Madiha Bouafia
email: madihabouafia@univ-evry.fr

Olivier Daube

Rayleigh-Bénard convection in 3 He near its critical point

Keywords: Anelastic approximation, Rayleigh-Bénard convection, supercritical fluid, transient flow, piston effect

We study by direct numerical simulation the Rayleigh-Bénard convection in supercritical 3 He using an anelastic approximation. The latter is based on scaling analysis associated with asymptotic expansions of the full governing equations which has an important consequence for numerical integration of the model. The approximate equations are supplemented by a parametric state equation and are solved numerically by a finite difference method coupled with a projection method. Numerical results giving time evolutions of the temperature difference between the horizontal walls are calculated and compared to experimental data. The convection onset is examined for the studied configuration.

Transport properties of pure fluids display large variations when approaching the gas-liquid critical point. In such fluids, the thermal diffusivity tends to zero while the isothermal compressibility, the thermal expansion coefficient and the isobaric specific heat diverge. These behaviors lead to a specific mechanism of heat transfer called the piston effect (PE) which induces a rapid homogenization of the temperature by thermoacoustic effects. The PE was initially observed experimentally in micro-gravity by [START_REF] Nitsche | The critical hump of Cv under microgravity, results from D-1 spacelab experiment 'Wärmekapazität[END_REF] then evidenced theoretically by [START_REF] Onuki | Fast adiabatic equilibration in a singlecomponent fluid near the liquid vapor critical point[END_REF]- [START_REF] Garrabos | Piston effect in a supercritical fluid sample cell : A phenomenological approach of the mechanisms[END_REF].

The interest shown the last two decades on the hydrodynamic stability of supercritical fluids is reflected in a significant number of experimental [START_REF] Kogan | Heat transfer and convective onset in a compressible fluid: 3 He near the critical point[END_REF]- [START_REF] Furukawa | Convection in a very compressible fluid: Comparison of simulations with experiments[END_REF], theoretical [START_REF] Carlès | The onset of free convection near the liquidŰvapour critical point.: Part II: Unsteady heating[END_REF]- [START_REF] Khouri | Transition convective dans les fluides supercritiques, 16ème congrès de mécanique[END_REF] and numerical works [START_REF] Amiroudine | Direct numerical simulation of instabilities in a two-dimensional near-critical fluid layer heated from below[END_REF]- [START_REF] Daube | Déclenchement de la convection Rayleigh Bénard dans l'He 3 au voisinage du point critique, 19ème Congrès Français de Mécanique[END_REF]. One of the configurations that quickly emerged as a study model is the Rayleigh-Bénard convection because of the interaction between two stability criteria: the classical Rayleigh criterion valid in Boussinesq and the Schwarzschild criterion valid for atmospheric flows at large scales. In supercritical fluids, the Schwarzchild criterion becomes relevant on small scales of length, including cells with very small dimensions due to the divergence of the compressibility [START_REF] Meyer | Onset of convection in a very compressible fluids: the transient toward steady state[END_REF]- [START_REF] Furukawa | Convective heat transport in compressible fluids[END_REF]. A modified Rayleigh number was proposed by [START_REF] Carlès | The onset of free convection near the liquidvapour critical point-part I: Stationary initial state[END_REF] including the difference between the real gradient and the adiabatic temperature gradient. The latter, AT G = ρg(∂T /∂P ) s , is related to an adiabatic process and corresponds to the temperature gradient obtained by moving a fluid particle along the hydrostatic pressure gradient. It has a stabilizing effect in the convection onset and its role is becoming increasingly important when approaching the critical point [START_REF] Kogan | Heat transfer and convective onset in a compressible fluid: 3 He near the critical point[END_REF].

The primary goal of this paper is to validate the use of the anelastic approximation for supercritical fluids. The paper basically consists of two parts. The first one is devoted to describe the set of approximations applied to full compressible Navier-Stokes equations based on an anelastic approximation. Another important point of our work lies in the use of a parametric state equation of supercritical 3 He. It has the advantage to reproduce accurately physical properties of the fluid near the critical point. The anelastc equations allow to simulate the Rayleigh-Benard convection in supercritical fluids driven by a weak heating from below. A method is proposed to solve the derived equations. The second part is devoted to 2D numerical results obtained in the same conditions as in experiments described in [START_REF] Furukawa | Convection in a very compressible fluid: Comparison of simulations with experiments[END_REF]. The validation of the code is done by comparing numerical solutions to experimental data. The convection onset is also examined through the influence of the aspect ratio on the total kinetic energy, and temperature fields during the transient phase.

CONFIGURATION

Following the experimental studies [START_REF] Furukawa | Convection in a very compressible fluid: Comparison of simulations with experiments[END_REF], we are interested in the onset of the Rayleigh-Bénard convection in the supercritical 3 He, for modified Rayleigh numbers above the instability threshold. A thin layer of 3 He (H = 1.06mm) is bounded by two horizontal plates. The fluid is initially at rest with conditions close to the critical point (ρ c , p c , T c )= (41.45kg/m 3 , 1.1510 5 P a, 3.31K).

• The initial temperature in the cavity is uniform and slightly greater than T c . The distance to the critical point is characterized by ϵ = (T i -Tc) Tc .

• The fluid is initially stratified with an mean value equal to the critical density ρ c .

The bottom wall is heated with a uniform heat flux while the upper one is maintained at the initial temperature T i (fig. 1). The considered values of the heat flux q are such as (T -T i )/(T i -T c ) is always « 1. This allowed us to consider that the dynamic viscosity µ, the thermal conductivity k, the specific heat c p and the coefficient of the isobaric thermal expansion β remain constant in the considered temperature interval with values taken at the initial temperature T i .

GOVERNING EQUATIONS

The values of the heat flux q and the parameter ϵ considered in this study allow us to assume that:

• the physics of the phenomena considered in this work may be described in the framework of continuum mechanics. The flow is therefore governed by the full compressible Navier-Stokes equations. We have chosen to use the enthalpy form of the energy equation and the equation of state in a parametric form fitted to experimental data [START_REF] Rudnick | Test of a new field-theoretical crossover equation of state[END_REF].

• the dynamic viscosity µ, the thermal conductivity k, the specific heat c p and the isobaric thermal expansion coefficient β remain constant in the considered temperature interval and equal to their values at the initial temperature T i .

Using the following reference quantities (the subscript c refers to values at the critical point):

• length: L 0 = H, the fluid layer thickness;

• Pressure: P 0 = p c ; Density: ρ 0 = ρ c ; Temperature: T 0 = T c

• Velocity: V 0 = a characteristic velocity of the flow which tends to zero when the heating flux q responsible for the flow tends to zero.

• Time: t 0 = L 0 /V 0 the governing equations in dimensionless form read:

∂ρ ∂t + ∇ (ρ -→ V) = 0 ρ d -→ V dt = -Eu∇p + 1 Re ∇ τ - 1 F 2 ρ -→ z ρ dT dt = 1 PrRe ∇ 2 T + G h β(T i )T i dp dt p = f (ρ, T ) where β = -1 ρ ( ∂ρ ∂T )
p is the isobaric thermal expansion coefficient and the stress tensor τ is defined by: τ = 1 2

( ∇ -→ V + ∇ -→ V t ) + ∇ -→ V 3 I
with the following dimensionless parameters:

Re = ρ c V 0 H µ Reynolds number Eu = p c ρ c V 2 0 Euler number G h = p c ρ c c p T c Pr = µc p k Prandtl number F = V 0 √ gH Froude number γ = c p c v ratio of specific heats

THE ANELASTIC APPROXIMATION

In the context of a numerical simulation, the main difficulties arise from the fact that the compressible Navier-Stokes equations support acoustic waves. Though these waves are not important in this Rayleigh-Bénard configuration as they do not contribute in a significant way to energy transfer compared to convective effects, they involve very restrictive stability criteria for the numerical simulation. In order to overcome these drawbacks, they are filtered out by using a so-called low Mach number approximation (LMNA), taking advantage of the low speed nature of the convective effects. More precisely, a particular kind of LMNA is used, namely anelastic approximation used for instance in stratified geophysical flows.

For this purpose, an analysis of the orders of magnitude of the different terms shows that Eu ≫ 1. A regular asymptotic expansion is then performed by expanding all the primary variables in powers of the small parameter η = 1/Eu:

p = p (0) + ηp (1) + O(η 2 ) ρ = ρ (0) + ηρ (1) + O(η 2 ) -→ V = - → V (0) + η -→ V (1) + O(η 2 ) T = T (0) + ηT (1) + O(η 2 )
Inserting these expansions into the Navier-Stokes equations, a sequence of an O(η -1 ) and of an O(1) problems is obtained:

4.1. O(η -1
) order problem

∇p (0) + 1 Eu F 2 ρ (0) + 1 Eu Re ∇ τ (0) = 0 (1)
where

1 Eu F 2 = ρ c gH p c and 1 Eu Re = µV 0 p c H
The first term of ( 1) is a pure O(η -1 ) order term and will thus be kept. The second and third terms of (1) behave differently when q increases:

• In the framework of continuum mechanics the Knudsen number is ≪ 1. Thus, the kinetic gas theory involves that the parameter 1 Eu Re is ≪ 1 .

• The parameter 1 Eu F 2 is small but its value is fixed since it does not depend on the distance to the critical point nor on the input heat flux, Therefore, only the two first terms of (1) are retained in the zero th problem yielding:

∇p (0) + 1 Eu F 2 ρ (0)-→ z = 0
This equation involves that p (0) and the density ρ (0) do not depend on x nor y. The pressure therefore may be split into two parts:

p (0) (z, t) = P (t) + p s (z)
where P (t) = ∫ 1 0 p (0) (z, t) dz is the average thermodynamic pressure and (p s (z), ρ s (z) = ρ (0) (z)) are the initial pressure and density stratification, solutions of the system:

dp s dz + 1 Eu F 2 ρ s (z) = 0
(2)

p s = f (ρ s , T i ) (3)
subject to the constraints:

∫ 1 0 ρ s (z) dz = 1 (4) ∫ 1 0 p s (z) dz = 0 (5)

Zero (th) order problem

Once the η -1 order problem is solved, the zero (th) order problem reads:

∂ρ (0) ∂t + ∇ (ρ (0) -→ V (0) ) = 0 ρ (0) d -→ V (0) dt = -∇p (1) + 1 Re ∇ τ (0) - 1 EuF 2 ρ (1)-→ z ρ (0) dT (0) dt = 1 PrRe ∇ 2 T (0) + G h (βT ) T i ( dP dt + -→ V (0) ∇p (0)
)

p (0) (z) = f (ρ (0) , T (0) )
Replacing ρ (1) by its first order approximation (ρ -ρ (0) )/η and taking into the fact that 1 Eu F 2 is finite and that ρ (0) = ρ s is independent of the time t, the first order problem finally reads:

∇ (ρ s -→ V) = 0 continuity equation (6) ρ s d -→ V dt = -∇π + 1 Re ∇ τ - 1 F 2 (ρ -ρ s ) -→ z momentum equation (7)
ρ s dT dt = 1 PrRe ∇ 2 T + G h (βT ) T i ( dP dt + -→ V ∇p s
) energy equation ( 8)

P (t) + p s (z) = f (ρ, T ) equation of state (9) ∫ V ρdυ = L/H
global mass conservation [START_REF] Accary | An adaptation of the low Mach number approximation for supercritical fluid buoyant flows[END_REF] Where the superscripts (0) and (1) have been dropped and π stands for p (1) . We can notice that this model derived from an anelastic approximation, differs slightly from the one proposed by Accary et al [START_REF] Accary | An adaptation of the low Mach number approximation for supercritical fluid buoyant flows[END_REF], in particular with the use of ρ s instead of ρ everywhere excepted in the buoyancy term. Our model may thus be seen as an extended Boussinesq approximation using a stratified density field instead of a uniform one.

BOUNDARY CONDITIONS

The classical no-slip condition -→ V = 0 on the walls is used for the velocity. Concerning the temperature, different sets of boundary conditions were used on the horizontal walls whereas the side boundaries are adiabatic:

1. Dirichlet: in this case, the horizontal lower plate is maintained at an uniform temperature T b (t), 2. In experimental data, the heating is performed using a uniform heat flux q(W/m 2 ). Two kind of boundary conditions were used in the numerical simulations to ensure the proper heat flux.

(a) The given heat flux q(t) is imposed pointwise by means of a Neumann condition, (b) Due to the huge discrepancy between the thermal conductivities of the fluid and of the copper plates used in the experiments, we assumed that the temperature T b of the bottom plate is uniform in space and depends only on the time t, i.e. T b = T b (t). An additional constraint has therefore to be imposed to ensure the correct overall heat flux, namely:

-k 1 A ∫ A 0 ∂T ∂z z=0 dx = q(t) (11)

NUMERICAL METHODOLOGY

Centered mimetic finite differences on a staggered MAC mesh are used for the spatial discretization [START_REF] Hyman | Natural discretization for the divergence, gradient and curl on logically rectangular grids[END_REF]. The grid is uniform in the x-direction and variable in z. The time derivatives are approximated by a second order backward Euler scheme in which the linear terms are treated implicitly while the non linear terms are treated explicitly with an Adams-Bashforth extrapolation. Giving the solution ( -→ V (n) , p (n) , T (n) , ρ (n) ) at time level n∆t, it is well known (see for instance [START_REF] Goda | A multistep technique with implicit difference schemes for calculating two or three dimensional cavity flows[END_REF]) that the solution at time level (n + 1)∆t may be obtained by solving the following sequence of problems:

1. Resolution of the energy equation

( ρ s σ T I -∇ 2 ) T n+1 = S n,n-1 T + G h [βT ] T =T i ( dP dt n+1 + -→ V n ∇p s ) (12)
2. Computation of ρ (n+1) , P (n+1) : the following system of nonlinear equations consisting of the equation of state written at each point of the mesh and of an additional condition imposing the conservation of total mass is solved by Newton-Raphston's method:

P n+1 (t) + p s (z) = f (ρ n+1 , T n+1 ) (13) ∫ V ρ n+1 dυ = L/H (14)

Computation of dP dt n+1

: along the lines of [START_REF] Le Quére | A Chebyshev collocation algorithm for 2D non-Boussinesq convection[END_REF] , a compatibility condition for dP dt n+1 is obtained by integrating on the whole domain Ω the energy equation and taking into account the continuity equation:

dP dt n+1 = 1 A ∫ ∂Ω ∂T ∂ - → n dl ( 15
)
4. Resolution of the momentum and continuity equations

∇ (ρ s -→ V n+1 ) = 0 (16) ( ρ s σ V I -∇ 2 ) -→ V n+1 + Re∇π n+1 = - → S n,n-1 V - Re F 2 (ρ n+1 -ρ s ) -→ z (17)
where σ V = 3Re/2∆t and σ T = 3PrRe/2∆t. The source terms are respectively given by:

S n,n-1 T = PrRe ( ρ s 4T n -T n-1 2∆t -2(ρ s - → V • ∇T ) n + (ρ s - → V • ∇T ) n-1 ) -→ S n,n-1 V = Re ( ρ s 4 - → V n - -→ V n-1 2∆t -2(ρ s -→ V • ∇ -→ V) n + (ρ s - → V • ∇ -→ V) n-1
)

The coupling -→ V-π is treated by a classical projection method for incompressible flows [START_REF] Guermond | An overview of projection methods for incompressible flows[END_REF] applied to ρ s -→ V. The resolution is split in two steps:

• prediction:

ρ s -→ V (n) -→ ρ s - → V ( * ) ( ρ s σ V I -∇ 2 ) -→ V * + Re∇π n = - → S n,n-1 V - Re F 2 (ρ n+1 -ρ s ) -→ z
supplemented by the no-slip condition -→ V * = 0 on the boundaries.

• correction:

ρ s - → V (n+1) = ρ s -→ V ( * ) + ∇φ, where φ is calculated in order to satisfy ∇ (ρ s -→ V (n+1) ) = 0
In order to ensure at each time step the correct heat flux [START_REF] Daube | Déclenchement de la convection Rayleigh Bénard dans l'He 3 au voisinage du point critique, 19ème Congrès Français de Mécanique[END_REF], the following procedure holds: In a preprocessing step, a particular problem is solved:

( ρ s σ T I -∇ 2 ) T = 0 in Ω (18) ∂ T ∂x (0, z) = ∂ T ∂x (A, z) = 0 (19) T (x, 0) = 1 (20)
T (x, 1) = 0

and its solution T is stored. During the time marching process described in section 6, the energy equation ( 12) is solved with an arbitrary value T b of the temperature along the bottom plate, yielding a provisional field T . The actual temperature filed T reads then

T = T + λ T
where λ is computed in order to satisfy the flux condition [START_REF] Daube | Déclenchement de la convection Rayleigh Bénard dans l'He 3 au voisinage du point critique, 19ème Congrès Français de Mécanique[END_REF].

STATE EQUATION

A parametric state equation defined in [START_REF] Rudnick | Test of a new field-theoretical crossover equation of state[END_REF] is used to describe the (P, ρ, T ) dependence for supercritical 3 He. This equation includes a regular part which matches the properties of the fluid far away of the critical point and a singular part containing the universality of the fluid behavior close to the critical point, especially the critical exponents.

VALIDATION

The results reported in this section are performed on a horizontal cell of aspect ratio A = L/H = 4. A grid points 769 × 129 is used on a uniform mesh in the x direction and on a non-uniform hyperbolic tangent mesh in the z direction.

Criterion for convection onset

The code has been tested first by finding the Rayleigh-Schwarzschild criterion of the convection onset. According to [START_REF] Carlès | The onset of free convection near the liquidvapour critical point-part I: Stationary initial state[END_REF], the threshold of the instability onset is given by the modified Rayleigh number:

Ra mod = ρ 2 c c p gβH 4 kµ ( ∆T H -g T i β c p ) ≥ Ra c
Where ∆T H is the temperature gradient between the horizontal walls and g T i β cp the adiabatic temperature gradient ATG. For a distance to the critical point ϵ = 0.02, ATG is equal to 0.034 mK/cm. The critical Rayleigh number Ra c which depends on the boundary layers is equal to 1708 for a configuration with two solid walls [START_REF] Akiyama | Experiments on the onset of longitudinal vortices in laminar forced convection between horizontal plates[END_REF]. The critical temperature difference between the horizontal walls at which the convection starts is then given by: ∆T onset = AT G × H + Ra c (kµ/ρ 2 c c p gβH 3 ). In order to determine the stability threshold, we plot the total reduced kinetic energy E c as a function of the modified Rayleigh number when the bottom wall is maintained at a uniform temperature or subjected to a uniform heat flux. The total kinetic energy is equal to 2 shows the variations of E k versus the modified Rayleigh number. With a uniform temperature, the transition to a convective motion occurs at a critical value Ra c ≃ 1811 and the corresponding temperature difference ∆T between the horizontal walls is equal to 0.041 mK. In the case of a uniform heat flux, the transition is located close to Ra c ≃ 1743 for the range 7.4 × 10 -5 < q < 7.5 × 10 -5 W/m 2 .

E k = 1 2 ∫ 1 0 ∫ A 0 ρV 2 dxdz. Figure

Impact of the piston effect

When the heating starts, the fluid temperature inside the cavity increases rapidly due to the piston effect. Owing to the high compressibility and the very small diffusivity, the heating from below induces the appearance of three distinct zones : two thermal boundary layers near the top and bottom walls in which heat transfer is done by diffusion and the bulk of cavity which heated up adiabatically and homogeneously. The presence of the piston effect modifies the temperature field compared with an ordinary process of diffusion.

Figure 3 shows profiles of the reduced temperature (T -T z=H )/θ at different instants, where θ = qH Tck is a scale of the temperature difference. In the diffusion regime, typical profiles of temperatures are characterized by a rapid and homogeneous temperature in the bulk region during action of the piston effect. The characteristic time of the piston effect is t ep = 0.18s while the diffusion time t D = 5.4 × 10 2 s. The piston effect is equal to t ep = t D (γ-1) 2 [START_REF] Onuki | Fast adiabatic equilibration in a singlecomponent fluid near the liquid vapor critical point[END_REF], and the diffusion characteristic time is equal

T D = H 2 k/ρccp
where k/ρ c c p denotes the thermal diffusivity at critical density for the ideal gas.

NUMERICAL SIMULATIONS

In this section, we are interested in fluid heated from below with a uniform heating q = 1.69 × 10 -3 W/m 2 and for a distance to the critical point ϵ = 0.02. This configuration allows comparison between our numerical results and experiments available in the literature [START_REF] Furukawa | Convection in a very compressible fluid: Comparison of simulations with experiments[END_REF]. The simulations are based on thermophysical properties :

c p = 2.19 × 10 5 J/kg/K, k = 1.89 × 10 -2 W/m/K; µ = 1.83 × 10

Comparison with experimental data

Figure 4 displays time evolutions of the temperature difference ∆T (t) obtained from computations and experimental data of reference [START_REF] Furukawa | Convection in a very compressible fluid: Comparison of simulations with experiments[END_REF]. The simulations were carried out with different state equations of 3 He near its critical point : the parametric law according to [START_REF] Rudnick | Test of a new field-theoretical crossover equation of state[END_REF] and analytic laws (Van der Walls, Redlich Kwong). One can observe that the profiles related to analytic laws are identical. All the relaxation curves show similar behavior : an initial phase with a quasi-linear evolution until attaining a maximum (first peak since the heating starts) followed by a second phase characterized by damped oscillations before reaching a quasi-steady state. These oscillations have also been observed experimentally and are attributed to the interaction between the diffusion and piston effect [START_REF] Amiroudine | Piston-effect-induced thermal oscillations at the Rayleigh Benard threshold in supercritical 3 He[END_REF]. Note that the curve relating to the parametric law shows better agreement with the experimental results, in particular the period of pseudo oscillations and the quasi-steady value of ∆T (t). On the other hand, the return "from below" to the asymptotic state observed experimentally is not found in the calculations as in all published numerical simulations. Note finally that the relaxation curves strongly depend on the heating flux q and the proximity to the critical point ϵ as shown in experiments of Kogan and Meyer [START_REF] Kogan | Heat transfer and convective onset in a compressible fluid: 3 He near the critical point[END_REF], [START_REF] Meyer | Onset of convection in a very compressible fluids: the transient toward steady state[END_REF]. To examine the impact of aspect ratio on the ∆T (t) profiles, simulations were carried out with three values A = 4, 8 and 16. We point out that the experiments were conducted in a shallow cavity with aspect ratio equal to 57. The numerical results displayed in figure 5 reveal once again deviations between experiment and simulations during the transient phase. The high of the first peak remains larger in simulations and does not vary with the aspect ratio. For A = 16, the amplitudes of damped oscillations are lower than for A = 4 or A = 8 but the locations of extrema are not well synchronized with experimental data.

Convection onset

We examine first the influence of aspect ratio on the convection onset. Figure 6 shows transient profiles of ∆T and total kinetic energy as function of time for three values (A = 4, 8, 16) on a short period up to 40s. The figure shows principally two phases: a first one where the kinetic energy is insignificant, followed by a second one where the kinetic energy increases rapidly and attains a maximum which coincides with the maximum of ∆T profile. As can be seen, the convection is triggered at the same time whatever the aspect ratio before the profiles merge during the ascent phase. Snapshots of the kinetic energy are displayed in figure 7 at t ≃ 17s to evidence this point. Only the left half of each cavity is represented since the profiles of kinetic energy are symmetric. One can see that the convective starts first at the edges in the same proportions regardless the aspect ratio. Figure 8 shows snapshots of temperature fields at different instants for a cavity with aspect ratio A = 8. The corresponding times are marked on figure 9 to locate them on the ∆T profile. During the initial phase, figures 8(A,B) exhibits temperature fields still dominated by the diffusive regime although weak irregularities appear on the isotherms of fig. 8(B). Figure 8(C) shows the development of thermal plumes at the extremities then gradually cover the whole space between the horizontal walls as ∆T increases. On figure 6, the first peak of kinetic energy located at t ≃ 30s indicates that convection has developed substantially which nearly coincides with the maximum of ∆T (t).

at time t = 32s , figure 8 (D) shows that a cooling is initiated as a result of the fluid movement from the cold top region to the bottom. When approaching the second pick (minimum), an excess cooling leads to an homogeneous temperature in the bulk which is the signature of the piston effect (fig. 8(E) at t ≃ 36s). Figures 8(F,G) give the temperature profiles corresponding to moments approaching the quasi-steady state. Isotherms display upward and downward thermal plumes arising from the horizontal walls. The role of the piston effect (PE) on the damped oscillations has been described and argued by Amiroudine and Zappoli in [START_REF] Amiroudine | Piston-effect-induced thermal oscillations at the Rayleigh Benard threshold in supercritical 3 He[END_REF]. According to their description, when the bulk temperature increases sufficiently (thermal plumes cover the whole space after the heating starts), the temperature gradient at the cold top boundary increases. The cold piston effect is then operative driving the cold fluid downwards. It leads to a decrease of the temperature and to the first peak in the ∆T profile. An excess cooling of the bulk increases the temperature gradient at the bottom boundary. The hot piston effect becomes then dominant driving the hot fluid upwards, thus producing a minimum in ∆T , and so on.

Conclusion

We presented a hydrodynamic model to study Rayleigh-Bénard convection in supercritical fluids within an anelastic approximation. The model is then applied to two-dimensional numerical simulations of a thin layer of supercritical 3 He heated from below, in the same conditions as in experiments mentioned in [START_REF] Furukawa | Convection in a very compressible fluid: Comparison of simulations with experiments[END_REF]. A parametric state equation is used which has the advantage to reproduce accurately physical properties of the fluid near the critical point. The main results in this study are summarized as follows:

• Rayleigh-Schwarzchild instability criterion for the convection onset has been highlighted in the presence of the piston effect.

• Numerical profile of ∆T (t) exhibits deviations with experimental curve during the initial phase but agree well at quasi-steady state. The use of a parametric state equation gives better results than do analytic laws.

• Convection onset does not change with the the aspect ratio.

  Greek symbols β isobaric thermal expansion, K -1 γ ratio of specific heats ∆T Temperature difference between the horizontal walls, µK ε reduced temperature parameter, ε = T i -Tc Tc θ scale of the temperature difference, θ = qH Tck κ thermal conductivity, W -1 K -1 µ dynamic viscosity, kgm -1 s -1

Figure 1 :

 1 Figure 1: Supercritial 3 He in Rayleigh-Benard configuration.

Figure 2 :

 2 Figure 2: Total kinetic energy versus the modified Rayleigh number.

Figure 3 :

 3 Figure 3: Vertical profiles of temperature at x = 0.5 for q = 1.69 × 10 -3 W/m 2 and ϵ = 0.02.

  -6 m 2 /s and β = -1 ρ ∂ρ ∂T = 22.1K -1 . The other dimensionless parameters are : Re = 139, P r = 21.2, Eu = 8 × 10 7 , F = 3 × 10 2 and γ = 55.4. The time step ∆t is equal to 1/10 of the characteristic time of the piston effect t ep . The values of time scales are 0.18s and 540s for t ep and T D respectively.

Figure 4 :

 4 Figure 4: Experimental and numerical profiles ∆T (t) from 2D computations for q = 1.69 × 10 -3 W/m 2 , ϵ = 0.02 and aspect ratio A = 2.

Figure 5 :

 5 Figure 5: Comparison between experimental and numerical profiles of ∆T (t) for q = 1.69 × 10 -3 W/m 2 at ϵ = 0.02 and aspect ratios A = 4, 8, 16.

Figure 6 :

 6 Figure 6: Time evolution of the kinetic energy E c and ∆T for A = 4, 8, 16.

Figure 7 :

 7 Figure 7: Snapshot of Kinetic energy for A = 4, 8, 16 at time t ≃ 17s.

Figure 8 :Figure 9 :

 89 Figure 8: Temperature fields at different instants : q = 1.69 × 10 -3 W/m 2 , ϵ = 0.02 and A = 8.

Acknowledgements

We are grateful to Pierre Carlès for his contribution and thank him for providing us with experimental data.

List of Figures


François Rodrigues

Jean-Baptiste Philit

Irina Giurgea

Dany Anglicheau

Jean-Jacques Roux

Nadia Hoyeau

Gilles Grateau

Laurence Cuisset

Sophie Georgin- Lavialle

Sophie Georgin-Lavialle
email: sophie.georgin-lavialle@aphp.fr

AA amyloidosis revealing mevalonate kinase deficiency: A report of 20 cases including two new French cases and a comprehensive review of literature

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

Manuscript (1237 words)

Introduction

Mevalonate kinase deficiency (MKD) is a rare monogenic autosomal recessive autoinflammatory disease [START_REF] Schulert | Mevalonate kinase deficiency: current perspectives[END_REF] caused mutations in MVK, the gene for coding the mevalonate kinase protein. The disease typically starts during the first months of life. The common features include recurrent fever associated with one or more of the following features: lymphadenopathy, mouth ulcers, arthralgia, headache, vomiting, abdominal pain, vaccine reaction and rash. In absence of accurate diagnosis and persistence of systemic chronic inflammation, MKD may be complicated by inflammatory A amyloidosis (AA) that can result in kidney failure and death.

To study the occurrence and prognosis of AA in MKD patients we performed a literature review of all published cases from 1947 to 2019 and a retrospective study of all French cases collected through the national referral center for inflammatory amyloidosis and hereditary recurrent fevers.

Methods

Pubmed and Medline databases were searched from 1947 to May 20th, 2019 for relevant articles using the keywords "amyloidosis" "mevalonate kinase deficiency" and "hyper IgD syndrome". All relevant articles were retrieved, and additional references quoted in these articles were checked by manual research. Abstracts from the congress of Familial Mediterranean Fever and Systemic Auto-inflammatory Diseases (ISSAID) and from the congress of Pediatric Rhumatology European Society were searched on titles from 2001 to 2019 and 1994 to 2019, respectively, for relevant articles.

Case reports

A 62-year old female patient of Spanish origin suffered since the age of 18 months from bouts of fever, abdominal pain, vomiting, arthromyalgias, cervical lymphadenopathy and oral ulcers, lasting one week and occurring twice monthly. She was referred to a nephrology clinic with proteinuria and AA was diagnosed by renal biopsy. Nephrotic syndrome and end stage renal failure requiring hemodialysis occurred respectively four and seven years later. At the age of 71 she presented to the emergency department for abdominal pain and constipation. CT scan showed a colic occlusion with sigmoid stenosis caused by an endoluminal mass.

Duodenal and sigmoid biopsies were positive for AA (figure 1). She refused any intervention and died two months later. Next-generation sequencing of a panel of 62 genes linked to autoinflammatory syndromes revealed two heterozygous mutations (I268T and V377I) in the MVK gene.

A 33-year old male of North African origin was referred to our reference center for exploration of renal and digestive AA amyloidosis. His parents were consanguineous. One brother and one sister had died at the ages of 8 and 5 respectively and had both been suffering from unexplained recurring fever since the first months of life. The patient suffered from fever, abdominal pain, vomiting, otitis and odynophagia episodes since the age of one. He displayed a growth delay and proteinuria since childhood. AA amyloid deposits were demonstrated on renal, duodenal and rectal biopsies at the age of 13 (figure 2). He went on to develop end-stage renal disease requiring hemodialysis at the age of 20. At that time he was not eligible for renal transplantation because of severe cachexia and malabsorption due to AA amyloidosis. Colchicine had been given since childhood with no effect. At the age of 28 years he started monthly injections with tocilizumab, which resulted in marked diminution of febrile episodes, diarrhea and weight gain. One year later the patient underwent renal transplantation.

To date, he continues the treatment with tocilizumab. Targeted Sanger sequencing of MEFV, MVK, NLRP3, TNFRSF11A revealed two heterozygous variants (N205D and G336S) in MVK gene.

Results

Our keyword research found 44 references, of which 7 were relevant [START_REF] Obici | First report of systemic reactive (AA) amyloidosis in a patient with the hyperimmunoglobulinemia D with periodic fever syndrome[END_REF][START_REF] Cavoli | Renal amyloidosis due to hyper-IgD syndrome[END_REF][START_REF] Lane | AA amyloidosis complicating the hereditary periodic fever syndromes[END_REF][START_REF] Kolsky | P02-015 -A novel MVK mutation in a child with AA amyloid[END_REF][START_REF] Kallianidis | Amyloid A amyloidosis secondary to hyper IgD syndrome and response to IL-1 blockage therapy[END_REF][START_REF] Lachmann | AA amyloidosis complicating hyperimmunoglobulinemia D with periodic fever syndrome: A report of two cases[END_REF][START_REF] Rowczenio | Two cases of AA amyloidosis complication Hyper-IgD and periodic fever syndrome (HIDS) diagnosed at the UK national amyloidosis centre[END_REF] . Manual research allowed five additional references to be added [START_REF] Ostuni | Atypical hypergammaglobulinaemia D syndrome with amyloidosis: an overlap with familial Mediterranean fever?[END_REF][START_REF] Siewert | Hereditary Periodic Fever With Systemic Amyloidosis: Is Hyper-IgD Syndrome Really a Benign Disease?[END_REF][START_REF] Dusunsel | Amyloidosis in a child with Hyperimmunoglobulin D syndrome[END_REF][START_REF] Ter Haar | The Phenotype and Genotype of Mevalonate Kinase Deficiency: A Series of 114 Cases From the Eurofever Registry: PHENOTYPE AND GENOTYPE OF MKD[END_REF] . Nineteen patients suffering from both MKD and AA amyloidosis were described in the literature, and we retained MKD diagnosis in eighteen of them. The excluded patient was clinically asymptomatic at the age of 47, carried two nonpathogenic MVK variants (S52N a likely benign variant and D386N a variant of unknown significance) and no measurement of mevalonate kinase enzymatic activity was available [START_REF] Lane | AA amyloidosis complicating the hereditary periodic fever syndromes[END_REF] .

A total of 20 cases were studied, two novel French patients and eighteen cases from literature described in eleven articles from 1996 to 2017 (table 1). Given a current estimate of 300 patients suffering from MKD worldwide [START_REF] Ter Haar | Recommendations for the management of autoinflammatory diseases[END_REF] , the prevalence of AA is thus roughly estimated at about 6% of all MKD cases. Among the 20 patients with AA and MKD, 13 were men and 7 women with a median age of 26.5 years at AA diagnosis (extremes 4-62 years). The origin of the patients was varied: Northern Europe (n = 7), Italy (n = 3), Eastern Europe (n = 3), Great Britain (n = 3), Germany (n = 1), Spain (n = 1), Algeria (n=1) and Turkey (n = 1). With the exception of one patient [START_REF] Ter Haar | The Phenotype and Genotype of Mevalonate Kinase Deficiency: A Series of 114 Cases From the Eurofever Registry: PHENOTYPE AND GENOTYPE OF MKD[END_REF] , the diagnosis of MKD was always made after that of AA in this series. MKD clinical signs had always started in the first 4 years of life. The median delay between the first symptoms and MKD diagnosis was 24 years ranging from 4 to 70 years.

MVK gene sequencing was performed in all but one patient and systematically revealed two pathogenic heterozygous mutations. The most common genotype was V377I/I268T (n=9).

The main clinical signs of amyloidosis were nephrotic syndrome (n=15), isolated end stage renal disease (n=5) or nephrotic syndrome with end stage renal disease (n=8) and, less frequently, intestinal occlusion (n=1) or malabsorption (n=1). AA was histologically proven on kidney biopsy (n=18), digestive tract biopsy (n=5), as well as thyroid (n=1) and bronchial (n=1) tissue samples. The youngest patient was a 4 years girl, who was misdiagnosed with PFAPA syndrome [START_REF] Kolsky | P02-015 -A novel MVK mutation in a child with AA amyloid[END_REF] . Interestingly, two patients from Turkey and Algeria were wrongly diagnosed with familial Mediterranean fever because the prevalence of this autoinflammatory disease is particularly high in this regions [START_REF] Dusunsel | Amyloidosis in a child with Hyperimmunoglobulin D syndrome[END_REF] .

Five patients died including two before the era of biotherapy; nine underwent a kidney transplant. Colchicine was tried in 7 patients, in the hypothesis of familial Mediterranean fever or PFAPA syndrome but was never effective. Several biotherapies have been used effectively: anti interleukine-1 type anakinra (n = 8, one success, five partial responses, two failures); anti-TNF alpha fusion protein etanercept (n = 7, four successes, one partial response, two failures); anti-interleukin 6 tocilizumab (n = 5, four successes, one partial response). AA amyloidosis relapsed on three kidney grafts.

Discussion

This study describes clinical, biological and genetic characteristics of 20 patients with mevalonate kinase deficiency and AA amyloidosis. Diagnosis of MKD can be made late in life, secondary to the diagnosis of AA amyloidosis. To date we estimate that around 6% of all patients with MKD, in whom the diagnosis was missed, develop AA amyloidosis with a mortality rate of 25%. This estimation must be met with caution, since the actual prevalence of MKD is unknown and since our analysis of case reports is subject to selection and publication bias. Our results are congruent with those of Ter Haar et al [START_REF] Ter Haar | The Phenotype and Genotype of Mevalonate Kinase Deficiency: A Series of 114 Cases From the Eurofever Registry: PHENOTYPE AND GENOTYPE OF MKD[END_REF] , who described 5 patients with amyloidosis among a cohort of 114 MKD patients belonging to the Eurofever registry. In Ter Haar's series, rough prevalence estimate was of 4.3%, two patients out of five died of amyloidosis, and four patients out of five were diagnosed MKD after AA amyloidosis.

In our series, all reported cases but one [START_REF] Ter Haar | The Phenotype and Genotype of Mevalonate Kinase Deficiency: A Series of 114 Cases From the Eurofever Registry: PHENOTYPE AND GENOTYPE OF MKD[END_REF] received the MKD diagnosis after AA amyloidosis discovery, underscoring that this autoinflammatory disorder is still underdiagnosed. We highlight the importance of an early targeted gene sequencing to begin treatment and prevent the onset of AA, especially as the clinical presentation of MKD can mimic other autoinflammatory disease such as PFAPA and familial Mediterranean fever. Misdiagnosis is therapeutically relevant since colchicine is inefficient in mevalonate kinase deficiency in contrast to the two former autoinflammatory conditions [START_REF] Schulert | Mevalonate kinase deficiency: current perspectives[END_REF][START_REF] Ter Haar | Recommendations for the management of autoinflammatory diseases[END_REF] . Patients with AA complicating MKD can benefit from a kidney transplant. Nevertheless, all MKD patients with AA should receive biotherapy targeting proinflammatory cytokines including anti-IL-1, anti-TNF or anti-IL6 receptor. Indeed, this data show that AA amyloidosis can relapse on the grafted kidney if the disease is not controlled after transplantation.

Regarding genotypes, 83% (15/18) of patients had variants located between the 205 to 268 aminoacids and 50% (9/18) of patients harbored the V3771/I268T genotype, which is fairly common in MKD.

In conclusion, early diagnosis of MKD is essential to start an effective treatment, such as a biotherapy targeting interleukins 1 or 6, in order to avoid systemic inflammation and thus to prevent AA occurrence.

Figure

  Figure's legends:

Figure 1 .

 1 Figure 1. Rectal mucosa biopsies of patient 19 showing amorphous eosinophilic amyloid deposits green-apple birefringence in polarized light. A: rectal mucosa, HES. B: zoom on vascular deposits, HES. C: Red Sirius without polarization microscopy. D: Red Sirius applegreen refringence with polarization microscopy. E: thioflavin-T staining with fluorescent microscopy. Staining was positive with anti-AA antibody and negative with anti-kappa and anti-lambda antibodies (not shown).

Figure 2 .

 2 Figure 2.

Table 1 :

 1 Main features of the 16 patients.

	.

Table 1 :

 1 Main features of the 16 patients..

	Patient	Se	Age on	Age on	Age on	Diagno	MVK mutation Origin	Death Treatme
	number	x	AA	MKD	first	sis				nt by a
	[and		diagno	diagno	MKD	delay				biologic
	referen		sis	sis	sympto	(years)				agent
	ce]		(years)	(years)	ms
					(years)
	1 9	M 28	33	1	33	NA	Italian		No
	2 2	M 27	27	1	27	V377I/L265R	Italian		No
	3 7	M 19	19	1	19	V377I/I268T	British		Anti IL1
	4 12	M 37	27	3	24	V377I/I268T	British		Anti IL1
	5 7	M 22	22	1	22	V377I/L234P	Germa		Anti TNF
								n
	6 10	M 22	22	1	22	H20P/V250I	Wester	yes	Anti TNF
								n
								Europe
								an
	7 3	M 29	29	1	29	NA	Italian		Anti IL1
	8 11	M 7	7	1	7	G326R/V377I	Turkish		Anti TNF
	9 4	M 23	23	NA	23	V377I/L234P	Northe		Anti IL1
								rn		Anti IL6
								Europe
								an
	10 4	M 15	15	1	15	V377I/I268T	Northe	yes	Anti IL1
								rn
								Europe
								an
	11 4	F	26	26	1	26	V377I/I268T	Northe		Anti TNF
								rn
								Europe
								an
	12 6	F	62	62	NA	62	V377I/I268T	Europe	yes	Anti IL1
								an
	13 12	M 39	43	2	41	V377I/L234P	Europe		Anti IL1
								an		Anti IL6
										Anti TNF
	14 12	F	27	27	4	23	V377I/I268T	Europe	yes	No
								an
	15 12	F	8	18	0.1	18	V377I/I268T	Europe	yes	No
								an
	16 5	F	4	4	2	4	V377I/C152W Europe		Anti IL1
								an
	17 8	F	32	32	1	31	V377I/I268T	Europe	no	No
								an
	18 8	M 42	42	3	39	G336S/V377I/	Europe	no	No
							S52N	an


Ambre Lauret

Anna Moltó

Vered Abitbol

Loriane Gutermann

Ornella Conort

François Chast

Claire Goulvestre

Claire Le Jeunne

Stanislas Chaussade

Christian Roux

Frédéric Batteux

Maxime Dougados

Yannick Allanore

Jérôme Avouac
email: jerome.avouac@cch.aphp.fr

Pr Jérôme Avouac

Effects of successive switches to different biosimilars infliximab on immunogenicity in chronic inflammatory diseases in daily clinical practice

Keywords: infliximab, CT-P13, SB2, biosimilar, immunogenicity, anti-drug antibodies

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

The use of targeted biological treatments has transformed the entire management of chronic inflammatory disorders. Since a few years, the expiration of their patents had led to the deveopment of biosimilar products, allowing a reduction of health expenditure. Biosimilars being complex molecules, their development need strict comparability study. [START_REF] Gabbani | CT-P13: design, development, and place in therapy[END_REF] Regarding Infliximab, the first biosimilar CT-P13 entered the market in Europe in 2013 and United

States in 2016, with the same indications than the innovator. Biosimilarity between CT-P13 and its innovator has been demonstrated by non-clinical and clinical studies including two pivotal clinical studies (PLANETRA and PLANETAS). [START_REF] Yoo | A randomised, double-blind, parallel-group study to demonstrate equivalence in efficacy and safety of CT-P13 compared with innovator infliximab when coadministered with methotrexate in patients with active rheumatoid arthritis: the PLANETRA study[END_REF][START_REF] Park | Comparable long-term efficacy, as assessed by patient-reported outcomes, safety and pharmacokinetics, of CT-P13 and reference infliximab in patients with ankylosing spondylitis: 54-week results from the randomized, parallel-group PLANETAS study[END_REF] In addition, systematic nonmedical switch from innovator Infliximab to its biosimilar CT-P13 in inflammatory chronic diseases in real clinical practice setting was associated with no significant changes in objective clinical parameters. [START_REF] Avouac | Systematic switch from innovator infliximab to biosimilar infliximab in inflammatory chronic diseases in daily clinical practice: The experience of Cochin University Hospital, Paris, France[END_REF][START_REF] Glintborg | Drug concentrations and anti-drug antibodies during treatment with biosimilar infliximab (CT-P13) in routine care[END_REF] Then, other biosimilars have been approved, such as SB2 in 2017. [START_REF] Smolen | Safety, immunogenicity and efficacy after switching from reference infliximab to biosimilar SB2 compared with continuing reference infliximab and SB2 in patients with rheumatoid arthritis: results of a randomised, doubleblind, phase III transition study[END_REF] Currently, immunogenicity constitutes one important concern about these therapies. Indeed, it is known that the presence of anti-drug antibodies (ADA) is associated with a decrease of trough-serum drug levels, lower clinical response and more side effects. [START_REF] Park | Comparable long-term efficacy, as assessed by patient-reported outcomes, safety and pharmacokinetics, of CT-P13 and reference infliximab in patients with ankylosing spondylitis: 54-week results from the randomized, parallel-group PLANETAS study[END_REF][START_REF] Tanaka | Safety and efficacy of CT-P13 in Japanese patients with rheumatoid arthritis in an extension phase or after switching from infliximab[END_REF] Infliximab is one of the most immunogenic anti-tumor necrosis factor (anti-TNF)-α therapies; thus the prevention of the immunization and the clinical management of its consequences is a key clinical issue. [START_REF] Braun | Switching to biosimilar infliximab (CT-P13): Evidence of clinical safety, effectiveness and impact on public health[END_REF] According to previous clinical studies, ADA directed against innovator Infliximab recognize and bind CT-P13, illustrating that these two treatments may have common immunodominant epitopes. [START_REF] Becciolini | A review of the literature analyzing benefits and concerns of infliximab biosimilar CT-P13 for the treatment of rheumatologic diseases: focus on interchangeability[END_REF] For this reason, it is necessary to ensure that switch to biosimilar is not associated with increased risk of immunisation. Although previous studies were reassuring, they did not evaluate successive switches in the same patient and follow-up period was limited.

Therefore, the main objective of this study was to evaluate in a usual care setting the risk and factors influencing immunogenicity i) in patients who experienced successive non-medical switches from innovator infliximab to a first then a second biosimilar infliximab, and ii) in patients who switched from a first to a second biosimilar infliximab. Another objective of this study was to integrate these results to previous published data through a comprehensive metaanalysis following a systematic literature research.

METHODS

Study design:

A prospective observational usual care study was conducted in Rheumatology, Gastroenterology and Internal Medicine departments of Cochin Hospital.

Study population: Two independent cohorts were constituted; the first cohort, named cohort-1, included patients who were on maintenance therapy with the original treatment before the successive non-medical switches to biosimilars. [START_REF] Avouac | Systematic switch from innovator infliximab to biosimilar infliximab in inflammatory chronic diseases in daily clinical practice: The experience of Cochin University Hospital, Paris, France[END_REF] The second cohort, named cohort-2, included biologic-naive patients who received a first infliximab biosimilar before being nonmedically switched to a second.

Inclusion criteria: All patients followed-up in Cochin Hospital, on maintenance therapy with innovator infliximab, and considered controlled for their disease according to their treating physician, were systematically screened for inclusion in cohort-1. Adult patients who agreed to switch to CTP-13, and who had received at least 3 infusions of innovator infliximab prior to the switch, were eligible for inclusion in this cohort. [START_REF] Avouac | Systematic switch from innovator infliximab to biosimilar infliximab in inflammatory chronic diseases in daily clinical practice: The experience of Cochin University Hospital, Paris, France[END_REF] Adult patients, naive of infliximab, who initiated CT-P13 and agreed to participate to the study were eligible for inclusion in cohort-2.

All included patients agreed to participate in the study after receiving informed consent, which was recorded in the medical source file. The protocol and the informed consent document have received Institutional Review Board/Independent Ethics Committee (IRB/IEC) approval before initiation of the study ("Comité de Protection des Personnes", Paris Ile de France I). Clinical and laboratory data: Data were collected at each patient visit through a face-to-face interview and with the validation from the medical file in a standardized case-report form that included: diagnoses; demographic parameters (age, gender, disease duration, body mass index, BMI) ; current and past medication use (including concomitant treatment with methotrexate), duration of treatment with innovator infliximab, number of infusions and dose of the last infusion.

Setting

Infliximab trough levels and anti-drug antibodies (ADA) were assessed in the morning prior to each infusion using a validated enzyme-linked immune-absorbent assay (ELISA, LISA-TRACKER Duo Infliximab, Theradiag, Croissy-Beaubourg, France). This kit which has been validated for the detection of ADA and the measurement of infliximab trough levels in patients treated with innovator and biosimilar infliximab. The Intra-assay coefficient of variation ranged from 4.1% to 8.5% for the detection of ADA and from 3.9% to 11% for the measurement of infliximab trough levels. The Inter-assay coefficient of variation ranged from 10.2% to 15.8% for the detection of ADA and from 8.2% to 17.3% for the measurement of infliximab trough levels. Immunogenicity was defined by the detection of positive anti-drug antibodies (ADA ≥10 ng/mL), at least at two consecutive time points.

Primary Outcome of the study:

The primary outcome of the study was the development of immunogenicity during the observation period.

Secondary outcomes: Secondary outcomes were i) the point prevalence of positive ADA at baseline visit in cohort-1, ii) the influence of the successive switches to biosimilars on the risk of immunogenicity in both cohorts, iii) factors associated with ADA generation in both cohorts, iv) the impact of ADA positivity on treatment discontinuation and v) the retention rate of biosimilar infliximab at the end of the observation period in both cohorts.

Statistical analysis:

All data are expressed as mean values ± standard deviation (SD) or number and percentage (%) for continuous and categorical variables, accordingly. Statistical analysis was performed using Medcalc (v18.9.1). To seek for associations between the presence of ADA and potential risk factors of immunization at baseline in cohort 1, we used the unpaired t-test for two-group comparisons (continuous variables) and the chi-square test for differences in frequency (binary variables). Retention rate of biosimilar infliximab was estimated by Kaplan-Meier survival curves. To identify predictive factors of ADA generation in cohorts 1 and 2, we used cox proportional-hazard regression.

Systematic literature research and meta-analysis:

Eligible studies were studies reporting the incidence of ADA occurrence in patients who switched from innovator to a biosimilar infliximab or who were initiated with a biosimilar infliximab. We included observational studies, for whom The Meta-analyses of Observational Studies in Epidemiology (MOOSE) guidelines were followed and randomized controled trials (RCTs). [START_REF] Stroup | Meta-analysis of observational studies in epidemiology: a proposal for reporting. Meta-analysis Of Observational Studies in Epidemiology (MOOSE) group[END_REF] We searched MEDLINE and Embase databases between January 1960 and April 2019 using the terms (biosimilar OR infliximab OR CT-P13 OR SB2) AND (immunogenicity OR anti-drug antibodies). The Medical subject heading (MeSH) terms were used for all databases, and a keyword search was substituted when the MeSH search was not available.

All MeSH search terms were exploded. In addition, reference lists of the papers initially detected were searched by hand to identify additional relevant reports. No language restriction was applied. Eligibility of references retrieved by the search was assessed independently by two of the authors (A.L. and J.A.) and disagreements resolved at each step. We selected studies that reported sufficient data to calculate the incidence of ADA seroconversion. Data were extracted from the selected studies using a predefined standardized form. Quality assessment of individual observational studies was performed using the Newcastle-Ottawa Scale. This scale, specific for cohort or case-control studies, uses a star rating system (range: 0-9 stars) scoring three aspects of the study: selection of groups, comparability and ascertainment of the outcome of interest. The quality of RCTs was evaluated with the Jadad scale. [START_REF] Jadad | Assessing the quality of reports of randomized clinical trials: is blinding necessary?[END_REF] It contains two questions for randomization and masking and one question evaluating the reporting of withdrawals and dropouts. Each question entails a yes or no response option. In total, five points can be awarded, with higher scores indicating superior quality.

We calculated in each study a proportion based on the number of patients with positive ADA among the total number of patients. Each individual prevalence was first transformed into a quantity via the Freeman-Tukey variance-stabilizing transformation. A weighted mean of the transformed proportions was calculated, using a DerSimonian-Laird random effects model.

The combined prevalence was calculated as the back-transform of this weighted mean. [START_REF] Freeman | Transformations Related to the Angular and the Square Root[END_REF][START_REF] Dersimonian | Meta-analysis in clinical trials[END_REF] Statistical heterogeneity was tested by Q-test (χ2). This test allows description of the percentage of total variation across trials that is attributable to statistical heterogeneity rather than chance. I2-values of 25, 50 and 75% correspond to low, moderate and high between-trial heterogeneity of results, respectively. [START_REF] Higgins | Quantifying heterogeneity in a meta-analysis[END_REF][START_REF] Higgins | Measuring inconsistency in metaanalyses[END_REF] Fixed and random-effects models based on Qstatistics for heterogeneity were used for homogeneous and heterogeneous trials, respectively. MedCalc software Medcalc (v18.9.1) was used for all these analyses.

RESULTS

Study population

Cohort-1 was constituted of 265 patients on maintenance therapy with innovator infliximab who systematically switched to a first biosimilar infliximab (CT-P13) (Table 1): 135 patients had axial spodyloarthrits (axSpA) (51%), 64 inflammatory bowel diseases (IBD) (24%), 31 reumatoid arthritis (RA), 22 psoriatic arthrits (PsA) (8%), 8 uveitis (3%) and 5 other chronic inflammatory diseases (3 vasculitis and 2 AA amyloidosis) (2%). Among these 265 patients, 140 patients switched to the second biosimilar infliximab (SB2), starting from December 2017 (including 72 patients with axSPA, 38 with IBD and 15 with RA) (Table 2), 26 remained treated with CT-P13, and innovator infliximab was re-established in 55 patients, mainly due to experienced inefficacy of CT-P13 (47/55, 85%) (Figure 1A). Of note, innovator infliximab was re-established in 19 patients after the first biosimilar infusion, 14 after the second infusion, 17 after the third infusion and 5 after >3 infusions.

A total of 60 patients experienced treatment discontinuation during the observation period. At the time of treatment discontinuation, 39 patients were receiving CT-P13, 8 SB2 following CT-P13, and 13 innovator infliximab. Discontinuation was related to primary or secondary loss of efficacy (n=26), side effects (n=20, including 4 infusion-related reactions), diagnosis of neoplasia (n=6), sustained remission (n=6), and death (n=2).

Cohort-2 consisted of 44 patients naive of infliximab who initiated a treatment with CT-P13: 20 with AxSpA (45.5%), 9 with IBD (20.5%), 9 with RA (20.5%), 4 with PsA (9%) and 2 with other chronic inflammatory diseases (one patient with Behcet disease and one with undifferentiated arthritis) (4.5%) (Table 1). Among these patients, 29 switched to SB2 (including 11 with AXSpA, 8 with IBD and 7 with RA) (Table 2), 5 remained treated with CT-P13 and 10 discontinued the treatment before the switch to SB2 (Figure 1B). A total of 15 patients experienced treatment discontinuation during the observation period, including 5 patients who have interrupted their treatment after the switch. Causes of discontinuation were primary or secondary lack of efficacy (10 patients), occurrence of side effects (n=4, including 2 infusion-related reactions) and diagnosis of lymphoma in a single patient.

Analysis of the primary outcome

Cohort-1

Among the 235 ADA negative patients at baseline, 20 patients developed ADA during the 3year observation period (8.5%), corresponding to a rate of 3 for 100 patient years. All patients with positive ADA had undetectable infliximab trough levels (<0.30 µg/mL). ADA titers ranged from 10 to >200 ng/mL, and 15/20 patients had titers >200 ng/mL. The incidence of ADA development was 11% in AxSpA (13/120 patients), 3.5% in IBD (2/57 patients), 8% in RA (2/25 patients) and 10% in PsA (2/20 patients). Positive ADA were detected in 10 patients during exposition to CT-P13 and 6 during exposition to SB2. Four patients were back to innovator INF at the time of ADA seroconversion. The mean time to ADA seroconversion was 22±13 months (range: 1-36 months). The majority of patients who developed ADA during the observation period (16/20, 80%) had received innovator infliximab for more than 24 months prior to the switch (Table S1).

Cohort-2

In infliximab-naive patients, 11/44 (25%) patients developed ADA during the observation period, corresponding to a rate of 14 for 100 patients years. All patients with positive ADA had undetectable infliximab trough levels (<0.30 µg/mL). The incidence of ADA development was 20% in AxSpA (4/20 patients), 22% in IBD (2/9 patients), 44% in RA (4/9 patients) and 25% in PsA (1/4 patients). The mean time to positive ADA detection was 13±11 months (range: 1-31 months).

Analysis of secondary outcomes

Point prevalence and outcome of patients with positive ADA at baseline visit in cohort-1

Positive ADA were detected in 30 patients (11.3%, 16 females) at baseline visit (first infusion of CT-P13). All these patients had and undetectable infliximab trough levels (<0.30 µg/mL). Among these 30 patients, 15/135 had axSpA (11%), 6/31 RA (19%), 7/64 IBD (11%) and 2/21 PSa (10%). No significant association was observed between presence of ADA and age, gender, type of disease and concomitant methotrexate or other conventional synthetic disease modifying anti-rheumatic drugs (DMARDs). No association was observed between ADA detection and treatment with methotrexate after adjustment to disease type. Patients with positive ADA at baseline visit were more likely to have a BMI >30 (14/30, 45% vs. 40/235, 17%, p<0.001) and received less innovator infliximab infusions (28±20 vs. 40±25 infusions, p=0.012) than patients with negative ADA. Among these 30 patients, 13 (43%) discontinued infliximab during the observation period (11 treated with CTP-13 and 2 with innovator infliximab), due to loss of efficacy (n=10), side effects (n=2 infusion-related reactions) and diagnosis of neoplasia (n=1). 12 of these patients switched from CT-P13 to SB2, which was maintained until the end of the observation period. Interstingly, 7 of these patients had gradual conversion to seronegative status, with parallel increase of infliximab trough levels, whereas ADA seropositivity persisted in 5 patients with undetectable infliximab trough levels.

In addition, 5 patients were maintained with innovator infliximab up to the end of the obervation period with a good clinical response according to their treating physician, despite all of them had constant positive ADA detection and undetectable infliximab trough levels (<0.30 ug/mL).

Influence of the successive switches to biosimilars on the risk of immunogenicity

Kaplan Meyer curves illustrating ADA-free survival of the 235 ADA negative patients at baseline from cohort-1 showed no influence of the number of received INF biosimilars on ADA development during the observation period (Figure 2).

In cohort-2, among the 29/44 (66%) CTP13-treated patients who switched to SB2, only a single patient developed ADA (Figure 1B).

Factors associated with ADA generation

No predictive factor of immunogenicity was identified in cohort-1, including type of disease, age, sex, BMI or concomitant methotrexate or other conventional synthetic DMARD intake.

In cohort-2, a BMI >30 at baseline visit and mean infliximab through levels <2 ug/mL from baseline visit to seroconversion were predictive of the development of ADA with Hazard Ratio (95% confidence interval, CI) of 5.54 (1.30-23.65) and 5.53 (1.30-23.43), respectively (Table S2).

Influence of immunogenicity on treatment maintenance

Cohort-1

The risk of treatment discontinuation was significantly higher in patients with positive ADA at baseline visit or during follow-up compared to patients without ADA (Hazard Ratio 2.37, 95% confidence interval 1.38-4.05, p=0.002) (Figure 3A). Moreover, patients who discontinued infliximab (n=60) were more likely to have positive ADA (20/60, 33%) compared to patients still treated with infliximab (30/205, 15%) (p=0.002).

Among the 26 patients who discontinued infliximab because of primary or secondary loss of efficacy, 12 had positive ADA. Four patients stopped infliximab because of an infusionrelated reaction, and all of them were ADA positive.

Cohort-2

The risk of treatment discontinuation was also significantly higher in patients with positive ADA during the observation period compared to patients without ADA (Hazard Ratio 2.79, 95% confidence interval 1.04-7.52, p=0.042) (Figure 3B). Among the 10 patients who stopped infliximab because of of primary or secondary loss of efficacy, 4 were tested positive for ADA. Two patients stopped their treatment because of an infusion-related reaction, and both were tested positive for ADA.

Retention rate of biosimilar infliximab at the end of the observation period

The retention rate of biosimilar infliximab in cohort-1 was 58% (155/265) at the end of observation period, including 132 patients treated with SB2 and 23 who remained treated with CT-P13 (Figure S1A).

The retention rate of biosimilar infliximab in cohort-2 was 66% (29/44) at the end of observation period, including 24 patients treated with SB2 and 4 who were treated with CT-P13 (Figure S1B).

Meta-analysis integrating our results to data collected from a systematic literature search

The selection of studies included in the meta-analysis is summarized in Figure S2 and Table S3. Out of 263 articles identified, 16 were finally included, representing a total of 2979 patient. We identified 6 studies (1 RCT and 5 observational studies) that analyzed the incidence of ADA development after the switch from innovator infliximab to CTP-13, representing 971 patients. The pooled incidence of ADA occurrence in this population was 5.2% (95% CI 2.8-8.3%). This result was based on random effects model because of significant heterogeneity (Cochran Q=16.53 for 5 degrees of freedom, DF, p=0.006). After removing the RCT, the pooled incidence was 3.8% (95% CI 2.6-5.2%) and no heterogeneity was observed (Q=3.09 for 4 DF, p=0.543). After inclusion of our results obtained from cohort-1, the incidence was 4.7% (95% CI 3.5-6.1%; Figure 4A), with no significant heterogeneity (Q=10.9 for 5 DF, p=0.052).

Twelve studies assessed the occurrence of ADA in innovator infliximab-naive patients that received CPT-13, representing 2008 patients. The pooled incidence of ADA occurrence in this population was 28% (95% CI 17.8-39.2). This result was also based on random effects model because of substantial heterogeneity (Cochran Q=320 for 11 DF, p<0.001). When considering observational studies, and after incusion of our results obtained from cohort-2, the incidence was 21.1% (95% CI 13.1-30.3%; Figure 4B), with reduced but still significant heterogeneity (Q=11.02 for 3 DF, p=0.012). When considering RCTs, the incidence was 30.7% (95% CI 18.2-44.9%) with substantial heterogeneity (Q=289 for 8 DF, p<0.001).

DISCUSSION

Our study brings some original and relevant specificities, including the inclusion of patients that received 3 different infliximab molecules, allowing the demonstration of a comparable immunization rate regardless of the number of biosimilars received. In addition, patients were followed during observation period of 3 years, which is longer than in most previous studies.

We also assessed the mean time to ADA detection, which was 21.19±13.7 months in cohort-1 and 12.8±10.8 months in cohort 2, supporting that ADA seroconversion occurs during the first months in infliximab-naive patients.

The rate of ADA seroconversion was 8.5% in patients receiving biosimilars Infliximab who were previously receiving the original molecule. In previous studies assessing the switch from innovator to biosimilar Infliximab, this rate varied from 2.4% to 14.8%, [START_REF] Smolen | Safety, immunogenicity and efficacy after switching from reference infliximab to biosimilar SB2 compared with continuing reference infliximab and SB2 in patients with rheumatoid arthritis: results of a randomised, doubleblind, phase III transition study[END_REF][START_REF] Smits | Drug Survival and Immunogenicity After Switching From Remicade to Biosimilar CT-P13 in Inflammatory Bowel Disease Patients: Two-year Follow-up of a Prospective Observational Cohort Study[END_REF][START_REF] Smits | Long-Term Clinical Outcomes After Switching from Remicade® to Biosimilar CT-P13 in Inflammatory Bowel Disease[END_REF][START_REF] Smits | Clinical Outcomes Following a Switch from Remicade® to the Biosimilar CT-P13 in Inflammatory Bowel Disease Patients: A Prospective Observational Cohort Study[END_REF] and the pooled incidence was 4.7% in our meta-analysis. This is concordant with our results, considering also the variability of diagnoses, patients'characteristics, concomitant immunosuppressive therapies and treatment duration. Moreover, the successive use of 2 biosimilars in our cohort did not increase the risk of immunogenicity compared to previous studies that analyzed the use of a single biosimilar only. PLANETRA and PLANETAS studies found higher immunization rates: 44.8% and 27.4% at 48 weeks after the switch, respectively, [START_REF] Yoo | A randomised, double-blind, parallel-group study to demonstrate equivalence in efficacy and safety of CT-P13 compared with innovator infliximab when coadministered with methotrexate in patients with active rheumatoid arthritis: the PLANETRA study[END_REF][START_REF] Park | Comparable long-term efficacy, as assessed by patient-reported outcomes, safety and pharmacokinetics, of CT-P13 and reference infliximab in patients with ankylosing spondylitis: 54-week results from the randomized, parallel-group PLANETAS study[END_REF] but they include patients already immunized at baseline. Including patients with positive ADA at baseline visit, the rate of immunization in cohort 1 was 19%, close to what was observed in PLANETAS, considering that the majority of patients had axSpA in our cohort. These results are reassuring for clinical practice in case of interchangeability between innovator to biosimilars, as reported in the literature. [START_REF] Glintborg | Drug concentrations and anti-drug antibodies during treatment with biosimilar infliximab (CT-P13) in routine care[END_REF][START_REF] Smolen | Safety, immunogenicity and efficacy after switching from reference infliximab to biosimilar SB2 compared with continuing reference infliximab and SB2 in patients with rheumatoid arthritis: results of a randomised, doubleblind, phase III transition study[END_REF][START_REF] Tanaka | Safety and efficacy of CT-P13 in Japanese patients with rheumatoid arthritis in an extension phase or after switching from infliximab[END_REF][START_REF] Smits | Drug Survival and Immunogenicity After Switching From Remicade to Biosimilar CT-P13 in Inflammatory Bowel Disease Patients: Two-year Follow-up of a Prospective Observational Cohort Study[END_REF][START_REF] Smits | Long-Term Clinical Outcomes After Switching from Remicade® to Biosimilar CT-P13 in Inflammatory Bowel Disease[END_REF][START_REF] Smits | Clinical Outcomes Following a Switch from Remicade® to the Biosimilar CT-P13 in Inflammatory Bowel Disease Patients: A Prospective Observational Cohort Study[END_REF][START_REF] Eberl | Switching maintenance infliximab therapy to biosimilar infliximab in inflammatory bowel disease patients[END_REF][START_REF] Yoo | Efficacy and safety of CT-P13 (biosimilar infliximab) in patients with rheumatoid arthritis: comparison between switching from reference infliximab to CT-P13 and continuing CT-P13 in the PLANETRA extension study[END_REF][START_REF] Park | Efficacy and safety of switching from reference infliximab to CT-P13 compared with maintenance of CT-P13 in ankylosing spondylitis: 102week data from the PLANETAS extension study[END_REF][START_REF] Plevris | Implementation of CT-P13 via a Managed Switch Programme in Crohn's Disease: 12-Month Real-World Outcomes[END_REF][START_REF] Alten | Randomised, double-blind, phase III study comparing the infliximab biosimilar, PF-06438179/GP1111, with reference infliximab: efficacy, safety and immunogenicity from week 30 to week 54[END_REF] The rate of ADA seroconversion was 25% in infliximab-naive patients who received biosimilars Infliximab during the observation period. In the literature, immunization rates ranged from 8.0% to 62.4% in this population and the pooled incidence was 21% in our meta-analysis of observational studies. [START_REF] Jørgensen | Switching from originator infliximab to biosimilar CT-P13 compared with maintained treatment with originator infliximab (NOR-SWITCH): a 52-week, randomised, double-blind, non-inferiority trial[END_REF][START_REF] Smolen | Comparing biosimilar SB2 with reference infliximab after 54 weeks of a double-blind trial: clinical, structural and safety results[END_REF] These measures were highly variables across studies since they depended of the study power, patients'characteristics or methods of ADA detection. We observed a higher rate of ADA seroconversion in cohort-2 compared to cohort-1. This difference may partly be explained by the exlusion of the 30 patients with positive ADA at baseline visit in cohort-1. Thus, we followed patients who did not developed ADA within a long exposition period upon innovator infliximab, and these patients may have a lower probability of further having ADA, given that ADA seroconversion usually occurs during the first months of treatment. BMI>30 was associated with ADA positivity at baseline visit in cohort-1 and predicted ADA seroconversion in cohort-2. The impact of high BMI on ADA development and reduction of anti-TNF-α efficacy has already been reported. A higher BMI could be responsible of an inflammatory role of fat tissues by the production of multiple pro-inflammatory cytokines. [START_REF] Hwang | Higher body mass index and anti-drug antibodies predict the discontinuation of anti-TNF agents in Korean patients with axial spondyloarthritis[END_REF][START_REF] Højgaard | The influence of obesity on response to tumour necrosis factor-α inhibitors in psoriatic arthritis: results from the DANBIO and ICEBIO registries[END_REF][START_REF] Gremese | Body weight, gender and response to TNF-α blockers in axial spondyloarthritis[END_REF] Thus, this parameter is primordial and needs to be taken into account in clinical practice, by tighter monitoring or dose adaptation, in order to avoid treatment discontinuation.

In cohort-2, a low concentration of infliximab trough serum levels was predictive of ADA seroconversion. This is consistent with previous data showing a reduced risk of immunization with higher doses of infliximab, leading to increased infliximab trough serum levels. [START_REF] Tanaka | Safety and efficacy of CT-P13 in Japanese patients with rheumatoid arthritis in an extension phase or after switching from infliximab[END_REF][START_REF] Braun | Switching to biosimilar infliximab (CT-P13): Evidence of clinical safety, effectiveness and impact on public health[END_REF][START_REF] Vande Casteele | The relationship between infliximab concentrations, antibodies to infliximab and disease activity in Crohn's disease[END_REF] Concomitant treatment with Methotrexate or other conventional synthetic DMARDs was not found as a potent protective factor of immunogenicity in both cohorts, considering the entire population of after adjustment to disease type, illustrating the disparate findings of previous study results about the protective role of these treatments on immunogenicity. [START_REF] Braun | Switching to biosimilar infliximab (CT-P13): Evidence of clinical safety, effectiveness and impact on public health[END_REF][START_REF] Maini | Infliximab (chimeric anti-tumour necrosis factor α monoclonal antibody) versus placebo in rheumatoid arthritis patients receiving concomitant methotrexate: a randomised phase III trial[END_REF][START_REF] Baert | Influence of immunogenicity on the long-term efficacy of infliximab in Crohn's disease[END_REF][START_REF] Bendtzen | Individualized monitoring of drug bioavailability and immunogenicity in rheumatoid arthritis patients treated with the tumor necrosis factor alpha inhibitor infliximab[END_REF][START_REF] Strik | Suppression of anti-drug antibodies to infliximab or adalimumab with the addition of an immunomodulator in patients with inflammatory bowel disease[END_REF][START_REF] Mellstedt | Clinical considerations for biosimilar antibodies[END_REF] However, in cohort 2, a non-significant trend for a protective effect of MTX was observed, and the absence of significativity may be explained by the limited sample size of this cohort.

Patients with ADA had an increased risk of treatment discontinuation, which was mainly due to primary or secondary lack of efficacy. Of note, a subset of patients who interrupted infliximab because of insufficient efficacy were tested negative for ADA (14 in cohort 1, 6 in cohort 2), suggesting either a failure of the mechanism of action of TNF-α inhibitors or a potential lack of sensitivity of the assay. Infusion-related reactions were not frequently observed (4 in cohort-1, 2 in cohort-2), and all occurred in patients with positive ADA, as previously reported. [START_REF] Tanaka | Safety and efficacy of CT-P13 in Japanese patients with rheumatoid arthritis in an extension phase or after switching from infliximab[END_REF][START_REF] Yoo | Efficacy and safety of CT-P13 (biosimilar infliximab) in patients with rheumatoid arthritis: comparison between switching from reference infliximab to CT-P13 and continuing CT-P13 in the PLANETRA extension study[END_REF][START_REF] Strand | Immunogenicity of Biologics in Chronic Inflammatory Diseases: A Systematic Review[END_REF][START_REF] Reinisch | Evaluation of the Cross-reactivity of Antidrug Antibodies to CT-P13 and Infliximab Reference Product (Remicade): An Analysis Using Immunoassays Tagged with Both Agents[END_REF] It is important to note that physicians were not blinded for ADA status, and ADA positivity may have influenced the choice of treatment discontinuation.

The retention rates of patients treated by biosimilars were 58% in cohort-1 and 55% in cohort-2 at the end of the observation period. The retention rates were 66% at 2 years in patients suffering from inflammatory bowel diseases, [START_REF] Smits | Drug Survival and Immunogenicity After Switching From Remicade to Biosimilar CT-P13 in Inflammatory Bowel Disease Patients: Two-year Follow-up of a Prospective Observational Cohort Study[END_REF] 44% at 2 years in PLANETRA, [START_REF] Yoo | Efficacy and safety of CT-P13 (biosimilar infliximab) in patients with rheumatoid arthritis: comparison between switching from reference infliximab to CT-P13 and continuing CT-P13 in the PLANETRA extension study[END_REF] and 64,8% in PLANETAS, [START_REF] Park | Efficacy and safety of switching from reference infliximab to CT-P13 compared with maintenance of CT-P13 in ankylosing spondylitis: 102week data from the PLANETAS extension study[END_REF] and differences with our study may be related to variable obervation periods and inclusion of a larger panel of chronic inflammatory disorders.

Our study is limited by the small size of the second cohort, making difficult to compare across disease populations. Patients from cohort-1 were all correctly controled with innovator infliximab before the switch. Therefore, our results may not be extrapolated to a random population of patients who receive biosimilar infliximab or who are inadequately managed with innovator infliximab. Being observational, our study lacks the proper control of continuing originator infliximab ,without switching to biosimilars infliximab, in to provide framework to the observations noted. Moreover, we had insufficient data to robustly examine the relationship between doses of infliximab and ADA generation.

ADAs were detected only in patients with undetectable infliximab trough levels and patients with detectable infliximab trough levels all have negative ADAs, which may suggest that the presence of the drug may interfere with the detection of antibodies.

In summary, our study shows that immunogenicity occurrence is not favored by the switch to biosimilars infliximab. However, our data highlight that consequences of immunogenicity are not negligible, with increased risk of allergic reactions and treatment discontinuation.

:

  Patients from cohort-1 were switched at inclusion visit to biosimilar infliximab CT-P13 at the same dose and frequency as innovator infliximab, between October and December 2015. Then, the second switch from CT-P13 to the second biosimilar infliximab SB2 started in December 2017 (minimum exposure time on CT-P13 before the second switch to SB2: 23 months). Patients were then evaluated at each infusion visit until the end of the observation period in December 2018. Patients from cohort-2 received their first infusion of bisimilar infliximab CT-P13 between November 2015 and October 2017. The switch to the second biosimilar infliximab SB2 occured in December 2017 (minimum exposure on CT-P13 time before the switch to SB2: 2 months) and patients were evaluated at each infusion visit until December 2018.

Figure 1 :Figure 2 :

 12 Figure 1: Flow Chart illustrating the switch to the different biosimilars infliximab (INF: Infliximab) Figure 2: Immunogenicity-free survival illustrating the influence of the number of received INF biosimilars on immunogenicity in cohort-1, in the 235 patients ADA-free at baseline

Figure 3 :Figure 4 :

 34 Figure 3: Influence of immunization on treatment discontinuation in cohort-1 (A) and cohort-2 (B) (FU: Follow-up) Figure 4: forest plots illustrating the meta-analysis of observational studies of the incidence of ADA development after the switch from innovator infliximab to CTP-13 (A) and the incidence of ADA development in patients who were initiated with a biosimilar infliximab (B).

Jerome Avouac has received reseach grant and honoraria from PFIZER Maxime Dougados has participated to advisory boards related to biosimilars organized by BIOGEN, AMGEN and PFIZER Financial support: None

TABLES AND FIGURES:


S Marty-Quinternet

L Puget

A Debernardi

R Aubry

N Magy-Bertrand

J L Prétet

C Chirouze

K Bouiller

Dr Quentin Lepiller
email: q1lepiller@chu-besancon.fr

Electrostatic wipes as simple and reliable methods for influenza virus airborne detection

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

INTRODUCTION

Transmission of respiratory viruses is mediated by large secreted droplets (> 5 µm), released by cough, sneeze, talk or breath, that fall rapidly by gravitational settling in front of the infected subject, and by small aerosol particles (also called droplet nuclei, < 5 µm) which remain suspended longer in air and spread over greater distances [START_REF] Pan | Collection, particle sizing and detection of airborne viruses[END_REF].

Aerosol transmission of common respiratory viruses, such as influenza virus, is often neglected in healthcare setting compared to droplet transmission, although growing evidence supports its role in epidemic and/or nosocomial spread of viruses [START_REF] Blachere | Measurement of airborne influenza virus in a hospital emergency department[END_REF][START_REF] Leung | Quantification of Influenza Virus RNA in Aerosols in Patient Rooms[END_REF][START_REF] Lindsley | Distribution of airborne influenza virus and respiratory syncytial virus in an urgent care medical clinic[END_REF].

One hurdle to overcome for identifying and managing aerosol transmission is the lack of simple and inexpensive samplers for airborne viruses. Here, we assessed the relevance of commercialized electrostatic wipes (EW) as simple and reliable supports for the detection of virus-containing aerosols. We particularly characterized the performance of an in-house protocol for virus elution and detection from this support and investigated its possible application during a seasonal flu outbreak through a pilot study.

METHODS

Virus preparation

Viral stocks of cytomegalovirus (CMV) and adenovirus (ADV), dedicated to validate the performance of our protocol for virus detection on EW, were obtained by virus propagation on MRC5 fibroblasts as previously described [START_REF] Lepiller | HCMV activates the IL-6-JAK-STAT3 axis in HepG2 cells and primary human hepatocytes[END_REF]. Influenza A virus (IAV) was obtained from a respiratory sample, collected for routine molecular analysis in our institution. Viral nucleic acid extraction and amplification by (RT)-PCR were performed using commercial kits listed below.

Study population of the pilot study

Detection of IAV-containing aerosols on EW was performed in the hospital rooms of influenza-infected patients in the Departments of Geriatrics and Internal Medicine, Besançon University Hospital, France. All patients were informed of the presence of the wipes and agreed. Since the presence of the wipes did not interfere with patient care, the local ethics committee was not consulted for this pilot study.

Electrostatic wipes contamination and exposure

Four types of commercialized EW (surface 315 cm²) were tested (brands APTA®, CEDAR®, TOUS LES JOURS®, and CASINO®) for virus detection. To validate the protocol, EW were impregnated with suspensions of CMV, ADV or IAV, dried at room temperature from 1 to 4 days depending on the experiment, and stored at -80°C until viral nucleic acid extraction. For the pilot study, EW were placed in open plastic boxes, 1.80 m above the headboard, in influenza-infected patients' rooms during the acute phase of infection (< 48h after symptom onset). After 48h of exposure, EW were collected and stored in their plastic boxes at -80°C.

Plastic boxes were disinfected (Surfanios®, Anios®, Lille-Hellemmes, France) after each use and residual contamination by IAV RNA was checked by swabbing the plastic surface and performing an influenza-specific RT-PCR.

Viral elution from electrostatic wipes and nucleic acid amplification

After viral exposure or experimental contamination, each wipe was put in a sealed plastic bag with 5 mL of a washing solution (PBS) containing 0.1% Tween 80 (Merck®, Darmstadt, Germany) and shaken for 10 minutes in a Stomacher® (AES®, Combourg, France). Two (± 0.5) mL of washing solution was collected and centrifuged (60 minutes; 9500 g; 4°C). Viral RNA and DNA were extracted from 500 µL of the pellet using the Nucleospin® RNA virus and the NucleoSpin® DNA blood (Macherey-Nagel) kits, respectively, and amplified by (RT)-PCR using the R-DiaFlu® (Diagenode), CMV R-gene® (Biomérieux) and Adenovirus R-gene® (Biomérieux) kits. Since our protocol includes a detergent solution (washing solution) that may greatly impact the infectivity of viruses (especially in the case of enveloped viruses), we did not try to isolate the biologically active viruses by cell culture after the elution step.

RESULTS AND DISCUSSION

Analytical performance of the protocol

To estimate the recovery efficiency and the repeatability of our protocol, 4 types of commercialized EW were impregnated in quadruplicate with 100 µl of a suspension of CMV (5.87 log10 copies/ml) or ADV (5.86 log10 copies/ml) and dried at room temperature for one day until virus elution and DNA extraction. CMV and ADV were chosen as model for enveloped and non-enveloped viruses, respectively, to validate the protocol due to their ease of use, propagation in cell culture and quantification. The mean concentrations of CMV DNA and ADV DNA eluted from these 16 wipes were 4.48 log10 copies/ml (average loss of CMV DNA by the elution protocol = -1.39 log10 copies/ml; concentration ratio = 76.3%) and 4.21 log10 copies/ml (average loss of ADV DNA = -1.65 log10 copies/ml; concentration ratio = 71.7%), respectively. Standard deviations (SD) between the 16 measures were 0.21 log10 copies/ml (coefficient of variation CV = 4.79%) and 0.29 log10 copies/ml (CV = 6.85%) for CMV and ADV, respectively, resulting in a mean SD of 0.25 log10 copies/ml (CV = 5.82%). To confirm these results for IAV, 2 types of wipes were impregnated in triplicate with a suspension of IAV (5.11 log10 copies/ml). The average loss of IAV RNA during the elution protocol was -1.27 log10 copies/ml (concentration ratio = 75.1%), and SD between the measures was 0.27 log10 copies/ml (CV = 7.05%).

To estimate the detection limit of our protocol, EW were impregnated with serial dilutions of CMV, ADV or IAV suspensions, with amounts ranging from 2 to 6 log10 gene copies of viral nucleic acid, in 7 distinct trials, and dried for one day at room temperature prior to viral elution and nucleic acid extraction. The detection limit was defined as the smallest amount of nucleic acid detectable in 7/7 trials [START_REF] Hospodsky | Accuracy, Precision, and Method Detection Limits of Quantitative PCR for Airborne Bacteria and Fungi[END_REF]. With our protocol, this limit was obtained at 4.7 log10 gene copies (50 000 gene copies), for both CMV and ADV suspensions, and 4 log10 gene copies (10 000 gene copies) for IAV (Table I).

Since IAV has only a brief survival on porous surfaces [START_REF] Bean | Survival of influenza viruses on environmental surfaces[END_REF], we aimed to estimate the duration of influenza RNA stability on the EW. For that purpose, two types of EW (brands APTA® and CEDAR®) were impregnated with a suspension of IAV (5.11 log10 copies/ml) and dried at room temperature from 1 to 4 days. The amount of influenza RNA eluted from the EW did not significantly differ during this period, suggesting a good stability of the viral RNA on EW during at least 4 days (Figure 1).

EW have been proposed as interesting surrogates for the assessment of indoor airborne microbial exposure (i.e., with bacteria and fungi) [START_REF] Frankel | Comparison of sampling methods for the assessment of indoor microbial exposure[END_REF]. However, no data is currently available for virus detection on EW and no comparison with other sampling methods has been performed. Comparing the performance between available samplers for airborne viruses is impeded by the variety of their designs (mainly based on impaction, liquid impingement, filtration, and electrostatic precipitation of viral particles [START_REF] Pan | Collection, particle sizing and detection of airborne viruses[END_REF]) and by the lack of standardized performance criteria. Repeatability, recovery efficiency, detection limit, and RNA stability, were chosen as main parameters to validate the performance of our in-house protocol for virus detection on EW. Since the repeatability of our protocol was close to the required repeatability of PCR assays dedicated to human diagnostic (SD < 0.25 log10 copies/ml according to the French guidelines [9]) we conclude in suitable repeatability of our technique. A relevant sampler for virus-containing airborne particles should be sensitive enough to detect the infectious doses of virus inhaled by exposed subjects. Previous work has estimated that the inhalation doses of IAV ranged from 1.35 x 10 4 to 1.07 x 10 5 gene copies of virus for exposures of 1h to 8h [START_REF] Nikitin | Influenza virus aerosols in the air and their infectiousness[END_REF]. With an observed detection limit at 1 x 10 4 gene copies of viral RNA, we suggest that our protocol is sensitive enough to detect airborne infectious doses of IAV. This suggestion was further confirmed through a pilot study in influenza-infected patients' rooms.

Pilot study in influenza-infected patients' rooms

Thirty-two EW were placed in the hospital rooms of influenza-infected adult patients (mean age = 85 years, range: 42 -101 years), during the acute phase of infection (< 48h after symptom onset), high enough to exclude any droplet contamination (1.80 m above the headboard). After 48h of exposure, IAV RNA was detectable in 75% (n=24) of EW. The mean concentration of IAV RNA eluted from these wipes was 3.36 log10 copies/ml, ranging from 2.14 to 4.43 log10 copies/ml. This result suggests that our method detects IAV-containing aerosols in a hospital setting.

Several methods have been proposed to detect airborne influenza in healthcare settings. By using NIOSH cyclone or 6-stage Andersen samplers, IAV was detectable in 17.4% to 50% of samples obtained in emergency departments or in influenza-infected patients' rooms [START_REF] Blachere | Measurement of airborne influenza virus in a hospital emergency department[END_REF][START_REF] Leung | Quantification of Influenza Virus RNA in Aerosols in Patient Rooms[END_REF][START_REF] Lindsley | Distribution of airborne influenza virus and respiratory syncytial virus in an urgent care medical clinic[END_REF].

Most of these studies highlighted a high proportion of influenza RNA in aerosols < 4 µm, suggesting an important part of small aerosols during IAV transmission. Our technique does not measure the size distribution of virus-containing airborne particles or the fraction of biologically active virus inside, and it requires a longer time of exposure than cyclone-based methods. However, its low cost and ease of use make it an attractive alternative to traditional samplers for monitoring airborne IAV contaminations.

COMPETING INTERESTS: None declared

TABLES AND FIGURES

Table I: Detection limit of viruses on electrostatic wipes. EW were impregnated with suspensions of CMV, ADV and IAV, containing from 2 to 6 log10 gene copies of viral nucleic acid. The detection limit was defined as the smallest amount of DNA detectable in 7/7 trials [START_REF] Hospodsky | Accuracy, Precision, and Method Detection Limits of Quantitative PCR for Airborne Bacteria and Fungi[END_REF].