Imad Aharchaou

Jean-Sébastien Py

Sébastien Cambier

Jean-Luc Loizeau

Geert Cornelis

Philippe Rousselle

Eric Battaglia

Davide Anselmo

Luigi Vignati

Davide A L Vignati

Chromium hazard and risk assessment: New insights from a detailed speciation study in a

Keywords: Trace metals, Chromium, Metal speciation, Algae, Hazard/Risk assessment

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

INTRODUCTION

The bioavailability and ecotoxicity of trace elements in natural environments are determined by the complex interplay among the ecological traits of living organisms, the toxicodynamics and toxicokinetics of trace elements, and the elemental speciation in environmental matrices [START_REF] Fairbrother | Framework for Metals Risk Assessment[END_REF][START_REF] Mason | Trace Metals in Aquatic Systems[END_REF][START_REF] Harris | Principles of Sound Ecotoxicology[END_REF]. Elemental speciation refers to various physico-chemical forms in which trace elements occur in a given environment and, in some cases, includes the presence of different oxidation states with contrasting environmental biogeochemistry. In the specific case of chromium, the importance of speciation is well appreciated with regard to its biogeochemical cycle [START_REF] Masscheleyn | Chromium Redox Chemistry in a Lower Mississippi Valley Bottomland Hardwood Wetland[END_REF][START_REF] Dominik | Speciation and Environmental Fate of Chromium in Rivers Contaminated with Tannery Effluents[END_REF][START_REF] Saputro | Speciation of dissolved chromium and the mechanisms controlling its concentration in natural water[END_REF]) and biological effects (WHO 2009;WHO 2013). In surface waters, chromium mainly occurs in two oxidation states, namely Cr VI and Cr III , with contrasting environmental and biological behavior. Hexavalent chromium, a recognized human carcinogen, forms negatively charged chemical species, interacts little with colloidal and particulate material, has a high environmental mobility, and easily crosses biological membranes (WHO 2013). In contrast, Cr III preferentially forms positively charged chemical species, tends to associate with colloids or suspended particulate matter and is considered of less ecotoxicological concern (WHO 2009;WHO 2013). In most environmental settings, both redox forms occur simultaneously, albeit in variable proportions [START_REF] Bobrowski | Chromium speciation study in polluted waters using catalytic adsorptive stripping voltammetry and tangential flow filtration[END_REF][START_REF] Saputro | Speciation of dissolved chromium and the mechanisms controlling its concentration in natural water[END_REF] and interconversions between them have been documented along with the corresponding controlling factors [START_REF] Rai | Environmental chemistry of chromium[END_REF][START_REF] Richard | Aqueous geochemistry of chromium: A review[END_REF][START_REF] Lin | The Chemical Transformations of Chromium in Natural Waters -A Model Study[END_REF].

However, experimental research on Cr speciation in standardized ecotoxicological test media has received limited attention. Thermodynamic speciation calculations are increasingly used to predict the Cr forms likely to exist in ecotoxicological exposure media, thus aiding experimental planning and data interpretation [START_REF] Dazy | Antioxidant enzyme activities as affected by trivalent and hexavalent chromium species in Fontinalis antipyretica Hedw[END_REF][START_REF] Didur | Alteration of chromium effect on photosystem II activity in Chlamydomonas reinhardtii cultures under different synchronized state of the cell cycle[END_REF][START_REF] Liu | An experimental and thermodynamic equilibrium investigation of the Pb, Zn, Cr, Cu, Mn and Ni partitioning during sewage sludge incineration[END_REF]. These calculations also suggest that insoluble species of Cr III (mostly Cr oxyhydroxides) can form in ecotoxicological test media for algae, daphnids and aquatic plants [START_REF] Dazy | Antioxidant enzyme activities as affected by trivalent and hexavalent chromium species in Fontinalis antipyretica Hedw[END_REF][START_REF] Vignati | Chromium(VI) is more toxic than chromium(III) to freshwater algae: A paradigm to revise? Ecotoxicol[END_REF][START_REF] Ponti | How reliable are data for the ecotoxicity of trivalent chromium to Daphnia magna?[END_REF]. The presence of such chemical species can modify the fraction of Cr III that is potentially bioavailable for the test organisms during the exposure period, because in most cases it is assumed that the bio-availability of metals is related to the free ion activity [START_REF] Morel | Freshwater Alga and Cyanobacteria, Growth Inhibition Test[END_REF]. Insoluble species also explain the often large differences between total and total filterable (< 0.45 µm) Cr concentrations found in test media spiked with Cr III , the extent depending on medium composition [START_REF] Chapman | Effects of water hardness on the toxicity of metals to Daphnia magna: status report -January[END_REF][START_REF] Vignati | Temporal Decrease of Trivalent Chromium Concentration in a Standardized Algal Culture Medium: Experimental Results and Implications for Toxicity Evaluation[END_REF][START_REF] Ponti | How reliable are data for the ecotoxicity of trivalent chromium to Daphnia magna?[END_REF]. It should also be noted that filterable (< 0.45 µm) Cr concentrations do not equal the sum of concentrations of truly dissolved Cr species, because the initial formation of precipitates may result in solids having particle sizes below this size cut-off. Furthermore, certain studies present results supporting the conclusion that Cr III is more ecotoxic than Cr VI [START_REF] Holdway | The toxicity of chromium to fish[END_REF][START_REF] Thompson | Comparison of the Toxicity of Chromium III and Chromium VI to Cyanobacteria[END_REF][START_REF] Vignati | Chromium(VI) is more toxic than chromium(III) to freshwater algae: A paradigm to revise? Ecotoxicol[END_REF][START_REF] Lira-Silva | Removal, accumulation and resistance to chromium in heterotrophic Euglena gracilis[END_REF][START_REF] Kováčik | Physiology and methodology of chromium toxicity using alga Scenedesmus quadricauda as model object[END_REF]; in contrast with the current consensus considering Cr VI as the most ecotoxic redox form (WHO 2013). A more detailed understanding of Cr speciation in (standardized) laboratory test media used for ecotoxicity testing will help to both reconcile contrasting ecotoxicological results in controlled settings and improve our ability to extrapolate laboratory results to real-field risk assessment situations.

On the basis of the above considerations, three aspects related to Cr speciation, and its changes during a given (standardized) test, appear of particular importance for an improved understanding of the relative ecotoxicity of Cr III and Cr VI : a) the stability of (filterable) Cr concentrations added to the test medium, b) the possibility of redox interconversions between Cr III and Cr VI , and c) the formation of Cr oxyhydroxides (i.e., Cr-bearing nanoparticles). In the present study, the ecotoxicity of three Cr III salts and one Cr VI salt commonly used in ecotoxicological studies was investigated using the standard algal medium ISO 8692 (OECD 2011), hereinafter test medium, as exposure matrix and the green alga Raphidocelis subcapitata as test organism. The behavior and speciation of both Cr III and Cr VI forms, including their possible interconversions, were investigated in detail over 72 h; corresponding to the typical duration of a standard algal test (OECD 2011). Our results showed rapid changes (i.e., within hours) in Cr III speciation which calls for a thorough reconsideration of the current knowledge about the relative ecotoxicity of Cr III and Cr VI in terms of both hazard and risk assessment.

MATERIALS AND METHODS

Chemicals

All chemicals used were of highest purity. For the various experiments, the test medium ISO8692 was prepared as described in OECD guideline 201 (OECD 2011) All filtrations were performed using 0.22 µm syringe filters (Millex 33 mm diameter, PVDF, Millipore, reference number SLGV033NB) prewashed one time with 10 mL of diluted (10% v/v) hydrochloric acid (HCl Suprapur 30%, Merck Millipore, lot number Z0309518344) and three times with 10 mL of ultrapure water (Millipore, Q-POD®). A preliminary experiment showed that Millex syringe filters with nominal pore sizes of 0.22 and 0.45 µm yielded comparable results for aliquots of test medium amended with 60 µg Cr III /L (data not shown).

All samples for the analysis of total Cr concentration were acidified at 1% v/v with concentrated nitric acid (HNO 3 67%, Prolabo, VWR, batch number 1108110). A solution of 0.4 M nitric acid (Chemlab, suprapur 70%, batch: 221831609) spiked with 1 µg/L of rhodium was used as internal standard during the analyses of Cr speciation.

Chromium ecotoxicity

The ecotoxicity of Cr VI and Cr III salts to the green alga Raphidocelis subcapitata (strain 278/4 originally obtained from the Culture Collection of Algae and Protozoa -CCAP -Argyll, Scotland, United Kingdom; formerly known as Pseudokirchneriella subcapitata) was evaluated according to OECD guideline 201 (OECD 2011). Tests were performed as previously described [START_REF] Vignati | Chromium(VI) is more toxic than chromium(III) to freshwater algae: A paradigm to revise? Ecotoxicol[END_REF]) using inoculums of 20,000 cells/mL and nominal exposure concentrations of 9,18,35,70,140,280,560,1125,2250 µg Cr/L. The effects of Cr salts on algal growth were expressed as the effective exposure concentrations (ECs50) that produced a 50% decrease in algal fluorescence (BMG LabTechnologies, Fluostar), considered as a proxy for algal biomass. The ECs50 were calculated by performing a nonlinear regression on Hill's model with the macro REGTOX (Version EV7.0.4., E. Vindimian) (Vindimian 2010). In the case of Cr III , ECs50 were estimated based on both nominal concentrations and Time-Weighted Mean (TWM) dissolved measured concentrations (OECD 2012). Starting from this point, the terms total and dissolved concentrations will indicate the unfiltered and filtered (0.22 µm) portions of measured Cr levels.

Temporal evolution of Cr concentration in the test medium

Aliquots (50 mL) of freshly prepared test medium were transferred to acid-washed Erlenmeyer flasks (150 mL) and spiked with a Cr concentration corresponding to the ECs50 of either Cr III (added as CrCl 3 •6H 2 O) or Cr VI (added as K 2 Cr 2 O 7 ) in the presence or absence of an initial algal inoculum of 20,000 cells/mL. Aliquots were analyzed for total and dissolved Cr after 0.5, [START_REF] Montaño | Improvements in the detection and characterization of engineered nanoparticles using spICP-MS with microsecond dwell times[END_REF][START_REF] Tuoriniemi | new peak recognition algorithm for detection of ultra-small nano-particles by single particle ICP-MS using rapid time resolved data acquisition on a sector-field mass spectrometer[END_REF][START_REF] Tuoriniemi | Size Discrimination and Detection Capabilities of Single-Particle ICPMS for Environmental Analysis of Silver Nanoparticles[END_REF]8,24,48, and 72 h of incubation under continuous light (90 -110 µE/m 2 /s) at 21 ± 2 °C and, for biotic samples only, rotary agitation (100 rpm). For dissolved Cr determination, the first 5 mL of filtered solution were used for preconditioning the filters and discarded. Preconditioning aimed at removing possible residues of ultrapure water from filter pores and saturate possible sorption sites for Cr. Total and dissolved Cr concentrations were determined by flame atomic absorption spectrometry (FAAS, Perkin-Elmer AAnalyst 100) or, for concentrations < 20 µg/L, graphite furnace atomic absorption spectrometry (GFAAS, Varian spectra 300, using 0.1% Mg(NO 3 ) 2 as matrix modifier according to manufacturer instructions). Quantification limits were 10 µg/L for FAAS and 0.2 µg/L for GFAAS. Certified reference materials SPS-SW1 (2.00 ± 0.02 µg/L) and WW1 (200 ± 1 µg/L), both from SpectraPure standards (Manglerud, Norway), were used as quality controls.

All analytical results are expressed in µg Cr/L.

The statistical significance of the temporal changes in Cr concentrations was evaluated by one-way ANOVA with Tukey post-hoc comparison. Visual Minteq modelling (ver 3.1) was done to investigate Cr III speciation in test medium amended with an initial total concentration of 60 µg Cr/L . No redox transformations were assumed, because it will be argued based on experimental proof that these did not occur. Calculations were performed using experimentally measured Cr concentrations and pH values, and the test medium composition as reported in OECD (2011). No modifications were made to the Visual Minteq default database and the Debye-Hückel equation was used for activity corrections.

Chromium redox speciation

To investigate Cr redox speciation and the possible interconversion between Cr III and Cr VI , aliquots (50 mL) of the test medium were spiked with either Cr VI or Cr III (added as chloride) both in absence (abiotic medium) and presence (biotic medium) of algal inoculums (20,000 cells/mL). Nominal Cr concentrations in the spiked solutions were 60 µg/L for Cr III and 115 µg/L for Cr VI , corresponding to the calculated 72 h ECs50 (see section Chromium ecotoxicity in Results and discussion). Samples were analyzed immediately after spiking (t=0) or incubated at 23 ± 1 °C, under continuous light (90 -110 µE/m 2 /s) and, for biotic samples only, rotary agitation (100 rpm) for 24, 48 and 72 h prior to analysis (Figure S1). At the end of each incubation period, sample aliquots for Cr speciation were filtered as described above.

After preconditioning the filters with 5 mL (subsequently discarded) of Cr-amended test medium, 10 mL of filtrate was collected in polystyrene sample vials and immediately analyzed by ion chromatography-inductively coupled plasma mass spectrometry (IC-ICP-MS). Samples were kept at between 4 and 6 °C in a refrigerated sample tray during analysis.

An additional abiotic sample of test medium (2 L) was prepared in an acid-washed lowdensity polyethylene bottle and spiked with 60 µg/L of Cr III to follow more closely the kinetics of the changes in Cr III speciation [START_REF] Sacher | Simultaneous Determination of Cr(III) and Cr(VI) in Ground and Drinking Waters by IC-ICP-MS[END_REF][START_REF] Séby | Chromium speciation by hyphenation of high-performance liquid chromatography to inductively coupled plasma-mass spectrometry-study of the influence of interfering ions[END_REF]. Aliquots for analysis were recovered every 20 min over the first 6 hours after spiking and again after 24, 48, and 72 hours of incubation in the same conditions described above.

Trivalent Cr and hexavalent Cr species were separated and quantified by IC-ICP-MS using a Thermo ICS 5000+ pump coupled with an anion exchange column (Thermo AG7 2x50 mm) and connected to the nebulizer of an ICP-MS (Thermo, Series XII) (Table S1). A solution of 0.4 M nitric acid spiked with 1µg/L of rhodium was used to elute the Cr species from the anion exchange column (see Table S1 for more details). The analyses were carried out according to the method developed by the French Agency for Food, Environmental & Occupational Health & Safety (ANSES) on the basis of the application note from the supplier [START_REF] Sacher | Simultaneous Determination of Cr(III) and Cr(VI) in Ground and Drinking Waters by IC-ICP-MS[END_REF]; ANSES/LHN/MT-CrVI). Chromium detection was performed at m/z 52 and 53. Experimental IC-ICP-MS results were compared with those of speciation modeling carried out as described previously (section Temporal evolution of Cr concentration) using Visual Minteq.

Formation of Cr nanoparticles in the test medium

Aliquots of test medium were spiked with 60 µg/L of Cr III (added as chloride or nitrate) and the formation of Cr-containing particles was investigated by Nanoparticle Tracking Analysis (NTA), spICP-MS (single particle ICP-MS) and Single Particle Counting (SPC) over 72 h; that is the typical duration of an algal ecotoxicological test. Blank samples consisting of unspiked test medium were systematically analyzed along with the corresponding samples.

Total and dissolved Cr concentrations were determined by FAAS during the various experiments.

For NTA (Nanosight NS500; Malvern instruments Ltd, UK), spiked samples were aged for 0, 0.5, 1, 2, 24, 48, and 72 h and assayed (before and after filtration) for particle concentration and particle size distribution (PSD). The NS500 provides detailed analysis of the concentration and size distribution of all types of nanoparticles from 10 nm to 1000 nm in diameter [START_REF] Carr | Nanoparticle Tracking Analysis[END_REF] using the properties of both light scattering and Brownian motion in liquid suspensions. Particles in suspension in the sample chamber (volume = 0.3 mL) were visualized using a 20x magnification microscope equipped with a camera operated at 25 frames per second for 60 s. The resulting video files were elaborated using the built-in software (NTA 2.3 build 0033) to calculate the hydrodynamic diameter of the individually tracked particles. After each measurement, the sample chamber was flushed with milliQ water and reloaded with the next sample aliquot. All measurements were done in triplicate and the mean (± one standard deviation) of particle concentration and average size calculated (see supplementary information for protocol optimization).

While NTA determines the total particle count, spICP-MS (Perkin Elmer NexION 350D ICP-MS) was used to specifically measure Cr-containing particles. Samples were aged for 0, 24, 48 and 72 h and diluted to a theoretical concentration of 0.06 µg/L total Cr before analysis.

The transport efficiency was calculated based on a dissolved standard curve of Au stabilized by 0.1 % cysteine and on the TEM-based median size (56 nm) of gold nanoparticles (NIST8013, nominal diameter 60 nm) using the method of [START_REF] Pace | Determining Transport Efficiency for the Purpose of Counting and Sizing Nanoparticles via Single Particle Inductively Coupled Plasma Mass Spectrometry[END_REF]. Data acquisition was performed in fast acquisition scanning technique (FAST) mode with a dwell time of 50 µs over 100 s. Raw data (two million readings per sample) were extracted and loaded into the Nanocount software (http://blogg.slu.se/nanocount/) for the determination of particle number and particle size distribution. Correction for dissolved concentrations was performed using outlier analysis based on a 5 × σ criterion specifically developed for FAST data (Tuoriniemi et al. 2015). Peak integration time was set to 20 ms and the minimum detectable cluster was set at 4 ions. Distributions of the corresponding spherical size were calculated assuming a Cr(OH) 3 ( = 3.11 g/cm 3 ) composition and a spherical shape. It should be noted that these were assumptions as the exact composition and shape of the formed particles are unknown.

However, considering the measured pH range of the test medium initially spiked with 60 µg Cr/L (7.8-7.9 units), trivalent chromium is expected to rapidly undergo hydrolysis and form amorphous oxyhydroxides [START_REF] Rai | Environmental chemistry of chromium[END_REF][START_REF] Iso ; Kotaś | Water quality --Guidelines for algal growth inhibition tests with poorly soluble materials, volatile compounds, metals and waste water[END_REF]. The assumption on particle shape would allow comparison with the results obtained using other methods.

To detect the presence of particles outside the NTA and spICP-MS measuring range, samples were analyzed after 0, 24, 48, and 72 hours of incubation using three Single Particle Counters (SPCs): a high sensitivity in-situ monitor (HSLIS) Model M50 for the range 50 to 200 nm and two Volumetric Spectrometers (LiQuilaz-S02 and LiQuilaz-S05, Particle Measuring Systems, Boulder, CO, U.S.A) for the ranges 200 to 2000 nm and 500 nm to 20 µm, respectively. The SPCs use light scattering to count individual particles across 31 size classes with some overlapping between the LiQuilaz-S02 and S05 [START_REF] Rossé | Use of single particle counters for the determination of the number and size distribution of colloids in natural surface waters[END_REF]. Results for spiked medium were corrected for blank values.

RESULTS AND DISCUSSION

Chromium ecotoxicity and temporal evolution of Cr concentrations

Results of ecotoxicity tests were highly reproducible with ECs50 at 72 h (mean value ± one standard deviation) of 113 ± 3 µg/L (n = 3) for K 2 Cr 2 O 7 , 59 ± 3 µg/L for CrCl 3 •6H 2 O (n = 6), 61 ± 8 µg/L for Cr(NO 3 ) 3 •9H 2 O (n = 3) and 62 ± 3 µg/L for KCr(SO 4 ) 2 •12H 2 O (n=3). The ECs50 values reported in the literature for freshwater algae range from 130 to 470 µg/L for Cr VI and from 30 µg/L to over 1000 µg/L for Cr III (WHO 2009; Vignati et al. 2010; OECD 2011; WHO 2013). In the case of Cr VI , a ring test involving 16 laboratories determined a range of 72h-ECs50 between 70 and 260 µg Cr/L for Scenedesmus subspicatus and Selenastrum capricornutum (a former name for R. subcapitata) based on algal biomass endpoint [START_REF] Munn | Chromium trioxide, sodium chromate, sodium dichromate, ammonium dichromate, potassium dichromate, EUR 21508 EN[END_REF]WHO 2013); which agrees with our results. In the case of Cr III , our results are in the low range of the values reported in the literature and indicate a higher toxicity of Cr III compared with Cr VI ; an occurrence also reported in previous research [START_REF] Holdway | The toxicity of chromium to fish[END_REF][START_REF] Thompson | Comparison of the Toxicity of Chromium III and Chromium VI to Cyanobacteria[END_REF][START_REF] Vignati | Chromium(VI) is more toxic than chromium(III) to freshwater algae: A paradigm to revise? Ecotoxicol[END_REF][START_REF] Lira-Silva | Removal, accumulation and resistance to chromium in heterotrophic Euglena gracilis[END_REF][START_REF] Kováčik | Physiology and methodology of chromium toxicity using alga Scenedesmus quadricauda as model object[END_REF]. Further insights in the relative ecotoxicity of the two redox forms of Cr can be gained by examining their behavior in the test medium. In particular, the detailed examination of Cr VI and Cr III behavior added to the test medium at concentrations corresponding to their respective ECs50 allows to exactly determine the actual concentrations responsible for the observed effects.

At t = 0 h, the measured total and dissolved Cr concentrations (added as Cr III ) were similar and corresponded to the expected nominal values in both abiotic and biotic media. In the absence of algae, total Cr concentrations remained within 20% of the initial value over the first 24 hours and had decreased by about 40% after 72 h. In the same experiment, dissolved Cr concentrations remained within 20% of the initial values only over the first two hours, but had dropped by 40% eight hours after spiking and by 83% after 72 h (Figure 1). The decrease in total Cr concentrations indicates that some of the added Cr may be lost to the walls of the test vessel over time. However, comparison of total and dissolved concentrations indicates that ca. 50% of the added Cr likely occurs in the form of colloidal or particulate form (most likely amorphous Cr oxyhydroxides) starting from 24 hours after spiking (i.e., for over 2/3 of the test duration). Calculations in Visual Minteq for an initial concentration of 60 µg/L as Cr III predicted that, in the observed pH range of 7.8 to 7.9, the Cr(OH) 3 species should account for 92-94 % of the total Cr. Furthermore, about 80% of the initially added Cr III was predicted to precipitate in the form of amorphous Cr(OH) 3 , in very good agreement with the 80% decrease of the corresponding dissolved Cr concentration over 72h (Figure 1). Colloid/nanoparticle formation was indeed confirmed using NTA and spICP-MS (see section Formation of Cr nanoparticles in Results and Discussion). Analogous calculations using the dissolved Cr concentration measured at 72h (11±0.25 µg/Cr L, n=3) also predicted that Cr(OH) 3 would account for over 90% of the measured Cr concentration, but with less than 2% occurring in the precipitated phase. In both cases, the sum of the positively charged species Cr(OH) 2 + and CrOH 2+ was predicted to represent about 3.5% of the total dissolved Cr and EDTA complexes were about 2.5%. Further comparison between speciation calculations and analytical results is presented in the next section.

The difference between total and dissolved Cr concentrations becomes statistically significant starting from 8 h after spiking (one-way Anova with Tukey post-hoc comparison, p < 0.01).

Considering the temporal decrease of the dissolved Cr concentration, assumed as a better dissolved Cr concentrations [START_REF] Vignati | Temporal Decrease of Trivalent Chromium Concentration in a Standardized Algal Culture Medium: Experimental Results and Implications for Toxicity Evaluation[END_REF][START_REF] Vignati | Chromium(VI) is more toxic than chromium(III) to freshwater algae: A paradigm to revise? Ecotoxicol[END_REF]).

In the presence of algae, both total and dissolved Cr concentrations decreased with time (Figure 1) and the decrease was more marked for the dissolved concentrations (over 95% after Analogous experiments performed with aliquots of test medium amended with Cr VI at the corresponding EC50 concentration (115 µg/L) did not show significant changes in total or dissolved Cr concentration neither in the absence nor in the presence of algae (Figure S5).

The above observations lead us to the conclusion that Cr III is 4 to 10 times more toxic than

Cr VI when the 72 h EC50 for Cr III is expressed as the TWM dissolved concentration estimated from measurements in the absence or presence of algae, respectively. However, the presence of algae had no measurable effect on dissolved Cr VI concentrations (Figure S6). One possibility is that the entrance of minimal quantities of Cr VI into the cells may suffice to reduce algal biomass, which would support the current consensus that Cr VI is more toxic than Cr III . On the other hand, exposure to Cr VI has been shown to cause lysis of R. subcapitata cells at concentrations of 1.75 mg/L or higher added to an algal inoculum of 2 × 10 5 cells/mL [START_REF] Labra | Toxic and genotoxic effects of potassium dichromate in Pseudokirchneriella subcapitata detected by microscopy and AFLP marker analysis[END_REF]; which corresponds to an initial quantity of 8.75 ng of Cr VI per algal cell at the beginning of the experiment (our calculation). This figure compares favorably with the value of 5.75 ng of Cr VI per algal cell in our experimental conditions for an initial spike of 115 µg/L. Upon cell lysis, the initially internalized Cr VI would be released back to the test medium resulting in an apparent stable total (dissolved) Cr concentration over the duration of the experiment. Note that Cr VI can undergo intracellular reduction to Cr III [START_REF] Cheung | Mechanism of hexavalent chromium detoxification by microorganisms and bioremediation application potential: A review[END_REF][START_REF] Volland | Intracellular chromium localization and cell physiological response in the unicellular alga Micrasterias[END_REF][START_REF] Kováčik | Physiology and methodology of chromium toxicity using alga Scenedesmus quadricauda as model object[END_REF]) which could also be released back to the test medium upon cell lysis; possibly in association with intracellular constituents preventing its precipitation in the test medium. While no experiments were performed to determine if cell lysis had occurred, we verified possible changes in the redox state of Cr in the test medium over the exposure duration.

Chromium redox speciation

Aliquots of test medium spiked with Cr VI exhibited a single peak, corresponding to the one observed in a standard solution of Cr VI , with a retention time of about 50 s regardless of the presence of algae and of the incubation time (Figures 2A andS6). The total Cr VI concentration, determined from total peak area, was 118 µg/L at t=0 and 120 µg/L after 72h of incubation in the abiotic test medium and 137 µg/L at t=0 and 120 µg/L after 72h in the biotic medium. No peaks corresponding to Cr III were observed in either abiotic or biotic test medium (Figures 2A and S6). While this result does not provide information on possible Cr VI to Cr III interconversion in the intracellular environment [START_REF] Shanker | Chromium toxicity in plants[END_REF][START_REF] Viti | Molecular mechanisms of Cr(VI) resistance in bacteria and fungi[END_REF][START_REF] Kováčik | Physiology and methodology of chromium toxicity using alga Scenedesmus quadricauda as model object[END_REF], it shows that algal cells are exposed to a practically constant concentration of Cr VI throughout the test duration. The corresponding ECs50 values for Cr VI can therefore be confidently ascribed to this specific redox form and calculated from the concentrations initially added to the test medium.

On the other hand, marked and rapid changes in Cr speciation occurred in medium aliquots amended with Cr III . At t=0 and in the absence of algae, a single peak at a retention time of about 100 s, corresponding to the hydrated Cr III ion, was observed (Figure 2B). The corresponding dissolved Cr III concentration determined by IC-ICP-MS was 57 µg/L, in agreement with the expected value of 60 µg/L. However, after 24 h of incubation, the peak area at 100 s had dropped by 99% and the corresponding dissolved Cr III concentration at 72 h was only 0.39 µg/L (Figure 2B). Starting from 24 h after spiking, two additional peaks were observed at retention times around 45 s and 75 s (Figure 2B). Considering the measured pH range of the test medium (7.5-7.9 for medium aliquouts amended with Cr III concentrations between 20 and 1250 µg Cr/L), Cr III is expected to rapidly undergo hydrolysis [START_REF] Rai | Environmental chemistry of chromium[END_REF][START_REF] Richard | Aqueous geochemistry of chromium: A review[END_REF][START_REF] Iso ; Kotaś | Water quality --Guidelines for algal growth inhibition tests with poorly soluble materials, volatile compounds, metals and waste water[END_REF] and the peaks at 45 and 75 s likely correspond to the hydrolytic Cr III complexes Cr(OH) 2+ and Cr(OH) 3 0 [START_REF] Séby | Chromium speciation by hyphenation of high-performance liquid chromatography to inductively coupled plasma-mass spectrometry-study of the influence of interfering ions[END_REF].Addition of 5 µg/L of Cr VI to an aliquot of the solution initially spiked with 60 µg/L of Cr III and aged for 4 h resulted in the expected Cr VI peak at 50 s, thus confirming that the peak at 45 s was not the results of an oxidation of Cr III to Cr VI during the experiment (Figures 2C andS6).

As already seen in the previous section, for an initial concentration of 60 µg/L of Cr III , speciation calculations using Visual Minteq suggest that, at equilibrium, the positively charged species Cr(OH) 2 + and CrOH 2+ should represent about 3.5% of the total in the observed pH range of 7.8-7.9. Assuming a dissolved Cr concentration of 11 µg Cr/L after 72h of incubation (see previous section and figure 1), the theoretical concentration of positively charged Cr species at the end of the exposure period would be 0.2-0.4 µg/L; in agreement with the IC-ICP-MS speciation results (Figure 2B).

Samples spiked with Cr III in the presence of algae showed the three distinct peaks at retention times of about 100 s, 75 s, and 45 s already at t = 0 (Figure S6). The area of all peaks rapidly decreased and became practically negligible after 24 hours of incubation (Figure S6). In the presence of algae, the concentration of hydrated Cr III (peak at 100 s) decreased from 30 µg/L at t = 0 to 0.14 µg/L at t = 72 h (Figure S6). The discrepancy between the measured (30 µg/L) and expected concentration (60 µg/L) at t = 0 can be explained by a more rapid formation of hydrolysis products. Indeed, the presence of particular microenvironments with increased pH around algal cells and colonies was reported to enhance Fe hydrolysis [START_REF] Sunda | Effect of pH, light, and temperature on Fe-EDTA chelation and Fe hydrolysis in seawater[END_REF] and an analogous phenomenon may occur in the case of Cr III . Again, no peak indicative of the formation of Cr VI was identified throughout the experiment duration so that the ecotoxicological effects discussed previously (section Chromium ecotoxicity in Results and Discussion) can be ascribed to Cr III .

The disappearance of the chromatographic peak of hydrated Cr III (t = 100 s) between 0 and 24 h of incubation prompted us to examine the changes in Cr III speciation at shorter time intervals. Note that, given the absence of calibration standards for the peaks at 45 and 75 s, the changes in the relative importance of the chromatographic peaks can be discussed solely on the basis of their signal intensities. Immediately after spiking, 84% of dissolved Cr was present as hydrated Cr III (retention time 100 s) with the peaks at 75 s and 45 s representing about 8% of the total signal each (Figures 2C and3). The peak of hydrated ionic Cr III at 100 s decreased very rapidly and was only 2% of the initial dissolved Cr concentration after 6 hours of incubation (Figure 3). At the same time, the peak at 75s increased up to 56% of the total signal 1 hour after spiking and then slowly decreased to 40% after 6 h. The peak at 45 s accounted for 7 and 10% of the total signal regardless of the incubation time (Figure 3). Both the sum of the signals of the three peaks and the corresponding dissolved Cr signal (assayed by ICP-MS) decreased by 50% and 40% compared with their respective initial values (Figure 3).

Samples collected after 24, 48, and 72 h of incubation confirmed the initial decreasing trend and, in the case of dissolved Cr, were comparable with the results obtained by FAAS (Figure 1). The difference between dissolved Cr (ICP-MS) and the sum of various Cr peaks (IC-ICP-MS) may be due to nanoparticle formation depositing in the column and going undetected. On the other hand, the signal of total Cr (in terms of relative intensity measured by ICP-MS) remained within 20% of the initial value (Figure 3). Overall, the rapid changes in Cr III speciation added to the test medium (particularly the disappearance of ionic Cr III in less than 2 h) arise the question of which Cr III species are actually responsible for the observed decrease in algal biomass during ecotoxicity testing. These considerations will be developed later in the text (section Implications for Cr hazard and risk assessment) after the presentation of the results confirming the formation of Cr-bearing particles in the test medium.

Formation of chromium (nano)particles

NTA analysis showed that colloidal particles formed within minutes after adding soluble Cr III into the test medium. Particle concentration and size ranged between 9.64 × 10 8 and 29.7 × 10 8 particles/mL and 80 and 140 nm, respectively (Figure 4). The particle concentration was 0.17 ± 0.10 × 10 8 particles/mL in test medium without added Cr III (Figure 4). Filtration (0.22 µm) of Cr III -amended aliquots of test medium lowered particle concentration to around 0.6 × 10 8 particles/mL, but did not decrease their size by more than 25% (Figure 4). Total Cr concentration remained within ± 20% of initial value over the entire experiment duration.

Dissolved Cr concentrations also did not change during the first 2 h of incubation, but then progressively decreased to 26% of the initial value after 72h (Figure 4). The concomitant removal of particles and decrease in dissolved Cr concentration (Figure 4) confirms the formation of Cr containing (nano)particles starting from initially soluble Cr III salts for incubation times > 24 h (Figure 4). The experimental decrease of dissolved Cr concentrations is in agreement with the theoretical calculation performed with Visual Minteq (see Chromium ecotoxicity in Results and discussion).

Analysis by spICP-MS confirmed that the nanoparticles formed immediately after spiking actually contained Cr (Figure S11). The orders of magnitude of size is similar to those measured using NTA (Figure S11 and Figure 4), at least when using the assumed composition and shape (Table S3). On the other hand, spICP-MS detected an increase in particle number from 5 × 10 6 (t ≤ 24 h) to 2 × 10 8 (t ≥ 72 h), suggesting that the mass percentage of Cr III occurring as particles increased from 4% at 0 h to 20% at 72 h to 76% at 96 h. Differences in particle numbers estimated by spICP-MS and NTA likely arise from the specific technical features of the two methods. Large particles do not manage to pass a spray chamber and are therefore not measured during spICP-MS [START_REF] Tuoriniemi | Size dependence of silver nanoparticle removal in a wastewater treatment plant mesocosm measured by FAST single particle ICP-MS[END_REF], which therefore tends to favor small particles as long as they are larger than the detection limit of approx. 90 nm.

NTA, in contrast, preferentially detects relatively large particles that scatter more light and is less accurate in detecting relatively small particles. Note also that the particle size distributions detected with spICP-MS abruptly stop at the size detection limit. Thus, despite the two techniques yielding similar average particle sizes, NTA likely observes a fairly constant number concentration of relatively large particles that are mostly removed by filtration, while spICPMS observes an increase in the number of (relatively small) particles with time (Figure 4 and S11). At short incubation times, a very large mass of Cr may reside in the particle fraction that can pass a 0.22 µm filter without being detected by neither NTA nor spICP-MS. Hence, a decrease Cr mass concentration is not observed when filtering samples at 0.22 µm at short incubation times (Figure 4). Measurement of total and dissolved Fe (data not shown) allowed to exclude the formation of Fe-bearing particles (including mixed Cr-Fe(oxy)hydroxides) [START_REF] Sass | Solubility of amorphous chromium(III)-iron(III) hydroxide solid solutions[END_REF] and thus the possibility of indirect ecotoxic effect of Cr III via sequestration of the essential nutrient Fe. Interestingly, model calculations with

Visual Minteq predicted that the test medium should be oversaturated with respect to different mineral phases including several Fe-containing minerals and hydroxyapatite. The exact chemical nature of particles formed in Cr-spiked test medium clearly deserves further experimental investigation, especially at short incubation times for which the assumption of equilibrium is unlikely to be valid. Finally, removal of particles with sizes between 80 and 140 nm by filters with a 0.22 µm nominal cut-off can be explained by an actual smaller cutoff of the filters' pores [START_REF] She | Calculation of effective pore diameters in porous filtration membranes with image analysis[END_REF] or by the formation of larger particles undetectable via NTA and spICP-MS.

Measurements by SPC confirmed the presence of particles in the same range identified by NTA and spICP-MS, but also of particles larger than 300 nm in unfiltered test medium spiked with Cr III and incubated for 24, 48, and 72 hours (Figure 5 and S7). At t=0, only particles between 50 and 150 nm were observed at a concentration of 3.2  10 5 particles/mL. After 24 hours, the concentration of particles between 50 and 200 nm increased to 6.1  10 6 particles/mL and particles larger than 300 nm (8.5  10 3 particles/mL) had also appeared.

Particles in the range 50-200 nm were still present after 48 (6.5  10 6 particles/mL) and 72 h (9.8  10 6 particles/mL) of incubation, while particles larger than 300 nm eventually disappeared after 72 h (Figure 5). The latter observation suggests the formation of particles too large to be measured by the instruments or, more likely, settling too quickly to be effectively sampled by the instrument.

Based on the analysis of total and dissolved Cr in the samples subject to SPC measurements (figure S7), 45 µg of Cr (75% of the Cr III initially added to the test medium) had been incorporated in the observed particles after 72 hours. This result agrees well with the corresponding Visual Minteq calculations (see section Cr ecotoxicity in Results and discussion for details). Assuming a density of 3.11 g/cm 3 for the amorphous Cr oxyhydroxides likely occurring in the medium, the total volume of the particles would be approx. 1.45 × 10 -14 m 3 /mL. Given an approximate volume of 5.24 × 10 -22 m 3 for an individual (spherical) particle with a diameter of 100 nm, a mass of Cr of 45 µg would be enough to form 2.76 × 10 7 particles/mL. The presence of larger particles, unaccounted for in the previous calculation, can be invoked to explain the difference between calculations and SPC measurements.

Implications for Cr hazard and risk assessment

Our results show that Cr III speciation into a standardized ecotoxicological test medium for algae changes within a few hours after spiking; even when the total Cr III concentration remains comparatively stable. Similar, although less detailed, investigations on daphnids [START_REF] Ponti | How reliable are data for the ecotoxicity of trivalent chromium to Daphnia magna?[END_REF]) and bacteria [START_REF] Bencheikh-Latmani | Toxicity of Cr(III) to Shewanella sp. Strain MR-4 during Cr(VI) Reduction[END_REF]) suggest that such behavior may be common in ecotoxicological media whose composition favors the formation of Cr III hydroxides. Thus, new ecotoxicological data for the hazard assessment of Cr III must be obtained by considering the recommendations originally developed for sparingly soluble substances (ISO 14442 2006) [46]. In particular, in the case of marked differences (> 20%)

between nominal and actual concentration, the corresponding EC50 for Cr III must be calculated as the TWM of the dissolved concentration (OECD 2012). The excellent agreement between experimental results and thermodynamic modeling of speciation equally suggests that our observations could have a broader validity, although the kinetics of temporal speciation changes may vary across media and as a function of initial Cr III concentration.

Furthermore, following our IC-ICPMS results, the question of the actual Cr III species responsible for the observed ecotoxicological effects in living organisms deserves additional study. An application of the biotic ligand model to the study of root elongation in barley [START_REF] Song | Development of a Multi-Species Biotic Ligand Model Predicting the Toxicity of Trivalent Chromium to Barley Root Elongation in Solution Culture[END_REF] suggested Cr 3+ and Cr(OH) 2+ as the two biologically active chemical species in controlling the effects of Cr III . However, the rapid disappearance (< 2 h) of ionic Cr from the test medium questions the role of such species in determining the observed algal response. One possibility is that a pulse exposure to 60 µg/L of truly dissolved Cr III at the beginning of the test can cause a 50% reduction in algal biomass after incubation over 72 h.

Alternatively, the residual concentration of ionic Cr III after 2 h (less than 1 µg/L) determines the effect observed at the end of the test or the other Cr III species also contribute to the observed toxicity. The formation of some Cr-bearing (nano)particles over the course of the test also points to a possible nano-ecotoxicological dimension in the toxicity of Cr III to algae.

In particular, freshly formed Cr(OH) 3 particles can lead to the formation of "transiently available Cr III species" which may be highly toxic [START_REF] Bencheikh-Latmani | Toxicity of Cr(III) to Shewanella sp. Strain MR-4 during Cr(VI) Reduction[END_REF]). The existence of monomeric and polymeric Cr III being documented in environmental samples [START_REF] Hu | Occurrence and speciation of polymeric chromium(III), monomeric chromium(III) and chromium(VI) in environmental samples[END_REF], both Cr hydroxides and Cr-bearing (nano)particles may have an ecotoxicological role outside laboratory settings and deserve consideration in risk assessment for Cr III .

The present study does not question the high ecotoxicity of Cr VI , but it adds to the growing evidence that the biological effects of Cr III strongly depend on the composition of the medium used for testing and are likely underestimated [START_REF] Lira-Silva | Removal, accumulation and resistance to chromium in heterotrophic Euglena gracilis[END_REF][START_REF] Ponti | How reliable are data for the ecotoxicity of trivalent chromium to Daphnia magna?[END_REF]. In this context, the paradigm 'Cr VI is more toxic than Cr III ' increasingly appears as an oversimplified representation of environmental reality. In this context, more detailed studies on the speciation Cr III in standardized ecotoxicological laboratory settings are highly desirable for at least three reasons. First, reduction of Cr VI to Cr III is a typical strategy for remediation of Crcontaminated matrices and environments; second Cr contamination remains a serious environmental problem in several low to middle income countries whose economic activity is linked with the material demands of the current lifestyle in developed countries (Pure Earth and Green Cross 2016); third the safe perspective use of Cr 2 O 3 nanoparticles is linked to their intrinsic properties, but also to the possible release of soluble Cr in either redox forms [START_REF] Horie | Chromium(III) oxide nanoparticles induced remarkable oxidative stress and apoptosis on culture cells[END_REF][START_REF] Da Costa | Effect of chromium oxide (III) nanoparticles on the production of reactive oxygen species and photosystem II activity in the green alga Chlamydomonas reinhardtii[END_REF][START_REF] Puerari | Synthesis, characterization and toxicological evaluation of Cr2O3 nanoparticles using Daphnia magna and Aliivibrio fischeri[END_REF]. In all cases, the appropriate knowledge of the actual ecotoxicity of Cr VI and Cr III necessary to assess the environmental risks of Cr appears incomplete. Identifying the exact chemical species responsible for ecotoxicological effects, especially in the case of Cr III , will facilitate extrapolation of laboratory findings to complex environmental realities and the associated remediation/management decision.

Supplemental data-The Supplemental Data are available on the Wiley Online Library at DOI: 10.1002/etc.xxx. Details for IC-ICP-MS experiments and analytical procedures, temporal evolution of dissolved Cr III and Cr VI concentrations, complementary IC-ICP-MS results, optimization and details of NTA and spICP-MS procedures and additional measurements of particle size distribution and number by SPC, NTA and spICP-MS. Table S3: Conditions and ICP-MS parameters for spICP-MS analysis. S2 for the full compilation of the measured values at t = 0). Measurements were done in triplicate for C1, C2, C4 and C9 after 0 and 48 h of incubation. The relative standard deviations (RSD) for these measurements were usually below 10 % except for C1 at 48 h (RSD = 70%) and C2 at 48 h (RSD = 40%) and C3 at 48 h (RSD = 20%). The high RSD were obtained for analytical concentrations close to the instrumental quantification limit for FAAS. Also note that, with increasing concentrations, total dissolved Cr levels were lower than the corresponding total ones already at t = 0 (see Table S2). No particles were detected in the ultrapure water (MQW) used to prepare the test medium.

Particle concentration in the blank sample (freshly prepared ISO medium) was low (0.14 ± 0.07 × 10 8 particles/mL) and particle size distribution (PSD) covered a large spectrum between 0 and 900 nm (Figure S9). In ISO medium spiked with Cr III and regardless of the incubation time, particle concentrations ranged between 7.85 × 10 8 and 27.5× 10 8 particles/mL with relative standard deviations (RSD) between 6 and 59 % (Figure S8 and S9). Particles detected by NTA had a mean size between 100 and 135 nm with RSD between 1% and 12%

(Figure S9). The high RSD of some particle concentration measurements were caused by the systematic decrease in particle number between the first and the third replicate measurement (Figure S9 A, B and C). The total (unfiltered) Cr concentration was stable over 72 h and ranged between 62 µg/L at t=0 and 66 µg/L 72 h after spiking. However, the total filterable Cr concentration decreased over time from 60 µg/L at t=0 to 16 µg/L after 72 h (Figure S10).

Examination of the videos recorded during NTA showed that the number of particles visible in the field of the camera was stable during data acquisition for the first replicate, but increased with time for replicates two and three. nanoparticle arrives at the detector. The intensity of this peak can be calculated into some measure of size, provided that a composition and shape are assumed for the particles (Table S3). Only one isotope ( 52 Cr) was measured simultaneously, whereas any Cr-containing particles formed because of hydrolysis most likely also contained oxygen atoms and protons.

No collision cell gas was used to remove 40 Ar 12 C interferences on the 52 Cr signal. Hence, a continuous background signal was recorded, not consisting of 52 Cr but of the 40 Ar 12 C interference. However, by using short dwell times, the intensity of any background signal reduces proportionally more than the short but intense nanoparticle signals [START_REF] Montaño | Improvements in the detection and characterization of engineered nanoparticles using spICP-MS with microsecond dwell times[END_REF]. It was thus hypothesized that better size detection limits could be obtained by using a relatively small dwell time, but still measuring in standard mode, where the sensitivity towards the most abundant Cr isotope ( 52 Cr) is highest. The used dwell time of 50 µs and the absence of settling time cause nanoparticle events to be spread over multiple subsequent measurement events that need to be integrated separately for each event. Moreover, distinguishing non-dissolved from dissolved signals was needed, because interferences still caused a relatively high background signal. Both requirements were achieved using a previously published method [START_REF] Tuoriniemi | new peak recognition algorithm for detection of ultra-small nano-particles by single particle ICP-MS using rapid time resolved data acquisition on a sector-field mass spectrometer[END_REF]. This method calculates an intensity cut-off value based on a number of times the standard deviation of the background signal. Integrated peak surfaces below this cut-off value are considered to stem from dissolved events and are not taken into account when recalculating S3.

Figure S12. Temporal evolution in the distribution of the corresponding spherical diameter. The diameters are corresponding to spherical diameters calculated using the setting in Table S3.

  proxy of the Cr potentially available to the algae (see[START_REF] De Paiva Magalhães | Metal bioavailability and toxicity in freshwaters[END_REF] and references therein for a detailed discussion), the time-weighed mean (TMW)(OECD 2012) exposure concentration of the algae to Cr (added as Cr III ) was about 25 µg/L for an initial addition of 60 µg/L as Cr III . Similar behavior of total and dissolved Cr concentration was observed over the concentration range 20 -7,000 µg/L for CrCl 3 and for selected concentrations of Cr(NO 3 ) 3 and CrKSO 4 (FiguresS2-S4); confirming that the decrease in the dissolved exposure concentrations must be considered and quantified when testing Cr III toxicity in standardized laboratory media. These observations corroborate previous findings obtained by measuring the decrease in Cr concentrations in test medium directly in 96-well microplates in the absence of algae and without actually providing information on the total vs.

  72 hours). The incomplete recovery of total Cr was likely caused by attachment of algal cells to the vessel's walls despite the constant agitation. Most importantly, the differences between dissolved Cr concentrations in the absence and presence of algae became statistically significant starting from 24 h after spiking (one-way Anova with Tukey post-hoc comparison, p < 0.01), indicating adsorption onto or absorption into the algal cells of most of the available dissolved Cr. Based on the dissolved Cr concentrations in the presence of algae, the 72 h TMW effect concentration (EC50) for algal growth (in terms of biomass) was 11.5 µg/L.

Figure 1 .

 1 Figure 1.

Figure 1 .

 1 Figure 1. Temporal evolution (expressed as percentage of the value measured at t = 0) of total and dissolved (< 0.22 µm) Cr concentrations in ISO medium amended with CrCl 3 •6H 2 O at an initial concentration of 60 µg Cr/L (nominal value). Error bars indicate one standard deviation (SD). Large SD after 72 h of incubation were caused by Cr concentration decreasing to values close to the instrumental detection limit. C 0 and C t refer to total or dissolved Cr concentration measured at t=0 and at the various incubation times, respectively. All data points were calculated on the basis of measured total and dissolved Cr values. The measured pH was 7.8-7.9 over the entire duration of the experiment. Data points for different incubation times were slightly nudged to visualize the corresponding error bars.

Figure 2 .

 2 Figure 2.

Figure 2 .

 2 Figure 2. Chromatograms of test medium (without added algae) at different incubation times. Panels A and B: test medium amended with 115 µg/L of Cr VI (K 2 Cr 2 O 7 ) (A) or 60 µg/L of Cr III (CrCl 3 •6H 2 O) (B) at 0 h, 24 h, 48 h or 72 h after spiking. Panel C: temporal evolution of chromatograms of test medium containing 60 µg/L of Cr III with measurements performed every 20 min during 6 h. Note the peak of added Cr(VI) (5 µg/L) at 50 s. All solutions were filtered (0.22 µm) immediately before analysis; cps (counts per second). Note the different scales on the y axes.

Figure 3 .

 3 Figure 3.

Figure 3 .

 3 Figure 3. Temporal evolution of the relative abundances of three Cr III species (Cr(OH) 2+ , yellow circles; Cr(OH) 3 0 , turquoise circles; Cr 3+ , green triangles) in ISO medium spiked with 60 µg Cr/L of Cr III (CrCl 3 •6H 2 O) determined by IC-ICP-MS. The sum of the three Cr species (pink squares) and the signals of total chromium (black crosses) and total dissolved chromium (filtered at 0.22 µm; blue crosses) are also indicated.

Figure 4 .

 4 Figure 4.

Figure 4 .

 4 Figure 4. Particle concentrations (bars), particle size (triangles) and Cr concentration (lines) in unfiltered and filtered (0.22 µm) aliquots of ISO medium spiked (except for the sample 'Blank') with 60 µg/L of Cr III (CrCl 3 • 6H 2 O) at different incubation times. Particle concentration and size measured by nanoparticle tracking analysis, Cr concentration measured by atomic absorption spectrometry.

  Figure 5.

Figure 5 .

 5 Figure 5. Particle size distribution and number of particles (in mL -1 nm -1 ) in test medium spiked with Cr III (CrCl 3 • 6H 2 O) after 0 (black circles), 24 (red circles), 48 (green triangles) and 72 h (yellow triangles) of incubation. All measurements were performed by Single Particle Counter (SPC) at a sample flow rate of 64 mL/min. Results for each size class have been corrected for particle concentration in ISO medium without added Cr III (see figureS7for the corresponding comparisons). To obtain the number of particles per mL in a given size range, the values on the y-axis must be multiplied for the corresponding size range (in nm) on the x-axis.

Figure S6 :

 S6 Figure S6: Chromatograms of standard ISO 8692 biotic (presence of algae) medium amended with Cr VI or with Cr III at different times between 0 and 72 h

Figure S10 :

 S10 Figure S10: Temporal evolution of chromium concentrations with and without filtration in ISO medium amended with Cr III during 72 hours.

Figure S11 :

 S11 Figure S11: Temporal evolution of particle number and % of total mass occurring as particle mass or Number average and mass average particle diameter.

Figure S12 :

 S12 Figure S12: Time-dependent changes in the distribution of the corresponding spherical diameter.

Figure S1 .

 S1 Figure S1. Experimental plan for speciation experiments with Ion Chromatography ICP-MS (IC-ICP-MS). Abiotic (absence of algae) and biotic (presence of algae) samples were prepared in advance or immediately prior to analysis (d0). All samples were analyzed on day 0 to optimize the analyses course in day 0.

Figure S2 .

 S2 Figure S2. Temporal evolution (expressed as a percentage of the value measured at t=0) of total dissolved Cr concentrations (filtered at 0.22 µm) in standard (ISO8692) medium amended with Cr III (CrCl 3 •6H 2 O (square) or Cr(NO 3 ) 3 •9H 2 O (cross) or KCr(SO 4 ) 2 •12H 2 O (triangle)) or Cr VI (K 2 Cr 2 O 7 (circle)) during 72 hours. Initial concentration of each salt was 140 µg/L (A) or 560 µg/L (B).

Figure S3 .

 S3 Figure S3. Temporal evolution (expressed as a percentage of the value measured at t=0) of total dissolved Cr concentrations (filtered at 0.22 µm) in standard (ISO 8692) medium amended with initial total concentrations of CrCl 3 •6H 2 O between 20 (C1) and 7000 (C9) µg/L (see TableS2for the full

Figure S4 .

 S4 Figure S4. Temporal evolution (expressed as a percentage of the value measured at t = 0) of total Cr concentrations in standard (ISO 8692) medium amended with initial concentrations of CrCl 3 •6H 2 O between 20 (C1) and 7000 (C9) µg/L (see TableS2for the full compilation of the measured values at t = 0). Measurements were done in triplicate for C1, C2, C4 and C9 after 0 and 48 h of incubation. The relative standard deviations (RSD) for these measurements were usually below 10 % except for C1 at 48 h (RSD = 20%) and C2 at 48 h (RSD = 15%).

Figure S5 .

 S5 Figure S5. Temporal evolution (expressed as a percentage of the values measured at t = 0) of Cr concentrations (total Cr concentrations (black circles) and total dissolved Cr concentrations (filtered at 0.22 µm) (white circles) in biotic (presence of algae) ISO medium amended with Cr VI (K 2 Cr 2 O 7 ) during 72 hours. Initial Cr concentration is 115 µg/L.

Figure S6 .

 S6 Figure S6. Chromatograms of standard ISO 8692 biotic (presence of algae, initial density ~ 20,000 cell/mL) medium amended with 115 µg/L of Cr VI (K 2 Cr 2 O 7 ) (A) or with 60 µg/L of Cr III (CrCl 3 •6H 2 O) (B) at 0 h (green), 24 h (brown), 48 h (orange) or 72 h (blue) after spiking. Chromatograms of standard ISO 8692 medium containing 60 µg/L of Cr III (CrCl 3 •6H 2 O) during 24 h (brown), and then amended with Cr VI (K 2 Cr 2 O 7 ) (green) (C). All solutions were filtered (0.22µm) immediately before analysis; cps (counts per second).

Figure S7 .

 S7 Figure S7. Particle size distribution and number of particles (in mL -1 nm -1 ) determined with Single Particle Counter (SPC) measurements in ISO algal test medium with and without addition of 70 µg/L of Cr III (added as CrCl 3 .6H 2 O) at different incubation times. To obtain the number of particles per mL in a given size range, the values on the y-axis must be multiplied for the corresponding average size value (in nm) on the x-axis.

Figure S9 .

 S9 Figure S9. Comparison of reproducibility of results profiles before (A, B and C) and after (D, E and F) measurement parameters modification by adding a waiting step of 60 s before data acquisition for replicates 2 and 3. This edit to the experimental procedure aimed to harmonize the waiting time before each replicate measurement; i.e. to increase the waiting time for replicates two and three from 5 seconds to 60 s. This experiment was realized in ISO test medium spiked with 60 µg/L of Cr III , corresponding to the previously determined EC50 at 72 h

  When nanoparticles arrive in the ICP-MS plasma they are turned into ions thus forming a cloud of ions. Truly dissolved ions are homogeneously distributed in solution and when injected into the plasma thus cause a continuous, yet fluctuating, stream of ions to be detected by the detector. Nanoparticles can thus be distinguished from dissolved ions as the former cause intensive peaks in the detected time dependent signal, each time a cloud of ions from a

Figure S11 .

 S11 Figure S11. Temporal evolution of particle number and % of total mass occurring as particle mass (left) or number average and mass average particle diameter (right). The diameters are corresponding spherical diameters calculated using the setting in TableS3.

  and spiked with either Cr VI as potassium dichromate (K 2 Cr 2 O 7 , VWR, purity 99.8% min, CAS number 7778-50-9) or with one of the following Cr III salts: chromium chloride (CrCl 3 •6H 2 O; Alfa Aesar,

	99.5% min, Crystalline, CAS number 10060-12-5), chromium potassium sulfate
	(KCr(SO 4 ) 2 •12H 2 O; VWR, 99%, CAS number 7788-99-0) or chromium nitrate
	(Cr(NO 3 ) 3 •9H 2 O; Alfa Aesar, 98.5%, Crystalline, CAS number 7789-02-8).

Table S1 :

 S1 Summary of the IC-ICP-MS parameters and conditions used in Cr speciation experiments

	IC conditions
	pump	Thermo ICS 5000+
	separation column	Dionex Thermo AG7 2x50 mm
	column temperature	20 °C
	eluent	0.4 mol/L HNO 3 spiked with 1µg/L of Rh, isocratic system
	flow rate	500 µL/min
	sample volume	200 µL
	flushing volume	1,500 µL
	duration	10 min
	ICP-MS parameters
	ICP-MS	Thermo XII series
	nebulizer	PFA-LC
	gas flow	0.87 L/min
	plasma power	1,500 W
	plasma gas flow	13.5 L/min
	auxiliary gas flow	0.77 L/min
	detector mode	pulse counting
	KED	He/H 2
	CCT -KED flow rate	3.5 mL/min -3 V
	Data acquisition
	ions (m/z)	52 Cr, 53 Cr, 103 Rh
	measurement unit	counts
	sweps/reading	1
	replicates	1
	dwell time	100 ms
	integration time	600,000 ms

Table S2

 S2

	. Measured Cr concentration at t = 0 in standard (ISO 8692) medium amended with different
	initial concentrations (C1-C9) of CrCl 3 •6H 2 O with and without filtration at 0.22 µm. All values are in
	µg/L of Cr.
		Measured total	Measured filterable (0.22 µm)
		concentration at t = 0	concentration at t = 0
	C1	18	20
	C2	40	42
	C3	82	78
	C4	186	179
	C5	436	379
	C6	789	717
	C7	1745	1477
	C8	3596	2700
	C9	6877	5489

Acknowledgment

This work is part of the PhD thesis of I. Aharchaou who is supported by the French Ministry of Education. The financial support of the CNRS (project EC2CO Insokintox) is greatly acknowledged. We thank A. Garnier (LHN, ANSES, Nancy) for help with IC-ICP-MS analysis. The contributions of S. Cambier were in part made possible within NANION (FNR/12/SR/4009651-Fonds National de la Recherche Luxembourg). We are grateful to E. Szalinska (AGH University of Science and Technology, Krakow, Poland) for her help in some experiments. D. Vignati and G. Cornelis acknowledge the support of COST action ES1205 (STSM 35421).

Supporting information

Chromium speciation in a standardized ecotoxicological medium: implications for hazard and risk assessment Imad Aharchaou a* , Jean-Sébastien Py b , Sébastien Cambier c , Jean-Luc Loizeau d , Geert the average signal and the standard deviation of the background signal. The method converges when no new particle events are identified and the particle size distribution is then calculated from the particle events intensities. Such a single cut-off value is known to lead to both false positives (peaks mistakenly considered particle events) and false negatives (peaks mistakenly considered dissolved events) [START_REF] Cornelis | signal deconvolution method to discriminate smaller nanoparticles in single particle ICP-MS[END_REF]. The goal of the spICP-MS measurement was to verify the hypothesis of the presence of Cr-containing particles in the samples. Hence, a high and thus conservative number of standard deviations (5) was used to minimize false positives, rather than to minimize false negatives [START_REF] Tuoriniemi | Size Discrimination and Detection Capabilities of Single-Particle ICPMS for Environmental Analysis of Silver Nanoparticles[END_REF].

The calculations were realized with a software called Nanocount, which is freely available at http://blogg.slu.se/Nanocount.


Youcef A Bioud
email: y.bioud@usherbrooke.ca

Abderraouf Boucherif
email: a.boucherif@usherbrooke.ca

Maksym Myronov

Ali Soltani

Gilles Patriarche

Nadi Braidy

Dominique Drouin

Richard Arès

High-quality Ge/Si virtual substrates fabricated by a low cost and scalable process

Summary

In this presentation, we propose a new defect engineering strategy in highly mismatched heteroepitaxy to simultaneously achieve low dislocation density and epi-ready Ge/Si virtual substrate using a highly scalable process. By self-assembling nanovoids around the Ge/Si interface from both sides through dislocation-selective electrochemical deep etching and thermal annealing, a continuous Ge layer is obtained, in which, a large portion of the original threading dislocations are pinned and annihilated close to a free surface (see Fig. 1), giving a new configuration so-called "Nanovoids-based Ge/Si Virtual Substrate (NVS)".

Introduction

Developing inexpensive, high-performance epitaxial devices with the hope of achieving widespread market adoption, depends critically on production costs and ultimate material quality. Any process that meets these challenges successfully provides solutions for a wide range of leading-edge applications. Due to the large difference in the lattice constant between the epitaxial materials and heterosubstrates, strain is introduced in epitaxial layer, which leads to the generation of a high density of misfit dislocations. Dislocations act as recombination centers for carriers and have a detrimental effect on device performance. Devices like photodetectors, multi-junction solar cells, transistors, modulators, based on Ge-on-Si (001) technology are facing these issues. To this end, several approaches have been proposed for reducing the TD density. However, many of these techniques are limited to small-scale processes and require the use of expensive and complex processing technologies. In addition, the TD density remains high for many device applications [START_REF] Ye | Germanium epitaxy on silicon[END_REF].

Results

Ge/Si (001) samples with high TDD are anodically porosified by the bipolar electrochemical etching technique [START_REF] Bioud | Fast growth synthesis of mesoporous germanium films by high frequency bipolar electrochemical etching[END_REF]- [START_REF] Bioud | Chemical composition of anodically formed p-type porous GaAs in HF based electrolyte[END_REF]. The layer structure shows selectively distributed mesopores obtained by selective dislocations deep etching. The porosification front reaches the Ge/Si heterointerface, forming a porous layer in the Si substrate, as shown in Fig. 2. The resulting mesoporous Ge/Si structure is transformed into quasi-monocrystalline voided Ge on voided Si during thermal annealing [START_REF] Bioud | Low cost Ge/Si virtual substrate through dislocation trapping by nanovoids[END_REF]- [START_REF] Bioud | MESOPOROUS GERMANIUM BY HIGH FREQUENCY BIPOLAR ELECTROCHEMICAL ETCHING FOR OPTICAL SENSOR APPLICATIONS[END_REF].

Fig. 3a. indicates the location where a dislocation segment ends at the nanovoid with no propagation beyond. A reasonable explanation for the TD reduction is that two dislocations with opposite Burgers vectors having the same magnitude have reached the void, according to fusions, complete and half annihilation reactions (See Fig. 3b-d). In such structure, the TDs have an interaction radius higher than the interaction radius in the conventional structure without voids, which in turn increases their recombination probability.

Fig. 4 ab. shows TEM micrographs from the Ge/Si reference and the NVS, respectively. A high defect density region, extending from the heterointerface towards the surface may be observed for the Ge/Si reference. A dense dislocation network confined in a region of 50 nm close to the Ge/Si interface of the NVS, and almost nonexistent defects within the Ge layer. In the NVS configuration, TDs bend towards the voids in Si onto the glide plane in order to minimize their length, causing their elimination at the nearest free surface. The averaged TDD is reduced significantly from ~10 7 cm -2 to ~10 4 cm -2 for 1.5 µm thick Ge layers, which is considered low for such a thin epitaxial layer (see Fig. 4a).

Conclusion

Ultra-low TDD in mismatched Ge on Si films is produced by a simple and inexpensive process, which consists on tuning the dislocation motion by selfassembling nanovoids close to the Ge/Si interface. It shows that introducing nanovoids favors recombination of dislocations by increasing their interaction radius. The voids located at the Si substrate act as a free surface for inhibiting threading dislocation propagation towards the active layer of the device, leading to the creation of an almost defect free Ge layer on Si.

Fig. 1 .

 1 Fig. 1. Schematic illustration of the nanovoid based Ge/Si virtual substrate architecture.

Fig. 2 .

 2 Fig. 2. TEM image of porous Ge/Si formed using a current density of 4 mA/cm 2 during 30 min shows a thick porous Ge layer with weakly branched pores crossing threading dislocation cores up to full uprooting of misfit dislocations.

Fig. 3 .

 3 Fig.3. BF-STEM image shows gliding dislocations in the Ge layer join the void area until its complete annihilation (a). Possible processes for annihilation of TDs at the void surface by interaction of several threading segments from: the same slip system (b), the parallel slip system (c), by a combination of glide and slip motion (d) and by fusion (e).

Fig. 4 .

 4 Fig. 4. TEM images of the Ge/Si reference substrate (a) and the nanovoid based Ge/Si virtual substrate (b) show the annihilation of dislocation segments coming from the Ge/Si interface at the void located in the Si substrate. (c) Etch-pit density taken from the edge of the NVS shows the TDD reducing from ~10 7 cm -2 to ~10 4 cm -2 for 1.5 µm thick Ge layer.


Karim Tout
email: karim.tout@utt.fr

Rémi Cogranne
email: remi.cogranne@utt.fr

Florent Retraint
email: florent.retraint@utt.fr

FULLY AUTOMATIC DETECTION OF ANOMALIES ON WHEELS SURFACE USING AN ADAPTIVE ACCURATE MODEL AND HYPOTHESIS TESTING THEORY

Keywords: Anomaly detection, Nondestructive testing, Adaptive image model, Hypothesis testing theory. Center Zone Ventilation

HAL is

INTRODUCTION

During the past decades computer-vision based non-destructive testing have been broadly used for inspection of wide range of "objects" such as fabrics [START_REF] Kumar | Computer-vision-based fabric defect detection: a survey[END_REF][START_REF] Stojanovic | Real-time vision-based system for textile fabric inspection[END_REF], nuclear fuel rods [START_REF] Cogranne | Statistical detection of defects in radiographic images using an adaptive parametric model[END_REF] or even food to cite few. However, such systems are usually designed to help and ease an operator who has to do the inspection "manually" which might be subjective and labor intensive. Thus, there is a great need for fully automatic detection methods. However, depending on the inspected object such a detection may be difficult due to the non-anomalous "background".

Prior methods for defect detection using computer-vision can be divided into three categories [START_REF] Kumar | Computer-vision-based fabric defect detection: a survey[END_REF][START_REF] Mery | A review of methods for automated recognition of casting defects[END_REF]: 1) Generic methods that are highly flexible since they do not need any prior The Ph.D thesis of Karim Tout is partially funded by the Conseil Régional de Champagne-Ardenne under Collaborative Research Program. knowledge on the inspected object. Such methods are usually based on tools for image processing and defect enhancement (contrast enhancement, edge detection, etc. . . ) and pattern recognition [START_REF] Stojanovic | Real-time vision-based system for textile fabric inspection[END_REF]. 2) Specific methods that are based on ground-truth or examples of a reference [START_REF] Mery | A review of methods for automated recognition of casting defects[END_REF]. The detection is then merely based on the observed differences between the reference and the inspected image. This approach is efficient but also very sensitive to experimental conditions, such as object position, illumination, etc. . . 3) Methods based on computer-vision and image processing [START_REF] Cogranne | Statistical detection of defects in radiographic images using an adaptive parametric model[END_REF][START_REF] Mery | A review of methods for automated recognition of casting defects[END_REF], that usually require prior information on the non-anomalous object. Two main approaches have been proposed to introduce statistical prior knowledge: Bayesian and non-Bayesian approaches. Statistical Bayesian approach allows the design of efficient and rather simple methods for anomaly detection. However those methods require 1) that the defect occurs with known prior probability and, 2) that the non-anomalous object is also random with known apriori distribution. Those requirements limit the application of Bayesian methods.

In this paper, it is proposed to design a non-Bayesian method based on an adaptive model of the non-anomalous wheel image, referred to as the "background". The model is sufficiently accurate and flexible for inspection of a wide range of wheels. The main contributions of the present paper are the following: 1) An adaptive statistical model is proposed to represent the imaged wheels. This model only requires knowledge of geometry which makes the proposed method fully-automatic and applicable to a wide range of wheels.

2) The proposed model is accurate enough, to ensure high detection performance and computationally simple, for realtime application.

3) The statistical properties of the method are explicitly provided. Hence, the operator can, for instance, prescribe a false-alarm probability easily and can know which type of anomalies can be detected with which probability. The present paper is organized as follows. Section 2 describes the different elements of a wheel. Then, in Section 3, the proposed adaptive model of the wheels is detailed. Section 4 presents the proposed statistical method for anomaly detection and studies its statistical properties. Finally Section 5 presents numerical results and Section 6 concludes the paper.

WHEEL'S ELEMENTS DETECTION

The face of the wheel is a complicated surface to inspect because each wheel is made of different parts (zones). The methodology proposed in this paper is applied on each zone separately, hence the first step is to split the image of a wheel into those different parts, see Fig. 1a. Besides, a wheel also contains some key elements among which the most important are the pilot hole, the countersinks, the valve hole and the ventilation holes, see Fig. 1b. Those elements must be localized for the two following reasons 1) because those are used to perform a geometrical re-adjustment, which can be considered as a self-calibration and 2) those element must be taken into account into the detection of anomalies. Hence, let us first briefly describe how those key elements are detected. It is important to note that, the design of each wheel is known, thus the parameters describing the geometry of inspected wheels, especially the key elements mentioned above, are known.

The pilot hole, the countersinks, and the valve hole, all have a circular shape. Thus, their detection and localization is carried out using the Circular Hough Transform (CHT). This is one of the most robust methods for circular shape detection [START_REF] Illingworth | A survey of the hough transform[END_REF]. In our case, the CHT is also computationally very efficient since it is applied on a limited search area and, because the radius of each element is known, only two unknown parameters have to be found: the coordinates (x 0 , y 0 ) of the center of each element.

The last and most complicated step is the detection of the ventilation holes. Those elements exhibit a wide range of different designs for aesthetic reasons but also to reduce the weight of the wheel. This high variety in shapes of the ventilation holes explain the choice of the active contour models, or snakes, for their detection [START_REF] Kass | Snakes: Active contour models[END_REF]. Such models have been exten-Fig. 2: Illustration of results for detection of all the holes sively used in image segmentation in order to detect complex geometrical forms. The final result of the detection procedure to localize all those elements is shown in Fig. 2 3. ADAPTIVE MODEL OF THE WHEEL Once the key elements described above are localized, one can split the wheel within several areas, see Fig. 1a.

Background model

For each inspected area, an original adaptive model is applied to subtract the anomaly-free image of the wheel. In fact this "background" acts here as a nuisance as it has no interest for defect detection while must be carefully taken into account. The present paper proposes to use a parametric linear model to represent the background. Such a model has, indeed, indisputable advantages: it is simple and, hence, usually computationally efficient and can be used within the well-founded statistical theory of invariance.

Due to space limitation, the rest of this paper focuses on the galbe zone. For clarity and simplicity, the galbe zone is unfolded to a rectangular image, denoted Z = {z m,n }, of size M × N . The inspected area corresponding to image Z is split into non-overlapping small blocks of size w × h (for width and height resp.). Let us also denote z k the k-th block from Z. Because the image Z is corrupted with additive Gaussian noise, each block z k can be modeled as:

z k ∼ N (µ k , Σ k ).
(

) 1
where N represents the Gaussian distribution, which expectation µ k and covariance matrix Σ k . The idea of a linear model is to represent the expectation as a sum of non-anomalous "basis vector" µ k = Hx k . However, the present paper uses an original model for the background expectation, which is adaptive in the sense that the basis vectors H are actually changed to model better each block. This paper also uses a realistic noise model, discussed in subsection 3.2.

The proposed parametric background model is based on the following two dimensional algebraic polynomial:

f (x, y) = dx i=0 dy j=0 c i,j x i y j (2)
with d x and d y the degree of the polynomial. For simplicity, the block z k is represented as a vector, reading pixels lexicographically. The same applies for the (discrete) coordinates, denoted as x and y, and for the coefficients c i,j of the polynomial (2), denoted as vector c k of (d x +1)×(d y + 1) dimension. Denoting as matrix F the polynomial model, which is detailed in [START_REF] Cogranne | Statistical detection of defects in radiographic images using an adaptive parametric model[END_REF][START_REF] Cogranne | An asymptotically uniformly most powerful test for LSB matching detection[END_REF][START_REF] Sedighi | Content-Adaptive Steganography by Minimizing Statistical De-tectability[END_REF] but not in this paper due to space limitation, the model of the background (2) can be written as:

µ k = F c k , (3)
The model ( 1) -( 3) is simple and efficient enough for several applications [START_REF] Cogranne | Statistical detection of defects in radiographic images using an adaptive parametric model[END_REF][START_REF] Cogranne | An asymptotically uniformly most powerful test for LSB matching detection[END_REF][START_REF] Sedighi | Content-Adaptive Steganography by Minimizing Statistical De-tectability[END_REF]. However, the non-anomalous background of a wheel is too much complex, with multiple light reflection and artifacts, to be represented with a simple polynomial model. To tackle this difficulty it is proposed in this paper to design an adaptive model, for which the matrix F changes to take into account the specificity of each block. For this purpose, it is proposed to exploit the circularity of the wheel. Roughly speaking, along the angle, pixels should share similar profiles. The design of an adaptive linear model based on this idea is done using the Principal Component Analysis (PCA). In fact, without subtracting the empirical mean, the first principal components account for the most significant components (eigenvector with highest eigenvalues) of the signal and can be added to the model (3). One can note that sparse dictionary learning methods are also efficient to this purpose but we observed that the PCA provides good results for a much lower computational complexity.

Let us denote P k the part of the first principal components that corresponds to the locations along the rows of the extracted block z k . With the addition of the adaptive part due to the few first principal components, the proposed model for representing the background, that is the expectation of the block z k (1), can be written as :

µ k = H k d k . ( 4
)
where the matrix H k is given by the concatenation:

H k = (F|P k ) .
Similarly the weighting vector d k represents the contribution of those different basis vectors. Roughly speaking, the principal components allow us to model with high accuracy the complexity of the background, and the polynomial part models the remaining part that changes from block to block.

Noise model

A usual model for the noise corrupting raw images (that are not processed) can be obtained by considering separately the shot noise, due to Poissonian process of photo-counting, and the various electronic noises. While the variance of the Poissonian process equals its expectation, the electronic noises are well modeled as a Gaussian random variable with constant variance [START_REF] Foi | Practical poissonian-gaussian noise modeling and fitting for single-image raw-data[END_REF][START_REF] Thai | Camera model identification based on the heteroscedastic noise model[END_REF]. Due to the very high number of counted photons, the Poissonian process can be approximated as a Gaussian distribution [START_REF] Foi | Practical poissonian-gaussian noise modeling and fitting for single-image raw-data[END_REF][START_REF] Thai | Camera model identification based on the heteroscedastic noise model[END_REF]. Hence, the value of pixel at location (m, n) can be modeled as a Gaussian random variable whose variance is given by:

σ 2 m,n = a µ m,n + b. (5)
These parameters (a, b) of the heteroscedastic noise model ( 5) only depend on the imaging system and acquisition settings. Thus, because neither the camera nor the acquisition settings change, parameters (a, b) remain constant for all pixels from all the images of wheels. After camera calibration, this paper assumes that the noise model parameters (a, b) are known. The model of the noise (5) allows us to take into account the variance of each pixel in the ensuing statistical test, to improve its accuracy [START_REF] Thai | Camera model identification based on the heteroscedastic noise model[END_REF][START_REF] Thai | Statistical detection of data hidden in least significant bits of clipped images[END_REF]. An example of this model ( 5) is illustrated in Fig. 3. This Figure shows the variance of pixels as a function of estimated expectation from the same pixels highlighting the linear relation between them [START_REF] Illingworth | A survey of the hough transform[END_REF].

Since the pixels do not share the same variance, the estimation of expectation of block z k is made difficult. To tackle this estimation problem without applying a time-consuming optimization algorithm, a two step approach is proposed in this paper. A first estimation of pixels expectation and variance is obtained with a simple Least-Square (LS):

µ ls k = H k H T k H k -1 H T k z k , Σ ls k = I w×h × (a µ ls k + b),
where I w×h denotes identity matrix of size w × h. This rough estimation of the covariance is thus re-used to update the estimation of the expectation using the well-known Weighted Least-Square (WLS) given by:

     µ k = H k H T k Σ ls -1 k H k -1 H T k Σ ls -1 k z k , Σ k = I w×h × (a µ k + b). (6)
It is of course possible to continue this procedure. It has been observed that this two-steps method is a good trade-off between accuracy and computational time.

STATISTICAL DETECTION OF ANOMALIES

As described above, see Eq. ( 4), when there is no anomaly, the expectation of block z k is given by H k d k . On the opposite, when an anomaly is present in the block z k , its expectation is modified and is modeled by H k d k + θ k with θ k the expectation of the anomaly. For simplicity, it is assumed in this paper that the presence of the anomaly has no effect on the variance.

Hence the goal of anomaly detection problem studied in the present paper is to decide between these two following composite hypotheses:

H 0 : {z k ∼ N (H k d k , Σ k ), ∀k ∈ {1, . . . , K}} H 1 : {z k ∼ N (H k d k + θ k , Σ k ), ∀k ∈ {1, . . . , K}} , (7)
with of course, θ k = 0 for some k.

Formally, a statistical test δ is a mapping δ : R w.h → {H 0 ; H 1 }. The false alarm probability of a test is defined as:

α 0 (δ) = P H0 (δ(Z) = H 1 )
where P H0 denotes the probability under hypothesis H 0 . Conversely, the power function of a test δ is defined as:

β(δ; θ k ) = P H1 (δ(Z) = H 1 ).
Note that the power β(δ; θ k ) depends on the anomaly θ k . In this paper it is proposed to apply the invariance principle to remove the nuisance parameters H k d k and to design a Uniformly Best Constant Power (UBCP) test [START_REF] Fouladirad | Optimal fault detection with nuisance parameters and a general covariance matrix[END_REF]. To this end, the observations z k are projected onto the orthogonal complement of the sub-space spanned by the columns of H k by using the projector:

P ⊥ H k = I w×h -H k H T k Σ -1 k H k -1 H T k Σ -1 k . (8)
However, because the variance is not constant over all the pixels, it is necessary to normalize the "residuals" by dividing each residual by its standard deviation. Those normalized residuals can be written as follows:

r k = Σ -1/2 k P ⊥ H k z k . (9)
It is then easy to establish [START_REF] Fouladirad | Optimal fault detection with nuisance parameters and a general covariance matrix[END_REF][START_REF] Cogranne | Statistical detection of defects in radiographic images using an adaptive parametric model[END_REF] that the norm of the normalized "residuals" r k follows the distribution

r k 2 2 ∼ χ 2 Υ (0) , ∀k ∈ {1, . . . , K} under H 0 χ 2 Υ ( k ) , ∀k ∈ {1, . . . , K} under H 1 , (10)
where χ 2 Υ ( k ) denotes the non-central χ-squared distribution with Υ = w × h -p degree of freedom, here p denotes the number of columns of H k , and the non-central parameter k under hypothesis H 1 is given by :

k = Σ -1/2 k P ⊥ H k θ k 2 2 . (11)
Here k denotes the "anomaly-to-noise" ratio [START_REF] Cogranne | Statistical detection of defects in radiographic images using an adaptive parametric model[END_REF] and is essential to define how detectable the anomaly is.

Based on the residuals r k and their distribution, see Eq. ( 10), the UBCP test can be written as follows

δ = H 0 if r k 2 2 ≤ τ H 1 if r k 2 2 > τ, (12)
where, in order to guarantee the false-alarm probability α 0 , the decision threshold τ is set as follows:

τ = F -1 χ 2 Υ (1 -α 0 ; 0) (13)
where F χ 2 Υ (x, k ) and F -1

χ 2 Υ (x, k ) resp.
represent the noncentral χ 2 cumulative distribution function with non-centrality parameter k and its inverse.

Similarly the power function of the test is given by:

β(δ, θ k ) = F χ 2 Υ (τ, k ). (14)
One can note from the previous results, Eq. ( 13)-( 14), two important things. First, the threshold τ depends only on the false-alarm probability α 0 and is thus constant for all the blocks. Second, the detectability of the anomaly depends only on the "anomaly-to-noise ratio" k . More precisely, Eq. [START_REF] Thai | Statistical detection of data hidden in least significant bits of clipped images[END_REF] shows that it is crucial for the model to represent the expectation of z k with high accuracy but also ensure that the anomaly θ k remains in the residuals (orthogonal complement of H k ).

EXPERIMENTS AND RESULTS

Because of the space limitation, only a limited number of results can be presented. To show the accuracy of the proposed adaptive model, Fig. 4 presents two examples of galbe zones, with typical defects intended to be detected. Note that the defects are highlighted with red circles and that we picked, on purpose, defects which are difficult to see from naked eyes.

First, Fig. 4c and4d show the normalized residuals r k , see Eq. ( 9), for the second example of anomaly. The image from Fig. 4c has been obtained using the proposed adaptive model over blocks with size h = 23 (height) and w = 50 (width). The degree of the polynomial used is d y = 5 (along the height) and d x = 1 (along the width) and the number of Principal Components added to this model is 3. The defect is clearly visible which confirms that the proposed adaptive model has the ability to describe with accuracy the background while preserving the anomaly in the "residuals". Second, it is wished to show the relevance of the proposed statistical test and the accuracy of the theoretical results. The first example of defect, see Fig. 4a, has been used to perform a Monte-Carlo simulation on 1 000 images. Because it is hardly possible to obtain many images with similar anomalies, we picked randomly a set of 1 000 images without any defect on which the anomaly has been superimposed. Fig. 5 presents the empirical distribution of the normalized residuals norm r k 2 2 , see Eq. [START_REF] Fouladirad | Optimal fault detection with nuisance parameters and a general covariance matrix[END_REF]. One can note from Fig. 5 that the two hypothesis are separable without any classification error. Beside, Fig. 5 also compares the empirical distribution under H 0 with the theoretical one [START_REF] Thai | Camera model identification based on the heteroscedastic noise model[END_REF]. A non-negligible discrepancy can be observed which may be explained by two reasons. First, the estimation of pixels expectation has a non-zero variance which is not yet taken into account in the proposed test. Second, the proposed adaptive model, though efficient, is not perfect and, hence, may sometime put a small part of the nonanomalous background among the residuals.

CONCLUSION

This paper studies the problem of fully automatic anomaly detection on wheels. The proposed method analyzes the different zones of a wheel separately. The main originalities of the proposed approach are the use of an adaptive linear model for the non-anomalous background and the heteroscedastic noise model. The proposed adaptive model is simple, accu-

Fig. 1 :

 1 Fig. 1: Description of the different elements of a wheel.

σ 2 Fig. 3 :

 23 Fig. 3: Illustration of the noise model showing, for several images, pixels' variance as a function of expectation.

j

  (a) First example of circular shape anomaly. j (b) Second example of rectilinear shape anomaly.

j

  (c) Normalized residuals obtained from Fig.4bwith the proposed model.

j

  (d) Normalized residuals obtained from Fig. 4b with wavelet decomposition.

Fig. 4 :

 4 Fig. 4: Example of typical anomalies it is aim at detecting.

Fig. 5 :

 5 Fig. 5: Empirical and theoretical distributions of the proposed test over 1000 of images with and without anomaly. rate and preserves the anomaly within the residuals. Because the adaptive model is linear, it can be used easily with theory of hypothesis testing taking into account the noise model. The proposed method allows a fully-automatic detection scheme in real time. Numerical results show the high accuracy of the model and the relevance of the statistical test.