Mariem Ghayaza

Lydie Le Forestier
email: lydie.leforestier@univ-orleans.fr

Fabrice Muller

Christophe Tournassat

Jean-Michel Beny

Pb(II) and Zn(II) adsorption onto Na-and Ca-montmorillonites in acetic acid/acetate medium: Experimental approach and geochemical modelling Authors

Keywords: adsorption, lead, zinc, cation exchange, surface complexation

Smectites are usually used as a clay barrier at the bottom of subsurface waste landfills due to their low permeability and their capacity to retain pollutants. The Na-and Ca-saturated SWy2 montmorillonites were interacted with initial Zn(NO 3 ) 2 or Pb(NO 3 ) 2 concentrations ranging from 10 -6 to 10 -2 M with a solid/liquid ratio of 10 g L -1 , and using acetic acid/acetate as buffer at pH 5 in order to reproduce a biodegradable leachate of a young landfill. These experiments revealed that Zn and Pb sorption onto Na-SWy2 is higher than onto Ca-SWy2 in the whole range of concentrations. Metal retention into both montmorillonites increases with the decrease in acetic acid/acetate concentration. The two site protolysis model with no electrostatic term (2SPNE model) was used to model these experiments. As the experimental data of Zn sorption were well fitted, this model was validated and has been improved by taking into account the metal-acetate complexation in solution. In order to validate the model for Pb sorption, new selectivity coefficients have been determined, namely log K c (Pb-Na) = 0.5 for Na-montmorillonite and log K c (Pb-Ca) = 0.3 for Ca-montmorillonite.

Introduction

The major potential environmental impacts related to landfill leachate are pollution of groundwater and surface water. European legislation requires the presence of a clay barrier at the bottom of waste landfills to prevent contamination. Smectites are usually used for this purpose because of their low permeability, their expansion ability and their capacity to retain pollutants. When refuse is buried in a landfill, a complex series of biological and chemical reactions occur as the refuse decomposes. It is generally accepted that landfills undergo five phases of decomposition: (1) an initial aerobic phase, which lasts only a few days, (2) an anaerobic acid phase, (3) an initial methanogenic phase, (4) a stable methanogenic phase, and

(5) an additional aerobic or humic phase of decomposition [1]. Leachate composition mainly depends on the biodegradation phase of the organic matter, and hence on the age of the waste disposal. Consequently, three types of leachate have been distinguished [2]: biodegradable for a young landfill (< 5 years old), intermediate for a medium landfill (5-10 years), and stabilized for an old landfill (> 10 years). The biodegradable leachate is characterized by a decrease in pH (4.5 < pH < 6.5), due to the accumulation of volatile fatty acids, principally carboxylic acids, resulting from bacterial activity. Harmsen [3] estimated that 95% of the total organic carbon comes from these acids. As the pH is acidic, this leachate is chemically aggressive and will increase the solubility of many compounds, in particular of heavy metals (up to 2 g L -1 ). The organic acids are then progressively converted to methane and carbon dioxide by methanogenic bacteria, leading to an increase in pH. Thus, the intermediate leachate is characterized by a neutral environment (6.5 < pH < 7.5) and a low biodegradability due to a lower content of volatile fatty acids. Finally, the stabilized leachate contains fulvic and humic acids of a high molecular weight, and also low molecular weight compounds, all of which are resistant to biodegradation. The leachate produced by an old landfill is basic with a pH between 7.5 and 9. Consequently, the major potential pollution of surface water and groundwater may be caused by the acidic leachates of young landfills containing high amounts of toxic metals. Two of the most abundant metallic pollutants present in waste landfill leachates are lead and zinc. Pb occurs predominantly as Pb 2+ species up to pH 6, with also the presence of a nitrate species PbNO 3 + (less than 10%) [4], whereas all zinc is in the form of Zn 2+ at pH 5. Zinc is known to be essential to plants, humans and animals, but it can have adverse effects if its availability in soils exceeds a certain threshold value. Acute toxicity arises from the ingestion of excessive amounts of zinc salts, either accidentally or deliberately after the consumption of more than 500 mg of zinc sulfate. Lead is known to be hazardous even at low concentrations. To avoid the contamination of the water table and consequently the contamination of living beings, it is essential to predict the behaviour of these metals in the clay barrier of waste landfills. The mean landfill concentration values are 5 mg L -1 (7.6x10 -5 mol L -1 ) for zinc and 0.09 mg L -1 (4.3x10 -7 mol.L -1 ) for lead [5]. The maximum reported concentrations can however reach 1000 mg L -1 (1.5x10 -2 mol L -1 ) for zinc and 5 mg L -1 (2.4x10 -5 mol L -1 ) for lead. All these values exceed international standards for drinking water, which are 3 mg L -1 (= 4.6x10 -5 mol L -1 ) for Zn and 0.01 mg L -1 (=4.8x10 -8 mol L -1 ) for Pb [START_REF]World Health Organization, Guidelines for drinking-water quality[END_REF].

Numerous experimental studies have investigated the interaction between clays and lead or zinc, where factors such as pH [START_REF] Abollino | [END_REF]8], ionic strength [9,10], or clay adsorbents such as kaolinite, illite or montmorillonite [4,8,11,12] affect the extent of adsorption of these metals onto clays. However, these metallic pollutants are in contact with other compounds in leachates (dissolved organic matter, inorganic macro components, and xenobiotic organic compounds), which may influence the interactions of metals with clay. Gautier et al. [13] have shown that carboxylic acids may interact with smectite, while Huang et al. [14] have studied the influence of low molar mass acids on the adsorption of Cd 2+ and Pb 2+ by goethite and montmorillonite. To our knowledge, however, no study has been done to experiment and model the adsorption of metals onto smectite in the presence of carboxylic acids.

Both sorption and precipitation are believed to be significant mechanisms for the immobilization of metals and the subsequent low leachate concentrations. The electrostatically bound cations (interlayer cations) can undergo exchange with the cations in solution in reactions which are fast, stoichiometric and reversible [15][START_REF] Van Olphen | An introduction to clay colloid chemistry[END_REF][START_REF] Bolt | Thermodynamics of cation exchange[END_REF]. The cation exchange reaction of a metal B (Pb or Zn), of valency Z B (2 in this study), exchanging with a cation A (Na or Ca), of valency Z A (1 or 2, respectively), in the interlayer of a clay mineral (here the montmorillonite SWy2) can be expressed as:

Z B . (A ZA -clay) + Z A . B ZB ↔ Z A . (B ZB -clay) + Z B . A ZA
Sorption by cation exchange is characterised by a strong dependency on background electrolyte concentration, a weak dependency on pH and linear sorption. The second category of reactive sites is perceived as being amphoteric surface hydroxyl groups (≡SOH) situated along the edges of the clay platelets [START_REF] Sposito | The surface chemistry of soils[END_REF]. These "edge" or "broken bond" sites, consistent with a surface complexation mechanism, exhibit a strong pH dependence and a weak dependence on ionic strength. As they can protonate and deprotonate, the concentrations of neutral (≡SOH), protonated (≡SOH 2

+

) and de-protonated (≡SO -) edge sites change as a function of pH.

The objective of this work is to reproduce the chemical conditions of an acidic leachate in a young subsurface waste landfill (pH = 5) and to understand and model the mechanisms of interaction between metallic pollutants (Pb, Zn) and smectite with a fixed ionic strength and in the presence of organic molecules such as acetic acid/acetate.

Materials and methods

Clay material

The Part of the Na-SWy2 stock was saturated with Ca using the same procedure as above but with a 1M CaCl 2 solution instead of NaCl. This sample is hereafter named Ca-SWy2. The BET specific surface area is 45.4 m 2 g -1 for Na-SWy2 [START_REF] Forestier | [END_REF] and 46 m 2 g -1 for Ca-SWy2. Cation exchange capacity (CEC) determined using the triethylenetetramino copper II complex method [20] is 0.850 ± 0.027 mol c /kg for Na-SWy2 [START_REF] Forestier | [END_REF] and 0.851 ± 0.001 mol c /kg for Ca-SWy2.

Solutions preparation

All solutions were prepared from analytical grade products with Millipore Milli-Q then added to reach a solid to liquid ratio (r S/L ) of 10 g L -1 . After 16 hours, the tubes were centrifuged at a relative centrifugal field of 4500 g for 15 min. Supernatant solutions were filtered through a Millipore filter (0.2 µm nitrocellulose membrane) and analyzed by atomic absorption spectrometry (AAS) using a Hitachi Z-8100 spectrophotometer. A flame spectrometer was used to measure Pb concentrations ranging from 5x10 -6 to 10 -3 M and Zn concentrations ranging from 1.5x10 -6 to 6x10 -5 M. A graphite atomizer enabled the measurements of Pb concentrations from 7x10 -8 to 4x10 -6 M. From measurements of the pollutant concentration in solution before and after interaction with smectite, the amount of metal adsorbed on the clay was quantified. Concentrations of sorbed Zn and Pb onto clay ([Zn] sorbed and [Pb] sorbed in mol kg -1 ) were calculated according to:

L S eq tot sorbed r Zn Zn Zn / ] [ ] [ ] [ - = L S eq tot sorbed r Pb Pb Pb / ] [ ] [ ] [ - =
where [i] tot stands for the total concentration of metal i measured in the initial solution and

[i] eq stands for the concentration at equilibrium.

Error bands were calculated according to Danzer [START_REF] Danzer | Analytical chemistry, Theoretical and metrological fundamentals[END_REF]. The extended combined uncertainty

U([i]

) represents an interval that contains a large part of the values of series of measurements:

U([i]) = k x u([i])
where the selected coverage factor k was 2, to cover an interval in which 95.5% of the values are found.

Where

u([i] eq ) = 2% [i] eq ; u([i] tot ) = 2% [i] tot And ( ) 2 2 ) ] ([ ) ] ([ ) ] ([ tot eq sorbed i u i u i u + =
Since the results are presented as log [i] sorbed versus log [i] eq , the error bands become:

U + = log ([i] + 2 u([i])) -log([i]) U -= log ([i] -2 u([i])) -log([i])

Infrared spectroscopy

Fourier-transform infrared (FTIR) spectra were recorded in transmission mode using a NICOLET Magna-IR 760 Fourier transform spectrometer and a NICOLET Nic-Plan microscope. The powder sample was directly deposited on the NaCl window of the microscope stage without further preparation to avoid K + -clay cation exchange within the sample during analysis [START_REF] Pelletier | [END_REF] and to prohibit contributing absorbed water from KBr pellets in the stretching O-H range. Prior to and during measurement, the spectrometer and microscope chambers were purged with dry compressed air to remove most of the atmospheric H 2 O and CO 2 . The sample area analysed was a 100 µm diameter circle selected under the microscope 15 X Cassegrainian objective. Operating conditions were 128 scans with 2 cm -1 resolution without CO 2 -H 2 O corrections. The studied wave number ranged from 650 to 4000 cm -1 according to the spectrometer beamsplitter and the microscope detector (Nicolet MCT-A).

Modelling

Various thermodynamic sorption models based on cation exchange and/or surface complexation mechanisms have been developed [23][24][25][26][27]. Bradbury and Baeyens [23] chose the diffuse double layer (DDL) model described by Stumm and Morgan [START_REF] Stumm | Aquatic Chemistry[END_REF] to develop the two site protolysis model with no electrostatic term (2SPNE model). This empirical 2SPNE model, developed by fitting titration and metal sorption data on Na-montmorillonite, was used in this study. The total ≡SOH site capacity for Na-montmorillonite, determined by titration experiments [START_REF] Baeyens | [END_REF], is 0.08 mol sites kg -1 . The non-linearity of the sorption processes indicated that at least two types of sites with different affinities are involved in the overall sorption on Na-montmorillonite [23]. The so-called "strong" sites (≡S S OH) have a low capacity and a high sorption affinity, whereas the "weak" sites (≡S W OH) have a considerably larger capacity but a much lower sorption affinity. From the 2SPNE modelling of the titration results, Bradbury and Baeyens [23] deduced fixed values for ≡S S OH and ≡S W OH site capacities and protolysis constants, which are reported in Table 2. The geochemical PHREEQC2 code [START_REF] Parkhurst | User's guide to PHREEQC (Version 2) -A computer program for speciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations[END_REF] was used in all of the fitting/modelling work described further in this study. The PHREEQC2 thermodynamic database was used throughout. The approach was to model the sorption of lead or zinc on the Na-or Ca-SWy2 clay in the same conditions as in batch experiments. For this, the CEC value measured for Na-and Ca-SWy2 was incorporated in the code, as well as the background electrolyte concentration, the concentration of the initial metal solution, the fixed solid/liquid ratio and the fixed pH value. Selectivity coefficients for Zn-Na and Zn-Ca exchange reactions (Table 3), determined by Bradbury and Baeyens [23,31], were included in the code to model cation exchange and surface complexation reactions of zinc with Na-and Ca-montmorillonites. In contrast to zinc, only few thermodynamic data are available for lead in the literature. The procedure adopted here was to model Pb adsorption isotherms by using Zn thermodynamic coefficients and then to find the best fit which reproduced our experimental data. The objective was to determine new thermodynamic data for Pb sorption onto montmorillonite after validating the model.

Results

Influence of ionic background and metal concentration on the adsorption of metals onto montmorillonite

The experimental results at fixed ionic strength (I = 0.04 M) and high buffer concentration (0.01 M CH 3 COOH and 0.03 M CH 3 COONa) show that the sorbed metal concentration increases with the increase in the equilibrium metal concentration (Fig. 1).

The sorption of zinc on Na-SWy2 was better than Ca-SWy2, for an equilibrium concentration between 10 -5 and 10 -2 M (Fig. 1a and1c). The same results were obtained for lead (Fig. 1b and1d). These results are in agreement with Bradbury and Baeyens [32] who determined for Eu sorption a weaker intrinsic surface complexation constant in the case of Camontmorillonite compared to the Na-clay and confirmed that the same trend was also true for Zn. Indeed, the binding constants of the Na-montmorillonite system are greater than those of Ca-montmorillonite. Alvarez-Ayuso and Garcia-Sanchez [33] also highlighted a lower sorption capacity of Ca-bentonite than Na-bentonite for all the metal cations studied (Cd 2+ , Cr 3+ , Cu 2+ , Ni 2+ , Zn 2+ ), which seems related to the higher charge of Ca 2+ and its lower H + adsorption capacity. The replacement of low-charge (e.g. Na + ) by high-charge (e.g. Zn 2+ ) cations is favored relative to the exchange of same-charge cations (e.g. Ca 2+ by Zn 2+ ).

The comparison of metal adsorption onto the same clay shows that lead is slightly less adsorbed than zinc onto Na-SWy2. Although Pb 2+ has the same valence as Zn 2+ , this cation is characterised by a larger ionic radius so its introduction in interlayers and complexation with surface sites is limited by steric hindrance and lower electrostatic attraction [START_REF] Abollino | [END_REF]. On the contrary, Stefan et al. [34] found a greater affinity of Pb 2+ compared to Zn 2+ for Namontmorillonite. For Ca-SWy2 the difference between lead and zinc is not significant, since the same amounts of Pb and Zn were adsorbed on this smectite. This result is in agreement with Helios Rybicka et al. [11] and Auboiroux et al. [10] who showed that for trace metal concentrations, no significant difference could be discerned between lead and zinc fixation.

Influence of acetic acid/acetate concentration on the adsorption of metals onto montmorillonite

The adsorption of zinc and lead onto smectite in the presence of acetic acid/acetate was evaluated. For this, batch experiments were performed under the same conditions by changing only the buffer concentration. A low buffer concentration was then fixed ten times lower (0.001 M CH 3 COOH, 0.003 M CH 3 COONa) than the high buffer concentration (Table 1).

Both for zinc and for lead, metal adsorption on Na-SWy2 significantly increased with the decrease in acetic acid/acetate concentration (Fig. 1 and2). This difference was more pronounced for Zn with a higher adsorption by a logarithmic unit in the case of low buffer concentrations (Fig. 1a and2a). Baeyens and Bradbury [START_REF] Baeyens | [END_REF] asserted that the presence of acetic acid/acetate had no influence on the sorption of Ni and Zn on Namontmorillonite, but this was demonstrated only in the case of low buffer concentration (0.001 M). The same trend was observed for Pb sorption onto Na-SWy2 (Fig. 1b and2b), where the difference was more significant for low equilibrium Pb concentrations (<10 -6 M).

The influence of acetic acid/acetate concentration of Zn and Pb adsorption onto Ca-SWy2 was less pronounced than onto Na-SWy2 (Fig. 1c-d and2 c-d). Huang et al. [14] confirmed that an increase in acetic acid concentration in solution leads to a decrease in Pb 2+ adsorption by goethite and Ca-montmorillonite. At low acid concentrations, the organic anions adsorb onto the mineral particles so that the negative surface charges increase. This weakens the ability of the acetic acid molecules to complex with Pb 2+ ions in solution and promotes the adsorption of Pb 2+ . At high acetic acid concentrations, however, the concentration of Pb or Zn remaining in solution increased with increasing acid concentration and promoted the complexation of Zn 2+ or Pb 2+ by acid and reduced the quantity of metal ion adsorbed:

2 HCH 3 COO + Zn 2+ = Zn(CH 3 COO) 2 + 2 H + (1) 2 HCH 3 COO + Pb 2+ = Pb(CH 3 COO) 2 + 2 H + (2)

FTIR results

A sample of Ca-SWy2 clay powder was analyzed under the microscope to obtain the clay spectrum as reference (Fig. 3a). The band at 1640 cm -1 was identified as water vibration. With the addition of the buffer, peaks appeared at 1552, 1460 and 1420 cm -1 (Fig. 3b). The 1420 and 1552 cm -1 peaks correspond respectively to symmetric and anti-symmetric stretching of [COO] -species, characteristic of acetate. The band at 1460 cm -1 represents asymmetric CH 3 bending modes of acetate. When zinc (10 -4 M) was added to the system, another band appeared near 1700 cm -1 in addition to those described above (Fig. 3c). The same results were observed for lead onto Ca-SWy2 (Fig. 3d), and also for Zn and Pb onto Na-SWy2 (data not presented). This band is attributed to the stretching of the HO-C=O bond [35], which reveals the adsorption of acetic acid onto the clay, instead of the metals.

Modelling and discussion

Modelling Zn sorption onto montmorillonite surfaces

Since all the parameters describing Zn sorption on conditioned Na-montmorillonite are fixed (Tables 2 and3), the first test for the model was to compare the Zn sorption isotherm calculated at pH = 5 with the experimental measurements (Fig. 1a). The modeled curve reproduces the general trend of the experimental data well but could be improved. As previously shown by infrared spectroscopy, the acetic acid/acetate concentrations have a significant effect on the adsorption of zinc onto the clay. The equation of Zn acetate formation was therefore added in the model, as well as its thermodynamic constant (PHREEQC2 database) 2 HCH 3 COO + Zn 2+ = Zn(CH 3 COO) 2 + 2 H + With log K c (Zn -acetate) = -6.5 Fig. 1a clearly shows that the overall agreement between calculated and measured data is better in the new simulation, which validates the model. The thermodynamic data of this simulation were applied to simulate the adsorption of zinc in Na-SWy2 with a low buffer concentration; the result is shown with the continuous line in Fig. 2a. This simulation reflects, once again, the experimental data, thus confirming the model. Consequently, the mechanisms of zinc adsorption on clay can be understood as a function of Zn concentration in solution (Fig. 4a).

For low equilibrium zinc concentration, 90% of adsorbed zinc is fixed by surface complexation in the strong sites ≡S S OH. The remaining 10 % is adsorbed by cation exchange, while the influence of the weak sites is negligible. From 10 -6 M of Zn eq , adsorption by cationic exchange increases rapidly while the surface complexation onto the strong sites ≡S S OH decreases. For high equilibrium zinc concentration (> 10 -4 M), all the zinc is retained in smectite by cation exchange. The same approach was adopted to model the Zn sorption data on Ca-SWy2. The first test was done by choosing the selectivity coefficient for Zn-Ca exchange in Ca-montmorillonite, log K c (Zn-Ca) = 0, as previously determined by Bradbury and Baeyens [31] (Table 3). The modeled curve exhibits the same shape as the experimental data but slightly shifted downward in the range of high Zn concentrations (Fig. 1c). The addition of the effect of Zn-acetate formation leads to a better fit of the experimental data in the range of low Zn equilibrium concentrations. Modeling the mechanisms of zinc adsorption on Ca-SWy2 shows the same trends as for Na-SWy2 (Fig. 4b). Surface complexation by the strong sites ≡S S OH is the main mechanism involved for low equilibrium zinc concentration, whereas zinc is mostly retained by cation exchange beyond 10 -4 M. It is noticeable that around 10% of zinc is adsorbed in the weak sites ≡S W OH in the case of 10 -2 M [Zn eq ], and the contribution of the strong sites ≡S s OH is almost negligible due to their saturation.

Modelling Pb sorption onto montmorillonite surfaces

Unlike zinc, thermodynamic data of lead adsorption onto clays are sparse in the literature. The approach was as follows: first, the thermodynamic parameter of zinc for Na-SWy (log K c = 0.59) [23] was introduced in the model, and the first simulation was compared to the experimental data of lead adsorption on Na-SWy2 (Fig. 1b, dotted line). The overall shape of the curve was incorrectly predicted. The second step was, as in the other simulations, to add the effect of lead acetate in the model:

2 HCH 3 COO + Pb 2+ = Pb(CH 3 COO) 2 + 2 H + With log K c (Pb -acetate) = -5.5 (PHREEQC2 database)
This second simulation is shifted downward compared to the first, indicating that part of the lead is complexed with acetate in solution (Fig. 1b, dash dotted line). While it better reproduces the shape of the experimental data, this result remains unsatisfactory, meaning that the thermodynamic data cannot be the same for zinc and lead. This was followed by an optimization procedure in which the selectivity coefficient of Pb to Na in Na-SWy2, K c (Pb-Na), was varied to yield the best fit to the experimental data (Fig. 1b, continuous line). A good correspondence between calculated and measured values was obtained for log K c (Pb-Na) = 0.5 (Table 3). This value was used to model the lead adsorption experiment with a low buffer concentration in Fig. 2b. The fit corresponds very well with experimental data. Ferrell et al. [36] applied a geochemical transport model to predict lead retention by clay liners, but they only considered cationic exchange and not complexation mechanisms in the edges. Moreover, to model the cation exchange between Pb and clay, they used the database of PHREEQC2 with log K c equal to 1.05, without experimental data to confirm this selectivity constant.

The calculated sorption isotherm of Pb on Na-SWy2 can exhibit three distinct regions depending on the Pb equilibrium concentration (Fig. 5a).

At low Pb equilibrium concentrations (< 5x10 -6 M), sorption occurs mainly on the strong sites, with a maximum of 80% of Pb retained in the ≡S S OH sites for [Pb eq ] = 10 -7 M. From [Pb eq ] = 5x10 -6 M, the strong sites are saturated, so the retention of lead on the weak sites and by cation exchange increases. Pb adsorption in the ≡S W OH sites reaches a maximum of 60% of the total adsorbed amount for [Pb eq ] = 10 -4 M then decreases rapidly. The contribution of Pb uptake by cation exchange is dominant for the highest Pb equilibrium concentrations (> 10 -3 M), with nearly 80% of lead retained by cation exchange at [Pb eq ] = 10 -2 M. The same approach was used to model the adsorption of lead onto Ca-SWy2. First, the model of Bradbury and Baeyens [31] was applied with log Kc = 0, corresponding to Ca-SWy2 in interaction with Zn (Table 3), then the effect of acetic acid/acetate was taken into account by adding the equation of lead acetate formation, log K c (Pb -acetate) = -5.5 (Fig. 1d, fine-dotted line and dash dotted line, respectively). Finally, the selectivity constant of lead for Ca-SWy2 was modified until the best agreement with the experimental data was achieved (Fig. 1d, continuous line). The best fit was found for log K c (Pb-Ca) equal to 0.3 (Table 3). The calculated sorption isotherm of Pb on Ca-SWy2 reveals that lead is differently adsorbed onto the calcic clay compared to the sodic one (Fig. 5b). Here the contribution of the weak sites is more visible over all the range of Pb equilibrium concentrations. For low Pb equilibrium concentrations (< 10 -6 M), 70% of lead uptake is located in the ≡S S OH sites, 30% in the ≡S W OH sites and cation exchange is not involved in this concentration range. From 10 -5 M to 10 -4.5 M [Pb eq ], the contribution of strong sites decreases and conversely the adsorption by the weak sites increases for a maximum of 85% lead adsorbed by the weak sites. For [Pb eq ] > 10 - 4.5 M, the proportion of lead adsorbed by complexation mechanisms in the edges decreases rapidly, and is replaced by the cation exchange mechanism. For the highest Pb equilibrium concentration (10 -2 M), 60% of the adsorbed lead is retained by the Ca-Pb exchange mechanism, while the weak sites contribute 40% and adsorption by the strong sites, which are already saturated, is insignificant.

Linear free energy relationship

The general form for hydrolysed species of a metal Me with a valency Z Me can be written as

x ZMe x OH Me - ) (
where x is an integer greater than or equal to unity. Consequently, the general form of the surface complex can be expressed as For example, for x = 2, the hydrolysed form of Zn is Zn(OH) 2 and its surface complex is ≡S s OZn(OH). It is well established that relationships can be found between the free energies Similarly, the thermodynamic data obtained in this study for lead adsorption onto the weak sites of Na-SWy2 and Ca-SWy2 (black circles) were plotted on Fig. 7.

These two points established for lead are superimposed and do not fit so well with the correlation line. As explained by Bradbury and Baeyens [37], the pool of data suitable for determining weak site surface complexation constants is much smaller, and thus the confidence in the correlation in LFERs between the surface complexation constants and hydrolysis constants is not as high as in the case of the strong sites.

Conclusion

Zn(II) and Pb(II) adsorptions onto Na-and Ca-saturated Wyoming montmorillonites were separately investigated in acidic conditions with a fixed pH value of 5. For a given metallic cation (Zn 2+ or Pb 2+ ), adsorption onto the sodic smectite is higher than onto the calcic one, over the whole range of metal concentrations investigated (10 -6 to 10 -2 M). Besides, zinc has a slightly better affinity for Na-SWy2 than lead, whereas no significant difference between the two metals was observed in the case of Ca-SWy2. The amount of metal (either zinc or lead) adsorbed onto both montmorillonites increases with the decrease in acetic acid/acetate concentration, due to the probable formation of zinc and lead acetate complexes in solution.

In addition to batch experiments, the two site protolysis model with no electrostatic term (2SPNE model) was used to fit the experimental data. In the case of zinc, the selectivity coefficients characterizing cation exchange and surface complexation reactions with Na- [23] or Ca-saturated montmorillonite [31] were incorporated in the code, as well as the thermodynamic constant of Zn-acetate formation. As the experimental data of Zn sorption were well fitted, this model was validated and used afterwards for lead. New selectivity coefficients have been determined for Pb adsorption onto Na-montmorillonite: first for cation exchange with log K c (Pb-Na) = 1.5, and then for surface complexation into the strong sites with log S K int = 1.5, and into the weak sites with log W K int = -0.5. Concerning the modelling of Pb(II) adsorption onto Ca-montmorillonite, the best fit was found for log K c (Pb-Ca) equal to 0.3. The surface complexation constants of Pb sorbing on the strong sites of Na-and Casaturated montmorillonites are well correlated with the corresponding hydrolysis constants, as Pb data verified the Linear Free Energy Relationship previously established by Bradbury and Baeyens [37].

For both Na-and Ca-saturated montmorillonites, zinc is mostly retained by cation exchange for high equilibrium zinc concentration, whereas surface complexation by the strong sites ≡S S OH is the main mechanism involved below 10 -4 M, which corresponds to zinc concentrations of the most biodegradable leachates in subsurface waste landfill. The main mechanisms involved in lead adsorption differ from Na-to Ca-saturated montmorillonites, and depend also on Pb equilibrium concentrations. In the range of the mean Pb concentrations in leachates (10 -7 to 10 -6 M), sorption occurs mainly on the strong sites. However, the retention of lead on the weak sites is dominant in the case of the maximum Pb concentration reported in leachates (2.4x10 -5 M), then cation exchange takes over for the highest Pb equilibrium concentrations (10 -2 M). This study shows that calcic montmorillonite and especially sodic montmorillonite have a good capacity to retain zinc as well as lead, which ensures the durability of the retention performances of the clayey barriers. However, leachates of waste landfill also contain organic molecules such as acetic acid and acetate which may inhibit the adsorption of heavy metals. It should be borne in mind that the biodegradable and acidic leachates produced during the first phase of waste decomposition may contribute to the main potential risk of pollution. ■: experimental data. Fig. 1a and 1b: the dotted line is obtained using the Bradbury and Baeyens model [23] with the fixed parameters: log K c (Zn-Na) = 0.59, log S K int (Zn) = 1.6 and log W K int (Zn) = -2.7. Fig. 1c and1d: the dotted line is obtained using the Bradbury and Baeyens model [31] with the fixed parameters: log K c (Zn-Ca) = 0, log S K int (Zn) = 1.2 and log W K int (Zn) = -2.9. Fig. 1a-b-c-d: the dash dotted lines are obtained by using the same model and by adding the potential formation of Zn acetate (log K c (Zn -acetate) = -6.5) or Pb acetate (log K c (Pb -acetate) = -5.5), with no fitted parameters. Fig. 1b: the continuous line is the best fit to the data, with the following fit parameters: log K c (Pb-Na) = 0.50, log S K int (Pb) = 1.5 and log W K int (Pb) = -0.5. Fig. 1d: the continuous line is the best fit to the data, with the following fit parameters: log K c (Pb-Ca) = 0.30, log S K int (Pb) = 1.2 and log W K int (Pb) = -0.5. □: experimental data. The continuous lines correspond to the fit with the selectivity coefficients for Zn-Na and Pb-Na equilibria on Na-SWy2, and Zn-Ca and Pb-Ca equilibria on Ca-SWy2 (Table 3). Zn sorption onto Na-SWy2. □: experimental data. The continuous line is calculated using the Bradbury and Baeyens model [23] with the fixed parameters (log K c (Zn-Na) = 0.59, log S K int (Zn) = 1.6 and log W K int (Zn) = -2.7), and by adding the potential formation of Zn acetate (log K c (Zn -acetate) = -6.5). Dotted line: cation exchange (CE-Zn); fine-dotted line: complexation in the strong sites (≡S S OZn + ); dash dotted line: complexation in the weak sites (≡S W OZn + ). (b) Zn sorption isotherm onto Ca-SWy2. □: experimental data. The continuous line is calculated using the Bradbury and Baeyens model [31] with the fixed parameters (log K c (Zn-Ca) = 0., log S K int (Zn) = 1.2 and log W K int (Zn) = -2.9), and by adding the potential formation of Zn acetate (log K c (Zn -acetate) = -6.5). Dotted line: cation exchange (CE-Zn); fine-dotted line: complexation in the strong sites (≡S S OZn + ); dash dotted line: complexation in the weak sites (≡S W OZn + ). Correlation of surface complexation constants of species sorbing on the strong sites of montmorillonite with the corresponding hydrolysis constants. Gray circles: Mn(II), Co(II), Cd(II), Ni(II), Zn(II); gray diamonds Eu(III), Am(III); gray squares: (Sn(IV), Th(IV); light gray triangles: Np(V); gray inverted triangles: U(VI) (from Bradbury and Baeyens [37]).

Figure captions

Black circles: Pb(II) on Na-SWy2 and on Ca-SWy2 (this study). Fig. 7 Correlation of surface complexation constants of species sorbing on the weak sites of montmorillonite with the corresponding hydrolysis constants. Gray circles: Ni(II), Zn(II); gray diamonds: Eu(III); and gray inverted triangles: U(VI) (from Bradbury and Baeyens [37]). Black circles: Pb(II) on Na-SWy2 and on Ca-SWy2 (this study). Table 3 Summary of reactions (cation exchange and surface complexation) and selectivity coefficients for Zn-Na and Pb-Na equilibria on Na-SWy2, and Zn-Ca and Pb-Ca equilibria on Ca-SWy2. a From Bradbury and Baeyens [23] b From Bradbury and Baeyens [31]

Na-SWy2

Fig. 1 Metal

 1 Fig.1

Fig. 2 Metal

 2 Fig.2

Fig. 3 FTIRFig. 4 Zn

 34 Fig.3

Fig. 5 Pb

 5 Fig. 5

Fig. 6

 6 Fig.6

Acknowledgements

The authors are grateful to Fabien Veillon for technical assistance. The two anonymous reviewers are gratefully acknowledged for their useful comments. The authors also express their gratitude to the French National Agency for Research (ANR) for the financial support.

This publication is a contribution to the ANR-07-JCJC-0013-01 (Metalclay) project allocated to L. Le Forestier.

of formation of metal complexes and thermodynamic properties of the metal ions or ligands.

Such dependencies are commonly termed linear free energy relationships (LFER). Bradbury and Baeyens [37] determined a linear correlation between the logarithms of surface complexation constants of some metals adsorbed on the strong sites (log S K x-1 ) of montmorillonite and their hydrolysis constants (log OH K x ): log S K x-1 = 8.1 ± 0.3 ± (0.90 ± 0.02) log OH K x Consequently, our thermodynamic data obtained for lead adsorption onto the strong sites of Na-SWy2 and Ca-SWy2 (black circles) were plotted on Fig. 6.

They are positioned very well on this correlation line. This indicates that the chemical bonding mechanisms of metal cations with the surface hydroxyl groups of montmorillonite and aqueous hydrolysis are similar. The same approach can be applied for the weak adsorption sites. Fig. 7 shows the linear correlation between surface complexation constants of species adsorbed on the weak sites of montmorillonite exchanged with various cations and the corresponding hydrolysis constants [37]: log w K x-1 = 6.2 ± 0.8 ± (0.98 ± 0.09) log OH K x


R Fodil

F Lellouche

J Mancebo

G Sbirlea-Apiou

D Isabey

L Brochard

Bruno Louis
email: bruno.louis@inserm.fr

COMPARISON OF PATIENT-VENTILATOR INTERFACES BASED ON THEIR COMPUTERIZED EFFECTIVE DEAD SPACE

Keywords: interfaces/masks, non-invasive ventilation, dead space

Purpose: Non-invasive ventilation is largely used to treat acute and chronic respiratory failure. This ventilation encounters a non negligible rate of failure related to the used interface/mask, but the reasons for this failure remain unclear. In order to shed light into this issue and to better understand the effects of the geometrical design of interfaces, we aimed to quantify flow, pressure and gas composition in terms of CO 2 and O 2 at the passage through different types of interface (oronasal mask, integral mask and helmet). Especially, we postulated that due to specific gas flow passing throughout interface, the effective dead space added by the interface is not always related to the whole gas volume included in the interface.

Methods: Numerical simulations, using computational fluid dynamics, were used to describe pressure, flow and gas composition during ventilation with the different interfaces.

Results: Between the different interfaces the effective dead spaces differed only modestly (110 to 370ml) while their internal volumes were markedly different (110 to 10000ml). It was limited to half the tidal volume for the most voluminous interface, while it was close to the interface gas volume for the less voluminous interfaces. Pressure variations induced by the flow ventilation throughout the interface were negligible.

Conclusions: Effective dead space is not related to the internal gas volume included in the interface, suggesting that this internal volume should not be considered as a limiting factor for their efficacy during non-invasive ventilation. Patient's comfort and synchrony have also to be taken into account.

INTRODUCTION

Non-invasive ventilation (NIV) defines a method of mechanical ventilation that does not require endotracheal intubation. Using this technique, pressurized gas is delivered to the airways through one of a variety of interfaces, such as a mouthpiece or a nasal or facial mask.

Over the last two decades, the use of NIV has increased markedly in the treatment of both acute and chronic respiratory failure [1,2]. In an acute setting, NIV reduces the risk of endotracheal intubation [3] and facilitates the weaning process from mechanical ventilation [4]. Nevertheless for various reasons, NIV is not always successful. The rate of failure for this procedure in acute patients ranges from 7% to 49% [2,[5][START_REF] Girault | Noninvasive mechanical ventilation in clinical practice: a 2-year experience in a medical intensive care unit[END_REF][START_REF] Robino | Effectiveness of non-invasive positive pressure ventilation differs between decompensated chronic restrictive and obstructive pulmonary disease patients[END_REF]. One of the reasons reported in the literature to explain this failure rate is the poor patient tolerance to the NIV interface [START_REF] Chiumello | Is the helmet different than the face mask in delivering noninvasive ventilation?[END_REF][START_REF] Cuvelier | Cephalic versus oronasal mask for noninvasive ventilation in acute hypercapnic respiratory failure[END_REF]. Mask discomfort, sensation of excessive air pressure, intolerance, skin lesions, leakage and rebreathing have been cited as the most relevant parameters to explain the interfacerelated failure of NIV. A large variety of interfaces are presently available ranging from the simple nasal or oronasal mask to the helmet recently proposed [START_REF] Antonelli | New treatment of acute hypoxemic respiratory failure: noninvasive pressure support ventilation delivered by helmet--a pilot controlled trial[END_REF][START_REF] Bellani | The use of helmets to deliver non-invasive continuous positive airway pressure in hypoxemic acute respiratory failure[END_REF]. To our knowledge, the efficacy of these different interfaces has essentially been tested in clinical trials or in bench studies based upon the comparison of clinical indexes such as breathing pattern, airway pressure, neuromuscular drive, inspiratory muscle effort, work of breathing (WOB), arterial blood gases and dyspnea [1,[START_REF] Cuvelier | Cephalic versus oronasal mask for noninvasive ventilation in acute hypercapnic respiratory failure[END_REF][START_REF] Chiumello | Noninvasive positive pressure ventilation delivered by helmet vs. standard face mask[END_REF][START_REF] Mortimore | Comparison of nose and face mask CPAP therapy for sleep apnoea[END_REF][START_REF] Navalesi | Physiologic evaluation of noninvasive mechanical ventilation delivered with three types of masks in patients with chronic hypercapnic respiratory failure[END_REF][START_REF] Pelosi | Non-invasive ventilation delivered by conventional interfaces and helmet in the emergency department[END_REF][14][15][START_REF] Vargas | Helmet with specific settings versus facemask for noninvasive ventilation[END_REF]. All these interfaces allow successful non-invasive ventilation. Especially, clinical efficacy was not found different during NIV conducted with interfaces whose volumes very much differed [1,[START_REF] Cuvelier | Cephalic versus oronasal mask for noninvasive ventilation in acute hypercapnic respiratory failure[END_REF][START_REF] Chiumello | Noninvasive positive pressure ventilation delivered by helmet vs. standard face mask[END_REF][START_REF] Vargas | Helmet with specific settings versus facemask for noninvasive ventilation[END_REF]. Only WOB and inspiratory muscle effort were slightly less decreased with the helmet, by comparison to the other interfaces [START_REF] Chiumello | Noninvasive positive pressure ventilation delivered by helmet vs. standard face mask[END_REF][START_REF] Vargas | Helmet with specific settings versus facemask for noninvasive ventilation[END_REF] but these differences were abolished by a specific ventilator setting [START_REF] Vargas | Helmet with specific settings versus facemask for noninvasive ventilation[END_REF]. In first view, this fact is surprising since some of these interfaces have a large internal volume associated with dead space that should not permit successful ventilation. In theory, the dead inserm-00595406, version 1 -24 May 2011 space should remain as small as possible because any increase of it, induces a raise in patient's WOB [START_REF] Lellouche | Effect of the humidification device on the work of breathing during noninvasive ventilation[END_REF].

We presently postulate that due to the streaming effects of the gas passing throughout the interface, the effective dead space of the interface could be quite different from the volume delimited by the interface and the part of the body embedded in this interface (called interface gas region). To test this assumption, we used numerical simulations with computational fluid dynamic (CFD) software to describe pressure, flow and gas composition in four types of interfaces regularly used to deliver NIV in the intensive care unit (ICU). In contrast with clinical trials, CFD presents the advantage to test this set of interfaces in strictly identical conditions. In a previous in vitro bench study, Saatci and al. [START_REF] Saatci | Dynamic dead space in face masks used with noninvasive ventilators: a lung model study[END_REF] estimated the interface dead space without flow or pressure measurements. However, these authors tested several face masks but not the helmet interface.

MATERIAL AND METHOD

We studied four interfaces commonly used in ICU (see Table 1 for interface characteristics): two oronasal face masks (masks #1 and #2), an integral mask (mask # 3) and a helmet-type interface which covers the entire head and neck (mask # 4). Each interface was successively positioned upon the same adult mannequin head made of polystyrene. Each setup, i.e., the mannequin-interface, was numerically reconstructed in three dimensions by using computed tomography (CT) images. In each three dimensional (3D) geometry, breathing flow was simulated for successive cycles (i.e. inspiratory + expiratory phases) by using CFD software (FLUENT Fluent Inc., Lebanon, TN, USA) until an "equilibrium state" was reached. The equilibrium state is defined as the moment where the parameters (i.e., pressure, flow and gas composition) become identical from one breathing cycle to the next breathing cycle. Details about 3D reconstruction and CFD procedure are described in the online inserm-00595406, version 1 -24 May 2011 electronic supplementary material (ESM). The inspiratory phase consisted of blowing a constant 600 ml/sec flow rate during 1.25 sec through the inlet of the interface. The expiratory phase consisted of blowing a constant 300 ml/sec flow rate during 2.5 sec through the mouth of the mannequin. This setting corresponds to a breathing pattern of 750 ml tidal volume (VT), 16 beats/min frequency and a ratio of 2 between inspiratory and expiratory times.

During the inspiratory phase, the insufflated gas called "fresh air" was normal air, fully humidified and heated at 37°C (Figure 1). During the expiratory phase, the gas blown in the interface, called in Figure 1 "exhaled air", was air enriched with CO 2 (see Table 2 for the exact compositions of fresh air and exhaled air). At the initial time of the first breathing cycle, the interface gas region was totally filled with fresh air. The CFD procedure allows estimating gas composition, flow and pressure at any locus of the interface gas region and at any time of the breathing cycle. Gas composition was described as the mass fraction of each gas species, especially for oxygen (MF O2 ) and carbon dioxide (MF CO2 ). Then, we determined the effective dead space (VD) of the interface gas region defined as the rebreathed gas volume resulting from the exhaled gas trapped in this interface gas region as well as the volume of fresh air (V fresh ) that are inhaled by the mannequin during each inspiratory cycle

The pressure in the interface is composed by a mean pressure (e.g. atmospheric pressure, pressure support, positive end-expiratory pressure) and by the variation of pressure induced by the flow. This variation of pressure, which is computed by the CFD procedure, does not depend on the mean pressure as long as the thermodynamical properties of gas are not affected by the mean pressure. Therefore, our results theoretically apply to the different pressure regimes or ventilator settings, constant or intermittent, used in clinical practice during NIV.

inserm-00595406, version 1 -24 May 2011

RESULTS

The equilibrium state was estimated from the time course of MF O2 at the mouth from one cycle to the following cycle. For the first 3 interfaces shown in Table 1, the equilibrium state was quickly reached: the MF O2 curves become identical after less than 6 breathing cycles. To reach the equilibrium state with the helmet took a little more time: approximately 2 minutes (i.e., after 32 breathing cycles).

During the inspiratory phase, MF O2 at the mouth of the mannequin globally increases with time, while MF CO2 decreases (see Figure 2). MF O2 represents the quantity of oxygen available for the lung at the equilibrium state while MF CO2 quantifies the amount of CO2 rebreathing. With the two oronasal masks (#1 and #2), that are the smaller, the MF O2 tended to reach the maximum theoretical value (22.2%, i.e., the oxygen concentration of the total fresh air) by the end of the inspiration time. By contrast, with the two other interfaces (#3 integral and #4 helmet), MF O2 at the mouth of the mannequin was never above 20% during the inspiratory cycle. The MF CO2 behaviour was to decrease throughout the inspiratory phase from its maximum value (7.2%) to zero (0%) for the two oronasal masks, and to remain always positive for the two other masks: 2.4% for integral mask and 3.2% for helmet, (see Figure 2).

The effective dead space characterizing the four interfaces varied from 110 ml to 370 ml (see Figure 3). The larger VD corresponds to the helmet, and represents only 4% of the volume of the interface gas region. In this case, the effective dead space increases linearly with time and inspired volume (see Figure 4). The smallest VD was obtained with the oronasal mask #1 which has the smallest interface gas volume, and the VD was about 100% of the interface gas volume (see Figure 3). For this oronasal mask #1, VD was attained within the first 0.35 sec of the inspiratory cycle, before following a plateau during the remaining of the cycle (see Figure 4). The two others masks i.e., oronasal mask #2 and integral mask, behaved inserm-00595406, version 1 -24 May 2011 intermediately. The VD profile (see Figure 3) of oronasal mask # 2 during the inspiration was close to that of oronasal mask # 1, with a VD reaching 93% of the interface gas volume. The integral mask behaviour was not far from that of helmet, with a VD equal to only 35% of the interface gas volume (see Figure 3). For all tested interfaces, the pressure field was found relatively homogeneous with a maximum pressure variation not exceeding 0.3 cm H 2 O.

DISCUSSION

The main finding of this study is that the effective dead space, which is never higher than the interface gas volume, can be much smaller due to the streaming effect presently calculated by CFD. For all the interfaces the effective dead space was under 370 ml for a tidal volume of 750 ml. This is of clinical interest because it suggests that even interfaces with extremely high internal volumes (10 liters) might yet be used in patients. This holds true to the extent that patients are capable to inhale an inspired gas slightly enriched with CO 2 (a maximum 2.1% of CO 2 in volume for the helmet). The finding that effective interface dead space is not linked to the interface gas volume is consistent with several clinical studies.

These studies have reported a lack of differences, in terms of patient's respiratory effort, breathing pattern and gas exchange, among interfaces with disparate internal volumes [1,[START_REF] Cuvelier | Cephalic versus oronasal mask for noninvasive ventilation in acute hypercapnic respiratory failure[END_REF]14,[START_REF] Vargas | Helmet with specific settings versus facemask for noninvasive ventilation[END_REF][START_REF] Tarrega | Acute physiologic effects of nasal and full-face masks during noninvasive positive-pressure ventilation in patients with acute exacerbations of chronic obstructive pulmonary disease[END_REF][START_REF] Gregoretti | Evaluation of patient skin breakdown and comfort with a new face mask for noninvasive ventilation: a multi-center study[END_REF]. Importantly, our results also show that with a tidal volume of 750 ml, the less voluminous mask (oronasal mask #1) clearly remains the most favorable in terms of rebreathing, since the VD is reduced by a factor of 3.4 when compared to the VD of the most voluminous masks (helmet) (Figure 3). Nevertheless, this beneficial effect decreases quasi linearly as tidal volume decreases (Figure 4). For example, with a tidal volume of 400 ml, the previous factor is as low as 1.8. This means that the choice of an interface based only on the inserm-00595406, version 1 -24 May 2011 effective VD, is probably questionable. Factors such as comfort, tolerance and leaks should also be taken into account during the decision-making process.

In the extreme case of tidal volumes below 200 ml, the most efficient interface in terms of re-breathing becomes the most voluminous (the helmet). Of course, such a small tidal volume does not fit standard adult ventilation. However, if we consider the non-invasive high-frequency oscillatory ventilation at low tidal volume, as recently proposed in neonatalogy [START_REF] Colaizy | Nasal high-frequency ventilation for premature infants[END_REF], our results suggest that a helmet interface could be potentially more effective than a nasal or oronasal interface due to the lower CO 2 rebreathing. It is not in disagreement with the fact that the helmet is not the interface of choice for NIV in COPD patients with acute exacerbation. Indeed, a 200 ml tidal volume is too low in breathing adult COPD patients to results in adequate alveolar ventilation. With these patients the required tidal volume is higher, i.e., in range where the helmet is the less efficient interface in terms of re-breathing.

The streaming effect behind effective dead space can be physically understood on the basis of the ratio between tidal volume and interface gas volume. When the interface gas volume is much larger than the tidal volume, the convective flows are reduced and the gas composition in the interface, i.e., the mass fraction of each gas species, is poorly affected by a single breathing cycle. The quasi-constancy of MF O2 and MF CO2 at the mouth in the helmet mask throughout the entire inspiratory phase illustrates this phenomenon (Figure 2). This assumption was already implicitly developed by Taccone et al. [15] who described the helmet functions as a semi-closed environment. Accordingly, the corresponding mass fraction becomes, at the equilibrium point, the mean between the mass fractions of fresh air and exhaled air and the VD is half the tidal volume, (e.g., VD = 49% of VT in the helmet). On the inserm-00595406, version 1 -24 May 2011 basis of a negligible convective flow it suggests that this result (VD  50% of VT) may be generalized to the other helmets.

By contrast, when the interface volume is small as compared to the tidal volume (oronasal mask #1 and #2), the convective flows are important. In this scenario, the recirculation velocities are relatively high and are also present in the quasi-totality of the interface gas region. In this case, the interface gas volume is washed out by the breathing flow (i.e., both the inhaled and the exhaled gas) and the dead space gets closer to the interface internal volume, (e.g., 100 % of the interface gas volume for the oronasal mask # 1 and 93 % for the oronasal mask #2). On this basis, we can predict that the "small" masks (oronasal) have a VD close to their internal volume.

With the integral mask, where the gas entry is at the level of the chin, the role of convection is intermediate and the tidal volume is close to the interface gas volume. In the first part of an inspiration, (i.e., for the first 0.35 sec, corresponding to about 200 ml of inspired gas), the inferior part of the mask (from the chin to the mouth) is rapidly washed out.

During this time, MF O2 and VD are close to the values observed with the 2 smallest masks (see oronasal masks #1 and #2 in Figure 2 and4). After this short period of time, MF O2 at the mouth reaches a plateau resulting from gas mixture made of the gas flow coming directly from the ventilator (fresh air) and partial entrainment of the gas residing between the mouth and forehead (see the video showing the time course of the MF O2 during the inspiration and expiration in the online ESM). The fact, that VD is impacted by both convective and diffusive phenomena, suggests that the results of our simulation cannot be generalized to the other integral mask to predict the VD. Changing geometry may change the balance between convective and diffusion phenomena that will result in a different VD.

Noteworthy, the physical streaming effects do not require important pressure variations in the interface gas region. It confirms that these interfaces are slightly resistive and inserm-00595406, version 1 -24 May 2011 are not responsible for a significant amount of resistive work. Chiumello et al. [START_REF] Chiumello | Noninvasive positive pressure ventilation delivered by helmet vs. standard face mask[END_REF] found that helmet induced an increase of WOB associated with an increase of the time to reach the pressure support without any increase of the tidal volume while Vargas et al. [START_REF] Vargas | Helmet with specific settings versus facemask for noninvasive ventilation[END_REF] found that using a specific settings (increase of the pressure support and PEEP with the highest pressurization rate) allowed to abolish this greater inspiratory muscle effort. It suggests that this increased WOB observed with the helmet is explained in part by trigger and pressurization difficulties and not only to a large dead space problem. Such assumption is in agreement with the relative low value of VD that we obtained.

The present findings can be partially extended to clinically-relevant changes in oxygen and carbon dioxide concentrations. In this study we used normal air, heated and humidified, as inspiratory gas and we used air enriched with 5% of CO 2 as the expired gas. Oxygentherapy as well as O 2 -CO 2 exchange within the lung modify gas composition. As long as physical and thermodynamic properties of the gas are not affected by gas composition and/or temperature, the effective dead space inferred in this study remains unchanged. This means that if convective and diffusive phenomena are unchanged, the effective dead space is also unchanged. Considering the slight modification in thermodynamic properties of the gas (less than 10% for gas density and less than 4% for gas kinematic viscosity) induced by either a variation of O 2 concentration (from 15% to 100%) or a variation of CO 2 concentration (from 0 to 5%), we can postulate that our results remain valid whatever the oxygen-therapy level administered. Note that, a change in O 2 concentration in the fresh air only requires changing the maximal and minimal values corresponding to fresh and exhaled air, in the scales of One of the limitations of this study was that the numerical tool did not allow us to simulate non-intentional leak. Nevertheless, it is clear that a bias-flow leak tends to decrease inserm-00595406, version 1 -24 May 2011 the rebreathing problem, but it also tends to induce auto-triggering and to decrease the effective tidal volume inspired by the patient [START_REF] Fauroux | Performance of ventilators for noninvasive positive-pressure ventilation in children[END_REF][START_REF] Louis | Effect of manufacturers inserted mask leaks on ventilator performance[END_REF]. However, the importance of these phenomena is extremely contingent upon a set of conditions as ventilator mode, trigger algorithms or maximum flow deliverable by the ventilator. Another limitation of this study is that we implicitly assumed the rigidity of the wall interface. This assumption is particularly questionable with the helmet. However, a recent study [START_REF] Vargas | Helmet with specific settings versus facemask for noninvasive ventilation[END_REF] concluded that increasing both pressure-support level and positive end-expiratory pressure may be clinically advisable when providing NIV via a helmet. Such a higher pressurization, that reduces the compliance of the helmet, tends to justify our rigidity assumption.

In summary, we have shown that mathematical modelling and computational fluid dynamics can estimate the effective dead space of NIV interfaces by analysing the pressure field/flow pattern and variations in gas composition inside these interfaces. New research efforts will be dedicated in the future to the translation of these mathematical modelling to clinical environments so as to increase efficiency while decreasing the side-effects of the clinical treatments. The effective dead space of the interfaces used for NIV was not directly related to the internal volume of the interface. For the most voluminous interfaces, effective dead space is limited to half the tidal volume while the effective dead space is close to the interface gas volume only for the less voluminous interfaces. These findings allow physicians to choose among a large number of masks which may be suitable for an individual patient and also allow physicians to take into consideration other parameters such as comfort and synchrony when choosing an interface. Effective dead space volume, volume of inspired fresh air and interface gas volume for the four masks presented in Table 1. These data are given once the equilibrium state is reached between two successive cycles. In addition, a no-slip condition was assumed at the inner walls. Inspiratory and expiratory flow cycles were simulated using constant flow rates with a temporal step of 0.025 sec.

inserm-00595406, version 1 -24 May 2011

LEGEND OF FIGURES

Set-up of CFD problem: 3D numerical model. Inspiratory and expiratory airflows were generated in the 3D mesh model. Governing equations for momentum and mass conservation were solved by a commercial CFD software package, FLUENT (Fluent Inc., Lebanon, TN, USA), using a control-volume based method. The solution algorithm used was a segregated solver. The governing equations were made linear with an implicit method. The local mass fraction of each gas species (O 2 -CO 2 ) at a given time was predicted through the solution of a inserm-00595406, version 1 -24 May 2011 convection-diffusion equation included in the FLUENT software. A uniform velocity profile was used as a boundary condition at the inlet of the mesh model. The CFD software package, FLUENT (Fluent Inc., Lebanon, TN, USA), is a commercial software. It is extensively used in industry and academic fields. Our team used this software for several years. In previous studies we validated our use of this software measuring pressure drop and flow in nasal airway and human proximal airway tree [4,5].

CFD Postprocessing: effective dead space

The CFD procedure allows estimating gas composition, flow and pressure at any locus of the interface gas region and at any time of the breathing cycle. Especially, gas composition at the mouth of the mannequin, allows determining the effective dead space (VD) of the interface gas region defined as the rebreathed gas volume resulting from the exhaled gas trapped in this interface gas region. Gas composition was described from CFD estimation of the mass fraction of each gas species, especially for oxygen (MF O2 ) and carbon dioxide (MF CO2 ). The knowledge of the mean MF O2 at the mouth of the mannequin (calculated via CFD as shown in the online ESM), allows to estimate the inspired volume of oxygen (V O2 ):

V V vF V vF V vF V V vF vF V V V V V V                 

Figure 2 .

 2 Figure 2.

Figure 1 Schematic 2

 12 Figure 1

Figure 3

 3 Figure 3

Figure 4 Evolution

 4 Figure 4

Figure1Figure2Figure 3

 3 Figure1

  t 2 are the beginning and the end of the inspiratory time respectively,  air and  O2 the density of air and oxygen respectively and, V is the flow rate.V O2 allowed to estimate the volume of fresh air (V fresh ) and the VD that are inhaled by the mannequin during each inspiratory cycle:

  inserm-00595406, version 1 -24 May 2011

  Figure 1

Table 1

 1 Non invasive ventilation interfaces

		Mask	Name / Compagny		Mask type		Interface volume (ml)
		# 1	Airvie / Peters		oronasal		111
		# 2	Full Face / Koo		oronasal		205
		# 3	Inspir'aid / Fernez-Bacou		integral mask	978
		# 4	Castor-R / Starmed		helmet		10220
			Non invasive ventilation interfaces. The interface volume is the internal volume of
		each interface estimated in presence of the mannequin head.
	inserm-00595406, version 1 -24 May 2011	Table 2 Gas compositions Inspiratory flow (fresh air) Mass Fraction (%) Volume Fraction (%) Expiratory flow (exhaled air) Mass Fraction (%) Volume Fraction (%)	N 2 72.5 73.3 71.1 73.3	O 2 22.2 19.7 16.6 15.0	Ar 1.2 0.9 1.2 0.9	CO 2 0.0 0.0 7.2 4.7	H 2 O 3.9 6.2 3.9 6.2

COMPARISON OF PATIENT-VENTILATOR INTERFACES BASED ON THEIR COMPUTERIZED EFFECTIVE DEAD SPACE

R. Fodil 1,2 , F. Lellouche 3 , J. Mancebo 4 , G. Sbirlea-Apiou 1,2 , D. Isabey 1,2 , L. Brochard 1,2,5 , B. Louis 1,2

(1) Inserm Unite U955, Cell and Respiratory Biomechanics Group, Créteil, F-94010, France ; (2) Université Paris-Est, Faculté de Médecine, UMR_S955, Créteil, F-94010, France ; (3) Université Laval, Centre de Recherche de l'Institut Universitaire de Cardiologie et de Pneumologie de Québec, G1V4G5 Québec, QC, Canada ; (4) Servei Medicina Intensiva, Hospital Sant Pau, Barcelona, Spain (5)

THREE-DIMENSIONAL SURFACE RECONSTRUCTION AND SET-UP OF A COMPUTATIONAL FLUID DYNAMICS (CFD) PROBLEM

Data acquisition and three-dimensional (3 D) surface reconstruction: The 3D computational geometry used for this numerical study was derived from computed tomography (CT) scan images, except in the case of the helmet type where the interface was reconstructed using a 3D modeller (3ds Max, Autodesk, Inc., CA, USA). The same mannequin head was used to delimitate the internal volume of each interface. Scans provided contiguous axial images which were 0.5mm apart. The stack of CT images in DICOM format was imported into a commercial software package: AMIRA  (VisageImaging, Richmond, Australia) for segmentation. Segmentation assigns a label to each pixel of the image, defining whether the pixel is in a solid or in an air region of the interface. Segmentation is a prerequisite for 3D-surface model generation. We used AMIRA software to successively construct, for each interface, a triangular surface and a volumetric tetrahedral grid of the segmented object (see Figure 1).

Set-up of CFD problem: Mesh model. This original mesh, Amira normal mesh (A-NM), was used in a preliminary airflow simulation. The result was used to adapt the mesh via the CFD software to resolve large pressure gradients in the flow field. The quality of the resulting mesh (F-AM) was estimated by the triangle aspect ratio (< 10) and tetra aspect ratio (< 10), as usually reported in the literature [1]. To eliminate artifacts due to the boundary conditions, we added two further elements to each model. The first was a virtual cylindrical tube of 15 cm in length and a diameter equal to the inlet interface ( 1.9 cm). This was situated at the junction between the interface and the ventilator circuit. The second element was a virtual elliptical duct (3.6 cm in length, a 2 cm major axis and a 1 cm minor axis) at the inserm-00595406, version 1 -24 May 2011

where vF O2fresh and vF O2exhaled are the volume fraction of oxygen of fresh air (heated and humidified) and exhaled air (which contains CO 2 ) respectively and, VT is the tidal volume.