J Bouvard

F Moisy

H Auradou

Ostwald-like ripening in the two-dimensional clustering of passive particles induced by swimming bacteria

Clustering passive particles by active agents is a promising route for fabrication of colloidal structures. Here, we report the dynamic clustering of micrometric beads in a suspension of motile bacteria. We characterize the coarsening dynamics for various bead sizes, surface fractions and bacterial concentrations. We show that the time scale τ for the onset of clustering is governed by the time of first encounter of diffusing beads. At large time (t τ ), we observe a robust cluster growth as t 1/3 , similar to the Ostwald ripening mechanism. From bead tracking measurements, we extract the short-range bacteria-induced attractive force at the origin of this clustering.

I. INTRODUCTION

Phase separation and formation of dense domains of self propelled particles are fascinating phenomena in active matter [START_REF] Theurkauff | Dynamic Clustering in Active Colloidal Suspensions with Chemical Signaling[END_REF][START_REF] Palacci | Living Crystals of Light-Activated Colloidal Surfers[END_REF][START_REF] Redner | Structure and Dynamics of a Phase-Separating Active Colloidal Fluid[END_REF][START_REF] Buttinoni | Dynamical clustering and phase separation in suspensions of self-propelled colloidal particles[END_REF][START_REF] Wysocki | Cooperative motion of active Brownian spheres in threedimensional dense suspensions[END_REF][START_REF] Stenhammar | Phase behaviour of active Brownian particles: the role of dimensionality[END_REF][START_REF] Stenhammar | Activity-Induced Phase Separation and Self-Assembly in Mixtures of Active and Passive Particles[END_REF][START_REF] Cates | Motility-Induced Phase Separation[END_REF][9][START_REF] Ginot | Aggregation-fragmentation and individual dynamics of active clusters[END_REF][START_REF] Driscoll | Leveraging collective effects in externally driven colloidal suspensions: experiments and simulations[END_REF][START_REF] Paoluzzi | From motility-induced phase-separation to glassiness in dense active matter[END_REF]. The structural and dynamical properties of the clusters depend on the particle density, their motility characterized by the persistence time of their trajectories and the existence of attractive mutual interactions. When passive particles are placed in a bath of active particles, numerical simulations show the emergence of clusters of passive particles [START_REF] Stenhammar | Activity-Induced Phase Separation and Self-Assembly in Mixtures of Active and Passive Particles[END_REF][START_REF] Mccandlish | Spontaneous segregation of self-propelled particles with different motilities[END_REF][START_REF] Dolai | Phase separation in binary mixtures of active and passive particles[END_REF][START_REF] Omar | Swimming to Stability: Structural and Dynamical Control via Active Doping[END_REF][START_REF] Rodriguez | Phase behaviour and dynamical features of a two-dimensional binary mixture of active/passive spherical particles[END_REF][START_REF] Omar | Phase Diagram of Active Brownian Spheres: Crystallization and the Metastability of Motility-Induced Phase Separation[END_REF]. Beyond the interest in this fundamental problem, such clustering may be highly promising for practical applications, such as the realization of assemblies like crystals, gels and micelles from colloidal passive elements [START_REF] Stenhammar | Activity-Induced Phase Separation and Self-Assembly in Mixtures of Active and Passive Particles[END_REF][START_REF] Omar | Swimming to Stability: Structural and Dynamical Control via Active Doping[END_REF][START_REF] Kraft | Surface roughness directed self-assembly of patchy particles into colloidal micelles[END_REF][START_REF] Schwarz-Linek | Phase separation and rotor self-assembly in active particle suspensions[END_REF][START_REF] Massana-Cid | Active apolar doping determines routes to colloidal clusters and gels[END_REF].

Swimming bacteria are known to transfer part of their activity to passive particles. This has been observed for micron size objects such as beads [START_REF] Wu | Particle Diffusion in a Quasi-Two-Dimensional Bacterial Bath[END_REF][START_REF] Miño | Enhanced Diffusion due to Active Swimmers at a Solid Surface[END_REF][START_REF] Valeriani | Colloids in a bacterial bath: simulations and experiments[END_REF][START_REF] Patteson | Particle diffusion in active fluids is non-monotonic in size[END_REF], ellipsoids [START_REF] Peng | Diffusion of Ellipsoids in Bacterial Suspensions[END_REF] or more complex shapes such as gears [START_REF] Leonardo | Bacterial ratchet motors[END_REF][START_REF] Sokolov | Swimming bacteria power microscopic gears[END_REF] that exhibit rotation when placed in a bacterial bath. Such an active bath can also mediate short-range effective attractions similar to depletion forces between suspended particles, causing the particles to stick together and form pairs [START_REF] Angelani | Effective Interactions between Colloidal Particles Suspended in a Bath of Swimming Cells[END_REF] and small clusters [START_REF] Gokhale | Dynamic clustering of passive colloids in dense suspensions of motile bacteria[END_REF]. However, these experiments show limited growth and absence of phase separation, questioning the possibility to form large-scale clusters in a bacterial system.

In this paper, we report continuously growing clusters forming from up to 10 5 beads suspended in a bacterial bath with apparently no limitation in size. We show that, after a transient governed by the bacteria-induced bead diffusivity, the cluster growth follows a power law ∼ t 1/3 , compatible with the Lifshitz-Slyozov-Wagner theory [START_REF] Lifshitz | The kinetics of precipitation from supersaturated solid solutions[END_REF][START_REF] Wagner | Theorie der alterung von niederschlägen durch umlösen (ostwald-reifung)[END_REF][START_REF] Voorhees | The theory of ostwald ripening[END_REF] describing the Ostwald coarsening mechanism for the growth of grains in a supersaturated solution. * harold.auradou@universite-paris-saclay.fr

II. EXPERIMENTAL SETUP

Our system, sketched in Fig. 1, consists in fluorescent polystyrene beads (PS-FluoGreen) of diameters D B ranging between 2 and 40 µm added to a suspension of Burkholderia contaminans, a motile bacterium ubiquitous in the environment (see Appendix A for details). The bacterial cell size is approximately 3 µm long, 1 µm diameter, and the average swimming velocity is V s 20 µm s -1 , with a typical run duration τ run 0.8 s and run length V s τ run 16 µm [START_REF] Bouvard | Direct measurement of the aerotactic response in a bacterial suspension[END_REF]. A drop of the beadbacteria mixture is injected in a chamber placed on the stage of an inverted microscope.

The chambers were made by bonding a 25 µL Frame-Sealed Chamber (Bio-Rad), height 310 µm and side length 9 mm, on a glass slide covered by a silicon sheet (Gel-Film). This substrate limits the beads adhesion (see Appendix F for details). The chamber is closed by a PDMS (polydimethylsiloxane) cover to ensure a good oxygenation of the suspension, and placed on the stage of an inverted microscope (Leica DMI4000B) equipped with a (2048 × 2048) pixels 2 camera (Hamamatsu Orca Flash 4). Because the beads are denser than the culture medium, they rapidly settle on the bottom surface of the chamber within minutes. The bead concentration is therefore expressed in terms of surface fraction, Φ B , ranging from 3.7 × 10 -4 to 0.7. Two bacterial concentrations are used, corresponding to optical densities OD = 1 and 5, with 1 OD ∼ 1.8 × 10 6 bact µL -1 . These high concentrations ensure an intense swimming activity (and hence a large bead diffusivity), but they remain below the onset of collective motion [START_REF] Martinez | A combined rheometry and imaging study of viscosity reduc-tion in bacterial suspensions[END_REF].

The large-scale dynamics of the clustering is investigated from image sequences with a large field of view (5.3 × 5.3) mm 2 and a resolution of 2.6 µm per pixel, and images are acquired every 30 s over 1 h. We checked that the bacterial concentration and the ensuing bead activity remain constant during that time (see Appendixes C and E for details). To track individual beads, images are acquired at a higher frame rate, between 1 and 20 fps, with a smaller field of view, between (0.21 × 0.21) mm 2 and (5.3 × 5.3) mm 2 , chosen according to the bead diameter.

III. DYNAMIC CLUSTERING

The sequence of images in Fig. 2, obtained for a bead diameter D B = 5 µm and a surface fraction Φ B = 0.12, illustrates the dynamics of the cluster formation (only the fluorescent beads are visible). Starting from uniformly distributed beads at short time (a), denser domains rapidly form at small scale (b), and then gradually evolve toward larger clusters separated by depleted regions (c). A 1-hour time-lapse of this experiment (see Suppl. Movie 1) illustrates the clustering dynamics, showing dense concentrations of beads highly fluctuating in size and continuously exchanging beads. Additional movies with higher magnification and acquisition rates (see Suppl. Movie 2, Suppl. Movie 3) emphasize this continuous exchange of beads between clusters, with freely diffusing beads in the depleted areas between the clusters.

We observe that the clustering dynamics remains essentially two-dimensional during most of the clustering process, except in the densest regions at large time, where beads occasionally overlap in two or more layers. Experiments performed without bacteria or with non-motile (bleach-inactivated) bacteria do not show any clustering, confirming that the clustering dynamics is driven by the swimming of bacteria. Additional experiments performed with wild type E. coli show a similar clustering dynamics but on a slower time scale (see Appendix D for details). This results in smaller clusters at the end of the experiments, which led us to favor experiments with B. contaminans.

The clustering dynamics, similar to that observed with self-propelled particles [4-10, 12, 17, 35], is reminiscent of the Ostwald ripening mechanism [START_REF] Lifshitz | The kinetics of precipitation from supersaturated solid solutions[END_REF][START_REF] Wagner | Theorie der alterung von niederschlägen durch umlösen (ostwald-reifung)[END_REF][START_REF] Voorhees | The theory of ostwald ripening[END_REF]. In the Ostwald ripening model, individual constituents are subject to a short-range attraction, and an excess of concentration around the clusters, proportional to their curvature, generates a diffusive flux from small to large clusters. In other words, the constituents "evaporate" from small clusters and "condense" on larger clusters, leading to a growth as t 1/3 at large time [START_REF] Stenhammar | Phase behaviour of active Brownian particles: the role of dimensionality[END_REF][START_REF] Cates | Motility-Induced Phase Separation[END_REF][START_REF] Lifshitz | The kinetics of precipitation from supersaturated solid solutions[END_REF][START_REF] Wagner | Theorie der alterung von niederschlägen durch umlösen (ostwald-reifung)[END_REF][START_REF] Zhang | Active phase separation by turning towards regions of higher density[END_REF]. To check to what extent this picture holds in the present study, we quantify in the following the time evolution of the cluster size, and determine the bacteria-induced attractive force between beads from bead tracking measurements.

To characterize the cluster size, we have developed a robust image-based method, applicable even when the beads are too small to be resolved individually (see Appendix B for details). We define an image heterogeneity index as

σ n (t, L F ) = σ(I(x, t) * G L F (x)) σ(I(x, t)) , (1)
i.e., as the standard deviation of the intensity levels I(x, t) of the image at time t convoluted with a Gaussian filter G L F (x) of width L F , normalized such that To examine the robustness of this growth at large time, we performed an additional experiment lasting 16 h in the particular case of D B = 5 µm, OD = 5, and Φ B = 0.6 [black symbols in Fig. 3(a)]. Although the bacterial density is not constant over this long duration, this test experiment confirms the continuous increase of L c , up to a factor of 30 at the end of the experiment, corresponding to clusters made of ∼ 10 3 beads. The final image after 16 hours (Fig. 4) shows large clusters, characterized by a cluster size L c = 150 µm. These clusters are themselves organized in structures of an even larger size, up to 2 -3 mm, making them visible to the naked eye.

The earlier onset of clustering at larger surface fraction observed in Fig. 3(a) suggests that the clustering time is governed by the time of first encounter of freely diffusing beads. Accordingly, this crossover time must be governed by the bead concentration and the bacteriainduced bead diffusion coefficient µ B . To estimate µ B , we track isolated beads in experiments performed with a lower surface fraction, as illustrated in Fig. 5. We compute the mean square displacement

|δr| 2 = |r i (t) -r i (0)| 2 , ( 2
)
where r i (t) is the position of the bead i and the brackets • is the average over time and beads (see Appendix E for details). In the diffusive regime (large times), we observe a linear dependence, |δr| 2 4µ B t, from which we compute µ B . Figure 6 summarizes the values of µ B for various bead diameters and the two bacterial concentrations. We obtain µ B between 2 and 25 µm 2 s -1 , with a weak non-monotonic dependence on the bead diameter. This bacteria-induced diffusivity is 10 2 to 10 3 larger than the thermal diffusivity expected for beads of the same diameter shown in dotted line, µ T = k B T /(6πηR B ), with k B the Boltzmann constant, T the temperature and η the fluid viscosity [START_REF] Einstein | Über die von der molekularkinetischen theorie der wärme geforderte bewegung von in ruhenden flüssigkeiten suspendierten teilchen[END_REF]. This strong diffusivity, in agreement with previous studies [START_REF] Wu | Particle Diffusion in a Quasi-Two-Dimensional Bacterial Bath[END_REF][START_REF] Miño | Enhanced Diffusion due to Active Swimmers at a Solid Surface[END_REF][START_REF] Patteson | Particle diffusion in active fluids is non-monotonic in size[END_REF], highlights the strong bead-bacteria coupling for bead diameters of the order of the swimming persistence length V s τ run .

From this bacteria-induced bead diffusivity, we finally estimate the characteristic time of first encounter, τ = 2 /µ B , for two beads separated by a distance . At short time, the beads are randomly distributed on the bottom surface of the cell, so that At short time, in the freely diffusing bead regime (t τ ), the data plateau to a constant value. This plateau takes the expected value L c /R B 1 for the largest beads, but is significantly larger for D B ≤ 10 µm. This originates from the diffraction limit of optical microscopy [START_REF] Wolf | The optics of microscope image formation[END_REF]: for beads smaller than the microscope resolution, the apparent cluster size is given by the Airy diffraction diameter rather than the true bead diameter, yielding an overestimation of the apparent cluster size.

R B / √ Φ B with R B the
At large time, in the clustering regime (t τ ), the data approximately follow a power law with an exponent consistent with 1/3 (dotted line), in agreement with the Lifshitz-Slyozov-Wagner prediction [START_REF] Lifshitz | The kinetics of precipitation from supersaturated solid solutions[END_REF][START_REF] Wagner | Theorie der alterung von niederschlägen durch umlösen (ostwald-reifung)[END_REF][START_REF] Bray | Theory of phase-ordering kinetics[END_REF], with no apparent saturation. These results are confirmed by the experiments performed with various bead sizes (D B = 2 -40 µm) and two bacterial concentrations [see Fig. 3(b)]. In this figure, each data set is averaged over 4 to 8 experiments, with vertical bars reflecting the dispersion between experiments. At large time, t/τ > 100, all data follow a power-law growth L c ∼ t a with a 0.35 ± 0.05.

IV. BACTERIA-INDUCED ATTRACTIVE FORCE

We now address the key question of the effective bacteria-induced attractive force at the origin of the large-scale clustering of the beads. The beads being essentially freely diffusing at short time suggests that this attractive force acts only when the beads are very close. To characterize this short-range attraction, we analyze the relative motion of bead pairs at low surface fraction Φ B and high acquisition rate (see Fig. 5 and Suppl. Movie 4 for details). For each pair of beads (i, j), we compute their velocity difference projected along the pair separation [see Fig. 7(a)],

δV ij = (v i -v j ) • r i -r j |r i -r j | . ( 4
)
Two contributions are expected in δV ij : a large stochastic contribution reflecting the bacteria-induced diffusivity, which should average to zero, and a small deterministic negative contribution reflecting the attraction. We extract this deterministic contribution by computing the relative velocity δV (d) averaged over the pairs (i, j) separated by a given distance d = |r i -r j |-2R B . To deduce the bacteria-induced effective force, we assume that this force is balanced by the viscous drag, which writes in the form

F (d) = -κηR b δV (d), (5)
with η the liquid viscosity and κ a friction factor that characterizes the motion of the bead over the bottom surface of the chamber (κ = 6π for an isolated sphere far from the walls). We determine empirically κ by measuring the velocity of beads drifting in a chamber tilted by a small angle (see Appendix F for details).

The resulting force, plotted in Fig. 7(b), shows a clear attraction at short range, up to d 15 µm, and fluctuations around zero at larger d, as expected for pure diffusion. An increase as d → 0 is also observed, corresponding to the steric interaction between beads. To extract the characteristic range of the attraction, we fit the attractive part of F with F (d)

-F 0 e -d/d0 . This fit gives a length scale d 0 7 ± 1 µm of the order of the bacteria size (including flagella), with weak dependence on the bead diameter. The characteristic force is F 0 0.6 ± 0.2 pN, a value close to the hydrodynamic force induced by the swimming of bacteria [START_REF] Drescher | Fluid dynamics and noise in bacterial cell-cell and cell-surface scattering[END_REF]. This force magnitude and range are much larger than those expected for the van der Waals force for polystyrene beads [START_REF] Ohshima | Van der waals interaction between colloidal particles[END_REF][START_REF] Haliyo | An overview on robotic micromanipulation[END_REF], confirming that the swimming activity of bacteria is the dominant process in the bead clustering.

We finally discuss to what extent the Ostwald ripening mechanism describes the observed cluster growth. In the classical Ostwald ripening, the "evaporationcondensation" quasi-equilibrium state is governed by the ratio between the short-range attractive potential E 0 and the kinetic energy k B T . In our system, an effective potential can be estimated from the bacteria-induced attractive force as E 0 F 0 d 0 , and an effective kinetic temperature can be defined from the bead diffusivity using a Stokes-Einstein law modified by the wall-bead friction factor [START_REF] Wysocki | Cooperative motion of active Brownian spheres in threedimensional dense suspensions[END_REF], k B T eff κηR B µ B . We obtain a ratio σ = E 0 /k B T eff ranging from 0.15 for the 25 µm beads, which slowly form compact clusters, and 1.6 for the 5 µm beads, which rapidly form loosely packed and highly fluctuating clusters. According to the Ostwald mechanism, the deficit of bounding energy for beads in small clusters generates a small excess of concentration of free beads proportional to the cluster curvature, ∆Φ B σR B /L c , leading to a preferential diffusion toward larger clusters. This results in a self-similar growth given by the Lifshitz-Slyozov-Wagner relation [START_REF] Lifshitz | The kinetics of precipitation from supersaturated solid solutions[END_REF][START_REF] Wagner | Theorie der alterung von niederschlägen durch umlösen (ostwald-reifung)[END_REF][START_REF] Voorhees | The theory of ostwald ripening[END_REF],

L c R B = β 1 + α t τ 1/3 , ( 6
)
with α and β of the order of unity. Our data is well described by this law for large beads [see Fig. 3(b)], with β 1.1 ± 0.1 and α 0.4 ± 0.2. The data for smaller beads show a higher plateau at short time due to the diffraction limit, but collapse on the predicted power-law growth at large time. We therefore conclude that the Ostwald ripening mechanism provides a good description of the bacteria-induced bead clustering in our system.

V. CONCLUSION

In this paper, we show that the swimming activity of bacteria produces a clustering of passive beads over a wide range of sizes and concentrations, following an Ostwald ripening-like dynamics with no apparent saturation. Our experiments demonstrate that very large clusters can be formed, raising the possibility of using bacterial motility to generate large structures of passive colloidal particles.

Our ever-growing clusters differ from the small quasistationary clusters recently reported by Gokhale et al. [START_REF] Gokhale | Dynamic clustering of passive colloids in dense suspensions of motile bacteria[END_REF]. This difference may originate from the much larger bead diffusivity measured in our system, resulting in a shorter time of first encounter and hence a faster dynamics. Several parameters may explain this larger diffusivity, among which the use of a highly motile bacterial strain, a weak vertical confinement, and a strongly reduced wall-bead friction achieved by adding a silicone substrate on the bottom of the chamber.

Our experiments allowed us to provide an estimate for the bacteria-induced attractive force between beads. This force may combine a steric effect originating from the depletion of bacteria between close beads, similar to particles suspended in a solution of macromolecules [START_REF] Omar | Phase Diagram of Active Brownian Spheres: Crystallization and the Metastability of Motility-Induced Phase Separation[END_REF][START_REF] Harder | The role of particle shape in active depletion[END_REF][START_REF] Ray | Casimir effect in active matter systems[END_REF][START_REF] Ni | Tunable long range forces mediated by self-propelled colloidal hard spheres[END_REF][START_REF] Asakura | On Interaction between Two Bodies Immersed in a Solution of Macromolecules[END_REF][START_REF] Asakura | Interaction between particles suspended in solutions of macromolecules[END_REF], and a hydrodynamic effect, originating from the viscous stress induced by the swimming of bacteria. Close to a solid boundary, this stress tends to maintain bacteria on the surface [START_REF] Berke | Hydrodynamic Attraction of Swimming Microorganisms by Surfaces[END_REF][START_REF] Sipos | Hydrodynamic trapping of swimming bacteria by convex walls[END_REF], yielding an attractive force between beads. This picture is confirmed by our force estimate, of magnitude matching the hydrodynamic thrust of a swimming of bacteria and range of the order of typical bacteria size [START_REF] Drescher | Fluid dynamics and noise in bacterial cell-cell and cell-surface scattering[END_REF].

Appendix A: Bacterial strains and culture

The main bacterial strain used in this study is Burkholderia contaminans, an environmental strain characterized from the sequencing of 16S and recA gene fragments [START_REF] Bouvard | Direct measurement of the aerotactic response in a bacterial suspension[END_REF][START_REF] Bouvard | Dynamics of bacterial suspensions, from aerotaxis to cluster formation[END_REF]. Bacteria were grown overnight in YEB (Yeast Extract Beef) medium at 28 °C in an orbital shaker at 200 rpm. A certain volume of this suspension is added to YEB containing fluorescent polystyrene beads (PS-FluoGreen, from microParticles GmbH). The volume is chosen to obtain a suspension containing 1.8 or 9 × 10 6 bacteria per microliter, corresponding to an optical density (OD) of 1 and 5, respectively. The solution is then homogenized with an orbital vortex mixer and placed in the chamber.

Additional experiments were conducted with another bacterial species, Escherichia coli RP 437. The bacteria were cultured in CAM-M9G (1:1000 ratio) medium in an incubator shaker at 240 rpm and 30 °C. The culture was stopped at an OD close to 0.1 and washed twice by centrifugation (2300 g for 10 min). The bacteria were then re-suspended into a minimal buffer (0.1 M EDTA, 0.001 M Methionine, 1 M Sodium Lactate and 0.1 M Phosphate buffer dissolved in milliQ water at pH = 7.0). This medium provides the salts needed for the bacterial swimming, but it does not contain any nutrient for bacterial growth. The bacteria were concentrated at an OD of 7 and then diluted to OD = 5, before adding 2 µm fluorescent beads.

Appendix B: Measurement of the characteristic cluster size

To compute the characteristic size of the clusters L c , the images are blurred with a low pass Gaussian filter of varying width (see Fig. 8). When the filter width exceeds the characteristic size of the clusters, the blurred image becomes nearly uniform, which provides an estimate of the cluster size. This method applies for all bead sizes and magnifications, even for small beads under the microscope resolution.

The blurring is achieved by convoluting each image I(x, t) (of size 2048 × 2048 pixels) with a Gaussian kernel G L F (x) of width L F increasing from 1 to 1000 pixels. The standard deviation σ(I(x, t) * G L F (x)) of the resulting image is then computed. We define the heterogeneity index as the ratio between this standard deviation and the standard deviation of the initial image,

σ n (t, L F ) = σ(I(x, t) * G L F (x)) σ(I(x, t)) . ( B1
)
This quantity is 1 for the original (non-blurred) image, and tends to 0 for L F L c (uniform image), where L c is the characteristic size of the clusters. Because of the finite size of the image, and because of residual heterogeneity in the illumination, σ n tends to a small value σ * n of the order of 0.05, which we subtract from σ n .

Figure 9 tion of the filter width L F at increasing times during the clustering process. The decrease of σ n is shallower at large time, indicating the presence of patterns of increasing size. We define the cluster size L c (t) as the filter size for which σ n (L c (t)) reaches a chosen threshold σ 0 n . The time evolution of L c (t) obtained for various thresholds σ 0 n is illustrated in Fig. 9(b), in the case OD = 5, D B = 5 µm and Φ B = 0.24. All curves show a similar behavior, with a transition from a constant value at short time to a power-law growth ∼ t 1/3 at large time. This indicates that the heterogeneity index (B1) provides a robust description of the dynamics of the cluster growth. The threshold σ 0 n = 0.5 is chosen because for large beads (when diffraction effects can be neglected), it yields L c R B at short time.

Other image processing methods were tested, such as the image correlation method, and gave similar results [START_REF] Bouvard | Dynamics of bacterial suspensions, from aerotaxis to cluster formation[END_REF]. The present method was found to be more robust to the presence of defects on the images, such as scratches on the glass slide or non-uniform illumination.

Appendix C: Control experiments

Two experiments were conducted to check that the clustering of beads is induced by the swimming activity of the bacteria. First, a suspension containing only beads and no bacteria did not show any clustering. Secondly, we used a suspension of beads mixed with bleachinactivated bacteria. Again, no clustering of the beads was observed here.

To check that the bacterial concentration was not changing significantly during the experiments, two suspensions with an initial optical density (OD) of 1 and were placed in conical flasks and at room temperature reproduce the conditions under which the suspensions are maintained during the clustering experiments. Figure 10(a) shows the OD measured on samples taken during one hour. For both experiments, we can see that the OD remains almost constant over the whole duration of the sampling. Beyond one hour, the bacterial concentration increases and saturates at an OD close to 10 [see Fig. 10(b)]. These measurements indicate that the bacterial concentration for the 16-hour experiment performed at initial OD = 5 [shown in Fig. 3(a)] almost doubled over the duration of the experiment.

Appendix D: Clustering experiments with E. coli

To check if the observed bead clustering is specific to the bacterial species B. contaminans, we performed experiments with another species, Escherichia coli RP 437. Figure 11(a,b) shows images recorded at the beginning of the experiment and after 1 h. The final image shows a clear clustering of beads, similar to that observed with B. contaminans. Figure 11(c) shows the evolution of the cluster size L c computed using the image processing method as described in Section B. As for B. contaminans, L c is first constant and then increases in time. The increase is consistent with the power-law ∼ t 1/3 observed with B. contaminans.

An important difference between the two bacterial species is the duration of the plateau before the growth regime. The crossover between these two regimes is governed by the time of first encounter of diffusing beads, which is shorter for B. contaminans than for E. coli under the same conditions. This may be due to a difference in swimming activity between the two species, and led us to select B. contaminans rather than E. coli for our study.

Appendix E: Effective diffusion of beads in a bacterial bath

To determine the effective diffusion coefficient of the beads, we analyze their trajectories when placed in a bacterial bath at OD = 1 and 5. A low surface fraction is chosen to minimize their interaction and to prevent the formation of clusters. The bead tracking is performed using Trackmate [START_REF] Tinevez | Trackmate: An open and extensible platform for single-particle tracking[END_REF], from which we compute the mean square displacement

|δr| 2 = |r i (t) -r i (0)| 2 , ( E1
)
where r i (t) is the position of the bead i and the brackets • denote the average over time and beads. For a Brownian particle performing a 2D random walk of steps of duration τ B and length B = v B τ B , the mean square displacement follows a ballistic regime |δr| 2 = v 2 B t 2 for t < τ B and a diffusive regime |δr| 2 = 4µ B t for t > τ B .

Figure 12(a) shows |δr| 2 as a function of time for the set of experiments summarized in Tab. I. Our data shows a first regime of slope larger than 1 followed by a diffusive regime, a behavior which is consistent with previous studies [START_REF] Wu | Particle Diffusion in a Quasi-Two-Dimensional Bacterial Bath[END_REF][START_REF] Valeriani | Colloids in a bacterial bath: simulations and experiments[END_REF][START_REF] Patteson | Particle diffusion in active fluids is non-monotonic in size[END_REF]. To highlight the diffusive regime at large time, we plot the ratio |δr| 2 /4t in Fig. 12(b). After 2 to 30 seconds, all curves tend to a constant value, yielding the diffusion coefficient µ B reported in Tab. I alongside the experimental conditions. They are plotted as a function of the bead diameter in Fig. 6.

Finally, we checked that the bead diffusion coefficient remained constant during the clustering experiments. An experiment was conducted with 5 µm beads at a surface fraction Φ B = 0.006 at OD = 5. Measurements in Fig. 13 show a nearly constant µ B during 1 h, which is consistent with the nearly constant bacterial concentration observed in Fig. 10, indicating that the 1-h clustering experiments are performed under stationary bacterial conditions. The diffusion coefficient µB is given by |δr| 2 /4t at large time.

Appendix F: Wall-bead friction coefficient κ

To determine the effective attractive force between beads from our bead velocity measurements, we assume that this force is balanced by the viscous friction. This assumption requires to know the force-velocity relation for a bead moving close to a surface. The bead motion is a combination of rolling and sliding, and depends on several parameters such as the roughness of the beads and substrate.

In order to determine the force-velocity relation, we performed experiments with beads drifting under gravity along the bottom surface of a chamber tilted by a small angle θ with respect to the horizontal. The chamber is prepared following the same protocol as in Appendix A, and is filled with the same culture medium as in the clustering experiments but without bacteria. The chamber is mounted on the microscope stage, which is tilted at an angle θ between 5°and 17°. The component of the bead weight along the surface is 4/3 πR 3 B ∆ρg sin θ, with g = 9.81 m s -2 the gravitational acceleration, η = 1 mPa s the fluid viscosity and ∆ρ = ρ B -ρ f the density difference between the beads (ρ B = 1.06 g cm -3 ) and the fluid (ρ f = 1.007 g cm -3 ). We write the friction force as F = κηR B V drift , with V drift the drift velocity of the bead, and κ a constant accounting for the wall-bead interaction (the standard Stokes force yields κ = 6π far from the walls). The drift velocity is therefore given by:

V drift = 4πR 2 B ∆ρg 3κη sin θ. (F1)
The drift velocity was determined from the tracking of dozens of beads for different tilt angles. Figure 14 shows V drift as a function of sin θ for different bead diameters. For a given bead diameter, V drift grows linearly with sin θ, as predicted by Eq. (F1). From the measured slope we determine the friction coefficient, and obtain κ = 34, 52 and 77 (±10%) for beads of diameter 5, 10 and 25 µm, respectively. These values are used to compute the effective force F defined in Eq. ( 5) and plotted in Fig. 7.

Figure 1 .

 1 Figure1. Experimental setup. A drop of a suspension containing polystyrene beads and B. contaminans bacteria is placed in a 25 µL frame-sealed chamber (height 310 µm, length 9 mm) on a glass slide covered by a silicon sheet to minimize adhesion. The chamber is closed by a PDMS (polydimethylsiloxane) cover to ensure a good oxygenation of the suspension, and placed on the stage of an inverted microscope.

Figure 2 .

 2 Figure 2. Image sequence showing the clustering of beads of diameter DB = 5 µm and surface fraction ΦB = 0.12 induced by the activity of the bacterial bath at bacterial concentration OD = 5 (about 10 5 beads present on the images). Image (d) is a zoom of image (c), showing freely diffusing beads in the depleted regions between clusters.

Figure 3 .

 3 Figure 3. (a) Cluster size Lc as a function of time at large bacterial concentration (OD = 5) for beads of diameter DB = 5 µm and various surface fractions ΦB. Inset: Normalized cluster size Lc/RB as a function of t/τ for DB = 5 µm. (b) Lc/RB as a function of t/τ for various bead diameters DB and bacterial concentrations (filled symbols: OD = 1; empty symbols: OD = 5). The vertical bars reflect the dispersion for each bead diameter. The black dashed line shows a best fit using Eq. (6) with α = 0.4 ± 0.2 and β = 1.1 ± 0.1. The colored dashed lines emphasize the larger apparent cluster size for small bead diameters due to the diffraction limit.

  σ n (0, t) = 1. With this definition, one has σ n (L F , t) → 0 when the filter width L F exceeds the largest scale present in the image. We finally define the cluster size L c (t) as the filter width such that σ n (L c (t)) = 1/2.

Figure 3 (

 3 a) shows the temporal evolution of the cluster size L c for beads of diameter 5 µm at various surface fractions Φ B . For the lowest Φ B , L c remains close to the bead diameter, and shows only a slight increase after about ten minutes, corresponding to small clusters made of 2 -4 beads only. As the surface fraction is increased, the transition to the growth regime starts earlier, and the cluster size increases by a factor of almost 10 after 1 hour, indicating clusters made of typically 100 beads, with no visible saturation.

Figure 4 .

 4 Figure 4. Giant bead clustering after 16 hours, obtained for beads of diameter DB = 5 µm and initial bacterial concentration of OD = 5 and surface fraction ΦB = 0.6.

Figure 5 .

 5 Figure 5. Sequence of phase-contrast images taken from the Suppl. Movie 4 showing a freely diffusing bead (blue track) and two interacting beads (yellow and red tracks). Bead diameter DB = 5 µm, bacterial concentration OD = 5.

Figure 6 .

 6 Figure 6. Effective diffusion coefficient µB of the beads as a function of their diameter DB for bacterial concentrations OD = 1 (filled symbols) and OD = 5 (empty symbols). The dashed line shows the Stokes-Einstein prediction µT = kBT /(6πηRB) for thermal diffusion.

bead radius, yielding τ R 2 BΦ

 2 B µ B . (3) Normalizing the time t with τ and the cluster size L c with R B yields a good collapse of our data at D B = 5 µm and OD = 5 for various surface fractions [see inset of Fig. 3(a)], confirming that the onset of clustering is governed by τ .

Figure 7 .

 7 Figure 7. (a) Sketch of the velocity difference δVij for a pair of beads (i, j). (b) Average force between two beads as a function of their separation d, for beads of diameter DB = 5, 10, 25 µm at OD = 1 and 5. Black dashed line: exponential fit F (d) = -F0 e -d/d 0 with F0 = (0.6 ± 0.2) pN and d0 = (7 ± 1) µm.

Figure 8 .

 8 Figure 8. (a) Image (size 2048 × 2048 pixels) of fluorescent polystyrene beads of diameter DB = 5 µm with surface fraction ΦB = 0.24, in a suspension of B. contaminans. (b,c,d) Same image convoluted with a Gaussian filter GL F (x) of width LF = 10, 50 and 100 pixels, used to determine the characteristic cluster size.

Figure 9 .

 9 Figure 9. (a) Heterogeneity index σn as a function of the filter size LF in pixels (1 pixel = 2.6 µm). Data obtained for beads of diameter DB = 5 µm at a surface fraction ΦB = 0.24 in a bacterial at OD = 5. σn(LF ) is plotted every δt = 90 s from t = 0 (blue) to t = 60 min (red). The black dashed line shows the threshold σ 0 n = 0.5 defining the cluster size Lc(t). (b) Evolution of the normalized characteristic cluster size Lc/RB, as a function of the normalized time t/τ for various values of the threshold σ 0 n .

Figure 10 .

 10 Figure 10. Time evolution of the bacterial concentration of B. contaminans of initial optical density 1 (filled squares) and 5 (empty circles). The suspensions were kept under conditions close to those of the experiments. (a) OD values measured during the first hour, corresponding to the duration used in the clustering experiments. (b) OD values measured over twenty-five hours. These measurements show that the OD saturates to 10 beyond ten hours.

Figure 11 .

 11 Figure 11. Clustering of beads in a suspension of E. coli RP437 bacteria (bead diameter DB = µm, surface fraction ΦB = 0.30, OD = 5), at = 0 (a) and t = 60 min (c) Time evolution of the cluster size Lc(t), showing a dynamics similar to the one observed for B. contaminans: a plateau at short time followed by an increase at large time, compatible with a t 1/3 power law.

Figure 12 .

 12 Figure 12. (a) Mean square displacement |δr| 2 of beads for bacterial concentrations OD = 1 (filled symbols) and OD = 5 (empty symbols). See Tab. I for experimental conditions. (b)The diffusion coefficient µB is given by |δr| 2 /4t at large time.

n

  OD D B C B N tracks MAG f aq µ B (µm) (g mL -1 ) (Hz) (µm 2 s -1 )TableI. Summary of the experimental conditions for the determination of the bead diffusivity µB: bead diameter DB, bacterial concentration OD, bead concentration CB, number of trajectories N tracks , acquisition frequency faq and magnification (MAG). The diffusion coefficient µB is computed from the mean square displacement of beads at low concentration, as shown in Fig.12.

Figure 13 .

 13 Figure 13. Time evolution of the effective diffusion coefficient of the beads µB during one hour, in the case OD = 5, DB = 5 µm and ΦB = 0.006.

Figure 14 .

 14 Figure 14. Average drift velocity V drift of the beads as a function of the sine of the tilt angle θ, for three bead diameters DB = 5, 10 and 25 µm.

ACKNOWLEDGEMENTS

We thank A. Gargasson for experimental help, and G. Dietze and M. Jarrahi for fruitful discussions. This work is supported by the French National Research Agency (ANR) through the "Laboratoire d'Excellence Physics Atom Light Mater" (LabEx PALM) as part of the "Investissements d'Avenir" program (ANR-10-LABX-0039).


MD1 Christoph Bacri

MD1 Robin Chastant

MD2 Lucien Chassin-Trubert

Hireche Kheira

Pierre Md

Ludovic Alric

Canaud

Kheira Hireche

MD, PhD1 Pierre Alric

MD, PhD1 Ludovic Canaud
email: l-canaud@chu-montpellier.fr

Fenestrated Physician-Modified Endovascular Grafts for Aberrant Right Subclavian Artery and/or Kommerell's diverticulum

Keywords: ARSA, aberrant right subclavian artery, Lusoria, homemade endograft, physician-modified stent graft, TEVAR, endovascular repair

published or not. The documents may come

Introduction

Aberrant right subclavian artery (ARSA), also known as arteria lusoria, is an important aortic arch branching pattern variation. The prevalence is between 0.4% and 1.8%1,2 in the general population. The right subclavian artery arises from the aortic arch distal to the origin of the left subclavian artery (LSA) and takes a retro-esophageal path in 80% of patients. Other paths can be between the esophagus and the trachea in 15% and anterior to the trachea or main stem bronchus patch in 5%.1 Approximately, 20% to 60% of individuals are with ARSA associated with an aneurysmal dilatation of the proximal portion of the subclavian artery known as Kommerell's diverticulum (KD). Symptoms are reported to occur in around 5% of cases and are most commonly due to compression of the esophagus (dysphagia lusoria) or the trachea (dyspnea, chronic cough, stridor, recurrent pneumonia, obstructive emphysema, or chest pain).3 Current recommendations for repair of ARSA and/or KD are for symptomatic patients and/or asymptomatic patients with subclavian artery aneurysm >3 cm or KD >5.5 cm. [START_REF] Czerny | Clinical cases referring to diagnosis and management of patients with thoracic aortic pathologies involving the aortic arch: a companion document of the 2018 European Association for Cardio-Thoracic Surgery (EACTS) and the European Society for Vascular Surgery (ESVS) expert consensus document addressing current options and recommendations for the treatment of thoracic aortic pathologies involving the aortic arch[END_REF] Operative treatment modalities include resection and ligation of the symptomatic or aneurysmal ARSA, to release compression, and subclavian-carotid transposition or bypass, to reestablish arterial circulation to the right arm. Furthermore, KD can be treated by stent-graft implantation or descending thoracic aorta replacement. Thoracic endovascular aortic repair (TEVAR) might be challenging due to steep arches, which are often present in these patients.

The aim of this report was to evaluate midterm results of the current series of 6 patients treated with fenestrated physician-modified endograft (PMEG) for ARSA and/or KD.

Methods

Ethics

The study was conducted according to the principles of the Helsinki II Declaration and informed consent was obtained from all patients: before surgery, for the use of PMEG, and during follow-up, for the use of data.

This study was approved by the local institutional review board that is registered at the Office for Human Research Protections. The potential risks and benefits of PMEG and manufactured stent grafts were discussed clearly and without bias before surgery. The theoretical increased risk of infection associated with PMEG, the lack of standardization, and the lack of long-term data were clearly explained.

Patients

Protocol and informed consent were approved by the institutional review board. All patients gave written consent, and the local authorities approved the study. From January 2018 through November 2022, all patients presenting with ARSA and/or KD were enrolled and treated in one tertiary referral center. Multidisciplinary teams were involved in the decisionmaking. Demographic, anatomic, intraoperative, and postoperative data were recorded.

Planning, Sizing, and Device Preparation

A vascular imaging workstation is used to accurately define and measure patient's anatomic criteria from computed tomography angiography images. An appropriate stent graft is selected to achieve the seal and modifications planned. Stent-graft fenestrations are fashioned on the back table during anesthetic induction. The Valiant Captivia stent-graft (Medtronic, Santa Rosa, Calif, USA) is used for all PMEGs. The endograft is completely unsheathed. The fenestration is placed as it is not crossed by stent struts. The proximal fenestration is a large fenestration that follows the shape of the proximal stent, made with a scalpel. The distance between the fenestrations depends on the distance between the left common carotid and the subclavian artery. A cautery device is used to fashion the fenestration with a standard diameter of 8 mm. A nitinol wire (loop of a snare, EV3 Amplatz Goose Neck Snare; Medtronic, Santa Rosa, California) is sutured around the fenestration both to reinforce seal (dilation of a covered stent against the nitinol ring) and to mark the position. A Terumo 0.035 stiff is used as preloaded wire. It is introduced after fenestration of the endograft from the distal part through the endograft and externalized through the LSA fenestration. The endograft is resheathed, using snugger and cotton vessel loop. The technical steps of the endograft modification are illustrated in another publication. 5 A modified endograft is shown in Figure1.

Technical Steps

All procedures were performed in 2 stages, under general anesthesia. During the first stage, revascularization of the right upper limb is performed by a carotid-subclavian bypass, with an 8 mm prosthetic graft, and the proximal segment of the ARSA is ligated. If needed, a left carotidsubclavian bypass is made. The endovascular stage is performed during the same procedure, through either surgical exposure or percutaneous access of the common femoral arteries and left brachial artery. Left carotid access is used in case of bilateral carotidsubclavian bypass instead of left brachial access (the rest of the procedure is described with the left brachial access but is transposable to the carotid access). The origin of the ARSA is occluded by an endovascular plug (Amplatzer) and, in case of bilateral bypass, the subclavian artery was also plugged. A 24 French (Fr) 33 cm length introducer sheath is placed retrograde through the common femoral access. A 6 Fr 45 cm sheath introducer is placed through the retrograde left brachial access into the ostium of the LSA. A double curved 300 cm extra stiff 0.035 wire is positioned against the aortic valve through the femoral access. The proximal side of the preloaded guide wire is advanced through the femoral access sheath, delivered to the LSA using a 6 Fr 25 mm snare loop, and exteriorized establishing a through-and-through wire. The PMEG is moved forward over the Lunderquist wire and the preloaded guidewire is progressively pulled by the second operator from the left brachial access, orientating the fenestrations superiorly to face the supra-aortic trunks originating off the superior arch. The first angiographic run, perpendicular to the LSA, is performed through the left brachial sheath. Deployment is started and completed under visualization. Neither rapid pacing nor decreased blood pressure are used. The accuracy of the deployment comes from the good alignment of the fenestration with the target artery and a correct traction on the through-andthrough wire. A 9 Fr 80 cm sheath is advanced with its dilatator through the LSA fenestration over the preloaded guidewire into the stentgraft lumen from the femoral access. A 9 to 12 mm diameter, 38 or 59 mm in length balloon expandable covered stent (LifeStream, Bard, Tempe, Arizona), brought through the femoral access, is inflated, protruding approximately 5 mm into the aortic stent-graft lumen, with the remaining length in the LSA. The covered stent is flared, using a 14 mm balloon. The second fenestration is never catheterized nor stented. Completion angiography was performed to verify the correct position of the PMEGs and patency of all supraaortic vessel trunks.

Follow-up

Study follow-up time is defined as the date of the last postoperative clinical evaluation. All surviving patients underwent at least postoperative surveillance imaging at 1 month, 6 months, and then annually.

Statistical Analysis

Categorical data are presented as frequencies; continuous variables are expressed as median and range or standard deviation. All statistical analyses were performed using IBM SPSS Statistics 24 software (Version 24.0.0.0).

Results

Between 2018 and 2022, 6 patients with ARSA were treated with physician-modified endovascular graft by the same surgeon. The baseline characteristics are shown in Table 1. Patients' mean age was 49 (24-78) years. Mean proximal aortic diameter was 29 (23-34) mm. Table 2 gives a resume of the main details of the 6 patients. Two patients were symptomatic with dysphagia Lusoria. One patient was treated in the emergency setting for isthmus rupture in a context of high-velocity trauma. A case report was published about this case by Freycon-Tardy et al in 2022.6 Two had aneurysm of the aortic arch and one of the right subclavian artery in a patient with right-sided arch. Another patient had a right descending thoracic aorta. In case of situs inversus, the right subclavian artery is stented instead of the LSA; the rest of the procedure is unchanged.

Each aortic repair was landing in zone 0. Five patients were treated by double-fenestrated homemade endografts (83%). The standard double-fenestrated PMEG was used in 5 patients because the distance between the subclavian artery and the carotid was too short to obtain a sufficient landing zone for long-term sealing. If zone 2 would have been long enough to assure a good sealing, a single-fenestrated endograft could have been used. The emergency had a double fenestration on left and right carotid, which brought the landing zone to zone 0. It is also zone 0 for the bovine arch because of the right carotid-subclavian bypass.

Perioperative details are shown in Table 3. Mean operative time was 138 (111-216) minutes. All right upper limbs were revascularized with prosthetic carotid-subclavian bypass. Two patients required an additional left carotidsubclavian bypass. In the emergency case, the distance between the aortic rupture and the LSA was too short, which jeopardizes a long-term efficient sealing. The PMEG was double-fenestrated on the left and right carotid and stented in the left carotid. With regard to the patient with aortic arch aneurysm and bovine arch, because of the additional anatomic complexity, the double-fenestrated PMEG was not suitable. The PMEG was single-fenestrated on the bovine arch with a large fenestration of a diameter of 14 mm. As no stent with such a diameter was available, an Endurant limb was shortened and delivered through carotid access into the fenestration up to the bifurcation. These 2 patients had an additional proximal embolization of LSA. The distal landing zone was zone 4 because there was no need to go lower to achieve sufficient sealing. Stent-graft diameter ranged from 24 to 38 mm, and the mean length of aortic coverage was 133 mm (range, 100-150 mm). Technical success was achieved in 100% of patients. Preoperative imaging with reconstruction of the patient with bovine arch and aneurysm is presented in Figure 2. Post-therapeutic reconstruction at 1 month follow-up is presented in Figure 3.

Thirty Days Outcomes

The mean length of hospital stay was 7 (range, 5-13) days. There was no in-hospital death. No major morbidity nor mortality rates were reported. The dysphagia disappeared in symptomatic patients (100%). No patient had cerebrovascular complications or retrograde dissection. One patient (17%) was complicated with lower limb ischemia: it was diagnosed and treated by femoro-femoral bypass during the same procedure. One patient (17%) had operative site complications (1 seroma) but no patient requires surgical reintervention.

Follow-up

During a mean follow-up of 16 (range, 3-50) months, the overall mortality in this series was 0% (0). Every bypass was patent. No Type 1, 2, or 3 endoleak was reported. Overall, no reintervention was performed within the followup. The aneurysm does not have a significant reduced diameter during follow up (62-59 mm, 43-43 mm, and 68-67 mm), but the 3 patients presenting aneurysm were followed up only on a short period: 8, 4, and 3 months respectively.

Discussion

Aberrant right subclavian artery and KD are an anatomic anomaly but often linked to aortic arch diseases and can be symptomatic in a few cases. Most studies comparing treatment with and without thoracic open access showed similar results in safety and patency (mortality of 1.62 and 100% patency).7,8 As the actual trends are to be less invasive in the treatment of pathologies, even in presence of anatomic anomalies, some teams used celioscopic9 or robotic10 approaches to respect the lusoria. Other groups improved the hybrid or full endovascular way, showing feasibility, efficiency, and safety even in the emergency setting. Hybrid technique consists mainly of TEVAR covering the origin of the ARSA, ligation, or plugging of it and revascularization or not of the right subclavian artery by debranching of the ARSA or carotid-subclavian bypass. The full endovascular approach consists of TEVAR with revascularization of the right upper limb by chimney,11 fenestration,12 or branched grafts.13 However, there are still some limitations for these advanced devices, such as technical challenge, manufacturing lead time, and high cost; therefore, the physician-modified fenestrated stent graft could be considered to be an alternative option that is suitable and always accessible.

There are few data currently available concerning hybrid repair in the specific area of pathologic aortic arch in patients with ARSA and/or KD. As there are only few people presenting those pathologies and needing a treatment, there are even less people needing emergency treatment. These facts make it complicated to run studies. The current literature is diverging when it comes to the management of emergencies, with some teams encouraging endovascular or hybrid repair and others considering it as a bridge to a more stable solution.14

This study is the first to report the results of hybrid treatment with physician-modified fenestrated endograft and tries to clarify the value of this approach in terms of feasibility, morbidity, mortality, and medium-term outcomes.

The current trend in this institution is to propose endovascular therapy for all pathologies of the aortic arch, except for infections, because it provides less comorbidity than open surgery (5%-10% mortality, 6%-12% of stroke, 7.6% of bleeding requiring reintervention, 3% of renal failure requiring dialysis, or readmission within 30 days of primary operation up to 13%)15 and it does not need cardiopulmonary bypass or circulatory arrest.

The less invasive therapeutic approach with good exclusion efficiency was chosen. [START_REF] Canaud | Minimum 10-year follow-up of endovascular repair for acute traumatic transection of the thoracic aorta[END_REF] Therefore, there was no open surgery within the 6 cases treated in the past 4 years, even for the youngest patients who are aged only 24 and 32 years. Some long-term studies, with more than 10 years follow-up of endovascular aortic isthmus rupture, show that this endovascular therapy lasts over time without any device-related issues.

All patients in this case series benefit from total aortic arch repair with proximal landing in zone 0 because in 4 patients the distance between LSA and left carotid was too short to propose a single-fenestrated endograft. The standard double fenestrated PMEG includes in the second fenestration the left carotid and the brachiocephalic trunk (here only the right carotid). If aortic arch anatomy was suitable, single-fenestrated PMEG could have been used, avoiding a total aortic arch repair. The single-fenestration on the bovine arch brings the proximal landing zone to zone 1. The isthmic rupture at the bottom of the LSA made a long-term sealing uncertain if a single-fenestrated endograft was used. A longer proximal landing zone is preferred, even if total aortic arch repair is needed, to ensure a good sealing for long-term efficiency even in young patients.

With a technical success rate of 100% and the absence of in-hospital or 30 days mortality, this study shows encouraging early results. With regard to the technical success rate and the patency of 100%, it is comparable to the current literature.17, 18 The morbidity is low (3%), especially regarding stroke (0), endoleaks (0), and necessity of reintervention (0). The results are mostly satisfactory and similar to those reported by Wooster et al.19 Mostly, the ARSA originated distal to LSA. To obtain an adequate proximal landing zone for TEVAR, excluding 2 subclavian arteries could be suggested. It has been shown that covering one subclavian artery could be unharmful,20 however, bilateral occlusion is not recommended, not because of the risk of subclavian steal syndrome or upper limb ischemia but because of the higher risk of spinal ischemia or stroke. Therefore, it is possible to cover both the subclavian arteries and make a bilateral carotid-subclavian bypass or revascularize with some off-label techniques such as chimney or in situ laser fenestrations.

The physician-modified stent-graft is an off-label use of the Valiant Captivia thoracic stentgraft. Concerns about its integrity and durability can be raised, but in this study and in other series conducted by the team with the same technic, no stent fracture or endoleak on the fenestration have been seen.5, 21, 22 As the technique is quite new, further data are needed to establish its durability. All patients require longterm follow-up to identify any complication related to a device failure.

Currently, branched devices of the aortic arch are not available routinely and therefore not suitable for emergencies in contrast with the standard Valiant Medtronic endograft that can be off-the-shelf in most aortic centers. The endografts are modified preoperatively after analysis of the CT-scan, but, as shown in a previous study, all supra-aortic branches originate from 2 areas in the aortic arch in 97% of cases.2 This could lead to the development of a standard single-fenestrated or double-fenestrated endograft easily available.

The technique has been improved during the past years to be easier and shorter.

We can note that the preloading of the guidewire through the small fenestration during graft modification allows a step less during the procedure and is time saving. Indeed, the catheterization of the fenestration can sometimes be tricky.

The through-and-through wire in the small fenestration permits an easy, secure, and precise alignment of the fenestration and the target vessel. An example with the LSA as target vessel:

The through-and-through wire has been used and the PMEG is placed in the aortic arch with the small fenestration proximal to the LSA. The markers of the fenestrations aligned.

The traction on the through-and-through wire tends to bring the wire to the inferior wall of the subclavian artery and pull the fenestration (and with it the PMEG) while delivering. During this maneuver, we noticed no ripping of the endograft nor lesion of the LSA.

There are several limitations of this case series. The outcomes highlights experience obtained in a single center and with only 6 patients. As there are only few patients with ARSA and moreover with symptomatic ARSA and/or KD, it is complicated to perform a prospective study. Even in 6 patients, different approaches were used as different ways to modify the endografts, making it harder to compare with other technics. However, it shows the great adaptability to each situation and the range of applications PMEGs induce.

Finally, even if the early results are quite encouraging, the mean follow-up is short (8 months) and should be continued.

Conclusion

The use of PMEGs for the treatment of pathological aortic arch in patients with ARSA and/or KD is an effective and reproducible alternative approach with a 100% technical success rate and 100% patency without endoleaks. It is associated with no mortality and low adverse events in short-term and midterm follow up. However, long-term follow-up is necessary to determine the durability of this technique.

Acknowledgments

I am grateful to all of those with whom I have had the pleasure to work during this and other related projects.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Author Contributions

The authors confirm contribution to the article as follows: L.C. contributed to study conception and design, C.B. contributed to data collection, C.B. and L.C-T. contributed to analysis and interpretation of results, and P.A., R.C., and K.H. contributed to draft manuscript preparation and reviewing. All authors reviewed the results and approved the final version of the manuscript.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Ethical Statement

The study was conducted according to the principles of the Helsinki II Declaration and informed consent was obtained from all patients. This study was approved by the local institutional review board (IRB No. 0001158), which is registered at the Office for Human Research Protections. When obtaining consent from patients, potential risks and benefits of PMEG and manufactured stent grafts were discussed in detail and without bias. Furthermore, the theoretical increased risk of infection associated with PMEG, the lack of standardization, and the lack of long-term data were clearly explained.


G Libourel

P Michel

M Delbo

C Ganino

A Recio-Blanco

P De Laverny

M E Zolensky

A N Krot

SEARCH FOR PRIMITIVE MATTER IN THE SOLAR SYSTEM

Introduction: Recent astronomical observations and theoretical modeling led to a consensus regarding the global scenario of the formation of young stellar objects (YSO) from a cold molecular cloud of interstellar dust (organics and minerals) and gas that, in some cases, leads to the formation of a planetary system. In the case of our Solar System, which has already evolved for ~4567 Ma, the quest is to access, through the investigation of planets, moons, cometary and asteroidal bodies, meteorites, micrometeorites, and interplanetary dust particles, the primitive material that contains the key information about the early Solar System processes and its evolution. However, laboratory analyses of extraterrestrial samples, astronomical observations and dynamical models of the Solar System evolution have not brought yet any conclusive evidence on the nature and location of primitive matter in the Solar System, preventing a clear understanding of its early stages.

As a statement of the obvious, the primitive matter in the Solar System being still unknown, it is difficult to define its signature, to identify where it is preserved in the Solar System, and what it is made of. Furthermore, the primitive matter is not defined in a unique way and there is currently no real convergence in the definition of primitive Solar System materials in closely related scientific fields of astronomy, astrochemistry, cosmochemistry, planetary science, and possibly astrobiology. These disciplines use different approaches: astronomy focuses on both observations and modeling of celestial objects, astrochemistry exploits radio observations of complex organics molecules in molecular clouds, cosmochemistry relies on meteorite and asteroid/comet sample analysis, planetary science investigates the evolution and properties of small bodies and planets, while astrobiology addresses more generally the question of whether life exists beyond Earth. Primitiveness is therefore a wide-ranging concept whose definition and scaling vary from one community to another with different tools and, therefore, different criteria.

Planetary scientists qualify as primitive the asteroids of taxonomic types D, P, T and of the taxonomic C-complex (Ch-, Cb-, C-, G-, B-, Cgh-types) because their reflectance spectra and their low albedo values are consistent with those of carbonaceous chondrites, although the generally featureless spectra of these objects permit alternative interpretations. Collisional studies and analyses of astronomical observations indicate that some of these asteroids may be rubble piles that endured collisions and re-accumulation. Thus, these bodies, which possibly mixed and endured major structural changes, cannot be considered primitive by themselves. However, although these small bodies have been repeatedly destroyed and reformed, the intensity of the chemical, thermal, and physical processes they underwent may still be weak and/or localized enough to preserve some primitive matter within them.

Results: We propose that the evolution the Solar System should be instead described based on the physical processes in action through time and at the different spatial scales rather than using (supervised) classification techniques. By analogy with stellar and galactic physics in which automated parameterizations are considered for stars, we define primitive matter in our Solar System through a parameterization scheme based on the amount and intensity of processes the matter underwent since its delivery to or its formation in the Solar System instead of defining it on the basis of its age only. Of course at some point, the time of formation comes into play, but first, the matter considered the most primitive in terms of a specific process should show little evidence for subsequent modification by other processes. The selected parameters are those involved in a canonical view of YSO formation and evolution towards planetary systems based on the current understanding of processes and transformations of solids and gases in the early Solar System . These include (i) irradiation from the young Sun, (ii) evaporation and gas-solid condensation, (iii) dust agglomeration, (iv) melting of dust agglomerates during transient heating events (e.g., shock waves, current sheets, etc.), (v) accretion of thermally processed and unprocessed solids and ices into pebble-and planetesimal-sized bodies, (vi) core-mantle differentiation, (vii) thermal metamorphism and aqueous alteration, and to some extent (viii) regolith formation and space weathering. In this order, these processes and transformations define different levels of primitiveness with respect to the primordial (thermally unprocessed in the Solar System) protosolar molecular cloud matter. The fact that a given process may have occurred once or several times and in differ-ent environments (e.g., hot/cold, dry/wet, low/high energy) does not count for our purpose. Other processes like extrasolar irradiation, extrasolar grain implantations, low and moderate energy impacts and, to a certain extent, regolith formation and space weathering are not considered here as discriminating criteria as they could occur along the entire lifetime of our Solar System, and are not expected to modify the material properties in a way that may alter its primitiveness. This approach allows us to define in a new way the level of primitiveness intrinsic to our Solar System (Table 1). The most primitive is not necessarily the oldest, as usually considered, but the least affected in the number or kind of processes it underwent inside the limit of our Solar System. Accordingly, some old objects/matter may be primitive, but some other old objects/matter may not be, on this basis. Conversely, some younger objects/matter may still be primitive, on this same basis. For instance, the second largest asteroid (4) Vesta is the likely source of howarditeseucrites-diogenites (HEDs) meteorites, and has thus experienced melting and differentiation processes that drastically altered the composition of its original components. Although (4) Vesta accreted very early in the Solar System history, its matter cannot be considered primitive as a whole, while other smaller carbonaceous and/or undifferentiated asteroids may be more primitive despite being accreted later (Table 1).

Discussion: Though perfectible, this new parameterization scheme of primitiveness in our Solar System already presents several advantages. i) It is a relative scale that takes into consideration the wide-ranging concept of primitiveness, and that can be used by vari-ous communities involved in this quest about the origins of our Solar System. ii) It allows us to rank the primitiveness of any celestial objects and of the matter they are made of on a same scale. iii) It establishes new criteria for studying the evolution of the primitive object or matter, which may or may not be related to its age. iv) It permits avoiding some contradictions, such as the fact that carbonaceous chondrites or C-type asteroids are commonly called "primitive", in the usual definition, and yet most of them are probably not primitive as a whole, even if some of their material is primitive, justifying that they are good candidates to sample primitive material. v) It avoids the investigation of the early evolution of the Solar System to be limited by the analytical precision related to radiometric ages, and by isotope heterogeneity at a specific time in the Solar System.

Conclusion:

We show that neither the age of an object, nor its mineralogy is discriminant enough for revealing its primitiveness, and propose a new parameterization scheme based on the processes the matter underwent since its delivery to the Solar System [1]. By ranking celestial objects and their constituents, two antagonistic sources of primitive materials in the protoplanetary disk emerge, one close to the Sun resulting from evaporation, condensation and melting of the protosolar molecular cloud dust followed by accretion into asteroidal bodies, and the other at large heliocentric distances resulting from agglomeration of the protosolar and solar dust into cometary bodies, the latter reservoir remaining poorly sampled so far.

Reference:

  [1] Libourel et al. (2017) Icarus, 282, 375-379.

Table 1 :

 1 Example of chronological sequence of processes experienced by selected extraterrestrial objects ranked according to their inferred primitiveness. G.L., P.M. and M.D. acknowldegde support from the French Space Agency CNES.