Nicolas Demanget
email: nicolas.demanget@gmail.com

Pierre Latil

Laurent Orgéas

Pierre Badel

Stéphane Avril

Christian Geindreau

Jean-Noël Albertini

Jean-Pierre Favre

Severe Bending of Two Aortic Stent-Grafts: an Experimental and Numerical Mechanical Analysis

Keywords: Endograft, Finite Element Analysis, X-Ray Microtomography

and key terms

Stent grafts (SGs) are commonly used for treating abdominal aortic aneurysms (AAAs) and numerical models tend to be developed for predicting the biomechanical behavior of these devices. However, due to the complexity of SGs, it is important to validate the models. In this work, a validation of the numerical model developed in Demanget et al. (J. Mech. Behav. Biomed. Mater. 5:272-282, 2012) is presented. Two commercially available SGs were subjected to severe bending tests and their 3D geometries in undeformed and bent configurations were imaged from X-ray microtomography. Dedicated image processing subroutines were used in order to extract the stent centerlines from the 3D images. These skeletons in the undeformed configurations were used to set up SG numerical models that are subjected to the boundary conditions measured experimentally. Skeletons of imaged and deformed stents were then quantitatively compared to the numerical simulations. A good agreement is found between experiments and simulations. This validation offers promising perspectives to implementing the numerical models in a computer-aided tool and simulating the endovascular treatments.

Introduction

A widely used and minimally invasive technique to prevent abdominal aortic aneurysm (AAA) rupture, endovascular aneurysm repair (EVAR), involves the endovascular insertion of a stent-graft (SG) via the femoral arteries in order to exclude the aneurysm sac from the main blood flow. Most recent SGs consist of a combination of Nitinol stents stitched onto a polymeric woven fabric. EVAR is associated with lower post-operative morbidity and mortality compared with the invasive traditional surgical procedure to treat AAA. However, SG durability remains a significant issue. During the patient's follow-up, complications requiring secondary interventions may occur, such as endoleaks [START_REF] Albertini | Pathophysiology of proximal perigraft endoleak following endovascular repair of abdominal aortic aneurysms: a study using a flow model[END_REF][START_REF] Baum | Endoleaks after endovascular repair of abdominal aortic aneurysms[END_REF] , stent fracture [START_REF] Jacobs | Mechanical failure of prosthetic human implants: A 10-year experience with aortic stent graft devices[END_REF] , wear of the polymeric woven fabric [START_REF] Beebe | Results of an aortic endograft trial: Impact of device failure beyond 12 months[END_REF][START_REF] Chakfe | Influence of the textile structure on the degradation of explanted aortic endoprostheses[END_REF] as well as stenosis or thrombosis of the SG [START_REF] Carroccio | Predicting iliac limb occlusions after bifurcated aortic stent grafting: Anatomic and device-related causes[END_REF][START_REF] Cochennec | Limb graft occlusion following EVAR: Clinical pattern, outcomes and predictive factors of occurrence[END_REF] . Insufficient flexibility of the devices was often considered as one of the main causes responsible for these complications, especially when the SGs are deployed in tortuous AAAs. This evidence clearly emphasizes the critical need to better understand and model the mechanical behavior of SGs.

In that sense, finite element (FE) analyses can be suitable to better study the deformation mechanisms responsible for the above-mentioned SG-related complications, to compare the clinical and mechanical performances of manufactured SGs and/or to guide choices during the SG design process. Though a fair amount of work was devoted to the FE modeling of the mechanics of stents alone [START_REF] Auricchio | Carotid artery stenting simulation: From patient-specific images to finite element analysis[END_REF][START_REF] Favier | Influence of manufacturing methods on the homogeneity and properties of Nitinol tubular stents[END_REF][START_REF] Pelton | Fatigue and durability of Nitinol stents[END_REF] , very few numerical studies have been conducted on the assessment of SGs mechanics [START_REF] Demanget | Computational comparison of the bending behavior of aortic stent-grafts[END_REF][START_REF] Kleinstreuer | Computational mechanics of Nitinol stent grafts[END_REF][START_REF] Vad | Determination of Coefficient of Friction for Self-Expanding Stent-Grafts[END_REF] . This is partially due (i) to the complexity of SGs which combine stents stitched onto thin anisotropic and deformable membranes and (ii) to the difficulty to properly obtain the initial geometry of the SGs: (i) With the help of some simplifying assumptions (in particular for the stitching model), the first point can be overcome [START_REF] Demanget | Computational comparison of the bending behavior of aortic stent-grafts[END_REF][START_REF] Kleinstreuer | Computational mechanics of Nitinol stent grafts[END_REF][START_REF] Vad | Determination of Coefficient of Friction for Self-Expanding Stent-Grafts[END_REF] . For example, numerical models (including both stents and grafts) of manufactured SGs were developed to analyze the influence of the stent architecture on the bending behavior of SGs [START_REF] Demanget | Computational comparison of the bending behavior of aortic stent-grafts[END_REF] . However, no study was carried out to validate finely these SG numerical models and/or confront simulation results with experimental data.

(ii) A possible solution to prevent from the second difficulty consists in obtaining the initial geometries of SGs directly from 3D images, e.g. with X-ray microtomography. This imaging technique is an attractive tool for experimental mechanics [START_REF] Buffiere | In Situ Experiments with X ray Tomography: an Attractive Tool for Experimental Mechanics[END_REF][START_REF] Stock | X-ray microtomography of materials[END_REF][START_REF] Stock | Recent advances in X-ray microtomography applied to materials[END_REF] . Within the field of medical devices, it was purposely used in order to image the in-vitro deployment steps of coronary stents [START_REF] Connolley | X-ray micro-tomography of a coronary stent deployed in a model artery[END_REF] or to model their initial geometry after suitable image analysis subroutines [START_REF] Mortier | Automated generation of a finite element stent model[END_REF] . Furthermore, an automatic method has been recently developed to segment the stents of SGs from CT data [START_REF] Klein | Automatic segmentation of the wire frame of stent grafts from CT data[END_REF] . Besides, it is important to notice that if a proper mechanical testing device could be inserted inside a microtomograph, X-ray microtomography could also be used to catch SGs geometries when the SGs are subjected to a mechanical loading, as already carried out for other fibrous structures and architectures [START_REF] Badel | Simulation and tomography analysis of textile composite reinforcement deformation at the mesoscopic scale[END_REF][START_REF] Latil | Towards the 3D in situ characterisation of deformation micro-mechanisms within a compressed bundle of fibres[END_REF][START_REF] Le | X-ray phase contrast microtomography for the analysis of the fibrous microstructure of SMC composites[END_REF] . These in situ 3D observations could thus provide useful data in order to check the validity of SG numerical models. Within this context, the aim of the present study is to validate the numerical technique developed by Demanget et al. [START_REF] Demanget | Computational comparison of the bending behavior of aortic stent-grafts[END_REF] in order to predict the deformation of SGs. To do so, the methodology sketched in figure 1 was followed. Two commercially available SGs were subjected to bending tests and their geometries in the undeformed and bent configurations were scanned with an X-ray microtomograph. The image analysis subroutines developed in Latil et al. (2011) [START_REF] Latil | Towards the 3D in situ characterisation of deformation micro-mechanisms within a compressed bundle of fibres[END_REF] were then used in order to extract descriptors of the stent centerlines from the 3D images. The skeletons of the initial stent were also used to process relevant numerical models of the SGs that were subjected to the boundary conditions very close to those measured experimentally. The skeletons of the deformed and imaged stents were finally used to validate the numerical simulations.

b. 3D in situ observations of SGs bending

As sketched in figure 1, the aim of this experimental analysis was (i) to provide initial (undeformed) geometries of the two considered stents and (ii) to assess some quantitative comparison criteria from 3D images of the deformed stents. The whole process to perform experimental SG bending and to post-process tomographic data is reported hereafter. i. X-ray microtomography set-up 3D images of the undeformed and deformed SGs were obtained using a laboratory X-ray microtomograph (3SR Lab, Grenoble, France, RX Solutions apparatus). As illustrated in figure 3, it consists of a microfocus enclosed tube (1) (conical X-ray source, voltage from 40 to 150 kV, current intensity up to 500 µA) and a large detector (2) (195.07 × 243 mm 2 with a field of view of 1920 × 1536 pixels 2 ). For the present experiments, the generator voltage and current were respectively set to 100 kV and 290 µA. The acquisition rate was set to 10 images/s and 900 images were acquired on a 360° rotation (3) of the scanned SG. Besides, the 3D images of the sample were obtained from the 900 radiographs by using commercial reconstruction software (using backprojections algorithm, DigiCT, Digisens, France). Finally, a voxel size of 57 x 57 x 57 µm 3 was chosen in order to have the full structure of the SG together with rather good spatial definition of stent cross sections. If these settings could not provide a good representation of the polymer graft, it provides in return a very nice imaging of the stents together with short scanning times. ii. Detection of stent centerlines After proper denoising operations (standard smoothing and filtering algorithms), the 3D images could be segmented (with the software ImageJ) in order to have 3D representations of the stents (see figure 1). SG centerlines were then obtained by using the skeletonization algorithms implemented in the commercial software Avizo (VSG). The centerlines then consisted of a list of points whose spatial coordinates were expressed in the 3D image reference frame. As shown in figure 4, the noisy poly-lines defined from these points were finally smoothed using a homemade Matlab routine based on a moving average. iii. Bending device An experimental bending device was designed, manufactured and used to perform bending tests on the considered SG limbs. It is illustrated in figure 3. Most of its components were made up of polyvinyl chloride (PVC) in order not to disturb the X-ray beam during the SGs scans. The SG limbs ends were embedded on the brackets (6) and then mounted on the support bar (7) (see figure 3). For the Ao-SG limb, only the portion of the stent with a global diameter approximately equal to 12 mm was studied: the SG distal end was rolled up and fixed on a bracket. As a consequence, the length of the considered Ao stent which was subjected to the bending was about 100 mm. Proximal and distal Z-stents of Zs-SG were fully embedded on the brackets so that both Z-spiral stent ends were also attached on the brackets.

Only the central continuous Z-spiral stent was considered and studied in the present work: the length of the considered stent was about 100 mm.

The experimental device allowed to subject each SG end to opposite rotations about the xaxis, until a bending angle 1 2of 180° was reached (see figure 3). The maximum value of 180° for 1 was based on clinical data provided by our surgical team [START_REF] Albertini | Endovascular repair of abdominal aortic aneurysms in patients with severe angulation of the proximal neck using a flexible stent-graft: European Multicenter Experience[END_REF] . In order to maintain the SG in the yz-plane, the other two rotations were locked. Only the translation of the SG ends along the z-axis, i.e. the longitudinal direction of the SG, was let free in order to avoid spurious tension in the fabric during SG bending. Once the deformed SG reached its equilibrium on the experimental bending device, the translation along z-axis was locked in order to have a stable experimental device during tomographic acquisitions.

c. Bending simulation

Both geometry and mechanical behavior of the two considered SG limbs were modeled using the finite element analysis software Abaqus 6.8/Explicit ® (Simulia). The whole methodology to simulate SGs bending was similar to that carried out previously [START_REF] Demanget | Computational comparison of the bending behavior of aortic stent-grafts[END_REF] . It is briefly recalled hereafter.2 i. Material properties Stents of both limbs were made up of NiTi whose the superelastic properties were taken from literature [START_REF] Kleinstreuer | Computational mechanics of Nitinol stent grafts[END_REF] and given in table 1. The tension/compression asymmetry often observed in NiTi alloys [START_REF] Orgéas | Non-symmetric tension-compression behavior of NiTi alloy[END_REF][START_REF] Orgéas | Stress-induced martensitic transformation of a NiTi alloy in isothermal shear, tension and compression[END_REF] was neglected in this study for simplicity. In addition, it was assumed that stents' material points were subjected to a monotonic loading during the SGs bending, i.e. without unloading. As in Demanget et al. (2012) [START_REF] Demanget | Computational comparison of the bending behavior of aortic stent-grafts[END_REF] , this assumption was checked a posteriori and enabled us to use a simple and standard elasto-plastic constitutive model for the NiTi stents. Doing so, as sketched in figure 5, the standard yield stress corresponded to the onset of the forward stress-induced martensitic transformation 3 L S , below which the behavior corresponds to the elasticity of the austenite phase (Young's modulus E A , Poisson's ratio 1 A ).

Above the yield stress, a bilinear strain hardening was chosen to describe both the forward stress-induced martensitic transformation (up to a transformation strain 4 L ) and the elasticity of the martensite phase (Young's modulus E M , Poisson's ratio 1 M ). [START_REF] Demanget | Computational comparison of the bending behavior of aortic stent-grafts[END_REF] , by assuming as a first approximation that the fabrics behaved as orthotropic elastic plates, this methodology combines:

• several pure and plane strain tensile tests, to determine the in-plane orthotropic elastic behavior of the fabrics with longitudinal E L and transverse E T Young's moduli, a

Poisson's ratio 1 LT and a shear modulus G (see table 2),

• "nail tests", to estimate the longitudinal D L and transverse D T bending stiffnesses of the fabrics (see table 2). [START_REF] Hall | Comparison of element technologies for modeling stent expansion[END_REF] showed that this approximation yielded acceptable results when studying the global stent stress state.

Stents

Wire radius r (mm) 0.125 0.17

Number of elements 2756 2282

As in Elliott et al. (2002), undeformed stent geometries were directly derived from the smoothed list of points generated through tomographic data post-processing (see figure 1). A homemade Matlab routine was created purposely to sample these coordinates and generate the nodes as well as the connectivity of the B31 elements of the stent.

Since the 3D-reconstruction of the textile from tomography was not available, it was necessary to create geometry and mesh of the graft which was fixed onto the stent. The following procedure was chosen to perform this complex operation. A cylindrical tube meshed with linear triangular shell elements (S3 in Abaqus) was modeled and pressurized within the stent (considered as a rigid body at this stage) in order to fit stent geometry as close as possible (see figure 6). During the pressurization, translation about the z-axis was fixed at both graft ends. This first step of graft positioning was improved by changing temporally the fabric mechanical properties, i.e. E L was increased while E C was decreased in order to avoid graft bulging between stent turns. Once the graft was well positioned onto the stents, the stress field in the graft was set to zero. This configuration was defined as the undeformed configuration for the bending simulations. Likewise, sutures securing the stents and the graft together were modeled through the imposition of a bonding between graft and stent outer surfaces (tie constraint in Abaqus), i.e.

no sliding was allowed between stent and graft. Lastly, a self-contact algorithm was added in order to avoid self-penetration of SG components.

iii. Boundary conditions Numerical boundary conditions were applied on two reference points (RP1 and RP2) controlling both SG ends considered as rigid bodies. RP1 and RP2 were placed at the exact location of both pivot links, as depicted on figure 3. The SG portions mounted on brackets in the experimental device were considered as rigid bodies. Boundary conditions consisted in applying opposite rotations (until reaching 1 = 180°) about the x-axis at each RP while locking the two other rotations together with the x and y-axes translations. The displacement of SG ends along the z-axis was measured during experimental bending and then imposed numerically to adjust numerical boundary conditions to the nearest experimental measurements.

d. Quantitative comparison between experiments and simulations

This comparison was based on the analysis of the stents' centerline geometries in the deformed experimental and numerical configurations. As summarized in figure 1, these centerlines were obtained from 3D images as well as from simulation results. Thus, by noting s the curvilinear abscissa of the considered centerlines, the position x(s) of each centerline was characterized, together with its corresponding Frenet basis (t,n,b) [START_REF] Latil | Towards the 3D in situ characterisation of deformation micro-mechanisms within a compressed bundle of fibres[END_REF] , as shown in figure 4:

, , d d 1 , d d n t b t n x t × = = = s s κ (2)
where 6(s) is the local curvature of the considered centerline. A similar procedure was also carried out for the undeformed configurations, where the local centerline curvature was noted 6 0 (s). Note that the chosen spatial resolution together with the skeletonization/smoothing procedure induced a small systematic error 26 ≈ ±0.01 mm -1 on the estimation of the curvatures. Thereafter, by noting that the experimental and numerical length of the considered stents remained constant after bending, i.e. that stents' centerlines were subjected to negligible tensile elongation, it was then possible to follow the material points of the centerlines from the undeformed to the deformed experimental and numerical configurations.

The comparison of the experimental and numerical curvature 6(s) could then be achieved at each of these material points in the deformed configurations. Besides, the distance 2x(s)

between each associated couple of material points of the experimental (x exp (s)) and the numerical (x num (s)) deformed centerlines was also calculated (2x(s) = ||x exp (s) -x num (s)||), and a 3D position error

7(s) = 2x(s) / R (3)
was defined from the largest displacement along the stent, corresponding approximately to the global radius of curvature R of the bent stent (see figure 8). Lastly, from the knowledge of the stent wire radius r and the local curvatures in the initial 6 0 (s) and deformed 6(s) configurations, it was also possible to estimate the local maximal bending strain 4 b max (s) the stents were subjected to during their deformation:

0 max κ κ ε - = r b (4)
Taking into account the error induced during the estimation of the curvatures, note that such maximal bending strain were estimated with a very small error 24 b max = 2.10 -3 . Figure 8 strengthens the above-mentioned remarks, by comparing the 3D experimental and simulated shapes of deformed stents' centerlines for both SGs. As obvious from this figure, the simulated centerlines are close from experimental ones. However, some differences can be noted. For example, as revealed from the front views displayed in figure 8, the overall bending of the SGs, i.e. the bending of the SGs' centerlines, is somewhat more pronounced for the experimental SGs than for the numerical ones. Besides, by looking more closely at the deformed shapes of the stents in the case of Ao-SG, a significant difference between experimental and numerical centerlines is observed and concerned the fifth turn from the SG end #1: the turn of experimental stent seems to get inside the SG and generated a localized stent deformation while the global shape of numerical stent remained fairly homogeneous.

Results

a. Qualitative comparison

b. Quantitative comparison

To better analyze the results, the evolution of position error 7 along the curvilinear abscissa s of the bent stent centerlines was plotted for each SG in figure 9. The global radii of curvature R of the SGs were found to be equal to 20.5 mm and 24 mm for Ao-SG and Zs-SG, respectively (see figure 8). Results presented in this figure confirm the observations stated in the last subsection. Indeed, for Ao-SG (resp. Zs-SG), the position error oscillated between 0 and 20% (resp. 0 and 16%) with a mean value of 8.53% (resp. 6.41%) and the most important position error was approximately located at 570 mm (490 mm, respectively) from SG end #1. All these results are supported by figure 10 that plots the evolution of experimental and numerical curvatures 6 2along the curvilinear abscissa s of the bent stent centerlines. For Ao-SG, the curvature of the numerical (resp. experimental) stent centerline generally oscillates between 0.06 and 0.22 mm -1 (resp. 0.03 and 0.22 mm -1 ) with a mean of 0.143 mm -1 (resp.

0.144 mm -1 ). For Zs-SG, the curvature of the numerical (resp. experimental) stent centerline oscillates between 0 and 1.17 mm -1 (resp. 0 and 1.17 mm -1 ) with a mean of 0.278 mm -1 (resp.

0.275 mm -1 ). For both SGs, the comparison between experimental data and simulated results is satisfactory, keeping in mind the systematic error 26 ≈ ±0.01 mm -1 induced during the estimation of the curvatures. To strengthen the above remarks, the experimental and numerical maximal bending strains 4 b max recorded along the curvilinear abscissa s of the stents were finally estimated and compared (result not plotted here). For the two SGs, the experimental and numerical bending strains were found to be very close and very small, i.e. within the systematic error of 2.10 -3 .

This proves that during the studied bending of the SGs, no noticeable stent bending was observed. This also emphasizes the fairly good comparison between the experiments and the simulations.

Discussion

The objective of this study was to validate a numerical tool dedicated to predict the deformation of endovascular SGs, by comparing simulation results to what was observed from experiments. To run such a comparison, special attention was paid in order to minimize most of the possible error sources.

The mechanical behaviors of the stents and the grafts were modeled with appropriate constitutive laws, taking into account the possible superelastic behavior of NiTi and the strong anisotropy of polyester. In this last case, special mechanical tests were required and achieved prior to the simulation in order to gauge the stiffness and the anisotropy of the grafts.

The initial geometries of the experimental and numerical stents were set identical. This was possible thanks to the X-ray microtomography combined with dedicated image analysis subroutines.

The SGs were deformed with a special bending apparatus that was mounted within the microtomograph. This allowed (i) proper boundary conditions for the simulation to be captured directly from the experiments and (ii) the full final stent geometries to be determined to constitute an exhaustive experimental database for the comparison with the simulations.

By adopting this careful methodology, the very promising results that were obtained in this study bring the following comments.

The qualitative results displayed in figures 7 and 8 highlight an overall good agreement between experiments and numerical simulations of SGs' bending, except in some zones such as the fifth turn of the Ao stent: the observed difference is mainly due to the thick graft seam line, which was not modeled numerically. Indeed, Ao graft was composed of two pieces of graft sewn together along the entire length of the SG. It generated a high degree of heterogeneity and caused the penetration of the fifth turn of the spiral stent within the Ao-SG during the bending.

Regarding the quantitative results, i.e. the position errors 7 (see figure 9), the centerline curvatures 6 (see figure 10) and the maximal bending strains 4 b max , the agreement is still satisfactory. The mean (< 9 %) and maximal (< 20 %) position error between the simulated and imaged deformed stents remained fairly low for both SGs. Knowing that the mean position error for both SGs does not exceed 1.8 mm, the results of this work are acceptable if this value is compared to the observation scale commonly used in medical imaging.

Furthermore, curvatures of experimentally and numerically bent stents were very close. Thus, maximal experimental and numerical bending strains were identical and negligible.

By using the results of the simulations, the corresponding maximal Von Mises strain was found to be equal to 0.37 % for Ao-SG and 0.36 % for Zs-SG. These very low strains entirely validate our initial basic choice concerning the stent constitutive behavior: during the considered SG bending, the whole stents remained elastic.

To the best of the authors' knowledge, very few studies were carried out on the experimental validation of numerical models of stents alone from a quantitative point of view wrinkling, non-linear constitutive laws, self-contact problems), it is fair to consider that our SG numerical models are accurate and reliable enough to correctly reproduce the mechanical behavior of actual SG samples. Obviously, there are some differences between experimental and numerical results. However, these differences could be minimized by considering the following points in future simulations.

Most of the observed differences between the deformed imaged and numerical SGs probably come from the difficulty to model the initial shape of the grafts. Looking at the initial actual SG samples, one can clearly see that their fabrics form wrinkles (see figure 2)

while the modeled SGs exhibit a rather smooth fabric surface without wrinkle (see figure 6).

These initial real wrinkles constitute additional material available in the outer curvature region during the bending. Thus, they are suspected to induce a higher radius of curvature for the imaged SGs than for the numerical ones (see figure 8). A possible way to get rid of this would consist in improving the 3D imaging of the SGs, e.g. by enhancing the x-ray absorption of the grafts with contrast agents [START_REF] Davit | Imaging biofilm in porous media using X-ray computed microtomography[END_REF] .

Differences also come from the elementary model used for the stent/graft connection.

Indeed, the sutures between stent and graft were not modeled rigorously because this would have increased dramatically the complexity and the duration of calculations. This connection was considered perfect, although Ao sutures were coarse and allowed stent micro-movements.

The numerical boundary conditions were adjusted to the nearest experimental ones.

However, in the case of the Zs-SG, some technical problems were encountered during the experiments and induced some slight differences between experimental and numerical boundary conditions. Indeed, the extremities of Zs-SG were not modeled while they were used for the embedding of the SG in the experiments, leading to a slight shear of the fabric in the non-embedded part of the Zs-SG (see figure 8).2

Keeping in mind that the previous mentioned points should be tackled in future studies to improve the accuracy of the numerical SG models, this work has proven the relevance of the presented simulations from a mechanical viewpoint. To illustrate their usefulness, each bent SG was also subjected to an intraluminal pressure varying between the diastolic (75 mmHg) and systolic (150 mmHg) pressures (representative of a hypertensive patient). As an example, figure 11 shows the simulated deformed SGs with and without an intraluminal pressure of 150 mmHg. For both SGs, the visual comparison between pressurized and pressure-free geometries does not reveal any remarkable difference. For instance, by increasing the pressure, the fabric swells between stent turns, especially for Ao-SG whose fabric is softer and more flexible than the Zs-SG fabric (see table 2). Furthermore, the local curvature of the stent centerline was computed following the procedure adopted previously, showing a slight increase of this curvature (less than 10 % of the mean value) for both SGs. Likewise, the maximal stress value 3 S max and the maximal variations of stresses max(23 S ) in the stents for diastolic and systolic pressures were assessed and compared. First of all, for both SGs, 3 S max values revealed that the stents remained elastic for this loading case (3 S max = 238 MPa for Ao-SG and 3 S max = 241 MPa for Zs-SG). Thus, no marked martensitic transformation was observed within the stents. The intraluminal pressure variation is such that max(23 S ) = 123 MPa for Ao-SG and max(23 S ) = 70 MPa for Zs-SG. These values corresponded to a maximal variation of strain max(24 S ) of 0.31 % for Ao-SG and 0.17 % for Zs-SG. Even if such tests and related results are still quite far from the clinical reality, these type of results could be useful for predicting stents' fatigue and durability [START_REF] Miyazaki | Fatigue life of Ti-50 at.% Ni and Ti-40Ni-10Cu (at.%) shape memory alloy wires[END_REF][START_REF] Pelton | Optimisation of processing and properties of medical grade Nitinol wire[END_REF] .

Conclusion

Thanks to proper bending experiments achieved inside a x-ray microtomograph, the numerical approach used to model aortic SGs and developed in Demanget et al. (2012) [START_REF] Demanget | Computational comparison of the bending behavior of aortic stent-grafts[END_REF] could be validated. Indeed, skeletons of imaged and deformed stents were quantitatively compared to the numerical simulations, and a good agreement was found between experiments and simulations. This validation offers promising perspectives to implementing the numerical models in a computer-aided tool and simulating the endovascular treatments.

Figure 1 -

 1 Figure 1 -Scheme of the study outline.

Figure 2 -

 2 Figure 2 -Pictures of the two considered SG limbs.

Figure 3 -

 3 Figure 3 -Picture and scheme of the in situ bending device mounted in the X-ray

Figure 4 -

 4 Figure 4 -3D representation of the raw and smoothed data obtained from the Ao-SG

Figure 6 -

 6 Figure 6 -Graft positioning step by SG pressurization: 3D views and associated cross-

Figure 7

 7 Figure 7 gives a first qualitative comparison of deformed and simulated Zs-SG. A similar

Figure 7 -

 7 Figure 7 -Global shapes of actual (upper picture) and simulated (lower picture) bent Zs-SGs.

Figure 8 -

 8 Figure 8 -3D (left hand side) and 2D (right hand side) views of experimental and numerical

Figure 9 -

 9 Figure 9 -Evolution of the position error 7 along the stent centerline curvilinear abscissa s for

Figure 10 -

 10 Figure 10 -Curvatures 6 of both experimental and numerical deformed stent centerlines as

Figure 11 -

 11 Figure 11 -Deformed Ao (upper pictures) and Zs-SGs (lower pictures) after simulations with

Table 1 Material properties of Nitinol Parameters Values

 1 The lack of data concerning the mechanical properties of the SGs polyester fabrics led us to perform our own mechanical tests with fabric samples obtained from manufacturers. As described inDemanget et al. (2012)

	Austenite elasticity E A (MPa)	40000
	Austenite Poisson's ratio 5 A	0.46
	Martensite elasticity E M (MPa)	18554
	Martensite Poisson's ratio 5 M	0.46
	Transformation strain 4 L	0.04
	Start of transformation loading 3 L S (MPa)	390
	End of transformation loading 3 L E (MPa)	425
	Ultimate tensile strength 3 R (MPa)	827 -1172

Figure 5 -Schematic stress-strain curve of a superelastic Nitinol.

2

Table 2 Material properties of both fabrics

 2 Stent geometries were meshed with beam elements (B31 in Abaqus) instead of volume elements in order to reduce the computational cost of simulations (see table3). This simplification of stent modeling was used in several studies sinceHall and Kasper (2006)

	Parameters			Ao-fabric	Zs-fabric
	E L (MPa)			260 ± 4%	225 ± 10%
	E T (MPa)			110 ± 12%	1000 ± 10%
	5 LT			0.2	0.2
	G (MPa)			0.4	3.6
	Longitudinal ultimate strain 4 R	L		0.40	0.23
	Circumferential ultimate strain 4 R	C	0.13	0.18
	Longitudinal bending stiffness D L (10 -4 Nmm)	4.6	4.0
	Circumferential bending stiffness D C (10 -4
				2.0	18
	Nmm)
	ii. Geometry and mesh

Table 3 Geometrical and computational features of numerical SG models

 3

		Ao-SG	Zs-SG
	Degrees Of Freedom (DOF)	77676	75090
	Graft
	Fabric thickness (mm)	0.10	0.08
	Number of elements	26600	20336

Acknowledgements

The authors gratefully acknowledge the Région Rhône-Alpes and the ANR (research program ''3D discrete ANAlysis of micromechanisms of deformation in highly concentrated FIBre suspensions'', ANAFIB, ANR-09-JCJC-0030-01) for their financial support.


Charlotte Fillon
email: charlotte.fillon@ujf-grenoble.fr

Cécile Gautheron
email: cecile.gautheron@u-psud.fr

Pieter Van Der Beek

Peter Van Der Beek

Oligocene-Miocene burial and exhumation of the Southern Pyrenean foreland quantified by low-temperature thermochronology

Oligocene-Miocene burial and exhumation of the

Southern Pyrenean foreland quantified by low-temperature thermochronology

Introduction

The southern central Pyrenees have figured prominently in studies of orogenic wedge building, thrusting sequences and interactions between tectonics and surface processes, in part because of the exceptional exposure of syn-tectonic strata [START_REF] Puigdefàbregas | Tecto-sedimentary cycles and depositionnal sequences of the Mesozoic and Tertiary from the Pyrenees[END_REF][START_REF] Vergés | Thrust sequences in the southern central Pyrenees[END_REF]) and the quality of the ECORS seismic profile [START_REF] Ecors Pyrenees | The ECORS deep seismic profile reflection survey across the Pyrenees[END_REF] shot through this area.

Low-temperature thermochronology (mainly apatite fission-track; AFT) data [START_REF] Fitzgerald | Asymmetric exhumation across the Pyrenean orogen: implications for the tectonic evolution of a collisional orogen[END_REF][START_REF] Sinclair | Asymmetric growth of the Pyrenees revealed through measurement and modeling of orogenic fluxes[END_REF] provide evidence for a phase of rapid exhumation of the Axial Zone of the central Pyrenees during Late Eocene -Early Oligocene times, accompanied by the development of a crustalscale duplex (Muñoz 1992;[START_REF] Beaumont | Factors controlling the Alpine evolution of the central Pyrenees inferred from a comparison of observations and geodynamical models[END_REF]. The conglomeratic erosional products of this phase of rapid exhumation were hypothesized to have buried the southern flank of the Axial Zone in a late orogenic stage of its evolution, and to have been removed ~20 Myr later as post-orogenic incision of the Ebro drainage system reached the area [START_REF] Coney | Syntectonic burial and posttectonic exhumation of the southern Pyrenees foreland fold-thrust belt[END_REF]. Recent magnetostratigraphic studies [START_REF] Beamud | A middle to late Eocene continental chronostratigraphy from NE Spain[END_REF]2011) have confirmed the depositional ages of these conglomerates, while the link to exhumation of the Axial Zone is clearly established by their sedimentology [START_REF] Vincent | The Sis palaeovalley: a record of proximal fuvial sedimentation and drainage basin development in response to Pyrenean mountain building[END_REF].

However, the amount, extent and timing of excavation of these conglomerates have yet to be quantified in the foreland basin where low-temperature thermochronological data are scarce. The only currently available data are AFT ages and track-length distributions from the conglomeratic deposits themselves [START_REF] Beamud | Magnetostratigraphy and detrital apatite fission track thermochronology in syntectonic conglomerates: constraints on the exhumation of the South-Central Pyrenees[END_REF][START_REF] Rahl | Links between orogenic wedge deformation and erosional exhumation: Evidence from illite age analysis of fault rock and detrital thermochronology of syn-tectonic conglomerates in the Spanish Pyrenees[END_REF], which confirm the timing of rapid erosional unroofing of the Axial Zone and suggest that the deposits were sufficiently thick to result in partial AFT annealing in samples from their base. Two of us have recently constrained the thickness of the conglomerate deposits and the timing of their re-incision, using thermo-kinematic modelling constrained by the existing thermochronology dataset in the Southern Axial Zone [START_REF] Fillon | Post-orogenic evolution of the southern Pyrenees: constraints from inverse thermo-kinematic modelling of low-temperature thermochronology data[END_REF]. These models predict a thickness of the deposits of ~2 km on the southern flank of the Axial Zone, which was reached shortly after 30 Ma.

Valley incision is predicted to have occurred from Late Miocene times (9 Ma) onward, which we link to the base-level drop resulting from opening of the Ebro Basin to the Mediterranean [START_REF] Garcia-Castellanos | Interplay between tectonics, climate, and fluvial transport during the Cenozoic evolution of the Ebro Basin (NE Iberia)[END_REF][START_REF] Urgelés | New constraints on the Messinian sealevel drawdown from 3D seismic data of the Ebro Margin, western Mediterranean[END_REF]. We thus have proposed a scenario of topographic evolution from Axial Zone data that we extrapolated to the southern Pyrenean foreland, but no data were available to test our model predictions.

Low temperature apatite fission-track (AFT) and (U-Th)/He (AHe) thermochronology provides a powerful tool to constrain the thermal history of the foreland. The AFT and AHe thermochronometers are sensitive to the 50-120 °C and 40-110 °C temperature ranges respectively [START_REF] Farley | Helium diffusion from apatite: general behavior as illustrated by Durango fluorapatite[END_REF][START_REF] Shuster | The influence of artificial radiation damage and thermal annealing on helium diffusion kinetics in apatite[END_REF], therefore their combination can be used to constrain burial and exhumation in the fold-and-thrust belt from depths between ∼1.5 and 3.5 km, depending on the local geothermal gradient.

We present new AFT and AHe data from Late Cretaceous-Palaeocene "Garumnian" sandstones collected in the Tremp-Graus and Ager basins of the southern central Pyrenees (Fig. 1), in order to provide direct estimates of the thickness and extent of the overlying conglomerate deposits, as well as to further constrain the timing of excavation of the basin. The AHe thermochronometer is very sensitive and requires high-quality samples, rendering the application of this method challenging in sedimentary samples. However, we will show that despite limited and relatively scattered AHe ages, we are able to obtain consistent Mesozoic to Cenozoic exhumation histories for three samples located in the north, centre and south of the fold-and-thrust belt. We use a new thermal-history inversion code [START_REF] Gallagher | Transdimensional inverse thermal history modeling for quantitative thermochronology[END_REF]) that allows incorporation of variable AFT-annealing and AHe-diffusion kinetics.

Tectono-sedimentary evolution of the South Central Pyrenees

The south-central Pyrenean fold-and-thrust belt (also called South Central Unit, SCU) developed with the collision of the Iberian and European plates in the Late Cretaceous. Underthrusting of the Iberian plate below the European plate created a doubly-vergent Pyrenean wedge. The southern Pyrenees evolved as the pro-wedge by inversion of Cretaceous extensional structures [START_REF] Puigdefàbregas | Tecto-sedimentary cycles and depositionnal sequences of the Mesozoic and Tertiary from the Pyrenees[END_REF][START_REF] Bond | Inversion of a Lower Cretaceous extensional basin, south central Pyrenees, Spain. Basin Inversion[END_REF] followed by in-sequence thrust propagation towards the south [START_REF] Vergés | Thrust sequences in the southern central Pyrenees[END_REF]Muñoz 1992;[START_REF] Vergés | Eastern Pyrenees and related foreland basins: pre-, syn-and postcollisional crustal-scale cross-sections[END_REF][START_REF] Beaumont | Factors controlling the Alpine evolution of the central Pyrenees inferred from a comparison of observations and geodynamical models[END_REF]. The fold-andthrust belt propagated further in the SCU, compared to the regions east and west of it, by sliding on a thick Triassic evaporite layer (Fig. 1c). Thrusting is in-sequence at first order, with activation of the Boixols thrust initiated in the Late Cretaceous, followed by the Montsec thrust, which transported the Tremp-Graus Basin in a piggy-back manner from Paleocene to Late Eocene times (Puigdefàbregas et al. 1992), and finally the frontal Sierras Marginales thrust sheet, active from Middle Eocene to Late Oligocene times (see Fig. 1 for locations).

From the ECORS seismic profile (ECORS Pyrenees Team 1988; [START_REF] Choukroune | The ECORS Pyrenean deep seismic profile reflection data and the overall structure of an orogenic belt[END_REF], as well as modelling and thermochronological studies of the Southern Axial Zone [START_REF] Beaumont | Factors controlling the Alpine evolution of the central Pyrenees inferred from a comparison of observations and geodynamical models[END_REF][START_REF] Sinclair | Asymmetric growth of the Pyrenees revealed through measurement and modeling of orogenic fluxes[END_REF][START_REF] Fitzgerald | Interpretation of (U-Th)/He single grain ages from slowly cooled crustal terranes: A case study from the Transantarctic Mountains of southern Victoria Land[END_REF][START_REF] Gibson | Late-to post-orogenic exhumation of the Central Pyrenees revealed through combined thermochronological data and modelling[END_REF][START_REF] Metcalf | Thermochronology of a convergent orogen: Constraints on the timing of thrust faulting and subsequent exhumation of the Maladeta Pluton in the Central Pyrenean Axial Zone[END_REF], rapid exhumation of the internal units (Nogueres, Orri and Rialp, Fig. 1c) is known to have occurred by vertical stacking (Muñoz 1992;[START_REF] Vergés | Eastern Pyrenees and related foreland basins: pre-, syn-and postcollisional crustal-scale cross-sections[END_REF] during Middle Eocene to Early Oligocene times.

Thermo-kinematic modelling of the in-situ low-temperature thermochronology (AFT and AHe) dataset predicts exhumation rates of 2.8±0.3 km Myr -1 between 37 and 30 Ma in that area [START_REF] Fillon | Post-orogenic evolution of the southern Pyrenees: constraints from inverse thermo-kinematic modelling of low-temperature thermochronology data[END_REF]. This rapid exhumation was associated with strong erosion of the southern Axial Zone, the products of which were deposited in pre-existing palaeo-valleys as a thick pile of conglomerates currently mainly exposed in the Sis, Gurp and La Pobla massifs (Fig. 1b). These palaeo-valleys probably represented sediment transfer zones, supplying the Huesca fan system [START_REF] Vincent | The Sis palaeovalley: a record of proximal fuvial sedimentation and drainage basin development in response to Pyrenean mountain building[END_REF], one of the main drainage systems of the Southern Central Pyrenees (with the Luna fan system to the West) during Oligocene-Miocene times. The link between exhumation of the internal massifs and deposition of the conglomerates has been confirmed by provenance studies [START_REF] Vincent | The Sis palaeovalley: a record of proximal fuvial sedimentation and drainage basin development in response to Pyrenean mountain building[END_REF] and by AFT analysis of pebbles from the Sis conglomerates [START_REF] Beamud | Magnetostratigraphy and detrital apatite fission track thermochronology in syntectonic conglomerates: constraints on the exhumation of the South-Central Pyrenees[END_REF][START_REF] Rahl | Links between orogenic wedge deformation and erosional exhumation: Evidence from illite age analysis of fault rock and detrital thermochronology of syn-tectonic conglomerates in the Spanish Pyrenees[END_REF], which both reveal unroofing of the Axial Zone and deposition of its erosional products in the basin.

Present-day remnants of these extensive syn-to post-tectonic conglomerate deposits include the Senterada and La Pobla basins [START_REF] Beamud | A middle to late Eocene continental chronostratigraphy from NE Spain[END_REF][START_REF] Beamud | Magnetostratigraphy and detrital apatite fission track thermochronology in syntectonic conglomerates: constraints on the exhumation of the South-Central Pyrenees[END_REF], the Sis conglomerates [START_REF] Vincent | The Sis palaeovalley: a record of proximal fuvial sedimentation and drainage basin development in response to Pyrenean mountain building[END_REF], the Oliana fan (to the east of the CSU; Burbank et al. 1992b) and the Huesca fan (southwest of our study area; [START_REF] Friend | Evolution of the central part of the northern Ebro basin margin, as indicated by its Tertiary fluvial sedimentary infill. Tertiary Basins of Spain[END_REF]; they reach a maximum thickness of ~1000 m.

Magnetostratigraphic studies constrain deposition of the Sis conglomerates at ~40 to 27 Ma [START_REF] Beamud | A middle to late Eocene continental chronostratigraphy from NE Spain[END_REF][START_REF] Beamud | Magnetostratigraphy and detrital apatite fission track thermochronology in syntectonic conglomerates: constraints on the exhumation of the South-Central Pyrenees[END_REF], deposition of similar conglomerates to the east of the CSU, in the Oliana area, at ~40 to 36 Ma (Burbank et al. 1992a), and in the Sierras Marginales thrust sheet between 36.5 and 24.7 Ma [START_REF] Meigs | Ten-million-year history of a thrust sheet[END_REF]. The period of strong exhumation/erosion/deposition was synchronous with closure of the Atlantic connection of the Ebro foreland basin at 36 Ma [START_REF] Costa | Closing and continentalization of the South Pyrenean foreland basin (NE Spain): magnetochronological constrains[END_REF]. The basin became endorheic at that time and remained so until Late Miocene times [START_REF] Arenas | Latest Oligocene-Late Miocene lacustrine systems of the northcentral part of the Ebro Basin (Spain): sedimentary facies model and palaeogeographic synthesis[END_REF][START_REF] Garcia-Castellanos | Interplay between tectonics, climate, and fluvial transport during the Cenozoic evolution of the Ebro Basin (NE Iberia)[END_REF][START_REF] Arche | Some considerations on the initiation of the present SE Ebro river drainage system: Post-or pre-Messinian?[END_REF][START_REF] Urgelés | New constraints on the Messinian sealevel drawdown from 3D seismic data of the Ebro Margin, western Mediterranean[END_REF]. During its endorheic phase, the basin was progressively filled by conglomeratic deposits at its borders, grading to lacustrine sediments in its centre, and developed into a large overfilled foreland basin.

Mesozoic pre-depositional history

Recently, two independent studies have reported zircon fission-track (ZFT), U-Pb and (U-Th)/He (ZHe) ages of samples from the SCU (Filleaudeau et al. 2011;[START_REF] Whitchurch | Sediment routing system evolution within a diachronously uplifting orogen: Insights from detrital zircon thermochronological analyses from the South-Central Pyrenees[END_REF]. ZHe analysis of Garumnian sandstones of the Tremp Basin (sample ORC2; Filleaudeau et al. 2011) shows three main age populations (Triassic, Early Cretaceous and Late Cretaceous), interpreted to reflect distinct Mesozoic exhumation events affecting the source area(s). [START_REF] Whitchurch | Sediment routing system evolution within a diachronously uplifting orogen: Insights from detrital zircon thermochronological analyses from the South-Central Pyrenees[END_REF] applied detrital ZFT dating to Garumnian sandstones of the Ager basin and found the same Early and Late Cretaceous exhumation events, together with Carboniferous (Variscan) ZFT ages. A sample collected from the Aren formation (the stratigraphic unit just below the Garumnian in the Tremp Basin) presents Early Cretaceous and Carboniferous ZFT age peaks, lacking Late Cretaceous ages. The combination of these two datasets shows an important phase of Early Cretaceous source-area exhumation at 134±15 Ma (all uncertainties combined), with less well expressed events at ~80 Ma, ~225 Ma and 300-330 Ma. We will discuss later the imprint of these pre-depositional exhumation phases on our sample ages.

Low-temperature thermochronology

Five samples (AN01 to AN05) were collected along a N-S profile in Garumnian facies sandstones.

These continental deposits of Maastrichtian-Middle Palaeocene (65-60 Ma) age crop out extensively throughout the fold-and-thrust belt (Fig. 1b). Other lithologies were also sampled, including Eocene sandstones, Santonian turbidites and volcanic rocks of the Nogueres zone, but none of these provided sufficient high-quality apatite grains for thermochronological analysis.

Apatite Fission-Track thermochronology

Samples were prepared and analyzed at ISTerre (Grenoble, France). Apatite grains were separated from fine-to medium-grained sandstone samples using standard heavy-liquid and magnetic separation techniques. Apatite aliquots were mounted in epoxy, polished to expose internal crystal surfaces, and etched with 5.5 M HNO 3 for 20 s at 21 °C. Low-U muscovite sheets were fixed to the mounts, to be used as external detectors, and samples were irradiated in the FRM II Research Reactor at the Technische Universität München (Germany). Apatite samples were irradiated together with IRMM 540R dosimeter glasses and Durango and Fish Canyon Tuff age standards. After irradiation, the mica detectors of all samples and standards were etched for 18 minutes at 21 °C in 48% HF. The samples and standards were counted dry at 1250× magnification, using an Olympus BH2 optical microscope and the FTStage 4.04 system of [START_REF] Dumitru | A new computer-automated microscope stage system for fission-track analysis[END_REF]. Due to the low yield of apatite grains, all datable grains were counted for each sample. Fission-track ages were calculated using the zeta-calibration method and the standard fission-track age equation [START_REF] Hurford | The zeta age calibration of fission-track dating[END_REF]. The χ²-test and age dispersion [START_REF] Galbraith | Estimating the component ages in a finite mixture[END_REF][START_REF] Galbraith | Statistical models for mixed fission track ages[END_REF] were used to assess the homogeneity of AFT ages. We were able to measure horizontal confined track lengths and the lengths of the track etch pits that outcrop on the etched internal surface (D par ) in four samples.

Apatite (U-Th)/He analysis

Apatite grains were carefully selected according to their morphology at ISTerre. Each grain was placed into a platinum basket for He-extraction at Paris-sud University (Orsay, France). Two to five replicates were analyzed per sample. The platinum baskets were heated using a diode laser to 1030±50 °C during 5 minutes, allowing total He degassing; a reheat under the same conditions allowed checking for the presence of He trapped in small inclusions. The 4 He content was determined by comparison with a 1-2×10 -7 ccSTP 3 He spike. After He extraction, platinum baskets were placed into single-use polypropylene vials. Apatite grains were dissolved one hour at 90 °C in a 50 µl HNO 3 solution containing a known concentration of 235 U and 230 Th, and then filled with 1 ml of ultrapure MQ water. U and Th measurements followed a procedure similar to [START_REF] Evans | Determination of uranium and thorium in zircon, apatite, and fluorite: Application to laser (U-Th)/He thermochronology[END_REF]. The final solution was measured for U and Th concentrations by quadrupole ICP-MS (series II CCT Thermo-Electron at LSCE, Gif-sur-Yvette, France). Analytical accuracy and reproducibility for U-Th isotope measurements by using ICP-QMS were better than ±0.5% at 2j [START_REF] Douville | Rapid and accurate U-Th dating of ancient carbonates using inductively coupled plasma-quadrupole mass spectrometry[END_REF]). The analysis was calibrated using internal and external age standards, including Limberg Tuff, Durango and FOR3, which provided mean AHe ages of 16.8±0.7 Ma, 31.8±0.5 Ma, and 110.7±7.0 Ma respectively. These values are in agreement with literature data, i.e. 16.8±1.1 Ma for the Limberg Tuff [START_REF] Kraml | A new multi-mineral age reference material for 40Ar/39Ar, (U-Th)/He and fission track dating methods: The Limberg t3 tuff[END_REF]), 31.02±0.22 Ma for Durango (McDowell et al. 2005) and 112±10 Ma for the internal FOR3 standard.

Individual ages were corrected by each grain's ejection factor F T , determined using the Monte Carlo simulation technique of [START_REF] Ketcham | Accounting for long alpha-particle stopping distances in (U-Th-Sm)/He geochronology: Refinement of the baseline case[END_REF]; the equivalent-sphere radius has been calculated using the procedure of Gautheron and Tassan-Got (2010). The 1j error on AHe age should be considered at 8%, reflecting the sum of errors in the ejection-factor correction and age dispersion of the standards.

Results

Apatite fission tracks were counted and measured in 4 samples located in the north (AN04), centre (AN03, AN02) and south (AN01) of the fold-and-thrust belt (see Fig. 1 for location); the results are reported in Fig. 2 and Table 1. Only sample AN01, collected south of the Montsec thrust (Fig. 1), close to the Ager basin sample of ( 2011), shows a single age component (144±11 Ma). The other samples, for which more grains were counted, fail the χ 2 -test and have age dispersions >20%, with central ages between 64±5 and 77±6 Ma. Individual samples contained insufficient dated grains to deconvolve the sample ages into age components. However, since the samples were collected in the same stratigraphic unit and show similar age structures, we calculated age components from the combined data, using the radial-plotter software of [START_REF] Vermeesch | RadialPlotter: a Java application for fission track, luminescence and other radial plots[END_REF]. Three age peaks are found when pooling all single-grain ages: the major age component is Late Cretaceous in age (76.1±3.7 Ma), the second peak age is Late Paleocene (i.e., younger than the depositional age; 51.7±3.2 Ma), and a minor Early Cretaceous peak age is found at 142±10 Ma, with Early Cretaceous single-grain ages encountered in all samples (Fig. 2).

The youngest age population is clearly younger than the depositional age and single-grain ages <60 Ma are found in all samples except AN01, suggesting that they have been partially reset by postdepositional burial. Mean track lengths (MTL) are very short, ranging from 10.1 µm in AN01 to 12.2 µm in AN03 with standard deviations between 1.0 and 2.2 µm, indicating relatively slow long-term exhumation rates. Note, however, that only between 10 and 27 track lengths could be measured in these samples due to the low apatite yield.

Apatite (U-Th)/He analyses were also performed on four samples: AN01, 02, 03 and AN05 (Fig. 3, Table 2). A striking feature of the AHe ages is their large scatter; single-grain ages vary from 3.9 to 169 Ma. There appears to be some correlation between AHe ages and the effective uranium content (eU = [U]+0.24× [Th], expressed in ppm) of the grains, which varies between 4 and 25 ppm in samples AN01, 02 and 03 (Fig. 3a). The relationship between single-grain AHe ages and eU content reflects the increase of closure temperature as a function of the amount of α-recoil damage, for which eU content is a convenient proxy [START_REF] Shuster | The influence of natural radiation damage on helium diffusion kinetics in apatite[END_REF][START_REF] Shuster | The influence of artificial radiation damage and thermal annealing on helium diffusion kinetics in apatite[END_REF]. Moreover, the rapidly increasing ages for eU > 15 ppm, with less variation below this value (Fig. 3a), are consistent with a model in which He-retention increases non-linearly with the amount of α-recoil damage [START_REF] Shuster | The influence of natural radiation damage on helium diffusion kinetics in apatite[END_REF][START_REF] Flowers | Apatite (U-Th)/He thermochronometry using a radiation damage accumulation and annealing model[END_REF]. Only sample AN05 does not fit this correlation; we suspect that this may be related to its very high eU content and, in particular, quite extreme Th concentration compared to the other samples. Thus, the AHe ages cannot be interpreted directly, but the Late Miocene-Pliocene ages measured in samples AN01, AN02 and AN03 imply post-depositional burial and exhumation of the basin. We will test the timing and amount of burial / exhumation through numerical inversion of the data in the next section.

Thermal-history modelling

In order to test what constraints the data provide on the post-depositional thermal history of the samples, we use an inversion model [START_REF] Gallagher | Markov chain Monte Carlo (MCMC) sampling methods to determine optimal models, model resolution and model choice for Earth Science problems[END_REF][START_REF] Gallagher | Transdimensional inverse thermal history modeling for quantitative thermochronology[END_REF]) that allows extracting both optimal thermal histories and AFT annealing/AHe diffusion parameters by a Markov chain Monte Carlo (MCMC) sampling method. The inversion code incorporates recent kinetic models of He diffusion proposed by [START_REF] Flowers | Apatite (U-Th)/He thermochronometry using a radiation damage accumulation and annealing model[END_REF] and [START_REF] Gautheron | Effect of alpha-damage annealing on apatite (U-Th)/He thermochronology[END_REF], as well as the most recent multi-kinetic AFT annealing model of [START_REF] Ketcham | Improved modeling of fission-track annealing in apatite[END_REF]. The modelling proceeds from an initial randomly chosen time-temperature path and set of kinetic parameters, for which a probability that the model fits the data is calculated. Then the parameters are slightly perturbed, the probability of fitting the data is recalculated and compared to the initial model. The model with the highest probability is retained. This procedure is repeated a large number of times (the number of iterations being chosen by the user), providing a large collection of models with their associated probabilities that allow calculating model statistics (probability distributions of model parameters, etc.). A full explanation of the modelling procedure is provided in Gallagher (2012).

Model set-up

The parameter space (time, t and temperature, T) has been subdivided into three T-t boxes: from 300 Ma (beginning of the model run) to 70 Ma with temperatures between 140 °C and 0 °C, from 70 to 60 Ma with a temperature of 10±10 °C (e.g. surface conditions), and finally from 60 Ma to present, with a temperature range of 140 °C to 0 °C. By doing this, the only constraint we impose on the model is the deposition time. The results are the product of 200,000 iterations, which is a sufficient amount to obtain a stable and robust solution (see discussion in [START_REF] Gallagher | Transdimensional inverse thermal history modeling for quantitative thermochronology[END_REF]. We present results of inversions for samples AN01, 02 and 03, which were analysed with both AFT and AHe thermochronology; samples AN04 and AN05, which come from the same structural position but for which only AFT (AN04) or AHe (AN05) measurements were available, were combined for a test model but do not provide sufficient thermal constraints to obtain a well-defined T-t path.

As we use a multikinetic AFT annealing algorithm [START_REF] Ketcham | Improved modeling of fission-track annealing in apatite[END_REF]) in this study, the single grain-age counting data and track-length measurements were incorporated in the model and combined with the average D par (i.e. we do not take potential intra-sample kinetic variation into account). We acknowledge that the number of track lengths measured in the samples is less than optimal for inverse thermal history modelling; however, this limitation is offset by the fact that we have both AFT and AHe data and exploit variable annealing and diffusion kinetics.

The He-diffusion models of [START_REF] Gautheron | Effect of alpha-damage annealing on apatite (U-Th)/He thermochronology[END_REF] and [START_REF] Flowers | Apatite (U-Th)/He thermochronometry using a radiation damage accumulation and annealing model[END_REF] were used to reproduce He-diffusion behaviour in apatite. These two models include the influence of g-recoil damage and its annealing on He-diffusion kinetics; in particular, they predict He retentivity to increase either linearly [START_REF] Gautheron | Effect of alpha-damage annealing on apatite (U-Th)/He thermochronology[END_REF] or non-linearly [START_REF] Flowers | Apatite (U-Th)/He thermochronometry using a radiation damage accumulation and annealing model[END_REF] with the amount of g-recoil damage.

Predicted AHe ages by the two models mainly differ for low eU contents (15-25 ppm), because this is the range where the amount of g-recoil damage corresponds to the slope change in the diffusion law defined by natural and experimental data [START_REF] Shuster | The influence of natural radiation damage on helium diffusion kinetics in apatite[END_REF][START_REF] Shuster | The influence of artificial radiation damage and thermal annealing on helium diffusion kinetics in apatite[END_REF]. The simulations therefore predict slightly different thermal histories depending on which He-diffusion model is used; we will only present models using the [START_REF] Flowers | Apatite (U-Th)/He thermochronometry using a radiation damage accumulation and annealing model[END_REF] diffusion algorithm here; modelling results obtained using the [START_REF] Gautheron | Effect of alpha-damage annealing on apatite (U-Th)/He thermochronology[END_REF] diffusion algorithm are presented in Supplementary Figure 1.

The inversion procedure used here implicitly assumes that all grains share a single pre-depositional thermal history, whereas the zircon data discussed in Section 3 show that these sediments were derived from multiple sources with different pre-depositional histories. We will assess the effect of this simplification in the discussion (Section 7.2).

Inferred thermal histories

The models predict very similar T-t paths for all three samples (Fig. 4), in accordance with their similar stratigraphic and structural position, showing burial from their time of deposition until Miocene-Pliocene times, followed by exhumation until the present-day. The pre-deposition T-t path is poorly constrained for samples AN01 and AN02, in contrast to the model for sample AN03, which predicts a well-constrained pre-depositional history with linear cooling from the Early Cretaceous (130 °C at 100 Ma) to the time of Garumnian sandstone deposition. For this sample, the model predicts burial to a temperature of ~70 °C reached between 11 and 5 Ma, before final exhumation. Sample AN01 produced the widest range of single-grain AHe ages (7 Ma and 77 Ma); although the AFT age (144±11 Ma) suggests a single source age. The sample is also furthest from the preserved conglomeratic massifs. Nevertheless, the model predicts significant burial, to a maximum temperature of 80 °C, and an onset of Miocene exhumation between 20 and 10 Ma. The T-t path of sample AN02 is quite similar, although this sample appears to have been buried most deeply, reaching a temperature of up to 95 °C. The predicted onset of final exhumation is well constrained at 7 Ma. Finally, we observe that the maximum Cenozoic burial temperatures predicted by the models are consistent with their corresponding AFT ages; maximum predicted burial temperatures are higher for samples with younger central AFT ages.

Discussion

Sensitivity to eU variations

To test the thermal histories provided by inverse modelling and the match with our AHe ages, the "expected" thermal histories (i.e. the weighted-average T-t path for the probability distributions shown in Fig. 4; cf. Gallagher 2012) for the three samples have been introduced in a forward model [START_REF] Ketcham | Forward and reverse modeling of low-temperature thermochronology data. Low-Temperature Thermochronology:Techniques, Interpretations and Applications[END_REF] to predict AHe ages for a grain size equal to the average size of our analysed crystals (equivalent-sphere radius of 57 µm) and eU contents varying from 5 to 30 ppm, using the He-diffusion model of [START_REF] Flowers | Apatite (U-Th)/He thermochronometry using a radiation damage accumulation and annealing model[END_REF]. A comparison of predicted ages with our AHe data (Fig. 5) shows that both single-grain ages of sample AN02, as well as most single-grain ages of sample AN03 are in good agreement with the modelled path. Therefore, this test shows that the age scatter of these samples can be largely explained by their varying eU content. Conversely, some grains of samples AN01 and AN03 do not fit the modelled relationship between age and eU; therefore the measured ages could have been influenced by another parameter, such as a different pre-depositional history. We will test that possibility in the following section.

Influence of the pre-depositional history

The inverse modelling procedure we used cannot take into account variable pre-depositional histories of these detrital grains. However, the detrital ZFT and ZHe data of [START_REF] Whitchurch | Sediment routing system evolution within a diachronously uplifting orogen: Insights from detrital zircon thermochronological analyses from the South-Central Pyrenees[END_REF] and [START_REF] Filleaudeau | Thermo-tectonic evolution of the south-central Pyrenees from rifting to orogeny: insights from detrital zircon U/Pb and (U-Th)/He thermochronometry[END_REF] provide evidence for variability in timing and rates of source-area exhumation, as discussed in Section 3. We thus test to what degree such variable pre-depositional exhumation histories could explain the encountered dispersion of AHe ages.

The ZFT and ZHe data presented in Section 3 show pre-depositional exhumation ages between ~80 and ~300 Ma. From this starting point, we tested the influence of the pre-depositional history and eU content by performing forward modelling [START_REF] Ketcham | Forward and reverse modeling of low-temperature thermochronology data. Low-Temperature Thermochronology:Techniques, Interpretations and Applications[END_REF], using the AFT annealing model of [START_REF] Ketcham | Improved modeling of fission-track annealing in apatite[END_REF] and the AHe-diffusion model of [START_REF] Flowers | Apatite (U-Th)/He thermochronometry using a radiation damage accumulation and annealing model[END_REF], with the same parameter values as in Section 7.1. We imposed the post-depositional scenario from the inversion results presented previously and tested how the final AHe age varies as a function of eU, maximum postdepositional temperature (T max ) and onset time of initial (pre-depositional) exhumation (Fig. 6a). The results are presented as contours of predicted AHe ages as a function of eU and onset time in Fig. 6b and 6c, for T max of 70 and 80 °C respectively. This forward modelling differs from the inverse modelling presented previously in two important aspects, therefore inducing somewhat different results: first, the forward models use fixed values for the diffusion parameters, whereas the inverse models allow varying these within the uncertainties propagated from the original experiments [START_REF] Gallagher | Transdimensional inverse thermal history modeling for quantitative thermochronology[END_REF]. Second, we fix T max as well as its timing and the overall shape of the thermal history path in the forward models, whereas these have more degrees of freedom in the inversions and show, for instance, clear tradeoffs between T max and timing of initial (pre-depositional) cooling. We use these forward models to illustrate the effects of variable T max , eU and pre-depositional history on the measured AHe ages rather than to provide additional constraints on these parameters.

For the two burial temperatures tested, the modelling reveals the same patterns, in agreement with the relationship we expect between AHe age, eU content and T max . The modelled ages are older when initial exhumation starts earlier and for higher eU contents. The predicted ages are younger when T max increases; the maximum modelled AHe ages are 155 and 120 Ma for T max of 70 and 80 °C, respectively. Moreover, for the same eU, the age scatter decreases with increasing T max . For example, for an eU of 16 ppm (the average eU value of our grains), modelled ages vary from 10 to 105 Ma as a function of onset time of initial exhumation for T max = 70 °C, but only from 10 to 40 Ma for T max = 80 °C.

These forward models confirm the hypothesis that the pre-depositional history of the detrital grains can have a major effect on AHe age variations. With these results, we can also identify what variability in timing of pre-depositional exhumation would be required to explain the scatter in our AHe ages, by plotting the ages and eU values of our samples on the contour plots (Fig. 7b). First of all, we note that the forward model with T max = 70 °C provides the best fit to the combined data; this value is within the range of predictions of all inverse models. Secondly, when looking at the T max = 70 °C plot, we can conclude that all grains except AN011 fit with a pre-depositional exhumation phase starting between 150 and 90 Ma, which is in good agreement with the ZHe and ZFT age distributions of [START_REF] Filleaudeau | Thermo-tectonic evolution of the south-central Pyrenees from rifting to orogeny: insights from detrital zircon U/Pb and (U-Th)/He thermochronometry[END_REF] and [START_REF] Whitchurch | Sediment routing system evolution within a diachronously uplifting orogen: Insights from detrital zircon thermochronological analyses from the South-Central Pyrenees[END_REF], which record a major Early Cretaceous (~120-150 Ma) exhumation phase and a less well-expressed phase in the Late Cretaceous (~80 Ma).

These results are also in agreement with the expected model from the thermal-history inversion of AN02 and AN03, predicting an onset of initial exhumation before the Late-Cretaceous (i.e. >100 Ma).

Only the age of AN011 is outside of this range and suggests Triassic initial cooling, consistent with the occurrence of Triassic ZHe ages, which may result from a major volcanic episode associated with the emplacement of the Central Atlantic Magmatic Province [START_REF] Marzoli | Extensive 200-millionyear-old continental flood basalts of the central Atlantic magmatic province[END_REF]. Our previous observations showed that the age dispersion between the two grains of this sample could not be explained by their respective eU contents alone. We thus propose that variable pre-depositional exhumation histories, with at least one grain recording Triassic initial cooling, constitute another factor to explain the variable AHe grain ages.

To conclude, our forward modelling shows that the pre-depositional history of a detrital sample can considerably influence the measured AHe ages as well as the inferred temperature of burial. In our case, it seems that a combination of variable eU and variable timing of initial exhumation, consistent with higher-temperature detrital ZHe and ZFT data, can explain the scatter in AHe ages. Moreover, the forward models suggest that most apatite grains record an Early Cretaceous pre-depositional exhumation phase.

Cenozoic Burial and exhumation scenario

The inverse modelling results provide values for the amount and timing of Cenozoic burial heating that range from 70 to 95 °C, with final exhumation starting between 20 and 5 Ma. Even though the modelling predicts a variable range of maximum burial temperatures and associated timing, the firstorder pattern of the T-t paths in all cases shows significant burial during post-Eocene times, with subsequent exhumation starting in the Late Miocene-Early Pliocene.

We interpret the burial recorded by the samples as being due to deposition of the Late Eocene-Oligocene conglomerates produced by rapid erosion of the Axial Zone, and explain the subsequent exhumation by excavation of the modern southern Pyrenean river valleys. In this scenario, we do not take into account any tectonic activity that could be responsible for late-stage exhumation of the SCU (i.e., during Miocene times). The main reason for this choice is that there is no clear evidence for such tectonic activity in the SCU, mainly because no Miocene sediments are exposed in that area.

Moreover, as shown in Fig. 7, our AFT and AHe ages and the corresponding burial estimates predicted by the thermal modelling are homogeneous for all samples, despite their provenance from different thrust sheets. A few very young (Middle Miocene) AFT and AHe ages were reported further west, in the Bielsa massif [START_REF] Jolivet | Thermochronology constraints for the propagation sequence of the south Pyrenean basement thrust system (France-Spain)[END_REF]) and to the north of the study area in the Barruera massif [START_REF] Gibson | Late-to post-orogenic exhumation of the Central Pyrenees revealed through combined thermochronological data and modelling[END_REF], which have been interpreted as recording Miocene out-of-sequence thrusting. However, it is unclear how these results could be extrapolated to the SCU.

Estimating the thickness of the conglomerate cover requires knowledge of the local geothermal gradient. A previous interpretation of AFT data from the SCU [START_REF] Beamud | Magnetostratigraphy and detrital apatite fission track thermochronology in syntectonic conglomerates: constraints on the exhumation of the South-Central Pyrenees[END_REF]) used a geothermal gradient of 30 °C km -1 , as constrained by numerical modelling [START_REF] Zeyen | Integrated lithospheric modeling combining thermal, gravity, and local isostasy analysis: Application to the NE Spanish Geotransect[END_REF]) supposing a value for the thermal conductivity of sediments of 2.5 W m -1 K -1 . According to [START_REF] Fernàndez | Heat flow, heat production, and lithospheric thermal regime in the Iberian Peninsula[END_REF], however, the average present-day geothermal gradient for the SCU is 22±4 °C km -1 , significantly lower than the value for the Pyrenean Axial Zone (~33 °C km -1 ); this discrepancy is apparently due to the high thermal conductivity (2.47 to 3.22 W m -1 K -1 ) measured in the sediments.

As there is no consensus on the subject, we will use in the following a 30 °C km -1 geothermal gradient to estimate the sediment thicknesses, thus providing a conservative estimate of the amount of burial.

Using this value for the geothermal gradient and a surface temperature of 20 °C, the minimum amount of burial required to reach the T max recorded by our Garumnian samples can be estimated at 2.3 km for sample AN03, 2.6 km for sample AN01 and to 3.2 km for sample AN02, with final exhumation rates of 0.13 to 0.5 km Myr -1 . As the thickness of the Palaeocene-Middle Eocene sediments deposited in the Tremp-Graus Basin ranges from 1.2 km in the Montsec footwall area (sample AN01) to 1.6 km in the Tremp area (samples AN02 and AN03), our results imply a minimum thickness of post-Middle Eocene sediments of 700 m for sample AN03, 1.6 km for the sample AN02 and 1.4 km for sample AN01, as represented in Fig. 7. Note that, because the Late Eocene-Oligocene conglomerates are discordant on the Middle-Eocene and older sediments, it is difficult to estimate the exact thickness of the latter. Note also that for a lower geothermal gradient of 22 °C km -1 (see paragraph above), inferred burial depths are significantly higher and require 1.6, 2.4 and 2.7 km of post-Middle Eocene sediments, respectively, for samples AN03, AN01 and AN02.

Thermo-kinematic modelling of the in-situ AFT and AHe dataset in the Axial Zone of the central Pyrenees [START_REF] Fillon | Post-orogenic evolution of the southern Pyrenees: constraints from inverse thermo-kinematic modelling of low-temperature thermochronology data[END_REF] suggested that ~2 km of conglomeratic deposits once covered the southern flank of the central Axial Zone. The model also predicted re-incision and erosion of the conglomerates during the Tortonian (9.2±0.5 Ma), implying late-stage exhumation rates of ~0.3 km Myr -1 in the valley bottoms. The AHe ages confirm this interpretation and show continuous excavation of the basin from the Late Miocene-Pliocene to the present.

Finally, it is interesting to note that our inverse models do not reproduce an Eocene signal of exhumation linked to tectonic activity of the fold-and-thrust belt. However, the Late Eocene conglomerates rest unconformably on the earlier syn-tectonic sediments, implying an initial period of burial and unroofing between the Late Cretaceous and Late Eocene. We tested for this by forcing the thermal history models to reach near-surface temperatures in the Eocene but found that this did not affect the models to any significant extent. Therefore, if there was exhumation in the Eocene it could not have been very large (>1 km) otherwise the AFT and AHe systems would have recorded this event. Our modelling results thus support the idea of a strongly overfilled Ebro basin in the Oligocene-Miocene, characterised by up to 1.6 km of sediment aggradation at its northern edge.

Extent of late orogenic conglomerate deposits

The inferred amounts of burial are consistent with what we expected for samples AN02 and AN03, as these were collected close to the remnant conglomeratic massifs and the Axial Zone. A more surprising result is obtained for sample AN01, which is located in another structural unit, south of the Montsec thrust, and quite far from the Axial Zone. The closest conglomeratic outcrops to this sample are located further east and have been dated by magnetostratigraphy at 40 to 36 Ma (Oliana conglomerates; Burbank et al. 1992a). Nevertheless, the inversion results for sample AN01 suggest 2.6 km of burial before an onset of final exhumation between 10 and 20 Ma. These values are comparable to those obtained for the northern samples. Thus, the Ager Basin, south of the Montsec thrust (Fig. 1), seems to record the same post-Eocene burial/exhumation history as the Tremp Basin, implying that infilling by the Huesca fan sediments extended to that basin. The burial of the Ager Basin, which is not drawn in most paleo-geographic reconstructions (see Jones 2004 for example), could result from an extension of the Huesca fan further to the east, or from extension of the Oliana fan towards the west.

Conclusions

We have succeeded in modelling our dataset of AFT and AHe ages of detrital apatites to obtain consistent T-t paths using He-diffusion kinetics that are a function of radiation damage and its annealing. Our models show that the significant AHe-age scatter can be explained by variable eU content together with variable pre-depositional exhumation histories, consistent with inferences from published higher-temperature ZFT and ZHe data. Modelling of three samples predicts burial from the Late-Cretaceous to the Miocene-Pliocene to reach maximum temperatures of 70 to 95 °C, requiring at least 0.7 to 1.6 km of Late Eocene-Oligocene overburden. The inferred timing for the onset of exhumation ranges from 20 to 5 Ma, with exhumation rates of 0.13 to 0.5 km Myr -1 . These modelling results thus show similar post-orogenic burial and exhumation in the southern Pyrenean foreland as previously inferred for the southern Axial Zone and suggest a Late Miocene (pre-Messinian) onset of Ebro Basin incision. They confirm that several km of sediments covered the southern Pyrenean flank and filled the Ebro Basin, consequently to the onset of endorheism in the basin.

Acknowledgements:

This study was supported by INSU-CNRS through the European Science Foundation Topo-Europe programme "Spatial and temporal coupling between tectonics and surface processes during lithosphere

  inversion of the Pyrenean-Cantabrian mountain belt (PyrTec)". It forms part of CF's PhD project at Université Joseph Fourier, supported by the French Ministry for Research and Higher Education. Vincent Bouvier, Rosella Pinna and Louise Bordier are thanked for AFT sample preparation, U-Th chemistry and help during ICP-MS measurement at LSCE (Gif sur Yvette), respectively. Eric Douville is thanked for providing access to the ICP-MS. AHe age measurements at Orsay were funded by the ANR-06-JCJC-0079 project granted to C. Gautheron. The fission-track lab at ISTerre is supported by Université Joseph Fourier and INSU-CNRS. We thank Kerry Gallagher for providing a prepublication version of the QTQt thermal-history inversion code and for advise in running it.Constructive reviews by Hugh Sinclair and an anonymous reviewer, as well as comments by editor Andy Carter, significantly improved the manuscript.

Figure captions Figure 1 .

 captions1 Figure captions

Figure 2 .

 2 Figure 2. Radial-plot and histogram representations (Vermeesch 2009) of the AFT counting data of samples AN01, 02, 03, and 04 combined. The radial plot is centred on the central age of the combined samples (79 Ma); grey lines indicate peak ages and the black dashed line represents the depositional age (65 Ma). Samples are individualised by different grey-shading of the data points.

Figure 3 .

 3 Figure 3. a) AHe ages plotted as a function of effective uranium content (eU = [U]+0.24×[Th]) for the four samples analysed; gray dashed line in a) represents exponential fit to the data. b) Sample AN05has been separated from the others due to its high eU content and lack of correlation between eU and AHe ages, which contrasts with the other samples.

Figure 4 .

 4 Figure 4. Modelled T-t paths from joint AFT and AHe data for samples AN01, 02 and 03 (note variable timescales for these plots, constrained by the oldest single-grain AFT age). The black curves represent the expected model (weighted mean model) and its 95% confidence interval for the T-t paths; the yellow curve is the maximum likelihood model (best data fit). T-t paths are coloured according to their probability (scale on the right-hand side, which varies between samples). The gray boxes represent the prior constraints on the explored parameter space (see text for discussion) and dotted gray lines refer to the values of T max and burial time discussed in the text.

Figure 5 .

 5 Figure 5. Sensitivity of AHe ages to eU variations. The curves represent predicted AHe ages as a function of eU for the T-t paths of the expected models (cf. Fig. 4), and for eU varying from 5 to 30 ppm. The dots represent the AHe data shown in Fig. 3 and Table2.

Figure 6 .

 6 Figure 6. Effect of pre-depositional exhumation history on AHe ages. a) Forward model set up: AHe ages are predicted using the He-diffusion model of Flowers et al. (2009) for varying eU contents, T max and starting times of pre-depositional exhumation ("exhumation 1"). b) AHe ages modelled as a function of eU content and starting time of the pre-depositional phase of exhumation, for two different maximum burial temperatures (T max = 70 and 80 °C respectively). Measured ages of our samples are plotted as black squares, or represented as dashed lines when they do not resolve a starting time.

Figure 7 .

 7 Figure7. Topographic profile along the same transect as A-A' in Figure1b, showing the inferred palaeo-elevation of the Oligocene-Miocene deposits inferred from thermal-history modelling of the AHe and AFT data for samples AN02, AN03 and AN01 (dashed line is best estimate, orange band is uncertainty), compared to the inferred maximum elevation over the southern Axial Zone from inversion of in-situ thermochronology data[START_REF] Fillon | Post-orogenic evolution of the southern Pyrenees: constraints from inverse thermo-kinematic modelling of low-temperature thermochronology data[END_REF]. Yellow shading in Sierra de Gurp represents current exposure of Late Eocene-Oligocene conglomerates. Locations of major thrust faults in the SCU fold-and-thrust belt are indicated for comparison to Fig.1c.

Table 1

 1 Apatite Fission-Track results. s and i are the spontaneous and induced track densities measured; d is the induced track density in the external detector, the number of tracks counted(Ns, Ni, Nd) are in brackets; P(χ²) is χ²-probability (in %), D is the single-grain age dispersion. A P(χ²)<5 and/or D > 0.15 indicates that the data distribution contains multiple age populations ; MTL is the mean track length, with sd its standard deviation; Dpar is the average etch-pit width measured parallel to the C-axis. Measurements were performed by CF with a -factor =217.9±3.5 for IRMM-540 dosimeter glasses.

	Sample	position (lat/long)	Elevation (m)	no of grains	s (Ns) (10 6 cm -2 )	i (Ni) (10 6 cm -2 )	d (Nd) (10 6 cm -2 )	Pχ² (%)	D	Central age (± 1j, Ma)	MTL (µm)	sd (µm)	no tracks	Dpar (µm)	sd (µm)	no Dpar
	AN01	41.96/00.85	624	8	1.133 (489)	0.632 (273)	0.74 (4262)	32.34 0.02	144 ± 11	10.1	1.0	10	2.2	0.4	24
	AN02	42.16/00.89	436	20	0.7641 (999)	0.8513 (1113)	0.75 (4262)	<< 1	0.26	76.9 ± 6.2	11.3	1.4	19	2.1	0.2	36
	AN03	42.18/00.89	504	22	1.264 (1639)	1.493 (1936)	0.75 (4262)	<< 1	0.26	64.2 ± 4.6	12.2	1.6	27	2.2	0.2	61
	AN04	42.22/00.84	902	13	1.0715 (810)	1.205 (911)	0.75 (4262)	<< 1	0.20	74.1 ± 7.6	11.3	2.2	19	2.1	0.1	18