E Martin
email: martin@lcts.u-bordeaux.fr

D Leguillon

A Catapano

N Carrère

Prediction of interfacial debonding between stiff spherical particles and a soft matrix with the coupled criterion

Keywords: Particle reinforced polymer, Interfacial debonding, Coupled criterion, Finite Fracture Mechanics

The tensile load at debonding onset between stiff particles and a soft matrix is predicted with the coupled criterion which combines a stress and an energy conditions. A finite element model of a representative volume element is implemented in order to consider the influence of the size of the particles, the particle volume fraction, mixed mode conditions at the interface and the presence of residual stresses. It is also shown how this approach can be used in order to analyze experimental data for the identification of the interfacial fracture parameters.

Introduction

Reinforcing a matrix with rigid particles is an attractive way to increase its mechanical properties. Spherical particles have been demonstrated to improve the stiffness, tensile strength, and toughness of polymeric and ceramic matrices [START_REF] Argon | Toughenability of polymers[END_REF][START_REF] Cotterell | Fracture mechanisms and fracture toughness in semicrystalline polymer nanocomposites[END_REF][START_REF] Taya | Toughening of a Particulate-Reinforced Ceramic-Matrix Composite by Thermal Residual Stress[END_REF][START_REF] Bao | Effects of residual stresses on strength and toughness of particle-reinforced TiN/Si3N4 composite: Theoretical investigation and FEM simulation[END_REF]. Enhancement of the global mechanical properties of these composites depend on the component properties and their volume fractions but also on the strength and toughness of the interface between the matrix and the particles.

For polymer filled with stiff particles, there is a consensus that interfacial debonding which facilitates matrix shear yielding is a pre-requisite to obtain high toughness [START_REF] Cotterell | Fracture mechanisms and fracture toughness in semicrystalline polymer nanocomposites[END_REF][START_REF] Chen | Critical particle size for interfacial debonding in polymer/nanoparticle composites[END_REF]. As verified experimentally under tensile loading [START_REF] Vollenberg | Experimental determination of thermal and adhesion stress in particle filled thermoplasts[END_REF][START_REF] Bai | Interfacial debonding behavior of a rigid particle-filled polymer composite[END_REF][START_REF] Tjernlund | Length-scale effects on damage development in tensile loading of glass-sphere filled epoxy[END_REF][START_REF] Cho | Effect of inclusion size on mechanical properties of polymeric composites with micro and nano particles[END_REF][START_REF] Hosseinpour | Stress/strain development around a spherical inclusion in a polymeric matrix: The effects of particle and matrix mechanical characteristics and thermal expansivity difference[END_REF], at debonding onset, an area first develops instantaneously from the poles of the particles and extends progressively along the interface with increasing applied stress. Previous works [START_REF] Pukánszky | Stress distribution around inclusions, interaction, and mechanical properties of particulate-filled composites: Stress Distribution Around Inclusions[END_REF] estimate the debonding stress D σ by evaluating the energy necessary to create the debonding area with

2 c T i D G C R σ σ = - (1)
where c i G is the interfacial fracture energy, R is the particle radius, T σ is the thermal stress resulting from the thermal expansion mismatch between the particles and the matrix, C is a coefficient depending on component properties. Eq. [START_REF] Argon | Toughenability of polymers[END_REF] shows that the debonding stress exhibits a size effect as it depends on the particle radius. Comparing D σ with the composite tensile strength indicates that there is a critical size below which no interface debonding and thus little toughening can develop. Similar expressions were derived for a hydrostatic loading [START_REF] Cotterell | Fracture mechanisms and fracture toughness in semicrystalline polymer nanocomposites[END_REF][START_REF] Chen | Critical particle size for interfacial debonding in polymer/nanoparticle composites[END_REF][START_REF] Gent | Detachment of an elastic matrix from a rigid spherical inclusion[END_REF][START_REF] Chen | Theoretical analysis on the local critical stress and size effect for interfacial debonding in particle reinforced rheological materials[END_REF][START_REF] Chen | Size effect of particles on the damage dissipation in nanocomposites[END_REF] but it must be noted that the value of the debonding surface is always postulated or taken as the complete interfacial area. To get rid of this assumption, only justified under hydrostatic loading, a finite fracture approach can be used as already demonstrated by several authors [START_REF] García | A model for the prediction of debond onset in spherical-particle-reinforced composites under tension. Application of a coupled stress and energy criterion[END_REF][START_REF] Gentieu | Size effect in particle debonding: Comparisons between finite fracture mechanics and cohesive zone model[END_REF]. More precisely, combining a stress and an energy conditions gives access to the debond stress and the debonding area. The present work uses such a coupled criterion to describe the nucleation of interfacial debonding between stiff particles and a soft matrix. The previous studies are now extended by considering the particle volume fraction and taking into account the presence of residual stresses.

The paper is organized as follows: the coupled criterion is outlined in Section 2 while Section 3 examines the choice of a proper representative cell. Numerical results are presented in Section 4 including the influence of mixed mode conditions and residual stresses. Section 5 is devoted to the analysis of experimental results.

Prediction of interfacial debonding

The geometry considered for the presentation of this section is the one that will be analyzed afterwards: a spherical particle (radius R) embedded in a matrix and submitted to a tensile loading σ in the z direction (Fig. 1a). A given point at the particle/matrix interface is located by the angle θ measured from the z axis. Particle and matrix are elastic and isotropic materials with Young's moduli ( )

, p m E E
and Poisson's ratios ( )

, p m
υ υ . It is assumed that the particle is stiffer than the matrix with p m E E > . This elastic mismatch induces a stress concentration along the interface around the top and bottom poles. Upon a critical loading, two symmetric debonds (angle D θ ) are nucleated at the poles (Fig. 1b). Experimental observations may indicate that interfacial debonding occurs firstly at one pole followed shortly by a second crack initiated at the other pole of the same particle. In any case, the difference in predicted applied stress between both debonded modes is weak as shown by García et al. [START_REF] García | A model for the prediction of debond onset in spherical-particle-reinforced composites under tension. Application of a coupled stress and energy criterion[END_REF].

Assuming a brittle behavior of the interface, the coupled criterion (CC) which combines an energy and a stress conditions is used to describe the initiation of this interfacial fracture mechanism [START_REF] Leguillon | Strength or toughness? A criterion for crack onset at a notch[END_REF][START_REF] Cornetti | Finite fracture mechanics: A coupled stress and energy failure criterion[END_REF]:

a) The energy condition requires the change in potential energy δ Π to be larger than the energy necessary for the nucleation of the interfacial crack of surface ( )

S θ with ( ) ( ) ( ) ( ) 0 c i S S G δ θ θ -Π = Π -Π ≥ , (2)
where c i G is the interfacial fracture energy. Note that the constant c i G denotes here a generic parameter that will be specified in Section 4.1 taking into account the concept of mixed-mode.

Eq. ( 2) can be written in order to introduce the incremental energy release rate (IERR)

( ) ( ) ( ) inc G S S θ δ θ = -Π leading to ( ) ( ) c inc i G S G θ ≥ . ( 3
)
The relationship between the IERR and the differential energy release rate ( )

i G S d dS =-Π is [19] ( ) ( ) ( ) ( ) 0 1 (
)

S inc i G S G A dA S θ θ θ = ∫ , (4) which induces
( )

( ) ( ) inc i inc dG S S G S G S dS = - , (5)
where θ has been omitted in the expression of S for sake of simplicity.

b) The stress condition stipulates that the opening normal stress all along the anticipated crack path must exceed the interfacial strength c i σ . A local coordinate system ( ) , x y along the interface is used to define x  as the normal direction and the stress condition is expressed as ( )

for c xx i σ α σ α θ ≥ ≤ . (6)
A similar inequality is valid for mixed-mode,

c i
σ is then a generic constant and the role of tensile and shear strengths will be specified further in Section 4.1.

Eq. ( 3) and ( 6) are the CC inequalities that must be solved to determine the applied tensile stress D σ and the angle D θ at onset of debonding. They can be modified to take into account mixed- mode condition or thermal residual stresses as will be shown in section 4.

Selection of a Representative Volume Element (RVE)

As recently pointed out [START_REF] Doitrand | Numerical implementation of the coupled criterion: Matched asymptotic and full finite element approaches[END_REF], the CC can be implemented with the help of a matched asymptotic approach or a full finite element approach. A full field finite element analysis is used here but we mention that the matched asymptotic approach may also be used for very small values of the particle volume fraction [START_REF] Quesada | Multiple failures in or around a stiff inclusion embedded in a soft matrix under a compressive loading[END_REF]. To avoid time-consuming 3D calculations, we have opted for 2D calculations based on axial symmetry. The simplest of the volumes we can consider contains a single particle. The major challenge is then to choose a model that takes satisfactorily into account the interactions between neighboring particles. We must also determine how to evaluate the change in potential energy necessary to apply the energy condition.

The spherical RVE

The simplest shape of the RVE is made of two concentric spheres. Taking into account the axial symmetry and the symmetry of geometry and loading, the RVE reduces to two concentric quarter of disk as shown in Fig. 2a. For the sake of simplicity, the radius of the inner disk is set to 1 (with the appropriate changes in the equations), and the dimensionless outer one

is 1/ 3 m P 1/ R V =
, where P V is the volume fraction of particles. Along the Oz axis, no conditions have to be prescribed due to the axial symmetry formulation of the problem. Along the Or axis (Fig. 1), usual symmetry conditions are applied to the displacement field U and stress field σ 0 0

z rz U σ = =
on Or (the horizontal axis). [START_REF] Bai | Interfacial debonding behavior of a rigid particle-filled polymer composite[END_REF] To simulate the remote loading, a unit macroscopic strain 1

zz ε = is prescribed along the outer circle out Γ by imposing z U z = . (8)
Theoretically, there exists an alternative approach prescribing a force corresponding to a unit unidirectional stress field 1 zz σ = but it has been checked that it is not as effective. For the thermal loading, the outer circle remains free of forces reflecting the fact that the macroscopic (homogenized) stress field is zero.

Let us define the following functional spaces

{ } { } { } 1 out 0 1 out 1 H ( ), 0 on , on , H ( ), 0 on , 0 on , H ( )
, 0 on .

z z z z z W W Or W z W W Or W W W Or = ∈ Ω = = Γ = ∈ Ω = = Γ = ∈ Ω = U U V
Here 1 H ( ) Ω is the Sobolev space ensuring enough smoothness and integrability to the functions over the whole domain Ω (i.e. the domain filled by the RVE). The variational formulation for an auxiliary elastic problem with prescribed strain can be written

Find el W ∈ U such that el 0 : : d 0 W V s V Ω ∇ ∇ = ∀ ∈ ∫ C U , ( 9
)
where C is the elastic fourth order tensor and where the generic element of surface ds denotes of course the weighted integration element r dr dz taking into account the axial symmetry of Ω.

The variational formulation for the auxiliary thermo-elastic problem (pure residual stresses without any mechanical loading) can be written The actual solution is then

Find th W ∈ V such that th in : : d : : d W V s V s V ε Ω Ω ∇ ∇ = ∇ ∀ ∈ ∫ ∫ C C V , (10)
el th zz U W TW ε = + ∆ , ( 11
)
where zz ε is the remote strain and T ∆ the actual temperature change. The potential energy associated with U can be expressed as

( ) ( ) ( ) ( ) (
)

in
zz zz U T U T s T W W s W W s T W W s ε ε ε ε ε ε ε Ω Ω Ω Ω Π = ∇ -∆ ∇ -∆ ∆ = ∇ ∇ + ∇ - ∇ - + ∆ ∇ ∇ - ∫ ∫ ∫ ∫ C C C C (12)
The last term vanish as a consequence of Eq. ( 10) and the nesting of the functional spaces, then ( ) ( )

2
T W W s W W s T T W W s W W s s T W s T T W W s W W s s ε ε ε ε ε ε ε ε ε ε Ω Ω Ω Ω Ω Ω Ω Ω Ω ∆ Π = ∇ ∇ + ∇ - ∇ - ∆ ∆ = ∇ ∇ + ∇ ∇ + -∆ ∇ ∆ ∆ = ∇ ∇ - ∇ ∇ + ∫ ∫ ∫ ∫ ∫ ∫ ∫ ∫ ∫ C C C C C C C C C (13)
The last term is unchanged for two states of the representative cell, i.e. with or without debonding, thus the change in potential energy is ( δ should be read "the change of")

T W W s W W s ε δ δ δ Ω Ω ∆ Π = ∇ ∇ - ∇ ∇ ∫ ∫ C C (14)
Once ( 9) and [START_REF] Hosseinpour | Stress/strain development around a spherical inclusion in a polymeric matrix: The effects of particle and matrix mechanical characteristics and thermal expansivity difference[END_REF] are discretized by finite elements, this term can be computed

2 2 el el th th . 2 2 zz T ε δ δ δ ∆ Π = - X X X X   ( 15
)
where  is the stiffness matrix of the discretized systems, the same in both cases, el X and th X are the vectors of nodal unknowns of the auxiliary elastic and thermo-elastic problems.

Eq. ( 15) shows a very simple form without coupling terms, easy to implement. Unfortunately, as seen further when comparing with results from experiments, this spherical RVE works well only for small volume fraction of particles. Indeed, such a RVE is very convenient and commonly used in homogenization but does not really takes into account the interaction between neighboring particles.

The cylindrical RVE

An alternative is to select a cylindrical RVE (Fig. 2b). The radius of the cylinder being equal to the half-height to preserve the distance between particles. The symmetry conditions are the same as above, then the RVE reduces to a square with dimensionless half side

1/ 3 m P (2 / 3 ) R V =
embedding the quarter disk with radius 1 that represents the particle.

Now the boundary conditions on the upper T Γ and lateral R Γ boundaries should reflect both the remote load and the proximity of neighboring cells. To ensure the latter condition and taking into account the symmetries of the mechanical and thermal loadings, the upper and lateral faces must remain straight and move parallel to themselves. To this aim let us first define the following functional spaces

{ } { } { } 1 R 1 R 0 1 T R
H ( ), 0 on , 0 on , on , H ( ), 0 on , on , 0 on , H ( ), 0 on , 0 on , 0 on .

r z z T r z z z T r z z r W W Or W W r W W Or W z W W W Or W W = ∈ Ω = = Γ = Γ = ∈ Ω = = Γ = Γ = ∈ Ω = = Γ = Γ U U U
Two auxiliary elastic problems are defined as

Find r r W ∈ U such that 0 : : d 0 r W V s V Ω ∇ ∇ = ∀ ∈ ∫ C U . ( 16
)
Find

z z W ∈ U such that 0 : : d 0 z W V s V Ω ∇ ∇ = ∀ ∈ ∫ C U . ( 17
)
The solution to the elastic problem can be written

el r z r zz U a W W ε = + , ( 18
)
where zz ε is the remote prescribed strain and where r a is obtained imposing a vanishing horizontal resultant force, reflecting the fact that the lateral boundaries of the specimen remain

free el ( ) ( ) ( ) 0 r z r r r zz r R U a R W R W ε = + = , (19)
here r R holds for the resultant force in the Or direction.

Let

th W be the solution to the auxiliary thermo-elastic problem with a unit temperature change, the upper and lateral faces being fixed (i.e. 0 displacements)

Find th 0 W ∈ U such that th in 0 : : d : : d U W V s V s V ε Ω Ω ∇ ∇ = ∇ ∀ ∈ ∫ ∫ C C . ( 20
)
The solution to the thermo-elastic problem can be written

th th r z r z U T W b W b W = ∆ + + . ( 21
)
The coefficients r b and z b are determined such that horizontal and vertical resultant forces vanish, reflecting, as above, the fact that the macroscopic (homogenized) stress field is zero

th th ( ) ( ) ( ) 0, ( ) ( ) ( ) 0. r z r r r z r r z z r z z z R U b R W b R W R U b R W b R W = + = = + = (22)
The full solution can be written th el th with and .

r z r z r r r z zz z U U U T W A W A W A a b A b ε = + = ∆ + + = + = + (23)
The change in potential

energy δ Π is in in 2 in in in 1 : ( ) : ( ) d 2 1 : : d : : d : : d . 2 2 U T U T s T U U s T U s s δ δ ε ε δ δ ε δ ε ε Ω Ω Ω Ω Π = ∇ -∆ ∇ -∆ ∆ = ∇ ∇ -∆ ∇ + ∫ ∫ ∫ ∫ C C C C (24)
The last term vanishes because it does not change between the two states (without and with debonding) of the RVE, then substituting Eq. ( 23) leads to

: : d . r r r z z r z z r z r z r z T A W W s W W s A W W s A A W W s T W s T A W s T A W s δ δ δ δ δ δ ε δ ε δ ε Ω Ω Ω Ω Ω Ω Ω ∆ Π = ∇ ∇ + ∇ ∇ + ∇ ∇ + ∇ ∇ -∆ ∇ -∆ ∇ -∆ ∇ ∫ ∫ ∫ ∫ ∫ ∫ ∫ C C C C C C C (25)
and finally

: : d . r r r z z r z z r z r z r z T A W W s W W s A W W s A A W W s T A W s T A W s δ δ δ δ δ δ ε δ ε Ω Ω Ω Ω Ω Ω ∆ Π = - ∇ ∇ + ∇ ∇ + ∇ ∇ + ∇ ∇ -∆ ∇ -∆ ∇ ∫ ∫ ∫ ∫ ∫ ∫ C C C C C C (26)
Using the previous notations, r X , z X et th X being the vectors of nodal unknowns associated respectively with r W , z W et th W and B being the right hand side vector of the thermo-elastic system Eq. ( 20), it comes

2 2 2 th th 2 2 2 . r r z z r z r z r z r z r z T A A A A T A T A δ δ δ δ δ δ δ ∆ Π = - + + + -∆ -∆ X X X X X X X X BX BX    (27)
Even if each term is rather simple and can be easily computed, it may be better, first to combine the terms applying Eq. ( 23) and then to use Eq. [START_REF] Banks-Sills | On the effect of particle shape and orientation on elastic properties of metal matrix composites[END_REF] to compute the change in potential energy th ,

1 . 2 r z r z T A A T δ δ δ = ∆ + + Π = -∆ X X BX BX XX BX  (28)
In order to evaluate the efficiency of the spherical and cylindrical RVEs, prediction of Young's modulus estimated in the z direction as a function of the particle volume fraction is compared with experimental data. Careful measurements of this property for a composite consisting of glass spheres embedded in epoxy resin are available in the literature [START_REF] Smith | Experimental values for the elastic constants of a particulate-filled glassy polymer[END_REF]. Fig. 3 shows that both RVE are equivalent for P 10% V < but the cylindrical one must be preferred for higher values. We thus adopt this axisymmetric geometry which has also been demonstrated sufficiently accurate when compared with a three-dimensional analysis [START_REF] Agarwal | Three-dimensional finite element analysis of spherical particle composites[END_REF]. However, this approach is not entirely free of drawbacks. Obviously, the Or and Oz directions are not equivalent. This is not perceptible for small volume fractions, but for larger fractions it can be seen, for example, that the tension acting along the interface in case of pure thermal loading is not strictly constant. It exhibits a slight maximum at the pole of the particle, on the Oz axis. As mentioned by previous authors [START_REF] Banks-Sills | On the effect of particle shape and orientation on elastic properties of metal matrix composites[END_REF], a particulate composite can be modeled as a matrix filled with a periodic array of particles. Assuming an hexagonal array and simplifying the hexagon to a cylinder allows to perform an axisymmetric analysis. Nevertheless, the usual conditions of the theory of homogenization are not exactly realized and it is not possible to reconstruct exactly the entire structure by repeating the pattern formed by the RVE.

Numerical results

Finite element calculations are now performed with the cylindrical RVE in order to estimate the applied stress at decohesion onset using the CC.

Single mode failure analysis

We first consider a tensile loading in the direction z. As already mentioned, the representative displacement field requires the superposition of two elastic solutions Eq. [START_REF] Cornetti | Finite fracture mechanics: A coupled stress and energy failure criterion[END_REF].

The link between the CC inequalities (Eq. (3), Eq. ( 6)) and the applied uniaxial strain zz ε is established by introducing the stress concentration factor (SCF) ( ) xx k θ and the dimensionless IERR ( )

A θ with ( ) ( ) ( ) ( ) ( ) ( ) 2 ,
.

xx xx i zz inc inc i zz k E G S G RE A σ θ θ ε θ θ θ ε =    = =   (29)
where ( ) ( )

1 2 2 2 1 1 i p p m m E E E ν ν -   = - + - 
 is an interfacial effective modulus [START_REF] García | Debonding at the fibre-matrix interface under remote transverse tension. One debond or two symmetric debonds?[END_REF].

The SCF ( )

, , , ,

xx p p m p m k V E E θ ν ν
only requires one calculation with the perfectly bonded interface. It was checked that the finite element model allows to recover the analytical solution originated by Goodier [START_REF] Goodier | Concentration of Stress Around Spherical and Cylindrical Inclusions and Flaws[END_REF] and also reported elsewhere [START_REF] Hosseinpour | Stress/strain development around a spherical inclusion in a polymeric matrix: The effects of particle and matrix mechanical characteristics and thermal expansivity difference[END_REF][START_REF] Wang | Criteria of Craze Initiation in Glassy Polymers[END_REF] for a rigid particle embedded within an infinite matrix (i.e for Vp < 0.01%). The dimensionless IERR ( ) , , , ,

p p m p m A V E E θ ν ν
requires several computations with a successive release of the interfacial nodes to vary the debonding length. A mesh refinement must be introduced along the selected crack path (i.e the particle/matrix interface) in order to capture accurately the angle D θ at initiation [20]. This value is proportional to the interfacial characteristic length c i L as will be shown by Eq. [START_REF] Hutchinson | Mixed Mode Cracking in Layered Materials[END_REF]. A convergence study was performed and leads to select a minimum mesh size (expressed here in terms of minimum discretized angle)

1 θ ∆ < deg. provided that 0.005 c i L R ≥ . A contact zone
may appear near the crack tip of an interfacial crack [START_REF] París | Kinking of Transversal Interface Cracks Between Fiber and Matrix[END_REF]. This means that contact would take place in case of debonding and therefore further debonding cannot develop. The overlapping of crack faces was thus checked but was not detected with the selected discretization if the decohesion angle is smaller than the maximum angle M θ which is now defined. 3) is first satisfied for

M M W θ θ θ = = if ( ) ( ) 2 M M c inc i zz i G RE A G θ θ ε = = . ( 30
)
The initiation of a debonding crack also requires the stress condition Eq. ( 6) to be fulfilled

( ) ( ) M M c xx xx i zz i k E σ θ θ ε σ = ≥ . ( 31
)
Combining Eq. ( 30) and Eq. ( 31) leads to compare the characteristic interfacial length ( )

2 c c c i i i i L E G σ = to the structural length R β with ( ) ( ) 2 M M xx A k θ β θ = . ( 32
)
If c i L R β ≥
, the energy condition Eq. ( 30) is governing. The debonding angle at initiation reaches its maximum value M θ which only depends on the structural geometry. The debonding strain ( )

M c M D i i G RE A ε θ =
does not depend on the interfacial strength. The debonding stress is thus

( ) c M i D c M i G E RE A σ θ = , (33)
where c E is the homogenized composite modulus.

If we exclude the presence of residual stress (which will be considered in the next section), it is worthy of note that Eq. ( 33) is similar to Eq. (1). Further, Eq. ( 5) indicates that the nucleated interfacial crack is stable since ( )

( ) 0 M inc dG d θ θ θ θ = = implies that ( ) ( ) M M c i inc i G G G θ θ = = . ( 34
)
Then, according to Eq. ( 5), ( )

c i i G G θ < for M θ θ >
which means a priori crack arrest.

( ) ( ) 2 c D i xx D A L R k θ θ = . ( 35
)
The debonding stress

M D D σ σ > is now ( ) c i D c i D G E RE A σ θ = . ( 36
)
In that case [START_REF] Doitrand | Comparison between cohesive zone and coupled criterion modeling of crack initiation in rhombus hole specimens under quasi-static compression[END_REF], the nucleated crack is unstable, at least in an initial phase, since Eq. ( 5)

indicates that ( ) ( ) ( )
( ) i inc inc G S G S S dG S dS = + which leads to ( ) c i i G S G > as ( ) 0 inc dG S dS > for M D θ θ
< . Finally, Eq. ( 33) and ( 36) can be written as ( )

1 c c i D c i i D E L E R A σ σ θ = (37)
with ( ) ( )

2 = if c c D xx D i i A k L R L R θ θ β < and if M c D i L R θ θ β = ≥ .
0 c c i D xx i E k E σ σ = (38)
which corresponds to the horizontal line in Fig. 6a. This plot also depicts the debonding stress provided only by the energy condition Eq. ( 33) which is similar to Eq. ( 1) largely used in the literature. It is clear that using only the energy condition leads to underestimate the debonding stress for larger particles. For the typical configuration defined by 10 33) and the stress condition Eq. ( 38) can be easily determined with:

( ) ( ) 2 2 0 M c i xx A L R k θ γ = = . ( 39
)
Eq. ( 39) defines the parameter γ which is plotted versus the particle volume fraction in Fig. 6b.

This structural value decreases with p V and with the elastic contrast p m E E . L R , at least in part through an increase in the stiffness of the structure, we draw attention to its unexpected decrease for small values of the ratio. Indeed, increasing the volume fraction of particles also increases the total length of interfaces which is the weak point of the structure in case of very small values of interface toughness, which could explain this phenomenon (see also Fig. 10b).

Mixed mode conditions

The opening mode is predominant for small values of the debonding angle but it is to be noted that the amplitude of the interfacial shear stress increases with D

θ . The influence of these mixed-mode conditions on the debonding onset can be evaluated with the CC.

The stress condition is modified by introducing an equivalent stress eq σ which combines the interfacial normal and shear stresses

( ) ( ) ( ) , xx xy
σ θ τ θ . A Coulomb law can be preferred [START_REF] Fitoussi | Determination of a tridimensional failure criterion at the fibre/matrix interface of an organic-matrix/discontinuous-reinforcement composite[END_REF] but a quadratic expression is also commonly used [START_REF] García | A model for the prediction of debond onset in spherical-particle-reinforced composites under tension. Application of a coupled stress and energy criterion[END_REF][START_REF] Ogihara | Investigation of combined stress state failure criterion for glass fiber/epoxy interface by the cruciform specimen method[END_REF][START_REF] Greco | A two-scale failure analysis of composite materials in presence of fiber/matrix crack initiation and propagation[END_REF][START_REF] Carraro | Modelling fibre-matrix debonding under biaxial loading[END_REF]: Introducing the SCF ( ) eq k θ , the stress condition is now given by ( ) ( ) ( ) ( )

2 2 xy c eq xx i zz eq i zz i k k E k E θ σ θ θ ε θ ε σ µ = + = ≥ , (40)
where ( ) ( )

xy xy i zz k E τ θ θ ε = .
The energy condition ( ) ( )

c inc i G G θ ψ
≥ must now take into account the dependence of the interfacial fracture energy on the fracture mode mixity angle ψ defined by

( ) ( ) ( ) ( ) 1 tan xy xx ψ θ τ θ σ θ - =
. Using a phenomenological characterization law [START_REF] Hutchinson | Mixed Mode Cracking in Layered Materials[END_REF] provides the increase of the interfacial fracture energy versus θ with

( ) ( ) ( ) ( ) ( ) 2 1 tan 1 c c c i i i G G M G θ λ ψ θ θ   = + - =   ( 41
)
where λ ( )

0 1 λ ≤ ≤ is a material parameter. Setting θ θ θ = .
The debonding stress is now expressed as

( ) ( ) c D c i D c i i D N E L E R A θ σ σ θ = (44) with ( ) ( ) ( ) 2 = if c D c i i D eq D A L L R R N k θ β θ θ < and if M c D i L R θ θ β = ≥ .
Fig. 8 plots the predictions of the CC obtained with mixed-mode conditions defined by ( )

1, 0.1 µ λ = =
. Comparing with the results that ignore the mixed-mode ( )

10, 1 µ λ = =
, the debonding angle is higher with mixed-mode conditions (Fig. 8a) but the influence on the debonding stress remains weak (Fig. 8b).

Presence of residual stresses

If the particle has a larger CTE ( )

p
( ) ( ) ( ) ( ) ( )( ) 2 , , T c xx xx i c i T c inc i c i k E T G RE A T G σ θ θ α σ θ θ α  = -∆ ≥   = -∆ ≥   (
2 = if T D c c T i i T xx A L R L R k θ β < , ( 46
)
with if

M c T D T i L R θ θ β = ≥ and
( ) 2 T T M T T xx A k β θ = .
The temperature change ( ) D T ∆ at initiation of debonding is given by ( ) ( )

1 c i c i c D T i D E L T R A α σ θ - ∆ = . ( 47
( ) ( ) ( ) ( ) ( ) ( ) ( )( ) 2 2 , . T c xx xx i zz xx i c i T c inc i zz c i k E k E T G RE A A T G σ θ θ ε θ α σ θ θ ε θ α  = + -∆ ≥     = + ∆ ≥     (48)
The IERR in Eq. ( 48b) is here simply obtained by adding the values corresponding to the tensile loading (Eq. (29b)) and the temperature change (Eq. (45b)). We have checked numerically that the coupling terms which are present in Eq. ( 28) can be ignored.

Results show that

) ( ) ( ) 2 2 2 1 c D T T i xx D xx D A L k A R k θ κ θ κ θ   - + =       , (49)
with

M D TM θ θ ≤ , T c i κ σ σ = and T i c E T σ α = - ∆ .
Comparing to Eq. ( 35) reveals an additional term involving the stress ratio κ . Finally, the debonding strain D ε can be estimated and the corresponding debonding stress is given by ( ) ( )

1 2 2 1 1 c T D c i D c c i i i D E L R A E R L A σ κ θ σ θ   = -     (50)
It is to be noted that this expression reduces to Eq. ( 37) if 0 κ = and that ( ) account the thermal residual stresses also depends on the interfacial fracture properties (and not only on the thermal expansion mismatch between the particles and the matrix).

2 1 T D c i R A L κ θ > as D T T ∆ < ∆ .

Analysis of experimental results

In this section, the numerical results from the previous section are now used to analyze experimental data. More precisely, the objective is to show how the interfacial fracture parameters ( )

, c c i i G σ
can be extracted from experimental records. Polymer matrices strengthened by glass particles are considered first.

In the study reported by Bai et al. [START_REF] Bai | Interfacial debonding behavior of a rigid particle-filled polymer composite[END_REF], samples were made with polyethylene reinforced with glass beads. A coupling agent was used to promote interfacial adhesion and both untreated (GH1) and treated (GH2) reinforcements were tested. The angle D θ and the applied stress D σ at debonding onset were estimated with the help of in situ tensile tests. In this case, the identification procedure is straightforward. Eq. ( 30) and Eq. ( 31) respectively provide the estimation of the interfacial strength and toughness with ( )

c i xx D D k σ θ σ = and ( ) 2 . c i D D i R G A E θ σ =
Corresponding estimations are indicated in Table 1 for GH1 andGH2 composites. These interfacial properties characterize a very weak interface but it is worthy of note that similar magnitude orders were also determined in [START_REF] Bai | Interfacial debonding behavior of a rigid particle-filled polymer composite[END_REF] as reported in Table 1. It is expected that the CC provides a better accuracy as these authors used more approximate models. As pointed out by the authors, the interfacial debonding is difficult to detect and may occur earlier so that the experimental debonding stress is an upper limit which is consequently also the case for the estimated interfacial properties.

In their experimental work, Cho et al. [START_REF] Cho | Effect of inclusion size on mechanical properties of polymeric composites with micro and nano particles[END_REF] have also observed the nucleation of interfacial debonding within composites made with a vinyl ester resin reinforced with glass particles of various diameters. Their results indicate that the debonding stress can be taken as about 90% (respectively 70%) of the tensile strength of each composite if 70 μm R ≥ (respectively 70 μm R <

). Following the procedure proposed by Martin et al. [START_REF] Martin | Understanding the tensile strength of ceramics in the presence of small critical flaws[END_REF], Eq. ( 37) is used to produce isovalues of the debonding stress in the ( )

, c c i i G σ plane.
For each particle radius, a search procedure then allows to estimate the values of the interfacial parameters which provide the best fit of the predicted values with the experimental data as indicated in Table 1. Fig. 10a plots the predicted ratio . The CC predicts a larger applied stress for a small particle ( )

6 μm R =
. It is very likely that the experimentally found values in this case are not initially caused by particle/matrix debonding but by matrix cracking. In fact, the values of the debond load are deduced from the loading at final failure (weighted by a coefficient of 70 or 90%) without it being possible in reality to know precisely the origin of the mechanism. The tensile strength of the matrix (50 MPa) is obviously an upper bound for the predicted values for debonding. This upper bound is clearly visible on Fig. 10a.

It reveals difficult to find in the literature experimental data indicating debond thresholds for various particle volume fractions. We use data from Papanicolaou and Bakos [START_REF] Papanicolaou | The Influence of the Adhesion Bond between Matrix and Filler on the Tensile Strength of Particulate-Filled Polymers[END_REF] who reported the tensile strength of composites made with glass beads embedded in an epoxy resin. Table 1 indicates that various volume fractions up to 30% were used. Based on the observations by Cho et al. [START_REF] Cho | Effect of inclusion size on mechanical properties of polymeric composites with micro and nano particles[END_REF], the debonding stress was taken as 90% (respectively 70%) of the tensile strength if 70 μm R ≥ (respectively 70 μm R <

). These experimental data are analyzed with a search procedure (based on Eq. ( 37)) in order to identify the interfacial parameters (Table 1). Fig. 10b compares the CC prediction of the debonding stress versus the particle volume fraction with the experimental results. As already shown in Fig. 7 and Section 4.1, a low value of the ratio c i L R is required to reproduce the decrease of the debonding stress with p V .

Finally, we consider ceramic matrix composites reinforced with particles based on the results of Davidge and Green [START_REF] Davidge | The strength of two-phase ceramic/glass materials[END_REF]. These authors fabricated several glass composites with a 10% volume fraction of ThO2 spheres. Several batches with particles of varying radius between Assuming that the interfacial properties are identical for every batch, these experimental results indicate that the energy condition (which depends explicitly on the particle radius) controls the interfacial debonding. Following Eq. ( 46), we can thus consider that the debonding angle is

M D T θ θ = with min max for c T i L R R R R β ≥ ≤ ≤
. Applying the energy condition Eq. (45b) provides estimations of the interfacial fracture energy with

( ) ( )( ) ( ) ( )( ) 2 1 min 2 2 max , . c c T M i i i T c c c T M i i i T c G G R E A T G G R E A T θ α θ α  > = -∆   ≤ = -∆   (51)
An upper bound of the interfacial strength is obtained with the help of the condition ( ) ( )

max min max for c T c c c i i i i L R G G G β ≥ ≤ ≤
which leads to ( ) ( )

1 min max max c T M i i T c i i c T T E G A R E T R R θ σ α β β ≤ = ∆ . ( 52
)
The estimations of the interfacial properties through Eq. ( 51) and ( 52) only require the structural parameters ( ) ( )

, T M T T A θ
β which can be easily computed as described in the previous section.

Table 2 reports the values corresponding to the experimental results obtained with two different matrices.

Conclusion

Interfacial debonding between stiff particles and a soft matrix submitted to tensile loading is analyzed with a finite fracture mechanics approach. A finite element model of a cylindrical representative cell is used to apply the CC which couples stress and energy conditions. This method does not require any assumption regarding the crack size at debonding

Table 1

Analysis of experimental data (polymer matrices reinforced with glass particles) Analysis of experimental data (glass matrices reinforced with thoria particles [START_REF] Davidge | The strength of two-phase ceramic/glass materials[END_REF])

Ep (GPa) νp Em (GPa) νm Vp (%) R (µm) D θ (1) (°) D σ (1) (MPa) D σ (2) (MPa) c i σ (1) (MPa) c i G (1) (Jm -2 ) c i σ (2) (MPa) c i G (2) (Jm -2 ) [7] 52
Ep (GPa) νp p α (10 -6 °C-1 ) Em (GPa) νm m α (10 -6 °C-1 ) Vp (%) T ∆ (°C) 1 R (µm) 2 R (µm) ( ) max c i σ (MPa) ( ) min c i G (Jm -2 ) ( ) max c i G (Jm -2 ) G1 250

  temperature change) where α is the coefficient of thermal expansion (CTE) and I the second order identity tensor.

=

  The stress concentration is maximum for 0 θ = and xx k is a decreasing function of θ .For low values of the particle volume fraction, results indicate that the SCF may become negative for . Inversely, ( ) A θ exhibits a local maximum with an increase up to the angleM W θ θ = .As pointed out by previous authors[START_REF] García | Debonding at the fibre-matrix interface under remote transverse tension. One debond or two symmetric debonds?[END_REF][START_REF] París | Kinking of Transversal Interface Cracks Between Fiber and Matrix[END_REF][START_REF] Weißgraeber | Crack nucleation in negative geometries[END_REF], the presence of this maximum coincides with the progressive change from mode I to mode II of the interfacial crack opening. Results reveal that M applied strain, the energy condition Eq. (

Fig. 4a depictsθ

  Fig. 4a depicts the typical evolution of

  point between the energy condition Eq. (

Fig. 7 L

 7 Fig. 7 describes the influence of the particle volume fraction on the debonding stress for

τ

  is the interfacial shear strength. A high value of µ leads to neglect the influence of shear.

α

  than the matrix ( ) m α , interfacial tensile stress is generated upon cooling from the fabrication temperature. Introducing the CTE of the composite c α and 0 T ∆ < the temperature change permits to derive the stress and energy conditions for interfacial debonding during the cooling step:

  estimated with the help of a modified finite element procedure which now requires the superposition of three elastic solutions Eq.[START_REF] Quesada | Multiple failures in or around a stiff inclusion embedded in a soft matrix under a compressive loading[END_REF]. For this geometry, the stress state at the interface is hydrostatic and T xx k does not depend on θ . It was checked that the FE model allows to recover the analytical solution of the SCF for a rigid particle embedded within an infinite matrix and submitted to a uniform temperature change[START_REF] Selsing | Internal stresses in ceramics[END_REF]. However we detected that the cylindrical cell induces a stress concentration at 0 θ = for higher values of p V . This artefact limits the use of the cell to low values of the particle volume fraction with 10%. Using the CC provides the debonding angle at initiation by solving

  Fig. 9a illustrates Eq. (47) by plotting ( ) D T -∆ versus c i L R for selected values of the elastic

  still a decreasing function of θ and that the IERR possesses a maximum ifM TM θ θ = .The debonding angle at initiation is obtained by solving

(

  Fig. 9b plots the ratio c D i σ σ as a function of c i L R for various values of the stress ratio κ . It is clear that the presence of residual stresses decreases the debonding stress but this influence is weaker for higher values of c i L R as the mechanical loading becomes predominant. Comparing Eq. (50) with Eq. (1) reveals that the additional term T σ taking into

min 22 . 5

 225 μm R =and max 355 μm R = were elaborated with vacuum hot-pressing. Micrographic examination of the specimens after cooling revealed cracks that originate at the matrix/particle interface. The presence of cracks was found dependent on the sphere radius: an upper bound 1 absence and the presence of cracks.

  onset and is very efficient to derive the debonding stress for various interfacial properties. The key parameters are the length ratio c i L R and the structural parameter β as the condition c i L R β ≥ delimitates the energy dominant domain for which the debonding stress scales with c i G R . Additional results reveal that the influence of interfacial mixed-mode conditions on the value of the debonding stress is weak. Taking into account the cooling phase after elaboration at high temperature allows to estimate the amplitude of the temperature change responsible for debonding. Superposing residual stresses and mechanical loading introduces an additional term proportional to the stress ratio κ which decreases the applied stress at debonding. Finally, it is shown that experimental data can be used to estimate bounds or values of the interfacial fracture properties.

Fig. 1 :Fig. 2 :Fig. 3 :Fig. 4 :Fig. 5 :Fig. 7 :Fig. 8 :Fig. 9 : 10 :

 1234578910 Fig. 1: a) A spherical particle bonded to a surrounding matrix and subjected to a tensile loading in the z direction, b) Nucleation of interfacial debonding (angle D θ ) for an applied debonding stress D σ .

Table 2

 2

			0.22	1.03	0.38	5
	GH1					10	23	3.81	6.6	28.0 10 -3	6.0	65.3 10 -3
	GH2					13	20.5	5.0	8.6	63.0 10 -3	8.3	133.4 10 -3
	[9]	70	0.25	3.5	0.35	5				25-50	62	35.7
						6		46.2	168.7
						72		51.2	53.4
						210		42.9	38.4
						521		32.7	34.4
	[38]	53.3	0.27	4.21	0.35	108				71.1	1.0
						5		47.6	39.0
						10		40.7	38.7
						15		37.1	38.0
						20		34.8	37.1
						25		33.1	36.0
						30		31.8	34.6
						10.5
						5		56.7	51.8	93.3	0.8
						10		52.2	51.3
						15		49.8	50.5
						20		48.1	49.5
						25		46.8	48.1
						30		45.8	46.5
	(1) experimental value -(2) identified value


Louise C Lemonnier

A Courouce

M Cessans

L Petit

J M Cardwell

M- P Toquet

E A Richard

Variability of fungi detection in the respiratory tract of racehorses according to the sampling site

INTRODUCTION

The potential involvement of fungi in equine asthma was previously investigated based on tracheal wash (TW) rather than bronchoalveolar lavage (BAL) (1). However, the reliability of airway samples and laboratory methods has not been investigated and the clinical relevance of fungal detection in equine airways still remains controversial.

OBJECTIVES

Preliminary study to 1) characterize fungi from upper and lower airways of racehorses and 2) determine the most reliable methodology for fungal detection -12/22 (55%) with both spores and hyphae, frequently phagocyted BAL -Comparison between aliquots (Table 2):

-Poor agreement between BAL L and BAL R (κ= 0.015) -Poor agreement between culture and cytology (κ=0.015) (Figure 1) -Substantial agreement between BALP and separate lungs (κ= 0.627; Se = 0,58 ; Sp = 1,00) -7/7 BALP positive on cytology were positive on BALL or BALR -5 BALp negative on cytology were positive on BALL or BALR

Table 1 )

 1 TW:

	METHODS
	• 30 Standardbred racehorses in active training, aged 4.6 ± 1.6	• Fungi detection, identification and characterization
	years, from 3 different training stables	by cytology and culture
	• TW, followed by BAL from each lung separately, collected	• Comparison was made between:
	through a guarded catheter and gastroscope
	RESULTS
	• Fungal culture
	TW: 28/30 (93%) positive ; BALP: 4/30 (13%) positive
	-4/4 positive in TW
	-3/4 with same fungi in BALP and TW
	-9 genus (alone or concomitant)
	-Aspergillus (5 genus) 13/28 (46%)
	-Penicillium 12/28 (43%)
	-Chrysosporium, Cladosporium, Scopulariospsis
	• Fungal cytology (

• Cytology and culture of TW vs BAL P • Cytology of BALP vs BALL and BALR CONCLUSION BAL is preferred over TW for fungal analysis. Pooled BAL is a highly specific while fairly sensitive alternative to combined cytology of individual left/right samples for mold/fungi detection. DISCUSSION Despite a similar prevalence of fungi detection in left and right BAL, a large disparity and a poor agreement were found between lungs. BALP cytology however exhibited a substantial agreement with corresponding samples from each lung. TW fungal culture was overly positive amongst healthy individuals and most likely poorly specific for fungal detection ECEIM Virtual Congress, 22 nd -23 rd October 2021 HYPOTHESIS Fungal cytology of a pooled BAL (BALP) is representative of corresponding left (BALL) and right (BALR) samples, and is more reliable than TW for fungal detection. REFERENCES 1) Dauvillier J, ter Woort F, van Erck-Westergren E. Fungi in respiratory samples of horses with inflammatory airway disease. J Vet Intern Med. 2019;33:968-975

Table 1 :

 1 Cytology of pooled and individual BALF, and of TW

						25
						20					TWcyt +
						15					TWcult -
						10					TWcult +
						5					TWcyt -
						0					TWcyt +
							BALp	BALp	TW	TW
							cu lt	cyt	cu lt	cyt
						Figure 1: Distribution of results based on sampling site and method of
						analysis (cyt: cytology ; cult: culture ; -: negative ; + : positive)
	TW	Cytology positive 22/30	Spores 18/22	Hyphae 16/22	Phagocyted 14/22	BALL only	BALR only	BALL+R	Agreement (κ)
		7/30				Cytology	4/7	5/8	3	0,015
	BAL P	3 bilateral 4 unilateral	7/7	2/7	6/7	Culture only	Cytology only	Culture + cytology	Agreement (κ)
	BALR	8/30	5/8	6/8	5/8	BAL P	3/4	6/7	1/7	0,015
	BAL L	7/30	7/7	0/7	6/7

Table 2 :

 2 Comparison of BALF sample sites, and of BALF methods of analysis


domain: chim sdv

text:
Fabien Fillesoye

Méziane Ibazizène

Nicolas Marie

Florence Noble

Cécile Perrio

Evaluation of Specific Binding of [ 11 C]RTI-97 to KOR by Autoradiography and PET Imaging in Rat

Keywords: Kappa opioid receptor, RTI-97, JDTic, carbon-11, autoradiography, positron emission tomography

Kappa opioid receptor (KOR) PET imaging remains attractive to understand the role of KOR in health and diseases, and to help the development of drugs especially for psychiatric disorders such as depression, anxiety and addiction. The potent and selective KOR antagonist RTI-97 labelled with carbon-11 was previously demonstrated to display specific KOR binding in mouse brain by ex vivo autoradiography studies. Herein, we evaluated [ 11 C]RTI-97 in rat by in vitro autoradiography and by in vivo PET imaging. The radiosynthesis of [ 11 C]RTI-97 was optimized to obtain high molar activities. Despite a low cerebral uptake, the overall results showed an heterogeneous repartition and specific KOR binding of [ 11 C]RTI-97 in brain, and a high and specific accumulation of [ 11 C]RTI-97 in pituitary in accordance with KOR expression.

Kappa opioid receptors (KORs) are known to play an important role in many physiological and pathological functions including immunomodulation, mood control, sensation of pain, anxiety, depression, drug abuse and psychiatric disorders. [START_REF] Van't Veer | ole of kappa-opioid receptors in stress and anxiety-related behavior[END_REF][START_REF] Browne | Targeting opioid dysregulation in depression for the development of novel therapeutics[END_REF][3][START_REF] Tejeda | The dynorphin/k-opioid receptor system and its role in psychiatric disorders[END_REF] They belong to G-protein-coupled receptor family and are the most abundant ORs in the human brain. [START_REF] Feng | Current Research on Opioid Receptor Function[END_REF] Although homology with MOR and DOR subtypes, KORs display a unique pharmacology with aversive effects produced by KOR agonists whereas MOR and DOR agonists are rewarding and reinforcing. [START_REF] Merrer | Reward processing by the opioid system in the brain[END_REF] Potent KOR antagonists such as JDTic have been proposed as chemotherapy for cocaine, morphine and nicotine addiction as well as alcohol seeking. [START_REF] Thomas | Identification of the first trans-(3R,4R)-dimethyl-4-(3-hydroxyphenyl)piperidine derivative to possess highly potent and selective opioid K receptor antagonist activity[END_REF][START_REF] Beardsley | Differential effects of the novel kappa opioid receptor antagonist, JDTic, on reinstatement of cocaine-seeking induced by footshock stressors vs cocaine primes and its antidepressant-like effects in rats[END_REF][START_REF] Carroll | Effects of JDTic, a selective κ-opioid receptor antagonist, on the development and expression of physical dependence on morphine using a rat continuous-infusion model[END_REF][START_REF] Jackson | Effect of the selective kappa-opioid receptor antagonist JDTic on nicotine antinociception, reward, and withdrawal in the mouse[END_REF][START_REF] Schank | The kappa opioid receptor antagonist JDTic attenuates alcohol seeking and withdrawal anxiety[END_REF] As a result, efforts have been made to develop KOR PET imaging in order to better understand in vivo KOR pharmacology, to measure the KORs density, to investigate disease states and to evaluate new therapeutics. [START_REF] Cumming | A survey of molecular imaging of opioid receptors[END_REF][START_REF] Kaur | Classics in neuroimaging: shedding light on opioid receptors with positron emission tomography imaging[END_REF] The past decades have seen progress in the validation of KORs radioligands (Figure 1). Among them, [ [START_REF] Schank | The kappa opioid receptor antagonist JDTic attenuates alcohol seeking and withdrawal anxiety[END_REF] C]GR103545, [ 11 C]EKAP and [ 11 C]LY2795050 have been assessed in clinical trials. [ 11 C]GR103545 displayed slow binding kinetics and ultra-potency leading to risk of side effects such as dysphoria, sedation and psychosis due to its KOR agonist property. [START_REF] Naganawa | Evaluation of the agonist PET radioligand [ 11 C]GR103545 to image kappa opioid receptor in humans: kinetic model selection, testretest reproducibility and receptor occupancy by the antagonist PF-04455242[END_REF][START_REF] Martinez | Kappaopioid receptors, dynorphin, and cocaine addiction: a positron emission tomography study[END_REF] The novel KOR agonist [ 11 C]EKAP was recently reported to display faster tissue kinetics than [ [START_REF] Schank | The kappa opioid receptor antagonist JDTic attenuates alcohol seeking and withdrawal anxiety[END_REF] C]GR103545 in test-retest reproducibility studies. [START_REF] Li | Development and in vivo evaluation of a κ-opioid receptor agonist as a PET radiotracer with superior imaging characteristics[END_REF][START_REF] Matuskey | Social status and demographic effects of the kappa opioid receptor: a PET imaging study with a novel agonist radiotracer in healthy volunteers[END_REF][START_REF] Naganawa | Kinetic modeling and test-retest reproducibility of 11 C-EKAP and 11 CFEKAP, novel agonist radiotracers for PET imaging of the kappa opioid receptor in humans[END_REF] [ 11 C]LY2795050, identified as a KOR antagonist with short term effects, was shown to possess favorable brain uptake, pharmacokinetic properties and binding profiles but poor stability and moderate KOR selectivity. [START_REF] Zheng | Synthesis and Evaluation of 11 C-LY2795050 as a k-Opioid Receptor Antagonist Radiotracer for PET Imaging[END_REF][START_REF] Naganawa | Kinetic modeling of 11 C-LY2795050, a novel antagonist radiotracer for PET imaging of the kappa opioid receptor in humans[END_REF][START_REF] Vijay | PET imaging reveals lower kappa opioid receptor availability in alcoholics but no effect of age[END_REF][START_REF] Naganawa | Receptor occupancy of the κ-opioid antagonist LY2456302 measured with positron emission tomography and the novel radiotracer 11 C-LY2795050[END_REF][START_REF] Naganawa | Test-retest reproducibility of binding parameters in humans with 11 C-LY2795050, an antagonist PET radiotracer for the kappa opioid receptor[END_REF][START_REF] Yang | Radiosynthesis of [ 11 C]LY2795050 for preclinical and clinical PET imaging using Cu(II)-mediated cyanation[END_REF] The analogue [ 11 C]/[ 18 F]LY2459989 recently evaluated in non-human primates was suggested to display a similar in vivo behavior. [START_REF] Li | Novel 18 F-labeled -opioid receptor antagonist as PET radiotracer: synthesis and in vivo evaluation of 18 F-LY2459989 in nonhuman primates[END_REF][START_REF] Cai | Fluorine-18-labeled antagonist for PET imaging of kappa opioid receptors[END_REF] Thus, characterization of KOR radiopharmaceuticals with antagonism properties and high target specificity is still desirable. 27

(3R)-7-hydroxy-N-((1S)-1-{[(3R,4R)4-(3- hydroxyphenyl)-3,4-dimethyl-1-piperidinyl]methyl}- 2methylpropyl)-1,2,3,4-tetrahydro-3- isoquinolinecarboxamide]
established as the most potent and selective KOR antagonist reported so far (Figure 1). [START_REF] Poisnel | 11 C]-MeJDTic: a novel radioligand for κopioid receptor positron emission tomography imaging[END_REF][START_REF] Schmitt | 18 F]-FluoropropylJDTic for κ-opioid receptor PET imaging: Radiosynthesis, pre-clinical evaluation, and metabolic investigation in comparison with parent JDTic[END_REF] Among them, the N- ]methyl-1,2,3,4tetrahydro-3-isoquinolinecarboxamide) was reported to exhibit a high specific binding to KOR in brain by ex vivo studies in mouse using competition and counting method. [START_REF] Poisnel | 11 C]-MeJDTic: a novel radioligand for κopioid receptor positron emission tomography imaging[END_REF] RTI-97 was also reported to display advantageous pharmacological properties compared to JDTic. In vitro experiments from rodent brain tissues [RTI-97: K i (KOR) = 0.053 ± 0.03 nM, K i (MOR) / K i (KOR) = 700, K i (DOR) / K i (KOR) = 1162; JDTic: K i (KOR) = 0.32 ± 0.05 nM, K i (MOR) / K i (KOR) = 12, K i (DOR) / K i (KOR) = 940] and human cloned receptors [RTI-97: K i (KOR) = 1.01 ± 0.14 nM, K i (MOR) / K i (KOR) = 8.8, K i (DOR) / K i (KOR) = 117; JDTic: K i (KOR) = 0.41 ± 0.10 nM; K i (MOR) / K i (KOR) = 2.3, K i (DOR) / K i (KOR) = 72] revealed that RTI-97 was more potent and selective than JDTic. [START_REF] Thomas | Identification of (3R)-7-hydroxy-N-((1S)-1-{[(3R,4R)-4-(3hydroxyphenyl)-3,4-dimethyl-1-piperidinyl]methyl}-2methylpropyl)-1,2,3,4-tetrahydro-3-isoquinolinecarboxamide as a novel potent and selective opioid κ receptor antagonist[END_REF] RTI-97 was also found to have a shorter duration of antagonism than JDTic in models of analgesia in mouse and in diuresis in rat, suggesting that pharmacokinetics would remain appropriate for imaging studies. [START_REF] Owens | Pharmacodynamic relationships between duration of action of JDTic-like kappa-opioid receptor antagonists and their brain and plasma pharmacokinetics in rats[END_REF] The long duration of action of JDTic and its derivatives, producing measurable antagonism for several weeks at minimally-effective doses, raised questions of mechanism, especially since brain penetration was low and clearance from plasma was rapid. [START_REF] Munro | Long-acting κ opioid antagonists nor-BNI, GNTI and JDTic: pharmacokinetics in mice and lipophilicity[END_REF] Lysosomes sequestration was proposed as explanation for JDTic brain persistence. However, such a hypothesis would lead to nondisplaceable KOR binding, which was not in accordance with the previously cited [ 11 C]RTI-97 evaluation. [START_REF] Poisnel | 11 C]-MeJDTic: a novel radioligand for κopioid receptor positron emission tomography imaging[END_REF] Thus, the overall findings prompted us to further investigate KOR binding properties of [START_REF] Schank | The kappa opioid receptor antagonist JDTic attenuates alcohol seeking and withdrawal anxiety[END_REF] 2). [ 11 C]RTI-97 was purified and isolated by normal phase HPLC, then concentrated to dryness and formulated. This method was advantageous for time saving reasons (See Supporting Information). The overall production was performed on a commercial automated carbon-11 synthesis unit (TRACERlab FX MeI GE Healthcare). Ready to use [ 11 C]RTI-97 was obtained within 33 min from end of bombardment in 11-16% radiochemical yield (not decay corrected and relative to [START_REF] Schank | The kappa opioid receptor antagonist JDTic attenuates alcohol seeking and withdrawal anxiety[END_REF] CH 4 ) with > 99% radiochemical and chemical purities and 111-259 GBq/mol molar activities. Molar activities were 50-100 times higher than those obtained according to previously reported procedure (1.4-4.5 GBq/μmol). [START_REF] Poisnel | 11 C]-MeJDTic: a novel radioligand for κopioid receptor positron emission tomography imaging[END_REF] In vitro experiments were performed on healthy male Wistar rat brain slices with the radiotracer alone (baseline conditions) and with the addition of a large excess (x 2500) of naloxone, a non-selective OR antagonist, or U-50,488, a selective KOR agonist (blocking conditions) for the determination of [ 11 C]RTI-97 binding selectivity. All experiments were performed in triplicate with three different productions of [ 11 C]RTI-97. Autoradiography images revealed that the radioactivity was distributed heterogeneously over brain sections under baseline conditions and that radioactivity levels were significantly reduced under blocking conditions (Figure 3, Table 1). Under baseline conditions, the highest concentration of [ 11 C]RTI-97 was found in OT (olfactory tubercle), TH (thalamus), SC (superior colliculi) and CPU (caudateputamen), with radioactivity ratios relative to CB (cerebellum) known to be poor in KORs reaching 1.5-1.7. Less binding was observed in ACB (nucleus accumbens), SNR (substantia nigra), CTX (cortex), HIP (hippocampus) and HY (hypothalamus), corresponding to radioactivity ratios relative to CB in the 1.4-1.2 range; and the lowest radioactivity levels were measured in CC (corpus callosum), AMY (amygdala) and CB as expected. This distribution was in accordance with KOR expression in rat brain regions. [START_REF] Mansour | Opioidreceptor mRNA expression in the rat CNS: anatomical and functional implications[END_REF][START_REF] Zukin | Characterization and visualization of rat and guinea pig brain  opioid receptors: Evidence for 1 and 2 opioid receptors[END_REF] In the competition studies using either naloxone or U-50,488, [ 11 C]RTI-97 binding was significantly reduced in all cerebral regions except CC and CB. Binding inhibition rates were in the 30-50% range in KOR expressing regions, while they were below 20% in KOR devoided structures such as CC and CB. These results indicated [ 11 C]RTI-97 binding specificity. Globally, naloxone and U-50,488 displayed a similar inhibition effect in [ 11 C]RTI-97 binding. The absence of a significant difference between naloxone and U-50,488 was in agreement with the specificity of [ 11 C]RTI-97 for KOR. The in vivo specific binding of [ 11 C]RTI-97 was then assessed by in vivo PET/CT imaging in healthy male Wistar rats. Rats were injected (iv, tail vein) with 34.2±8.0 MBq of [ 11 C]RTI-97 (corresponding to 0.2 to 12.1 g/kg of RTI), and dynamic PET imaging was acquired over 30 min. In competition experiments, rats received naloxone or U-50,488 (1 mg/kg, iv, tail vein) 10 min prior injection of [ 11 C]RTI-97, or JDTic (10 mg/kg, ip) 30 min prior injection of [ 11 C]RTI-97. The use of different blockers was important as discrepancies in KOR radioligand binding has previously been revealed. [START_REF] Placzek | Discrepancies in Kappa Opioid Agonist Binding Revealed through PET Imaging[END_REF] PET Images under baseline conditions (injection of only [ 11 C]RTI-97) showed that brain uptake of [ 11 C]RTI-97 was very low, and that [ 11 C]RTI-97 accumulated in pituitary gland (Figure 4). Thus, time-activity curves (TACs) were extracted for whole brain, pituitary gland and muscle as reference.

[ 11 C]-methylated derivative [ 11 C]RTI-97 (or [ 11 C]RTI-5989-97, [ 11 C]-MeJDTic, (3S)-7-hydroxy-N- ((1S)-1{[(3R,4R)-4-(3-hydroxyphenyl)-3,4-dimethyl-1- piperidinyl]methyl}-2-methylpropyl)-2-[
[ 11 C]RTI-97 uptake in pituitary gland was rapid with the maximum peak SUV values of about 1.6 reached from 3.5 min post-injection. These values remained constant until the end of 30 min acquisition, and they were 4 times higher than the SUV values for muscle uptake. TAC for muscle uptake displayed a similar profile of that for pituitary gland but with a lesser magnitude as the maximum peak SUV value also reached at 3.5 min was only 0.4. For pituitary gland and muscle, no wash out was observed during acquisition time. Uptake in brain was lower than in muscle with SUV values that did not exceed 0.4 at 1 min, and decreased to 0.2 to stay stable from 3 to 30 min.

For competition studies, TACs were determined for whole brain, pituitary gland and muscle by pooling all data obtained with naloxone, U-50,488 and JDTic. The pre-injection of the blockers had significant influence on [ 11 C]RTI-97 uptake in pituitary gland with SUV values of about 1.15 during the 3.5-30 min plateau, corresponding to 30% inhibition rate. In contrast, no difference between baseline and blocking conditions was observed in muscle and whole brain. As remark, the low radioactivity levels in brain were not appropriate to detect any significant inhibition.

In order to refine and complete the in vivo results, we undertook ex vivo experiments. Animals were euthanized at the end of the PET imaging session for brain and cerebral regions dissection and radioactivity counting, and also for evaluation of [ 11 C]RTI-97 stability in blood (Table 2). Ex vivo data were expressed as uptake index to correct for differences in animal body weight and injected dose (see Supporting Information). Radioactivity amounts in blood corresponding to uptake index of 0.25-0.33, were similar under baseline and blocker preinjection conditions, confirming that the pharmacokinetics of [ 11 C]RTI-97 was not modified by the blockers. Moreover, HPLC analyses revealed that more than half of [ 11 C]RTI-97 was recovered intact in the circulation, and radiometabolites were found to be more polar than [ 11 C]RTI-97 and not to cross the BBB. These findings were in accordance with our previously reported studies carried out in mouse. [START_REF] Poisnel | 11 C]-MeJDTic: a novel radioligand for κopioid receptor positron emission tomography imaging[END_REF] As expected following PET imaging results, [ 11 C]RTI-97 concentration was high in pituitary gland with an uptake index reaching around 8 under baseline conditions. The uptake index decreased to 5.6 under blocking conditions with naloxone and U-50,488 as blockers, corresponding to around 30% inhibition, and dropped to 4.6 using JDTic, leading to inhibition rate of 43%. The inhibition rate was found to be significantly higher with JDTic than with naloxone and U-50,488. This difference could not be shown from PET imaging data due to a lack of sensibility compared to counting measurement, but globally the overall ex vivo results were of the same magnitude as those in vivo.

The radioactivity level for half brain remained very low with uptake index of 0.5-0.6 under both baseline and blocking conditions, value in the same order than that for CB. Once again, these results are in accordance with the low brain penetration determined by PET imaging. Interestingly, data for cerebral sub-structures displayed a significant heterogeneous radioactivity repartition despite the low radioactivity levels. Under baseline conditions, [ 11 C]RTI-97 uptake was high in HY and OT with radioactivity ratios relative to CB of 3.70 and 2.09 respectively, and it was lower in CPU, HIP and CTX with radioactivity ratios relative to CB ranging from 1.61 to 1.31. Radioactivity levels in TH were similar to that in CB. In HY and OT, 40% of [ 11 C]RTI-97 uptake was inhibited by preinjection of U50,488. These inhibition results are coherent with those obtained by autoradiography (Table 1). The uptake inhibition in HY and OT was lower with naloxone and JDTic as blockers. In contrast, naloxone and JDTic lead to 28-37% of [ 11 C]RTI-97 binding inhibition in CPU whereas no effect was observed with U50,488. Inhibition by naloxone, U50,488 and JDTic below 25% was not significant in the other brain regions. In summary, we have successfully developed the radiosynthesis of [ 11 C]RTI-97 with high molar activities. In vitro autoradiography studies demonstrated KOR specific binding in rat brain in accordance with KOR cerebral distribution. In vivo PET imaging and ex vivo studies in rats revealed a low brain penetration but a high uptake of [ 11 C]RTI-97 in pituitary. It has been largely shown that the implication of the KOR system in several physiopathological states such as addiction, stress and anxiety-related behaviors was related to the modulation of the hypothalamic-pituitary-adrenal (HPA) axis. [START_REF] Zhao | Functional copioid receptors on oxytocin and vasopressin nerve terminals isolated from the rat neurohypophysis[END_REF][START_REF] Fjalland | k-Opioid receptor agonists differentially affect the release of neurohypophysial hormones[END_REF] It was also well established that pituitary gland displayed high density of KORs. [START_REF] Mansour | Immunohistochemical localization of the cloned 1 receptor in the rat CNS and pituitary[END_REF] MORs have also been found to be expressed but not DORs. Thus, the high accumulation of [ 11 C]RTI-97 in pituitary was expected, especially since this brain region was not protected by the blood-brain barrier (BBB). However, a non-specific entry could occur due to the significant vascularization and to hydrophobic properties of RTI-97. Both in vivo and ex vivo data demonstrated a significant [ 11 C]RTI-97 binding inhibition in pituitary by either naloxone, U-50,488 and JDTic. The higher inhibition effect measured in ex vivo studies using JDTic was also consistent with a higher affinity and specificity of JDTic for KORs compared to naloxone and U-50,488, and also confirmed [ 11 C]RTI-97 specific KOR binding. The high uptake and specific binding of [ 11 C]RTI-97 in pituitary was also nicely correlated to the significant concentration and specific binding revealed in HY by ex vivo experiments, according to the known KOR enriched expression in these two strongly attached structures.

These results may raise the question of whether KOR pituitary binding may be related to centrally mediated effects induced by RTI-97 and drugs from the same class of compounds.

To our knowledge, binding in pituitary was poorly investigated in the evaluation of KOR PET radiotracers, and the consideration of this structure may be underestimated.

[ 3 H]Cyclofoxy, a ligand with high affinity for both MOR and KOR, was shown to label pituitary in ex vivo autoradiography studies. 39 A decreased binding of non-selective OR [ 11 C]diprenorphine in pituitary was revealed in undernourished restrictive anorexia nervosa patients compared to controls. [START_REF] Galusca | Decreased cerebral opioid receptors availability related to hormonal and psychometric profile in restrictive-type anorexia nervosa[END_REF] This latter study was a typical example suggesting that a focus on the quantification of ORs and especially KORs in pituitary could bring rapid and important information in PET imaging of neurologic diseases, while avoiding the problems of BBB permeability and subsequent low brain uptake throughout cerebral sub-structures. In this regard, [ 11 C]RTI-97 with its high pituitary labeling and its unambiguous KOR specificity, would remain a valuable radiotracer for at least preliminary investigation by preclinical PET imaging.

Table of Contents

Figure 1 .

 1 Figure 1. Structure of main KOR PET radioligands and JDTic derivatives. Few years ago, we developed KOR radiotracers derived from JDTic [(3R)-7-hydroxy-N-((1S)-1-{[(3R,4R)4-(3hydroxyphenyl)-3,4-dimethyl-1-piperidinyl]methyl}-2methylpropyl)-1,2,3,4-tetrahydro-3isoquinolinecarboxamide]established as the most potent and selective KOR antagonist reported so far (Figure1).[START_REF] Poisnel | 11 C]-MeJDTic: a novel radioligand for κopioid receptor positron emission tomography imaging[END_REF][START_REF] Schmitt | 18 F]-FluoropropylJDTic for κ-opioid receptor PET imaging: Radiosynthesis, pre-clinical evaluation, and metabolic investigation in comparison with parent JDTic[END_REF] Among them, the N-[[START_REF] Schank | The kappa opioid receptor antagonist JDTic attenuates alcohol seeking and withdrawal anxiety[END_REF] C]-methylated derivative [ 11 C]RTI-97 (or [ 11 C]RTI-5989-97, [ 11 C]-MeJDTic, (3S)-7-hydroxy-N-((1S)-1{[(3R,4R)-4-(3-hydroxyphenyl)-3,4-dimethyl-1piperidinyl]methyl}-2-methylpropyl)-2-[ 11C]methyl-1,2,3,4tetrahydro-3-isoquinolinecarboxamide) was reported to exhibit a high specific binding to KOR in brain by ex vivo studies in mouse using competition and counting method.[START_REF] Poisnel | 11 C]-MeJDTic: a novel radioligand for κopioid receptor positron emission tomography imaging[END_REF] RTI-97 was also reported to display advantageous pharmacological properties compared to JDTic. In vitro experiments from rodent

Figure 2 .

 2 Figure 2. Radiosynthesis scheme of [ 11 C]RTI-97 from cyclotron produced [ 11 C]CH 4 (A) with representative semipreparative HPLC (high performance liquid chromatography) chromatogram at the end of the radiosynthesis for the purification and isolation of [ 11 C]RTI-97 (B).

Figure 3 .

 3 Figure 3. Representative autoradiography images of coronal brain sections after incubation with [ 11 C]RTI-97 (0.7 ± 0.2 GBq/L, i.e. 4.3 ± 0.8 nM; baseline conditions) or after coincubation of [ 11 C]RTI-97 with naloxone (10 μM) or U-50,488

[ 11 C

 11 ]RTI-97 (10 μM) (blocking conditions). Tissue sections were counterstained with thionine for brain structure identification.

Figure 4 .

 4 Figure 4. Representative axial and sagittal plans of fusion PET/CT (up), CT (middle) and PET (down) images with [ 11 C]RTI-97 under baseline (A) and blocking (B, using JDTic as blocker) conditions. Time-activity curves (TACs; SUV: standardized uptake value) of [ 11 C]RTI-97 obtained for pituitary (blue, * for p < 0.05), muscle (green) and whole brain (red) under baseline (solid lines, n = 4) and blocking (dotted lines, taken in account all results with naloxone (n = 5), U-50,488 (n = 5) and JDTic (n = 6) as blockers) conditions (C). Data were reported as mean values ± standard error of the mean (SEM).

  [START_REF] Schank | The kappa opioid receptor antagonist JDTic attenuates alcohol seeking and withdrawal anxiety[END_REF]

  C]RTI-97. Here, we report results for KOR specificity of[START_REF] Schank | The kappa opioid receptor antagonist JDTic attenuates alcohol seeking and withdrawal anxiety[END_REF] C]RTI-97 by in vitro autoradiography, in vivo PET imaging and ex vivo experiments in rats. First of all, we revisited the radiosynthesis of [ 11 C]RTI-97 in order to obtain high molar activities. The radiolabeling was realized by 11 C-methylation of JDTic with [ 11 C]-methyl triflate obtained from 11 CH 4 instead of 11 CO 2 (Figure

Table 1 . Brain structure (BS) distribution of radioactivity after incubation of rat brain slides with [ 11 C]RTI-97

 1 Incubation of [ 11 C]RTI-97 (0.7 ± 0.2 GBq/L, i.e. 4.3 ± 0.8 nM) alone. c Coincubation of [ 11 C]RTI-97 (0.7 ± 0.2 GBq/L, i.e. 4.3 ± 0.8 nM) with naloxone (10 μM) or U50,488 (10 μM).

	Brain structure		Radioactivity (10 3 xDLU/mm 2 ± SEM)	BS/CB ratio d	Binding inhibition (%) e
	(BS) a		Baseline	blocking with	blocking with	(baseline)	naloxone	U50,488
		Conditions b		naloxone c	U50,488 c
	OT		8.07 ± 0.27	3.54 ± 0.70	3.10 ± 0.55	1.7 ± 0.6	47	43
	TH		7.98 ± 0.18	4.97 ± 0.57	4.26 ± 0.13	1.6 ± 0.4	34	31
	SC		7.79 ± 1.71	4.80 ± 0.47	3.94 ± 0.18	1.6 ± 0.4	35	35
	CPU		7.62 ± 1.09	4.87 ± 1.03	3.28 ± 0.24	1.5 ± 0.3	37	49
	ACB		6.86 ± 0.81	4.59 ± 0.83	2.98 ± 0.35	1.4 ± 0.3	33	51
	SNR		6.79 ± 1.55	4.97 ± 0.40	3.86 ± 0.53	1.4 ± 0.1	20	27
	CTX		6.41 ± 0.72	4.29 ± 0.94	3.57 ± 0.16	1.3 ± 0.2	32	38
	HIP		6.29 ± 0.93	4.01 ± 0.56	3.51 ± 0.33	1.2 ± 0.2	35	34
	HY		5.68 ± 1.08	4.14 ± 0.63	3.08 ± 0.54	1.2 ± 0.3	26	32
	CC		5.67 ± 0.70	4.67 ± 0.63	4.03 ± 0.22	1.1 ± 0.1	18	22
	AMY		5.31 ± 0.71	3.49 ± 0.59	2.56 ± 0.31	1.1 ± 0.2	35	44
	CB		5.23 ± 0.91	5.11 ± 0.94	4.39 ± 0.67	1.0 ± 0.1	3	17
									and blocking
	experiments	with	naloxone	or	U50,488	(significant	inhibition	>	30%).

a BS are listed by decreasing radioactivity level. b d BS/CB ratios calculated from values obtained under baseline conditions. e Calculated from values obtained under baseline conditions

Table 2 . Radioactivity distribution 30 min post-injection determined by counting after dissection

 2

	Tissue		Uptake index (± SEM)		BS/CB ratio	Uptake inhibition (%) d
	or	baseline	blocking with	blocking with	blocking with	(baseline)	naloxone	U50,488 JDTic
	BS	conditions	naloxone a	U50,488 b	JDTic c
	Blood	0.25 ± 0.04	0.33 ± 0.09	0.24 ± 0.03	0.27 ± 0.04	na e	na e	na e	na e
	Pituitary	8.06 ± 0.28	5.58 ± 0.48	5.61 ± 0.19	4.59 ± 0.67	na e	31	30	43
	½ Brain	0.06 ± 0.01	0.05 ± 0.01	0.05 ± 0.01	0.06 ± 0.01	na e	-	-	-
	HY	0.23 ± 0.07	0.17 ± 0.02	0.13 ± 0.02	0.17 ± 0.02	3.70 ± 1.31	-	43	-
	OT	0.15 ± 0.03	0.17 ± 0.08	0.09 ± 0.01	0.13 ± 0.02	2.09 ± 0.30	-	40	-
	CPU	0.12 ± 0.04	0.08 ± 0.01	0.13 ± 0.04	0.09 ± 0.01	1.61 ± 0.23	37	-	-
	HIP	0.10 ± 0.01	0.09 ± 0.02	0.10 ± 0.01	0.10 ± 0.02	1.59 ± 0.39	-	-	-
	CTX	0.09 ± 0.01	0.11 ± 0.05	0.08 ± 0.01	0.09 ± 0.01	1.31 ± 0.30	-	-	-
	TH	0.08 ± 0.02	0.11 ± 0.06	0.06 ± 0.01	0.06 ± 0.01	1.11 ± 0.31	-	-	-
	CB	0.07 ± 0.02	0.06 ± 0.01	0.07 ± 0.01	0.06 ± 0.01	1.00 ± 0.01	-	-	-

a Pre-injection of naloxone (1 mg/kg; iv; 10 min). b Pre-injection of U-50,488 (1 mg/kg; iv; 10 min). c Pre-injection of JDTic (10 mg/kg; ip; 30 min). d Only values for significant inhibition (P < 0.041). e Not applicable.

ACKNOWLEDGMENT

The authors thank gion ormandie, CNRS, CEA, Labex IRON (ANR-11-LABX-0018-01) and FR3038 INC3M. They are grateful to the cyclotron operators Mr Olivier Tirel and Mr Jérôme Delamare for production of carbon-11, and to Mrs Martine Dhilly and Mr Laurent Chazalviel from biology laboratory.

ASSOCIATED CONTENT Supporting Information

The Supporting Information is available free of charge on the ACS Publications website.

Experimental details, and HPLC analyses (PDF)

AUTHOR INFORMATION Corresponding Author

* Cécile Perrio -Normandie Univ, UNICAEN, CEA, CNRS, UMR 6030, LDM-TEP, Cyceron, Boulevard Henri Becquerel, 14000 Caen, France; Email: perrio@cyceron.fr

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Notes

The authors declare no competing financial interest.