Marie Naudot

Alejandro Garcia Garcia

Nicolas Jankovsky

Anaïs Barre

Luciane Zabijak

Zakaria Soufiane

Louison Azdad

Fahmi Collet

Anne Bedoui

Guy Hébraud

Schlatter

The combination of a poly-caprolactone/nano-hydroxyapatite honeycomb scaffold and mesenchymal stem cells promotes bone regeneration in rat calvarial defects

Keywords:

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1

The combination of a poly-caprolactone/nanohydroxyapatite honeycomb scaffold and mesenchymal stem cells promotes bone regeneration in rat calvarial defects Running title : PCL-nHA honeycomb scaffold with MSCs promotes bone regeneration in vivo Marie Naudot 1 , Alejandro Garcia Garcia 2 , Nicolas Jankovsky 3 , Anaïs Barre 1 , Luciane Zabijak 4 , Soufiane Zakaria Azdad 5 , Louison Collet 3 , Fahmi Bedoui 6 , Anne Hébraud 7 , Guy Schlatter 7 , Bernard Devauchelle 1,8,9 , Jean-Pierre Marolleau 3,10 , Cécile Legallais 2 , Sophie Le

Introduction

Over the last few decades, tissue-engineered bone substitutes have been developed as alternatives to autografts and allografts; bone grafts are often only available in limited quantities, and are associated with a risk of donor site morbidity and infection. The use of an appropriate biomaterial-based scaffold is crucial for accurately restoring, maintaining and improving the bone tissue regeneration process in space and time. The scaffold has to provide an architectural blueprint for cell regeneration and must possess osteoconductive, osteoinductive and/or osteointegration properties. A number of efficient scaffolds have been developed from natural or synthetic polymers and ceramics. The most commonly used synthetic polymers are poly (α-hydroxyesters) such as poly(ε-caprolactone) (PCL), polylactic acid and poly(lactic-co-glycolic) acid (PLG). The poly (α-hydroxyesters)' architecture (porosity, degradability, and pore size) and mechanical properties can be tailored for specific applications, including bone tissue engineering [START_REF] Borden | Structural and human cellular assessment of a novel microsphere-based tissue engineered scaffold for bone repair[END_REF][START_REF] Mankani | In Vivo Bone Formation by Human Bone Marrow Stromal Cells: Effect of Carrier Particle Size and Shape[END_REF][START_REF] Yao | Electrospun Poly(-glutamic acid)/-Tricalcium Phosphate Composite Fibrous Mats for Bone Regeneration[END_REF]. Although PCL has a slow biodegradation rate and a high osteointegration capacity [START_REF] Rao | Natural and Synthetic Polymers/Bioceramics/Bioactive Compounds-mediated Cell Signaling in Bone Tissue Engineering[END_REF], it suffers from a lack of biological functionality at the scaffoldcell interface. Hence, PCL is typically combined with other natural or synthetic polymers and/or with ceramics [START_REF] Shor | Precision extruding deposition (PED) fabrication of polycaprolactone (PCL) scaffolds for bone tissue engineering[END_REF][START_REF] Xu | Surface functionalization of polycaprolactone films via surface-initiated atom transfer radical polymerization for covalently coupling celladhesive biomolecules[END_REF]. Bioceramics like hydroxyapatite (HA) and tricalcium phosphate (TCP) have been widely used in bone repair, in view of their chemical similarity to bone. In particular, HA mechanically reinforces other polymers and improves the scaffold's osteoconductive and osteoinductive properties [START_REF] Dorozhkin | Bioceramics of calcium orthophosphates[END_REF][START_REF] Zhang | Three dimensional printed macroporous polylactic acid/hydroxyapatite composite scaffolds for promoting bone formation in a critical-size rat calvarial defect model[END_REF]. Three-dimensionally printed and electrospun scaffolds made from appropriate materials therefore appear to be highly promising tools for bone regeneration, due to their ability to mimic the native extracellular matrix environment via their morphology, surface modification, and/or bulk incorporation of biomolecules [START_REF] Leijten | From Nano to Macro: Multiscale Materials for Improved Stem Cell Culturing and Analysis[END_REF][START_REF] Ye | Three-dimensional electrospun nanofibrous scaffolds displaying bone morphogenetic protein-2-derived peptides for the promotion of osteogenic differentiation of stem cells and bone regeneration[END_REF]. Electrospinning techniques can produce nano-or microfibers by applying a high potential voltage difference between a liquid polymer and a collecting target.

Oriented or structured nanofiber mats can be prepared by adjusting the direction of the electric field and micropatterning the collector [START_REF] Criscenti | 3D screening device for the evaluation of cell response to different electrospun microtopographies[END_REF][START_REF] Yang | Electrospinning of nano/micro scale poly(L-lactic acid) aligned fibers and their potential in neural tissue engineering[END_REF].

Researchers have reported that such structured electrospun polymer nanofibers can induce cell differentiation in vitro, which suggests that applications in bone tissue engineering are possible [START_REF] Baudequin | The Osteogenic and Tenogenic Differentiation Potential of C3H10T1/2 (Mesenchymal Stem Cell Model) Cultured on PCL/PLA Electrospun Scaffolds in the Absence of Specific Differentiation Medium[END_REF][START_REF] Brennan | 3D cell culture and osteogenic differentiation of human bone marrow stromal cells plated onto jet-sprayed or electrospun micro-fiber scaffolds[END_REF]. Recently, more complex, bioinspired multi-layered composite scaffolds have been produced by electrospinning/electrospraying on micropatterned collectors thanks to an electrostatic template assisted deposition (ETAD) process [START_REF] Nedjari | Electrospun Honeycomb as Nests for Controlled Osteoblast Spatial Organization[END_REF]. When using honeycomb micropatterned collectors, the resulting scaffolds with controlled pore size mimic the hemi-osteon structure [START_REF] Nedjari | Electrospun Honeycomb as Nests for Controlled Osteoblast Spatial Organization[END_REF]. A PCL scaffold integrating HA nanoparticles with a honeycomb macrostructure (referred to henceforth as a "honeycomb PCL-nHA scaffold") proved to be biocompatible, osteoconductive and osteoinductive in vitro using the C3H10 cell line and organotypic culture [START_REF] Garcia | Poly(ε-caprolactone)/hydroxyapatite 3D honeycomb scaffolds for a cellular microenvironment adapted to maxillofacial-bone reconstruction[END_REF] has not yet been tested in vivo.

In bone tissue engineering, the cellular component is usually composed of stem cells. When seeded into a scaffold, these cells have crucial roles by secreting growth factors and/or by directly differentiating into the desired osteogenic cell type [START_REF] Alford | Extracellular matrix networks in bone remodeling[END_REF][START_REF] Zhang | The potential of human fetal mesenchymal stem cells for off-the-shelf bone tissue engineering application[END_REF]. Mesenchymal stem cells (MSCs) are multipotent stromal cells present in most adult connective tissues and most neonatal tissues. The most commonly used MSCs are isolated from the bone marrow (BM), adipose tissue or dental pulp [START_REF] Chamieh | Accelerated craniofacial bone regeneration through dense collagen gel scaffolds seeded with dental pulp stem cells[END_REF][START_REF] Chen | Mesenchymal stem cell sheets: a new cell-based strategy for bone repair and regeneration[END_REF]. The MSCs are able to differentiate into multiple cell types, including osteoblasts, chondroblasts and adipocytes in particular [START_REF] Oryan | Role of Mesenchymal Stem Cells in Bone Regenerative Medicine: What Is the Evidence ?[END_REF][START_REF] Sousa | Human adult stem cells from diverse origins: an overview from multiparametric immunophenotyping to clinical applications[END_REF]. These cells are known to release cell survival and proliferative factors and to have immunomodulatory properties-thus controlling inflammation and modifying nearby immune cells [START_REF] Kiernan | The Immune Response to Allogeneic Differentiated Mesenchymal Stem Cells in the Context of Bone Tissue Engineering[END_REF]. The positive effect of adding MSCs to a PCL scaffold on bone regeneration has already been demonstrated in (for example) a rabbit knee defect model (with a PCL-TCP scaffold) [START_REF] Shao | Repair of Large Articular Osteochondral Defects Using Hybrid Scaffolds and Bone Marrow-Derived Mesenchymal Stem Cells in a Rabbit Model[END_REF], a rat calvarial defect model (with a PLG-HA scaffold) [START_REF] Orbay | The Effects of Adipose-Derived Stem Cells Differentiated Into Endothelial Cells and Osteoblasts on Healing of Critical Size Calvarial Defects[END_REF], and a porcine critical-size bone defect model (with a PCL-TCP/HA scaffold) [START_REF] Jensen | Dental pulp-derived stromal cells exhibit a higher osteogenic potency than bone marrow-derived stromal cells in vitro and in a porcine critical-size bone defect model[END_REF].

In the present study, we investigated the osteocompatibility, osteoconductive and osteoinductive properties of a honeycomb PCL-nHA scaffold seeded (or not) with rat BMderived MSCs (BM-MSCs) in a rat calvarial defect (Figure 1).

We first analyzed the in vitro adhesion and viability of BM-MSCs seeded on the scaffold. In vivo bone regeneration in calvarial defects was then assessed using micro-computed tomography (μ-CT) after 2, 4, 6 and 8 weeks of implantation of the honeycomb PCL-nHA with or without BM-MSCs, and at 8 weeks (the end of experiment) using histological techniques. Our experimental protocol enabled us to evaluate the respective effects of the biomaterial itself (compared with the empty space that nevertheless follows a healing process) and the additional presence of BM-MSCs seeded prior to implantation.

Materials and methods

Synthesis of the PCL honeycomb by electrospinning and electrospraying

A 6% electrospinning solution of PCL (molecular weight=80 kg.mol -1 , Sigma Aldrich, France) was obtained by dissolving the polymer in dichloromethane (Sigma-Aldrich) and N,N-dimethylformamide (ReagentPlus Sigma-Aldrich) (70/30 v/v) for 24 h. A 10% by weight HA nanopowder (Sigma-Aldrich, ref 677418) with a particle size ≤200 nm was prepared in ethanol (Sigma-Aldrich) 48 h before electrospraying. The obtained nHA solution was ultrasonicated for 5 min (Branson Sonifier, Switzerland) just before the deposition.

We used a custom vertical electrospinning device comprising a 18G needle connected to a Spellman SL 10 high voltage supply , a syringe pump and a rotating collector (100 rpm) within which a honeycomb micropattern collector was fixed. The micropattern has been described previously [START_REF] Nedjari | Electrospun Honeycomb as Nests for Controlled Osteoblast Spatial Organization[END_REF]. The mean diameter of the honeycomb cavities was 160 µm, and the honeycomb walls were 20 µm wide and 60 µm high. Thirteen layers of PCL (flow rate: 1.5 ml/h; needle-collector distance: 18 cm; voltage: 25 kV) and 13 layers of nHA (flow rate: 0.6 ml/h; needle-collector distance: 15.5 cm; voltage: 25 kV) were deposited alternately, as described previously [START_REF] Garcia | Poly(ε-caprolactone)/hydroxyapatite 3D honeycomb scaffolds for a cellular microenvironment adapted to maxillofacial-bone reconstruction[END_REF] (Figure 1A). After processing, the resulting membrane was peeled off from the honeycomb micropattern collector, transferred into 6-well inserts (diameter: 12 mm; no membrane, Costar, Corning, France), sterilized in 70% ethanol for 1 h, and then rinsed three times with phosphate-buffered saline (PBS, Sigma-Aldrich).

Isolation and culture of rat BM-MSCs

Mesenchymal stem cells were harvested from 12-week-old male Sprague-Dawley rats (Janvier Labs, France). The femurs were dissected and the BM was flushed with Eagle's minimum essential medium alpha modification (αMEM, Sigma-Aldrich) supplemented with 10% fetal bovine serum (Eurobio, France), 2 mM L-glutamine (Eurobio), 100 U/ml penicillin, 100 pg/ml streptomycin (both from Eurobio), and 250 ng/mL amphotericin B (Gibco, France).

The cell suspension was transferred into 6-well cell culture plates and cultured in a humidified 5% CO 2 atmosphere at 37°C. Thereafter, the medium was replaced twice a week to remove non-adherent cells and refresh the culture. Once 80% confluence had been reached (typically after 7 to 10 days), cells were detached (using 0.25% trypsin) and replated in T175 flasks (Sigma-Aldrich).

Phenotyping of rat BM-MSCs

Cultured cells were harvested, suspended in PBS, and phenotyped using flow cytometry with FITC-conjugated anti-rat CD90, FITC-conjugated anti-rat CD45 antibodies or primary antibody IgG mouse anti-CD73 and then with the secondary PE-conjugated anti-mouse IgG antibody (all purchased from BD Pharmingen TM , BD Biosciences, France). Cells incubated with PE-conjugated or FITC-conjugated mouse IgG1 isotype antibodies (BD Biosciences) were used as negative controls. The cells were analyzed on a BD FACSCanto TM II (BD Biosciences) and the results were analyzed using FlowJo software (version 10, Tree Star, USA).

Cell seeding on the scaffold

In order to assess cell attachment on the honeycomb PCL-nHA scaffold, 1.2x10 6 BM-MSCs were seeded into scaffolds in inserts with culture medium and allowed to adhere for 24 hours at 37°C in a 5% CO 2 atmosphere. Subsequently, the medium was changed and non-adherent cells were removed. The inserts were examined under an SEM (Philips XL30 ESEM-FEG, FEI, The Netherlands). Scaffolds seeded (or not) with cells were cleaned with ethanol and coated with gold prior to observation. In order to evaluate cell viability in the honeycomb scaffold, the scaffolds were removed from the inserts and placed in a 24-well plate. One hour before the assay, the medium was replaced with αMEM medium containing Hoechst 33342 (2 µg/ml) and ethidium homodimer 1 (EthD-1, 4 µM) (both from ThermoFisher Scientific, France). The scaffolds were then rinsed with PBS and observed under a confocal microscope (Zeiss LSM 710, 20x, France).

2.5 Surgical procedures and graft preparation in the rat critical-sized calvarial bone defect model All procedures for animal experiments were evaluated and approved by the local animal care and use committee and by the French Ministry of Research (registration number: APAFIS 6019-2016070615199279). Twenty-two male Sprague-Dawley rats (8 weeks of age, body weight: ≈ 350g, Janvier Lab) were used. Twenty-four hours after cell seeding (or not), the scaffolds were grafted into a calvarial bone lesion. Rats were anesthetized by isofluorane inhalation (induction with 5% isofluorane and an airflow of 1L/min; 3% at 0.5 L/min thereafter; Isovet, Piramal HealthCare, UK). The scalps covering the calvarial vault were shaved, scrubbed with an antiseptic solution (Biseptine, Bayer Healthcare, France), and infiltrated with 0.1-0.5 ml of a local anesthetic (2% lidocaine, Lurocaïne, Vetoquinol, France). A sagittal skin incision was made over the calvarium, the soft tissues were raised, and the periosteum was dissected to expose the calvarial bone surface. A circular bone defect (diameter: 5 mm) was created on each side of the sagittal suture, using a diamond bur (Fig1.C). Honeycomb PCL-nHA scaffolds with BM-MSCs (in the scaffold+MSCs group of rats, n=11) or scaffolds alone (the scaffold group, n=11) were placed into the defects on the left side; the right side remained empty and served as a control (n=22). Next, the soft tissues were lowered and skin was closed with 5-0 braided absorbable suture (Vicryl 5/0, Ethicon, France). After surgery, analgesia was provided through subcutaneous injections of buprenorphine (0.05 mg/kg, Buprecare, Axience, France). The animals were housed 1 per cage for 2 weeks post-op and then 2 per cage. They had ad libitum access to water and chow, in an enriched environment. At the study end point (8 weeks after scaffold implantation), all animals were euthanized by overdose CO 2 inhalation. After skin dissection, the calvarium was removed and immediately fixed in 4% neutral buffered formalin (VWR, France).

In vivo µCT assessment and radiomorphometric analysis

Prior to each µCT assessment of bone regeneration, rats were anesthetized with isofluorane (induction at 5% and an airflow of 1 L/min, and then maintenance with 3% at 0.5 L/min). The animals were imaged using an X-ray µCT device (SKYSCAN 1176,; X-ray source: 65 kV, 380 µA, 1 mm Alu filter, and a 0.6° rotation step, Bruker, USA). Three-dimensional images were acquired with a maximum voxel size of 18 µm. An internal density phantom (calibrated in g/cm 3 of HA) was used to scale the bone density. The full 3D high-resolution raw dataset was obtained with a flat panel detector that moved 180° around the sample (scanning time: 5 min). Three-dimensional renderings were extracted from data frames using Dataviewer software (Bruker, USA). The amount of regenerated bone inside each defect was quantified using CTscan Analyser software (Bruker, USA). An overall volume of interest in the defect area was drawn by interpolating two-dimensional regions of interest on consecutive sections. This volume of interest comprised only the remodeled bone defect area. Overall thresholding was used to separate mineralized elements from background noise. We analyzed the bone mineral density (BMD, in g/cm 2 of HA) and the bone volume fraction (bone volume/tissue volume, BV/TV, expressed as a percentage). Three-dimensional images of bone were reconstructed with CTvox software (Bruker, USA).

Histological assessments

Harvested, fixed samples were immersed in Microdec EDTA A1 decalcification solution (Microm Microtech, France) for 4 days, dehydrated in graded ethanol solutions, embedded in paraffin, prepared as 3 µm sections, and stained with hematoxylin and eosin (H&E) reagent or Masson's trichrome reagent. The images were acquired using a Leica SCN 400 Slide Scanner (Leica, France).

Statistical analysis:

Quantitative variables were quoted as the mean ± standard deviation. The statistical significance of intergroup differences was probed in a one-way ANOVA test with Dunnett's post-test for multiple comparisons. The following thresholds for statistical significance were considered: *p<0.05, **p < 0.01, and *** p < 0.001. All statistical analyses were performed using GraphPad Prism software (version 6, GraphPad Software, USA).

Results

Characterization of rat BM-MSCs

Flow cytometry with antibodies against some specific markers commonly used to characterize human MSCs (namely CD90, CD73, and CD45) was realized to immunophenotype rat BM-MSCs. The latter were positive for CD90 (99.6%) and CD73 (54%) and negative for CD45

(5.36%) (Figure 2).

Adhesion and viability of BM-MSCs on the honeycomb PCL-nHA scaffold

In order to assess the behavior of BM-MSCs in contact with the matrix, cells were seeded on the honeycomb PCL-nHA scaffold for 24h and cultured. The spatial distribution and viability of BM-MSCs on honeycomb PCL-nHA scaffold were evaluated under the SEM (Figure 3

Bone remodeling processes in honeycomb PCL-nHA-filled defects

To evaluate in vivo the osteoconductive and osteoinductive properties of the honeycomb PCL-nHA scaffold seeded (or not) with BM-MSCs in calvarial defects, bone regeneration were assessed using µ-CT 2, 4, 6 and 8 weeks after implantation (Figure 4). In all groups, new bone emerged against the dura mater after two weeks, and an increase over time in bone regeneration was observed. The sagittal µCT views showed signs of bone bridging from the week 4 onwards, and bone bridging was more ample in the scaffold+MSCs group (as confirmed by coronal views). Under all conditions, bone reconstruction started at the margins and bottom of the defect and then became apparent in the center.

Irrespective of the condition, a quantitative analysis of bone regeneration by μ-CT revealed an increase in bone formation over time, with a plateau achieved at 6 weeks (Figure 5). At that time, we observed osteogenic activity with nearly complete closure of the defect and a bone volume fraction of approximately 80%.

At 2 weeks, the bone volume fraction was significantly greater in the scaffold+MSCs group than in the other two groups (Figure 5.A). At 4 weeks, we observed a slight increase of bone volume fraction in the scaffold+MSCs group (66.6 ± 12.4%) compare to the scaffold group (62.4 ± 11.2%, p=0.2831) that was significantly higher in comparison to the control group (55.4 ± 14%, p=0.0468) (Figure 5.B). Beyond 4 weeks, there were no significant intergroup differences. Irrespective of the condition, the BMD increased over time throughout the experimentdemonstrating the mineralization/maturation of newly formed bone (Figure 5.C). At all time points, the BMD was significantly higher in the scaffold+MSCs group than in the control group (Figure 5

.D).

A histological assessment revealed details of the tissue composition and bone formation in the defects (Figure 6).

In the control and scaffold groups, we observed disjointed bone formation and more fibrous connective tissue (visible as light green areas in the Masson's trichrome slides) in the defects (Figure 6.A). In defects filled with scaffold+MSCs, we observed greater bone mature regeneration and closure of the lesion. In all groups, we observed the typical structure of mature bone, with osteocytes (the yellow arrow in Figure 6.B) encased within bone substance and osteoblasts (the green arrow in Figure 6.B) at the borders. Vessels were visible under all conditions (black arrow). No residual material was seen within the defect region.

Discussion

Many novel biomaterials and tissue-engineered products for bone regeneration have been studied over the last decades. Electrospinning has been investigated as a means of producing a 3D matrix, with a porosity that is often limited in the absence of specific microstructuration.

Although most studies with electrospun biomaterials have been performed in vitro, some of the latest in vivo studies have given promising results in terms of bone regeneration in a calvarial defect model [START_REF] Wang | Bone remodelinginspired dual delivery electrospun nanofibers for promoting bone regeneration[END_REF][START_REF] Wu | Functionalization of silk fibroin electrospun scaffolds via BMSC affinity peptide grafting through oxidative self-polymerization of dopamine for bone regeneration[END_REF]. Several polymers can be used, and are frequently combined with a mineral material to enhance the matrix's osteopromotive properties. [START_REF] Garcia | Poly(ε-caprolactone)/hydroxyapatite 3D honeycomb scaffolds for a cellular microenvironment adapted to maxillofacial-bone reconstruction[END_REF] proved the in vitro value of a biomimetic structure inspired by the honeycomb structure of the osteons by combining PCL and nHA to promote the adhesion, proliferation and osteodifferentiation of the seeded cells. This scaffold had an elastic modulus of 4 MPa, which made it easy to handle and to shape into any form -as would be required in clinical practice.

In the present study, we first confirmed the in vitro biocompatibility of this honeycomb PCL-nHA scaffold seeded with rat BM-MSCs by analyzing cell adhesion, spatial distribution and viability. The cells completely covered the honeycomb PCL-nHA scaffold, and so there was no preference for a particular part of the honeycomb structure; this has previously been observed with C3H10T1/2 cells after 48 h of culture [START_REF] Garcia | Poly(ε-caprolactone)/hydroxyapatite 3D honeycomb scaffolds for a cellular microenvironment adapted to maxillofacial-bone reconstruction[END_REF]. This complete coverage could be explained by the honeycomb pattern's promotion of extracellular matrix synthesis and upregulation of type II collagen [START_REF] Eniwumide | The Morphology and Functions of Articular Chondrocytes on a Honeycomb-Patterned Surface[END_REF]. Alternatively, it might be due to the high seeding density -a strategy known to have delivering more cells while preserving the latter's viability and functions in vivo [START_REF] Ding | Increased stem cells delivered using a silk gel/scaffold complex for enhanced bone regeneration[END_REF].

We next assessed the scaffold's functional properties, i.e. its ability to promote new bone formation in a rat calvarial defect model. We created two defects per animal; one was filled with scaffold, and the other remained empty as a control. This protocol makes it possible to take into account inter-individual variability and thus increasing the statistical power.

Our µCT analysis of the defects at several time points enabled us to describe the time course of bone reconstruction. The honeycomb PCL-nHA scaffold appeared to have a significant effect on bone formation as early as the second week post-implantation, with a greater bone volume fraction and a greater BMD than in the no-scaffold control group. The bone volume fraction peaked at close to 80% at 6 weeks and remained stable at 8 weeks. This regeneration time course (a logarithmic curve) has already been described in the same rat model with a beta-TCP [START_REF] Chou | Bone regeneration of calvarial defect using marine calcareous-derived beta-tricalcium phosphate macrospheres[END_REF] and with nanogel-crosslinked materials [START_REF] Charoenlarp | The improvement of calvarial bone healing by durable nanogel-crosslinked materials[END_REF], although the investigators did not test cell-seeded scaffolds. In contrast, other studies have showed that bone reconstruction is linear (with a mean bone volume fraction of only 20% at 8 weeks) when 3D-printed PCL scaffolds were implanted in calvarial defects (Lee et al., 2019;[START_REF] Pae | 3D-printed polycaprolactone scaffold mixed with β-tricalcium phosphate as a bone regenerative material in rabbit calvarial defects[END_REF]. The disparities between our present results and the literature data might be due to differences in the materials' composition and/or architecture. To the best of our knowledge, a PCL electrospun scaffold (with or without seeded cells) has not previously been studied with µCT at several time points (rather than at sacrifice only). We confirmed that the honeycomb PCL-nHA scaffold was osteoinductive in vivo, and that it becomes involved in the bone regeneration process soon after implantation.

As reported previously [START_REF] Chamieh | Accelerated craniofacial bone regeneration through dense collagen gel scaffolds seeded with dental pulp stem cells[END_REF][START_REF] Jensen | Dental pulp-derived stromal cells exhibit a higher osteogenic potency than bone marrow-derived stromal cells in vitro and in a porcine critical-size bone defect model[END_REF][START_REF] Orbay | The Effects of Adipose-Derived Stem Cells Differentiated Into Endothelial Cells and Osteoblasts on Healing of Critical Size Calvarial Defects[END_REF], bone regeneration was enhanced when the scaffolds were seeded with MSCs. Our in vivo densitometry data evidenced a significantly greater bone volume fraction in the defect for the scaffold+MSCs group (compared with the control group) 2 and 4 weeks after implantation. Furthermore, the BMD in the scaffold+MSCs group was higher than the control value through the experiment. However, the quantitative bone tissue regeneration observed in scaffold+MSCs group did not differ significantly from that observed with the scaffold alone.

A histological assessment confirmed the µCT results; there was more bone tissue in scaffold+MSCs group, and the junction had closed completely. Hence, the addition of MSCs to a honeycomb PCL-nHA scaffold appeared to accelerate the bone healing process by increasing bone synthesis and mineralization.

It is thought that MSCs act through both direct bone formation and indirect paracrine effects that promotes extracellular matrix deposition and angiogenesis [START_REF] Yagyuu | Unique and reliable rat model for the assessment of cell therapy: bone union in the rat mandibular symphysis using the bone marrow stromal cells[END_REF]. In our experiments, we could not identify the origin of the cells in the new bone structures, since the BM-MSCs were isolated from syngeneic rats of the same sex. Hence, we cannot conclude whether the observed bone formation was attributable to paracrine/trophic effects and/or the direct engraftment of transplanted cells.

The ideal biodegradable material should provide sufficient support for cell adhesion while leaving space for tissue growth [START_REF] Kwon | Bone regeneration by means of a three-dimensional printed scaffold in a rat cranial defect[END_REF][START_REF] Zhang | Three dimensional printed macroporous polylactic acid/hydroxyapatite composite scaffolds for promoting bone formation in a critical-size rat calvarial defect model[END_REF]. Indeed, the growth of newly formed bone is limited by the initially available space and the scaffold's degradation rate. Degradation of the material is required for complete bone healing. For example, Seol et al. observed greater bone tissue regeneration with a printed HA/TCP template than with a more slowly degrading printed HA template [START_REF] Seol | Improvement of bone regeneration capacity of ceramic scaffolds by accerelated release of their calcium ions[END_REF]. In the present study, the μ-CT parameters did prevented us from detecting the honeycomb PCL-nHA scaffold and thus from evaluating its rate of degradation over time. However, given that the mean ± SEM thickness of our honeycomb PCL-nHA scaffold was 31 ± 5μm, [START_REF] Garcia | Poly(ε-caprolactone)/hydroxyapatite 3D honeycomb scaffolds for a cellular microenvironment adapted to maxillofacial-bone reconstruction[END_REF] we can assume that it did not fill the bone defect (500 µm in thickness). Hence, the scaffold left space for bone synthesis, which might have contributed to the rapid bone construction (with a bone volume fraction of more than 80% after 8 weeks) relative to most of the scaffolds tested in the same model [START_REF] Chamieh | Accelerated craniofacial bone regeneration through dense collagen gel scaffolds seeded with dental pulp stem cells[END_REF][START_REF] Chen | Mesenchymal stem cell sheets: a new cell-based strategy for bone repair and regeneration[END_REF][START_REF] Orbay | The Effects of Adipose-Derived Stem Cells Differentiated Into Endothelial Cells and Osteoblasts on Healing of Critical Size Calvarial Defects[END_REF][START_REF] Son | In vitro and in vivo evaluation of electrospun PCL/PMMA fibrous scaffolds for bone regeneration[END_REF][START_REF] Wang | Bone remodelinginspired dual delivery electrospun nanofibers for promoting bone regeneration[END_REF][START_REF] Wu | Functionalization of silk fibroin electrospun scaffolds via BMSC affinity peptide grafting through oxidative self-polymerization of dopamine for bone regeneration[END_REF][START_REF] Zhang | Three dimensional printed macroporous polylactic acid/hydroxyapatite composite scaffolds for promoting bone formation in a critical-size rat calvarial defect model[END_REF]. Moreover, we did not observe PCL fibers on the histological sections. In the same model, [START_REF] Son | In vitro and in vivo evaluation of electrospun PCL/PMMA fibrous scaffolds for bone regeneration[END_REF] demonstrated the osteoconductive properties of an electrospun PCL/poly(methylmethacrylate) scaffold. At the end point (8 weeks), they observed the presence of PCL fibers. We hypothesize that this disparity is due to two parameters: (i) the diameter of the fibers, with a mean value of 2 μm in Son et al.'s scaffold, vs. 145 ± 39 nm in our scaffold [START_REF] Garcia | Poly(ε-caprolactone)/hydroxyapatite 3D honeycomb scaffolds for a cellular microenvironment adapted to maxillofacial-bone reconstruction[END_REF], and (ii) the very slow degradation of poly(methylmethacrylate) [START_REF] Son | In vitro and in vivo evaluation of electrospun PCL/PMMA fibrous scaffolds for bone regeneration[END_REF], which is slower than that of HA nanoparticles. In view of the results obtained here, we considered that our honeycomb PCL-nHA scaffold provided sufficient support for cell adhesion and colonization and also left sufficient space for bone growth.

Overall, the scaffold's structure, composition and combination with BM-MSCs accelerated the bone regeneration process. However, the scaffold's mechanical properties in vivo remain to be determined. It would be interesting to evaluate the scaffold's bone regeneration capacity in a context of mechanical stress, such as animal models of mandibular or tibia defects.

Conclusion

We demonstrated the in vitro and in vivo biocompatibility and osteoconductive properties of an electrospun/electrosprayed honeycomb PCL-nHA scaffold. When implanted in a rat calvarial defect, the scaffold exhibited osteoinductive activity and thus promoted new bone formation. The honeycomb PCL-nHA scaffold accelerated the bone regeneration process during the immediate post-implantation period. The combination of honeycomb PCL-nHA scaffold and BM-MSCs significantly improved bone regeneration and bone mineralization in particular. This biomimicry-based MSC-seed scaffold appears to be a promising candidate for healing/repairing clinically relevant large craniofacial bone defects.

Finally, we acknowledge the contribution of the physico-chemical analysis platform at UTC (Frédéric Nadaud and Caroline Lefebvre), for confocal and SEM analysis.

  , CHIMERE. Jules Verne University of Picardie, Amiens, France 2: UMR 7338, BMBI. CNRS, University of Technology of Compiegne, Compiegne, France 3: EA4666, HEMATIM. Jules Verne University of Picardie, Amiens, France 4: Plateforme ICAP. Jules Verne University of Picardie, Amiens, France 5: Department of Pathology and Cytology, Amiens University Medical Center, Amiens, France 6: Laboratoire Roberval, FRE CNRS 2012, University of Technology of Compiegne, Compiegne, France 7: ICPEES UMR 7515. CNRS, University of Strasbourg, Strasbourg, France 8: Department of Maxillofacial Surgery, Amiens University Medical Center, Amiens, France 9: Facing Faces Institute, Amiens, France, 10: Department of Hematology, Amiens University Medical Center, Amiens, France

  .A, 3.B) and the fluorescence microscope, respectively (Figure 3.C-E). Scanning electron microscopy revealed that the scaffold was completely covered by several layers of cells (Figure 3.B). Indeed, the scaffold's honeycomb structure was no longer visible. The cells filled the cavities and also settled on the walls. Cell viability was assessed by Hoechst 33342 staining for total cells and EthD-1 staining for dead cells (Figure 3.C-E). Only a few dead cells were observed, and the estimated viability was 95%. Nuclear fluorescence also testified to complete occupation of the honeycomb PCL-nHA scaffold by BM-MSCs (Figure 3.C).

Figure 1 .

 1 Figure 1. The experimental protocol. The honeycomb PCL-nHA scaffold was produced by alternating electrospun PCL fiber layers (steps 2k-1 for k=1 to 7) and electrosprayed HA nanoparticle layers (steps 2k for k=1 to 6) (A). After the cells had been cultured for 24h, the MSCs' adhesion and viability were analyzed using fluorescence microscopy and scanning electron microscopy (SEM) (B). Honeycomb PCL-nHA scaffolds with or without BM-MSCs were engrafted into a calvarial bone lesion on one side of the body; the contralateral lesion remained empty and served as a control (C). Bone regeneration was analyzed using µCT after 2, 4, 6 and 8 weeks of implantation (D). The red frames delimit the areas analyzed (cf. Fig 4).After 8 weeks, the part of the skull containing the defects was recovered for histological assessment (E).

Figure 2 .

 2 Figure 2. Phenotyping of rat BM-MSCs. The expression of three cell surface markers associated with the MSC phenotype in humans (CD90, CD73, and CD45) was investigated

Figure 3 .

 3 Figure 3. Spatial distribution and viability of BM-MSCs seeded on a scaffold before implantation. Scanning electron micrographs of a honeycomb PCL-nHA scaffold with no cells (A) and one seeded with BM-MSCs (B). Scale bar in A and B: 100 µm. Fluorescence staining of BM-MSCs with Hoechst 33342 (blue) and EthD-1 (red) on a scaffold (C), the transmitted light image (D), and the merged images (E). Scale bar in C-E: 50 µm.

Figure 4 .

 4 Figure 4. Micro-CT of calvarial defects in the control, scaffold and scaffold+MSCs groups at 2, 4, 6 and 8 weeks post-implantation. For each condition, the left panel shows a sagittal view of the defect and the right panel shows a coronal view. Scale bar: 1 mm.

Figure 5 .

 5 Figure 5. Quantitative analysis of bone generation in the defect at 2, 4, 6 and 8 weeks, as evaluated by the bone volume fraction (the BV/TV ratio in %) (A, B) and the BMD (in g/cm 2 ) (C, D). *p < 0.05; **p < 0.01; ***p < 0.001.

Figure 6 .

 6 Figure 6. Representative histologic images of calvarial defects eight weeks after implantation in the control, scaffold and scaffold+MSCs groups (H&E staining on the left and Masson's trichrome staining on the right) (A). Scale bar = 1mm. A higher-magnification view of H&E stained sections from the control (1), scaffold-only (2) and scaffold+MSCs groups (3) (B), black arrow: vessel; green arrow: osteoblast; yellow arrow: osteocyte. Scale bar = 100 µm.

Acknowledgment

This research was funded by the French government via the "Investments for the Future" program (managed by the National Research Agency; reference: ANR-11-IDEX-0004-02), and by the Region Hauts de France (the INTIM project). We thank Sabine Siegwald for fabricating the micropatterned collectors at the STnano cleanroom facility (University of Strasbourg, Strasbourg, France). We also thank Julie Le Ber and Anaïs Jovelet (PlatAnN animal facility, Jules Verne University of Picardie, Amiens, France) for assistance with animal experiments, and Paulo Marcelo (ICAP cell engineering and protein analysis facility, Jules Verne University of Picardie, Amiens, France) for assistance with µCT. A. Hébraud and G. Schlatter thank the financial support of the project ANR MimHeart (ANR-15-CE08-0010).

Conflict of interest

The authors declare that they have no competing or commercial interests.

Authors


Hannes Zschiesche
email: hannes.zschiesche@im2np.fr

Ahmed Charai

Dominique Mangelinck

Claude Alfonso

A Charaï

Ti segregation at CoSi grain boundaries

Keywords: Cobalt disilicide, Ti excess at CoSi 2 grain boundary, Atom probe tomography, Transmission electron microscopy

come

Introduction

CoSi 2 films on Si substrates are widely used in microelectronic applications as contact material beside TiSi 2 and NiSi films, depending on the scale. Low electrical resistivity, high thermal stability and the good match of the crystal structure with Si are the main advantages of CoSi 2 [1]. The aim of the intro-5 duction of a Ti interlayer between the Co film and the Si substrate was to grow CoSi 2 as a single crystal in epitaxy on Si(100) or Si(111) by sputtering deposition and reactive diffusion [2].

The role of the Ti interlayer during the phase formation has been investigated and explanations were proposed. Two possibilities are considered: a) the reduction of native oxide on the silicon substrate b) the formation of a Ti rich phase acting as a diffusion or reaction barrier. Both possibilities should provide homogeneous diffusion and phase formation. The influence of parameters such as the deposition of an alloy instead of a bilayer [3], the substrate orientations [4], annealing environments [5], annealing temperatures [6], thickness of the Ti interlayer or the Co layer [7] or other elements for the interlayer [8] have been investigated to get a better understanding and a better process. The influence of a Ti capping layer instead of a Ti interlayer was also reported [9,10]. The Ti capping layer induced an increase of the nucleation temperature of CoSi 2 as well as a preferred texture in comparison to the growth without capping Ti. These effects can be explained by the diffusion of Ti from the capping layer to the interface.

As Ti is only slightly soluble in CoSi 2 , it was assumed that Ti has to be present in the grain boundaries (GBs) after the formation of CoSi 2 . However, to the best knowledge of the authors, the presence of Ti at the GBs after the formation of CoSi 2 has not been shown yet.

Atom probe tomography (APT) enables to detect single atoms and to reconstruct them in 3D volumes with atomic resolution. It allows to quantify tiny excess (number of atoms per unit area [11]) of elements at 2D structures such as GBs or interfaces [12]. An excess of elements can origin from strain fields induced by defects [13] as they are present on GBs. The combination of APT and transmission electron microscopy (TEM) is a powerful method to compare excess of elements with structural defects [14].

The aim of this work is the chemical investigation of CoSi 2 GBs by APT. The structure at different GBs is analyzed by TEM. A comparison of the determined Ti excess at GBs and the defect density estimated from high resolution transmission electron microscopy (HRTEM) investigations will be discussed.

Materials and Methods

Si(111) wafers have been immersed in a 5 % dilute HF for 1 min to remove native oxide before load in the sputtering system. Successive deposition of 5 nm Ti and 100 nm Co from two individual targets of Ti and Co (both 99.99 % purity) has been done by magnetron sputtering. The deposition was performed with a base pressure of about 10 -8 Torr using 99.9999 % pure Ar gas flow of 6.7 sccm at room temperature. Thermal annealing were performed in vacuum up to 850 • C to fully transform the as-deposited bilayer film into CoSi 2 .

X-ray diffraction (XRD) measurements (here not shown) performed in the Bragg-Brentano geometry, with a 1.5 • offset to avoid the signal from the substrate, show the presence of CoSi 2 with a strong peak of the (111) orientation and minor peaks of further orientations. TEM lamellas and APT tips have been prepared using a focused ion beam (FIB) FEI Helios 600. APT measurements were performed on a LEAP 3000 HXR. Voltage mode at 40 K, 200 kHz, 20 % pulse fraction and 0.2 % detection rate was applied in order to get optimal information in the compromise of resolution and volume size. IVAS software was used for the reconstruction following the common procedure [15,16]. TEM has been performed on a TECNA Ï G20 for microstructure investigations and energy dispersive X-ray spectroscopy (EDS) analysis and on a C s -corrected TI-TAN 80-300 equipped with a GIF Tridiem 863. The acceleration voltage was always chosen to be 200 kV. However, the comparison of the excess concentration at a GB is only semiquantitative. The spatial resolution in the APT is not isotropic and thus experimental broadening due to different spatial resolution can occur depending on the orientation of the grain boundary inside the APT tip volume. This can change the local excess concentration of identical grain boundaries. In contrast, the determination of the excess number of atoms projected on the GB plane allows a more quantitative comparison as it is not affected by anisotropic effects [11]. The value of the Ti excess at the GB can be specified as the number of atoms per unit area. Thus, experimental broadening of the GB plane has no influence on the excess quantity.

Results

APT

The accumulation of Ti atoms over the accumulation of all atoms along the z-axis of the cylinder is shown in the integral profile (Figure 2b). For a constant concentration, as seen in the grains, a linear behavior is verified: the concentration is determined from the slope of the fit. The Ti concentration in the grains is about 0.2 at %. The offset between the two slopes of the grains at the GB corresponds to the Ti excess at the analyzed GB area (red line). In this example it is determined to 415 atoms integrated over the base area of the cylinder.

Dividing the number of atoms by the base area of the cylinder gives the value of Ti excess at the GB per unit area. The same procedure was applied for the three different GBs from figure 1 and the Ti excess is visualized in figure 3. The Ti excess is significantly different for the three investigated GBs. 5). They have the ( 202) planes in common. Thus, the rotation axis is perpendicular to the ( 202) planes. Furthermore, the GB plane is aligned close to the ( 202) planes and so the rotation axis is almost perpendicular to the GB 110 plane. That identifies a main twist GB character. The misorientation of the two zone axis is 54.7 • . Figure 5b is the Bragg-filtered image of the ( 202) planes.

TEM

Defects in the ( 202) planes can be found and are highlighted. The distance is about 11.6 nm. Their origin is in the mismatch of the planes perpendicular to the GB plane. In parallel to the viewing direction these are the ( 24 2) planes for the grain on the left side of the figure and the (20 2) planes for the grain on the right side of the figure (normal vectors of planes indicated in figure 5b). EDS, energy-filtered transmission electron microscopy (EFTEM) and scanning transmission electron microscopy (STEM) electron energy loss spectroscopy (EELS) have been applied in order to investigate the presence of Ti at the GBs directly in TEM (not shown). However, no Ti excess was detected at different GBs. Since the APT results of section 3.1 show a systematic enrichment of Ti on GBs, the local concentration variation of Ti should be under the detection limit of these analytical TEM techniques and the combination of TEM and APT is crucial for this investigation.

Discussion

The values of Ti excess at CoSi 2 GBs investigated by APT determine a number of atoms per unit area. In the Gibbs approach, it is assumed that all the excess atoms are located on the GB plane with no thickness. The sharp peak at the GB in the concentration profile of figure 2a justifies that assumption.

The FWHM is about 1.5 nm and can be explained by experimental broadening. Furthermore, the defects in the GB plane can be energetically favorable positions for Ti atoms, as seen for other material system with excess on defects [13].

Thus, it is of interest to estimate a defect density per unit area on the GBs from the TEM investigations and compare them with the Ti excess.

Figure 4 shows that the distance between the defects along a low angle GB plane is about d dislo = 3.5 nm. Low angle tilt GBs are well described by edge dislocations parallel to the rotation axis [START_REF] Prieseter | Grain boundaries from theory to engineering[END_REF]. Their distance d dislo is geometrical predicted from the Read and Shockley expression d dislo = b/Θ where b is the norm of the Burgers vector and Θ is the misorientation of the GB [START_REF] Read | [END_REF]. With the measurement of the distance between the defects and the misorientation of the GB by HRTEM, the norm of the Burgers vector can be calculated to b = 0.31 nm, even if the quality of the HRTEM image is not sufficient for a direct determination. This value is in the order of the lattice plane distances of CoSi 2 (1 11) planes. Thus, it can be assumed that there are primary b=a( 1 Additional planes from edge dislocations are normal to the plane of the HRTEM image. Their distance is identical to the atomic spacing between the lattice planes in the viewing direction [10 1] (d (10 1) = 0.378 nm). From that, the unit area for one defect is calculated to d (10 1) ×d dislo = 1.33 nm 2 (compare scheme in figure 6). If every defect core is occupied by one Ti atom, an Ti excess of about 0.75 atoms/nm 2 is expected for the investigated low angle GB. This estimation of the excess value is in between the two Ti excesses determined by APT at the GB1 and GB2 (Figure 3). In figure 7, a schematic model of the relation between the Ti excess at the GB and their misorientation is drawn. As it is assumed that the Ti excess is correlated to the defect density, it is expected to be minimal for very low misorientation and at special GBs where the lattices of both adjacent grains are in high coincidence. From the calculation above, the Ti excess of GB1 and GB2 investigated by APT are slightly smaller and bigger than the defect density at the low angle GB investigated in TEM. It can be estimated that they are in the same misorientation region, as well as GB3.

The defects in the special GB (Figure 5) have a distance 3 times larger than the defects in the presented low angle GB. Thus, a significant lower defect density and by this Ti excess at the GB would be expected to be measured.

The measured defect distance can be verified by comparison of the distance between coincidence sites of the different planes parallel to the viewing direction perpendicular to the GB. Their normal vectors are drawn in figure 5b. For the grain on the left in [111] viewing direction it corresponds to the atomic spacing between ( 24 2) planes d ( 24 2) = 2.187 nm. For the grain on the right in [010] viewing direction it corresponds to the atomic spacing between (20 2) planes d (20 2) = 1.894 nm. Distances between defects along the GB are estimated to be at minimums of the differences in multiple atomic distances which are coincident sites for differences close to 0. After 7 and 6 atomic distances, respectively, the difference has a minimum. Thus, the distance of defects is estimated to be about 13.2 nm, that is in the order of the measured distance. The ( 24 2) planes are not resolved, thus a simultaneous Bragg-filtering of ( 24 2) and (202) planes is not possible. However, strong assumptions have been made to calculate the defect density on the GB plane from HRTEM image. The number of Ti atoms localized per defect might be also different from one. In addition, different kinds of defects (edge, screw or mixed dislocations, steps...) may have different behavior in view on Ti excess. Simulations could help to compare the proposed relationship to theoretical thermodynamic results.

To improve the interpretation of the presented results, a precise correlation of the Ti excess to the GB misorientation and the GB plane would be necessary.

In principal, acquired APT volumes can contain enough crystallographic information to determine the misorientation through the density variation along the crystallographic poles and lattice planes [20,21]. Nevertheless, obtaining this information is difficult and usually works easier for pure metals [20,21]. Moreover, there are limitations if the GB is at the border of the APT volume. In the volumes shown in figure 3b and3c, there is not enough information to determine the misorientation properly. Another method to determine the misorientation of the GB is the use of electron microscopy before the APT run. Indeed, orientation mapping of the tip by transmission Kikuchi diffraction (TKD) in a scanning electron microscope (SEM) or by nanobeam diffraction in a TEM has shown to be promising for systematic investigations between misorientation and excess at GBs [22,23].

Further studies are in progress to get better correlation between the misorientation and the Ti excess as well as correlation between the structure of CoSi 2 GBs and the Ti excess.

Conclusion

In conclusion, Ti segregates to grain boundaries of CoSi 2 . The amount of excess depends on the grain boundary characteristic as misorientation and defect structure. A relationship between defects and Ti localization is proposed. It could be verified by a correlated study of HRTEM and APT on identical GBs as well as by an exhaustive study of correlation between misorientation and Ti excess.

Figure 1

 1 Figure 1 presents three APT volumes which contain each one GB. The presence of the GB is indicated by an increased Ti concentration along a flat plane, as highlighted in figure 1 by the isoconcentration surface for Ti 1.5 at %. In order to determine the amount of Ti at the GBs, cylinders with a diameter of

Figure 1 :

 1 Figure 1: APT volumes of CoSi 2 contain GBs with excess of Ti (1.5 at. % isosurface highlighted). a) GB 1 b) GB 2 c) GB 3

Figure 2 :

 2 Figure 2: a) The concentration profile along the z-axis of the cylinder in figure 1a visualizes the increased concentration of Ti at the GB. b) The constant concentration inside the grains can be fitted with a linear function in the integral profile. The slope corresponds to the concentration (about 0.2 at. % for both grains). The step height at the GB is related to the number of Ti atoms on the base area of the cylinder (415 at).

  70

Figure 3 :

 3 Figure 3: The comparison of Ti excess at different GBs shows a significant variation.

Figure 4

 4 Figure 4 shows a low angle tilt GB. The fast Fourier transformations (FFT) (inset in figure 4a) demonstrates that both adjacent grains are in [10-1] zone

Figure 4 :

 4 Figure 4: HREM on low angle tilt GB. a) Two grains in [10-1] zone axis are slightly tilted around the [10-1] axis to each other (about 5 • ). b) Bragg filtering of (1-11) planes visualizes the misorientation of the grains. Furthermore, defects along the GB becomes visible.

Figure

  Figure 4b is an image obtained only from the (1-11) spots of the FFT. It shows the (1-11) planes of CoSi 2 . This Bragg-filtered image of selected planes,

Figure 5 :Figure 5

 55 Figure 5: HREM on special GB. a) Two grains in [111] and [010] zone axis are visible. The misorientation of the two zones is 54.7 • . Both grains have the ( 202) planes in common. b) Bragg filtering of the ( 202) planes shows defects at the GB in very large distance (about 11.6 nm) compared to figure 4.

Figure 6 :

 6 Figure 6: Schematic drawing of defect density calculation on low angle tilt GB with edge dislocations paralle to the rotation axis.

  11) edge dislocations at the [10 1] low angle tilt GB. For verification it is necessary to determine the orientation of the Burgers vector in a HRTEM image. Modeling the low angle tilt GB by the superposition of supercells in [10 1] orientation and 5 • misorientation verifies a distance of atomic positions in coincidence of about 3.5 nm.

Figure 7 :

 7 Figure 7: Schematic drawing of Ti excess over misorientation compared with estimated GB defect density.

Acknowledgment This work was supported by the French government through the program "Investissements d'Avenir A*MIDEX" (Project APODISE, no. ANR-11-IDEX-0001-02) managed by the National Agency for Research (ANR). The authors would like to thank M. Bertoglio for assistance with sample growth, M. Descoins for assistance with APT and T. Neisius, A. Campos, M. Cabie, L. Patout and C. Dominici for assistance with TEM and fruitful discussions.


Augustin Pouye
email: augustin.pouye@insa-lyon.fr

Laurent Maxit
email: laurent.maxit@insa-lyon.fr

Cédric Maury

Marc Pachebat

SYNTHESIS OF THE VIBROACOUSTIC RESPONSE OF A PANEL UNDER DIFFUSE ACOUSTIC FIELD USING THE SYNTHETIC ARRAY PRINCIPLE

The reproduction of the vibration and acoustic responses of structures under random excitation such as the diffuse acoustic field or the turbulent boundary layer is of particular interest to researchers and the transportation industry (automobile, aeronautics, etc.) as well. Indeed, the determination of these vibroacoustic responses requires making in-situ measurements or using test facilities such as the anechoic wind tunnel, which are complex and costly methods. Another drawback of these test means is the variability of the results when for instance; the same structure is tested in different facilities of the same kind. Based on the previous considerations, the necessity of finding a simple, cost-efficient and reproducible alternative method becomes obvious. In the present paper, a method of achieving this goal using a single acoustic source and the synthetic array principle is proposed. To assess the validity of this method, we propose an academic case study consisting of a baffled and simply supported aluminum panel under diffuse acoustic field and turbulent boundary layer excitations. The vibration response of the plate as well as the transmission loss are determined with the proposed process and compared to results from random vibration theory. These comparisons show good agreement between both the results obtained with the proposed approach and the theoretical ones.

INTRODUCTION

The experimental characterization of structures under random excitations such as the diffuse acoustic field (DAF) and the turbulent boundary layer (TBL) is of great interest to the transportation industry and the building sector. However, the test facilities used (reverberant chamber for the DAF and anechoic wind tunnel or in-situ tests for the TBL) can sometimes be complex and costly. Moreover, the results obtained for a given structure can be very different from one facility to another even though the same setup is implemented.

The experimental reproduction of the vibroacoustic response of structures under stochastic excitations using an array of acoustic sources has been theoretically shown some decades ago. But due to technical limitations, this method could not be experimentally validated back then. Since 2000, many researchers have addressed this problem using various approaches. Maury, Bravo, Elliott and Gardonio [START_REF] Maury | Turbulent Boundary-Layer Simulation with an Array of Loudspeakers[END_REF][START_REF] Elliott | The synthesis of spatially correlated random pressure fields[END_REF][START_REF] Bravo | The experimental synthesis of random pressure fields: Methodology[END_REF][START_REF] Maury | The experimental synthesis of random pressure fields: Practical feasibility[END_REF] have widely discussed the reproduction of a TBL excitation using an array of loudspeakers. This method works well when it comes to the reproduction of a DAF excitation but due to the limited number of sources in the array, it fails to simulate the wall-pressure fluctuations of a subsonic TBL excitation because of the high wavenumbers involved meaning that a denser source array would be needed. In this paper, an improvement of the previous approach using the synthetic array principle is proposed. This technique aims at simulating the vibroacoustic response of structures under these random excitations independently of the environment. This process has been used by Aucejo et al. [START_REF] Aucejo | Source Scanning Technique for Simulating TBL-Induced Vibrations Measurements[END_REF] under the name of Source Scanning Technique (SST) in order to reproduce the vibration response of a steel panel to a TBL excitation in the low frequency domain (up to 300 Hz).

This paper is organized as follows: first the theoretical background on the vibroacoustic response of a simple structure under random excitation is given. Secondly, the source scanning technique is briefly described. Finally, after presenting the experimental setup, some results are presented.

WAVENUMBER FORMULATION

This analysis considers the response of two dimensional rectangular structures to a random pressure field excitation. This pressure field is assumed to be stationary in time and homogeneous in space. We will be interested in two types of random excitations: the diffuse acoustic field and the turbulent boundary layer excitation.

The geometric configurations of the studied structure is shown in Fig. 1. In the following, we will assume that the wall-pressure fluctuations are not affected by the vibrations of the structure which means that the excitation is not modified by the structural re- sponse. Thus the random excitations considered in this paper are modeled by the wall pressure fluctuations that would be observed on a smooth rigid wall, also known as the blocked pressure p b [START_REF] Fahy | Sound and Structural Vibration: Radiation, Transmission and Response[END_REF].

L 1 L 2 h x 1 x 2 x 3 p b

Response of Panels to Random Pressure Fields

The response of the panel when excited by the blocked-pressure p b (y, t) is denoted α (x, t) and designates the panel velocity response v (x, t) if x is located on its surface Σ p . Otherwise, it corresponds to the radiated pressure by the panel p r (x, t) or the particle velocity response v 0 (x, t). It is given by the following convolution product

α (x, t) = t 0 Σp γ α (x, y, t -τ ) p b (y, τ ) dxdτ (1)
where γ α (x, y, t) is the space-time impulse response of the panel at point x when excited by a normal unit force at point y. With the previous assumptions made on the random processes involved, the crosscorrelation function R αα (x, t) can be written

R αα (x, t) = +∞ -∞ α (x, t) α (x, t + τ ) dτ (2)
where α (x, t) also designates v, p r or v 0 . Performing a time-Fourier transform of the cross-correlation function after introducing Eq. ( 1) in Eq. ( 2) yields the following space-frequency spectrum of the panel response (see Ref. [START_REF] Maury | A Wavenumber Approach to Modelling the Response of a Randomly Excited Panel, Part I: General Theory[END_REF] for details)

S αα (x, ω) = Σp Σp Γ α (x, y, ω) S p b p b (y, z, ω) ×Γ * α (x, z, ω) dydz (3)
where Γ α (x, y, ω) is the time-Fourier transform of γ α (x, y, t) and corresponds to the panel frequency response function at point x when excited by a normal force at point y; S p b p b (y, z, ω) is the time-Fourier transform of the blocked-pressure cross-correlation function and the superscript " * " represents the complex conjugate.

Defining the wavenumber-frequency spectrum of the blocked-pressure S p b p b (k, ω) as the wavenumber transform of its space-frequency spectrum S p b p b (x, y, ω) yields

S p b p b (x, y, ω) = 1 4π 2 +∞ -∞ S p b p b (k, ω) e jk(x-y) dk
(4) Introducing Eq. ( 4) in Eq. ( 3) and re-arranging, one obtains the following expression of the panel response

S αα (x, ω) = 1 4π 2 +∞ -∞ H α (x, k, ω) S p b p b (k, ω) ×H * α (x, k, ω) dk (5)
where

H α (x, k, ω) = Σp Γ α (x, y, ω) e -jky dy (6)
is called the sensitivity function and it characterizes the vibroacoustic behavior of the panel. In practice, this response is approximated by

S αα (x, ω) ≈ 1 4π 2 k∈Ωk H α (x, k, ω) S p b p b (k, ω) ×H * α (x, k, ω) δk (7)
where Ω k is a set of properly chosen wave-vectors.

The DAF is very well known random excitation. In fact, there is a closed-form solution that exactly describes it. The space-frequency spectrum of a DAF is defined by the following equation [START_REF] Cook | Measurement of Correlation Coefficients in Reverberant Sound Fields[END_REF]

S p b p b (r, ω) = Φ p b p b (ω) sin (k 0 r) k 0 r (8)
where r = |x -x |; ω is the frequency; k 0 = ω/c 0 is the acoustic wavenumber and c 0 the speed of sound in the medium. Φ p b p b (ω) designates the wall-pressure auto-spectral density function. The wavenumber transform of the space-frequency spectrum yields the frequency-wavenumber spectrum of the DAF blocked-pressure

S p b p b (k, ω) =      Φ p b p b (ω) 2π k 0 1 k 2 0 -|k| 2 if |k| < k 0 0 if |k| ≥ k 0 (9) where |k| = k 2 1 + k 2 2
, k 1 and k 2 are the wavenumbers in the x 1 and x 2 directions, respectively.

Radiated Power

The radiated power is defined by the following equation Π r (ω) =

Σp I act (x, ω) dx ( 10
)
where dx is the surface element and I act (x, ω) is the normal component of the active sound intensity at point x. The active sound intensity is directly related to the CSD function S pv0 (x, ω) between the sound pressure and the particle velocity at point x [9]

I act (x, ω) = [S pv0 (x, ω)] (11)
where designates the real part and from Eq. ( 7), one has

S pv0 (x, ω) ≈ 1 4π 2 k∈Ωk H p (x, k, ω) S pp (k, ω) H * v0 (x, k, ω) δk (12)
In practice, the radiated power will be estimated by an approximation of the integral of Eq. ( 10) with the rectangular rule

Π r (ω) ≈ x∈Σr I act (x, ω) δx (13)
where Σ r is an elemental surface at a distance x 3 on the radiating side of the panel.

SOURCE SCANNING TECHNIQUE

The Source Scanning Technique (SST) relies on the linearity of the involved phenomena and on the principle of wave superposition. SST also relies on the assumption that the random pressure fields of interest can be modeled as a set of uncorrelated wall-pressure plane waves. This technique is used for the measurement of the sensitivity functions which allow to compute the vibroacoustic response of the panel when the excitation is known, namely S p b p b (k, ω). The synthetic array principle consists in using a unique monopole source which is spatially displaced to different positions thereby creating virtually the array of monopole sources. It is closely related to the concept of Synthetic Aperture Radar (SAR), which consists in post-processing the signals received by a moving radar to produce fine resolution images from an intrinsically resolution-limited radar system in the alongtrack direction [START_REF] Curlander | Synthetic Aperture Radar: Systems and Signal Processing[END_REF]. The proposed approach is based on the mathematical formulation of the problem in the wavenumber domain. This formulation is appropriate because it allows an explicit separation of the contributions of the excitation via the wall-pressure cross-spectrum density function from those of the vibroacoustic behavior of the structure via the sensitivity functions. This formulation is also computationally more efficient than the space-frequency formulation [START_REF] Maury | A Wavenumber Approach to Modelling the Response of a Randomly Excited Panel, Part I: General Theory[END_REF]. Given a target pressure field p (x, k, ω) = e -ikx consisting of wall-pressure plane waves of wavevector k = (k 1 , k 2 ), there are three main steps for the reproduction of this target pressure field using SST (a) Characterization of the acoustic source: measurement of the transfer functions (G sp ) between source positions s and observation points p on the plate (microphones), see Fig. 2 x 1

x 2

G ps (ω) q s (k, ω) = p p (k, ω) (14)
(c) Synthesis of the target pressure field: in order to determine the vibroacoustic response of the structure, one needs to determine the following sensitivity functions

H α (x, k, ω) = s Q s (k, ω) Γ s α (x, ω) (15)
where α = (v, p, v 0 ) and Γ s α (x, ω) represents the frequency response function (FRF) of the structure at point x which is to be measured.

EXPERIMENTAL SETUP

The plate was manufactured using the protocol presented by Robin et al. [START_REF] Robin | A Plane and Thin Panel with Representative Simply Supported Boundary Conditions for Laboratory Vibroacoustic Tests[END_REF] and was placed in a baffle consisting of a 2 cm thick square plywood with a 1 m side and in which there is an aperture the size of the plate, see Fig. The measurements were done in a room where the three walls are covered with absorbing wedges and 10 cm absorbing foam panels were placed on the floor and around the structure inside the baffle in order to prevent the potential reflections and noises coming from the robot and acquisition system from polluting the measurements.

RESULTS AND DISCUSSION

In all the results shown below, there is a horizontal shift (along the frequency axis) which is due to the fact that in the theoretical model, the boundary conditions are considered perfect which they are not in practice.

Fig. 6 shows the auto-spectrum density function of the structural velocity response at point x = (0.06, 0.3, 0) m (in dB units) when excited by a DAF. It can be observed that the vibration response determined using SST do not match the theoretical ones under 300 Hz: this is due to the fact that the source is not efficient in that frequency range as stated before. The vertical offsets that can be observed at some frequencies are due to the fact that for the theoretical case, the modal damping of the plate is taken constant in the entire frequency range whereas it is not the case in real conditions. Fig. 7 shows the inverse of the radiated power (in dB units) by the panel when excited by a DAF. The radiated power was determined using the two microphone method. The experimental results do not match the theoretical ones under approximately 600 Hz: this is probably due to the fact that the monopole source was not very efficient to induce a sufficient radiation amplitude for the measurement of the pressure and particle velocity sensitivity functions. Above that frequency, there is a good agreement between the theoretical results and those obtained using SST.

CONCLUSION

The results obtained using SST for the simulation of the DAF induced vibrations of a rectangular panel were compared to numerical results. This comparison showed a fairly good agreement between both results. The process was automatized with two Cartesian robots controlled by a Matlab code: this will allow us to characterize more complex panels in the future.

Further details on this study as well as results for a turbulent boundary layer excitation will be available in the submitted journal paper [START_REF] Pouye | Reproduction ot the Vibroacoustic Response of Panels under Stochastic Excitations using the Source Scanning Technique[END_REF].

ACKNOWLEDGMENT

This work was funded by the French National Research Agency (VIRTECH project, ANR-17-CE10-0012) and was performed within the framework of the LABEX CeLyA (ANR-10-LABX-0060) of Université de Lyon, within the program "Investissements d'Avenir" (ANR-16-IDEX-0005) operated by the French National Research Agency (ANR).

Figure 1 .

 1 Figure 1. Simply supported plate on all edges.

Figure 2 .

 2 Figure 2. Measurement of G ps (ω)

Figure 3 .

 3 Figure 3. Measurement of the velocity FRF Γ s v (x, ω)

  [START_REF] Aucejo | Source Scanning Technique for Simulating TBL-Induced Vibrations Measurements[END_REF]. A mid-high frequency monopole source manufactured by Microflown is used to generate the sweep signals necessary for the determination of the transfer functions between the source and an array 1/4 ROGA RG-50 microphones. This source was placed on the arm of a 3 axis Cartesian robot in order to automatize the displacement of the source. The vibration response of the structure was measured using a Brüel & Kjaer type 4508 accelerometer. It is important to note that the monopole source used for the experiment was only efficient from approximately 300 Hz to 7000 Hz.

Figure 4 .

 4 Figure 4. Measuring the transfer functions G sp

Figure 5 .

 5 Figure 5. Baffled simply supported panel

Figure 6 .

 6 Figure 6. DAF vibration response: theory (thin black line), SST (thick gray line).

Figure 7 .

 7 Figure 7. Inverse of the radiated power under DAF: theory (thin black line), SST (thick gray line).