S Taileb
email: said.taileb@ensma.fr

J Melguizo-Gavilanes

A Chinnayya

Influence of the chemical modeling on the quenching limits of gaseous detonation waves confined by an inert layer

Keywords: Detonation dynamics, chemistry modeling, simplified kinetics, detailed chemistry, quenching limits, numerical simulation

The effect of chemistry modeling on the flow structure and quenching limits of detonations propagating into reactive layers bounded by an inert gas is investigated numerically. Three different kinetic schemes of increasing complexity are used to model a stoichiometric H 2 -O 2 mixture: single-step, three-step chainbranching and detailed chemistry. Results show that while the macroscopic characteristics of this type of detonations e.g. velocities, cell-size irregularity and leading shock dynamics, are similar among the models tested, their instantaneous structures are significantly different before and upon interaction with the inert layer when compared using a fixed height. When compared at their respective critical heights, h crit , i.e. the reactive layer height at which successful detonation propagation is no longer possible, similarities in their structures become apparent.

The numerically predicted critical heights increase as h crit, Detailed � h crit, 3-Step < h crit, 1-Step . Notably, h crit, Detailed was found to be in agreement with experimentally reported values. The physical mechanisms present in detailed chemistry and ne-

Introduction

A detonation is a combustion front coupled with a strong leading shock wave that travels supersonically with respect to reactants at rest. Its propagation mechanism can be summarized as follows: (i) the shock wave compresses and heats up fresh reactants; (ii) due to the high temperature sensitivity of the chemistry this abrupt temperature increase results in very fast chemical reactions; and (iii) the volumetric expansion of the burnt gases across the reaction zone drives the leading shock wave forward. A strong coupling between the leading shock wave and the reaction zone is a key feature of self-sustained detonation waves [START_REF] Zel | On the theory of detonation propagation in gaseous systems[END_REF]. The one-dimensional laminar structure of a detonation is then composed of an induction length, l ind (i.e. the distance between the leading shock and the start of heat release), and a reaction zone across which temperature increases and density decreases resulting in flow expansion until the flow velocity reaches the speed of sound in burnt products in a frame of reference attached to the shock, i.e. sonic point. The distance between the leading shock and the sonic plane is typically referred to as the hydrodynamic thickness, h t [START_REF] Lee | On the hydrodynamic thickness of cellular detonations[END_REF][START_REF] Radulescu | The hydrodynamic structure of unstable cellular detonations[END_REF].

In reality, detonations exhibit an unsteady multidimensional cellular structure that departs significantly from its laminar description [START_REF] Strehlow | Nature of transverse waves in detonations[END_REF] drawn by the triple points formed by the interaction of the leading shock, and transverse waves traveling along the height of the wave. As a result, l ind and h t (characteristic length scales of detonations) become dynamic entities. Any disturbance coming towards the leading shock and reaction zone complex from regions downstream of the hydrodynamic thickness will not affect the dynamics of the detonation wave. However, it remains vulnerable to the influence of the boundaries confining the wave. The nature of these boundaries and their length scale ratios to the detonation cell size, λ, and/or h t , result in a detonation velocity deficit, defined as a percentage of the ideal detonation propagation velocity (Chapman-Jouguet -CJ), D/D CJ , and eventual quenching. Various boundary conditions have been investigated in literature.

They can be classified in two main categories: (i) smooth boundaries, such as constant cross section tubes [START_REF] Brochet | Contribution à l'étude des détonations instables dans les mélanges gazeux[END_REF], divergent channels [START_REF] Radulescu | Dynamics of detonations with a constant mean flow divergence[END_REF] and yielding confinements [START_REF] Sommers | Simulation of condensed explosive detonation phenomena with gases[END_REF]; and (ii) rough boundaries, such as tubes with obstacles [START_REF] Teodorczyk | Detonation attenuation by foams and wire meshes lining the walls[END_REF] and porous walls [START_REF] Radulescu | The failure mechanism of gaseous detonations: experiments in porous wall tubes[END_REF]. The main failure mechanisms described are lateral expansion waves and attenuation of transverse waves that lead to the decoupling of the leading shock wave and the reaction zone. Experimental evidence shows that the quenching process differs depending on the mixture regularity. In [START_REF] Radulescu | The failure mechanism of gaseous detonations: experiments in porous wall tubes[END_REF] the critical dimension for detonation propagation in porous walls was determined to be 11λ and 4λ, for mixtures exhibiting a regular and irregular cellular structures, respectively. This outcome was attributed to stronger transverse waves that are able to compensate for the losses, hence rendering the detonation more resilient to failure.

Another relevant boundary condition comes from the presence of compressible confinement [START_REF] Reynaud | Interactions of a detonation wave confined by a high-temperature compressible layer[END_REF][START_REF] Reynaud | Numerical Study of Detonation Confined by an Inert Gas[END_REF][START_REF] Houim | The influence of acoustic impedance on gaseous layered detonations bounded by an inert gas[END_REF][START_REF] Mi | Effect of spatial in-homogeneities on detonation propagation with yielding confinement[END_REF]. In this configuration, the detonation front propagates in a layer of reactive mixture bounded at the top by inert gas. Lateral expansion of the products, streamline divergence, as well as triple point absorption/reflection at the interface lead to a very complex detonation front structure whose resulting curvature has been recently argued to be the main energy loss mechanism [START_REF] Chiquete | The effect of curvature and confinement on gas-phase detonation cellular stability[END_REF]. This canonical configuration also has implications for propulsion applications such as Rotating Detonation Engines, and safety. For the former, understanding non-idealities and predicting the detonation quenching limits is of prime importance for optimization and practical implementation of these devices. For the latter, understanding the mechanisms that lead to quenching and re-ignition is vital to mitigate the consequences of accidental leaks in industries such as nuclear, chemical processing plants, among others [START_REF] Rudy | Critical conditions of hydrogen-air detonation in partially confined geometry[END_REF].

Classical experiments using the latter configuration were carried out using a rectangular cross-section composed of three rigid walls and a film separating reactive and inert mixtures [START_REF] Sommers | The interaction of a detonation wave with an inert boundary[END_REF][START_REF] Dabora | The influence of a compressible boundary on the propagation of gaseous detonations[END_REF][START_REF] Dabora | The influence of a compressible boundary on the propagation of gaseous detonations[END_REF]. Schlieren visualization revealed the main features of the wave complex which consist of a curved detonation front coupled to a transmitted oblique shock wave in the inert gas and a mixing layer separating shocked inert gas from hot detonation products. Special attention was given to the velocity deficit as a function of the height of the channel, the reactive layer height and the acoustic impedance ratio of inert to reactive gas. The authors found that the velocity deficit is proportional to the reactive layer height. Furthermore, the acoustic impedance was found to influence the structure of the propagating wave complex. As the confinement becomes lighter, i.e. lower acoustic impedance, the oblique shock in the inert gas detaches and moves ahead of the detonation. The critical height, h crit , obtained for stoichiometric H 2 -O 2 bounded by N 2 was 3λ, and corresponded to a velocity deficit of 10% (D/D CJ = 0.9) prior to quenching.

Murray and Lee [START_REF] Murray | The influence of yielding confinement on large-scale ethylene-air detonations[END_REF] showed that transition from a rigid tube to a yielding confinement undergoes a first transient with partial quenching and re-ignition followed by steady propagation. The transition phase is characterized by generation of the ignition centers at the interface which sweep between the shock and the de-coupled reaction zone to re-establish the detonation wave. Quenching occurs if the detonation is not able to overcome the expansion losses coming from the presence of the interface. Experiments conducted by Rudy et al. [START_REF] Rudy | Critical conditions of hydrogen-air detonation in partially confined geometry[END_REF][START_REF] Rudy | Detonations in hydrogen-methaneair mixtures in semi confined flat channels[END_REF][START_REF] Rudy | Experimental determination of critical conditions for hydrogen-air detonation propagation in partially confined geometry[END_REF] and Grune et al. [START_REF] Grune | Detonation wave propagation in semi-confined layers of hydrogen-air and hydrogenoxygen mixtures[END_REF] to determine the propagation limits of detonations in H 2 -O 2 and H 2 -Air using the same experimental configuration as Dabora et al. [START_REF] Dabora | The influence of a compressible boundary on the propagation of gaseous detonations[END_REF] confirmed their findings, namely a h crit ∼ 3λ for stoichiometric H 2 -Air, and 2.4λ

≤ h crit ≤ 3.6λ for H 2 -O 2 .
Reynaud et al. [START_REF] Reynaud | Interactions of a detonation wave confined by a high-temperature compressible layer[END_REF][START_REF] Reynaud | Numerical Study of Detonation Confined by an Inert Gas[END_REF] and Mi et al. [START_REF] Mi | Effect of spatial in-homogeneities on detonation propagation with yielding confinement[END_REF] carried out numerical simulations of detonation propagation into a reactive gas bounded by an inert gas for mixtures exhibiting regular and irregular cellular structures. Single-step chemistry with the same thermodynamic and kinetic parameters for the inert and reactive mixtures were used in both studies. The inert confinement influences the detonation propagation differently depending on the mixture regularity, and more importantly, h crit , was found to be lower for regular than irregular mixtures, characterized by low and high activation energies, respectively. These results are in disagreement with the experimental observations in [START_REF] Radulescu | The failure mechanism of gaseous detonations: experiments in porous wall tubes[END_REF]; the discrepancy can be attributed to the use of inviscid models that fail to capture the mixing and burning of shocked unburnt mixture left behind the leading shock as argued in [START_REF] Radulescu | A detonation paradox: Why inviscid detonation simulations predict the incorrect trend for the role of instability in gaseous cellular detonations?[END_REF]. The presence of unburnt pockets is a characteristic feature of the structure of irregular detonations [START_REF] Radulescu | The ignition mechanism in irregular structure gaseous detonations[END_REF]. However, all the numerical work known to the authors and cited in [START_REF] Radulescu | A detonation paradox: Why inviscid detonation simulations predict the incorrect trend for the role of instability in gaseous cellular detonations?[END_REF] share an extra common assumption apart from an inviscid description of the flow: the chemistry is modeled assuming that the fuel is directly converted into products following a single irreversible reaction. When attempting to numerically predict quenching limits in real systems, in addition to the competition between cooling due to expansion and chemical heat release, the production/consumption of intermediates (active radicals) could also play an important role in extending or reducing the detonation propagation envelopes.

To gain some insight into the role of chemical modeling on the prediction of quenching limits, the present work uses three different models of increasing complexity: single-step, three-step chain-branching and detailed chemistry, to assess their effect on h crit for detonation propagation in a semi-confined environment.

The detonation front dynamics and the two-dimensional structure of the front during steady propagation and quenching are examined.

Computational methodology

Governing equations

The flow is assumed to be inviscid and non-conducting hence described by the 2-D compressible Euler equations.

∂ρ ∂t + ∂ρu i ∂x i = 0 (1)
∂ρu i ∂t + ∂(ρu i u j + pδ ij ) ∂x i = 0 (2)
∂ρe t ∂t + ∂(ρu i (e t + p/ρ)) ∂x i = 0 (3)
∂ρY k ∂t + ∂ρu i Y k ∂x i = ωk , k = 1, ..., N (4)
where ρ, u, p, e t , Y k , ωk are the density, velocity, pressure, specific total energy, the mass fraction of species k in a mixture composed of N species, and the net production/consumption of species k, respectively. δ ij is the Kronecker delta, and

x i are the horizontal and vertical components of space with i = 1, 2, respectively.

The total energy is expressed as

e t = e s + 1 2 u i u i + q (5)
which includes the sensible internal energy, e s , the kinetic energy, 1 2 u i u i , and the local heat release, q. The system of equations above is closed with an equation of state following the ideal gas law, p = ρ RT , where R = R u /W is the specific gas constant, R u the universal gas constant, W the molecular weight of the mixture, and T is the gas temperature. The expressions for e s and q are dependent on the chemical modeling used.

Chemistry modeling 2.2.1. Single-step kinetics

The fuel, F, is directly converted into products P following a single irreversible Arrhenius reaction:

F As -→ P
The species conservation equation for the fuel, Y F , is:

∂ρY F ∂t + ∂ρu i Y F ∂x i = ωF = -ρY F A s exp(-E a /R u T ) (6)
A s and E a are the pre-exponential factor and the activation energy, respectively.

The mixture is assumed to have a constant ratio of specific heats, γ, whose sensible internal energy and local heat release are given by e s = p/[(γ -1)ρ], and q = -(1 -Y f )Q; Q is the energy content of the mixture.

Three-step chain-branching kinetics

In reality, chemical conversion of reactants into products does not take place in a single step, but through a sequence of intermediate stages which typically include chain-initiation, chain-branching and termination steps [START_REF] Birkan | The unified theory for chain branching thermal explosions with dissociation-recombination and confinement effects[END_REF]. Therefore, we account for a few elementary reactions using a three-step chain-branching scheme originally proposed in [START_REF] Short | On the nonlinear stability and detonability limit of a detonation wave for a model three-step chain-branching reaction[END_REF]. To retain the essential dynamics of a real chainbranching reaction, the model consists, at first, of a thermally neutral initiation step with high activation energy in the Arrhenius term, which produces a small concentration of chain-carriers, R, from the fuel, F. Followed by a branchingstep, also thermally neutral and of Arrhenius type, with lower activation energy to allow for the concentration of chain-carriers to increase rapidly. Finally, an exothermic termination step in which chain-carriers are converted into products, P, at a constant rate. Note that heat release could be associated with any/all steps, however here, heat release is only associated with the termination step. This assumption is a good approximation for H 2 mixtures, whereas for some hydrocarbons, e.g. acetylene, the branching steps may also release significant heat [START_REF] Varatharajan | Chemical-kinetic descriptions of hightemperature ignition and detonation of acetylene-oxygen-diluent systems[END_REF].

Three-step models [START_REF] Birkan | The unified theory for chain branching thermal explosions with dissociation-recombination and confinement effects[END_REF][START_REF] Sharpe | Homogeneous explosion and shock initiation for a three-step chain-branching reaction model[END_REF][START_REF] Short | On the nonlinear stability and detonability limit of a detonation wave for a model three-step chain-branching reaction[END_REF][START_REF] Melguizo-Gavilanes | A comparison between constant volume induction times and results from spatially resolved simulation of ignition behind reflected shocks: implications for shock tube experiments[END_REF] allow much more flexibility than single-step kinetics which unavoidably associates heat release with initiation, and offer additional physical insight with a rather negligible increase in computational cost.

The reaction steps are represented by

Initiation F k I -→ R (7)
Branching

F + R k B -→ 2R (8)
Termination

R k T -→ P (9)
The species equations and net production/consumption rates of fuel, ωF , and chain-carriers, ωR , based on the scheme above are:

∂ρY F ∂t + ∂ρu i Y F ∂x i = ωF = -r I -r B ∂ρY R ∂t + ∂ρu i Y R ∂x i = ωR = r I + r B -r T with r I = k I (ρY F ) exp (-E I /R u T ) r B = k B (ρY F )(ρY R )/W exp (-E B /R u T ) r T = k C (ρY R )
The corresponding pre-exponential reaction constants for initiation, branching and Finally, the expression for e s is the same as for the single-step model, and the local heat release is given by q

termination are k I = k C exp (E I /R u T I ) , k B = k C (W/ρ) exp (E B /R u T B ), and
k T = k C , respectively. E I /R u ,
= -(1 -Y F -Y R )Q.

Detailed kinetics

The detailed mechanism of Mével for the oxidation of hydrogen was used [START_REF] Mével | Fundamental combustion properties of oxygen enriched hydrogen/air mixtures relevant to safety analysis: Experimental and simulation study[END_REF],

which includes 9 species and 21 reactions. This model has been extensively validated against experimental databases for laminar burning speeds, ignition delay times and detonation relevant conditions [START_REF] Gallier | Detonation wave diffraction in H2-O2-Ar mixtures[END_REF]. For detailed kinetics, the sensible internal energy and local heat release are given by e s = � T T ref c v dT , and q = -� N k=1 ωk Δh o f,k ; c v and Δh o f,k are the specific heat at constant volume of the mixture and the entalphy of formation of species k. JANAF polynomials are used to account for temperature dependent thermodynamics, i.e. specific heats, internal energy and enthalpy of the mixture.

Determination of model parameters for simplified kinetics

To model the behavior of a stoichiometric H 2 -O 2 mixture, the kinetic parameters were determined, for single-step chemistry, by varying A s and E a /R u to match the constant volume ignition delay times, τ ind , obtained using the detailed mechanism of Mével et al. [START_REF] Mével | Fundamental combustion properties of oxygen enriched hydrogen/air mixtures relevant to safety analysis: Experimental and simulation study[END_REF]. For three-step chain branching chemistry, the same methodology was used to tune k C , E I /R u , E B /R u , T I and T B . The calibration comprises two steps: first, τ ind at the von Neumann state (T vN , p vN , ρ vN ) was targeted; the kinetic parameters were varied to match it to within 0.1%. Second, at fixed ρ vN , the process was repeated for 900 K ≤ T ≤ 2000 K (1.6 MPa ≤ p ≤ 3.6 MPa). For single-step chemistry, A s and E a /R u respectively control the τ ind value and the rate at which it decreases/increases as a function of T (i.e. the slope). For the three-step chain-branching, E I /R u controls the slope for the high temperature range, whereas E B /R u does it for the low temperature range. k C , shifts τ ind to higher/lower values, and T B is the chain-branching cross-over temperature (location where the change of slope in Fig. 1 is observed). This calibration procedure yields a good compromise with regards to matching both, the high and low temperature ranges, with the available degrees of freedom. Special attention was paid to the high temperature range, and particularly to the von Neumann state.

The parameters found are A s = 6.0 × 10 9 s -1 , and delay times with average deviations of less than 20%, and shows a maximum deviation of less than 50% at T ∼ 1250 K. For lower temperatures (T < 1250 K), the differences in ignition delay times increase from one to three orders of magnitude for single-step chemistry.

E a /R u = 14160 K, for single step; and k C = 2 × 10 7 s -1 , E I /R u = 25000 K, E B /R u = 8500 K, T I = 2431 K, T B =

Numerical methods

The governing equations were integrated using our parallel in-house code RESIDENT (REcycling mesh SImulation of DEtonations). Spatial discretization is performed using finite differences together with directional splitting; operator splitting couples the hydrodynamics and the chemistry. The characteristic variables are reconstructed at the cell boundaries using a ninth order monotonicity preserving scheme [START_REF] Suresh | Accurate monotonicity-preserving schemes with Runge-Kutta time stepping[END_REF], which allows for a reduction of dissipation and provides improved accuracy even in the presence of strong flow discontinuities, i.e shocks and contact surfaces, [START_REF] Xu | High resolution numerical simulation of ideal and non-ideal compressible reacting flows with embedded internal boundaries[END_REF][START_REF] Mignone | High-order conservative finite difference GLM-MHD schemes for cell-centered MHD[END_REF]. The Approximate Riemann solver of Toro (HLLC) [START_REF] Toro | Restoration of the contact surface in the HLL-riemann solver[END_REF] with the fix of Shen et al. [START_REF] Shen | A robust HLLC-type riemann solver for strong shock[END_REF] for the shear wave is used to compute the numerical fluxes. A third-order TVD explicit Runge-Kutta is selected for the temporal integration with a CFL number of 0.2. Additionally, a sliding window technique was used to follow the detonation as it propagated into mixture at rest. This allowed us to have a fixed number of cells in the computational domain at all times, irrespective of the length of the channel computed [START_REF] Sow | On the viscous boundary layer of weakly unstable detonations in narrow channels[END_REF][START_REF] Reynaud | A computational study of the interaction of gaseous detonations with a compressible layer[END_REF]. Special care was taken to ensure that the size of the window used did not influence the flow structure and quenching limits reported.

The chemistry is integrated as follows: using an analytical solution that entails freezing the Arrhenius term during the chemical time step for single-step; explicitly for three-step chain-branching; and using a semi-implicit preconditioned iterative method based on a diagonal approximation of the chemical Jacobian for detailed chemistry, (see Savard et al. [START_REF] Savard | A computationally-efficient, semi-implicit, iterative method for the time-integration of reacting flows with stiff chemistry[END_REF]). This numerical integration method has been validated for stiff chemistry, and shown to be stable and to provide good convergence rates for time steps larger than 1 µs. Note that this is useful in the context of direct numerical simulation of turbulent flames, where low Mach number approximations are the norm, and time steps are often restricted by the chemistry instead of the convective time scale. For high speed compressible flow however, the convective and chemical time scales are comparable and typical time steps are significantly lower than 1 µs, hence the species lifetimes contained in the diagonal preconditioner will necessarily capture all critical small chemical time scales. In our calculations, only one iteration step is required.

Domain, initial and boundary conditions

A schematic of the simulation setup is shown in Fig. Second, the resulting fields were used as initial conditions for separate simulations in which the channel height was filled with a layer of inert mixture. In order to have a meaningful comparison with the simplified models the acoustic impedance ratio, (ρa) inert /(ρa) react where a is the speed of sound, was kept con- Different reactive layer heights, h, were tested to determine the height at which successful detonation propagation is no longer possible, h crit . The resolution used was uniform and set to Δx = Δy = l ind /10 pts. A detailed numerical convergence study, included in Appendix A, was carried out to ensure the resolution chosen was sufficient. The computations were performed using ∼ 400-500 processsors with an average of 70 million cells per case; the full study took 2.5 million CPU hours.

stant to a value representative of stoichiometric H 2 -O 2 bounded by N 2 (Y N 2 ,o = 1) at T o , [(γ inert W inert T react )/(γ react W react T inert )] 1/2 = 1.52

Results

Ideal detonation

The simulations run in uniform mixture allow to highlight the differences in global features among the chemical models. Therefore, in this subsection, we compare their detonation front dynamics, instantaneous flow fields and numerical soot foils. The pdf for three-step chain-branching lies above and below that of detailed and single-step chemistry, respectively. Finally, note that when D/D CJ < 0.86 for thee-step chain-branching chemistry, the post-shock temperature is below the crossover temperature (T s < T B ) hence the production of active intermediates is slow resulting in a significant increase in τ ind with values that are about two orders of magnitude longer than those associated with constant volume ignition behind detonation fronts (∼ 1 µs). This will be shown to affect the nature of the flow fields. Overall the front dynamics seems to be reasonably captured by both simplified kinetics schemes. present. This is in line with the observations of Taylor et al. [START_REF] Taylor | The influence of chemical kinetics on the structure of hydrogen-air detonations[END_REF]. Finally, the unburned pockets are larger and seem to last longer downstream of the leading shock for both simplified models considered, whereas detailed chemistry shows a more uniform burned gas temperature downstream of the front. The changes in induction length, l ind , along the height of the front for all chemical models, as seen from these fields, seem to have comparable sizes. The smaller cell size predicted by detailed chemistry is somewhat expected and not due to lack of resolution (see Appendix A) but rather due to potential vibrational non-equilibrium effects [START_REF] Taylor | The influence of chemical kinetics on the structure of hydrogen-air detonations[END_REF][START_REF] Shi | Assessment of vibrational non-equilibrium effect on detonation cell size[END_REF], reaction model uncertainties and/or threedimensional effects [START_REF] Mével | Structure of detonation propagating in lean and rich dimethyl ether-oxygen mixtures[END_REF].

Semi-confined detonation

The differences between the three models in the semi-confined case are investigated in this subsection. The quasi-steady detonation computed above will now propagate into reactive mixture bounded by an inert layer. Based on previous work performed in our group [START_REF] Reynaud | Numerical Study of Detonation Confined by an Inert Gas[END_REF] with single-step chemistry fitted to match the numerically determined cell size and steady detonation velocity with those reported experimentally [START_REF] Kaneshige | Detonation database: GALCIT Report FM97-8[END_REF], the critical height for a stoichiometric H 2 -O 2 mixture bounded by N 2 was found to be h crit = 18 mm. However, since E a /R u is higher for the current fitting in which we take τ ind as a target, h crit is expected to increase [START_REF] Reynaud | Interactions of a detonation wave confined by a high-temperature compressible layer[END_REF][START_REF] Reynaud | Numerical Study of Detonation Confined by an Inert Gas[END_REF][START_REF] Mi | Effect of spatial in-homogeneities on detonation propagation with yielding confinement[END_REF]. Using a layer height slightly above this value, h = 20 mm, we carried out simulations to compare the main features among the three chemical models.

Global features

Figure 6 shows a comparison of the flowfields obtained after 20 µs of propagation. In all cases, characteristic traits of detonations propagating under yielding confinement are recovered, namely a curved front, an oblique transmitted shock and a shear layer separating shocked inert gas from detonation products. However, significant differences appear. While the detonation seems to propagate comfortably in the detailed chemistry case, the structure in the single-step and three-step cases exhibits a more irregular behavior with sizable pockets of unburnt gas distributed over the flow field, as well as larger distances between the leading shock and the reaction zone in the vicinity of the interface. The detonation front is curved for all chemical models which is an inherent signature of a velocity deficit.

Detailed chemistry seems to be less affected by the inert boundary showing less curvature, whereas single-step and three-step chemistry shows larger bulbs and more pronounced cusps.

Further examination of the flow field at longer times (Fig. 7), after ∼ 100 µs of interaction with the interface, reveals that the detonation continues to propagate without any issues for detailed chemistry; single-step and three-step chainbranching chemistry, on the other hand, are incapable of sustaining a detonation at this layer height. This outcome suggests that the quenching limits, characterized here using h crit , are dependent on the choice of chemical modeling used.

We emphasize however, that alternative calibration methods using fitting targets other than τ det could lead to different results. In order to find h crit , the value of h should be increased for single-step and three-step chain-branching, and decreased for detailed chemistry. Since for the former two cases the detonation failed to 21 propagate, whereas for the latter it transmitted successfully. Fifteen additional simulations were run, progressively increasing and decreasing the value of h, to quantify the differences in h crit among the chemical models.

Critical heights and quenching dynamics

The values of h crit found are 24, 20 and 6 mm for single-step, three-step and detailed chemistry, respectively. While the differences in flow structure were more pronounced when comparing the models at fixed heights (Figs. 6 and7), close to h crit , the flow fields show some similarities (Fig. 8), namely increased curvature and presence of unburnt pockets, as well as two distinct zones: (i) decoupling of the leading shock and reaction zone close to the interface; and (ii) nearly undisturbed propagation as the bottom wall is approached. To further investigate the quenching dynamics, numerical soot foils for heights slightly above h crit were examined to observe how the detonation wave experiences losses. The reactive-inert layer complex is located 10 mm away from the left boundary (x = 10 mm) for all the chemical models tested.

Figure 9 displays soot foil records with single-step for h = 28 mm (top) and h crit = 24 mm (bottom). For h > h crit , the detonation successfully propagates, the initial interaction with the interface results in oblique streaks traveling toward the bottom wall along which the cell size increases. This increase in cell size is caused by unsteady expansion waves coming from the interface which partially decouple the leading shock and reaction zone. Upon reflection at the bottom wall (x ∼ 100 mm) a new curved streak of cells is formed, now oriented towards the interface (x = 140 -150 mm); upstream of it, re-ignition occurs accompanied by smaller cells suggesting the presence of a locally overdriven front that subsequently propagates without failing through the reactive layer. For h = h crit , the dynamics is similar to that described above, except that after the first reflection from the bottom wall, the detonation is not able to continue propagating. The thermodynamic state (p, T ) generated at the wall upon reflection, and the chemical time scale associated with it, is not strong enough to compete with the expansion induced cooling coming from the interface which results in total quenching of the front. The distance to quenching, x Q , defined as the first location where full decoupling is observed after interaction with the interface, lies around 200 mm for single-step chemistry. The evolution obtained for detailed chemistry seems to be more rich including some of the features observed in single-step and three-step chain-branching chemistry. For h = 10 mm > h crit (Fig. 11 -top) shortly after the interaction with the interface (10 mm < x < 55 mm), the cell size increases gradually without local quenching in line with the dynamics described for single-step chemistry; for 50 mm < x < 115 mm the thick clear band is evidence of full local quenching of the front, now in line with the dynamics described for three-step chain-branching chemistry. In contrast with the two previous cases, re-establishment of the det-onation wave takes place through several quenching and re-ignition steps. Final successful re-ignition occurs upon reflection from the bottom wall at x ∼ 105 mm; ignition centers emerging from the yielding confinement re-initiate the detonation wave [START_REF] Dabora | The influence of a compressible boundary on the propagation of gaseous detonations[END_REF][START_REF] Dabora | The influence of a compressible boundary on the propagation of gaseous detonations[END_REF]. For h = h crit = 6 mm (Fig. 11 -bottom), the failure of the front occurs through a gradual separation between the reaction zone and leading shock as cooling induced expansion emanating from the interface quenches the chemistry. No local quenching or re-ignition attempts were observed at this reactive layer height. x Q , for detailed chemistry was 60 mm. Three-step chain-branching and detailed chemistry show similar re-initiation dynamics. Table 1 summarizes the critical heights and quenching distances obtained. The value of h crit predicted by detailed chemistry is in very good agreement with experimentally reported values [START_REF] Grune | Detonation wave propagation in semi-confined layers of hydrogen-air and hydrogenoxygen mixtures[END_REF]. Simplified kinetics yield h crit values that are more than three times (single-step), and four times (three-step) larger than those obtained with detailed chemistry. Finally, the quenching distances, x Q , increase with decreasing chemical modeling complexity as Experimental [START_REF] Dabora | The influence of a compressible boundary on the propagation of gaseous detonations[END_REF] 4.6 -

x Q, Detailed � x Q, 3-Step < x Q, 1-Step .

Unburnt pocket analysis

In an attempt to understand the increased resistance that detailed chemistry exhibits we analyze in detail one of the mechanisms whereby unburnt pockets get consumed, i.e. constant volume explosion, and also provide a simple estimate of the time scales for diffusive burning. Figure 12 shows an overview of the full flow field shortly after interaction with the inert interface, and a zoom to the region of interest.

Using the thermodynamic state (p and T ) in five different locations inside the unburnt pocket (see close-up to normalized density gradient) constant volume delay times were computed in two different ways: (i) assuming the composition to be that of fresh mixture (Y H 2 ,o and Y O 2 ,o ) -case 1; (ii) using the actual local compositions (Y i ) -case 2. This was done to assess the effect of incipient intermediates on the delay times. For single-step and three-step chemistry, only case 1 can be considered using Y f = 1.

The presence of intermediates expectedly resulted in faster τ ind (see Fig. 13) but the differences are not significant to provide any clue regarding the increased resistance of the wave to failure. Bear in mind however that the thermodynamic state of this pocket is constantly changing as it is subjected to transverse and expansion waves of various strengths whose overall effect could result in an effective decrease in τ ind . Moreover, there are variations of more than one order of magnitude in τ ind across the points examined that single-step chemistry does not capture.

A simple order of magnitude estimate to determine whether the time scales for diffusive burning are comparable with those computed above for the chemistry, is W varies from 12 g/mol in shocked fresh mixture to 14-16 g/mol in burnt mixture (due to dissociation) leading to an increase in temperature of the products, whereas γ shows more significant variations within the pocket itself (1.33-1.36) followed by a decrease toward ∼ 1.21 in burnt products. None of these observations allow to provide conclusive answers regarding the differences in h crit obtained among the chemical models. The pressure and density profiles show only slight differences at the von Neumann state (vNx/l ind = 0) with simplified kinetics overpredicting it. The CJ (x/l ind ∼ 7) is well captured by all models. The temperature profiles show the opposite behavior as T is higher for detailed chemistry at CJ and essentially the same at the vN state for all models. The higher value of T at CJ for detailed chemistry is simply a consequence of accounting for changes in W . This can be shown using the ideal gas law: T CJ = (p/ρR u ) CJ W Detailed , since the value of the first term on the right-hand side of the expression is approximately the same for all chemical models. Another evident difference in all the profiles given by simplified kinetics are the trajectories taken to expand the mixture from vN to CJ.

The thermicity profiles, σ, shed some light as to why this is the case and exhibit the most interesting behavior. The rates at which heat is released, their maxima, as well as the lengths associated to the induction phase and heat release differ significantly for simplified kinetics as compared to detailed chemistry. This suggests that the stability of the mixture characterized by the parameter χ [START_REF] Ng | Assessment of detonation hazards in highpressure hydrogen storage from chemical sensitivity analysis[END_REF][START_REF] Radulescu | The propagation and failure mechanism of gaseous detonations: experiments in porous-walled tubes[END_REF] is different even though the simplified models are fitted to supposedly mimic the same reactive gas (i.e. stoichiometric H 2 -O 2 at atmospheric conditions).

The χ stability parameter [START_REF] Ng | Assessment of detonation hazards in highpressure hydrogen storage from chemical sensitivity analysis[END_REF][START_REF] Radulescu | The propagation and failure mechanism of gaseous detonations: experiments in porous-walled tubes[END_REF] is defined as χ = T vN /τ ind • (∂τ ind /∂T ) vN • l ind /l reac where l reac = u CJ / σmax is the reaction length; T vN and u CJ are the temperature and flow speed at the von Neumann and Chapman-Jouguet state, respectively. To compare the values of χ among the chemical models, we can write a generic ratio as follows:

χ a χ b = � T vN,a T vN,b � � τ ind,b τ ind,a � � ∂τ ind,a ∂τ ind,b � � l ind,a l ind,b � � u CJ,b u CJ,a � � σmax,a σmax,b � (10)
where a and b are subscripts corresponding to the models being compared. Since the von Neumann temperature and associated delay times, as well as their slopes in the high temperature range are approximately the same for all mechanisms, the first three ratios in Eq. 10 are unity. This simplifies the expression to:

χ a χ b ∼ � l ind,a l ind,b � � u CJ,b u CJ,a � � σmax,a σmax,b � (11)
The values of the remaining ratios can then be computed using Fig. 14.

χ 1-Step χ 3-Step ∼ (4.12) • (0.996) • (0.893) ∼ 3.664 χ Detailed χ 3-Step ∼ (2.06) • (1.115) • (2.176) ∼ 4.998 χ Detailed χ 1-Step ∼ χ Detailed χ 3-Step • χ 3-Step χ 1-Step ∼ 1.364
The results obtained show that while the χ values for single-step and detailed chemistry are rather close, the differences are large when compared to three-step chain-branching chemistry. The discrepancy seems to arise from the differences in l ind and σmax among the mechanisms.

Discussion and conclusion

Two-dimensional simulations were conducted to assess the influence of the chemical modeling on the detonation structure and its quenching limits. Three different kinetic schemes were used to model a stochiometric H 2 -O 2 mixture at ambient conditions. Additionally, two configurations were investigated: ideal propagation in a channel and non-ideal semi-confined propagation with eventual quenching.

Three-step chain-branching chemistry reproduces accurately the spectrum of induction times as compared to detailed chemistry, in the high and low temperature regions. Single-step chemistry only captures the high temperature range.

In the ideal case, the range of numerically predicted cell sizes was in agreement with experimental observations, which means that this characteristic length is most probably determined by the high temperature kinetics, as suggested by the phenomenological relations between the cell size and the induction length, computed at the vN state.

The dynamics of the leading shock for both simplified kinetics models and Another differentiating feature between the simplified models in this temperature range is that for three-step chain-branching chemistry the rate of production of radicals decreases significantly and heat release to the mixture stops abruptly. This is in contrast with single-step chemistry where energy deposition continues over a longer spatial scale as evidenced from the thermicity profiles. In real H 2 systems however, there is a change in chemical pathways for T < T B where linear chains take over, partially converting the H 2 to HO 2 that in the presence of enough H atoms can replenish the radical pool through H+HO 2 → OH+OH, ultimately resulting in ignition of the mixture and associated heat release.

Analysis of the induction times of different samples within an unburnt pocket indicates that the presence of active radicals cannot solely explain the observed resistance to losses. As hydrogen is consumed, the molecular weight increases resulting in temperature rising at a higher rate within the reaction zone than in the simplified kinetics models. This results in enhanced reactant consumption.

Nevertheless, the effective activation energy of the mixture is reduced whose regularizing effect may not completely explain the emergence of reactive transverse waves.

In terms of χ the mixture stability increases (values of χ decrease) as χ Detailed > χ 1-Step � χ 3-Step . The increase of χ (or equivalently of the reduced activation energy in the case of single-step models) and associated instabilities are not sufficient to explain the higher critical height. However, the h crit results seem to correlate well with the values of σmax obtained, i.e. σmax / σmax, Detailed ∝ h crit /h crit, Detailed .

This suggests that improved simplified models could be developed by using the thermicity profiles together with ignition delay times as fitting targets.

Furthermore, due to the hydrogen depletion, the ratio of specific heats γ approaches one, crossing over the critical value [START_REF] Mach | Mach reflection bifurcations as a mechanism of cell multiplication in gaseous detonations[END_REF] for which inert and reactive shock bifurcations give rise to the spontaneous appearance of triple points [START_REF] Lau-Chapdelaine | Viscous solution of the tripleshock reflection problem[END_REF][START_REF] Lau-Chapdelaine | Viscous triple shock reactions relevant to detonation waves, and Detonation dynamics predicted by the Fickett model[END_REF]. These gasdynamics features together with the transverse reactive waves observed in the detailed chemistry results may provide the necessary feedback to promote fuel consumption within unburnt pockets, and ultimately account for its observed resistance to losses.

The critical height predicted with detailed chemistry (h crit = 6 mm) is in good agreement with experimental data (h crit � 4.6 mm) [START_REF] Dabora | The influence of a compressible boundary on the propagation of gaseous detonations[END_REF], despite the fact that we neglect three-dimensional effects. This advocates for the predictive capabilities of detailed chemistry as compared to simplified kinetics. Nonetheless, we acknowledge that this outcome is specific to H 2 mixtures and direct extrapolation of our results to hydrocarbons may not be applicable as their cellular structure is very ir-regular. For the latter it may be necessary to assess whether diffusive consumption of unburnt pockets plays a role.

A natural extension of our work would be to allow the three-step chain-branching model to include molecular weight and ratio of specific heats variations; also, extension of the simplified kinetics to include competition for radicals as discussed in [START_REF] Liang | Detonation front structure and the competition for radicals[END_REF] may provide the missing physics to improve the predictive capabilities of simplified models.

  and E B /R u are the initiation and branching activation temperatures, and T I and T B are the crossover temperatures at which the chain-initiation and branching rates become equal to the chain-termination rate.

Figure 1 :

 1 Figure 1: Top: constant volume induction times as a function of inverse temperature. Initial conditions (von Neumann stateρ vN ) computed for a stoichiometric H 2 -O 2 mixture at p o = 100 kPa and T o = 295 K. At fixed ρ vN , temperature was varied in the range 900 K ≤ T ≤ 2000 K, resulting in associated pressure variations of 1.6 -3.6 MPa. Bottom: percent deviation for singlestep and three-step chain-branching with respect to detailed chemistry.

Figure 1

 1 Figure1shows the ignition delay times predicted by each of the three chemical models, and the percent deviation computed for single-step and three-step chain-branching chemistry using the ignition delay times from detailed chemistry, τ det , as a reference. Both kinetic models predict approximately the same ignition delay time as detailed chemistry in the high temperature range (T ≥ 1429 K) with average deviations of less than 10 % and 5 % for single-step and three-step chainbranching chemistry, respectively. The change of activation energy typical of H 2 chemistry, i.e. change of slope in black line, is expectedly not captured by the single-step model. The three-step on the other hand predicts the low temperature

2 .

 2 The simulations were run in two steps. First, a detonation was initiated and allowed to propagate in a channel completely filled with reactive mixture, i.e. stoichiometric H 2 -O 2 , until a quasi-steady structure was achieved (∼ 100 µs of propagation). The initial conditions used were p o = 100 kPa, T o = 300 K with mass fractions of fuel, Y F ,o = 1, for single-step kinetics; and fuel and radical species Y F ,o = 1 and Y R,o = 0, for three-step chain-branching kinetics. For detailed chemistry, the initial mass fractions of H 2 and O 2 are Y H 2 ,o = 0.1112 and Y O 2 ,o = 0.8888.

Figure 2 :

 2 Figure 2: Simulation setup and computational strategy to determine the critical height.

Figure 3 :

 3 Figure 3: Normalized instantaneous shock front velocity as a function of distance (top), and probability density function of the leading shock velocity (down) for single-step, three-step chainbranching and detailed chemistry -ideal detonation. The detonation has propagated about 100 µs.

Figure 3

 3 Figure 3 shows the normalized instantaneous detonation velocity, D/D CJ , and its probability density function (pdf) measured at the bottom wall of the channel. The velocity peaks arise from transverse wave and triple point collisions. The latter collisions give rise to local Mach stems that subsequently decay and evolve to an incident shock as the speed of the front drops below D CJ , inducing a local decoupling with the reaction zone. A new cycle begins, upon new triple point collisions, resulting in an abrupt acceleration of the front. This behavior is characteristic of detonations and all chemical models capture it.

3. 1 . 2 .

 12 Instantaneous structure Instantaneous two-dimensional fields of normalized temperature (T /T o ), and magnitude of the density gradient (|∇ρ|/|∇ρ max |) are displayed in Fig. 4 for the three models. The fields are taken after ∼ 100 µs corresponding to ∼ 300 mm of propagation. This guarantees that a quasi-steady structure, independent of the initiation transient, was achieved. Mach stems and incident shocks are linked with transverse waves which propagate back and forth along the detonation front, becoming weaker as they get away from the front. Unburnt pockets result from their collisions. Three different physical mechanisms contribute to the consumption of these pockets: (i) constant volume explosion enhanced by transverse waves that repeatedly change their thermodynamic state; (ii) transverse waves; (iii) mixing and diffusive burning. The former two are the only ones the inviscid model used in this work would capture. In the normalized density gradient fields for detailed chemistry, smaller flow structures and seemingly stronger transverse waves than those observed for single-step and three-step chain-branching chemistry are

Figure 4 :

 4 Figure 4: Instantaneous fields for the three chemical models considered. Top: single-step; center: three-step chain-branching; bottom: detailed chemistry.

Figure 5 :

 5 Figure 5: Numerical soot-foils and histograms showing the distribution of cell sizes (λ) for singlestep (top), three-step chain-branching (center) and detailed chemistry (bottom). The height of the reactive layer is h = 20 mm.

Figure 6 :

 6 Figure 6: Instantaneous detonation structure for single-step (top), three-step chain-branching (center) and detailed chemistry (bottom) after 20 µs of propagation into the reactive/inert layer complex. The height of the reactive layer is h = 20 mm. The solid horizontal line in normalized magnitude of density is a visual aid showing the location of the reactive/inert interface.

22

 22

Figure 7 :

 7 Figure 7: Instantaneous detonation structure for single-step (top), three-step chain-branching (center) and detailed chemistry (bottom) after 100 µs of propagation into the reactive/inert layer complex. The height of the reactive layer is h = 20 mm. The solid horizontal line in normalized magnitude of density is a visual aid showing the location the reactive/inert interface.

Figure 8 :

 8 Figure 8: Comparison of flow structures at heights slightly above h crit for single-step (lefth = 28 mm), three-step chain-branching (centerh = 24 mm) and detailed chemistry (righth = 10 mm).

Figure 9 :

 9 Figure 9: Numerical soot foils for single-step chemistry for two reactive layer heights: h = 28 mm -top; h crit = 24 mm -bottom.

Figure 10 :

 10 Figure 10: Numerical soot foils for three-step chain-branching chemistry for two reactive layer heights: h = 24 mm -top; h crit = 20 mm -bottom.

Figure 11 :

 11 Figure 11: Numerical soot foils for detailed chemistry for two reactive layer heights: h = 10 mm -top; h crit = 6 mm -bottom. Note that the horizontal and vertical scales are different to ease visualization of the cellular structure.

Figure 12 :

 12 Figure 12: Top: normalized magnitude of density gradient, ∇ρ/∇ρ max , of full flow field. Bottom: close-up to unburnt pocket on one pocket of unburnt gas.

Figure 13 :

 13 Figure 13: Constant volume delay times, τ ind , computed at different locations inside the unburnt pocket.

3. 2 . 4 .

 24 Comparison among the ZND profilesThe ZND (Zel'dovich-von Neumann-Döring) structure obtained with all chemical models is shown in Fig.14. The characteristic lengths for each are: a half reaction length of l 1/2, 1-Step = 70 µm for single-step, defined as the distance from the leading shock to the location where half of the fuel is consumed. As mentioned earlier, single-step models do not have a clearly defined thermally neutral zone before heat release; for three-step chain-branching and detailed chemistry: l ind, 3-Step = 17 µm and l ind, Detailed = 35 µm, respectively, formally defined as the distance from the leading shock to maximum thermicity σmax .

Figure 14 :

 14 Figure 14: ZND structure obtained using single-step, three-step chain-branching and detailed chemistry. Pressure, density and temperature are normalized by their values in fresh mixture; distance by l ind, Detailed = 35 µm. Thermicity, σ, is kept in its dimensional form.

  detailed chemistry were similar, as shown by the pdf of the normalized detonation velocity, D/D CJ . Detailed chemistry also shows a flat region around the CJ value, up to values of D/D CJ corresponding to the crossover temperature. Below this temperature, the ignition times are no longer commensurate with those associated with adiabatic shock-induced ignition behind detonation fronts. This may explain the presence of bulbs and cusps in the front for three-step chain-branching chem-istry. However, this increased curvature is not present in detailed chemistry, which also exhibits reactant consumption downstream of the transverse waves along the front. These are the most remarkable features that could explain the resilience of H 2 mixtures to failure.The critical heights obtained increase as h crit, Detailed � h crit, 3-Step < h crit, 1-Step .h crit, Detailed was by far the lowest among the three chemical models. Although the simplified kinetics schemes and detailed chemistry share the same ignition delays and shock dynamics in the high temperature range, their predicted critical heights differ significantly (h crit, 3-Step /h crit, Detailed ∼ 3.33). The critical height for singlestep, h crit, 1-Step , on the other hand, is only 20% more than h crit, 3-Step . However, the excursion of the detonation wave to low velocities and corresponding post-shock temperatures below the crossover temperature should favor quenching to occur at a height lower than that of the single-step model whose induction time is shorter.

Table 1 :

 1 Critical heights, h crit , and quenching distances, x Q , predicted with different chemical models.

	Chemistry modeling h crit (mm) x Q (mm)
	Single-step	24	200
	Three-step	20	140
	Detailed	6	60

Acknowledgements

The computations were performed using HPC resources from the cluster of Pprime, the Mésocentre de Calcul Poitevin and from GENCI-CINES (Grant 2018-A0052B07735). This work was supported by the CPER FEDER Project of Région Nouvelle Aquitaine.

Appendix A. Numerical convergence

A convergence study was performed to determine an adequate spatial resolution to run our simulations. Here, we only show results for three-step chainbranching and detailed chemistry because the numerical convergence for singlestep has been thoroughly presented in previous work by our group using the same in-house code [START_REF] Reynaud | A computational study of the interaction of gaseous detonations with a compressible layer[END_REF]. The computational domain used is a channel of L x = 100 mm by L y = 2 mm corresponding to ∼ 120 l ind and ∼ 60 l ind along the height of the channel for three-step chain-branching and detailed chemistry, respectively.


Julian Biau
email: julian.biau@clermont.unicancer.fr

E Thivat

E Chautard

M Boone

B Chauffert G , C Bourgne

D Richard

I Molnar

S Levesque

R Bellini

F Kwiatkowski

P Verrelle

Godfraind

X Durando

Phase 1 trial of ralimetinib (LY2228820) with radiotherapy plus concomitant temozolomide in the treatment of newly diagnosed glioblastoma

Keywords: ralimetinib, radiotherapy, temozolomide, glioblastoma, phase I clinical trial

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

Introduction

Glioblastoma (GBM) is the most common and aggressive adult primary brain tumor [START_REF] Ricard | Primary brain tumours in adults[END_REF][START_REF] Louis | The 2016 World Health Organization Classification of Tumors of the Central Nervous System: a summary[END_REF].

Although radiotherapy (RT) with concomitant and adjuvant temozolomide (TMZ) has increased patient survival, long-term prognosis remains poor, with a median survival of 15 months [START_REF] Stupp | Radiotherapy plus concomitant and adjuvant temozolomide for glioblastoma[END_REF][START_REF] Stupp | Effects of radiotherapy with concomitant and adjuvant temozolomide versus radiotherapy alone on survival in glioblastoma in a randomised phase III study: 5-year analysis of the EORTC-NCIC trial[END_REF]. Tumor progression most often occurs inside the irradiated tumor volume [START_REF] Bleehen | A Medical Research Council trial of two radiotherapy doses in the treatment of grades 3 and 4 astrocytoma. The Medical Research Council Brain Tumour Working Party[END_REF], showing the high radioresistance of these tumors. Mitogen-activated protein kinase (MAPK) cascades are key signaling pathways involved in the regulation of cell proliferation, survival and differentiation. Activation of p38-MAPK has been associated with a poor prognosis in GBM [START_REF] Patil | High levels of phosphorylated MAP kinase are associated with poor survival among patients with glioblastoma during the temozolomide era[END_REF]. P38-MAPK activation represents a compensatory response by tumor cells to environmental stressors such as RT and chemotherapy [START_REF] Hideshima | Targeting p38 MAPK inhibits multiple myeloma cell growth in the bone marrow milieu[END_REF][START_REF] Hideshima | p38 MAPK inhibition enhances PS-341 (bortezomib)-induced cytotoxicity against multiple myeloma cells[END_REF]. Therefore, combining the current treatment of GBM with p38-MAPK inhibition represents a promising opportunity.

Ralimetinib (LY2228820), a selective inhibitor of and -isoforms of p38-MAPK, reduces phosphorylation of its cellular direct target, MAPK-activated protein kinase 2 (MAPKAP-K2).

Preclinical studies demonstrated that ralimetinib had antitumor activity [START_REF] Campbell | Characterization of LY2228820 dimesylate, a potent and selective inhibitor of p38 MAPK with antitumor activity[END_REF] and enhanced sensitivity to TMZ in GBM xenograft models [START_REF] Starling | P38 MAPK inhibitor, LY2228820, causes significant chemopotentiation of temozolomide in U87MG human glioblastoma xenografts[END_REF]. Ralimetinib has also been tested in different phase 1 or 2 clinical trials alone or combined with hormono/chemotherapy [START_REF] Patnaik | A First-in-Human Phase I Study of the Oral p38 MAPK Inhibitor, Ralimetinib (LY2228820 Dimesylate), in Patients with Advanced Cancer[END_REF][START_REF] Vergote | A randomized, double-blind, placebo-controlled phase 1b/2 study of ralimetinib, a p38 MAPK inhibitor, plus gemcitabine and carboplatin versus gemcitabine and carboplatin for women with recurrent platinum-sensitive ovarian cancer[END_REF][START_REF] Bendell | A phase 1 dose-escalation study of checkpoint kinase 1 (CHK1) inhibitor prexasertib in combination with p38 mitogen-activated protein kinase (p38 MAPK) inhibitor ralimetinib in patients with advanced or metastatic cancer[END_REF]. However, before this study, no clinical trials had tested ralimetinib in combination with RT ± chemotherapy.

Here, we report the results of the first phase 1 trial to evaluate the combination of ralimetinib (a p38-MAPK inhibitor) with RT and chemotherapy (TMZ) in the treatment of newly diagnosed GBM.

The primary objective was to determine the recommended dose of ralimetinib in combination with TMZ and RT. The secondary objectives were to characterize the pharmacokinetics drug-drug interaction and impact of ralimetinib on MAPKAP-K2 activation in peripheral blood mononuclear cells (PBMC).

Materials and Methods

Patients

Eligible patients were 18 to 75 years of age with newly diagnosed and histologically confirmed GBM, with a recursive partitioning analysis (RPA) of class III or IV [START_REF] Li | Validation and simplification of the Radiation Therapy Oncology Group recursive partitioning analysis classification for glioblastoma[END_REF], and adequate hematologic and hepatic function. Patients receiving corticosteroids were eligible if they received a stable or decreasing dose for at least 14 days before enrollment.

Patients with a history of other malignancy within 5 years prior to enrollment, diagnosis of inflammatory bowel disease, diarrhea of any cause  CTCAE grade 2, a major bowel resection that would alter oral drug absorption, and/or concurrent administration of immunosuppressive therapy were excluded. All patients provided written informed consent prior to enrollment.

Study design and treatment plan

The study was approved by the ethics committee and the national regulator and registered with www.clinicaltrials.gov (NCT02364206). This phase I study was an open-label, multicenter dose-escalation study with an expansion cohort. The dose escalation was driven by a Tite-CRM (Time to event Continual Reassessment Method) [START_REF] Cheung | Sequential designs for phase I clinical trials with late-onset toxicities[END_REF] method with 3 ralimetinib dose levels. Cohorts of 3 to 6 patients were treated, with a minimum of 6 patients at the recommended dose.

Ralimetinib. Ralimetinib was given orally every 12 hours, 7 days a week, for 2 cycles of 2 weeks [START_REF] Patnaik | A First-in-Human Phase I Study of the Oral p38 MAPK Inhibitor, Ralimetinib (LY2228820 Dimesylate), in Patients with Advanced Cancer[END_REF] (Figure 1), at 100 (dose 1), 200 (dose 2) or 300 mg/12h (dose3). The first cycle started one week before the beginning of RT and the second during the 4 th and 5 th weeks of RT.

Radiotherapy. For irradiation, all patients were immobilized with custom thermoplastic masks. Target volume and organs at risk delineation was done by a dedicated CT-scan in the treatment position matched and fused with contrast-enhanced T1-weighted and Flair MRI sequences. The gross tumor volume (GTV) was defined as the contrast enhancement area in the T1-weighted MRI sequence, including the tumor bed for patients with partial or complete resection. The clinical target volume (CTV) was defined as the addition of a geometric tridimensional 1-cm margin around the GTV that was corrected to the anatomical borders. The CTV also included hyperintensity in the Flair MRI sequence.

The planning target volume (PTV) was defined as the addition of a geometric tridimensional 4-mm margin around the CTV. RT consisting of fractionated focal irradiation at a dose of 2 Gy per fraction was given once daily five days per week over a period of 6 weeks, for a total dose of 60 Gy. Threedimensional conformal RT and Intensity-Modulated RT (IMRT) were allowed.

Temozolomide: Concomitant TMZ at a dose of 75 mg/m 2 per day was given 7 days per week from the first day of RT until the end of RT. Four weeks after RT, patients received a maximum of 6 cycles of adjuvant TMZ according to the standard 5-day schedule every 28 days (at a dose of 150 mg/m²/day for the first cycle and then at 200 mg/m²/day in the absence of toxicity).

Patient evaluation

Toxicity was graded according to the National Cancer Institute's Common Toxicity Criteria Disease evaluations were based on RANO criteria (Response Assessment in Neuro-Oncology) [START_REF] Wen | Updated response assessment criteria for highgrade gliomas: response assessment in neuro-oncology working group[END_REF]. Magnetic Resonance Imaging (MRI) was performed within 28 days before the initiation of the study treatment, 4 weeks after the end of RT, every 8 weeks during the adjuvant period, and subsequently every 3 months during the first 2 years.

Biomarkers assessment

A central pathology review and biomarker assessment has been implemented on FFPE blocks used for diagnosis. ATRX, PTEN protein scoring, CD34, IDH1 R132H mutation, and pMAPKAPK-2 were detected by immunohistochemistry. MGMT promoter methylation was performed by a pyrosequencing methylation assay [START_REF] Villalva | O6-Methylguanine-methyltransferase (MGMT) promoter methylation status in glioma stem-like cells is correlated to temozolomide sensitivity under differentiation-promoting conditions[END_REF][START_REF] Mcdonald | The T genotype of the MGMT C>T (rs16906252) enhancer single-nucleotide polymorphism (SNP) is associated with promoter methylation and longer survival in glioblastoma patients[END_REF].

Pharmacokinetic assay

Ralimetinib and TMZ concentrations were determined by a multiparameter method using a liquid chromatography/tandem mass spectrometry assay. Whole blood samples were collected on days (D) 7 (ralimetinib), 28 (TMZ) and 35 (ralimetinib and TMZ) with a 10-point kinetic analysis at 10h (Figure 1). Pharmacokinetic analyses included the area under the plasma concentration/time curve to the last sampling time point (AUC), peak observed concentration (Cmax), and time to Cmax (Tmax).

To explore the passage of ralimetinib across the blood-brain barrier, an optional substudy was proposed with a ralimetinib dosage in cerebrospinal fluid 7 days after administration.

Pharmacodynamic assay

The pharmacodynamic of ralimetinib was explored through the assessment of pMAPKAP-K2 on anisomycin-stimulated PBMC by flow cytometry. Pharmacodynamic analyses were conducted on plasma samples collected at the predose on D1, and after treatment administration on D7 (ralimetinib), D28 (TMZ), D35 (ralimetinib and TMZ) (Figure 1).

Statistical considerations

The recommended dose was the maximum tolerated dose (MTD) of ralimetinib. The MTD was defined as the highest dose tested in which a dose-limiting toxicity (DLT) was experienced by no more than 33% of patients. DLT was defined as any grade 3-4 toxicity except alopecia, nausea, and vomiting which can be rapidly controlled with appropriate measures. Only toxicities occurring between the first day of ralimetinib until 2 weeks after the end of RT were considered for DLT assessment.

Due to the exploratory nature of the current study and the relatively low number of patients, mainly descriptive statistics were used. The safety population consisted of all patients who received any dose of ralimetinib.

Progression-free survival (PFS) and overall survival (OS) were measured from study enrollment. PFS and OS curves and estimates were constructed using the Kaplan-Meier method.

Predictive factors of PFS were investigated using univariate Cox regressions and a multivariate model including parameters with p < .25 in the univariate analysis.

Comparisons of pharmacokinetic and pharmacodynamic parameters at different times and doses

were assessed by paired t-test, Welch's t-test or Wilcoxon's rank test (depending on the distribution of data and without multiple-comparisons correction due to the exploratory nature of the analysis and very small sample size).

The statistical significance threshold was set at 5%. Statistical analyses were performed using R software.

Results

Between June 2015 and December 2016, 9 patients were enrolled in the phase 1 study (cohort 1 at dose 1: n=6; cohort 2 at dose 2: n=3); and 9 patients in the expansion cohort dose 1). Patient characteristics at baseline are presented in Table 1. All enrolled patients received at least one dose of ralimetinib: 15 received ralimetinib at 100 mg/12h and 3 at 200 mg/12h. 15 completed the 2 cycles of ralimetinib through radiochemotherapy and 15 completed the 6 cycles of adjuvant TMZ. A dose reduction of ralimetinib (between cycles) was implemented for 2 patients (treated at 200 mg) due to toxicity. In addition, six patients interrupted ralimetinib treatment due to toxicity (n=4: 2 for each dose), the patient's decision (n=1) and non-respect of the treatment schedule (n=1). This last patient was withdrawn from the study for non-compliance with the administration schedule (without concomitant administration of ralimetinib with chemoradiotherapy due to RT offset for technical reasons) but was evaluated for safety. One patient treated at 200 mg/12h permanently discontinued ralimetinib treatment for toxicity.

In the Phase 1 part, none of the first 3 patients treated at dose 1 had a DLT, allowing for dose 2 assessment. The three patients treated at 200 mg/12h presented a DLT: one patient had a grade 3 face edema, and two patients had a grade 3 rash and grade 3 hepatic cytolysis (Table 2). According to study design, 3 more patients were treated at dose 1. Of these three patients, only one patient presented a DLT consisting of grade 3 lymphopenia. None of the DLT was related with RT. All these DLT were reversible with appropriate measures. The MTD of ralimetinib was then considered to be 100 mg/12h (dose 1) and was used in the expansion cohort. Three of the 9 patients of the expansion cohort presented a DLT: 2 had hepatic cytolysis (1 of grade 3, another of grade 4 with cholestasis, and 1 with a rash (grade 3). Among the 15 patients (6 in phase 1 and 9 in the expansion cohort) treated at 100 mg/12h, DLT occurred in a total of 4 patients (27%) which confirmed the recommended dose of 100 mg/12h. Overall, the most common adverse events (AE) (all grades and for the entire study period) were asthenia (78%), nausea/vomiting (72%), dermatitis/rash (61%), headache (61%), constipation (44%), hepatic cytolysis (44%), and alopecia (39%) (Table 3). Twelve patients experienced one or more severe (grade ≥ 3) AE (67%). The most frequently severe AE for the entire study period were dermatitis/rash in 22% (4/18), hepatic cytolysis in 22% (4/18), and lymphopenia in 11% (2/18) of patients. Considering only patients treated at the recommended dose of 100 mg, severe AE were observed in 5 patients during the concomitant period (33%): hepatic cytolysis in 13% (2/15), cholestasis in 7% (1/15), dermatitis/rash in 7% (1/15), lymphopenia in 7% (1/15), and nausea/vomiting in 7% of patients (1/15). No death related to treatment was reported. No patient presented a grade ≥ 3 radio-induced toxicity.

Concerning pharmacokinetic, mean Cmax after ralimetinib alone at 100 mg/12h was 300 ± 64 ng/mL vs 827 ± 144 ng/mL at 200 mg/12h (p=0.048) (Figure 2). Mean AUC0-10 after ralimetinib alone at 100 mg/12h was 1725 ± 292 ng.h/mL vs 3598 ± 673 ng.h/mL at 200mg/12h (p=0.09). Tmax was not significantly different between both doses. No interaction of TMZ and ralimetinib when administrated concomitantly has been noted, just as no significant differences have been observed in Cmax, Tmax and AUC for both drugs when administrated concomitantly than when administrated alone (ralimetinib: D7 vs D35; TMZ: D28 vs D35), but the study is under-powered for this type of analysis (supplementary data). Patient No. 8 presented an accumulation of 2 molecules ralimetinib and TMZ at D35. One patient treated at 100 mg/12h had cerebral fluid detection of ralimetinib. Ralimetinib dosage was 29 ng/mL in cerebral fluid vs 125 ng/ml in plasma at the same time (180 min post administration). Concerning pharmacodynamic, as shown in Figure 3, ralimetinib induced a strong inhibition of pMAPKAP-K2 (54%) in PBMC as early as 1 hour after the first oral intake. A similar effect was observed on D7 (52%) and D35 (56%) with TMZ. The results obtained for one patient at 200 mg were very close to those observed at 100 mg and were therefore pooled to present the data (on average 62%).

We reported the efficacy outcomes of the 15 patients treated at the recommended dose (100 mg/12h). At the last follow-up (median of 41.4 months), 10/15 patients had a progression and 9/15 were dead. The 6-month, 1-year, and 2-year PFS rates were, respectively, 92.9% (95% CI [80-100]), 50% (95% CI ), and 35.7% (5% CI ). The median PFS was 12.8 months IC95 (7.9 lower boundary of 95% CI), whereas the median overall survival was 24.5 months (16.5 lower boundary of 95% CI). In multivariate analysis, we found a link between the IDH1 mutation and a better prognosis (HR of 0.116; 95% CI, 0.014-0.995 for PFS), as widely described, in addition to an association between PTEN expression in the tumour and a poorer prognosis (HR of 10.5; 95%CI, 1.12-10.5 for PFS).

Discussion

Our trial was the first to evaluate the combination of ralimetinib, a p38-MAPK inhibitor, with RT and TMZ in the treatment of newly diagnosed GBM. We met our primary objective with a recommended dose (RD) of ralimetinib at 100 mg/12h. This dose was lower than the RD of ralimetinib determined in previous phase I trials. In the first phase I study in advanced cancer, the RD was 300 mg/12h [START_REF] Patnaik | A First-in-Human Phase I Study of the Oral p38 MAPK Inhibitor, Ralimetinib (LY2228820 Dimesylate), in Patients with Advanced Cancer[END_REF] as monotherapy or with tamoxifen. In a randomized phase Ib/II test on the combination of gemcitabine and carboplatine +/-ralimetinib for women with ovarian cancer, the RD was 200 mg/12h (D1-10 q21d) [START_REF] Vergote | A randomized, double-blind, placebo-controlled phase 1b/2 study of ralimetinib, a p38 MAPK inhibitor, plus gemcitabine and carboplatin versus gemcitabine and carboplatin for women with recurrent platinum-sensitive ovarian cancer[END_REF]. Another phase I study assessing the combination of ralimetinib with prexasertib (checkpoint kinase 1 inhibitor) in patients with advanced or metastatic cancer [START_REF] Bendell | A phase 1 dose-escalation study of checkpoint kinase 1 (CHK1) inhibitor prexasertib in combination with p38 mitogen-activated protein kinase (p38 MAPK) inhibitor ralimetinib in patients with advanced or metastatic cancer[END_REF] did not succeed in establishing a RD of ralimetinib. With a model-based 3+3 dose escalation, no DLT was observed in the cohort of 3 patients treated at 100 mg/12h, though 3/6 patients experienced DLT at a dose of 200 mg/12h (D1 to 14).

In the current trial, DLTs were consistent with the known toxicities of ralimetinib (asthenia, nausea, rash, constipation, vomiting, pruritus and hepatic cytolysis) and well-established side effects of RT and TMZ. All patients treated at 200 mg/12h experienced a grade 3 rash (/edema) and only one (7%) at 100 mg/12h with a 9% grade ≥ 3 rash, as described in the first ralimetinib phase 1 trial [START_REF] Patnaik | A First-in-Human Phase I Study of the Oral p38 MAPK Inhibitor, Ralimetinib (LY2228820 Dimesylate), in Patients with Advanced Cancer[END_REF]. One patient (treated at 100 mg/12h) had grade 3 lymphopenia. Even if this toxicity is well established with TMZ [START_REF] Stupp | Radiotherapy plus concomitant and adjuvant temozolomide for glioblastoma[END_REF][START_REF] Stupp | Effects of radiotherapy with concomitant and adjuvant temozolomide versus radiotherapy alone on survival in glioblastoma in a randomised phase III study: 5-year analysis of the EORTC-NCIC trial[END_REF], it has also been described with ramelitinib [START_REF] Patnaik | A First-in-Human Phase I Study of the Oral p38 MAPK Inhibitor, Ralimetinib (LY2228820 Dimesylate), in Patients with Advanced Cancer[END_REF]. Four patients (22%) experienced grade ≥ 3 hepatic cytolysis during concomitant period (all resolved after stopping ralimetinib and TMZ, allowing restarting of TMZ and TMZ maintenance). Hepatic cytolysis has been recently observed in conjunction with ralimetinib use and was also a potential side effect of TMZ, with up to 26% grade 3 enzyme elevations associated with TMZ in GBM patients [START_REF] Clarke | Randomized phase II trial of chemoradiotherapy followed by either dose-dense or metronomic temozolomide for newly diagnosed glioblastoma[END_REF][START_REF] Yang | Temozolomide chemotherapy in patients with recurrent malignant gliomas[END_REF][START_REF] Pérez-Larraya | Temozolomide in elderly patients with newly diagnosed glioblastoma and poor performance status: an ANOCEF phase II trial[END_REF][START_REF] Dixit | Temozolomide-related idiosyncratic and other uncommon toxicities: a systematic review[END_REF][START_REF] Niewald | Toxicity after radiochemotherapy for glioblastoma using temozolomide--a retrospective evaluation[END_REF][START_REF] Wick | Temozolomide chemotherapy alone versus radiotherapy alone for malignant astrocytoma in the elderly: the NOA-08 randomised, phase 3 trial[END_REF]. Other series have reported fewer rates of liver enzyme elevation [START_REF] Clarke | Randomized phase II trial of chemoradiotherapy followed by either dose-dense or metronomic temozolomide for newly diagnosed glioblastoma[END_REF][START_REF] Yang | Temozolomide chemotherapy in patients with recurrent malignant gliomas[END_REF][START_REF] Pérez-Larraya | Temozolomide in elderly patients with newly diagnosed glioblastoma and poor performance status: an ANOCEF phase II trial[END_REF][START_REF] Dixit | Temozolomide-related idiosyncratic and other uncommon toxicities: a systematic review[END_REF][START_REF] Niewald | Toxicity after radiochemotherapy for glioblastoma using temozolomide--a retrospective evaluation[END_REF]. Also, several cases of severe cholestatic hepatitis have been reported [START_REF] Grewal | Fatal reactivation of hepatitis B with temozolomide[END_REF][START_REF] Goldbecker | Hepatic encephalopathy after treatment with temozolomide[END_REF][START_REF] Sarganas | Severe sustained cholestatic hepatitis following temozolomide in a patient with glioblastoma multiforme: case study and review of data from the FDA adverse event reporting system[END_REF][START_REF] Dixit | Temozolomide induced liver injury[END_REF] with the onset of injury within 1 to 7 months of starting TMZ. In the randomized double-blind placebo-controlled phase Ib/II study of gemcitabine and carboplatin +/-ralimetinib in recurrent ovarian cancer, grade 3-4 elevated alanine aminotransferase was more frequent in the ralimetinib arm (19.7% vs 3.8%) [START_REF] Vergote | A randomized, double-blind, placebo-controlled phase 1b/2 study of ralimetinib, a p38 MAPK inhibitor, plus gemcitabine and carboplatin versus gemcitabine and carboplatin for women with recurrent platinum-sensitive ovarian cancer[END_REF]. In our study, the occurrence of grade 3 hepatic cytolysis on 2 patients (66%) treated at 200 mg/12h, with one at D14 (7 days after TMZ start) raises the question of a potential increased liver toxicity with ralimetinib and TMZ. However, among the 15 patients treated at 100 mg/12h, only 13% experienced severe hepatic cytolysis, both rapidly reversible with appropriate measures. Nevertheless, appropriate liver monitoring seems essential in future trials, especially as TMZ might also induce sever hepatotoxicity. No severe toxicity related to RT was reported, demonstrating that ralimetinib was well tolerated in combination with RT.

Despite the small number of patients, the PK parameters were in accordance with previous PK analysis of ralimetinib [START_REF] Patnaik | A First-in-Human Phase I Study of the Oral p38 MAPK Inhibitor, Ralimetinib (LY2228820 Dimesylate), in Patients with Advanced Cancer[END_REF]. No evidence of significant drug-drug interaction between ralimetinib and TMZ has been highlighted. One patient presented an accumulation of ralimetinib and TMZ at D35, attesting to an idiosyncratic metabolic problem. While UGT enzymes were involved in the metabolic clearance of ralimetinib, the genotype of UGT1A1*1/*1 and UGT1A4*1a/*1b of this patient, with a usual glucoroconjugation capacity, does not explain the observed accumulation.

In our study, ralimetinib administrated at 100 mg/12h demonstrated a pharmacodynamic response with a significant inhibition of pMAPKAP-K2 in PBMC of around 50-60% as observed with a 300 mg/12h dose [START_REF] Patnaik | A First-in-Human Phase I Study of the Oral p38 MAPK Inhibitor, Ralimetinib (LY2228820 Dimesylate), in Patients with Advanced Cancer[END_REF]. A critical issue in brain tumor therapy is whether the drug penetrates the blood-brain barrier to reach the target. Dosage of ralimetinib in the cerebral fluid was possible for only one patient, but it showed that ralimetinib could go across the BBB with a favorable ratio of approximately 24% (vs blood). Further studies would be needed to determine the pharmacodynamic response of ralimetinib within the tumor and tumor microenvironment; however, technical issues in obtaining GBM biopsies create limitations.

The small sample size of the expansion cohort with a total of 15 patients treated at the RD of ralimetinib represents an important limitation of these data. The planned phase II trial (n=40) was discontinued due to an industry decision to stop providing ralimetinib before the end of recruitment.

However, the first results of the efficacy of the association of a p38-MAPK inhibitor alongside RT and TMZ for the treatment of GBM were encouraging, with a PFS rate at 6 months of 93%, a PFS of 12.6 months and a OS of 24.5 months compared with historical data of the standard of care [START_REF] Stupp | Radiotherapy plus concomitant and adjuvant temozolomide for glioblastoma[END_REF][START_REF] Stupp | Effects of radiotherapy with concomitant and adjuvant temozolomide versus radiotherapy alone on survival in glioblastoma in a randomised phase III study: 5-year analysis of the EORTC-NCIC trial[END_REF]. These results should be interpreted with caution, taking into account the high percent of IDH-1 mutant GBM (27%) and of MGMT methylated patients (31% of known methylation status). Future randomized trials are needed to evaluate the efficacy of ralimetinib in combination with chemoradiotherapy in GBM.

These results represent the first proof-of-concept study to report the outcomes of a p38-MAPK inhibitor with RT and chemotherapy in newly diagnosed GBM. Another p38-inhibitor compound, LY3007113, has been tested in advanced cancer patients. Further development is not planned because its toxicity, which produced symptoms such as tremors and rashes, precluded achieving a biologically effective dose [43]. Grade ≥ 3 treatment-related adverse events included upper gastrointestinal hemorrhage and increased hepatic enzyme. SCIO-469 (Talmapimod), BIRB-796 (Doramapimod) and Losmapimod have shown interesting anti-tumoral activity in preclinical models of multiple myeloma [START_REF] Hideshima | p38 MAPK inhibition enhances PS-341 (bortezomib)-induced cytotoxicity against multiple myeloma cells[END_REF][START_REF] Navas | Inhibition of p38alpha MAPK enhances proteasome inhibitor-induced apoptosis of myeloma cells by modulating Hsp27, Bcl-X(L), Mcl-1 and p53 levels in vitro and inhibits tumor growth in vivo[END_REF][START_REF] Vanderkerken | Inhibition of p38alpha mitogen-activated protein kinase prevents the development of osteolytic bone disease, reduces tumor burden, and increases survival in murine models of multiple myeloma[END_REF] [32], epidermoid carcinoma [START_REF] He | BIRB796, the inhibitor of p38 mitogen-activated protein kinase, enhances the efficacy of chemotherapeutic agents in ABCB1 overexpression cells[END_REF] and cervical cancer [START_REF] Jin | The p38 MAPK inhibitor BIRB796 enhances the antitumor effects of VX680 in cervical cancer[END_REF] or NSCLC (PDX mouse model) [START_REF] Yeung | Losmapimod Overcomes Gefitinib Resistance in Non-small Cell Lung Cancer by Preventing Tetraploidization[END_REF].

So far, however, its administration in men has only been tested in the field of anti-inflammatory research [START_REF] Schreiber | Oral p38 mitogen-activated protein kinase inhibition with BIRB 796 for active Crohn's disease: a randomized, double-blind, placebocontrolled trial[END_REF] or in patients with myelodysplastic syndrome [START_REF] Sokol | Randomized, dose-escalation study of the p38α MAPK inhibitor SCIO-469 in patients with myelodysplastic syndrome[END_REF], post-myocardial infarction [START_REF] Newby | Losmapimod, a novel p38 mitogen-activated protein kinase inhibitor, in non-ST-segment elevation myocardial infarction: A randomised phase 2 trial[END_REF], or facioscapulohumeral muscular dystrophy (recent orphan drug status of losmapimod by FDA). This phase I trial showed that combining ralimetinib with standard chemoradiation for newly diagnosed GBM was feasible. The most frequent and critical dose-limiting toxicity was hepatic cytolysis. The MTD of ralimetinib was determined at 100 mg/12h. These results represent the first proofof-concept of an association of a p38-MAPK inhibitor with RT and chemotherapy justifying further randomized trials.

Figure captions

version 4 .

 4 03 (NCI-CTCAE v4.03). The neurologic status of patients was evaluated by clinical assessment and Mini-Mental State Examination (MMSE) and evaluation of corticoid dosage.

Figure 1 :

 1 Figure 1: Treatment scheme during the concurrent phase. Radiotherapy (RT), Temozolomide (TMZ), pharmacokinetic (PK).

Figure 2 : 1 Figure 3 :

 213 Figure 2: Pharmacokinetic profiles at 100 and 200 mg/12h on Day 7 of cycle 1

Acknowledgement

This study was supported by INCa (Institut National du Cancer) and the foundation ARC. Ralimetinib was provided by Eli Lilly and Company. The authors would like to thank Xavier Paoletti of the Department of Biostatistics at the Institut Curie for providing statistical assistance for the Tite-CRM Method.