Martin Genet
email: martin.genet@lmt.ens-cachan.fr

Dr Wenyi Yan

Pr Thanh Tran-Cong

Investigation of a hydraulic impact -a technology in rock breaking

Keywords: Finite element simulation, Dimensional analysis, Rock breaking, Non-explosive method, Hydraulic impact

The finite element method and dimensional analysis have been applied in the present paper to study a hydraulic impact, which is utilized in a non-explosive rock breaking technology in mining industry. The impact process of a high speed piston on liquid water, previously introduced in a borehole drilled in rock, is numerically simulated. The research is focused on the influences of all the parameters involved in the technology on the largest principal stress in the rock, which is considered as one of the key factors to break the rock. Our detailed parametric investigation reveals that the variation of the isotropic rock material properties, especially its density, has no significant influence on the largest principal stress. The influences of the depth of the hole and the depth of the water column are also very small. On the other hand, increasing the initial kinetic energy of the piston can dramatically increase the largest principal stress and the best way to increase the initial kinetic energy of the piston is to increase its initial velocity. Results from the current dimensional analysis can be applied to optimize this non-explosive rock breaking technology.

Introduction

Explosives are commonly used to fragment large rock masses in modern mining practice.

From the technical point of view, although explosive method is powerful, it does not produce fragments with homogeneous size distribution. In many situations the amount of very fine rocks is high, while in other situations the amount of oversized boulders could be excessive. Furthermore, explosive method involves complex drilling, blasting, scaling, ground support and the evacuation of people and equipment before blasting. Such a multi-activity cycle is time-consuming, inefficient and unproductively expensive [START_REF] Singh | Non-explosive applications of the PCF concept for underground excavation[END_REF]. Another major concern with explosive blasting is the associated danger and undesirable impact on the environment such as fly rocks, air blast, noise pollution and toxic fumes. When blasting occurs close to residential areas, or during tunnel construction, environmental protection regulation could seriously affect the rate of rock excavation. In some cases, blasting would be excluded as an acceptable method of rock breaking. Apart from the breaking of large rock masses for transportability purposes, tunnelling requires more carefully controlled rock breaking. Oversized boulders often cause blockage of mine draw points. When such blockage occurs, extensive shutdown of mine operation will result, causing loss of millions of dollars per hour. Thus, fast, simple, safe and clean methods of breaking boulders are required in some cases to make total mining operation efficient.

To overcome the drawbacks of explosive methods, several non-explosive technologies have been developed in the past, see Singh [START_REF] Singh | Non-explosive applications of the PCF concept for underground excavation[END_REF]. Young [START_REF] Young | Controlled foam injection for hard rock excavation[END_REF] provided an overview and compared the pros and cons of various methods of pressurising a borehole in a rock mass, including small charge explosive and propellant, water jets, firing of high speed water slugs, mechanical splitters, and high pressure gases. McCarthy [START_REF] Mccarthy | Method apparatus and cartridge for non-explosive rock fragmentation[END_REF] proposed the use of propellant cartridge in a predrilled hole to provide the breaking force. In the latest patent by Young [START_REF] Young | Controlled foam injection method and means for fragmentation of hard compact rock and concrete[END_REF], a highpressure foam was utilized to replace explosive technology. The controlled-foam injection (CFI) method invented by Young [START_REF] Singh | Non-explosive applications of the PCF concept for underground excavation[END_REF][START_REF] Young | Controlled foam injection method and means for fragmentation of hard compact rock and concrete[END_REF] has a number of advantages, including lower maximum pressure and the maintenance of pressure during fracture by virtue of the compressibility of the foam. Another non-explosive rock breaking method was invented and patented by Denisart et al. [START_REF] Denisart | Method of breaking a hard compact material, means for carrying out the method and application of the method[END_REF], which is illustrated in Fig. 1. The hydraulic fluid, such as water, is introduced in a pre-drilled borehole and is impulsively loaded by a high speed piston. The highly pressurized water, with the reflection of the pressure wave, will result in huge stresses in the rock mass, especially at the bottom of the hole, which is a stress raiser.

Consequently, cracks will be initiated around the borehole, especially at the bottom, and the pressurized water will penetrate into the cracks, providing the driving force for crack propagation. Eventually, cracks will propagate back to the surface due to free surface effect and a volume of the hard material will be removed.

All the available inventions and patents focused on the principle of the rock breaking methods, i.e., different approaches are used to answer the basic question of how to break a rock mass. In terms of the application of the non-explosive technology, we need to quantify many parameters, such as the depth of the borehole and the initial velocity of the piston, etc.

In the current investigation, the dimensional analysis and numerical method are applied to quantify the hydraulic impact process, which is involved in a non-explosive rock breaking technology as shown in Fig. 1. The efficiency of the impact is evaluated by the maximum principal stress in the rock during an impact process. Numerical results from the investigation will assist industry to quantitatively apply this non-explosive rock breaking technology and, therefore, to improve rock breaking efficiency. This paper is structured as follows. The finite element model to simulate the hydraulic impact is presented in Section 2. The functional relationship between the largest principal stress in the rock and all the processing parameters from dimensional analysis is discussed in Section 3. In Section 4, detailed numerical results on the influences of all the parameters on the largest principal stress are discussed. Finally, conclusions are given in Section 5.

Impact simulation

Finite element mesh

The finite element method has been applied to simulate the hydraulic impact process. We use a finite element package, CASTEM, to create the finite element mesh, a PERL script to translate CASTEM meshes into ABAQUS meshes, the commercial package ABAQUS/Explicit to do the simulations, and a PYTHON script to automate the simulation process.

The borehole, as shown in Fig. 1, can be idealized as a cylinder. Therefore, this problem can be treated as axisymmetric. Moreover, the rock body can be considered as semi-infinite.

Infinite elements are utilized to simulate the semi-infinite body. Fig. 2 shows the finite element mesh generated by using CASTEM. The definition of the geometrical parameters shown in Fig. 2 can also be found in Table 1.

As shown in Fig. 2, there is an arc with the radius of a R at the bottom of the borehole. The reason to introduce the arc is to avoid singularity, which implies an infinite stress. Moreover, it is a good representation of the reality. It is impossible to have a perfect right angle practically when we drill a hole and we always have the trace of the tool on the machined part. Further explanation of this assumption can be found in Section 3.

As shown in Fig. 2, very fine meshes are generated around the corner of the bottom of the hole. Many simulation tests with different mesh densities have been carried out to eliminate the influence of mesh density and determine the final mesh for the calculations. In the end, there are 122 four-node bilinear elements and 4349 three-node linear elements in the final model. The only initial condition in this problem is the initial velocity of the piston, which is an additional parameter of the problem.

Material properties

The piston is normally made of steel, which is assumed to be a homogeneous and isotropic material. We also assume that the piston stays in its elastic domain during the impact process. In the current investigation, the rock in this simulation is simplified as an elastic, homogeneous and isotropic solid. In reality, rock, as a natural material, consists of crystal, grains, cementitious materials, voids, pores and flaws, see [START_REF] Jaeger | Fundamentals of rock mechanics. 3 rd Edition[END_REF]. At the first stage of investigating this non-explosive rock breaking technology, our current objective is to understand and quantify the impact process. Considering the influence of the inhomogeneous microstructure of rock material will be our next task. On the other hand, because of the uncertainty of the microstructure and its inhomogeneity, the assumed isotropic rock in our model can be treated as a representative of the real material and the results from this assumption will still be practically useful, especially for companies which intend to develop relevant universe equipments for this non-explosive technology. Furthermore, we do not take into account the possible plastic deformation of the rock in the present research, neither the creation nor the propagation of cracks, which will be our future study. Consequently, we have three parameters to describe the rock: Young's modulus r E , Poisson's ratio r ! and it's density r ! .

Contact simulation

As shown in Fig. 1 and Fig. 2(a), there are three pairs of contacts involved in the impact process, i.e., the contact between the piston and the water, the contact between the piston and the rock, and the contact between the water and the rock. We use the hard contact algorithm from ABAQUS without damping to simulate these contacts. The friction is also neglected in our simulation. Practically, the friction between water and piston or rock should be very low.

Further study will be carried out after we obtain reliable friction value involved in the contact between piston and rock.

All the impact simulations were carried out by using ABAQUS/Explicit. The effect of the hydraulic impact is evaluated by the largest principle stress in the rock. As an example of our finite element simulation results, Fig. 3 shows the distribution of the maximum principal stress field in the structure at the instant when the shockwave arrives at the end of the bottom of the hole. It clearly indicates that the largest maximum principal stress, the largest principal stress in short, occurs at the bottom of the hole. Irrespective of microstructures, cracks will possibly initiate at this position with this largest stress in the rock. Fig. 4 shows the corresponding direction field of the maximum principal stress at this local area in the rock. On the surface, the direction of the maximum principal stress is perpendicular to the surface. One can imagine, once cracks initiate, the highly pressurized water will penetrate into the cracks and drive the cracks to propagate, which will be the core of the investigation to understand the rock breaking in our future study.

Dimensional analysis

All the parameters involved in the simulation are listed in Table 1. Here, the radius of the piston is the same as the radius of the borehole. Dimensional analysis is a powerful method to systematically carry out parametrical study on a complicated problem involving many parameters, see examples [START_REF] Anderson | Fracture mechanics: Fundamentals and applications[END_REF][START_REF] Tunvisut | Use of scaling functions to determine mechanical properties of thin coatings from microindenation tests[END_REF][START_REF] Yan | Analysis of Spherical Indentation of Superelastic Shape Memory Alloys[END_REF]. This method is applied in the current investigation. The objective variable in our dimensional analysis is chosen as the largest principal stress in the rock, m ! , during an impact process. The rock material can be roughly considered as brittle material. According to Coulomb's criterion of maximum normal stress, the largest principal stress will initiate cracks in the rock and lead to the fragmentation of rock mass. Generally, the largest principal stress is a function of all the parameters listed in Table 1, i.e., ( )

p p p p p w w w w h h a r r r L ,E , , ,V ,D ,E , , ,R ,D ,R ,E , , m f ! " # " # " # = . ( 1
)
According to the Buckingham ! -theorem for dimensional analysis, we can reduce the number of parameters. For this purpose, we choose h D , the depth of the hole, p ! , the density of the piston and p E , the Young modulus of the piston as the primary quantities. Therefore, the dimensionless function for the largest principal stress is

p p w w w h a r r 1 p w r 1/ 2 1/ 2 h p h p h h p L V D E R R E , , , , , , , , , , , D D D
D m p p p p E E E E ! " # = $ % & % & ' ( ) * + + , , , + + + . (2)
Among all the dimensionless parameters that we have just created, some values can be considered as unchanged in this physical problem. The piston is generally made from steel and water is normally used as the liquid in this technology. Therefore, the material data for the piston and the water can be treated as constant. Consequently, the following dimensionless parameters will be considered constant in our model:

0.3 p ! = , 0.4995 w ! = , (3)
w p ! ! = = . (4)
Therefore, the dimensionless function ( 2) can be simplified as

p p w h a r r 2 r 1/ 2 1/ 2 h p h h h p L V D R R E , , , , , , , D D D D m p p p E E E ! " # = $ % & % & ' ( ) * + , + + . ( 5
)
After this dimensional analysis, the number of variables involved in the stress analysis has reduced from 15 in the original Eq. ( 1) to 8 in Eq. ( 5).

We now define the domains of the dimensionless variables based on our understanding of this physical problem. The following limits of the domains for geometrical parameters are appropriated for this problem:

[ ] 0.1;0.8 p h L D ! , [ ] 0.1;0.8 w h D D ! . (6)
[ ] 0.01;0.5

h h R D ! , [ ] 0.001;0.05 a h R D ! . ( 7
)
Referring to [11], the domains of the mechanical properties of different types of rocks are shown in Table 2 , we can define the domains for dimensionless variables linked to the rock material as follows:

[ ] 0.05;0.5 r p E E ! , [ ] 0.1;0.35 r ! " , [ ] 0.25;0.4 r p ! ! " . (8)
According to Denisart et al. [START_REF] Denisart | Method of breaking a hard compact material, means for carrying out the method and application of the method[END_REF], the initial velocity of the piston can vary from 10 / m s to 200 / m s , which corresponds to the following domain of the dimensionless initial velocity:

[ ]

p 1/ 2 1/ 2 p V 0.0020;0.0395 p E ! " # $ . (9)
In our numerical simulations, we have to adjust the limits of some parameters' domains because of numerical instability problem. The Poisson's ratio of water is 0.4995, which is close to the value of 0.5 of imcompressible materials. Additionally, the water is highly confined in the borehole and exposed to a highly compressive load from the impact of the high speed piston. Due to these factors, the stiffness matrix in a finite element simulation is almost singular, which can sometimes lead to numerical instability [START_REF]Analysis/Theory Manuals[END_REF]. A unsuccessful numerical instability calulcation can be easily detected by observing large abnormally distorted and penetrated deform meshes. To overcome this instablility problem, we sometimes have to choose some values lower than the upper limit or higher than the lower limit of the domains defined in above Eqs (6-9). In the following section, only the correct results from the stable calculations are reported. We can believe that the fitted laws in the restricted domains of study in the following section are valid in the entire domains defined in Eqs (6-9).

Results and discussions

Influence of rock properties

The effect of rock density is considered first. Fig. 5 shows the influence of the normalized rock density, / r p ! ! , on the normalized largest principal stress, /

m p E !
, in the rock during the impact process. We have considered the two limit values of the domains of all the dimensionless parameters in Eq. ( 5), one by one from Fig. 5(a) to Fig. 5(g), while fixing the values of all the others dimensionless parameters at the middle values of their domains, which are defined in Eqs. [START_REF] Wilson | Three-dimensional static and dynamic analysis of structures[END_REF][START_REF] Jaeger | Fundamentals of rock mechanics. 3 rd Edition[END_REF][START_REF] Anderson | Fracture mechanics: Fundamentals and applications[END_REF][START_REF] Tunvisut | Use of scaling functions to determine mechanical properties of thin coatings from microindenation tests[END_REF]. For example, the two curves in Fig. 5(a) are obtained for / 0.17 ! ! from 0.25 to 0.4 in all the studied cases is negligibly small. Because all the studied cases have covered the domains of this physical problem, one can deduce that it is generally correct that the influence of the variation of rock density on the maximum largest principal stress in the rock can be neglected.

Consequently, the dimensionless rock density in Eq. ( 5) can be removed and the dimensionless stress function can be further simplified as

p p w h a r 3 r 1/ 2 1/ 2 h p h h h L V D R R E , , , , , , D D D D m p p p E E E ! " # = $ % & % & ' ( ) * + , . (10)

Influence of borehole dimensions 4.2.1 Borehole depth

The depth of the borehole, h D , is chosen as the primary length in the dimensional analysis. Its influence on the problem can be implicitly reflected in the parametric study of other dimensionless length parameters, such as the dimensionless piston length and the dimensionless water depth. But it is understandable that the depth of the borehole has no direct influence on the largest principal stress in the rock, and that is the reason to choose it as the primary length to normalize the other parameters. when the borehole radius evolves from 5 cm to 30 cm according to the numerical results.

Borehole radius

It is interesting to plot the instantaneous average velocity and the instantaneous kinetic energy of the piston over the impacting time for several values of the dimensionless radius of the hole. Fig. 9 and Fig. 10 show these results. In Fig. 9, we can see that at the beginning, the piston is moving down, that is why the average velocity is negative. Then its average velocity decreases, and at

1/ 2 1/ 2 7 h p p t D E ! " = # #
, the piston has zero averaged velocity. After that, the piston is coming up, so its average velocity is increasing. We can also follow this in Fig. 10:

the piston starts with its kinetic energy, which decreases until

1/ 2 1/ 2 7 h p p t D E ! " = # #
where it is null, and then increases because the piston is coming up. Additionally, we can see from Fig. 9 that the average velocity of the piston does not depend on the borehole radius, and from Fig. 10 that the kinetic energy of the piston depends on the radius of the hole, which is obvious because the radius of the hole is also the radius of the piston and the initial kinetic energy strongly depends on the radius of the piston. However, we can see that its evolution is quite similar from one value to another, which is obviously linked to the fact that the average velocity is the same for all curves in Fig. 9. We can explain this by saying that both the kinetic energy of the piston and the energy that is transmitted to the water depend on the radius of the piston in the same way: they both are proportional to the cross section area of the piston, i.e., the square of its radius. Then, if the piston has a larger radius, it will have more initial kinetic energy, but it will also transmit more energy to the water, so its kinetic energy will decrease faster. This remark is important, and we will explain below that the kinetic energy of the piston is a key factor to determine the largest principal stress in the rock.

To understand this, we discuss an impact process by following Fig. 11, which shows the first principal stress in the element that has the largest principal stress and the instantaneous average velocity of the piston versus impacting time for 0.0167

h h R D = :
-The piston hits the water with its initial velocity at the beginning of the simulation, which starts the impact process.

-The created shockwave comes down in the water, and arrives at the bottom of the borehole at

1/ 2 1/ 2 2 h p p t D E ! " = # # .
Here is the first peak in the stress curve, with -Then the shockwave climb back to the surface (the material behaviour of the water is very different from the others material behaviours, so the transmission of energy is low) and the stress at the bottom of the hole reduces because of the dispersion of energy.

-When the shockwave arrives at the surface at

1/ 2 1/ 2 4 h p p t D E ! " = # #
, it is reflected and comes down again, but with more energy because the piston is still coming down.

-Thus, the second peak in the stress curve will be greater, with 3 1.7 10

p E ! = " # at 1/ 2 1/ 2 6 h p p t D E ! " = # # .
-And when the shockwave climb back and arrives at the surface for the second time,

at 1/ 2 1/ 2 8 h p p t D E ! " = # #
, the piston has no more velocity downward and is going up.

-So the shockwave comes down again with less energy, and the third peak in the stress curve will be smaller, with We can conclude that we have the largest principal stress in the rock when the shockwave arrives at the bottom of the hole the last time while the piston still having some velocity downward. It indicates that the kinetic energy of the piston plays an important role in the determination of the largest principal stress.

Arc radius at borehole bottom

This parameter, the arc radius at the borehole bottom, as shown in Fig. 2, is introduced to avoid the problem of infinite stress at the corner and allow a better modelling of the geometry of the hole in a real situation. Obviously, it will have a substantial influence on the largest principal stress in the rock. Fig. 12 shows its influence on the problem. The thick curve in Fig.

12 represents an exponential function to fit the numerical dots. We can see that the stress tends to infinity when the radius of the arc closes to zero, which is normal because of the problem of singularity when 0

Water depth

Fig. 13 shows the influence of w D on the largest principal stress in the rock and on the time to reach this value, when all the other dimensionless parameters are fixed at the middle values of their domains. We can see that the largest principal stress decreases and that the time to reach that stress increases when the depth of water increases. This conclusion can be explained by the fact that the deeper the water is, the more the energy can disperse from the water to the rock, and therefore, it results to a smaller largest principal stress in the rock at the bottom of the hole. This relationship depends on the distance travelled by the shockwave, and Fig. 13 indicates that the normalized stress curve consists of two linear parts with the corner at 0.35

w h D D = .
Furthermore, the slope of the normalized stress curve depends on the number of return trips that the shockwave has made before the largest principal stress is reached and the change of the curve's slope is linked to the discontinuity of the curve for the time to reach the largest stress, and is explained in detail below.

The variation of the time to reach the maximum principal stress with the change of the water depth, shown in Fig. 13, is due to the combination of two facts:

-when the depth of water increases, the time for the shockwave to travel from the surface of the water to the bottom of the hole increases too, so the time to reach the largest principal stress increases.

-and when the water becomes deep enough, the largest principal stress is not reached at the third time when the shockwave arrives at the bottom of the hole, but the second time.

We can follow this in Figs. 14(a , 60

h D cm = , 20 p L cm = , 60 / p V m s = , 5 a R mm = , 50 r E GPa = , 5 h R cm = , 0.2 r ! =
, the largest principal stress in the rock increases from 773 MPa to 1207 MPa when the depth of water in the hole reduces from 50 cm to 10 cm. In terms of the entire rock breaking technology, we need pressurized water to drive crack propagation once cracks are initiated in the rock. Therefore, it is not recommended to increase the largest principal stress in the rock, the crack initiation forcing, by reducing the water depth.

Influence of piston dimensions 4.3.1. Piston length

The radius of the piston is the same as h R , the radius of the hole. Its influence has been studied in the previous subsection. Now, let's consider the influence of piston length. Fig. 15 shows that the normalized largest principal stress increases continuously with the increasing of the normalized piston length. The longer the piston is, the higher its initial energy is because of the fixed initial velocity. Therefore, the stress in the rock increases. Such an influence is significant. For example, in the case of 200

p E GPa = , 3 7800 / r Kg m ! = , 60 h D cm = , 30 w D cm = , 60 / p V m s = , 5 a R mm = , 50 r E GPa = , 5 h R cm = and 0.2 r ! = ,
we obtain from Fig. 15 that the largest principal stress in the rock evolves from 690 MPa to 1202 MPa if the piston length evolves from 10 cm to 50 cm .

Initial kinetic energy of the piston

We have investigated the influence of the dimensions of the piston and its initial velocity on the largest principal stress in the rock. We will now try to understand the global influence of its initial kinetic energy, which embrace all these parameters:

2 2 1 2 p p p p p K R L V ! " = # # # # # . (12)
Fig. 18 shows the evolution of the normalized largest principal stress in the rock during the impact with respect to the normalized initial kinetic energy of the piston. The initial kinetic energy is changed by three approaches separately, i.e., changing the piston length, changing the piston radius and changing the initial velocity of the piston, while keeping the other parameters fixed at the middle values of their domains. Numerical results from the three approaches are depicted by three curves in Fig. 18. All these curves indicate that increasing the initial kinetic energy can increase the largest principal stress in the rock, which is not a surprise. For the purpose of increasing the largest stress in the rock over 800 MPa for 200 p E GPa = through increasing the initial kinetic energy, Fig. 18 indicates that the most effective way is to increase the piston's initial velocity.

Conclusions

The hydraulic impact problem of a non-explosive rock breaking technology has been studied.

Dimensional analysis and the finite element method have been applied to systematically investigate the influence of all the parameters involved in the impact process, which includes the geometrical parameters and the properties of rock, piston and water. Major conclusions from our investigation are summarized below:

-The rock density has a negligible influence on the largest principal stress in the rock.

-The influences of rock's Poisson's ratio and Young's modulus on the largest principal stress in the rock are small.

-The shape of the bottom of the hole has a substantial impact on the problem. For example, the closer it is to a right angle, the larger will be the largest stress in the rock.

-The largest principal stress in the rock decreases if the depth of water is increased.

-Increasing the initial kinetic energy of the piston has a significant influence on the problem: it implies an increase of the largest principal stress in the rock and a variation of the time to reach that value.

-The best way to increase the largest principal stress in the rock by increasing the initial kinetic energy of the piston is to increase its initial velocity.

Figs. 5

 5 Figs.5(a-g) clearly indicate that the variation of the normalized largest principal stress

Fig. 6 . 6 ,Fig. 7

 667 Fig.6shows the numerical results of the normalized largest principal stress in the rock during

Fig. 8

 8 Fig. 8 shows the influence of the normalized borehole radius / h p R D on the normalized

  this parameter will never be equal to zero, and its value can be estimated from the documentation of the active part of the tool used to drill the hole, in addition to the consideration of the rock material, or from experimental tests. We can achieve the dimensional values from Fig.12. For instance, if 200 principal stress in the rock reduces from 1860 MPa to 538 MPa when the radius of the arc at the bottom of the hole increases from 1 mm to 10 mm .

  Fig.13indicates that reducing the water depth can increase the largest stress in the rock. For

Fig. 15 4 . 3 . 2 .

 15432 Fig. 15 also shows that the time to reach the largest stress has an irregular relationship with

Fig. 1 .Fig. 2 .

 12 Fig. 1. Illustration of the hydraulic rock breaking technology.

Fig. 3 .

 3 Fig. 3. Maximum principal stress field, in the structure.

Fig. 4 .

 4 Fig. 4. Direction field of the maximum principal stress, in the rock at the bottom of the hole.

Fig. 5 Fig. 5 .

 55 Fig. 5(a)

Fig. 6 .

 6 Fig. 6. Influence of Poisson's ratio of the rock on the normalized largest principal stress in the

Fig. 7 .

 7 Fig. 7. Influence of normalized Young's modulus of the rock on the normalized largest

Fig. 8 .

 8 Fig. 8. Influence of normalized borehole radius on the normalized largest principal stress in

Fig. 9 .

 9 Fig. 9. Normalized average velocity of the piston versus normalized impacting time for

Fig. 10 .

 10 Fig. 10. Normalized kinetic energy of the piston versus normalized impacting time for several values of normalized borehole radius.

Fig. 11 .Fig. 12 .

 1112 Fig. 11. Normalized energy of the piston and the normalized maximum principal stress in the

Fig. 13 .

 13 Fig. 13. Influence of normalized water depth on the normalized largest principal stress in the

FigFig. 14 .

 14 Fig.14(a)

Fig. 15 .

 15 Fig. 15. Influence of normalized piston length on the normalized largest principal stress in the

FigFig. 16 .Fig. 17 .

 1617 Fig.16(a)

Fig. 18 .

 18 Fig. 18. Influence of normalized initial kinetic energy of the piston on normalized largest

  . According to this table, after choosing 200

			E	p	=	GPa	and
	7800	/	3

p Kg m ! =

Table 1 .

 1 List of all the parameters involved in the impact simulation.

	Piston	Water	Rock	Borehole
	p E : Young's modulus	w E : Young's modulus	r E : Young's modulus

h R : radius p ! : Poisson's ratio w ! : Poisson's ratio r ! : Poisson's ratio h D : depth p ! : density w ! : density r ! : density a R : arc radius p L : length w D : depth p V : initial velocity

Table 2 .

 2 Mechanical properties of typical rock materials.

	Rock material	Density (Kg / m 3 )	Young modulus (GPa)	Poisson's ratio
	Granite	2500 -2800	35 -80	0.1 -0.2
	Basalt	2400 -2900	20 -100	0.1 -0.3
	Sandstone	2200 -2700	10 -40	0.2 -0.3
	Dolerite	2900 -3100	40 -90	0.1 -0.3
	Limestone	2000 -2800	10 -50	0.2 -0.35
	Andesine	2500 -2800	30 -60	0.1 -0.25

This work has been partially supported by the Australia Research Council. Many thanks to

Laurent Champaney for his useful Perl scripts.

Acknowledgement


Gauthier Derenty-Camenen

Olivier Chadebec

Olivier Pinaud

Laure-Line Rouve

Steeve Zozor

Multipolar bases of equivalent magnetic sources on arbitrary surfaces

Keywords: Double-layer potential, multipolar expansion, near magnetic field computation, spherical Harmonic Functions

Decreasing Spherical Harmonic Functions (DSHF) provide a natural base for the magnetic scalar potential far enough from the sources. This multipolar expansion orders the magnetic field according to its decreasing rate and spatial periodicity. Unfortunately, this representation is not valid close to the sources. In this paper we will construct a basis for double-layer potential distributions on a surface, as close to the sources as needed, which is valid next to the sources while exhibiting a multipolar expansion property.

I. INTRODUCTION

O UTSIDE any surface enclosing magnetic sources, if the exterior volume is simply connected, the magnetic field derives from a scalar potential ϕ that verifies Laplace equation ∆ϕ = 0. In spherical coordinates, far enough from the sources, we can express this potential (and the associated field) in their multipolar expansion using the Decreasing Spherical Harmonic Functions (DSHF) [START_REF] Stratton | Electromagnetic theory, mcgrow-hill book company[END_REF]:

(1) ϕ(r, θ, φ) = ∞ k=1 k m=-k a km Y m k (θ, φ)/r k+1 .
For a chosen center of expansion, the spherical harmonic coefficients a km depend only on the source, Y m k (θ, φ)/r k+1 being the DSHF of order k and degree m with the typical spatial decreasing law 1/r k+1 . Because of this decreasing law any desired level of precision can be achieved at any distance by truncation of the DSHF basis.

Due to its expression with only a few degrees of freedom, this representation is commonly used to solve inverse problem [START_REF] Whaler | Spherical harmonic analysis of the geomagnetic field: an example of a linear inverse problem[END_REF] or to get a compact model of complex sources in the context of numerical methods coupling [START_REF] Tavernier | Realtime numerical dosimetry of low-frequency electromagnetic fields by using multipoles[END_REF], [START_REF] Van Hoang | Near Magnetic Field Coupling Prediction Using Equivalent Spherical Harmonic Sources[END_REF].

However, this representation is only valid outside the Brillouin Sphere (BS), the smallest sphere which encloses all sources [START_REF] Costin | On the Domain of Convergence of Spherical Harmonic Expansions[END_REF]. As a consequence, the BS limits the use of the DSHF representation when the field must be determined close to sources that are located in a volume with a dimension smaller or greater than the others [START_REF] Tavernier | Realtime numerical dosimetry of low-frequency electromagnetic fields by using multipoles[END_REF], [START_REF] Van Hoang | Near Magnetic Field Coupling Prediction Using Equivalent Spherical Harmonic Sources[END_REF].

In this paper we propose a method to construct a basis of distributions for double-layer potentials on an arbitrary surface closer than the BS which produce a valid field inside the BS while producing a field with similar decreasing property as the DSHF outside the BS.

II. A MULTIPOLAR BASIS ON ARBITRARY SURFACES

A. Layer potentials

Let S be any arbitrary surface which encloses all the sources. We can find a double-layer potential τ (equivalent to a normal dipoles distribution) on this surface that produces the same magnetic field (and scalar potential) outside the surface [START_REF] Stratton | Electromagnetic theory, mcgrow-hill book company[END_REF].

The scalar potential is then expressed at any exterior point P using Green function's normal derivative ∂ n G, with:

(2)

ϕ(P ) = M ∈S τ (M ) ∂ n G(P, M ) dS
The Green's function for any two points M and P in 3D is:

(3) G(P, M ) = 1 4π 1 ∥P M ∥ .

B. Construction of the multipolar basis

From the harmonic decomposition of (2), we choose an initial basis for the double-layer potential defined by the projection of the base of increasing spherical harmonic functions on the surface S:

(4)

τ 0 km (r, θ, φ) = r k Y m k (θ, φ)
If the surface S has some regularities, the family of distribution τ 0 km remains a basis of the distributions for the double layer potential [START_REF] Brelot | Sur l'approximation et la convergence dans la théorie des fonctions harmoniques ou holomorphes[END_REF].

This basis produces the same field as the DSHF in ([?]) if S is a sphere, but has no noticeable multipolar properties in other cases.

With this starting basis, we use the inner product defined in [START_REF] Legris | Identification de l'état magnétique d'un système ferromagnétique à partir de mesures du champ proche[END_REF]:

(5) ⟨τ 1 |τ 2 ⟩ = M ∈S σ[τ 1 ](M )τ 2 (M )dS Where σ[τ 1 ]
is the single-layer potential on the surface S that produces the same field as τ 1 outside of S.

Using the inner product (5) we orthonormalize the basis τ 0 km to get the new the basis τ km using Gram-Schmidt method. The distributions of τ 0 km are orthonormalized from the lowest order k.

This orthonormalization process induces an orthogonality property between the initial basis and the orthonormal one, the distribution of the new orthonormal basis are orthogonal to all the previous distributions of the initial basis.

As the spherical harmonic coefficients a k ′ m ′ of the multipolar expansion of any distribution τ km are given by: (6) a k ′ m ′ = τ 0 k ′ m ′ |τ km , All the spherical harmonic coefficients a k ′ m ′ of order k ′ strictly lower than k are set to 0. Thus, the scalar magnetic potential produced by the new ditribution τ km presents no contribution of order strictly inferior to k, meaning that the spatial decreasing law is at least 1/r k+1 . This property is illustrated in 2D on Fig 1, using the order k spatial periodicity of the circular harmonic field. In the extended paper, further theoretical development on the validity of this basis will be presented as well as another basis for multipolar single-layer potential. Both multipolar bases properties will be compared.

III. NUMERICAL APPLICATION

We consider a numerical model of a simplified ship hull mock-up, with one dimension higher than the others (4.4 m × 0.65 m × 0.6 m). The magnetic hull, placed in a low uniform vertical field (-15.92 A/m), is magnetized and produces its own field in the surroundings (magnetic anomaly).

We enclose the mock-up in a box (4.5 m × 0.75 m × 0.7 m) which defines the surface S where the double-layer potential is located. The expected distribution (or reference distribution), shown in figure 2, can be determined using (2) on the surface S. We will then project this expected equivalent double-layer potential of the anomaly on the new layer harmonics basis. The box is meshed with 2400 quadrangles (2402 nodes) so the reference distribution is represented with 2401 degrees of freedom by linear nodal shape functions. For the multipolar basis the number of degrees of freedom is K(K + 2) with K the order for the truncation, here the maximum amount of degrees of freedom is 168 (K = 12).

For the results, the relative error presented is the absolute difference between the module of the field produced by the reference distribution and the one produced by the layer harmonic truncated basis, divided by the maximum (on the computation surface) of the module of the field produced by the reference distribution.

A. Results outside the Brillouin Sphere

We compute the field produced by the layer harmonics on a sphere of radius 12.5 m. As expected, only the lowest orders are needed to correctly describe the field. In particular, the first order of the surface bases reconstructs the field with an error lower than 3%, with the associated decreasing law of a magnetic dipole.

B. Results inside the Brillouin Sphere

We compute the field produced by the layer harmonics on a rectangle of dimensions 2 m × 7 m along x and y axis and located 1 m below the box. Results (Table I) show that the field close to the mockup, inside the BS, is obtained with a precision lower than 1% with a maximum truncation order for the surface basis, superior or equal to 8. This means that only 80 layer harmonic coefficients must be determined to describe the field so close to the mock-up, which is very convenient for a future purpose of identification of these terms by solving an inverse problem from close field measurements.

Fig. 1 .

 1 Fig. 1. 2D spatial representation of a fourth order source vector (k = 4), field lines (red) produced by the distribution on a non-circular surface S (blue), before the orthonormalization (left) and after (right).

Fig. 2 .

 2 Fig. 2. Mock-up and visualisation of the reference distribution for doublelayer potential on the box.

TABLE I MAXIMUM

 I RELATIVE ERROR ON THE PLANE INSIDE THE BS AGAINST THE MAXIMUM ORDER OF TRUNCATION

	Order for the	maximum relative	Order for the	maximum relative
	truncation	error (%)	truncation	error (%)
	1	22.6	7	1.6
	2	16.3	8	0.8
	3	8.5	9	0.9
	4	6.3	10	0.8
	5	5.4	11	0.6
	6	3.9	12	0.4


Mohamed I Ghenai

Ronan Perrussel

Olivier Chadebec

Frédéric Vi

Jean-Michel Guichon

Gérard Meunier

Jonathan Siau

Domain decomposition for 3D nonlinear magnetostatic problems: Newton-Krylov-Schur vs. Schur-Newton-Krylov methods

Domain decomposition is a strategy designed to be used on parallel machines. This strategy leads to hybrid methods between direct and iterative solvers and allows users to benefit from the advantages of both. Lately, the growing size of simulations in electromagnetics brought to light the interest of using domain decomposition. Nonlinearity is also one of the problems specificities where the need for an efficient solver is high. This paper provides a comparison between two techniques of domain decomposition for solving 3D nonlinear magnetostatic problems. A test case illustrates the results that can be expected.

Index Terms-Domain decomposition, FETI method, Nonlinear magnetostatic, Parallel computing.

I. INTRODUCTION

D OMAIN decomposition is a strategy that seeks to decom- pose the problem into subdomains in order to be able to process them independently by relying on parallelization. Each subdomain will thus have its own local system to solve and will rely on solving methods adapted to its specificities (size, matrix properties...). For the case of nonlinear problems, most of the time, the nonlinearity is localized. This enables the domain decomposition method to distribute the workload resulting from the nonlinearity on some subdomains and have linear subdomains, where no need to calculate the tangent operator at each Newton-Raphson step. Hence, a local nonlinear solution can be performed on smaller problems instead of solving a much bigger global problem, while executing the full simulation in parallel. The originality of this paper is to provide a comparison between two non-overlapping domain decomposition techniques developed initially to treat nonlinear mechanics simulations. This paper details the implementation of these methods and shows an application of its use on a 3D contactor with nonlinear ferromagnetic materials.

II. PROBLEM DESCRIPTION

A 3D magnetostatic problem using a scalar potential formulation will be considered in the reminder of this paper [START_REF] Meunier | The finite element method for electromagnetic modeling[END_REF]. Using the finite element method, for a domain Ω with a magnet as source, ferromagnetic materials and the device surrounded by air, the system to be solved is written as

K(u)u = b(u), (1)
where

• K(u) is the finite element matrix of the magnetic scalar potential formulation, • u contains the values of the scalar potential at each node of the mesh, • b(u) is the source vector. The Newton-Raphson iterative method is usually considered to solve (1). This method consists of computing the tangent matrix DK as well as the residual r u at every iteration n and solving successive linear systems of the form

DK(u n )δu n = -r u (u n ).
(

) 2
The residual is given by r

u (u n ) = K(u n )u n -b(u n ).

III. DOMAIN DECOMPOSITION

For this study, we consider non-overlapping domain decomposition methods. They are caracterized by the absence of a shared surface (2D) or volume (3D) connecting neighboring subdomains [START_REF] Spillane | Méthodes de décomposition de domaine robustes pour les problèmes symétriques définis positifs[END_REF]. This choice was motivated by the parallel computing capabilities that it offers.

A. FETI : Finite Element Tearing and Inteconnecting

This method was introduced by Farhat and Roux in 1991 [START_REF] Farhat | A method of finite element tearing and interconnecting and its parallel solution algorithm[END_REF]. The domain is decomposed into subdomains and each subdomain is processed independently on a processor. The subdomain problems are usually solved by a direct solver, while an iterative method enables to solve a global problem condensed on the interface between subdomains. With the use of a proper preconditionner, it has been shown that the FETI method is optimal for a scalar diffusion problem [START_REF] Farhat | Optimal convergence properties of the FETI domain decomposition method[END_REF].

If the domain Ω is decomposed into N sd subdomains, on a subdomain s, a Poisson type problem has to be solved

(3) K s u s = b s + B t s λ,
where K s , u s , and b s are respectively matrix, solution and right-hand-side relative to subdomain s, B s is the signed Boolean matrice that extract from the vector u s its signed restriction to the subdomain interface shared with its neighbors (opposite signs between two neighboring subdomains) and λ is the Lagrange multiplier vector required to enforce the continuity conditions (4) for all couples of neighbors, ( 4)

N sd s=1 B s u s = 0.
Floating subdomains need also to be defined. They are subdomains without Dirichlet-type boundary conditions: the pseudo inverse matrix K + is then used instead of the inverse K -1 . The bases of the kernel of each matrix K s are concatenated in the rigid body mode matrix R. For a scalar problem the kernel of K s is at most of dimension 1. R i is the restriction of R on the interface. The problem condensed on the global interface between subdomains can then be written as ( 5)

F i R i (R i ) t 0 λ α =    - N sd s=1 B s K + s b s R t b    ,
where α is of size the number of floating subdomains and ( 6)

F i = N sd s=1 B s K + s B t s .

B. Newton-Krylov-Schur methods

The Newton-Krylov-Schur (NKS) methods can be implemented straightforwardly: at each Newton-Raphson iteration, the FETI method is considered to solve the tangent linear system (2). As in FETI, the Schur complement in NKS describes the interface problem. The global problem is never assembled and the residual computation is partitioned on the subdomains [START_REF] Pebrel | A nonlinear dual-domain decomposition method: Application to structural problems with damage[END_REF].

C. Schur-Newton-Krylov

The Schur-Newton-Krylov (SNK) methods were developed based on the observation that NKS methods do not take advantage of domain decomposition to solve the nonlinear problem, but only to solve the resulting tangent linear systems. In SNK methods the global nonlinear problem is decomposed into small nonlinear problems with continuity conditions imposed on the interface unknowns across the subdomains, resulting in a condensed nonlinear interface problem with tangent system (7)

DF i R i (R i ) t 0 δλ δα = -r λ 0 .
Problem (7), just as [START_REF]Altair Flux TM[END_REF], is solved using a preconditioned conjugate projected gradient (PCPG) algorithm as in [START_REF] Farhat | A method of finite element tearing and interconnecting and its parallel solution algorithm[END_REF]. The algorithm of SNK methods is summarized in Algorithm 1.

IV. APPLICATION

Both NKS and SNK algorithms have been implemented in Altair Flux TM software [START_REF]Altair Flux TM[END_REF]. They have been tested and compared to the standard Newton-Raphson method commonly used for this type of simulations. The linear solver used in Newton Raphson by default is a direct solver (LU factorisation). The test case is illustrated in Fig. 1 and represents a 3D magnetic contactor. It was decomposed into 4 subdomains: 1 air (linear), 2 upper pallet (nonlinear), 3 magnet (linear) and 4 E shape (nonlinear). The size of the test case is 2432 nodes.

Table I sums up the results. An adaptive convergence criteria has been used to obtain less PCPG iterations with a Dirichlet preconditioner [START_REF] Farhat | Optimal convergence properties of the FETI domain decomposition method[END_REF]. The project was solved using 4 cores.

Algorithm 1 SNK with FETI algorithm

Require: n = 1, λ 0 = R i (R it R i ) -1 R t b while ∥δλ n ∥/∥λ n ∥≤ tol g do K s (u n s ) = b s (u n s ) -B t
λ n+1 ← λ n + δλ n α n+1 ← α n + ((R i ) t R i ) -1 (R i ) t (-DF i (λ n )δλ n -r n λ ) n ← n + 1 end while

Fig. 1 .

 1 Fig. 1. Contactor test case with nonlinear materials.

  s λ n s ▷ Solve local NL problems p = 1; u n 1 s = (R i ) t α n s while δu ≤ tol N R do Solve DK s (u n p s )δ p u = b p s (u n p s ) -B t s λ n

	u n p+1 s	← u n p s + δ p u	s
	p ← p + 1
	end while
	r n λ ←	N sd s=1 B s u n s	▷ Compute residual
	Solve FETI interface problem with PCPG

TABLE I

 I

	RESULTS COMPARISON FOR THE CONTACTOR TEST CASE
	Item	NR NKS SNK
	Max local NL iterations	/	/	5
	Global NL iterations	6	6	7
	Speedup	1	1.3 0.4


A Thiolat

L Semerano

Y M Pers

J Biton

D Lemeiter

P Portales

J Quentin

C Jorgensen

P Decker

M.-C Boissier

P Louis-Plence

N Bessis

Interleukin-6 Receptor Blockade Enhances CD39ϩ Regulatory T Cell Development in Rheumatoid Arthritis and in Experimental Arthritis

Objective. The rationale for blocking interleukin-6 (IL-6) in rheumatoid arthritis (RA) lies chiefly in the proinflammatory effect of this cytokine. Few studies have evaluated the consequences of anti-IL-6 receptor (IL-6R) antibody treatment on Treg cells. This study was undertaken to elucidate the mechanism of action of anti-IL-6R antibody treatment by studying the effects on Treg cells in an experimental arthritis model and in patients with RA. Methods. Mice with collagen-induced arthritis (CIA) were treated with a mouse anti-IL-6R antibody (MR16-1), and changes in Treg, Th1, and Th17 cells were assessed at key time points during the course of the disease. Peripheral blood from 15 RA patients was collected on day 0 and after 3 months of tocilizumab treatment for flow cytometry analysis of Th17 and Treg cells. Results. In MR16-1-treated mice, Th17 cell frequencies were unchanged, whereas Treg cell frequencies were increased. The Treg cell phenotype showed marked changes, with an increase in the frequency of CD39؉ Treg cells in the lymph nodes and spleen. Interestingly, similar CD39؉ Treg cell expansion was observed in RA patients who were tocilizumab responders at 3 months, with no change in Th17 cell frequency. Moreover, fluorescence-activated cell-sorted CD39؉ Treg cells from responder RA patients were functionally able to suppress the proliferation of conventional T cells. Conclusion. In both CIA and RA, the frequency of functionally suppressive CD39؉ Treg cells is increased as a result of anti-IL-6R treatment, whereas Th17 cells are unaffected. The modification of Treg cell frequency and phenotype may be one of the mechanisms involved in the therapeutic effect of IL-6 blockade in RA.

Interleukin-6 (IL-6) plays a central role in the pathogenesis of rheumatoid arthritis (RA). This cytokine targets multiple cells, including B cells, T cells, macrophages, neutrophils, synoviocytes, and osteoclasts. Signaling through the IL-6 receptor (IL-6R) leads to a combination of systemic and joint inflammation, resulting in pannus formation, osteoclast activation, and chronic synovitis. IL-6-deficient mice are resistant to collagen-induced arthritis (CIA) [START_REF] Alonzi | Interleukin 6 is required for the development of collageninduced arthritis[END_REF], and early administration of the anti-mouse IL-6R monoclonal antibody MR16-1 inhibits CIA [START_REF] Takagi | Blockage of interleukin-6 receptor ameliorates joint disease in murine collagen-induced arthritis[END_REF]. IL-6 is abundantly expressed in the synovium of RA patients [START_REF] Madhok | Serum interleukin 6 levels in rheumatoid arthritis: correlations with clinical and laboratory indices of disease activity[END_REF]. These data provide a strong rationale for targeting IL-6, and the humanized anti-IL-6R antibody tocilizumab is now used to treat moderate-to-severe RA [START_REF] Tak | Advances in rheumatology: new targeted therapeutics[END_REF].

IL-6 is also involved in the adaptive immune response. IL-6 influences T cell differentiation into effector T cells (Th1, Th2, and Th17 cells) or regulatory T cells (Treg cells) [START_REF] Dienz | The induction of antibody production by IL-6 is indirectly mediated by IL-21 produced by CD4ϩ T cells[END_REF]. Th17 cells and Treg cells have opposite roles in rheumatoid inflammation [START_REF] Boissier | Cell and cytokine imbalances in rheumatoid synovitis[END_REF]. Th17 cells are important mediators of inflammation in animal Supported in part by the Socie ´te ´Franc ¸aise de Rhumatologie and Universite ´Paris 13. Unrestricted grants were provided by Roche and Chugai Pharma France. Drs. Thiolat, Semerano, and Pers contributed equally to this work.

Address correspondence to Marie-Christophe Boissier, MD, PhD, EA 4222, Li2P, Universite ´Paris 13, 74 Rue Marcel Cachin, 93017 Bobigny, France. E-mail: marie-christophe.boissier@avc. aphp.fr. models of RA [START_REF] Hirota | T cell self-reactivity forms a cytokine milieu for spontaneous development of IL-17ϩ Th cells that cause autoimmune arthritis[END_REF][START_REF] Geboes | Proinflammatory role of the Th17 cytokine interleukin-22 in collagen-induced arthritis in C57BL/6 mice[END_REF][START_REF] Nakae | Suppression of immune induction of collagen-induced arthritis in IL-17-deficient mice[END_REF]. In contrast, CD4ϩCD25ϩFoxP3ϩ Treg cells are essential for maintaining immune homeostasis, preventing autoimmunity, and limiting chronic inflammatory diseases. A Treg/Th17 cell imbalance has been documented in RA [START_REF] Samson | Inhibition of interleukin-6 function corrects Th17/Treg cell imbalance in patients with rheumatoid arthritis[END_REF]. In mice, Th17 cells and induced Treg (iTreg) cells arise from the same CD4ϩ naive T cell precursor in distinct cytokine milieus. IL-6, and probably other proinflammatory cytokines, may determine whether an immune response is dominated by either Treg cells or Th17 cells [START_REF] Bettelli | T(H)-17 cells in the circle of immunity and autoimmunity[END_REF]. Treg cells express IL-6R [START_REF] Doganci | The IL-6R alpha chain controls lung CD4ϩCD25ϩ Treg development and function during allergic airway inflammation in vivo[END_REF][START_REF] Oberg | Differential expression of CD126 and CD130 mediates different STAT-3 phosphorylation in CD4ϩCD25Ϫ and CD25high regulatory T cells[END_REF], and administration of a mouse monoclonal antibody to inhibit IL-6R in CD4ϩ T cell cultures potently inhibits Th17 cell differentiation in response to transforming growth factor ␤ and conditioned medium, and partially restores the induction of Treg cells [START_REF] Fujimoto | Interleukin-6 blockade suppresses autoimmune arthritis in mice by the inhibition of inflammatory Th17 responses[END_REF].

The role of Treg cells in RA has been investigated in both patients and animal models. In murine CIA, Treg cell depletion aggravates the disease [START_REF] Morgan | CD25ϩ cell depletion hastens the onset of severe disease in collagen-induced arthritis[END_REF], whereas adoptive Treg cell transfer has a protective effect. Similarly, the absence of Treg cells in K/BxN scurfy mice is associated with faster onset and greater severity of arthritis [START_REF] Nguyen | Where FoxP3dependent regulatory T cells impinge on the development of inflammatory arthritis[END_REF]. The proportion of Treg cells in RA patients is increased in the synovium but unchanged in the peripheral blood, when compared to that in healthy individuals and patients with other joint diseases [START_REF] Jiao | Accumulation of FoxP3-expressing CD4ϩCD25ϩ T cells with distinct chemokine receptors in synovial fluid of patients with active rheumatoid arthritis[END_REF][START_REF] Lin | The quantitative analysis of peripheral blood FOXP3-expressing T cells in systemic lupus erythematosus and rheumatoid arthritis patients[END_REF]. Importantly, the Treg cell phenotype and suppressive activity of Treg cells are altered in RA. Rheumatoid Treg cells exhibit diminished suppressive capabilities, are unable to inhibit the production of tumor necrosis factor ␣ (TNF␣) and interferon-␥ (IFN␥) by CD4ϩ conventional T (Tconv) cells or macrophages [START_REF] Ehrenstein | Compromised function of regulatory T cells in rheumatoid arthritis and reversal by anti-TNFalpha therapy[END_REF][START_REF] Cao | CD25brightCD4ϩ regulatory T cells are enriched in inflamed joints of patients with chronic rheumatic disease[END_REF], and do not accumulate CTLA-4 on their surface [START_REF] Flores-Borja | Defects in CTLA-4 are associated with abnormal regulatory T cell function in rheumatoid arthritis[END_REF]. Similarly, another study showed resistance of CD4ϩ T cells to Treg cell-mediated suppression in the peripheral blood of RA patients [START_REF] Van Amelsfort | CD4(ϩ)CD25(ϩ) regulatory T cells in rheumatoid arthritis: differences in the presence, phenotype, and function between peripheral blood and synovial fluid[END_REF]. Moreover, TNF␣ compromises Treg cell function in RA [START_REF] Ehrenstein | Compromised function of regulatory T cells in rheumatoid arthritis and reversal by anti-TNFalpha therapy[END_REF][START_REF] Nadkarni | Anti-TNF-alpha therapy induces a distinct regulatory T cell population in patients with rheumatoid arthritis via TGF-beta[END_REF].

Our group [START_REF] Biton | Interplay between TNF and regulatory T cells in a TNF-driven murine model of arthritis[END_REF][START_REF] Biton | TNFalpha: activator or inhibitor of regulatory T cells?[END_REF] and other investigators (23) have shown that TNF␣ antagonist therapy leads to a modification in the Treg cell phenotype, accompanied by an increase in suppressive activity. In this study, we hypothesized that IL-6R blockade could act via effects on Treg cells. Most of the studies on the effects of anti-IL-6R treatment on Treg cells have focused only on Treg cell frequency [START_REF] Samson | Inhibition of interleukin-6 function corrects Th17/Treg cell imbalance in patients with rheumatoid arthritis[END_REF][START_REF] Fujimoto | Interleukin-6 blockade suppresses autoimmune arthritis in mice by the inhibition of inflammatory Th17 responses[END_REF][START_REF] Aricha | Blocking of IL-6 suppresses experimental autoimmune myasthenia gravis[END_REF].

Our objective in the present study was to elucidate the consequences of anti-IL-6R treatment in terms of its effects on the Treg cell phenotype and the activation of Treg cells in both a mouse model of RA (CIA) and in human patients with RA [START_REF] Nadkarni | Anti-TNF-alpha therapy induces a distinct regulatory T cell population in patients with rheumatoid arthritis via TGF-beta[END_REF], in order to determine whether Treg cells are involved in the mode of action of this targeted therapy.

PATIENTS AND METHODS

Patients. Patients meeting the American College of Rheumatology/European League Against Rheumatism (EULAR) revised criteria for RA [START_REF] Aletaha | rheumatoid arthritis classification criteria: an American College of Rheumatology/European League Against Rheumatism collaborative initiative[END_REF] and qualifying for anticytokine therapy were invited to participate in a prospective, open-label, 12-week study of intravenous tocilizumab. Eligible patients were required to have a 28-joint Disease Activity Score (DAS28) of Ն3.2 and to have been treated unsuccessfully with at least 2 synthetic and/or biologic diseasemodifying antirheumatic drugs (DMARDs). The study was approved by the local ethics committee (approval no. DC-2012-1579), and informed consent was obtained from all patients prior to study entry. Tocilizumab was given with approval of the French Drug Agency, in a dose of 8 mg/kg as a 60-minute intravenous infusion every 4 weeks.

We included 15 patients (13 women, 2 men) whose median age was 58 years and mean disease duration was 17.6 years (a detailed list of the patients' main characteristics at baseline is available from the corresponding author upon request). A history of an inadequate treatment response to methotrexate was noted in all 15 patients, an inadequate response to leflunomide was observed in 7 patients, and an inadequate response to TNF␣ antagonist therapy was observed in 8 patients (etanercept in 8, infliximab in 2, and adalimumab in 8). A list of the concomitant therapies (steroids or DMARDs) is available from the corresponding author upon request. After 12 weeks of tocilizumab therapy, 7 patients were good responders and 8 were nonresponders, according to the EULAR response criteria [START_REF] Van Gestel | Development and validation of the European League Against Rheumatism response criteria for rheumatoid arthritis: comparison with the preliminary American College of Rheumatology and the World Health Organization/International League Against Rheumatism criteria[END_REF]. For the functional suppression assay, 8 patients were recruited, including 6 of the 7 good responders in the CD39 expression study, and 2 other patients whose disease was in sustained remission or whose disease activity had been low for at least 6 months.

Mice. Clinical and histologic assessments of CIA. DBA/1 mice (6 weeks old) were purchased from Janvier. All procedures were approved by the Animal Care and Use Committee of the Universite ´Paris 13 (Bobigny, France).

Arthritis was induced with native bovine type II collagen (CII) (MD Biosciences) in male DBA/1 mice. Clinical and histologic scores of arthritis were evaluated in each mouse, as described elsewhere [START_REF] Clavel | Relationship between angiogenesis and inflammation in experimental arthritis[END_REF][START_REF] Denys | Intra-articular electrotransfer of mouse soluble tumour necrosis factor receptor in a murine model of rheumatoid arthritis[END_REF]. Briefly, the animals were killed and their legs were dissected free and processed for histologic studies. At least 4 serial sections were cut from each paw to ensure extensive evaluation of the arthritic joints. The lesions were evaluated in each joint as previously described, using a 4-point scale (scores of 0-3, where 0 indicates normal and 3 indicates severe). This global histologic score reflects both the extent of synovitis (synovial proliferation, inflammatory cell infiltration) and the extent of joint destruction (bone and cartilage thickness and irregularity and presence of erosions). We also separately evaluated the presence of articular destruction, by taking into account the degradation of bone and cartilage regardless of inflammation. For this assessment, we again used a 4-point scale (scores of 0-3, where 0 indicates no destruction and 3 indicates the presence of subchondral bone erosions).

Treatment of mice. IL-6 blockade was achieved using an intraperitoneal injection of 8 mg of MR16-1, a rat IgG1specific monoclonal antibody against murine IL-6R. Control animals received an intraperitoneal injection of IgG purified from the serum of unimmunized rats or an intraperitoneal injection of phosphate buffered saline (PBS). The injection was given on the day of CII immunization (day 0) to enable assessment of therapeutic effects in early disease. MR16-1 was a gift from Chugai Pharma France, and control IgG was purchased from Jackson ImmunoResearch.

Cell and tissue preparation. Mice. Spleen leukocytes were prepared using a homogenizer, and red blood cells were lysed in hemolysis buffer (NH 4 CL, KHCO 3 , and EDTA). Afferent popliteal and axillary lymph nodes were dissected out of the limbs, and node leukocytes were prepared using a homogenizer. Thymus leukocytes were prepared using a homogenizer, and then frozen at Ϫ80°C in heat-inactivated fetal calf serum (FCS) containing 10% dimethyl sulfoxide until staining. Blood was collected by heart puncture.

RA patients. For monitoring of the immune response, blood samples from RA patients were collected just before the first and fourth tocilizumab infusions (8 mg/kg each). For the functional suppression assay, 25-40 ml of blood from responder patients was collected and peripheral blood mononuclear cells (PBMCs) were obtained by Ficoll gradient centrifugation.

Flow cytometry. Mice. The cell surfaces were stained with one of the following: fluorescein isothiocyanate (FITC)labeled anti-CD25 (clone 3C7), FITC-labeled anti-CD4 (clone RM4-5), R-phycoerythrin (PE)-labeled anti-CTLA-4 (clone UC10-4F10-11), PE-labeled anti-CD62L (clone MEL-14) (all from BD Biosciences), PE-labeled anti-glucocorticoidinduced TNF receptor (anti-GITR; clone DTA-1), PE-labeled anti-inducible T cell costimulator (anti-ICOS; clone 7E.17G9) (all from eBioscience), PE-labeled anti-CD39 (clone 24 DMS1; eBioscience) or PE-labeled anti-Helios (clone 22F6; BioLegend), and PerCP-Cy5.5-labeled anti-CD4 (clone RM4-5) or PerCP-Cy5.5-labeled anti-CD8 (clone 53-6.7) (both from BD Biosciences). The cells were stained at 4°C in PBS containing 4% heat-inactivated FCS and 0.01M sodium azide, and then incubated for 30 minutes with appropriate dilutions of the various monoclonal antibodies coupled to FITC, PE, or PerCP-Cy5.5. The allophycocyanin (APC)labeled anti-FoxP3 (clone FJK-16s) staining set (eBioscience) was used for intracellular staining, in accordance with the manufacturer's recommendations. Staining for intracellular cytokines (IL-17 and IFN␥) was performed as described previously [START_REF] Biton | Interplay between TNF and regulatory T cells in a TNF-driven murine model of arthritis[END_REF].

Flow cytometry was performed on a 4-color FACSCalibur (Becton Dickinson). Dead cells were excluded on the basis of forward-scatter and side-scatter characteristics. Reported statistical data are based on at least 1,000 events gated on the cell population of interest. Results were analyzed using Cell-Quest Pro software (BD Biosciences). The WEASEL program (version 2. ). The antibodies were detected after fixation and permeabilization with reagents from eBioscience. For Th17 cell staining, PBMCs were first stimulated with anti-CD3/anti-CD28-coated beads (Invitrogen) for 24 hours.

Flow cytometry was performed on a FACSCanto II (BD Biosciences). Data were analyzed using DIVA version 6, and further processed using Prism version 5.0 (GraphPad Software).

Assessment of the suppressive effects of Treg cells on CD4؉CD25؊ Tconv cells. Spleen CD4ϩCD25Ϫ and CD4ϩCD25ϩ T cells were purified using a Regulatory T Cell Isolation Kit (Miltenyi Biotec) according to the manufacturer's protocol [START_REF] Biton | Interplay between TNF and regulatory T cells in a TNF-driven murine model of arthritis[END_REF]. Flow cytometry demonstrated 90-95% purity of the CD4ϩCD25Ϫ and CD4ϩCD25ϩ T cell-enriched fractions. The proliferation of carboxyfluorescein succinimidyl ester (CFSE)-stained CD4ϩCD25Ϫ T cells (Tconv cells) with or without CD4ϩCD25ϩ cells was then assessed, as described previously [START_REF] Biton | Interplay between TNF and regulatory T cells in a TNF-driven murine model of arthritis[END_REF].

Assessment of the suppressive effects of CD39؉ and CD39؊ Treg cells on CD4؉CD25؊ Tconv cells. Isolation of human T cell subsets was carried out by labeling 25-80 million PBMCs with APC-H7-conjugated anti-CD4, PerCP-Cy5.5conjugated anti-CD25, PE-conjugated anti-CD127, and PE-Cy7-conjugated anti-CD39. Viable cells were cell-sorted on a FACSAria (MRI platform) in 3 various populations: CD4ϩCD127ϩCD25Ϫ T cells (Tconv cells), CD4ϩ CD127 low CD25ϩCD39ϩ T cells (CD39ϩ Treg cells), and CD4ϩCD25ϩCD127 low CD39Ϫ T cells (CD39Ϫ Treg cells). Cell-sorted populations were routinely Ͼ98% pure.

CFSE-labeled Tconv cells (10 5 ) were cultured with titrated numbers of CD39ϩ Treg cells, CD39Ϫ Treg cells, or unlabeled Tconv cells in the presence of allogeneic APC (5 ϫ 10 5 ) and 10 g/ml anti-CD3 monoclonal antibody 2C11. After 4 days of culture, proliferation of Tconv cells was assessed by fluorescence-activated cell sorting (FACS) analysis. Data were analyzed using FlowJo software to determine the percentage of original cells that divided, and further processed using Prism version 5.0 (GraphPad Software).

ATP hydrolysis assay. The ATPase activity of Treg cells from MR16-1-treated or control IgG-treated mice was evaluated 9 days after the induction of CIA. CD4ϩCD25ϩ cells were purified as described above, and ATPase activity was determined as described previously [START_REF] Borsellino | Expression of ectonucleotidase CD39 by Foxp3ϩ Treg cells: hydrolysis of extracellular ATP and immune suppression[END_REF].

Cytokine assay. For detection of TNF␣ in the sera, a FlowCytomix kit (eBioscience) was used in accordance with the manufacturer's instructions. Samples were analyzed by flow cytometry. FlowCytomix Pro software (eBioscience) was used for cytokine quantification.

Enzyme-linked immunosorbent assay (ELISA) for IFN␥. Levels of IFN␥ in the culture supernatants were measured using commercially available ELISA kits (R&D Systems), in accordance with the manufacturer's instructions.

Statistical analysis. Depending on the distribution of the data, parametric or nonparametric tests with appropriate comparisons were used to compare groups. Clinical scores and log-transformed histologic scores were compared using oneway analysis of variance (ANOVA) with comparison using post hoc Student-Newman-Keuls test.

The impact of MR16-1 treatment during the course of CIA on thymus, spleen, and lymph node Treg cells or Th17 cell populations, in terms of the number, frequency, ratio, and expression of various molecules (assessed as the mean fluorescence intensity [MFI]), was evaluated using two-way ANOVA (treatment group and time). Serum cytokine (TNF␣) levels were compared between MR16-1-and IgG-treated mice using the Mann-Whitney test with Bonferroni correction. All statistical analyses were performed with MedCalc software version 10.4, unless otherwise specified.

RESULTS

Improvement in CIA following early IL-6R blockade.

A single intraperitoneal injection of 8 mg of MR16-1 on day 0 attenuated the clinical manifestations of arthritis (P Ͻ 0.05) (Figure 1A) and the histologic arthritis scores (Figures 1B andC), as compared to IgG- and PBS-treated control mice. TNF␣ was detectable in the serum of mice with late-stage CIA (after day 28), and TNF␣ levels were higher in the IgG group than in the MR16-1 group (mean Ϯ SEM 25.4 Ϯ 2.4 pg/ml versus 13.9 Ϯ 11.1 pg/ml; P Ͻ 0.05) on day 42.

Increased frequency of thymic Treg cells in MR16-1-treated mice. Treg cells can be generated either in the thymus from CD4ϩCD8ϩ double-positive thymocytes (natural Treg [nTreg] cells) or peripherally (induced Treg [iTreg] cells) from conventional CD4ϩ FoxP3Ϫ T cells (Tconv cells) [START_REF] Bilate | Induced CD4(ϩ)Foxp3(ϩ) regulatory T cells in immune tolerance[END_REF]. In MR16-1-treated mice compared to IgG-treated control mice, we found increases in both the count and frequency of nTreg cells (CD4ϩCD8ϪFoxP3ϩ cells) among whole thymocytes during the course of arthritis (Table 1), mainly attributable to differences observed at the begining (day 8) and at the end (day 42) of the analysis. Similarly, the frequency of thymic CD4ϩCD8ϪFoxP3ϩ cells expressing Helios and the level of Helios expression by thymic Treg cells were significantly increased in MR16-1treated mice compared to controls (Table 1).

Increased Treg:Th17 and Treg:Tconv cell ratios in MR16-1-treated mice. In the spleen, the percentage of Tconv cells among leukocytes from day 18 to day 42 was lower in MR16-1-treated mice compared to IgGtreated controls, whereas the percentage of Treg cells was similar in both groups. Thus, the Treg:Tconv cell ratio was unmodified (results available from the corresponding author upon request). In the lymph nodes, MR16-1 treatment decreased the Tconv cell percentage among leukocytes from day 18 to day 42 as compared to that in the control groups, whereas the Treg cell per- centage was not different between groups. Thus, the Treg:Tconv cell ratio increased in the lymph nodes of MR16-1-treated mice compared to control mice globally over time (results available from the corresponding author upon request). IL-6 acts as a decision point that determines whether the immune response is dominated by either Treg cells or Th17 cells. We found no significant change in the frequency of either Th17 cells (Figures 2A andB) or Treg cells (Figure 2C) among CD4ϩ cells in the lymph nodes after MR16-1 treatment. Nevertheless, the ratio of Treg cell frequencies to Th17 cell frequencies among CD4ϩ cells was significantly increased in favor of Treg cells in the lymph nodes of MR16-1-treated mice (Figure 2D).

Modification of the Treg cell phenotype by IL-6R neutralization in mice with CIA. We characterized the Treg cell phenotype throughout the development of CIA, from day 8 to day 28, by evaluating the expression levels of CTLA-4, CD62L, GITR, ICOS, Helios, and CD39. Levels of ICOS, GITR, and Helios were not modified on Treg cells from the lymph nodes or spleen of mice at any time after MR16-1 treatment (results not shown). In contrast, MR16-1 treatment increased the percentage of CTLA-4ϩ Treg cells (results available from the corresponding author upon request) and in- creased the intensity (MFI) of CTLA-4 expression in the lymph nodes (Figure 3A), but not in the spleen (results not shown), when compared to IgG treatment during the course of CIA.

Furthermore, IL-6R neutralization increased the frequency of CD39ϩ Treg cells in both the lymph nodes and spleen, as compared to that in the IgG control group (results available from the corresponding author upon request). The intensity (MFI) of CD39 expression on Treg cells from the spleen, but not the lymph nodes, was increased throughout the course of CIA in the MR16-1 group compared to the IgG control group (Figures 3B andC). MR16-1 treatment had no effect on the ability of Treg cells to suppress the proliferation of Tconv cells or production of IFN␥, nor did it have any effect on the ATPase activity of Treg cells (results not shown).

Lack of effect on Th17 cells, but increase in CD39؉ Treg cells, following tocilizumab treatment in RA patients. Of the 15 RA patients treated with tocilizumab, 7 met the EULAR criteria for a very good response (defined as a change in the DAS28 of Ͼ1.2) (results available from the corresponding author upon request). The frequency of peripheral blood Th17 cells (defined as CD4ϩIL-17ϩCCR6ϩ cells) was not significantly modified by tocilizumab therapy. Moreover, the frequency of Th17 cells did not differ between responders and nonresponders (mean Ϯ SEM 0.53 Ϯ 0.22% versus 0.23 Ϯ 0.09%) (Figure 4A).

With regard to Treg cells, CD39 is constitutively expressed on ϳ50% of human CD25ϩFoxP3ϩ nTreg cells in healthy controls [START_REF] Fletcher | CD39ϩFoxp3ϩ regulatory T cells suppress pathogenic Th17 cells and are impaired in multiple sclerosis[END_REF]. The percentage of CD39ϩ cells among CD4ϩCD25ϩFoxP3ϩ T cells was signifi- cantly higher in the responders than in the nonresponders after 3 months of tocilizumab therapy (mean Ϯ SEM 72 Ϯ 4% versus 44 Ϯ 8%; P Ͻ 0.05). Importantly, as a consequence, the frequency of CD39ϩ Treg cells among CD4ϩ cells was significantly higher in responders compared to nonresponders (mean Ϯ SEM 1.17 Ϯ 0.12% versus 0.78 Ϯ 0.12%; P Ͻ 0.05) (Figure 4B). Interestingly, this increase in the frequency of CD39ϩ Treg cells was observed as early as 1 month (results not shown) following treatment with tocilizumab, but the increase only reached a statistically significant difference at 3 months of treatment.

Suppressive function of CD39؉ and CD39؊ Treg cells in responder patients. To assess the functionality of Treg cells in a suppression assay, CD39ϩ and CD39Ϫ Treg cells from 8 responder patients (mean Ϯ SEM DAS28 2.2 Ϯ 0.8; mean Ϯ SEM duration of tocilizumab treatment 22.6 Ϯ 7.2 months) were FACSsorted based on the expression of CD25, CD127, and CD39, to separate both Treg cell populations from Tconv cells. First, we found that in all tested patients, both Treg cell populations suppressed, in a very efficient manner, the proliferation of CD4ϩ Tconv cells, even at a Treg:Tconv cell ratio of 1:2 (Figure 5A).

Based on the percentage of original cells that had divided, we calculated the relative suppression activity of both Treg cell populations. FACS-sorted CD39ϩ Treg cells from the 8 responder RA patients were functionally able to suppress the proliferation of Tconv cells. It may be noted that in 5 of the 8 responders, the suppressive function of CD39ϩ Treg cells was higher than that of CD39Ϫ Treg cells (Figure 5B).

DISCUSSION

The results of the present study demonstrate, for the first time, the involvement of the CD39ϩFoxP3ϩ Treg cell population following administration of an anticytokine treatment in arthritis. We show that blockade of the IL-6 pathway modified the Th17/Treg cell balance and led to induction of a functional CD39ϩFoxP3ϩ Treg cell population that was associated with an attenuation of disease severity in both humans with RA and mice with CIA.

Since IL-6 is a key factor in Th17 cell differentiation [START_REF] Bettelli | Reciprocal developmental pathways for the generation of pathogenic effector TH17 and regulatory T cells[END_REF], the protective effect of anti-IL-6R antibody treatment against arthritis was hypothesized to involve the suppression of Th17 cells [START_REF] Fujimoto | Interleukin-6 blockade suppresses autoimmune arthritis in mice by the inhibition of inflammatory Th17 responses[END_REF][START_REF] Yoshida | IL-6 blockade preferentially inhibits Th17 differentiation in collagen-induced arthritis[END_REF], as has been seen in other models of autoimmune disease. Studies in various autoimmunity models, such as experimental autoimmune encephalomyelitis [START_REF] Serada | IL-6 blockade inhibits the induction of myelin antigenspecific Th17 cells and Th1 cells in experimental autoimmune encephalomyelitis[END_REF], uveoretinitis [START_REF] Hohki | Blockade of interleukin-6 signaling suppresses experimental autoimmune uveoretinitis by the inhibition of inflammatory Th17 responses[END_REF], CIA [START_REF] Takagi | Blockage of interleukin-6 receptor ameliorates joint disease in murine collagen-induced arthritis[END_REF][START_REF] Lissilaa | Although IL-6 trans-signaling is sufficient to drive local immune responses, classical IL-6 signaling is obligate for the induction of T cell-mediated autoimmunity[END_REF], and glucose-6-phosphate isomerase-induced arthritis [START_REF] Iwanami | Crucial role of the interleukin-6/interleukin-17 cytokine axis in the induction of arthritis by glucose-6-phosphate isomerase[END_REF], showed that anti-IL-6R antibody treatment suppressed antigen-specific Th17 cell differentiation. In our study, Th17 cell frequencies were not significantly different between tocilizumab responders and nonresponders, and no significant changes were observed throughout the course of CIA in MR16-1-treated mice. An important difference in comparison with other studies is that we evaluated non-antigen-specific Th17 cells. Therefore, our results in CIA may more accurately reflect the events in human RA, whose pathogenesis likely involves several different autoantigens.

Rather than conducting separate measurements of the frequencies of Th17 cells and Treg cells, an assessment of the balance between these 2 T helper cell subsets is needed, since IL-6 is the key cytokine directing the differentiation process toward one or the other cell type [START_REF] Bettelli | T(H)-17 cells in the circle of immunity and autoimmunity[END_REF]. An appropriate Th17/Treg cell balance is crucial for maintaining immune homeostasis, whereas an excess of Th17 cells relative to Treg cells causes the onset of various autoimmune and chronic inflammatory diseases [START_REF] Tanaka | Immunotherapeutic implication of IL-6 blockade[END_REF].

Our study shows that anti-IL-6R antibody treatment modifies the Th17/Treg cell balance by modifying the Treg:Tconv cell ratio, but not by acting on the Th17 cell subset (neither in mice nor in humans). In a study by Fujimoto et al [START_REF] Fujimoto | Interleukin-6 blockade suppresses autoimmune arthritis in mice by the inhibition of inflammatory Th17 responses[END_REF], the Th17:Treg cell ratio was modified in mice with CIA treated with MR16-1, although contrary to our study findings, this modification could be attributed to a decreased Th17 cell frequency rather than a modified Treg cell percentage. In addition, in a study by Samson et al, treatment of RA patients with tocilizumab induced a decreased frequency of Th17 cells as compared to that in healthy donors [START_REF] Samson | Inhibition of interleukin-6 function corrects Th17/Treg cell imbalance in patients with rheumatoid arthritis[END_REF]. This apparent discrepancy with our data can be explained by the different types of controls used in the 2 studies. In our study, all patients received tocilizumab, and we compared responder RA patients to nonresponder RA patients. In contrast, in the study by Samson et al [START_REF] Samson | Inhibition of interleukin-6 function corrects Th17/Treg cell imbalance in patients with rheumatoid arthritis[END_REF], tocilizumab-treated RA patients were compared to untreated patients with active RA. Nevertheless, similar to our findings, the study by Samson et al showed that tocilizumab induced an increased percentage of Treg cells, and in both studies, inhibition of the IL-6 pathway restored the Th17/Treg cell balance.

IL-6 pathway inhibition also modified the Treg cell phenotype. In particular, we found that the Heliosϩ Treg cell population was increased within the thymus of MR16-1-treated mice. Helios was initially described as a specific marker for discriminating thymus-derived nTreg cells (Heliosϩ) from peripherally differentiated iTreg cells (HeliosϪ) [START_REF] Thornton | Expression of Helios, an Ikaros transcription factor family member, differentiates thymic-derived from peripherally induced Foxp3ϩ T regulatory cells[END_REF]. However, results of recent studies have suggested that Helios may be unable to distinguish nTreg cells from iTreg cells, as Helios expression may be induced during the activation of T cells regardless of their origin [START_REF] Akimova | Helios expression is a marker of T cell activation and proliferation[END_REF][START_REF] Gottschalk | Response to comment on "expression of Helios in peripherally induced Foxp3ϩ regulatory T cells[END_REF]. The relevance of Helios as a marker for Treg cell activation needs to be further investigated. Nevertheless, assuming that Helios is a Treg cell activation marker, our results suggest that IL-6 pathway inhibition in CIA may lead to either increased re-entry of activated Treg cells into the thymus or, more probably, to increased intrathymic activation of Treg cells [START_REF] Akimova | Helios expression is a marker of T cell activation and proliferation[END_REF].

Given that MR16-1 inhibited the clinical, histologic, and biologic signs of CIA, we studied whether these effects were related to an enhanced Treg cell suppression of Tconv cell proliferation. In vitro, the degree of suppression in the spleen was similar in the MR16-1 and control mice (results not shown). To study another Treg cell suppressive phenotype, we investigated whether anti-IL-6R antibody treatment modified CD39 expression on Treg cells. In mice with CIA, MR16-1 treatment expanded the CD39ϩ Treg cell population. Interestingly, tocilizumab treatment induced a CD39ϩ Treg cell population in responder patients with RA after 1 month, and this increase reached a statistically significant difference at 3 months after treatment. This CD39ϩ Treg cell population was functionally able to suppress Tconv cell proliferation in responder patients.

Membrane-expressed CD39 catalyzes extracellular ATP hydrolysis and, together with CD73, results in production of the antiinflammatory mediator adenosine [START_REF] Borsellino | Expression of ectonucleotidase CD39 by Foxp3ϩ Treg cells: hydrolysis of extracellular ATP and immune suppression[END_REF]. CD39 expression on Treg cells has thus been associated with increased suppressive potency, one effect of which is suppression of Th17 cell activity [START_REF] Fletcher | CD39ϩFoxp3ϩ regulatory T cells suppress pathogenic Th17 cells and are impaired in multiple sclerosis[END_REF][START_REF] Ye | CD39ϩ regulatory T cells suppress generation and differentiation of Th17 cells in human malignant pleural effusion via a LAP-dependent mechanism[END_REF]. Moreover, alterations in the CD39/CD73 machinery lead to loss of Treg cell function and to autoimmunity [START_REF] Sauer | Alterations in the adenosine metabolism and CD39/CD73 adenosinergic machinery cause loss of Treg cell function and autoimmunity in ADA-deficient SCID[END_REF]. FoxP3ϩCD39ϩ Treg cells are impaired in patients with multiple sclerosis [START_REF] Fletcher | CD39ϩFoxp3ϩ regulatory T cells suppress pathogenic Th17 cells and are impaired in multiple sclerosis[END_REF]. Conversely, the CD39ϩ Treg cell population expands during remission of multiple sclerosis and after antiinflammatory treatment in CIA [START_REF] Kochetkova | IL-35 stimulation of CD39ϩ regulatory T cells confers protection against collagen II-induced arthritis via the production of IL-10[END_REF][START_REF] Kochetkova | Segregated regulatory CD39ϩCD4ϩ T cell function: TGF-beta-producing Foxp3-and IL-10-producing Foxp3ϩ cells are interdependent for protection against collagen-induced arthritis[END_REF]. Moreover, a very recent study has shown that an efficient therapy based on stem cell adoptive transfer mostly depended on CD39/CD73 signals and partially on the induction of CD4ϩCD39ϩFoxP3ϩ Treg cells in CIA [START_REF] Chen | Adoptive transfer of human gingiva-derived mesenchymal stem cells ameliorates collagen-induced arthritis via suppressing Th1 and Th17 cells and enhancement of regulatory T cell differentiation[END_REF]. These findings are consistent with the increased CD39 expression on Treg cells in CIA as well as in responder patients after anti-IL-6R blockade. We can therefore hypothesize that this anti-IL-6R antibody allows the generation of a potent suppressive Treg cell population capable of inducing metabolic changes that protect against joint inflammation. Overall, our results support the hypothesis that one mechanism underlying the control of arthritis via IL-6 pathway blockade may be both the restoration of a nonpathogenic Th17/Treg cell balance and the generation of a suppressive CD39ϩ Treg cell population. Further studies are warranted to determine whether IL-6R inhibition acts directly on Treg cells or involves other cell populations acting on Treg cells.

1 A

 1 . Thiolat, PhD, J. Biton, PhD, D. Lemeiter, MRS, P. Decker, PhD, N. Bessis, PhD: INSERM U1125 and Sorbonne Paris Cite ´Universite ´Paris 13, Bobigny, France; 2 L. Semerano, MD, PhD, M.-C. Boissier, MD, PhD: INSERM U1125, Sorbonne Paris Cite Úniversite ´Paris 13, and AP-HP, Bobigny, France; 3 Y. M. Pers, MD, PhD, C. Jorgensen, MD, PhD: INSERM U844, Universite ´Montpellier 1, and CHU Ho ˆpital Lapeyronie, Montpellier, France; 4 P. Portales: Hopital Saint-Eloi, Montpellier, France; 5 J. Quentin, PhD, P. Louis-Plence, PhD: INSERM U844 and Universite ´Montpellier 1, Montpellier, France.

3 ;

 3 Walter ϩ Eliza Hall, Institute of Medical Research, Parkville, Australia) was used for graphic representations. Patients with RA. For assessment of cells from RA patients, we used antibodies to surface markers, from either BD PharMingen (PE-labeled anti-CD127 [clone HIL-7R-M21], PE-labeled anti-CCR6 [clone 11A9], PerCP-Cy5.5labeled anti-CD25 [clone M-A251], V450-conjugated anti-CD4 [clone RP-T4], and V500-conjugated anti-CD45 [clone HI30]) or eBioscience (PE-Cy7-labeled anti-CD39 [clone A1], Alexa Fluor 647-conjugated anti-FoxP3 [clone 259D/C7], and anti-IL-17 [clone SCPL1362]

Figure 1 .

 1 Figure1. Interleukin-6 receptor (IL-6R) blockade with anti-IL-6R monoclonal antibody inhibits murine collagen-induced arthritis (CIA). On day 0, type II collagen was injected into mice to induce CIA, followed by intraperitoneal injection with anti-IL-6R monoclonal antibody MR16-1 (8 mg; n ϭ 8) or with IgG (8 mg; n ϭ 8) or phosphate buffered saline (PBS; n ϭ 8) as controls. A and B, Clinical arthritis scores (A) and histologic joint inflammation and destruction scores (B) were compared between groups. The incidence of CIA was 6 (75%), 6 (75%), and 5 (62%) in the MR16-1, IgG, and PBS groups, respectively. Results are the mean Ϯ SEM. P values were determined by one-way analysis of variance. C, Representative histologic slides of knee sections (stained with hematoxylin and eosin) show the extent of inflammatory synovitis and joint destruction in mice treated with MR16-1, compared with mice in the IgG or PBS control groups. Original magnification ϫ 50. Color figure can be viewed in the online issue, which is available at http://onlinelibrary.wiley.com/doi/10.1002/art.38246/abstract.

Figure 2 .

 2 Figure 2. Interleukin-6 receptor (IL-6R) neutralization increases the Treg:Th17 cell ratio in murine collagen-induced arthritis (CIA). Lymph node cells (from the same mice as described in Figure 1) were labeled with fluorochrome-conjugated anti-CD4, anti-IL-17, and anti-FoxP3. Th17 and Treg cells, defined as CD4ϩIL-17ϩ cells and CD4ϩFoxP3ϩ cells, respectively, were monitored in the lymph nodes. A, Representative dot plot showing the percentage of IL-17ϩ cells on gated CD4ϩ cells in an MR16-1-treated mouse on day 8. B and C, Percentages of IL-17ϩ (B) and FoxP3ϩ (C) cells among CD4ϩ cells in the lymph nodes of MR16-1-treated mice and IgG control mice during the course of CIA. D, Ratio of FoxP3ϩ cells to Th17ϩ cells among CD4ϩ cells in the lymph nodes from MR16-1-treated mice compared with IgG controls during the course of CIA. Results are the mean Ϯ SEM. ء ϭ P Ͻ 0.05 versus IgG, by two-way analysis of variance.

Figure 3 .

 3 Figure 3. Interleukin-6 receptor (IL-6R) blockade in mice with collagen-induced arthritis (CIA) increases the intensity of CD39 Treg cell expression in the spleen. Leukocytes in the lymph nodes (LN) (A and B) or spleen (C) from mice with CIA (same mice as described in Figure 1) were labeled with fluorochrome-conjugated anti-CD4, anti-FoxP3, and anti-CTLA-4 (A) or anti-CD39 (B and C), and expression of CTLA-4 and CD39 on gated CD4ϩFoxP3ϩ cells was analyzed using flow cytometry. For each day, histograms are shown for 1 representative mouse in the MR16-1-treated group and control IgG group, as well as the isotype control (shaded histograms). Mean Ϯ SEM values are the mean fluorescence intensity (MFI) of CTLA-4 (A) or CD39 (B and C) expression. Differences between groups were significant (P Ͻ 0.05 by two-way analysis of variance) throughout the course of CIA.

Figure 4 .

 4 Figure 4. Tocilizumab treatment does not affect the frequency of Th17 cells, but increases the frequency of CD39ϩ Treg cells, in patients with rheumatoid arthritis (RA). Flow cytometry was used to analyze the percentage of Th17 cells (CD4ϩIL-17ϩCCR6ϩ cells) (A) and Treg cells (CD4ϩCD25ϩFoxP3ϩCD127 low CD39ϩ cells) among CD4ϩ cells (B) from 15 patients with RA at baseline and 3 months after treatment with tocilizumab. Each symbol represents an individual patient. Bars show the mean Ϯ SEM. After treatment, the frequency of CD39ϩ Treg cells differed significantly (as determined by Mann-Whitney test) between responders (R) and nonresponders (NR).

Figure 5 .

 5 Figure 5. CD39ϩ Treg cells suppress the proliferation of conventional T (Tconv) cells in patients with rheumatoid arthritis (RA) who are tocilizumab responders. A, Unlabeled titrated numbers of CD4ϩ Tconv cells or CD39ϩ or CD39Ϫ Treg cells were cocultured with carboxyfluorescein succinimidyl ester (CFSE)-labeled Tconv cells (in ratios of 1:2 or 1:4) in the presence of allogeneic allophycocyanin and anti-CD3 antibody. Gray histograms represent proliferation of activated CD4ϩ T cells cocultured with Tconv cells. Blue and red histograms represent proliferation of activated CD4ϩ T cells cocultured with fluorescence-activated cell-sorted CD39Ϫ Treg cells or CD39ϩ Treg cells, respectively. Representative results from 1 of 8 experiments are shown. B, CFSE dilution data obtained (at a ratio of 1 Treg cell to 2 Tconv cells) from 8 responder patients (P1-P8) were analyzed by FlowJo to determine the percentage of original cells that divided. Thereafter, the percentage of inhibition of proliferation was assessed following the addition of CD39ϩ Treg cells or CD39Ϫ Treg cells in 8 independent experiments.

Table 1 .

 1 Effects of anti-interleukin-6 receptor monoclonal antibody MR16-1 on thymic Treg cells in mice with collagen-induced arthritis* The MR16-1 treatment group comprised 8 mice, and the IgG control group comprised 10 mice on all days except day 42 (n ϭ 8). Thymic Treg cells, defined as CD4ϩCD8ϪFoxP3ϩ cells, were monitored using flow cytometry in all mice on days 8, 18, 28, and 42 after arthritis induction. Helios

		Days after arthritis induction
	8	1 8	2 8	4 2

* expression was assessed on gated CD4ϩCD8ϪFoxP3ϩ cells. Results are the mean Ϯ SEM. Differences between groups were significant (P Ͻ 0.05 by two-way analysis of variance) on all days throughout the development of collagen-induced arthritis. MFI ϭ mean fluorescence intensity.

ACKNOWLEDGMENTS

We thank Clement Lourdes Maguimey (Sorbonne Paris Cite ´Universite ´Paris 13) and Ste ´phane Chambris and Sonia Varela (animal facilities of Sorbonne Paris Cite ´Universite ´Paris 13) for their outstanding technical assistance. We also thank Myriam Boyer (Montpellier RIO Imaging platform) for performing the cell-sorting experiment with the FACSAria. We thank Roche Shugai for providing the monoclonal antibody MR16-1.

AUTHOR CONTRIBUTIONS

All authors were involved in drafting the article or revising it critically for important intellectual content, and all authors approved the final version to be published. Dr. Boissier had full access to all of the data in the study and takes responsibility for the integrity of the data and the accuracy of the data analysis. Study conception and design. Thiolat, Semerano, Biton, Jorgensen, Decker, Boissier, Plence, Bessis. Acquisition of data. Thiolat, Semerano, Biton, Lemeiter, Quentin, Boissier, Plence, Bessis. Analysis and interpretation of data. Thiolat, Semerano, Pers, Biton, Lemeiter, Portales, Decker, Boissier, Plence, Bessis.

ROLE OF THE STUDY SPONSOR

Unrestricted grants were provided by Roche and Chugai Pharma France. These companies had no role in the study design or in the collection, analysis, or interpretation of the data, the writing of the manuscript, or the decision to submit the manuscript for publication. Publication of this article was not contingent upon approval by Roche and Chugai Pharma France.