Laura Marcela

Forero Ramirez

Elise Gobin

Rachida Aid-Launais

Clément Journe

Fernanda C Moraes

Luc Picton

Didier Le Cerf

Didier Letourneur

Cédric Chauvierre

Frédéric Chaubet

Didier LETOURNEUR a , Cédric CHAUVIERRE a , Frederic Chaubet
email: frederic.chaubet@univ-paris13.fr

Gd(DOTA)-grafted submicronic polysaccharide-based particles functionalized with fucoidan as potential MR contrast agent able to target human activated platelets

Keywords: Dextran, fucoidan, MRI, human platelets, crosslinking, submicronic particles conceptualization, investigation, methodology, formal analysis, writing - investigation, R. AID-LAUNAIS : investigation, methodology, C. JOURNE : investigation, methodology, F. C. MORAES : investigation, methodology, L. PICTON : conceptualization, validation, writing -review conceptualization, validation, resources, D. LETOURNEUR : conceptualization, validation, funding acquisition, C. CHAUVIERRE : conceptualization, validation, resources, writing -review conceptualization, project administration, funding acquisition, supervision

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

Introduction

Atherothrombosis remains the leading cause of morbidity and mortality worldwide and represents a major economic burden on health care systems [START_REF] Herrington | Epidemiology of Atherosclerosis and the Potential to Reduce the Global Burden of Atherothrombotic Disease[END_REF][START_REF] Lozano | Global and regional mortality from 235 causes of death for 20 age groups in 1990 and 2010: a systematic analysis for the Global Burden of Disease Study 2010[END_REF]. Its underlying cause is atherosclerosis, a chronic inflammatory disease characterized by the formation of lipid-rich plaques in the intima of medium and large arteries. While stable plaques remain asymptomatic and relatively harmless, vulnerable plaques may rupture and thrombose causing myocardial infarction, stroke, or sudden death [START_REF] Schroeder | Vulnerable and dangerous coronary plaques[END_REF][START_REF] Waxman | Detection and Treatment of Vulnerable Plaques and Vulnerable Patients: Novel Approaches to Prevention of Coronary Events[END_REF]. There is thus a medical need for noninvasive tests allowing to early detect high-risk plaques and thrombus formation in order to prevent major cardiovascular events.

Magnetic resonance imaging (MRI) has been successfully used to characterize plaque composition, detect arterial thrombi and monitor plaque progression and regression in several animal models of atherosclerosis and in humans [START_REF] Corti | Imaging of atherosclerosis: magnetic resonance imaging[END_REF][START_REF] Leiner | Magnetic resonance imaging of atherosclerosis[END_REF]Raggi et al., 2016;[START_REF] Sannino | Non-invasive vulnerable plaque imaging: how do we know that treatment works?[END_REF]. In routine practice, MRI often requires the use of Gadolinium-based (Gd) contrast agents to enhance relaxation rates of water molecules, which results in better contrast between different biological tissues [START_REF] Caravan | Gadolinium(III) Chelates as MRI Contrast Agents: Structure, Dynamics, and Applications[END_REF][START_REF] Yon | Gadolinium-based contrast agents: From gadolinium complexes to colloidal systems[END_REF][START_REF] Zhou | Gadolinium-based contrast agents for magnetic resonance cancer imaging: Gadolinium-based CA for MR cancer imaging[END_REF]. Nevertheless, these contrast agents have major limitations including a short circulation time, a low diffusion and affinity with the interstitial space and a lack of tissue specificity. Important doses are thus necessary to improve imaging contrast, exposing patients to potential side effects [START_REF] Kuo | Gadolinium-based MR Contrast Agents and Nephrogenic Systemic Fibrosis[END_REF][START_REF] Rogosnitzky | Gadolinium-based contrast agent toxicity: a review of known and proposed mechanisms[END_REF]. These limitations can be addressed by combining nanotechnology and molecular imaging strategies.

Nanosystems having paramagnetic properties and bearing targeting molecules able to bind specifically to thrombus have gained increased attention as potential imaging probes. Ultra-small particles of iron oxide, micelles, liposomes, and perfluorocarbon nanoparticles have been designed for MRI visualization of several inflammation-related targets, such as macrophages, oxidized low density lipoproteins, endothelial cell expression, plaque neovasculature, apoptosis, and activated platelets [START_REF] Amirbekian | Detecting and assessing macrophages in vivo to evaluate atherosclerosis noninvasively using molecular MRI[END_REF][START_REF] Barkhausen | Detection of Atherosclerotic Plaque With Gadofluorine-Enhanced Magnetic Resonance Imaging[END_REF][START_REF] Briley-Saebo | Targeted Molecular Probes for Imaging Atherosclerotic Lesions With Magnetic Resonance Using Antibodies That Recognize Oxidation-Specific Epitopes[END_REF][START_REF] Cai | MR Molecular Imaging of Aortic Angiogenesis[END_REF][START_REF] Li | Molecular Imaging of Atherosclerotic Plaques Targeted to Oxidized LDL Receptor LOX-1 by SPECT/CT and Magnetic Resonance[END_REF][START_REF] Mcateer | An approach to molecular imaging of atherosclerosis, thrombosis, and vascular inflammation using microparticles of iron oxide[END_REF][START_REF] Suzuki | Ultrasmall superparamagnetic iron oxide nanoparticles coated with fucoidan for molecular MRI of intraluminal thrombus[END_REF][START_REF] Te Boekhorst | Molecular MRI of Inflammation in Atherosclerosis[END_REF][START_REF] Van Tilborg | Annexin A5-Functionalized Bimodal Nanoparticles for MRI and Fluorescence Imaging of Atherosclerotic Plaques[END_REF]. P-selectin (140 kDa membrane glycoprotein) is an adhesion molecule overexpressed on the surface of activated platelets and inflamed endothelium of atherothrombotic lesions [START_REF] Bachelet | Affinity of low molecular weight fucoidan for P-selectin triggers its binding to activated human platelets[END_REF][START_REF] Saboural | Purification of a Low Molecular Weight Fucoidan for SPECT Molecular Imaging of Myocardial Infarction[END_REF]. P-selectin allows the recruitment of leucocytes through the interaction with its main ligand, PSGL-1 (McEver, 2001). Interestingly, fucoidan is a natural sulfated polysaccharide obtained from brown seaweed extract, which has shown a strong and specific affinity for P-selectin [START_REF] Bachelet | Affinity of low molecular weight fucoidan for P-selectin triggers its binding to activated human platelets[END_REF][START_REF] Chollet | Fucoidans in Nanomedicine[END_REF][START_REF] Saboural | Purification of a Low Molecular Weight Fucoidan for SPECT Molecular Imaging of Myocardial Infarction[END_REF]. In this context, P-selectin and fucoidan appear as an appropriate target-ligand system for the diagnosis of atherothrombosis. One can therefore hypothesize that the assembly of several molecules of fucoidan with particles containing Gd material will result in MRI contrast probes with increased binding on activated platelets. The aim of the present study was to develop novel and biospecific polysaccharide-based submicronic particles (SPs) functionalized with fucoidan and able to bind to human activated platelets for atherothrombosis imaging by MRI (Scheme 1).

Dextran, another polysaccharide widely used in the biomedical field [START_REF] Abir | Efficacy of Dextran Solutions in Vascular Surgery[END_REF][START_REF] Ferreira | Dextran-based materials for biomedical applications[END_REF][START_REF] Naessens | Leuconostoc dextransucrase and dextran: production, properties and applications[END_REF], was chosen as polymer carrier for Gd(DOTA) groups as the contrast moieties. The polysaccharide nature of the designed objects was expected to ensure their haemocompatibility and low toxicity. Among all the works dealing with micro/nanoparticles exclusively composed of polysaccharides, very few examples were designed for MRI and almost all of them were developed for cancer diagnostics. Chitosan and hyaluronic acid have been by far the most employed polysaccharides to get Gd-loaded nanoparticles [START_REF] Chan | Long-Lasting and Efficient Tumor Imaging Using a High Relaxivity Polysaccharide Nanogel Magnetic Resonance Imaging Contrast Agent[END_REF][START_REF] Gheran | Biocompatibility of Gd-Loaded Chitosan-Hyaluronic Acid Nanogels as Contrast Agents for Magnetic Resonance Cancer Imaging[END_REF][START_REF] Huang | Magnetic resonance imaging of contrast-enhanced polyelectrolyte complexes[END_REF][START_REF] Na | T1-Weighted MR imaging of liver tumor by gadolinium-encapsulated glycol chitosan nanoparticles without non-specific toxicity in normal tissues[END_REF][START_REF] Nam | Tumor Targeting Chitosan Nanoparticles for Dual-Modality Optical/MR Cancer Imaging[END_REF][START_REF] Payne | Multimodal Imaging Nanoparticles Derived from Hyaluronic Acid for Integrated Preoperative and Intraoperative Cancer Imaging[END_REF][START_REF] Rigaux | Characterization of Gd loaded chitosan-TPP nanohydrogels by a multi-technique approach combining dynamic light scattering (DLS), asymetrical flow-field-flow-fractionation (AF4) and atomic force microscopy (AFM) and design of positive contrast agents for molecular resonance imaging (MRI)[END_REF][START_REF] Zhang | Hyaluronic Acid-Chitosan Nanoparticles to Deliver Gd-DTPA for MR Cancer Imaging[END_REF], but alginate and pullulan-based ones have also been described [START_REF] Kim | Gadolinium-chelate nanoparticle entrapped human mesenchymal stem cell via photochemical internalization for cancer diagnosis[END_REF][START_REF] Podgórna | Gadolinium alginate nanogels for theranostic applications[END_REF]. They were mainly prepared by self-assembly of amphiphilic polysaccharide derivatives, formation of polyelectrolyte complexes or ionic gelation with sodium tripolyphosphate. To the best of our knowledge, no polysaccharide-based submicronic particle combining fucoidan and Gd-based contrast agent has been developed yet, which contributes to the originality of the present work.

As a first step, a chemical modification of native dextran to introduce Gd(DOTA) groups was performed.

Next, SPs were synthesized by co-crosslinking of fucoidan and former dextran macrocomplexes within the droplets of a water-in-oil emulsion. SPs were characterized in terms of morphology, size and zeta potential. In vitro assays were performed to evaluate the cytotoxicity, contrast properties and targeting capacity of the obtained objects.

Scheme 1. Preparation of polysaccharide submicron particles via a combined inverse emulsion-crosslinking method.

Materials and methods

Materials

Dextran T70 ( = 55 000 g/mol, Đ = 1.12) was purchased from Pharmacosmos (Holbaek, Denmark), Low molecular weight fucoidan ( = 4 400 g/mol, Đ = 1.49, 16.8 wt% sulfates) was obtained from

Algues & Mer (Ouessant, France) in the framework of a partnership for the pharmaceutical development of a GMP-grade fucoidan for molecular diagnosis of cardiovascular diseases [START_REF] Chauvierre | Pharmaceutical Development and Safety Evaluation of a GMP-Grade Fucoidan for Molecular Diagnosis of Cardiovascular Diseases[END_REF]. France). Tyrode-Hepes buffer (0.3 wt% BSA, pH 7,24) contained 137 mM NaCl, 2 mM KCl, 12 mM NaHCO3, 0.3 mM Na2HPO4, 5.5 mM glucose and 5 mM Hepes. All materials were used without further purification. Dialysis membranes of 10 000 Da were purchased from Spectrum Laboratories (New Brunswick, NJ, USA).

Preparation of DexNH2-Gd(DOTA) complexes

Dextran derivatives bearing Gd(DOTA) groups were synthesized in three steps (Scheme 2). In the first step, the attachment of primary amine functions (NH2) onto dextran was performed in aqueous basic media. Typically, 5 g of dextran (31 mmol of anhydroglucopyranose unit (AGU)) were dissolved in 25 mL of water. 25 mL of NaOH (6.2M) were added and the mixture was stirred during 30 minutes. The reaction flask was then immersed in a thermostated oil bath at 55 °C before the addition of 8 g of 3chloropropylamine hydrochloride (62 mmol, 2 equivalents per AGU) and the mixture was maintained under stirring during different reaction times. After neutralization, the polymer (DexNH2), was extensively dialyzed against ultrapure water (cut-off: 10 000 Da) and finally freeze-dried. Degree of substitution of primary amine groups per 100 AGU (DSNH2) was estimated by elemental analysis of nitrogen.

In the second step, DOTA groups were linked to aminated dextran using classical EDC/NHS reaction.

Typically, DOTA (1 equivalent per primary amine group) was dissolved in 10 mL of water and pH was adjusted to 3.5 with diluted HCl (0.5M). After 30 min of stirring, EDC and NHS were added at a molar ratio DOTA/EDC/NHS of 1/5/1.25. The pH was raised to 7 and DexNH2 previously dissolved in 10 mL of water was added in small amounts for 1h. The mixture was stirred at room temperature for 2h.

Resulting DexNH2-DOTA derivative was dialyzed against EDTA (0.05M) to avoid the complexation of contaminating metal ions by DOTA then against water (cut-off: 10 000 Da) before freeze-drying. Degree of substitution of DOTA moieties per 100 AGU (DSDOTA) was estimated from the increase of nitrogen content with respect to the one of DexNH2 precursor.

In the third step, the chelation of Gd 3+ ions by DOTA groups along the dextran backbone was performed by mixing GdCl3.6H2O (1 Gd 3+ per DOTA group) with DexNH2-DOTA in water as previously described [START_REF] Nguyen | Gadolinium/terbium hybrid macromolecular complexes for bimodal imaging of atherothrombosis[END_REF]. After adjusting the pH to 6.5 with NaOH, the solution was maintained at room temperature overnight followed by heating at 60 °C for 4h. Chlorides were removed by dialysis (cut-off: 10 000 Da) and white fluffy products were obtained after freeze-drying. Dextran gadolinium chelates were called DexNH2-Gd(DOTA). Degree of substitution of Gd 3+ ions per 100 AGU (DSGd) was determined by total reflection X-ray fluorescence (TRXF) spectrometry (S2 Picofox, Bruker, Germany).

Polysaccharide submicron particles synthesis

Dextran T70 particles were obtained via a water-in-oil emulsification-crosslinking method inspired from our previous works [START_REF] Bonnard | Leukocyte mimetic polysaccharide microparticles tracked in vivo on activated endothelium and in abdominal aortic aneurysm[END_REF]. Typical experimental conditions were as follows: 1.2 g of dextran and 1.4 g of NaCl were solubilized in 4 mL of water. 1.2 g of this solution were then mixed with 120 µL of NaOH (10M) and 240 µL of trisodium trimetaphosphate (STMP) (30% (w/v) in water). 300 µ L of the mixture were slowly injected into 15 ml of sunflower oil containing 6.0% (w/v) of polyglycerol polyricinoleate (PGPR) as emulsion stabilizer and dispersed with a homogenizer at 30,000 rpm for 4 min (Polytron PT 3100, dispersing aggregate PT-DA 07/2EC-B101, Kinematica, Luzernerstrasse, Switzerland). The resulting emulsion was then transferred to an oven (50 °C) wherein the crosslinking step took place for 20 min. Polysaccharide particles were recovered by ultracentrifugation (15,000 g, 45 min), washed once with PBS 1X, twice with SDS (0.04% (w/v)) and four times with water. The resulting pellets were resuspended in water and stored at 4 °C until use. To prepare Gd-loaded particles (Gd-SPs), dextran was replaced by DexNH2-Gd(DOTA). Fucoidan-functionalized particles (FUCO-Gd-SPs) were prepared with 60 mg of fucoidan and 1.14 g of DexNH2-Gd(DOTA).

Physico-chemical characterizations

1 H NMR spectra were recorded on a Bruker-400 Ultrashield (Bruker, Germany). Samples were prepared in D2O at a concentration of 20 mg/mL.

Average molecular weight of dextran derivatives was determined by size exclusion chromatography coupled to a multi-angle laser light scattering detector (SEC-MALLS) in NaNO3/NaN3 (0.15 M/0.02% (w/v)). Refractive index increment (dn/dc) of 0.146 mL.g -1 was used (See Supporting).

The viscosities of sunflower oil and dextran solutions were measured at 25 °C using a rotational rheometer with a concentric cylinder geometry (TA instrument HR2, Delaware, USA).

Nitrogen content was estimated by elemental analysis (Service de Microanalyse du CNRS, ICSN, Gif-sur-Yvette, France). Phosphorus and gadolinium contents were determined by total reflection X-ray fluorescence (TRXF) spectrometry (S2 PICOFOX, Bruker, Germany). Fucoidan content was assessed by colorimetric quantification of sulfates as previously described [START_REF] Li | Development of Polymer Microcapsules Functionalized with Fucoidan to Target P-Selectin Overexpressed in Cardiovascular Diseases[END_REF].

Particle size distribution was measured by using Laser Diffraction Particle Size Analyzer (Mastersizer 3000, Malvern Instruments, UK) and number distributions are reported. The obtained size (D50) and span values were an average of at least three consecutive measurements.

Zeta potential of particles was measured in 1mM KCl at 25°C using a Zetasizer Nano-ZS (Malvern Instruments, Malvern, UK).

The morphology of particles was investigated by Transmission Electron Microscopy (TEM, Tecnai 12, 80 kV; FEI; Hillsboro, OR, USA), Scanning Electron Microscopy (SEM, Philips XL30 ESEM-FEG, Netherlands) and confocal microscopy (Zeiss LSM 780 with 63× oil objective, Carl Zeiss Microscopy, Oberkochen, Germany). For TEM observation, 3 μL of particles suspension were dropped onto a 400 mesh copper grid and positive stained with uranyl acetate (1% (w/v)) and allowed to air-dry at room temperature.

For SEM images, one drop of particles suspension was dropped onto a silicon wafer, then air-dried and coated with a thin layer of gold before observation.

Cytotoxicity tests

Human Umbilical Vein Endothelial Cells (HUVECs) were grown in DMEM supplemented with 10% (v/v) fetal bovine serum, 4mM of L-glutamine, 100 U/mL penicillin and 100 µg/mL streptomycin. Cells were cultivated at 37 °C under 5% CO2 (v/v) in a humidified incubator. HUVECs were seeded at 10,000 cells per well in 96-well plates and incubated for 24h. After that, culture medium was removed and 100 µL of particle suspensions at different concentrations (200, 500 and 1 000 µg/mL) were added. Cells metabolic activity was determined after 24h by resazurin assay. Cells were incubated with medium containing 10% resazurin for 2h at 37 °C and fluorescence intensity (λex = 560 nm; λem = 590 nm) was read in an Infinite M200 PRO microplate (TECAN Group Ltd, Switzerland). Metabolic activity in the presence of particles was compared to the control condition.

To assess cells morphology, samples were fixed with PFA and incubated with TRITC-phalloidin and DAPI to stain for F-actin and nuclei respectively.

MRI phantoms

DOTAREM, DexNH2-Gd(DOTA) and FUCO-Gd-SPs gel phantoms (Gd concentrations ranging between 0.12 and 1.0 mM) were prepared in 0.5 mL tubes using 2% (w/v) agarose. These tubes were put inside of a larger container, which was itself filled with agarose gel.

Longitudinal relaxation (T1) and transversal relaxation (T2) times were acquired on a 7 Tesla animal MR imager (Pharmascan 70/16, Bruker Biospin, Ettlingen, Germany), and analyzed with Bruker software Paravision 6.0.1. In order to calculate T1 map, a rapid acquisition with relaxation enhancement (RARE) sequence was used, with echo time (TE) of 8.5 ms, variable repetition time (TR, 200, 400, 800, 1500, 3000, 5500 ms), matrix (MTX): 128x128, field of view (FOV): 30x30 mm and slice thickness of 1 mm.

For T2 map calculation, a multislice multiecho (MSME) sequence was employed with TR of 2200 ms and TE between 6.8 to 170 ms (25 echoes; echo spacing: 6.8 ms). MTX, FOV and slice thickness were as before. The slope of the line obtained by plotting the relaxation rates R1 and R2 (R1= 1/T1; R2 = 1/T2) at different concentration, provided the relaxivity r1 and r2 respectively.

Interaction of SPs with human activated platelets 2.7.1 Under static conditions

The interaction between three groups of PE-Cy5 labeled platelets (non-activated platelets (PRP), activated platelets (PRP + TRAP) and P-selectin blocked activated platelets (PRP + TRAP + anti-CD62P)) and FUCO-Gd-SPs was measured by flow cytometry. Protocol was adapted from [START_REF] Li | Development of Polymer Microcapsules Functionalized with Fucoidan to Target P-Selectin Overexpressed in Cardiovascular Diseases[END_REF]. Briefly, 5 mL of blood from healthy adult volunteers were collected in sodium citrate 3.8% (w/v). Platelet-rich plasma (PRP) was obtained by centrifugation at 200 g for 15 min (5702RH centrifuge Beckman Coulter, Villepinte, France) and platelet concentration was adjusted to 1×10 8 ml -1 with Tyrode-HEPES buffer (0.3 wt% BSA). Platelets were labeled by incubation with PE-CyTM5 mouse anti-human CD41a for 15 min.

Conjugate excess was then eliminated by a wash step. Activated PRP was obtained by stimulation of PRP with 20 μM TRAP. In some experiments, activated then P-selectin-blocked PRP were obtained by incubation with a non-labeled anti-human CD62P at high concentration (0.04 mg/mL). Before assessing the interaction with particles, P-selectin expression level at the platelet surface was assessed using an antihuman CD62P-FITC and measuring FITC signal by flow cytometry. To evaluate the binding ability of particles to P-selectin expressed onto platelets, 5 μL of nonactivated PRP, activated PRP with TRAP or anti P-selectin-treated activated PRP were incubated for 20 min with 5 μl of FITC-labeled FUCO-Gd-SPs (10 mg/mL). Sample volume was then completed to 100 µL using Tyrode-HEPES buffer (0.3 wt% BSA).

Samples were analyzed on a LSRII flow cytometer (BD Biosciences, Le Pont de Claix, France), 10,000 PE-Cy5 positive platelets were collected per sample, and the mean fluorescence intensity (MFI) of FITC channel was measured in these platelets. FITC-labeled Gd-SPs were used as negative control.

Under arterial flow conditions

Binding ability of FUCO-Gd-SPs to P-selectin expressed on activated platelet aggregates was as well evaluated in vitro as previously reported [START_REF] Li | Development of Polymer Microcapsules Functionalized with Fucoidan to Target P-Selectin Overexpressed in Cardiovascular Diseases[END_REF][START_REF] Juenet | Thrombolytic therapy based on fucoidanfunctionalized polymer nanoparticles targeting P-selectin[END_REF]. Briefly, micro-channels of Vena8 Fluoro+ chambers (Cellix Ltd, Dublin, Ireland) were coated overnight with 50 µg/mL of collagen and then washed with NaCl 0.9%. Human whole blood labeled with DiOC6 (a green fluorescent dye) was perfused under arterial flow conditions for 5 min to induce platelet activation and aggregation on the collagen-coated channel. TRITC labeled FUCO-Gd-SPs at 1 mg/mL in NaCl 0.9% were then perfused during 5 min. Their accumulation onto preformed platelet aggregates was monitored in real time by fluorescence microscopy (Axio Observer, Carl Zeiss Microscopy, Oberkochen, Germany). Fluorescence images were taken along each micro-channel after washing with NaCl 0.9%. Gd-SPs were used as negative control.

Statistical Analysis

Data are presented as mean ± SEM (n≥3). Flow cytometry results were analyzed statistically with a oneway ANOVA with Bonferroni post-tests to compare data obtained with Gd-SPs and Fuco-Gd-SPs. A difference of p < 0.05 was considered significant.

Results

Synthesis of dextran gadolinium chelates.

A series of aminated dextran (DexNH2), dextran ligands (DexNH2-DOTA) and their corresponding gadolinium complexes (DexNH2-Gd(DOTA)) were synthesized in three consecutive steps (Scheme 2).

All modifications were done in aqueous media. Three sets of reaction conditions were used (Conditions-1, 2, 3), resulting in three final macrocomplexes named Complex-1, 2, 3, respectively. The substitution degrees (DS) of primary amines, DOTA groups and Gd 3+ ions were expressed as the number of introduced groups per 100 AGU. All physicochemical characterizations are reported in Table 1.

Amination of dextran was performed in basic solution (3.1 M NaOH) by reaction with 3chloropropylamine leading to DexNH2 derivatives (1 st step, Table 1). Successful introduction of amine moieties was confirmed by elemental analysis of nitrogen content (%N) and 1 H NMR spectroscopy.

The characteristic peaks of methylene protons of propylamine group (-CH2-CH2-CH2-NH2) were clearly visible at 1.9 ppm and 3.1 ppm (Figure S1). Substitution degree of amine (DSNH2) could be tuned from 5.6 to 23.9% by increasing reaction time (1.5, 3 and 14 h) at constant amine/AGU feeding ratio (2/1).

These results are in agreement with those reported by De Nooy et al. for the amination of scleroglucan [START_REF] De Nooy | Synthesis and preliminary characterisation of charged derivatives and hydrogels from scleroglucan[END_REF]. Furthermore, no degradation of the dextran backbone under basic conditions (pH≈13) was evidenced at early times and only a slight decrease in molecular weight was observed at 14 h as attested by SEC-MALLS analysis (Table S1).

Scheme 2. Synthesis of DexNH2-Gd(DOTA) complexes.

Table 1. Physicochemical characteristics of DexNH2-Gd(DOTA) complexes. Table 1). Initial quantity of amine functions (DSNH2) was shown to influence both the degree of substitution DSDOTA and the grafting yield. As expected, the number of DOTA groups linked to dextran chains increased with the initial amine content, all other conditions being the same. In all cases, DOTA grafting was incomplete leaving unreacted propylamines along dextran backbone. Coupling yields were in about 50-60% for initial DSNH2 values below 8%

(Conditions-1 and 2, Table 1) and of less than 30% when DSNH2 was equal to 23.9%

(Conditions-3). This low yield was likely due to steric hindrance effects.

DexNH2-Gd(DOTA) macrocomplexes were finally produced by reacting former DexNH2-DOTA ligands with gadolinium chloride (3 rd step, Table 1). An aminated dextran (without DOTA groups) was used as negative control. The amount of complexed Gd 3+ was assessed by TXRF. According to X-ray fluorescence emission spectra, Gd was effectively chelated by DexNH2-DOTA ligands while no Gd was detected in the case of aminated dextran (Figure S2). These results further demonstrated the presence of DOTA moieties covalently linked to the polysaccharide. In addition, DSGd calculated from Gd content (%Gd) matched well with DSDOTA previously estimated from N content, indicating the presence of one Gd 3+ ion per DOTA group. Three DexNH2-Gd(DOTA) complexes having 2.4 (Complex-1), 5.0 (Complex-2) and 6.7 (Complex-3) Gd(DOTA) groups per 100 AGU were obtained corresponding to 8, 17 and 23 Gd(DOTA) groups per dextran chain, respectively.

Preparation of polysaccharide-based submicronic particles

Optimization of crosslinking and emulsion conditions

Polysaccharide-based particles were prepared in one-step using a combined water-in-oil emulsion/co-crosslinking process. This process was solvent-free in both production and purification steps. Sunflower oil was used as continuous phase instead of organic solvents commonly reported in the literature. Furthermore, STMP and PGPR, safe materials with no reported adverse effects on humans [START_REF] Abed | Influence of polysaccharide composition on the biocompatibility of pullulan/dextran-based hydrogels[END_REF][START_REF] Nikolovski | HOW TO FORMULATE A STABLE AND MONODISPERSE WATER-IN-OIL NANOEMULSION CONTAINING PUMPKIN SEED OIL: THE USE OF MULTIOBJECTIVE OPTIMIZATION[END_REF], were used as crosslinking agent and emulsion stabilizer respectively.

Native dextran (Dextran T70) was used as a model polysaccharide to optimize the preparation of particles. Crosslinking reaction was performed at 50°C at constant 1M NaOH concentration. SEC/MALLS measurements indicated that no degradation of dextran backbone occurred during 5h under these conditions (Table S2). The use of sodium chloride (4M)

appeared to increase the reaction rate. NaCl screened phosphate negative charges coming from STMP reaction keeping macromolecular chains closer, thus improving the crosslinking process.

We determined the lower polysaccharide and STMP concentrations required to succesfully crosslinked dextran chains. For a dextran solution at about or below 120 g/L no gelation was noted. This result was expected as the critical overlap concentration (C*) of Dextran T70 in water is reported at about 112 g/L at 40°C [START_REF] Antoniou | Solution properties of dextran in water and in formamide[END_REF]. Stable 3D networks were obtained for dextran concentrations equal or above 200 g/L since the entanglement density of dextran chains was sufficient in such conditions. Minimal [STMP]/[AGU] molar ratio required for crosslinking was equal to 0.02. Below this value, no reaction occurred.

The viscosity of both dispersed (ηd) and continuous phases (ηc), and more specifically the viscosity ratio (ηd/ηc) play an important role in droplets size, dispersity and stability.

Typically, the emulsification process is highly intensified when that ratio tends to 1 and smaller droplets can be obtained [START_REF] Vananroye | Effect of Confinement on Droplet Breakup in Sheared Emulsions[END_REF]. On one hand, regarding continuous phase, sunflower oil viscosity was 16 mPa.s at 25 °C and increased slightly to 19 mPa.s with the addition of 6% (w/v) of PGPR. On the other hand, dextran solutions containing 4M NaCl behaves like Newtonian fluids (i.e. viscosity does not depend on the shear rate) in the concentration range studied (50-500 g/L) (Figure S3a). As the concentration of solutions increased from 50 to 500 g/L, the relative viscosity increased exponentially from 1.6 to 163 (Figure S3b). An aqueous phase containing 200 g/L of dextran, giving a viscosity of 12 mPa.s and a viscosity ratio ηd/ηc of ~0.6, was finally chosen for the preparation of particles.

Tuning particles size

Table 2 summarizes experimental conditions used in the present study (Runs 1-5), as well as the average size of the particles after purification and resuspension in water. In all formulations, aqueous phase contained 200 g/L of polysaccharide and 1M NaOH while continuous phase was composed of sunflower oil and PGPR (6% (w/v)). Water to oil phases ratio was kept to 30/150 (v/v). Phosphorus content (%P) in as-obtained particles was used as indicator of the actual amount of phosphoester groups incorporated in the polymer network (i.e. intermolecular, intramolecular and monografted) [START_REF] Lack | High-resolution nuclear magnetic resonance spectroscopy studies of polysaccharides crosslinked by sodium trimetaphosphate: a proposal for the reaction mechanism[END_REF][START_REF] Dulong | Pullulan-STMP hydrogels: a way to correlate crosslinking mechanism, structure and physicochemical properties[END_REF].

Particles size was tuned by varying STMP concentration and consequently [STMP]/[AGU]

molar ratio (Runs 1-3). Unsurprisingly, the higher the initial [STMP]/[AGU] ratio, the smaller the particle size. This observation can be correlated to the increase of crosslinking as suggested by the rise of P content. More densely packed particles with lesser swelling in water were obtained at higher STMP feeding amount. Because of the anionic charges brought by STMP, all particles exhibited negative zeta potential. Submicronic particles (SPs) of about 790 nm with narrow size distribution can be achieved in a reproducible way by using

[STMP]/[AGU]=0.17 (6.0 % (w/v) STMP, Run 3). Production yield was of about 35%. (a) Width of the distribution calculated using = ( (0.9 -(0.1 / (0.5 . D(0.1), D(0.5) and D(0.9) were the particle diameters at 10%, 50% and 90% of the particle number size distribution. (b)Determined by Total Reflection X-ray Fluorescence (TXRF).

Synthesis of Gd-SPs and FUCO-Gd-SPs

The optimized emulsion conditions described above (Run 3) were applied to gadolinium Complex-2 (Table 1) to obtain two types of SPs: non-functionalized/Gd-loaded SPs (Gd-SPs, Run 4) and fucoidan-functionalized/Gd-loaded SPs (FUCO-Gd-SPs, Run 5). For dextran derivatives with higher modification degrees (Complex-3), no gel was obtained. This was likely due to a reduced amount of hydroxyl groups available for crosslinking and to steric hindrance. Complex-2 was chosen over Complex-1 because of its higher Gd content.

Size distribution, zeta potential and %P of Gd-SPs and FUCO-Gd-SPs were roughly like those obtained with model SPs (Run 3). Gd content was similar for both types of SPs (2.3-2.6 wt%)

but almost 2-times lower than the one of dextran complex precursor (4.0 wt%). Alkaline 20 crosslinking conditions would led to some hydrolysis of amide bonds linking Gd(DOTA) groups to dextran and to a loss of Gd(DOTA) moieties. This hypothesis was supported by the decrease in nitrogen content (around 1.70 wt% in SPs compared to 2.12 wt% in Complex-2).

FUCO-Gd-SPs contained 23±5 µmol S/g which corresponded to a fucoidan content of 1.3 wt% (about 26 wt% of the fucoidan initially dissolved in the aqueous phase). those measured by laser diffraction (~800 nm) whereas smaller average sizes were detected by TEM (~700 nm) and SEM (~400 nm). These differences arise from sample preparation (in hydrated or dried states) and observation conditions (vacuum).

The FUCO-Gd-SPs were stable for at least two weeks when stored in aqueous suspension at 4 °C. In addition, the effective protection of particle size during freeze-drying can be ensured with 5% (w/v) sucrose as cryoprotectant since no aggregation was observed after resuspension in aqueous medium. This allowed long-term storage of SPs. As expected, FUCO-Gd-SPs average size was found to be smaller in physiological saline solution (0.9% NaCl) because of the screening of phosphate negative charges (Figure 1a). The FUCO-Gd-SPs remained stable at room temperature and 37 °C for at least 72h under such conditions.

Cytotoxicity

Cytocompatibility of Complex-2 (Table 1) toward HUVECs was checked and compared with the one of free Gd 3+ ions (concentration ranging from 8 to 80 µg/mL). Cell viability was assessed by measuring metabolic activity of the mitochondria using resazurin reagent.

Complex-2 did not affect cell viability after 24h. In contrast, metabolic activity decreased down to 50% in the presence of free Gd 3+ (Figure S4). Mitochondrial dysfunction induced by Gd 3+ and other lanthanide ions has been already reported [START_REF] Feng | Impaired mitochondrial function and oxidative stress in rat cortical neurons: Implications for gadolinium-induced neurotoxicity[END_REF][START_REF] Gil | La 3+ , Gd 3+ and Yb 3+ induced changes in mitochondrial structure, membrane permeability, cytochrome c release and intracellular ROS level[END_REF][START_REF] Zhao | Mitochondrial dysfunction induced by different concentrations of gadolinium ion[END_REF]. These results further proved the successful chelation of Gd 3+ by DOTA groups of DexNH2-DOTA derivatives.

FUCO-Gd-SPs also showed excellent cytocompatibility even at concentrations at high as 1 mg/mL (Figure 2a). No major morphological changes of HUVECs were evidenced when compared to control conditions (Figure 2b). Furthermore, FUCO-Gd-SPs appeared to be internalized by endocytosis. Particles engulfment by HUVECs was clearly seen by confocal microscopy (Figure 2c). Further in vitro and in vivo studies will be required for a complete understanding of the mechanism involved in internalization, as well as the fate of the particles.

Proton relaxation effects of dextran derivatives and FUCO-Gd-SPs

The efficiency of an MRI contrast agent is correlated to its relaxivity. That is, its ability to accelerate longitudinal (1/T1) or transversal (1/T2) relaxation rates of the protons of hydrogen atoms from the surrounding water molecules [START_REF] Jacques | High-Relaxivity Magnetic Resonance Imaging Contrast Agents Part 2: Optimization of Inner-and Second-Sphere Relaxivity[END_REF]. Relaxometric properties of Complex-2 and FUCO-Gd-SPs were assessed in vitro on agarose phantoms at 7 Tesla.

Commercially available contrast agent DOTAREM (containing free Gd(DOTA) complex)

was used for comparison. Relaxation times, T1 and T2, were measured at a concentration range of 0.12-1 mM of chelated Gd 3+ . The relaxivities r1 and r2 were then calculated from the linear regression slope of 1/T1 and 1/T2 vs. Gd 3+ concentration and are depicted in Figure 3.

When Gd(DOTA) complex was attached to the dextran backbone of macromolecular Complex-2 or to the polysaccharide matrix of FUCO-Gd-SPs, both r1 and r2 relaxivities were enhanced with respect to DOTAREM. This effect was more pronounced in the case of FUCO-Gd-SPs with about twofold and fivefold increase in r1 and r2, respectively. As previously observed for other macromolecular or nanoparticulate contrast agents [START_REF] Fransen | r 1 and r 2 Relaxivities of Dendrons Based on a OEG-DTPA Architecture: Effect of Gd 3+ Placement and Dendron Functionalization[END_REF][START_REF] Huang | Chitosan oligosaccharide based Gd-DTPA complex as a potential bimodal magnetic resonance imaging contrast agent[END_REF][START_REF] Courant | Hydrogels Incorporating GdDOTA: Towards Highly Efficient Dual T1/T2 MRI Contrast Agents[END_REF], this relaxation rate enhancement can be ascribed to the restriction of the rotational motion of Gd(DOTA) complex inside polysaccharide matrix.

In addition, the highly hydrated nature of FUCO-Gd-SPs network, would enhance Gd-water molecule interactions and favor the transfer of magnetic effect to the bulk water [START_REF] Courant | Hydrogels Incorporating GdDOTA: Towards Highly Efficient Dual T1/T2 MRI Contrast Agents[END_REF][START_REF] De Sarno | Effect of crosslinking agent to design nanostructured hyaluronic acid-based hydrogels with improved relaxometric properties[END_REF].

In order to check how the relaxometric properties translated in image contrast, the signal intensity of both T1 and T2-weighted images (Figure 4a-b) was as well quantified. While T1enhancing agents result in positive/brighter contrast, T2 ones give predominantly negative/dark contrast. As shown in Figure 4c, positive contrast properties of FUCO-Gd-SPs were comparable to those of DOTAREM. However, FUCO-Gd-SPs appear to be a better

Targeting properties

The binding capacity of Gd-SPs and FUCO-Gd-SPs for P-selectin expressed onto the surface of human activated platelets was assessed by flow cytometry in three conditions: platelet-rich plasma (PRP), PRP with TRAP-activated platelets, and PRP with TRAP-activated platelets after blocking P-selectin with a specific antibody (anti-CD62P). As shown on Figure 5a, FITC-labeled FUCO-Gd-SPs strongly bound to activated platelets in absence of the antibody, in agreement with the expression level of P-selectin in each condition (Figure S5). These results proved both the availability of some fucoidan chains at the surface of the polysaccharide matrix for interacting with P-selectin on activated platelets and the specificity of the interaction between fucoidan-functionalized SPs and P-selectin.

The binding of Gd-SPs and FUCO-Gd-SPs to platelet aggregates under arterial blood flow conditions was evaluated as well (Figure 5b). Experiments were performed in a flow chamber mimicking arterial blood flow conditions (wall shear stress of 67.5 dyn/cm 2 ) on activated platelet aggregates. FUCO-Gd-SPs (TRITC labeled) significantly accumulated at the surface of the aggregates whereas Gd-SPs showed almost no binding. Moreover, FUCO-Gd-SPs remained attached even after washing with 0.9% NaCl at arterial shear rate. These results confirmed the targeting ability of fucoidan-functionalized SPs under dynamic physiological conditions. conditions [START_REF] Li | Development of Polymer Microcapsules Functionalized with Fucoidan to Target P-Selectin Overexpressed in Cardiovascular Diseases[END_REF][START_REF] Juenet | Thrombolytic therapy based on fucoidanfunctionalized polymer nanoparticles targeting P-selectin[END_REF]. Human whole blood labeled with DiOC6 (green) was injected into a collagen-coated microchannel to get platelets aggregates expressing P-selectin (left images). TRITC-labeled particles (red) were then injected during 5 minutes (middle images). Channels were washed with 0.9% NaCl after each step. Particles and platelets aggregates co-localization was evaluated by merged fluorescence microscopy (right images). Gd-SPs (without fucoidan) were used as control. White scale bar corresponds to 50 µm.

Discussion

The driven idea of the approach presented here was to prepare a new diagnostic platform with the potential for Health agencies approval and human use. That's why we used non-harmful, biocompatible and biodegradable materials as both final particle constituents and preparation process raw materials. STMP was for instance preferred over conventional glutaraldehyde, a crosslinker with documented cytotoxicity [START_REF] Oryan | Chemical crosslinking of biopolymeric scaffolds: Current knowledge and future directions of crosslinked engineered bone scaffolds[END_REF][START_REF] Reddy | Crosslinking biopolymers for biomedical applications[END_REF].

Biocompatible vegetable oil was, for its part, chosen as emulsion continuous phase instead of commonly used organic solvents. This choice supposed a challenge for the obtention of smaller particles as a highly viscous polysaccharide aqueous phase needed to be dispersed in a viscous oily phase. Reducing the size of our previous micrometric polysaccharide particles [START_REF] Bonnard | Leukocyte mimetic polysaccharide microparticles tracked in vivo on activated endothelium and in abdominal aortic aneurysm[END_REF] to submicronic range, required the optimization of several processing parameters including vegetable oil and surfactant type, polysaccharide molecular weight and concentration, and so on. We obtained a final size of about 800 nm far above 100 nm widely admitted as a limit to efficiently avoid a rapid clearance from the reticuloendothelial system (RES). In previous studies we have evidenced in vivo interaction of fucoidan-bearing microparticule of 2.5 µm with aneurysmal thrombi [START_REF] Bonnard | Leukocyte mimetic polysaccharide microparticles tracked in vivo on activated endothelium and in abdominal aortic aneurysm[END_REF][START_REF] Li | Development of Polymer Microcapsules Functionalized with Fucoidan to Target P-Selectin Overexpressed in Cardiovascular Diseases[END_REF].

Another key-parameter to limit the risk of quick RES uptake is the nature of the surface [START_REF] De | Drug delivery and nanoparticles: Applications and hazards[END_REF]. A polysaccharide coating may provide steric protection against protein adsorption (more particularly opsonins) and early macrophage uptake [START_REF] Lemarchand | Polysaccharide-decorated nanoparticles[END_REF]. Anyway, the biological responses and biodistribution of our submicronic particles remained to be investigated in vivo. Additional process optimization could further reduce, if needed, particle size.

Encapsulation of Gd-based contrast agents into polysaccharide nanoparticles have already been approached in three ways: by conjugation with polysaccharide precursor [START_REF] Huang | Magnetic resonance imaging of contrast-enhanced polyelectrolyte complexes[END_REF][START_REF] Kim | Gadolinium-chelate nanoparticle entrapped human mesenchymal stem cell via photochemical internalization for cancer diagnosis[END_REF][START_REF] Na | T1-Weighted MR imaging of liver tumor by gadolinium-encapsulated glycol chitosan nanoparticles without non-specific toxicity in normal tissues[END_REF][START_REF] Nam | Tumor Targeting Chitosan Nanoparticles for Dual-Modality Optical/MR Cancer Imaging[END_REF][START_REF] Payne | Multimodal Imaging Nanoparticles Derived from Hyaluronic Acid for Integrated Preoperative and Intraoperative Cancer Imaging[END_REF][START_REF] Zhang | Hyaluronic Acid-Chitosan Nanoparticles to Deliver Gd-DTPA for MR Cancer Imaging[END_REF] , by ionic trapping during particles preparation [START_REF] Gheran | Biocompatibility of Gd-Loaded Chitosan-Hyaluronic Acid Nanogels as Contrast Agents for Magnetic Resonance Cancer Imaging[END_REF][START_REF] Huang | Magnetic resonance imaging of contrast-enhanced polyelectrolyte complexes[END_REF][START_REF] Podgórna | Gadolinium alginate nanogels for theranostic applications[END_REF][START_REF] Rigaux | Characterization of Gd loaded chitosan-TPP nanohydrogels by a multi-technique approach combining dynamic light scattering (DLS), asymetrical flow-field-flow-fractionation (AF4) and atomic force microscopy (AFM) and design of positive contrast agents for molecular resonance imaging (MRI)[END_REF], or by post-modification of particles surface [START_REF] Chan | Long-Lasting and Efficient Tumor Imaging Using a High Relaxivity Polysaccharide Nanogel Magnetic Resonance Imaging Contrast Agent[END_REF]. Nevertheless, Huang et al. demonstrated that Gd 3+ ionically trapped into chitosan/dextran sulfate polyelectrolytes (PECs) is rapidly released after one day of incubation in PBS buffer at 37°C. In contrast, no release was detectable from Gd(DTPA)grafted PECs under the same conditions during at least 6 days. Besides limiting the potential toxicity of free Gd ions, grafting of Gd-chelates to polysaccharide offers also the possibility to adjust Gd-cargo during particles synthesis. Herein, we gave the priority to the well-known and already clinically approved Gd(DOTA) complex. Gd(DOTA) was conjugated to an aminated dextran via a carbodiimide reaction and the resultant macrocomplexes were employed to synthesize both Gd-SPs and FUCO-Gd-SPs via the optimized emulsion-crosslinking method.

By doing so, Gd(DOTA) groups were successfully incorporated to the designed platform conferring it dual positive and enhanced negative contrast properties (r1= 6.7 mM -1 s -1 and r2= 37.6 mM -1 s -1 at 7 T). Similar relaxation rates (r1= 5.4 mM -1 s -1 and r2= 36.4 mM -1 s -1 ) were observed under the same magnetic field for self-assembled chitosan nanogels post-modified with Gd(DOTA) moieties [START_REF] Chan | Long-Lasting and Efficient Tumor Imaging Using a High Relaxivity Polysaccharide Nanogel Magnetic Resonance Imaging Contrast Agent[END_REF]. Increasing Gd cargo per particle would be particularly interesting to eventually improve T1 relaxometric properties and decrease necessary doses for patients. This would probably require the optimization of the current dextran modification protocol or the implementation of another chemistry route leading to chemical bonds less sensitive to crosslinking in basic media. It is worth noting that our imaging strategy is not only based on the contrast properties of the resulting SPs but also on their biospecificity. Low molecular weight fucoidan employed here as targeting agent recently passed preclinical evaluation as radiotracer for in vivo detection of cardiovascular pathologies [START_REF] Chauvierre | Pharmaceutical Development and Safety Evaluation of a GMP-Grade Fucoidan for Molecular Diagnosis of Cardiovascular Diseases[END_REF], and early stages of Phase I and Phase II clinical trials for its safety and validation of its ability to detect acute thrombosis in patients with suspected acute deep vein thrombosis are ongoing. Preferential accumulation of fucoidan-functionalized SPs onto thrombosed areas can be expected because of their binding affinity to activated platelets. This should rise the local concentration of contrast agent and increase thrombus imaging sensitivity of the FUCO-Gd-SPs compared to the commercial and non-biospecific DOTAREM at the same Gd dose.

Conclusions

Early detection of atherothrombotic lesions remains a big medical challenge. In this work, we developed novel biospecific polysaccharide submicronic particles containing Gd-based MR contrast agent. First, Gd(DOTA) moieties were successfully conjugated to dextran. The resulting macrocomplexes were then used to prepared Gd-loaded and fucoidan-functionalized particles by an emulsion-crosslinking method. This method was solvent-free in both production and purification steps. Particles exhibited good colloidal stability and were cytocompatible with human endothelial cells. The affinity of fucoidan-bearing particles for human activated platelets was evidenced under static and dynamic conditions. The particles exhibited good MR contrast properties with a significant signal enhancement of T2-weighted images when compared to DOTAREM. These results indicated their high potential as a diagnostic probe for molecular imaging of atherothrombosis by MRI. As a next step, the biospecificity of the particles and their capacity to image atherothrombosis will be checked invivo in experimental models of the disease.

  3chloropropylamine hydrochloride, 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide hydrochloride (EDC.HCl), N-hydroxysuccinimide (NHS), Gadolinium(III) chloride hexahydrate (GdCl3.6H2O) and Paraformaldehyde (PFA) were purchased from Fisher Scientific (Illkirch, France). 1,4,7,10-Tetraazacyclododecane-1,4,7,10-tetraacetic acid (DOTA) was provided by Leap Labchem (Hangzhou, China). Ethylenediaminetetraacetic acid (EDTA), Trisodium Trimetaphosphate (STMP), Sodium Dodecyl Sulfate (SDS), Triton X-100, 7-hydroxy-10-oxidophenoxazin-10-ium-3-one (resazurin), 3,3′-Dihexyloxacarbocyanine iodide (DiOC6), 4',6-diamidino-2-phenylindole (DAPI) and Phalloidin-TRITC were from Sigma Aldrich (Saint-Quentin-Fallavier, France). Dextran-FITC ( = 70 000 g/mol) and Dextran-TRITC ( = 40 000 g/mol) were from TdB Consultancy (Uppsala, Sweden). Polyglycerol polyricinoleate (PGPR 4150) was a gift from Palsgaard SAS (Lyon, France). Sunflower oil (Lesieur, France) is a mixture of saturated fatty acids (palmitic acid ~5 wt%-and stearic acid ~6 wt%) and unsaturated fatty acids (mainly oleic acid ~37 wt% and linoleic acid ~51 wt%). Thrombin receptoractivating-peptide (TRAP) was obtained from PolyPeptide laboratories (Strasbourg, France). PE-CyTM5 mouse anti-human CD41a was provided by BD Pharmingen, (Le Pont de-Claix, France), mouse antihuman CD62P and mouse anti-human CD62P-FITC were obtained from Beckman Coulter (Villepinte,

  (a) Nitrogen content estimated by elemental analyses. (b) Degree of substitution of initial primary amines (NH2), residual primary amines (NH2r, not modified with DOTA groups) and grafted DOTA moieties (DSDOTA) per 100 AGU were calculated from N content (DSNH2r + DSDOTA = DSNH2). (c) Gadolinium content determined by total reflection X-ray fluorescence (TRXF) spectrometry. (d) Degree of substitution of gadolinium ions per 100 glucopyranose units estimated from Gd content. (e) Evaluated from SEC-MALLS in NaNO3/NaN3 (0.15 M/0.02% (w/v)) with dn/dc=0.146 mL/g. EDC/NHS chemistry was used to graft DOTA ligands to amine functions of DexNH2. Higher nitrogen content of resultant DexNH2-DOTA derivatives (with respect to the corresponding DexNH2 precursors) confirmed the incorporation of the DOTA tetraazamacrocycle (2 nd step,

Figure 1 .

 1 Figure 1. a) Size distribution in water and NaCl 0.9% and b) TEM c) Confocal microscopy and d) SEM-Micrographs of FUCO-Gd-SPs. In the case of confocal microscopy, sample was analyzed in its hydrated state. For the other techniques (TEM and SEM), SPs were air-dried and submitted to vacuum conditions.

Figure 2 .

 2 Figure 2. a) Cytocompatibility of FUCO-Gd-SPs towards HUVECs after 24 h incubation at 37°C. 100% of mitochondrial metabolic activity (resazurin reduction assay) corresponds to control cells incubated without particles. n = 3. b) Fluorescent images of HUVECs. F-actin is shown in red (TRITC-Phalloidin) and nuclei are shown in blue (DAPI), white scale bar corresponds to 20µm c) Zoom on an isolated cell evidences the internalization of the fluorescent particles. White scale bar corresponds to 10µm.

Figure 3 .

 3 Figure 3. a) Longitudinal (r1) and b) transversal (r2) relaxation rates vs. Gd 3+ concentration for DOTAREM, Complex-2 and FUCO-Gd-SPs at 7 Tesla. The solid lines represent the linear regression of the data. The slopes of the curves corresponding to relaxivity (r1 or r2) are indicated. Longitudinal and transversal proton relaxivities of FUCO-Gd-SPs were 1.7 and 5.0 times higher than those of DOTAREM.

Figure 4 .

 4 Figure 4. a) T1 and b) T2 weighted MRI acquisitions at 7 Tesla of DOTAREM, Complex-2 and FUCO-Gd-SPs phantoms (agarose 2% (w/v)) used for relaxivity calculations. Background corresponds to control (agarose gel with no Gd). Relative c) T1 and d) T2 weighted signal intensities versus Gd concentration. FUCO-Gd-SPs showed enhanced negative contrast effect compared to DOTAREM.

Figure 5 .

 5 Figure 5. a) Flow cytometry assessment of interactions of FITC-labeled Gd-SPs and FITC-labeled FUCO-Gd-SPs with either non-activated platelet-rich plasma (PRP), PRP activated with TRAP (PRP+TRAP) and PRP activated with TRAP and blocked with P-selectin antibody (PRP+TRAP+anti-CD62P) (Li et al., 2017). The mean fluorescence intensity (MFI) on the FITC channel was measured for 10,000 events of PE-Cy5 labeled platelets at a particles concentration of 10 mg/mL (n=3; ***p<0.001). b) Evaluation of FUCO-Gd-SPs binding on activated platelets under arterial flow

Table 2 .

 2 Formulation and physico-chemical characterization of polysaccharide submicronic particles.

	Crosslinking reaction was performed at 50°C during 20 min with [Polysaccharide]=200 g/L
	[NaOH]=1M, [PGPR]= 6% (w/v).
	R.	Polysaccharide		D(nm)	Span (a)	Zeta	%P (b)	%Gd (b)
						potential
						(mV)
	1	DexT70	0.043	1720±50 0.61±0.01	-18±3	0.6±0.1	-
	2	DexT70	0.087	1230±45 0.67±0.03	-22±3	0.8±0.1	-
	3	DexT70	0.170	790±30	0.61±0.01	-30±3	1.1±0.1	-
	4	Complex-2	0.170	720±35	0.67±0.03	-28±5	1.0±0.1	2.6±0.2
	5	Complex-2/Fuco	0.170	840±45	0.60±0.02	-25±4	1.1±0.1	2.3±0.1

Acknowledgments

The authors express their highest gratitude to Murielle Maire (LVTS, Villetaneuse, France) for fucoidan content determination, to Alina Zenych (LVTS, Paris, France) for some preliminary experiments, to Christine Choqueux (LVTS, Paris, France) and UTC (Compiègne, France) for SEM images, to Samira Benadda and CRI U1149 imaging facilities for confocal imaging training and to Stéphane Loyau and Kevin Guedj (LVTS, Paris, France) for flow cytometry experiment design and data analysis. We also thanks Rémi Le Borgne from the ImagoSeine facility (Jacques Monod Institute Paris, France), and the France BioImaging infrastructure supported by the French National Research Agency (ANR-10-INSB-04, « Investments fit the future ») for their precious help with TEM images. This work was supported by INSERM, Université de Paris, Université Paris 13 and UMS34 FRIM, and received the financial support of the ANR-16-CE18-0031 NANOPACT.


Hocine Menana

Bruno Douine

Yazid Statra

Optimization of Fully HTS Ironless Axial Flux Electrical Machines

Keywords: Fully HTS ironless axial flux electrical machine, three-dimensional semi-analytical modeling approach, Volume integral method, Maxwell stress tensor method, Multi objective optimization

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

INTRODUCTION

Recently, fully high temperature superconducting (HTS) electrical machines have aroused worldwide research efforts due to their high power densities, making them good candidates for embedded applications, such as wind power generation and electrical aircrafts [START_REF] Ainslie | Recent advances in superconducting rotating machines: an introduction to the 'Focus on Superconducting Rotating Machines[END_REF][START_REF] Zhang | Design and Modeling of 2G HTS Armature Winding for Electric Aircraft Propulsion Applications[END_REF]. HTS are characterized by high current densities and low power losses, allowing to increase the linear current loading and thus the torque density and the global efficiency of the HTS electrical machines, compared to conventional ones. In addition, the air gap in a fully HTS machine can be made much smaller, compared to hybrid ones (superconductingcopper machines), resulting in a higher magnetic field density [START_REF] Dezhin | System Approach of Usability of HTS Electrical Machines in Future Electric Aircraft[END_REF]. Furthermore, the elimination of the iron core increases the efficiency, due to absence of core losses, and reduces the weight [START_REF] Ravaud | Ironless permanent magnet motors: Three-dimensional analytical calculation[END_REF]. However, the strong nonlinear behavior of HTS materials makes the sizing and optimization procedures of HTS electrical machines delicate operations, where local electromagnetic quantities have to be evaluated generally in 3D. Numerical approaches are generally inevitable, facing the limitations of conventional numerical tools which struggle in some cases to provide accurate solutions in reasonable computation times, despite the high performances of the recent computers. The development of specific modeling approaches is thus needed to speed up the sizing and optimization procedures of HTS systems. In this context, a volume integral approach is proposed in this work for a rapid 3D modeling of forces and torques in a fully HTS ironless axial flux machine (IAFM). The calculation of the magnetic field using the integral equations is obtained in very short times thanks to the use of particular volumetric basis elements for which the solution is obtained analytically. The developed model is then used in a multi objective optimization, based on genetic algorithms, aiming to maximize the magnetic torque and to minimize the superconducting wire length in the considered structure, respecting the constraints related to the critical bending radius of the superconducting tape and the dependence of the critical current density on the magnetic field. A comparison with 3D finite element analysis on the optimal solution confirms the accuracy and the rapidity of the proposed approach.

The studied HTS-IAFM and the modeling approach are presented in the next section. Section III describe the multi objective optimization procedure. The obtained results for the optimal solution are presented and compared with finite element computation in Section IV. In Section V, a mechanical study is carried out to define the volume of the machine and its torque density, which is then compared to conventional ones.

THE MODELLING APPROACH

The structure of the studied HTS-IAFM is shown in Fig. 1. It consists of an axial flux synchronous machine constituted of two sets of triangular shaped HTS coils mounted on nonmagnetic supports. The structure parameters are given in Table I. The inductor coils are supplied by DC currents I in a way to obtain alternatively north and south poles. This is the rotating part of the machine. The stator with three-phase double-layer concentrated nonoverlapping armature windings is supplied by AC currents. The use of concentrated nonoverlapping coils has certain advantages: shorter end-turn length and reduced stator winding cost due to the reduced number of coils and the simplicity of the winding [START_REF] Geng | Analysis and Implementation of New Ironless Stator Axial-Flux Permanent Magnet Machine With Concentrated Nonoverlapping Windings[END_REF][START_REF] Kamper | Analysis and Performance of Axial Flux Permanent-Magnet Machine With Air-Cored Nonoverlapping Concentrated Stator Windings[END_REF]. This choice is more appropriate when using HTS materials, where it is necessary to take into account the limitations of the HTS related to the critical current and bend radius. The ironless windings are fixed on the anterior sides of epoxy resin supports (G11) containing guide-track grooves for coils embedding, as shown in Fig. 1(a).

A magneto-static modeling of the machine is performed. The aim is to evaluate the forces and torque between the two set of coils, taking into account the dependence of the critical current density in the HTS coils on the magnetic field. The Biot-Savart's law is used to compute the magnetic field produced by the HTS coils. The three-phase windings are fed with electrical current such as Ia = I and Ib = Ic = -I/2 corresponding to AC operation at a given instant of the time variation of the three phase currents. As shown in Fig. 1(b), the coils are discretized into rectangular beam or circular arc segment volume elements of rectangular cross sections. The magnetic field created by the structure is then the superposition of the magnetic fields created by the basic elements. Figure 1(c) gives more details on the rotor coils dimensions and orientation.

Magnetic field calculation

Let (x, y, z) be a field point and in Cartesian coordinates system; then, the magnetic flux density for a straight beam with rectangular cross section, parallel to the z axis, with a cross section (x2-x1)×(y2-y1), length (z2-z1), carrying a constant current density J oriented in the positive z direction, is given as follows [START_REF] Urankar | Vector potential and magnetic field of current-carrying finite arc segment in analytical form, Part III: Exact computation for rectangular cross section[END_REF]:

( ) ( ) 2 0 , , 1 , , 1 ( , , ) , 4 i j k m m i j k J B x y z A x y z m x y µ π + + = = - = ∑ (1) 1 1 1 1 2 5 1 1 1 1 3 4 ( , , ) sinh sinh tanh , ( , , ) sinh sinh tanh , x i k j y j k i A x y z u w v θ θ θ - - - - - -  = - - +   = + -   (2) Where: , 2 , 1 , , / , / , / , / , / , , , , , , 5 4 3 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 = = = = = = + + = + = + = + = - = - = - = k j i r v w u r u w v v u w w v u r u w w v v u z z w y y v x x u j k i i k j ki j jk i ij k k j i i k ki k j jk j i ij k k j j i i θ θ γ θ β θ α θ γ β α (3)
The expressions of the components of the magnetic field for a circular arc segment are also available in [START_REF] Urankar | Vector potential and magnetic field of current-carrying finite arc segment in analytical form, Part III: Exact computation for rectangular cross section[END_REF]. However, in this work, we use the expressions given by (Eq. 4) which are simpler to implement [START_REF] Capelluto | Algorithm for the Fast Calculation of Magnetic Fields Generated by Arc-Shaped Conductors With Rectangular Cross Section[END_REF]. Indeed, in this case, the analytical integration of the Biot-Savart's law was performed along two coordinates, obtaining a 1-D integrand (thus avoiding the use of elliptic integrals). The result is very satisfying in terms of rapidity and precision.

( ) ( ) ( ) 2 1 2 1 2 1 0 0 0 1 , , cos( ) 4 , , sin( ) 4
, , ( 0.5 .ln( ) . ) 4

x xy

y xy z z A J B x y z L d J B x y z L d J B x y z L T M f R d ϕ ϕ ϕ ϕ ϕ ϕ µ ϕ ϕ π µ ϕ ϕ π µ ϕ π = = - = + + ∫ ∫ ∫ (4)
The analytical expressions of Lxy, Lz, T1, M, f and RA depend directly on the geometrical parameters of the studied structure [START_REF] Capelluto | Algorithm for the Fast Calculation of Magnetic Fields Generated by Arc-Shaped Conductors With Rectangular Cross Section[END_REF].

Force and torque calculations

The axial force (Fz) and the static torque (Γ) are obtained by the integration of the Maxwell stress tensor on a surface (S) located in the middle of the air gap between the two sets of coils:

( )

2 2 2 0 1 1 2 z z x y S F B B B dxdy µ = - - ∫∫ (5)
( )

0 1 y z x z S B B x B B y dxdy µ Γ = - - ∫∫ (6)

Operating current of the HTS coils

The critical current density of a superconducting coil does not only depend on the temperature, but also on the applied magnetic field. The increase of the magnetic field lead to a decrease of the critical current density, and thus the degradation of the HTS material performances. Indeed, superconducting materials have a nonlinear behavior represented by [START_REF] Urankar | Vector potential and magnetic field of current-carrying finite arc segment in analytical form, Part III: Exact computation for rectangular cross section[END_REF], where E and Ec are the electrical field and its critical value respectively; J and Jc are the electric current density and its critical value respectively, and n is the creep exponent that defines the steepness of the transition from the superconducting to the normal state. The critical current density and the creep exponent depend on both the temperature and the magnetic field.

( )

( ) n B c c J E E J B   =     (7)
The considered HTS coils are assumed to be made of 1G BSCOO tape. In such material, the critical current density and the creep exponent exhibit an anisotropic dependence on the magnetic field, which can be modelled by the Kim's model, given by [START_REF] Capelluto | Algorithm for the Fast Calculation of Magnetic Fields Generated by Arc-Shaped Conductors With Rectangular Cross Section[END_REF], where Jc0 and n0 are the values of the critical current density and the creep exponent at zero magnetic field [START_REF] Statra | A volume integral approach for the modelling and design of HTS coils[END_REF].

( )

0 / / 1 2 2 2 0 / / 0 / / 1 2 2 2 0 / / ( , ) 1
( , ) (1 )
c c J n J J B B B k B B n n B B B k B B δ ⊥ - ⊥ ⊥ - ⊥  =  + +    =  + +  (8)
The width and thickness of the used BSCCO tape are respectively: lw = 4.3 mm and ew = 0.23 mm. The critical bending radius of the tape is: Rc = 35 mm. Its main characteristics at 30 K are listed in Table II [START_REF] Belguerras | Study of HTS Magnetic Coupler Using Analytical and Numerical Computations[END_REF]. The critical value of the electric field is usually set to: Ec=1μV/cm [START_REF] Statra | A volume integral approach for the modelling and design of HTS coils[END_REF][START_REF] Belguerras | Study of HTS Magnetic Coupler Using Analytical and Numerical Computations[END_REF]. The operating current is obtained for a maximum value of the electric field applied locally on the coil that is equal to Ec, i.e. max(E/Ec)=1. This requires some iterations using [START_REF] Urankar | Vector potential and magnetic field of current-carrying finite arc segment in analytical form, Part III: Exact computation for rectangular cross section[END_REF] and [START_REF] Capelluto | Algorithm for the Fast Calculation of Magnetic Fields Generated by Arc-Shaped Conductors With Rectangular Cross Section[END_REF]. The current is increased as long as max(E/Ec)<1. However, in the optimization procedure this takes a lot of time. Therefore, an alternative method to calculate the operating current is adopted: the operating current is obtained by the intersection between the load line representing the current as a function of the maximum magnetic field applied locally on the coil and the curves ( ⊥, ∥). This method provides a faster estimation of the operating current. Indeed, obtaining the load line requires the knowledge of only one operating point of the coil.

MULTI OBJECTIVES OPTIMIZATION

The developed semi-analytical model is used in a multi objective optimization procedure based on the Non-Dominated Sorting Genetic Algorithm (NSGA II) [START_REF] Deb | A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II[END_REF]. The goal is to maximize the magnetic torque (Eq.6), and to minimize the superconducting wire length (Lsup) which is the sum of L1 and L2, where:

r r r 1 (2Tw -W ) ( + + ) 4p N cos( /2) 2 2 r r L H L α π = (9) s s s 2 (2Tw -W ) ( + + ) 2Q N cos( /2) 2 2 s s L H L β π = (10)
In ( 9) and ( 10), Q is the number of stator coils, while Ns and Nr represent the number of turn in a coil of the stator and the rotor respectively. The other parameters are given by the following equations:

p π α = (11) 2 Q π β = (12) int sin( / 2) 1 sin( / 2) s R Tw β β = - int sin( / 2) 1 sin( / 2) r R Tw α α = - int 2 * s out s H R R Tw = - - (15)
int 2 * r out r H R R Tw = - - (16)
2 tan( / 2) III. The optimization procedure consists to determine the vector V= [p x1 x2 x3] of optimal variables that verify the objective functions, respecting the constraints related to bending radius given in table IV and critical current density. To avoid local transition and quench in the HTS coils, especially in the armature windings (working at low frequencies), only 80% of the critical current is injected in the HTS coils.

s s L H β = (17) 2 tan( / 2) r r L H α = (18)
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 1 / 2 / 2 2 1 / 2 / 2 c w out w out M R e sin R sin R e sin R s x in a α α β β             + -  - 1 1 ( ) 2 / 2 1 / 2 2 / 2 1 / 2 1 ( ) ( ) 1
( )

M n n s i in sin si sin α α β β - -         -                + -    + x2 2 w s e Tw 1 c s R Tw - x3 2 w r e Tw 1 c r R Tw -
The block diagram shown in Fig. 2 presents the general structure of the optimization procedure, in which the main steps are: i.

Definition and insertion of the vector of the optimization variables in the semi-analytical model.

ii.

Evaluation the superconducting wire length Lsup=L1+L2.

iii.

Evaluation the critical current density Jc for the position (φ = 0°), corresponding to the worst case.

iv.

For J = 80% Jc, determine the maximum value of the torque corresponding to the displacement angle φ = π/(2p).

The algorithm verifies the objective functions and satisfies the imposed constraints by repeating the steps i-iv.

RESULTS

The algorithm gives possible compromises between the two criteria (torque and superconducting wire length) as shown in Fig. 3 which represent the evolution of the Pareto front according to the number of generations for a population of 30 individuals. These compromises strongly depend on the constraints imposed. We notice that the algorithm converges after 145 generations.

The configuration for which the couple is maximum in Fig. 3 is selected. The values of the corresponding optimization variables are given in Table V. The results of the torque and the axial forces calculated by the semi analytical model have then been compared with 3D finite element analysis performed on COMSOL software [START_REF] Comsol | Finit-element software package comsol multiphysic version 4[END_REF], in the aim of validation. A formulation in terms of the magnetic vector potential is used in the 3D FEM.

Figures 4 and5 show, respectively, the axial force and the static torque as a function of the mechanical rotor position φ. The axial force reaches a maximum value of 23.5 kN for φ = 0°, while the torque has a maximum value of 4.52 kN.m for φ = 18°. We also notice that the axial force has no mean value due to the absence of ferromagnetic materials in the studied structure. The axial force and static torque calculated with the proposed approach are in good accordance with those obtained by 3D FEM simulation. However, for one point of computation, the computing time is in the order of few seconds using the proposed approach, while it is around ten minutes for the FEM.

Figure 6 shows a comparison between semi-analytical and finite element calculations of the operating current density of the superconducting coils for φ = 0°, which corresponds to the worst case, by using the maximum electric field criterion: max(E/Ec)=1. The obtained critical current density is about 268 A/mm 2 . It can be seen that the results of the semi-analytical model are close to those obtained by the finite elements analysis. The difference between the analytical and numerical calculations of the operating current density, for both methods described above (section 2.3), is less than 0.4 % as shown in table VI.

MECHANICAL STUDY

This part aims to estimate the thickness of the mechanical supports of the two sets of HTS coils in order to resist to the axial forces. As already mentioned above, the coils are placed on supports made from G11 material. This kind of support ensures the thermal insulation between the superconducting coils and the motor shaft which is at the room temperature. Figure 7 (a) shows the shape of the support structure. It has an inner and outer diameter of 56mm and 740mm respectively. The inner diameter which represent the diameter of the motor shaft is calculated using the following relation [START_REF] Fanchon | Guide de mécanique[END_REF]:

1 3 16 D πτ Γ   ≥     (19)
Where, τ and Γ represent, respectively, the maximum shear stress and the torque supported by the shaft. Using a safety factor of two, the diameter is calculated to be able to transmit twice the maximum torque calculated previously with the maximum stress equal to the half of the tensile strength of the steel used to make the shaft (565 MPa) [START_REF] Carl | SUPERCONDUCTING ACCELERATOR MAGNETS: An Introduction to Mechanical Design and Construction Methods[END_REF].

The volume axial forces obtained for a position (φ=0°) on COMSOL software, are illustrated in Fig. 7(b). It can be seen that these forces are not applied equally on all the coils. The force is greater in the coils of phase (a). Indeed, the latter is supplied by a current I, while the other phases are supplied by currents equal to ±I/2. To evaluate the maximum stress applied on the supports, the worst case is considered:

-By integrating the greatest force applied on one coil, we find an axial force of 6300 N. -We applied on the two set of coils a total force of 63 kN which represents the force applied to a coil multiplied by the maximum number of coils in one set (10 in this case).

The distribution of the stress applied to one of the supports for a thickness of 30 mm, is represented in Fig. 8. It can be noticed that the highest stress occurs on the surface close to the motor shaft, where fixed constraint is applied. Figure 9 shows the evolution of the maximum stress applied locally on the support and the displacement between the two supports as a function of the support thickness. The thickness of the mechanical support is chosen so that the displacement and the stress do not exceed 10% the thickness of the air gap, and the half of the tensile strength of the used material (Von Mises Criteria) respectively (Table VII). The result is a thickness of 35 mm, leading to an approximate torque density of the machine of 156 kN.m/m 3 , which is much higher than that of conventional machines [START_REF] Dubois | Comparison of generator topologies for direct-drive wind turbines[END_REF]. This result takes into account only the volume of the active parts.

CONCLUSION

The design and optimization of superconducting electrical machines is mainly based on the evaluation of local quantities, due to the strong dependence of superconductive material performances to the magnetic field, and rapid modeling approaches are needed. In this context, this paper presents a three-dimensional semianalytical approach based on the volume integral method for the forces and torque calculations in a fully HTS ironless axial flux synchronous machine. The performances of the developed model and its advantages, compared to 3D FEM analysis, have been shown on a multi-objective optimization example. The considered example allowed also to appreciate the performances of the fully HTS electrical machines compared to conventional ones. The evaluation of AC losses in the HTS coils, and the cryogenic system sizing will be studied in future work.

Fig. 1 .

 1 Fig. 1. Geometry of the modelled HTS ironless axial flux machine (p=5, Q=9) (a) Topology (b) Coils structure and dimensions (c) details on the rotor coils dimensions and orientation

Fig. 2 .

 2 Fig. 2. Process of the optimization

Fig. 3 .

 3 Fig. 3. Evolution of the Pareto front according to the number of generations

Fig. 4 .Fig. 5 .Fig. 6 .

 456 Fig. 4. Axial force versus mechanical rotor position (φ)

Fig. 7 .

 7 Fig. 7. (a) Support structure (b) Volume axil force distribution (N/m 3 )

Fig. 8 .

 8 Fig. 8. The distribution of the stress en MPa for a thickness of 30 mm.

Fig. 9 .

 9 Fig. 9. Maximum stress and displacement versus the thickness of the support.

TABLE I .

 I PARAMETERS OF THE STUDIED HTS-IAFM

	Parameter	Description	Value
	Rout	Outer radius	350 mm
	lw	Coils thickness	4.3 mm
	e	Thickness of the air gap	5 mm
	ke	Filling factor	0.83

TABLE II .

 II CHARACTERISTICS OF THE HTS TAPE @ 30K

	Parameter	Jc0	BJ0	k	δ	n0	Bn0

Value

537 A/mm

2

1.01 T 0.182 0.87 31 2 T

TABLE III .

 III RANGE OF VARIATION OF THE OPTIMISATION VARIABLES

	Parameter	Description	Range	Nature
	p	Number of pole pairs	[2-8]	Integer
	x1 = Rint /Rout	Coefficient which defines the inner radius	[0.1-0.6]	Real
	x2 = Ws /Tws	Coefficient which defines the stator coil's width	[0.1-0.6]	Real
	x3 = Wr /Twr	Coefficient which defines the rotor coil's width	[0.1-0.7]	Real
	TABLE IV.	CONSTRAINTS ON THE OPTIMISATION VARIABLES
	Parameter	Min Value	Max Value
	x1

TABLE V .

 V PARAMETERS OF THE HTS-IAFM AFTER OPTIMIZATION

	Parameter	Description	Value
	p	Number of pole pairs	5
	Rin	Inner radius	149 mm
	Wr	Rotor coil's width	42.26 mm
	Ws	Stator coil's width	31.5 mm
	Γ	Torque value	4.52 kN.m
	Lsup	Superconducting wire length	1.23 km
	Jc	Critical current density	268.22 A/mm 2

TABLE VI .

 VI RESULTS OF THE OPERATING CURRENT DENSITY

	Jc (A/mm 2 )	Max(E/Ec)	Load line	Difference
	Semi-analytical	268	267.9	0.037 %
	FEM	267	267.36	0.135 %
	Difference	0.37 %	0.2 %

TABLE VII .

 VII EXTRAPOLATED MECHANICAL PROPERTIES OF THE USED MATERIAL[START_REF] Carl | SUPERCONDUCTING ACCELERATOR MAGNETS: An Introduction to Mechanical Design and Construction Methods[END_REF]

	G11-CR	Young's Modulus	Poisson's	tensile strength
		(E) (GPa)	ratio, ν	(MPa)
	Temperature :		0.216	856
	(30 K)