T Deleau

J-J Letourneau

S Camy

F Espitalier

J Aubin

H Helouvry

N Macedo Portela Da Silva

A transparent micro-device to study mass transfer and thermodynamics in two-phase flows at high pressure

Concentration data and mass transfer coefficients between supercritical CO2 and water in microfluidic capillaries are still scarce in the literature, although they are a big asset for the understanding of green chemical processes using water and supercritical CO2.

In this study, a transparent, inexpensive and pressure resistant microsystem is developed to investigate mass transfer of a two-phase flow of water and CO2 under high-pressure (P > 70 bar). It is based on microcapillary technology [1] and allows 2D axisymmetric modelling.

INTRODUCTION

Since the early 1980s, microfluidics has proven to be an effective means to intensify chemical processes. Indeed, the decrease in characteristic length scales leads to shorter diffusional paths increased surface area to volume ratios, thereby decreasing the characteristic times for heat and mass transfer and enhancing transport phenomena. With the emergence of high-pressure applications in microfluidics, the development of highly resistant microfluidic chips has been the focus of a number of studies. Amongst these, glass/glass [START_REF] Tiggelaar | Fabrication, mechanical testing and application of high-pressure glass microreactor chips[END_REF] and silicon/glass microreactors [START_REF] Trachsel | Transparent silicon/glass microreactor for high-pressure and high-temperature reactions[END_REF][START_REF] Murphy | Solder-based chip-to-tube and chip-to-chip packaging for microfluidic devices[END_REF][START_REF] Marre | Design and packaging of microreactors for high pressure and high temperature applications[END_REF] have shown to resist pressures of up to 400 bar. The microchannels are constructed using either wet or dry etching methods and then are sealed to glass via anodic bonding. These microchips have the advantage of resisting high-pressures and also allow optical access to the flow for in-situ characterization. In addition, silicon/glass chips have the asset of enabling very good temperature control due to the high thermal conductivity of the silicon wafer [START_REF] Marre | Design and packaging of microreactors for high pressure and high temperature applications[END_REF]. However, the fabrication methods employed require clean room facilities, specific equipment and expertise, and entail relatively high operating and fabrication costs, which are limiting when rapid prototyping is required. Some simpler glass devices based on fused-silica capillaries have also been proposed for high-pressure applications [START_REF] Portela Da Silva | Transparent and Inexpensive Microfluidic Device for Two-Phase Flow Systems with High-Pressure Performance[END_REF][START_REF] Marre | Dripping to jetting transitions observed from supercritical fluid in liquid microcoflows[END_REF]. Marre et al. [START_REF] Marre | Dripping to jetting transitions observed from supercritical fluid in liquid microcoflows[END_REF] showed the use of silica capillaries under pressure conditions ranging from 80-180 bar. Macedo Portela da Silva et al. [START_REF] Portela Da Silva | Transparent and Inexpensive Microfluidic Device for Two-Phase Flow Systems with High-Pressure Performance[END_REF] demonstrated that operating pressures up to 300 bar could be achieved by embedding silicon capillaries in epoxy resin. Both of these studies also showed that two-phase flow can be easily visualized and characterized by shadowgraphy in such capillaries. However more elaborate optical characterization techniques, such as micro Particle Image Velocimetry, would be limited in these devices because of problems related to optical distortion, poor light transmission and focal depth. Recently, Martin et al. [START_REF] Alexandre | Fast and Inexpensive Method for the Fabrication of Transparent Pressure-Resistant Microfluidic Chips[END_REF] developed systems based on the use UV-curable off-stoichiometry thiol-ene epoxy (OSTE+) polymer chemically bonded to glass that proved to be resistant to CO2 without failure up to at least 200 bar and could be used at high pressure for several hours. However, such devices are up to now limited in terms of channel size and lengths. The purpose of this study is to develop capillary-based microfluidic devices, which are reinforced by the use of UV-curable off-stoichiometry thiol-ene epoxy (OSTE+) polymer and allow sufficient channel lengths in order to investigate mass transfer occurring in a two-phase CO2-water system.

MATERIALS AND METHODS

Microreactor design

The microreactor developed in this study (Figure I(a)) is based on the pressure-resistant microreactor technology developed by [START_REF] Portela Da Silva | Transparent and Inexpensive Microfluidic Device for Two-Phase Flow Systems with High-Pressure Performance[END_REF] and [START_REF] Alexandre | Fast and Inexpensive Method for the Fabrication of Transparent Pressure-Resistant Microfluidic Chips[END_REF], whereby a capillary tubing is embedded in a transparent resin and supported by a polymethyl methacrylate (PMMA) chassis. In this new prototype OSTEMER resin, which has high optical quality and has shown to be resistant to pressure [START_REF] Alexandre | Fast and Inexpensive Method for the Fabrication of Transparent Pressure-Resistant Microfluidic Chips[END_REF], is used for embedding the capillary tubes and ensuring optical access to the flow via a glass window.

Fabrication

A PMMA block (270 x 140 x 20 mm 3 ) is machined with a digital milling machine (Charlyrobot -Charly4U CNR3) to order to hold a glass window (40mm x 40mm) and house the coiled capillary system. A transparent box is also made in order to contain the reactor and a heating fluid. The milling process takes approximately 4 hours.

3 m of fused-silica capillary tubing (ID = 530 µm and OD = 665 µm) is coiled and inserted into the chassis and held in place with a guiding support, in which sleeves are inserted (region B in figure II). The plastic coating around the capillary is then carefully burned using a flame and removed with a cotton swab under a microscope in order to improve the optical transparency of the observation zone (region A in figure II).

OSTEMER resin (Mercene Labs) is then poured over the top of the capillary system into the PMMA/glass support, such that it entire covers the capillary tubes. The ensemble is then exposed to UV light for 35 s at 25 mW/cm 2 .Crystal Clear OSTEMER resin has been chosen because of its transparency and low shrinkage properties as reported by Martin et al. [START_REF] Alexandre | Fast and Inexpensive Method for the Fabrication of Transparent Pressure-Resistant Microfluidic Chips[END_REF].

Stainless-steel connectors for high pressure applications (Upchurch Scientific, USA) are used to connect the capillary reactor to the external network pipes (pumps etc.). Two phase flow is generated in the capillary using a coaxial contacting setup with a T-junction.

Experimental rig

The microreactor is integrated into a high-pressure circuit, which is fed by two syringe pumps (ISCO 260 ISCO 100 D and HLX) to reach pressures up to 20 MPa. The pumps are filled with water and with CO2 (purity 99.995%; Linde, France), and control the volume flow rates (approximately 10 -2 mL.min -1 ) and the fluids temperature (20°C for water and 5°C for CO2). A third syringe pump (ISCO 260 D) is placed at the outlet of the microreactor output in order to maintain and control the output pressure in the system (up to 20 MPa). The microreactor is put into a transparent box and immerged in a circulating heat transfer fluid in ordain to maintain a constant temperature in the reactor. The box has been setup to force the fluid circulation everywhere around the micro-reactor. Inlet/outlet for this heat transfer fluid is shown in figure II (region C).

A Coriolis-type micro-flowmeter is used to control CO2 mass flowrate at the microreactor inlet. Indeed, the mass flowrate is not so easy to control because of CO2 temperature change between the pump and the microreactor inlet which involves density change. Furthermore, the pressure change affects a lot fluid properties.

Figure III shows in what extend the density [START_REF] Span | A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple-Point Temperature to 1100 K at Pressures up to 800 MPa[END_REF], viscosity [START_REF] Fenghour | The Viscosity of Carbon Dioxide[END_REF] and surface tension of CO2 [START_REF] Georgiadis | Interfacial Tension Measurements of the (H2O + CO2) System at Elevated Pressures and Temperatures[END_REF] vary between atmospheric pressure and 200 bar. These changes of properties have to be taken into account to understand behaviour of fluid phase in the different parts of the experimental set-up (pump, tubing, microsystem). Formation of the flow can be recorded by a CCD camera (Baumer HXC13) with a resolution of 1280 x 1021 pixels2. The videos can be acquired at 2000 frames per second. The microchannel is lit with LED lamps that have a light intensity of 2200 lumen. As an example, Figure IV, reports a photo of a stable two-phase Taylor flows of CO2 and water obtained at 20 MPa using a microcapillary set-up identical to the one described in [START_REF] Portela Da Silva | Transparent and Inexpensive Microfluidic Device for Two-Phase Flow Systems with High-Pressure Performance[END_REF]. Optical access to the flow makes it possible to quantify the volume change of bubbles (due mass transfer between the gas and the liquid phases). The main advantage of this kind of device is the high pressure resistance, ease of fabrication and rather low price, with the "T" and "U" junctions that can be recovered after reactor failure (the lifetime of micro-reactors is not infinite due to the high pressure use).

Other advantages for hydrodynamics and mass transfer investigations lie in the circular cross section (creating an axial symmetrical system and makes CFD simulations and modelling easier), the coiling system that allows a reactor up to 10 meters long and an inner surface that is perfectly smooth. Moreover, the cylindrical fused-silica tubing (Polymicro, USA) is coated with polyimide cladding as a protection and provides a great flexibility. When the coating is removed, the capillary is completely transparent which allows an optical access.

Finally, it should be pointed out that attention was paid to curvature effects. Indeed, curvature effects can lead to flow instabilities or to coalescence of the dispersed phase and can even be used to separate phases. For this device, the Bond number Bo = Δ𝜌 𝑎 𝐿 /𝜎 with 𝑎 = 𝑣/𝑅 , is calculated with centrifugal acceleration. Considering identical mixtures, with identical operating conditions and with the same channel surface sections, the Bond number of the onchip microdevices (bending radius 𝑅 = 0.3 mm) is 100 times higher than of the presented device (bending radius = 30 mm).

A few disadvantages still remain on this device: the only possible kind of entry is a coaxial one. The effect of a T-junction on high pressure can't be investigate as carried out in Yao et al. [START_REF] Yao | The Effect of System Pressure on Gas-Liquid Slug Flow in a Microchannel[END_REF]. Moreover, the current system of temperature regulation does not allow a spectroscopic access such as Raman spectroscopy some technical solutions are presently under investigations (heating film, warm air box…).

CONCLUSION AND FUTURE WORK

This work describes the fabrication of a microreactor that is able to resist pressures up to 20MPa and suitable for the use of high-pressure CO2. The target of such a device is to use it to investigate mass transfer between gaseous CO2 and an aqueous liquid phase. The next step of this work will consist in implementing optical techniques and/or spectroscopic techniques, which will enable concentrations of the different components to be measured along the microchannel. In combination with phenomenological modelling, this set-up will be used as a tool to calculate mass transfer coefficients between components at high pressure.

  The dimensions of the microreactor and the different elements, i.e. chassis, resin, and glass window, are shown in Figure I(b).

Figure

  Figure I. (a) Schematic diagram of the microreactor with lighting system; (b) dimensions of the reactor with the 40mm x 40 mm viewing window and guide supports (dark blue).

Figure II .

 II Figure II. The transparent high pressure micro-reactor.

Table 1 :

 1 Values of surface tension between water and CO2 for different pressures.

Figure III .

 III Figure III. Fluid properties of CO2 changing with pressure.

Figure

  Figure IV. P = 20 MPa; T=308 K; VCO2= 0.02 mL.min-1; VH2O= 0.02 mL.min-1 in a 530 µm capillary.


Delphine Bertin
email: d.bertin@hotmail.fr

Pierre Labadie

J D Ferrari

Alexandre Sapin
email: asapin@rovaltainresearch.com

Jeanne Garric

Olivier Geffard

Hélène Budzinski

Marc Babut
email: marc.babut@irstea.fr

Potential exposure routes and accumulation kinetics for poly-and perfluorinated alkyl compounds for a freshwater amphipod: Gammarus spp. (Crustacea)

Keywords: perfluorinated compounds, sediment, Gammarus spp., exposure route, uptake rate, clearance, BSAF

 Gammarids were exposed to field sediments from downstream of a fluoropolymer plant.

 The steady state was not achieved after 21 days.

 Elimination rates were dependent on the perfluorinated carbon chain length.

 Clearance was high -up to 8-9 perfluorinated carbons.

 Kinetic BSAFs exceeded 1 for compounds having more than 8 perfluorinated carbons.

Introduction

Poly-and perfluorinated alkyl compounds (PFASs) are present in all media (water, sediment, biota, humans) and are subject to large-scale distribution as far as the polar regions [START_REF] Giesy | Global Distribution of Perfluorooctane Sulfonate in Wildlife[END_REF][START_REF] Houde | Biomagnification of perfluoroalkyl compounds in the bottlenose dolphin (Tursiops truncatus) food web[END_REF][START_REF] Houde | Monitoring of Perfluorinated Compounds in Aquatic Biota: An Updated Review[END_REF]. Many studies have shown PFASs' bioaccumulation in various species, including top-predators, and a few of them point to sediment as a PFAS source [START_REF] Martin | Perfluoroalkyl contaminants in a food web from lake Ontario[END_REF][START_REF] Armitage | Modeling global-scale fate and transport of perfluorooctanoate emitted from direct sources[END_REF][START_REF] Loi | Trophic Magnification of Poly-and Perfluorinated Compounds in a Subtropical Food Web[END_REF]. In Although they are located at the basis of many food webs, little is known about PFAS transfer from sediment to benthic organisms. The oligochaete Lumbriculus variegatus accumulated seven perfluoroalkyl carboxylic acids (PFCAs; carbon chain length ranging from C 7 to C 14 ) and three perfluoroalkane sulfonates (perfluorobutane sulfonic acid -PFBS, perfluorooctane sulfonic acid -PFOS and perfluorodecane sulfonic acid -PFDS) from sediment in two laboratory experiments [START_REF] Higgins | Bioaccumulation of perfluorochemicals in sediments by the aquatic oligochaete Lumbriculus variegatus[END_REF][START_REF] Lasier | Perfluorinated chemicals in surface waters and sediments from northwest Georgia, USA, and their bioaccumulation in Lumbriculus variegatus[END_REF]. However, the PFAS accumulation pathways and the factors influencing their bioaccumulation were not identified.

Two studies of midge (Chironomus riparius) larvae exposed to field sediment showed rapid accumulation and elimination of two PFCAs (C 11, perfluoroundecanoic acid [PFUnDA] and C 13 acid perfluorotridecanoic [PFTrDA]), PFOS and its perfluorooctane sulfonamide precursor (FOSA) [START_REF] Bertin | in prep. Accumulation and depuration of perfluoroalkyl compounds (PFASs) by midge larvae (Chironomus riparius, Diptera, Chironomidae) exposed to contaminated sediments[END_REF]Bertin et al., submitted). Like oligochaetes, chironomid larvae are in direct contact with sediment, and accumulation occurs through food ingestion

Author-produced version of the article published in Chemosphere (2016), vol. 155, p. 380-387 The original publication is available at http://www.sciencedirect.com doi:10.1016/j.chemosphere.2016.04.006 ©. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ and diffusion from pore water (PW) through the tegument. Biota to sediment accumulation factors (BSAFs) for chironomids were lower than BSAFs reported previously for Lumbriculus variegatus [START_REF] Higgins | Bioaccumulation of perfluorochemicals in sediments by the aquatic oligochaete Lumbriculus variegatus[END_REF][START_REF] Lasier | Perfluorinated chemicals in surface waters and sediments from northwest Georgia, USA, and their bioaccumulation in Lumbriculus variegatus[END_REF]. This difference could be related to the respective experimental designs (uncontaminated food added to chironomids experiments), to physiology, or to differing life traits, in particular feeding habits (Bertin et al., submitted). We found no study addressing these issues for PFASs.

The Gammarus sp. is a freshwater invertebrate widely used in ecotoxicology. It is a widespread epi-benthic species, present throughout the Northern hemisphere. Furthermore, this species is an important food source for fish, amphibians and birds [START_REF] Macneil | The trophic ecology of freshwater Gammarus spp.(Crustacea: Amphipoda): problems and perspectives concerning the functional feeding group concept[END_REF].

It feeds mainly by shredding the leaf litter (Tachet et al., 2010). This behaviour plays an important role in the nutrient cycle and contributes to redistributing organic matter in the riverine ecosystem. In addition, gammarids graze organic biofilm at the litter surface, and ingest fine organic matter particulates from sediment deposits. They can also adopt a predator position [START_REF] Macneil | The trophic ecology of freshwater Gammarus spp.(Crustacea: Amphipoda): problems and perspectives concerning the functional feeding group concept[END_REF]. Gammarids are also known for their capacity to accumulate various organic and inorganic contaminants [START_REF] Amiard | Comparative study of the patterns of bioaccumulation of essential (Cu, Zn) and non-essential (Cd, Pb) trace metals in various estuarine and coastal organisms[END_REF][START_REF] Ashauer | Bioaccumulation kinetics of organic xenobiotic pollutants in the freshwater invertebrate Gammarus pulex modeled with prediction intervals[END_REF][START_REF] Lebrun | Waterborne nickel bioaccumulation in Gammarus pulex: Comparison of mechanistic models and influence of water cationic composition[END_REF][START_REF] Tlili | Bioaccumulation of polybrominated diphenyl ethers by the freshwater benthic amphipod Gammarus pulex[END_REF].

The aim of the present study was to determine the PFAS accumulation pathways and kinetics in a benthic species, Gammarus sp. in realistic conditions, because its biology and life traits differ from those previously studied. The objectives were (i) to identify the contamination routes in the accumulation of PFASs by gammarids, (ii) to describe PFAS accumulation and elimination kinetics and (iii) to compare the kinetic constants and BSAFs obtained for gammarids to those available for other benthic species and to discuss the differences according to the respective life traits and physiology.

Materials and methods

Sediments

In October 2013, a sample of approximately 60 L of sediment was taken from the river bed of a deposition site in the Rhone River (eastern central France, N45°28′17.0″E4°46′43.4″). This site is located 40 km downstream of a fluoropolymer manufacturing plant, where polyvinylidene fluoride (PVDF) and various fluorinated polymers have been synthesized since the 1980s [START_REF] Dauchy | Relationship between indusrial discharges and contamination of raw water ressources by perfluorinated compounds. Part I: Case study of a fluoropolymer manufacturing plant[END_REF]. The known releases from this site include mainly a range of perfluoroalkyl acids, in particular the perfluorohexanoic (PFHxA) and perfluorononanoic acids (PFNA), used as a carrier (solvent) of fluorinated polymers. Some longer chain perfluoroalkyl acids, such as the perfluoroundecanoic and perfluorotridecanoic acids (PFUnDA, PFTrDA respectively), are believed to be impurities of the technical PFNA.

Surface sediment was collected using a Van-Veen grab, sieved at 2 mm, pooled in a polypropylene (PP) jar and stored at 4°C in the laboratory. Twelve aquaria (38 x 20 x 24.5 cm in polystyrene) were prepared with 4 L of homogenized sediment and 15 L of groundwater with 400-500 µS.cm -1 conductivity. Each aquarium was allowed to settle for 1 week before introducing the gammarids. Twelve aquaria were prepared with only groundwater for the controls.

Collection and maintenance of gammarids

Three weeks before the start of the experiment, adult gammarids, i.e. a mixture of Gammarus fossarum and Gammarus pulex, (9.5 ± 0.8 mm) were collected with a hand net at a remote/uncontaminated site (La Mouge River, N46°50'97.2"E4°75'63.9"). Gammarids were kept in a bucket on ice, and brought to the laboratory. They were acclimatized for 3 weeks in aquaria with continuously renewed groundwater under constant aeration; a 16:8 h light:dark photoperiod was maintained and the temperature was kept at 12°C. Organisms were fed ad libitum with alder leaves (Alnus glutinosa).

Gammarus sp. exposure

One experiment was conducted in two phases: the first step examined PFAS accumulation kinetics while the second step considered PFAS elimination (Figure S1 in SI). Only male gammarids were selected, in order to eliminate potential biases due to neonate release by females. For the accumulation step, 450 individuals were added to nine sediment aquaria (50 per aquarium) and 150 individuals were added to three control aquaria (50 organisms per aquarium). All the aquaria were made in polystyrene (PS) materials; flexible pipes were made of low-density poly-ethylene (PE, Versilic ®). Gammarids were collected at 7 (T1), 15 (T2) and 21 (T3) days, one aquarium being sacrificed at each time. For the elimination step, 450 gammarids were added to three sediment aquaria (150/aq.) and exposed for 21 days. After 3 weeks of sediment exposure, the organisms were transferred to a clean media (about 450 organisms in three flow-through aquaria filled with groundwater completely renewed four times per day). About 50 gammarids were killed at 7 (T4), 15 (T5), and 21 (T6) days after the transfer. The control gammarids were also killed after 42 days (Te, about 50 organisms). For both experiments, overlying water (OW) was continuously renewed (four times a day) under constant aeration. A 16:8 h light:dark photoperiod and a temperature of 12°C were maintained during the experiments. The organisms were fed ad libitum with alder leaves (Alnus glutinosa), previously conditioned for 3 days in groundwater; freshly pre-conditioned leaves were added once a week. Each week the water quality parameters (pH, temperature, concentration of dissolved oxygen, conductivity, NO 2 -and NH 4 + ) were monitored (experimental design shown in Fig. S1).

Sample collection

Overlying water (OW) was sampled directly in a 1 L polyethylene (PE) bottle at T1, T2, T3, T4, T5, T6 and in the controls. PW was obtained with Rhizon® systems (SDEC, Reignac-sur-

Author-produced version of the article published in Chemosphere (2016), vol. 155, p. 380-387 The original publication is available at http://www.sciencedirect.com doi:10.1016/j.chemosphere.2016.04.006 ©. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Indre, France) following the method developed in (Seeberg-Elverfeldt et al., 2005) and was sampled at T1, T2 and T3. Sediment was also sampled at T1, T2 and T3. Leaves were sampled at T0, T1, T2, T3, T4, T5, T6 and once in the controls. Before freezing, leaf samples were rinsed with groundwater to remove sediment particles. Like the leaf samples, organisms were sampled at T0, T1, T2, T3, T4, T5, T6 and in the controls. Then these biota samples were cryopreserved in liquid nitrogen and stored at -21°C [START_REF] Reiner | Determination of perfluorinated alkyl acid concentrations in biological standard reference materials[END_REF].

PFAS extraction

For sediment, gammarid samples, leaf samples and the fish tissues used as reference matrix (NIST SRM 1947[START_REF] Reiner | Determination of perfluorinated alkyl acid concentrations in biological standard reference materials[END_REF], PFASs were extracted using sonication following the method described in [START_REF] Bertin | in prep. Accumulation and depuration of perfluoroalkyl compounds (PFASs) by midge larvae (Chironomus riparius, Diptera, Chironomidae) exposed to contaminated sediments[END_REF]. The OW and PW samples were processed using Strata-X-AW cartridges as described by [START_REF] Labadie | Partitioning behaviour of perfluorinated alkyl contaminants between water, sediment and fish in the Orge River (nearby Paris, France)[END_REF]. Sediment or tissue samples were extracted by sonication using methanol (MeOH), concentrated under a nitrogen stream, purified on ENVI-Carb cartridges and eluted with MeOH. Eluates were concentrated to 400 µl under a nitrogen stream and transferred into injection vials. Details are provided in SI.

LC-MS/MS analysis and chemicals

PFASs (list of compounds and acronyms in SI, table S1) were analysed by LC-MS/MS using an Agilent 1200 LC system (Agilent Technology, Massy, France) interfaced with an Agilent 6490 triple quadrupole mass spectrometer (details in SI, Table S2). The purchase of the chemicals and their source are described in the supplementary data; most were purchased from Wellington Laboratories (via BCP Instruments, Irigny, France) and Sigma-Aldrich (St Quentin Fallavier, France).

Quality control and method performance

Analyte recovery was determined using spiked samples for each matrix (OW and PW, sediment and gammarids). Native PFAS recovery ranged from 73% to 122% with a relative standard deviation below 33% for fish and spiked sand except for perfluoropentanoic acid (PFPeA) and PFBS. Native PFAS recovery for spiked waters (OW and PW) ranged from 65% to 118% with a relative standard deviation below 12% except PFTrDA, perfluorotetradecanoic acid (PFTeDA), 6:2 fluorotelomer sulfonic acid (6:2 FTSA), N-ethyl perfluorooctane sulfonamidoacetic acid (EtFOSAA), N-methyl perfluorooctane sulfonamide (MeFOSA) and N-ethyl perfluorooctane sulfonamide (EtFOSA) (Table S3 in SI).

Replicate procedural blanks were analysed for each series of samples (details in Table S4 in SI). For the water sample procedure, the predominant compound was PFPeA (mean level: 160 ± 8 pg, n=4) and perfluorodecanoic acid (PFDA) (mean level: 34 ± 5 pg, n=4). For tissue, sediment and leaf samples, the prevailing analytes in blanks were PFPeA (123 pg) and PFDA (31 pg). PFAS concentrations were therefore blank-corrected when applicable. For compounds present in blanks, the limits of detection (LDs) were defined as three times the standard deviation, and the limits of quantification (LQs) were set at 10 times the standard deviation of the blank (Muir and Sverko, 2006;Munoz et al., 2015). For analytes not detected in blanks, LDs and LQs were determined as the concentration with a signal-to-noise ratio of 3 and 9, respectively. This was calculated on matrices spiked at 0.3-1.8 ng g -1 (sediment and Gammarus spp.) and 0.9-17.3 ng L -1 (Vittel® mineral water samples) (Table S6). The PFASs measured in NIST SRM 1947 Lake Michigan Fish Tissue compared well with reference values (SI Table S6).

Data analyses and modelling

Author-produced version of the article published in Chemosphere (2016), vol. 155, p. 380-387 The original publication is available at http://www.sciencedirect.com doi:10.1016/j.chemosphere.2016.04.006 ©. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Data were checked for normality using the Shapiro-Wilk test and were analysed using the Kruskal-Wallis test (a non-parametric test) and the Mann-Whitney test using R language (R Core Team, 2014a, b).

Assuming sediment was the main source of PFASs for the gammarids, accumulation data were adjusted to a two-compartment model [START_REF] Spacie | Bioaccumulation[END_REF][START_REF] Landrum | Bioavailability and toxicokinetics of polycyclic aromatic hydrocarbons sorbed to sediments for the amphipod Pontoporeia hoyi[END_REF].

Equation ( 1) was used to estimate the uptake and elimination coefficients (k u and k e , respectively).

Eq. ( 1) with the PFAS concentration in organisms (ng.g -1 ww), the PFAS concentration in sediment (ng g -1 dw), expressed in g g -1 ww .d -1 and in d -1 . In the selected size range, gammarids do not grow significantly within the experiment duration, so there is no need to correct for growth.

Elimination data can also be adjusted directly to an exponential decrease model (Eq. 2).

Eq. ( 2)

where C 0 is the PFAS concentration at the start of the elimination phase (ng g -1 ww).

Conceptually, k e values obtained from Eqs. 1 and 2 are identical: Eq. 2 corresponds to the integrated form of Eq. 1 when Cs ed is set to 0. Nevertheless k e values obtained from the two approaches can differ when fitted on independent data sets. Model calculations were performed in R language using the <<ode>> function, and k u and k e were optimized simultaneously with the least square method using the <<optim>> function implemented in the <<Desolve>> package (R Core Team, 2014a). When k u and k e are processed in this way, the whole data set including both uptake and elimination experimental data can be used, avoiding differences in k e values derived from separate adjustments.

The kinetic biota-to-sediment accumulation factor (BSAF kinetic ) is derived from the uptake and elimination rate constants (Eq. 3):

Eq. ( 3)

The elimination half-life (T 1/2 ) is obtained according to Eq. ( 4):

Eq. ( 4)

Results

PFAS distribution in water, sediment and leaves

Water in control aquaria displayed low concentrations of PFHpA, PFOA, PFNA, PFDA, PFUnDA, as well as perfluorohexane sulfonate (PFHxS), PFOS and 6:2FTSA (0.01 -0.07 ng L -1 ) while PFBA, PFPA and PFHxA reached higher concentrations (1.35, 0.25 and 0.24 ng L - 1 , respectively). The contamination profile in sediments (test aquaria, T1 to T3) was dominated by PFUnDA (1.19 ± 0.15 ng g -1 dry weightdw) and PFTrDA (2.09 ± 0.10 ng g -1 dw); PFHxA, PFNA, PFDA, perfluorododecanoic acid (PFDoDA), PFOS and 6:2FTSA ranged from 0.1 to 0.5 ng g -1 dw, while other compounds, such as PFOA, N-methyl perfluorooctane sulfonamidoacetic acid (MeFOSAA) and FOSA, ranged from <LD (0.003-0.013 ng g -1 dw) to 0.1 ng g -1 dw. In PW the dominant compounds were PFHxA (97.95 ± 17.41 ng L -1 ), PFNA (7.10 ± 1.98 ng L -1 ) and PFUnDA (6.05 ± 0.97 ng L -1 ); PFPA, PFOA, PFBS and PFOS were within the range 1.0-5.0 ng L -1 , with other compounds undetected (e.g.

PFDA, PFTrDA, PFBS, FOSA, 6:2FTSA) to ≤1.0 ng L -1 (PFHpA, MeFOSAA). PFHxA (2.59 ± 0.23 ng L -1 ) was still the most concentrated compound in OW; PFBA, PFPA, PFHpA, PFOA, PFTrDA, PFBS, PFHxS and PFOS concentrations were within the range 0.5-1.5 ng L - (0.63 ± 0.38 ng g -1 dw) displayed the highest concentrations in alder leaves; PFPA, PFOA, PFNA, and EtFOSAA ranged from 0.05 to 0.5 ng g -1 dw. PFHxA, PFDoDA, PFHxS, MeFOSAA and FOSA were measured at levels <0.05 ng g -1 dw; other compounds such as PFDA or 6:2FTSA remained undetected in this matrix. Details are shown in SI (Table S6).

Gammarid survival, PFAS accumulation and elimination

Organisms from the reference site (La Mouge) displayed a limited contamination by a range of PFCAs (PFOA, PFNA, PFDA, PFDoDA and PFTrDA, all around 0.1-0.0.3 ng g -1 (ww),

and PFOS (0.93  0.2 ng g -1 ww). After acclimatization for 3 weeks, all concentrations remained similar, except for PFUnDA, which increased to 0.19 ng g -1 (ww) and PFOS, which fell to 0.09 ± 0.002 ng g -1 ww (Table S7 in SI). Gammarid survival was > 75% in control aquaria, and > 80% in test aquaria except at T6 (54%, 66% and 6% respectively). Organisms from this aquarium with a low survival rate were not considered further. Nine of ten compounds (PFCAs: PFNA, PFUnDA, PFDoDA, PFTrDA; PFOS and precursors:

PFAS concentrations in

PFOS, MeFOSAA, EtFOSAA, FOSA; 6:2FTSA) displayed significantly higher concentrations in test gammarids at 21 days (T3) compared with control organisms (Table 1).

The most accumulated compounds were PFUnDA and PFTrDA, and PFOS to a lesser extent.

Author-produced version of the article published in Chemosphere (2016), vol. 155, p. 380-387 The original publication is available at http://www.sciencedirect.com doi:10.1016/j.chemosphere.2016.04.006 ©. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Concentrations of most PFASs were still increasing at T3 (21 days), so the steady state was not reached at 3 weeks of exposure (Figure 1).

Author-produced version of the article published in Chemosphere (2016), vol. 155, p. 380-387 The original publication is available at http://www.sciencedirect.com doi:10.1016/j.chemosphere.2016.04.006 ©. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ The results from the accumulation and elimination experiments fitted the two-compartment model well (Eq. 1; Figures 1 andS3 and S4 in SI): the distance between the observed and simulated data ranged from 0.0001 to 0.039, and R 2 ranged from 0.78 to 0.97 except for FOSA (R 2 = 0.54) and PFDoDA (R 2 = 0.29) (Table 2). The uptake rates (k u ) ranged from 0.053 to 0.242 g.g ww .d -1 and the elimination rates (k e ) from 0.042 to 0.276 d -1 (Table 2). Given that elimination was not significant for PFDoDA and PFTrDA, the k e values provided by the model calculations for these compounds are indicative, as are the corresponding BSAFs. BSAF kinetic values tended to increase as the PFCA chain length increased. In addition, BSAF is also higher for PFOS than for PFNA, which has the same number of perfluorinated carbons (Table 2). All compounds with more than 8 perfluorinated carbons display BSAF kinetic values above 1, with the exception of EtFOSAA. Note that EtFOSAA concentrations varied between LD and LQ during the elimination phase, so both k e and BSAF kinetic values could not be determined.

Discussion

4.1. PFAS distribution in water, sediment, food and Gammarus sp.

Author-produced version of the article published in Chemosphere ( 2016), vol. 155, p. 380-387 The original publication is available at http://www.sciencedirect.com doi:10.1016/j.chemosphere.2016.04.006 ©. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

The comparison of PFAS concentrations in each compartment (OW, PW, sediment, leaves and gammarids) in control and test aquaria at the beginning and end of the experiment makes it possible to identify the transfers between the compartments and design a conceptual diagram of PFAS transport (Figure 2). A transfer from one compartment to another is assumed when a compound is present in both compartments in test aquaria, but undetected in one of them in controls. PFBA, MeFOSAA and EtFOSAA are present at similar concentrations in both control and test OWs throughout the experiment, while other PFAS concentrations increase by several orders of magnitude, suggesting transfers from PW (e.g. PFHxA, PFHpA, PFHxS) or sediment particles via PW (e.g. PFUnDA). Thus PFUnDA was presumably transferred from sediment to leaves. PFUnDA is both associated to sediment particles and dissolved in PW: therefore gammarids may have taken PFUnDA from both PW and leaves or sediment. PFTrDA concentrations varied widely in OW (range <LD -2.62 ng L -1 ) but remained undetected in PW. Since the water was not filtered prior to extraction and analysis, the concentrations measured in OW and PW represented the total concentrations (dissolved + sorbed to suspended particles). On the other hand, PFTrDA concentrations could be underestimated in PW, as a consequence of sorption to Rhizon ® materials.

Notwithstanding these uncertainties concerning PFTrDA measurements in water compartments, the higher load on sediment particles as well as its K OC value (Munoz et al., 2015) supports the hypothesis that PFTrDA uptake occurred much more through the ingestion of contaminated particles than from water. This hypothesis is consistent with previous conclusions about the PFCA benthic source signature for Lake Ontario Diporeia (an amphipod species) [START_REF] Martin | Perfluoroalkyl contaminants in a food web from lake Ontario[END_REF].

During the exposure period, gammarid activity mobilized particles, which deposited on the leaves' surface. Two PFAS transfer pathways to the leaves are therefore possible: (i) by diffusion from water, or (ii) from sediment particles and water. These transfers could involve the microbial biofilm on the leaves' surface. Indeed, the leaf conditioning before their addition to the aquaria led to the microorganism's colonization [START_REF] Abelho | From Litterfall to Breakdown in Streams: A Review[END_REF][START_REF] Aßmann | Consequences of the colonisation of leaves by fungi and oomycetes for leaf consumption by a gammarid shredder[END_REF] and biofilms are known for accumulating trace elements [START_REF] Farag | Concentrations of metals associated with mining waste in sediments, biofilm, benthic macroinvertebrates, and fish from the Coeur d'Alene River Basin, Idaho[END_REF][START_REF] Van Hullebusch | Metal immobilisation by biofilms: Mechanisms and analytical tools[END_REF] as well as organic compounds [START_REF] Widenfalk | Sediment microbes and biofilms increase the bioavailability of chlorpyrifos in Chironomus riparius (Chironomidae, Diptera)[END_REF][START_REF] Writer | Role of biofilms in sorptive removal of steroidal hormones and 4-nonylphenol compounds from streams[END_REF]. Nevertheless, PFAS transfer to the leaves themselves was probably limited, because leaves were renewed every week. Like PFUnDA and PFNA, PFOS accumulation by gammarids could have occurred via water (OW) and leaves concurrently. In summary, gammarids accumulate PFASs by two potential contamination routes: the trophic route, i.e. ingestion of leaves and sediment particles, and the respiratory route. The former was predominant for long-chain compounds such as PFTrDA and PFDoDA, while the latter was also involved for PFOS, PFNA and PFUnDA (Figure 2). As a consequence, the k u values are overestimated for these three compounds, because the derivation process assumed sediment was the main source. The k e values are not affected.

PFAS bioaccumulation

The concentrations observed in gammarids in the present experiment are within the same range as in the few studies that reported PFAS concentrations in crustaceans from the field [START_REF] Kannan | Perfluorinated compounds in aquatic organisms at various trophic levels in a Great Lakes food chain[END_REF][START_REF] Haukås | Bioaccumulation of per-and polyfluorinated alkyl substances (PFAS) in selected species from the Barents Sea food web[END_REF]. FOSA concentrations (<2 ng g -1 ww) were lower in freshwater amphipods from a Great Lake food web [START_REF] Kannan | Perfluorinated compounds in aquatic organisms at various trophic levels in a Great Lakes food chain[END_REF] than those found in gammarids in our study. PFOS and PFOA concentrations were higher in marine gammarids (Gammarus wilkitzkii) from the Barents Sea than in the present study, whereas the opposite was found for 6:2 FTSA (0.48 ± 0.24 ng g -1 ww) [START_REF] Haukås | Bioaccumulation of per-and polyfluorinated alkyl substances (PFAS) in selected species from the Barents Sea food web[END_REF]. Long chain compounds were not often measured in monitoring studies, except in two shrimp species (Peneaus monodon and Metapenaeus ensis) [START_REF] Loi | Trophic Magnification of Poly-and Perfluorinated Compounds in a Subtropical Food Web[END_REF]. [START_REF] Martin | Perfluoroalkyl contaminants in a food web from lake Ontario[END_REF]) also analysed a range of PFCAs in the Ontario food-web, observing decreasing concentrations with increasing chain length, but they did not report the respective concentrations in sediments. They stated that the contamination profile observed in Diporeia and sculpin (a benthic-feeding fish species) reflected a benthic source signature. Such comparisons nevertheless remain difficult, because (i) different species were considered and (ii) the exposure concentrations were different and did not necessarily involve water and sediment in all cases.

According to accumulation kinetics, the steady state was not reached at 3 weeks of exposure.

For the pesticides chlorpyrifos and pentachlorophenol [START_REF] Ashauer | Uptake and elimination of chlorpyrifos and pentachlorophenol into the freshwater amphipod Gammarus pulex[END_REF], the steady state was achieved between 48 and 72h for Gammarus pulex: for chlorpyrifos resulted from a decline of the exposure concentration in the test vessel, while for carvedilol and fluoxetine the steady state was not reached in 48 hours [START_REF] Meredith-Williams | Uptake and depuration of pharmaceuticals in aquatic invertebrates[END_REF]. [START_REF] Ashauer | Uptake and elimination of chlorpyrifos and pentachlorophenol into the freshwater amphipod Gammarus pulex[END_REF] explained the differences between pentachlorophenol and chlorpyrifos by hydrophobicity. Furthermore, [START_REF] Meredith-Williams | Uptake and depuration of pharmaceuticals in aquatic invertebrates[END_REF] assigned the variations in uptake rates of several pharmaceuticals (5-fluorouracil, carbamazepine, diazepam, moclobemide, carvedilol and fluoxetine) at an estimated steady state to the respective ionization state. Nevertheless, both studies were conducted in water, with neither sediment nor food present, which presumably lead to different kinetics compared to the present study.

These observations and the need for longer equilibration times for PFASs suggest that transport mechanisms across membranes are more complex than simple diffusion. The failure to achieve steady state within 3 weeks could also be due to the formation of PFCAs (or PFSAs) in sediment or gammarids from unanalysed precursors. We nevertheless discarded this hypothesis, bcause (i) PFCA and PFSA concentrations remained steady in sediment during the experiment, and (ii) the corresponding kinetics in sediments are deemed to be very low (Liu and Mejia Avendaño, 2013).

In spite of the failure to achieve the steady state, the determination of the uptake and elimination constant rates allowed determining kinetic BSAFs. For PFCAs, these BSAFs are positively correlated with the number of perfluorinated carbons (Pearson correlation coefficient, 0.958; p-value 0.042; when all compounds including PFOS, its precursors and 6:2 FTSA are accounted for, the Pearson coefficient is still 0.797, and the p-value = 0.01).

Moreover, the BSAF for PFOS was higher than for PFNA, which has the same number of fluorinated carbons, as already shown in previous studies (Martin et al., 2003a, b;[START_REF] Lasier | Perfluorinated chemicals in surface waters and sediments from northwest Georgia, USA, and their bioaccumulation in Lumbriculus variegatus[END_REF].

Comparison between gammarids and chironomids

Despite the inherent spatial and temporal variability of the PFAS sediment concentrations in the field, the sediment molecular profile contamination in this study and in studies with the midge Chironomus riparius using a similar design [START_REF] Bertin | in prep. Accumulation and depuration of perfluoroalkyl compounds (PFASs) by midge larvae (Chironomus riparius, Diptera, Chironomidae) exposed to contaminated sediments[END_REF]Bertin et al., submitted) are comparable (Table S8). Uptake and elimination rates were estimated with the approach in both studies. The respective kinetics presented several differences between these two species: chironomids did not accumulate PFNA, unlike gammarids. Despite a shorter exposure (4 days) according to its life cycle, chironomids' k u for PFUnDA (0.70 g g ww .d -1 ), PFTrDA (0.93 g g ww .d -1 ), PFOS (1.27 g g ww .d -1 ) and FOSA (2.02 g g ww .d -1 ) were higher than for gammarids (Table 2). PFAS elimination by chironomids was faster than for gammarids and complete after 42 h. In addition, PFCAs k e values for chironomids were negatively correlated with the carbon chain-length for compounds with more than nine perfluorinated carbons in gammarids. BSAFs were also higher for all PFASs for gammarids than for chironomids, consistent with the gammarids' slower elimination. These differences between these two invertebrates could be explained by different exposure routes related to the organisms' lifestyles and physiology. The chironomid is a benthic invertebrate feeding on organic matter associated with sediment particles, whereas the gammarids are shredder epi-benthic organisms, living in the water column with occasional contact with sediment. For chironomids, the trophic pathways were identified as the main PFAS exposure route [START_REF] Bertin | in prep. Accumulation and depuration of perfluoroalkyl compounds (PFASs) by midge larvae (Chironomus riparius, Diptera, Chironomidae) exposed to contaminated sediments[END_REF]Bertin et al., in prep.) while for gammarids the trophic route was predominant for longer chain (>11) PFCAs, and both respiratory and trophic routes were involved for C8-C10 compounds.

Conclusion

The study results reported here show an accumulation by gammarids of four long-chain PFCAs (PFNA, PFUnDA, PFDoDA and PFTrDA), one PFSA (PFOS), three precursors (MeFOSAA, EtFOSAA, FOSA) and one fluorotelomer (6:2 FTSA) from the sediment. The steady state was not reached at 3 weeks of exposure. In addition, the depuration of PFOS, precursors and 6:2 FTSA was almost complete in 21 days but not for the long-chain PFCAs.

The PFCA depuration time increases as the chain length increases. Moreover, in agreement with previous studies (Martin et al., 2003a, b;[START_REF] Lasier | Perfluorinated chemicals in surface waters and sediments from northwest Georgia, USA, and their bioaccumulation in Lumbriculus variegatus[END_REF], the BSAFs of PFCA values also seem to increase as the chain length increases. The PFAS pathway follows digestive and respiratory routes. In comparison with PFAS bioaccumulation by chironomids, where the PFAS accumulation and elimination were fast and complete after 42 h, and the behavioural differences existing between these two organisms, it is clear that lifestyle has an impact on PFAS exposure routes and subsequent bioaccumulation.

Figure captions

Table captions

Table 3: Mean PFAS concentration in gammarids in control aquaria and at T3 (ng.g -1 wet weight (ww)) (± standard deviation, n=3). (*) significant difference between test and control (p-value < 0.05). Author-produced version of the article published in Chemosphere (2016), vol. 155, p. 380-387 The original publication is available at http://www.sciencedirect.com doi:10.1016/j.chemosphere.2016.04.006 ©. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Potential exposure routes and accumulation kinetics for poly-and perfluorinated alkyl compounds for a freshwater amphipod: Gammarus spp. (Crustacea)

Figure captions

Figure captions

Author-produced version of the article published in Chemosphere ( 2016 (2016), vol. 155, p. 380-387 The original publication is available at http://www.sciencedirect.com doi:10.1016/j.chemosphere.2016.04.006 ©. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Potential exposure routes and accumulation kinetics for poly-and perfluorinated alkyl compounds for a freshwater amphipod: Gammarus spp. (Crustacea) Delphine Bertin, Pierre Labadie, Benoît J. D. Ferrari, Alexandre Sapin, Jeanne Garric, Olivier Geffard, Hélène Budzinski, Marc Babut ( (2016), vol. 155, p. 380-387

  //chm.pops.int/TheConvention/ThePOPs/TheNewPOPs/tabid/2511/Default.aspx).

  OW remained steady during the course of the experiment (FigureS2-A in SI), except PFOA (decrease at day 21), PFTrDA (<LD at day 7, 2.62 ng L -1 at day 15, and 0.14 ng L -1 at day 21) and PFBS (increase at day 21). PFAS concentrations in PW were in the 1-10 ng L -1 range (PFPA, PFHpA, PFOA, PFNA, PFUnDA, PFHxS, PFOS) or below (PFDA, PFBS), and steady (FigureS2-B), with two exceptions: PFHxA, which decreased from 116 ng L -1 at day 7 to 81 ng L -1 at day 21 (FigureS2-B), and PFTrDA which remained undetected. PFAS concentrations were also steady in the sediment (FigureS2-C).

Figure 1 :

 1 Figure 1 : Accumulation and elimination kinetics of selected PFAS; errors bars represent the standard deviation of measurements (n = 3, except for the last depuration point T6) -Curves represent model outputs.

  Author-produced version of the article published in Chemosphere(2016), vol. 155, p. 380-387 The original publication is available at http://www.sciencedirect.com doi:10.1016/j.chemosphere.2016.04.006 ©. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Figure 2 :

 2 Figure 2: Conceptual diagram of PFAS distribution between compartments

Figure 2 :

 2 Figure 2 : Accumulation and elimination kinetics of selected PFAS; errors bars represent the standard deviation of measurements (n = 3, except for the last depuration point T6) -Curves represent model outputs.

Figure 2 :

 2 Figure 2: Conceptual diagram of PFAS distribution between compartments

Figure 1 :

 1 Figure 1 : Accumulation and elimination kinetics of selected PFAS; errors bars represent the standard deviation of measurements (n = 3, except for the last depuration point T6) -Curves represent model outputs.

Figure 2 :

 2 Figure 2: Conceptual diagram of PFAS distribution between compartments

Table 1 :

 1 Mean PFAS concentration in gammarids in control aquaria and at T3 (ng g -1 wet weight (ww)) (± standard deviation, n=3). (*) significant difference between test and control (p-value < 0.05).

	Compounds	Concentration in gammarids in control aquaria (ng g -1 ww)	Concentration in gammarids (ng g -1 ww) at 21 days
	PFOA	0.43 ± 0.14	0.36 ± 0.04
	PFNA	<0.09 (LQ)	0.20 ± 0.01	(*)
	PFUnDA	0.11 ± 0.02	2.29 ± 0.60	(*)
	PFDoDA	0.12 ± 0.01	0.39 ± 0.03	(*)
	PFTrDA	<0.02 (LD)	3.18 ± 0.19	(*)
	PFOS	0.17 ± 0.07	0.84 ± 0.17	(*)
	6:2 FTSA <0.01 (LD)	0.13 ± 0.06	(*)
	MeFOSAA <0.04 (LQ)	0.11 ± 0.03	(*)
	EtFOSAA < 0.02 (LD)	0.16 ± 0.05	(*)
	FOSA	<0.02 (LQ)	0.14 ± 0.01	(*)

Table 2 :

 2 Model outcomes. The values in brackets for PFDoDA and PFTrDA are tentative, because elimination was not significant for these compounds.

			PFCAs		PFOS, 6:2 FTSA and PFOS precursors
	Compounds	PFNA PFUnDA PFDoDA PFTrDA PFOS	6:2 FTSA	MeFOSAA EtFOSAA FOSA
	Distance	0.001	0.013	0.004	0.039	0.023	0.002	0.0001	0.001	0.001
	R 2	0.899	0.965	0.290	0.968	0.804	0.782	0.947	0.821	0.537
	k u (g g ww .d -1 )	0.094	0.141	0.078	0.089	0.202	0.242	0.129	0.053	0.218
	k e (d -1 )	0.087	0.048	(0.015)	(0.011)	0.042	0.276	0.060	nd	0.066
	BSAF	1.08	2.92	(5.05)	(8.13)	4.76	0.88	2.13	nd	3.32
	N
	perfluorinated	8	10	11	12	8	6	8	8	8
	C

Table 4 :

 4 Model outcomes. The values in brackets for PFDoDA and PFTrDA are tentative, because elimination was not significant for these compounds.

Pore water Sediment Overlying water Gammarids Alder leaves Suspended par cles

  ), vol. 155, p. 380-387 The original publication is available at http://www.sciencedirect.com doi:10.1016/j.chemosphere.2016.04.006 ©. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Figure Author-produced version of the article published in Chemosphere (2016), vol. 155, p. 380-387 The original publication is available at http://www.sciencedirect.com doi:10.1016/j.chemosphere.2016.04.006 ©. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Figure Author-produced version of the article published in Chemosphere (2016), vol. 155, p. 380-387 The original publication is available at http://www.sciencedirect.com doi:10.1016/j.chemosphere.2016.04.006 ©. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Potential exposure routes and accumulation kinetics for poly-and perfluorinated alkyl compounds for a freshwater amphipod: Gammarus spp. (Crustacea) Delphine Bertin, Pierre Labadie, Benoît J. D. Ferrari, Alexandre Sapin, Jeanne Garric, Olivier Geffard, Hélène Budzinski, Marc Babut

	(Table 1)
	Compounds	Concentration in gammarids in control aquaria (ng.g -1 ww)	Concentration in gammarids (ng.g -1 ww) at 21 days
	PFOA	0.43 ± 0.14	0.36 ± 0.04
	PFNA	<0.09 (LQ)	0.20 ± 0.01	(*)
	PFUnDA	0.11 ± 0.02	2.29 ± 0.60	(*)
	PFDoDA	0.12 ± 0.01	0.39 ± 0.03	(*)
	PFTrDA	<0.02 (LD)	3.18 ± 0.19	(*)
	PFOS	0.17 ± 0.07	0.84 ± 0.17	(*)
	6:2 FTSA <0.01 (LD)	0.13 ± 0.06	(*)
	MeFOSAA <0.04 (LQ)	0.11 ± 0.03	(*)
	EtFOSAA < 0.02 (LD)	0.16 ± 0.05	(*)
	FOSA	<0.02 (LQ)	0.14 ± 0.01	(*)
	PFPA PFHxA (PFHpA) PFOA PFNA PFUnDA (PFTrDA ?) PFHxS PFOS MeFOSAA	(PFPA) PFHxA PFOA PFNA PFDA PFUnDA PFDoDA PFTrDA PFTeDA PFOS (MeFOSAA) (EtFOSAA) (FOSA) (6:2FTSA)
	?
	PFBA PFPA PFHxA PFHpA
	PFOA (PFNA) (PFDA)
	(PFUnDA) (PFTrDA) PFBS PFHxS PFOS	?	?
		PFOA (PFNA) PFUnDA PFDoDA
		PFTrDA
		PFOS (MeFOSAA) (EtFOSAA)
		(FOSA) (6:2FTSA)	PFPA (PFHxA) PFOA (PFNA)
			PFUnDA PFDoDA PFTrDA
	?		PFTHxS PFOS (MeFOSAA)
			EtFOSAA (FOSA)

Table Click here to download Table: Table-1_Bertin-et-al_2016_revised-final.docx

 Click Author-produced version of the article published in Chemosphere

Table 2 )

 2

			PFCAs		PFOS, 6:2 FTSA and PFOS precursors
	Compounds	PFNA PFUnDA PFDoDA PFTrDA PFOS	6:2 FTSA	MeFOSAA EtFOSAA FOSA
	Distance	0.001	0.013	0.004	0.039	0.023	0.002	0.0001	0.001	0.001
	R 2	0.899	0.965	0.290	0.968	0.804	0.782	0.947	0.821	0.537
	k u (g.g ww .d -1 )	0.094	0.141	0.078	0.089	0.202	0.242	0.129	0.053	0.218
	k e (d -1 )	0.087	0.048	(0.015)	(0.011)	0.042	0.276	0.060	nd	0.066
	BSAF	1.08	2.92	(5.05)	(8.13)	4.76	0.88	2.13	nd	3.32
	N
	perfluorinated	8	10	11	12	8	6	8	8	8
	C

Table Click here to download Table: Table-2_Bertin-et-al_2016_revised-final.docx

 Click Author-produced version of the article published in Chemosphere

Author-produced version of the article published in Chemosphere(2016), vol. 155, p. 380-387 The original publication is available at http://www.sciencedirect.com doi:10.1016/j.chemosphere.2016.04.006 ©. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

. The concentrations of other compounds, including PFNA, PFUnDA and 6:2FTSA were < 0.5 ng L -1 . PFUnDA (0.53 ± 0.34 ng g -1 dw), PFTrDA (0.40 ± 0.23 ng g -1 dw) and PFOSAuthor-produced version of the article published in Chemosphere(2016), vol. 155, p. 380-387 The original publication is available at http://www.sciencedirect.com doi:10.1016/j.chemosphere.2016.04.006 ©. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

The original publication is available at http://www.sciencedirect.com doi:10.1016/j.chemosphere.2016.04.006 ©. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Acknowledgements

This study was funded by the Rhone-Mediterranean and Corsica Water Agency and the Rhone-Alps Region within the Rhone ecological restoration plan. The Aquitaine Region and the European Union (CPER A2E project) are acknowledged for their financial support. This study also benefitted from grants from the French National Research Agency (ANR) as part of the Investments for the Future Program, within the Cluster of Excellence COTE (ANR-10-LABX-45). We thank Linda Northrup (English Solutions, Voiron, France) for copy editing the text.


Clément Genty
email: clement.genty@ensam.eu

Henri Samier

Jean-Manuel Gaget

Simon Richir

Does Mc Donald's properly manage its domain names ? Time management : proposal of the iceberg method for domain name categorization

Keywords: Domain Name, Time Management, Attention Management, Valuation

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

Science Arts & Métiers (SAM)

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible.

This is an author-deposited version published in: http://sam.ensam.eu Handle ID: .http://hdl.handle.net/null

To cite this version :

Simon R RICHIR, Clément GENTY, Henri SAMIER, Jean-Manuel GAGET -Does Mc Donald's properly manage its domain names ? Time managagement : proposal of the iceberg method for domain name categorization -In: CONFERE, Hongrie, 2018-07-05 -Confere -2018 INTRODUCTION Domain Names are intangible assets used by every Internet users since 1986. Their value, correlated to their importance for the communication field and the information system. But while we are in a period where we connect factories to the Internet, the domain name remains the link between the company and the Internet. It is thus a need for decision makers to have a tool ready to use.

HISTORY AND INTEREST

Invented in 1983 and presented by Paul Mockapetris through the Request For Content 882 [1] and 883 [2], the Domain Name System is an alphanumeric tool used in order to give trust through the Internet.

The development of the industry 4.0 and more globally the digitalization of our economy gives to Internet a central point for economical development. Therefore, valuation, financial or not, is going to be developped.

A need for a method

State of Art

The state of art concerning the domain name management remains thin. According to the ISO 10668 norm, there are three approaches to valuate an intangible assets like a brand: the Market, Cost and Income approaches.

Using this method to valuate domain names, we can consider that the market approach is the most common one. A second market exists and the price of the domain name is given because of its semantic.

Auctions-based websites and valuation tools usually process by giving a value because of the interest of the characters : number of words, length, meaning, trending, a lot of of settings are used even if no any scientifical method exists.

The technical aspect of the domain name is not developped in the scientifical litteracy. In 2016, the loss aspect was used in order to have an idea of what technical development is lost [START_REF] Genty | La valorisation des actifs immatériels numériques , une pratique nécessaire. Revue des méthodes existantes et proposition d'une analyse technico-économique[END_REF]. According to this paper, the income aspect can be given due to a combination of traffic, average basket and purchase rate. PROPOSAL Because the domain name has a visible shape, the semantic, and a hidden one, the criticality, we suggest to use a method using these two axes, named Iceberg method. Using two rates, each one being rated from zero to one, the position of the domain name will be possible according to the X-and the Y-axes.

Figure 1. Iceberg Method

The definition of semantic and criticality ratings must be done with caution : the charge of the domain name evolves with time and the '1' rating has to be given to the most important value of the sample.

Four cells exist, 1-2-3-4, and management of the domain name has to be done according to its cell location :

Cell Location Designation Management

Presentation of McDonald's

McDonald's is typically the company concerned by Internet. At a time where every consumer decides where he should eat by surfing on the Internet, the biggest restaurant in the world has to be present.

Historically, brothers 'Dick' and 'Mac' McDonald opened their restaurant in 1940. Fifteen years later, it was the first time that a restaurant used the Golden Arches design : it was located in Des Plaines [START_REF] Badal | McDonald's Corporation -2015[END_REF].

CONFERE'18/N°

In 1994, a journalist of Wired asked the PR department of McDonald's why the do not register MCDONALDS.COM which was, at this time, available. The answer, « Are you finding that the Internet is a big thing » [START_REF] Quittner | Billions Registered[END_REF] appears to be colorful in 2018.

Given the fact that McDonalds's has withdrawn the project of using two Top Level Domains dedicated to the company [START_REF]mcd Registry Agreement -Terminated[END_REF] [7], we can conclude that McDonald's is going to keep its wallet of domain names and thus will need to manage it.

Presentation of the domain names wallet

McDonald's, due to its history, used several names to describe its activity: Golden Arches, the symbol, McDonald's, its brand, MCD, its ticker symbol, also used for emailing,… Given the fact that McDonald's is a name commonly used as a familiy name, the brand had to register and to deal with domain names registered for a private purpose. It means that McDonald's has an important wallet of domain names and is an excellent candidate for the interest of the management by the Iceberg method.

X-AXIS : SEMANTIC

Semantics is the oldest valuation method. Indeed, a domain name is above all a name and a name corresponds to a value. The examples of SEX.COM, MUTUELLE.FR or FB.COM are three examples.

Y-AXIS : CRITICALITY

Once the domain name is acquired, an infrastructure develops: links, mail servers, and content are developed, bringing SEO, and reputations.  The domain name can be considered as a digital brand : the semantic is important and the typosquatting, represented by 'MCDONALD.FR' shows that the asset has to be kept for a long time, while has not to be technically developped ;  'GOLDENARCHES.COM' represents an historical brand : the domain name is registered but not used, but has to be maintened into the wallet ;  On the other side, 'MCD.COM', not well known by a lot of Internet users, should be strenghtened due to its criticality ;  Finally, 'MCDONALDS.COM' is the main brand name and is critical : used in communication, marketing and information system fields, the most developped name of the wallet has to be managed with high precaution.

CONCLUSION

Begging on a need to domain name management, the Iceberg Method is the first model and is ready to be used for international brands. The importance of the size of domain names wallets is going to need logarithmic axes. This proposition has to remain open source in order to become a standard in intangible assets management.

A third axis can tomorrow bring an interesting visualization to this method: compliance with naming rules. Indeed, the commercial policy of domain names being liberal, it is advisable to carry out preventive deposits because of various factors: risky TLD because of the absence of recovery procedures, TLD known in the UDRP/SYRELI statistics, sectoral TLD,... The scale will thus provide an indication of the status of the name in relation to the naming policy. Case to follow.

7 AFigure 2 .

 72 Figure 2. Iceberg Method -Application to McDonald's


Chao Liu
email: liu@lirmm.fr

Jing Guo
email: jing.guo@gdut.edu.cn

Philippe Poignet
email: poignet@lirmm.fr

Nonlinear Model-Mediated Teleoperation for Surgical Applications under Time Variant Communication Delay

Keywords: Bilateral teleoperation, Hunt-Crossley model, communication delay, robotic surgery

  L'archive ouverte pluridisciplinaire

INTRODUCTION

Robotic technologies have found their way to the surgery area since long time, but only until recent two decades robot-assisted surgery has seen its revolutionary developments and wide applications in medical practice. Minimally invasive surgery (MIS), as the most recent revolution in manual surgery, has shown numerous advantages over traditional open surgery, such as less trauma, less pain, shortened hospital stay and reduced cost, etc. Robotic minimally invasive surgery (RMIS) has further sharpened the edge of MIS by providing more stable and more dexterous manipulation, new task-specific tools, reduced physical and mental burden for the surgeon and correspondingly improved safety and comfortability for the patient. Encouraged by the success of RMIS, with the representative example of the world-wide use of da Vinci R robotic surgery system, robot-assisted surgery has stepped towards single-port laparoscopy (SPL) and natural orifice transluminal endoscopic surgery (NOTES) attempting to further enhance the cosmetic benefits of minimally invasive surgery while minimizing the potential morbidity associated with multiple incisions.

In most robot-assisted surgeries, the surgeon is isolated from the operating site inside the patient body and his operation is executed by the robotic instrument(s) via a unilateral teleoperation manner, i.e. the robotic instrument purely executes the surgeon's commands without sending back any haptic information about the working environment and the operation consequence. The lack of feedback information has been observed and evaluated by researchers in surgical robotics [START_REF] Okamura | Haptic Feedback in Robot-Assisted Minimally Invasive Surgery[END_REF]), and numerous bilateral teleoperation approaches have been proposed in literature to address this problem [START_REF] Dobbelsteen | Indirect measurement of pinch and pull forces at the shaft of laparoscopic graspers[END_REF], [START_REF] Kuchenbecker | VerroTouch: high-frequency acceleration feedback for telerobotic surgery[END_REF], [START_REF] Mcmahan | Tool contact acceleration feedback for telerobotic surgery[END_REF]). For most of the developed bilateral telesurgery schemes, the communication delay has been ignored. It can be explained that in most RMIS the surgeon stays close to the patient and robotic surgery system such that delay in communication is negligible. However, for new robotic intervention methods as SPL and NOTES, all robotic instruments (including actuator, sensors, etc.) need to be miniaturized. The existence of communication cables/wires appear cumbersome and limit the maneuverability of operating tools, and in some cases even not feasible, e.g. in swallowable capsule robots for monitoring or diagnosis purposes. The most promising solution is to replace the wired communication by wireless communication, as has been implemented in miniaturized modular robots for endocavitary surgery [START_REF] Tortora | Array of Robots Augmenting the Kinematics of Endocavitary Surgery[END_REF]). But as a downside, the wireless communication inevitably introduces considerable communication delay.

Different from general time-delayed system control which mainly considers system stability, the time-delayed bilateral teleoperation design should consider both stability and transparency, which are usually two conflicting objectives [START_REF] Hokayem | Bilateral teleoperation: An historical survey[END_REF]). Without time delay, it has been shown that perfect stability and transparency can be achieved [START_REF] Lawrence | Stability and transparency in bilateral teleoperation[END_REF], Hashtrudi-Zaad and Salcudean (2001)). But with the presence of time delay, Anderson and Spong showed that even small time delay in communication can destroy system stability based on scattering theory, and they proposed an active control method to alleviate this problem with constant time delay [START_REF] Anderson | Bilateral Control of Teleoperators with Time Delay IEEE Trans[END_REF]). A conceptually similar wave variable formulation has been proposed by Niemeyer and Slotine in [START_REF] Niemeyer | Stable adaptive teleoperation[END_REF]), which can guarantee system passivity against theoretically arbitrary time delay. Later on, many passivity-based schemes such as wavevariable transformation [START_REF] Franken | Bilateral telemanipulation with time delays: A two-layer approach combining passivity and transparency[END_REF], [START_REF] Kawashima | Bilateral teleoperation with time delay using modified wave variable based controller[END_REF], [START_REF] Bate | Reducing wave-based teleoperator reflections for unknown environments[END_REF], [START_REF] Li | Achieving stable tracking in wave-variable based teleoperation[END_REF], [START_REF] Guo | Stable and enhanced position-force tracking for bilateral teleoperation with time delay[END_REF]) and time domain passivity approach [START_REF] Hannaford | Time-domain passivity control of haptic interfaces[END_REF], [START_REF] Ryu | A passive bilateral control scheme for a teleoperator with time-varying communication delay[END_REF], [START_REF] Ryu | Bilateral control with time domain passivity approach under time-varying communication delay[END_REF]), have been proposed in literature. However, all these passivity-based methods guarantee system stability at the cost of sacrificing transparency to certain extent. In [START_REF] Hannaford | A design framework for teleoperators with kinesthetic feedback[END_REF]), an online environment estimation scheme was proposed for teleoperation system with time delay. In this approach, non-delayed force feedback signal is provided to the operator directly using an online estimated environment model and hence presents an alternative type of information exchange between the master and slave. This kind of teleoperation design concept is referred to as model-based, model predictive/prediction based, or model-mediated teleoperation (MMT). Different from the conventional teleoperation architecture wherein the force signals or wave variables are transmitted in the backward channel (Fig. 1a), MMT systems send the estimated model parameters back to the master instead (Fig. 1b). The main interesting properties of MMT system lie in that: first of all, the overall system is separated into two decoupled subsystem (master loop and slave loop) and therefore system stability can be studied separately on the master side and slave side, which is obviously much more convenient than conventional passivity based teleoperation system design; secondly, given a fast and accurate environment modelling method, the haptic force rendered to the human operator well mimics the real interaction on the slave side and presents trivial time delay if the environment properties change slowly or in a predictable way, and therefore high operation transparency can be achieved; also, MMT reduces transmission data complexity thanks to its increased level of abstraction and therefore allows relatively lower system update rate (more robustness to time delay) since environment model parameters are transmitted instead of high bandwidth force signals [START_REF] Mitra | Model-mediated telemanipulation[END_REF]). Many MMT methods have been proposed in literature including Smith-predictor based methods [START_REF] Love | Force reflecting teleoperation with adaptive impedance control[END_REF], [START_REF] Tzafestas | Telehaptic perception of delayed stiffness using adaptive impedance control: Experimental psychophysical analysis[END_REF], [START_REF] Yoon | Modelbased space robot teleoperation of ETS-VII manipulator[END_REF], Smith and Hashtrudi-Zaad (2005), [START_REF] Sheng | Model predictive control for bilateral teleoperation systems with time delays[END_REF], Willaert et al. (2012), [START_REF] Smisek | Naturallytransitioning rate-to-force controller robust to time delay by model-mediated teleoperation[END_REF], Li et al. (2016)).

For our targeted surgical application where miniaturized robotic instruments are controlled wirelessly, MMT presents a very promising solution due to its robustness to relatively large and time variant communication delay and intrinsic advantage to tolerate limited bandwidth communication constrained by wireless transmission protocols, such as ZigBee [START_REF] Guo | Scaled Position-Force Tracking for Wireless Teleoperation of Miniaturized Surgical Robotic System[END_REF]). The major challenge for this MMT implementation is to choose a suitable environment model for human living tissue, which should be both accurate in interaction description and efficient for real-time calculation. Recent result in [START_REF] Guo | Viscoelastic Model Based Bilateral Teleoperation for Robotic-assisted Telepalpation[END_REF]) employs linear Kelvin-Boltzmann model for teleoperated robotic palpation. In [START_REF] Achhammer | Improvement of model-mediated teleoperation using a new hybrid environment estimation technique[END_REF]), a physically more accurate nonlinear Hunt-Crossley model has been used for bilateral teleoperation, but the time delay in communication is not considered. Non-parametric neural network (NN) modelling has also been used in (Smith and Hashtrudi-Zaad (2005b), Li et al. (2016b)), but such kind of NN-based methods suffer problems such as the reciprocal relationships among the computational complexity, estimation accuracy and convergence rate and therefore is not suitable for surgical applications. In this paper, as to the authors' knowledge, we propose the first nonlinear Hunt-Crossley model based bilateral teleoperation scheme taking into account time variant communication delay. Efficient parameter estimation can be realized using log linearization technique and recursive least squares (RSL) method for real-time calculation purpose. The system stability is investigated by analysing the dissipation energy and the system transparency is evaluated through simulation studies under different conditions. The system analyses and simulation studies are carried out considering real surgical practice and requirements towards solving the targeted surgical application.

ROBOT-TISSUE INTERACTION MODEL SELECTION

A realistic and accurate robot-tissue interaction model is essential to achieve a model-mediated bilateral teleoperation which can provide the surgeon with high operation transparency (true operation feeling).

Model Selection

Several models have been developed in literature to describe the viscoelastic behaviour of soft tissues [START_REF] Kobayashi | Modeling of viscoelastic and nonlinear material properties of liver tissue using fractional calculations[END_REF]). The most complete study on viscoelastic tissue model is addressed in [START_REF] Fung | Biomechanics: mechanical properties of living tissue[END_REF]). Although accurate for off-line analysis, this model is complex and difficult to be used for applications with real time requirement. One simple and intuitive way to describe the interaction between robotic tools and soft tissues is to analytically build the force-displacement (or stress-strain) relationship. Analytical models are usually presented as combinations of springs and dampers [START_REF] Fung | Biomechanics: mechanical properties of living tissue[END_REF]), and are defined by the following components: the exerted force by the tissue, F e (t), when a strain is applied; the indentation (or penetration), x(t), computed as the amount of displacement of the tissue from the rest position; the velocity of the deformation ẋ(t); the elastic and damping coefficients K and b respectively.

Following this modelling method, several linear models have been developed:

• Elastic model: F e (t) = Kx(t). (1) • Maxwell model: F e (t) = b ẋ(t) -α Ḟe (t) (2)
where Ḟe (t) is the derivative of the exerted force and

α = b K . • Kelvin-Voigt model: F e (t) = Kx(t) + b ẋ(t). (3) • Kelvin-Boltzmann: F e (t) = Kx(t) + η ẋ(t) -γ Ḟe (t) (4)
where K = k1k2 k1+k2 , η = bk2 k1+k2 , γ = b k1+k2 with k 1 , k 2 and b denoting the elastic and damping coefficients respectively.

The above linear models may apply to contacts with objects of linear and homogeneous properties, but physical limitations can be observed when contact with soft tissue is considered. Combining the loading and unloading behaviours, a hysteresis loop should be observed as the force-displacement relationship for soft tissue during the contact. However, linear models predict a discontinuous sudden jump force during the switch between these two modes. Also, by analysing the power flow during contact as calculated by P (t) = F e (t) ẋ(t), it is found that during the unloading phase linear viscoelastic models indicate the existence of a positive energy meaning that power still flows from the end-effector to the tissue after separation, which is physically impossible [START_REF] Diolati | Contact impedance estimation for robotic system[END_REF]).

To address the aforementioned problems with linear viscoelastic models, a nonlinear Hunt-Crossley (HC) model has been proposed by replacing the spring/damper linear combination in (3) with a nonlinear one [START_REF] Hunt | Coefficient of restitution interpreted as damping in vibroimpact[END_REF]):

F (t) = Kx β (t) + λx β ẋ(t), x ≥ 0 0 x < 0 ( 5
)
where β is a positive scalar and normally ranges from 1.1 to 1.3 for soft tissues. The main characteristic of HC model is the effect of deformation depth on the damping term.

With the HC model, the contact force evolves from zero reaching the maximum value during the loading phase and returns to zero during the unloading phase. Accordingly, a physically correct power flow can be obtained. Therefore, in this work this more realistic model will be employed to serve as the estimator of robot-tissue (environment) interaction.

Real-Time Model Parameter Identification

Since the Hunt-Crossley model is nonlinear, it is not straightforward to online identify the model parameters.

The model equation ( 5) can be further written for positive deformation x as:

F e (t) = Kx β (t)(1 + λ K ẋ(t)) = Kx β (t)(1 + δ ẋ(t)) (6)
where δ = λ K . Then by taking natural logarithm of both sides, it has ln(F e (t)) = ln(K) + βln(x(t)) + ln(1 + δ ẋ(t)). ( 7) For soft tissue, generally the elastic coefficient K is much higher than the damping coefficient resulting in a small δ. Also, in robotic surgery, the surgeon moves the instruments slowly which leads to low interaction velocity ẋ(t) especially considering that the unit of velocity is in m/s. Therefore, in most cases, it has ln(1

+ δ ẋ(t)) δ ẋ(t) (8) so that ln(F e (t)) ln(K) + βln(x(t)) + δ ẋ(t) = [1, ln(x(t)), ẋ(t)] • [ln(K), β, δ] T (9)
which presents the following form y = Φ T θ (10) with y = ln(F e (t)) measurable with the force sensor equipped on the robotic tool, Φ T = [1 ln(x(t)) ẋ(t)] measurable from the robot actuator encoders, and θ = [ln(K) β δ] T being the model parameters to be online identified and fed to the estimated interaction model on the master side.

Therefore, various signal processing algorithms could be applied to solve this parameter estimation problem, such as exponentially weighted recursive least squares (RLS), self-perturbing RLS, etc. In this work, a standard recursive least squares method is used because of its easy implementation and efficient calculation in real time. The performance of this online estimation is shown in Section 4.

Remark 1 : Regarding the persistent excitation condition for parameter estimation convergence, it is known that for identification of n parameters at least n/2 non-zero frequencies are required [START_REF] Ioannou | Adaptive Control Tutorial[END_REF]). Considering the small number of Hunt-Crossley model parameters to be estimated and the complex movement trajectory involved in surgical operations, the persistent excitation condition could be easily met for estimation of constant or slowly time varying Hunt-Crossley model parameters.

Remark 2 : Sudden and significant changes in model parameters and the contact model itself may cause sudden and significant changes in the estimated model parameters, which consequently leads to a sudden change to the force rendered to the human operator. This phenomenon is called model-jump effect (Willaert et al. (2012b)). Although such kind of parameter change rarely happens in surgical operations, smooth transition and safety switch/threshold should be considered in the parameter updating.

NONLINEAR MODEL-MEDIATED TELEOPERATION DESIGN

Based on the selected nonlinear robot-environment interaction model, a Hunt-Crossley model-mediated teleoper-ation under communication delay can be synthesize as in Fig. 2.

Fig. 2. Nonlinear model-mediated teleoperation with time delay

As seen from the system diagram, the human operator's motion command in position (x m ) or velocity ( ẋm ) is sent to the slave robot through the communication channel. Instead of sending back directly the high bandwidth signal of environment force (F e ) or wave variable (v s ), only estimated environment parameters from an online RLS estimator are fed back to the master side. This is particularly interesting for wireless telesurgery applications where wireless communication boards with limited data transmission bandwidth are used. As model parameter information is higher in terms of abstraction level compared to environment force information, it is possible to update them at a lower rate as long as the environment model is not changing fiercely, which is hardly possible during surgical operations.

Moreover, since this teleoperation scheme is not passivity based and does not resort to wave transformation, position movement command can be sent directly to the slave instead of velocity and therefore avoids the common problem of position drift due to velocity integration as in most conventional passivity-based bilateral teleoperation approaches.

System Stability

As shown in Fig. 2, the overall teleoperation system constitutes two decoupled sub-systems (sub-loops) on the master and slave side, denoted by "loop 1" and "loop 2" respectively. There exists no force/motion feedback from the slave to the master but only estimated contact model parameter information. Therefore, instead of considering the overall system closed over the communication channel, system stability can be analysed separately based on the two sub-systems. As long as the stability of the two subloops can be guaranteed, the overall teleoperation system is ensured to be stable.

The master sub-system (loop 1) can be considered as a cascade connection of human operator, master device and the Hunt-Crossley model approximator. The human operator and master device are considered to possess passive mechanical impedances (Hashtrudi-Zaad and Salcudean (2001)). So if the Hunt-Crossley model approximator with updated model parameters is passive, the master subsystem is passive as well.

The passivity of the Hunt-Crossley interaction model can be evaluated by investigating its dissipation energy using equation ( 6) as

t 0 F e • ẋdt = t 0 Kx β (1 + δ ẋ) ẋdt = t 0 (Kx β ẋ + δx β ẋ2 )dt = t 0 Kx β ẋdt + t 0 δx β ẋ2 dt = x(t)
x(0)

Kx β dx + t 0 δx β ẋ2 dt = K(x β (t) -x β (0)) + t 0 δx β ẋ2 dt (11)
It is noted that above analysis stands only when the robot is in contact with the soft tissue, i.e. x > 0, otherwise the robot is in free motion and correspondingly works in another mode. Hence if δ > 0 it has

t 0 δx β ẋ2 dt ≥ a t 0 δ ẋ2 dt ≥ 0 ( 12
)
where a represents the minimum value of x β (t) over whole time duration [0, t], which is clearly non-negative.

By substituting inequality ( 12) into ( 11), it has

t 0 F e • ẋdt ≥ K(x β (t) -x β (0)) ≥ -Kx β (0) (13)
for non-negative K and thus shows that the Hunt-Crossley interaction is passive.

In fact, K, β and δ = λ K are all positive model parameters with physical meanings in reality, and their positiveness guarantees the passivity of Hunt-Crossley interaction. Therefore, if the estimated model parameters K, β, δ converge to their true values or lower bounded by a positive threshold during updating, the master side Hunt-Crossley model estimator is also passive. In consequence, the master sub-system (loop 1) is stable.

For the slave sub-system (loop 2), no matter the received master command is in motion (position/velocity) or in force, various control methods have been proposed in literature for stable interaction between robot and soft working environment [START_REF] Moreira | Soft Tissue Force Control Using Active Observers and Viscoelastic Interaction Model[END_REF], [START_REF] Golovin | Position/Force Control of Medical Robot Interacting with Dynamic Biological Soft Tissue[END_REF]). With both master and slave sub-systems stable, the proposed Hunt-Crossley model-mediated teleoperation system is guaranteed to be stable.

System Transparency

Ideal system transparency is defined as a perfect match between master and slave position and force signals (Yokokohji and Yoshikawa (1994)), or a match between the environment impedance and the perceived impedance by the operator [START_REF] Lawrence | Stability and transparency in bilateral teleoperation[END_REF]).

For model-mediated bilateral teleoperation, the system transparency essentially depends on the preciseness of environment description model and efficiency of model parameter identification. The nonlinear Hunt-Crossley model has been proved to be accurate in soft tissue modelling and efficient in model-based force control [START_REF] Pappalardo | Hunt-Crossley model based force control for minimally invasive robotic surgery[END_REF]). As commented in Remark 1, the model parameters can be identified accurately if the excitation signals are rich enough in frequency. If the environment model remains constant during operation, the operator can perceive exactly the same environment dynamics as if there exists no communication delay after the convergence time of model parameter estimation plus one backward communication delay (time variant or not). If the environment model parameters are changing at a relatively lower rate compared with the communication delay, the operator can still be rendered with almost ideal transparency of the environment dynamics. The system transparency of our proposed teleoperation scheme is evaluated in different situations as shown in next section.

PERFORMANCE EVALUATION BY SIMULATION STUDIES

In this section, simulation studies are carried out to evaluate the performance of the proposed Hunt-Crossley modelmediated bilateral teleoperation scheme under variant time delay, mimicking an robotic telesurgery with wireless communication. For clearer presentation and without loss of generality when extended to multiple degrees of freedom (DOF) [START_REF] Anderson | Bilateral Control of Teleoperators with Time Delay IEEE Trans[END_REF], teleoperation system of one DOF is used in the simulation study. Two different situations are considered: interaction with environment of constant but unknown parameters, and with environment of time variant parameters. As shown in [START_REF] Guo | Scaled Position-Force Tracking for Wireless Teleoperation of Miniaturized Surgical Robotic System[END_REF]), the round trip communication delay for wireless ZigBee transmission is at the scale of few hundreds of milliseconds (ms). In the simulation, for both cases, the time variant communication delays are defined in ms as:

T com (t) = T 1 (t) = 200 + 55sin(2πt), forward T 2 (t) = 300 + 35sin(2πt + π/2), backward
Here, sinusoidal functions are used to simulate communication time variance. Theoretically the designed system can work with more complex (even arbitrary) time variances. The system transparency is evaluated by comparing the ratios between position and force signals of master and slave sides as Fm xm v.s. Fs xs (Yokokohji and Yoshikawa (1994)).

Constant Environment

In this study, the environment used as ground-truth is described by a constant model:

F e (t) = Kx β (t)(1 + δ ẋ(t)) = 2000x 1.23 (1 + 0.1 ẋ) (14)
The model parameters are roughly set based on the soft material estimation in [START_REF] Diolati | Contact impedance estimation for robotic system[END_REF]). The slave robot is assumed to start from the zero-contact position of the environment surface (x(0) = 0). For both the master side approximation model and the slave side RLS estimator, the initial values of unknown environment parameters are approximated as K = 665, β = 1 and δ = 0. And to avoid the violent parameter changes during the transition (convergence) period, the master model will wait for 1 second before starting to receive the updating model parameters from the RLS estimator.

From Fig. 3, it is shown that the three estimated model parameters by RLS converge to their true values quickly, where ln(K) = ln(2000) = 7.6. Consequently, it is seen in Fig. 4 that the master force follows exactly the same environment force after the 1 second transition period if the back-trip communication delay is compensated for comparison purpose. In the end, the environment dynamics ( Fm xm ) rendered to the human operator on the master side is faithful to the real one except a lead in phase as shown in Fig. 5, which reveals the predictive nature of model-mediated teleoperation approach.

Time Variant Environment

In this study, the parameters of ground-truth environment is time variant and defined as ln(K) = 7.6 + 0.1sin( π 4 t), β = 1.23 + 0.01sin( π 2 t), δ = 0.1 + 0.01sin( π 8 t). Note that the value of K varies in the range of [1808,2208] correspondingly.

Since the environment parameters are time variant, the estimated model parameters do not converge to the true parameters accurately in real time. However, the force rendering and environment dynamics matching still perform well as shown in Fig. 6 and7. Slight performance degradation are observed as compared to the first simulation study. This can be explained by the parameter mismatch between master side estimator and slave environment due to non-convergent online parameter estimation, and hence again emphasizes the importance of model accuracy in this kind of model-mediated teleoperation.

The simulation studies verify the efficiency of the proposed bilateral teleoperation scheme in providing stable and transparent performance and robustness against communication delay and environment parameter variance. A nonlinear model based bilateral teleoperation scheme has been developed in the work to address surgical applications where the working environment is soft tissue and the communication contains time variant delays due to the wireless communication protocol used (e.g. ZigBee), package loss, etc. The nonlinear Hunt-Crossley model has been chosen to describe the soft tissue environment which has been proved in literature to be more realistic and accurate than linear viscoelastic models. By resorting to online parameter identification technique, in this work recursive least square (RLS), the environment model parameters are estimated online and transmitted to the master side model which serves as a predictor and renders haptic force feedback to the human operator without delay. The overall system is guaranteed to be stable through passivity analysis. Simulation studies with both constant and varying contact environments show that the proposed teleoperation scheme can provide faithful interaction force to the operator and provide quite accurate matching between perceived and real environment dynamics.

Fig. 1 .

 1 Fig. 1. General diagrams of bilateral teleoperation systems

Fig. 3 .

 3 Fig. 3. RLS online estimation of environment parameters

Fig. 6 .

 6 Fig. 6. Master force v.s. delay-compensated environ. force