Giuseppe De Nisco

Paola Tasso

Karol Calò

Valentina Mazzi

Diego Gallo

Francesca Condemi

Solmaz Farzaneh

Stéphane Avril

Ph.D Umberto Morbiducci
email: umberto.morbiducci@polito.it

Deciphering ascending thoracic aortic aneurysm hemodynamics in relation to biomechanical properties

The degeneration of the arterial wall at the basis the ascending thoracic aortic aneurysm (ATAA) is a complex multifactorial process, which may lead to clinical complications and, ultimately, death.

Individual genetic, biological or hemodynamic factors are inadequate to explain the heterogeneity of ATAA development/progression mechanisms, thus stimulating the analysis of their complex interplay.

Here the disruption of the hemodynamic environment in the ATAA is investigated integrating patient-specific computational hemodynamics, CT-based in vivo estimation of local aortic stiffness and advanced fluid mechanics methods of analysis. The final aims are (1) deciphering the ATAA spatiotemporal hemodynamic complexity and its link to near-wall topological features, and (2) identifying the existing links between arterial wall degeneration and hemodynamic insult.

Technically, two methodologies are applied to computational hemodynamics data, the wall shear stress (WSS) topological skeleton analysis, and the Complex Networks theory. The same analysis was extended to the healthy aorta.

As main findings of the study, we report that: (1) different spatiotemporal heterogeneity characterizes the ATAA and healthy hemodynamics, that markedly reflect on their WSS topological skeleton features; (2) a clear link (stronger than canonical WSS-based descriptors) emerges between the variation of contraction/expansion action exerted by WSS on the endothelium along the cardiac cycle, and ATAA wall stiffness. The findings of the study suggest the use of advanced methods for a deeper understanding of the hemodynamics disruption in ATAA, and candidate WSS topological skeleton features as promising indicators of local wall degeneration.

Highlights

 Different levels of spatiotemporal heterogeneity characterize the aneurysmal and healthy ascending aorta hemodynamics, reflecting on wall shear stress topological skeleton.

 Peculiar wall shear stress topological skeleton features are linked to local ascending thoracic aortic aneurysms stiffness.

 The topological shear variation index, a measure of wall shear stress luminal contraction/expansion action variation along the cardiac cycle, is an indicator of local aortic wall degradation, performing better than canonical wall shear stress-based descriptors of flow disturbances.

 Wall shear stress topological skeleton analysis, combined with Complex Networks theory, contributes to better determine whether arterial wall degeneration, in combination with hemodynamic insult, leads to aneurysmal progression/rupture.

Introduction

Ascending thoracic aortic aneurysm (ATAA) is an unphysiological localized ballooning of the aorta at the ascending segment proximal to the brachiocephalic trunk, which can grow in size and eventually rupture, leading to serious complications and death. The common clinical treatment of ATAA consists in surgical repair by replacing the diseased aortic segment with a synthetic graft [START_REF] Isselbacher | Thoracic and abdominal aortic aneurysms[END_REF][START_REF] Erbel | ESC Guidelines on the diagnosis and treatment of aortic diseases: Document covering acute and chronic aortic diseases of the thoracic and abdominal aorta of the adult. The Task Force for the Diagnosis and Treatment of Aortic Diseases of the European[END_REF]. Due to significant mortality rates associated to prophylactic surgery (3-5 %) [START_REF] Isselbacher | Thoracic and abdominal aortic aneurysms[END_REF], indications for surgical treatment depend on the estimated maximum aortic diameter, with a suggested critical threshold value of 5.5 cm (except for patients with Marfan syndrome) [START_REF] Erbel | ESC Guidelines on the diagnosis and treatment of aortic diseases: Document covering acute and chronic aortic diseases of the thoracic and abdominal aorta of the adult. The Task Force for the Diagnosis and Treatment of Aortic Diseases of the European[END_REF][START_REF] Coady | Surgical intervention criteria for thoracic aortic aneurysms: a study of growth rates and complications[END_REF][START_REF] Johansson | Ruptured thoracic aortic aneurysms: a study of incidence and mortality rates[END_REF]. However, the diameter-based criterion for surgical intervention has been widely recognized as inadequate [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][START_REF] Chau | Natural history of thoracic aortic aneurysms: size matters, plus moving beyond size[END_REF].

To find complementary or alternative markers of ATAA risk of rupture, a plethora of studies have focused on, e.g., genetic, biological, structural and biomechanical factors involved in the ATAA wall dilatation/degeneration [START_REF] Elefteriades | Thoracic aortic aneurysm clinically pertinent controversies and uncertainties[END_REF][START_REF] Poullis | Ascending aortic curvature as an independent risk factor for type A dissection, and ascending aortic aneurysm formation: a mathematical model[END_REF][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][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] Pasta | In Vivo Strain Analysis of Dilated Ascending Thoracic Aorta by ECG-Gated CT Angiographic Imaging[END_REF][START_REF] Wagenseil | Bio-chemo-mechanics of thoracic aortic aneurysms[END_REF][START_REF] Petit | Review of the Essential Roles of SMCs in ATAA Biomechanics[END_REF]. However, current evidence is still insufficient to rely on biomechanical factors alone [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] Wagenseil | Bio-chemo-mechanics of thoracic aortic aneurysms[END_REF], and rather suggests a possible relation between ATAA hemodynamics and wall mechanical properties, which might better explain the complexity of ATAA development and progression.

In particular, the analysis of aortic hemodynamics, with the assessment of distinguishable intravascular flow features and wall shear stress (WSS) distribution on the luminal surface as obtained from in vivo [START_REF] Bollache | Aortic valvemediated wall shear stress is heterogeneous and predicts regional aortic elastic fiber thinning in bicuspid aortic valve-associated aortopathy[END_REF][START_REF] Suwa | Effect of Aortic Valve Disease on 3D Hemodynamics in Patients With Aortic Dilation and Trileaflet Aortic Valve Morphology[END_REF][START_REF] Dux-Santoy | Increased rotational flow in the proximal aortic arch is associated with its dilation in bicuspid aortic valve disease[END_REF][START_REF] Rodríguez-Palomares | Aortic flow patterns and wall shear stress maps by 4D-flow cardiovascular magnetic resonance in the assessment of aortic dilatation in bicuspid aortic valve disease[END_REF] and patient-specific computational studies [START_REF] Youssefi | Impact of Patient-Specific Inflow Velocity Profile on Hemodynamics of the Thoracic Aorta[END_REF][START_REF] Pasta | In Silico Shear and Intramural Stresses are Linked to Aortic Valve Morphology in Dilated Ascending Aorta[END_REF][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 patient-specific displacement-based FEA[END_REF][START_REF] Condemi | Ascending thoracic aorta aneurysm repair induces positive hemodynamic outcomes in a patient with unchanged bicuspid aortic valve[END_REF][START_REF] Condemi | Fluid-and Biomechanical Analysis of Ascending Thoracic Aorta Aneurysm with Concomitant Aortic Insufficiency[END_REF], have been suggested to derive markers of rupture risk, giving the supposed link between hemodynamic features and ATAA wall mechanical properties. For instance, previous follow-up studies reported a significant association between the luminal exposition to relatively low WSS values and ascending aorta wall weakening and dilatation in ATAA patients [START_REF] Condemi | Ascending thoracic aorta aneurysm repair induces positive hemodynamic outcomes in a patient with unchanged bicuspid aortic valve[END_REF][START_REF] Burk | Evaluation of 3D blood flow patterns and wall shear stress in the normal and dilated thoracic aorta using flow-sensitive 4D CMR[END_REF][START_REF] Guzzardi | Valve-Related Hemodynamics Mediate Human Bicuspid Aortopathy: Insights From Wall Shear Stress Mapping[END_REF].

In this context, we propose a framework combining patient-specific computational fluid dynamics (CFD), advanced fluid mechanics analysis and personalized in vivo estimates of the local aortic stiffness. The aims are to interpret the complex role played by local hemodynamics in ATAA and to decipher the existing links between near-wall features, intravascular flow structures and ATAA wall stiffness. More specifically, changes in hemodynamics associated with pathologic aortic dilatation were analyzed by applying two recently proposed methodologies on two subjectspecific (1 healthy -1 diseased) CFD models. The first approach relies on the analysis of WSS vector field topological skeleton, essentially consisting of a collection of critical points (i.e., locations at the luminal surface of the vessel where the WSS vanishes), and special lines which separate the luminal surface into areas of different WSS behavior, ultimately identifying where an expansion/contraction action is exerted by WSS on the endothelium (which is expected to have biological relevance) [START_REF] Mazzi | A Eulerian method to analyze wall shear stress fixed points and manifolds in cardiovascular flows[END_REF] [START_REF] Arzani | Wall shear stress fixed points in cardiovascular fluid mechanics[END_REF]. The second one exploits Complex Networks (CNs) theory to describe the spatiotemporal heterogeneity in near-wall and intravascular flow patterns, revealing information embedded in hemodynamic quantities waveforms (along the cardiac cycle) and useful to describe nonlinear phenomena involving them [START_REF] Calo | Spatiotemporal Hemodynamic Complexity in Carotid Arteries: an Integrated Computational Hemodynamics & Complex Networks-Based Approach[END_REF]. Both approaches were combined here to relate near-wall hemodynamics and intravascular flow patterns, which are expected to markedly affect WSS features [START_REF] De Nisco | The Atheroprotective Nature of Helical Flow in Coronary Arteries[END_REF][START_REF] De Nisco | The impact of helical flow on coronary atherosclerotic plaque development[END_REF]. Finally, ATAA local stiffness was obtained through a recently proposed inverse method based on gated CT scans [START_REF] Farzaneh | Inverse identification of local stiffness across ascending thoracic aortic aneurysms[END_REF]. Spatial correlations with WSS features were extracted from the topological skeleton analysis to ultimately associate ATAA complex hemodynamic features and wall mechanical properties.

Methods

One 36 years old healthy subject with no history of cardiovascular diseases, and one 59 years old subject with bicuspid aortic valve (BAV), moderate aortic valve insufficiency and a 6.03 cm x 5.95 cm ATAA were enrolled in the study after informed consent. An overview of the methods applied in this study is provided in Figure 1 and detailed onwards.

Medical imaging and geometry reconstruction

The two subjects were imaged by a 3T MR scanner (Siemens Magnetom Prisma) without contrast agent, using the same 4D flow MRI protocol exhaustively detailed elsewhere [START_REF] Condemi | Fluid-and Biomechanical Analysis of Ascending Thoracic Aorta Aneurysm with Concomitant Aortic Insufficiency[END_REF]. Based on 4D flow MRI images, the 3D geometries of each subject were reconstructed using CRIMSON (CardiovasculaR Integrated Modelling and SimulatiON) [START_REF] Dillon-Murphy | Multi-modality image-based computational analysis of haemodynamics in aortic dissection[END_REF]. The resulting geometries included the ascending thoracic aorta, the aortic arch, the descending thoracic aorta and the supra-aortic vessels (brachiocephalic artery -BCA, left common carotid artery -LCCA, and left subclavian artery -LSA, as shown in Figure 1).

Additionally, the diseased subject underwent ECG gated CT imaging in order to identify ATAA wall local stiffness with a recently proposed inverse method [START_REF] Farzaneh | Inverse identification of local stiffness across ascending thoracic aortic aneurysms[END_REF] detailed below.

In vivo aortic wall stiffness estimation

A recently proposed non-invasive inverse approach was applied here to identify aortic wall stiffness for the diseased subject. Briefly, ATAA geometries at ten phases along the cardiac cycle, including diastolic and systolic phases, were (1) reconstructed from gated CT scans using MIMICS (v.10.01, Materialise NV), and (2) meshed ensuring a set of nodes attached to the same material points at all the recorded cardiac phases. Based on the Fourier series analysis of temporal changes in position of each node, the local strain distribution was reconstructed and the wall stiffness at every location was derived by satisfying the local equilibrium equation under the acting tensions.

The strategy applied to estimate local wall stiffness in vivo is exhaustively detailed elsewhere [START_REF] Farzaneh | Inverse identification of local stiffness across ascending thoracic aortic aneurysms[END_REF].

Computational hemodynamics

The finite element-based open-source code SimVascular (http://simvascular.github.io/) was adopted to solve the governing equations of fluid motion in the two models. In detail, the Navier-Stokes equations, in their discretized form and under unsteady flow conditions, were solved using a stabilized finite element method supporting the use of linear tetrahedral elements (P1-P1) in the SimVascular flow solver for velocity and pressure [START_REF] Updegrove | SimVascular: An Open Source Pipeline for Cardiovascular Simulation[END_REF]. Newtonian blood rheology (with prescribed constant density and dynamic viscosity respectively equal to 1050 kg m -3 and 0.0035 Pa s) and rigid wall with no-slip condition were assumed. To ensure a grid-independent solution, based on a mesh sensitivity analysis, an average tetrahedral element size of 1.05•10 -3 m with a near-wall refinement consisting of 12 tetrahedral boundary layers with a decreasing ratio of 0.90 was adopted. The resulting computational grids consisted of 4.13 and 7.97 million elements for healthy and diseased model, respectively. Boundary conditions were prescribed using patient-specific 4D flow MRI measurements. In detail, measured fully 3D phase velocity data were extracted along the cardiac cycle and imposed in terms of Dirichlet inflow boundary conditions (BCs) at the ascending aorta (AAo) inlet section (as detailed in [START_REF] Morbiducci | Inflow boundary conditions for imagebased computational hemodynamics: impact of idealized versus measured velocity profiles in the human aorta[END_REF]). As regards outflow BCs, 4D flow MRI measured flow rates were prescribed at the supra-aortic vessels [START_REF] Gallo | On the use of in vivo measured flow rates as boundary conditions for image-based hemodynamic models of the human aorta: implications for indicators of abnormal flow[END_REF] in terms of fully developed velocity profiles. A three element Windkessel model was prescribed as BC at the descending aorta (DAo) outlet section, by applying a 3D-0D coupling scheme [START_REF] Condemi | Fluid-and Biomechanical Analysis of Ascending Thoracic Aorta Aneurysm with Concomitant Aortic Insufficiency[END_REF][START_REF] Dillon-Murphy | Multi-modality image-based computational analysis of haemodynamics in aortic dissection[END_REF]. The three element Windkessel model components (i.e., the impedance -ZC, the distal resistance -R, and the capacitor -C) were tuned as described in [START_REF] Condemi | Fluid-and Biomechanical Analysis of Ascending Thoracic Aorta Aneurysm with Concomitant Aortic Insufficiency[END_REF], obtaining patient specific values for the healthy (ZC = 1.36•10 7 kg m -4 s -1 ; R = 2.28•10 8 kg m -4 s -1 ; C = 1.50•10 -8 kg -1 m 4 s 2 ) and the pathologic subject (ZC = 5.32•10 6 kg m -4 s -1 ; R = 9.02•10 7 kg m -4 s -1 ; C = 3.18•10 -8 kg -1 m 4 s 2 ).

On the simulated flow fields in the healthy and diseased models, advanced post-processing tools were applied to better decipher the aortic hemodynamics complexity.

Deciphering aortic hemodynamics -WSS topological skeleton analysis

Based upon dynamical systems theory, the topological skeleton of a vector field is made of fixed points and manifolds, where: (1) a fixed point is a point where the vector field vanishes; (2) vector field manifolds, connecting fixed points, identify contraction/expansion regions (respectively, stable/unstable manifolds).

Here, a very recently proposed Eulerian method was considered to analyze the topological skeleton of the WSS vector field across the aortic luminal surface [START_REF] Mazzi | A Eulerian method to analyze wall shear stress fixed points and manifolds in cardiovascular flows[END_REF]. Based on the Volume Contraction Theory, it has been demonstrated [START_REF] Mazzi | A Eulerian method to analyze wall shear stress fixed points and manifolds in cardiovascular flows[END_REF] that specific features of the WSS vector field topological skeleton, i.e., WSS manifolds, can be easily captured using the divergence of the normalized WSS vector:

DIV = ∇ • 𝛕 𝑢 = ∇ ⋅ ( 𝛕 |𝛕| ), (1)
where 𝛕 𝑢 is the unit vector of WSS vector 𝛕. Eq. ( 1), neglecting the WSS vector magnitude variation, identifies the WSS spatial contraction/expansion configuration patterns [START_REF] Mazzi | A Eulerian method to analyze wall shear stress fixed points and manifolds in cardiovascular flows[END_REF]: negative values of DIV identify contraction regions, approximating attracting manifolds; positive values of DIV identify expansion regions, approximating repelling manifolds (Figure 2a).

According to the scheme proposed elsewhere for the complete WSS topological skeleton extraction [START_REF] Mazzi | A Eulerian method to analyze wall shear stress fixed points and manifolds in cardiovascular flows[END_REF], the identification of WSS fixed points location at the luminal surface was performed by computing a mesh-independent topological index, named Poincaré index. Then, the identified fixed points were classified using the eigenvalues of the Jacobian matrix, which provide information about fixed points nature (Figure 2). Technically, the adopted eigenvalue-based criterion allowed to distinguish between fixed point node or focus configurations. The combinations of the Poincaré index values and of eigenvalues 𝜆 𝑖 (i = 1, 2, 3) of the Jacobian matrix corresponding to the possible WSS fixed points configurations are summarized in Figure 2b.

As a first step, here the WSS topological skeleton of the cycle-average WSS vector field 𝛕 ̅ at the luminal surface of both the healthy and diseased model was analyzed. The unsteady nature of the WSS vector field fixed points along the cardiac cycle was investigated using the WSS fixed points weighted residence time along the cardiac cycle [START_REF] Mazzi | A Eulerian method to analyze wall shear stress fixed points and manifolds in cardiovascular flows[END_REF]:

𝑅𝑇𝛻 𝑥 𝑓𝑝 (𝑒) = 𝐴 ̅ 𝐴 𝑒 1 𝑇 ∫ 𝕀 𝑒 (𝒙 𝑓𝑝 , 𝑡) 𝑇 0 |(∇ • 𝝉) 𝑒 | 𝑑𝑡, (2)
where 𝒙 𝒇𝒑 (𝑡) is the WSS fixed point position at time t ∈ [0, 𝑇], e is the generic triangular element of the superficial mesh of area 𝐴 𝑒 , 𝐴 ̅ the average surface area of all triangular elements of the superficial mesh, 𝕀 is the indicator function and (∇ • 𝛕) 𝑒 is the instantaneous WSS divergence.

Eq. ( 2) quantifies the fraction of cardiac cycle spent by a fixed point inside a generic mesh surface element e on the aortic luminal surface emphasizing the contribution of fixed points surrounded by a marked local contraction/expansion action. In fact, from a physical point of view, the term 2) allows to measure the strength of the contraction/expansion action of shear on the wall.

|(∇ • 𝝉) 𝑒 | in eq. (
Additionally, here a quantity based on WSS divergence, named Topological Shear Variation Index (TSVI), is introduced to measure the amount of variation in WSS contraction and expansion action exerted at the luminal surface of the vessel. To do that, the root mean square of the normalized WSS divergence is computed as follows:

𝑇𝑆𝑉𝐼 = { 1 𝑇 ∫ [∇ • (𝛕 𝑢 ) -∇ • (𝛕 𝑢 ) ̅̅̅̅̅̅̅̅̅̅ ] 2 𝑇 0 𝑑𝑡} 1/2 , (3)
Roughly speaking, eq. ( 3) allows to localize regions on the luminal surface of the vessel exposed to large variations in the shear contraction/expansion action exerted by the flowing blood along the cardiac cycle.

Deciphering aortic hemodynamics -Complex Networks analysis

The spatiotemporal heterogeneity of intravascular and near-wall flow patterns was here investigated applying a recently introduced approach based on the application of the CNs theory to computational hemodynamics data [START_REF] Calo | Spatiotemporal Hemodynamic Complexity in Carotid Arteries: an Integrated Computational Hemodynamics & Complex Networks-Based Approach[END_REF][START_REF] Calò | Exploring wall shear stress spatiotemporal heterogeneity in coronary arteries combining correlation-based analysis and complex networks with computational hemodynamics[END_REF], where the nodes of the network are represented by the waveforms, along the cardiac cycle, of specific hemodynamic quantities at the nodes of the aortic computational grid.

Here, the CNs-based analysis was applied to the WSS vector magnitude (|τ|) waveforms along the cardiac cycle, whereas intravascular hemodynamics was described in terms of axial velocity (Vax)

and kinetic helicity density (Hk). In detail, Vax is the component of blood velocity vector along the local axial direction, identified as the direction of the tangent to the vessel's centerline [START_REF] Morbiducci | A rational approach to defining principal axes of multidirectional wall shear stress in realistic vascular geometries, with application to the study of the influence of helical flow on wall shear stress directionality in aorta[END_REF]. By definition, Vax is representative of the main flow direction. Hk is defined as the internal product between local velocity and vorticity vectors and its sign is an indicator of the (right-or left-handed) direction of rotation of helical blood flow patterns. The latter descriptor was involved in the analysis because of the established physiological significance of helical blood flow in main arteries [START_REF] De Nisco | The impact of helical flow on coronary atherosclerotic plaque development[END_REF][START_REF] Gallo | Segment-specific associations between local haemodynamic and imaging markers of early atherosclerosis at the carotid artery: an in vivo human study[END_REF][START_REF] Kilner | Helical and retrograde secondary flow patterns in the aortic arch studied by three-directional magnetic resonance velocity mapping[END_REF][START_REF] Morbiducci | In vivo quantification of helical blood flow in human aorta by time-resolved three-dimensional cine phase contrast magnetic resonance imaging[END_REF][START_REF] Liu | Physiological significance of helical flow in the arterial system and its potential clinical applications[END_REF][START_REF] Stonebridge | Spiral Laminar Flow: a Survey of a Three-Dimensional Arterial Flow Pattern in a Group of Volunteers[END_REF][START_REF] Gallo | Helical flow in carotid bifurcation as surrogate marker of exposure to disturbed shear[END_REF][START_REF] Gallo | An insight into the mechanistic role of the common carotid artery on the hemodynamics at the carotid bifurcation[END_REF][START_REF] Morbiducci | Helical flow as fluid dynamic signature for atherogenesis risk in aortocoronary bypass. A numeric study[END_REF][START_REF] Morbiducci | Mechanistic insight into the physiological relevance of helical blood flow in the human aorta: an in vivo study[END_REF][START_REF] De Nisco | The Atheroprotective Nature of Helical Flow in Coronary Arteries[END_REF].

For both investigated aortic models, three different CNs were built, starting from Vax, Hk and |τ| time-histories, respectively. In the here adopted approach [START_REF] Calo | Spatiotemporal Hemodynamic Complexity in Carotid Arteries: an Integrated Computational Hemodynamics & Complex Networks-Based Approach[END_REF], two generic nodes i and j of the CN are connected by a topological link {i, j} if the Pearson correlation coefficient Rij between the waveforms of each considered hemodynamic quantity at the two nodes is larger than a given threshold R ̂. In this sense, each CN can be represented by its adjacency matrix Aij containing the information about node connectivity as follows:

A 𝑖𝑗 = { 0, 𝑖𝑓 {𝑖, 𝑗} ∉ 𝐸 𝑜𝑟 𝑖 = 𝑗, 1, 𝑖𝑓 {𝑖, 𝑗} ∈ 𝐸. (4)
Here, for each aortic model, and for each of the three CNs based on the hemodynamic quantities Vax, Hk and |τ|, respectively, the median values of the single Rij distributions were set as threshold values R ̂ to build up adjacency matrices, as proposed elsewhere [START_REF] Calo | Spatiotemporal Hemodynamic Complexity in Carotid Arteries: an Integrated Computational Hemodynamics & Complex Networks-Based Approach[END_REF][START_REF] Calò | Exploring wall shear stress spatiotemporal heterogeneity in coronary arteries combining correlation-based analysis and complex networks with computational hemodynamics[END_REF].

Three metrics, based on Aij, were used to characterize the structure of each CN. In detail, here we considered the degree centrality DCi of node i, defined as the percentage of nodes of the network connected to node i, i.e., the so-called neighbors of i:

𝐷𝐶 𝑖 = 100 ( 1 𝑁-1 ∑ 𝐴 𝑖𝑗 𝑁 𝑗=1 ) = 100 ( 1 𝑁-1 𝑑𝑐 𝑖 ) . (5)
In eq. ( 5) dci is the non-normalized degree centrality of node i. To allow comparisons between the healthy and the diseased model networks, characterized by different number of nodes (N), dci was normalized to the total number (N-1) of possible neighbors of i. In summary, for a specific hemodynamic descriptor, DCi measures the fraction of time-histories correlated above threshold with the time-history in node i, quantifying the spatiotemporal homogeneity/heterogeneity of the considered hemodynamic quantity waveform in each node, with respect to the whole network (i.e., the fluid volume for Vax and Hk, or the luminal surface for |τ|).

The second CNs metric used in this study was applied to the Vax-and Hk-based networks to provide a quantitative measure of the anatomical length of persistence of the correlation of axial velocity and helical flow patterns inside the aorta. To do that, the so-called normalized average Euclidean distance (AEDi) [START_REF] Calo | Spatiotemporal Hemodynamic Complexity in Carotid Arteries: an Integrated Computational Hemodynamics & Complex Networks-Based Approach[END_REF][START_REF] Scarsoglio | Complex networks unveiling spatial patterns in turbulence[END_REF] of each node i of the network from all its neighbors n(i) was evaluated, defined as:

𝐴𝐸𝐷 𝑖 = 1 𝐷 𝑚𝑎𝑥 ∑ 𝑙 𝑖𝑗 𝑗∈𝑛(𝑖) 𝑑𝑐 𝑖 , ( 6
)
where Dmax is the maximum AAo diameter in the region upstream of the proximal supra-aortic trunk, and lij is the Euclidean distance between neighbor nodes i and j. In eq. ( 6), AEDi was normalized with respect to Dmax, in order to account for AAo geometric variability between the healthy and the diseased model. To investigate the effect that the presence of the ATAA has on the anatomical extent of the spatiotemporal correlations between Vax and Hk structures, in both models AEDi was computed only in the aortic region from the inlet section to the first supra-aortic vessel bifurcation point.

The length of persistence of the correlation of WSS spatiotemporal patterns at the aortic luminal surface was evaluated in topological terms in the |τ|-based network of the two aortic models. This was done computing the average shortest path length (𝑆𝑃𝐿 ̅̅̅̅̅ 𝑖 ) of node i, defined as:

𝑆𝑃𝐿 ̅̅̅̅̅ 𝑖 = 1 𝑁-1 ∑ 𝑑 𝑖𝑗 , 𝑗∈𝑉,𝑖≠𝑗 (7)
where V is the set of nodes of the network, and dij ∈ Z is the shortest topological distance between nodes i and j, i.e., the minimum number of links connecting node i with node j [START_REF] Boccaletti | Complex networks: Structure and dynamics[END_REF] (Figure 1). In synthesis, 𝑆𝑃𝐿 ̅̅̅̅̅ 𝑖 is a measure of the topological length of the correlation persistence of the |τ| waveform at each luminal surface node (i.e., the smaller the 𝑆𝑃𝐿 ̅̅̅̅̅ 𝑖 , the larger the topological persistence length of the correlation between i and the rest of the network). In order to be consistent with the computation of the anatomical persistence length of correlation (i.e., the AEDi metric), also 𝑆𝑃𝐿 ̅̅̅̅̅ 𝑖 was computed only in the aortic region from the inlet section to the first supraaortic trunk bifurcation point.

Deciphering aortic hemodynamics -Canonical WSS-based hemodynamic descriptors

In addition to the advanced methods for analyzing aortic hemodynamics introduced above, flow disturbances were evaluated here also in terms of canonical WSS-based descriptors (Table 1), namely the time-averaged wall shear stress (TAWSS), oscillatory shear index (OSI) [START_REF] Ku | Pulsatile flow and atherosclerosis in the human carotid bifurcation. Positive correlation between plaque location and low oscillating shear stress[END_REF], and relative residence time (RRT) [START_REF] Himburg | Spatial comparison between wall shear stress measures and porcine arterial endothelial permeability[END_REF]. Moreover, a descriptor of WSS multidirectionality was considered (Table 1), i.e., the transversal WSS (transWSS) [START_REF] Peiffer | Computation in the rabbit aorta of a new metric -the transverse wall shear stress -to quantify the multidirectional character of disturbed blood flow[END_REF], defined as the average WSS component acting orthogonal to the time-averaged WSS vector direction.

Aortic hemodynamics vs. wall stiffness

To investigate the existence of possible relations between ATAA hemodynamics and the mechanical properties of the aortic wall, an analysis of co-localization between exposure to "disturbed" hemodynamics vs. wall stiffness was carried out according to schemes proposed elsewhere [START_REF] De Nisco | The Atheroprotective Nature of Helical Flow in Coronary Arteries[END_REF][START_REF] De Nisco | The impact of helical flow on coronary atherosclerotic plaque development[END_REF][START_REF] Gallo | Insights into the co-localization of magnitude-based versus direction-based indicators of disturbed shear at the carotid bifurcation[END_REF]. More specifically, objective thresholds for WSS-based hemodynamic descriptors and for wall stiffness were identified as the 2 nd tertile of the respective luminal distribution (1 st tertile for TAWSS). The co-localization of luminal surface areas (SAs) characterized by stiffness and each one of OSI, RRT, transWSS, or TSVI values higher (lower for TAWSS) than the respective thresholds was quantitatively assessed by the similarity index (SI) [START_REF] Gallo | Insights into the co-localization of magnitude-based versus direction-based indicators of disturbed shear at the carotid bifurcation[END_REF]:

SI = 2(SA ℎ𝑖𝑔ℎ 𝑠𝑡𝑖𝑓𝑓𝑛𝑒𝑠𝑠 ∩ SA 𝑗 ) SA ℎ𝑖𝑔ℎ 𝑠𝑡𝑖𝑓𝑓𝑛𝑒𝑠𝑠 + SA 𝑗 , (8)
with j indicating a generic WSS-based hemodynamic descriptor. SI ranges between 0 (the SAs have no spatial overlap) and 1 (the SAs are equivalent and perfectly spatially overlapped).

Results

ATAA wall stiffness in vivo estimation

The in vivo estimated local wall stiffness distribution on the AAo of the diseased subject is presented in Figure 3. Consistent with previous observations [START_REF] Choudhury | Local mechanical and structural properties of healthy and diseased human ascending aorta tissue[END_REF][START_REF] Khanafer | Determination of the elastic modulus of ascending thoracic aortic aneurysm at different ranges of pressure using uniaxial tensile testing[END_REF], local variations in the wall mechanical properties are evident in the investigated model, where the highest values of the stiffness are observed at the outer AAo wall. For this reason, in order to investigate the possible role played by hemodynamic features in the development and progression of aneurysm disease, the analysis was here focused at the proximal AAo outer wall of both healthy and diseased models, where the biomechanical wall alteration mainly occurred in the ATAA subject.

WSS topological skeleton analysis

As suggested elsewhere [START_REF] Wagenseil | Bio-chemo-mechanics of thoracic aortic aneurysms[END_REF], here the analysis of the WSS vector field topological skeleton at the aortic luminal surface was applied in a two-step strategy.

As a first step, the aortic cycle-average WSS vector field topological skeleton was identified and analyzed (Figure 4a) aiming at identifying (on average) differences between the healthy and ATAA model. It emerged that on both models a line of marked WSS expansion was located at the proximal AAo outer wall, as identified by positive DIV values. However, the healthy aorta only presented there an unstable node. Moreover, marked contraction lines characterized the WSS topological skeleton on the ATAA outer wall, but they were not present on the luminal surface of the healthy aorta.

In the second step, the impact of the WSS vector field dynamics (along the cardiac cycle) on topological skeleton features was analyzed. The analysis of the luminal surface distribution of fixed points weighted residence time (𝑅𝑇𝛻 𝑥 𝑓𝑝 , Figure 4b) highlighted the presence of a wide region at the AAo outer-wall of the diseased model where instantaneous WSS fixed points appear and reside for a longer fraction of cardiac cycle. Such region is surrounded by luminal regions with a high local WSS contraction/expansion strength. On the other hand, a completely different distribution was observed on the outer wall of the healthy model (Figure 4b), mainly characterized by low 𝑅𝑇𝛻 𝑥 𝑓𝑝 values.

The analysis of the TSVI luminal distributions (Figure 4c) highlighted that: (1) the highest local variations in the contraction/expansion action exerted by the WSS on the endothelium along the cardiac cycle are located at two distinct regions of the AAo outer wall luminal surface, in both healthy and diseased models; (2) in the diseased model, high TSVI and high 𝑅𝑇𝛻 𝑥 𝑓𝑝 regions are markedly co-localized on the outer wall luminal surface.

CNs analysis

In the attempt to better describe differences between healthy and ATAA models accounting for possible links between the biomechanical alteration of the wall and hemodynamics, CNs were applied to the aortic flow and WSS fields.

The DC distributions of the Vax-, Hk-and |τ|-based CNs are displayed in Figure 5 for both models.

For visualization purposes, in each CN the DC values were classified in "high" and "low" based on the median value of the DC distribution of the healthy subject. Regarding the axial flow in the AAo of the diseased model (Figure 5a), a predominance of Vax waveforms with a neighborhood which is representative of a portion of the whole aortic axial flow smaller than in the healthy model emerged, as highlighted by the low value DC distribution in that region.

Regarding Hk, the DC distribution in the AAo (Figure 5b): (1) confirms the presence of counterrotating helical flow patterns both in the healthy and in the ATAA model [START_REF] Condemi | Fluid-and Biomechanical Analysis of Ascending Thoracic Aorta Aneurysm with Concomitant Aortic Insufficiency[END_REF][START_REF] Morbiducci | A rational approach to defining principal axes of multidirectional wall shear stress in realistic vascular geometries, with application to the study of the influence of helical flow on wall shear stress directionality in aorta[END_REF][START_REF] Morbiducci | In vivo quantification of helical blood flow in human aorta by time-resolved three-dimensional cine phase contrast magnetic resonance imaging[END_REF][START_REF] Morbiducci | Mechanistic insight into the physiological relevance of helical blood flow in the human aorta: an in vivo study[END_REF], as suggested elsewhere [START_REF] Calo | Spatiotemporal Hemodynamic Complexity in Carotid Arteries: an Integrated Computational Hemodynamics & Complex Networks-Based Approach[END_REF]; (2) highlights that helical flow (characterized considering Hk waveforms along the cardiac cycle) presents a spatiotemporal heterogeneity that in the ATAA model is markedly different from the healthy one, and which could be the consequence of the combination of the AAo dilatation and of the different shape of the (measured and imposed) inflow velocity profile (reminding that (1) the investigated ATAA subject is affected by BAV, and (2) that the presence of valvulopathy could markedly affect the AAo hemodynamics [START_REF] Pirola | Computational study of aortic hemodynamics for patients with an abnormal aortic valve: The importance of secondary flow at the ascending aorta inlet[END_REF].

Figure 5 confirms that the differences in the spatiotemporal intravascular complexity characterizing the ATAA and healthy models reflect WSS magnitude waveforms heterogeneity. In detail, the distal segment of the AAo of the ATAA model is characterized by an extended region of the luminal surface of the dilated aorta exposed to |τ| waveforms presenting a neighborhood which is smaller than in the healthy model (low DC values, Figure 5c). Therefore, in the diseased subject the pathologic expansion of the aortic wall where stiffness is higher (Figure 3) translates into WSS magnitude waveforms with a shape markedly different from the rest of the vessel.

The impact of ATAA on the spatiotemporal hemodynamic heterogeneity in the AAo was evaluated also in terms of anatomical persistence length of the correlation between neighbor waveforms.

AED maps (Figure 6a-b) highlight how the aortic dilation disrupts the persistence of the correlation of the Vax and Hk waveforms, breaking the topological connections among waveforms in the AAo and shortening the length of correlation, compared to the healthy model. Finally, the heterogeneity of WSS magnitude spatiotemporal features induced by AAo dilatation, already emerged from the DC maps, was confirmed by 𝑆𝑃𝐿 ̅̅̅̅̅ maps. More specifically, it was observed that the luminal surface of the distal dilated AAo presents larger areas where the functional length of correlation of WSS magnitude waveforms is smaller than the healthy AAo (Figure 6c).

Aortic hemodynamics vs. wall stiffness

Here we assess the co-localization of the in vivo estimated wall stiffness at AAo outer wall of the ATAA model with the WSS topological skeleton-based quantities, and with canonical WSS-based descriptors of disturbed shear. A visual inspection of Figure 7 suggests that an association might exist between instantaneous WSS fixed points dynamics at the luminal surface and the aortic stiffness. Interestingly, instantaneous WSS fixed points undergo longer combinations of residence time and marked contraction/expansion strength of the WSS vector field (as expressed by the quantity 𝑅𝑇𝛻 𝑥 𝑓𝑝 ) on those ATAA luminal surface areas where stiffness is high (Figure 7).

To explore more in depth the possible connections between peculiar WSS features and the altered biomechanical properties of the diseased aortic wall, the extent of the co-localization of high aortic wall stiffness regions with SAs exposed to presumably disturbed shear was quantified. By visual inspection of Figure 8a, it emerged that high stiffness co-localizes with high TSVI better than with canonical WSS-based descriptors. Of note, it was observed that SAs exposed to low TAWSS poorly co-localize with high stiffness regions. These observations were quantitatively confirmed by the SI values (Figure 8b), remarking the stronger capability of the WSS vector field divergencebased quantity TSVI as indicator of altered arterial wall mechanical properties, than the canonical WSS-based descriptors. Indeed, TSVI co-localizes with ATAA wall stiffness 206% more than TAWSS, 15% more than OSI and transWSS, and 45% more than RRT.

Discussion

Wall dilatation/degeneration of the ascending aorta is a complex multifactorial process promoted by a unique bio-chemo-mechanical environment, which may ultimately lead to aortic wall dissection/rupture [START_REF] Elefteriades | Thoracic aortic aneurysm clinically pertinent controversies and uncertainties[END_REF][START_REF] Poullis | Ascending aortic curvature as an independent risk factor for type A dissection, and ascending aortic aneurysm formation: a mathematical model[END_REF][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][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] Pasta | In Vivo Strain Analysis of Dilated Ascending Thoracic Aorta by ECG-Gated CT Angiographic Imaging[END_REF][START_REF] Wagenseil | Bio-chemo-mechanics of thoracic aortic aneurysms[END_REF][START_REF] Petit | Review of the Essential Roles of SMCs in ATAA Biomechanics[END_REF]. Despite a large body of literature focused on the role played by individual biological, chemical, or biomechanical factors in the ATAA development [START_REF] Wagenseil | Bio-chemo-mechanics of thoracic aortic aneurysms[END_REF], the heterogeneity characterizing ATAA disease cannot be exhaustively explained by individual features and the analysis of their complex interplay is still poorly investigated [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] Wagenseil | Bio-chemo-mechanics of thoracic aortic aneurysms[END_REF].

In this context, here we aim to highlight the possible links between ATAA hemodynamics, obtained by CFD simulations and explored with advanced methods, and in vivo estimated wall mechanical properties, inversely derived from gated CT scans [START_REF] Farzaneh | Inverse identification of local stiffness across ascending thoracic aortic aneurysms[END_REF].

The findings of this study confirm, on the basis of an in-depth quantitative exploration, that the near-wall and intravascular hemodynamic environment characterizing the ATAA model markedly differs from the healthy aorta.

More in detail, the analysis of the WSS topological skeleton highlighted peculiar features on the ATAA outer wall, which are not or are poorly present on the luminal surface of the healthy ascending aorta (Figure 4), i.e.: (1) the presence of localized marked WSS contraction regions; [START_REF] Erbel | ESC Guidelines on the diagnosis and treatment of aortic diseases: Document covering acute and chronic aortic diseases of the thoracic and abdominal aorta of the adult. The Task Force for the Diagnosis and Treatment of Aortic Diseases of the European[END_REF] the appearance and persistence of instantaneous WSS fixed points along the cardiac cycle (as quantified by 𝑅𝑇𝛻 𝑥 𝑓𝑝 , which additionally weights the strength of the local contraction/expansion action exerted by the WSS); (3) a large luminal surface area undergoing marked variation in the WSS contraction/expansion action on the endothelium over the cardiac cycle (as indicated by

TSVI).

From the CNs-based analysis, marked differences between ATAA and healthy aorta emerged in the organization of the intravascular hemodynamic patterns. In detail, here for the first time the disruption of spatiotemporal homogeneity of intravascular hemodynamic features induced by the AAo dilatation was quantified in terms of the Euclidian length of persistence of the correlation between flow quantities. As indicated by AED, the presence of aortic dilation seems to reduce the anatomical length of correlation persistence both for the axial velocity and kinetic helicity density waveforms, compared to the healthy case (Figure 6).

This induced-by-aortic-dilation increase in AAo intravascular hemodynamics spatiotemporal heterogeneity reflects on a reduced functional length of correlation in WSS magnitude waveforms , localized on the distal outer wall, as indicated by 𝑆𝑃𝐿 ̅̅̅̅̅ (Figure 6). Such differences between ATAA and healthy models are further confirmed by the observed WSS magnitude DC luminal distribution, which highlights that in the dilated aorta the topologically isolated region is more extended than in the healthy one (Figure 5c). The latter result can be explained by the demonstrated causative role of helical flow in determining WSS patterns at the aortic luminal surface [START_REF] De Nisco | The Atheroprotective Nature of Helical Flow in Coronary Arteries[END_REF][START_REF] De Nisco | The impact of helical flow on coronary atherosclerotic plaque development[END_REF].

The evidences emerged from the WSS topological skeleton analysis and from the CNs-based analysis support the hypothesis that a complex interplay exists between hemodynamic features, aortic wall dilatation and its degradation in terms of wall mechanical properties. This statement is supported by the main finding of the study, i.e., that in the distal AAo outer wall of the ATAA model, extended high stiffness regions (indicating a degradation of the mechanical properties of the wall), co-localize with luminal surface areas of: (1) high instantaneous WSS fixed points residence time (weighted by WSS divergence value) (Figure 7); (2) large variations in the WSS contraction/expansion action exerted by the flowing blood along the cardiac cycle, here quantified by TSVI (Figure 8).

It is worth noting that the cross-sectional nature of this study does not allow to establish whether the observed hemodynamic features are responsible for wall dilatation and degradation, or whether they are consequence of the dilated geometry. However, previous studies suggested that altered aortic flow predisposes the ascending thoracic aorta to wall dilatation/degradation [START_REF] Condemi | Ascending thoracic aorta aneurysm repair induces positive hemodynamic outcomes in a patient with unchanged bicuspid aortic valve[END_REF][START_REF] Burk | Evaluation of 3D blood flow patterns and wall shear stress in the normal and dilated thoracic aorta using flow-sensitive 4D CMR[END_REF] as a consequence of the purported role of endothelial shear in the pathogenesis of ATAA [START_REF] Michel | From genetics to response to injury: Vascular smooth muscle cells in aneurysms and dissections of the ascending aorta[END_REF]. In this sense, the findings of this study suggest that future studies addressing the role of hemodynamics in the ascending thoracic aorta to wall dilatation/degradation should include descriptors based on the WSS topological skeleton, such as TSVI (Figure 8). In fact, such descriptors show a higher co-localization with regions at the aortic wall characterized by high stiffness than canonical WSS-based descriptors. The hemodynamic quantities presented here may improve the prediction of ATAA development and progression and contribute to a deeper understanding of the underlying hemodynamics-driven processes.

Limitations

Several limitations could weaken the findings of this study. The main limitation is that the present analysis is based on only one ATAA model and one healthy aorta model. For this reason, we acknowledge that the here reported association between the WSS topological skeleton-based descriptor TSVI and ATAA wall weakening indicator should be confirmed on a larger dataset.

The inverse approach here adopted to estimate local wall stiffness in vivo is based on the assumption that the aortic wall behaves as a membrane with no through-thickness shear [START_REF] Farzaneh | Inverse identification of local stiffness across ascending thoracic aortic aneurysms[END_REF][START_REF] Farzaneh | Identifying Local Arterial Stiffness to Assess the Risk of Rupture of Ascending Thoracic Aortic Aneurysms[END_REF].

The regions near the supra-aortic branches may not satisfy such assumption and were therefore excluded from the wall stiffness analysis. Moreover, in the perspective of extending the analysis of aortic stiffness at different stages of ATAA growth, an extensive use of the inverse approach may be limited by the use of X-ray during the gated CT scans procedure. In this regard, other techniques, such as ultrasounds [START_REF] Wittek | Cyclic three-dimensional wall motion of the human ascending and abdominal aorta characterized by time-resolved three-dimensional ultrasound speckle tracking[END_REF] or MRI [START_REF] Arani | Cardiac MR elastography for quantitative assessment of elevated myocardial stiffness in cardiac amyloidosis[END_REF], may be adopted as a source of dynamic images of the aortic wall during the cardiac cycle.

Finally, the main limitation regarding the numerical settings of the CFD study is represented by the rigid wall assumption. However, recent observations have demonstrated that aortic wall motion has a minor impact on WSS-based descriptors of disturbed shear [START_REF] Lantz | Wall shear stress in a subject specific human aorta -Influence of fluid-structure interaction[END_REF], and on intravascular flow topology. Concerning the latter, for example, similar helical fluid structures have been observed in vivo [START_REF] Morbiducci | In vivo quantification of helical blood flow in human aorta by time-resolved three-dimensional cine phase contrast magnetic resonance imaging[END_REF][START_REF] Morbiducci | Mechanistic insight into the physiological relevance of helical blood flow in the human aorta: an in vivo study[END_REF][START_REF] Frydrychowicz | Interdependencies of aortic arch secondary flow patterns, geometry, and age analysed by 4dimensional phase contrast magnetic resonance imaging at 3 Tesla[END_REF] and in vitro both in rigid and distensible aortic phantoms [START_REF] Gallo | Analysis of thoracic aorta hemodynamics using 3D particle tracking velocimetry and computational fluid dynamics[END_REF][START_REF] Gulan | Experimental Investigation of the Influence of the Aortic Stiffness on Hemodynamics in the Ascending Aorta[END_REF]. Therefore, we believe that the assumption on aortic wall distensibility does not entail the generality of the present results.

Conclusions

In this study, the integration of computational hemodynamics, in vivo stiffness estimation and advanced fluid mechanics methods allowed to explore more in depth the existence of links between the altered hemodynamics in the ATAA and the wall biomechanical degradation.

Moreover, combining WSS topological skeleton analysis and CNs-based analysis has highlighted that WSS topological skeleton features across the luminal surface of the ascending aorta are markedly affected by the different level of spatiotemporal heterogeneity characterizing the ATAA and healthy subjects' hemodynamics.

In conclusion, despite the exploratory nature of the study, advanced methods of analysis of the aortic blood flow have shown their very strong potential to decipher the links between local hemodynamics and the degradation of the mechanical properties of the aortic wall. In this sense, WSS topological skeleton analysis [START_REF] Mazzi | A Eulerian method to analyze wall shear stress fixed points and manifolds in cardiovascular flows[END_REF][START_REF] Arzani | Wall shear stress fixed points in cardiovascular fluid mechanics[END_REF] and CNs-based analysis promise to be very effective tools [START_REF] Mazzi | A Eulerian method to analyze wall shear stress fixed points and manifolds in cardiovascular flows[END_REF][START_REF] Arzani | Wall shear stress fixed points in cardiovascular fluid mechanics[END_REF].

Tables Table 1: Definition of WSS-based hemodynamic descriptors of "disturbed flow".

𝛕 is the WSS vector; T is the period of the cardiac cycle; n is the unit vector normal to the arterial surface at each element.

WSS-based hemodynamic descriptors

Figure 1 .

 1 Figures captions

Figure 2 .

 2 Figure 2. WSS topological skeleton features. (a) Configuration of each fixed point-type and contraction and expansion regions, colored by blue and red respectively. (b) Identification and classification of fixed points based on Poincaré index and eigenvalues of the Jacobian matrix.

Figure 3 .

 3 Figure 3. Estimated wall stiffness distribution at the luminal surface of ATAA model.

Figure 4 .

 4 Figure 4. Luminal distributions of WSS topological skeleton-based metrics. Aortic luminal distributions of (a) cycle-average WSS topological skeleton, (b) WSS fixed points weighted residence time (𝑅𝑇𝛻 𝑥 𝑓𝑝 ), and (c) TSVI. In panel (a), contraction/expansion regions are colored by blue/red, respectively, and Line Integral Convolution technique is adopted to visualize WSS vector. The ATAA and healthy aortic models are displayed in the top and bottom panel, respectively.

Figure 5 .

 5 Figure 5. DC distributions of hemodynamic descriptors-based CNs. The DC distributions of the (a) Vax, (b) Hk, and (c) |τ| CNs are displayed for the diseased (top) and healthy (bottom) subjects.

Figure 6 .

 6 Figure 6. Anatomical and topological length of correlation persistence of hemodynamic spatiotemporal patterns. The AED distributions of the (a) Vax, and (b) Hk CNs, and (c) 𝑆𝑃𝐿 ̅̅̅̅̅ distribution of the |τ| CNs are displayed for the diseased (top) and healthy (bottom) subjects. AED and 𝑆𝑃𝐿 ̅̅̅̅̅ were computed at the ascending aorta segment of each model.

Figure 7 .

 7 Figure 7. Wall stiffness vs. weighted residence time analysis. Contour maps of estimated wall stiffness (left) and WSS fixed points weighted residence time (𝑅𝑇𝛻 𝑥 𝑓𝑝 -right) at the luminal surface of ATAA model. The black contour line represents the 2 nd tertile of stiffness luminal distribution at the ATAA outer wall.

Figure 8 .

 8 Figure 8. Wall stiffness vs. deranged aortic hemodynamics analysis. (a) co-localization maps of high stiffness and disturbed shear; (b) similarity indices quantifying the co-localization of luminal SAs characterized by high stiffness and each descriptor of deranged hemodynamics (i.e., low TAWSS; high OSI, RRT, transWSS, TSVI).

FiguresFigure 1 .

 1 Figures

Figure 2 .

 2 Figure 2. WSS topological skeleton features. (a) Configuration of each fixed point-type and contraction and expansion regions, colored by blue and red respectively. (b) Identification and classification of fixed points based on Poincaré index and eigenvalues of the Jacobian matrix.

Figure 3 .

 3 Figure 3. Estimated wall stiffness distribution at the luminal surface of ATAA model.

Figure 4 .

 4 Figure 4. Luminal distributions of WSS topological skeleton-based metrics. Aortic luminal distributions of (a) cycle-average WSS topological skeleton, (b) WSS fixed points weighted residence time (𝑅𝑇𝛻 𝑥 𝑓𝑝 ), and (c) TSVI. In panel (a), contraction/expansion regions are colored by blue/red, respectively, and Line Integral Convolution technique is adopted to visualize WSS vector. The ATAA and healthy aortic models are displayed in the top and bottom panel, respectively.

Figure 5 .

 5 Figure 5. DC distributions of hemodynamic descriptors-based CNs. The DC distributions of the (a) Vax, (b) Hk, and (c) |τ| CNs are displayed for the diseased (top) and healthy (bottom) subjects.

Figure 6 .

 6 Figure 6. Anatomical and topological length of correlation persistence of hemodynamic spatiotemporal patterns. The AED distributions of the (a) Vax, and (b) Hk CNs, and (c) 𝑆𝑃𝐿 ̅̅̅̅̅ distribution of the |τ| CNs are displayed for the diseased (top) and healthy (bottom) subjects. AED and 𝑆𝑃𝐿 ̅̅̅̅̅ were computed at the ascending aorta segment of each model.

Figure 7 .

 7 Figure 7. Wall stiffness vs. weighted residence time analysis. Contour maps of estimated wall stiffness (left) and WSS fixed points weighted residence time (𝑅𝑇𝛻 𝑥 𝑓𝑝 -right) at the luminal surface of ATAA model. The black contour line represents the 2 nd tertile of stiffness luminal distribution at the ATAA outer wall.

Figure 8 .

 8 Figure 8. Wall stiffness vs. deranged aortic hemodynamics analysis. (a) co-localization maps of high stiffness and disturbed shear; (b) similarity indices quantifying the co-localization of luminal SAs characterized by high stiffness and each descriptor of deranged hemodynamics (i.e., low TAWSS; high OSI, RRT, transWSS, TSVI).


L Derycke

J Sénémaud

D Perrin

S Avril

P Desgranges

J N Albertini

F Cochennec

S Haulon
email: s.haulon@hml.fr

Derycke Lucie
email: deryckelucie@gmail.com

Patient-specific computer modeling for automated sizing of fenestrated stent-grafts

Keywords: Fenestrated endovascular aneurysm repair (FEVAR), computational analysis, personalized medicine, numerical simulation

What this paper adds:

Fenestrated stent-grafting has become a standard endovascular approach to treat complex abdominal aortic aneurysms. Currently, accurate device planning requires significant operator's experience and a long manufacturing delay. This step is known to be crucial for surgical success. Computational modeling could prove helpful in providing more tailored and straightforward care in patients, especially for planification. This study explores the potential of simulation for fenestrated stent-graft sizing.

Introduction

In most high volume aortic European centers, stent-graft (SG) implantation is considered the first line treatment for thoracic and abdominal aortic aneurysms (AAA) in patients with suitable anatomies. [START_REF] Wanhainen | Editor's Choice -European Society for Vascular Surgery (ESVS) 2019 Clinical Practice Guidelines on the Management of Abdominal Aorto-iliac Artery Aneurysms[END_REF][START_REF] Riambau | Editor's Choice -Management of Descending Thoracic Aorta Diseases: Clinical Practice Guidelines of the European Society for Vascular Surgery (ESVS)[END_REF] Fenestrated stent-grafting (FEVAR) is a validated endovascular approach to treat complex AAA with unfavourable anatomies (short infra renal neck, supra-renal or type IV thoraco-abdominal aneurysms). [START_REF] Mastracci | Twelve-year results of fenestrated endografts for juxtarenal and group IV thoracoabdominal aneurysms[END_REF][START_REF] Marzelle | Results and factors affecting early outcome of fenestrated and/or branched stent grafts for aortic aneurysms: a multicenter prospective study[END_REF][START_REF] Verhoeven | Fenestrated stent grafting for short-necked and juxtarenal abdominal aortic aneurysm: an 8-year single-centre experience[END_REF][START_REF] Oderich | Results of the United States multicenter prospective study evaluating the Zenith fenestrated endovascular graft for treatment of juxtarenal abdominal aortic aneurysms[END_REF][START_REF]British Society for Endovascular Therapy and the Global Collaborators on Advanced Stent-Graft Techniques for Aneurysm Repair (GLOBALSTAR) Registry. Early results of fenestrated endovascular repair of juxtarenal aortic aneurysms in the United Kingdom[END_REF] FEVAR requires custom-made devices specifically tailored to each patient's anatomy. As a result, the delay for planning and manufacturing currently ranges from 6 to 8 weeks, which may preclude its use in patients presenting with large aneurysms. Accurate device planning requires the use of dedicated three-dimensional imaging software combined with high-resolution pre-operative CT scan to perform all the necessary measurements. In case of arterial tortuosity or important angulation, it is difficult to predict SG behaviour in the aorta and to modify the semi-automated arterial segmentation and centerline reconstructions accordingly.

The finite-element analysis (FEA) is a numerical method used to overcome biomechanical problems using displacements, strains and stresses analysis. [START_REF] Leach | Computational Models of Vascular Mechanics[END_REF] FEA can be used to predict the deployment of SGs in aortic aneurysms. [START_REF] Perrin | Patient-specific simulation of endovascular repair surgery with tortuous aneurysms requiring flexible stent-grafts[END_REF][START_REF] Perrin | Patientspecific numerical simulation of stent-graft deployment: Validation on three clinical cases[END_REF][START_REF] Auricchio | Patient-specific aortic endografting simulation: from diagnosis to prediction[END_REF][START_REF] Romarowski | Computational simulation of TEVAR in the ascending aorta for optimal endograft selection: A patient-specific case study[END_REF][START_REF] Derycke | Predictive Numerical Simulations of Double Branch Stent-Graft Deployment in an Aortic Arch Aneurysm[END_REF] Recent literature has highlighted the advancements in computational analysis applied to endovascular repair. Based on analyses focused on the mechanical behaviour of SGs [START_REF] Demanget | Computational comparison of the bending behavior of aortic stent-grafts[END_REF] , models of EVAR and supra-renal devices deployed in virtual models have been established; [START_REF] Perrin | Deployment of stent grafts in curved aneurysmal arteries: toward a predictive numerical tool[END_REF][START_REF] Bock | What if you stretch the IFU? A mechanical insight into stent graft Instructions For Use in angulated proximal aneurysm necks[END_REF] those patient-specific models have proved reliable. [START_REF] Perrin | Patient-specific simulation of endovascular repair surgery with tortuous aneurysms requiring flexible stent-grafts[END_REF][START_REF] Perrin | Patientspecific numerical simulation of stent-graft deployment: Validation on three clinical cases[END_REF][START_REF] Auricchio | Patient-specific aortic endografting simulation: from diagnosis to prediction[END_REF][START_REF] Romarowski | Computational simulation of TEVAR in the ascending aorta for optimal endograft selection: A patient-specific case study[END_REF][START_REF] Derycke | Predictive Numerical Simulations of Double Branch Stent-Graft Deployment in an Aortic Arch Aneurysm[END_REF] The aim of this study was to assess two different steps of a patient-specific finite-element model of Zenith® fenestrated device deployment in complex AAA to predict fenestrations positions.

Primary hypothesis was that simulation would provide accurate positioning of fenestrations in comparison to standard planning techniques and postoperative CT scan measurements.

Material and Methods

Study population

The study was approved by the Institutional Review Board of the French Society of Thoracic and Cardiovascular Surgery (Société Française de Chirurgie Thoracique et Cardio Vasculaire-SFCTCV).

The study population consisted of 51 consecutive patients who underwent implantation of a Zenith® Fenestrated AAA Endovascular Graft (Cook Medical, Bloomington, IN) to treat juxtarenal, para-renal or thoraco-abdominal aortic aneurysms between January 2016 and April 2018 at Henri Mondor Hospital and Marie Lannelongue Hospital.

Exclusion criteria were: unavailability of preoperative CT scan, poor pre-operative CT scans quality precluding modeling analysis (poor quality of the contrast agent injection or large slice thickness (>3mm)), post-dissection aneurysms, and devices combining branch(es) and fenestration(s).

Sizing process

The sizing of the SG was performed by the manufacturer (Cook Medical® planning center, London, UK).

Simulation strategy

High resolution pre-operative arterial-phase CT scans were used to generate patient-specific 3dimensionnal models of the aorta, from the descending thoracic aorta to the common iliac arteries, including the target arteries (celiac trunk, superior mesenteric and renal arteries) using the VMTK (Vascular Modeling Toolkit, www.vmtk.org) library. This open-source software semi-automatically segments DICOM datasets from the CT scan and creates 3D vascular models (aortic segmentation step). [START_REF] Sethian | A fast marching level set method for monotonically advancing fronts[END_REF] As calcifications of the aortic wall and intra-luminal thrombus were not included in the model, the aortic wall and the target vessels were considered as homogenous surfaces with a constant thickness of 1.5 mm and 1 mm respectively. The custom-made SGs were reproduced digitally on the basis of the graft plan data. Deployment of the personalized SG in its corresponding model of the aorta was retrospectively performed using the commercially available Abaqus/Explicit v6.14 finite element solver (Dassault Systèmes, Paris, France). Simulations were achieved using proprietary algorithms (Planop, PrediSurge, Saint-Etienne, France). Computational technology was based on finite-element analysis and assessed the deformations induced by the device-host interaction resulting in a prediction of SG behaviour and arterial displacement. Briefly, the aortic surface was virtually deformed until a cylindric shape of the aorta, was obtained. This step of numerical aortic deformation was called "morphing". Then, it was possible to deploy a stent-graft inside the cylindric aorta, and to reverse the deformation of the aortic surface while maintaining the stentgraft in place (Figure (1)). The validation of this model was previously reported by our group. [START_REF] Perrin | Patient-specific simulation of endovascular repair surgery with tortuous aneurysms requiring flexible stent-grafts[END_REF][START_REF] Perrin | Patientspecific numerical simulation of stent-graft deployment: Validation on three clinical cases[END_REF] The aortic wall was assigned an orthotropic elastic behaviour. Mechanical properties of stents and fabric were obtained either from literature or from in house mechanical testing of samples obtained from manufacturers. [START_REF] Demanget | Computational comparison of the bending behavior of aortic stent-grafts[END_REF] For the stents, a linear elastic material behaviour was used, reproducing the nitinol behaviour in its austenitic phase. [START_REF] Demanget | Computational comparison of the bending behavior of aortic stent-grafts[END_REF] The polyester fabric was modelled as an orthotropic elastic material. [START_REF] Demanget | Computational comparison of the bending behavior of aortic stent-grafts[END_REF]

Simulation analysis

For each visceral artery incorporated into the graft, two data parameters were measured by a blinded investigator: the longitudinal distance between the ostial centers along the centerline, measured in millimeters (mm), and the rotational clock angle between each visceral artery, measured in degrees (°). These two parameters encoded the position of the visceral arteries relative to one another. Automated fenestration positions were calculated by the software from the "morphing" step.

The different steps of the simulation methodology are illustrated in Figure (1).

Post-operative images analysis

One trained and independent observer performed the post-operative imaging analysis. The position of the fenestrations on the post-operative CT scan represents the "ideal" SG configuration because any sizing mismatch is compensated by the stent-graft's longitudinal (stents are not connected to each other) and rotational (10-20% oversizing) flexibility. The measures of relative angle and distance between each visceral artery were extracted using a dedicated imaging workstation (TeraRecon Inc., Santa Rosa, CA, USA.) and the modality previously described for pre-operative sizing. [START_REF] Banno | Inter-observer variability in sizing fenestrated and/or branched aortic stent-grafts[END_REF]

Statistical analysis

All statistical analyses were performed using R statistical software version 3.5.2 (R Foundation for Statistical Computing, Vienna, Austria). Contrary to the real process of deployment, the simulated SG was not deployed inside the aorta based on the position of one of the target arteries but with an automatic longitudinal position and an overall rotation of 0 degrees. A systematic measurement bias could have been induced by this method. In order to provide relevant comparisons between the implanted FEVAR and simulation processes, a constant shift was applied to all the fenestrations for each case to correct potential differences induced by these two parameters. However, the relative distances and angles between the fenestrations for each case was preserved, as illustrated in Figure (2).

The measures were compared with respect to the absolute longitudinal and rotational differences.

Agreement between the different measures was assessed by plotting the difference between each method relative to each other with the limits of agreement (± 1.96 standard deviations around the mean difference) as described by Bland and Altman. Quantitative variables were also analysed by linear regression test, used to calculate the bias, estimated by the mean difference and the standard deviation of the difference.

Longitudinal distance and clock face discrepancies >3 mm and >15°, respectively, were considered significant, according to the inter-observer variability of pre-operative sizing reported in the literature. [START_REF] Banno | Inter-observer variability in sizing fenestrated and/or branched aortic stent-grafts[END_REF][START_REF] Malkawi | Sizing fenestrated aortic stent-grafts[END_REF][START_REF] Oshin | Intra-and interobserver variability of target vessel measurement for fenestrated endovascular aneurysm repair[END_REF]

Results

Fifty-one FEVAR deployments were simulated with a total of 180 fenestrations and 15 scallops (195 target arteries). Details are reported in Table (1 In our current practice, numerical simulations required approximately 8 hours of computational analysis, including 2 hours of manual work. The automated fenestration positions extracted from the "morphing" step were obtained in approximately half an hour.

The mean slice thickness of the pre-operative CT scans was 1.2 ± 0.45 mm [0.5, 2.0]. Similar results were obtained when comparing infra-or millimetric CT scans and supra-millimetric CT scans.

Quantitative assessment:

The numerical results are summarized in Table (2).

Both Bland-Altman and linear regression showed good reproducibility for longitudinal and circumferential position between the three methods (Figure ( 4)).

The median absolute difference between the simulation and post-operative CT scan was 1.0 ± 1.1 mm for longitudinal distance measurements and 6.9 ± 6.1° for clock positions. The worst case was a longitudinal distance difference of 6.0 mm and an angle difference of 44.3°. 95% of the longitudinal deviances were shorter than 3 mm (43/51 cases) and 96% of the rotational deviances were under 15° (44/51 cases).

The median absolute difference between the planning center and post-operative sizing was 0.8 ± 0.8 mm for longitudinal distance measurements and 5.1 ± 5.0° for clock positions. The worst case was a longitudinal distance difference of 4.0 mm and an angle difference of 37.1°. 97% of the longitudinal deviances were shorter than 3 mm (46/51 cases) and 98% of the rotational deviances were under 15° (48/51 cases).

The median absolute difference between the simulation and the planning center was 0.96 ± 0.97 mm for longitudinal distance measurements and 4.8 ± 3.6° for clock positions. The worst case was a longitudinal distance difference of 5.0 mm and an angle difference of 21.8°. 98% of the longitudinal deviances were shorter than 3 mm (47/51 cases) and 99% of the rotational deviances were less than 15° (49/51 cases).

A subgroup analysis focusing on the number of fenestrations (group 1: 4 fenestrations or scallop (39/51) and group 2: 3 fenestrations or scallop (11/51)) showed similar results. The median absolute difference between the simulation and the post-operative sizing was approximately 1 mm (1.0 ± 1.2 mm and 1.0 ± 1.2 mm, respectively) for longitudinal distance measurements and 7.5° (7.0 ± 6.3° and 7.9 ± 5.2°, respectively) for clock positions. The median absolute difference between the simulation and the planning center was approximatively 1 mm (0.9 ± 1.2 mm and 1.2 ± 0.9 mm, respectively) for longitudinal distance measurements and 5° (4.8 ± 3.6° and 4.8 ± 3.8°, respectively) for clock positions.

Qualitative assessment:

Two cases of proximal suboptimal apposition were observed and one case presented with an excess graft oversizing (Figure (5) (A) and (B)). An inhomogeneous deployment of the SG was observed in six cases; it was also depicted on the post-operative CT scan. On the example, the posterior stent struts were tightened whereas the anterior struts were spread apart. This stent configuration was similar on the simulation and the post-operative CT scan (Figure (5)

(C)).
Two cases presented a SG shifted towards the aortic axis, due to a significant misalignment of the aneurismal sac and the aortic axis (Figure ( 6)). In 6 cases, pleated fabric was observed at the level of the visceral arteries and a similar aspect was found on the corresponding postoperative CT scan (Figure (5) (D) and (E)).

Automated sizing process:

The numerical results are summarized in Table (2).

The median absolute difference between automated and post-operative sizing was 3.0 ± 0.3 mm for longitudinal distance measurements and 11.0 ± 9.3° for clock positions. The worst case was a longitudinal distance difference of 16.7 mm and an angle difference of 56.0°. 93% of the longitudinal deviances were shorter than 3 mm (39/51 cases) and 91% of the rotational deviances were under 15° (38/51 cases).

The median absolute difference between automated sizing and the planning center was 1.2 ± 1.7 mm for longitudinal distance measurements and 7.4 ± 6.5° for clock positions. The worst case of each was a longitudinal distance difference of 15.5 mm and an angle difference of 44.9°. 93% of the longitudinal deviances were under 3 mm (40/51 cases) and 97% of the rotational deviances were under 15° (46/51 cases).

Discussion

Treatment of complex AAA with FEVAR has been proven feasible, effective and safe [START_REF] Mastracci | Twelve-year results of fenestrated endografts for juxtarenal and group IV thoracoabdominal aneurysms[END_REF][START_REF] Marzelle | Results and factors affecting early outcome of fenestrated and/or branched stent grafts for aortic aneurysms: a multicenter prospective study[END_REF][START_REF] Verhoeven | Fenestrated stent grafting for short-necked and juxtarenal abdominal aortic aneurysm: an 8-year single-centre experience[END_REF][START_REF] Oderich | Results of the United States multicenter prospective study evaluating the Zenith fenestrated endovascular graft for treatment of juxtarenal abdominal aortic aneurysms[END_REF][START_REF]British Society for Endovascular Therapy and the Global Collaborators on Advanced Stent-Graft Techniques for Aneurysm Repair (GLOBALSTAR) Registry. Early results of fenestrated endovascular repair of juxtarenal aortic aneurysms in the United Kingdom[END_REF] and has the potential to greatly reduce the mortality and morbidity risks, especially in the subgroup of patients at high risk for open repair. However, the use of fenestrated devices implies proper analysis of the patient's arterial geometry to design a custom-made SG. Physicians have to be trained to use dedicated sizing software and to be familiar with 3D imaging and its limitations. [START_REF] Moore | Fenestrated endovascular grafts for juxtarenal aortic aneurysms: a step by step technical approach[END_REF][START_REF] Greenberg | Beyond the aortic bifurcation: branched endovascular grafts for thoracoabdominal and aortoiliac aneurysms[END_REF] An automated, reproductible and precise sizing procedure could facilitate the clinical process and free up physician time.

Our model proved successful in providing fenestrations locations similarly to the current sizing performed by the planning center, confirmed by the comparison to the postoperative analysis.

The process has been successfully evaluated in 51 patients.

Accurate positioning of the fenestrations is determinant for procedural success and long-term patency. Numerical simulation of SG deployment offers other potential advantages. The behaviour of the deployed SG can be visualized and assessed, including adequate application of the fabric, proximal apposition, excessive oversizing or kinking, as seen in Figure (5). These results indicate the clinical relevance of numerical simulation of FEVAR to improve outcome by helping the physician to select appropriate graft diameters and fenestration positions that best fits the individual patient. In unfavorable aortic anatomies, a deployment simulation could be performed by the planning center to accept or reject cases. To allow relevant comparison, we performed an accurate digital reproduction of patient specific SGs based on the graft plan data. Standardized digital SG models are currently being constructed, in order to provide a quick and easy to use interface.

We noticed in less than 15% of cases longitudinal and rotational differences higher than 3 mm or 15°. There is no consensus regarding maximum tolerance level between fenestrations and target vessels positions. Some experienced endovascular specialists suggested that a rotational deviance of 15° between the fenestration and its target vessel was acceptable, as it was unlikely to lead to significant complications. [START_REF] Nordon | Toward an "off-the-shelf" fenestrated endograft for management of short-necked abdominal aortic aneurysms: an analysis of current graft morphological diversity[END_REF] Our results confirm the previous studies focused on interobserver variability when sizing FEVAR, which reported good agreement but also some critical discrepancies between observers. Oshin et al. reported an analysis of 25 FEVAR sizing performed by two experienced operators; they observed deviances of more than 3 mm in 18% of cases in longitudinal position, and of more than 15° in 12% of cases on clock position. [START_REF] Oshin | Intra-and interobserver variability of target vessel measurement for fenestrated endovascular aneurysm repair[END_REF] Banno et al. reported comparison of 268 FEVAR sizing between two experienced surgeons and the manufacturer. They observed more than 22.5° angle discrepancy in 9.8% of cases and more than 5 mm length discrepancy in 16.4% of cases. [START_REF] Banno | Inter-observer variability in sizing fenestrated and/or branched aortic stent-grafts[END_REF] Finally, Malkawi et al. reported results of comparison of 19 FEVAR sizing between four experienced observers. [START_REF] Malkawi | Sizing fenestrated aortic stent-grafts[END_REF] The overall interobserver measurement error for distance was 5.3 mm (4.4-6.2 95% CI) and for target vessel orientation 12.6° (10.8-14.4 95% CI). Maurel et al. reported comparison of FEVAR pre and post-operative sizing of renal artery distance and clock position and showed that an accommodation to sizing error up to 15° in clock position may be considered acceptable, without adverse consequences on patency. [START_REF] Maurel | Changes in Renal Anatomy After Fenestrated Endovascular Aneurysm Repair[END_REF] Our results compared favourably with these data.

Furthermore, discrepancies could be partly explained by the adjustment of the fenestrations designed by the manufacturer to fit with the 15-20% graft oversizing, the presence of reducing ties, and fenestration shift to avoid having a stent strut crossing the lumen of a fenestration. These rotational adjustments explain why longitudinal measurements showed less variability than circumferential measurements. The technique of clock position measurement, with its 7.5° accuracy, compared to the 1 mm accuracy of longitudinal measurements, also explains this difference.

A thorough examination of our cases has identified causes of discrepancy. An inhomogeneous deployment of the SG was observed in six cases associated with rotational position misalignment, which was also found on the post-operative CT scan (Figure ( 5)). In case of misalignment of the aneurysmal sac and aortic axis, the SG was shifted away from the aortic axis, especially in cases with prior EVAR. In Figure (6), one of these cases is presented: the SG, which is constrained above and below the aneurysm, is shifted forward in the aortic lumen at the level of the aneurysm. Different clock positions are obtained depending on whether the aortic lumen axis or the SG axis is used as a reference. In six cases with a longitudinal position misalignment, pleated fabric was observed at the level of the visceral arteries and a similar aspect was found on the corresponding post-operative CT scan, as shown in Figure (5). Finally, discrepancies were depicted in two cases with a large distance between the SG and the visceral artery ostium and three cases with large visceral artery diameter (larger than 10 mm). In such anatomies, accuracy is less crucial to achieve technical success.

The delay in producing a fenestrated device is related to both planning and manufacturing. The current eight weeks delay is inappropriate for urgent patients. Numerical simulations require nowadays approximately 8 hours of computational analysis, including 2 hours of manual work, which is similar to the time spent for planning by a trained operator. To further reduce the delay and provide an accurate and fast tool to physicians, computing capabilities improve at a very rapid pace. In a near future, it is likely that the time required to perform these simulations will fall below the hour.

The first step of the deployment simulation provides positions of the visceral arteries within half an hour. However, the aortic segmentation was inaccurate in some cases with arterial calcifications, previous EVAR with struts in front of visceral arteries and ostial stenosis. For such cases, checking the aortic segmentation is still required. A previous study highlighted the need for "human input" in automated sizing for EVAR. [START_REF] Wyss | Threedimensional imaging core laboratory of the endovascular aneurysm repair trials: validation of methodology[END_REF] Measurements accuracy appeared to be better in our study, probably due to the improved quality of the CT scans.

This study has several limitations. We focused our study on fenestrated devices and nondissected aortas. Branched device modelling is currently feasible and will be assessed in specific studies. Improvements are also in progress to extend the model to dissected aortas. Moreover, we only focused our study on the Zenith Cook Medical device because it is the most implanted fenestrated endograft in both centers, and because the position of the fenestration is critical on this device which is fully supported with stents. Simulation of other fenestrated devices, which require different planning methods, will be performed in a separate study. Our simulations could benefit from more sophisticated modeling including thrombus, calcifications of the aortic wall and environment. Current validation of simulation models remains a major issue. Simulation results were compared to post-operative sizing and pre-operative sizing, which have their own limitations, and CT images analysis and numerical models of SG deployment were performed retrospectively.

Numerical simulation of SG deployment in complex AAA was feasible in 51 patients and accurately determines patient-specific fenestration positions. When compared to post-operative sizing, the current process of sizing achieved by the planning center showed less variability than the simulation model and automated positions extracted directly from the "morphing" step still required manual corrections. It is currently being improved with new computational algorithms. This model is a reliable tool for FEVAR planning and has the potential to help physicians to select the device design that best fits the patient's aortic anatomy. Evaluation of the software in other conditions, such as unsuccessful cases, high arterial tortuosity cases and physician-modified stent-grafts, should be addressed in further studies. Moreover, prospective work should be realized to support these promising early results.

  ). Examples of simulation results are presented in Figure (3). Fifteen patients were excluded for unavailability of preoperative CT scan (3/15), poor pre-operative CT scans quality (5/15), post-dissection aneurysms (4/15), and devices combining branch(es) and fenestration(s) (3/15).

Figure 1 .

 1 Figure legends:

Figure 2 .

 2 Figure 2. Illustration of constant shift applied on simulation results. The relative distances and

Figure 3 .

 3 Figure 3. Illustration of the three different stent-grafts modeling and simulation results. (A)

Figure 4 .

 4 Figure 4. Longitudinal and clock position of target vessels depicted with the simulation and the

Figure 5 .

 5 Figure 5. Qualitative assessment examples: (A) excess of oversizing, (B) defect of proximal

Figure 6 .

 6 Figure 6. Challenging clock position analysis: (A) right lateral view: red arrow: the stent-graft

Table 1 .

 1 Distribution of fenestrations and scallops of the simulated stentgrafts.

	Tables:
	N of fenestration/scallop	N of cases N of fenestrations	N of scallops
	5/0	1	5	0
	4/0	28	112	0
	3/0	7	21	0
	4/1	1	4	1
	3/1	10	30	10
	2/1	4	8	4
	Total	51	180	15
	FEVAR, fenestrated endovascular abdominal aortic aneurysm repair

Table 2 .

 2 Comparison results of longitudinal and clock positions obtained by the two steps of the simulation model and the pre-and post-operative sizing; and percentage of longitudinal and clock position discrepancies below the significance limits of 3 mm and 15°.

		Longitudinal position, mm
		Post-operative sizing	Pre-operative sizing
		Median ± SD	N ≤ 3 mm	Median ± SD	N ≤ 3 mm
		[range]	(%)	[range]	(%)
	Simulation	1.0 ± 1.1 [-5.9, 6.0]	95	0.96 ± 0.97 [-4.6, 5.0]	98
	Pre-operative sizing	0.8 ± 0.8 [-4.0, 4.0]	97
	Automated positions	3.0 ± 0.3 [-9.5, 16.7]	93	1.2 ± 1.7 [-15.5, 9.5]	93
		Circumferential position, °
		Post-operative sizing	Pre-operative sizing
		Median ± SD	N ≤ 15°	Median ± SD	N ≤ 15°
		[range]	(%)	[range]	(%)
	Simulation	6.9 ± 6.1 [-44.3, 25.1]	96	4.8 ± 3.6 [-21.8, 19.

Disclosures:

JN. Albertini, D. Perrin and S. Avril are cofounders of the company PrediSurge SAS. S. Haulon is consultant for Cook Medical. F. Cochennec is proctor for Cook Medical.

The other authors have no conflict of interest.