scheme. To include patientspecific hemodynamics conditions, the transaortic jet velocity evaluated by Doppler echocardiography was set as the inflow velocity condition at the aortic valve plane. For each outlet, we first computed the global vascular resistance and arterial compliance of each patient from echocardiographic measurements and clinical demographic data. Then, these parameters were used to compute the outflow boundary conditions of a three-element

Windkessel model (comprising proximal resistance, compliance, and a distal resistance) coupled to each outflow branch. Boundary conditions were adjusted to match brachial artery pulse pressure.

After numerical solution, WSS values were obtained for the entire thoracic aorta, with further in-depth subanalysis in the ascending thoracic aorta by computing maxima at sinotubular junction (namely, analysis plane = AA1), proximal (AA2) and mid (AA3) ascending thoracic aorta for each quadrant (i.e., major, minor, anterior and posterior quadrants).

Statistical Analysis

The Rank Sum test was used to assess differences in the extensional stiffness between BAV ATAAs and TAV ATAAs. One-way Anova, followed by Holm-Sidak post-hoc test for all pairwise comparisons, was used to assess differences of extensional stiffness among aortic quadrants. The association of the extensional stiffness with patient age, aortic pulse pressure, aortic diameter, WSS, aortic strain and stress was explored by Pearson's correlation. Statistical analyses were performed using SigmaPlot (Systat Software Inc., San Jose, California), with statistical significance set at p=0.05 in all cases. Data are shown as Mean ± SEM.

In addition, Principal Component Analysis (PCA) was performed for dimensionality reduction of all data computed for each patient. First two principal components were analyzed to assess separation of BAV ATAA versus TAV ATAA. The tolerance ellipse based on Hotelling's T2 at a significance level of 0.05 was calculated and shown in the score plots.

Principal Component Analysis was performed using SPSS software (IBM SPSS Statistics v.17, New York, NY).

Results

Table 1 summarizes patient demographic data, systolic and diastolic pressures and aortic diameter. The distribution of age in BAV ATAAs differs significantly from that of TAV ATAAs patients (50.2 ± 7.5 years for BAV ATAAs vs 64.7 ± 7.8 years for TAV ATAAs, p<0.01), and this difference was confirmed by the analysis of the age on a different cohort of 159 patients [START_REF] Agnese | Patterns of ascending aortic dilatation and predictors of surgical replacement of the aorta: A comparison of bicuspid and tricuspid aortic valve patients over eight years of follow-up[END_REF]. The relationship of extensional stiffness as averaged among quadrants with the ascending aortic diameter and the aortic pulse pressure are shown in Fig. 5A and Fig. 5B. A strong positive correlation was found between the extensional stiffness and the aortic pulse pressure (R=0.644 and p<0.001), but was not significant between the extensional stiffness and the aortic diameter (R=0.341 and p=0.065). Interestingly, a significant positive correlation was found between extensional stiffness and patients age for BAV ATAAs (R=0.619 and p=0.032), but not for TAV ATAAs (R=-0.117 and p=0.645) as shown by Fig. 5C and Fig. 5D. Fig. 5E and Fig. 5F show the relationship of both strain and stress obtained in the circumferential direction with the average extensional stiffness. The extensional stiffness was inversely correlated with the circumferential strain (R=-0.522 and p=0.00324) and positively with the circumferential stress (R=0.474 and p=0.008). Correlation analysis of extensional stiffness with age (Fig. 5C) also revealed that BAV ATAAs can be divided into two subgroups: 1) patients younger than 50 years old who had a relatively low extensional stiffness, 2) patients older than 55 years old who had a relatively high extensional stiffness. All analysis in Fig. 5 were also broken down by aneurysm type, results are reported in Fig. A1.

Peak systolic WSSs were correlated to the average extensional stiffness for each ascending aortic level and aortic quadrant. The correlation analysis between extensional stiffness and WSS values evaluated at proximal ascending thoracic aorta (AA2) appears promising (R=0.343 and p=0.080 for AA2), but no significant correlation was found between stiffness and WSS evaluated locally for Major, Minor and Anterior quadrants. For the Posterior quadrant a correlation was identified although the obtained p-value was very close to the threshold (p=0.05) and a low coefficient was obtained. Results are presented in Fig. 6. All analysis were also broken down by aneurysm type, results are reported in Fig. A2.

A PCA based on patient's age, aortic diameter, aortic pulse pressure, extensional stiffness and WSS showed no separation of BAV ATAAs from TAV ATAAs (see Fig. 7). However, the loading plot revealed that the most important variables responsible for differences between BAV ATAAs and TAV ATAAs are the pulsed pressure and the patient's age.

Discussion

This study aimed to investigate the patterns of extensional stiffness from in vivo dynamic imaging of ATAAs and to evaluate potential correlations with clinical data and blood shear forces. The extensional stiffness did not show any significant difference between BAV ATAAs and TAV ATAAs. This supports recent evidence and observations for which there should be no distinction in the surgical management of BAV patients versus TAV patients (Agnese et al., 2019). Recently, we performed equibiaxial mechanical testing on ascending aortic tissues with either BAV or TAV [START_REF] Di Giuseppe | Identification of circumferential regional heterogeneity of ascending thoracic aneurysmal aorta by biaxial mechanical testing[END_REF] and found no difference in the mean values of the aortic tissue stiffness between BAV ATAAs and TAV ATAAs as reported here.

However, other groups who performed mechanical testing on ascending aortic tissues found differences in the mean values of the aortic tissue stiffness between BAV patients and TAV patients [START_REF] Choudhury | Local mechanical and structural properties of healthy and diseased human ascending aorta tissue[END_REF][START_REF] Duprey | In vitro characterisation of physiological and maximum elastic modulus of ascending thoracic aortic aneurysms using uniaxial tensile testing[END_REF][START_REF] Okamoto | Mechanical properties of dilated human ascending aorta[END_REF][START_REF] Pham | Biomechanical characterization of ascending aortic aneurysm with concomitant bicuspid aortic valve and bovine aortic arch[END_REF][START_REF] Pichamuthu | Differential tensile strength and collagen composition in ascending aortic aneurysms by aortic valve phenotype[END_REF]. We did not measure the extensional stiffness in non aneurysmatic subjects as healthy subjects cannot undergo CT scans. However the stiffness of healthy aortas was measured by a variety of other techniques in the literature and values in a range between 150 kPa and 1000 kPa were reported, with ATAA exhibiting generally a higher stiffness than healthy aortas [START_REF] Azadani | Biomechanical properties of human ascending thoracic aortic aneurysms[END_REF][START_REF] Walraevens | Correlation between compression, tensile and tearing tests on healthy and calcified aortic tissues[END_REF].

The correlation of patients' age with the extensional stiffness obtained by the LESI methodology was strongly affected by the valve phenotype. For TAV patients, the extensional stiffness did not vary with the patient age but increased with the age of BAV patients. This is likely a consequence of the significant difference in the age of BAV versus TAV patients. Indeed, TAV ATAAs were older than 50 years while most of patients with BAV were <50 years. We also found that BAV ATAAs can be divided into two subgroups: 1) patients younger than 50 years old who had a relatively low extensional stiffness, 2) patients older than 55 years old who had a relatively high extensional stiffness. Martin et al. (Martin et al., 2013b) showed that the biomechanical properties of dilated ascending aorta change between 50 and 60 years, and this could explain either the difference in the extensional stiffness of two subgroups of BAV ATAAs or the lack of correlation between the extensional stiffness and patient age for TAV ATAAs.

As expected, no significant correlation was found between extensional stiffness and shear stress for Major, Minor and Anterior quadrant, thereby suggesting there is no direct link between hemodynamics and biomechanical properties of ATAA wall. For the posterior quadrant, instead, a significant correlation was observed.

The extensional stiffness was significantly correlated with both the pulsed pressure and the circumferential strain and stress. Although these variables are directly involved in the derivation of the aortic stiffness in the LESI methodology, these significant correlations can also be interpreted with physiological principles.

Relations between the aortic stiffness and the pulsed pressure have been known for decades. Indeed, as the aorta becomes stiffer, the central pulsed pressure is higher due to the increase in the pulse wave velocity and the early return of reflected waves to the heart from following junctions [START_REF] Fung | Biomechanics: circulation[END_REF]. In a young and healthy aorta, the reflected wave tends to hit the aortic root during diastole, serving to increase diastolic pressure and hence improving perfusion of coronary arteries. In aged and stiffened aortas, the reflected hits the aortic root earlier, increasing the systolic pressure and decreasing the diastolic one. The amplitude of reflected waves increases as the arterial stiffness increases, further augmenting central systolic pressure (Chirinos and Segers, 2010a, b;[START_REF] Fung | Biomechanics: circulation[END_REF][START_REF] Laurent | Structural and genetic bases of arterial stiffness[END_REF][START_REF] Mackenzie | Assessment of arterial stiffness in clinical practice[END_REF][START_REF] O'rourke | Aortic diameter, aortic stiffness, and wave reflection increase with age and isolated systolic hypertension[END_REF]. The effects of this supplemental load onto the aorta, which are direct expressions of the stiffness increase, should be reckoned for estimating the risk of rupture or dissection of ATAAs.

As expected, the extensional stiffness was also significantly correlated to the circumferential strain since circumferential strains are a direct expression of the aortic stiffness. Stiffening often triggers degradation and/or loss of a fraction of elastin fibers, leading to a reduction of the wall extensibility [START_REF] Sokolis | Biomechanical response of ascending thoracic aortic aneurysms: association with structural remodelling[END_REF]. Another consequence is also a decrease of the axial stretch of the aorta, producing an increase of the aortic arch curvature named unfolding [START_REF] Redheuil | Age-related changes in aortic arch geometry: relationship with proximal aortic function and left ventricular mass and remodeling[END_REF]. The degradation of protein networks in the extracellular matrix of ATAAs can be explained by the unbalance between protein synthesis by vascular cells and protein destruction by matrix metalloproteases (MMPs) [START_REF] Lemaire | Matrix metalloproteinases in ascending aortic aneurysms: Bicuspid versus trileaflet aortic valves[END_REF]. In the cohort from which this study group was extracted, we found that the expression level of MMP-9 is altered in BAV ATAAs vs TAV ATAAs [START_REF] Gallo | On the prospect of serum exosomal miRNA profiling and protein biomarkers for the diagnosis of ascending aortic dilatation in patients with bicuspid and tricuspid aortic valve[END_REF]. The significant correlation between extensional stiffness and stress is very common for fibrous soft tissues, owing to their exponential stress-strain curve [START_REF] García-Herrera | Mechanical behaviour and rupture of normal and pathological human ascending aortic wall[END_REF]. This reflects reorientation and straightening of collagen bundles upon loading [START_REF] Sokolis | A structural basis for the aortic stress-strain relation in uniaxial tension[END_REF].

When analyzing BAV and TAV ATAAs together, the PCA analysis suggested that BAV ATAAs are likely forming a cluster in the lower quadrants of the multivariate score plot in the direction of the loading associated to patient age. This is not surprising because BAV patients are known to commonly develop ATAA at younger age than TAV [START_REF] Agnese | Patterns of ascending aortic dilatation and predictors of surgical replacement of the aorta: A comparison of bicuspid and tricuspid aortic valve patients over eight years of follow-up[END_REF][START_REF] Lemaire | Matrix metalloproteinases in ascending aortic aneurysms: Bicuspid versus trileaflet aortic valves[END_REF].

Limitations

The LESI approach relies on local equilibrium equations as it is based on the principle of virtual work [START_REF] Bersi | Novel methodology for characterizing regional variations in the material properties of murine aortas[END_REF]. As for the generalized Laplace's law, the LESI approach considers the local equilibrium between pressures and tensions in a membrane, indicating that the aortic wall experience no shear through the thickness. This may not be a realistic assumption in regions near the aortic branches but these were excluded from the analysis.

The peripheral pulsed pressure rather than central aortic pressure was used. However, the mismatch of aortic compliance between the brachial artery and the aorta should be likely reduced or even reversed with the advanced age of our patients. The effect of brachial blood pressure on the extensional stiffness evaluations will be likely minimal in this study.

Validation of in silico modeling has to be established. A large sample size including BAV ATAAs matched with the age of TAV ATAAs would be ideal to confirm observations. Unfortunately, we could not compare results with those relative of non aneurysmatic subjects because healthy control volunteers are not allowed to undertake multiphase gated CT scans due to x-ray radiations risks. We are trying to extend our methodology to other imaging modalities (ultrasounds, MRI).

Conclusions

We evaluated the patterns of extensional stiffness from the in vivo imaging of ATAAs on a cohort of 30 patients using the LESI methodology. We found no appreciable differences between BAV and TAV patients. Regional differences appeared marginal due to interindividual variability. The correlation of patients' age with the extensional stiffness strongly depended on the valve phenotype. Strong relationship of the extensional stiffness with the pulsed pressure was found, supported by biomechanical explanations.

  have presented a novel methodology, namely the LESI (local extensional stiffness identification) methodology, to non-invasively quantify local stiffness properties on the basis of ECG-gated CT scans and brachial arm pressure. The interrelationship between the obtained local stiffness with other established markers of aortic function remains unclear and this currently limits the methodology's potential impact. The aim of the current study was to determine the most sensitive markers of local ATAA stiffness estimation with the hypothesis that direct measures of local ATAA stiffness could better detect the high-risk patients. First, the patterns of extensional stiffness obtained by the LESI methodology in a cohort of 30 patients with ATAAs and different aortic valve phenotypes were analyzed. Then, the association of stiffness with demographic data and computationally derived wall shear stress (WSS) was investigated.

Fig. 2

 2 Fig. 2 and Fig. 3 show representative extensional stiffness and WSS maps obtained by the

Figure 1 :

 1 Figure 1: Representation of ATAA: anterior, posterior, major and minor regions are shown in

Figure 2 :

 2 Figure 2: Representative extensional stiffness maps of 6 patients reconstructed using LESI

Figure 3 :

 3 Figure 3: Representative wall shear stress maps of 2 patients obtained by CFD analysis for

Figure 4 :

 4 Figure 4: Comparisons of average extensional stiffness of BAV ATAAs and TAV ATAAs

Figure 5 :

 5 Figure 5: (A) Correlation between average extensional stiffness and ascending aortic

Figure 6 :

 6 Figure 6: Correlation between extensional stiffness and peak systolic WSSs evaluated at proximal ascending aorta from (A) major, (B) minor, (C) anterior and (D) posterior regions.

Figure 7 :

 7 Figure 7: Two-dimensional score plots of PC1 versus PC2 with loading showing the main

Figure A1 :

 A1 Figure A1: Correlation between average extensional stiffness vs circumferential strain data

Figure A2 :

 A2 Figure A2: Correlation between extensional stiffness and peak systolic WSSs evaluated at

  Figure 6 736

Acknowledgments

Stéphane Avril is grateful to the European Research Council (ERC grant Biolochanics, grant number 647067) for financial support. This work was supported by a "Ricerca Finalizzata" grant from the Italian Ministry of Health (GR-2011-02348129) to Salvatore Pasta, and by grant from PON FSE-FESR Ricerca Innovazione 2014-2020 to Marzio Di Giuseppe.

Conflict of interest statement

The authors confirm there are not conflict of interest associated with this publication.