DEN, A Chartier Cea

M.-C Marinica

Rearrangement of interstitial defects in alpha-Fe under extreme condition

In this study, by theoretical means, we reveal the main mechanisms that underpin the microstructure evolution driven by the formation of self-interstitial atoms (SIAs) clusters in body centered cubic iron under extreme conditions. Using Frenkel pairs accumulation simulations we point the complex interplay between the two families of interstitial defects, the dislocation loops with Burgers vectors <100> and ½<111> and the tridimensional C15 clusters. We reconcile the previous sparse understanding of microstructure evolution that put in opposition various mechanisms of defects formation by showing that both ½ <111> loops self-interactions and C15 clusters transformations produce <100> loops. Moreover, we exhibit the fact that these tri-dimensional clusters can form under irradiations with only the Frenkel pair accumulation that mimics electron irradiation and not only in high-energy cascades as it was previously stated. Finally, we show that the tridimensional C15 clusters even precede production of loops under irradiation.

I Introduction: 2D and 3D defects in irradiated bcc-iron

The performance of materials under extreme conditions is driven by the formation and the mobility of clusters of vacancies and interstitial atoms. Vacancies and self-interstitial atoms (SIAs) form either two or three-dimensional clusters depending on their sizes and mainly because of the competition between the interface and the bulk energies. In body centered cubic (bcc) metals, the clusters of vacancy behave similarly [START_REF] Matsukawa | One-dimensional fast migration of vacancy clusters in metals[END_REF], while the SIAs clusters underlay complex energetic landscape with plenteous morphologies [START_REF] Willaime | Stability and mobility of self-interstitials and small interstitials clusters in α-iron: ab-initio and empirical potential calculations[END_REF][START_REF] Nguyen-Manh | Self-interstitial defects in bcc transition metals: group specific trends[END_REF][START_REF] Terentyev | Self-Trapped Interstitial-Type Defects in Iron[END_REF][START_REF] Marinica | Energy landscape of small clusters of self-interstitial dumbbells in iron[END_REF], iron being one of the more exotic [6,[START_REF] Ma | Universality of point defect structure in body-centered cubic metals[END_REF]. In bcc transition metals, single SIA generally forms a crowdion that is a defect aligned along the <111> direction [START_REF] Domain | Ab initio calculations of defects in Fe and dilute Fe-Cu alloys[END_REF][START_REF] Derlet | Multiscale modeling of crowdion and vacancy defects in body-centered-cubic transition metals[END_REF][START_REF] Dudarev | Effect of the alpha-gamma Phase Transition on the Stability of Dislocation Loops in bcc Iron[END_REF][START_REF] Fu | Stability and mobility of mono-and di-interstitials in α-Fe[END_REF][START_REF] Amino | Detection of one-dimensional migration of single selfinterstitial atoms in tungsten using high-voltage electron microscopy[END_REF]. Few of these dumbbells can pack together into bundles, forming small dislocation loops. In iron, resistivity recovery as well as internal friction experiments and DFT computations show that the most stable configuration for single SIA is a <110> dumbbell. Packed dumbbells keep this orientation until around five SIAs and then change orientation above, into <111> direction according to DFT predictions [START_REF] Willaime | Stability and mobility of self-interstitials and small interstitials clusters in α-iron: ab-initio and empirical potential calculations[END_REF][START_REF] Fu | Multiscale modelling of defect kinetics in irradiated iron[END_REF][START_REF] Marinica | Irradiation-Induced Formation of Nanocrystallites with C15 Laves Phase Structure in bcc Iron[END_REF]. Dumbbells in iron may also transform into three-dimensional structures with symmetry corresponding to C15 Laves phase [6,[START_REF] Marinica | Irradiation-Induced Formation of Nanocrystallites with C15 Laves Phase Structure in bcc Iron[END_REF][START_REF] Dézerald | Stability of selfinterstitial clusters with C15 Laves phase structure in iron[END_REF]. These C15 structures are stable, immobile and exhibit large antiferromagnetic moments. However, for higher number of SIAs, they face competition with nanometric-sized dislocation loops. According to a recent DFT informed discrete-continuum model [6], C15 clusters may transform into ½ <111> loops for more than around 50 SIAs, or into <100> loops for more than around 90 SIAs. Indeed, transmission electron microscopy (TEM) observations in bcc transition metals reveal the existence of planar loops. They can have the Burgers vector aligned along either ½<111> (highly mobile) or <100> (immobile), depending on temperature [START_REF] Masters | Dislocation Loops in Irradiated Iron[END_REF][START_REF] Ehrhart | Physics of Radiation Effects in Crystals[END_REF][START_REF] Eyre | On the formation of interstitial loops in bcc metals[END_REF][START_REF] Arakawa | One-Dimensional Glide Motion of 'Naked' Nanoscale 1/2<111> Prismatic Dislocation Loops in Iron[END_REF][START_REF] Amino | Detection of one-dimensional migration of single selfinterstitial atoms in tungsten using high-voltage electron microscopy[END_REF]. Dislocation loops with ½<111> Burgers vector are dominant in most bcc metals, and are therefore presumed to be the most stable configurations for bundling crowdions. In iron, magnetism controls the relative stability of both morphologies. The ½<111> loops are the most stable at low temperature while above 800K it is the <100> loops [START_REF] Dudarev | Effect of the alpha-gamma Phase Transition on the Stability of Dislocation Loops in bcc Iron[END_REF]. These <100> loops are also observed in irradiated iron at low temperature. However, though numerous studies tackle their formation, as we will see below, the very details of the mechanisms at work are still subject of intense researches. Masters [START_REF] Masters | Dislocation Loops in Irradiated Iron[END_REF] investigated first experimentally the formation of <100> loops in irradiated iron in the absence of vacancy cluster. He suggested that the formation of these loops is based on the interaction between two ½<111> loops. Eyre and Bullough [START_REF] Eyre | On the formation of interstitial loops in bcc metals[END_REF] rather suggested that ½<110> loops are involved in the formation of <100> dislocation loops. Decades later, based on the seminal work of Osetsky et al [START_REF] Osetsky | Interactions between mobile dislocation loops in Cu and α-Fe[END_REF] on the ½<111> loops interaction, Marian et al [START_REF] Marian | Mechanism of Formation and Growth of <100> Interstitial Loops in Ferritic Materials[END_REF] explored the two possibilities by means of atomistic simulations. They showed that the formation of <100> segments may happen from the interaction between two ½<111> loops with appropriate sizes and specific orientations. They concluded that <100> loops can be formed from ½<111> loops. Xu et al [START_REF] Xu | Solving the Puzzle of ⟨100⟩ Interstitial Loop Formation in bcc Iron[END_REF] showed the complete transformation of two colliding ½<111> loops into <100> loop. This process is stochastic in nature according to Xu et al [START_REF] Xu | Solving the Puzzle of ⟨100⟩ Interstitial Loop Formation in bcc Iron[END_REF], and highly infrequent due to the strict conditions required. However, using TEM, Arakawa et al [START_REF] Arakawa | Direct observation of the coalescence process between nanoscale dislocation loops with different Burgers vectors[END_REF] did not put in evidence any <100> loops while examining tens of ½<111> loops reactions. Recently, Wang et al [START_REF] Wang | Formation of dislocation loop in bcc-Fe via the ternary loop reaction[END_REF] added another path for the formation of <100> loops, based on a ternary loops reaction which involves also ½<111> loops. In addition, Chen et al [START_REF] Chen | A new mechanism of loop formation and transformation in bcc iron without dislocation reaction[END_REF] pointed in their study that <100> loops may result from the re-arrangement and reorientation of a single crowdion cluster. Besides, other authors returned to the role of single events like thermal spikes or displacement cascades for the creation of <100> loops in iron. Thus, recent simulations by Khara et al [START_REF] Khara | Dislocation loop formation by swift heavy ion irradiation of metals[END_REF] showed that both ½ <111> loops and <100> loops may emerge from one single track induced by swift heavy ion. Further, Peng et al [START_REF] Peng | Shockwave generates <100> dislocation loops in bcc iron[END_REF] reminded that displacement cascades produce shockwaves around them. In iron, they promote the transformation of SIAs into <100> loops by a so-called punch out mechanism, at distance from the cascade cores. These loops also arise directly inside cascades according to Calder et al [START_REF] Calder | Effect of mass of the primary knockon atom on displacement cascade debris in α-iron[END_REF], with an increasing probability of formation with pka mass. Granberg et al [START_REF] Granberg | Cascade debris overlap mechanism of <100> dislocation loop formation in Fe and FeCr[END_REF] provided incremental insights on this point and evidenced that overlap of cascades on preexisting primary radiation damage readily produces <100> loops too. Alternatively, Zhang et al [START_REF] Zhang | Formation of prismatic loops from C15 Laves phase interstitial clusters in body-centered cubic iron[END_REF] called for the nucleation of very stable C15 clusters. This class of clusters, identified as "sessile" and "metastable" clusters in Gao et al [START_REF] Gao | Properties and evolution of sessile interstitial clusters produced by displacement cascades in α-iron[END_REF] or later as C15 clusters in Marinica et al [START_REF] Marinica | Irradiation-Induced Formation of Nanocrystallites with C15 Laves Phase Structure in bcc Iron[END_REF] -appear directly inside high-energy cascades as observed too by Zarkadoula et al [START_REF] Zarkadoula | The nature of high-energy radiation damage in iron[END_REF] or in overlapping cascades after Byggmästar et al [START_REF] Byggmästar | Effects of short-range repulsive potential on cascade damage in iron[END_REF]. Zhang et al [START_REF] Zhang | Formation of prismatic loops from C15 Laves phase interstitial clusters in body-centered cubic iron[END_REF] argued that once formed, C15 clusters grow by trapping small mobile interstitials induced by irradiation. C15 clusters subsequently transform into ½<111> loops or <100> loops at equivalent amount. While this scenario is based on empirical potential simulations, ab initio calculations performed later by Alexander et al [6] bring thorough support. One may also anticipate that <100> loops might form with a much lower probability since they require the stabilization and transformation of much bigger C15 clusters -by roughly forty SIAs -than ½<111> loops [6].

Using extensively molecular dynamics (MD) simulations in iron, we investigate the nucleation and growth of interstitials defects, such as C15 clusters and both ½<111> and <100> loops by irradiation. We apply a demarche introduced first by Limoge et al [START_REF] Limoge | Computer simulation studies of radiation induced amorphization[END_REF] in which periodic creation of Frenkel pairs is designed to mimic irradiation. Such methodology already provided valuable insights on mechanisms of irradiation induced amorphization in metallic systems, like copper-titanium intermetallics [START_REF] Sabochick | Radiation-induced amorphization of ordered intermetallic compounds CuTi, CuTi2, and Cu4Ti3: a molecular dynamics study[END_REF] or Ni-Zr solid solution [START_REF] Nagase | Electron-irradiationinduced solid-state amorphization caused by thermal relaxation of lattice defects[END_REF][START_REF] Nagase | Electron-irradiation-induced solid-state amorphization in supersaturated Ni-Zr solid solutions[END_REF], as well as in oxides [START_REF] Crocombette | Atomistic simulation of amorphization thermokinetics in lanthanum pyrozirconate[END_REF][START_REF] Chartier | Key role of the cation interstitial structure in the radiation resistance of pyrochlores[END_REF] or in graphite [START_REF] Chartier | Atomic scale mechanisms for the amorphisation of irradiated graphite[END_REF]. With this methodology, in nano-metric supercells, we scrutinize on the fly the evolution of defectsincluding C15 clusters and both ½<111> loops and <100> loops -as a function of dose up to 1.0 dpa. In addition to these integrated simulations, we rationalize our observations by applying dedicated calculations involving single C15 cluster. In this regard, we introduce SIAs only (without the counterdefect, vacancy) close to C15 clusters of different sizes, in a similar manner as performed recently by Monasterio et al [START_REF] Monasterio | Self-interstitial clusters in radiation damage accumulation: coupled molecular dynamics and metadynamics simulations[END_REF] and taking advantage of previous estimations [6]. Combination of both types of simulations allows us to provide a new route for the nucleation of <100> loops along with insights on formation and stability of C15 clusters as explained below.

II Methodology: Frenkel pairs accumulation

We perform all our molecular dynamics simulations using the LAMMPS code [START_REF] Plimpton | Fast parallel algorithms for short-range molecular dynamics[END_REF] with the M07 EAM potential for iron [START_REF] Marinica | Irradiation-Induced Formation of Nanocrystallites with C15 Laves Phase Structure in bcc Iron[END_REF][START_REF] Malerba | Comparison of empirical interatomic potentials for iron applied to radiation damage studies[END_REF]. This potential has the particularity of satisfactory reproducing relative formation energies of small loops with respect to C15 clusters, in agreement with 0 K ab initio calculations [6,[START_REF] Marinica | Irradiation-Induced Formation of Nanocrystallites with C15 Laves Phase Structure in bcc Iron[END_REF]. We design two sets of simulations: the first set explores the entire process of nucleation and growth of defect clusters and/or loops by irradiation while the second one targets the transformation of specific configurations of C15 clusters.

In the first set of simulations, irradiation is mimicked by performing Frenkel pair accumulation (FPA) in a chosen supercell, following previous studies [START_REF] Limoge | Computer simulation studies of radiation induced amorphization[END_REF][START_REF] Sabochick | Radiation-induced amorphization of ordered intermetallic compounds CuTi, CuTi2, and Cu4Ti3: a molecular dynamics study[END_REF][START_REF] Crocombette | Atomistic simulation of amorphization thermokinetics in lanthanum pyrozirconate[END_REF][START_REF] Chartier | Key role of the cation interstitial structure in the radiation resistance of pyrochlores[END_REF]. Herein, iron atoms are randomly chosen in the entire supercell and randomly displaced at a distance of more than 1.2 Å than any other atom. The time between each of these displacements is set to 2 ps. Interstitials and vacancies created lead to the increase of pressure and of temperature. Both are driven back to their target values (300K and 0 GPa) within 2 ps thanks to careful controls relying on Berendsen thermostat and barostat. In order to track finite size effects, we investigate two supercell sizes, one containing 11664000 atoms (called hereafter big supercell) of volume 51.5 × 51.5 × 51.5 nm 3 and the other one containing 1458000 atoms (called hereafter small supercell) of volume 25.7 × 25.7 × 25.7 nm 3 . 2500 and 400 Frenkel pairs were introduced in the big and small supercell, respectively, every 2 ps. This makes dose rates of 1.07 10 8 dpa/s and 1.37 10 8 dpa/s, respectively, by far higher than any experiments. Indeed, any long-range (thermal) diffusion is hindered for any defects in our FPA simulations. Hence, our simulations likely describe low temperature cases where kinetics effects can be neglected. In addition, they can describe cases where migration of defects is impeded by some external factors like trapping at impurities, for example vacancies in Fe-C or interstitials loops for Fe-Cr [START_REF] Schäublin | On the origin of primary ½ a0 <111> and a0 <110> loops in irradiated Fe(Cr) alloys[END_REF][START_REF] Schuler | Equilibrium vacancy concentration driven by undetectable impurities[END_REF]. However, local recombination of Frenkel pairs and reorganization of defects still operate within few picoseconds [START_REF] Olsson | Ab initio threshold displacement energies in iron[END_REF][START_REF] Nakashima | Recombination radius of a Frenkel pair and capture radius of a self-interstitial atom by vacancy clusters in bcc Fe[END_REF] and provide an annealing rate that counteracts the (high) dose rate of defects produced by FPA. In addition, dislocations can absorb defects in the entire supercell since capture radii are of the same order of magnitude as the size of the supercell, being 1 nm and 4 nm, respectively for vacancies and interstitials [START_REF] Shastry | The interaction between point defects and edge dislocations in BCC iron[END_REF][START_REF] Anento | Edge dislocations as sinks for sub-nanometric radiation induced defects in α-iron[END_REF].

In the second set of simulations, we explore the stability and the role of C15 clusters observed in FPA simulations. To do so, we partly follow recent works done by Monasterio et al [START_REF] Monasterio | Self-interstitial clusters in radiation damage accumulation: coupled molecular dynamics and metadynamics simulations[END_REF] for investigating the swelling induced by SIAs clusters in iron. We introduce single interstitials one after the other (up to 500 interstitials) with a time interval of 1 ps, in the vicinity of preexistent C15 clusters. We consider two sizes of C15 clusters, each of them embedded in supercells of 96.86 Å of thickness with a square base of 177.67 × 178.88 Å 2 . One C15 cluster contains 87 SIAs, and lies far above the stability limit of C15 cluster with respect to ½<111> loops [6], and close but slightly below the stability limit with <100> loops. The other C15 cluster is made of 49 SIAs, and is situated slightly below the stability limit given by the ½ <111> loops.

We perform the analysis of our simulations using Ovito [START_REF] Stukowski | Visualization and analysis of atomistic simulation data with OVITO -the Open Visualization Tool[END_REF]. Dislocations are determined using the DXA algorithm [START_REF] Stukowski | Automated identification of dislocations in crystal interfaces[END_REF] using default parameters. Densities of ½<111> and <100> dislocations are then evaluated by dividing their total length by the total volume of the supercell. In addition, knowing that C15 atoms exhibit icosahedral coordination, we use the polyhedral template matching method [START_REF] Mahler Larsen | Robust structural identification via polyhedral template matching[END_REF] to identify them. Once selected, we classify C15 clusters as a function of their size, starting from 12 C15 atoms, the smaller C15 cluster.

As explained extensively elsewhere [6,[START_REF] Dézerald | Stability of selfinterstitial clusters with C15 Laves phase structure in iron[END_REF][START_REF] Marinica | Irradiation-Induced Formation of Nanocrystallites with C15 Laves Phase Structure in bcc Iron[END_REF], C15 clusters exhibit complex geometry which calls for specific notations and clarifications that we recall hereafter. The building block of C15 cluster corresponds to a Z16 Frank-Kasper polyhedron having 12 atoms at interstitial positions together with 10 vacancies around a specified bcc atomic site. Larger C15 clusters gather a set of Z16 Frank-Kasper polyhedron having centers situated on one, among four, diamond network, which underlies the initial bcc structure. The C15 size refers to the atoms of the C15 cluster that are in interstitial positions as well as the centers of the Z16 polyhedra. The C15 Laves phase is obtained from the bcc phase by replacing 2n bcc atoms with 3n C15 atoms. This gives, in the infinite C15 cluster, a factor two between the overall interstitials contained in the cluster and the atoms in interstitials positions. However, in our analysis, beyond the atoms in the interstitial positions we count also the centers of Z16 polyhedra giving what will be reported in the following as the C15 size. The rough factor, in the infinite size limit, between the overall SIAs number of C15 cluster and the total number of counted atoms in C15 cluster is 3. In the following, C15 SIA clusters are denoted cluster, where n is the net number of SIAs, i.e., the number of additional atoms in the bcc lattice. For example, the smaller C15 cluster containing 12 C15 atoms (without the atom located in the center of the C15 cluster that shares a site from the bcc structure), has a net number of 2 SIAs (= 12 interstitials -10 vacancies) and is denoted cluster.

III Results: Nucleation and transformation of C15 clusters

We start with the analysis of the first set of simulations where we apply the FPA methodology. We report evolutions of dislocation densities and C15 sizes with dose (dpa) on Figure 1 and on Figure 2, respectively, for small and big supercells. We note that evolutions of densities of dislocations as well as number and size of C15 clusters behave identically with dose for both sizes of supercell. In addition, evolution of microstructures look very similar too, as illustrated on snapshots at different doses in Figure 3 and in Figure 4. This means that using a moderate size of supercell around one million atoms is sufficient to capture most meaningful information.

In both simulations, with big and small supercells, different stages emerge. We observe that the nucleation of C15 clusters -bigger than cluster -occurs first, and before any dislocation (Figure 1 and Figure 2). Then, their size (y axis) and their number (color scaling) increase gently with irradiation dose. At 0.01 dpa, ½<111> loops start to nucleate (see Figure 3 and Figure 4). Many of these loops are bound to an immobile C15 cluster (see Figure 3 and 4 at 0.02 dpa) conforming to observations done by Dérès et al [START_REF] Dérès | Dislocation depinning from nano-sized irradiation defects in a bcc iron model[END_REF]. At the same dose of 0.01 dpa, C15 clusters reach sizes of 40 C15 atoms or equivalently cluster. This size of cluster is much lower than the crossover between formation energies of ½<111> loops and C15 clusters. Nucleation of ½<111> loops from C15 clusters takes therefore a kinetic path rather than a thermodynamic one. Next, <100> loops come out for doses of around 0.02 dpa, with much lower density compared to ½<111> loops. Subsequently, densities of both types of dislocations increase with irradiation dose. They show maxima at different values of dose, being around 0.1 dpa for ½<111> loops with densities of 4 10 16 m -2 and between 0.2 and 0.4 dpa for <100> loops with densities of roughly 10 16 m -2 . In between, we observe that the number of C15 clusters shows its maximum at 0.03-0.04 dpa with sizes smaller than cluster. This number decreases while the density of ½<111> loops increases, likely because the former feeds the latter as we will see in the following. In parallel, sizes of some C15 clusters continue to increase with dose, even far above maxima of dislocations densities i.e. at above 0.4 dpa. Besides, loops interact to each other (at around 0.1 dpa and further) and progressively transform into forest of dislocations as can be seen on Figure 3 and on Figure 4. Some interactions belong to reactions suggested by Masters and Xu et al [START_REF] Masters | Dislocation Loops in Irradiated Iron[END_REF][START_REF] Xu | Solving the Puzzle of ⟨100⟩ Interstitial Loop Formation in bcc Iron[END_REF] and mentioned in introduction. These reactions yield to nucleation of <100> loops or to larger ½<111> loops. Densities of both ½ <111> and <100> dislocations decrease and reach steady state above 0.8 dpa, with density of dislocation of ½ <111> loops representing 90 % of the total, which is slightly more than seen by Peng et al [START_REF] Peng | Shockwave generates <100> dislocation loops in bcc iron[END_REF] of around 80%. This value is in line with some experiments (see Chen et al [START_REF] Chen | Dislocation loops in ultrahigh purity Fe(Cr) alloys after 7.2 MeV proton irradiation[END_REF] or Schäublin et al [START_REF] Schäublin | On the origin of primary ½ a0 <111> and a0 <110> loops in irradiated Fe(Cr) alloys[END_REF]) where a low amount of <100> loops is seen in irradiated iron below 300°C. Yet, comparisons remain not always relevant since the absolute ratio between 1/2<111> and <100> loops seen experiments can be biased by surfaces that readily eliminate 1/2<111> loops. Total density of dislocations stabilize at roughly 10 16 m -2 , around two orders of magnitude higher than experimental observations at room temperature [START_REF] Hernández-Mayoral | Heavy-ion irradiations of Fe and Fe-Cr model alloys Part 2: Damage evolution in thin-foils at higher doses[END_REF], but only 4 times higher than values obtained at 93K [START_REF] Schäublin | On the origin of primary ½ a0 <111> and a0 <110> loops in irradiated Fe(Cr) alloys[END_REF]. Combination of very high dose rates and temperature employed in our FPA simulations are certainly responsible for such overestimation, and it remains uneasy to rescale with temperature or dose rate [START_REF] Schäublin | On the origin of primary ½ a0 <111> and a0 <110> loops in irradiated Fe(Cr) alloys[END_REF][START_REF] Dunn | Displacement rate and temperature equivalence in stochastic cluster dynamics simulations of irradiated α-Fe[END_REF]. In addition, some C15 clusters of more than 153 C15 atoms survive, which corresponds to according to large-scale rules [6]. Few of them even reach sizes of more than 255 C15 atoms (or equivalently cluster size). At steady state, one observes a balance between creation of dislocations from C15 clusters and their formation.

We now turn to the second set of simulations in which are investigated the responses of and clusters to injection of interstitials in their vicinity. As we describe below, responses are strikingly different in term of C15 evolution as well as concerning the nature of dislocations that nucleate. We consider first the behavior of the smaller C15 cluster, i.e. the cluster (147 C15 atoms), reported on Figure 5. Under the injection of interstitials, the cluster increases first its size by trapping small mobile interstitials induced by irradiation, as already put in light by Zhang et al [START_REF] Zhang | Formation of prismatic loops from C15 Laves phase interstitial clusters in body-centered cubic iron[END_REF]. The growth continues up to roughly cluster (159 C15 atoms) at which a ½<111> loop nucleates (snapshots on Figure 6). While ½<111> loop develops, the C15 size drastically decreases, feeding its growth with the contribution of injected interstitials. Injection of interstitials stops at 500 ps (500 interstitials injected one after the other every 1 ps). Subsequently, the entire system smoothly evolves toward a steady state. Density of dislocation stabilizes at around 750 ps, namely 250 ps after the end of interstitials injection. In parallel, primary cluster stabilizes at roughly (69 C15 atoms) leaving also around some C15 clusters smaller than (21 C15 atoms). This is expected since, for the M07 potential, is situated at the limit of the cross point of C15 cluster stability (between and with 20-90 C15 atoms) with respect to ½<111> loops [6]. The picture is quite different concerning the evolution of cluster (261 C15 atoms), as can be seen on Figure 7. The cluster decreases in size and a <100> loop nucleates (snapshots on Figure 8) at around (159 C15 atoms). The <100> loop develops and reaches a steady state at around 100 ps after the interruption of the injection of interstitials. In between and 150 ps after the nucleation of <100>, a ½<111> loop nucleates too. In turn, this ½<111> loop develops by steps and then reaches a steady state lately, around 500 ps after the end of injection. Its density gets similar to the <100> loop. Meanwhile, primary cluster stabilizes -at a lower size than previously -at around (39 C15 atoms) and comparable residues are left around in the form of clusters smaller than (21 C15 atoms). Interestingly, both small and big C15 clusters contribute to the creation of loops at different degrees. While ½<111> loops come up from both cluster sizes, only the bigger one can help the nucleation of <100> loops. Therefore, their formation probability is obviously low since not all clusters can attain the required size. Nevertheless, FPA simulations show that some of them can reach large sizes dynamically, without their transformation into any loops.

IV Discussion: <100> loops nucleate from C15 clusters and ½ <111> loops

Our simulations suggest that the response of iron to irradiations can be decomposed into different stages. We have identified the following ones: (i) production of point defects by irradiation; (ii) their transformation into C15 clusters; then (iii) nucleation of ½ <111> loops (from C15 clusters) and; subsequently (iv) of <100> loops (from C15 clusters and ½<111> loops); finally (v) stabilization of a steady state in which all types of defects are present. Besides this sequence itself, some new features and mechanisms arise and may allow updating current knowledge on defects induced by irradiations in iron.

One of interesting results is the fact that nucleation of C15 clusters directly occurs from the accumulation of single SIAs. This result brings further support to previous observations that C15 clusters may (i) form in high-energy cascades as seen by Gao et al [START_REF] Gao | Properties and evolution of sessile interstitial clusters produced by displacement cascades in α-iron[END_REF], Marinica et al [START_REF] Marinica | Irradiation-Induced Formation of Nanocrystallites with C15 Laves Phase Structure in bcc Iron[END_REF] and Zarkadoula et al. [START_REF] Zarkadoula | The nature of high-energy radiation damage in iron[END_REF] or (ii) appear as the result of overlap of cascades as shown by Byggmästar et al. [START_REF] Byggmästar | Effects of short-range repulsive potential on cascade damage in iron[END_REF]. While not surprising according to the general picture based on formation energies [START_REF] Marinica | Irradiation-Induced Formation of Nanocrystallites with C15 Laves Phase Structure in bcc Iron[END_REF]6], the assertion that C15 clusters dynamically nucleates from primary defects in irradiated iron is therefore significantly strengthened. Additionally, since our simulations reproduce electron irradiation at low temperature, as claimed by other authors [START_REF] Sabochick | Radiation-induced amorphization of ordered intermetallic compounds CuTi, CuTi2, and Cu4Ti3: a molecular dynamics study[END_REF][START_REF] Nagase | Electron-irradiationinduced solid-state amorphization caused by thermal relaxation of lattice defects[END_REF][START_REF] Nagase | Electron-irradiation-induced solid-state amorphization in supersaturated Ni-Zr solid solutions[END_REF], we provide an additional regime -SIAs transformation into C15 clusters under electron irradiation -to the ballistic one found by Byggmästar et al [START_REF] Byggmästar | Effects of short-range repulsive potential on cascade damage in iron[END_REF]. Another interesting result of our simulations is the fact that C15 clusters precede the formation ofany -loops, being ½ <111> or <100> ones. This is different from the results proposed by Byggmästar et al [START_REF] Byggmästar | Effects of short-range repulsive potential on cascade damage in iron[END_REF] who showed that ½ <111> loops form directly inside cascades, and before any C15 clusters. Nevertheless, present work feeds the work hypothesis done by Zhang et al [START_REF] Zhang | Formation of prismatic loops from C15 Laves phase interstitial clusters in body-centered cubic iron[END_REF] that C15 clusters exist prior to loops. In addition, and besides the growth of C15 clusters itself which operates by capturing mobile interstitials as described by Zhang et al [START_REF] Zhang | Formation of prismatic loops from C15 Laves phase interstitial clusters in body-centered cubic iron[END_REF], their subsequent transformation -or not -into both ½ <111> and <100> loops is very informative. One observes that C15 clusters may readily transform into ½<111> loops when their size is above their stability limit. Wang et al [START_REF] Wang | Effects of temperature and point defects on the stability of C15 Laves phase in iron: a molecular dynamics investigation[END_REF] observed recently such a transformation with particular temperature / point defects conditions. These C15 clusters may also continue to grow and reach sizes that lead them to relax into <100> loops. Possibly, they may even further enhance their size, still fed by mobile interstitials produced by irradiation. Yet, C15 clusters appear as one of the seeds for the nucleation of loops and especially the <100> loops in iron under irradiation. This is further supported by the fact that most dislocations begin and end into C15 clusters. Indeed, the role of C15 clusters does not preclude any other well-known mechanism for the creation of <100> loops. Rather, we do see in our FPA simulations that complex self-interactions between ½<111> loops result in their formation as suggested by Masters [START_REF] Masters | Dislocation Loops in Irradiated Iron[END_REF] decades ago. While it is uneasy to decide if these interactions involve three ½<111> loops as pointed by Wang et al [START_REF] Wang | Formation of dislocation loop in bcc-Fe via the ternary loop reaction[END_REF] recently, the formation of <100> loops likely requires two as explained by Marian et al [START_REF] Marian | Mechanism of Formation and Growth of <100> Interstitial Loops in Ferritic Materials[END_REF] and by Xu et al [START_REF] Xu | Solving the Puzzle of ⟨100⟩ Interstitial Loop Formation in bcc Iron[END_REF].

Apart from these new features and mechanisms themselves, our results provide extra situations that promote nucleation of C15 clusters and of <100> loops from them. Recalling, our FPA simulations operate at high dose rates. It reasonably corresponds to electron irradiation at low temperature [START_REF] Sabochick | Radiation-induced amorphization of ordered intermetallic compounds CuTi, CuTi2, and Cu4Ti3: a molecular dynamics study[END_REF][START_REF] Nagase | Electron-irradiationinduced solid-state amorphization caused by thermal relaxation of lattice defects[END_REF][START_REF] Nagase | Electron-irradiation-induced solid-state amorphization in supersaturated Ni-Zr solid solutions[END_REF]. No long-range diffusion is therefore allowed, but this does not impede short-range movements. Indeed, Frenkel pairs recombination [START_REF] Olsson | Ab initio threshold displacement energies in iron[END_REF][START_REF] Nakashima | Recombination radius of a Frenkel pair and capture radius of a self-interstitial atom by vacancy clusters in bcc Fe[END_REF] as well as absorption of defects by dislocations [START_REF] Shastry | The interaction between point defects and edge dislocations in BCC iron[END_REF][START_REF] Anento | Edge dislocations as sinks for sub-nanometric radiation induced defects in α-iron[END_REF] act. Both ensure the entire transformations observed and therefore, short-range interactions alone explain the nucleation of C15 clusters and their transformation into loops and in particular <100> loops in irradiated iron.

V Conclusion

In the present work, we intensively use molecular dynamics simulations to investigate the response of iron to irradiation. For this purpose, we used the Frenkel pairs accumulation framework whose main characteristic is an accelerated introduction of damages. With these simulations, we expect to mimic reliably electron irradiation of iron at low temperature, knowing that thermal -i.e. long-range -diffusion is overlooked. In such conditions, we find a complex interplay between the two main families of interstitial defects in bcc iron, the 2D defects -namely ½<111> and <100> loops -and the 3D ones -, i.e. C15 clusters. The present investigation reveals that: (i) C15 clusters appear in the very early stage of the microstructure evolution of irradiated iron, and prior toany -loops and (ii) both ½<111> and <100> loops can directly nucleate from C15 clusters. Interestingly, some other well-known mechanismslike the interactions between ½<111> loops -still operate for the transformation of ½<111> loops into <100>. Hence, the present study does not exclude any previous proposed mechanisms. In addition, having proved that both C15 clusters and ½ <111> loops may yield <100> loops, we also establish that each mechanism envisioned previously as contradictory may rather collaborate. Further, C15 clusters may feed loops when thermal diffusion is hindered, while loops self-interactions may take over otherwise. This might explain the formation of <100> loops in dense systems as Fe-Cr [START_REF] Schäublin | On the origin of primary ½ a0 <111> and a0 <110> loops in irradiated Fe(Cr) alloys[END_REF], in which the diffusion of loops being blocked by the Cr, the formation of loops might happen via C15 clusters. In order to propose a hierarchy among these mechanisms more involved studies giving accurate statistics are needed.

Obviously, the effect of temperature and long-range diffusion are yet to be explored. In particular, one may wonder if high enough temperatures would modify the paths for the creation of C15 clusters and <100> loops as we describe above. Such a question could be addressed now, by implementing different mechanisms found herein in higher-level multi-scale simulations, like kinetic Monte-Carlo, cluster dynamics or mean-field approximation.

Figure 1 (

 1 Figure 1 (color online): Upper panel shows the evolution of dislocation ½<111> and <100> loops density (at 300K), represented respectively by red and green lines and calculated by dividing their total length by the total volume of the supercell of 1458000 atoms. Lower panel shows C15 size as a function of dose in simulation supercell. In the lower panel is plotted the number of C15 clusters (color scaling) for each given C15 size.

Figure 2 (

 2 Figure 2 (color online): Evolution of dislocation ½<111> and <100> loops density, in the upper panel and C15 size in the lower panel as a function of dose in a simulation supercell containing 11664000 atoms (eight times bigger than the one of Figure 1) at 300K. Colors and legends are the same as in Figure 1 except the color scaling of the lower panel that has been rescaled by eight for comparison.

Figure 3 .

 3 Figure 3. (color online) Selected snapshots of the evolution of dislocations and C15 clusters in iron as a function of doses for the small supercell (containing 1458000 atoms). Red and green lines represent respectively ½<111> and <100> loops. Yellow balls and sticks are for C15 atoms.

Figure 4 :

 4 Figure 4: (color online) Selected snapshots of the evolution of dislocations and C15 clusters in iron as a function of doses for the big supercell (containing 11664000 atoms). Legends are the same as in Figure 3.

Figure 5 :

 5 Figure 5: (color online) Evolution of dislocation density and C15 size as a function of time starting from a 49 SIA C15 cluster. 500 interstitials are injected, one after the other every 1 ps.

10

 10

Figure 6 :

 6 Figure 6: (color online) Nucleation of ½<111> dislocation from a 49 SIA C15 cluster. Legends are the same as in Figure 3.

Figure 7 :

 7 Figure 7: (color online) Evolution of dislocation density and C15 size as a function of time starting from an 87 SIA C15 cluster. 500 interstitials are injected, one after the other every 1 ps.

Figure 8 :

 8 Figure 8: (color online) Nucleation of <100> loop from an 87 SIA C15 cluster. Legends are the same as in Figure 3.

Acknowledgments

This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euroatom research and training program 2014-2018 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. The research leading to these results is partly funded by the European Atomic Energy Community's (Euratom) Seventh Framework Programme FP7/2007-2013 under grant agreement No. 604862 (MatISSE project) ) and in the framework of the EERA (European Energy Research Alliance) Joint Programme on Nuclear Materials. The author(s) MCM acknowledge the support of the French Agence Nationale de la Recherche (ANR) under project project EPigRAPH ANR-14-CE07-0001. MCM acknowledges support from the GENCI (CINES/CCRT/IDRIS) computer center under Grant A0050906973. MCM acknowledges François Willaime for encouraging C15 clusters studies. AC acknowledges Jean-Paul Crocombette for the fruitful discussions at the origin of the present work.


MD, MSc Sébastien Baillieul
email: sbaillieul@chu-grenoble.fr

PhD Charlotte Elsworth-Edelsten
email: dr.elsworthedelsten@gmail.com

PhD Arnaud Saj
email: arnaud.saj@hcuge.ch

MD, PhD Gilles Allali
email: gilles.allali@hcuge.ch

Sebastien Baillieul

C Elsworth

Neural substrates of reduced walking activity after supratentorial stroke: a voxel-based lesion symptom mapping study

Keywords: Stroke, Secondary prevention, Walking, Magnetic resonance imaging, Physical activity, Rehabilitation

Background: Most stroke patients exhibit low levels of walking activity, a key component of secondary stroke prevention. The predictors of walking activity may be multifactorial and are thus far partially understood. We aimed to study the neuroanatomic correlates of low levels of daily walking activity following hemispheric stroke.

Methods:

In this cross-sectional study, 33 community-dwelling stroke survivors (age: 63.9±12.9 years; % female: 36.4%; NIHSS at admission: 3.3±4.0) were prospectively recruited at least 3 months after a first ever, unilateral, supratentorial stroke confirmed by brain magnetic resonance imaging. Walking activity was measured by daily step counts (steps•day -1 ), recorded using an Actigraph GT3x+ triaxial accelerometer over 7 consecutive days. Voxel-based lesion-symptom mapping was performed to identify brain areas associated with walking activity following stroke.

Results: Participants presented 4491.9±2473.7 steps•day -1 . Lower levels of walking activity were related to lesions of the posterior part of the putamen, of the posterior limb of the internal capsule and of the anterior part of the corona radiata. No cortical region was associated with walking activity.

Conclusions:

Our preliminary results identify subcortical neuroanatomical correlates for reduced walking activity following stroke. If confirmed, these results could serve as a rationale for the development of targeted rehabilitative strategy to improve mobility after stroke.

INTRODUCTION

Physical activity is a key component of secondary stroke prevention [START_REF] Billinger | Physical activity and exercise recommendations for stroke survivors: A statement for healthcare professionals from the american heart association/american stroke association[END_REF]. Functional limitations experienced by post stroke patients often result in reduced physical activity, far below the recommended 10,000 daily steps required for health benefits [START_REF] Mahendran | Recovery of ambulation activity across the first six months post-stroke[END_REF][START_REF] Tudor-Locke | How many steps/day are enough? For adults[END_REF] and can lead to sedentariness (English, Manns, Tucak, & Bernhardt, 2014). If the degree of physical impairment may be an important factor driving sitting and physical activity time in people post stroke, the determinants and predictors of low levels of walking activity (WA) may be multifactorial and are not well studied (English et al., 2016). Thus, depression, fatigue and altered quality of life are negatively correlated with post-stroke physical activity [START_REF] Thilarajah | Factors associated with post-stroke physical activity: A systematic review and meta-analysis[END_REF].

Walking requires the complex interaction of several brain structures and functions that goes far beyond voluntary motor control [START_REF] Takakusaki | Functional neuroanatomy for posture and gait control[END_REF]. Studying the relationship between neuroimaging and mobility impairments can lead to a better understanding of the underlying pathophysiology of those impairments and can serve as biomarkers of recovery [START_REF] Stinear | An update on predicting motor recovery after stroke[END_REF]. Thus, initial damage to the corticospinal tract (CST) can predict decreased gait speed, even after a chronic delay following stroke [START_REF] Cheng | Does stroke location predict walk speed response to gait rehabilitation[END_REF][START_REF] Reynolds | Neuronal injury in the motor cortex after chronic stroke and lower limb motor impairment: A voxel-based lesion symptom mapping study[END_REF]. Lesions involving the posterolateral putamen are associated with temporal gait asymmetry after a chronic delay following stroke [START_REF] Alexander | Association between gait asymmetry and brain lesion location in stroke patients[END_REF].

When combined with lesions of neighbouring structures, lesions to the putamen are associated with poor recovery of gait post-stroke [START_REF] Cheng | Does stroke location predict walk speed response to gait rehabilitation[END_REF][START_REF] Lee | Brain lesions affecting gait recovery in stroke patients[END_REF]. The association between lesion location and reduced walking activity (WA) following stroke has never been studied. We hypothesized that a cluster of different lesion locations related to motor and non-motor determinants of gait control will be associated with lower WA levels.

This study aims to identify the neuroanatomic correlates of low levels of WA following stroke, based on a voxel-based lesion-symptom mapping (VLSM) approach.

MATERIAL AND METHODS

Participants

Thirty-three community-dwelling stroke survivors (age: 63.9±12.9 years; % female: 36.4%; NIHSS at admission: 3.3±4.0) were recruited in this cross-sectional study, at least 3 months after stroke onset (mean±1SD=182.4±74.9 days) from the Department of Neurology of the Geneva University Hospital between November 2012 and January 2016. Clinical characteristics are presented in Table 1. Inclusion criteria were: i) first ischemic, unilateral, supratentorial stroke (to overcome specific balance and gait impairments linked with brainstem or cerebellar lesions), ii) brain magnetic resonance imaging (MRI) confirming stroke diagnosis, iii) a Rivermead Mobility Index [START_REF] Antonucci | Rasch analysis of the rivermead mobility index: A study using mobility measures of first-stroke inpatients[END_REF] score of level 7 or above, ensuring participants with sufficient mobility skills, and iv) and absence of other neurological condition. Participants with contraindications to exercise participation, unable to walk, with language impairments including aphasia or who had an acute medical condition interfering with gait (except stroke) were not included in the study.

The protocol was approved by the Ethic Committee of the Geneva University Hospitals and each participant provided a signed informed consent.

Insert Table 1 about here

Clinical data and measurements

Participants underwent a complete medical examination at least 3 months after stroke onset, performed by a certified neurologist, including the evaluation of their cognitive status using the Montreal Cognitive Assessment (MoCA). Clinical acute stroke characteristics, including score on the National Institute of Health Stroke Scale (NIHSS) at admission were retrieved in patients' medical records. The Modified Charlson Comorbidity Index was used to quantify comorbidity (Goldstein, Samsa, Matchar, & Horner, 2004).

Functional independence and mobility for activities of daily living were assessed using the Barthel Index (Duffy, Gajree, Langhorne, Stott, & Quinn, 2013). Rivermead Mobility Index [START_REF] Antonucci | Rasch analysis of the rivermead mobility index: A study using mobility measures of first-stroke inpatients[END_REF], a sub-scale of the Rivermead Motor Assessment was used to evaluate mobility skills (i.e. gait, balance and transfers). For both scales, higher scores reveal higher functional status and mobility skills. As a major determinant of post stroke walking ability (Fulk, He, Boyne, & Dunning, 2017), gait speed was determined in the Willy Taillard Kinesiology Laboratory of the Geneva University Hospital using a GAITRite walkway system® (GAITRite Gold, CIR Systems, PA, USA) [START_REF] Bilney | Concurrent related validity of the gaitrite walkway system for quantification of the spatial and temporal parameters of gait[END_REF]. Participants were asked to walk at their comfortable gait speed. Each participant performed one evaluation trial at steady-state walking speed on a 10-meter walkway.

The main outcome for WA was the daily step counts (DSC) (Fulk et al., 2017) measured with an Actigraph GT3x+ triaxial accelerometer (ActiGraph, LLC, Pensacola, FL, USA). This device accurately discriminates movement over a broad range of gait speeds, including low gait speeds [START_REF] Bassett | Use of pedometers and accelerometers in clinical populations: Validity and reliability issues[END_REF] and is recognized as a valid step-count monitor for free-living condition (J. A. [START_REF] Lee | Concurrent validation of the actigraph gt3x+, polar active accelerometer, omron hj-720 and yamax digiwalker sw-701 pedometer step counts in lab-based and free-living settings[END_REF]. The accelerometer was worn over the fifth lumbar vertebra 24 hours a day during 7 consecutive days and removed only for water-based activities. Accelerometers were initialized and data downloaded using software provided by the manufacturer (v5.2.0, ActiLife, ActiGraph). Data were included if the participant had accumulated at least 10 hours of valid activity recordings per day for a minimum of 4 days (mean±SD duration of recording: 7±0 days).

MRI processing and lesion analysis

MRI scans were performed according to standard stroke protocols at the Radiology Department of Geneva University Hospitals on average within 3 days following stroke onset (2.9±2.7 days). MRI protocol included T1, T2 and fluid attenuated inversion recovery (FLAIR) images, obtained with standard parameters on a 1.5 T apparatus (Intera, Philips Medical Systems). MRI images were first processed using SPM12 (Wellcome Trust Centre for Neuroimaging, London, United Kingdom) for Matlab (Mathworks, Natick, MA). T1 native images were spatially normalized into Montreal Neurological Institute (MNI) space. The T2weighted images were then co-registered to the spatially normalized T1 images.

Lesion delineation was performed by the same trained clinician (SB) blinded for all clinical data, onto axial slices of the processed T2-weighted images using the MRIcron software package (http://www.mccauslandcenter.sc.edu/mricro/mricron/). Age-related white matter changes were rated by the same trained clinician on T2-weighted native images following the methodology proposed by Wahlund et al. [START_REF] Wahlund | A new rating scale for age-related white matter changes applicable to mri and ct[END_REF]. All right-sided lesion maps (n=14) were flipped onto the left hemisphere as reported before (Cheng et al., 2014).

VLSM is a voxel-by-voxel statistical method dedicated to the analysis of brain lesionbehavior relationship [START_REF] Bates | Voxel-based lesion-symptom mapping[END_REF]. VLSM analyses were performed using the uncorrected, with a cluster threshold of p<.05).

Results were displayed using MRIcron in radiological convention, with Montreal Neurological Institute coordinates provided in mm. To accurately describe the anatomical affected structures, the Automated Anatomic Labeling and the John Hopkins University white matter labels-1mm atlases were overlaid with the significant VLSM clusters.

Statistical analysis

All variables are reported as mean±1 standard deviation (SD) or number of observations and percentages when appropriate. All statistical analyses were performed using SPSS 23 (IBM SPSS Statistics, Version 23.0. Armonk, NY).

RESULTS

Clinical and walking activity assessment

We included patients without significant cognitive impairment, as reflected by scores from the MoCA. Scores from the Barthel Index revealed high functional independence and mobility for activities of daily living. Consistently, scores from the Rivermead Mobility Index revealed high functional mobility skills (Forlander & Bohannon, 1999) (Table 2). According to gait speed values, one participant (3%) was considered as home ambulator (gait speed<0.4 m⋅s -1 ), seven (21%) as limited community ambulators (0.4≤gait speed≤0.8 m⋅s -1 ) and 25 (76%) as full community ambulators (gait speed>0.8 m⋅s -1 ) (Fulk et al., 2017).

All participants had valid accelerometer recordings with a mean±1SD DSC of 4491.9±2473.7 steps•day -1 (Table 2).

Insert Table 2

DISCUSSION

We found that daily WA, a major health outcome in terms of secondary prevention following stroke, measured three months after stroke onset was negatively associated with a cluster of subcortical lesions in a group of patients with high functional independence and mobility skills. The reported DSC of 4491.9±2473.7 steps•day -1 is consistent with previous stroke studies (English et al., 2014;[START_REF] Mahendran | Recovery of ambulation activity across the first six months post-stroke[END_REF].

Consistent with our hypothesis, a cluster of lesions found in the posterior part of the putamen, the posterior limb of the internal capsule and the anterior part of the corona radiata were associated with lower daily WA after controlling for age, body mass index and agerelated white matter changes. The strongest association was observed in the posterior part of the putamen, a key structure involved in sub-cortico-cortical motor loops, and in particular in fronto-striatal connections, that span motor, cognitive and limbic cortical areas [START_REF] Leh | Fronto-striatal connections in the human brain: A probabilistic diffusion tractography study[END_REF]. From a motor point of view, stroke lesions involving the putamen are associated with gait impairments, such as gait asymmetry [START_REF] Alexander | Association between gait asymmetry and brain lesion location in stroke patients[END_REF] and negatively affect gait recovery post-stroke (Jones et al., 2016; K. B. [START_REF] Lee | Brain lesions affecting gait recovery in stroke patients[END_REF].Stroke lesions involving the putamen can also be associated with parkinsonism [START_REF] Mehanna | Movement disorders in cerebrovascular disease[END_REF][START_REF] Suri | Post-stroke movement disorders: The clinical, neuroanatomic, and demographic portrait of 284 published cases[END_REF]. We did not include patients with other neurological conditions but stroke. However, we did not quantify the presence of parkinsonism or mild parkinsonian signs that may have contribute to the observed WA limitation.

Other relevant structures were the internal capsule and the corona radiata, both part of the CST, previously described as being associated with lower gait speed [START_REF] Reynolds | Neuronal injury in the motor cortex after chronic stroke and lower limb motor impairment: A voxel-based lesion symptom mapping study[END_REF] and poor gait recovery (Cheng et al., 2014;[START_REF] Cheng | Does stroke location predict walk speed response to gait rehabilitation[END_REF] after stroke. In the study by Jones et al., higher lesion loads of the CST assessed by volumetric measurement were significantly associated with lower scores of gait and everyday functions of general mobility [START_REF] Cheng | Does stroke location predict walk speed response to gait rehabilitation[END_REF]. Beyond anatomical lesion, the relevance of CST functional integrity on predicting functional outcomes post-stroke such as walking remains unclear [START_REF] Stinear | Prediction of motor recovery after stroke: Advances in biomarkers[END_REF].

Recent results suggest that the absence of hemiparetic lower limb motor evoked potential from the ipsilesional hemisphere induced by transcranial magnetic stimulation did not affect walking speed in chronic stroke survivors [START_REF] Sivaramakrishnan | Absence of a transcranial magnetic stimulation-induced lower limb corticomotor response does not affect walking speed in chronic stroke survivors[END_REF]. Authors further suggest that walking recovery may rely on the recruitment of redundant motor pathways, such as reticulospinal tract or could arise from the development of rehabilitationinduced motor compensations [START_REF] Sivaramakrishnan | Absence of a transcranial magnetic stimulation-induced lower limb corticomotor response does not affect walking speed in chronic stroke survivors[END_REF]. The anatomical-functional discrepancies regarding the role of CST in predicting walking recovery post-stroke reinforce the statement that walking recovery post-stroke is a complex process at least partially understood.

We found no association between cortical lesion and WA levels. This result is supported by two interventional studies highlighting the strong subcortical contribution to rehabilitation-induced recovery of lower limb and walking function after stroke (Enzinger et al., 2009;[START_REF] Luft | Treadmill exercise activates subcortical neural networks and improves walking after stroke: A randomized controlled trial[END_REF]. However, other authors observed cortical activation changes (bilateral primary sensorimotor cortex, bilateral supplementary motor area) in rehabilitationassociated walking improvements (Enzinger et al., 2009). These discrepancies could be explained by the design of the studies (observational vs. interventional) and by the outcome chosen to evaluate walking performance. Thus, Enzinger et al. (Enzinger et al., 2009) evaluated their patients with a walking endurance test (2-minute timed walking test) after 4 weeks of treadmill training while we assessed spontaneous WA in free-living condition over seven days in a cross-sectional manner. The small sample size may prevent us to report cortical lesions associated with WA. Our results, together with those of the two aforementioned studies underpinned the involvement of widespread sub-cortico-cortical motor loops in functional walking recovery post-stroke. Thus, WA may be the result of a 'cross-talk' between several motor and non-motor brain functions including gait and postural control, cognitive functions as well as volitional behaviour. We thus hypothesize that the outlined lesions, found as being negatively associated with WA represent key nodes of a wider WA-related connectome. The main limitation of this preliminary work was the inclusion of minor strokes, preventing the generalization of our findings for all stroke patients. Moreover, as MRI scans were performed at least three months before evaluation, we could have overestimated the stroke size due to initial edema. Finally, we included patients with high functional and mobility skills, as reflected by Barthel Index and Rivermead Mobility Index scores. Unfortunately, while focusing on motor skills and mobility impairments, our work did not include comprehensive cognitive and behavioural evaluations.

Future work should investigate the contribution of cognition and behaviour to WA levels, while controlling for mobility skills.

CONCLUSIONS

Our results highlight that daily WA measured three months after stroke onset was negatively associated with a cluster of subcortical lesions. If confirmed, these results could serve as a rationale for the development of targeted rehabilitative strategies to improve mobility after stroke, especially when affecting the CST and the posterior part of the putamen.

Future studies should confirm these findings in a larger population while performing the MRI

  //www.mccauslandcenter.sc.edu/mricro/mricron/) included in the MRICron toolset. In each voxel, a T-test was conducted to compare the behavioral score of patients with or without a lesion in that voxel. Analyses were only conducted on voxels damaged in ≥5 subjects. All 3D lesion maps were fed into NPM along with the corresponding participant performance in terms of DSC. Age, body mass index, and age-related white matter changes, three variables linked with impaired walking skills, were used as covariates. The resulting statistical maps were thresholded voxelwise at conventional statistical values (p<.01

  artery territory as shown in Figure1. VLSM analyses showed that 3 subcortical brain regions, the posterior part of the putamen, the posterior limb of the internal capsule and the anterior part of the corona radiata were associated with low DSC (Figure2, MNI coordinates of peak value, -29, -10, 6, corresponding to the posterior part of the putamen). No cortical region was associated with WA levels.Insert Figure1about here Insert Figure 2 about here

Figure 1 :

 1 Figure 1: Lesion overlap map from the 33 participants. All right-sided lesions (n=14) are

Figure 2 :

 2 Figure 2: Voxel-based lesion symptom mapping study: cerebral correlates of the daily

  Stroke characteristics and quantification of age-related white matter changes are presented in Table1. The highest frequency of lesions was observed in the middle cerebral

	about here
	3.2. Imaging assessment -VLSM analysis

Table 1 :

 1 at the same time of the physical activity measurement. Clinical characteristics of the population (n=33)

	& Thomalla, G. (2014). Influence of stroke infarct location on functional outcome
	measured	by	the	modified	rankin	scale.	Stroke,	45(6),	1695-1702.
	doi:10.1161/STROKEAHA.114.005152
	Duffy, L., Gajree, S., Langhorne, P., Stott, D. J., & Quinn, T. J. (2013). Reliability (inter-rater
	agreement) of the barthel index for assessment of stroke survivors: Systematic review and
	meta-analysis. Stroke, 44(2), 462-468. doi:10.1161/STROKEAHA.112.678615
	English, C., Healy, G. N., Coates, A., Lewis, L. K., Olds, T., & Bernhardt, J. (2016). Sitting
	time and physical activity after stroke: Physical ability is only part of the story. Top Stroke
	Rehabil, 23(1), 36-42. doi:10.1179/1945511915Y.0000000009
	English, C., Manns, P. J., Tucak, C., & Bernhardt, J. (2014). Physical activity and sedentary
	behaviors in people with stroke living in the community: A systematic review. Phys Ther,
	94(2), 185-196. doi:10.2522/ptj.20130175
	Enzinger, C., Dawes, H., Johansen-Berg, H., Wade, D., Bogdanovic, M., Collett, J., Guy, C.,
	Kischka, U., Ropele, S., Fazekas, F., & Matthews, P. M. (2009). Brain activity changes
	associated with treadmill training after stroke. Stroke, 40(7), 2460-2467.
	doi:10.1161/STROKEAHA.109.550053
	Forlander, D. A., & Bohannon, R. W. (1999). Rivermead mobility index: A brief review of
	research to date. Clin Rehabil, 13(2), 97-100. doi:10.1191/026921599675502264
	Fulk, G. D., He, Y., Boyne, P., & Dunning, K. (2017). Predicting home and community
	walking		activity	poststroke.	Stroke,	48(2),	406-411.
	doi:10.1161/STROKEAHA.116.015309
	Goldstein, L. B., Samsa, G. P., Matchar, D. B., & Horner, R. D. (2004). Charlson index
	comorbidity adjustment for ischemic stroke outcome studies. Stroke, 35(8), 1941-1945.
	doi:10.1161/01.STR.0000135225.80898.1c

Table 2 :

 2 Functional and mobility performances of the patients, assessed at least 3 months after stroke onset

Table 1 :

 1 Clinical characteristics of the population (n=33)

	Clinical characteristics
	Females, n (%)

Data are reported as mean (1 standard deviation (SD)) or number of observations and percentages when appropriate. ARWMC: Age-Related White Matter Changes; BMI: Body Mass Index; L: Left; MOCA: MOntreal Cognitive Assessment; MRI: Magnetic Resonance Imagery; NIHSS: National Institute of Health Stroke Scale; R: Right; SD: Standard Deviation.

Table 2 :

 2 Functional and mobility performances of the patients, assessed at least 3 months after stroke onset

	Performances on functional scales
	Barthel Index, mean (SD)
		94.9 (10.2)
	(Range 0-100)
	Rivermead Mobility Index, mean (SD)
		14.6 (1.3)
	(Range 0-15)
	Gait speed
	Comfortable gait speed, mean (SD)
	(m⋅s -1 )	0.98 (0.26)
	Daily walking activity
	Valid accelerometers recordings, n (%)	33 (100%)
	Daily steps count, mean (SD)
		4491.9 (2473.7)
	(steps/day)
	Data are reported as mean±1 standard deviation (SD) or number of observations and
	percentages when appropriate.

ACKNOWLEDGEMENTS

Swiss National Science Foundation, Marie Heim Vogtlin grant (PMPDP3_151339) and Geneva University Hospitals (PRD 10-II-7).

DECLARATION OF CONFLICTING INTERESTS

Sébastien Baillieul was supported by a grant of the SOFMER (Société Française de Médecine Physique et de Réadaptation).

Gilles Allali was supported by the Baasch-Medicus Foundation.

Charlotte Edelsten and Arnaud Saj reports no disclosure.


PharmD Sophie Liabeuf

PhD Keith Mccullough

MD Eric W Young

PhD Ronald Pisoni

PhD Jarcy Zee

MD Helmut Reichel

MD Roberto Pecoits-Filho

MD Friedrich K Port

MD, PhD Bénédicte Stengel

PhD Philipp A Csomor

PhD Marie Metzger

MD Bruce Robinson

MD, PhD Ziad A Massy
email: ziad.massy@aphp.fr

Ziad Pr

Massy

International variation in the management of mineral bone disorder in patients with chronic kidney disease: Results from CKDopps

Keywords: mineral bone disease, chronic kidney disease, phosphate

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

INTRODUCTION

Chronic kidney disease (CKD) is commonly associated with disorders of mineral and bone metabolism, including abnormalities of serum calcium (Ca), phosphorus (P), parathyroid hormone (iPTH), and serum 25-hydroxyvitamin D (25-D). These abnormalities have been extensively investigated in patients with end-stage kidney disease where the disturbances and consequences of altered mineral metabolism are most apparent. [START_REF] Tentori | Recent changes in therapeutic approaches and association with outcomes among patients with secondary hyperparathyroidism on chronic hemodialysis: the DOPPS study[END_REF][START_REF] Block | CKD-Mineral and Bone Disorder and Risk of Death and Cardiovascular Hospitalization in Patients on Hemodialysis[END_REF][START_REF] Ureña-Torres | Association of kidney function, vitamin D deficiency, and circulating markers of mineral and bone disorders in CKD[END_REF] The cascade of pathophysiological events that results in CKD mineral bone disorders (MBD) progresses in parallel with CKD and contributes to parathyroid hyperplasia and impaired bone health. MBD alterations may also contribute to cardiovascular disease, through the development of vascular calcification, impaired arterial function, and left ventricular hypertrophy and fibrosis. [START_REF] Block | CKD-Mineral and Bone Disorder and Risk of Death and Cardiovascular Hospitalization in Patients on Hemodialysis[END_REF] The onset, rate, and severity of CKD-MBD biochemical abnormalities can be highly variable across patients. [START_REF] Moranne | Timing of onset of CKD-related metabolic complications[END_REF][START_REF] Levin | Prevalence of abnormal serum vitamin D, PTH, calcium, and phosphorus in patients with chronic kidney disease: results of the study to evaluate early kidney disease[END_REF] Additional characterization of MBD marker patterns and treatment practices across the CKD spectrum would assist in the development of prevention strategies.

The recently updated 2017 KDIGO guidelines [START_REF]KDIGO 2017 Clinical Practice Guideline Update for the Diagnosis, Evaluation, Prevention, and Treatment of Chronic Kidney Disease-Mineral and Bone Disorder (CKD-MBD)[END_REF] recommend initiating the evaluation of CKD-MBD markers in CKD Stage 3, with treatment decisions based on serial measurements of the full array of laboratory markers. We lack data on international practice with respect to the routine clinical frequency of MBD marker measurement and pharmacological treatment of MBD with phosphate binders, vitamin D, and related compounds in non-dialysis CKD patients.

To address these gaps in knowledge, we sought to examine and describe international variation in the assessment, prevalence, clinical targets, and treatment of MBD markers in non-dialysis (Stage 3-5) CKD patients.

METHODS

Sample

CKDopps is an ongoing, international, prospective cohort study of adults (≥18 years old) with estimated glomerular filtration rate (eGFR) <60 mL/min/1.73 m 2 receiving care in stratified random national samples of nephrology clinics. Patients were sequentially or randomly selected from national samples of nephrologist-run CKD clinics in Brazil, France, Germany, Japan, and the United States. The study rationale and design has been previously published [START_REF] Mariani | The CKD Outcomes and Practice Patterns Study (CKDopps): Rationale and Methods[END_REF] . Data for this analysis were drawn from Brazil (

Data

At study enrollment, patient demographics and comorbid conditions are collected on the baseline medical questionnaire. Comorbidities were determined based on ICD-10 codes in Germany, and via medical record abstraction in Brazil, France, and the US. Laboratory data up to six months prior to enrollment and until one year after the first lab were recorded. CKD-MBD laboratory markers of interest included serum levels of P, Ca, iPTH, and 25-D. In Brazil, Germany, and the US, we collected routinely measured laboratory data during longitudinal follow-up (to a maximum frequency of monthly). In France, laboratory measurements and prescription information were collected according to a pre-defined study protocol 8 , we did not analyze CKD-MBD lab-measurement frequency practices for this cohort. PTH is referred to as intact PTH (iPTH) because roughly 85%-90% of the PTH values were obtained through intact PTH assays. Whole PTH assay was used for about 10% of Brazilian and US patients, and 5% of Brazilian patients had missing assay type. The distributions of PTH were similar for patients with intact PTH and for patients with missing assay type, but the variability introduced by different assay types (even within iPTH assays) will render the reported iPTH values less accurate. Nephrologists in each clinic reported target MBD-related laboratory values using the Nephrologist Practice Questionnaire.

Medication use and dosage extracted from the paper or electronic medical records was collected, using a summary questionnaire, on a secure, web-based data collection system. Analysis of medication was performed at the time of patient inclusion and 30 days before, until up to one year after, the CKD stage index date.

We obtained ethics approval for CKDopps from a central institutional review board, supplemented by additional study approvals as required by national and local ethics committees. All patient data are used in accordance with the written informed consent of the patients.

Statistical Analyses

The unit of analysis was patient-stage, based on the patient's CKD stage at study entry or the first identified date of entry into another CKD stage during study follow-up (except in France, where one observation per patient, based on CKD stage at study entry, was used).

Baseline patient characteristics were provided by patient-stage. Timing of follow-up laboratory measurements within a particular CKD stage was assessed using Kaplan-Meier curves with censoring at the earliest of transition to a new CKD stage, initiation of renal replacement therapy, death, departure from the study for any reason, or the end of study follow-up. Timing of laboratory measurement was compared to the 2017 KDIGO recommendations [START_REF]KDIGO 2017 Clinical Practice Guideline Update for the Diagnosis, Evaluation, Prevention, and Treatment of Chronic Kidney Disease-Mineral and Bone Disorder (CKD-MBD)[END_REF][START_REF] Ketteler | Executive summary of the 2017 KDIGO Chronic Kidney Disease-Mineral and Bone Disorder (CKD-MBD) Guideline Update: what's changed and why it matters[END_REF] . Reported laboratory values were the first available, from 30 days before until up to one year after the CKD stage index date. Medication prescription (yes/no) was assessed as any recorded medication prescription from 30 days before until up to one year after the CKD stage index date We conducted statistical analyses using SAS version 9.4 (SAS Institute Inc., Cary, NC).

RESULTS

Our analysis cohort included 7,577 patients; we excluded 73 subjects who had out of range or missing eGFR values (Table 1). Allowing patients to be reassigned after transition to a new CKD stage (patient-stage analyses) yielded 9,904 patients-distributed as 32% from Germany, 30% from France, 24% from the US, and 14% from Brazil. Male patients were more common than women in most countries and CKD stages. Mean age was higher in Germany than in other countries. The most common comorbidity was hypertension, which varied from 82% to 97% by country and CKD stage. The US had the highest percentage of diabetic patients in each CKD stage. The prevalences of heart failure (HF) and coronary

CKD-MBD laboratory target levels as identified in the Nephrologist Practice

Survey

Nephrologists (n=273) associated with the participating clinics were asked to indicate their preferred target values for MBD laboratory values (Figures 1a-c). The reported maximum P target for CKD Stage 4/5 varied from a low of 4 mg/dl to a high of >7 mg/dl; the modal target value was 4.5 mg/dl for Brazil and France, 5.5 mg/dl for the US, and 6 mg/dl for Germany. The upper iPTH target for CKD Stage 4/5 also varied, with a modal target range of 200-500 pg/ml for all countries. The majority of respondents in each country selected a lower target of 30 ng/ml for 25-D.

Probability of repeat measurement of CKD-MBD-related labs over time

For each specific CKD-MBD marker value identified near the index date, we determined the patient's cumulative probability of a repeat lab measurement over the following 12months (Table 2). The probability of a repeat measurement increased over 12 months, and with increasing CKD stage, for all CKD-MBD markers. For example, the probability of a repeat serum phosphorous measurement among patients with CKD Stage 3a was 34% within three, 61% within six, 73% within nine, and 79% within 12 months.

In situations where KDIGO has published recommendations regarding time intervals for repeat testing, the recommendations were achieved or surpassed at least 69% of the time (Table 2). The probability of repeat lab measurement was typically higher in Germany than the US and Brazil (not shown). Despite the absence of a specific recommendation for repeat testing for iPTH in CKD Stage 3, the probability of repeat testing within 12 months was relatively high at 61% (Stage 3a) and 73% (Stage 3b). The probability of iPTH testing within 12 months increased further in CKD Stage 5 to 83%, although adherence to the KDIGO recommendation to test every 3-6 months in CKD Stage 5 was considerably lower (43% at three months, 69% at six months). Despite the absence of a specific KDIGO recommendation for frequency of 25-D testing, 25-D was assessed on a yearly basis in the majority of the patients, ranging from 55% (Stage 3a) to 80% (Stage 5).

CKD-MBD laboratory values, by eGFR level and country

. Increases in mean P and iPTH, and decreases in Ca, were generally gradual from eGFR 60 to 20 ml/min/1.73m 2 but accelerated at eGFR <20 ml/min/1.73m 2 . 25-D showed no relation to eGFR; the small deviations in 25-D at the eGFR extremes reflect lower sample size rather than pathophysiologic patterns. These trends were similar for all four countries. Supplementary Figure 1 shows median P, Ca, iPTH, and 25-D in relation to eGFR.

Categorical distributions of MBD laboratory markers by CKD stage are provided in Figure 2. Although median P increased with CKD stage, there were some patients with P <3.5 mg/dl in all CKD stages. The proportion of patients with iPTH <70 pg/ml declined steeply with increasing CKD stage. Ca values <8.5 mg/dl were seen across CKD stage but were more common in more advanced CKD stages. 25-D levels did not vary meaningfully by CKD stage. Of note, 25-D levels were not reported for 65%-71% of patients from the US and Brazil or for 45% of German patients. Overall, differences between countries in distributions of these four serum MBD laboratory markers were modest.

We explored the relation between iPTH and 25-D, the prohormone of calcitriol (Figure 3). Amid large variation, iPTH showed a negative association with 25-D. Median iPTH was 49 pg/ml lower for patients with 25-D 40-49 ng/ml versus 0-10 ng/ml. In a multivariable logistic model, iPTH >300 pg/ml was more common at 25-D <20 ng/ml than 30-44 ng/ml (OR=1.54, 95% confidence interval 1.25-1.90; Supplemental Table 1).

CKD-MBD treatments

We examined CKD-MBD treatment patterns in relation to relevant lab values, with a focus on patients with CKD Stage 4 or 5 (Figure 4). Phosphate binder use varied by P and country (Figure 4a). Among patients with P >5.5 mg/dl, phosphate binder use ranged from 14% in the US to 43% in France. Among patients with serum P <4.5 mg/dl, phosphate binder use ranged from 5% in Germany to 18% in France. Calcium-based phosphate binders were the primary treatment used in Germany, Brazil, and the US, whereas almost exclusively noncalcium-based binders were prescribed in France.

The prescription of nutritional and active (calcitriol and related analogs) vitamin D varied by iPTH and country (Figure 4b). Generally, use of active vitamin D was higher among patients with higher iPTH values, especially >300 pg/mL, while the use of nutritional vitamin D was more constant across iPTH values (Figure 4b). France had the highest use of nutritional vitamin D and Germany had the highest use of active vitamin D. France and Brazil had the lowest simultaneous use of active and nutritional vitamin D (Figure 4b). Among patients with iPTH >300 pg/ml, the use of active vitamin D ranged from 12% in France to 51% in Germany. The percentage of vitamin D use did not appear to be consistently related to 25-D levels (Figure 4c).

DISCUSSION

CKD-MBD is an important complication of CKD, and frequent monitoring of biomarkers is required to optimally guide treatment. The main findings of our study are that frequency of monitoring of CKD-MBD markers by nephrologists in CKDopps countries is in keeping with guidelines, but prescription of medications to treat CKD-MBD abnormalities is generally loweven in this study of patients under nephrologist care. Target MBD biomarker levels vary notably, and prescription patterns vary somewhat, across countries.

CKD-MBD affects a large number of persons with advanced CKD and influences the risk of bone, mineral, and cardiovascular complications. Block et al. (2013) found many phenotypes of abnormal iPTH, Ca, and P, each with its own risks of death, parathyroidectomy, and cardiovascular hospitalization. [START_REF] Block | CKD-Mineral and Bone Disorder and Risk of Death and Cardiovascular Hospitalization in Patients on Hemodialysis[END_REF] Similarly, DOPPS showed that abnormalities in CKD-MBD markers were linked with adverse outcomes in hemodialysis patients. [START_REF] Tentori | Recent changes in therapeutic approaches and association with outcomes among patients with secondary hyperparathyroidism on chronic hemodialysis: the DOPPS study[END_REF] Despite this increased risk, Liabeuf et al. found that a large proportion of HD patients have CKD-MBD biomarker values outside the KDIGO recommended targets. [START_REF] Liabeuf | Attainment of guideline targets in EURODOPPS haemodialysis patients: are differences related to a country's healthcare expenditure and nephrologist workforce?[END_REF] While the majority of epidemiological studies related to CKD-MBD focus on late stages of kidney disease, many reports illustrate the importance of studying CKD-MBD at earlier CKD stages.

Indeed, a recent study of bone histomorphometric data among persons with CKD Stages 2-5 reported a gradual increase in bone resorption, associated with decreased bone formation and impaired bone mineralization, with increasing CKD stage. [START_REF] Graciolli | The complexity of chronic kidney disease-mineral and bone disorder across stages of chronic kidney disease[END_REF] In 2017, KDIGO issued updated guidelines that recognized the complexity and challenges involved with management of CKD-MBD markers. [START_REF]KDIGO 2017 Clinical Practice Guideline Update for the Diagnosis, Evaluation, Prevention, and Treatment of Chronic Kidney Disease-Mineral and Bone Disorder (CKD-MBD)[END_REF][START_REF] Ketteler | Executive summary of the 2017 KDIGO Chronic Kidney Disease-Mineral and Bone Disorder (CKD-MBD) Guideline Update: what's changed and why it matters[END_REF] The 2017 guidelines are more specific than prior iterations regarding the recommended frequency of routine CKD-MBD lab measurements. In this study, we focused on the probability of repeat lab measurements within specific time intervals in order to accurately report on adherence to KDIGO measurement frequency recommendations, showing that the majority of patients underwent repeat lab testing in accordance with the 2017 KDIGO recommended timeline (Table 2). KDIGO also recommends that CKD patients receive an initial measurement of each of these MBD markers, ideally when the patient is still in Stage 3. It has been reported [START_REF] Roetker | Adherence to Kidney Disease: Improving Global Outcomes Mineral and Bone Guidelines for Monitoring Biochemical Parameters[END_REF] that the majority of Stage 3 patients do not receive these initial measurements for PTH, P, and 25-D, and investigations (not shown) using CKDopps data corroborate this. As the majority of our data were collected prior to publication of these guidelines, these results demonstrate that nephrologists were aware previously of the importance of careful monitoring for CKD-MBD, whether influenced by prior guidelines or for other reasons, but that these measurements were often not initiated immediately for new CKD patients.

The 2017 KDIGO guidelines encourage efforts to normalize laboratory markers but lack specific target recommendations. Clinical uncertainty about optimal and attainable lab targets is evident in the variation in the target lab values for P and PTH selected by nephrologists participating in CKDopps. As previously shown in HD patients [START_REF] Liabeuf | Attainment of guideline targets in EURODOPPS haemodialysis patients: are differences related to a country's healthcare expenditure and nephrologist workforce?[END_REF] , it appears to be difficult to attain target levels for all CKD-MBD markers simultaneously, a goal achieved in only 3% to 15% of CKD Stage 5 patients. This work expands our understanding of CKD-MBD and its management across the CKD stage and geographic spectrum. In the study cohort, the prevalence of MBD abnormalities increased as expected with CKD progression. The percentage of CKD Stage 4 patients with phosphorus >4.5 mg/dl was similar in Germany (14%), US (15%), and France (13%), but higher in Brazil (26%). The distribution of iPTH levels was similar across the four countries. The proportion of patients with 25-D <30 ng/ml was consistent across CKD stages, and was approximately 55% overall, though slightly higher in the US. Country differences could be explained by differences in sunlight exposure and intake of nutritional vitamin D , differences in costs of medications, or health coverage. Similarly, a study evaluating US patients with early stage CKD showed differences in mean and median iPTH levels, but not 25-D levels, across deciles of eGFR. [START_REF] Levin | Prevalence of abnormal serum vitamin D, PTH, calcium, and phosphorus in patients with chronic kidney disease: results of the study to evaluate early kidney disease[END_REF] In our analysis, iPTH levels varied inversely with 25-D levels, although with wide variation and a relatively small effect (Figure 4), a result similar to results found in prior analyses. [START_REF] Metzger | Relation between circulating levels of 25(OH) vitamin D and parathyroid hormone in chronic kidney disease: quest for a threshold[END_REF] Furthermore, a recent analysis of a prospective study showed that progressive reductions in iPTH were achieved as mean post-treatment serum 25-D rose from 13.9 ng/mL to 92.5 ng/mL, irrespective of CKD stage. [START_REF] Strugnell | Rationale for Raising Current Clinical Practice Guideline Target for Serum 25-Hydroxyvitamin D in Chronic Kidney Disease[END_REF] Interestingly, both studies [START_REF] Strugnell | Rationale for Raising Current Clinical Practice Guideline Target for Serum 25-Hydroxyvitamin D in Chronic Kidney Disease[END_REF][START_REF] Ennis | Current recommended 25hydroxyvitamin D targets for chronic kidney disease management may be too low[END_REF] found that 25-D levels far above 30ng/ml are needed to suppress iPTH in nondialysis CKD patients.

Only 15%-39% of patients with P >5.5 mg/dL in this study were prescribed phosphate binders. The type of phosphate binder used differed across countries. Few patients in Germany, Brazil, or the US received non-calcium-based phosphate binders, whereas these agents were the treatment of choice in France. The 2017 KDIGO guidelines suggest limiting the dose of calcium-based phosphate binders in adult patients with CKD G3a-G5D who are receiving phosphate-lowering treatment.

Studies evaluating use of phosphate binders in early CKD stages have shown significant decrease in phosphaturia without a large change in serum phosphate. [START_REF] Liabeuf | Randomized Clinical Trial of Sevelamer Carbonate on Serum Klotho and Fibroblast Growth Factor 23 in CKD[END_REF][START_REF] Block | Effects of phosphate binders in moderate CKD[END_REF] These data indicate that serum P may not accurately reflect phosphate balance in early CKD stages.

Nephrologists may avoid the use of phosphate binders in non-dialysis CKD patients because of the lack of reliable outcome-based clinical trials and from safety concerns related to a possible association of phosphate binder use, especially calcium-based binders, with vascular calcification. [START_REF] Block | Effects of phosphate binders in moderate CKD[END_REF] The CKDopps cohort demonstrates national differences in the use of nutritional vitamin D or calcitriol and related analogs. A substantial proportion of CKD Stage 4/5 patients with a potential clinical indication were not prescribed vitamin D (23%-51% of those with vitamin D <30; 13%-41% of those with iPTH >300 pg/ml across the four countries). Prescription of nutritional vitamin D appears to be inconsistently associated with 25-D and iPTH levels. The percentage of patients treated by vitamin D varied widely across the studied countries, with Germany having the highest prescription rate (Figure 5). National variations in clinical target preferences may contribute to these practice differences. Only 6%-7% of French and Brazilian patients received active vitamin D, while 15% of US and 32% of German patients did. This difference could be due to differences in national formularies and pharmacologic markets; for example, the French National Drug Agency and food and drug administration does not authorize paricalcitol use. The revised KDIGO recommendation suggested that calcitriol and vitamin D analogs should be routinely used only for CKD Stage 4-5 patients with severe and progressive hyperparathyroidism. This guideline's authors indicated that this revision was supported because recent randomized controlled trials of vitamin D analogs failed to demonstrate improvements in clinically relevant outcomes, while demonstrating increased risk of hypercalcemia. [START_REF]KDIGO 2017 Clinical Practice Guideline Update for the Diagnosis, Evaluation, Prevention, and Treatment of Chronic Kidney Disease-Mineral and Bone Disorder (CKD-MBD)[END_REF][START_REF] Hamdy | Effect of alfacalcidol on natural course of renal bone disease in mild to moderate renal failure[END_REF][START_REF] Thadhani | Vitamin D therapy and cardiac structure and function in patients with chronic kidney disease: the PRIMO randomized controlled trial[END_REF] In this international cohort, nutritional vitamin D was the most frequently used treatment.

Yet 34% to 61% of patients still had 25-D levels below 30 ng/ml (Figure 3A), often despite treatment with nutritional vitamin D, although dosage levels were not analyzed. Further investigation in clinical trials is necessary to determine whether more effective vitamin D replacement can ameliorate secondary hyperparathyroidism in CKD patients.

Readers should interpret these results in the context of study limitations-as this work was observational and cross-sectional in nature, we were unable to evaluate causal relationships. In addition, in some groups (including Stage 5 patients) the sample size is small, there was substantial missing data on medication use, and routine lab monitoring practices for French participants could not be included in the analysis because of their specific protocol. As included patients were prevalent, it was not possible to evaluate the date of mineral bone disease drug initiations and correlate this with a lab value. The medication use in relation to the serum biochemical parameters is difficult to interpret, as we do not have a record of medication at each laboratory value. Due to the period of inclusion (3% of patients included after July 2017), we could not evaluate the impact of the 2017 KDIGO CKD-MBD updated guidelines. Due to the limited time of follow up, we could not evaluate the changes over time for medications. These two points could be evaluated in CKDopps when longer follow up is available.

Laboratory values were routinely collected and not centrally measured, so differences between PTH and 25D assays could interfere with the interpretation of difference across countries. Despite these limitations, the present study expands our knowledge on the prevalence of MBD abnormalities and management in a large, international sample of CKD patients, allowing for comparisons between geographically and culturally disparate regions. We have shown that MBD practices among patients with kidney disease vary internationally and by CKD stages. Physicians are clearly aware of the need to monitor this multisystem interaction of pathophysiological events related to mineral and bone metabolism.

However, target levels vary notably and prescription of medications to treat abnormalities in these laboratory markers is generally low. While there are opportunities to increase treatment of hyperphosphatemia, hyperparathyroidism, and vitamin D deficiency in advanced CKD, the effect on longer-term complications of these conditions requires study. Early intervention and preventive efforts, perhaps begun while laboratory markers are within target limits, may result in better overall and longer-term management.

.Disclosures Sophie Liabeuf has no conflicts of interest to disclose; Helmut Reichel reports honoraria and consulting fees from Amgen and Hexal AG; Friedrich K. Port has consultancy contract with Arbor Research Collaborative for Health and no other conflicts to declare; Bénédicte Stengel reports grants for the CKD-REIN cohort study (which contributes French data to CKDopps) from Amgen, Baxter, Fresenius Medical Care, GlaxoSmithKline, Merck Sharp and Dohme-Chibret, Sanofi-Genzyme, Lilly, Otsuka, and Vifor Fresenius, as well as speaker honoraria at the French Society of Diabetology from Lilly, and at the French-speaking Society of Nephrology, Dialysis and Transplantation from MSD; Philipp A. Csomor is an employee of Vifor Pharma Management Ltd; Marie Metzger has no conflicts of interest to disclose; Ziad A. Massy reports grants for CKD REIN and other research projects from Amgen, Baxter, Fresenius Medical Care, GlaxoSmithKline, Merck Sharp and Dohme-Chibret, Sanofi-Genzyme, Lilly, Otsuka and the French government, as well as fees and grants to charities from Astellas, Baxter, Daichii, and Sanofi-Genzyme; these sources of funding are not necessarily related to the content of the present manuscript.

  1,009 patients from 21 CKD clinics, 2014-18 data), France (2,969 patients, 40 clinics, 2013-16 data), Germany (1,834 patients, 33 clinics, 2013-18 data), and the United States (US; 1,765 patients, 38 clinics, 2014-18 data).

  Percentages based on Kaplan-Meier curves of time to next lab measurement, censored on departure, death, and change to another CKD stage if not accompanied by the specific lab. Includes patients with an initial measurement after 30 days prior to and before 1 year after their entry into a given CKD stage during study follow-up. Suggested frequencies based on KDIGO 2017 guidelines 3.1.3 (not graded).*No time interval given in KDIGO 2017 guidelines. For iPTH, the guideline states that frequency should be based on baseline level and CKD progression. For 25OH vitamin D, the guideline states that 25OH vitamin D levels might be measured, and repeated testing determined by baseline values and therapeutic interventions.

  The nephrologist survey allowed inter-country comparisons of nephrologist preferences for biomarker targets.Studies of patients with end-stage renal disease contribute the majority of our knowledge regarding MBD in kidney disease patients. The treatment of CKD-MBD remains a challenging task, and the high frequency of MBD marker abnormalities among CKD patients warrants further study. Well-designed clinical trials based on hard outcomes have not yet tested the use of calcitriol and related analogs, nutritional vitamin D, or phosphate binders, leading to a lack of strong evidence to guide use of these therapies.

Figure Titles Figure 1 a

 Titles1 Figure Titles

Figure 2 a

 2 Figure 2 a-d: Baseline MBD marker lab measurements were used once per patient per CKD stage. If a patient, during follow-up, had multiple lab measurements in multiple CKD stages, at most one per stage was used. A lab measurement was used if it was taken between 30 days before or up to one year after the first lab during study followup indicating that the patient had entered a given CKD stage. N represents the number of patients with available data.

Figure 3 :

 3 Figure 3: Distributions of PTH within each category of 25-D indicated are shown, from 25th percentile to 75th percentile, with the median (line) and mean (diamond) indicated.

Figure 4 a

 4 Figure 4 a-c: Baseline MBD marker lab measurements and prescription information were used once per patient per CKD stage. At most one value for each patient per stage was used. A lab measurement or prescription was used if it was taken between 30 days before or up to one year after the first lab during study follow-up indicating that the patient had entered a given CKD stage. N represents the number of patients with available data.

  Figure 3

Table 1 : Patient sample and characteristics Country Brazil Germany United States France Sample

 1

	Consented patients		1012			1836			1769			3033
	GFR <60 and non-missing		1009			1834			1765			2969
	Patients in final dataset		1009			1834			1765			2969
	Patient-stages* in analyses		1367			3155			2413			2969
	CKD Stage	3a	3b	4	5	3a	3b	4	5	3a	3b	4	5	3a	3b	4	5
	N	126	351	612	278	193	620 1554 788	226	632 1075 480	471 1135 1240 123
	N from Prior Stage	0	65	163	130	0	157	438	726	0	125	266	257	0	0	0	0
	Age (mean, years)	64	66	66	62	68	71	72	72	66	69	69	67	64	67	68	69
	Male	62%	54%	51%	49%	64%	57%	57%	63%	61%	54%	50%	50%	71%	66%	63%	61%
	Comorbidities
	Diabetes	46%	45%	47%	50%	36%	41%	42%	40%	54%	55%	56%	58%	38%	44%	44%	42%
	Hypertension	89%	92%	91%	91%	82%	83%	82%	82%	92%	94%	93%	93%	86%	91%	92%	97%
	Heart Failure	11%	14%	19%	14%	8%	12%	14%	11%	11%	16%	18%	18%	9%	13%	15%	15%
	Coronary Artery
	Disease	19%	21%	24%	20%	23%	26%	29%	27%	30%	31%	34%	29%	22%	24%	28%	25%
	*Each time a patient entered a new CKD stage while in follow-up, their data during that stage was used to inform all tables relevant to that CKD stage.
	artery disease (CAD) increased from CKD Stage 3a to 3b to 4, then stabilized or declined in CKD Stage 5.

Table 2 : Probability of repeat measurements of MBD-related laboratory data, by CKD stage

 2

		KDIGO		% with repeat measure within:
		suggested
		frequency	3 months	6 months	9 months	12 months
	S. Phosphorus
	Stage 3a	6-12 months	34%	61%	73%	79%
	Stage 3b	6-12 months	31%	63%	77%	84%
	Stage 4	3-6 months	47%	77%	86%	89%
	Stage 5	1-3 months	70%	86%	91%	92%
	S. Calcium
	Stage 3a	6-12 months	37%	66%	78%	83%
	Stage 3b	6-12 months	36%	67%	81%	87%
	Stage 4	3-6 months	49%	80%	88%	92%
	Stage 5	1-3 months	73%	90%	94%	94%
	iPTH
	Stage 3a	*	17%	38%	53%	61%
	Stage 3b	*	16%	42%	61%	73%
	Stage 4	6-12 months	27%	53%	70%	78%
	Stage 5	3-6 months	43%	69%	80%	83%
	25OH vitamin D
	Stage 3a	*	14%	30%	49%	55%
	Stage 3b	*	12%	41%	63%	73%
	Stage 4	*	24%	49%	67%	76%
	Stage 5	*	40%	67%	80%	80%
	French data were not available for this table.

Acknowledgements

*CKDopps Investigators

We acknowledge and thank the following individuals for their contributions. CKDopps Steering Committee members and Country Investigators: Antonio Lopes, Roberto Pecoits-Filho (Brazil); Christian Combe, Christian Jacquelinet, Ziad Massy, Benedicte Stengel (France); Johannes Duttlinger, Danilo Fliser, Gerhard Lonnemann, Helmut Reichel (Germany); Takashi Wada, Kunihiro Yamagata (Japan); Ron Pisoni, Bruce Robinson (United States). Additional CKDopps Research Group members: Viviane Calice da Silva, Ricardo Sesso (Brazil); Elodie Speyer (France); Koichi Asahi, Junichi Hoshino, Ichiei Narita (Japan); Rachel Perlman, Friedrich Port, Nidhi Sukul, Michelle Wong, Eric Young, Jarcy Zee (United States). Acknowledgements for France (1) Country Investigators: Christian Combe, Christian Jacquelinet, Ziad Massy, Benedicte Stengel, Carole Ayav, Serge Briançon, Denis Fouque, Luc Frimat, Maurice Laville, (± Christophe Pascal, ±Yves-Edouard Herpe). (2) Coordinating center: Céline Lange, Karine Legrans, Sophie Liabeuf, Marie Metzger, Elodie Speyer. Jennifer McCready-Maynes, an employee of Arbor Research Collaborative for Health, provided editorial support for this paper.

Funding/Support

This work has been supported by specific funding from Vifor Fresenius Medical Care Renal Pharma. Please see www.dopps.org for additional funding details.