Finite-Element Model Reduction of Surface-Mounted Permanent Magnet Machines by Exploitation of Geometrical Periodicity

This paper presents a methodology that allows taking advantage of the geometrical periodicity of electrical machines together with the modeling of rotor motion. It enables by means of the discrete Fourier transform (DFT) to reduce the large-scale system obtained from the finite-element model to several smaller independent subsystems, allowing a shortening of the computational time. Due to DFT properties, the computational time can be more reduced especially when we consider the inter-dependence of the spectral components under either balanced or unbalanced supply condition. In addition, a further reduction is possible in the case of balanced regimes where the distribution of the eventual numerical solution is governed by a limited number of prevailing harmonics.

Index Terms-Discrete Fourier transform (DFT), electromagnetic fields, finite-element (FE) analyses, geometrical periodicity, model reduction, rotating electric machines, surface-mounted permanent magnet (SMPM) machines.

I. INTRODUCTION

I N ELECTROMAGNETIC field computation, when the interaction between electric and magnetic variables cannot be solved analytically, solution by numerical techniques such as finite-element (FE) [START_REF] Ida | Electromagnetics and Calculation of Fields[END_REF] or boundary element methods [START_REF] Brebbia | The Boundary Element Method for Engineers[END_REF] are often used. When a fine mesh and a small time step are used, such numerical techniques lead usually to a substantial calculation time which prevents the intensive use of such model in a design process. To tackle this issue, model reduction techniques are widely used; they have shown their efficiency in reducing both computational time and memory storage requirements. Some of these model reduction techniques are based on the subdomain reduction, namely, the ones dealing with the perturbation principle [START_REF] Sabariego | A perturbation approach for the modeling of eddy current nondestructive testing problems with differential probes[END_REF], [START_REF] Al Eit | Perturbation finite element method for efficient copper losses calculation in switched reluctance machines[END_REF]; they are usually used to determine the solution only in the most relevant areas. Besides, other techniques are dealing with the order reduction of the equation system. Among these, we can mention the proper orthogonal decomposition [START_REF] Chatterjee | An introduction to the proper orthogonal decomposition[END_REF], [START_REF] Al Eit | Model-order nonlinear subspace reduction of electric machines by means of POD and DEI methods for copper losses calculation[END_REF] which has proven its benefit in the electromagnetic simulation of numerical models with a very high number of unknowns. We can mention that there exist other approaches based on lookup table techniques that are widely used for an effective computational efficient in real time machine control and convertor design [START_REF] Rosu | Basics of electrical machines design and manufacturing tolerances[END_REF], [START_REF] Siami | A computationally efficient lookup table based FCS-MPC for PMSM drives fed by matrix converters[END_REF]. In fact, all the foregoing mentioned approaches are classified under the a posteriori reduction techniques since they require initially, at least, one full model solution. However, in this paper, we are interested in a priori model reduction technique that deals with the exploitation of the geometrical periodicity [START_REF] Bossavit | The exploitation of geometrical symmetry in 3-D eddycurrents computation[END_REF]- [START_REF] Lobry | Symmetry and TLM method in nonlinear magnetostatics[END_REF] based on the discrete Fourier transform (DFT).

In a practical way, if an FE model presents a kind of magnetic symmetry due to a common periodicity between the geometry and the source distribution (permanent magnet Manuscript received November 23, 2017; revised February 21, 2018; accepted April 16, 2018. Corresponding author: M. Al Eit (e-mail: moustafa.aleit@gmail.com).

Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMAG.2018.2830753 and current density), it is common to take full advantage of it by meshing only a portion of the electromagnetic device yielding therefore to substantial calculation benefits. We can go further by using the group representation theory [START_REF] Bossavit | The exploitation of geometrical symmetry in 3-D eddycurrents computation[END_REF], [START_REF] Lobry | Exploitation of the geometrical symmetry in the boundary element method with the group representation theory[END_REF], [START_REF] Hamermesh | Group Theory and its Application to Physical Problems[END_REF], [START_REF] Jansens | Theory of Finite Groups[END_REF] to take advantage of the geometrical symmetry even when the excitation sources do not share necessarily the same periodicity. This enables in the case of surface-mounted permanent magnet (SMPM) machines to reduce the mesh on a single section holding only one stator tooth.

To meet this objective in magnetostatic problems, this approach consists in constructing the full problem by duplicating the FE modeling of an elementary periodic cell. This elementary cell represents the smallest connected section that regenerates the complete model by a simple transformation. In this paper, we will not apply the group representation theory literally, but an equivalent approach based on the linear algebra theory and more particularly on the properties of the stiffness full FE model matrix which is in fact a block circulant matrix. By means of a DFT transformation, it has been shown in the linear case that we can reduce the original large FE problem to a series of independent subproblems with a reduced size [START_REF] Davis | Circulant Matrices[END_REF], [START_REF] Dickinson | Eigenvectors and functions of the discrete Fourier transform[END_REF]. In the non-linear case, some techniques have been proposed to keep the block circulant property by using iterative algorithms based on the fixed-point technique or the transmission-line method. Such techniques allow not only to apply the DFT but also to account for the non-linearity by introducing an additional fictitious source term on the righthand side of the equation system [START_REF] Lobry | Symmetry and TLM method in nonlinear magnetostatics[END_REF], [START_REF] Chiampi | A Jiles-Atherton and fixed-point combined technique for time periodic magnetic field problems with hysteresis[END_REF].

In this paper, we present a methodology to construct a reduced model of an SMPM whose geometry enables to take full advantage of the previous approach in the linear case. First, the full FE model of an SMPM is detailed in Section II. In Section III, the reduction approach is presented, and a dedicated method to take into account the movement is introduced; the rotor motion is considered within the subproblems using the spatial Fourier interpolation method (SFIM) [START_REF] Gersem | Harmonic weighting functions at the sliding interface of a finite-element machine model incorporating angular displacement[END_REF], [START_REF] Montier | Rotation movement based on the spatial Fourier interpolation method (SFIM)[END_REF] extended from the locked step method [START_REF] Preston | Induction motor analysis by time-stepping techniques[END_REF]. The dependence of Fourier components is also exploited to speed up the solution of the problem. Furthermore, in a balanced supply regime, the source has a regular distribution, leading to a limited number of DFT dominant components. In such case, it is sufficient to solve only the corresponding subsystems. Finally, the proposed methodology is applied to the study of a nine teeth/eight poles SMPM example that does not present in fact any common symmetry between the pure geometric model and the source distribution.

II. FINITE-ELEMENT MODELING

In a domain of boundary ( = 1 ∪ 2 and 1 ∩ 2 = {}), the magnetostatic equations and the associated constitutive medium relationship are

∇ × -→ H = -→ J s , ∇. -→ B = 0 ( 1 ) -→ H = ν -→ B -ν -→ B r (2)
where -→ B is the magnetic flux density vector, -→ H is the magnetic field vector, -→ J s is the current source density vector, -→ B r is the residual magnetization vector in the permanent magnets, and ν is the reluctivity. To impose the uniqueness of the solution, boundary conditions are set on 1 and 2

-→ H × -→ n = -→ 0 on 1 ; -→ B . -→ n = 0 on 2 (3)
with -→ n the outward boundary unit normal vector.

To solve (3), the magnetic vector potential

-→ A ( -→ B = ∇× -→ A ) is used.
Besides, to ensure the unicity of -→ A , we most often add the Coulomb gauge which is, however, implicitly verified in the case of 2-D modeling. The resulting vector potential formulation from (1) and ( 2) is now given by

∇ × ν(∇ × -→ A ) = ∇ × ν -→ B r + -→ J s . ( 4
)
In the following, we will clarify how to exploit the geometrical periodicity of the structure of an electrical machine. We consider, therefore, as an example, an SMPM consisting of nine stator teeth supporting a three-phase winding and eight rotor poles (Fig. 1). Due to the non-consistent periodicity between stator and rotor sources, this machine does not present effectively any magnetic symmetry. However, it presents a periodicity that holds on the material permeability, i.e., the geometry regardless of the source distribution (current and residual magnetic flux densities). Therefore, in this machine case, we can discern nine identical cells in space. The principle of the determination of the elementary periodic cell is given in Fig. 1: concerning only the permeability of the materials, this elementary cell is defined by a machine section involving a single stator tooth.

To generalize, let us consider now the case of an electromagnetic device made up of N periodical sections in space (Fig. 2). We suppose that the periodicity holds only on the permeability but not on the sources produced by the currents or the residual magnetic flux density.

We admit that all the sections are discretized by the same mesh and have thus the same number and distribution of nodes. Therefore, it can be shown that it is sufficient to model only an elementary section, as the one presented in Fig. 2, in such a way that the complete model can be deduced by a simple duplication of this elementary model. In each section, n is supposed to be the number of degrees of freedom. It represents the total number of inner nodes excepting: i) the ones on the boundary where a Dirichlet condition is imposed and ii) the ones on the common side with the previous section of the device (see Fig. 2).

Taking into account now the periodicity on the material characteristics of the N sections, the 2-D FE formulation of the linear magnetostatic problem, given in (4), leads to the following matrix system to solve:

⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ S S 0 • • • 0 S S S S 0 • • • 0 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • S 0 • • • 0 S S ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ A 0 A 1 . . . . . . . . . . . . A (N-1) ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ = ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ F 0 F 1 . . . . . . . . . . . . F (N-1) ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ (5)
[S c ][ A] = [F] (6)
where [S c ] is a block circulant matrix of the full FE model,

[ A] of size ([N ×n]×1
) is the set of unknown nodal magnetic potential, and [F] is the source term.

[S] of size (n × n) is the matrix accounting for the inner contribution of each section i , [S ] is the matrix accounting for the contribution on the section i of the previous section i -1, and [S ] is the matrix accounting for the contribution on the section i of the next section i + 1. [ A i ] and [F i ] of size (n × 1) are, respectively, the set of unknown nodal magnetic potential and the source term calculated in the section i (0 ≤ i ≤ N -1).

III. MODEL REDUCTION METHODOLOGY

A. Model Reduction at a Fixed Rotor Position

Using a DFT, the block circulant matrix [S c ] can be factorized under the following expression [START_REF] Chatterjee | An introduction to the proper orthogonal decomposition[END_REF], [START_REF] Davis | Circulant Matrices[END_REF], [START_REF] Olson | Circulant matrices and their application to vibration analysis[END_REF]:

[S c ] = [W ][S ][W ] -1 . ( 7
)
The matrix [W ] and the block diagonal matrix [S ] will be given, respectively, as follows:

[W ] = [U ] ⊗ [I dn ] (8)
[S ] =

⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ S 00 0 • • • • • • • • • • • • 0 0 S 11 0 • • • • • • • • • 0 0 0 S 22 0 • • • • • • 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 0 • • • • • • • • • • • • 0 S (N-1)(N-1) ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ( 9
)
where ⊗ is the Kronecker product and [I dn ] of size (n × n) is the identity matrix. The entries of the DFT matrix [U ] of size (N × N) are given in the following expression:

U (c, l) = 1 √ N e j 2π N (c-1)(l-1) ; 1 ≤ c ≤ N and 1 ≤ l ≤ N. ( 10
)
Combining now ( 6) and ( 7), we obtain

[W ][S ][W ] -1 [ A] = [F]. (11)
Multiplying the system (11) by the inverse matrix [W ] -1 , we retreive the following new system to solve:

[S ][Z ] = [C] (12)
with

[Z ] = [W ] -1 [ A] and [C] = [W ] -1 [F]. (13)
Since [S ] is a block diagonal matrix, we have, therefore, N independent subsystems of size n to be solved

[S ii ][Z i ] = [C i ]; 0 ≤ i ≤ N -1. ( 14
)
The original system (6) of size n × N is now transformed into a set of N independent subsystems of size n. From the solutions of these N subsystems, the solution of the full model on the N sections can be deduced from ( 13) and given by

[ A] = [W ][Z ].
Avoiding solving the full model system of dimension n × N by solving N independent subsystems of dimensions n each, leads effectively to a reduction in the computational time. The considered acceleration in the computational time is denoted γ in the following.

B. Model Reduction Considering the Rotor Motion

In this section, we suppose the general case of a rotating electromagnetic device, consisting of a fixed stator and a movable rotor, and having a periodical structure as described in Section II. To the author's knowledge, no method combining the rotor movement and the DFT approach has been already proposed in the literature. However, such method is required to fully model such rotating electromagnetic device. To tackle this issue, the consideration of the rotor motion in this paper will be combined to our model reduction approach using the SFIM [START_REF] Gersem | Harmonic weighting functions at the sliding interface of a finite-element machine model incorporating angular displacement[END_REF], [START_REF] Montier | Rotation movement based on the spatial Fourier interpolation method (SFIM)[END_REF] which is an extension of the locked step method [START_REF] Preston | Induction motor analysis by time-stepping techniques[END_REF]. To do so, the presence of a fictive interface between the stator and the rotor is defined (Fig. 3). Since the full model of the device represents N identical sections in space, the geometrical periodicity, as it has been said before, can be exploited to simplify the model to only one elementary section.

In Fig. 3, we can notice that in each section i (0 ≤ i ≤ N -1), we have the stator domain si whose number of degrees of freedom is n s and the rotor domain ri whose number of degrees of freedom is n r . The statorrotor interface, where the motion is taken into account, is duplicated to create dual si and ri separation interfaces which belong, respectively, to si and ri . The relationship between the discretization nodes of the two interfaces si and ri allows, according to the locked step method [START_REF] Preston | Induction motor analysis by time-stepping techniques[END_REF] or the SFIM [START_REF] Gersem | Harmonic weighting functions at the sliding interface of a finite-element machine model incorporating angular displacement[END_REF], [START_REF] Montier | Rotation movement based on the spatial Fourier interpolation method (SFIM)[END_REF], considering the rotor motion. When m D is the total number of nodes of the stator-rotor interface, we should denote that the number of degrees of freedom n g = m D /N, related to both interfaces si and ri in each section, is included, respectively, in both n s and n r .

On the basis of the foregoing, we can summarize that there are N periodic sections in the stator, the degree of freedom of each is n s , and N periodic sections in the rotor, and the degree of freedom of each is n r . The use of the geometrical periodicity which makes it possible to construct the full model of the electromagnetic device by concatenation of the elementary section model leads to obtain, according to ( 5) and ( 6); the following overdetermined system to be solved:

[S cS ] [0] [0] [S cR ] [ A SS ] [ A RR ] = [F SS ] [F RR ] (15)
where

[ A SS ] = ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ A S0 A S0 A S1 A S1 . . . . . . A S(N-1) A S(N-1) ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ; [A RR ] = ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ A R0 A R0 A R1 A R1 . . . . . . A R(N-1) A R(N-1) ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ [F SS ] = ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ F S0 F S0 F S1 F S1 . . . . . . F S(N-1) F S(N-1) ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ; [F RR ] = ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ F R0 F R0 F R1 F R1 . . . . . . F R(N-1) F R(N-1) ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ (16)
where

[ A SSi ] = [A Si , A Si ]
T represents the set of the total unknown nodal magnetic potential in the stator domain si of the section i . A Si represents the set of unknown nodal magnetic potential in the stator domain except the ones on the interface Si which are represented by the vector A Si .

[F SSi ] = [F Si , F Si ] T is the source term calculated on the stator domain si . F Si is the source term calculated on the stator domain but referring to the nodes belonging to the stator domain excepting those on the interface Si whose associated source term is given by F Si . As for the rotor terms A RRi , A Ri , A Ri , F RRi , F Ri , and F Ri , they are homologous to the previously defined stator terms A SSi , A Si , A Si , F SSi , F Si , and F Si .

[S cS ] and [S cR ] being block circulant matrices, they can be factorized separately under the following forms:

[S cS ] = [W S ][S S ][W S ] -1 [S cR ] = [W R ][S R ][W R ] -1 (17)
where [S S ] and [S R ] are two block diagonal matrices and the transformation matrices [W s ] and [W R ] will be given, respectively, in terms of the DFT matrix [U ] as follows:

[W S ] = [U ] ⊗ [I dn S ] (18) [W R ] = [U ] ⊗ [I dn R ] (19)
where [I dn S ] and [I dn R ] are the identity matrices of size (n S × n S ) and (n R × n R ), respectively. Combining now the system ( 15) with [START_REF] Gersem | Harmonic weighting functions at the sliding interface of a finite-element machine model incorporating angular displacement[END_REF], we obtain, in the harmonic domain, the new system to solve

[S S ] [0] [0] [S R ] [Z SS ] [Z RR ] = [C SS ] [C RR ] (20)
where the vectors

[Z SS ], [Z RR ], [C SS ],
and [C RR ] will be given in the following expressions:

[Z SS ] = [W S ] -1 [ A SS ] and [C SS ] = [W S ] -1 [F SS ] (21) [Z RR ] = [W R ] -1 [ A RR ] and [C RR ] = [W R ] -1 [F RR ]. (22)
Since [S S ] is a block diagonal matrix, we have, therefore, N independent overdetermined subsystems to solve, of size n S each, and since [S R ] is a block diagonal matrix, we have likewise, therefore, N independent overdetermined subsystems to solve, of size n R each

[S ii S ][Z SSi ] = [C SSi ]; 0 ≤ i ≤ N -1 [Z SSi ] = Z Si Z Si ; [C SSi ] = C Si C Si (23) [S j j R ][Z RRi ] = [C RRi ]; 0 ≤ j ≤ N -1 [Z RRi ] = Z Ri Z Ri ; [C RRi ] = C Ri C Ri . ( 24
)
To solve these different overdetermined independent subsystems in the stator and the rotor domains, they have to be coupled together, and thus we have to express different In fact, in our case, the relationship between [Z S ] and [Z R ] is determined in such a way as to take into account the rotor motion. The latter is performed using the SFIM. It allows considering effectively any rotation angle θ and not only the discrete few angle steps given by θ m = m θ , where m ∈ Z and θ is a previously fixed rotation angle step.

By this method, to take into account the continuous rotor motion, the vector assembling the nodes belonging to the interface solidary to the rotor [ A R ] is expressed as a function of that assembling the nodes of the interface solidary with the stator [ A S ]. This is done by assuming that the DFT of both vectors are given in the following expression:

[Z F R ] = [D(θ )][Z F S ] (25)
where

[D(θ )] is the diagonal matrix linking the DFT [Z F R ] of [ A R ] to the DFT [Z F S ] of [ A S ].
It allows adding a phase lag of amplitude θ to a signal, by multiplying its kth harmonic by e j θk . When m D is the total number of nodes of the stator-rotor interface, the entries of the matrix [D(θ )] of size (m D × m D ) are given in the following expression [START_REF] Montier | Rotation movement based on the spatial Fourier interpolation method (SFIM)[END_REF]:

D(i, i ) = e j θ(i-1) ; i 1, m + D e j θ(i-1-m D ) ; i m + D + 1, m D (26)
where

m + D = [(m D + 1)/2].
The particular form of the matrix [D(θ )] at it is given in ( 26) is due to the periodicity of the DFT. Now, given that [W F ] is the DFT matrix of size (m D × m D ), the vectors [Z F S ] and [Z F R ] are given in the following equations:

[Z F S ] = [W F ] -1 [ A S ] (27)
[Z F R ] = [W F ] -1 [ A R ] (28)
where vectors [ A S ] and [ A R ] are given in the following explicit expressions:

[ A S ] = ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ A S0 A S1 . . . . . . . . . A S(N-1) ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ; [A R ] = ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ A R0 A R1 . . . . . . . . . A R(N-1) ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ . ( 29
)
We should denote furthermore that the vectors [ A S ] and [ A R ] can be expressed in function of their DFT vectors [Z S ] and [Z R ] in the following expressions, respectively,

[Z S ] = [W S ] -1 [ A S ] (30) [Z R ] = [W R ] -1 [ A R ] (31)
where

[W S ] = [W R ] = [U ] ⊗ I d m D N . ( 32
)
Combining now (25), ( 27), ( 28), (30), and (31) leads to the following expression:

[Z R ] = [W R ] -1 [W F ][D(θ )][W F ] -1 [W S ][Z S ] [Z R ] = [Q][Z S ]. (33)
The matrix [D(θ )] being diagonal; therefore, the matrix

[W F ][D(θ )][W F ] -1
is circulant, which will lead furthermore to that in our case where

[W S ] = [W R ], the matrix [Q] = [W R ] -1 [W F ][D(θ )][W F ] -1 [W S ] is block diagonal.
The matrix [Q] being block diagonal, each subvector [Z Ri ] can be expressed as a function only of the corresponding vector [Z Si ], thus leading from ( 23) and (24) to resolve N independent coupled subsystems in the following form:

⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ [S ii S ] Z Si Z Si = C Si C Si [S ii R ] Z Ri Z Ri = C Ri C Ri [Z Ri ] = [Q ii ][Z Si ] ; 0 ≤ i ≤ N -1. (34)
We have then proved that the SFIM used to take into account the rotor motion does not affect the advantage of the exploitation of the geometrical periodicity for any rotation angle θ and leads always to N reduced independent subsystems.

We should denote that to take into account the rotor motion while ensuring a model reduction by means of the exploitation of the geometrical periodicity, the matrices [W S ] and [W R ] should be equals. In fact, this condition is verified when the number of stator and rotor sections are equal. In fact, the choice of the same number of sections N in both stator and rotor does not have any problem in the case of cylindrical rotor machine as in the case of SMPM, for example, since the rotor is without any saliency and thus the number N of the machine periodical sections can be chosen equal to the number of stator teeth N S , the elementary section presenting one stator tooth is effectively the smallest periodic section. However, in the case of salient pole rotor machines as for the cases of double-salient switched reluctance or buried permanent magnet machines, the rotor exhibits strong saliency: the machine consists now of N S stator teeth and N R rotor teeth (i.e., N R salient rotor poles). To ensure a geometrical periodicity, the number N of the machine periodical or congruent sections must be chosen now using the greatest common divisor GCD as in the following equation [START_REF] Larsen | Torque ripple reduction based on current control for a flux switching permanent magnet machine[END_REF]:

N = GCD (N S , N R ). ( 35
)

C. Additional Contribution of the DFT on the Model Reduction by Looking on Their Properties

As a summary, we have verified that the exploitation of the geometrical periodicity in some electromagnetic devices results in the transformation of a large system to be solved to several subsystems of small dimensions, thus leading to an acceleration in the computational time which is denoted γ . This was verified to be always true even when taking into account the continuous rotor motion using the SFIM.

Moreover, the normalized DFT has some particular characteristics such as the interdependence between the spectral components in the case of the DFT of real values. This type of interdependence will be studied in the following part, differentiating the two cases of sampling with an even or odd number N. In our case, the values undergoing the DFT are real numbers representing the nodal values of the magnetic potential. We can prove (see Appendix A) that if a vector [Z ] is the DFT of a real vector [ A] of dimension N, some components of [Z ] are interdependent. We can deduce that some subsystems in (34) do not need to be solved. For example, in the case where N is even, the vector [Z ] can be given by its general representation form

[Z ] = ⎡ ⎢ ⎢ ⎢ ⎣ Z 0 Z N 2 -α Z N 2 Z N 2 +α ⎤ ⎥ ⎥ ⎥ ⎦ where α ∈ [1; 2 . . . ; N 2 -1] ( 36
)
where

Z N 2 +α = Z N 2 -α ; α ∈ 1; 2 . . . ; N 2 -1 . ( 37
)
Only the (N/2 + 1) subsystems associated with the vectors Z 0 , Z (N/2)-α , and Z (N/2) are determined by solving (34). The other vectors Z (N/2)+α will be deduced in a post-processing step using the simple conjugate relationship (37). Avoiding that the solving of all the N subsystems, by solving only (N/2 -1) subsystems, increases, therefore, the acceleration in the computational time from γ to γ p = γ × (N/((N/2) + 1)).

However, in the case, where N is odd, the general representation form of the vector [Z] is now

[Z ] = ⎡ ⎢ ⎣ Z 0 Z N+1 2 -α Z N-1 2 +α ⎤ ⎥ ⎦ where α ∈ 1; 2 . . . ; N 2 -1 (38)
where

Z N-1 2 +α = Z N+1 2 -α ; α ∈ 1; 2 . . . ; N -1 2 . ( 39
)
Only the (N + 1)/2 subsystems associated with the vectors Z 0 and Z ((N+1)/2)-α are determined by solving (34). The other vectors Z ((N-1)/2)+α will be deduced in a post-processing step using the simple conjugate relationship (39). We retrieve, therefore, the same property as the one pointed out in the case when N is an even number and so the opportunity of speedup. However, the acceleration in the computational time when N is odd is now quite different and it is given by

γ p = γ × N/ N+1 2 .

D. Additional Contribution of the DFT on the Model Reduction by Looking on the Spectral Content of the Solution

In several particular cases characterized by a regular distribution of the sources (currents and/or permanent magnets), one spectral harmonic of this distribution can be dominant, and thus a prevailing spectral harmonic of the solution predominantly governs the overall distribution of the full model solution. It seems profitable then to solve only the subsystem associated with the DFT component related to this prevailing harmonic. To benefit from this advantage, it is necessary, therefore, to determine the relationship between a given harmonic k and a DFT component Z m of the vector [Z ].

In Appendix B, we have proven that the spectral information relating to the harmonic k is represented by the component m of the DFT vector such that the relation between m and k is described in the following expression:

k = |N × l ± m| where l ∈ N. ( 40
)
Knowing the prevailing harmonic k, then one can determine the dominant component m of the DFT vector [Z ]; the considered component Z m will represent the spectral content of the harmonic k. Coming back now to the solution of the system (34): if we are in the case where the full model solution is governed by the harmonic k, thus giving the advantage of solving only and sufficiently in (34), the single FE subsystem linked to the components [Z SSm ]and [Z RRm ]. This will increase effectively the speedup to γ p = γ × N.

All these different cases will be treated in the following part on an application example of an SMPM.

IV. APPLICATION EXAMPLES

The application example is a 9/8 SMPM (Fig. 4). It consists of nine stator teeth and eight rotor permanent magnets. Using the classical approach, there is no obvious magnetic symmetry and as a matter of fact the full geometry of the machine needs to be meshed. However, the rotor permeability (iron and magnet) is axisymmetric even though the residual magnetic flux density varies, but it does not alter the material characteristic, i.e., permeability and periodicity, as mentioned in Section II.

In fact, the studied machine represents a stator saliency with N s = 9 teeth and a cylindrical non-salient rotor. Therefore, the elementary periodic cell, as we have noticed in Section II, turns out to be only one stator tooth and representing 1/9 of the whole machine (Figs. 1 and4). However, the rotor presents N a = 8 permanent magnets; the symmetry, hence, is not consistent between the stator teeth and the rotor poles. To overcome this problem, the permanent magnets are subdivided each into q portions, d portions of which are modeled in the elementary section.q and d should verify the following equation:

d × 9 = q × 8 (41)
In the simplest case, we can choose d = 8 and q = 9; each permanent magnet should be subdivided, therefore, into nine portions from which eight portions only are modeled in the elementary 1/9 machine section (Fig. 4). The residual magnetic flux density distribution in nine different sections is shown in Fig. 5, while the stator phases are left unloaded. We should denote that the 2-D spatial mesh of the elementary cell is made of n = 625 nodes and 1158 elements.

From the mesh of one cell, we have reconstructed a full FE model (reference) that we have compared to the reduced model. The exploitation of the geometrical periodicity makes it possible to switch effectively from the large FE system to nine independent subsystems. In our case, the transformation from the real unknown values to the DFT values is given in the following relations

[Z SS ] = [W S ] -1 [ A SS ] and [Z RR ] = [W R ] -1 [ A RR ] (42) [Z SS ] = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ Z SS0 Z SS1 Z SS2 Z SS3 Z SS4 Z SS5 Z SS6 Z SS7 Z SS8 ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ and [Z RR ] = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ Z RR0 Z RR1 Z RR2 Z RR3 Z RR4 Z RR5 Z RR6 Z RR7 Z RR8 ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ . ( 43
)
Thanks to the particular properties of the DFT (see Section III-C), some spectral components are dependent. In our case, N is odd; then, the components: Z ((N-1)/2)+α = Z ((N+1)/2)-α where α ∈ [1 : ((N -1)/2)]. Therefore, if N = 9, the components Z SS8 , Z SS7 , Z SS6 , and Z SS5 are linked to Z SS1 , Z SS2 , Z SS3 , and Z SS4 and the corresponding subsystems can be not necessarily solved (same for [Z RR ] components). The remaining five subsystems are solved, while the unknowns of the other subsystems will be deduced in a post-processing step. If we admit that the transformation into nine independent subsystems leads to a speedup of γ , the solving, hence, of five subsystems instead of nine will lead in addition to an advantage acceleration in the calculation time theoretically equal to γ p = γ × 9/5.

A. Balanced Regime

The first application is the case of a balanced permanent magnet source distribution in the rotor, while the stator winding is kept unloaded. In fact, we have verified that the reduced model solution matches absolutely the one of the reference full model. The post-processing global quantity compared between both models is the magnetic flux flowing through a tooth coil (Fig. 6).

The local quantities are the flux line distribution (Fig. 7), the magnetic flux density (Fig. 8), and the magnetic potential calculated at the air-gap level in function of the angular position (Fig. 9). The flux lines, the flux density distributions, and the magnetic potential are calculated at a given rotor position, while the magnetic flux is calculated for a full rotor mechanical revolution. The speedup resulting from the transformation of the large system into nine independent subsystems has been The distribution of the source in the rotor has a particular shape: it consists of four pairs of permanent magnets leading to a source distribution in such a way that the fourth harmonic is dominant. This can be verified by looking at the distribution of the magnetic potential calculated at the air-gap level and its spectral representation (Figs. 7 and8). Since the fourth harmonic is dominant, the solution of the associated subsystem could be sufficient to obtain an acceptable accuracy compared to the full model (see Section III-D). According to (40), the spectral harmonics are projected into the DFT components as presented in Table I, where l N and [] + represents the positive value. According to Table I, the spectral representation of the magnetic potential shown in Fig. 9 is plotted in Fig. 10 as a function of the harmonics and the associated DFT components.

The prevailing fourth harmonic corresponds to the case where k = l × N +4 = 4, l = 0, m = 4, and N = 9. As shown in Fig. 10, the fourth harmonic is associated with the DFT component Z 4 . Therefore, the solution of the subsystem corresponding to Z 4 component seems to be sufficient to obtain an accepted accuracy. Generating now the global solution from the component Z 4 only, we have remarked that the model reduction solution matches very well the one of the reference full model.

The results are in agreement not only with respect to the global quantity of the magnetic flux (Fig. 11) where the error does not exceed 0.12% but also regarding the local ones (Figs. [START_REF] Hamermesh | Group Theory and its Application to Physical Problems[END_REF][START_REF] Jansens | Theory of Finite Groups[END_REF][START_REF] Davis | Circulant Matrices[END_REF], but now with a slight low precision where the error considering the calculation of the magnetic potential in the air gap, for example, is about 5% (Fig. 14). Solving a single subsystem instead of nine allows an acceleration in time of calculation of order γ p = 9 × 1.7 ≈ 15.

C. Unbalanced Regime With a Demagnetization of a Rotor Permanent Magnet

In this section, we will study the case of unbalanced regimes that can be characterized by one of the following three cases: 1) a demagnetization of a permanent magnet in the rotor; 2) a short circuit in the stator windings; 3) an unbalanced power supply to the stator. In our case, since the stator is not loaded, we will study the case of an unbalanced regime characterized by a defect of demagnetization of a permanent magnet in the rotor (Fig. 15). This defect causes the rupture of the particular balanced distribution of the rotor source, and thus we are no longer in the case of a dominant harmonic: five of the nine subsystems must be solved. The solution is compared between the The spectral representation of the magnetic potential distribution, as presented in Fig. 20, has shown that effectively there is not a single dominant harmonic, but many harmonics of important values. Now, to see the contribution of each DFT component to the construction of the full problem solution, the solution is computed separately from different modes Z 0 , Z 1 , Z 2 , Z 3 , and Z 4 . The corresponding flux line distribution and the magnetic potential calculated at the air-gap level are plotted in Fig. 21.

Finally, the acceleration in the computational time for the various problems treated previously is summarized in Table II.

V. CONCLUSION

The presented approach based on the geometrical periodicity, and using the DFT, allows an efficient reduction of the FE model of an SMPM. Moreover, it was verified that the SFIM technique enables to model the continuous rotor movement while retaining the advantage of the geometrical periodicity.

The particular characteristics of the DFT allow additional acceleration in the computational time due to the inter-dependence between the harmonic components. Besides, a further acceleration can adequately take place in the case of a balanced regime where the solution distribution is governed by a single dominant spectral harmonic.

We should denote that these accelerations in the computational time have been obtained while even using a sequential computation. Nevertheless, an optimal speedup can be achieved, and that when using a parallel computation since the yielding reduced subsystems are effectively independent.

APPENDIX

A. Conjugate Relationship Between DFT Components

Assuming the case of a vector X of dimension N given in the following form:

[X ] = [x 0 x 1 • • • x m • • • x (N-1) ] T . ( 44
)
The DFT vector [Z ] of [X] will be given in the following expression using the inverse DFT matrix [U ] -1 :

[Z ] = [U ] -1 [X ] = [Z 0 Z 1 • • • Z m • • • Z N-1 ] T (45)
where the entries of [U ] -1 are given by U -1 (l, c) = 1 √ N e -j × 2π N ×(l-1)×(c-1) 1 ≤ l ≤ N and 1 ≤ c ≤ N. (46)

From ( 45) and (46), the general term Z m of the vector [Z ] will be given, therefore, in the following expression:

Z m = N-1 n=0
x n e -j × 2π N ×m×n .

(47)

Let us first suppose the case where N, the number of samples is even; then, the vector [Z ] can be given by its general representation form

[Z ] = ⎡ ⎢ ⎢ ⎢ ⎣ Z 0 Z N 2 -α Z N 2 Z N 2 +α ⎤ ⎥ ⎥ ⎥ ⎦
where α ∈ 1; 2 . . .

; N 2 -1 . ( 48
)
Based on (47), the expressions of both general terms Z (N/2)-α and Z (N/2)+α will be given by

Z N 2 -α = N-1 n=0
x n e -j ×π×n × e j × 2π N ×α×n (49)

Z N 2 +α = N-1 n=0
x n e -j ×π×n × e -j × 2π N ×α×n . (

With n being an integer which takes the values 1, 2, . . . , N-1, the term e -j ×π×n is then a real number that can take the values 1 or -1. We can then deduce, from (49) to (50), that Z (N/2)+α and Z (N/2)-α are conjugate

Z N 2 +α = Z N 2 -α ; α ∈ 1; 2 . . . ; N 2 -1 . ( 51
)
In the other case, where the sampling number N is odd, the vector [Z ] can be given its general representation form

[Z ] = ⎡ ⎢ ⎣ Z 0 Z N+1 2 -α Z N-1 2 +α ⎤ ⎥ ⎦ where α ∈ 1; 2 . . . ; N 2 -1 . ( 52
)
In the same way, based on (47), the expressions of both general terms Z ((N+1)/2)-α and Z ((N-1)/2)+α will be given by

Z N+1 2 -α = N-1 n=0
x n e -j ×π×n × e -j × π N ×(1-2α)×n (53)

Z N-1 +α = N-1 n=0
x n e -j ×π×n × e j × π N ×(1-2α)×n .

(54)

We can then deduce from (53) and (54) that Z ((N+1)/2)-α and Z ((N-1)/2)+α are conjugate

Z N-1 2 +α = Z N+1 2 -α ; α ∈ 1; 2 . . . ; N -1 2 . ( 55
)

B. Spectral Content of DFT Components

Let us consider the case of a signal x(t) representing a sinusoidal function of frequency k f corresponding to the kth harmonic of a reference signal of frequency f . When this given kth harmonic signal whose mathematical representation is x (t) = A k sin(k2π f t) and is discretizing through a sampling frequency F s = N × f , the sampling vector consisting of the N samples will be given in the following form:

[X ] = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ 0 A k sin(k2π/N) . . .
A k sin(k2π/N × m) . . .

A k sin(k2π/N × (N -1)) ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ . ( 56
)
Performing now in a following step, the DFT of the vector [X] which leads to the vector [Z ] = U -1 [X ] whose general term, using (47), is given in the following expression:

Z m = N-1 n=0 A k 2 j
√ N e j ×2π ×(k-m) N

×ne -j ×2π ×(k+m) N ×n . (57) Indeed, terms e (( j ×2π×(k-m))/N) and e -(( j ×2π×(k+m))/N) represent, respectively, the Nth roots of the complex numbers: e j ×2π×(k-m) and e -j ×2π×(k+m) . Since (km) ∈ Z and (k + m) ∈ Z, both complex numbers e j ×2π×(k-m) and e -j ×2π×(k+m) are thus equal to 1, and therefore both series in (57) will be equal to zeros since they represent in fact the sum of the Nth roots of unity. However, one of these sums will be non-zero if there exists an integer l such that k ± m = N × l.

(58)

In the excepted cases presented by the relation (58), e (( j ×2π×(k-m))/N)×n or e -(( j ×2π×(k+m))/N)×n will be equal to 1 regardless the value of n; Z m will be not equal to zero, and it will include, therefore, the spectral on the harmonic k.

Fig. 1 .

 1 Fig. 1. 9/8 synchronous machine: highlighting different sources (left) and considering the permeability of materials regardless of sources (right).

Fig. 2 .

 2 Fig.2. Full model (left). Modeling of one elementary section: the crossed points represent the inner nodes, the round points represent the ones common with the previous section, and the squared points represent the ones subjected to Dirichlet conditions (right).

Fig. 3 .

 3 Fig. 3. Full model of a rotating electromagnetic device. The marked fictive interface separates the fixed part (stator) from the rotating part (rotor) (left). Modeling of one elementary section (right).

  [Z Ri ] as functions of different [Z S j ]. In other words, where [Z S ] and [Z R ] are, respectively, the set of [Z Si ] and [Z Ri ], we have to express [Z S ] as a function of [Z R ].

Fig. 4 .

 4 Fig. 4. Cylindrical SMPM 9/8 (left). Mesh of the 1/9 modeled section (right).

Fig. 5 .

 5 Fig. 5. Permanent magnet source distribution in the nine different sections.

Fig. 6 .

 6 Fig. 6. Magnetic flux through a tooth coil calculated with the reference full model and the reduced model in the balanced regime.

Fig. 7 .

 7 Fig. 7. Flux line distribution calculated with the reference full model (left) and the reduced model (right) in the balanced regime.

Fig. 8 .

 8 Fig. 8. Flux density distribution calculated with the reference full model (left) and the reduced model (right) in the balanced regime.

Fig. 9 .

 9 Fig. 9. Magnetic potential in the air gap in function of the angular position calculated with the reference full model and the reduced model in the balanced regime.

Fig. 10 .

 10 Fig. 10. Spectral representation of the magnetic potential distribution at the air-gap level in the balanced regime.

Fig. 11 .

 11 Fig. 11. Magnetic flux through a tooth coil calculated with the reference full model and the reduced model with only Z 4 .

Fig. 12 .

 12 Fig. 12. Flux line distribution calculated with the reference full model (left) and the reduced model with only Z 4 (right).

Fig. 13 .

 13 Fig. 13. Flux density distribution calculated with the reference full model (left) and the reduced model with only Z 4 (right).

Fig. 14 .

 14 Fig. 14. Magnetic potential in the air gap in function of the angular position calculated with the reference full model and the reduced model with only Z 4 .

Fig. 16 .

 16 Fig. 16. Magnetic flux through a tooth coil calculated with the reference full model and the reduced model in the unbalanced regime.

Fig. 17 .

 17 Fig. 17. Flux line distribution calculated with the reference full model (left) and the reduced model (right) in the unbalanced regime.

Fig. 18 .

 18 Fig. 18. Flux density distribution calculated with the reference full model (left) and the reduced model (right) in the unbalanced regime.

Fig. 19 .

 19 Fig. 19. Magnetic potential in the air gap in function of the angular position calculated with the reference full model and the reduced model in the unbalanced regime.

Fig. 20 .

 20 Fig. 20. Spectral representation of the magnetic potential distribution at the air-gap level in the unbalanced regime.

Fig. 21 .

 21 Fig. 21. Flux line distribution and air-gap magnetic potential calculated by means of different modes Z 0 , Z 1 , Z 2 , Z 3, and Z 4 separately.

  M. Al Eit , S. Clénet , and T. Henneron Université de Lille, Arts et Metiers ParisTech, Centrale Lille, HEI, EA 2697-L2EP-Laboratoire d'Electrotechnique et d'Electronique de Puissance, F-59000 Lille, France

  [S cS ] and [S cR ] are two block circulant matrices linked to stator and rotor geometrical domains, respectively. [ A SS ] and [ A RR ] which are, respectively, of size ([N × n s ] × 1) and ([N × n r ] × 1), represent the vectors of the magnetic potential unknowns, and [F SS ] and [F RR ] are the source terms. The vectors [ A SS ], [ A RR ], [F SS ], and [F RR ] are given with their following explicit forms:

TABLE I

 I

	HARMONIC CONTENT OF EACH DFT COMPONENT
	calculated; it is equal to γ = 1.7. Solving five instead of
	nine subsystems will lead moreover to a theoretical speedup
	of γ = 1.7 × 9 5 ≈ 3.
	B. Balanced Regime Considering Only Z 4

TABLE II SPEEDUP

 II IN THE FE COMPUTATIONAL TIME IN DIFFERENT CASES OF BALANCED AND UNBALANCED REGIMES


Cédric Ménard

Joelle Dulong

David Roulois

Benjamin Hebraud

Léa Verdière

Céline Pangault

Vonick Sibut

Isabelle Bezier

Nadège Bescher

Philippe ; Bourin

Direction Espagnolle Nicolas Csa21

Stromalab Tarte

Joëlle Dulong

Benjamin Hébraud

Céline Monvoisin

Mélanie Gadelorge

Nicolas Bertheuil

Erwan Flécher

Louis Casteilla

Philippe Collas

Luc Sensebé

Nicolas Espagnolle

Karin Tarte
email: karin.tarte@univ-rennes1.fr

Integrated transcriptomic, phenotypic, and functional study reveals tissue-specific immune properties of mesenchymal stromal cells

Keywords: Integrated Transcriptomic, Phenotypic, and Functional Study Reveals Tissue-Specific Immune Properties of Mesenchymal Stromal Cells Integrated transcriptomic, phenotypic, and functional study reveals tissue-specific immune properties of mesenchymal stromal cells adipose stem cells, Bone marrow stromal cells (BMSCs), Immunosuppression, Immunogenicity, Gene expression, Cell interactions

published or not. The documents may come   L'archive ouverte pluridisciplinaire

INTRODUCTION

Mesenchymal stromal cell (MSC) therapy has gained tremendous interest over the past decade, since the seminal proof of concept of its beneficial effect in steroidresistant graft-versus-host disease [START_REF] Shi | Immunoregulatory mechanisms of mesenchymal stem and stromal cells in inflammatory diseases[END_REF][START_REF] Galipeau | Mesenchymal Stromal Cells: Clinical Challenges and Therapeutic Opportunities[END_REF]. MSCs have thereafter been proposed as a valuable innovative approach in a wide array of inflammatory diseases, acute tissue injury syndromes, and chronic degenerative disorders, and more than 900 clinical trials involving MSCs have been registered (http://www.clinicaltrials.gov).

Nevertheless, the limited evidence of their effectiveness in prospective randomized phase III trials, the lack of defined in vivo mechanism of action allowing the design of relevant potency assays and patient monitoring strategies, together with the high cost of regulatory approved cell productions have hampered their development in the clinic [START_REF] Galipeau | Mesenchymal Stromal Cells: Clinical Challenges and Therapeutic Opportunities[END_REF][START_REF] Galipeau | The mesenchymal stromal cells dilemma--does a negative phase III trial of random donor mesenchymal stromal cells in steroid-resistant graft-versus-host disease represent a death knell or a bump in the road?[END_REF]. Besides heterogeneity of recipients, one possible explanation for the inconsistency in clinical results is the heterogeneity of transplanted MSC batches. In addition to inter-individual variability in MSC donors, several critical culture-related parameters affect MSC properties, including culture medium, scale of culture expansion, or cell freezing [START_REF] Sensebé | Good manufacturing practices production of mesenchymal stem/stromal cells[END_REF][START_REF] Mendicino | MSC-based product characterization for clinical trials: an FDA perspective[END_REF][START_REF] Moll | Do cryopreserved mesenchymal stromal cells display impaired immunomodulatory and therapeutic properties?[END_REF]. Accordingly, we have recently shown that replicative senescence associated with industrial-scale expansion of MSCs is associated with a decreased capacity to inhibit T-cell proliferation [START_REF] Loisel | Brief Report: Proteasomal Indoleamine 2,3-Dioxygenase Degradation Reduces the Immunosuppressive Potential of Clinical Grade-Mesenchymal Stromal Cells Undergoing Replicative Senescence[END_REF]. Moreover, cryopreservation may behave as an additive detrimental determinant of MSC function and potency [START_REF] Chinnadurai | Cryopreserved Mesenchymal Stromal Cells Are Susceptible to T-Cell Mediated Apoptosis Which Is Partly Rescued by IFNγ Licensing[END_REF].

The tissue source of MSCs was identified early as a major parameter modulating MSC functional properties. The two major sources of clinical-grade MSCs are adult bone marrow and adipose tissue. Both of them allow the generation of large number of cells expressing the minimal MSC phenotype, i.e. CD45 neg CD31 neg CD14 neg CD105 pos CD73 pos CD90 pos , and displaying anti-inflammatory properties in vitro [START_REF] Sensebé | Good manufacturing practices production of mesenchymal stem/stromal cells[END_REF].

Cultured adipose-derived stromal cells (ASCs) and bone marrow-derived stromal cells (BM-MSCs) have been proposed to exhibit specific phenotypes, differentiation potentials, secretomes, exosome contents, DNA methylation signatures, as well as transcriptomic, proteomic, and metabolomic profiles [START_REF] Cho | RNA sequencing reveals a transcriptomic portrait of human mesenchymal stem cells from bone marrow, adipose tissue, and palatine tonsils[END_REF][START_REF] De Almeida | Epigenetic Classification of Human Mesenchymal Stromal Cells[END_REF][START_REF] Jansen | Functional differences between mesenchymal stem cell populations are reflected by their transcriptome[END_REF][START_REF] Torensma | The impact of cell source, culture methodology, culture location, and individual donors on gene expression profiles of bone marrow-derived and adipose-derived stromal cells[END_REF][START_REF] Lee | Comparative study on metabolite level in tissuespecific human mesenchymal stem cells by an ultra-performance liquid chromatography quadrupole time of flight mass spectrometry[END_REF][START_REF] Reinisch | Epigenetic and in vivo comparison of diverse MSC sources reveals an endochondral signature for human hematopoietic niche formation[END_REF]. However these findings are not consistent, raising the hypothesis that in vitro culture could alter the impact of MSC tissue source. Importantly, MSC clinical efficacy relies on their paracrine activity including their ability to dampen innate and adaptive immune response [START_REF] Shi | Immunoregulatory mechanisms of mesenchymal stem and stromal cells in inflammatory diseases[END_REF].

Heterogeneity of MSC production processes but also of immunological assays used to evaluate the impact of MSC tissue sources on their anti-inflammatory and immunosuppressive properties have produced conflicting results [START_REF] Mattar | Comparing the Immunomodulatory Properties of Bone Marrow, Adipose Tissue, and Birth-Associated Tissue Mesenchymal Stromal Cells[END_REF][START_REF] Ménard | Immunoregulatory properties of clinical grade mesenchymal stromal cells: evidence, uncertainties, and clinical application[END_REF]. Nevertheless, several reports argue for a superiority of ASCs over BM-MSCs to inhibit T-cell activation, in relationship with an increased capacity to produce the immunosuppressive enzyme indoleamine-2,3 dioxygenase (IDO) [START_REF] Ménard | Clinical-grade mesenchymal stromal cells produced under various good manufacturing practice processes differ in their immunomodulatory properties: standardization of immune quality controls[END_REF][START_REF] Melief | Adipose tissue-derived multipotent stromal cells have a higher immunomodulatory capacity than their bone marrowderived counterparts[END_REF][START_REF] Ribeiro | Mesenchymal stem cells from umbilical cord matrix, adipose tissue and bone marrow exhibit different capability to suppress peripheral blood B, natural killer and T cells[END_REF].

Strikingly, comparative studies of ASC versus BM-MSC properties almost exclusively

analyze MSCs obtained from different donors, sometimes even propagated in different culture conditions, thus precluding any conclusion on the specific role of MSC tissue-of-origin on the observed variability [START_REF] Mattar | Comparing the Immunomodulatory Properties of Bone Marrow, Adipose Tissue, and Birth-Associated Tissue Mesenchymal Stromal Cells[END_REF]. In addition, they generally include low numbers of MSC batches, maximizing the influence of inter-individual variability. The only large comparison of ASCs and BM-MSCs obtained from the same donors exclusively focused on in vitro immunological functional assays without any evaluation of the molecular mechanisms underlying differences in MSC-driven immunosuppression [START_REF] Valencia | Comparative analysis of the immunomodulatory capacities of human bone marrow-and adipose tissuederived mesenchymal stromal cells from the same donor[END_REF]. Finally no study has checked whether the observed differences could be detected in situ in native MSCs. Overall, the decision to use ASCs versus BM-MSCs is typically motivated by proprietary concerns rather than by validation of their superiority in standardized assays.

The present work was designed to conclude on the biological significance of taking into account MSC tissue source in the design of MSC-based trials. For the first time, we combined transcriptomic, phenotypic, and functional analyses performed on ASCs and BM-MSCs obtained from the same 14 donors, and cultured under identical clinical grade-like conditions. We identified, using a combination of differential expression, pathway analysis, and weighted gene co-expression network analysis (WGCNA), a specific gene expression profile (GEP) of BM-MSCs versus ASCs with enrichment for niche-related versus immune related genes. Importantly, we highlighted the same specificities in sorted native BM-MSCs (nBM-MSCs) versus ASCs (nASCs), reinforcing the hypothesis of an imprinting of tissue source on MSC properties. Interestingly, these differences have direct functional consequences on the capacity of MSCs to interact with immune cells. Our results add a new rationale to support the use of adipose tissue as a source of MSCs for the treatment of immune-mediated diseases.

MATERIALS AND METHODS

Cultured MSC production and phenotypic characterization

Healthy donor recruitment followed institutional review board approval and written informed content process according to the revised Declaration of Helsinki was obtained. Fourteen donors were enrolled in this study (3 women and 11 men; median age: 36 ; Body Mass Index: 16.5 to 25) and provided bone marrow aspirates (iliac crest) and lipoaspirates (abdominal fat layer). ASCs were obtained after digestion with 0.4U/mL clinical grade-NB4 collagenase (Roche Diagnostics, Mannheim, Germany) for 45 min at 37°C, filtration, and centrifugation to obtain the stromal vascular fraction (SVF) [START_REF] Bourin | A first approach for the production of human adipose tissue-derived stromal cells for therapeutic use[END_REF]. SVF was seeded at 4.10 3 cells/cm 2 onto CellSTACK closed cell culture chambers (Corning, Lowel, MA) in MEM (Macopharma, Tourcoing, France) supplemented with 10% screened fetal calf serum (Hyclone, Logan, UT) and 10g/mL ciprofloxacin. Paired BM-MSCs were produced in parallel from unprocessed bone marrow seeded at 5.10 4 cells/cm 2 in the same culture dishes and medium as those used for ASCs. For both MSC types, medium was renewed twice weekly until cells reached confluence (end of passage 0 (P0)).

Cells were then detached using trypsin, reseeded at 1000/cm 2 until near confluence (end of P1) and subsequently harvested and cryopreserved until use. Additional ASC and BM-MSC batches were obtained with the same process from an independent set of healthy donors for validation experiments. For further use, MSCs were thawed, seeded at 1000 cells/cm 2 and cultured until 80% confluence. All subsequent phenotypic and functional experiments were performed at the end of P2. In particular, MSCs were assessed by flow cytometry for HLA-DR, CD14, CD90, CD73, CD45, CD34, CD105, CD146 (Beckman Coulter, Villepinte, France), CD31 (eBioscience, Paris, France), and VCAM-1 (Becton-Dickinson, Le Pont de Claix, France) as previously described [START_REF] Ménard | Clinical-grade mesenchymal stromal cells produced under various good manufacturing practice processes differ in their immunomodulatory properties: standardization of immune quality controls[END_REF]. Acquisition files were analyzed with Kaluza software (Beckman-Coulter) and data expressed as the ratio of mean fluorescence intensity (rMFI) obtained for each marker and its matched isotypic control antibody.

Gene expression profiling of cultured MSC

Whole genome gene expression profiling was performed on 14 BM-MSCs and 14 autologous ASCs at the end of P1 using Affymetrix Human Gene 1.0 ST microarrays (Affymetrix, Santa Clara, CA) and data were analyzed with R package Limma (v3.32.10). Non-redundant gene datasets were first generated after GCRMA normalization by retaining for each gene the probeset with the highest expression.

Normalized data were visualized by PCA analysis using the R package EMA.

Pearson correlation with pairwise complete observation was then performed and visualized using heatplot function of the R package made4. Euclidian distance was As a secondary method of analysis, we used the WGCNA R package [START_REF] Langfelder | WGCNA: an R package for weighted correlation network analysis[END_REF] to identify modules of co-expressed genes among the 13 paired MSC batches identified as correctly segregated by the unsupervised Pearson correlation analysis. For this analysis, we retained the top 25% most variable genes. Expression matrix was log2 transformed and the network was constructed by Pearson correlation considering a soft threshold power () value identified with the function Pick Soft Threshold in order to avoid the selection of an arbitrary cut-off. Then, a topological overlap metric (TOM) matrix was derived from the gene expression matrix and the dissimilarity of TOM was calculated. Hierarchical clustering tree was created and modules were generated by the dynamic tree cut method, with a minimum module size of 100 and a deepSplit of 2. Each module was marked by a color. The module eigengenes (ME) were then assigned to each cell type and visualized as a box-plot. To determine if coexpression modules were associated with tissue of origin, we performed a Wilcoxon Signed-Rank test. For the most relevant modules, gene expression was visualized with a heatmap using the heatplot function of the R package. Finally, module genelists were used for downstream enrichment pathway using the Ingenuity Pathway Analysis software (QIAGEN Bioinformatics).

For some genes, expression level was also assessed by Q-PCR, as previously described [START_REF] Ménard | Clinical-grade mesenchymal stromal cells produced under various good manufacturing practice processes differ in their immunomodulatory properties: standardization of immune quality controls[END_REF]. Briefly, after RNA extraction, gene expression was quantified using Taqman assay-on-demand reagents and an ABI Prism 7000 (Applied Biosystems, Courtaboeuf, France) with the CT calculation method. PCR data were normalized to the geometric mean of the two housekeeping genes (CDKN1B and EIF2B1). Results were further standardized by comparison to gene expression of a pool of 5 peripheral blood mononuclear cells (PBMC).

Analysis of native MSCs

VCAM-1 and HLA-DR expression was assessed on native MSCs after enzymatic digestion of 6 lipoaspirates and 6 BM aspirations with the same protocol. Briefly, unprocessed tissue samples were incubated for 45min at 37°C with 200IU/mL type IV collagenase, 1.6IU/mL neutral protease (Worthington, Lakewood, NJ), and S1) and VCAM-1 and HLA-DR expression was evaluated on both subsets.

For sorting of nBM-MSCs, BM mononuclear cells were first collected from enzymatically-digested BM using Ficoll gradient and depleted for CD45 pos cells using CD45-coupled magnetic beads (Dynabeads, Thermo Fisher Scientific). nBM-MSCs (n=7) and nASCs (n=10) were purified on a FacsAria II cell sorter (Becton Dickinson).

Gene expression level in native MSCs was assessed using the Fluidigm BioMark HD system. Briefly, cDNAs were obtained using the Fluidigm reverse transcription Master Mix and were then pre-amplified for 18 cycles in the presence of Pre-Amp Master Mix and pooled Taqman assay mix. Gene expression was then measured with the TaqMan Gene Expression Master Mix on a 48.48 Dynamic Array IFC. After quality control check, gene expression was calculated with the CT calculation method and CDKN1B and EIF2B1 as housekeeping genes.

Impact of MSCs on immune cell apoptosis and adhesion

MSC ability to support survival of immune cells was evaluated as described [START_REF] Ménard | Clinical-grade mesenchymal stromal cells produced under various good manufacturing practice processes differ in their immunomodulatory properties: standardization of immune quality controls[END_REF].

Briefly, paired ASCs and BM-MSCs obtained from the same donors were cocultured with peripheral blood B (1/1 B/MSC ratio), and T cells (10/1 T/MSC ratio) purified using negative selection kits (Miltenyi Biotec, purity >97%). After with HiPerfect Transfection Reagent (Qiagen). Briefly, 20.000 BM-MSC were plated in 96-wells flat-bottomed plates and incubated for 2 days with the transfection mix containing siRNA (50nM each). Efficient downregulation of VCAM-1 expression was confirmed by flow cytometry (Figure S2).

MSC chemoattractive properties

CXCL1 and CXCL16 were quantified in MSC supernatant at the end of P2 by ELISA (R&D Systems, Abington, UK) and expressed as the quantity per million of cultured MSCs.

Migration of neutrophils in response to conditioned MSC supernatants was assessed as previously described [START_REF] Grégoire | Neutrophils trigger a NF-κB dependent polarization of tumor-supportive stromal cells in germinal center Bcell lymphomas[END_REF] with slight modifications. Briefly, peripheral blood neutrophils freshly purified using whole blood CD15 microbeads on an AutoMACS ® apparatus (Miltenyi Biotech) were added to the upper compartment of Transwell chambers with 5-µm pore filters in migration medium (RPMI supplemented with 0.1% human albumin). Lower chambers contained MSC-conditioned supernatants obtained after 3 days of MSC culture in migration medium. The absolute number of viable DAPI neg CD66 pos CD16 pos neutrophils was quantified in the lower chamber after a 2-hour migration using FlowCount beads by flow cytometry.

MSC immunosuppressive properties

Inhibition of T and NK cells proliferation was performed as previously described [START_REF] Ménard | Clinical-grade mesenchymal stromal cells produced under various good manufacturing practice processes differ in their immunomodulatory properties: standardization of immune quality controls[END_REF].

Briefly, purified peripheral blood T and NK cells were stained with 0.2µM CFSE and activated for 6 days in coculture with MSCs at 10/1 and 1/1 ratios respectively. T cells were activated with 0.5µg/mL agonistic anti-CD3 and anti-CD28 antibodies (Sanquin, Amsterdam, The Netherlands) whereas NK cells were activated by 100IU/mL rhIL-2 (Proleukin ® , Novartis Pharma, Basel, Switzerland). The percentage of proliferating immune cells was quantified by flow cytometry as the proportion of cells having undergone more than one division using ModFit LT 3.0 software (Verity Software, Topsham, ME). This allowed for the calculation of the percentage of inhibition of proliferation with the following formula: (percentage of proliferation IDO activity was calculated after quantification of tryptophan and kynurenine catabolite by high-performance liquid chromatography using added 3-nitro-L-tyrosine as an internal standard, as previously described [START_REF] Tattevin | Enhanced indoleamine 2,3-dioxygenase activity in patients with severe sepsis and septic shock[END_REF]. Results were expressed as the kynurenine to tryptophan ratio in the supernatant of MSC primed or not with IFN (R&D Systems).

Statistical analysis

Differences between groups were analyzed with Prism software version 5.03 (GraphPad, La Jolla, CA) using the Wilcoxon test for matched pairs or the Mann-Whitney non-parametric U test for unpaired samples. Differences in dose-response to IFN stimulation in ASCs versus BM-MSCs were tested with a 2-way ANOVA using Bonferroni's post-hoc multiple comparisons tests. In all cases, a cutoff value of p<0.05 was used to reach statistical significance.

RESULTS

ASC and BM-MSC display tissue-specific molecular imprinting

To investigate the net impact of tissue source on cultured MSC properties while minimizing inter-individual variability, MSCs were produced in the same culture medium from paired adipose tissue and bone marrow samples collected from 14 healthy individuals. At the end of the first passage (P1), all MSC batches fulfilled the identity criteria including lack of residual hematopoietic and endothelial cells, homogeneous expression of CD90, CD105 and CD73 (Figure S3A). As previously reported CD34 was not expressed on BM-MSCs whereas it could be detected on 17.5 % [0.5-30.7%] of ASCs (n=14). All subsequent experiments were performed at the end of P2 to limit the additional variability associated with large-scale expansion, and closely mimic clinical grade-MSCs used in successful clinical trials.

We first performed an unbiased transcriptomic analysis using Affymetrix microarrays.

Principal Component Analysis including all normalized unique genes (20507 genes)

adequately segregated ASCs from BM-MSCs (Figure 1A). Interestingly, ASC GEP showed a higher heterogeneity than BM-MSC GEP, extending a previous report obtained on a limited number of unpaired allogeneic samples [START_REF] Torensma | The impact of cell source, culture methodology, culture location, and individual donors on gene expression profiles of bone marrow-derived and adipose-derived stromal cells[END_REF]. These data were confirmed by a Pearson correlation analysis in which paired ASCs and BM-MSCs were essentially segregated with a higher level of similarities between BM-MSCs than ASCs (Figure 1B). To better compare the impact of tissue origin versus interindividual variability, we further calculated the Euclidian distance between each BM-MSC and its paired ASC and compared it to the Euclidian distance between each BM-MSC and all the other BM-MSCs (Figure 1C). BM-MSCs were significantly closer to allogeneic BM-MSCs than to autologous ASCs confirming that MSC tissue source impacted MSC transcriptomic heterogeneity to a greater extent than inter-individual variability.

We next applied a WGCNA to identify transcriptional modules of co-expressed genes and evaluate whether they were related to MSC tissue source. First, the sample clustering based on Euclidian distance obtained with the WGCNA package (Figure S4A) is in accordance with our previous observations, showing a separation between ASCs and BM-MSCs and a higher heterogeneity of the ASCs population. The coexpression network was constructed by Pearson correlation considering a softthresholding power β of 8 (Figure S4B). Following dynamic tree cut, the gene clustering dendrogram identified 12 distinct gene modules including the grey module corresponding to unassigned gene (Figure 1D). After the modules were generated, we evaluated their relationship with MSC tissue of origin by using a Wilcoxon Signed-Rank test to determine whether the module eigengenes, defined as the principal component of each module and summarizing the gene expression profile of these modules, were significantly different in ASCs versus BM-MSCs (Figure 1E). Three modules were significantly associated with the MSC tissue source: Purple module (264 genes, P= 1.346e-06), Yellow module (459 genes, P= 1.92e-07), and Blue module (P= 1.92e-07) (Figure 1E and S4C). Heatmap representation of these gene modules revealed that, conversely to the Purple module, the gene expression profiles of the Yellow and Blue modules perfectly segregated ASCs and BM-MSCs (Figure S4D). In order to draw a functional profile of these 2 modules, we extracted two genelists per module, one corresponding to the genes overexpressed in ASCs and S1).

As expected, BM-MSC signature was strongly enriched for genes involved in osteogenic and chondrogenic differentiation programs and in the function of osteoblasts and chondrocytes. These include the osteoblastic marker BGLAP, the chondrocytic marker ACAN, the transcription factors RUNX3, RUNX2, DLX5, DLX6, and SOX9, the regulator of bone formation NRP3, the modulators of pyrophosphate metabolism ANKH and ENPP1, or TNFRSF19, described as a positive regulator of MSC differentiation into osteoblasts while decreasing adipogenesis [START_REF] Qiu | Tumor necrosis factor receptor superfamily member 19 (TNFRSF19) regulates differentiation fate of human mesenchymal (stromal) stem cells through canonical Wnt signaling and C/EBP[END_REF]. Similarly, RhoA signaling, identified as one of the most significant BM-MSC specific pathway using IPA (Figure 2C), has been proposed as a key driver of mechanotransduction in osteoblasts [START_REF] Nobis | A RhoA-FRET Biosensor Mouse for Intravital Imaging in Normal Tissue Homeostasis and Disease Contexts[END_REF]. Canonical Wnt signaling is also essential for osteoblast differentiation and several members of the Wnt pathway were overexpressed in BM-MSCs, whereas ASCs overexpressed some of the main Wnt inhibitors such as SFRP1 or DKK1 (Figure 2C and Table S1). BM-MSCs exhibited a higher capacity to differentiate into chondroblasts in vitro compared to ASCs whereas osteoblastic differentiation was similar (Figure S5A-C). Conversely, ASCs displayed activation of molecular pathways related to cholesterol biosynthesis and CD36, the most strongly upregulated ASC gene, is a marker of human adipocyte precursors [START_REF] Gao | CD36 Is a Marker of Human Adipocyte Progenitors with Pronounced Adipogenic and Triglyceride Accumulation Potential[END_REF]. Moreover, ASCs displayed a higher capacity to differentiate into adipocytes in vitro (Figure S5D). Altogether, these data definitively confirm that in vitro cultured MSCs retain the main tissue-specific features of their anatomic origin.

Interestingly, cultured BM-MSC overexpressed genes associated with pericytic BM niche, including a gene set associated with vascular smooth muscle contractility and pericyte identity (CSPG4, ACTA2, MCAM, ITGA7, NOTCH3, MYH9, and MYH11) [START_REF] Armulik | Pericytes: developmental, physiological, and pathological perspectives, problems, and promises[END_REF][START_REF] Astarita | Transcriptional profiling of stroma from inflamed and resting lymph nodes defines immunological hallmarks[END_REF] but also extracellular matrix components, including FNDC1, ACAN, COL4A1, COL4A2, HAPLN1, and SRGN; members of the TGF family (GDF5, GDF6, TGFB2); and numerous integrins (ITGA3, ITGA7, ITGA8, ITGA11, ITGB2) (Table S1). Overexpression of the pericytic marker CD146/MCAM was confirmed at the protein level (Figure S3B). Conversely, ASC-specific GEP revealed pathways related In agreement, numerous immune-related genes were found differentially expressed between ASCs and BM-MSCs (Table 1).

In order to determine whether these differences reflected features of native MSCs or represented a culture artifact, we sorted CD45 neg CD235a neg CD11b neg CD31 neg CD73 pos CD271 pos BM mononuclear cells, corresponding to nBM-MSCs, and CD45 neg CD235a neg CD11b neg CD31 neg CD34 pos CD146 neg cells from adipose tissue stromal vascular fraction, corresponding to nASCs (Figure S1) and analyzed the expression of 10 genes previously found differentially expressed on their cultured counterpart [START_REF] Li | Isolation and characterization of primary bone marrow mesenchymal stromal cells[END_REF][START_REF] Maumus | Native human adipose stromal cells: localization, morphology and phenotype[END_REF]. Interestingly, we demonstrated that nASCs significantly overexpressed PTGS1, involved in the production of the immunosuppressive molecule PGE2, the complement system members C3 and CD55, the adhesion molecular ICAM1, and the CXCR2 ligands CXCL1 and CXCL2. Similarly, nBM-MSCs significantly overexpressed VCAM1, antigen presentation molecules CD74 and HLA-DRA, and the chemokine CXCL16 (Figure 3). These data clearly argue for a strong imprinting of the tissue of origin on the immune properties of cultured MSCs. We thus decided to further examine the functional consequences of these molecular differences on tissue-specific MSC immune properties.

BM-MSCs and ASCs differentially trigger immune cell adhesion and recruitment

VCAM-1 was the second most strongly upregulated gene in BM-MSCs. At the protein level VCAM-1 was consistently detected only on BM-MSCs but not on paired ASC counterparts and we further validated this finding on independent MSC batches (Figure 4A-B). Interestingly, nBM-MSCs systematically but variably expressed VCAM-1 whereas nASCs were virtually VCAM-1 negative (Figure 4C). VCAM-1 plays a major role in the anti-apoptotic activity of stromal cells towards immune cells, in particular immature and mature B and T cells expressing the VCAM-1 ligand VLA-4.

Moreover, VCAM-1/VLA-4 interaction was proposed years ago as a main determinant of the interaction between pericytes and lymphocytes [START_REF] Navarro | Immune Regulation by Pericytes: Modulating Innate and Adaptive Immunity[END_REF]. We thus wondered whether cultured MSCs could differentially support B and T-cell survival depending on their tissue origin. Strikingly, BM-MSCs protected B and T cells from spontaneous apoptosis in vitro significantly better than their paired ASC counterparts (Figure 4D). In addition, efficient inhibition of VCAM-1 expression in BM-MSCs by siRNA reduced their capacity to trigger B-cell adhesion (Figure 4E). Apart from adhesion molecules, chemokines also orchestrate the interaction between MSCs and immune cells and both CXCL1, CXCL2, and CXCL16 belonged to the most strongly differentially expressed genes between cultured and native ASCs and BM-MSCs (Table 1 and Figure 3). We validated these differences at the protein level on our paired series of cultured BM-MSCs and ASCs as well as in independent MSC batches. As expected, ASCs secreted higher amounts of CXCL1, involved in the recruitment of innate myeloid cells in particular neutrophils, whereas BM-MSCs secreted higher amounts of CXCL16, the ligand for CXCR6-expressing memory T cells and monocytes (Figure 5 A-C). Moreover, we could show that, whereas BM-MSCs and ASCs produced the same amount of CXCL8/IL-8, ASCs were significantly more efficient in triggering neutrophil attraction, in agreement with their higher production of CXCL1 and CXCL2, the two other CXCR2 ligands (Figure 5D).

BM-MSCs and ASCs differentially elicit immune response suppression

The bidirectional crosstalk of infused MSCs with resident immune cells is pivotal for their clinical efficacy. The detection of humoral alloimmunization in recipients of allogeneic MSCs together with the lack of persistence of infused MSCs demonstrate that MSCs are not immune-privileged [START_REF] Galipeau | Mesenchymal Stromal Cells: Clinical Challenges and Therapeutic Opportunities[END_REF]. However, protecting MSCs from immune detection and prolonging their life-span in vivo may improve clinical outcome [START_REF] Ankrum | Mesenchymal stem cells: immune evasive, not immune privileged[END_REF].

Cultured and native BM-MSCs were found to overexpress HLA-DRA and CD74, both involved in antigen presentation to CD4 pos T cells (Table 1 and Figure 3). We could further confirm surface HLA-DR overexpression on BM-MSCs compared to ASCs in our paired MSC samples, but also on independent cultured MSC batches, and on native MSCs (Figure 6 A-C). HLA-DR is induced on MSCs upon exposition to inflammatory cues [START_REF] Ménard | Clinical-grade mesenchymal stromal cells produced under various good manufacturing practice processes differ in their immunomodulatory properties: standardization of immune quality controls[END_REF]. We thus tested whether the differential HLA-DR expression between ASCs and BM-MSCs was retained following stimulation by increasing doses of IFN. Cultured ASCs and BM-MSCs similarly enhanced their HLA-DR expression in response to inflammatory stimuli with a maximum of MHC class II expression at 100IU/mL of IFN, demonstrating their similar capacity to activate IFN-dependent signaling pathway. As a consequence, the level of expression of HLA-DR remained lower on inflamed ASC than on inflamed BM-MSC (Figure 6D). These data suggested that ASCs could better escape to recognition by CD4 pos T cells. In addition, their higher expression of the cell-surface complement inhibitor CD55 (Table 1), previously shown to crucially regulate MSC sensitivity to complement- dependent cytotoxicity [START_REF] Li | Mesenchymal stem cells are injured by complement after their contact with serum[END_REF], could favor their escape from initial immune attack in vivo.

We then used our previously established standardized tools to compare the capacity of paired ASCs and BM-MSCs to inhibit activated T cell and NK cell proliferation in vitro [START_REF] Ménard | Clinical-grade mesenchymal stromal cells produced under various good manufacturing practice processes differ in their immunomodulatory properties: standardization of immune quality controls[END_REF]. Strikingly, ASCs decreased significantly better T cell proliferation and BM-MSCs significantly better NK cell proliferation (Figure 6E). We and others have shown that IDO activity is the main mechanism supporting the capacity of human MSCs to suppress T cells, unlike NK cells [START_REF] Ménard | Clinical-grade mesenchymal stromal cells produced under various good manufacturing practice processes differ in their immunomodulatory properties: standardization of immune quality controls[END_REF]. IDO is not expressed by resting MSCs but is induced by IFN produced by activated T and NK cells. We thus assessed IDO activity in ASCs and BM-MSCs licensed with increasing doses of IFN.

We showed that ASCs required significantly less IFN to reach the maximum IDO activity than BM-MSCs (Figure 5 F-G). Thus, whereas ASCs and BM-MSCs have the same intrinsic capacity to respond to IFN signaling, as highlighted by parallel curves of HLA-DR induction, ASCs express higher functional immunosuppressive enzyme IDO in response to a low dose of IFN. 16 [START_REF] Bahr Von | Long-term complications, immunologic effects, and role of passage for outcome in mesenchymal stromal cell therapy[END_REF]. Of note, the IDO hi phenotype of ASCs could be further reinforced by the direct contact with innate myeloid cells, a key step in tissue repair and regeneration. In fact the interplay between MSCs and inflammatory macrophages was recently shown to trigger IDO expression and activity in MSCs in a CD54-dependent manner [START_REF] Espagnolle | CD54-Mediated Interaction with Proinflammatory Macrophages Increases the Immunosuppressive Function of Human Mesenchymal Stromal Cells[END_REF] and ASCs overexpressed CD54/ICAM-1 compared to BM-MSCs.

DISCUSSION

Second, resting ASCs overexpressed TSG-6, involved in the early inhibition of neutrophil and macrophage activity at sites of inflammation. Kynurenic acid, a tryptophan metabolite generated by IDO, was recently shown to enhance TSG-6 expression through the activation of aryl hydrocarbon receptor (AhR), which binds to TNFAIP6 promoter [START_REF] Wang | Kynurenic acid, an IDO metabolite, controls TSG-6mediated immunosuppression of human mesenchymal stem cells[END_REF]. This amplification loop between the two main MSC immunosuppressive mediators could contribute to the higher TSG-6 expression in ASCs primed by inflammatory stimuli. TSG-6 was proposed to directly impact the NF-B dependent activation of macrophages by TLR ligands [START_REF] Choi | Anti-inflammatory protein TSG-6 secreted by activated MSCs attenuates zymosan-induced mouse peritonitis by decreasing TLR2/NF-κB signaling in resident macrophages[END_REF] whereas IDO has been implicated in the differentiation of monocytes into IL-10-secreting immunosuppressive macrophages [START_REF] François | Human MSC suppression correlates with cytokine induction of indoleamine 2,3-dioxygenase and bystander M2 macrophage differentiation[END_REF]. It is thus tempting to speculate that, besides their strong capacity to inhibit T cells and their interest for the treatment of T cell-mediated immune disorders, ASCs would be particularly effective in modulating the inflammatory response mediated by macrophages. In addition, we revealed that ASCs recruited more efficiently neutrophils than BM-MSCs, whereas they overexpressed TSG-6, recently identified as a CXCL8-binding protein inhibiting neutrophil transendothelial migration and chemotaxis [START_REF] Dyer | TSG-6 inhibits neutrophil migration via direct interaction with the chemokine CXCL8[END_REF]. However, TSG-6 does not bind to CXCL1/CXCL2, both upregulated in ASCs, and has no effect on CXCL1-mediated neutrophil transmigration.

Finally, ASCs were virtually HLA-DR neg and retained a lower HLA-DR expression under inflammatory stimuli compared to BM-MSCs. This property could be clinically relevant in relationship with the increasing use of MSCs in allogeneic setting.

However, a comparison of alloimmunization rates in homogeneous patients receiving

ASCs versus BM-MSCs is currently lacking to conclude on the lower immunogenicity of ASCs. Interestingly, we highlighted for the first time an upregulation of components of the complement activation cascade in ASC transcriptomic profile. Complement components were recently identified as promoters of immunological tolerance through their capacity to promote development of myeloid-derived suppressor cells (MDSCs) [START_REF] Luque | Complement components as promoters of immunological tolerance in dendritic cells[END_REF]. In particular, liver stromal cells, like ASCs, produce C3, Factor B, and Factor D resulting in the formation of activation products iC3b and C3d that trigger shown to be induced upon inflammatory cytokine treatment of BM-MSCs, with a loss of H3K9me3 repressive mark and a gain of permissive acH3K9 mark [START_REF] Gonzalez | In vitro cytokine licensing induces persistent permissive chromatin at the Indoleamine 2,3-dioxygenase promoter[END_REF].

Methylation of the IDO1 promoter was also proposed as an additional level of regulation of IDO expression in breast cancer cells [START_REF] Dewi | Suppression of indoleamine-2,3-dioxygenase 1 expression by promoter hypermethylation in ER-positive breast cancer[END_REF]. A deeper evaluation of epigenetic regulation of IDO1 in ASCs versus BM-MSCs should shed new light on the regulation of this immunosuppressive mediator in the two cell subsets.

Importantly, we revealed for the first time, using purified nASCs and nBM-MSCs, that the differential immune profile of in vitro expanded MSCs obtained from BM and adipose tissue is essentially imprinted by their tissue of origin. Interestingly, murine

ASCs were proposed to be the precursors of lymphoid stromal cells that regulate immune cell recruitment and guided trafficking inside secondary lymphoid organs and ensure antigen delivery and B cell activation and selection [START_REF] Bénézech | Lymphotoxin-β Receptor Signaling through NF-κB2-RelB Pathway Reprograms Adipocyte Precursors as Lymph Node Stromal Cells[END_REF]. We highlighted here a lymphoid stroma signature, including LTBR, the NF-kB family members IRAK1, IRAK3, and TRAF3IP2; IL4R, IL13RA2, CLU, and CSTC in cultured human ASCs compared to BM-MSCs further confirming the relationship between in vitro expanded ASCs and their native counterpart and suggested that these cells are prone to interact with immune cells in vivo.

  with the R package stats with ward D2 parameter. Differentially expressed genes were identified based on an adjusted p-value <0.05 (by Benjamini-Hochberg method) and were visualized as an heatmap with the heatplot function in R.

  3 (B cells) or 7 (T cells) days of coculture, the percentage of apoptotic lymphocytes was assessed by flow cytometry with the Active Caspase-3 Apoptosis kit (Becton-Dickinson) after gating on CD45 pos events. This allowed for the calculation of the percentage of inhibition of apoptosis with the following formula: (percentage of caspase-3 pos without MSC -percentage of caspase-3 pos with MSC) / (percentage of caspase-3 pos without MSC)*100.For adhesion experiments, B cells were stained with 2µM CFSE (Interchim, Montluçon, France) and platted onto MSC layer for 2 hours as described[START_REF] Pandey | IL-4/CXCL12 loop is a key regulator of lymphoid stroma function in follicular lymphoma[END_REF]. After washing in PBS, fluorescence of residual adherent B cells was recorded on a Varioskan (Thermofisher) and the percentage of adherent cells was calculated by comparing with the fluorescence of the input. In some experiments, BM-MSCs were transfected with VCAM-1 siRNA (3 pooled Stealth iRNA, Life Technologies, Saint-Aubin, France) or a control siRNA (Negative Control Medium GC, Life Technologies)

  percentage of proliferation with MSC) / (percentage of proliferation without MSC)*100.

  one to the genes overexpressed in BM-MSCs, and analyzed them with IPA (Figure1F-G). Interestingly, both Yellow and Blue modules revealed a strong enrichment for immune-related pathways in ASCs. Altogether, our two unsupervised analysis methods clearly indicate that ASCs and BM-MSCs display strongly different transcriptomic profiles that could be functionally relevant for their clinical application.

  Differentially regulated functional pathways in BM-MSCs versus ASCsComparison of the GEP of the 28 paired BM-MSCs and ASCs revealed 3291 differentially expressed unique genes (adjusted P value <0.05 using Benjamini-Hochberg method, Figure2A-B), including 208 genes up-regulated more than 2-fold in BM-MSCs and 263 genes up-regulated more than 2-fold in ASCs (log2 FC >1 or <-1, Table

  immune response (Figures 2C).

  Tissue origin has been proposed for a long-time as a potential determinant of clinicalgrade MSC clinical efficacy. However, how intrinsic disparities between BM-MSCs and ASCs could be related to their capacity to interact with immune effectors and modulate immune response has not been extensively explored. In the present study, we demonstrated for the first time on a large series of ASCs and BM-MSCs obtained from the same donors and on purified nASCs and nBM-MSCs the strong impact of tissue origin on MSC properties. Moreover, we pinpointed that ASCs could be an interesting alternative to BM-MSCs for therapeutic applications considering their huge expression of anti-inflammatory and immunosuppressive molecules.First, ASCs endorsed stronger IDO activity in response to low dose IFN- stimulation, thereafter inhibiting more efficiently T-cell proliferation. Interestingly, ASCs display a higher proliferative capacity in vitro and enter senescence at a later time-point compared to BM-MSCs thus delaying the risk of proteasomal degradation of IDO that characterizes senescent MSCs[START_REF] Loisel | Brief Report: Proteasomal Indoleamine 2,3-Dioxygenase Degradation Reduces the Immunosuppressive Potential of Clinical Grade-Mesenchymal Stromal Cells Undergoing Replicative Senescence[END_REF]. In agreement, the clinical impact of culture expansion has been validated by the demonstration that late-passage MSCs were less effective than early-passage MSCs to control acute graft-versus-host-disease

  into MDSCs[START_REF] Hsieh | The role of complement component 3 (C3) in differentiation of myeloid-derived suppressor cells[END_REF]. The role of complement activation in the immunosuppressive activity of MSCs deserves further investigations. Importantly, it has to be noted that ASCs were conversely less potent than BM-MSCs at preventing NK cell proliferation, in agreement with the lack of reversion of MSC-dependent NKsuppressive activity by IDO inhibitors[START_REF] Davies | Mesenchymal Stromal Cell Secretion of Programmed Death-1 Ligands Regulates T Cell Mediated Immunosuppression[END_REF][START_REF] Chen | Stanniocalcin-2 contributes to mesenchymal stromal cells attenuating murine contact hypersensitivity mainly via reducing CD8+ Tc1 cells[END_REF]. In addition, BM-MSCs overexpressed PD-L1/CD274 and staniocalcin-2 (STC2), two suppressive molecules affecting CD8 pos T cell activation and synthesis of inflammatory cytokines[START_REF] Davies | Mesenchymal Stromal Cell Secretion of Programmed Death-1 Ligands Regulates T Cell Mediated Immunosuppression[END_REF][START_REF] Chen | Stanniocalcin-2 contributes to mesenchymal stromal cells attenuating murine contact hypersensitivity mainly via reducing CD8+ Tc1 cells[END_REF].The mechanisms underlying the higher IDO activity in ASCs in response to IFN are still unclear whereas IDO expression and activity has been reproducibly correlated with the capacity of human MSCs to inhibit T-cell proliferation[START_REF] Ménard | Clinical-grade mesenchymal stromal cells produced under various good manufacturing practice processes differ in their immunomodulatory properties: standardization of immune quality controls[END_REF][START_REF] François | Human MSC suppression correlates with cytokine induction of indoleamine 2,3-dioxygenase and bystander M2 macrophage differentiation[END_REF][START_REF] Chinnadurai | Potency Analysis of Mesenchymal Stromal Cells Using a Combinatorial Assay Matrix Approach[END_REF]. BM-MSCs and ASCs expressed IFN receptor at the same level (data not shown) and similarly upregulated HLA-DR in response to IFN stimulation, indicating a functional IFN signaling pathway. Of note IDO mRNA level was also reduced in primed BM-MSCs compared to primed ASCs (data not shown) suggesting a regulation at the transcriptional level. Recently, histone modifications at IDO1 promoter region were

CONCLUSIONFigure 1 .

 1 FIGURE LEGENDS

Figure 2 .Figure 3 .

 23 Figure 2. Paired ASC and BM-MSC differential gene expression pattern highlights tissue-specific functional pathways. (A) Venn diagram of the genes differentially expressed between paired BM-MSC and ASC (n=14). (B) Hierarchical clustering of paired ASCs and BM-MSCs performed on the 3291 differentially expressed genes. The relative level of gene expression is depicted according to the shown color scale. (C) Ingenuity Pathway Analysis of the up-and down-regulated genes. Shown are the top twenty pathways in ASCs (top, red bars) and BM-MSCs (bottom, blue bars) according to the p-value.

Figure 4 .

 4 Figure 4. ASCs and BM-MSCs differentially mediate immune cell adhesion and survival (A-C) VCAM-1 expression was assessed by flow cytometry on 7 paired cultured MSC samples (A), on an independent series of BM-MSCs and ASCs (n=10 each) (B), and on native BM-MSCs (nBM-MSCs) and ASCs (nASCs) (C, n=6 each). (D) The ability of MSC to support immune cells survival was assessed in a coculture assay with resting T and B cells. Survival of CD45 pos lymphocytes was evaluated by activated caspase-3 staining (n=7 independent experiments, each time with different paired MSC samples). (E) Purified B cells were labeled with CFSE and incubated for 2h on BM-MSC confluent cell monolayer. BM-MSCs have been transduced 48h before by VCAM-1 targeting siRNA or control siRNA. Adhesion percentage was calculated by comparing the residual fluorescence after adhesion with the fluorescence of the input (n=7 independent experiments). *p<0.05, **p<0.01, ***p<0.001.

Figure 5 .Figure 6 .

 56 Figure 5. ASCs and BM-MSCs have a distinct capacity to attract immune cells. (A) CXCL1 and CXCL16 concentrations were quantified in MSC supernatants by ELISA and normalized by the number of cultured MSCs (n=6 paired MSC samples). (B-C) CXCL1 and CXCL16 expression was quantified by Q-PCR (B) and ELISA (C) in an independent series of BM-MSCs and ASCs (n=10 each). (D). Neutrophil migration towards MSC conditioned medium was quantified by flow cytometry. The percentage of neutrophil migration is calculated as the number of DAPI neg CD66b pos CD16 pos viable neutrophils migrating in response to cell supernatant divided by their initial number (n=10 independent experiments). *p<0.05, **p<0.01

Figure 1 .

 1 Figure 1. Paired ASC and BM-MSC transcriptomic analysis reveal tissue-specific signatures

Figure 2 .Figure 3 .

 23 Figure 2. Paired ASC and BM-MSC differential gene expression pattern highlights tissue-specific functional pathways

Figure 4 .Figure 5 .Figure 6 .

 456 Figure 4. ASCs and BM-MSCs differentially mediate immune cell adhesion and survival

Table 1 : Immune-related genes differentially expressed in BM-MSC vs ASC

 1

	(Adjusted p-value < 0.05, I log2 FC I >1)

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ACKNOWLEDGEMENTS

This work was supported by grants from the CHU de Toulouse (Appel d'offre local 2008), the Etablissement Français du Sang (APR 2016), the Infrastructure program EcellFRANCE (ANR-11-INSB-005), the European Center for Transplantation Sciences and Immunotherapy (IHU CESTI, ANR-10-IBHU_0005), the French National Cancer Institute (INCa PLBIO-17-219). LV is a recipient of a fellowship from the Labex IGO and the Région Bretagne.

DATA AVAILABILITY STATEMENT

Data are available via the NCBI Gene Expression Omnibus (https://www.ncbi.nlm.nih.gov/geo/; accession number GSE122778). During the reviewing process the data are retained in private status and are available for reviewers only using the secure token shazuskolhcbtyb.

DISCLOSURE OF POTENTIAL CONFLICTS OF INTEREST

The authors declare no competing financial interest.

ASCs and BM-MSCs