effect was drastic when the ratio between humic and surface (iron oxide) sites exceeds a critical value. However, when HA were added after a 24 hours equilibration of the hematitethorium (IV) system, thorium (IV) was barely desorbed from the iron oxide surface.

Furthermore, no drastic effect of the ratio between humic and surface sites could be evidenced, as the increase of HA concentration only results in a slight monotonic decrease in Th(IV) retention. Increasing contact time between components of the systems only indicated slight Th(IV) retention variation. This was interpreted as a consequence of slow kinetic controls of both the Th(IV)-HA complexation and HA-hematite sorption.

Humic substances, humic acids, iron oxides, colloids, retention kinetics, thorium, tetravalent actinides, complexation.

The influence of addition order and contact time in the system hematite (α-Fe 2 O 3 ) -humic acid (HA) -thorium (IV) was studied in batch experiments. Thorium (IV) is considered here as a chemical analogue of other actinides (IV). The sorption isotherms were acquired varying pH in the range 2-10, and HA concentration in the range 1-100 mg/L. As already observed by numerous authors, thorium (IV) retention was hindered when HA and hematite were equilibrated beforehand during 24 hours. As it has been observed in a previous study, this

Introduction

Organic colloids can enhance the mobilisation of metallic pollutants in soils and sediments [START_REF] Miekeley | Some aspects of the influence of surface and ground water chemistry on the mobility of thorium in the "Morro do Ferro"environment[END_REF][START_REF] Fujikawa | Strong association of fallout plutonium with humic and fulvic acid as compared to uranium and 137 Cs in Nishiyama soils from Nagasaki, Japan[END_REF][START_REF] Kersting | Migration of plutonium in groundwater at the Nevada Test Site[END_REF][START_REF] Santschi | Organic nature of colloidal actinides transported in surface water environments[END_REF][START_REF] Wood | The role of humic substances in the transport and fixation of metals of economic interest (Au, Pt, Pd, U, V)[END_REF][START_REF] Artinger | Effects of humic substances on the 241 Am migration in a sandy aquifer: column experiments with Gorleben groundwater/sediment systems[END_REF]. Sorption phenomena of natural organic matter (NOM) are of a great importance on this account. The general affinity of NOM and its humic fractions towards mineral surfaces not only induces modifications of physico-chemical properties, as surface potential or colloidal stability [START_REF] Kretzschmar | Transport of humic-coated iron oxide colloids in a sandy soil: Influence of Ca 2+ and trace metals[END_REF][START_REF] Kretzschmar | Effects of adsorbed humic acid on surface charge and flocculation of kaolinite[END_REF], but also provokes modifications of the NOM itself [START_REF] Meier | Fractionation of aquatic natural organic matter upon sorption to goethite and kaolinite[END_REF][START_REF] Zhou | Size fractionation upon adsorption of fulvic acid on goethite: equilibrium and kinetic study[END_REF][START_REF] Korshin | Adsorption of natural organic matter (NOM) on iron oxide: Effects on NOM composition and formation of organo-halide compounds during chlorination[END_REF][START_REF] Gu | Adsorption and desorption of natural organic matter on iron oxide: mechanisms and models[END_REF].

Humic substances (HS) are the alkaline extractible fraction of NOM and are operationally defined from the extraction procedure: (i) humin is the insoluble fraction at whatever pH; (ii) humic acids (HA) are the insoluble fraction in acidic pH; (iii) fulvic acids (FA) are the soluble fraction whatever pH (sorbing on XAD resin) [START_REF] Maccarthy | The principles of humic substances[END_REF]. HS can be now represented as aggregates of aromatic molecules (mostly phenolic) carrying a large number of carboxylic functions [START_REF] Plancque | Molecular structure of fulvic acids by electrospray with quadrupole time-of-flight mass spectrometry[END_REF][START_REF] Mcintyre | Identification of compound classes in soil and peat fulvic acids as observed by electrospray ionization tandem mass spectrometry[END_REF][START_REF] Moulin | Direct characterization of iodine covalently bound to fulvic acids by electrospray mass spectrometry[END_REF]. The cohesion of these aggregates is through more or less weak bonding including van der Walls interactions or hydrogen bonding. Due their high functionality, HS can strongly complex multivalent elements and modify their retention by minerals [START_REF] Reiller | Retention behaviour of humic substances onto mineral surfaces and consequences upon thorium (IV) mobility: case of iron oxides[END_REF][START_REF] Takahashi | Comparison of adsorption behavior of multiple inorganic ions on kaolinite and silica in the presence of humic acid using the multitracer technique -A comparison with dissolved aluminum[END_REF][START_REF] Davis | Complexation of trace metals by adsorbed natural organic matter[END_REF][START_REF] Zachara | Influence of humic substances on Co 2+ sorption by a subsurface mineral separate and its mineralogic components[END_REF][START_REF] Labonne-Wall | Retention properties of humic substances onto amorphous silica: consequences for the sorption of cations[END_REF].

The association of thorium (IV) with HA is strong and has been observed on the field [START_REF] Miekeley | The importance of organic compounds on the mobilization and bioassimilation of thorium in the Morro do Ferro environment[END_REF][START_REF] Zeh | OECD NEA Proceedings[END_REF][START_REF] Dai | Colloidal organic carbon and 234 Th in the Gulf of Maine[END_REF][START_REF] Guo | Interactions of thorium isotopes with colloidal organic matter in oceanic environments[END_REF], and quantified [START_REF] Nash | Interaction of humic and fulvic acids with Th(IV)[END_REF][START_REF] Choppin | Complexes of actinides with naturally occurring organic compounds[END_REF][START_REF] Reiller | On the study of Th(IV)-humic acid interactions by competition sorption studies with silica and determination of global interaction constants[END_REF]. Thorium (IV) is often used as a chemical analogue for the other actinides (IV) [START_REF] Choppin | Utility of oxidation state analogs in the study of plutonium behavior[END_REF]. Solubility of actinides (IV) is fairly constant within the series, i.e. 10 -8 -10 -9 M if pH ≥ 4 [START_REF] Neck | Solubility and hydrolysis of tetravalent actinides[END_REF][START_REF] Guillaumont | Update on the chemical thermodynamics of uranium, neptunium, plutonium, americium and technetium[END_REF]. Thorium (IV) seems to be preferentially associated with the highest relative molecular weight fraction of the NOM, and this association seems to be kinetically governed [START_REF] Zhang | Selectivity in the complexation of actinides by humic substances[END_REF][START_REF] Quigley | Sorption irreversibility and coagulation behavior of 234 Th with marine organic matter[END_REF]. Humic acids are known to reduce redox sensitive actinides, i.e. Pa, Np and Pu [START_REF] Nash | Redox behavior, complexing, and adsorption of hexavalent actinides by humic acid and selected clays. Stiring marine disposal of high-level radioactive waste[END_REF][START_REF] Kim | A column experiment for the study of colloidal radionuclide migration in Gorleben aquifer systems[END_REF][START_REF] Marquardt | Complexation of neptunium(V) with humic acids at very low concentrations[END_REF][START_REF] Pirlet | The investigation of the neptunium complexes formed upon interaction of high level waste glass and Boom Clay media[END_REF][START_REF] Zeh | The reduction of Np(V) in groundwater rich in humic substances[END_REF][START_REF] André | Reduction of Pu(V) by humic acid. Radiochim[END_REF][START_REF] Kuczewski | Separation of plutonium and neptunium species by capillary electrophoresis-inductively coupled plasma-mass spectrometry and application to natural groundwater samples[END_REF], due either to the low redox potential of aqueous solution of HA [START_REF] Zauzig | Oxygen concentration and redox potential gradient in unsaturated model soil aggregates[END_REF][START_REF] Österberg | Oscillating, nonequilibrium redox properties of humic acids[END_REF][START_REF] Matthiessen | Evaluating the redox capacity and the redox potential of humic acids by redox titrations[END_REF][START_REF] Struyk | Redox properties of standard humic acids[END_REF] or/and by the preferential complexation of multicharged cations [START_REF] Kerndorff | Sorption of metals on humic acid[END_REF]. The +IV oxidation state of the actinides seems to be stabilised by the humic complexation.

Thermodynamic description of the metallic cation retention by mineral surface in the presence of HA has often led to a deviation from additivity rules of interactions models [START_REF] Vermeer | Metal ion adsorption to complexes of humic acid and metal oxides: deviation from the additivity rule[END_REF][START_REF] Robertson | Goethite/humic acid interactions and their effects on copper(II) binding[END_REF][START_REF] Christl | Interaction of copper and fulvic acid at the hematite-water interface[END_REF], if the modelling is performed in a sufficiently wide parametric interval. Fractionation of HA induced by sorption on mineral surfaces should imply modification of HA aggregates and therefore modification of complexing properties of these aggregates. On the other hand, some authors have reported an influence of addition order. If the influence noted by Davis [START_REF] Davis | Complexation of trace metals by adsorbed natural organic matter[END_REF] was moderate in the case of Cu(II) on γ-alumina, it was clearly strong in the case of Zr-Hf(IV) on kaolinite [START_REF] Takahashi | Comparison of adsorption behavior of multiple inorganic ions on kaolinite and silica in the presence of humic acid using the multitracer technique -A comparison with dissolved aluminum[END_REF]. These authors compared the systems where (i) mineral surface and HA were pre-equilibrated before any addition of metallic cation, and (ii) mineral surface and metallic cation were equilibrated beforehand and HA was added afterwards. Liu and Gonzales (49) did not detect any noticeable difference when HA was pre-equilibrated or added simultaneously with divalent metals on montmorillonite, but the authors did not equilibrate the metal with the mineral surface beforehand.

For a predictive modelling of metal (IV) retention by mineral surface in the presence of HA, one has to understand the mechanism of these phenomena. Therefore, in order to illustrate the different cases we have studied the following pre-equilibrated systems: (i) hematite and HA equilibrated before any addition of Th(IV); (ii) hematite and Th(IV) equilibrated before any addition of HA, (iii) Th(IV) and HA pre-equilibrated before any addition of hematite Experimental Materials. The colloidal hematite suspension and humic acids were the same as the one used in previous studies [START_REF] Reiller | Retention behaviour of humic substances onto mineral surfaces and consequences upon thorium (IV) mobility: case of iron oxides[END_REF][START_REF] Cromières | Sorption of thorium onto hematite colloids[END_REF][START_REF] Cromières | Physico-chemical characterization of the colloidal hematite/water interface: experimentation and modelling[END_REF]. Briefly, hematite was obtained from AEA Harwell and characterised by Cromières et al. [START_REF] Cromières | Sorption of thorium onto hematite colloids[END_REF][START_REF] Cromières | Physico-chemical characterization of the colloidal hematite/water interface: experimentation and modelling[END_REF] -diameter D = 55 nm, specific surface S sp = 19 m²/g, Proton Exchange Capacity = 3.8 × 10 -5 eq/g -; purified Aldrich HA was characterised by Kim et al. [START_REF] Kim | Characterisation and complexation of humic acids[END_REF] -PEC = 5.4 × 10 -3 eq/g -.

The initial solution of thorium ( 228 Th in 2 N HNO 3 ) was obtained from Amersham. This solution was diluted in order to obtain a 1.09 × 10 -9 M stock solution in 0.9 M NaClO 4 and 0.2 M HNO 3 . All other chemicals were reagent grade, and Millipore filtered water purged with Ar(g) was used (Milli-Q). pH measurement. The pH measurement was done using a TACUSSEL ® pH-meter (PHM 220 MeterLab) with a combined TACUSSEL ® electrode (Radiometer type XC 161, modified NaClO 4 0.1 M, NaCl 10 -2 M). Calibration in [H + ] is performed with commercial buffers (Prolabo, pH = 4, 7 and 9). The pH of the stock solution of colloidal hematite is about 1 which minimise the CO 2(g) dissolution. Nevertheless, the surface of solution was swept with Ar(g), in order to minimise the dissolution of CO 2 (g) in the suspensions.

Preparation of the suspension. The sorption experiments were conducted at room temperature according to a batch procedure in 10 ml polycarbonate vials sealed with screwcaps (Nalgene ® ).

Different modus operandi were used depending on the order of addition of the constituents.

In all the experiments, the hematite suspension was always prepared first.

Hematite suspension.

As the colloidal hematite suspension was stored under acidic conditions (pH ≅ 1), the colloidal phase was rinsed with Milli-Q water in order to eliminate excess acid, and to eliminate the last traces of chloride ions. An aliquot of the initial solution (1.5 g.L -1 ) was dispersed into Milli-Q water (9.5 ml) in centrifuge tubes and ultrasonically (Bioblock 35 kHz) shaken for 30 minutes. The obtained suspension was then ultracentrifuged at 50,000 rpm for 30 minutes and 6 ml of the supernatant were discarded: this operation is repeated 3 times. The concentration of the hematite suspension was fixed at the desired concentration by diluting the rinsed solution by the background electrolyte (NaClO 4 ). The pH was adjusted at the desired value. The obtained suspension was shaken for 24 hours to allow equilibration of the suspension.

Under the same conditions, inorganic carbon concentration has been estimated to be less than 5 × 10 -5 M (53, 54), which induces only a weak influence on Th(IV) speciation [START_REF] Reiller | On the study of Th(IV)-humic acid interactions by competition sorption studies with silica and determination of global interaction constants[END_REF][START_REF] Östhols | On the influence on mineral dissolution: III. The solubility of microcrystalline ThO 2 in CO 2 -H 2 O media[END_REF].

Depending on the order of addition, either HA of Th(IV) was added to the suspension. HA addition. When the hematite suspension was equilibrated, aliquots of the HA stock solution were added. The pH value was adjusted using freshly prepared 0.1 M HClO 4 or NaOH, and shaken for the appropriate time.

Thorium (IV) addition. When the suspension was equilibrated, an aliquot of the thorium (IV) stock solution was added to obtain a final concentration of 1.15 × 10 -12 M; the pH was adjusted at the desired value. The solution was shaken again for the appropriate time.

Separation of the colloidal suspension.

As in previous studies [START_REF] Reiller | Retention behaviour of humic substances onto mineral surfaces and consequences upon thorium (IV) mobility: case of iron oxides[END_REF][START_REF] Reiller | On the study of Th(IV)-humic acid interactions by competition sorption studies with silica and determination of global interaction constants[END_REF], we used the separation methods used by Cromières et al. [START_REF] Cromières | Sorption of thorium onto hematite colloids[END_REF], in order to minimise the thorium (IV) adsorption onto the vessel walls [START_REF] Cromières | Sorption d'éléments lourds (U(VI), Np(V), Th(IV), Am(III), Co(II), Cs(I)[END_REF][START_REF] Rydberg | Adsorption on glass and polythene from solution of thorium and thorium complexes in tracer concentration[END_REF]. The retention was calculated referring to the activity measured in the suspension and not referring to the total activity introduced in the ultracentrifuge tube.

After the appropriate equilibrium time, three 0.5 mL aliquots of the suspension were sampled for thorium activity measurement (A 1 is the mean of the measurements). The colloids were separated from the liquid phase by ultracentrifugation (90 min, 50,000 rpm), the pH of the supernatant was measured, and three other aliquots of 0.5 mL were sampled from the supernatant for thorium activity measurement (A 2 ). The activities of 228 Th were measured by liquid scintillation counting. The sample aliquots were added to 4 mL of liquid scintillator (Ultima Gold AB). The activity measurements were performed after one month in order to attain the secular equilibrium of 228 Th with its daughters. Sorption parameters. The sorption percentage R was calculated from the activities of the suspension (A 1 ) and of the supernatant (A 2 ) according to the following equation:

R (%) = © § ¹ • 1 - A 2 A 1 × 100 (1).
For the sake of comparison with independent results, the results are presented vs. the ratio of available biding site [≡HA] ÷ [≡SOH] defined as:

[≡HA]

[≡SOH] = C HA (g/L) × 5.4 10 -3 (eq/g) C α-Fe2O3 (g/L) × 3.8 10 -5 (eq/g)

(2),

where [≡HA] is the concentration of humic sites, and [≡SOH] is the concentration of surface sites.

Results and discussion

Pre-equilibration of hematite and HA. In figure 1 shown) show no differences with the results obtained in [START_REF] Reiller | Retention behaviour of humic substances onto mineral surfaces and consequences upon thorium (IV) mobility: case of iron oxides[END_REF]. Hence the sorption of Th(IV) on hematite can be directly compared in the two systems.

The results of HA retention in the systems were reported earlier [START_REF] Reiller | Retention behaviour of humic substances onto mineral surfaces and consequences upon thorium (IV) mobility: case of iron oxides[END_REF]. The decrease in metal retention when HA is pre-equilibrated with the solid is a classical observation [START_REF] Takahashi | Comparison of adsorption behavior of multiple inorganic ions on kaolinite and silica in the presence of humic acid using the multitracer technique -A comparison with dissolved aluminum[END_REF][START_REF] Davis | Complexation of trace metals by adsorbed natural organic matter[END_REF][START_REF] Zachara | Influence of humic substances on Co 2+ sorption by a subsurface mineral separate and its mineralogic components[END_REF][START_REF] Labonne-Wall | Retention properties of humic substances onto amorphous silica: consequences for the sorption of cations[END_REF][START_REF] Ticknor | The effect of fulvic acid on the sorption of actinides and fission products on granite and selected minerals[END_REF]. Takahashi et al. [START_REF] Takahashi | Comparison of adsorption behavior of multiple inorganic ions on kaolinite and silica in the presence of humic acid using the multitracer technique -A comparison with dissolved aluminum[END_REF] postulated that this phenomenon was due to the weak interaction of tetravalent cations, i.e. Zr(IV) and Hf(IV), with humic substances. The known interaction of thorium (IV) with natural organic matter observed in aquatic, marine and groundwater systems seems to contradict the latter hypothesis [START_REF] Miekeley | The importance of organic compounds on the mobilization and bioassimilation of thorium in the Morro do Ferro environment[END_REF][START_REF] Zeh | OECD NEA Proceedings[END_REF][START_REF] Dai | Colloidal organic carbon and 234 Th in the Gulf of Maine[END_REF]. Moreover, strong interaction constants were determined for Th(IV) and Np(IV) with humic acid in pH ranges relevant to natural waters [START_REF] Reiller | On the study of Th(IV)-humic acid interactions by competition sorption studies with silica and determination of global interaction constants[END_REF][START_REF] Pirlet | In 9 th International Conference on Chemistry and Migration Behavior of Actinides and Fission Products in the Geosphere[END_REF][START_REF] Reiller | Prognosticating the humic complexation for redox sensitive actinides through analogy, using the charge neutralisation model[END_REF]. Thus, the strength of the interactions between HA and metal ions does not seem to be the main factor implied. Under our conditions, humic sites are mainly present in solution, and their concentration in solution increases with pH as ionisation increases. When Th(IV) is added in the system, competition occurs between free humic sites and hematite surface sites. This competition is strongly in favour of HA in acidic-neutral pH range -high strength of complexation between Th(IV) and HA -, whereas for pH > 8 from ref. [START_REF] Reiller | Retention behaviour of humic substances onto mineral surfaces and consequences upon thorium (IV) mobility: case of iron oxides[END_REF] from ref. [START_REF] Reiller | Retention behaviour of humic substances onto mineral surfaces and consequences upon thorium (IV) mobility: case of iron oxides[END_REF] complexation by surface sites increases up to 50%. Hence in this system, where hematite is pre-equilibrated with HA, organic matter controls Th(IV) behaviour.

Decreasing the ionic strength to 10 -3 M (open diamonds on figure 1) does not seem to have any effect in this system. Similarly, ionic strength had no or very weak influence on HA retention onto this substrate as evidenced in the previous study [START_REF] Reiller | Retention behaviour of humic substances onto mineral surfaces and consequences upon thorium (IV) mobility: case of iron oxides[END_REF]. As a matter of fact, the actual colloidal state of this α-Fe 2 O 3 sample limits the effect of ionic strength [START_REF] Cromières | Sorption of thorium onto hematite colloids[END_REF][START_REF] Hunter | Equilibrium adsorption of thorium by metal oxides in marine electrolytes[END_REF].

Up to now the tentative modelling of ternary systems, i.e. solid-humic-metal, revealed that the additivity rule cannot be simply applied [START_REF] Vermeer | Metal ion adsorption to complexes of humic acid and metal oxides: deviation from the additivity rule[END_REF][START_REF] Robertson | Goethite/humic acid interactions and their effects on copper(II) binding[END_REF][START_REF] Christl | Interaction of copper and fulvic acid at the hematite-water interface[END_REF]. As a matter of fact, a large number of authors has clearly shown that slow sorption kinetic, fractionation phenomena and solid phase dissolution were implied [START_REF] Meier | Fractionation of aquatic natural organic matter upon sorption to goethite and kaolinite[END_REF][START_REF] Gu | Adsorption and desorption of natural organic matter on iron oxide: mechanisms and models[END_REF][START_REF] Van De Weerd | Modelling the dynamic adsorption/desorption of NOM mixture: Effects of physical and chemical heterogeneity[END_REF][START_REF] Van De Weerd | Modeling transport of a mixture of natural organic molecules: Effects of dynamic competitive sorption from particle to aquifer scale[END_REF][START_REF] Kaiser | Competitive sorption of dissolved organic matter fractions to soils and related mineral phases[END_REF][START_REF] Rose | Iron speciation in natural organic matter colloids[END_REF][START_REF] Vilgé-Ritter | Chemistry and structure of aggregates formed with Fe-salts and natural organic matter[END_REF][START_REF] Hur | Molecular weight fractionation of humic substances by adsorption onto minerals[END_REF]. Thus, a reliable thermodynamic modelling of these systems is difficult to assess without prior assessment of an actual equilibrium state.

Pre-equilibration of hematite and Th(IV).

The results obtained when Th(IV) is preequilibrated with hematite before any addition of HA (triangle symbols on figure 1) are illustrations of the modelling difficulty. The decrease in Th(IV) retention is clearly weaker than in the former case. This weaker influence of HA when added after hematite-metal equilibration was reported by only few authors [START_REF] Takahashi | Comparison of adsorption behavior of multiple inorganic ions on kaolinite and silica in the presence of humic acid using the multitracer technique -A comparison with dissolved aluminum[END_REF][START_REF] Davis | Complexation of trace metals by adsorbed natural organic matter[END_REF]. The effect was not that spectacular in the case of Cu(II) on γ-alumina (19), but seems equivalent in the case of Zr(IV)/Hf(IV) on kaolinite [START_REF] Takahashi | Comparison of adsorption behavior of multiple inorganic ions on kaolinite and silica in the presence of humic acid using the multitracer technique -A comparison with dissolved aluminum[END_REF]. This effect was not detected in the case of silica by Takahashi et al. [START_REF] Takahashi | Comparison of adsorption behavior of multiple inorganic ions on kaolinite and silica in the presence of humic acid using the multitracer technique -A comparison with dissolved aluminum[END_REF]. could not be evidenced when Th(IV) is equilibrated with hematite before any HA addition.

Even when [≡HA]/[≡SOH] ≈ 30, R(Th) is only decreased from 99.6 % to 93 % at pH ≈ 6.5.

Thorium (IV) retention in these systems still seems to increase with pH in this interval, as it was in Reiller et al. [START_REF] Reiller | Retention behaviour of humic substances onto mineral surfaces and consequences upon thorium (IV) mobility: case of iron oxides[END_REF], even if the R(Th) values could not be discriminated statistically.

In to the study of Takahashi et al. [START_REF] Takahashi | Comparison of adsorption behavior of multiple inorganic ions on kaolinite and silica in the presence of humic acid using the multitracer technique -A comparison with dissolved aluminum[END_REF] for the HA-kaolinite system, the ratio [≡HA]÷[≡SOH] can be calculated as:

[≡HA]

[≡SOH] = 30 10 -3 (g/L) × 6.1 10 -3 (meq/g) 2 (g/L) × 2.9 10 -5 (eq/g) = 3.2.

HA added first, From reference [START_REF] Reiller | Retention behaviour of humic substances onto mineral surfaces and consequences upon thorium (IV) mobility: case of iron oxides[END_REF] This value is lower than the one used in this study ([≡HA]÷[≡SOH] ≈ 30). In the case of our hematite sample, no difference in the addition order could be anticipated at a ratio of 3.2 from the results in figure 2. Nevertheless, one should keep in mind that kaolinite is less efficient in retaining HA than hematite [START_REF] Takahashi | Comparison of adsorption behavior of multiple inorganic ions on kaolinite and silica in the presence of humic acid using the multitracer technique -A comparison with dissolved aluminum[END_REF].

The results obtained are not easily interpreted. Nevertheless, given the preferential complexation of thorium (IV) by the highest molecular mass fraction of NOM [START_REF] Zhang | Selectivity in the complexation of actinides by humic substances[END_REF][START_REF] Quigley | Sorption irreversibility and coagulation behavior of 234 Th with marine organic matter[END_REF], and the kinetic control of the NOM sorption by mineral surface [START_REF] Gu | Adsorption and desorption of natural organic matter on iron oxide: mechanisms and models[END_REF][START_REF] Van De Weerd | Modelling the dynamic adsorption/desorption of NOM mixture: Effects of physical and chemical heterogeneity[END_REF][START_REF] Hur | Molecular weight fractionation of humic substances by adsorption onto minerals[END_REF], a tentative explanation of this comportment can be proposed. Van In our case, no fraction > 100 kDa can be anticipated with HA. But depending on the concentration, the fraction 3-100 kDa could reach sorption equilibrium after 500 hours for hydrophobic fractions and more than 900 hours for hydrophilic fractions [START_REF] Van De Weerd | Modelling the dynamic adsorption/desorption of NOM mixture: Effects of physical and chemical heterogeneity[END_REF]. Given the short time of our experiments (24 hours) the sorption of these fractions could have not reached equilibrium. This is further confirmed by the observation of Hur and Schlautman [START_REF] Hur | Molecular weight fractionation of humic substances by adsorption onto minerals[END_REF].

Therefore, when HA are pre-equilibrated with hematite over 24 hours, the higher mass fractions are not in equilibrium with the hematite surface and are thus present in "solution".

When Th(IV) is added to this suspension the complexation with higher mass fractions would lead to its presence in the supernatant. Moreover, the formation of inner-sphere surface complexes of thorium (IV) on this hematite sample, evidenced by Cromières et al. [START_REF] Cromières | Sorption of thorium onto hematite colloids[END_REF], could help to explain this unexpected behaviour.

When Th(IV) is pre-equilibrated with hematite, the complexation between the higher mass fraction in solution and sorbed Th(IV) seems less probable in the time frame of the experiment, and the metal retention by hematite would be more important. The question of Th(IV) sorption reversibility on the hematite sample must also be addressed also. Ho and Doern (67) showed that uranium (VI) was partly irreversibly bound onto hematite at pH = 6.2, where highly hydrolysed (UO 2 ) 3 (OH) + 5 was the major specie under these conditions [START_REF] Guillaumont | Update on the chemical thermodynamics of uranium, neptunium, plutonium, americium and technetium[END_REF][START_REF] Grenthe | Chemical thermodynamics of uranium[END_REF]. The total reversibility could only be obtained lowering pH to 4 within 24 h, where UO 2+ 2 is the major specie. Under our conditions, we can estimate, referring to Neck and Kim [START_REF] Neck | Solubility and hydrolysis of tetravalent actinides[END_REF], that Th(OH) + 3 and Th(OH) 4 (aq) are the major thorium (IV) species in solution in the interval 6 ≤ pH ≤ 9. As in the case of U(VI), the presence of strongly hydrolysed Th(IV) species can be responsible of the irreversible process. However, studies on sorption reversibility of thorium (IV) are scarce and this phenomenon is difficult to take into account without a proper analysis.

Influence of contact time. The influence of slow kinetics in HA chemistry has been evidenced either in the case of metal complexation [START_REF] Quigley | Sorption irreversibility and coagulation behavior of 234 Th with marine organic matter[END_REF]69), retention by mineral surface [START_REF] Gu | Adsorption and desorption of natural organic matter on iron oxide: mechanisms and models[END_REF][START_REF] Hur | Molecular weight fractionation of humic substances by adsorption onto minerals[END_REF], or even in the case of structural rearrangement [START_REF] Engebretson | Kinetic aspects of cation-enhanced aggregation in aqueous humic acids[END_REF][START_REF] Von Wandruszka | The role of selected cations in the formation of pseudomicelles in aqueous humic acid[END_REF]. Hence, contact time between HA and pre-equilibrated hematite-Th(IV) systems at pH ≈ 7 was increased from 24 hours to 1, 2 and 3 weeks (168, 336 and 504 hours). Results are reported in figure 3 is slightly higher in this series than in the one previously obtained. These differences cannot be interpreted, and further work is in progress to understand this behaviour.

The modelling of the interaction between metallic cations and HA has recently been presented as kinetically controlled (69). This kinetic control seems to lead to an irreversible part of the complexation. This seems to be in agreement with the complexation of Th(IV) in marine systems [START_REF] Quigley | Sorption irreversibility and coagulation behavior of 234 Th with marine organic matter[END_REF].

The influence of contact time between HA and thorium (IV) on the retention by α-Fe The influence of contact time between Th(IV)-HA complex and hematite surface is reported on figure 4b. In these series of experiments, Th(IV)-HA complex is equilibrated during about hematite-HA pre-equilibrated followed by Th(IV) addition; b. Th(IV)-HA pre-equilibrated for 1 month followed by hematite addition.

As in figure 4a, a slight increase in Th(IV) retention can be observed when increasing contact time of the humic complex with hematite. Nevertheless, as in figure 4a, this increase , from ref. [START_REF] Reiller | Retention behaviour of humic substances onto mineral surfaces and consequences upon thorium (IV) mobility: case of iron oxides[END_REF] from ref. [START_REF] Reiller | Retention behaviour of humic substances onto mineral surfaces and consequences upon thorium (IV) mobility: case of iron oxides[END_REF] A B

1

  Influence of addition order and contact time on thorium (IV) retention by hematite in the presence of humic acids. Pascal Reiller*, Florence Casanova CEA, CE Saclay, Nuclear Energy Division, DPC/SECR, Laboratoire de Spéciation des Radionucléides et des Molécules, bâtiment 391, BP 11, F-91191 Gif sur Yvette CEDEX, France. Valérie Moulin CEA, CE Saclay, Nuclear Energy Division, DDIN/MR, bâtiment 121, BP 11, F-91191 Gif sur Yvette CEDEX, France. tel: +33-1-6908-4312, fax: +33 1 6908 5411 pascal.reiller@cea.fr

[Figure 1 :

 1 Figure 1: Influence of the addition order for the system hematite-HA-Th(IV) with 24 hours equilibration time: circles, no HA added; diamonds, HA added first; triangles, Th(IV) added

  The influence of HA concentration on Th(IV) retention by colloidal hematite at different pH values reported by Reiller et al.[START_REF] Reiller | Retention behaviour of humic substances onto mineral surfaces and consequences upon thorium (IV) mobility: case of iron oxides[END_REF] is reported on figure 2 using closed symbols. The equilibration time was 24 hours for hematite-HA suspension and 24 hours after the addition of Th(IV). Comparable batch experiments were performed but equilibrating Th(IV) with hematite for 24 hours prior to addition of HA in the suspension. The final suspension was then shaken for another 24 hours. The results are plotted using open symbol on figure 2.

Figure 2 :

 2 Figure 2: Influence of HA on the sorption of thorium (IV) onto hematite and of the addition order after 24 hours equilibration time. Closed symbols from (17): HA added first; open symbols: Th(IV) added first; [Th] = 1 × 10 -12 M; [α-Fe 2 O 3 ] = 500 mg.L -1 ; I = 0.1 M

  de Weerd et al. (61) modelled the results of Gu et al. (12) and proposed different sorption kinetics for six fractions representing NOM: namely hydrophobic and hydrophilic fractions of size < 3kDa, 3-100 kDa and > 100 kDa. The lower mass fraction and the more hydrophobic fraction have faster kinetics. Through this modelling, the higher mass fractions reach sorption equilibrium in times ranging from 100 hours to more than 900 hours. These modelling results were experimentally confirmed by Hur and Schlautman (66) in the case of purified Aldrich humic acid Interestingly, the hematite sample used by Gu et al. (12) and the one used in Reiller et al. (17) and in this study too, have very similar properties except for the size of the particles, i.e. D = 150-300 nm, S sp = 10 m²/g, Anion Exchange Capacity = 3.86 × 10 -5 mol/g. Nevertheless, the experiments of Gu et al. (12) were performed at pH = 4.1. The comparison of our results with Gu et al. (12) experiments and with van de Weerd et al. (61) modelling results, can only be qualitative. The experiments by Hur and Schlautman (66) could be compared to our results apart from the lack of site density determination and the difference in specific surface area (7.41 m²/g).

Gu

  et al. (12) used a 1% hematite stock solution, diluted to 1/5 (i.e. ≈ 2g/L, or [≡SOH] = 7.7 × 10 -5 eq/L), and the high concentration postulated by van de Weerd et al. (61) was 14.4 mg of carbon/L (12 meq/g of carbon, or [≡HA] = 1.7 × 10 -4 eq/L). This leads to a ratio [≡HA]/[≡SOH] = 2.24. This value is very close to the retention drop evidenced in Reiller et al.[START_REF] Reiller | Retention behaviour of humic substances onto mineral surfaces and consequences upon thorium (IV) mobility: case of iron oxides[END_REF]. The experiments reported in figure2 -[≡HA]/[≡SOH] ≥ 5 -were thus performed in conditions where higher mass and hydrophobic fractions would not be in equilibrium with the hematite surface.

  compared to the results of Reiller et al. (17) (α-Fe 2 O 3 -HA 24h -Th(IV) 24h; pH = 7.16, closed squares) and to the results presented in figure 2 (α-Fe 2 O 3 -Th(IV) 24 h -HA 24 h; pH = 7.26, open squares) obtained at about the same pH value. A slight decrease in the R(Th) value could be evidenced in figure 3 when contact time is increased. The differences between the different contact times are only statistically significant when [≡HA]/[≡SOH] ≥ 30 (R(Th) ± 2.σ). As in the previous cases, the sorption decrease is more intense when the ratio [≡HA]/[≡SOH] increases.Nevertheless, the retention drop is undoubtedly less significant comparing to the Th(IV) sorption hindrance provoked by the formation of the organic layer as noted earlier (c.f. figure2). These results indicate that the slow sorption, or complexation, kinetics has only minor effect in the time frame of these experiments. It can be suggested that a longer equilibration time could induce a more intense desorption of Th(IV) from hematite surface.Pre-equilibration of HA and Th(IV) and influence of contact time. For these experiments, hematite concentration was lowered to 50 mg/L. The [≡HA]/[≡SOH] ratio was the same as in figure2and figure3, so the HA concentrations were lowered to the tenth of those used in Reiller et al.[START_REF] Reiller | Retention behaviour of humic substances onto mineral surfaces and consequences upon thorium (IV) mobility: case of iron oxides[END_REF] (figure4, closed squares). A similar retention pattern is obtained (figure4, grey squares). Nevertheless, it can be observed that the retention of Th(IV)

2 O 3 at pH ≈ 7 ,

 27 as well as the results obtained in Reiller et al.[START_REF] Reiller | Retention behaviour of humic substances onto mineral surfaces and consequences upon thorium (IV) mobility: case of iron oxides[END_REF] for the same conditions, are reported on figure4a. As in the preceding cases, the contact time in the time frame of the experiments has only a weak influence on the final result. Nevertheless, a slight increase of Th(IV) retention by the solid phase can be noticed. This effect is barely statically significant.In these experiments, the contact times between HA and hematite are the same, i.e. 24 hours. Consequently, these results only reflect the Th(IV) complexation by HA, assuming no effect on HA properties. Von Wandruszka et al.[START_REF] Von Wandruszka | The role of selected cations in the formation of pseudomicelles in aqueous humic acid[END_REF] evidenced an enhancement of the pyrene fluorescence in Th(IV)-HA systems when [Th(IV)] > 10 -5 M, indicating further aggregation of HA samples, but, as no pH indication is available in the original paper, the influence of ThO 2 solubility cannot be checked. Nevertheless, no such effect could be anticipated under our conditions where [Th(IV)] ≈ 10 -12 M.

9 [ 7 HAFigure 4 :

 974 Figure 4: Influence of contact time and HA concentration at pH ≈ 7, in the systems: a.

month (29 and 34 days) before any contact with hematite. The contact time of the preequilibrated Th(IV)-HA complex with hematite was increasing to 9

and 28 days (open symbols). The results obtained in Reiller et al. (17) (black squares), and the ones that were reported on figure4a(hematite-HA 24 h / Th(IV) 24 h, grey squares; Th(IV)-HA 37 days / hematite 24 h, grey circles) are reported for the sake of comparison.

Acknowledgment

This work has been carried out in the framework of the "HUMICS project" (FI4W-CT96-0027) and "HUPA project" (FIKW-CT-2001-00128), and MRTRA project of the Risk Control Domain (CEA/DEN/DDIN).

Interestingly, studying the leaching of borosilicate glasses, Dran et al. [START_REF] Dran | Leaching of borosilicate glasses by solutions containing humic acids: behaviour of metallic elements[END_REF] showed that, Zr(IV) was highly retained in the altered layer, but also leached from borosilicate glasses by solutions containing Aldrich humic acids as the concentration of Zr(IV) increased from 2.2 × 10 -7 M -0.02 mg Zr/L -with no HA, up to 1.1 10 -6 -0.1 mg Zr/L -with 80 mg HA/L. The authors also showed that the kinetic must be very slow at 90°C during 168 hours.

, from ref. [START_REF] Reiller | Retention behaviour of humic substances onto mineral surfaces and consequences upon thorium (IV) mobility: case of iron oxides[END_REF] is barely statistically significant. A tentative explanation could be linked to the discussion of preferential complexation of Th(IV) by higher mass fraction and to the kinetics control of Th(IV)-HA complex. On the one hand, it has been proposed that thorium (IV) is preferentially complexed by the higher sized and hydrophilic fractions of NOM [START_REF] Quigley | Importance of acid polysaccharides for Th-234 complexation to marine organic matter[END_REF]. On the other hand, from the works of van de Weerd et al. [START_REF] Van De Weerd | Modelling the dynamic adsorption/desorption of NOM mixture: Effects of physical and chemical heterogeneity[END_REF], these fractions have the slowest sorption kinetic that would imply not only a slow desorption of thorium (IV) from hematite surface, but also a slow sorption of pre-equilibrated Th(IV)-HA complex on the same hematite surface. A final step would be increasing contact times to larger values in order to test this hypothesis. Further works are in progress to test the validity of this hypothesis.


Mathilde Legrand

Nathanaël Jarrassé

Florian Richer

Guillaume Morel

A closed-loop and ergonomic control for prosthetic wrist rotation

Beyond the ultimate goal of prosthetics, repairing all the capabilities of amputees, the development line of upperlimb prostheses control mainly relies on three aspects: the robustness, the intuitiveness and the reduction of mental fatigue. Many complex structures and algorithms are proposed but no one question a common open-loop nature, where the user is the one in charge of correcting errors. Yet, closing the control loop at the prosthetic level may help to improve the three main lines of research cited above. One major issue to build a closed-loop control is the definition of a reliable error signal; this paper proposes to use body compensations, naturally exhibited by prostheses users when the motion of their device is inaccurate, as such. The described control scheme measures these compensatory movements and makes the prosthesis move in order to bring back the user into an ergonomic posture. The function of the prosthesis is no longer to perform a given motion but rather to correct the posture of its user while s/he focus on performing an endpoint task. This concept was validated and compared to a standard open-loop scheme, for the control of a prosthetic wrist, with five healthy subjects completing a dedicated task with a customized transradial prosthesis. Results show that the presented closed-loop control allows for more intuitiveness and less mental burden without enhancing body compensation.

I. INTRODUCTION

Upper limb prostheses aim at replacing the amputated limb of their users, to give them back some autonomy and capabilities. This substitution calls on developments in two main areas: mechatronics and control. Mechatronics now provides devices with multiple degrees of freedom (DOF), such as polydigital hands [START_REF] Cordella | Literature review on needs of upper limb prosthesis users[END_REF], [START_REF] Piazza | The softhand pro-h[END_REF], 2-DOF wrist [START_REF] Kyberd | Two-degree-of-freedom powered prosthetic wrist[END_REF] or whole multiple DOF arm [START_REF] Resnik | The deka arm: Its features, functionality, and evolution during the veterans affairs study to optimize the deka arm[END_REF] but the control of these devices still remains a challenge. Two main control approaches exist: myoelectric and movement-based; each one tries to bring a solution to the identified issues of prosthetic control, such as intuitiveness, reduced fatigue and mental burden, or robustness [START_REF] Castellini | Proceedings of the first workshop on peripheral machine interfaces: Going beyond traditional surface electromyography[END_REF]- [START_REF] Vujaklija | New developments in prosthetic arm systems[END_REF]. The most common one, used in daily life, is conventional myoelectric control, that takes the electrical signals of some flexor and extensor muscles of the residual limb to control the actuators of an externally-powered prosthetic joint [START_REF] Popov | The bio-electrically controller prosthesis[END_REF]. When there are several DOF to control, the user cannot make a simultaneous motion but has to switch from one joint to another, either with a co-contraction or by modulating finely the muscle contraction amplitude with proportional control approaches [START_REF] Roche | Prosthetic myoelectric control strategies: A clinical perspective[END_REF]. This sequential control is cumbersome and *This work was supported by ANR Byceps, ANR-18-CE19-0004 1 Mathilde Legrand, Nathanaël Jarrassé, Florian Richer and Guillaume Morel are with Institute of Intelligent Systems and Robotics, Sorbonne University, Paris, France {mathilde.legrand, nathanael.jarrasse, florian.richer, guillaume.morel}@sorbonne-universite.fr leads to muscular fatigue [START_REF] Castellini | Proceedings of the first workshop on peripheral machine interfaces: Going beyond traditional surface electromyography[END_REF]. To overtake these limitations, pattern recognition relies on muscular synergies to simplify the access to several joint motions and to reduce mental burden [START_REF] Vujaklija | New developments in prosthetic arm systems[END_REF], [START_REF] Herberts | Hand prosthesis control via myoelectric patterns[END_REF], [START_REF] Oskoei | Myoelectric control systems-a survey[END_REF], but without solving the issues of robustness and easy access to good electromyogram measurements. Movement-based control techniques choose to make use of joints motions instead of muscles signals, claiming for more intuitiveness and less complexity in signal processing. Some of them artificially link the motion of one functional joint to a prosthetic joint (joint-to-joint correspondence) [START_REF] Bennett | Imu-based wrist rotation control of a transradial myoelectric prosthesis[END_REF], [START_REF] Resnik | Controlling a multidegree of freedom upper limb prosthesis using foot controls: User experience[END_REF], others use functional joints as joystick to control the end-effector trajectory (for shoulder amputees only) [START_REF] Phillips | Endpoint control for a powered shoulder prosthesis[END_REF] and others employ models of joint synergies [START_REF] Merad | Intuitive prosthetic control using upper limb inter-joint coordinations and imu-based shoulder angles measurement: A pilot study[END_REF]- [START_REF] Farokhzadi | Online estimation of elbow joint angle using upper arm acceleration: A movement partitioning approach[END_REF]. Each of these techniques has pros and cons but one major issue remains common to all: they are open-loop control schemes. Whether the prosthesis motion corresponds to the user's intention is never considered by the system itself. Each technique leaves this correction step to the user, which increases his/her mental burden and leads to a high reaction time. To improve this aspect, two approaches can be developped: either optimizing the control algorithms in order to eliminate every possible errors, or finding ways to close the control loop. The first approach seems unrealistic: first, because achieving an effective intention decoding is a very complex challenge (particularly because of human variability); second because even the slightest error can discourage an everyday prosthesis user. Considering pattern recognition for instance, an algorithm that would achieve 99% of correct outputs would probably not be good enough: the 1% of error could put the user in uncomfortable or dangerous situations and thus still ask for a correction from the user him/herself. Alternatively, the closed-loop approaches may have not been developped yet because of the hurdle to define an error signal as the goal of the task is rarely known to the robotic limb. Indeed, how to perfectly determine the task to perform or the object to grasp in an unmonitored environment, where the only reliable source of information is the amputee him/herself and when the humanrobot communication channel relies on very limited signals (muscular contractions or joint motions)? An attempt to identify the intended motion is gaze-tracking-based solutions [START_REF] Maymo | Fastorient: Lightweight computer vision for wrist control in assistive robotic grasping[END_REF]. Still, they are not very accurate -making the control not very robust -because of the resolution of the cameras used and the intrinsic human eye limitation [START_REF] Kar | Towards the development of a standardized performance evaluation framework for eye gaze estimation systems in consumer platforms[END_REF]. They also force the user to lock his/her gaze on the target and to constantly wear eye-tracker glasses. When the movement of a prosthesis does not perfectly correspond to its user's intention, a common behavior stands out: the user tends to exhibit compensatory motions, in Fig. 1: Illustration of typical body compensations (use of trunk and upper-arm) exhibited to counteract an impaired or motionless wrist when rotating an object.

order to compensate the unadapted position/orientation of the end-effector [START_REF] Carey | Compensatory movements of transradial prosthesis users during common tasks[END_REF], [START_REF] Metzger | Characterization of compensatory trunk movements during prosthetic upper limb reaching tasks[END_REF] (see Figure 1). This often allows for faster, more accurate and less cumbersome correction than re-sending input signals (e.g. muscle contractions). We propose here to use these body compensations as an error signal to close the control loop. Oyama et al., in [START_REF] Oyama | Biomechanical reconstruction using the tacit learning system: Intuitive control of prosthetic hand rotation[END_REF], had build a control law for wrist prono-supination that aimed at minimizing body compensations. Yet, there is no error or closed-loop considerations, since the wrist rotation is merely proportional to a weighted combination of shoulder angles. We rather focus on these two aspects and consider that the function of the prosthesis is not to perform a given motion but to correct the posture of its user, while letting him/her executing an endpoint task. The control of the end-effector grasping function is then counted as a separate case.

In this paper, we present this concept we called ergonomic control, and apply it to the pronosupination of a prosthetic wrist. We setup an experiment in which we compare a standard open-loop with our closed-loop control. Considering that body compensations are physiologically armful and may lead to musculo-skeletal disorders [START_REF] Gambrell | Overuse syndrome and the unilateral upper limb amputee-consequences and prevention[END_REF], [START_REF] Ostlie | Musculoskeletal pain and overuse syndromes in adult acquired major upper-limb amputees[END_REF], this study does not only verify that the proposed concept is functional but also that it does not enhance compensatory motions, as suggested by recent upper limb motions assessments [START_REF] Kontson | An integrated movement analysis framework to study upper limb function: A pilot study[END_REF]- [START_REF] Hussaini | Refined clothespin relocation test and assessment of motion[END_REF].

II. METHODS

A. Closed-loop ergonomic control for wrist pronosupination

Conventional myoelectric control is kept for the grasping function as it seems good enough when used to control only the hand; the difficulty arises when additional DOF are added. We are thus interested in testing first our control approach on the wrist joint. Our hypothesis is that, if a prosthesis does not move or not as expected, a given task is still achieved by the subject but with body compensations. The approach described here, ergonomic control (EC), detects and employs these compensatory motions to control the robotic joint, whose motion will then make the user go back to a comfortable ergonomic position while s/he is performing the task. When wrist pronosupination is absent or not correct, it can be supplanted by trunk and arm compensatory motions [21], [START_REF] Metzger | Characterization of compensatory trunk movements during prosthetic upper limb reaching tasks[END_REF], [START_REF] Kontson | An integrated movement analysis framework to study upper limb function: A pilot study[END_REF]. However, (i) these compensations may differ depending on the subject's posture and (ii) all trunk and arm motions are not compensations. We could artificially map trunk and arm movements to the prosthesis' motions but this would create rigid coordinations between functional and robotic joints and limit the overall mobility of the subject.

We worked instead at a more distal level. To complete the uncorrect or replace the missing wrist pronosupination, trunk and arm compensatory motions aim at changing the hand orientation, rotating the forearm around its longitudinal axis (elbow-hand axis). We directly measure this rotation since it simplifies the data to record and thus the type and the number of sensors to use. When the forearm orientation is modified, it means that trunk and/or arm are moving to compensate; prosthetic wrist has to move to make the subject going back to a more ergonomic posture. The error signal is then set as

(t) = ω f a (t) -ω 0 (1)
with ω f a the forearm rotation angle around its longitudinal axis, i.e. the Z-Euler angle of XYZ sequence (see Figure 2), and ω 0 a reference forearm orientation, which defines the ergonomic posture to go back to. The reference definition is set here as the initial forearm orientation but can change if necessary, depending on the task. This generated error vector is simpler to measure than any spatial error related to an action in space. can be used as the input of a simple control law, which pilots the prosthetic wrist angular velocity, ω, as defined in the following equation:

ω(t) = 0 if | (t)| < 0 λ( (t) -δ 0 ) otherwise, ( 2
)
where 0 is a deadzone threshold (here set to 5 deg), δ = sign( (t) -0 ), and λ is a scalar gain (set to 2) that tunes the rate of correction. The frequency of the control loop is 100Hz. The values of 0 and λ were chosen experimentally to ensure stability.

B. Experimental set-up

Five healthy subjects (two females and three males, 22 to 25 years old, one left-handed and four right-handed) performed the wire loop task of the Powered Arm Prosthetic Race of the Cybathlon c [START_REF]Race Task Description Cybathlon 2020[END_REF]. The goal of the task is to bring the handle through the wire loop in a minimum time and without touching the wire. The shape of the wire requires the participants to continuously adjust their hand orientation with pronosupination. Attached to their left arm, the subjects wore a prosthetic prototype composed of a Touch Bionics hand (I-Limb TM Ultra) and a motorized wrist rotator. The hand was pre-positioned holding the handle and kept still during the experiment (see Figure 3); the wrist angular velocity was controlled by a DC motor driver (Ion motor control, Ltd), itself controlled by a Raspberry Pi 3 c . We used an Optitrack (NaturalPoints Inc.) motion capture system both for EC and for post-experiment analyses. Seven rigid bodies (or clusters), made of Optitrack markers, were tracked: two on the hips, one on the torso, two on the shoulders, one on the device's forearm and one on the handle. Two Inertial Measurement Units were also placed on the trunk and the upper arm respectively for post-experiment analyses (see Figure 4). Optitrack was convenient in lab environment and for post-experiment analyses but the data used for EC could have easily been replaced by gyroscope data from an Inertial Measurement Unit. Two control schemes of the device were compared:

1) an open-loop control (OL). A pair of push-buttons mounted on a handle was grasped by the free hand of the subjects (see Figure 4(a)). One push-button controlled the forward wrist rotation, the other the backward rotation. The joint angular velocity was fixed at 50 deg/s. When no push-button was pressed, the device stayed still. This command was used as a reference as it is a discrete open-loop control and thus mimicks most of the myoelectric controllers currently available for lower arm amputees (on/off, proportional switch or even pattern recognition) [START_REF] Farina | The extraction of neural information from the surface emg for the control of upper-limb prostheses: Emerging avenues and challenges[END_REF], while avoiding all the practical problems of EMG measurements [START_REF] Castellini | Proceedings of the first workshop on peripheral machine interfaces: Going beyond traditional surface electromyography[END_REF], [START_REF] Lobo-Prat | Non-invasive control interfaces for intention detection in active movement-assistive devices[END_REF]. 2) ergonomic control (EC). The forearm rotation, ω f a , was computed in the initial forearm frame, from quaternions of the Optitrack cluster placed on the device's forearm and sent in real time to the prosthesis. As subjects naturally tended to stay parallel to the wire during the whole experiment, the reference posture, ω 0 , was supposed to be fixed and was set as the initial position of the forearm. For more complex or changing tasks, the reference shall be updated, either in a very simple way, by the user himself with an external signal, or with a dedicated algorithm.

Before each recording session, subjects were allowed to train a few times on the wire loop task. They trained between two and five times. A recording session consisted in five trials and there were three recording sessions: one "natural" (N) with the own left forearm of the subjects, which provides a baseline from natural motions, one with OL, one with EC. Subjects always began with N while EC/OL order was randomized, to avoid measuring any effect of task learning.

Post-experiment analyses were conducted with Matlab, Mathworks Inc. This experiment was carried out in accordance with the recommendations of Université Paris Descartes ethic committee CERES, which approved the protocol. All participants gave their written informed consent in accordance with the Declaration of Helsinki.

III. RESULTS

EC was assessed on several criteria and compared to the standard OL control. The metrics characterize the good realization of the task but also the smoothness of the movement and the amount of generated body compensations.

A. Task realization

The task performance was described with the time of the task and the number of touches (see Figure 5). Figure 5(a) shows the time for each trial of the two modes, with the mean difference between the two modes and the 95% confidence intervals (CI). This representation was selected because it allows for a more transparent statistical analysis than the pvalue [START_REF] Ho | Moving beyond p values: data analysis with estimation graphics[END_REF], especially for small populations. If the 95% CI of the mean difference does not cross the zero dotted line, the two modes are statistically significantly different. The green lines are the minimum and maximum times obtained with N, during natural achievement of the task by each subject. It can be noticed that the natural times of the task are shorter for S1 because this subject was left-handed, but handedness did not affect any other results. We see here that for three out of five participants (S1, S2 and S4), the time is statistically significantly shorter with EC than with OL. For S5, the time with EC is longer but without a real significant difference. S3 stands out from the others as EC times are significantly longer than OL ones. On Figure 5(b), we observe that the number of touches does not really distinguish OL and EC, except for S1. The lattest touched the wire in four out of five trials with OL and never with EC, but this is partly due to the fact that this subject wanted to be fast before being precise. Overall, it can also be noticed that EC generates touches in

B. Smoothness of wrist motions

While healthy motions are naturally smooth [START_REF] Sejnowski | Making smooth moves[END_REF], prosthetic motions are often jerky, due to the discrete nature of the command [START_REF] Cowley | Movement quality of conventional prostheses and the deka arm during everyday tasks[END_REF]. Since EC allows for a continuous control of the movements, we infer that the smoothness of prosthetic motions with EC is improved, which would be a significant benefit. Figure 6 shows the wrist pronosupination angle and the wrist angular velocity of the prosthesis for one typical subject, for OL and EC respectively. We see on Figure 6(a) that the OL wrist angular velocity must be a series of pulses to obtain a motion as continuous as possible. Yet, it is clear that the wrist angular trajectory with OL is jerky (it is a step function) while the one with EC is smooth and continuous (see Figure 6(b)). This difference in smoothness can be illustrated by the high number of times the push-buttons were pressed compared to the low number of deadzone crossings with EC. These measures can also represent the involvement required from the subject, as pressing the push-buttons or exhibiting compensations to move the wrist increase the mental charge. Figure 7(a) shows these two metrics, with their mean and standard deviation, for all trials of the five participants. It highlights the fact that the prosthesis user is much more involved when using OL than when using EC: (i) s/he has to focus on individual wrist motions while EC allows to focus only on the end-effector motion and (ii) s/he is her/himself the corrector that closes the control loop.

To quantitatively evaluate smoothness, we used the spectral arc length of the wrist angular velocity [START_REF] Balasubramanian | A robust and sensitive metric for quantifying movement smoothness[END_REF] (Figure 7(b), the more negative, the less smooth). The same statistical representation as above, with 95% confidence intervals and difference mean, was employed. There is no doubt that for the five participants, EC wrist motions are significantly smoother than OL wrist motions. Yet, one can criticize the fact that the low smoothness of OL is intrinsic to its binary nature. As often done in on/off prosthetic control, finer velocity profiles, e.g. trapezoidal, could have been implemented. However, this would not have created a fully continuous control, as enabled by EC.

C. Joint motions

Another important point in upper limb motions assessment is to which extent the subject has to modify his/her joint movements and coordinations. It is particularly relevant in our case, where one may think that, due to its intrinsic characteristics, EC could potentially increase some trunk and arm compensatory motions. We focus on the study of the arm aperture angle, α, and the lateral bending of the trunk, ψ (see definitions on Figure 8(a)), to verify that the action of the prosthesis is fast enough to prevent any important and undesirable compensations. Figure 8(b) is the mean and standard deviation of the angular trajectories, normalized in time, for each participant. Green dashed lines represent the maximum and minimum values of each subject's natural angular trajectories. We first note that the timing of the angular variations are similar between the two modes of control. α (up panel) shows variations of amplitude between OL and EC but, except for S4, both always stay into the subject's natural baseline. For S4, even if α with EC shows higher values than with OL and exceeds the individual's natural values, the maximum is still lower than some natural maximum of other subjects. Contrary to α, ψ is a bit heightened with EC, especially for left-side bending (negative values). This observation points out the issue of the reference definition, which can affect the exhibited compensatory motions. Indeed, prosthetic wrist pronation is induced either by arm internal aperture (internal α, see Figure 8(a)) or by trunk left bending (negative ψ).

Because we chose, for this experiment, the reference as the initial position of the subject, with the arm along the body, the amplitude of internal α was limited. The latter was so difficult to perform that it was nearly not exhibited and, to induce wrist pronation, the subject used only left lateral bending. This phenomenon can be prevented by optimizing the choice of the reference position. If subjects were given the instruction to begin with a small external α, the amplitude of internal angle would have been increased, avoiding a too important use of the trunk to obtain pronation. We are currently working to find a reference posture that does not promote pronation or supination but allows an easy realization of both without enhancing trunk or arm compensations.

IV. CONCLUSIONS

Ergonomic control was used with a 1-DOF prosthetic wrist, by five subjects performing a dedicated task, the wire loop of Powered Arm Prosthetic Race of the Cybathlon c . EC was compared to OL, a discrete open-loop control that mimicks existing on/off prosthetic control, like myoelectric. EC shows better results than OL for the time of the task, the number of touches and also for mental burden, which is a great advantage over existing controls of prostheses. Moreover, closing the control loop on body compensations naturally reduces them. The wire loop experiment thus illustrates the interest for closed-loop ergonomic control for an artificial pronosupination joint. It exploits natural strategies of compensatory movements to close the control loop, without any necessity to know the environment or the task. The two main advantages of the proposed control are its intuitiveness and its simplicity. Indeed, it was mastered by all the participants without considerable training session and the control law has only two parameters to tune (the threshold, 0 , and the gain, λ). This ensures easy generalization to all users as well as robustness. The prosthesis user only has to focus on the endoint task while the prosthesis corrects his/her posture. EC is thus much less cumbersome than most of the existing open-loop control schemes with which the user has to focus on the motions of individual joints. The validation of ergonomic control was performed here on healthy subjects. Upcoming developments will thus include in-depth study with amputated participants. EC was also tested on only one task and for one DOF. Future works will aim at using Inertial Measurement Units instead of motion capture system for an easy transfer to daily life (raw gyroscope values can be sufficient, avoiding drift issues), studying EC use with a broader set of tasks and adapting it to more DOF (e.g. adding the elbow joint). This should allow for a simultaneous control of several prosthetic joints without more mental burden for the user.

ACKNOWLEDGMENT

We thank all the participants of the experiment.

Fig. 2 :

 2 Fig. 2: Diagram showing the definition of the reference frame used to compute XYZ Euler angles and obtained , and the definition of ω.

Fig. 3 :

 3 Fig. 3: Cybathlon wire-loop task with the adapted prosthetic device. The upper left insert shows the handle hold by the prosthetic hand.

Fig. 4 :

 4 Fig. 4: Experimental set-up. (a) OL control set-up. (b) EC set-up. 1: Optitrack markers; 2: Inertial Measurement Units.

Fig. 5 :

 5 Fig. 5: Task realization performance metrics. (a) Time of the task: all trials of each of the five subjects, with the 95% confidence interval and the mean difference between the two control modes. (b) Number of handle touching the wire for each trial. The green lines are (a) the maximum and minimum values of the time and (b) the maximum number of touches when the subject performed the task with his/her own hand. OL is open-loop and EC ergonomic control.

Fig. 6 :

 6 Fig. 6: Prosthetic wrist pronosupination angle and angular velocity for one trial of one typical subject with (a) open-loop control and (b) ergonomic control. The dashed lines indicate when the push-buttons are pressed (OL) or when the subject's forearm angle went out of the deadzone (EC).

Fig. 7 :

 7 Fig. 7: Wrist motion metrics. (a) Involvement of the subjects measured by the number of times the push-buttons are pressed (OL) and the number of deadzone crossings (EC). (b) Motion smoothness measured by the spectral arc length of wrist angular velocity: 95% of confidence interval and mean difference between the two control modes.

Fig. 8 :

 8 Fig. 8: Arm and trunk motions. (a) Definition of arm aperture and trunk lateral bending angles. (b) Mean and standard deviation of α (up panel) and φ (down panel), normalized in time, for all subjects. Green dashed lines are the maximum and minimum values of the subject's natural joint trajectories. OL is open-loop and EC ergonomic control.