Mathilde Orselly

Julien Devémy

Agathe Bouvet-Marchand

Alain Dequidt

Cédric Loubat

Patrice Malfreyt

Molecular interactions at the metal-liquid interfaces

We reported molecular simulations of the interactions between water, an epoxy prepolymer (DGEBA) and an hardener (IPDA) on an aluminum surface. This work proposes a comprehensive thermodynamic characterization of the adhesion process from the calculation of the different interfacial tensions. The cross-interactions between the atoms of the metal surface and the different molecules are adjusted so as to reproduce the experimental work of adhesion. Water nanodroplets on the metal surface are then simulated to predict its contact angle. Liquid-vapor surface tensions of the epoxy prepolymer (DGEBA) and hardener (IPDA) and the solidvapor surface tension of the aluminum surface are also calculated to provide the solid-liquid interfacial tension that remains very difficult to obtain from the mechanical definition.

I. INTRODUCTION

Understanding the behavior of a fluid in the vicinity of a surface is fundamental for many disciplines such as chemistry, physics, biology and medicine. It involves a macroscopic characterization of the phenomena at the interface and a complete description of the microscopic arrangements in the interfacial region. The knowledge of these interfacial interactions and structures is key to many applications involving adsorption, wetting properties of a surface, biocompatibility of a material and polymer materials such as nanocomposites and membranes.

To energetically characterize the affinity of a liquid for a surface, experiments usually measure the Young contact angle θ, which is related to different surface tensions through the Young's equation [1][2][3] . γ SL -γ SV + γ LV cos θ = 0 (1) where γ SL , γ SV and γ LV are the solid-liquid, solid-vapor and liquid-vapor surface tensions, respectively. For contact angle values less than 90 • , the liquid spreading over a large area on the solid surface, indicates that the wetting of the solid surface is favorable. The wetting is complete for θ = 0 • . For contact angles greater than 90 • , the liquid tries to minimize its contact with the surface by forming a compact liquid drop. A related but key property is the work of adhesion W SL per unit of area of the solid-liquid interface. This property can be defined as the reversible thermodynamic work needed to separate the solid-liquid interface from the equilibrium state of two coexisting phases to a separation distance of infinity [START_REF] Israelachvili | Intermolecular and surfaces forces[END_REF] .

W SL = γ LV + γ SV -γ SL (2)
a) Electronic mail: Mathilde.Orselly@specificpolymers.fr b) Electronic mail: Patrice.Malfreyt@uca.fr Using Eq.( 1), the work of adhesion can also be obtained in terms of the contact angle such as

W SL = γ LV (1 + cos θ) (3)
For positive values of W SL , we deduce that the higher the value of W SL is, the stronger the interaction between the solid and the liquid components are. Indeed, for optimum adhesion, W SL must be maximized which occurs when the solid-liquid interfacial tension γ SL approaches zero (Eq.( 2)). Molecular simulations [START_REF] Ghoufi | [END_REF][START_REF] Allen | Computer Simulation of Liquids : Second Edition[END_REF] have opened up important theoretical and methodological fields of investigation on interfacial systems with the aim of describing the interface and predicting surface tension. The link between the atomistic models and the surface tension is made through the statistical mechanics of inhomogeneous systems [START_REF] Rowlinson | Molecular Theory of Capillarity[END_REF] . The first simulation was carried out in the 1970s and focused on the liquid-vapor interface of a Lennard-Jones fluid [START_REF] Lee | [END_REF]9 . Many debates have animated this research activity because simulation results have suffered from many dependencies to input parameters. It took almost 50 years to solve all the methodological problems due to the modeling of an interface, namely the impact of the truncation of the potential [10][11][12] , the importance of the long range corrections to the surface tension 13 , the calculation of the surface tension through the mechanical and thermodynamic definition 14 and size-effects 15 . In conclusion, the calculation of surface tension is now under control in the case of liquid-vapor and liquid-liquid interfaces [START_REF] Ghoufi | [END_REF] .

The same cannot be said for the calculation of the interfacial tension between a solid and a fluid [START_REF] Allen | Computer Simulation of Liquids : Second Edition[END_REF] . Indeed, the interfacial thermodynamics in the solid-liquid and solid-vapor interfaces is different from that of liquidliquid and liquid-vapor interfaces. The calculation of the solid-liquid (γ SL ) and solid-vapor (γ SV ) is much more sophisticated, since it must consider the internal stress in the solid phase. The relationship between the surface tension and the surface stress tensor σ αβ , first given by Shuttleworth [START_REF] Shuttleworth | Proc. Phys. Soc. A[END_REF] , is

σ αβ = γ SL δ αβ + A ∂γ SL ∂ϵ αβ ( 4
)
where A is the cross-sectional area, ϵ αβ the αβ component of the elastic strain tensor [START_REF] Müller | [END_REF] and δ αβ the Kronecker delta. For interfacial systems involving only fluids, the second term in Eq.( 4) is considered null, and the surface tension is obtained from the stress profile. For solid-liquid interfaces, other alternatives have been developed to avoid the calculation of the elastic strain tensor. Capillary-wave oscillations can be used to estimate the solid-liquid interfacial energy 18 . The phantom-wall methodology [19][20][21][22] consists of using the thermodynamic integration method to calculate the Gibbs interfacial excess free energy between a solid-liquid interface and an unstructured phantom surface. The test-area method has also been applied to the calculation of the solid-liquid interfacial tension 23 . Another route 24 referred to as the cleaving method, consists of calculating the free energy required to create the solid-liquid interface from the separated bulk phases. This technique has been applied to the crystal-melt interfacial free energy 24 . Nevertheless, under facilitating conditions, the calculation of γ SL can be conducted by using the pressure tensor definition. In this case, a rigid surface with no intramolecular interactions is considered. The configuration of the atoms of the surface is not changed and no internal stresses are generated. We have performed this type of calculation on a sheet of graphene which is isotropic by nature. In this case, γ SL can be calculated in the same way as it is calculated in fluid-fluid interfaces. We have recently used this approach for the calculation of the solid-liquid interfacial tension in the graphene-liquids interface [25][26][27][28][29] . We have shown that the simulated graphene-water interfacial tension 27 was in line with that obtained from experiments 30 . For more complex surfaces, such as metallic ones, this mechanical approach can no longer be used.

In this paper, we aim to investigate the interfacial tensions that contribute to the energy balance of the adhesion between a solid and a fluid. We mainly focus on the adhesion of the components of epoxy resins onto metal surfaces. These systems are relevant for industrial processes due to the prominence of epoxies for a wide range of applications [START_REF] Pascault | General concepts about epoxy polymers[END_REF] . These thermosetting polymers can be used for structural components in aerospace applications or as various types of coatings. The adhesion between the substrate and the polymer is thus an undeniable aspect of the success of the resulting material, and its characterization is crucial.

To do so, we tackled the calculation of the work of adhesion of different metal-fluids interfaces by using the concept of Free Energy Perturbation (FEP) [START_REF] Zwanzig | [END_REF][33][34][START_REF] Chipot | Free Energy Calculations : Theory and Applications in Chemistry and Biology[END_REF] . This approach has been recently applied to the case of the interaction between a graphene sheet and water 21,36 . We also applied this approach to evaluate the solid-vapor interfacial tension of metal surfaces. From the calcula-tion of the liquid-vapor surface tension of components of resins, we proposed to determine the solid-liquid interfacial tension. We have measured the values of contact angle when they were not available in the literature. This study aims to show that it is possible to reproduce the work of adhesion of metal-fluid systems by playing on the cross-interactions.

The paper is organized as follows. Section II describes the simulation and experimental methods. Section III discusses the calculations of interfacial tensions of different systems. Section IV contains our conclusions.

II. EXPERIMENTAL AND SIMULATION METHODS

A. Description of the force field

The CHARMM General Force Field (CgenFF) [37][38][39] is used to describe the intra-and inter-molecular interactions of the thermosetting polymers. This Class I force field has the following functional form:

U = Bonds k r (r ij -r 0 ) 2 + Angles k θ (θ ijk -θ 0 ) 2 + Dihedrals n k φ,n [1 + cos(n φ ijkl -δ n )] + Impropers k ϕ (ϕ 0 -ϕ 0 ) 2 + U rey-Bradley k ub (r 1,3 -r 1,30 ) 2 + N onbonded atoms S(r ij ) q i q j 4π ϵ 0 r ij + N onbonded atoms S(r ij ) ε ij R min,ij r ij 12 -2 R min,ij r ij (5)
The total potential energy U sums then the bond (r ij ), valence angle (θ), Urey-Bradley (r 13 ), dihedral angle (φ) and improper angle (ϕ) interactions and non-bonded interactions modelled by Lennard-Jones and Coulombic potentials. k θ , k φ,n , k ub , k ϕ are the force constants and the variables with the subscript 0 represent the equilibrium values. The parameter R min used in the Lennard-Jones potential corresponds to 2 1/6 σ where σ is the atomic diameter. The CHARMM force field presents an additional component in the form of the Urey-Bradley term, which consists of a harmonic potential as a function of the distance between the non-bonded atoms 1 and 3 of an 1-2-3 angle. The Lennard-Jones parameters between pairs of different atoms are obtained from the Lorentz-Berthelot combination rules, in which ε ij values are calculated by using the geometric mean and R min values uses the arithmetic mean. The cut-off distance for van der Waals interactions is set to r c1 = 8.0 Å while the Particle-Particle Particle Mesh (PPPM) method with an accuracy of 1.0 × 10 -4 and a cut-off of 8 Å is considered for the long-range electrostatic interactions. For both the Lennard-Jones and Coulombic interactions, a force-switching function was applied between r c1 = 8 Å and r c2 = 10 Å. The S(r ij ) function, defined as

S(r ij ) = 1, if r ij ≤ r c1 (r 2 c2 -rij ) 2 (r 2 c2 +2 r 2 ij -3 r 2 c1 ) (r 2 c2 -r 2 c1 ) 3 , if r c1 < r ij ≤ r c2 (6
) yields a continuous potential energy and force at the cutoff radii r c1 and r c2 .

The Velocity-Verlet integrator was used to integrate the equations of motion using a time step of 1 fs. The SHAKE algorithm was applied to constrain the length of covalent bonds to hydrogen atoms to their equilibrium values. In order to control the temperature and pressure for NVT and NPT simulations, a Nosé-Hoover thermostat and barostat were applied 40 . Unless stated otherwise, the MD simulations were performed at 300 K and 1 atm. The molecular dynamics (MD) calculations were performed using the LAMMPS package 41 .

Aluminum was created by using the Atomsk software 42 . A repetition of the elementary mesh in the three directions of space XYZ was then possible. This makes it feasible to create a metal block for atomistic simulations based on the structure of the latter and its lattice parameters. It was chosen to investigate the {100} planes of this face-centered cubic crystal. The lattice parameters of aluminum is 4.0496 Å. [START_REF] Lide | CRC Handbook of Chemistry and Physics, Internet Version 2005[END_REF] Regarding the force field [START_REF] Heinz | [END_REF] associated with these types of atoms, metals are only linked together by non-covalent bonds, known as metallic bonds. In these simulations, each metallic atom is considered neutral. Lennard-Jones interactions are employed to maintain the system at equilibrium. For the aluminum surface, the parameters developed in Ref. 44 are transformed to fit the equations of the CHARMM force field as in Table I. Various molecules were modelled in order to estimate the influence of the chemical structure on the interface. In the framework of this study, the following molecules were used : DGEBA (diglycidic ether of bisphenol A) and IPDA (isophorone diamine) (see Figures 1a and1b). The force field of the molecules does not differ and is also based on the CHARMM General Force Field. The water molecules were modelled by using the flexible version of the SPC water model 45 .

B. Calculation of the work of adhesion W SL

In a classical system constituted by N identical particles of mass m defined by their coordinates r N and momenta p N , the Helmholtz free energy F is related to the partition function Q N V T in the constant-N V T ensemble by the following expression

F = - 1 β ln Q NVT = - 1 β ln 1 h 3N N ! dr N dp N exp (-β H(r N , p N )) = - 1 β ln 1 Λ 3N N ! dr N exp (-β U(r N )) (7)
where β = 1 k B T is the inverse temperature and h the Planck constant. The total Hamiltonian in Eq.( 7) can be written as the sum of the kinetic and potential energies of the system. Let us suppose that the potential energy U(r N ) is independent of the velocities, the double integral in Eq.( 7) can be separated in two integrals, one over the positions and one over the momenta. This latter can be written in terms of the de Broglie thermal wavelength, Λ. The resulting expression of the Helmholtz free energy is given by Eq.( 8).

∆F = F (1) -F (0) = - 1 β ln Q (1) NVT Q (0) NVT = - 1 β ln exp -β H (1) (r N , p N ) -H (0) (r N , p N ) (0) (8)
where H (1) (r N , p N ) and H (0) (r N , p N ) are the total Hamiltonian of the target and reference systems, respectively. The expression of Eq.( 8) is the fundamental expression of the Free Energy Perturbation (FEP) [START_REF] Zwanzig | [END_REF][33][34][START_REF] Chipot | Free Energy Calculations : Theory and Applications in Chemistry and Biology[END_REF] methodology. The reference system denoted as (0) is defined by the interaction between the solid and liquid phases characterized by γ SL . The target system (1) is then formed by a solid phase and a liquid phase in equilibrium with their vapor. Both phases no longer interact with each other and lead to two interfacial tensions γ LV and γ SV . We can describe the transformation with the following expression:

∆F = A W SL = A Nw-1 i=1 W SL (λ i ) = A γ LV +γ SV -γ SL (9)
where A is the surface area of the solid. Since the transformation does not involve any changes in terms of mass and temperature, it results that the kinetic term obtained through the de Broglie thermal wavelength cancels out. As a consequence, we replace the Hamiltonian by the potential energy U(r N ) and we will omit the dependence of U on the positions r N for simplicity of notation.

To improve the convergence of the calculation and to promote overlaps between consecutive steps, the calculation of the free energy difference ∆F between two states (0) and ( 1) is split into N w intermediate contiguous states or windows defined by a coupling constant λ i . The potential energy is a function of λ i as described by Eq.( 10)

U(λ i ) = λ i U(λ Nw ) + (1 -λ i ) U(λ 1 ) (10)
where 0 ≤ λ i ≤ 1, λ 1 = 0 and λ Nw = 1. Eq.( 7) can be rewritten in the context of the calculation over consecutive states (i) and (i + 1) by

∆F = F (1) -F (0) = Nw-1 i=1 ∆F (λ i ) = - 1 β Nw-1 i=1 ln exp -β U(λ i+1 ) -U(λ i ) λi (11) = + 1 β Nw i=2 ln exp -β U(λ i-1 ) -U(λ i ) λi (12)
The perturbations can be performed in both directions ("double-wide sampling") with N w windows over the entire simulation. In principle, for a reversible process, ∆F calculated in the forward direction with Eq.( 11) and backward direction with Eq.( 12) should be equal. The difference between the forward (∆λ = λ i+1 -λ i ) and backward (∆λ = λ i-1 -λ i ) simulations gives a lowerbound estimate of the error in the calculations. The transformation from state (i) to state (i+1) is achieved by changing the interactions between the solid and the liquid molecules and keeping identical the solid-solid and liquidliquid interactions. This is done by applying the following rules to the cross interactions between the atoms of the solid and liquid phases, such as

ε SL (λ i ) = (1 -λ i ) √ ε SS ε LL (13)
where S and L represent atoms of the solid and liquid phases, respectively. The removal of the interactions between the solid and liquid atoms (see Figure 1c) can lead to instabilities when the coupling parameter λ i approaches 0. A solution 46 is to modify the Lennard-Jones potential as

U LJ (r ij , λ i ) = (1 -λ i ) ε ij 1 µ (λ i ) 2 + Rmin,ij rij 6 2 - 1 µ (λ i ) 2 + Rmin,ij rij 6 ( 14
)
where µ was taken to 0.5. As λ i is 0, the solid and liquid molecules interact through the full strength of the Lennard-Jones potential. As λ i approaches 1, the Lennard-Jones potential is modified by a soft-core interaction µ λ 2 i .

C. Calculation of the surface tension 1. Mechanical definition

The surface tension γ, originally given by Kirkwood and Buff 47 , is defined by

γ = 1 2 p N -p T L z (15)
where p N and p T are the normal and tangential components of the pressure and L z is the length of the simulation cell in the z direction. Since a two phase simulation (see Figure 1d) with periodic boundary conditions consists of two interfaces, the surface tensions calculated from Eq.( 15) is divided by 2 to calculate γ for a single interface. For a planar interface, p N is given by p zz , whereas the tangential component p T is given by

1 2 (p xx + p yy ).
Irving and Kirkwood 7,47-51 have shown that γ can be calculated from p N (z) and p T (z), the components of the pressure tensor as a function of z;

γ = 1 2 Lz/2 -Lz/2 (p N (z) -p T (z)) dz (16)
This local definition of γ, based on the mechanical road, uses the force acting across a unit area in the z-plane for one interface. There is no unique way of calculating the forces across a particular area, since it is unclear which atoms contribute to this force. This has no effect on p N (z) but different choices of the contour can affect the definition of p T (z). However, these choices have no effect on the integral in Eq.( 16). We use here the Harasima definition 7,47,52 for the normal and tangential pressure components. The normal component of the pressure tensor can be written as

p N (z) = ⟨ρ(z)⟩ k B T + 1 2 A ∆z N -1 i=1 N j=i+1 z ij (f ij ) z × (δ(z -z i ) + δ(z -z j )) ( 17
)
where A is the surface area, ∆z is the thickness of the slab and ρ(z) is the local number density. The simulation box is divided into N z slabs of thickness δz. f ij is the force between atoms i and j defined as:

f ij = - r ij r ij dU(r ij ) dr ij (18)
where U represents all the intramolecular and intermolecular energy contributions described in the force field of Eq.( 5). The tangential component of the pressure tensor is then expressed as follows

p T (z) = ⟨ρ(z)⟩ k B T + 1 4 A ∆z N -1 i=1 N j=i+1 x ij (f ij ) x + y ij (f ij ) y × (δ(z -z i ) + δ(z -z j )) (19)
These equations indicate that half of the virial contributions arising between atom i and atom j is assigned to the slab where i is located and the other half to the slab where j is located. Since intermolecular energies and forces are modified by a switching function that makes energy and forces equations decrease smoothly to zero at the cutoff, no long-range corrections due to the truncated potentials need to be applied to the pressure components and surface tension.

Calculation of the solid-vapor surface γ SV

In order to obtain the solid-vapor surface tension, a methodology based on the difference of average total energy is used between two NVT simulations [START_REF] Heinz | [END_REF] . Two boxes are utilized : a split box with two slabs of metal separated by vacuum, and a unified box grouping these two slabs together. Both simulations cells have the same dimensions and the same total number of atoms. The difference in total energy between the separated structure (E S ) and the unified structure (E U ) corresponds to the cleavage energy per surface area. Two solid-vapor interfaces have been created during the cleavage process. This definition is based on the calculation of the energy and therefore neglects the entropy variations by considering that these contributions are negligible compared to the cohesive energy contribution, which is a fair approximation for metals at room temperature. The surface tension γ SV is then defined as

γ SV = E S -E U 2 A -T S S -S U 2 A ≈ E S -E U 2 A . ( 20
)
It is also possible to extend the calculation of W SL to W SV by adapting Eq.( 9) to the solid-vapor interface. In this case, by using the Free Energy Perturbation, Eq.( 9) becomes (21) where γ SS = 0 due to the energy/entropy compensation in the solid phase. By definition, this approach has the advantage of considering the entropic contribution. The initial state (λ 1 = 0) is defined by the two slabs of metal interacting with each other, and the final state (λ Nw = 1) by two slabs of metal that no longer interact and are separated by vacuum. The perturbation consists in annihilating progressively the cross interactions between the atoms of both metal slabs. The vanishing of the interactions between the two groups of metal atoms is carried out through Eq.( 22)

∆F = A W SV = A Nw-1 i=1 W SV (λ i ) = A (2 γ SV -γ SS ) = 2 A γ SV
ε SV (λ i ) = (1 -λ i ) √ ε (SS)1 ε (SS)2 (22)
where 1 and 2 refer to both groups of metal atoms.

During the transformation process, we can apply another methodology based on the concept of Thermodynamic Integration (TI) [START_REF] Chipot | Free Energy Calculations : Theory and Applications in Chemistry and Biology[END_REF] for the calculation of the free energy. This TI definition allows a faster convergence and a smaller number of windows.

∆F = 1 0 ∂F ∂λ dλ = - 1 β 1 0 1 Q NVT ∂Q NVT ∂λ dλ = 1 0 ∂U ∂λ λi dλ (23)
with

∂U ∂λ λi = U(λ i+1 ) -U(λ i ) δλ (24)
and λ i+1 = λ i + δλ with δλ = 2 × 10 -3 . In practice, the change in the cross-interactions between solid atoms is done by changing λ + ∆λ by λ + δλ in Eq.( 22). W SV is the contribution calculated from λ = 0 to λ = 1 but the following contribution W SV (λ) in Eq.( 25) calculated on intermediate states from λ = 0 to λ, although not physically meaningful, allows to check the accuracy of the calculation at each steps and to compare the value with that calculated with FEP.

W SV (λ) = λ 0 ∂U ∂λ λi dλ (25)

D. Experimental determination of the contact angle

Distilled water, DGEBA (diglycidic ether of bisphenol A) and IPDA (isophorone diamine) were used as contact angle measurement liquids on a 2024 aluminum alloy surface. The measurements were performed with an optical contact angle measuring system: OCA 50, DataPhysics Instruments GmbH. Measurements were made at room temperature (20 °C), except for DGEBA (70 °C) due to its viscosity. Sessile drop method was used to measure the contact angle by a direct measurement of the tangent angle at the three-phase contact point. For each system, five drops of each liquid were tested on the metallic surface.

III. RESULTS AND DISCUSSION

A. Calculation of the work of adhesion

We start this section with a methodological aspect of the calculation by showing in Figure 2 the dependence of the work of adhesion on the number of windows and the total simulation time. These calculations were performed in the forward and backward directions to check the reversibility of the transformation along the reaction path for systems. Regardless of the number of windows (N w = 20 or 40), Figure 2 shows that deviations on the work of adhesion between direct and reverse paths do not exceed 2 mJ m -2 over a total value of 299 mJ m -2 . This means that the amount of perturbation characterized by the value of ∆λ (0.05 or 0.025) between consecutive windows is adapted to provide the calculation of a reversible work. We observe in Figure 2 insignificant deviations between adhesion works calculated with 5, 20 and 40 ns. We use the set of simulations carried out with different input parameters to estimate a standard deviation of approximately 5 mJ m -2 which corresponds to a statistical uncertainty less than 2 % on this property. As a result, we take the route of applying 20 windows and 20 ns for the complete perturbation process. Subsequently, we first focus on the calculation of the work of adhesion of 300 molecules of water on an aluminum surface (5×5×5 units). The values reported in Figure 3a correspond to the averages performed over both directions. The result of this calculation is shown in Figure 3a with α = 1 where α is defined in Eq.( 26). In this case, the work of adhesion was found to be equal to (256 ± 1) mJ m -2 . By using Eq.( 3), an experimental surface tension of water 53 of 72 mJ m -2 and a contact angle measured experimentally of 85 • , we obtain an experimental work of adhesion of 78 mJ m -2 indicating that the simulated and experimental properties are by no means comparable. The large value obtained by simulation indicates that the cross interactions are too strong. An alternative to reproduce the experimental work of adhesion is to reduce the cross-interactions between the solid and liquid by introducing an α parameter less than or equal to 1, as expressed by the following equation:

ε SL = α √ ε SS ε LL (26)
The works of adhesion are also shown in Figure 3a for different α values. As expected, we observe that the work of adhesion decreases from 256 to 4.1 mJ m -2 as the strength of the interactions between the solid and liquid decreases. It is then possible to reproduce the experimental work of adhesion by choosing α = 0.469. This means that the cross-interactions must be significantly reduced by about 53 % to accurately predict the adhesion property of water on aluminum. This is not surprising, given the parameters of aluminum atoms [START_REF] Heinz | [END_REF] and water molecules 45 come from different force fields that have never been optimized together on this property. A microscopic view of the decrease of the crossinteractions between the metal and liquid can be observed on the density profiles of water molecules along the normal direction to the metal surface. These density profiles are shown in Figure 3b for decreasing interaction strength between metal and liquid. When the interaction is strongest (α = 1), the density profile of water molecules show a well-pronounced peak of adsorption, followed by a second peak with a lower but still significant amplitude. These two peaks inform us about a strong structuring of water molecules close to the metal surface through the formation of two ordered layers. The amplitude of the peaks weakens with decreasing α-values. A value of α = 0.469 leads to a good agreement between the experimental and simulated works of adhesion, without compromising the two well-ordered layers of water that results from an adaptation of the threedimensional hydrogen-bond network of bulk conditions to a two-dimensional geometry imposed by the interaction with a surface 29 . In the case of the metal-water interaction, it is then possible to combine a good reproduction of the work of adhesion and the structure of water close to the metal surface.

We extend the study to the interaction of 40 molecules of DGEBA and 60 molecules of IPDA with the aluminum surface, so as to simulate about 2000 atoms of liquid. We proceeded likewise and report the works of adhesion in Figure 4a for DGEBA molecules and in Figure 4b for IPDA molecules. The experimental works of adhesion are calculated via Eq.( 3) by considering the contact angles measured in this work. For the liquid-vapor surface tensions, the experimental values were not available and we replace them by the simulated ones.

The measured contact angles are respectively θ = 46 • and θ = 36 • for DGEBA and IPDA molecules. The corresponding work of adhesion are reported in Figure 4. We show again that the original cross-interactions parameters lead to a significant overestimation of the works of adhesion. For the interaction between DGEBA and the metal surface, we need to decrease the cross-interaction by about 58 % whereas a more drastic reduction of 73 % is required with IPDA to fit to the experimental property. The density profiles of Figure 4c show the local densities of DGEBA molecules in interaction with the aluminum surface. In the vicinity of the surface, we observe the adsorption is mainly characterized by only a single peak with a lower amplitude than that observed with water molecules. The same applies to IPDA molecules. This is due to the fact that these liquids are much less associated than water due to weaker interactions and a much less structured hydrogen bonding network. The reproduction of the experimental work of adhesion results in a decrease of the intensity of the peak of adsorption by 20 % whereas the vanishing of this peak requires weakening the cross-interactions by 80 % (see Figure 4c with α = 0.2).

B. Calculation of the contact angle

The contact angle is determined during post-treatment of the MD trajectories by fitting a spherical cap to the water atomic density. The fit is performed using the max- imum likelihood method. The log-likelihood to maximize is defined by

L = ln i ρ(⃗ r i ) = i ln ρ(⃗ r i ) ( 27
)
FIG. 5. Density profile used to determine the contact angle from simulation trajectories. The red curve is the density profile along the diameter of a spherical drop. The green curve is the density profile used to truncate the sphere. The functional definition of the full profile is given by Eq. ( 28).The angle θ is equal to (90

• + α) where sin α = z C -z S rg .
where the product and the sum run over all water atoms. The function ρ is chosen as

ρ = ε + 1 1 + exp (r 2 -r 2 g )/w 2 A 1 + exp (z S -z)/w ′ (28)
The notations are made explicit in Figure 5. The left bracket corresponds to a spherical profile whose section is drawn in red in Figure 5, where ε ≪ 1 is the relative density in the vapor, r is the distance to the center of the drop (x C , y C , z C ), r g is the drop curvature radius and w is the width of the liquid-vapor interface. The right bracket corresponds to a smooth step function which truncates the sphere and whose section is drawn in green in Figure 5, A is a normalization constant (not fitted) and z S and w ′ are the position and the width of the solid-fluid interface. The contact angle and contact radius are then obtained by:

θ = 90 • -arcsin( z S -z C r g ) ( 29
)

r d = r g sin θ (30)
These values are averaged over all the frames of an MD trajectory.

The size dependence of microscopic droplets is described by the modified Young-Dupré equation [START_REF] Gibbs | The Collected Works of J. Willard Gibbs[END_REF][START_REF] Weijs | [END_REF][56][57][58][59][60]

cos θ = cos θ ∞ - τ r d γ LV ( 31
)
where θ is the contact angle of a nanodroplet simulated at the atomic scale, τ is the line tension and r d is the radius of the contact surface between the nanodroplet and the material. θ ∞ is the equilibrium contact angle of a macroscopic angle corresponding to a droplet with r d that tends to infinity. Simulations were performed for 4 ns on systems comprising 500, 1000, 2000, 5000, 10 000 and 25 000 molecules of water on a 80×80×10 supercell of aluminum (about 324 Å in the x and y directions). 3). The contact angle (θ) was measured in this work and the simulated contact angle of water given in brackets is given for comparison. The surface tension (γLV) of water results from experiments 53 whereas the surface tensions of IPDA and DGEBA were calculated here by molecular simulations. The solid-vapor surface tension (γSV) was determined here by free energy perturbations. The solid-liquid surface tensions (γSL) were then deduced from Eq.( 2). Figure 6a shows the values of cos θ as a function of 1/r d for different nanodroplets of water wetting an aluminum surface. The cross-interaction between water molecules and the aluminum surface were calculated with α = 0.469 to match the experimental work of adhesion. Figure 6b shows the same relationship but in a different form. First, we find that cos θ decreases as the water nanodroplet size increases. The linear fit shown in Figure 6a confirms the agreement of our data with the Young's equation. Second, we observe that the simulated droplets show contact angles smaller to that of the macroscopic drop in line with a negative line tension τ . The linear regression yields a negative line tension τ of -9.1 × 10 -11 J m -1 and a value of θ ∞ = 81 • that agrees very well with the experimental value of 85 • . We also reproduce very well the magnitude of τ which is of the order of 10 -11 even if there are still many controversies about the sign of the line tension [58][59][60][61] . Typical configurations of nanodroplets are given in parts c) and d) of Figure 6.

WSL θ γLV γSV γSL (mJ m -2 ) ( • ) (mJ m -2 ) (mJ m -2 ) (mJ m -

C. Liquid-vapor surface tension

We report here the surface tensions of both constituents of the DGEBA-IPDA epoxy resin, with respectively simulating 400 and 600 molecules. We also report the surface tension of a mixture of these constituents (400 molecules of DGEBA and 200 of IPDA). The calculation was carried by using Eq.( 16). Figure 7 shows the differences between the normal and tangential pressures profiles of DGEBA and IPDA at two temperatures. The components of the pressure tensor are the same in the bulk liquid and vapor phases, with a few more oscillations around zero in the condensed phase. The two peaks are symmetric, and each peak contributes equally to γ(z). We also check that the bulk phases make no contribution to the local surface tension. The profiles of 16) is also shown for both molecules (right-axis).

Figure 8 shows that the surface tensions of DGEBA are higher than those of IPDA resulting in stronger intermolecular interactions for DGEBA in the liquid phase. This is in line with their respective density, which are of 1.17 g cm -3 for DGEBA and 0.92 g cm -3 for IPDA. The intermolecular interactions are stronger for DGEBA due to its aromaticity. We did not calculate the surface tension of water, since the calculation of its surface tension has been extensively studied with an accurate reproduction of the experimental property over a wide range of temperatures [START_REF] Ghoufi | [END_REF][62][63][64][65] .

We now pay attention to the temperature dependence For DGEBA and the DGEBA/IPDA epoxy mixture (2:1), the linear fits were performed by excluding the value at T = 300 K.

of the surface tension of DGEBA and IPDA systems. We observe that the temperature dependence of the surface tension is linear for IPDA and DGEBA with slopes of -0.08 ± 0.01 and -0.09 ± 0.01 mJ m -2 K -1 , respectively. For the DGEBA/IPDA epoxy mixture with a 2:1 mixing ratio, the slope was estimated to be equal to -0.075 ± 0.005 by excluding the value at 300 K that deviates from the linearity. These values of slopes match very well with those found in liquids and molten polymers 66 .

D. Solid-vapor surface tension

In a first step, the surface tension γ SV was estimated by using the energy difference between the initial and final states of the cleavage process and neglecting the entropic contribution (Eq (20)). We considered a simulation cell formed by 49 000 aluminum atoms with L x = L y = 141.61 Å and L z = 120 Å. The average energy of the unified structure E U is equal to -6 327 179 kJ mol -1 and that of the separated structure E S = -6 027 946 kJ mol -1 leading to a solid-vapor surface tension γ SV of 1239 mJ m -2 . The corresponding experimental surface tension 67 was found to be equal to 1180 mJ m -2 .

We now apply the concept of perturbation and integration thermodynamics to mimic progressively the cleavage process from λ = 0 to λ = 1. However, the relatively strong value of γ SV requires to increase significantly the number of windows to respect the reversibility between successive steps. We then apply 200 windows to calculate γ SV by using the FEP formalism. We also introduce the calculation of this property by applying the TI definition to check the accuracy of both methods. The results are shown in Figure 9a in the forward and backward direction for the FEP method. For the TI method, we give only the average on both directions. W SV is equal to 2322 and 2325 mJ m -2 in the forward and backward directions respectively, whereas TI provides values of 2322 and 2323 mJ m -2 for direct and reverse directions, respectively. We obtain an excellent agreement between both directions and methods, indicating that the number of windows and simulation time are adapted to the calculation of the solid-vapor surface tension of aluminum atoms. The values of γ SV are then 1162 and 1161 mJ m -2 for FEP and TI methodologies and are in a perfect agreement with experiments 67 with a deviation less of 2 %. The comparison with the method using the difference in energy would show an entropy term T ∆S of about 78 mJ m -2 at T = 300 K

We now pay attention to the entropic term. It is possible to have an estimation of this property by considering the melting entropy of aluminum [START_REF]CRC Handbook of Chemistry and Physics[END_REF] ) is perturbed by the melting at the atomic level by increasing translational degrees of freedom, the entropic contribution to the solid-vapor surface tension would be about 69 mJ m -2 . By using Eq.( 32), it is possible to calculate the entropic contribution by doing free energy calculations at different temperatures. We have calculated W SV at 290 and 310 K and reported the values in Figure 9b with the FEP and TI techniques.

T ∆S = -T ∂∆G ∂T ≈ -T ∆W SV ∆T ( 32
)
The choice of the temperature range is dictated by a significant response to the perturbation and the fact that the heat capacity of the metal is constant over this interval. We take ∆T = 20 K. The values of the surface free energies are given in Figure 9b and differ by about 8 mJ m -2 over this temperature range. We find that T ∆S is equal to 59 and 62 mJ m -2 for FEP and TI formalism. These calculated values confirm the order of magnitude of the previous estimates. We show here that both FEP and TI methods are able to provide the solid-vapor surface tension by doing no approximation on the entropic term. Figure 9c shows the values of the solid-vapor surface tensions of the aluminum surface at two different temperatures. The value of γ SV calculated from the energy difference at 450 K shows an unexpected increase of the interfacial property with the temperature whereas the method considering the entropy in the calculation exhibits a decrease of γ SV with increasing temperature. We estimate the entropy contribution T ∆S to be equal to 171 mJ m -2 at 450 K. The variation of entropy in the range of 300..450 K is larger than that of the energy (see Figure 9c) and therefore explains the inversion of the trend of γ SV with temperature. We conclude that only the method based on the calculation of the free energy can be used to predict this interfacial property at high temperatures at which neglecting the entropic term is no longer valid. FIG. 9. a) Cumulative surface energy of aluminum metal surface calculated at 300 K by using the FEP and TI methods. For the FEP method, the values are given in the direct and reverse directions. For the TI method, we average the values in both directions. Calculations were performed over 200 windows; b) surface energy values calculated with FEP and TI at 290, 300 and 310 K and c) solid-vapor surface tensions at 300 and 450 K calculated by using the energy difference (∆U ) and the Gibbs free energy (∆G) methods. The points calculated at 440 K and 460 K were used to calculate the entropy at 450 K .

E. Solid-liquid surface tension

The solid-liquid surface tension γ SL can be calculated by an indirect way by using the definition of the work of adhesion as follows

γ SL = γ LV + γ SV -W SL (33)
This calculation avoids using the mechanical definition of the interfacial tension and considering the relationship between γ SL and the elastic strain tensor (see Eq.( 4)).

The values of the solid-liquid interfacial tensions are given in Table II for water, DGEBA and IPDA liquids interacting with the aluminum surface. We establish here that the calculation of W SL and γ SV are under control through perturbation and integration thermodynamic methods. The calculation of γ LV is also under control through the mechanical definition of the surface tension, provided that the molecular models are well transferable to this property. It results that Eq.( 33) represents an accurate way of calculating γ SL . Since the values of γ LV and W SL are small compared to γ SV , the value of γ SL is imposed by γ SV and we find values ranging 1126 to 1155 mJ m -2 for the interaction of water, DGEBA and IPDA with an aluminium surface. These strong γ SL values indicate that the interface between these liquids and the aluminium atoms of the surface is highly ordered and not very fluid.

IV. CONCLUSION

We report molecular simulations of the interaction between liquids and an aluminum metal surface. Some keyproperties for understanding and characterizing the solidliquid interface are the work of adhesion and the contact angle. The primary objective of this work was not to reproduce the experimental work of adhesion as we are aware that this property depends on the transferability of the molecular models but rather to show that the calculation of the Gibbs free energy performs very well in line with the calculations of contact angle and interfacial tensions. It is then possible to characterize the adhesion process through the different interfacial tensions.

We applied the methodology of the perturbation thermodynamic to calculate the work of adhesion of water, DGEBA and IPDA on an aluminum surface. Since the molecular models of these molecules were developed independently of those of the metal atoms, the crossinteractions between liquid and metal atoms were not expected to reproduce the experimental work of adhesion. Indeed, we showed here that these cross-interactions should be weakened by a factor α ranging from 0.47 to 0.27 depending on the liquid studied. The analysis of the molecular density profiles along the direction normal to the surface confirms a layering of molecules at the interface of metal atoms. By using these modified cross-interactions, we demonstrated that it is possible to calculate the contact angle of water molecules interacting with the aluminum surface by considering the size-dependence of the nanodroplet.

We extended the study to the calculation of the liquidvapor surface tension of DGEBA and IPDA at different temperatures. We also investigated a 2:1 DGEBA/IPDA mixture. These simulations reproduce the fact that the surface tensions of DGEBA are greater than those of IPDA in agreement with their densities. We also calculated the slope of the temperature dependence of the surface tension for these systems, which were found to match with the slopes of many liquids and molten polymers.

We completed the study of the solid-liquid interface by the calculation of the surface free energy of aluminum by using the perturbation and integration thermodynamics approaches. The simulations showed an excellent agreement with experiments and also the ability of calculating the entropy contribution. This approach performed successfully for the calculation of the solid-vapor interfacial tension. We showed that it was possible to deduce the solid-liquid interfacial tension without needing to consider the components of the elastic strain tensor through a mechanical definition of the interfacial tension.

The methodologies described in this paper opens promising perspectives since they will help us in characterizing the solid-liquid interface through all its contributions γ SL , γ SV and γ LV . The knowledge of the work of adhesion and its different contributions is fundamental to test the validity of molecular force-fields used for the modelling of adsorption processes. A possible extension of this work could be the calculation of the percolation threshold in polymer composites filled with conductive metal particles by using mesoscopic models. This interfacial property can thus be used to develop realistic and accurate coarse-grained force-fields needed to represent the polymer composites with a representative system-size.

FIG. 1 .

 1 FIG. 1. Molecular representations of a) the DGEBA epoxy monomer and b) the IPDA hardener; c) IPDA molecules interacting with an aluminum metal surface; d) slab of IPDA liquid in equilibrium with its vapor at 298 K. The z-axis is indicated for each geometry and corresponds to the axis perpendicular to the solid-liquid and liquid-vapor interfaces.

FIG. 2 .

 2 FIG. 2. Cumulative work of adhesion of IPDA molecules on an aluminum surface as a function of the coupling parameter λ for two numbers of windows (Nw= 20 and 40) and a total simulation time ranging from 5 to 40 ns. The value of the work of adhesion reads at λ = 1.

FIG. 3

 3 FIG. 3. a) Cumulative work of adhesion of water on an aluminum surface as a function of the coupling parameter for different cross-interactions between aluminum atoms and atoms of water molecules at 300 K; b) atomic density profiles along the normal direction to the metal surface as a function of the reduced z * -position defined by z * = z/Lz where Lz is the box dimension of the simulation cell. The density profiles are shown for various values of α.

FIG. 4 .

 4 FIG. 4. Cumulative work of adhesion of a) DGEBA and b) IPDA on an aluminum surface as a function of the coupling for different cross-interactions between aluminum atoms and atoms of the liquid phase at 300 K; c) atomic density profiles of the DGEBA molecules along the normal to the metal surface as a function of the reduced z-position. The density profiles are shown at different α values.

FIG. 6

 6 FIG. 6. a) Dependence of the cosine of the contact angle of water nanodroplets wetting an aluminum surface on the inverse of the radius of contact r d .; b) dependence of the contact angle on r d . The fits are shown in red broken lines. The macroscopic contact angle θ∞ was calculated by extrapolating cos θ to (1/r d = 0) in part a); snapshots of water nanodroplets formed by c) 1000 and d) 25 000 water molecules.

FIG. 7 .

 7 FIG. 7. Difference between the local normal pN(z) and tangential pT(z) components of the pressure tensor as a function of z calculated in the liquid-vapor interfaces of IPDA at 300 K and DGEBA at 450 K (left axis). The surface tension profile calculated with Eq.(16) is also shown for both molecules (right-axis).

FIG. 8 .

 8 FIG.8. Surface tensions of IPDA and DGEBA molecules as a function of the temperature. The error-bars were calculated by using block-averages on five independent simulations. The dotted lines represent the linear fit of the simulated values. For DGEBA and the DGEBA/IPDA epoxy mixture (2:1), the linear fits were performed by excluding the value at T = 300 K.

  T ∆S o melting = T ∆H o melting T melting = 11.6 J mol -1 where T melting = 933 K and T = 300 K. By considering that only the first layer of atoms (400 atoms) of the metal surface (A = 40.46 × 40.46 Å2

  = 440 K and 460 K)

TABLE I .

 I Parameters from the CHARMM force field[START_REF] Heinz | [END_REF] for the aluminum atoms

	Metals	Mass	σ	ε
		(g)	( Å)	(kJ mol -1 )
	Al	26.98	2.6059	16.83

TABLE II .

 II Experimental values of work of adhesion (WSL) calculated via Eq.(

ACKNOWLEDGMENTS

MO, ABM and CL would like to thank all the members of SimatLab for stimulating discussions about this work. SimatLab is a joint public-private laboratory dedicated to the multi-scale modelling of polymer materials. This laboratory is supported by Michelin, Clermont Auvergne University (UCA), CHU of Clermont-Ferrand and CNRS. We are also grateful to the Mésocentre Clermont Auvergne University for providing computing and storage resources.

DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.


Dr Beth A Davison
email: bethdavison@momentum-research.com.

PhD Stefanie Senger

PhD; Iziah E Sama

PhD Gary G Koch

PhD Alexandre Mebazaa

MD Kenneth Dickstein

PhD ; Nilesh

J Samani

PhD; Marco Metra

PhD Stefan D Anker

PhD; John G Cleland

PhD ; Leong

L Ng

MD; Ify R Mordi

MD Faiez Zannad

PhD ; Gerasimos

S Filippatos

PhD Hans L Hillege

PhD; Piotr Ponikowski

PhD Dirk J Van Veldhuisen

PhD; Chim C Lang

PhD; Peter Van Der Meer

PhD Julio Núñez

PhD Antoni Bayés-Genís

PhD ; Christopher Edwards

BS Adriaan A Voors

PhD Gad Cotter

Is Acute heart failure a distinctive disorder? An analysis from BIOSTAT-CHF

Keywords: Acute heart failure, acute heart failure diagnosis, acute heart failure treatment

Aims: This retrospective analysis sought to identify markers that might distinguish between acute heart failure (HF) and worsening HF in chronic outpatients.

Methods and Results:

The BIOSTAT-CHF index cohort included 2516 patients with new or worsening HF symptoms: 1694 enrolled as inpatients (acute HF) and 822 as outpatients (worsening HF in chronic outpatients). A validation cohort included 935 inpatients and 803 outpatients. Multivariable models were developed in the index cohort using clinical characteristics, routine laboratory values, and proteomics data to examine which factors predict adverse outcomes in both conditions and to determine which factors differ between acute HF and worsening HF in chronic outpatients, validated in the validation cohort.

Patients with acute HF had substantially higher morbidity and mortality (6 months mortality was 12..3% for acute HF and 4..7% for worsening HF in chronic outpatients). Multivariable models predicting 180-day mortality and 180-day HF re-admission differed substantially between acute HF and worsening HF in chronic outpatients. CA-125 was the strongest single biomarker to distinguish acute HF from worsening HF in chronic outpatients, but only yielded a C-index of 0..71. A model including multiple biomarkers and clinical variables achieved a high degree of discrimination with a C-index of 0..913 in the index cohort and 0..901 in the validation cohort.

Conclusion:

The study identifies different characteristics and predictors of outcome in acute HF patients as compared to outpatients with chronic HF developing worsening HF. The markers identified may be useful in better diagnosing acute HF and may become targets for treatment development.

Introduction

Acute heart failure (AHF) is defined as a worsening of symptoms and signs of heart failure (HF) requiring urgent care inclusive (but not limited to) intravenous therapy and hospital admission.(1) Following a series of neutral studies in which new interventions for AHF were not shown in large studies to be associated with improvements in either patients' symptoms or shortand long-term outcomes,(2) some opinion leaders have raised doubt whether AHF is a separate condition or just a part of the natural course of chronic heart failure.(3) At the same time doubts have been raised that some of the failure in demonstrating positive effects in large AHF studies relates to dilution of the patient population;(4) i.e., that patients enrolled in larger confirmatory studies may not have "true" AHF but have other disorders, chiefly chronic HF that has slightly deteriorated. [START_REF] Davison | Mega-studies in heart failure -effect of dilution in examination of new therapies[END_REF] On the one hand some argue that the decision to admit a patient with AHF is subjective and variable and hence HF deterioration managed in the outpatient setting is not a different entity than AHF leading to hospital admission, while others argue that those are different conditions, the latter having a distinct pathophysiological mechanismassociated with inflammatory activation, more congestion, and end organ damage. [START_REF] Metra | Effect of serelaxin on cardiac, renal, and hepatic biomarkers in the Relaxin in Acute Heart Failure (RELAX-AHF) development program: correlation with outcomes[END_REF] One of the obstacles in resolving these differences, and possibly developing effective therapies for AHF, is that there are no objective measures that help determine whether a patient is truly "acute", i.e., has AHF. All objective measures utilized in the diagnosis of AHF to date (natriuretic peptides levels, chest Xray or lung ultrasound) can also be found to be affected in patients with stable chronic HF who have slight outpatient deterioration.

In the current analysis we have examined the characteristics of patients enrolled in the BIOSTAT-CHF study (A systems BIOlogy Study to Tailored Treatment in Chronic Heart Failure) study where patients with both AHF requiring hospital admission and worsening of HF managed in an outpatient clinic were enrolled and followed. [START_REF] Voors | A systems BIOlogy Study to TAilored Treatment in Chronic Heart Failure: rationale, design, and baseline characteristics of BIOSTAT-CHF[END_REF] While the absolute risk of adverse clinical outcomes overlapped in these two patient groups, the characteristics and prognosis of patients enrolled in the inpatient versus the outpatient setting in this study were found to differ. [START_REF] Ferreira | Heart failure in the outpatient versus inpatient setting: findings from the BIOSTAT-CHF study[END_REF] The objective of this retrospective analysis was to identify markers that may distinguish between AHF and chronic HF patients with outpatient exacerbations and determine whether predictors of adverse outcomes in the two groups differed in the BIOSTAT-CHF database.

Methods

Index and validation cohorts

The BIOSTAT-CHF project provided access to data from an index cohort of 2516 heart failure patients enrolled between December 2010 and December 2012 in 69 centers in 11 European countries. In the Index Cohort adult patients with new or worsening heart failure symptoms, objective evidence of cardiac dysfunction, treated with at least 40 mg/day furosemide or equivalent, and receiving 50% or less the target doses of evidence-based therapies were enrolled in either the inpatient or outpatient setting and patients were followed for a median of 21 months. [START_REF] Voors | A systems BIOlogy Study to TAilored Treatment in Chronic Heart Failure: rationale, design, and baseline characteristics of BIOSTAT-CHF[END_REF]. For the Validation cohort inclusion criteria were similar, although outpatients could have been recruited without worsening of heart failure. Data were available from a validation cohort of 1738 patients enrolled in either the inpatient or outpatient setting between October 2010 and April 2014 in six centers in Scotland, UK. Patients in the validation cohort had a heart failure diagnosis and a previous admission with heart failure requiring diuretic therapy, and were treated with at least 20 mg/day furosemide or equivalent and 50% or less the target doses of evidence-based therapies at entry. The study design of BIOSTAT-HF, baseline characteristics of the two cohorts and various modeling results have been described previously [START_REF] Voors | A systems BIOlogy Study to TAilored Treatment in Chronic Heart Failure: rationale, design, and baseline characteristics of BIOSTAT-CHF[END_REF][START_REF] Ferreira | Heart failure in the outpatient versus inpatient setting: findings from the BIOSTAT-CHF study[END_REF][START_REF] Voors | Development and validation of multivariable models to predict mortality and hospitalization in patients with heart failure[END_REF].

Patient characteristics and clinical outcomes

In order to develop a discriminatory model for acute HF and outpatient worsening HF (OP-WHF) we used reported hospitalization status (inpatient or outpatient) as surrogate. Model development was based on basic patient characteristics collected at study entry and baseline (age, sex, LVEF, BMI, vital signs, medical history), as well as baseline laboratory test values from blood samples analyzed locally or from blood samples that were frozen for shipment to central laboratories for analysis:

1. Local and routine central laboratory: Local laboratory results considered in the models included white blood cell count, red blood cell count, platelet count, hemoglobin, urea, glomerular filtration rate estimated from local creatinine using the CKD-EPI equation, [START_REF] Levey | A new equation to estimate glomerular filtration rate[END_REF] sodium, potassium, total bilirubin, glucose, AST, ALT, GGT, ALP, HDL, LDL, and triglycerides. NT-proBNP, high-sensitivity troponin T (hsTnT), and GDF-15 were centrally measured using a Roche Elecsys® cobas analyzer (Roche Diagnostics, Mannheim, Germany); aldosterone, renin, FGF23, urea, creatinine, calcium, phosphate, albumin, iron, ferritin, transferrin, hepcidin, and sTFR were also measured centrally.

2. Specialty biomarkers: Three biomarkers (TnI, ET-1, and IL-6) were measured using enzyme-linked immunosorbent assays (Singulex Inc.) on a Luminex platform. pro-ENK and bio-ADM were measured on a Sphingotec platform (Spingotec GmbH). CA125 was measured using a chemiluminescent microparticle immunoassay on an ARCHITECTi system (Abbott Laboratories). [START_REF]UniProt: a worldwide hub of protein knowledge[END_REF] For model development, we excluded 4 biomarkers from analysis as the same proteins were measured on more than 1 panel (1 copy each of AREG and SCF, and two copies of IL-6), leaving a total of 364 unique proteins for analysis.

In a preliminary step, we excluded baseline parameters with mostly missing observations in the index cohort and selected representative parameters in case of highly correlated or collinear variables. Olink measures were nearly perfectly correlated with other central measures of the same parameter. When both were available models were developed considering only the Olink parameter; for example, only MUC16 and not CA125 was considered in multivariable Model 3 for distinguishing AHF from OP-WHF. A differential expression analyses of the Olink proteins was performed using the Linear Models for Microarray data analysis (Limma) software (version 3.34.9). [START_REF] Ritchie | limma powers differential expression analyses for RNA-sequencing and microarray studies[END_REF] Proteins were considered differentially expressed in inpatients relative to outpatients if the absolute value of the fold change exceeded 1.24 (|log 2 FC|>0.31), the p-value for the t-test that the log 2 FC differs from zero and the false discovery rate (FDR) <0.05. A volcano plot [a plot of -log 10 (p-value) versus log 2 fold change] was used to visualize the differential expression of these markers in patients enrolled in the inpatient versus the outpatient setting. Clinical endpoints considered for analysis were the two components of the primary endpoint of BIOSTAT-CHF: all-cause death and first re-admission for heart failure. For the development of prognostic models, the time to the first occurrence of each clinical endpoint was evaluated through 180 days after baseline. Partially missing re-admission or death dates were imputed with the 15 th of the month if only day was missing, or July 1 st if both day and month were missing. Re-admission dates before and up to (≤) the respective baseline visit dates were excluded from analysis. Time to event was computed for all patients with a recorded event. Time to event for patients without a recorded event was censored at the earlier of 180 days after baseline or the individual end of study date. For the analysis of time to first occurrence of HF re-admission, time was censored at date of death for subjects who were not re-admitted for HF as the primary cause.

Statistical model development

Hospitalization status (inpatient versus outpatient) was analyzed using logistic regression. Time to all-cause death through 180 days and time to first HF re-admission through 180 days were analyzed using Cox proportional hazards models. We examined a number of classification methods in addition to logistic and Cox regression including Boosted Logistic Regression (LogitBoost), linear discriminant analysis with stepwise feature selection (stepLDA), neural networks (nnet), k-nearest neighbors (knn), CART (rpart), C5.0, and random forest (rf) (Supplementary Tables 12345). We noted that performance characteristics of C5.0 and random forest appeared best, with generally the highest area under the receiver operator characteristic curves (AUCs) and highest scaled Brier scores (which can be interpreted as correlation coefficients). Thus, pre-selection of Olink candidate predictors for the logistic regression models was based on the average variable importance rank for these two methods. We used the set of index cohort patients with complete Olink data as a training set for building classifiers that would predict inpatient status. Variable importance for each Olink marker was calculated by independently using C5.0 [START_REF]Programs for Machine Learning[END_REF] as well as Random Forests [START_REF] Breiman | Random Forests[END_REF] as classification methods in a repeated 5-fold cross-validation approach using R package "caret" [START_REF] Kuhn | caret: Classification and Regression Training[END_REF]. Variable importance measures within each method were ranked using sports ranking; markers were then sorted by their average rank across the two methods. The top 50 Olink markers were selected as candidates for the inpatient status model (Supplementary Table 6), and the top 20 markers as candidates for the outcome models except for the top 10 in the case of outpatient mortality.

The full set of candidate predictors for each of the five models is given in Supplementary Table 11. For discriminating between in-and outpatients, in Model 1 we considered only patient characteristics, vital signs and locally-and centrally-measured laboratory values; we additionally considered medical history for prognostic models. For model 2, we further considered specialty biomarker measures; for model 3, we added the pre-selected Olink proteins. Missing values in the final analysis data set were imputed using a multi-chain Monte Carlo approach (R package "mice"( 15)) and 10 imputed data sets were generated for the index cohort.

For each model, each continuous candidate baseline variable was first tested for non-linearity of its association with the model outcome by assessing the significance of the non-linear components of a restricted cubic spline transformation applied to the baseline variable in the index cohort while adjusting for the remaining candidate variables. In cases where the association was deemed significantly non-linear and this behavior was observed consistently across the 10 imputed data sets of the index cohort, appropriate non-linear transformations were selected from a set of pre-specified transformations (such as quadratic, cubic, or linear spline transformations). Selection was based on values of Akaike's Information Criterion and visual inspection of plotting the predicted outcome against the baseline values. Baseline variables with highly skewed distributions were log2 transformed for analysis. Logistic or Cox regression with backwards selection was run on the 10 imputed data sets computing pooled p-values according to Rubin's algorithm [START_REF] Rubin | Multiple imputation in health-care databases: an overview and some applications[END_REF] in each selection step and with the p-value criterion of 0.01 for staying in the inpatient models, and 0.05 for staying in the prognostic models. Estimated effect sizes, their 95% confidence intervals and p-values were pooled using Rubin's algorithm.

As a measure of discriminatory ability, the C-index pooled across the 10 imputed data sets was computed for each model. We further derived "final" models by combining the regression coefficients using Rubin's algorithm, applied each final model on the imputed data sets and derived the C-index for the final models as the average C-index across the imputed data sets. For internal validation, bootstrap samples of the imputed data sets of the index cohort were drawn, each time using the same random sample of patients for all imputations. Backwards selection and model fitting were repeated for each bootstrap sample in order to estimate bias-corrected Cindices and confidence intervals for each multivariable model. For external validation, the final models were applied to the imputed data sets of the validation cohort and pooled C-indices estimated. We further examined discrimination and calibration of our models through receiveroperator characteristics (ROC) curves and calibration plots.

The model for inpatient versus outpatient status was externally validated in the validation cohort.

A few of the baseline characteristics included in the final models were not accessible or not reported in the validation cohort and were thus multiply imputed. We successively added a small random sample of validation patients (n=11) to each of the 10 imputed data sets of the index cohort. We then imputed missing data for each subset of 11 validation patients in each imputed data set, repeated this step 158 times, thus generating 10 imputed data sets for the 1738 subjects in the validation cohort as well.

To further explore differences in prognostic factors between inpatients and outpatients, we applied the final multivariable models in inpatients to the outpatients. For HF readmission, all variables in the final model were used, while for death due to the limited number of events in outpatients the top 8 predictors were chosen. We further compared the fit of the final inpatient and outpatient models in the inpatients using partial likelihood ratio tests [START_REF] Fine | Comparing nonnested Cox models[END_REF] as implemented in R package nonnestcox; for each clinical endpoint, the two final models were fitted within the inpatients and separately for 10 imputed data sets. SAS® version 9.4 (SAS Institute, Cary, NC, USA) and R version 3.5.1 [START_REF] Core | R: A language and environment for statistical computing[END_REF] software was used for all analyses.

Data availability

The data that support the findings of this study are available from University Medical Center Groningen but restrictions apply to the availability of these data, which were used under license for the current study, and so are not publicly available. Data are however available from the authors upon reasonable request and with permission of University Medical Center Groningen.

Results

Inpatients versus outpatients

Summary statistics for selected baseline characteristics are presented in Table 1 by cohort and patient status. A volcano plot showing the differential expression of the Olink panel proteins in inpatients versus outpatients is presented in Figure 1. Mucin-16 (MUC16), also known as CA125, appears to be the most differentially expressed, when considered without simultaneous adjustment for other proteins (i.e., univariably). In BIOSTAT-CHF, a doubling of CA125 (ARCHITECTi) as a continuous measure increased the odds of being an inpatient by 50% (OR 1.50, 95% CI 1.42-1.58, p<0.0001) with an AUC of 0.6983 (Table 2); results for MUC-16 measured on the Olink platform were similar (OR 1.58, 95% CI 1.48-1.69, p<0.0001). MUC-16 was selected for inclusion in the multivariable model (Table 3) with a somewhat smaller association with inpatient status (OR 1.30, 95% CI 1.17-1.46). At a threshold of 100 U/mL, [START_REF] Nunez | Carbohydrate Antigen-125-Guided Therapy in Acute Heart Failure: CHANCE-HF: A Randomized Study[END_REF] CA125 (ARCHITECTi) greater than the threshold had an AUC of 0.6278, sensitivity of 0.3832, specificity 0.8725, positive predictive value (PPV) 0.8610 and negative PV (NPV) 0.4070. ....... We also examined the ability of the traditional marker of HF severity -NT-proBNPto discriminate between inpatients and outpatients. A doubling of NT-proBNP (cobas) was associated with an OR of 1.32 (95% CI 1.25-1.39, p<0.0001) for inpatient status with an AUC of 0.6395. Using a cut-point of 400 pg/mL [START_REF] Mueller | Heart Failure Association of the European Society of Cardiology practical guidance on the use of natriuretic peptide concentrations[END_REF] resulted in an AUC of 0.5421, sensitivity 0.9400, specificity 0.1442, PPV 0.6936, and NPV 0.5384. Thus, the traditional cut-point displayed high sensitivity and very low specificity. .......Note that when adjusted simultaneously for other proteins (Table 3), patients with a higher NT-proBNP were less likely to be an in-patient (OR 0•87 per 1-log increase, 95% CI 0•78-0•96).

We examined the ability of other biomarkers identified as potential markers of acutely ill heart failure patients including ST2, troponin T, troponin I, GDF-15, and ADM. Each of these markers individually was unable to discriminate between inpatients and outpatients, with AUCs of about 0.500 signifying an ability no better than chance to predict the status. Table 3 presents the selected multivariable logistic regression models for inpatient versus outpatient; Supplementary Figures 1 and2 show in the index and validation cohorts the receiveroperator-characteristic (ROC) and calibration curves, respectively. The discrimination of the final multivariable model 3, which included 21 of the 50 Olink proteins considered, was excellent, with a c-index (AUC) of 0.9133 in the index cohort and of 0.9011 in the validation cohort. The performance characteristics of this modelincluding AUC and scaled Brier scorewere better than those using classification methods (Supplementary Table 1).

Death through Day 180

In the Index cohort a total of 208 (12.3%) patients enrolled in the inpatient setting, and 39 (4.7%) patients enrolled in the outpatient setting, died by day 180. In the validation cohort 162 (17.3%) of the patients enrolled in the inpatient setting died at 6 months versus 25 (3.1%) in the outpatient setting. Final multivariable prognostic models are presented in Tables 4 and5 for inpatients and outpatients, respectively. The full models (Model 3) had good discrimination with c-indexes of 0.8281 and 0.8460, respectively. Although difficult to compare directly because the paucity of events among outpatients restricted the number of candidate predictors that could be considered for that outcome, the prognostic factors differed for the two patient groups. When only considering patient characteristics and local and central laboratory data (Model 1), for example, FGF23, NT-proBNP, renin, and troponin T were all highly prognostic in inpatients, while platelet count, peripheral arterial disease, and age were most prognostic in outpatients.

The 8 most prognostic factors from the inpatient multivariable Model 3 for death provided much less discrimination in outpatients with a c-index 0.7464 (Supplementary table 12). And the inpatient and outpatient models were found to be distinguishable, and the fit of the inpatient model significantly better than the outpatient model, in inpatients.

Heart failure hospitalization through Day 180

In the Index Cohort, a total of 254 (15.0%) patients enrolled as inpatients, and 73 (8.9%) patients enrolled as outpatients, were hospitalized for heart failure by day 180. In the Validation Cohort, 6-month HF admission was observed in 166 (17.8%) inpatients and 57 (7.1%) outpatients. Final multivariable prognostic models are presented in Tables 6 and7 had similar discrimination with a c-index of 0.7395 for both. Discrimination for the models in outpatients was better, with c-indexes of 0.7966, 0.7984, and 0.8234 for Models 1, 2, and 3, respectively. NT-proBNP was a strong prognostic factor in both inpatients and outpatients.

The inpatient Model 3 applied to outpatients provided less discrimination than the model developed in the outpatients, with a c-index of 0.8055 (Supplementary table 13). And the inpatient and outpatient models were found to be distinguishable, and the fit of the inpatient model significantly better than the outpatient model, in inpatients.

Discussion

AHF research has been limited in the last decades by three major issues. The first is the lack of an objective definition of AHF. The currently used definition is a subjective one (worsening symptoms and signs requiring urgent care) which has been an impediment to distinguishing between patients with "true" AHF versus those with out-patient HF exacerbations not requiring urgent care. This had led to significant problems in enrolling AHF patients in large studies. [START_REF] Davison | Mega-studies in heart failure -effect of dilution in examination of new therapies[END_REF] Second, related to the lack of ability to define AHF we also know little of its pathophysiology.

And third, as a consequence of our lack of ability to define AHF and our lack of knowledge of its pathophysiology the treatment targets for AHF are also not defined. In the last two decades, most therapies developed for AHF were either vasodilators or diureticswhich have both failed to show substantial benefit beyond some improvement in very short-term symptoms.

In the current analysis, AHF and OP-WHF were found to differ in three major domains. First, patients with AHF had much higher morbidity and mortality rates. The 180-day mortality and HF readmission rates were 12.3% and 15% for the AHF cohort and 4.7% and 8.9% for the OP-WHF cohort, respectively. Second, prognostic models for adverse outcomes differ for patients with AHF versus outpatient exacerbation of HF and models that predict adverse outcomes in AHF do not predict well adverse outcomes in outpatient exacerbations of HF. Third and lastly, the characteristics and prognosis of patients enrolled in the inpatient versus the outpatient setting in this study were found to differ. [START_REF] Ferreira | Heart failure in the outpatient versus inpatient setting: findings from the BIOSTAT-CHF study[END_REF] The current analysis suggests that patients admitted for AHF have a different biomarker profile from patients with HF exacerbation not requiring admission.

These findings suggest that different pathophysiological mechanisms leading to different patterns of activation of neurohormonal and inflammatory protein markers may be involved in AHF and differ from those in out-patient exacerbations of heart failure. If confirmed, these may enable development of new diagnostic platforms that would lead to better ability to diagnose patients with true AHF. The exact components and details of such diagnostic platforms should be elucidated in further prospective studies. In line with this limitation, as seen above, none of the currently proposed biomarkers (natriuretic peptides, CA125, ST2 or troponin) by itself can differentiate between AHF and outpatient exacerbation to the degree that the full model can.

However, more data are required to better elucidate which variables and biomarkers would best discriminate the different disorders. As described in the current manuscript the models provided may help illuminate new paths in developing better models, but are not in themselves ready to be applied immediately in clinical studies.

In addition, some biomarkers that are differentially activated in AHF or those that seem to be associated with adverse outcomes in AHF patients specifically may become targets for therapeutic interventions or proxies to therapeutic intervention success enabling more targeted therapy for AHF to be developed. Oncological development plans have for the last 20 years been successful in targeting specific phenotypes with specific tailored therapies targeting the pathways most activated in those phenotypes. Novel approaches assessing in parallel multiple targeted interventions in specific phenotypes should be adopted in AHF research. It is possible that the lack of success we have encountered in developing new therapies for AHF is not related to the proposal that AHF does not exist, but rather to our limited attempts to develop tailored phenotype specific treatments.

Study Limitations

The current analysis is limited by the moderate size of the BIOSTAT study which was designed mainly to examine the importance of treatment optimization in patients with worsening HF. Some of the outcomes were sparseespecially in the group of patients with exacerbation of HF not requiring admission -. This was especially true in the Validation Cohort where some patients could have been enrolled in the outpatient setting without worsening of HF. Moreover, the BIOSTAT study included a cohort of European mostly Caucasian patients mostly with left ventricular systolic dysfunction. Therefore, our models need validation in other cohorts of more diverse patient populations. The prognostic models developed have relatively low predictive value especially when it comes to HF readmissions. Therefore, they cannot be suggested to replace currently validated models in acute and chronic HF.

Conclusions

Our analysis suggests that patients who present with AHF differ from patients who develop HF exacerbation not requiring hospital admission. Patients with AHF are characterized by different clinical and biomarker profiles, have substantially worse outcomes and different predictors of adverse outcomes. The biomarkers that differ between patients with AHF and outpatients with HF exacerbation as well as the predictors of adverse outcome in AHF patients can serve to improve AHF diagnosis and potentially become therapeutic targets for AHF.

Funding

BIOSTAT-CHF was funded by the European Commission [FP7-242209-BIOSTAT-CHF;

EudraCT 2010-020808-29].

3 .

 3 Proteinomics/Olink panels: The BIOSTAT-CHF project included a comprehensive proteomic database measured by the Olink Proseek analysis service (Olink Proteomics, Uppsala, Sweden). The Olink platform utilizes a high-throughput multiplex immunoassay based on a proprietary Proximity Extension Assay (PEA) technology, where each biomarker is addressed by a matched pair of antibodies, coupled to unique, partially complementary oligonucleotides, and measured by quantitative real-time polymerase chain reaction (PCR). Results are expressed in the form of relative quantification (Normalized Protein eXpression or NPX) which are logarithmically related to protein concentration but cannot be converted to absolute protein concentrations. The BIOSTAT-CHF database comprised data from four Olink panels: Cardiovascular II, Cardiovascular III, Immune Response, and Oncology II, providing baseline measurements for a total of 368 proteins for most patients of both cohorts. Proteins can be recognized by a UniProt identifier.

  for inpatients and outpatients, respectively. Model discrimination was modest in inpatients, with a c-index of 0.7322 for the full model (Model 3); the model including only patient characteristics and local or central laboratory data (Model 1) and the model additionally considering specialty laboratory parameters (Model 2)

Figure 1 (

 1 Figure 1 (Central Illustration). Differential protein expression in inpatients relative to

  Heart rate, bpm 79.0 (70.0, 92.0) 72.0 (64.0, 82.0) 75.0 (64.0, 88.0) 69.0 (60.0, 79.0)

Table 1 . Baseline characteristics by cohort and patient status

 1

	Index Cohort	Validation Cohort

Table 2 . Ability of selected biomarkers to discriminate between patients with worsening heart failure enrolled in the inpatient versus the outpatient setting

 2 Results are presented as frequency and percentage for discrete variables and as median, lower quartile (Q1), and upper quartile (Q3) for continuous variables. *Result presented in Ferreira JP, Metra M, Mordi I, Gregson J, Ter Maaten JM, Tromp J, Anker SD, Dickstein K, Hillege HL, Ng L, van Veldhuisen DJ, Lang CC, Voors AA, Zannad F. Heart failure in the outpatient versus inpatient setting: findings from the BIOSTAT-CHF study. Eur J Heart Fail. 2019;21(1):112-20.Results from logistic regression models, modeling the probability for inpatient. *Parameters followed by a UniProt ID were measured on Olink. The remainder were measured using Singulex assays. †Model parameters and optimal cut-point allowed to vary and averaged across imputation datasets. ‡Same cut-point applied in each imputation dataset and resulting parameters averaged across imputation datasets.

	(LVEF <40%)	1167 (79.0%)	652 (85.2%)	345 (41.4%)	381 (51.8%)
	HFmrEF (LVEF 40-<50%)	187 (12.7%)	95 (12.4%)	209 (25.1%)	192 (26.1%)
	HFpEF (LVEF ≥50%)	124 (8.4%)	18 (2.4%)	279 (33.5%)	162 (22.0%)
	NYHA class
	Class I	31 (1.9%)	25 (3.1%)	6 (0.6%)	11 (1.4%)
	Class II	456 (28.0%)	412 (50.6%)	235 (25.1%)	477 (59.5%)
	Class III	874 (53.6%)	354 (43.4%)	477 (51.0%)	295 (36.8%)
	Class IV	270 (16.6%)	24 (2.9%)	217 (23.2%)	19 (2.4%)
	Extent of peripheral edema
	Not Present	477 (33.2%)	366 (55.1%)	204 (24.2%)	385 (54.9%)
	Ankle	443 (30.9%)	189 (28.5%)	284 (33.7%)	199 (28.4%)
	Below Knee	375 (26.1%)	99 (14.9%)	278 (33.0%)	97 (13.8%)
	Above Knee	140 (9.8%)	10 (1.5%)	77 (9.1%)	20 (2.9%)
	Pulmonary congestion
	No	579 (34.8%)	575 (73.4%)	292 (32.3%)	627 (83.7%)
	Single base	219 (13.2%)	92 (11.7%)	59 (6.5%)	36 (4.8%)
	Bi-basilar	864 (52.0%)	116 (14.8%)	554 (61.2%)	86 (11.5%)
	Orthopnea	745 (44.1%)*	134 (16.3%)*	..	..
	Rales >1/3 up lung fields	229 (21.2%)	19 (9.1%)	43 (11.1%)	7 (3.3%)
	Elevated jugular venous pressure	435 (39.4%)*	119 (21.6%)*	281 (36.0%)	169 (24.5%)
	Hepatomegaly	270 (16.0%)	88 (10.8%)	34 (3.9%)	26 (3.8%)
	Aldosterone antagonists	913 (53.9%)	426 (51.8%)	274 (29.4%)	286 (35.8%)
	ACEi/ARB	1170 (69.1%)	650 (79.1%)	587 (63.0%)	632 (79.1%)
	Beta blocker	1356 (80.0%)	737 (89.7%)	644 (69.1%)	608 (76.1%)
	Loop diuretics	1684 (99.4%)	820 (99.8%)	..	..
	Diuretics	1692 (99.9%)	822 (100.0%)	920 (98.7%)	791 (99.0%)
	Digoxin	320 (18.9%)	171 (20.8%)	171 (18.3%)	138 (17.3%)

Table 3 . Backward selection results Inpatient vs. Outpatient Multivariable Model 1 Local and central data Multivariable Model 2 Local, central, and Singulex data Multivariable Model 3 Local, central, Singulex, and Olink data Parameter Effect size for a change of Odds ratio (95% CI) P-value Odds ratio (95% CI) P-value Odds ratio (95% CI) P-value

 3

	Age, years	5	0.93 (0.88, 0.97)	0.0017	0.94 (0.89, 0.98)	0.0100	0.89 (0.83, 0.95)	0.0008
	LVEF, %	5	1.08 (1.03, 1.15)	0.0050	1.10 (1.04, 1.17)	0.0009	1.11 (1.04, 1.20)	0.0040
	Diastolic blood pressure ≤ 70 †	5	0.70 (0.62, 0.79)	<.0001	0.69 (0.61, 0.78)	<.0001	0.74 (0.64, 0.85)	<.0001
	Diastolic blood pressure > 70 †	5	0.96 (0.90, 1.01)		0.97 (0.91, 1.03)		1.00 (0.93, 1.08)
	Heart rate, bpm	5	1.11 (1.08, 1.15)	<.0001	1.11 (1.07, 1.15)	<.0001	1.10 (1.05, 1.14)	<.0001
	Albumin, g/L	1	0.88 (0.86, 0.91)	<.0001	0.92 (0.90, 0.94)	<.0001	0.93 (0.91, 0.96)	<.0001
	Aldosterone, pg/mL, log2	Doubling	0.91 (0.86, 0.97)	0.0023
	ALT, U/L, log2	Doubling	1.25 (1.10, 1.42)	0.0007	1.28 (1.12, 1.46)	0.0004
	Hepcidin, nmol/L, log2	Doubling	1.17 (1.10, 1.24)	<.0001	1.09 (1.03, 1.16)	0.0041
	Serum iron, μmol/L, log2	Doubling	0.68 (0.58, 0.79)	<.0001	0.77 (0.66, 0.90)	0.0013
	Phosphate, mmol/L, log2	Doubling	3.42 (2.49, 4.69)	<.0001	3.30 (2.39, 4.56)	<.0001	2.28 (1.48, 3.49)	0.0002
	sTfR, mg/L, log2	Doubling	1.38 (1.15, 1.65)	0.0005	1.48 (1.24, 1.77)	<.0001
	Total bilirubin, μmol/L, log2	Doubling	1.30 (1.10, 1.53)	0.0041
	Troponin T, pg/mL, log2	Doubling	1.44 (1.31, 1.60)	<.0001
	Potassium, mmol/L	1	0.68 (0.55, 0.83)	0.0002	0.67 (0.55, 0.82)	0.0002
	Transferrin, g/L	1	1.98 (1.45, 2.70)	<.0001
	Urea, mmol/L, log2	Doubling			1.31 (1.13, 1.53)	0.0007
	CA125, U/mL, log2	Doubling			1.25 (1.16, 1.35)	<.0001
	IL-6, pg/mL, log2	Doubling			1.26 (1.15, 1.38)	<.0001
	NT-proBNP, pg/mL, log2	Doubling			0.87 (0.81, 0.94)	0.0004	0.87 (0.78, 0.96)	0.0076
	Troponin I, pg/mL, log2	Doubling			1.30 (1.21, 1.39)	<.0001	1.31 (1.20, 1.42)	<.0001
	ADM (P35318)	1					0.70 (0.56, 0.87)	0.0014
	AGRP (O00253)	1					2.28 (1.65, 3.16)	<.0001
	BOC (Q9BWV1)	1					0.45 (0.28, 0.73)	0.0012
	FABP2 (P12104)	1					0.75 (0.64, 0.89)	0.0010
	FGF-21 (Q9NSA1)	1					0.77 (0.70, 0.86)	<.0001

Table 5 . Backward selection results for Death through Day 180 -Outpatients Multivariable Model 1 Local and central data Multivariable Model 2 Local, central, and Singulex data Multivariable Model 3 Local, central, Singulex, and Olink data Parameter Effect size for a change of Hazard ratio (95% CI) P-value Hazard ratio (95% CI) P-value Hazard ratio (95% CI) P-value

 5

	Age, years	5	1.32 (1.09, 1.60)	0.0046	1.22 (1.02, 1.46)	0.0263	1.23 (1.02, 1.48)	0.0329
	Hypertension	Yes vs.	0.42 (0.20, 0.88)	0.0217
		No
	Myocardial infarction	Yes vs.	2.14 (1.08, 4.26)	0.0300
		No
	Peripheral artery disease	Yes vs.	3.73 (1.52, 9.15)	0.0044
		No
	LVEF ≤ 35 % †	1	0.94 (0.89, 0.99)	0.0240
	LVEF > 35 % †	1	1.06 (1.00, 1.11)
	Hemoglobin, g/dL	1	0.75 (0.60, 0.94)	0.0130	0.72 (0.57, 0.90)	0.0039	0.72 (0.57, 0.91)	0.0056
	Potassium, mmol/L	1	2.05 (1.04, 4.05)	0.0407
	Platelet count, 10 9 /L, log2	Doubling	4.88 (2.25, 10.61)	0.0001	3.90 (1.54, 9.88)	0.0069	3.59 (1.31, 9.83)	0.0186
	Total bilirubin, μmol/L, log2	Doubling	2.05 (1.23, 3.42)	0.0098
	Male sex	Yes vs.			4.12 (1.51, 11.26)	0.0060	4.47 (1.57, 12.70)	0.0051
		No
	CA125, U/mL, log2	Doubling			1.47 (1.21, 1.78)	0.0001	1.45 (1.21, 1.74)	<.0001
	pro-ENK, pmol/L, log2	Doubling			1.88 (1.12, 3.14)	0.0213
	Red blood cell count, 10 12 /L	1			1.90 (1.10, 3.30)	0.0259	1.94 (1.11, 3.39)	0.0235
	CNTN1 (Q12860)	1					0.53 (0.29, 0.96)	0.0409
	SCGB3A2 (Q96PL1)	1					1.81 (1.31, 2.52)	0.0005
	Pooled C-index in Index Cohort		0.8277		0.8156		0.8460
	C-index of final model in Index Cohort		0.8244		0.8127		0.8428

A.A.V. received consultancy fees and/or research grants from Amgen, AstraZeneca, Bayer, Boehringer Ingelheim, Cytokinetics, Merck, Novartis, Novonordisk, Roche diagnostics, Vifor .

G.C. is an employee of Momentum Research who received research grants from Abbott

Laboratories, Amgen, Celyad, Cirius Therapeutics, Roche Diagnostics, Sanofi, and Windtree Therapeutics Inc.

Conflicts of Interest

B.A.D. is an employee of Momentum Research who received research grants from Abbott

Laboratories, Amgen, Celyad, Cirius Therapeutics, Roche Diagnostics, Sanofi, and Windtree Therapeutics Inc. S.S. is a former employee of Momentum Research who received research grants from Abbott Laboratories, Amgen, Celyad, Cirius Therapeutics, Roche Diagnostics, Sanofi, and Windtree Therapeutics Inc. I.S. reports no conflicts. G.G.K. is the principal investigator of a biostatistical agreement between Momentum Research, Inc. and the University of North Carolina at Chapel Hill, and that agreement provided the structure for his activity for this article. He is also the principal investigator of many such biostatistical agreements with other biopharmaceutical sponsors, including AbbVie, Amgen, Arena, AstraZeneca, Eli Lilly & Co., Forest Research Institute (Allergan), GlaxoSmithKline, Merck, Novartis, Otsuka, Pfizer, and Sanofi, although his activities for those sponsors are not related to the content of this article. Information concerning all biostatistical agreements for which Gary Koch is the principal investigator is publicly available through the University of North Carolina at Chapel Hill.

A.M. received personal fees and/or research grants from Novartis, Orion, Roche, personal fees from Servier, Adrenomed, from Abbott, Sanofi. K.D. reports no conflicts. N.J.S. reports no conflicts. M.M. received consulting or speaker fees from Amgen, AstraZeneca, Bayer, Novartis, Relypsa, Servier, Stealth Therapeutics, Trevena, Abbott Vascular.

Author contributions

The study was conceived by G. All authors critically reviewed the manuscript and contributed to the interpretation of results.