J.-P Groby

) C Lagarrigue

B Brouard

O Dazel

V Tournat

B Nennig

Using simple shape three-dimensional inclusions to enhance porous layer absorption

Keywords: numbers: 43.55.Ev, 43.20.Fn, 43.20.Ks, 43.20.Gp

The absorption properties of a metaporous material made of nonresonant simple shape three-dimensional inclusions (cube, cylinder, sphere, cone and torus) embedded in a rigidly backed rigid frame porous material is studied. A nearly total absorption can be obtained for a frequency lower than the quarter-wavelength resonance frequency due to the excitation of a trapped mode. To be correctly excited, this mode requires a filling fraction larger in the three-dimensions than in the two-dimensions for purely convex (cube, cylinder, sphere, and cone) shapes. At low frequencies, a cube is found to be the best purely convex inclusion shape to embed in a cubic unit cell, while the embedment of a sphere or a cone cannot lead to an optimal absorption for some porous materials. At fixed position of purely convex shape inclusion barycentre, the absorption coefficient only depends on and filling fraction and does not depend on the shape below the Bragg frequency arising from the interaction between the inclusion and its image with respect to the rigid backing. The influence of the angle of incidence is also shown. The results, in particular the excitation of the trapped mode, are validated experimentally in case of cubic inclusions.

I. INTRODUCTION

Acoustic porous materials are widely used in noise control applications because of their good sound absorbing properties in the middle and high frequency range. Nevertheless, porous materials suffer from a lack of absorption at low frequencies, when compared to their absorption capabilities at higher frequencies. The usual way to solve this problem is by multi-layering, while trying to keep the thickness of the treatment relatively small compared to the incident wavelength that has to be absorbed. The purpose of the present article is to investigate an alternative to multi-layering by embedding non-resonant simple shape three-dimensional inclusions in a rigidly backed porous sheet, thus creating a diffraction grating and therefore extending to 3-dimensional configurations previous studies [START_REF] Groby | Enhancing absorption coefficient of a backed rigid frame porous layer by embedding circular periodic inclusions[END_REF][START_REF] Nennig | A mode matching approach for modeling two dimensional porous grating with infinitely rigid or soft inclusions[END_REF] already conducted in 2-dimensional ones.

These last decades, several ways to avoid the problem of the porous material low frequency absorption have been proposed, mainly by combining resonant phenomena with the traditional viscous and thermal losses. Whatever the frequency, the idea behind is to excite modes of the structure that will trap the energy inside it and therefore enhance the absorption of the whole structure. The material properties were modeled either through homogenization procedures or by accounting for the whole wave phenomena: double porosity materials, whose properties are due to the microporous material resonance between the macro-pores [START_REF] Olny | Acoustic wave propagation in double porosity media[END_REF] , or porous materials with small radius (compared to the wavelength) cylindrical inclusions embedded in [START_REF] Tournat | Multiple scattering of acoustic waves and porous absorbing media[END_REF] , have been analyzed in the long wavelength limit, while metaporous materials [START_REF] Groby | Enhancing absorption coefficient of a backed rigid frame porous layer by embedding circular periodic inclusions[END_REF][START_REF] Lagarrigue | Parametric study of a metaporous made of inclusions embedded in a rigid frame porous material glued on a rigid backing[END_REF][START_REF] Nennig | A mode matching approach for modeling two dimensional porous grating with infinitely rigid or soft inclusions[END_REF] have been studied either semi-analytically or numerically in the entire frequency range of audible sound. In particular, the effect of the periodic embedment of both non-resonant and resonant inclusions in a porous layer on the absorption properties were studied in two-dimensions when the porous layer either is backed by a rigid backing [START_REF] Groby | Enhancing absorption coefficient of a backed rigid frame porous layer by embedding circular periodic inclusions[END_REF][START_REF] Lagarrigue | Parametric study of a metaporous made of inclusions embedded in a rigid frame porous material glued on a rigid backing[END_REF][START_REF] Nennig | A mode matching approach for modeling two dimensional porous grating with infinitely rigid or soft inclusions[END_REF] , possibly incorporating cavities [START_REF] Groby | Absorption of a rigid frame porous layer with periodic circular inclusions backed by a periodic grating[END_REF] , or radiates in a semi-infinite half-space [START_REF] Groby | Acoustic response of a periodic distribution of macroscopic inclusions within a rigid frame porous plate[END_REF] . Different inclusion shapes were studied [START_REF] Groby | Enhancing absorption coefficient of a backed rigid frame porous layer by embedding circular periodic inclusions[END_REF][START_REF] Hyun | Effects of inclusion shapes within rigid porous materials on acoustic performance[END_REF][START_REF] Lagarrigue | Parametric study of a metaporous made of inclusions embedded in a rigid frame porous material glued on a rigid backing[END_REF][START_REF] Nennig | A mode matching approach for modeling two dimensional porous grating with infinitely rigid or soft inclusions[END_REF] showing similar results at low frequencies.

a) Electronic address: Jean-Philippe.Groby@univ-lemans.fr

The increased absorption was explained by the excitation of local mode of the inclusion or of the cavities of the rigid backing, by the excitation of a trapped mode (TM) that traps the energy between the inclusion and the rigid backing, and by the excitation of the modified mode of the layer by coupling the layer mode with the Bloch waves originated by the added periodic heterogeneities. The effects of the inplane periodicity, whose main effect is the different excitation of modified mode of backed layer (MMBL), discussed in detail in [START_REF] Groby | Enhancing the absorption of a rigid frame porous layer by use of a rigid backing with three-dimensional periodic multi-irregularities[END_REF] in case of parallelepipedic irregularities of the rigid backing, will not be investigated here.

In this article, the influence of the periodic embedment of three-dimensional elementary shape inclusions in a porous layer rigidly backed is studied by use of an in-house Finite Element (FE) code. These simple shape three-dimensional inclusions cover a wide range of topological characteristics. For instance, cube, cylindre, sphere and cone have purely convex geometry, while the torus is not convex and presents some concave faces. Furthermore, the cone does not possess geometric symmetry with respect to its barycenter contrary to the other. The absorption coefficient of the whole structure for different shapes and orientations of the inclusions is calculated. Only square lattice are considered, i.e., the periodicities are identical in both directions of the plane.

The present paper is organized as follows. The problem is described in section II. The FE method is then validated numerically and experimentally in section III. In section IV, various numerical examples with different inclusion shapes are discussed.

II. FORMULATION OF THE PROBLEM

A. Description of the configuration

A parallelepipedic unit cell of the 3D scattering problem is shown in Fig. 1. Before the addition of the inclusions, the layer is a rigid frame porous material saturated by air (e.g., a foam) which is modeled as a macroscopically homogeneous equivalent fluid M p using the Johnson-Champoux-Allard model respectively. The upper semi-infinite material M a , i.e., the ambient fluid that occupies Ω a , and M p are in a firm contact at the boundary Γ L , i.e., the pressure and normal velocity are continuous across Γ L . A Neumann type boundary condition is applied on Γ 0 , i.e. the normal velocity vanishes on Γ 0 . Inclusions, with a common spatial periodicity d =< d 1 , d 2 , 0 >, are embedded in the porous layer and create a two-dimensional diffraction grating in the plan x 1 -x 2 . The periodicities d 1 and d 2 along the x 1 and x 2 directions are identical, d 1 = d 2 = d. In the following, five different infinitely-rigid simple-shape inclusions, depicted in Fig. 2, are considered : a cubic inclusion of edge a, a cylindrical inclusion of radius r and length h, a spherical inclusion of radius r, a conic inclusion of radius r and height h, and toric inclusions of neutral axis radius r and tore radius r t . A Cartesian coordinate system, with the three unit vectors i j , j = 1, 2, 3, is attached to each inclusion barycenter. The position and orientation of the inclusion are refered to by its barycenter x inc , its azimuth ψ inc , and its elevation θ inc = (i 3 , x 3 ).

The incident wave propagates in Ω a and is expressed by In each domain Ω α (α = a, p), the pressure field fulfills the Helmholtz equation

p i (x) = A i e i(k i 1 x 1 +k i 2 x 2 -k ai 3 (x 3 -L)) , wherein k i 1 = -k a sin θ i cos ψ i , k i 2 = -k a sin θ i sin ψ i , k ai 3 = k a cos θ i and A i = A i (ω) is the a) b) c) d) e) a h r r r h i i i 1 2 3 r r t 1 i 2 i 3 i x inc i 1 i 3 i 2 x inc x inc i 3 2 1 i i x inc i 1 i 2 3 i x inc
∇ • 1 ρ α ∇p α + (k α ) 2 ρ α p α = 0, (1)
with the density ρ α and the wavenumber k α = ω/c α , defined as the ratio between the angular frequency ω and the sound speed c α .

As the problem is periodic and the excitation is due to a plane wave, each field (X) satisfies the Floquet-Bloch relation

X(x + d) = X(x)e ik i ⊥ •d , (2)
where

k i ⊥ =< k i 1 , k i 2 ,
0 > is the in-plane component of the incident wavenumber. Consequently, it suffices to examine the field in the elementary cell of the material to get the fields, via the Floquet relation, in the other cells. The periodic wave equation is solved with a FE method. This FE method as well as the absorption coefficient calculation method are described in the appendix.

B. Material modeling

The rigid frame porous material is modeled using the Johnson-Champoux-Allard model.

The compressibility and density, linked to the sound speed through c p = 1/ (K p ρ p ) are 4,15

1 K p = γP 0 φ γ -(γ -1) 1 + i ω ′ c Pr ω G(Pr ω) -1 , ρ p = ρ a α ∞ φ 1 + i ω c ω F (ω) , (3)
wherein ω c = σφ/ρ a α ∞ is the Biot frequency, ω ′ c = σ ′ φ/ρ a α ∞ is the adiabatic/isothermal crossover frequency, γ the specific heat ratio, P 0 the atmospheric pressure, Pr the Prandtl number, ρ a the density of the fluid in the (interconnected) pores, φ the porosity, α ∞ the tortuosity, σ the flow resistivity, and σ ′ the thermal resistivity. The correction functions G(Pr ω) [START_REF] Champoux | Dynamic tortuosity and bulk modulus in air-saturated porous media[END_REF] and F (ω) [START_REF] Johnson | Theory of dynamic permeability and tortuosity in fluid-saturated porous media[END_REF] are given by

G(Pr ω) = 1 -iηρ a Pr ω 2α ∞ σ ′ φΛ ′ 2 , F (ω) = 1 -iηρ a ω 2α ∞ σφΛ 2 , (4)
where η is the viscosity of the fluid, Λ ′ the thermal characteristic length, and Λ the viscous characteristic length. The thermal resistivity is related to the thermal characteristic length [START_REF] Champoux | Dynamic tortuosity and bulk modulus in air-saturated porous media[END_REF] through σ ′ = 8α ∞ η/φΛ ′2 .

III. NUMERICAL AND EXPERIMENTAL VALIDATION

A large tortuosity (α ∞ = 1.42) 20 mm thick foam (Fireflex) sheet S1 and a medium resistivity (σ = 11500 N.s.m -4 ) 22 mm thick foam (Melamine) sheet S2 are used thorough the article. The parameters of these two porous materials are reported in Table I. These parameters have been evaluated using the traditional methods (Flowmeter for the resistivity and ultrasonic methods for the 4 other parameters, together with a cross-validation by impedance tube measurement) described in 2 . Extruded 2D configuration has first been used to validate the proposed 3D FE method by comparison with 2D results. This 2D configuration has been extensively validated with the multipole method 10 , with a modal approach [START_REF] Nennig | A mode matching approach for modeling two dimensional porous grating with infinitely rigid or soft inclusions[END_REF] and with FE method [START_REF] Groby | Enhancing absorption coefficient of a backed rigid frame porous layer by embedding circular periodic inclusions[END_REF] . This 2D FE method was based on a slightly different approach. This configuration consists in a 2 cm thick foam S1 with rigid circular inclusion of radius r = 7.5 mm embedded in with a spatial periodicity d = 2 cm. The comparision of the absorption coefficient calculated with the present FE method and the multipole method is presented in Fig. 3, showing a good agreement for both oblique an normal incidences. Around 10 linear elements per edges (2 cm) on the elementary cell leads to less than 1% of error on the absorption coefficient below 10 kHz and around 5% above. With the same mesh, quadratic elements yield to less than 1 % of error on the absorption curves thorough 20 kHz. Quadratic elements are used through this paper when calculations are run through 20 kHz, while linear elements are used when calculations are run for frequencies lower than 10 kHz. These results are in line with standard FE rules of thumbs, i.e., 10 linear elements per wavelength for around 1% of error.

The proposed method has also been validated by comparison with experimental results I) as the porous matrix and four aluminum cubes of 15 mm length edges as shown Fig. 4. The sample also contains 4 unit cells. The initial 22 mm-thick melamine foam was sliced and the material volumes that are then occupied by the inclusions were removed. The different elements are then gathered together with thin glue layers. The sample is placed at the end of an impedance tube, with a square cross-section and a side length of 42 mm, against a copper plug that closes the tube and acts as a rigid boundary. The tube cut-off frequency is 4200 Hz.

By assuming that only plane waves propagate below the cut-off frequency, the infinitely rigid boundary conditions of the tube act like perfect mirrors and create a periodicity pattern in the x 1 and x 2 directions with a periodicity of 21 cm, because 4 inclusions are embedded in the sample. This technique was previously used in [START_REF] Groby | Enhancing the absorption of a rigid frame porous layer by use of a rigid backing with three-dimensional periodic multi-irregularities[END_REF][START_REF] Lagarrigue | Parametric study of a metaporous made of inclusions embedded in a rigid frame porous material glued on a rigid backing[END_REF] and allows to determine experimentally the absorption coefficient of a quasi-infinite inplane periodic structure just with one or a correctly arranged small number of unit cells.

IV. NUMERICAL RESULTS

Numerical simulations have been performed for various geometric parameters, various shape inclusions and within the frequency range of audible sound, particularly at low frequencies. One of the main constraints in designing acoustically absorbing materials is the size and weight of the configuration. In this sense, a low frequency improvement implies good absorption for wavelength larger than the thickness of the structure.

The dimensions of the main studied configurations are listed in Table II.

A. Cubic inclusions

First, a a-edge cubic inclusion is considered in a cubic unit cell (d, d, L) = (2 cm, 2 cm, 2 cm). The cube is centered in the unit cell, i.e. x inc = (d/2, d/2, L/2). The inclusion is oriented such that (θ inc , ψ inc ) = (0, 0), i.e., the faces of the cube are parallel to those of the unit cell. Figure 6 depicts the evolution of the absorption coefficient at normal incidence for various edge lengths a from 0 mm to 17.5 mm leading to different filling fractions ff from 0 to ≈ 0.67.

Similarly to the analysis carried out in the two-dimensional case [START_REF] Groby | Enhancing absorption coefficient of a backed rigid frame porous layer by embedding circular periodic inclusions[END_REF][START_REF] Nennig | A mode matching approach for modeling two dimensional porous grating with infinitely rigid or soft inclusions[END_REF] , a trapped mode (TM) is excited by the presence of the inclusion. The TM excitation frequency ν t becomes lower when the filling fraction increases for fixed position of the barycenter. This frequency is always lower than the quarter wavelength resonance one, when the barycenter is higher or equal to half of the layer thickness L. The absorption coefficient possesses a maximum as a function of the edge of the cube. The absorption is nearly total for a = 16 mm edge cubic inclusion (configuration C1), which corresponds to a filling fraction of ff ≈ 0.51. When compared to the results obtained in the 2D case [START_REF] Groby | Enhancing absorption coefficient of a backed rigid frame porous layer by embedding circular periodic inclusions[END_REF] for a r = 7.5 mm infinitely long cylinder centered in the same matrix material with identical geometry (Figure 3), the required filling fraction for the absorption peak to be total is larger in the 3D case, i.e. ff ≈ 0.51, than in the 2D case, ff ≈ 0.44. In the same way, when the nearly total absorption peak is reached, ν t is higher in the 3D case (ν t = 2860 Hz) than in the 2D case (ν t = 2680 Hz).

Figure 7 depicts a cross-sectional view (x 1 -x 3 plane) of the pressure field magnitude inside the unit cell at x 2 = d/2 of the configuration C1 at ν t = 2860 Hz, showing that the wave is trapped between the inclusion and the rigid backing. Similarly to the 2D case, at fixed edge a, ν t becomes smaller when the distance between the inclusion and the rigid backing is larger, i.e., when x inc 3 increases. Therefore, this increased absorption could be explained by the first Fabry-Perot interference between the inclusions and its image with respect to the rigid backing, as can be shown in the transmission case. Nevertheless, the Fabry-Perot interference appears when the vertical distance between two adjacent inclusions is equal to the quarter of the projection on the vertical axis of the wavevector, which is impossible for two reasons: 1. because a quarter-wavelength is not possible with the rigid backing 2. because ν t would be identical for each cube edges and equal to the quarter-wavelength resonance frequency for a centered inclusion, if true.

Once the optimal edge size is determined to have a nearly total absorption peak at ν t , the absorption coefficient is calculated for the total frequency range of audible sound in Fig. 8. The first Bragg interference, which corresponds to the maximum of reflected energy leads to a minimum of absorption around 6000 Hz. This corresponds to constructive interferences between the scattered waves by the inclusion and its image with respect to the rigid backing. This minimum appears when 2x inc 3 is equal to half of the wavelength in case of normal incidence.

The modified mode of the backed layer (MMBL), which traps the energy inside the porous plate and corresponds to an evanescent wave in the upper half plate and a propagative wave inside the porous plate is excited at ν M M BL ≈ 17000 Hz. This corresponds to the intersection of the longitudinal mode of the porous plate, which cannot be excited by a plane incident wave without heterogeneity, with the first Bloch wave, as explained in [START_REF] Groby | Total absorption peak by use of a rigid frame porous layer backed with a rigid multi-irregularities grating[END_REF][START_REF] Groby | Enhancing absorption coefficient of a backed rigid frame porous layer by embedding circular periodic inclusions[END_REF][START_REF] Groby | Enhancing the absorption of a rigid frame porous layer by use of a rigid backing with three-dimensional periodic multi-irregularities[END_REF] . This mode is excited at relatively high frequency because the periodicity is here relatively small (d = 2 cm). The enhanced absorption due to MMBL was extensively explained in case of parallelepiped irregularities of the rigid backing in [START_REF] Groby | Enhancing the absorption of a rigid frame porous layer by use of a rigid backing with three-dimensional periodic multi-irregularities[END_REF] and used in [START_REF] Molerón | Control of absorption and directivity properties of noise barriers using periodic surfaces[END_REF] .

The absorption coefficients calculated in the case of a centered a = 12.5 mm (ff ≈ 0.24) edge cube with upper and lower interfaces parallel to Γ L and Γ 0 rotated around i 3 are almost identical below the first MMBL. In particular, the absorption coefficients calculated for ψ inc = 0 and ψ inc = π/4 (θ inc = 0) are identical, while it is well known, [START_REF] Goffaud | Theoretical study of a tunable phononic band gap system[END_REF][START_REF] Pichard | Experimental demonstrations in audible frequency range of band gap tunability and negative refraction in two-dimensional sonic crystal[END_REF] , that a 2D sonic crystal composed of square cross-section scatterers possesses full bandgap when ψ inc = π/4 and only a bandgap at normal incidence (ΓX), when ψ inc = 0. Some differences can be noticed near grazing incidence, but are not significant in case of an acoustic excitation by an airborne plane wave impiging the structure from the upper half-space. The bandgap were shown and were clearly of interest because the excitation was performed in between the parallelepipedic scatterers in [START_REF] Molerón | Sound propagation in periodic urban area[END_REF] .

Parallelepiped scatterers were tested, exhibiting similar influence on the absorption. The advantage is that ν t can be smaller because the parallellepiped can be placed further from the hard backing Γ 0 , letting x inc 3 being larger, but the filling fraction is then lower and a nearly total absorption peak is then difficult to reach at this frequency.

B. Other simple shape inclusions at normal incidence

We first focus on the three purely convex simple inclusion shapes that possesse geometric symmetry with respect to their barycenter.

The absorption coefficients for different simple shape inclusions embedded in the same porous material with the same periodicity and at identical filling fraction are calculated and compared. For identical material layer and dimension of the unit cell, the large filling fraction required, ff ≈ 0.51, to reach an almost total absorption coefficient at ν t in case of cube would impose a r ≈ 9.9 mm radius sphere. Such a filling fraction is also impossible to realize in practice when spheres are embedded with a periodicity d = 2 cm. This also means that in a cubic unit cell, a cubic inclusion seems to be the best choice in the sense that this inclusion shape enables large filling fraction when compared with other simple shape inclusions, like sphere or cylinder. While the embedment of spheres in a porous materials probably do not lead to an optimal absorption, i.e. a unit amplitude absorption, at low frequency, this solution is used in practice [START_REF] Fuller | Sound absorption using poro-elastic acoustic metamaterials[END_REF] .

The cube edge is also decreased to a = 15 mm in order for the filling fraction to be ff ≈ 0.42. A comparison between the absorption coefficients calculated for centered inclusions in the unit cell of a a = 15 mm cube (configuration C2), h = 15 mm and r = 8.5mm cylinder with different orientations (configuration C3: θ inc = 0 vertical cylinder and θ inc = π/2 horizontal cylinder), and a r = 9.3 mm sphere (configuration C4) is shown in figure 9. Several observations can be made. First, for fixed properties of material layer, inclusion barycenter position periodicity and filling fraction, the absorption coefficient is identical for the different inclusion shapes below the first Bragg frequency. This means that the absorption coefficient is mainly driven by the filling fraction below this frequency.

Second, whatever the inclusion shape, the MMBL is excited at the same frequency ν M M BL , because it only depends on the layer material properties and periodicity. Thirdly, absorption coefficients are almost identical between a vertical cylinder (configuration C3, θ inc = 0) and a cube (configuration C2). This means that at higher frequency flat interfaces parallel with the boundaries Γ 0 and Γ L have more influence on the absorption coefficient than the lateral shape. Fourthly, absorption coefficients for flat interface inclusions parallel with Γ L and Γ 0 are completely different from those for non-flat interface inclusions. Fifthly, while cubic inclusion enable a larger filling fraction, spherical and horizontal cylindrical inclusions lead to larger absorption at higher frequency. The higher order Bragg interferences seem to be more excited than in case of cube and vertical cylinder. This is in accordance with the conclusion of 23 in which it is shown in 2D that square cross-section scatterer in square lattice provides a larger bandgap, than other scatterer shapes. The absorption is almost always larger than the one of the homogeneous layer between the Bragg frequency and the first MMBL frequency for spheres and horizontal cylinders. In average, the best absorption coefficient is obtained with an horizontal cylindrical inclusion.

Calculations were also perform for each inclusion shape when the filling fraction increases. For each inclusion shape, ν t decreases and the absorption amplitude increases with increasing ff at fixed barycenter position. For cylinders, it was possible to find a possible to manufacture configuration leading to a nearly total absorption peak, while it was not the case of a sphere. Once the optimum is reached, if the filling fraction ff is still increased, both frequency ν t and amplitude of the associated absorption peak decrease.

The last two shapes studied here present particularities: the cone does not present geometric symmetry with respect to its barycenter and the torus is not of convex shape.

Concerning conic inclusions, besides an apparent dependance of ν t on the orientation of the cone, all the phenomena are in accordance with the previously studied shapes. Figure 10(a) depicts the absorption coefficient of a h = 15 mm, r = 8.5 mm cone, configuration C5, embedded in a porous sheet S1, and geometrically centered in the unit cell for different orientations: cone up, x inc = (10 mm, 10 mm, 6.25 mm), θ inc = 0; cone horizontal, x inc = (6.25 mm, 10 mm, 10 mm), θ inc = -π/2; and cone down, x inc = (10 mm, 10 mm, 13.25 mm), θ inc = π. The corresponding filling fraction is ff ≈ 0.15. It is impossible to reach a sufficiently large filling fraction to obtain a nearly total absorption peak with the conic inclusion in this case. When the cone is horizontal, the x 3 -coordinate of the barycenter is located in the middle height unit cell, i.e. x inc 3 = L/2. The configuration being periodic, it is possible to find a unit cell such that the barycenter is the center of the unit cell. In this case, the absorption peak associated with the excitation of the trapped mode is very close to the one of a a = 10 mm cube, ff = 0.125 (rigorously the edge of the cube should be a = 10.5 mm for ff ≈ 0.15). When the cone is oriented towards the air medium, i.e. cone up, the barycenter is lower than the middle of the unit cell, while when the cone is oriented towards the rigid backing, i.e. cone down, the barycenter is higher than the middle of the unit cell. This dependence is identical to the one already noticed in case of a cube, a sphere and a cylinder, i.e. ν t decreases when x inc 3 increases.

The toric shape is more interesting and more complex. The absorption coefficients of r = 5 mm and r t = 4.75 mm torus (configuration C6) embedded in the same S1 porous sheet, centered in the unit cell, i.e., x inc = (10 mm, 10 mm, 10 mm), with two different orientations, θ inc = 0 and θ inc = π/2 (ψ inc = 0), are shown in Figure 10(b). For this shape, a nearly total absorption peak can be obtained at ν t = 2680 Hz and for a filling fraction ff ≈ 0.28, i.e., both frequency and filling fraction are lower than those obtained in the case of purely convex shapes. This phenomenon is due to the non-convex shape which enables the volume below the inclusions to be larger in case of a torus than in case of purely convex shapes. This relatively low filling fraction associated with the toric shape also allows to reach a nearly total absorption peak at a very low frequency (ν t = 2100 Hz) when x inc 3 is increased at x inc 3 = 3L/4, Fig. 10(b). Nevertheless, this last shape should be considered as a particular case of a simple 3D shape, and can be considered at high frequency as a resonant one.

C. Numerical results at oblique incidence

The structure is obviously anisotropic, first because of the periodicity patterns itself, but also because of the inclusion shape. Figure 11 depicts the absorption coefficient of the configuration C1 when the layer material is the foam S1 for θ i ∈ [0, π/3] (ψ i = 0) and for ψ i ∈ [0, π/4] with θ i = π/4. For symmetry reason, performing calculation for larger ψ i is useless. The absorption coefficients for ψ i = π/3 and ψ i = π/6 when θ i = π/4, were found to FIG. 10. Absorption coefficients of a) a h = 15 mm and r = 8.5 mm cone, configuration C5, in a 2 cm thick S1 layer, when the cone is up θ inc = 0, cone horizontal θ inc = -π/2, and cone down θ inc = π (the absorption coefficient of a a = 10 mm cube is also plotted (o)) and b) a r = 5 mm and r t = 4.75 mm torus, configuration C6 in a 2 cm thick S1 layer, centered in the unit cell when θ inc = 0 (dashed-dotted line) and θ inc = π/2 (solid line), and when

x inc 3 = 3L/4 for θ inc = 0 (dotted line). The absorption coefficient of the homogeneous layer is depicted by the dashed line on a) and b). be identical, which provides another validation of the method. The frequency of excitation of the trapped mode is slightly modified when θ i increases: ν t increases when θ i increases.

The absorption is nearly total up to θ i ≈ π/3. At fixed θ i , ψ i only influences the results for frequencies higher than the first Bragg frequency. Similar results were found for the other inclusion shapes. for ψ i = 0 and θ i = 0, θ i = π/6, θ i = π/4, and θ i = π/3, and b) for θ i = π/4 and ψ i = 0, ψ i = π/6, and ψ i = π/4.

V. CONCLUSION

The influence of the periodic embedment of non-resonant three-dimensional simple shape inclusions (cube, cylinder, sphere, cone and torus) in a rigidly backed porous layer modeled in the rigid frame approximation is studied numerically and experimentally. Similarly to the 2D case, the absorption coefficient of these structures is enhanced, because of the excitation of different type of modes in particular at low frequency because of the excitation of a trapped mode that traps the energy between the inclusions and the rigid backing. This entrapment is nearly total for a specific filling fraction which is larger in 3-D than in 2-D and the frequency of excitation of this trapped mode goes down when the filling fraction increases.

The FE results are validated experimentally in case of cubic inclusions. Focusing on the absorption enhancement at low frequency, a cube is better than a sphere in a cubic unit cell because it allows a larger filling fraction. It is shown that in some cases, it is impossible to obtain a nearly total absorption peak by embedding spheres because the required filling fraction cannot be reached. At a fixed filling fraction and position of the barycenter, the absorption coefficients are identical below the first Bragg frequency for the various nonresonant inclusions. In other words, for only convex inclusions, the absorption coefficient only depends on the filling fraction and position of the barycenter and not on the shape of the inclusions below the first Bragg frequency. The torus required a lower filling fraction in order to reach a nearly total absorption peak at a frequency which is smaller than for the other shapes. Differences in terms of absorption coefficient are particularly noticeable at higher frequencies than the first Bragg frequency, and allow to classify the inclusion shape, either possessing faces parallel to the interface porous/air or the the rigid backing, or not. In particular, horizontal cylinders and torus lead to larger absorption coefficients than the other shape inclusions. The so-designed structures are obviously anisotropic. The trapped mode is poorly affected by the angle of incidence, when compared to the modified mode of the backed layer. At a fixed elevation angle of incidence, the trapped mode is not affected by the azimuthal angle. These results offers large persepctives in terms of absorption enhancement of porous layer through optimization procedures and embeddement of 3D resonant inclusions.

APPENDIX A: NUMERICAL MODEL 1. Finite element formulation

The weak form associated to the Helmholtz equation (1), required for FE resolution, is

- Ω α 1 ρ α ∇q α • ∇p α dΩ + Ω α (k α ) 2 ρ α qα p α dΩ = - ∂Ω α 1 ρ α qα ∇p α • n dΓ (A1)
for all the test functions q α , α = a, p. The bar qα denotes the complex conjugate of q α . The solution being periodic, the pressure fields p α and the test function q α are demodulated so as to use the periodic part of the pressure denoted pα such that pα = e -ik i ⊥ •d p α , and of the test function qα = e ik i ⊥ •d qα . Introducing these expressions in the weak form (A1) leads to

- Ω α 1 ρ α ∇q α • ∇p α dΩ + Ω α (k α ) 2 ρ α qα pα dΩ = - ∂Ω α 1 ρ α qα ∇p α • n dΓ, (A2)
where the shifted gradient operator reads as ∇ = ∇ -ik i ⊥ , ∇ = ∇ + ik i ⊥ . The normal derivative of the pressure vanishes on the bottom surface Γ 0 and on Γ inc because the scatterer is infinitely rigid. The boundary term pairs on the lateral boundaries Γ r , Γ l and Γ b , Γ f vanish due to the periodicity of p and q. The pressure and the normal velocity are continuous on the coupling boundary between the air and the porous material

Γ L , p a = p p , (A3) 1 ρ a ∂p a ∂n = 1 ρ p ∂p p ∂n . ( A4
)
The second condition is automatically accounted for by removing the boundary integral on Γ L . The continuity of the pressure or more precisely of pa = pp is ensured by the use of Lagrange multiplier λ and its associated test function ς. To do that, the two following integrals are evaluated on the boundary Γ L

Γ L ς(p a -pp ) dΓ + Γ L ( qa -qp )λ dΓ. ( A5
)
Note that using Lagrange multiplier is not mandatory here and algebraical condition or penalization can be used. The main interests are to deal with Hermitian matrix and to ease the implementation.

For the sake of computation, the radiating boundary Γ ∞ of height L ∞ that truncate Ω a is introduced, Fig. 1. The radiation of the elementary cell can be handled in the FE method with (i) DtN map, (ii) PML or (iii) modal expansion. Note PML is not suitable for the long wave limit (λ ≫ d) and are not safe for this application. In this paper, the last solution is preferred for its robustness and because the modal coefficient are required to compute the absorption coefficient. In practice, only a few modes are propagative. The FE degree of freedom on Γ ∞ are removed from FEM matrix in favor of modal amplitude.

The boundary term on Γ ∞ is easily computed thanks to Floquet mode orthogonality. On the plane boundary Γ ∞ , the total pressure reads p a = p i + p ∞ and the scattered pressure can be expanded as

p ∞ (x, ω)| Γ∞ = m,n∈Z 2 A mn φ mn , (A6)
with

φ m,n = 1 √ S e i(k 1m x 1 +k 2n x 2 ) , (A7)
where A mn are the amplitudes of the Floquet mode (n, m),

k 1m = k i 1 + m 2π d , k 2n = k i 2 + n 2π d , k a 3mn = (k a ) 2 -k 2 1m -k 2 2n
, and S = d 2 is the surface of the elementary cell. To satisfy the radiation condition, i.e. the field remains bounded when x 3 → ∞, the values of k a 3mn are chosen to consider both propagative and evanescent waves in Ω a .

It is worth noting that the FE discretization of Ω a encapsuled by Γ ∞ is not mandatory if the interface Γ L is a plane surface. In this case, the radiation condition can be applied directly on Γ L instead of Γ ∞ . The general formulation proposed here can tackle with corrugated porous material surface.

The modal expansion for the periodic part of the pressure field reads as

p| Γ∞ = m,n∈Z 2 A mn φmn + A i e ik ai 3 L∞ , (A8) with φmn = 1 √ S e i m 2π d 1 x 1 +n 2π d 2 x 2 . (A9)
The modal profile is changed but the value of k a 3mn remains the same. The coefficient A mn can be used to compute the absorption of the material, see sec. A.2. These coefficient are cast in the vector A.

The weak formulation arising from (A2) yields after FE discretization (the boundary integral on Γ ∞ will be stated later)

V t KU = VF. (A10)
The unknowns vector U can be cast into a vector U ∞ containing the FE degree of freedom (dof) on the radiation boundary Γ ∞ and a vector U ′ containing the other dof. The unknown vector can be expressed with (A8)

   U ′ U ∞    =    I 0 0 P ∞    T    U ′ A    +    0 0 0 P i    G    0 A i    . (A11)
Here, P stands for the modal projection matrix. The Floquet modes are stored in columns and the raw contains the nodal value. The same form is chosen for the test function

V = T *    V ′ B    , (A12)
where V ′ and B are associated to the FE and to the modal dof, respectively.

Introducing (A11) and (A12) in (A10) leads to the modified system

T † KT K    U ′ A    Ũ = T † F -T † KG    0 A i    F , ( A13
)
where † is for the hermitian transpose. The boundary term on Γ ∞ , using the modal expansion from (A8) and for the associated test function from (A12), yields

Γ∞ 1 ρ a qa ∇p a • n dΓ = m,n∈Z 2 Bmn ik a 3mn ρ a A mn -B00 ik ai 3 √ Se -ik ai 3 L∞ ρ a A i . (A14)
These terms can be easly added at the end of F and on the diagonal of K. The last step is to solve the modified FE matrix K Ũ = F with a sparse solver

4 , 15 .

 415 FIG. 1. Example of a d-periodic fluid-like porous sheet backed by a rigid wall with a periodic inclusion embedded in.

FIG. 2 .

 2 FIG. 2. Sketch of the different simple shape inclusions considered (of barycenter x inc ): cubic inclusions (a), cylindrical inclusions (b), spherical inclusions (c), conic inclusion (d) and toric inclusion (e)

FIG. 3 .

 3 FIG. 3. Absorption coefficient for an infinitely long cylinder inclusion, when the layer is occupied by the foam S1, see Table I, excited at normal incidence (black) or with θ i = π/3 (gray): reference results from Ref. 10, i.e., 2D results (solid line), linear elements (o) and quadratic elements ( ). The inset shows the snapshot of the pressure field magnitude at 2674 Hz.

FIG. 4 .

 4 FIG. 4. Picture of the characterized sample, configuration C2: a 2.2 cm thick Melamine foam with four 15 mm edge cube embedded in.

Figure 5 FIG. 5 .

 55 Figure5shows a comparison between the absorption coefficient of this sample measured experimentally and calculated with the present FE method. Both absorption coefficients are in good agreement. The small differences can be attributed to the glue layers and possible thin air layers inside the sample. The absorption coefficient of the corresponding homogeneous layer is also depicted in Figure5. Measurement of the initial 2.2 cm-thick

FIG. 6 .

 6 FIG.6. Absorption coefficient (linear elements) of a cubic inclusion of edge length a centered in a cubic unit cell (d 1 , d 2 , L) = (2 cm, 2 cm, 2 cm) occupied by the foam S1 when excited at normal incidence: from the thinest to the thickest curves a = 0, a = 5 mm, a = 7.5 mm, a = 10 mm, a = 12.5 mm, a = 15 mm, a = 16 mm, and a = 17.5 mm.

FIG. 7 .

 7 FIG. 7. Snapshot of the pressure field magnitude (linear elements) along a cross-sectional (x 1 -x 3 plan) plan view at x 2 = d/2 in the configuration C1, when the layer is occupied by the foam S1, excited at normal incidence at ν = 2860 Hz.

  FIG. 8. Absorption coefficient (quadratic elements) of the configuration C1, when the layer is occupied by the foam S1, excited at normal incidence. The absorption coefficient of the homogeneous layer is depicted by the dashed line.

FIG. 9 .

 9 FIG. 9. Absorption coefficients (quadratic elements) of the configuration C2 ( ), C3 θ inc = 0 (⊲) and θ inc = π/2 (△), and C4 (o), when the layer is occupied by the foam S1, excited at normal incidence. The absorption coefficient of the homogeneous layer is depicted by the dashed line.

FIG. 11 .

 11 FIG. 11. Absorption coefficient of a layer with cubic inclusions of a = 16 mm edge length centered in a cubic unit cell (d, L) = (2 cm, 2 cm) occupied by the foam S1 when excited a)

FIG. 1 5 FIG. 2 6 FIG. 3 8 FIG. 4 9 FIG. 5 10 FIG. 6 11 FIG. 7 13 FIG. 8 13 FIG. 9 16 FIG. 10 inc 3 = 18 FIG. 11

 152638495106117138139161031811 FIG. 1 Example of a d-periodic fluid-like porous sheet backed by a rigid wall with a periodic inclusion embedded in. . . . . . . . . . . . . . . . . . . . . . . . . . 5

TABLE I .

 I Acoustical parameters of the porous material constituting the sheet of thickness

		φ	α ∞	Λ (µm)	Λ ′ (µm)	σ (N.s.m -4 )
	S1	0.95	1.42	180	360	8900
	S2	0.99	1.02	120	240	11500

[START_REF] Amestoy | Multifrontal parallel distributed symmetric and unsymmetric solvers[END_REF]

.

Absorption computation

Once the wave amplitudes have been evaluated, the integration of the acoustic intensity leading to the energy balance can be done. This integration is performed over the unit cell using the orthogonality relation of the Floquet modes. In practice, the number of propagating modes in Ω a is very small and often reduced to the fundamental mode (m, n) = (0, 0) (specular reflection) and the first modes.

Thanks to the conservation of the energy, the absorbed power is given by P abs = P i -P r , where the reflected power in the x 3 direction is

to the incident power is

The absorption coefficient is then defined as the ratio of the absorbed power to the incident power

Implementation note

The


Stanislas Du Manoir

Béatrice Orsetti

Rui Bras-Gonçalves

Tien-Tuan Nguyen

Laurence Lasorsa

Florence Boissière

Blandine Massemin

Pierre-Emmanuel Colombo

Frédéric Bibeau

William Jacot

Charles Theillet
email: charles.theillet@inserm.fr

Breast tumor PDXs are genetically plastic and correspond to a subset

Keywords: PDX, patient derived xenografts, CNC, copy number changes, CGH, comparative genomic hybridization, RFS, recurrence free survival breast cancer, patient derived xenografts, genetic stability, adverse prognosis

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Considerable progress has been made in understanding the molecular mechanisms underlying breast cancer development. A number of new therapeutic strategies are currently being devised aiming at targeting specific oncogenic pathways. However, a significant gap still exists between the experimental work and the development of effective clinical treatments. To validate the antitumor potential of candidate drugs, preclinical studies based on model systems must be performed, and it is paramount that these models accurately reproduce the biological features of the cancer in the patients [START_REF] Hait | Anticancer drug development: the grand challenges[END_REF].

Preclinical research traditionally relies on cell lines established from tumor specimens.

Cancer cell lines have yielded highly valuable and informative data, and remain indispensable models for molecular genetics and biochemistry studies [START_REF] Kao | Molecular profiling of breast cancer cell lines defines relevant tumor models and provides a resource for cancer gene discovery[END_REF]. However, cancer cell lines only partially recapitulate the biology of the original tumors, because they propagate as adherent monolayers in vitro, in conditions that differ drastically from those in the tumor.

Furthermore, a number of cell lines used routinely have been established decades ago and passed along from one laboratory to another, thus encountering changes in culture conditions that may lead to the derivation of subsets with genetic and phenotypic differences [START_REF] Nugoli | Genetic variability in MCF-7 sublines: evidence of rapid genomic and RNA expression profile modifications[END_REF]. Finally, patient tumor material is available in small amounts, which limits the number of experiments that can be performed with primary cultures.

Human tumors propagated in immunocompromised animals, called patient derived xenografts (PDXs) or tumor grafts, could be interesting alternatives to cancer cell lines.

Research on colorectal and breast cancer has shown that grafts from primary tumors faithfully reproduce the histology and morphology of the tumor they stemmed from [START_REF] Fiebig | Clonogenic assay with established human tumour xenografts: correlation of in vitro to in vivo activity as a basis for anticancer drug discovery[END_REF][START_REF] Marangoni | A New Model of Patient Tumor-Derived Breast Cancer Xenografts for Preclinical Assays[END_REF]. These pioneer studies were the proof of principle that PDXs could be an excellent bridge between clinical material and cancer cell lines, and recent research shows that established PDXs are permanent sources of tumor material that can be subjected to treatment and monitored for response [START_REF] Landis | Patient-derived breast tumor xenografts facilitating personalized cancer therapy[END_REF]. Furthermore, breast cancer PDXs faithfully reproduce tumor pathology, growth and metastasis of breast cancer [START_REF] Derose | Tumor grafts derived from women with breast cancer authentically reflect tumor pathology, growth, metastasis and disease outcomes[END_REF], and also seem to maintain the genetic characteristics of their original tumors [START_REF] Petrillo | Xenografts faithfully recapitulate breast cancer-specific gene expression patterns of parent primary breast tumors[END_REF][START_REF] Reyal | Molecular profiling of patient-derived breast cancer xenografts[END_REF][START_REF] Zhang | A Renewable Tissue Resource of Phenotypically Stable, Biologically and Ethnically Diverse, Patient-derived Human Breast Cancer Xenografts[END_REF]. Together these studies demonstrate the power of PDX models for cancer research.

We describe here a collection of 20 established breast cancer PDXs that resulted from engraftment of 130 primary tumors. To investigate what differentiates tumors that produce PDXs from those that do not, we have carefully analyzed the determinants of graft take in breast cancer, and characterized the primary tumors and their resulting PDXs by array-CGH and transcriptome analysis. We show that tumor grafts from breast cancer display remarkable conservation of the morphological and genetic features of the tumor they stem from. CNC profiles remained stable over several passages, but a small fraction of CNCs in the primary tumor that corresponded to oligoclonal events were gradually lost during sequential passaging.

As expected, grade 3 and ER-breast tumors were positively selected in the grafting process [START_REF] Landis | Patient-derived breast tumor xenografts facilitating personalized cancer therapy[END_REF][START_REF] Petrillo | Xenografts faithfully recapitulate breast cancer-specific gene expression patterns of parent primary breast tumors[END_REF][START_REF] Zhang | A Renewable Tissue Resource of Phenotypically Stable, Biologically and Ethnically Diverse, Patient-derived Human Breast Cancer Xenografts[END_REF]. Finally, we show that breast tumors that give rise to stabilized PDXs derive from a subset of aggressive cancer prone to relapse and have a transcriptomic signature clearly distinct from tumors that fail to produce PDXs.

Materials and Methods

Patients and tumor material

A total of 130 fresh breast cancer samples were collected from the pathology department upon macroscopic dissections, transferred to the animal facility and implanted within a maximum of 60 minutes after surgical removal. Full description of all the tumors grafted is provided in Supplementary Table 1. This study was reviewed and approved by the Montpellier Cancer Center -Val d'Aurelle Institutional Review Board and informed consent was obtained from all patients. Samples were systematically anonymized. Mean follow-up time was of 34 months.

Grafting, passaging and preservation of PDXs

This project was first reviewed and approved by an internal animal ethics committee, and then by the University of Montpellier animal ethics committee. There was always a minimum of three mice per experimental group. We implanted a single fragment of fresh or frozen tumor (~8 mm 3 ) into the inter-scapular fat pads of 3 to 4-week-old female Swiss-nude mice. For ER + tumors, mice were supplemented with estrogen by weekly application on the skin of 10µl of a 15mg/ml estrogen (Sigma-Aldricht, St Louis, MI, USA) solution in ethanol. Tumor growth was measured weekly using calipers. Tumors were passaged onto a further cohort of mice once grafts reached a maximum of 2,000 mm 3 . At each passage, fragments were (1) frozen at -180°C in L15 culture (Sigma-Aldricht) medium, with 40% FCS serum, 10% DMSO, for eventual retransplantation, (2) frozen dry at -80°C for DNA, RNA or protein extraction, (3) fixed into 4% buffered formaldehyde and embedded in paraffin.

Histological analysis

Histology was assessed on hematoxylin-eosin stained sections. Immunochemistry was performed on standard sections, deparaffinized, rehydrated and treated for epitope retrieval in boiling EDTA (pH 9). Neutralization of endogenous peroxidase was done with H2O2. Sections were incubated for 20 minutes at room temperature with anti-ERa (clone 6F11, 1:100, LeicaBiosystems, St Germain en Laye, France), anti-PR (clone PgR636, 1:400, Dako, Glostrup, Denmark) mouse monoclonal antibodies. Antibody binding was amplified using the EnVision™ FLEX detection system (Dako). Endogeneous biotin and avidin were saturated with a blocking kit (Vector Laboratories-CliniSciences, Nanterre, France). Sections were then incubated with primary antibodies or mouse isotype control (Mouse IgG1κ, Sigma-Aldrich) overnight at 4°C. Sections were then washed 3X in 0.1% Tween20-PBS solution at 25°C for 3 hours and incubated 10 minutes with the secondary antibody. Amplification of the signal was done using the ABC kit (Vector Laboratories-CliniSciences). Sections were washed as above. Binding was visualized by incubating with DAB (3,3-diaminobenzidine) substrate. The sections were then counterstained with haematoxylin, dehydrated and permanently mounted. Slides were scanned with a digital slide scanner NanoZoomer (Hamamatsu). Pictures were visualized and exported using NDP.view 1 software. Slides were read by a pathologist (F.B.). The presence of invasive carcinoma was assessed and histology of the tumors and corresponding PDX was compared.

Immunohistochemistry results were evaluated according to standard practice.

DNA and RNA extraction

DNA and RNA were isolated from frozen tissues using the QIAmp DNA Mini kit and Rneasy Mini Kit (Qiagen S.A. France, Courtaboeuf, France). Each DNA sample was quantified by nanospectrophotometry (NanoView, GE Healthcare, Orsay, France) and qualified by 0.8% agarose electrophoresis. Qualification of mRNA was performed using a Bioanalyser (Agilent, Santa Clara, CA, USA).

Array-CGH

The genomic profiles were obtained by array comparative genomic hybridization (array-CGH) using HG18 CGH 385K Whole Genome v2.0 array (Roche NimbleGen, Madison, WI, USA).

DNA from a pool of 20 normal females was used as reference. For hybridization, 1μg of genomic DNA and reference DNA were labeled using NimbleGen Dual-Color DNA Labeling Kit (Roche Diagnostics, Meylan, France). Labeling products were precipitated with isopropanol and resuspended in water. Test (Cy3) and reference (Cy5) samples were combined in 40μl of NimbleGen Hybridization buffer. Hybridization was performed in a NimbleGen Hybridization system 4 for 48 hours at 42°C with agitation mode B and washed using NimbleGen Wash Buffer kit according to manufacturer's instructions. Arrays were scanned at 5μm resolution using the GenePix4000B scanner (Axon Instruments, Molecular Devices Corp., Sunnyvale, CA). Data were extracted from scanned images using NimbleScan 2.5 extraction software (Roche NimbleGen, Madison, WI, USA), which allows automated grid alignment, extraction, normalization, and export of data files. Normalized files were used as input for the Nexus 6.1 Software (Biodiscovery, El Segundo, CA, USA). Analysis settings for data segmentation and calling were the following: significant threshold for FASTST2 Segmentation algorithm: 1.0E-7, Max Continuous Probe Spacing: 1000, Min number of probes per segment: 10, high level gain: 0.485, gain: 0.17, loss:-0.2, homozygous copy loss:-0.485. Hierarchical clustering was done using Nexus 6.1 using average linkage setting.

Expression profiling and molecular classification

Expression profiling was performed on Affymetrix Human Genome GeneChip U133Plus2 and Biotinylated cRNA were prepared according to the Affymetrix IVT Express protocol from 100 or 200ng total RNA and hybridization was done as follows. CRNA were fragmented, 12µg hybridized for 16 hr at 45°C, washed and stained in the Affymetrix Fluidics Station 450 with Hybridization Wash & Stain kit. GeneChips were scanned using the Affymetrix GeneChip Scanner 3000 7G. Raw feature data were normalized using Robust Multi-array Average (RMA) method (R package affy). All subsequent analyses were performed on normalized datasets. For the CIT/Guedj classification we applied a classical distance-to-centroid approach, implemented in the citbcmst R package available at http://cran.rproject.org/web/packages/citbcmst/ index.html). For further details see [START_REF] Guedj | A refined molecular taxonomy of breast cancer[END_REF]. For the Hu, PAM50 and Sorlie classifications we implemented the script published by Alan Mackay available at http:// rock.icr.ac.uk/collaborations/Mackay/centroid.correlations.Eset/ExpressionSet Nearest Centroid Correlations.pdf). For the BasalA/B classification we used the gene centroid list as in [START_REF] Neve | A collection of breast cancer cell lines for the study of functionally distinct cancer subtypes[END_REF]. Pearson metrics was employed for all classifications except for Sorlie (Spearman metric). For the VEGF and IL8 signatures the function sig.score from the R program package Genefu was used to compute a signature score after MAS5 normalization of the data (R package affy). Probes list are included in the IL8 [START_REF] Hu | A compact VEGF signature associated with distant metastases and poor outcomes[END_REF], VEGF [START_REF] Waugh | The interleukin-8 pathway in cancer[END_REF] and proliferation [START_REF] Rody | A clinically relevant gene signature in triple negative and basal-like breast cancer[END_REF] lists are shown in Supplementary Table 2.

Survival analyses

On grafted tumors we performed Univariate Kaplan-Meier analysis with a log-rank (cox-Mantel-Haenzel) test using the GenePattern package. The CIT cohort dataset was dowloaded from Arrayexpress (E-MTAB-365) and the 428 samples stratified with survival follow-up data as ER+ or basal-like subtype. Univariate Kaplan-Meier was performed with a log-rank (cox-Mantel-Haenzel) test using GenePattern package with the VEGF signature.

Exome sequencing

High-throughput exome sequencing was performed by Integragen (Evry, France) using the Human All Exon v4 -70 Mb kit (Agilent) followed by 75 base end-sequencing on an Illumina HiSEQ 2000 on 6 samples at a mean 60X depth from three primary/PDXs pairs [START_REF] Gnirke | Solution hybrid selection with ultra-long oligonucleotides for massively parallel targeted sequencing[END_REF]. Bioinformatic analysis used the pipeline provided by Illumina (CASAVA1.8) on the build37 of the human genome and with ELANDv2e alignment algorithm. Annotation includes gene (Refseq), polymorphism (dbsnp132, 1000 genomes) and frequency of mutation in Integragen database (IGdb) of 150 expected to be normal Exome sequenced at Integragen facilities. For each mutation, localization (exon, intron) as well as effect (missense, no-sense, synonymous ) was annotated. Variant detection was done by pair (Primary/PDX) with CASAVA1.8 (Theta =0.01). This is the standard pipeline for output delivered by our contractor (Integragen SARL, Evry). Due to the absence of Normal blood DNA sequencing from the patient the filtering was done according to a stringent strategy in three steps as described below. (1) Mutations present in the 1000 genomes database or in IGdb were excluded from analysis as they represent polymorphisms or sequencing errors. (2) Only missense or nonsense mutations were considered. (3) Only the 518 genes previously found to be mutated twice in [START_REF] Banerji | Sequence analysis of mutations and translocations across breast cancer subtypes[END_REF] or in the Significantly mutated genes list of (Koboldt et al., 2012) were included. This filtering process in three steps resulted in the approval of 35 mutations for B3977 samples and 28 mutations for B3029 and 5 for the B3921 case (SupTable 3). Due to this low number of mutations in B3921, we considered this sample as unsuitable to determine a general trend in the comparison between primary and PDX. Frequency of the mutated allele was calculated in the primary and the PDX on the basis of respective read numbers.

Statistical Analysis

Anova or t-test were performed when appropriate using the Rcmdr R package. Multivariate logistic regression analysis was performed to identify independent predictors of the "PDX take".

Results

Establishment of the breast tumor PDX collection

With the aim to establish stabilized breast cancer PDXs, we grafted a total of 130 fresh breast tumor specimens into the inter-scapular fat pad of Swiss-Nude mice within an hour of surgical resection. We chose to graft into the inter-scapular fat pad rather than the mammary gland because of quicker and easier handling, as our strategy was to graft rapidly a large number of tumors within a limited time span. We rarely observed macroscopic metastases to the lung and never to the liver. All grafted breast tumors were primary tumors, except one tumor that was a local recurrence from a primary breast cancer treated three years earlier in our institution. We observed take (tumor regrowth at first graft) in 39 (30%) cases and stabilization (after at least three serial passages) of 20 (15%) PDX lines. Thus, 19 grafts that initially took were not sustained beyond one or two passages. The majority of these grafts (15/19) were ER+ tumors with a slow growth rate. Indeed, while established PDXs required on average 130 to 150 days of growth between each passage (and 63 days for a group of fast growers; Figure 1), nonestablished grafts took about 15 months to become palpable. These slow-growing grafts were therefore at increased risk of being lost because of premature death of the recipient animal. We found a significant correlation between PDX take and/or establishment, and steroid receptor levels and SBR grade (Table 1). Indeed, a majority of PDXs were of the ER/PR/HER2 triple negative (TN) phenotype (14/20) and predominantly mutated at the TP53 gene (65%), while only five PDXs were ER+ and three were HER2+ (two ER+/HER2+ and one ER-/HER2+) (Figure 2, Supplementary Figure 1B and1C).

PDXs reproduce the phenotype of the tumors they originate from

We next investigated whether the PDXs retained the phenotypic features of the tumors of origin.

We found that indeed they showed remarkable conservation of histological and morphological features (Supplementary Figure 1A). Furthermore, immunohistochemical staining in PDXs originating from ER+ tumors showed that ER and PR expression was stably conserved during passages (Supplementary Figure 1B). We also detected matching HER2 overexpression patterns in HER2+ primary tumors and their corresponding PDXs (Supplementary Figure 1C).

To further assess the phenotypic stability of the PDXs in reference to the primaries, we examined their respective assignments into molecular subtypes. We established expression profiles for the primary tumors and PDXs on Affymetrix U133 Plus 2 GeneChips, and then classified them according to the CIT/Guedj classification [START_REF] Guedj | A refined molecular taxonomy of breast cancer[END_REF]. Next, we compared these results with four other nearest centroid classifiers (Figure 2). Of the 20 tumors that gave rise to grafts, 13 were assigned to the Bas-L (in coherence with their TN phenotype), two to the ER-mApo (one had been diagnosed HER2 3+, while the second was determined HER2 1+) and five to ER+ Lum-B or Lum-C molecular subgroups of the CIT/Guedj classification [START_REF] Guedj | A refined molecular taxonomy of breast cancer[END_REF]. Subgroup assignments using these classifiers were globally concordant, thus confirming the conservation of the expression characteristics between primaries and PDXs (Figure 2).

Together these results show that breast cancer PDXs faithfully reproduce the phenotype of the tumor of origin.

PDXs preserve copy number change profiles of the original tumor

To assess the genomic stability of the PDXs, we established copy number change (CNC) profiles of primary tumors and their PDXs by array-CGH on high density oligo-chips. Similar patterns of genomic aberrations in PDXs and the primary tumors they originated from suggest that CNC profiles evolve in parallel in primary tumors and their grafts (Supplementary Figure 2A). However, in a number of cases the CNC profile of the primary tumor was less accentuated than the corresponding PDX profile, which resulted in a higher number of aberration call in the grafts (Supplementary Figure 2A). This effect could be explained by variable contingents of contaminating normal stromal cells in the primary tumors, resulting in the dilution and subsequent attenuation of the CNC signal. In the PDXs, contamination by normal tissue should not occur because stromal cells do not interfere with the tumor DNA signal, as they have murine origin and there is limited homology on our arrays. We estimated the fraction of normal cells present in each primary tumor and then inferred the level of dilution of tumor DNA by normal DNA in the CNC profiles of primary tumors. CNC profiles of primary tumors and PDXs were then normalized taking this dilution factor into account. Indeed, normalization led to a significant decrease in the divergence between CNC profiles from primary tumors and their corresponding PDXs (Supplementary Figure 2B,2C). Furthermore, clustering analysis performed on corrected profiles revealed that PDXs and their cognate primaries were systematically co-clustered, thus showing a high level of correlation (Figure 3).

Next, we analyzed the genetic stability of the PDXs during passages. Visual inspection revealed that CNC profiles of different grafts obtained from the same tumor were almost interchangeable (Figure 4C). Consistent with this, when compared to the primary tumor, the concordance ratio of CNC profiles of PDXs from passages 0, 1 or 2 suggests that changes occurred mainly during the initial graft (Figure 4B). These data indicate that propagation of breast tumors as xenografts on immunocompromised mice preserves preexisting genomic features, and that these genomic features change little during passages.

PDXs uncover limited levels of oligoclonality in breast tumors

Despite the genomic conservation of the PDXs and their tumors of origin, a detailed analysis of the CGH-profiles revealed that a fraction of the CNCs showed divergence at specific loci (examples are shown in Supplementary Figure 3A and Supplementary Figure 3B). We were interested in CNCs present in the tumors of origin but absent in the PDXs, which were clear signs of oligoclonality in the primary tumor. According to the tumor analyzed, these events represented up to 6% of the human genome (Figure 5A) and reached at least 2% in about half of the tumors. These findings suggest that a limited but sizeable level of oligoclonality is present in our breast cancer set. We next determined the precise fraction of de novo occurring anomalies in the PDXs when compared to the original tumors, as these de novo events are representative of ongoing genetic instability. We compared the CGH profiles of the PDXs and their cognate primary tumors after correction for normal stromal cells contamination (Supplementary Figure 2).

Similarly to oligoclonal anomalies, de novo events fluctuated from one PDX line to another, representing 0.3 to 9% of the human genome, with a quarter of the lines encompassing at least 4% of the genome (Figure 5B). Importantly, we observed no correlation between elevated oligoclonality and high occurrence of de novo CNCs. Results obtained from CGH profiles were confirmed by exome sequencing performed on a subset of three primary tumor/PDX pairs that we selected because of their CNC profile differences. However, since we could not obtain normal tissue from the patients to use as reference, our determination of somatic mutations could not be definitive. To circumvent this pitfall, we restricted our analysis to a subset of genes with mutations and indels described in previous high-throughput sequencing studies on breast cancer [START_REF] Banerji | Sequence analysis of mutations and translocations across breast cancer subtypes[END_REF]Koboldt et al., 2012). We were able to identify in each of the three breast tumors analyzed 5, 28 and 32 genes with deleterious mutations, respectively (Supplementary Table 3), and to compare the mutation frequency in the primary tumor vs the PDX (Supplementary Figure 4). In the primary tumor/PDX pairs with sufficient numbers to perform a statistical analysis, we found that mutation frequencies in the PDXs and in their original tumors were highly correlated (R 2 coefficient 0.65 and 0.80). In particular, we observed a general trend toward an enrichment of mutation frequencies in the PDXs, probably as a consequence of the elimination of normal stromal cells. While a minority of the mutations (possibly representing founder or essential events such as TP53) was selected to homogeneity in the PDXs, a large fraction of the mutations remained at an intermediary frequency rate (0.25 to 0.7) indicating that they were not subjected to a drastic selection process. Mutations restricted to the primary tumor (and lost in the PDX) represented 5.7% and 17% for B3977 and B3029 respectively. These results confirm our CNC data showing sizable levels of oligoclonality in these tumors. A limited set of de novo events (seven events in two cases) were also found.

Together these data show that there are differences in clonality in our breast cancer PDX collection, but that there is a general tendency for the gradual emergence of a dominant clone in the PDXs after three passages. Limited genetic drift could also be observed.

Breast tumors that take correspond to a subset of aggressive breast cancer.

The prevalence of grade 3 and TP53-mutated tumors in our PDX collection suggested that stable grafts could represent a subset of aggressive breast cancers. A multivariate regression logistics analysis showing that PDX take was significantly associated to Grade 3, ER-and metastatic disease further supported this model (Supplementary Table 4). To investigate the link between PDX take and aggressive breast cancer, we compared recurrence-free survival (RFS) in the breast cancer patients. Indeed, we found that patients whose primary tumor gave rise to a PDX had a lower RFS than patients whose tumor did not take (Supplementary Figure 5A). RFS may reflect known differences in outcome between TN basal cancers (predominant in the Take group) and ER+ luminal cancers (overrepresented in the No Take group). However, when we stratified the patients in TN and ER+ tumors, we still found a significant difference between RFS in the Take and the No Take groups in ER+ tumors, and an observable trend in TN breast cancers (Supplementary Figure 5B,5C).

The contrast between outcome in patients from Take and No Take groups raised the possibility that tumors that produce PDXs have distinct gene expression signatures from tumors that do not take. Our first attempt to identify a set of genes differentially expressed in the breast primary tumors using a supervised approach did not succeed because of limited sample size and insufficient statistical power. We therefore selected 16 expression signatures with reported prognostic significance in breast cancer to test for significant transcriptomic differences in the primary tumors used in our set. Five of these expression signatures showed a significant increase in the Take group, namely GGI-grade [START_REF] Sotiriou | Gene expression profiling in breast cancer: understanding the molecular basis of histologic grade to improve prognosis[END_REF], proliferation [START_REF] Rody | A clinically relevant gene signature in triple negative and basal-like breast cancer[END_REF], wound healing [START_REF] Chang | Gene expression signature of fibroblast serum response predicts human cancer progression: similarities between tumors and wounds[END_REF], VEGF [START_REF] Hu | A compact VEGF signature associated with distant metastases and poor outcomes[END_REF] and IL8 [START_REF] Waugh | The interleukin-8 pathway in cancer[END_REF](Figure 6). To avoid a confounding effect due to compositional differences, we classified the tumors according to molecular subtypes (namely Bas-L and Lum-B/Lum-C for the two subtypes with a sufficiently large sample size) and repeated the signature analysis. Remarkably, GGI-grade was significantly increased in the Take vs the No Take groups in both Bas-L and Lum tumors, while three signatures showed a restricted pattern. The wound healing signature was significantly increased in the Take group in Lum-B/Lum-C tumors, whereas VEGF and IL8 signatures were restricted to the Take group in Bas-L tumors. Interestingly, the proliferation signature showed differential expression in Lum tumors but did not reach significance, likely due to small sample size. Taken together, these results show that tumors that give rise to PDXs correspond to a distinct subgroup of aggressive breast cancers irrespective of the molecular subtype they belong to.

Discussion

Grafting efficiency

In comparison to other cancers, such as colorectal cancer, breast cancer PDXs are characterized by a relatively low take rate upon grafting on immunocompromised mice. In particular, several studies have shown that high grade and ER-negative tumors are overrepresented in breast PDXs [START_REF] Derose | Tumor grafts derived from women with breast cancer authentically reflect tumor pathology, growth, metastasis and disease outcomes[END_REF][START_REF] Landis | Patient-derived breast tumor xenografts facilitating personalized cancer therapy[END_REF][START_REF] Marangoni | A New Model of Patient Tumor-Derived Breast Cancer Xenografts for Preclinical Assays[END_REF][START_REF] Zhang | A Renewable Tissue Resource of Phenotypically Stable, Biologically and Ethnically Diverse, Patient-derived Human Breast Cancer Xenografts[END_REF]. Our work is consistent with these findings, given that from the 20 stabilized PDXs we established, 14 stemmed from TN breast cancers and 18 were grade 3.

Furthermore, the number of takes at first graft (39 take out of 130 grafts) was almost double the number of stabilized PDXs (at least three passages). Grafts that we could not stabilize were predominantly slow-growing ER+ tumors. It therefore appears that despite estradiol supplementation and grafting on female mice, ER+ breast tumors (predominantly of grade 2 in our series) are negatively selected in this system.

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Research on melanoma shows that some xenografts may require severely immunosuppressed animals, such as NOD-SCID gamma-delta mice, and it has therefore been proposed that the level of immunosuppression of recipient mice is a determinant factor for graft stabilization [START_REF] Quintana | Efficient tumour formation by single human melanoma cells[END_REF]. However, our attempt to graft on severely immunocompromised mice did not lead to a clear breakthrough, consistent with what others reported for breast cancer grafts [START_REF] Derose | Tumor grafts derived from women with breast cancer authentically reflect tumor pathology, growth, metastasis and disease outcomes[END_REF][START_REF] Landis | Patient-derived breast tumor xenografts facilitating personalized cancer therapy[END_REF]. It has also been suggested that the graft site could make a difference in graft take rates. For instance, breast cancer orthotopic grafting in cleared mammary fat pads has been preferred by several groups, but did not lead to a clear increase of ER+ tumor take rate [START_REF] Derose | Tumor grafts derived from women with breast cancer authentically reflect tumor pathology, growth, metastasis and disease outcomes[END_REF][START_REF] Zhang | A Renewable Tissue Resource of Phenotypically Stable, Biologically and Ethnically Diverse, Patient-derived Human Breast Cancer Xenografts[END_REF]. Another alternative could be to graft into the renal capsule [START_REF] Cutz | Establishment in Severe Combined Immunodeficiency Mice of Subrenal Capsule Xenografts and Transplantable Tumor Lines from a Variety of Primary Human Lung Cancers: Potential Models for Studying Tumor Progression-Related Changes[END_REF], however, this is a complex procedure and it is therefore not very commonly used. Hence, primary breast tumor grafting is still open for improvement and co-grafting of mesenchymal feeder cells or engineered mice expressing cocktails of cytokines could represent interesting leads.

PDXs represent a subset of aggressive and recurrence-prone breast tumors

In our collection the permanently stabilized PDXs corresponded to a subset of aggressive breast cancers associated to a lower RFS. This correlation between graft stabilization and cancer aggressiveness is in line with reports showing that metastatic lesions, such as pleural effusions, have a high take rate [START_REF] Landis | Patient-derived breast tumor xenografts facilitating personalized cancer therapy[END_REF]. We found that the potential to take and produce xenografts is inherent to the primary tumors, as demonstrated by the clear differences at the RNA expression level between tumors that took and those that did not. Overall, tumors producing stable PDXs showed increased expression of several gene signatures associated with adverse prognosis, namely GGI, wound healing, proliferation, IL8 and VEGF [START_REF] Chang | Gene expression signature of fibroblast serum response predicts human cancer progression: similarities between tumors and wounds[END_REF][START_REF] Hu | A compact VEGF signature associated with distant metastases and poor outcomes[END_REF][START_REF] Rody | A clinically relevant gene signature in triple negative and basal-like breast cancer[END_REF][START_REF] Sotiriou | Gene expression profiling in breast cancer: understanding the molecular basis of histologic grade to improve prognosis[END_REF][START_REF] Waugh | The interleukin-8 pathway in cancer[END_REF]. The core of the first three signatures is built around genes governing cell cycle progression, DNA synthesis and repair genes, which suggests there is increased proliferation in the tumors of the Take group. Elevated expression of IL8 and VEGF is characteristic of aggressive breast tumors.

In particular, elevated VEGF expression is known as a marker of adverse prognosis in breast cancer and is associated with hypoxia and increased vasculature [START_REF] Dhakal | Expression of vascular endothelial growth factor and vascular endothelial growth factor receptors 1 and 2 in invasive breast carcinoma: prognostic significance and relationship with markers for aggressiveness[END_REF][START_REF] Gasparini | Prognostic value of vascular endothelial growth factor in breast cancer[END_REF] (Supplementary Figure 6). Furthermore, increased IL8 signaling in breast cancer has been shown to favor cancer stem cell maintenance and propagation [START_REF] Ginestier | CXCR1 blockade selectively targets human breast cancer stem cells in vitro and in xenografts[END_REF][START_REF] Fernando | IL-8 Signaling Plays a Critical Role in the Epithelial-Mesenchymal Transition of Human Carcinoma Cells[END_REF], by way of cross-connections with PI3K/AKT and SRC [START_REF] Hartman | Growth of Triple-Negative Breast Cancer Cells Relies upon Coordinate Autocrine Expression of the Proinflammatory Cytokines IL-6 and IL-8[END_REF][START_REF] Singh | Targeting CXCR1/2 Significantly Reduces Breast Cancer Stem Cell Activity and Increases the Efficacy of Inhibiting HER2 via HER2-Dependent and -Independent Mechanisms[END_REF]. It is reasonable to assume that elevated production of IL8 and/or VEGF by tumor cells [START_REF] Hu | A compact VEGF signature associated with distant metastases and poor outcomes[END_REF][START_REF] Rody | A clinically relevant gene signature in triple negative and basal-like breast cancer[END_REF][START_REF] Waugh | The interleukin-8 pathway in cancer[END_REF]) could be critical for the grafting process and thus contribute to the higher take rate of basal-like breast tumors, for instance, by favoring cancer stem cell renewal and the angiogenic shift necessary to the long-term establishment of tumors of large size [START_REF] Waugh | The interleukin-8 pathway in cancer[END_REF].

PDXs reproduce the phenotypic and genetic characteristics of the grafted tumor fragment

An excellent conservation of the histological features of the tumor of origin in breast cancer PDXs was first shown by Marangoni and colleagues [START_REF] Marangoni | A New Model of Patient Tumor-Derived Breast Cancer Xenografts for Preclinical Assays[END_REF], and then repeatedly observed by others [START_REF] Derose | Tumor grafts derived from women with breast cancer authentically reflect tumor pathology, growth, metastasis and disease outcomes[END_REF][START_REF] Landis | Patient-derived breast tumor xenografts facilitating personalized cancer therapy[END_REF]. Our results are in agreement with these observations, thus confirming that PDXs perfectly recapitulate the morphological characteristics of primary tumors. Because sporadic loss of ER expression in PDXs established from ER+ breast tumors has been reported [START_REF] Bergamaschi | Molecular profiling and characterization of luminal-like and basal-like in vivo breast cancer xenograft models[END_REF], we carefully checked ER expression in our PDXs. However, we could not observe any reversion of ER expression in our ER+ PDXs (Supplementary Figure 1B). Importantly, these findings were corroborated by transcriptome analysis in the primary tumors and corresponding PDXs, which show very similar expression profiles and molecular classification assignments, in concordance with recent research [START_REF] Petrillo | Xenografts faithfully recapitulate breast cancer-specific gene expression patterns of parent primary breast tumors[END_REF].

Besides transcriptomic stability, the PDXs show remarkable stability at the genomic level, as clearly demonstrated by the excellent conservation of the CNC profiles of the tumors of origin. These results differ slightly from that of Reyal and coworkers, however, who observed a global increase in the number of CNCs in the PDXs [START_REF] Reyal | Molecular profiling of patient-derived breast cancer xenografts[END_REF]. Our analysis suggests that this discrepancy can be attributed to the presence of large contingents of contaminating stromal cells in the primary tumors, which dilutes out the tumors' DNA signal. Interestingly, we found that the CNC profiles in different PDXs established in parallel from the same tumor are nearly identical. These findings are very reassuring concerning the genetic stability of breast PDXs and their reliability as cancer models. We also found that oligoclonal CNC differences represent 0.2 to 6% of the genome, depending on the primary tumor, which is significantly less than what others reported for some breast tumors [START_REF] Nik-Zainal | Breast Cancer Working Group of the International Cancer Genome Consortium[END_REF]. It is possible that our assessment of oligoclonality levels based on CNC profile differences is an underestimation, when compared to the levels detected by whole genome sequencing. Nevertheless, our data are consistent with findings by Nik-Zainal and colleagues (2012) showing that oligoclonality varies appreciably from one breast tumor to another, and that the genetic structure of each tumor stabilizes around a dominant clone [START_REF] Nik-Zainal | Breast Cancer Working Group of the International Cancer Genome Consortium[END_REF]. The analysis of different PDXs established from the same tumor revealed that there is gradual loss of the minor clones over sequential passages. This result is however not surprising, as grafting onto immunocompromised mice represents a change of environment and selective pressure. In addition, gradual loss of minor clones could also result from the outgrowth of de novo occurring mutations.

In summary, our results show that PDXs are a faithful representation of the tumor of origin, but sequential passages are associated with gradual selection of a dominant genetic clone and some models can show limited genetic drift. These data suggest that PDXs are dynamic biologic elements that should therefore be regularly checked for genetic and phenotypic stability.

PDXs as cancer models

Grafts established from clinical tumor material are increasingly appreciated models for preclinical testing because they are closer representations of the disease than cancer cell lines. PDXs are particularly well suited to test targeted therapy, as they can be comprehensively characterized at the molecular level. PDXs also allow detection of the oncogenic cascades that fuel the tumor.

One could therefore expect that grafts will be increasingly used for the definition of therapeutic combinations, and they should play an important role in the current therapeutic evolution toward personalized medicine. Furthermore, PDXs could be key for unraveling the causes and the mechanisms underlying treatment failure, and for testing alternative therapies to overcome tumor resistance. Indeed, resistant and sensitive sublines can be derived from tumors with a clinically documented response to therapy, and sublines with variable levels of treatment sensitivity can be further established in vivo [START_REF] Landis | Patient-derived breast tumor xenografts facilitating personalized cancer therapy[END_REF]. Hence, a precise assessment of the tumor's level of oligoclonality and/or genetic plasticity could be of great value. Combined with short term ex vivo culture, it is foreseeable that PDXs will give rise to families of genetically modified models expressing shRNA, specific target genes or reporter genes, which will open the way to functional assays similar to those currently performed in cancer cell lines. For instance, fluorescent or luminescent models will be of special interest to monitor metastatic dissemination using in vivo imaging and to test compounds for the reduction of the tumor burden.

In summary, we have established a valuable collection of breast cancer PDXs that faithfully reproduce the tumors of origin. We have shown that breast PDXs retain transcriptomic and genomic stability over sequential passages, with gradual selection of a dominant genetic clone. Our results show that breast tumors producing stabilized PDXs derive from a subset of aggressive cancers associated with a poor clinical outcome, and that despite of an excellent conservation of original features, they remain genetically dynamic elements. We conclude that our PDX collection could be an important model for breast cancer research and preclinical testing. Figure 6: Expression differences between primary tumors that give rise to PDX (Take) and those that did not (No Take). Number of cases in each category are indicated in brackets. We analyzed 5 expression signatures with known prognostic showed significant expression differences. The tumor set was stratified according to molecular subtypes to verify whether these differences

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were not due to differences in composition of the Take and the No Take groups. GGI identifies the molecular grade signature.

2.Legend to Table 1

Table 1: Clinical and pathological characteristics that differentiate breast tumors that give rise to a PDX from those which fail to do so. Distribution of characteristics showing significant differences are presented for tumors that gave rise to primary take (passage 1) and tumors that reached passage 3 (a stage at which the PDXs were stabilized). Tumor Grade was determined according to the EE-SBR guide lines. Estrogen and progesterone receptor status was assessed by immunohistochemistry and scored as defined in the Materials and Methods section.

Figure 2 :

 2 Figure 2: Molecular classification of PDX and tumors of origin are highly concordant. Identical assignment were found in 87 % of the cases with at least 3/5 identical classifications for each PDX. Divergences were restricted to the luminal subtypes. Transcriptomes of PDX and corresponding tumor of origin were classified using the Guedj, Hu, PAM 50, Sorlie and Neve breast cancer classifiers and assignments were indicated by a color code. Red: Basal or Bas-L, Orange: M-Apo (ER-/HER2+), Pink: Lum-C (ER+/PR-), light blue: Lum-B (ER+/PR+/HER2-), dark blue: Luminal A. ER, PR status determined by IHC is presented in red for ER-, in green for ER+. HER2 status was noted negative in green when scored <2+, positive in red score = 3+.TP53 mutation status determined by DNA sequencing, mutated in red, wt in green.

Figure 3 :

 3 Figure 3: Breast tumors of origin and corresponding PDXs show elevated similarity at the genomic level. CNC profiles of all PDXs (* indicates corrected profiles) and breast tumors of origin were determined by array-CGH and convergence tested by clustering analysis. Breast tumors and their cognate PDXs were systematically clustered together (pairs, triplet or quadriplet according to profile availability).

Figure 4 :Figure 5 :

 45 Figure 4: CNC profiles of different grafts from the same primary tumor remain remarkably stable .A: Graft tree indicating the position of the analyzed PDXs which have been highlighted by a color code. B: Histograms showing the fraction of overlapping events in the tumor of origin and the corresponding PDX which are identified by color codes indicated in the graft tree. C: whole genome CNC profiles, gains are shown in blue, losses in red, chromosomes by alternating light blue and white bars. Samples are identified as shown in the tree

Acknowledgements: this work was supported by grants from INCa MOPRECLI and INCa "Role of cancer stem cells during metastatic progression of breast cancer" as well as Ligue Contre le Cancer comité du Haut-Rhin grant 2010 and Ligue Contre le Cancer Comité de l'Hérault grant 2011. The authors wish to thank the personnel of the IRCM animal facility team, the histology (RHEM) platform, the Affymetrix platform of Montpellier and Dr Caroline Mollevi from the Biostatistics platform at ICM for their help in this project. The constant support of ICM and SIRIC Montpellier-Cancer is gratefully acknowledged.