Alexander Rassloff
email: alexander.rassloff@tu-dresden.de

Sascha Heitkam
email: s.heitkam@hzdr.de

Gaetan Dalongeville

Christian Gauthier
email: christian.gauthier@ics-cnrs.unistra.fr

Thierry Roland
email: thierry.roland@ics-cnrs.unistra.fr

Alexander Raßloff

Gaëtan Dalongeville

FEM-simulation of gas diffusion in solid closed-cell porous materials

Keywords: Gas diffusion, Void material, Numerical simulation, Finite element method, Gas diffusion coefficient

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

Introduction

Solid foams and other porous closed-cell structures are of great interest in engineering [START_REF] Gibson | Cellular Solids: Structure and Properties[END_REF]. They are lightweight, insulating and shock-absorbing. The advancement in production techniques paves the way to new structures and geometries. For this reason, understanding porous materials' properties and applications is of significant interest. The objective of this paper is to provide a method for the simulation of gas diffusion in closed-cell porous material under mechanical load and to document first findings. Within this work, all materials are considered to contain only closed pores or cells. This gas diffusion phenomenon has been experimentally shown in several polymeric natures of foams, among them polypropylene foams [START_REF] Bouix | Polypropylene foam behaviour under dynamic loadings: Strain rate, density and microstructure effects[END_REF]. In this work, using specific compression tests in a fluid chamber, Bouix et al. pointed up a progressive and slow gas escapes during the whole deformation process of foams subjected to quasi-static compression. In the same manner, putting a closed-cell foam in a reduced environmental pressure we showed by X-ray tomographic reconstruction a tendency for the pore structure to collapse as gas diffuse out. Figure 1 is an illustration of the evolution of the structure. It shows on the left side the initial state of the thermoplastic closed-cell foam and on the right one the collapse configuration as pores are empty of gas and experience ambient pressure. This demonstrates how diffusion can be related to problem of dimensional stability during storage of foam or semifoam product. Also, this diffusivity process may be quite fast. For instance, the PU foam blown with CO 2 shows some shrinkage within two months after its production as a significant reduction of the pore pressure is attained [START_REF] Alsoy | Modeling of diffusion in closed cell polymeric foams[END_REF].

Knowing about the degassing behaviour of porous materials, especially about the time scale, is of major importance to industry as the lifetime of such products is strongly related to it. Elasticity and insulation properties depend on the kind and amount of gas contained in the material's pores. Also, since several blowing agents are about to phased out under recent international regulations for chemical uses (REACH), understanding how different gases affect the ageing behaviour is a prerequisite for the development of foam with alternative CBA. Thermal insulation boxes lose rigidity and their insulation properties with time, especially under load, when filled with ice, fish or heavy content, as the gas diffuses out of the pores. The same applies to foam sealing, cushioning and many more applications, where porous materials, such as foams, are exposed to long-term loads. In industrial packaging foam-like materials are used to absorb shocks to protect the packed content. Hereby, the absorption behaviour is mainly determined by the amount of gas stored in the wrap or fill material [START_REF] Song | Strain-rate effects on elastic and early cellcollapse responses of a polystyrene foam[END_REF]. The following equation relates the collapse stress to the relative density [START_REF] Gibson | Cellular Solids: Structure and Properties[END_REF]: where σ * pl is the collapse stress of the foam, σ pl the one of the solid material, φ the volume fraction of cell edges in a unit volume and (1 -φ) the remaining fraction of the solid contained in the pore faces, φ * the density of the foam and φ the density of the solid material. Considering this equation ( 1), it was shown that compression at low strain rate leads to plateau stress data lying close to line for φ = 1. This suggests that pores deform primarily through plastic buckling and bending of their edges. However, for high strain rate, collapse stress comes closer to the linear term of the equation (line for φ = 0) which refers to compression and stretching of the pore faces. This apparent higher contribution of the pore faces is mainly due to inertia effects and to the fact that gas bubbles cannot escape from the foam due to the short time. Therefore, the foam strength increases during dynamic loading because of the entrapped gas in the closed pores. As a constantly high absorption level is demanded, there should be no or low change regarding the properties of this material, i.e. negligible gas diffusion. Thus, gas diffusion is a major issue for several applications. To provide reliable and realistic behaviour laws there is a need for a temporal analysis taking into account both mechanics and gas diffusion. This problematic concerns polymer foams but beyond that others materials as cork stoppers for which oxygen transfer across the pore walls was demonstrated to follow a Fickian mechanism [START_REF] Lequin | Diffusion of oxygen in cork[END_REF]. However, comparatively few attempts have been made to numerically simulate gas diffusion in realistic porous materials. Previous research concentrated on theoretical models to predict effective diffusion coefficients. Alsoy [START_REF] Alsoy | Modeling of diffusion in closed cell polymeric foams[END_REF] compares existing approaches for this calculation for closed-cell polymeric foams.

σ * pl σ pl = 0.3 φ ρ * ρ 1.5 + 0.4 (1 -φ) ρ * ρ (1)
She makes comparisons between their theoretical predictions and experimental values. An algorithm for a one-dimensional simulation of pore concentration change due to diffusion is presented, relying on several as-sumptions. It requires a network of cubic pores with constant wall thickness, i. e. uniform and constant pore sizes, a homogeneous and isotropic foam and diffusion in only one direction. Pilon et al. [START_REF] Pilon | Gas diffusion in closed-cell foams[END_REF] present, likewise on the idea of a cubic unit cell model, an engineering model to predict diffusion coefficients in closed-cell foams. Briscoe and Savvas [START_REF] Briscoe | Gas diffusion in dense poly(ethylene) foams[END_REF] use elastic models with springs and arrays of rectangular pores in a row for the prediction. The idea of the application of the Finite Element Method (FEM) to simulate Fickian mass transport was mentioned by Wadiak [8]. This work shows the usage for a multi-layered polymeric body with no porosity. Nonetheless, it introduced the idea to use existing and effective thermal solvers for diffusion problems. Many projects focus on an experimental approach [START_REF] Rodríguez-Pérez | Gas diffusion in polyolefin foams during creep test. effect on impact behaviour and recovery after creep[END_REF][START_REF] Rodríguez-Pérez | Measuring the time evolution of the gas pressure in closed cell polyolefin foams produced by compression moulding[END_REF][START_REF] Modesti | New experimental method for determination of effective diffusion coefficient of blowing agents in polyurethane foams[END_REF][START_REF] Svanström | Determination of effective diffusion coefficients in rigid polyurethane foam[END_REF] to calculate diffusion coefficients or to investigate gas pressure changes in porous materials.

So far, prior theoretical research was limited to fixed geometries with approximations of wall thickness and areas. It has neglected to provide insight into the diffusion process going on in the material. There are no methods documented that consider directly the interaction between mechanical deformation of the porous material and the diffusion process, especially under changing loads. Therefore, a method is presented to integrate gas diffusion processes into structural mechanic FEM simulations. It allows arbitrary geometries and gas diffusion in three dimensions, is not limited to high foam-porosities and can calculate the process under different, time-dependent load-scenarios. Embedded in a commercial FEA program, MSC Marc, it is comfortable and efficient to use. Major advantage of the present numerical model is the possibility to evaluate the effect of foam structure (pore wall thickness, pore size, porosity distribution, topological arrangement) and possible anisotropic pore shape (often met with industrial foam). But also, to quickly take into account the influence of the polymer material constitutive laws by which we may implicitly reflect different physical states of the material as changes of crystallinity or cross-linking.

Using the analogy between Fickian diffusion and thermal conduction, the thermal solver of the FEA software is used to simulate the diffusion. Due to deformation of the pores and due to gas diffusion, the pore pressures change. In a parallel approach, both are calculated and accumulated for each time step. By this, gas pressure and stress distributions throughout the whole domain are obtained for every time step. Post-processing allows the extraction of characteristic values, e.g. an effective diffusion coefficient.

The method is implemented to simulate two-dimensional configurations under constant load as depicted in figure 2. In particular, the effect of geometrical pore shape on both the ageing profile and the effective diffusion coefficient is discussed based on results from the simulation. When closed-cell foams are produced by expansion, usually at high strain rate, pore elongation is induced in one direction which may results in anisotropic effect of the mass transfer in the polymer.

Methods

Theory of Gas Diffusion in Solid Closed-Cell Porous Materials

Gas diffusion describes the transport of gas in gas, liquid or solid due to the Brownian motion of gas molecules. It is a process in which gas passes from locations of higher concentration to ones of lower concentration. If the locations are separated by a solid, the gas needs to permeate it and diffuse through this material. Diffusion through condensed matter depends on the concerning material, the permeating gas, and on the temperature. Polymers are a group of materials where gas diffusion is relatively fast. Free volume that arises from the gaps left between entangled polymer chains is responsible for this aspect and usually a good correlation is found between diffusion rate and the degree of the macromolecular chains flexibility. Indeed any external force field acting on the molecular chain mobility has an important effect by opening or closing pathways for diffusion. Boersma et al. [START_REF] Boersma | Mobility and solubility of antioxidants and oxygen in glassy polymers. iii. influence of deformation and orientation on oxygen permeability[END_REF] studied the effects of tensile stress applied to plastic films on their oxygen permeation properties and reported an increase in permeation rate with stress. Nonetheless, it can often be neglected for most non-porous materials upon a certain thickness. Gas diffusion in gases is usually several orders of magnitudes faster than diffusion in solids or liquids. Thus, the time scale for diffusion is usually determined by the way gas diffuses through the pore wall. Gas diffusion as consequence of transient chemical bonding is not considered for this paper on solid closed-cell materials.

The basis for all models is Fick's law of diffusion

J = -D∇c (2)
with J the flux of gas mass, c the concentration of gas and D the diffusion coefficient. By taking the massbalance into account Fick's first law of diffusion can be transferred to the fundamental differential equation of diffusion or Fick's second law of diffusion

∂c ∂t = D∇ 2 c. (3)
In this work, it is assumed that the diffusion coefficient D in the solid material is constant, i. e. independent of the local gas concentration and mechanical stress in the solid material. Gas diffusion inside the pores is considered to be infinitely high, yielding homogeneous pressure and concentration inside each pore. For this work, the gaseous environment is considered to consist of a single gas.

The derivation of an analytical solution c( x, t) of this differential equation for complex boundary conditions is not feasible. For this reason, several models for the prediction of effective diffusion coefficients have been developed as mentioned above. We are not aware of any study that simulates complex structures under mechanical load to gain insight into diffusion in porous materials. Nonetheless, prior research helps to understand the basic mechanism that needs to be modelled.

The foam or porous material has either due to its production or due to an external load a higher pressure in its pores than ambient pressure. This causes a concentration imbalance because gas pressure and concentration are linked. In the present study (above the glass transition temperature), Henry's law is applied for this relation

c = S • p (4)
with S being the solubility of the gas in the solid material S s or in the pore S p and p the local gas pressure.

Due to the pressure gradients, the gas diffuses through the walls of the porous solid. By this, it evokes a change of pressure in the pores until an equilibrium is reached. The solubility in pore and solid is considered to be constant. Here, the polymer is considered to be in its rubbery state. It is generally agreed that the solubility depends neither on the gas concentration nor on the hydrostatic pressure applied to the polymer [START_REF] Crank | Diffusion in Polymers[END_REF][START_REF] Crank | The Mathematics of Diffusion[END_REF]. Also, for a wide range of temperature, it appears that variations of the solubility coefficient are less important than variations of the diffusion coefficient. Thus, the variations of D mainly affect the values of the permeability.

Set-up

The two-dimensional model for the numerical simulation is illustrated in figure 2. A block of porous material with a certain width w, height h and porosity φ is subjected to a vertical, mechanical load p load .

Either spherical or elliptical pores of equal volume are arranged either on a Cartesian lattice or are randomly distributed. Pores are well separated from each other and from the boundaries to diminish possible distortion of the meshed domains.

Figure 3 illustrates the boundary and initial conditions applied on the material as collected in table 1. At the top boundary, the integral normal force F load is prescribed on a rigid plate, leading to a timedependent and homogeneous normal displacement of the top boundary. Tangential stress at each node of the top boundary is set to zero. At the bottom boundary, zero normal displacement and zero tangential stress is prescribed by using a rigid plate with fixed displacement. No gas diffusion is allowed at the top and bottom boundary. At the side boundaries, the ambient pressure is applied as a normal mechanical load and tangential load is set to zero. Dimensional quantities are used for the simulations as collected in table 2. They are chosen to represent typical structures and do not resemble any particular porous material. Triangular finite elements of first order (linear -3 nodes) are used for the simulations.

Numerical Method

Fourier's law of thermal conduction and Fick's law share the same structure. Wadiak [START_REF] Wadiak | Application of the finite-element method to the diffusion and reaction of chemical species in multilayered polymeric bodies[END_REF] proposed in 1985 to adapt existing FEM code to solve Fickian mass transport through polymers. Thermal conduction is already implemented in many FEA programs, so in MSC Marc. Exploiting the thermal solver for simulating gas diffusion is the idea behind this approach. For this purpose, both equations are compared, and the quantities of the mass transport are expressed in quantities of Fourier's law.

Assuming constant density ρ, constant specific heat capacity c p and constant thermal conductivity k, as well as no thermal sources, the law of thermal conduction denotes

∂T ∂t = k ρc p ∇ 2 T (5)
with temperature T . For a better comparison Fick's second law of diffusion is written here again, with Henry's law (4) already applied to substitute the concentration c by the pressure p:

∂p ∂t = DS S ∇ 2 p (6)
Comparing both equations ( 5), ( 6) leads to the analogies as collected in table 3. Using the analogy, a thermal analysis is set up to represent a gas diffusion set-up. Gas pressures for the diffusion process (4) are applied in the framework of temperatures and therefore called pseudo-temperature hereafter. The material's diffusion coefficient is linked to the thermal conductivity. At the left and right boundary of the domain the pseudo-temperature is set to ambient pressure. Zero thermal gas flux is prescribed at the top and bottom boundary because the gas must not penetrate these boundaries.

A structural-thermal analysis can be run in MSC Marc and calculates the results. This is a big advantage, as two Marc-inherent solving capabilities can be used. No additional code has to be written for this purpose.

However, to avoid non-physical effects, any influence from the temperature on the mechanical model has to be disabled. To that end, the coefficient of thermal expansion and the dependency of Young's modulus on the temperature are set to zero.

The mechanical pressure has to be linked with the pseudo-temperature around the pores. As temperature and mechanical pressure are two different, but necessary quantities in the FEA, a parallel approach is chosen.

On the one hand, to calculate the mechanically induced change of pressure ∆p mech due to change of volume ∆V in the pore. On the other hand, to obtain the diffusion-induced change ∆p diff from the thermal solver.

Assuming isothermal compression, ideal gas law is applied to determine the pressure in a pore for the next

p i+1 = p i + ∆p i diff + ∆p i mech = p i + ∆p i diff + ∆V i • p i V i . (7)
Based on this idea, a Python script is written to set up and control a diffusion analysis in MSC Marc.

Figure 4 illustrates the algorithm chosen to perform the simulation. The simulation starts by loading and meshing a geometry. The material is defined as pure elastic with a mass density of ρ = 0 to avoid dynamical effects. For the thermal properties of the material the specific heat capacity is set ρ therm c p = S s , too. The thermal conductivity is set to the product of the diffusion coefficient and gas solubility of the bulk material k = DS s (see table 3).

Next, the boundary and initial conditions for mechanical stress, strain and pseudo-temperature are set and one time step is simulated. Now, the new gas pressure inside each pore is calculated with equation [START_REF] Briscoe | Gas diffusion in dense poly(ethylene) foams[END_REF] taking into account the results from the mechanical and thermal simulation.

Since the pores are not material, they are not captured by the meshing, thereby allowing the application of a mechanical pressure on the boundaries of the pores as needed for the simulation. Thus, one supplementary artificial element for each pore is generated to account for the material of the gas. It models the energy content of the respective pore in the thermal solver. From the comparison made between thermal conduction and mass diffusion (table 3) the artificial volume V art of the supplementary element equals V art S s = V pore RT .

Therefore, the specific heat capacity of the supplementary element's material is set c p = V pore /V art • RT /S s .

By linking the supplementary element with the boundary of the respective pore, the correct initial condition for the pseudo-temperature can be imposed. However, mechanical pressures at the interface of the pores can only be applied in the form of boundary conditions, which is not possible during run-time with MSC Marc.

For this reason, the simulation has to be halted after one time step to update the boundary conditions.

Nodal displacement and pseudo-temperature are transferred to the next time step by the help of initial conditions. With this framework, the structural-thermal analysis can be run. The simulated process can be divided into two phases. In the first ten time steps a rather short time step of 10 s is chosen to simulate the yielding due to the mechanical load properly. In this short time, gas diffusion is negligible. After these first steps the time step is increased, so that diffusion effects can be observed.

PDE ∂ t T = (k/ρc p )∇ 2 T S∂ t p = DS∇ 2 p T ↔ p k ↔ DS ρc p ↔ S Storage Q = V c p dT E = V • RT /S s dp in pore V c p ↔ V • RT /S s

Post-Processing

The numerical results are analysed to obtain characteristic values, e. g. characteristic time scales and an effective diffusion coefficient. The results of the simulation are values of pressure at the nodes of the meshed model and in the pores. For an efficient post-processing of the data, the local pressures at the nodes of the unstructured mesh are interpolated to an equidistant, Cartesian mesh. Based on this data, a one-dimensional pressure distribution along the x-direction is obtained by averaging over the y-direction.

As the gas cannot diffuse through the top and bottom side of the model, the diffusion in x-direction is the representative one for this process. Relaxation processes lead to a homogenisation of the pressure distribution in y-direction. It justifies the use of a one-dimensional model for the post-processing, as effective values for the whole structure are of special interest here. Figure 5 shows the contour plot and the corresponding one-dimensional gas-pressure distribution at two different times for a model with 54.4 % porosity and 200 pores. Since the random distribution of pores results is partially imbalanced in vertical direction also the initial amount of gas shows a vertical gradient. This gradient is still present in figure 5 after 6 months. one-dimensional pressure distribution is derived for each time step. The set of these pressure distributions is used to derive characteristic scalars for the diffusion process. A general solution of the diffusion equation ( 6) for homogeneous material is the series of exponentially decaying harmonic functions

p(x, t) = ∞ n=1 Ãn sin πn 2w x exp -D n πn 2w 2 t + p amb (8)
in which Ãn is a constant amplitude and D n the effective diffusion coefficient. The curves of the onedimensional pressure distribution are well presented by one sine-function after a short relaxation time. For this reason, coefficients of higher frequency can be neglected as they give only small distribution. Therefore, the period L of the sine-function in [START_REF] Wadiak | Application of the finite-element method to the diffusion and reaction of chemical species in multilayered polymeric bodies[END_REF] has to equal two widths 2w. From this condition, the relevant sine-function or index n can be determined

L = 2π/ nπ 2w ! = 2w ⇒ n = 2.
The evolution of the second coefficient is relevant for the calculation of an effective diffusion coefficient D eff .

Performing a fast Fourier transform (FFT) in space for each time step of the one-dimensional pressure distribution leads to the values of

A 2 (t) = Ã2 exp -D eff 2π 2w 2 t . (9)
The argument of the exponential function -D eff (2π/2w) 2 t in ( 9) is obtained by fitting the Fourier coefficients in time to an exponential function

A 2 (t) = Ã2 exp - t τ eff (10)
as illustrated in figure 6. Using the characteristic time τ eff of this exponential function, the effective diffusion coefficient D eff for the simulated porous material is derived by

D eff = w 2 τ eff π 2 . ( 11
)
In some cases, the pressure cannot be fitted well to a sine-function, e. g. for inhomogeneously distributed pores. To derive a characteristic time nonetheless, another approach is chosen. A characteristic diffusion time scale τ diff can be derived from the decay of pressure. For this purpose, the pressure distribution is averaged in each time step over the porous material including pores and solid material, resulting in a mean pressure p(t). This mean pressure shows an exponentially decaying behaviour in time. Fitting it to such an exponential function

p(t) = p 0 • exp - t τ diff ( 12
)
leads to the characteristic time τ diff . Similarly, a time scale τ pore can be defined taking into account only the pressure inside all pores to derive the mean pressure ppore .

Grid study

In order to assess the influence of spatial resolution, a convergence study on the mesh is conducted. For this purpose, a simulation is performed using three different resolutions (a, b, c) with increasing numbers of elements. Figure 7 shows sections of the discretized geometries. converge. As the extensive additional cost for the finer discretisation is not justified by this difference, the coarsest element size (a) has been used for this work.

A convergence study in time is conducted as well. Figure 9 shows the mean pressure evolution p(t) on a geometry with 200 randomly distributed pores and a porosity of φ = 50 % for three different lengths of the time step with ∆t = 7, 15, 30 d, respectively. Interpolating the results to the time steps of the simulation with the coarser time discretisation, equation ( 13) is used to calculate the mean deviation. It shows that the influence of the chosen time step is below 0.1 % on the mean pressure.

Results

In the first step, simulations of diffusion through a porous material under load are performed on twodimensional domains (w = h = 100 mm) with either 200 randomly distributed pores or with 25 to 225 pores, arranged equidistantly on a Cartesian lattice.

The one-dimensional pressure curves of all simulations show a characteristic sinusoidal profile after a short relaxation time. This demonstrates that the results agree to the Fickian diffusion model. Thus, the effective material approach according to equation ( 8) can be applied to determine effective properties.

Figure 10 shows the relative effective diffusion coefficients D eff /D bulk obtained from equation [START_REF] Modesti | New experimental method for determination of effective diffusion coefficient of blowing agents in polyurethane foams[END_REF]. The diffusion coefficient increases with increasing porosity. It meets the expectation that an increasing amount of bulk material constitutes increasing diffusion resistance. The data suggest a possible exponential relation grid-arranged and randomly distributed pores. Analytical values from an approximation by Pilon [START_REF] Pilon | Gas diffusion in closed-cell foams[END_REF] and exponential fits [START_REF] Crank | Diffusion in Polymers[END_REF].

between diffusion coefficient and porosity. An exponential fit

D(φ) D bulk = D o + D 1 exp φ φ 1 ,      D o = 0.5663, D 1 = 0.4589, φ 1 = 29.60% random D o = 0.8289, D 1 = 0.2511, φ 1 = 24.34% 10x10 (14)
is shown in figure 10. For a porosity of φ = 0, equation ( 14) yields

D eff /D bulk =      1.0252 random 1.08 10x10
, values close to the theoretical result of 1. This again demonstrates the validity of the method. Besides of its quantitative meaning, the effective diffusion coefficient describes the rate of diffusion through the material. It can be used to compare materials with different topologies or porosities. Figure 11 shows, how the resulting D eff relies on the number of pores in the computational domain. Already a small amount of 25 pores gives a reasonable estimate of the effective material properties. However, D eff still rises by 7 % if the number of pores is increased. Above 100 pores, the variation is below 2 %, proving the effective material behaviour of the material. For large domains or computationally demanding micro-structures, the simulation of long physical times might not be feasible. In that case, simulations of only a few time steps and extrapolation would be beneficial.

Figure 12 reports on the relative deviation of the effective diffusion coefficient when the simulation is stopped after a certain fraction of τ diff . To that end, materials with 200 randomly distributed pores at 30 %, 38 %, and 54 % gas fraction, respectively, have been simulated and post-processed, taking only a certain fraction of the simulated time into account. Already after 50 % of τ diff , the resulting effective diffusion coefficients show deviations smaller than 0.5 %.

Averaging the pressure in all pores at a given instant yields the mean pore pressure ppore . Figure 13 shows its evolution over time for simulations with different porosities, presented in figure 10 as well. The mean pore pressure decays approximately exponentially in time, which is in line with experimental findings [START_REF] Ruiz-Herrero | Effective diffusion coefficient for the gas contained in closed cell polyethylene-based foams subjected to compressive creep tests[END_REF].

The characteristic decay times τ pore are obtained from fitting the mean pore pressure ppore (t) evolution to an exponential function ppore (t) = p amb + p 1 exp (-t/τ pore ) [START_REF] Crank | The Mathematics of Diffusion[END_REF] starting after a certain number of time steps. Figure 14

Figure 14 shows a slight decrease of τ pore for an increasing number of pores in case of material with grid-arranged pores. This might be due to more homogeneous and thus, more efficient distribution of gas flux. However, no significant qualitative change of behaviour is detected. Therefore, the consideration of the structure as an effective material seems legitimate for the deployed number of cells.

After measuring the influence of porosity, now the influence of pore shape is considered. To that end, four additional simulations are conducted using randomly distributed elliptical pores. The ratio of the semi axes of all pores is set either to 0.5 or to 2, yielding horizontally or vertically oriented ellipses, respectively. Figure 15 shows the relative effective diffusion coefficients D eff /D bulk for domains with circular pores compared to ones with horizontally or vertically elongated pores at two different levels of porosity φ.

This bar chart suggest significantly faster diffusion for domains with horizontally arranged pores than for vertically arranged ones or for domains for circular pores. The difference in the diffusion coefficient between the latter ones are small. The figure shows a slight decrease in the diffusion coefficient if the pores are elliptical and vertically arranged, and not circular. In interpreting this tendency, one should, however, be cautious. The pore centers do not coincide. Thus, randomly occurring lines of pores may bias this result. Nonetheless, one could carefully venture a first explanation: The horizontal alignment of the pores, i. e. alignment in the direction of the diffusion, may enable the gas to diffuse through less bulk material in 'choosing' its way through the pores. This could accelerate the diffusion since the gas is considered to diffuse through the pores instantaneously, whereas the diffusion through the solid is slow. By this, the slower diffusion in case of vertically orientated, elliptical cells could be explained as well. In that case the gas might be forced to diffuse through effectively more bulk material.

In a third step, the influence of inhomogeneous pore distribution is investigated. To that end, the pores are arranged on a Cartesian lattice and shifted horizontally, leaving either a band of solid material of size λ • w in the middle, or leaving a band of size λ/2 • w at both sides (see figure 16). This is done for a constant overall porosity of φ = 40 % and constant dimension of the material w = h = 100 mm, to investigate the influence of this shifting. Due to the inhomogeneous distribution sinusoidal ansatz functions according to equation ( 8) do not represent the gas distribution. Consequently, characteristic times of exponential decay according to equation ( 12) are employed here. The characteristic diffusion time τ diff for different widths of the shifting λ are presented in figure 16. The diffusive decay for accumulation of solid material on the outside is slower than for accumulation in the middle of the material. In case of positive shift, the diffusion time is well represented by a linear function

τ diff = 2.958 a + 0.04352 a % • λ. (17)
The slope of the linear fit corresponds to the constitution of an additional diffusion barrier with growing thickness.

In case of negative shift, two effects have to be considered here. Firstly, the gas diffusion within the bubble cluster increases because of decreasing wall thickness between the bubbles. Secondly, the bubbles are shifted towards the sides, so the contained gas has to cover smaller diffusion lengths to reach the outside.

The combination of both effects results in a nonlinear decrease of the diffusion time with increasing shifting.

In this case, the diffusion time might by estimated by a second order polynomial function

τ diff = 2.938 a + 0.03200 a λ % • -0.00153 a λ % 2 . (18)
Interestingly, the positive and the negative shifting results in a comparable slope at zero shifting and a continuous and smooth curve. A linear fit over the whole simulated range of λ yields

τ diff = 2.940 a + 0.04496 a λ % • . (19)

Discussion

The method developed to simulate diffusion using a FEA program is successfully implemented in a Python script. The approach to employ the thermal solver proofs to be working. A stable code is developed and leads to quantitatively plausible results. For the simulation ideal gas law is used and isothermal compression is assumed. In that way, temperature dependencies are neglected. This is reasonable for long-term relaxation processes in polymer foam construction parts. However, in case of fast diffusion, e. g. for hydrogen storage in foams, thermal effects should be considered.

As the diffusion coefficient is set to a constant value, its dependency on the concentration and local mechanical stress is neglected. It would be difficult to implement the latter, because there is no direct interaction between diffusive flux and mechanical stress during a time step. The interaction is implemented by synchronizing initial and boundary conditions between the time steps. However, if the time steps are short enough, the results converge as demonstrated by the convergence study. Due to this parallel approach, the FEA program must stop after each time step and needs to be updated. Consequently, the simulation requires rather long computation times to perform. Nevertheless, it could be demonstrated that reliable diffusion coefficients can be determined by simulating only 0.5 diffusive time scales and thereby reducing the computational effort significantly (see figure 12).

The diffusion through the pores is considered to be taking place instantaneously, as the pore pressure is set to a constant value. In case of single component gases, the pressure equalises inside a pore with the speed of sound. And also, in case of gas mixtures the approach is reasonable because diffusion coefficients in gas are approximately seven orders of magnitude [START_REF] Cussler | Diffusion: Mass Transfer in Fluid Systems, 3rd Edition[END_REF] higher than for diffusion in polymers. Consequently, considering homogeneous conditions inside each pore is reasonable.

The influence of the solubility was neglected by setting its ratio S s /S gas = S s /RT to the value of 1.

Smaller solubility in the solid material would reduce the gas flux and thus, decrease the effective diffusion coefficient. Depending on the type of gas and solid, the chosen solubility ratio is in the range of realistic values [START_REF] Alsoy | Modeling of diffusion in closed cell polymeric foams[END_REF]. Note that here diffusion within the void is not the rate-determining step in the permeation process, and the chosen ratio value of 1 is consistent with previous studies [START_REF] Pilon | Gas diffusion in closed-cell foams[END_REF] showing no influence of the solubility of the gas in the condensed phase on the effective diffusion coefficient.

Compared to realistic foam, the present simulation is restricted to two dimensions, purely elastic material, spherical or elliptical pores, and the absence of struts, open pores, or other imperfections. This work considers only diffusion of a single gas. In case of mixtures of gases with different diffusion coefficients more complex processes such as demixing or diffusion from ambient gases into the void material could take place. Still, the results show reasonable agreement to experimental investigations of gas diffusion in porous media [START_REF] Alsoy | Modeling of diffusion in closed cell polymeric foams[END_REF].

The results also show the same magnitudes and tendency in the effective diffusion coefficient as the model developed by Pilon et al. [START_REF] Pilon | Gas diffusion in closed-cell foams[END_REF] (figure 10).

The program is used to predict effective diffusion coefficients. Offering a tool, that can determine a diffusion coefficient without complex, long and expensive experiments is of significant value. Since it computes the distribution of the gas, it could also determine effective positions for probes in experimental investigations, yielding highest sensitivity. However, for the simulations done so far, the pores are considered spherical, limiting the porosity geometrically to φ = 91 % in two dimensions and φ = 74 % in three dimensions. Due to the decreasing wall thickness for increasing porosity, the geometry must be meshed finer, resulting in increasing numbers of elements and high computational effort. In the present study, porosity is limited to φ = 60 %. For higher porosities, the initial solid foam structure should be computed considering the generation process of foams [START_REF] Dabo | Ad-hoc modeling of closed-cell foam microstructures for structure-properties relationships[END_REF] or surface evolver simulations [START_REF] Brakke | The surface evolver[END_REF].

Usually, two-dimensional resolution is instructive about the tendency observed in the principal directions

Figure 1 :

 1 Figure 1: Closed-cell foam observed at atmospheric pressure using X-ray tomography. Initial state (a) and collapse configuration once gas escaped by diffusion (b). A reduction by about 50% is observed in width and 7% in height. Thick polymeric skin present at the top and bottom of the sample may explain the difference in the size reduction regarding the direction.

Figure 2 :

 2 Figure 2: Basic set-up: Deformed two-dimensional porous material between two plates under compressive force F . Gas diffuses through pores and bulk material (polymer) to both sides (left and right).

Figure 3 :

 3 Figure 3: Boundary and initial conditions. Mechanical boundary conditions: Two-dimensional closed-cell porous material subjected to compressive force F load . Material is compressed in between to rigid plates, of which the bottom one is fixed in displacement and the top one fixed in normal displacement. A mechanical pressure p pore,i is acting on pore i. Mechanical ambient pressure p amb acting on both sides. Diffusion/temperature boundary conditions: Ambient pseudo-temperature T amb applied to the sides. Zero flux over the top and bottom boundary. Initial pseudo-temperature ic T pore,i applied to pore i.

Figure 4 :

 4 Figure 4: Flow chart: Main steps for a diffusion process simulation using a structural-thermal FEA

Figure 5 :

 5 Figure 5: One-dimensional gas-pressure distribution and contours plots of the gas pressure in a two-dimensional porous material (100 mm x 100 mm, 200 pores, φ = 54.4 %, D bulk = 5 E-12 m 2 s ) after: 6 month (left) and 36 months (right)

Figure 6 :

 6 Figure 6: Fourier coefficients A 2 (t) (9) for three models with different porosity φ = 20, 38, 54 % in time with exponential fit (10) to an exponentially decaying function. Fit parameters: Ã2 = 2.6538, 6.7925, 12.8915 kPa; τ eff = 50.6930, 34.8971, 22.1224 month.

Figure 7 :

 7 Figure 7: Section of the discretized mesh for a geometry with 200 randomly distributed pores with a porosity of φ = 45 %.Three different discretisations (a, b, c) with n elem = 100 000, 200 000, 400 000.

Figure 8 (p α -pβ ) 2 pβ -p amb   /n ts . ( 13 )Figure 8 :

 82138 Figure8shows the mean pressure evolution p(t) on a geometry with 200 randomly distributed pores and a porosity of φ = 45 % for three different meshes with n elem = 100 000, 200 000, 400 000 elements, respectively. The relative deviation between two configurations α and β is calculated by

Figure 9 :

 9 Figure 9: Convergence study in time for a model of 200 randomly distributed pores with a porosity of φ = 50 %. Mean pressure curves for three different time steps (a, b, c) with ∆t = 7, 15, 30 d. Relative deviations according to (13).

Figure 10 :

 10 Figure 10: Relative effective diffusion coefficients D eff /D bulk for different porosities φ from simulations on domains with

Figure 11 :

 11 Figure 11: Relative effective diffusion coefficients D eff /D bulk for certain numbers of pores npore from simulations on materials with grid-arranged pores

Figure 12 :Figure 13 :

 1213 Figure 12: Deviation of the effective diffusion coefficient after certain times from final value after all increments. For three models with 200 randomly distributed pores and porosities of φ = 30, 38, 54 %. Total number of time steps nts = 180, time step ∆t = 20, 15, 7 d.

Figure 14 :τ o = 5 .

 145 Figure 14: Characteristic diffusion time τpore from pore pressures for models with 200 randomly distributed pores and with grid-arranged pores as function of the porosity φ. Including linear fits given in equation (16).

Figure 15 :

 15 Figure 15: Comparison of relative effective diffusion coefficients of structures with horizontally aligned elliptical pores, vertically aligned elliptical pores and with 200 randomly distributed, circular pores. (φ = 40, 50 %)

Figure 16 :

 16 Figure 16: Characteristic diffusion time τ diff for structures with 10x10 grid-aligned circular pores for different shifting. Negative λ: Space in the middle. Positive λ: Space at the sides.

Table 1 :

 1 Boundary and initial conditions

	Boundary Condition	Top	Bottom	Left/right	Pore
	Normal displ.	free, same for whole area	zero	free	free
	Normal stress	F (t)	free	ambient pressure	pore pressure
	Tangent. disp.	free	free	free	free
	Tangent. stress	zero	zero	zero	zero
	Gas pressure	zero gradient	zero gradient const ambient pressure const for each pore

Table 2 :

 2 Quantities and values used in the numerical simulations

	Quantity	Symbol Value	Unit
	Young's modulus	E	5	MPa
	Poisson's ratio	ν	0.35
	Diffusion coefficient of the bulk material D bulk	5 • 10 -12	m 2 /s
	Solubility in bulk material	S s	4.2 • 10 -4	mol/Pa/m 3
	Solubility ratio	S s /RT	1
	Ambient pressure	p amb	10 5	Pa
	Pressure load	p load	15, 20	p amb
	Porosity	φ	0.15 . . . 0.6
	Width	w	100	mm
	Height	h	100	mm
	Time step	∆t	1 . . . 31	days
	Number of time steps	n ts	100 . . . 200
	Number of elements	n elem	100 000 . . . 200 000
	Number of pores	n pore	200

Table 3 :

 3 Comparison of the heat equation with Fick's second law

	Thermal conduction	Mass diffusion

of three dimensional configurations. For more realistic results pure elastic material behaviour could be replaces by viscoelastic one to simulate creep-experiments. Also, expansion to larger, non-square models with higher porosity could be part of further improvement. Transferring the method into three dimensions is easily possible, because the thermal and the structural solver of many FE programs are implemented in three dimensions as well. Future research could use the programs ability to simulate set-ups with time-dependent boundary conditions and complex geometries, making use of the universal character of the approach.

For the simulated geometries and a porosity ranging from 30 % to 60 %, a nearly linear correlation between characteristic diffusion time and porosity can be observed (figure 14). Quick estimations about the time scale for a certain model can be made with equation [START_REF] Ruiz-Herrero | Effective diffusion coefficient for the gas contained in closed cell polyethylene-based foams subjected to compressive creep tests[END_REF]. Subsequently, significant influence of the pore shape (figure 15) and pore distribution (figure 16) have been identified. In the considered parameter range, variations up to 30 % on the diffusion rate are to be observed.

Regarding the results, one can state, that diffusion is a non-negligible factor for long-time loaded solid closed-cell porous materials; though strongly depending on the material, the dimension of the model, its porosity and the gas chosen. For the structures simulated a major change in pore pressure caused by diffusion acts on the time scale of the order of months or few years.

Summarising, one can say that a tool is created that can handle complex loadings, cyclical deformation and other loads, limited only by the computer power to handle fine meshes. It can be used for manifold setups and may help for the design of porous materials such as polymer foam. Using simplifying assumptions like presence of a single gas, constant solubility and isothermal state, it simulates the pressure, respectively concentration, change inside the material. In that way, it offers insight into the diffusion process going on and allows to derive effective diffusion coefficients.

Competing interest. The authors declare that they have no competing financial interest.


MD Charlée Nardin
email: cnardin@chu-besancon.fr

MD Anne Jeand'heur

MD Kévin Bouiller

Marie Blanche Valnet-Rabier

MD Flora Dresco

MD Julie Castagna

Clémentine Adrien Mareschal

MD Marie Blanche Valnet-Rabier

MD Clémentine Carlet

MD Virginie Nerich

MD, PhD Samuel Limat

MD Eve Puzenat¹

MD François Aubin
email: francois.aubin@univ-fcomte.fr

Prof. François France Aubin

Vitiligo under anti-programmed cell death-1 therapy is associated with increased survival in melanoma patients

Keywords: melanoma, immune checkpoint inhibitor, adverse event, vitiligo, survival, anti-PD-1

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

MANUSCRIPT TEXT

To the Editor:

Anti-programmed cell death-1 (anti-PD-1) agents have demonstrated their efficacy in the treatment of advanced melanoma with reasonable toxicities [START_REF] Weber | Nivolumab versus chemotherapy in patients with advanced melanoma who progressed after anti-CTLA-4 treatment (CheckMate 037): a randomised, controlled, open-label, phase 3 trial[END_REF]. Although anti-PD-1 related adverse events (AEs), especially vitiligo, have been reported as associated with higher response rates and prolonged survival, this association remains controversial due to conflicting results [START_REF] Postow | Immune-Related Adverse Events Associated with Immune Checkpoint Blockade[END_REF]. Consequently, the impact of AEs under anti-PD-1 on survival in patients treated for advanced melanoma in the setting of daily practice was investigated.

All patients treated with anti-PD-1 agents for stage III-IV melanoma between 2011 and 2018 were retrospectively reviewed. Type and severity of AEs according to the CTCAE v5.0 and interval from anti-PD-1 initiation to AEs occurrence were collected. Using Cox-regression models, the prognostic impact of clinical factors including AEs on progression free survival (PFS) and overall survival (OS) was investigated. Additionally, a landmark analysis at 3 time points to address lead-time bias inherent to the time dependence of the occurrence of AEs was performed.

Overall, 111 patients treated with anti-PD-1 were evaluated. Patients' characteristics are listed in Table 1. Over a median follow-up of 438 days (range 8-1687), 61 patients experienced AEs (55%) after a median time of 51 days (range, 1-758). Cutaneous (n=32, 29%) including vitiligo (n=15, 13.5%), endocrine (n=35, 32%), and gastrointestinal (n=17, 15%) AEs were the most frequent. Specifically, vitiligo occurred at a median time of 256 days (range, 30-758). Severe AEs occurred in 12 patients (11%) leading to therapy discontinuation in 8 patients (7%).

Median OS was 22.5 months (CI95% 14.9-30.1). Median OS in patients experiencing vitiligo, other AEs and no AE were not reached, 28 months (CI95% 11.1-46.9) and 12 months (CI95% 4.7-20.3, p<001) respectively. Upon multivariable analysis, experiencing vitiligo (HR=0.099, CI95% 0.013-0.737, p=0,024) and serum LDH level (HR=3.514, CI95% 1.787-6.962, p<0.001) were independently associated with OS. Median PFS was 8.9 months (CI95% 9.2-11.6). Upon multivariable analysis, experiencing vitiligo (HR=0.109, CI95% 0.025-0.471, p=0.003) and serum LDH level (HR=3.077, CI95% 1.702-5.561, p<0.001) were independently associated with PFS. Using a landmark analysis, we confirmed that vitiligo was associated with prolonged OS as compared to patients experiencing other AEs or no AEs (Figure 1).

In daily practice, AEs under anti-PD-1 are frequent with a predominance of endocrine, cutaneous and gastrointestinal AEs as previously described [START_REF] Weber | Nivolumab versus chemotherapy in patients with advanced melanoma who progressed after anti-CTLA-4 treatment (CheckMate 037): a randomised, controlled, open-label, phase 3 trial[END_REF]. Regarding vitiligo, while its occurrence varies among series it

Figure legends Figure 1 .

 1 Figure legends Figure 1. Overall survival (OS) in patients treated with anti-PD-1 with vitiligo, other adverse events (AEs) and

Table 156 Table 1 Characteristics of patients with or without adverse events (AE)..

 1561

	157
	158	¹Percentages of total patients (111), ²percentages of patients with AEs (61), ³percentages of patients without
	159	AEs (50), ⁴ Patients who previously received a targeted therapy were either in treatment failure or experienced a
	160	toxicity contraindicating targeted therapies. ⁵Patients who previously received ipilimumab. AID: autoimmune
	161	disease; BMI: body mass index; ICI: checkpoint inhibitor; IPI: ipilimumab; LDH: lactate dehydrogenase; NIVO:
	162	nivolumab; n = number ; OR: Odds Ratio and confidence interval at 95% ; PBZ: pembrolizumab.
	163
			Total¹	Patients with AE²	Patients without AE³	Univariable
			n=111(100%)	n=61 (55%)	n=50 (45%)
						p-value
		Age
		Median age, [range] (years)	67 [25-89]	66 [32-89]	68 [25-88]	0.585
		Sex ratio
		Male (%)	58 (52)	33	25	0.667
		Female (%)	53 (48)	28	25
		BMI
		Median, [range], (kg/m²)	25.5 [15.7-45.4]	27.0 [15.7-45.5]	25.4[18.3-39.5]	0.229
		History of AID (%)
		Yes	9 (8)	5	4	0.970
		No	102 (92)	56	46
		Use of steroids
		Yes	15 (14)	10	5	0.327
		No	96 (86)	51	45
		AJCC Stage
		III (%)	30 (27)	14	16	0.285
		IV (%)	81(73)	47	34
		Brain metastases (%)
		Yes	35(32)	17	18	0.359
		No	76 (68)	44	32
		LDH level (UI/L)
		Median, [range] (UI/L)	250 [139-2367]	242 [139-2367]	250 [156-1876]	0.092
		BRAF V600 mutation (%)
		Yes	37 (21)	18	19	0.345
		No	74 (79)	43	31
		Targeted therapies 4 (%)
		Yes	30 (17)	15	15	0.523
		No	81 (73)	46	35
		IPI monotherapy 5 (%)
		Yes	44 (24)	26	18	0.478
		No	67 (76)	35	32
		Anti-PD-1 monotherapy (%)
		PBZ monotherapy	85	47	38	0.897
		NIVO monotherapy	26	14	12
	164
	165
	166

Acknowledgments

The authors thanks Alexandre Doussot and the Association A fleur de Peau (Besançon, France) for their technical assistance.

Charlée Nardin has acted as a consultant for Novartis, BMS and MSD.

IRB approval status: study approved by the authors' Institutional Review Board (DRCI of Besançon).

has been correlated with disease response [START_REF] Weber | Nivolumab versus chemotherapy in patients with advanced melanoma who progressed after anti-CTLA-4 treatment (CheckMate 037): a randomised, controlled, open-label, phase 3 trial[END_REF][START_REF] Nardin | Vitiligo Repigmentation with Melanoma Progression During Pembrolizumab Treatment[END_REF][START_REF] Hua | Association of vitiligo with tumor response in patients with metastatic melanoma treated with pembrolizumab[END_REF]]. Yet, its association with survival remains disputed [START_REF] Hua | Association of vitiligo with tumor response in patients with metastatic melanoma treated with pembrolizumab[END_REF][START_REF] Teulings | Vitiligo-like depigmentation in patients with stage III-IV melanoma receiving immunotherapy and its association with survival: a systematic review and meta-analysis[END_REF]. In the current study, patients who developed vitiligo under anti-PD-1 experienced longer survival. However, analyzing the correlation between AEs such as vitiligo should take into account the lead-time-bias due to the fact that patients dying of disease especially early after anti-PD-1 initiation will not develop AEs. This issue has been addressed using a landmark analysis. Further, the occurrence of any AEs other than vitiligo was not associated with any survival benefit as compared to patients experiencing no AEs. This observation highlighted the relevance of monitoring vitiligo under anti-PD-1 therapy.

While inherently limited by its retrospective nature and single-center design, the current study showed that the occurrence of vitiligo under anti-PD-1 therapy seems relevant as a surrogate of treatment efficacy and prolonged survival in daily practice.

Abbreviations and acronyms


Mathieu Puyade

Céline Labeyrie

Manuela Badoglio

Pascal Cintas

Sarah Guenounou

Pauline Lansiaux

Zora Marjanovic

Guillaume Nicolas

Amélie Pomies

Louis Terriou

Jose-Miguel Torregrosa Diaz

Clément Baron

Cristina Castilla Llorente

Ibrahim Yakoub-Agha

Dominique Farge
email: dominique.farge-bancel@aphp.fr

'autogreffe de cellules souches hématopoïétiques dans la polyradiculonévrite inflammatoire démyélinisante chronique : recommandations de la Société francophone de greffe de moelle et de thérapie cellulaire (SFGM-TC)

Keywords: Chronic inflammatory demyelinating polyneuropathy, Autologous hematopoietic cell transplantation, Mobilization, Conditioning regimen, Post autologous stem cell transplantation follow-up

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

Indications de l'autogreffe de cellules souches hématopoïétiques dans la polyradiculonévrite inflammatoire démyélinisante chronique : recommandations de la Société francophone de greffe de moelle et de thérapie cellulaire (SFGM-TC).

Résumé

La polyradiculonévrite inflammatoire démyélinisante chronique (PIDC) est une maladie autoimmune affectant le système nerveux périphérique caractérisée par une démyélinisation segmentaire et focale à l'origine d'un déficit neurologique clinique. Son diagnostic nécessite la présence de plusieurs éléments associant des critères cliniques, des critères de démyélinisation à l'électro-neuro-myogramme (ENMG), voire des critères de support au diagnostic (dissociation albumino-cytologique, anomalies nerveuses en IRM, autres anomalies mineures à l'ENMG, biopsie nerveuse avec signes de démyélinisation, amélioration sous traitement de première ligne dit immuno-modulateur). En cas d'échec à deux traitements successifs immuno-modulateurs de première ligne (corticoïdes, immunoglobulines à doses immuno-modulatrices ou échanges plasmatiques), le traitement immunosuppresseur de 2ème intention est mal codifié. Dans ce cadre, l'autogreffe de cellules hématopoïétiques (CH) est une alternative efficace chez des patients sélectionnés selon des critères spécifiques. L'objectif de ces recommandations, élaborées par un groupe d'experts de la Société Française de Greffe de Moelle osseuse et thérapie Cellulaire (SFGM-TC), du groupe Maladies Autoimmunes et Thérapie Cellulaire (MATHEC) et de la Filière de santé maladies rares Neuromusculaire (FILNEMUS), est de préciser les critères d'éligibilité des patients atteints de PIDC en vue d'une autogreffe de CH, les modalités pratiques des procédures de mobilisation, du conditionnement et du suivi standardisé après autogreffe de CH, ainsi que l'adaptation du traitement neurologique tout au long de la procédure d'autogreffe de CH et au cours du suivi.

Mots clés : Polyneuropathie inflammatoire démyélinisante chronique ; Autogreffe de cellules hématopoïétiques ; Mobilisation ; Conditionnement ; Suivi post autogreffe Summary Chronic Inflammatory Demyelinating Polyneuropathy (CIDP) is a chronic autoimmune disease involving the peripheral nervous system, characterized by focal and segmental demyelination accounting for neurological deficit. CIDP diagnosis is based on several criteria and requires the presence of specific clinical symptoms and of demyelinating criteria on the electroneuromyogram (ENMG) or of additional supportive criteria (spinal fluid examination with dissociation between albumin level and cellular abnormalities, nervous abnormalities on MRI or other minor abnormalities on ENMG, demyelinating features on nerve biopsy or patient improvement under so-called first-line therapy with immunodulator treatment). After failure of two successive first line immunomodulating drug therapies (corticosteroids, immunomodulating immunoglobulins, or plasma exchange), several options can be considered as second line therapies. The efficacy of autologous hematopoietic cell transplantation (AHCT) has been shown in CIDP patients. The aim of these recommendations established by a working group of experts from the "Société Française de Greffe de Moelle osseuse et thérapie Cellulaire (SFGM-TC)", the group "Maladies Auto-immunes et Thérapie Cellulaire (MATHEC)" and the "Filière de santé maladies rares Neuromusculaire (FILNEMUS)" is to specify the eligibility criteria for AHCT in CIPD patients, to describe the mobilization and the conditioning regimen for the AHCT procedure, as well as the patient standardized post-transplant follow-up and the management of neurological treatment throughout the all procedure.

QUESTIONS POSEES

1. Quels sont les patients atteints de polyneuropathie inflammatoire démyélinisante chronique (PIDC) candidats à une autogreffe de cellules hématopoïétiques (CH) ? Quel est le bilan à effectuer et quelles sont les mesures à prendre avant l'autogreffe de CH ? Quels sont les contre-indications à la procédure d'autogreffe de CH ? o Potentiels évoqués somesthésiques : présence d'anomalies de la conduction proximale.

o Biopsie nerveuse : présence de signes de démyélinisation/remyélinisation segmentaire [START_REF]Research criteria for diagnosis of chronic inflammatory demyelinating polyneuropathy (CIDP). Report from an Ad Hoc Subcommittee of the American Academy of Neurology AIDS Task Force[END_REF].

o Anomalies ENMG portant sur les paramètres de conduction sensitive.

o Amélioration clinique objective après traitement de 1 ère ligne dit immuno-modulateur. -Elimination des diagnostics différentiels : maladie de Lyme, diphtérie, exposition à un toxique ou à un traitement potentiellement neurotoxique, neuropathie héréditaire démyélinisante neuropathie motrice multifocale à blocs de conduction persistants, neuropathie médiée par les anticorps anti glycoprotéine associée à la myéline (anti-MAG), syndrome POEMS (Polyneuropathie, Organomégalie, Endocrinopathie, Immunoglobuline Monoclonale et atteinte cutanée (Skin)), radiculo-plexopathie diabétique et non diabétique, lymphome du système nerveux périphérique et amylose. L'évaluation du retentissement de l'atteinte neurologique repose sur les résultats des scores de handicap (Annexe III) évaluant la marche et la gêne gestuelle des membres supérieurs (Overall Neuropathy Limitation Scale (ONLS) [START_REF] Graham | A modified peripheral neuropathy scale: the Overall Neuropathy Limitations Scale[END_REF], Inflammatory Neuropathy Cause and Treatment (INCAT) disability score) ou plus largement l'autonomie dans la vie quotidienne (Score de Rankin modifié [START_REF] Banks | Outcomes Validity and Reliability of the Modified Rankin Scale: Implications for Stroke Clinical Trials: A Literature Review and Synthesis[END_REF]), ainsi que des scores cliniques permettant d'évaluer l'examen clinique moteur (Medical Research Council (MRC) [START_REF] Kleyweg | Interobserver agreement in the assessment of muscle strength and functional abilities in Guillain-Barré syndrome: Muscle Strength Assessment in GBS[END_REF]), l'examen sensitif (INCAT sensory sumscore [START_REF] Merkies | Psychometric evaluation of a new sensory scale in immune-mediated polyneuropathies. Inflammatory Neuropathy Cause and Treatment (INCAT) Group[END_REF]) ou la marche (tests de marche de 6 min ou sur 10m) [START_REF] Guyatt | The 6-minute walk: a new measure of exercise capacity in patients with chronic heart failure[END_REF].

La pathogénie de la PIDC demeure encore incertaine. La présence d'infiltrats inflammatoires sur la considérés alors en rémission de leur maladie, tandis que 40% restent dépendants des traitements [START_REF] Viala | A current view of the diagnosis, clinical variants, response to treatment and prognosis of chronic inflammatory demyelinating polyradiculoneuropathy[END_REF][START_REF] Rabin | Chronic inflammatory demyelinating polyradiculoneuropathy: search for factors associated with treatment dependence or successful withdrawal[END_REF]. Les patients réfractaires aux thérapeutiques de 1 ère ligne sont volontiers sévères, avec un handicap important (Score de Rankin modifié à 3 dans l'étude de Cocito [START_REF] Cocito | Immunosuppressive treatment in refractory chronic inflammatory demyelinating polyradiculoneuropathy. A nationwide retrospective analysis: The effect of immunosuppressive treatment in patients with CIDP[END_REF]).

En cas d'échec ou de dépendance à 2 traitements (simultanés ou successifs de 1ère ligne), différents traitements de 2 ème ligne peuvent être proposés. Aucun n'a démontré d'efficacité à un niveau de preuve satisfaisant pour ces patients atteints de PIDC en situation d'échec ou de dépendance aux traitements immuno-modulateurs de première ligne [START_REF]Joint Task Force of the EFNS and the PNS. European Federation of Neurological Societies/Peripheral Nerve Society Guideline on management of chronic inflammatory demyelinating polyradiculoneuropathy: report of a joint task force of the European Federation of Neurological Societies and the Peripheral Nerve Society--First Revision[END_REF][START_REF] Mahdi-Rogers | Immunomodulatory treatment other than corticosteroids, immunoglobulin and plasma exchange for chronic inflammatory demyelinating polyradiculoneuropathy[END_REF]. Ces différents traitements immunosupresseurs ou biothérapies, pouvant être utilisés en 2 ème ligne, sont les suivants [START_REF]Joint Task Force of the EFNS and the PNS. European Federation of Neurological Societies/Peripheral Nerve Society Guideline on management of chronic inflammatory demyelinating polyradiculoneuropathy: report of a joint task force of the European Federation of Neurological Societies and the Peripheral Nerve Society--First Revision[END_REF][START_REF] Vallat | Natalizumab as a Disease-Modifying Therapy in Chronic Inflammatory Demyelinating Polyneuropathy -A Report of Three Cases[END_REF] :

-immunosuppresseurs oraux : azathioprine, mycophénolate mofétil, méthotrexate, fingolimod.

-immunosuppresseurs injectables : cyclophosphamide, interféron alpha ou bêta.

-anti-TNF alpha : étanercept.

-anticorps monoclonaux : rituximab (anti-CD20), natalizumab (anti-alpha4 integrine), alemtuzumab (anti-CD52).

Le risque à trop différer un traitement efficace dans les formes sévères est la survenue d'une perte axonale nerveuse souvent irréversible, secondaire à une inflammation nerveuse avec démyélinisation prolongée [START_REF] Bouchard | Clinicopathologic findings and prognosis of chronic inflammatory demyelinating polyneuropathy[END_REF].

Actuellement, le niveau de preuve EBMT pour la réalisation de l'autogreffe de cellules hématopoïétiques (CH) est de III en option clinique [START_REF] Pdwp | Haematopoietic SCT in severe autoimmune diseases: updated guidelines of the European Group for Blood and Marrow Transplantation[END_REF]. Dans la littérature, 21 cas de patients traités par autogreffe de CH pour une PIDC ont été rapportés. Le taux de réponse précoce est de 100%, avec un risque de rechute à 33% (Tableau 1 [START_REF] Burman | Autologous haematopoietic stem cell transplantation for neurological diseases[END_REF]). [START_REF] Press | Autologous haematopoietic stem cell transplantation: a viable treatment option for CIDP[END_REF][START_REF] Mahdi-Rogers | Autologous peripheral blood stem cell transplantation for chronic acquired demyelinating neuropathy[END_REF][START_REF] Vermeulen | Successful autologous stem cell transplantation in a patient with chronic inflammatory demyelinating polyneuropathy[END_REF][START_REF] Vermeulen | Relapse of chronic inflammatory demyelinating polyneuropathy 5 years after autologous stem cell transplantation[END_REF][START_REF] Axelson | Successful repeated treatment with high dose cyclophosphamide and autologous blood stem cell transplantation in CIDP[END_REF][START_REF] Oyama | NONMYELOABLATIVE AUTOLOGOUS HEMATOPOIETIC STEM CELL TRANSPLANTATION FOR REFRACTORY CIDP[END_REF][START_REF] Barreira | Nonmyeloblative autologous hematopoietic stem cell transplantation for chronic inflammatory demyelinating neuropathy treatment[END_REF][START_REF] Kamat | Autologous peripheral blood progenitor cell transplantation in refractory chronic inflammatory demyelinating polyradiculopathy[END_REF][START_REF] Bregante | Sjögren's syndrome associated chronic inflammatory demyelinating polyradiculoneuropathy (CIDP) treated with autologous and subsequently allogeneic haematopoietic SCT (HSCT)[END_REF]) Au niveau du registre de l'European Bone Marrow Transplantion (EBMT), 56 patients atteints de PIDC ont déjà été traités par autogreffe de CH.

Un essai randomisé comparant l'autogreffe de CH au traitement standard après échec d'une 2ème ligne est en cours (https://clinicaltrials.gov/ct2/show/NCT00278629).

METHODOLOGIE SUIVIE

Cet atelier a été conduit selon la méthodologie des ateliers d'harmonisation des pratiques de la Société Française de Greffe de Moelle osseuse et thérapie cellulaire (SFGM-TC) [START_REF] Tipton | How we harmonize HSCT clinical practices among the SFGM-TC centers[END_REF]. Critères de non-indication à l'autogreffe de CH 1) En cas de neuropathie non auto-immune et notamment :

-neuropathie héréditaire dont amylose à transthyrétine.

-neuropathie secondaire à un médicament ou à un produit toxique.

-neuropathie attribuable à une autre étiologie [START_REF]Joint Task Force of the EFNS and the PNS. European Federation of Neurological Societies/Peripheral Nerve Society Guideline on management of chronic inflammatory demyelinating polyradiculoneuropathy: report of a joint task force of the European Federation of Neurological Societies and the Peripheral Nerve Society--First Revision[END_REF][START_REF] Magy | étude français des PIDC. [Diagnostic strategy for chronic inflammatory demyelinating polyradiculoneuropathy. Recommendations of the French working group[END_REF][START_REF] Group | Recommendations on diagnostic strategies for chronic inflammatory demyelinating polyradiculoneuropathy[END_REF]: -Bilan biologique infectieux : sérologies HIV, HTLV-1/2, HBV, HCV, HHV8, CMV, EBV, VZV, toxoplasmose, syphilis, antigénémie aspergillaire, Quantiferon®.

o
-Bilan biologique immunologique : électrophorèse des protides, immuno-électrophorèse des protides, dosage pondéral des immunoglobulines, immunophénotypage lymphocytaire (T, B, NK).

-Consultation stomatologique + ORL de moins de 1 mois avec panoramique dentaire et radiographie des sinus.

-Echographie cardiaque transthoracique et ECG.

-Explorations Fonctionnelles Respiratoires (EFR) avec mesure du transfert de l'oxyde de carbone (DLCO).

-Scanner thoraco-abdomino-pelvien.

-Consultation gynécologique avec échographie pelvienne et mammographie de moins d'un an chez les femmes, dosage de l'antigène spécifique de la prostate (PSA) et toucher rectal chez l'homme.

-Consultation diététicienne et évaluation nutritionnelle.

-Préservation de la fertilité.

-Prélèvement pour biothèque si disponible sur site.

Contre-indications à l'autogreffe de CH

-Grossesse ou absence de contraception adaptée pendant toute la procédure.

-Affection(s) concomitante(s) sévère(s) : Quelles sont les modalités de l'autogreffe de CH chez les patients atteints de PIDC ?

o

Mobilisation :

Attitude vis-à-vis des traitements neurologiques avant et pendant la mobilisation :

-

Le protocole classique de mobilisation des cellules souches périphériques est le suivant :

-Cyclophosphamide IV 1g/m² J1 et J2.

-GCS-F 5µg/kg/j en sous cutané dont la durée est fonction des habitudes des centres.

-Pas de sélection CD34+.

Entre le recueil de cellules souches hématopoïétiques périphériques et le conditionnement, selon l'évaluation du neurologue référent et l'état clinique du patient, les traitements possibles sont : les corticoïdes, les immunoglobulines IV ou SC et les échanges plasmatiques.

Conditionnement

En se basant sur les recommandations nationales éditées en 2017 sur la pratique de l' autogreffe de CH chez les patients atteints de maladies auto-immunes [START_REF] Pugnet | Indications et suivi des autogreffes de cellules souches hématopoïétiques dans les maladies auto-immunes et auto-inflammatoires : recommandations de la Société francophone de greffe de moelle et de thérapie cellulaire (SFGM-TC)[END_REF] un conditionnement non myeloablatif de type cyclophosphamide 50 mg/Kg de J-5 à J-2 soit une dose totale de 200 mg/kg, associé à du sérum antilymphocytaire (SAL) 0,5 mg/Kg à J-5, 1,5 mg/kg de J-4 à J-1 sous couvert d'une prémédication par corticoïdes, anti-histaminique, antipyrétique et en perfusion lente [START_REF] Barreira | Nonmyeloblative autologous hematopoietic stem cell transplantation for chronic inflammatory demyelinating neuropathy treatment[END_REF]. Ce protocole est disponible sur le site MATHEC (www.mathec.com).

En cas de contre-indication absolue ou relative au conditionnement standard, un conditionnement par fludarabine 30 mg/m² J-5 J-4 J-3 J-2 et cyclophosphamide 60 mg/m² à J-2 associés à du SAL 0,5 mg/kg à J-5, 1,5 mg/kg de J-4 à J-1 sous couvert d'une prémédication par corticoides, antihistaminique, antipyrétique et en perfusion lente (36) peut être envisagé. L'utilisation de G-CSF postgreffe se fera selon les protocoles habituels du service où se déroulera la greffe.

Soins de support pendant l'autogreffe de CH:

-Prophylaxie anti-infectieuse pendant la greffe : du fait du risque infectieux fungique et viral, une prophylaxie anti-pneumocystose et herpès est nécessaire. L'administration de fluconazole (anti-candida), et amoxicilline (anti-pneumococcique) est parfois débutée pendant la greffe selon les habitudes du centre.

-La kinésithérapie à visée neurologique de mobilisation devra être maintenue 3 fois par semaine.

-L'évaluation diététique est nécessaire pour adapter le régime alimentaire.

-Le suivi ergothérapeutique doit être maintenu, ainsi que le port des orthèses.

-Le neurologue participe au suivi pendant toute la durée de la greffe, en évaluant régulièrement le malade sur le plan clinique, en modifiant si nécessaire en fonction du contexte le traitement de fond neurologique et en s'assurant de la mise en place des mesures de supports à visée neurologique.

- Quel est le suivi spécifique hématologique et neurologique d'un patient atteint de PIDC après autogreffe de CH ?

Modalités :

La spécificité du suivi neurologique justifie une évaluation systématique en centre de référence FILNEMUS en lien avec le neurologue référent et couplé au suivi hématologique post-greffe pour :

-évaluer l'évolution de la PIDC -évaluer la reconstitution immunologique -prévenir les complications (www.mathec.com) [START_REF] Pugnet | Indications et suivi des autogreffes de cellules souches hématopoïétiques dans les maladies auto-immunes et auto-inflammatoires : recommandations de la Société francophone de greffe de moelle et de thérapie cellulaire (SFGM-TC)[END_REF].

Le rythme des consultations et des évaluations doit être de 3 mois pendant un an. Au-delà d'un an, le suivi sera réalisé dans un centre structuré pour le suivi pluridisciplinaire des patients traités par thérapie cellulaire pour maladie auto-immune ou auto-inflammatoire (MATHEC) tous les 3 à 6 mois selon l'évolution clinique.

Au cours de chaque consultation du suivi doit être réalisée une évaluation avec recueil standardisé :

-des données cliniques et électrophysiologiques nécessaires au suivi de la PIDC.

-des données cliniques et biologiques de la greffe avec prélèvement pour biothèque si disponible.

Ces données doivent être rapportées au registre national MATHEC et européen de l'EBMT.

Suivi de l'état général :

-Performance Status

Suivi Neurologique :

-A chaque visite (tous les 3 mois la première année puis tous les 3 à 6 mois) et en cas de -Réponse : baisse d'un point ou plus de l'ONLS.

-Stable : ONLS stable.

-Aggravation : augmentation d'un point ou plus de l'ONLS ou apparition d'une nouvelle manifestation clinique.

Suivi Immunologique :

Suivi de la reconstitution immunologique : Numération formule sanguine -plaquettes, taux de gammaglobulines et des sous populations lymphocytaires T/B/NK à 3, 6, 12, 18 et 24 mois, puis de manière annuelle en fonction du profil immunologique.

Suivi Biothèque :

Un suivi en biothèque est recommandé à M3, M6, M12, M18, M24 puis chaque année puis en cas de rechute clinique :

• 1 tube de 10 mL EDTA pour phénotypage T approfondi

Recommandations de prévention des complications (tirées des recommandations précédentes [43])

• Calendrier vaccinal à réaliser : https://www.hcsp.fr/explore.cgi/avisrapportsdomaine?clefr=504

• Surveillance EBV et CMV : PCR bimensuelle pendant 3 mois, puis une fois par mois pendant la première année. En cas de réactivation virale EBV (PCR EBV > 5 log à 2 examens confirmés avec ou sans symptôme clinique), un traitement préemptif par rituximab sera institué avec répétition des doses selon le protocole local. En cas de réactivation virale à CMV : un traitement par valganciclovir 900 mg x 2 par jour pendant 14 jours, puis 900 mg par jour pendant 14 jours (ou selon l´évolution de la charge virale) sera instauré.

• Prophylaxie anti-VZV et HSV par valaciclovir 500mg x 2/jour ou aciclovir 400mg x2/ jour pendant 1 an minimum (ou plus si non-récupération des CD4 > 200/mm 3 .

• Prophylaxie anti-pneumocystis par sulfaméthoxazole/triméthoprime fort 1 comprimé x 3/semaine ou faible quotidien associé à de l'acide folinique. En cas d'allergie au sulfaméthoxazole/triméthoprime , sont préconisés des aérosols de pentamidine mensuels ou un traitement par atovaquone. Cette prophylaxie sera maintenue pour une durée minimale de 6 mois (ou plus si non-récupération des CD4 > 200/mm 3 )).

• En cas d'infection fongique, un traitement antifongique adapté est à instaurer selon les protocoles locaux.

Quelles sont les questions résiduelles ?

Comment organiser la biothèque nationale pour les patients atteints de PIDC ? Comment diffuser l'information auprès des neurologues et des patients ?

Déclaration de liens d'intérêts

Les auteurs ne déclarent pas de lien d'intérêts.

2 . 3 . 4 . 5 .

 2345 Quelle Réunion de Concertation Pluridisciplinaire doit valider l'indication de l'autogreffe de CH chez un patient atteint de PIDC et comment organiser l'autogreffe de CH ? Quelles sont les modalités de l'autogreffe de CH chez les patients atteints de PIDC ? Quel est le suivi hématologique et neurologique spécifiques d'un patient atteint de PIDC après autogreffe de CH ? Quelles sont les questions résiduelles ? ETAT ACTUEL DE LA QUESTION La polyradiculonévrite inflammatoire démyélinisante chronique (PIDC) est une maladie auto-immune, affectant le système nerveux périphérique, caractérisée par une démyélinisation segmentaire et focale à l'origine d'un déficit neurologique d'expression clinique variable. Elle touche 2 à 9 personnes pour 100 000 habitants[1]. La présentation clinique typique est d'installation progressive ou par poussées successives sans récupération entre les poussées, sur plus de 8 semaines, et associe l'apparition d'un déficit moteur symétrique (proximal et/ou distal), d'une atteinte sensitive des 4 extrémités et d'un syndrome neurogène périphérique (diminution voire abolition des réflexes ostéo-tendineux). Une atteinte des nerfs crâniens est possible. Des formes atypiques existent avec atteinte distale, motrice pure, sensitive pure, asymétrique (type Lewis Sumner) et focale. Le diagnostic de PIDC définie par l'European Federation of Neurological Society/ Peripheral Nerve Society (EFNS/PNS) repose sur l'association des critères suivants (Annexe I)[2,3] : -Critère clinique : forme typique ou variante. -Critère électro-neuro-myographique : présence d'anomalies de la conduction motrice permettant d'affirmer la démyélinisation. -Critères de support au diagnostic si nécessaires : o Ponction lombaire : présence d'une dissociation albumino-cytologique o Imagerie plexique (IRM) : présence d'anomalies des segments nerveux (hypertrophie et/ou prise de contraste).

Lo

  'autogreffe de CH ayant montré des bénéfices durables pour le traitement des patients atteints de PIDC, le groupe MATHEC (Maladies auto-immunes et thérapie cellulaire) au sein de la SFGM-TC a réuni des spécialistes francophones d'horizons différents : 2 internistes experts dans la procédure d'autogreffe de CH dans les maladies auto-immunes, 4 hématologues et 1 infirmière experts de la thérapie cellulaires et de l'auto et allogreffe dans les pathologies hématologiques et auto-immunes, 3 neurologues experts en neuromusculaire membres actifs de la filière de santé maladies rares neuromusculaires (FILNEMUS), les coordinatrices d'étude du groupe MATHEC et de EBMT office pour les maladies auto-immunes. Une revue exhaustive de la littérature a été réalisée par MP et CL, partagée par l'ensemble des membres du groupe de travail durant le printemps 2018. Une conférence téléphonique en septembre 2018 a permis de faire la synthèse des avis, des expériences et des connaissances tirées de la littérature. Le niveau de preuve utilisé dans ces recommandations suit les normes établies par l'EBMT : 1) niveau I : au moins un essai clinique randomisé -méta-analyse d'essais randomisés, 2) niveau II : essais cliniques non randomisés -cohortes ou études cas-contrôle -méta-analyse de cohortes, 3) niveau III : analyse d'experts sur la base d'autres données disponibles et la gradation de recommandations de l'EBMT, avec 1) Option clinique : peut être envisagée après évaluation minutieuse du rapport bénéfice/risque, 2) en développement RATIONNEL L'autogreffe de CH permet la réinitialisation du système immunitaire avec reconstitution d'une réponse immune de novo et modification du répertoire lymphocytaire, avec l'apparition d'un répertoire T et B de novo[40] après l'administration d'un conditionnement intensif immunosuppresseur ou myéloablatif, suivi de la réinjection de CH autologues préalablement collectées. Ces données ont été démontrées lors du traitement par autogreffe de CH de nombreux patients atteints de MAI (sclérose en plaques, sclérodermie systémique, maladie de Crohn). Même si il n'y a pas encore d'analyses immunologiques rapportées chez les patients atteints de PIDC dans ce contexte, l'efficacité de l'autogreffe de CH dans la PIDC est probablement sous-tendue par une modification des répertoires lymphocytaires T et B. RECOMMANDATIONS DE L'ATELIER Quels sont les patients atteints de polyneuropathie inflammatoire démyélinisante chronique (PIDC) candidats à une autogreffe de cellules hématopoïétiques (CH) ? Quel est le bilan à effectuer et quelles sont les mesures à prendre avant l'autogreffe de CH ? Quels sont les contre-indications à la procédure d'autogreffe de CH ? Patients atteints de PIDC ayant une indication à l' autogreffe de CH -Age ≤ 65 ans. -PIDC prouvée (critères EFNS/PNS) (2) avec, si possible, preuve histologique par biopsie nerveuse. -PIDC sévère : score ONLS ≥ 3 aux membres supérieurs (au moins une fonction des mains impossible) et/ou un score ≥ 2 aux membres inférieurs (au moins marche paraissant anormale à l'examen clinique sans nécessité d'une canne sur courte distance). -PIDC avec signes de démyélinisation et sans perte axonale massive : o Déficit moteur sans amyotrophie majeure, laissant présager une réserve axonale o Signes de démyélinisation majeure à l'EMG : bloc de conduction selon les critères EFNS/PNS. Réponse clinique fluctuante ou insuffisante aux traitements. -PIDC en échec de deux traitements de première ligne (échanges plasmatiques, corticoïdes, immunoglobulines polyvalentes) et après échec ou en cas de contre-indication à un traitement de 2ème ligne.

  maladie de Lyme, o POEMS Syndrome, o myélome multiple, une maladie de Waldenström, une maladie de Castelman, o neuro-lymphomatose. 2) Lorsque le bénéfice neurologique attendu est faible, c'est-à-dire en cas de perte axonale importante. Bilan pré-thérapeutique -Performance Status. -Evaluation neurologique : o scores fonctionnels (ONLS, Rankin modifié) et cliniques (MRC, INCAT sensory sumscore), o test de marche de 6 min o ElectroNeuroMyoGramme (ENMG) de référence datant de moins de 3 mois est nécessaire (Annexe II) -Bilan biologique standard : Numération Formule Sanguine -plaquettes, Na+, K+, Cl-, Urée créatininémie, clairance de la créatinine, ECBU, protéinurie 24h, ASAT, ALAT, GGT, Bilirubine T, TP TCA, Fibrinogène, CRP T4, TSHus, (βHCG si femme en âge de procréer).

  Il est nécessaire d'arrêter tous les autres immunosuppresseurs au moins 1 mois avant la mobilisation. Il convient d'arrêter toute biothérapie, éventuellement utilisée, au moins 3 mois avant la mobilisation. -Il n'y a pas de nécessité d'arrêter les corticoïdes et les Ig IV ou SC avant ou pendant la procédure de mobilisation -Les échanges plasmatiques ou le rituximab peuvent être réalisés jusqu'à la veille de la mobilisation. Il ne doit pas y avoir d'échanges plasmatiques entre la mobilisation et le recueil de cellules souches hématopoïétiques périphériques.

  Le traitement de sortie du patient doit être validé par l'hématologue et le neurologue : une réévaluation en hospitalisation en service spécialisé de neurologie pour la CIDP et en sortie d'hospitalisation de greffe est nécessaire. -Après la sortie d'aplasie, la nécessité ou non du maintien et les modalités d'utilisation du(des) traitement(s) immunosuppresseur(s) et/ou immuno-modulateur(s) préalablement utilisé(s) par chaque patient seront ré-évalués par le neurologue référent, lors du suivi tous les 3 mois pendant 1 an en fonction de l'évaluation clinique et électrophysiologique. En cas de corticothérapie prolongée, un sevrage sera programmé sur quelques semaines, les IgIV/SC et les échanges plasmatiques seront arrêtés. En cas d'impossibilité absolue de sevrage, il faut rechercher la dose minimale efficace. -Il est nécessaire de prévoir un séjour d'aval pour le patient en Médecine Physique et Réadaptation afin d'optimiser la réhabilitation du patient.

o

  réalisation des scores fonctionnels (ONLS, Rankin modifié) et cliniques (MRC, INCAT sensory sumscore). o recueil de toute nouvelle atteinte neurologique par rapport à l'atteinte initiale (nerf crânien, sensibilité…). o nécessité d'introduction d'un traitement à visée neurologique spécifique (type, date d'introduction, doses de ce traitement). o évaluation globale par le neurologue de l'état du patient (amélioration / stable / dégradation). o Auto-évaluation globale par le patient de son état (amélioration / stable / dégradation). -A 3, 6, 12, 18 mois puis annuellement et en cas de rechute : o ENMG (protocole minimal en annexe).o test de marche de 6 minutes. -La rééducation, l'ergothérapie et le port des orthèses doivent être analysés et évalués, chaque évaluation devant être répétée et tracée dans le dossier médical du patient. -La nécessité et les bénéfices attendus d'un suivi en Médecine Physique et Réadaptation doivent être évalués et proposés en concertation avec le patient Les critères SFGM-TC-MATHEC et FILNEMUS proposés pour évaluer la réponse des patients atteints de PIDC au traitement par autogreffe de CH sont :

• 1

 1 tube sec de 4 mL pour conservation du sérum en congélation à -20°C • 4 tubes héparinés de 10 mL pour Ficoll puis division en 3 échantillons pour Congélation des PBMC à -80° Congélation en ARN total à -80°C Congélation en ADN copie à -80° Suivi Immunologique et Infectieux : Compte tenu de l'immunosuppression liée aux traitements antérieurs (durée et intensité des traitements antérieurs sont les principaux facteurs de risque), les complications infectieuses sont à surveiller particulièrement. La reconstitution immunitaire post autogreffe de CH se fait progressivement pendant la première année et est généralement acquise vers 12-18 mois mais peut être retardée. Les infections bactériennes, virales et fongiques peuvent survenir quelques mois après la greffe et doivent être systématiquement dépistées dans la 1 ère année et jusqu'à 2 ans après la greffe en fonction de la qualité de la reconstitution immunitaire. Les complications les plus fréquentes sont les primoinfections ou les réactivations à EBV, HSV, VZV, CMV et la pneumocystose. Le risque d'une infection à pneumocystis est plus important dans les 6 mois suivant la greffe surtout si une corticothérapie est maintenue, d'où l'importance des prophylaxies adaptées.

  En France, la RCP MATHEC, coordonnée par le Centre de Référence Maladies auto-immunes systémiques Rares d'Ile de France sous l'égide de la SFGM-TC, a lieu deux fois par mois (le 1 er et le 3 ème mercredi de chaque mois, modalités de connexion sur www.mathec.com). Une fiche spécifique pour la PIDC disponible sur www.mathec.com (annexe IV) doit être préalablement remplie pour l'évaluation collégiale multidisciplinaire du dossier. Cette RCP en téléconférence permet de réunir neurologues, spécialistes des maladies auto-immunes, hématologues des équipes de greffe, thérapeutes cellulaires et autres médecins et paramédicaux des centres experts impliqués dans la coordination des soins et le suivi immuno-clinique spécifique de ces patients. L'objectif de cette RCP MATHEC est

	de:
	a) s'assurer de la bonne indication à l'autogreffe de CH,
	b) vérifier l'absence de contre-indications (absolues ou relatives / définitives ou temporaires) à cette
	procédure,
	c) proposer le conditionnement le plus adapté en fonction des caractéristiques du patient.
	atteinte respiratoire : insuffisance respiratoire définie par une pression artérielle en
	oxygène au repos (PaO2) < 8 kPa (< 60 mmHg) et/ou une pression artérielle en
	dioxyde de carbone au repos (PaCO2) > 6,7 kPa (> 50 mmHg) sans oxygénothérapie,
	DLCO < 30 % de la théorique,

o atteinte cardiaque : signe clinique d'insuffisance cardiaque congestive réfractaire, fraction d'éjection ventriculaire gauche <45%, coronaropathie sévère non revascularisée, résistance artérielle pulmonaire >3 unités Wood, arythmie ventriculaire non contrôlée, épanchement péricardique avec retentissement hémodynamique sévère évalué par l'échocardiographie ou la présence à l'IRM cardiaque d'un aplatissement septal diastolique ou « D sign », o atteinte hépatique persistante ou évolutive définie comme une augmentation durable du taux des transaminases ou de la bilirubine >2 fois la normale, o dénutrition significative : indice de masse corporelle (IMC) <18 kg/m², albuminémie <20 g/L, o néoplasie active ou myélodysplasie concomitante. En cas de néoplasie en rémission complète depuis moins de 5 ans : l'autogreffe peut se discuter au cas par cas, en fonction du cancer (type, localisation, extension) et de ses traitements (chimiothérapie, radiothérapie, hormonothérapie...) toujours en concertation avec l'oncologue référent du patient, les hématologues et le spécialiste de la PIDC au cours de la RCP nationale MATHEC.

Quelle Réunion de Concertation Pluridisciplinaire doit valider l'indication de l'autogreffe de CH chez un patient atteint de PIDC et comment organiser l'autogreffe de CH ?

Conformément aux recommandations de bonnes pratiques cliniques de la SFGM-TC en France et à l'international (JACIE/EBMT), l'indication de l' autogreffe de CH doit être évaluée et validée en RCP.

  Ateliers de la SFGM-TC Lille 20 et 21 septembre 2018 Autogreffe et PIDC Tableau 1. résumé de la littérature de l'ACSH dans la PIDC (d'après Burman et col. [29]) anti-lymphocytaire ; ICT = irradiation corporelle totale ; BEAM = carmustine + etoposide + sytarabine + melphalan ; Cy = cyclophosphamide ; G-CSF = granulocyte colony stimulating factor ; MRC = Medical Research Council Scale for Muscle Strength ; INCAT = Inflammatory Neuropathy Cause and Treatment Scale

		n	Age au début	Sexe	Durée de la PIDC depuis le diagnostic (mois)	Conditionnement	Réponse clinique (score pré-post ACSH)	Durée de suivi après ACSH (mois)	Rechute (mois post-ACSH)
	Vermeulen et col. [32,33]	1	38	H	120	BEAM	Bonne récupération, sous prednisone 5mg/jour	>60	30
	Kamat et col. [37]	2	42 72	H H	24 120	Cy + SAL Cy + SAL	Récupération de la marche Stabilisé	18 3	Non Non
	Oyama et col. [35]	1	32	F	30	Cy + SAL	Rankin 4-1	22	Non
	Barreira et col. [36]	1	24	H	144	Cy + SAL	Réponse transitoire	2	1
	Mahdi-Rogers et col. [31]	3	29 58 72	F F H	252 156 72	Cy + SAL Cy + SAL Cy + SAL	MRC 39-48-29 MRC 58-62 MRC 46-34	26 6 19	18 Non Non
	Axelson et col. [34]	1	56	H	11 36	Cy Cy + SAL	INCAT 10-2 INCAT 6-2	101	25 Non
	Press et col. [30]	1 1	16-67	10H, 1F	11-228	Cy + SAL (7) BEAM (3) Melphalan (1)	INCAT médian 6-1	6-101	23 14 14
	Bregante et col. [38]	1	24	H	7	Thiotepa+Cy+G-CSF Fluda+Cy+ICT	Récupération de la marche Récupération de la marche	60	6 Non
	SAL = sérum

biopsie[START_REF] Rizzuto | Focal lesions area feature of chronic inflammatory demyelinating polyneuropathy (CIDP)[END_REF] et l'efficacité des traitements immuno-modulateurs[START_REF]Joint Task Force of the EFNS and the PNS. European Federation of Neurological Societies/Peripheral Nerve Society Guideline on management of chronic inflammatory demyelinating polyradiculoneuropathy: report of a joint task force of the European Federation of Neurological Societies and the Peripheral Nerve Society--First Revision[END_REF] font fortement suspecter un mécanisme immunologique. Les infiltrats inflammatoires dans le nerf, lorsqu'ils sont retrouvés, sont périvasculaires, polymorphes lymphocytaires T plus que B, non monotypiques[START_REF] Rizzuto | Focal lesions area feature of chronic inflammatory demyelinating polyneuropathy (CIDP)[END_REF]. Le ou les autoantigènes ne sont pas encore clairement identifiés[START_REF] Devaux | Nodal proteins are target antigens in Guillain-Barré syndrome[END_REF]. Quelques auto-anticorps ont été décrits dans la PIDC, en faveur d'un rôle pathogénique de l'immunité humorale médiée par les lymphocytes B : antigangliosides[START_REF] Chavada | Autoantibodies in immune-mediated neuropathies[END_REF] et plus récemment anti-contactine et anti-neurofascine[START_REF] Devaux | Nodal proteins are target antigens in Guillain-Barré syndrome[END_REF][START_REF] Querol | Neurofascin IgG4 antibodies in CIDP associate with disabling tremor and poor response to IVIg[END_REF][START_REF] Querol | Antibodies to contactin-1 in chronic inflammatory demyelinating polyneuropathy: Contactin-1 in Aggressive CIDP[END_REF], qui ne sont pas retrouvés chez tous les patients. L'étude du répertoire lymphocytaire T, aussi bien dans le sang que dans les infiltrats cellulaires de biopsie de nerf, a montré une restriction oligo-clonale chez les patients avec PIDC par rapport aux témoins normaux[START_REF] Schneider-Hohendorf | CD8+ T-cell immunity in chronic inflammatory demyelinating polyradiculoneuropathy[END_REF]. Le traitement par immunoglobulines intraveineuses diminue cette restriction d'hétérogénéité du répertoire lymphocytaire T CD4 et T CD8.[START_REF] Mausberg | Recovery of the Tcell repertoire in CIDP by IV immunoglobulins[END_REF] Le traitement de 1 ère intention repose sur l'immuno-modulation[START_REF]Joint Task Force of the EFNS and the PNS. European Federation of Neurological Societies/Peripheral Nerve Society Guideline on management of chronic inflammatory demyelinating polyradiculoneuropathy: report of a joint task force of the European Federation of Neurological Societies and the Peripheral Nerve Society--First Revision[END_REF] au choix entre les immunoglobulines polyvalentes par voie intraveineuse ou sous-cutanée (IgIV/SC)[START_REF] Dyck | A plasma exchange versus immune globulin infusion trial in chronic inflammatory demyelinating polyradiculoneuropathy[END_REF][START_REF] Eftimov | Intravenous immunoglobulin for chronic inflammatory demyelinating polyradiculoneuropathy[END_REF], la corticothérapie[START_REF] Hughes | Randomized controlled trial of intravenous immunoglobulin versus oral prednisolone in chronic inflammatory demyelinating polyradiculoneuropathy[END_REF][START_REF] Hughes | Corticosteroids for chronic inflammatory demyelinating polyradiculoneuropathy[END_REF] ou les échanges plasmatiques[START_REF] Mehndiratta | Plasma exchange for chronic inflammatory demyelinating polyradiculoneuropathy[END_REF]. Ces trois traitements ont démontré leur efficacité sans supériorité l'un par rapport à l'autre[START_REF] Oaklander | Treatments for chronic inflammatory demyelinating polyradiculoneuropathy (CIDP): an overview of systematic reviews[END_REF]. Le choix de ce traitement immuno-modulateur de 1 ère ligne est laissé à l'appréciation du prescripteur selon le terrain et la présence de contre-indications. Dans ce cadre, les recommandations européennes proposent les échanges plasmatiques qu'en cas d'échecs préalables aux IgIV ou corticoides, et ce compte-tenu des effets secondaires possibles des échanges plasmatiques[START_REF]Joint Task Force of the EFNS and the PNS. European Federation of Neurological Societies/Peripheral Nerve Society Guideline on management of chronic inflammatory demyelinating polyradiculoneuropathy: report of a joint task force of the European Federation of Neurological Societies and the Peripheral Nerve Society--First Revision[END_REF].En cas de non-réponse au traitement par immuno-modulateur, un autre traitement de 1 ère ligne est recommandé, car les patients peuvent répondre électivement à l'une ou à l'autre de ces thérapeutiques.En cas d'échec persistant, l'association de deux de ces traitements immuno-modulateurs peut être proposée[START_REF]Joint Task Force of the EFNS and the PNS. European Federation of Neurological Societies/Peripheral Nerve Society Guideline on management of chronic inflammatory demyelinating polyradiculoneuropathy: report of a joint task force of the European Federation of Neurological Societies and the Peripheral Nerve Society--First Revision[END_REF]. Environ 80 % des patients sont répondeurs à un traitement de 1 ère ligne. Parmi ces patients répondeurs au premier traitement immuno-modulateur, 60% peuvent ensuite être sevrés et

Remerciements

La SFGM-TC remercie les partenaires industriels pour leurs soutiens financiers qui ont permis la réussite de cette neuvième édition des ateliers d'harmonisation des pratiques : ASTELLAS, BIOTEST, CELGENE, GILEAD, JAZZPHARMACEUTICAL, KEOCYT, MACOPHARMA, MALLINCKRODT THERAKOS, MSD FRANCE, NEOVII, NOVARTIS, OCTAPHARMA, PFIZER, SANOFI.

Bibliographie