Marie Simonin

Jean M F Martins
email: jean.martins@univ-grenoble-alpes.fr

Gaëlle Uzu

Lorenzo Spadini

Aline Navel

Agnès Richaume

Low mobility of CuO and TiO2 nanoparticles in agricultural soils of contrasting texture and organic matter content

Keywords: Contrasted soils, Nanomaterials, Transfer, Dissolved organic carbon, CDE modelling, Nanoparticles' fate. Highlights

The fate of nanoparticles (NPs) in soil under relevant environmental conditions is still poorly understood. In this study, the mobility of two metal-oxide nanoparticles (CuO and TiO2) in contrasting agricultural soils was investigated in water-saturated soil columns. The transport of TiO2 and CuO-NPs were assessed in six soils with three different textures (from sand to clay) and two contrasted organic matter (OM) contents for each texture. TiO2 mobility was very low in all soils, regardless of texture and OM content. Mass recoveries were always less than 5%, probably in relation with the strong homo-aggregation of TiO2-NPs observed in all soil solutions, with apparent sizes 3-6 times larger than their nominal size. This low mobility suggests that TiO2-NPs present a low risk of direct groundwater contamination in contrasted surface soils. Although their retention was also generally high (more than 86%), CuO nanoparticles were found to be mobile in all soils. This is probably related to their smaller apparent size and low capacity of homo-aggregation of CuO-NPs in all soil solutions. No clear influence of neither soil texture or soil total organic matter content could be observed on CuO transport. However, this study shows that in contrasted agricultural soils, CuO-NPs transport is mainly controlled by the solutes dissolved in soil solution (DOC and PO4 species), rather than by the properties of the soil solid phase.

Introduction

Metal oxide engineered nanoparticles (NPs) are now integral elements of a myriad of consumer and industrial products. Copper oxide (CuO) NPs are widely used in catalysts, superconductors or paints for their biocidal properties [START_REF] Zhu | Highly dispersed CuO nanoparticles prepared by a novel quickprecipitation method[END_REF][START_REF] Ren | Characterisation of copper oxide nanoparticles for antimicrobial applications[END_REF][START_REF] Keller | Global life cycle releases of engineered nanomaterials[END_REF].

Titanium dioxide (TiO2) NPs are commonly incorporated in personal care products, paints or food packaging [START_REF] Keller | Global life cycle releases of engineered nanomaterials[END_REF]. As a result, soils are exposed to these components through various exposure routes, which may result in potential risks to human and ecosystems health.

Their release into soils can occur during industrial production, landfills, agricultural amendments of sewage sludge, abrasion of materials and accidental spill [START_REF] Nowack | Potential scenarios for nanomaterial release and subsequent alteration in the environment[END_REF].

Thus, there appears to be an urgent need to improve our current knowledge of the fate and transport of NPs in soils in order to better assess the risks for groundwater and agricultural soils.

Transport of NPs has been extensively investigated in poorly-reactive and well-defined porous media, such as glass beads or quartz sand, but only a few investigations have addressed the transport of metallic NPs in natural soils (e.g. [START_REF] Fang | Stability of titania nanoparticles in soil suspensions and transport in saturated homogeneous soil columns[END_REF][START_REF] Fang | Transport of copper as affected by titania nanoparticles in soil columns[END_REF][START_REF] Cornelis | Transport of silver nanoparticles in saturated columns of natural soils[END_REF][START_REF] Braun | Transport and deposition of stabilized engineered silver nanoparticles in water saturated loamy sand and silty loam[END_REF][START_REF] Simonin | Combined Study of Titanium Dioxide Nanoparticle Transport and Toxicity on Microbial Nitrifying Communities under Single and Repeated Exposures in Soil Columns[END_REF]. Soils are porous systems consisting of complex structured assemblages of mineral and organic particles combined with liquid and gaseous phases [START_REF] Spadini | Soil aggregates: a scale to investigate the densities of metal and proton reactive sites of organic matter and clay phases in soil[END_REF]. Several soil components such as clay and organic matter (OM) are known to influence the mobility of various pollutants or colloids due to their large reactive surfaces, which can interact with them, thus modifying their physicochemical behavior [START_REF] Pan | Applications and implications of manufactured nanoparticles in soils: a review[END_REF]. Some studies have demonstrated the influence of these factors on the aggregation, surface charge and stability of NPs [START_REF] Fang | Stability of titania nanoparticles in soil suspensions and transport in saturated homogeneous soil columns[END_REF][START_REF] Thio | Influence of natural organic matter on the aggregation and deposition of titanium dioxide nanoparticles[END_REF][START_REF] Zhou | Clay Particles Destabilize Engineered Nanoparticles in Aqueous Environments[END_REF]. Dissolved OM is known to promote NPs dispersion and potentially their mobility in simple porous media [START_REF] Ben-Moshe | Transport of metal oxide nanoparticles in saturated porous media[END_REF][START_REF] Thio | Influence of natural organic matter on the aggregation and deposition of titanium dioxide nanoparticles[END_REF][START_REF] Simonin | Influence of soil properties on the toxicity of TiO2 nanoparticles on carbon mineralization and bacterial abundance[END_REF], while clay particles can destabilize positively and negatively charged NPs and thus decrease their mobility [START_REF] Zhou | Clay Particles Destabilize Engineered Nanoparticles in Aqueous Environments[END_REF]. In addition, these processes are strongly influenced by the chemistry of soil solution, such as pH, ionic strength and electrolytes such as inorganic ions [START_REF] Wang | Transport of titanium dioxide nanoparticles in saturated porous media under various solution chemistry conditions[END_REF][START_REF] Cornelis | Fate and Bioavailability of Engineered Nanoparticles in Soils: A Review[END_REF][START_REF] Vitorge | Comparison of three labeled silica nanoparticles used as tracers in transport experiments in porous media. Part I: Syntheses and characterizations[END_REF]. [START_REF] Fang | Transport of copper as affected by titania nanoparticles in soil columns[END_REF] demonstrated that TiO2-NPs could act as a metal carrier and facilitate for instance the mobilization of metals, such as copper, in soil. These results raise concerns about the potential environmental risk associated with increased migration rates of co-contaminants and increased bioavailability of some toxic metals in the presence of NPs [START_REF] Chekli | Evaluating the mobility of polymer-stabilised zero-valent iron nanoparticles and their potential to co-transport contaminants in intact soil cores[END_REF][START_REF] Fang | Co-transport of Pb2 + and TiO2 nanoparticles in repacked homogeneous soil columns under saturation condition: Effect of ionic strength and fulvic acid[END_REF]. Because of the interactions between these multiple environmental factors in natural soils, it is difficult to predict the fate of NPs in soil based on investigations conducted in simple and poorly reactive porous media. In particular, it remains very difficult to hierarchize the dominant factors controlling the transfer of manufactured nanoparticles in natural soils, since most of these factors are closely related in such media. Studies evaluating the simultaneous effects of several soil factors on NPs mobility are clearly needed to elucidate the key soil properties that control NPs transport.

The objective of this study is to determine the influence of soil texture and OM content on the transport of two relevant manufactured nanoparticles, CuO-NPs and TiO2-NPs in contrasted soils. We conducted water-saturated column experiments with six agricultural soils with contrasted physicochemical properties. For this, we implemented 3 different soil textures: from sandy to clayey soils, and two OM contents for each soil texture. The measured NP breakthrough curves were fitted with the Convection Dispersion Equation (CDE) to identify the dominant processes involved in the transfer of these two NPs in the soils and to quantify the corresponding parameters.

Material and methods

Soils

This study was conducted with soils belonging to three different textural classes: sandy-loam, loam and silty-clay. Soils were collected from the upper 20 cm layer of three different agricultural sites located in the Rhône-Alpes and Burgundy regions of France (see [START_REF] Simonin | Influence of soil properties on the toxicity of TiO2 nanoparticles on carbon mineralization and bacterial abundance[END_REF] for further details). At each site, the sampling was performed in two plots with low and high OM contents distant of less than 500 m. Therefore, the experiments were performed with six test soils with three different textures and two different OM contents for each texture.

After collection, visible rocks, roots and plant litter of poor reactivity were manually removed.

The soils were sieved (2 mm) and homogenized before storage at 4°C. These soils were previously characterized [START_REF] Simonin | Influence of soil properties on the toxicity of TiO2 nanoparticles on carbon mineralization and bacterial abundance[END_REF] and some soil physicochemical properties are presented in Table 1.

Soil solutions from the six soils were prepared following the protocol described by [START_REF] Simonin | Influence of soil properties on the toxicity of TiO2 nanoparticles on carbon mineralization and bacterial abundance[END_REF] and used as background leaching solutions in the column breakthrough experiments.

Briefly, soil solutions were prepared by agitating 10 g of fresh soil dispersed in 50 mL of ultrapure water during 30 minutes at 180 rpm and 20°C in a refrigerated incubator shaker (New Brunswick -Eppendorf, Hamburg, Germany). The solutions were then centrifuged for 20 min at 8000 g, 20°C (Centrifuge 5804R, Eppendorf, Hamburg, Germany) to eliminate particles larger than 20 nm according to the Stokes' law. The supernatants were collected and stored at 4°C before characterization (Table 2) and used for NPs suspensions preparation (dispersion by vortexing the suspension 2 min. at maximum speed) and application in column experiments. In these soil solutions, orthophosphate concentrations were determined by Ion chromatography (Metrohm 732/733 separation center).

Nanoparticles

TiO2-NPs were provided in powder form by Sigma Aldrich (St Louis, USA) with crystal structure of anatase (80%) and rutile (20%) and 99.5% purity. These TiO2-NPs presented a specific surface area of 35-65 m² g -1 and a mean particle size of 21 nm as assessed by Transmission Electron Microscopy. CuO-NPs were also purchased from Sigma Aldrich in powder form with a nominal size around 50 nm and a specific surface area of 23 m² g -1 , according to the manufacturer's information. Both NPs were used as bare NPs without any coating and were characterized for intrinsic primary particle size using a ZEISS Ultra 55 scanning electron microscopy -field emission gun (SEM-FEG). In average, TiO2-NPs measured 28.7 ± 7.1 nm and CuO-NPs measured 57.0 ± 18 nm.

The apparent hydrodynamic diameter and zeta potential of the NPs were characterized using Dynamic Light Scattering (DLS) with a NanoZS (Malvern) directly in the soil solutions.

The measurements were performed in triplicate after dispersion through ultrasonication for 5 min in the spiking suspensions of NPs prepared at 50 mg L -1 in soil solutions.

Column experiments

The soil solutions were used as background leaching solutions for the duplicated column experiments. Spiking suspensions of NPs at 50 mg L -1 were prepared and injected in columns only after ultrasonication for 5 min. This NPs concentration is in the lower range of concentrations found in literature for similar transport studies in natural soils (e.g. [START_REF] Cornelis | Fate and Bioavailability of Engineered Nanoparticles in Soils: A Review[END_REF]. The transport experiments were performed in small glass columns (C10/10, GE Healthcare) of 1 cm in diameter and 10 cm long, homogeneously packed with 8 cm of wet soil as described by Martins and Mermoud (1999), corresponding to approximately 8 g of dry soil.

Flow adaptors (AC 10, GE Healthcare) were adjusted on the top of the columns to ensure a constant soil height during experiments. Soil bulk density values are presented in Table 3, along with the values of porosity and volume of pore water. At the beginning of the experiments, soil columns were saturated and leached from bottom to top with 100 mL of freshly prepared soil solution. The effluents were collected using a fraction collector (Gilson 203A) to check for the turbidity of the outflow by measuring the absorbance at 600 nm (Spectrometer Biowave II, Biochrom WPA). The absorbance was very low for all soils (< 0.02), indicating that the amount of soil colloids in the effluents was negligible. Bromide (Br) ion was used as water tracer to assess the hydrodynamic properties of the soils before NPs injection. About two pore volumes of bromide tracer (KBr 1 g L -1 also prepared in soil solution) were injected in each soil column and followed by 2 pore volumes injection of bromide-free soil solution. The concentrations of Br -in the soil column effluents were measured by Ion chromatography (Metrohm 732/733 separation center) with a detection limit of 4 µg L -1 .

The spiking suspensions of NPs (TiO2 or CuO) prepared at 50 mg L -1 (C0) in soil solution were injected in the columns at a flow rate of 0.1 mL min -1 during around 4 to 6 pore volumes. After NPs spiking, the columns were continuously leached with soil solution for at least 15 pore volumes. The column effluents were sampled in 15 mL centrifuge tubes every 10 minutes (~1 mL collected). Total concentrations of titanium (Ti) or copper (Cu) were measured in the spiking suspensions (C0) and in the effluents (C). The breakthrough curves of NPs are presented in a dimensionless form: C/Co as a function of V/Vo, the dimensionless eluted volume, with V normalized by Vo, the total pore water volume in the saturated column. All column experiments were performed in duplicate.

Metal concentration analyses were performed using microwave-assisted (Novawave, SCP Science) strong acid extraction (for Ti: hydrofluoric acid + nitric acid and for Cu: aqua regia).

Cu and Ti concentrations were determined using inductively coupled plasma optical emission spectrophotometer (ICP-OES; Varian 700-ES, Varian Inc. Scientific Instruments, Palo Alto, USA). With this methodology, Ti and Cu concentrations measured in a certified soil reference material (sandy loam 10, RTC-CRM027, lot HC027, Sigma-Aldrich) were in good agreement with certified values (95-102%). The detection limit was 50 µg L -1 for both Cu and Ti measurements. For each soil, breakthrough experiments were performed in control columns by injecting only soil solutions without NPs to determine the background concentration of Ti and Cu in the effluents. This background concentration was then subtracted from the measured concentrations of Ti and Cu in the effluents. The main characteristics of the soil columns are provided in Table 3.

Determining concentration profiles of Ti and Cu along the soil columns after NPs breakthrough was an important objective of the work. However, the soils used contain naturally relatively high background concentrations of Ti and Cu (measured at 2400-5300 mg kg -1 and 10-26 mg kg -1 , respectively, Table 1). For Ti, the injected amount of ~ 175 µg by soil column represents about 0.3-0.7% of the natural background Ti concentration present in the column. For Cu, the same injected quantity is close to the soil Cu background concentration. Consequently, as already reported [START_REF] Nickel | Mobility of coated and uncoated TiO 2 nanomaterials in soil columns-Applicability of the tests methods of OECD TG 312 and 106 for nanomaterials[END_REF] who used concentrations several orders of magnitude higher than in this study (5 g/L), due to solid Ti and Cu contents in these and in other soils, it is not possible to quantify the metals sorbed from the spiking solution, when using environmentally relevant NP concentrations, at least without specific NPs labeling (Vitorge et al. 2013), which was indeed not the case in this work.

To evaluate the occurrence of CuO dissolution in spiking suspensions during each column experiment, a dissolution test was performed. The six NPs spiking suspensions (one for each soil) were prepared and sampled (5 mL) after 6 hours corresponding to the maximum duration of the NPs column transport experiments. Dissolved Cu concentration in samples were determined by ICP-OES (Varian 700-ES) after centrifugation for 20 min at 6000 g in a 5 kDa ultrafiltration device (Vivaspin tube, Sartorius). Soil solutions without CuO-NPs were used as controls. The dissolution of TiO2-NPs in spiking suspensions was not assessed because these NPs are not soluble in water [START_REF] Chen | Titanium Dioxide Nanomaterials: Synthesis, Properties, Modifications, and Applications[END_REF][START_REF] Duester | Translocation of Sb and Ti in an undisturbed floodplain soil after application of Sb2O3 and TiO2 nanoparticles to the surface[END_REF].

Transport parameters estimation

The CXTFIT code implemented in the STANMOD software (USDA) [START_REF] Toride | The CXTFIT code for estimating transport parameters from laboratory and field tracer experiments[END_REF] was used to fit the tracer and NPs breakthrough curves. The pore water velocity (v, cm h -1 ) and dispersion (D, cm 2 s -1 ) in the NPs transport simulations were determined from the bromide tracer breakthrough curves obtained in the same soil. The analytic solution of the Convection Dispersion Equation (CDE) with a first-order loss term, µ, presented in Eq.1 was fitted to the bromide and NPs breakthrough curves using the Levenberg Maquardt algorithm (e.g. Martins and Mermoud 1999 ;[START_REF] Martins | Role of macropore flow in the transport of Escherichia coli cells in undisturbed cores of a brown leached soil[END_REF][START_REF] Vitorge | Size-and concentration-dependent deposition of fluorescent silica colloids in saturated sand columns: transport experiments and modeling[END_REF][START_REF] Lakshmanan | Nanoparticle transport in saturated porous medium using magnetic resonance imaging[END_REF].

𝑅 = 𝐷 -𝑣 -μC

Eq.1

where C is the NPs or tracer concentration, R is the retardation factor (dimensionless) of NPs (ratio of NPs and tracer residence times in soil columns), t is time, z is the distance from the inlet, v is the average pore water velocity calculated by dividing the water flow by the column section and the soil volumetric water content, D is the soil dispersion coefficient and µ is the NPs decay coefficient, related to their irreversible retention on solid collectors (soil constituents). For bromide experiments, only v, R and D parameters were calculated. For NPs experiments the parameters v, R, D and µ were calculated for the fitting of the breakthrough curves, using the values determined for the tracer as initial fitting values.

Characterization of soil organic matter by infrared spectroscopy

To evaluate the differences in organic matter quality between the 6 soils in relation to soil interactions with CuO-NPs, both soils samples and soils solutions were analyzed by MIR-ATR spectroscopy. Prior to infrared soil spectra acquisition, the six soil samples were prepared as follows: soils were air-dried for 10 days after dry sieving at 2 mm. The fine soil fraction was then finely ground (0.25 mm) using an ultra-centrifugal mill (ZM 200, Retsch) and further dried over-night at 40 °C without altering soil organic matter. MIR measurements were performed using Fourier-transform diamond attenuated total reflectance (MIR-ATR) on ca. 50 mg aliquots with an iS10 spectrometer (Thermo Scientific). MIR-ATR spectra were obtained after correction for interferences by H2O and CO2, by averaging 16 scans per sample at a 4 cm -1 resolution over the spectral range [4000-400 cm -1 ]. MIR-ATR measurements of the six soil solutions were performed using Fourier-transform diffuse reflectance on 50µL (1 drop) with the same equipment from Thermo Scientific. Deionized water was used as background solution.

The ATR spectrum of water was automatically deduced from the samples spectra for normalization.

Statistical analysis

The results of NPs hydrodynamic diameter, zeta potential and dissolution in soil solutions are presented as means (± standard errors) of 3 replicates. The influence of soil texture and OM content on NPs hydrodynamic diameter and zeta potential was investigated with a two-way Anova using the R software.

Results and discussion

Physicochemical properties of nanoparticles in soil solutions

Apparent size

CuO and TiO2-NPs were characterized in the six soil solutions used for preparing the spiking suspensions in the transport experiments (Figure 1). The values of hydrodynamic diameter of TiO2-NPs ranged from 73.9 to 128.1 nm, which is 2.7 to 4.6 times their intrinsic size of 28.7 ± 7.1 nm measured by SEM.

The content of solid OM in soil appears to only weakly affect the hydrodynamic parameters of NPs (Figure 1A): A marked difference is noted only for the Silty-Clay soil (Figure 1A). The difference relates probably more to the contrasted DOC and Ca content in these two soils (Table 2). DOC is known to facilitate colloids dispersion and stabilization [START_REF] French | Influence of Ionic Strength, pH, and Cation Valence on Aggregation Kinetics of Titanium Dioxide Nanoparticles[END_REF] 1B). These results evidence that CuO-NPs are less aggregated than TiO2-NPs in all soil solutions, except in that of the loam soil with high OM (Figure 1B). The point of zero net proton charge (PZNPC) of Rutile and Anatase is 5.3 and 5.4

( Machesky et al., 1994;Kosmulski, 2002), so TiO2-NPs are negatively charged at circumneutral pH in pure water [START_REF] Simonin | Influence of soil properties on the toxicity of TiO2 nanoparticles on carbon mineralization and bacterial abundance[END_REF]. On the other hand, the PZNPC of native CuO-NPs is equal to 10, they are therefore positively charged in pure water at circumneutral pH. Supposedly the association of the CuO NP's with soil DOM decreases their charge down to negative values, favoring their stabilization. Such a charge inversion effect was observed for CuO NP -humic acid suspensions [START_REF] Sousa | Aggregation kinetics and surface charge of CuO nanoparticles: the influence of pH, ionic strength and humic acids[END_REF]. Possibly, this charge relationship explains the observed higher stability of CuO NPs versus TiO2-NPs.

Zeta potential

Both TiO2 and CuO-NPs presented negative zeta potentials in all soil solutions (Figure 1C and 1D). The zeta potential of TiO2-NPs ranged from -23.9 to -15.5 mV whereas that of the CuO-NPs ranged between -20.8 nm and -13.8 mV. For CuO-NPs in contact with Aldrich humic acids, similar negative zeta potentials were observed at similar pH and ionic strength [START_REF] Sousa | Aggregation kinetics and surface charge of CuO nanoparticles: the influence of pH, ionic strength and humic acids[END_REF]. This comparison suggests that dissolved OM and Aldrich humic acids have similar effects on NPs zeta potential. This result is conceptually in agreement with recent findings, which show that humic acids are constituted as loosely bound molecules of relatively small size, which compare to DOM in terms of composition and acid-base reactivity and consequently charge density [START_REF] Hruška | Is a universal model of organic acidity possible: Comparison of the acid/base properties of dissolved organic carbon in the boreal and temperate zones[END_REF][START_REF] Sutton | Molecular structure in soil humic substances: the new view[END_REF][START_REF] Causse | Xanthan exopolysaccharide: Acid-base reactivity related to structure and conformation. A model for understanding the reactivity of degraded and colloidal soil organic matter[END_REF].

The zeta potential of CuO-NPs in soil solutions with high OM content were consistently more negative than in solutions of low OM content, while the observation is reverse for TiO2-NPs.

This surprising behavior is probably related to the high affinity of Cu for OM [START_REF] Jacobson | Electron Microprobe and Synchrotron X-ray Fluorescence Mapping of the Heterogeneous Distribution of Copper in High-Copper Vineyard Soils[END_REF][START_REF] Morel | Speciation study in the sulfamethoxazole-copper-pH-soil system: Implications for retention prediction[END_REF][START_REF] Navel | Effect of long term organic amendments and vegetation of vineyard soils on the microscale distribution and biogeochemistry of copper[END_REF], which can result in a greater OM coating effect on CuO-NPs compared to TiO2-NPs and consequently decreased surface charge and zeta potential. Such effects are known to possibly lead to variable NPs surface charge in distinct soils [START_REF] Simonin | Influence of soil properties on the toxicity of TiO2 nanoparticles on carbon mineralization and bacterial abundance[END_REF].

Hydrodynamic properties of the soils

The hydrodynamic properties of the six soils were determined by fitting the breakthrough curves of the water tracer, the bromide ion, with the CXTFIT code (Figure 2A). The corresponding transport parameters are presented in Table 4 with those adjusted for the CuO-NPs and TiO2-NPs. All bromide breakthrough curves presented mass recoveries close to 100%, as expected with an inert water tracer. Retardation factors (R) of bromide were all close to 1, except that calculated in the silty-clay-high OM soil. In this soil, R was 0.81, which indicates that some of the pore water was not traced by the water tracer, probably in relation with the high clay content of this soil and/or ionic exclusion or poorly accessible immobile water (Monrozier et al. 1993). Dispersion values (D) fitted to the breakthrough curves are quite low (below 10 -7 cm 2 s -1 ) and almost similar for all soils. These parameter values were used as initial D values in CXTFIT to fit the breakthrough curves of the NPs in the corresponding soils.

Transport of TiO2-NPs in soil columns

The mobility of TiO2-NPs was found to be very low in all soils, with mass recoveries ranging between 1.9 and 5.5% (Table 4). These NPs breakthrough curves measured in the six soils were very noisy, indicating that the measured Ti concentrations were in the range of Ti background concentration in the leachates (Figure 2B). Consequently, transport modelling was not possible for the TiO2-NPs breakthrough curves. In all soils the irreversible retention of TiO2-NPs was higher than CuO-NPs. This strong retention probably relates to the observed higher homoaggregation of TiO2-NPs in soil solutions, which increased the apparent NPs' size by a factor of 2.5 to 4.5 (Figure 1

Chemical stability and transport of CuO-NPs in soil columns

In order to calculate accurate mass balances for the column NPs-displacement experiments, the ability of CuO-NPs to dissolve in the six soils solutions was first assessed in the spiking suspensions through a 6-hour kinetic study. CuO-NPs dissolution was found to be negligible in all soil solutions, ranging from 0.22 and 0.49 % of the NPs applied mass (50 mg/L), after 6 hours of contact, which represents the maximum residence time of the NPs in the columns during transport experiments (Table 2). The measured aqueous Cu concentrations ranged from 0.112 to 0.243 mg L -1 that situate all below the PHREEQC-calculated Cu solubility limits toward Tenorite [START_REF] Parkhurst | Description of Input and Examples for PHREEQC Version 3: A Computer Program for Speciation, Batch-Reaction, One-Dimensional Transport, and Inverse Geochemical Calculations[END_REF]. This evidences a slow dissolution kinetic of the NPs. Consequently, Cu concentrations measured in the effluents can be attributed to CuO-NPs and not to dissolved Cu species.

All CuO-NPs breakthrough curves were fitted with the Convection Dispersion Equation, using the hydrodynamic parameters determined with the water tracer. The observed and CDE-Fitted breakthrough curves of CuO-NPs are presented in Figure 2A together with those of the water tracer (Br). The corresponding parameters are presented in Table 4. The CuO-NPs breakthrough curves (Figure 2A) show that these NPs are only partially mobile in the six soils, as important amounts of NPs were irreversibly retained in all soils, with NPs mass recoveries ranging from 5.2 to 14% (Table 4). Unlike TiO2-NPs, the partial mobility of CuO-NPs provided breakthrough curves that can be used to assess the influence of the studied factors on the transport of CuO-NPs. In all soils, the eluted CuO-NPs presented a fast transport through soil columns with no or low retardation as compared to the bromide tracer (Table 4). No clear effect of soil texture could be observed with the tested soils and, in particular, CuO-NPs were not specifically more mobile in the sandy-loam soils than in the loam or silty-clay soils as commonly observed for other types of pollutants (pesticides, PAH, heavy metals...) and as expected from previous work [START_REF] Fang | Stability of titania nanoparticles in soil suspensions and transport in saturated homogeneous soil columns[END_REF]). In the sandy-loam soils, CuO-NPs were transported slightly faster than the tracer (R = 0.98 and 0.91) indicating that in this type of soil, the NPs do not "see" all the water present in the soil presumably due to size exclusion processes or exclusion from immobile water zone during their transport (Table 4). In the loam and silty-clay soils, the CuO-NPs were transported slightly slower than water and presented a retardation factor slightly higher than 1, especially in the low OM soils. As for the tracer, the retardation factor measured in the high OM soils appeared always lower than in the low OM soils, indicating a clear relation between NPs mobility and soil OM content. This is possibly related to an increased soil structuration induced by the higher OM content in soil compared to the low OM soils [START_REF] Jastrow | Soil aggregate formation and the accrual of particulate and mineral-associated organic matter[END_REF][START_REF] Álvaro-Fuentes | Soil Aggregation and Soil Organic Carbon Stabilization: Effects of Management in Semiarid Mediterranean Agroecosystems[END_REF]. Such soil structuration improvement is indeed known to increase soil permeability through the formation of slightly bigger pores, which can facilitate the transfer of colloids or bacteria [START_REF] Martins | Role of macropore flow in the transport of Escherichia coli cells in undisturbed cores of a brown leached soil[END_REF][START_REF] Vitorge | Size-and concentration-dependent deposition of fluorescent silica colloids in saturated sand columns: transport experiments and modeling[END_REF][START_REF] Bagheri | Modeling the transport of nitrate and natural multi-sized colloids in natural soil and soil amended with vermicompost[END_REF]. Under our conditions, the different apparent size and zeta potential values of CuO-NPs measured in the different soil solutions do not seem to significantly affect NPs mobility whatever the soil. In the two loam soils of low and high OM contents, the CuO-NPs breakthrough curves were indeed very similar (Figure 2A), although their zeta potential values were the most contrasted (Figure 1), indicating that electrostatic interactions are probably not the dominant NPs retention process in the tested soils.

While in loam soils the NPs breakthrough curves were very similar in both low and high OM content conditions, in the sandy-loam and silty-clay soils, the breakthrough curves varied oppositely between the high and low OM condition (Figure 2). Interestingly, the mobility (recovery rate) of CuO-NPs increased by 62% in the high OM -sandy-loam soil compared to the low OM one, while in the silty-clay soil, CuO-NPs mobility decreased by 44% in the high OM soil compared to the low OM soil (Table 4, Figure 2A).

In the sandy-loam (high OM) and the silty-clay (low OM) soils, where CuO-NPs transport was enhanced, the concentration of dissolved organic carbon (DOC) in soil solutions was significantly higher than in the four other soils (Table 2). DOC concentration in soil solution appears thus as an important factor in NPs mobility, as has already been demonstrated in less complex porous media (e.g. [START_REF] Ben-Moshe | Transport of metal oxide nanoparticles in saturated porous media[END_REF][START_REF] Rastghalam | Nanoscale titanium dioxide (nTiO2) aggregation and transport in the co-presence of dissolved phosphate, illite colloid, and Fe oxyhydroxide coating[END_REF]. Other factors are probably also involved in the higher mobility of CuO-NPs in these two soils (e.g., low Ca and Mg concentrations in soil solutions). Although several studies have evaluated the mobility of CuO-NPs in columns of glass beads or sand material (Ben-Moshe, Dror and Berkowitz 2010; [START_REF] Wu | Transport and retention of copper oxide nanoparticles under unfavorable deposition conditions caused by repulsive van der Waals force in saturated porous media[END_REF], this study is one of the first studies on the transport of CuO-NPs in a series of 6 agricultural soils. We have shown here that CuO-NPs are partly mobile in all the contrasted soils studied, although the majority (86 to 94.2%) of these NPs are retained in the 8 cm top layer of these soils.

Spectral characteristics of soils and soils solutions

To further assess the observed differences in the effects of solid and dissolved OM levels on CuO-NPs mobility, a comparison of the MIR-ATR spectra of the six soils and of the six soil solutions is presented in Figure 3. For the solid phase, all the MIR-ATR spectra are mainly dominated by the strong absorption of soil minerals, which are very similar for the six soils.

Only slight insignificant spectral differences can be observed between the spectra obtained with low and high OM soils (Figure 3A), which do not explain the observed differences in the mobility of CuO-NPs. According to [START_REF] Stenberg | Chapter Five -Visible and Near Infrared Spectroscopy in Soil Science[END_REF] and [START_REF] Erktan | Comparison of infrared spectroscopy and laser granulometry as alternative methods to estimate soil aggregate stability in Mediterranean badlands[END_REF], the most frequent peaks in the MIR-ATR spectra of soils correspond to phyllosilicates (3622, 1635, 988, and 795 cm -1 ) and/or iron (oxy)hydroxydes (3622 and 795 cm -1 ) and tannins (1612, 1450, and 669 cm -1 ), with carboxylate (1592 and 1417 cm -1 , respectively), alkyl (CH2 and CH3 bending vibrations at 1455 and 1380 cm -1 , respectively) and aromatic moieties (phenol O-H bend at 1370 cm -1 ). The relatively low organic carbon content (a few %) of soils (Table 1) may explain the dominant absorption of soil minerals in mid-infrared.

For soils solutions (Figure 3B), although the MIR spectra appear very similar, slight differences can be observed in the 1200-980 cm -1 IR range of interest (black rectangles). Although incomplete correction of the background atmosphere (CO2) could have occurred, this is particularly visible in the wavelength ranges relating to dissolved inorganic phosphorus species(e.g. [START_REF] Tammer | Infrared and Raman Characteristic Group Frequencies: Tables and Charts[END_REF]Elzinga and Sparks 2007;[START_REF] Klein | Abiotic phosphorus recycling from adsorbed ribonucleotides on a ferrihydrite-type mineral: Probing solution and surface species[END_REF]. In this range, slightly higher or lower absorptions, corresponding to different Phosphate species were observed for the Sandy-Loam (high OM) and Silty-Clay (low OM) soil solutions, which are precisely the soils in which the mobility of CuO-NPs was highest (Figure 2). On the contrary, MIR absorption was lowest or highest in this range for the Sandy-Loam (low OM) and Silty-Clay (high OM) in which CuO-NPs mobility was lowest. In the 980 to 1200cm -1 range, IR absorption was very similar for the solutions of the two loam soils, in which CuO-NPs transport was very similar. For the sandy-Loam (high OM) and silty-Clay (low OM) soils, chemical analysis of P in soil solutions (Table 2) is in agreement with these IR trends and confirms the presence of higher concentrations of dissolved phosphate in the soils in which CuO-NPs are the more mobile. These results clearly suggest the existence of interactions between CuO-NPs and dissolved phosphorous (P) species in the soils that could explain the better stability of NPs in solution and therefore their slightly higher mobility in soils.

Phosphate effect on NPs transport

Phosphate is known to strongly sorb on metal oxides (e.g. Fe, Cu and Al oxides) even in acidic natural environments [START_REF] Mahdavi | The removal of phosphate from aqueous solutions using two nano-structures: copper oxide and carbon tubes[END_REF][START_REF] Claudio | Iron Oxide Nanoparticles in Soils: Environmental and Agronomic Importance[END_REF][START_REF] Klein | Abiotic phosphorus recycling from adsorbed ribonucleotides on a ferrihydrite-type mineral: Probing solution and surface species[END_REF]).

These properties have been used for various purposes, such as in agronomy to enhance phosphorus phytoavailability in soil [START_REF] Zahra | Metallic Nanoparticle (TiO2 and Fe3O4) Application Modifies Rhizosphere Phosphorus Availability and Uptake by Lactuca sativa[END_REF] or in wastewater treatment to eliminate phosphorus species [START_REF] Acelas | Selective removal of phosphate from wastewater using hydrated metal oxides dispersed within anionic exchange media[END_REF].

Our data suggest that phosphate species increase the mobility of CuO-NPs in the soils studied.

Several studies performed in quartz sand columns suggested a similar positive influence of phosphorus species on several types of NPs and especially of TiO2-NPs [START_REF] Hou | Transport, retention, and long-term release behavior of polymer-coated silver nanoparticles in saturated quartz sand: The impact of natural organic matters and electrolyte[END_REF][START_REF] Rastghalam | Fine particle attachment to quartz sand in the presence of multiple interacting dissolved components[END_REF][START_REF] Xu | Facilitated transport of nTiO2-kaolin aggregates by bacteria and phosphate in water-saturated quartz sand[END_REF]. Xu et al. (2018) studying a TiO2 NP's -phosphatebacteria ternary system showed that phosphate species generally facilitates the transport of TiO2

NPs linked on bacteria except in the presence of Fe oxide coatings or of low phosphate concentrations.

The main effect of phosphate appears to be the decrease of NPs surface charge induced by phosphate sorption. The stronger negative zeta potential of NPs probably results in enhanced repulsion of similarly charged soil constituents and, consequently, in the better stability and facilitated transfer of NPs in soil. In addition, the high complexing capacity of P may enable the formation of ternary complexes and, consequently, bridges between positively charged moieties, which are relevant for soils [START_REF] Sheng | Metal cation saturation on montmorillonites facilitates the adsorption of DNA via cation bridging[END_REF][START_REF] Mendez | Ternary Complex Formation of Phosphate with Ca and Mg Ions Binding to Ferrihydrite: Experiments and Mechanisms[END_REF]Hiemstra 2020). Zhara et al. (2015) suggested that positively charged TiO2-NPs, are destabilized by inter-particular phosphate bridges. Concerning Xu et al (2018), supposedly phosphate species bridge NPs to positively charged Fe oxide surfaces, as long as sorbed phosphate does not inverse the Fe oxide surface charge.

Globally, the effect of phosphate on NPs appears to be diverse. A facilitation of transport and dispersion effect linked to the negative charge of the sorbed phosphate species is potentially associated with an opposite immobilizing and aggregation effect linked to phosphate ternary bridging. Based on our observations, this study suggests that the apparent charge effect appears to be the dominant process under our conditions.

In conclusion, this study demonstrated a low or very low mobility of CuO and TiO2-NPs in agricultural soils, respectively. When differences in NP mobility were observed between soils, they seemed to be mainly due to dissolved OC and phosphate concentrations in soil solution.

Globally, the low mobility of NPs observed in an 8 cm soil layer in this study suggests that these two NPs present a low risk of direct groundwater contamination in a wide range of surface soils, although mobilization mechanism effects, probably involving P species, could increase this mobility and thus the associated risk for water supply. This low mobility also raises concerns about the long-term impacts of NPs on plants and soil biodiversity in agroecosystems that would require to be investigated under realistic field conditions.

  ) in agreement with[START_REF] Vitorge | Size-and concentration-dependent deposition of fluorescent silica colloids in saturated sand columns: transport experiments and modeling[END_REF]. No clear influence of the soil OM content on TiO2-NPs mobility could be evidenced in the six soils, because of their very low mobility. These results contrast with previous studies on the mobility of TiO2-NPs conducted in columns of glass beads or sand material, which usually present these NPs as mobile especially at alkaline pH (Ben-Moshe, Dror and Berkowitz 2010;[START_REF] Solovitch | Concurrent Aggregation and Deposition of TiO2 Nanoparticles in a Sandy Porous Media[END_REF][START_REF] Chowdhury | Combined Factors Influencing the Aggregation and Deposition of nano-TiO2 in the Presence of Humic Acid and Bacteria[END_REF][START_REF] Rastghalam | Nanoscale titanium dioxide (nTiO2) aggregation and transport in the co-presence of dissolved phosphate, illite colloid, and Fe oxyhydroxide coating[END_REF]. However, our results are consistent with previous works conducted in natural soils by[START_REF] Wang | Laboratory assessment of the mobility of water-dispersed engineered nanoparticles in a red soil (Ultisol)[END_REF] or[START_REF] Nickel | Mobility of coated and uncoated TiO 2 nanomaterials in soil columns-Applicability of the tests methods of OECD TG 312 and 106 for nanomaterials[END_REF], although these experiments were performed with positively charged TiO2-NPs. A study performed in natural soils is in significant disagreement with strong retention of TiO2 NPs[START_REF] Fang | Stability of titania nanoparticles in soil suspensions and transport in saturated homogeneous soil columns[END_REF]. They used negatively charged TiO2-NPs as in our study but observed a significant transport of these NPs, especially in soils with low clay, high DOM content and low ionic strength. Their DOC values are all much higher than those of our study (factor ~ 7), which could indicate a dominant effect of this factor on NPs mobility, especially considering their rather similar or even decreased Ca ++ values. In this study, NPs are transferred as a tracer especially at high DOM content.[START_REF] Fang | Co-transport of Pb2 + and TiO2 nanoparticles in repacked homogeneous soil columns under saturation condition: Effect of ionic strength and fulvic acid[END_REF] observed a similar behavior of TiO2 NPs in the presence of fulvic acids. Since in our experiments, the retention of TiO2-NPs was very high in the six soils studied, it was not possible to observe any influence of the soil texture (soil clay content) or of the ionic strength of soil solution. In our six soils, TiO2-NPs were not transported deeper than 8 cm. This result may relate to the relatively low DOM content of the soils, low NPs input concentration and/or other parameters such as soil aggregation column size and setup. Studying the fate of TiO2-NPs in soil is very challenging as Ti is abundant in soils and presents a very heterogeneous distribution. The findings obtained with laboratory saturated soil columns give a first assessment of the risk of NPs migration to deeper soil layers or groundwater, which appears very low. However, further work is clearly needed to assess the mobility potential of TiO2-NPs at environmentally relevant concentrations, in undisturbed soils or under unsaturated conditions and simulating repeated exposures in order to be closer to expected field conditions[START_REF] Duester | Translocation of Sb and Ti in an undisturbed floodplain soil after application of Sb2O3 and TiO2 nanoparticles to the surface[END_REF][START_REF] Cornelis | Fate and Bioavailability of Engineered Nanoparticles in Soils: A Review[END_REF][START_REF] Conway | Gravity-driven transport of three engineered nanomaterials in unsaturated soils and their effects on soil pH and nutrient release[END_REF][START_REF] Simonin | Combined Study of Titanium Dioxide Nanoparticle Transport and Toxicity on Microbial Nitrifying Communities under Single and Repeated Exposures in Soil Columns[END_REF].

FIGURESFigure 1 :

 1 FIGURES

Figure 2 :

 2 Figure 2: A) Breakthrough curves of the Bromide water tracer and CuO-NPs in columns of the

Figure 3 :

 3 Figure 3: A) MIR-ATR spectra of the 6 soils. B) MIR-DR spectra of the 6 soil solutions. Each

  ;[START_REF] Badawy | Impact of Environmental Conditions (pH, Ionic Strength, and Electrolyte Type) on the Surface Charge and Aggregation of Silver Nanoparticles Suspensions[END_REF][START_REF] Simonin | Influence of soil properties on the toxicity of TiO2 nanoparticles on carbon mineralization and bacterial abundance[END_REF][START_REF] Qiu | The aggregation and sedimentation of two different sized copper oxide nanoparticles in soil solutions: Dependence on pH and dissolved organic matter[END_REF] whereas Ca is known to complex and neutralize, i.e. to precipitate DOC. Coherently, the soil of lowest DOC is that of highest Ca content (the high OM silty-clay soil, Table2) and the NP's hydrodynamic diameter differs significantly from its sister soil (Low OM silty-clay soil). DOC thus appears to affect the hydrodynamic parameters of NPs more than soil texture.In comparison, the CuO-NPs hydrodynamic diameter values of 53.3 to 84.1 nm are lower than those of TiO2-NPs. These values measured in the soil solutions were close to the intrinsic value

of 57 ± 18 nm measured by SEM. No significant influence of soil texture or OM content on CuO-NPs aggregation was observed (Figure

Table 1 :

 1 Main characteristics of the six studied soils

		% sand % loam % clay % OM WHC (%)	pH	Ionic strength (mM)	CEC (cmol + kg -1 )	Cu (mg kg -1 )	Ti (g kg -1 )
	Sandy-loam -Low OM	68.4	14.7	16.9	2.09	20	7.0	0.98	11.5	20.1	2.4
	Sandy-loam -High OM	65.6	16.1	18.3	4.46	20	6.9	1.59	15.4	21.9	2.4
	Loam -Low OM	37.5	42.7	19.8	2.23	30	6.4	0.60	8.79	13.2	2.7
	Loam -High OM	40.3	40.8	18.9	6.77	30	6.3	1.31	15.3	10.4	2.4
	Silty-clay -Low OM	8.2	49.8	42.0	4.72	47	6.9	0.51	17.4	23.2	5.3
	Silty-clay -High OM	10.1	50.8	39.1	7.87	51	7.7	1.37	20.1	26.2	4.5

TABLES

Table 2 :

 2 Characteristics of the soil solutions used for the transport experiments (all concentrations are expressed in mg L -1 ) and results of Cu dissolution test in soil solutions conducted for 6 hours at 50 mg/L CuO-NPs.

		pH	Ionic strength (mM)	DOC	Ca	K	Mg	Na	Al	Fe	Mn	PO4	Solubility PO4_Th	% of dissolved Cu after 6h	PhreeqC Calc. CuTh Solubility
	Sandy-loam -Low OM	6.7	1.0	11.6	21.7	5.25	2.43	8.89	4.70	1.45	0.02	2.72	1.18	0.27 %	0.68
	Sandy-loam -High OM	6.4	2.0	18.6	12.2	6.84	1.11	12.06	7.62	1.69	0.02	3.67	7.47	0.49 %	1.19
	Loam -Low OM	6.2	1.2	8.2	28.8	3.84	3.23	13.18	11.35	1.90	0.09	1.19	6.48	0.37 %	3.46
	Loam -High OM	5.4	2.4	10.5	38.2	15.57	2.59	21.78	6.66	2.79	0.04	3.85	442.18	0.28 %	64.01
	Silty-clay -Low OM	6.3	1.5	25.2	33.5	3.69	1.40	11.41	4.35	1.79	0.01	0.74	3.73	0.24 %	2.74
	Silty-clay -High OM	7.1	1.6	8.9	80.8	4.15	4.28	5.48	2.66	3.53	0.04	0.00	0.03	0.22 %	0.4

PO4_Th : Calculated total orthophosphate solubility toward Apatite ; CuTh : Calculated Cu(II) solubility toward Tenorite without OM.

Table 3 :

 3 Main characteristics of the soil columns

		Pore volume (mL)	Bulk density (g cm -3 )	Effective Porosity	Darcy velocity (cm h -1 )	Average soil collector diameter* (µm)
	Sandy-loam -Low OM	2.90	1.27	0.51	14.9	122.9
	Sandy-loam -High OM	3.32	1.08	0.59	13.0	118.3
	Loam -Low OM	3.85	0.83	0.68	11.3	74.5
	Loam -High OM	3.80	0.86	0.67	11.4	78.9
	Silty-clay -Low OM	3.47	1.01	0.61	12.5	24.9
	Silty-clay -High OM	3.62	0.94	0.64	12.0	28.4

* Calculations based on

[START_REF] Ley | Soil water monitoring and measurement[END_REF]

Table 4 :

 4 Transport parameters for bromide, CuO-NPs and TiO2-NPs experiments.

				Bromide			CuO-NPs		TiO2-NPs
			MR	D	R	MR	D	R	µ	MR
			(%)	(cm 2 /s)	(-)	(%)	(cm 2 /s)	(-)	(h -1 )	(%)
		Low OM	97.4	1.0E-07	1.03	5.2	1.35E-05	0.98	7.27	2.1
	Sandy-loam	High OM	98.8	7.1E-08	0.97	14.0	2.52E-07	0.91	1.97	5.5
		Low OM	97.3	1.0E-07	0.99	11.4	1.10E-08	1.06	2.29	2.3
	Loam	High OM	95.1	5.9E-08	0.96	9.7	8.30E-08	0.99	2.37	3.4
		Low OM	96.4	1.2E-07	0.90	12.1	1.04E-05	0.92	2.37	1.9
	Silty-clay	High OM	94.8	5.5E-08	0.81	6.8	9.47E-07	0.88	3.28	2.2

MR: Mass Recovery (%), D: Dispersion value, R: Retardation factor

Acknowledgments

Marie Simonin was supported by a Ph.D grant from Rhône-Alpes Region -ARC

Environnement. This work was funded by a grant from the French National Program Microbien EC2CO-CNRS. The authors thank the lab assistance of Erwann Vince and Sophie Sebastianutti (MOME and AirOsol platforms at IGE) and also of Alix Dumay for modelling assistance. Special thanks are due to Lauric Cécillon and Alejandro Fernandez-Martinez for Infrared spectra measurements and help for interpretation. IGE is part of the Labex OSUG@2020 (ANR10 LABX56). We thank the Equipex NanoID (ANR-10-EQPX-39) for the access to the NanoZS (ISTerre).

Conflict of interest

The authors declare no conflict of interest.


Amina Ghrissi

Douglas Almonfrey

Fabien Squara

Johan Montagnat

Vicente Zarzoso

Identification of Spatiotemporal Dispersion Electrograms in Atrial Fibrillation Ablation Using Machine Learning: A comparative Study

Keywords: Atrial fibrillation, spatiotemporal dispersion, catheter ablation, multipole catheter, multichannel electrogram, machine learning, transfer learning

Atrial Fibrillation (AF) is the most widespread sustained arrhythmia in clinical practice. A recent personalized AF therapy consists in ablating areas displaying spatiotemporal dispersion (STD) electrograms (EGM) with the use of catheters. Interventional cardiologists use a multipolar mapping catheter called PentaRay to identify visually atrial sites with STD pattern by visual inspection. In this contribution, we propose to automatize the identification of STD EGMs using machine learning while comparing several features. The aim is to design a data representation and an adapted classification algorithm for accurate EGM detection with affordable computational resources and low prediction time. Four data formats are considered: 1) EGM matrices; 2) EGM plots; 3) three-dimensional EGM plots; 4) maximal voltage absolute values. Convolutional neural networks and transfer learning based on the VGG16 architecture are benchmarked. Classification results on the test set show that extracting features automatically with VGG16 is possible and yields comparable results to classifying raw EGM recordings with values of accuracy and AUC of 90%. However, the overall precision and F1 score are low (50%), which can be explained by the high class imbalance ratio. This issue is addressed with data augmentation. Due to its low computational cost, our solution can also be deployed in real time.

I. INTRODUCTION

During the last decade, artificial intelligence models [START_REF] Yao | Multi-class arrhythmia detection from 12-lead varied-length ECG using attention-based timeincremental convolutional neural network[END_REF], [START_REF] Dreiseitl | Logistic regression and artificial neural network classification models: a methodology review[END_REF] have intensively been used as decision-aid solutions in biomedical data analysis. In the current study, we are interested in helping cardiologists to automatically identify potential ablation sites in persistent atrial fibrillation (AF) using machine learning (ML) tools. AF represents the most frequent sustained arrhythmia experienced in clinical practice and it rises in prevalence with advancing age [START_REF] Zarzoso | Non-invasive prediction of catheter ablation outcome in persistent atrial fibrillation by fibrillatory wave amplitude computation in multiple electrocardiogram leads[END_REF]. AF is associated with a 5-fold stroke risk increase and a 2-fold increased risk of both mortality and dementia [START_REF] January | AHA/ACC/HRS focused update of the 2014 AHA/ACC/HRS guideline for the management of patients with atrial fibrillation: a report of the American College of Cardiology/American Heart Association Task Force on Clinical Practice Guidelines and the Heart Rhythm Society[END_REF]. Hence, AF entails an important economic burden. Among the existing treatments of persistent AF, ablation interventions beat drug therapies in terms of long-term effectiveness. Ablation consists in burning with radiofrequency (RF) energy cardiac tissue areas estimated to be responsible for the presence This work was supported in part by the French government Investments in the Future program, through IDEX UCA JEDI (ANR-15-IDEX-0001) and 3IA Côte d'Azur (ANR-19-P3IA-0002) projects. V. Zarzoso holds the Chair "IAblation" from 3IA Côte d'Azur.

1 Université Côte d'Azur, CNRS, I3S Laboratory, Sophia Antipolis, France (e-mail: {amina.ghrissi, vicente.zarzoso, fabien.squara, johan.montagnat}@univ-cotedazur.fr) 2 Federal Institute of Espírito Santo, Vitoria, Brazil (e-mail: dalmonfrey@ifes.edu.br).

3 Université Côte d'Azur, CHU Pasteur, Cardiology Department, Nice, France (e-mail: squara.f@chu-nice.fr).

and maintenance of AF. The classical ablation approach, called sequential stepwise ablation, yields poor clinical results [START_REF] Verma | Approaches to catheter ablation for persistent atrial fibrillation[END_REF]. A novel wholly patient-tailored ablation protocol, giving 95% of procedural success rate, consists in identifying ablation sites based on a signal pattern called spatiotemporal dispersion (STD) [START_REF] Seitz | AF ablation guided by spatiotemporal electrogram dispersion without pulmonary vein isolation: a wholly patient-tailored approach[END_REF]. Multipolar mapping catheters are used to record electrograms (EGM) in the atria thus targeting areas of STD as potential AF drivers. The high-density PentaRay catheter is used for STD localization. It has a five-branch star design with two bipoles on each spline. According to preliminary guidelines for STD identification from visual inspection, the 10-channel EGM recording acquired by the PentaRay would display a cardiac activation delay of 70% of AF cycle length (AFCL) on a minimum of three neighboring bipoles (channels) [START_REF] Seitz | AF ablation guided by spatiotemporal electrogram dispersion without pulmonary vein isolation: a wholly patient-tailored approach[END_REF]. However, this visual inspection may be biased by the difficulty for the interventional cardiologist to precisely quantify the STD pattern at each single mapped location in real time, as hundreds and even thousands of cardiac sites are mapped in a typical ablation intervention.

To overcome these limitations, the present contribution aims to design a decision-aid solution that helps interventional cardiologists detect STD patterns automatically thanks to both baseline ML and modern deep learning tools [START_REF] Goodfellow | Deep Learning[END_REF]. We seek the most optimal EGM classification model, formed by the combination of a data representation and an adapted classification algorithm, in order to detect STD locations with the highest performance and lowest computational cost in terms of prediction time and resources. The study dataset includes a cohort of over 35000 10-channel EGM signals acquired from 15 different persistent AF patients.

Our preliminary results in a previous study on automatic detection of STD from multichannel EGM recordings were promising [START_REF] Ghrissi | Data augmentation for automatic identification of spatiotemporal dispersion electrograms in atrial fibrillation ablation using machine learning[END_REF]. The classification performance on the test dataset reached 90% of accuracy and 80% of AUC using a shallow convolutional neural network (CNN). But values of precision were low because of the lack of STD samples. We also addressed the issue of class imbalance and lack of training samples from STD class through adapted data augmentation (DA) methods [START_REF] Agnieszka | Data augmentation for improving deep learning in image classification problem[END_REF] [START_REF] Shorten | A survey on image data augmentation for deep learning[END_REF]. In a complementary recent study, we addressed the classification of handcrafted features from EGM data [START_REF] Ghrissi | Identification of spatiotemporal dispersion electrograms in persistent atrial fibrillation ablation using maximal voltage absolute values[END_REF]. As suggested in [START_REF] Seitz | AF ablation guided by spatiotemporal electrogram dispersion without pulmonary vein isolation: a wholly patient-tailored approach[END_REF], we studied a time series computed from multichannel EGM signals to perform STD detection. The time series is called maximal voltage PentaRay absolute values (VAVp). Classification results were promising in simulated data but disappointing in real data.

The present contribution updates, completes and consolidates our preliminary results in [START_REF] Ghrissi | Data augmentation for automatic identification of spatiotemporal dispersion electrograms in atrial fibrillation ablation using machine learning[END_REF], [START_REF] Ghrissi | Identification of spatiotemporal dispersion electrograms in persistent atrial fibrillation ablation using maximal voltage absolute values[END_REF] by putting Authors' manuscript Accepted for publication in Biomedical Signal Processing and Control forward a feature selection technique for a more optimal EGM classification solution. For this purpose, we design and benchmark different data representations: 1) raw EGMs stored in matrices; 2) two-dimensional (2D) images obtained by subplotting the curves of the 10 leads one under the other, as it is currently done by the mapping system in the hospital; 3) three-dimensional (3D) image, tensor as a result of stacking three shifted images of EGM curves; 4) one-dimensional (1D) VAVp time series used as a compact representation of the multichannel recordings. These data representations are combined with suitable classifiers including multivariate logistic regression (MLR) [START_REF] Dreiseitl | Logistic regression and artificial neural network classification models: a methodology review[END_REF], dimensionality reduction with principal component analysis (PCA) [START_REF] Jolliffe | Principal component analysis: a review and recent developments[END_REF] followed by support vector machines (SVM) [START_REF] Boser | A training algorithm for optimal margin classifiers[END_REF], CNN [START_REF] Lecun | Gradient-based learning applied to document recognition[END_REF], transfer learning (TL) [START_REF] Goodfellow | Deep Learning[END_REF] of the VGG16 model [START_REF] Simonyan | Very deep convolutional networks for large-scale image recognition[END_REF]. The originality of this contribution is three-fold: first, to our knowledge this is the first systematic application of state-of-the-art ML techniques to EGM classification for STD identification; second, different data representations are benchmarked and TL is applied for the first time to the identification of dispersion pattern in multichannel EGMs; third, our decisionaid solution can be implemented in real time with moderate computational resources, thus potentially improving catheter ablation success rates while reducing the duration of STDbased ablation interventions for treating persistent AF.

II. AF ABLATION

A. Catheter Ablation of Persistent AF 1) AF Diagnosis: The heart is a vital muscle that pumps blood to irrigate the body thus providing oxygen and nutrients to body tissues. It is composed of four chambers, the two upper ones are called atria and the two lower ones are called ventricles. However, the heart mechanisms for a patient suffering from AF is different from that of a normal one, said to be in sinus rhythm. AF is characterized by an irregular activation in the atria that start quivering or fibrillating, causing non-synchronous fluctuations in the associated electrical baseline. Therefore, the ventricular rate becomes more rapid and disorganized [START_REF] Malmivuo | Bioelectromagnetism: Principles and Applications of Bioelectric and Biomagnetic Fields[END_REF].

2) AF Therapies: The severity degrees of AF differ according to the arrhythmogenic episode duration and the response to treatment. In case of persistent AF, pharmacotherapy proves less effective than catheter ablation due to the complexity of this arrhythmia. Ablation is an invasive procedure that consists in burning the cardiac myocytes displaying irregularities with RF energy delivered with the use of catheters. The classical ablation protocol of persistent AF uses bipolar mapping catheters. It is called stepwise and consists: in 1) burning the triggers around the pulmonary veins thought to be responsible for initiating AF; 2) ablating areas of the atrial substrate harboring drivers maintaining and self-perpetuating the arrhythmia, such as complex fractionated electrograms (CFAE) [START_REF] Nademanee | A new approach for catheter ablation of atrial fibrillation: mapping of the electrophysiologic substrate[END_REF]. However, a growing number of reports show the limitations of the stepwise approach, as several ablation interventions are typically required to terminate AF or at least to transform it to a more stable tachycardia [START_REF] Verma | Approaches to catheter ablation for persistent atrial fibrillation[END_REF].

B. STD-Guided Ablation

A recent discovery in AF ablation therapy shows that targeting only cardiac areas displaying STD EGMs can terminate AF in 95% of a cohort of 105 patients [START_REF] Seitz | AF ablation guided by spatiotemporal electrogram dispersion without pulmonary vein isolation: a wholly patient-tailored approach[END_REF]. The resulting recurrence rate within 18 months of follow-up is only 15%. STD is a visually discernible AF pattern that guides interventional cardiologists in ablating persistent AF drivers. STDbased ablation uses PentaRay mapping catheter (Biosense Webster Inc, Irvine, CA, USA) as shown in Fig. 1(A). Before ablation with RF energy, interventional cardiologists first position sequentially the PentaRay in different sites of the atria. Ten bipolar EGMs are then simultaneously recorded per location by maintaining the catheter stable for a few seconds. Finally, atrial sites displaying an irregular cardiac activity are annotated as dispersion points and tagged for ablation. According to guidelines in [START_REF] Seitz | AF ablation guided by spatiotemporal electrogram dispersion without pulmonary vein isolation: a wholly patient-tailored approach[END_REF], dispersion areas refer to clusters of electrograms, either fractionated or not, displaying interelectrode time and space dispersion at a minimum of three contiguous leads [START_REF] Seitz | AF ablation guided by spatiotemporal electrogram dispersion without pulmonary vein isolation: a wholly patient-tailored approach[END_REF], as shown in Fig. 1(B). Hence, STD-based ablation is a fully patient-tailored therapy.

However, quantifying visually if the delay of the intracardiac activation through neighboring bipoles can be approximated by 70% of the AFCL is a difficult and timeconsuming task. Thousands of atrial locations are mapped with the PentaRay catheter in a typical ablation intervention and all multichannel EGM recordings acquired at these locations must be evaluated visually by the practicing cardiologists in real time. Hence, the visual identification of STD areas is prone to errors and lack of reproducibility. Instead, the present work aims to design an optimized decision-aid solution that helps interventional cardiologists detect STD patterns automatically thanks to ML tools.

III. METHODS

A. Data Acquisition

The process of data acquisition consists in several steps: 1) selecting patients suffering from persistent AF and mapped with PentaRay for STD-based ablation; 2) exporting intervention data from BioSense CARTO system, including electrocardiogram (ECG), EGM and annotated dispersion points; 3) decompressing, anonymizing and preparing data of interest; 4) structuring data for classification purposes.

During the mapping phase, the PentaRay catheter is maintained stable for 2.5 s at each location. A location refers to an anatomical point inside the heart. Multichannel EGMs are sampled at 1 kHz and displayed through the CARTO system monitor, to be analyzed by the cardiologist. Hence, EGM data exported from CARTO system can be stored in a matrix of dimension 10 × 2500.

1) Data Labeling: Data labeling is performed by interventional cardiologists such that EGMs presenting spatiotemporal dispersion are annotated as "STD", also called gradient or substrate. We automatically merge remaining labels into the "non-STD" class. Moreover, a meticulous work is needed for standardizing the labels because the annotation nomenclature exported from CARTO system (encoded labels) differ from one patient to another. 2) Circularity Transformation: Circularity transformation consists in replicating for each sample the first two channels (matrix rows) at the end of the sample. The new sample, originally with dimensions 10×2500, becomes 12×2500. This transformation allows us to mimic the circular arrangement of the PentaRay branches. Indeed, it captures the neighborhood information between bipoles of splines A and E of the catheter, as shown in Fig. 1(A).

B. Data Representations

Starting from the basic matrix format presented above, data can be reformatted in different ways to match different classification algorithms:

1) Matrix: The first classification scheme uses matrices of dimensions 12 × 2500, the result of applying the circularity transformation on raw recordings of the 10-lead EGMs. Matrices can also be treated as images with 2D CNN models like LeNet-STD, as proposed in [START_REF] Yang | Deep convolutional neural networks on multichannel time series for human activity recognition[END_REF] for a human activity recognition task.

2) 2D image: The image format consists in subplotting the curves of the 10 leads, one under the other, as it is currently done by CARTO system during the mapping phase.This 2D plot of EGMs is used in the hospital and represents the most easily understandable representation by the eye of an interventional cardiologist. We will check in the present study if this format is also convenient for ML classifiers.

3) 3D image: This format enables the use of CNN models conceived to train on 3D RGB images like in ImageNet [START_REF] Deng | ImageNet: A large-scale hierarchical image database[END_REF] dataset (natural colored images). Hence, this data format enables the use of TL [START_REF] Goodfellow | Deep Learning[END_REF]. The 3D tensor is the result of stacking three 2D images along the depth dimension. The first slice (image) is a subplot of the ordered leads { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 }, similarly to 2D image format. The second slice is the subplot of the leads shifted in a circular way. The leads order becomes { 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 1 }. The third slice represents a subplots of leads shifted twice as follows { 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 1 , 2 }. Similarly to the circularity transformation, the idea comes from the circularity of the PentaRay branches. The interest in shifting the leads remains in allowing the 3D filter to systematically analyze neighboring leads along the depth dimension as it already does along the spatial dimensions (matrix slice). For instance the first convolutional window captures leads { 1 , 2 , 3 } across the three slices. This data format allows us to represent EGMs in a 3D tensor with a depth of three thus mimicking the shape of RGB images and allowing the use of algorithms requiring this input shape.

4) 1D signal: VAVp times series is a compact representation of multichannel recordings that has shown promising results in [START_REF] Ghrissi | Identification of spatiotemporal dispersion electrograms in persistent atrial fibrillation ablation using maximal voltage absolute values[END_REF]. The VAVp distribution is also claimed to depend on STD pattern in [START_REF] Seitz | AF ablation guided by spatiotemporal electrogram dispersion without pulmonary vein isolation: a wholly patient-tailored approach[END_REF]. As claimed in [START_REF] Seitz | AF ablation guided by spatiotemporal electrogram dispersion without pulmonary vein isolation: a wholly patient-tailored approach[END_REF], VAVp time series is calculated as follows: 1) the VAV matrix contains in its rows the absolute values of each channel of the multilead EGM recording; 2) one-dimensional VAVp signal is computed as the maximal values at each time sample of VAV matrix over the leads (rows) dimension. The histograms of VAVp distribution (h(VAVp)) are shown in [START_REF] Seitz | AF ablation guided by spatiotemporal electrogram dispersion without pulmonary vein isolation: a wholly patient-tailored approach[END_REF] to significantly depend on the presence of STD patterns. Numerical results showed that h(VAVp) is peaky and concentrated around zero if the virtual PentaRay is positioned in non-STD areas but it gets more spread for EGMs recorded in STD areas of the heart as shown in Fig. 2. However, a recent study [START_REF] Ghrissi | Identification of spatiotemporal dispersion electrograms in persistent atrial fibrillation ablation using maximal voltage absolute values[END_REF] showed that h(VAVp) distribution is not a key feature in STD detection when analyzing the database used in the present study. However, the supervised classification of raw VAVp time series itself into STD vs. non-STD categories is promising. Results on the test set are good with values of accuracy, AUC, sensitivity and specificity around 90% with low variability (10 -3 ). Complementary metrics such as precision and F1 score are also computed and analyzed in the present work. Besides, a larger dataset of 35000 EGMs are included in the present paper compared to 23000 in [START_REF] Ghrissi | Identification of spatiotemporal dispersion electrograms in persistent atrial fibrillation ablation using maximal voltage absolute values[END_REF].

C. Classification Algorithms

The ML algorithms trained to identify STD locations are the following:

1) SVM: SVM is widely used in biomedical data analysis like electrocardiogram classification [START_REF] Melgani | Classification of electrocardiogram signals with support vector machines and particle swarm optimization[END_REF]. The model maps the input feature space into a higher-dimensional space so Fig. 2: VAVp distributions (histograms) obtained by positioning a virtual PentaRay in a human atrias with homogeneous substrate (A) at the center of the driver, reminiscent of patients' dispersion areas, and (B) at the periphery of the driver. (C) In the interstitial fibrosis condition [START_REF] Seitz | AF ablation guided by spatiotemporal electrogram dispersion without pulmonary vein isolation: a wholly patient-tailored approach[END_REF].

that data samples from different classes become separable. Data is divided by a hyperplane in the original n-dimensional space, with a large gap [START_REF] Boser | A training algorithm for optimal margin classifiers[END_REF]. SVM aims at maximizing the distance, called margin, between data points situated near the hyperplane, called support vectors. Maximizing the margin provides some confidence that new data points can be classified with more accuracy. Then, new samples are mapped into the new space and predicted to belong to a class or another based on the side of the hyperplane on which they fall. Looking for a suitable separable representation of data is called kernel trick.

2) PCA: PCA explores linear relationships between features and defines variables significance on the basis of their variance contribution. It projects data in a new space model formed by synthesized variables called principal components (PC). This is useful when large amounts of information may be approximated by a moderately complex model structure. Based on the estimation of the correlation structure of the variables, PCA evaluates the importance of a variable in a PC model through the size of its residual variance [START_REF] Jolliffe | Principal component analysis: a review and recent developments[END_REF]. The choice to be examined is how many PC's (r) adequately account for the total variation in the n-dimensional data sample x. Among the existing criteria for choosing r, we opt for the cumulative percentage of total variation, also called hard threshold (t). The optimal number of PC's is chosen as the smallest integer r for which the cumulative percentage of total variation reaches or exceeds t. PCA allows us to reduce the dimensions of the input space by projecting the input data onto a space formed only by the first r PCs 3) MLR: In statistics, logistic regression [START_REF] Dreiseitl | Logistic regression and artificial neural network classification models: a methodology review[END_REF] estimates the probability of a given class or event by using the logistic function. MLR is identical to univariate logistic regression, but it considers more than one covariate. Let p(x) be the model's estimation of the probability of an event that depends on n covariates or independent variables. Then, inverting the logit formulation for modeling the probability gives:

p : R n → (0, 1) p(x) = e β 0 +β 1 x 1 +β 2 x 2 +•••+βn xn 1+e β 0 +β 1 x 1 +β 2 x 2 +•••+βnxn .
The estimates of the unknown parameters β i , i = 0, 1, 2, . . . , n, are derived through the maximization of a likelihood function. MLR is a baseline classifier in biomedical data analysis and electrograms classification [START_REF] Dreiseitl | Logistic regression and artificial neural network classification models: a methodology review[END_REF]. Furthermore, MLR can be implemented as a fully connected (FC) neural network. 4) CNN: Artificial neural networks (NN) are commonly used in biomedical data classification [START_REF] Dreiseitl | Logistic regression and artificial neural network classification models: a methodology review[END_REF], [START_REF] Pyakillya | Deep learning for ECG classification[END_REF], [START_REF] Hannun | Cardiologistlevel arrhythmia detection and classification in ambulatory electrocardiograms using a deep neural network[END_REF]. A NN consists of a series of connected layers, each layer composed of a number of artificial neurons, called nodes, that have learnable weights. A CNN is a special NN composed of convolutional and pooling layers followed by FC ones. Each node of the convolutional (conv) layer receives some inputs, performs a dot product and optionally follows it with a nonlinearity. The output of each conv filter is called feature map. In pooling layers, the resolution of feature maps is reduced to increase the invariance of features to distortions.

(a) LeNet-STD architecture is inspired by the state of the art LeNet5, a baseline CNN that is both a good classifier and a computationally-affordable algorithm [START_REF] Lecun | Gradient-based learning applied to document recognition[END_REF]. It has 60,000 parameters compared to AlexNet for instance that has 60 million parameters [START_REF] Goodfellow | Deep Learning[END_REF].

(b) VGG16 is a deep CNN designed by the Visual Geometry Group Lab, trained for ImageNet Large Scale Visual Recognition Challenge (ILSVRC) and achieving 92.7% top-5 test accuracy. ImageNet dataset contains 14 million images that belong to 1000 classes. VGG16 is composed of 5 conv blocks alternated by pooling layers and followed by FC ones. In total VGG16 has 16 layers with trainable weights [START_REF] Simonyan | Very deep convolutional networks for large-scale image recognition[END_REF] 5) TL: In terms of ML, TL is a process where a NN (M 1 ) is trained on a first problem then re-used in some way in a related problem. A new model is then formed by aggregating one or several layers from the trained model M 1 to additional layers, generally FC layers with trainable weights. The main benefits of TL consist in decreasing the training time for the new model and achieving a lower generalization error [START_REF] Goodfellow | Deep Learning[END_REF].

D. Cross-Validation

Cross-validation (CV) is a statistical tool commonly used in ML to quantify the generalization power of a classifier [START_REF] Kohavi | A study of cross-validation and bootstrap for accuracy estimation and model selection[END_REF]. k-fold CV consists in: first, partitioning the entire datasets into k subsets called folds; second, repeating model training k times while considering, at each round, the k th fold as the test dataset and the remaining samples as the training dataset; finally, the estimation of the classifier's performance is given by averaging the validation results over the k rounds. A rule of thumb is to choose k equal to 5 or 10 [START_REF] Kuhn | [END_REF]. Regarding the size of our dataset and the small number of STD samples (only 5% of non-STD samples), we opt for 5-fold CV in order to keep an acceptable amount of STD test samples. In each CV round, the test dataset is partitioned into two equal-sized subsets that will form the new validation and test sets. This guarantees that the model does not see the test samples during the training phase.

E. Performance Metrics

A cost function is minimized during the learning phase of a classifier. In order to evaluate the model's classification performance, several metrics are assessed. The accuracy (Acc) metric is computed as the result of dividing the total number of correct predictions by the total number of predictions. However, accuracy is not enough to quantify classification performance when learning from imbalanced datasets. For this, it remains important to compute the confusion matrix whose elements are the true positives (TP), true negatives (TN), false positives (FP) and false negatives (FN). From these values, the following metrics are evaluated: 1) sensitivity, recall or true positive rate (TPR), measuring the proportion of actual STD samples that are correctly identified as such; 2) specificity or true negative rate (TNR), quantifying the proportion of actual non-STD samples that are correctly identified as such; 3) precision or positive predictive value (PPV), assessing how trustable the result is when the model answers that a point belongs to the STD class; 4) negative predictive value (NPV), or probability that a sample is actually non-STD when the model has classified it as such; and 5) F 1 -score which stands for the harmonic mean of precision and sensitivity. The F1 score quantifies the balance between precision and recall values such that high recall accompanied with high precision values reflect that the STD class is perfectly handled by the model, low recall accompanied by high precision values reflect that the model cannot detect the STD class well but is sufficiently trustable when it does; high recall accompanied with low precision values reflect that the STD class is well detected but the model output for that class also includes non-STD samples, and low recall accompanied with low precision values reflect the STD class is poorly handled by the model. Then, the area under the Receiver Operating Characteristic (ROC) curve shortly named AUC is computed. The ROC curve is a graphical tool widely used to evaluate the performance of a binary classifier when varying the discrimination threshold [START_REF] Hajian-Tilaki | Receiver operating characteristic (ROC) curve analysis for medical diagnostic test evaluation[END_REF].

F. Data Augmentation

One of the biggest and most frequent challenges encountered in deep learning remains the insufficient amount of data or the uneven class balance of samples within the training dataset. The high misrepresentation of STD samples in the multichannel EGM dataset leads to poor classification results in terms of sensitivity, precision and AUC. This data imbalance issue can be handled through adapted DA solutions. DA is a signal preprocessing tool that applies transformations to original samples of the minority STD class in order to synthesize new samples. It consists in forming a balanced super-dataset by replicating randomly STD samples until they reach the number of non-STD ones [START_REF] Agnieszka | Data augmentation for improving deep learning in image classification problem[END_REF] [START_REF] Shorten | A survey on image data augmentation for deep learning[END_REF]. A recent study benchmarked a set of DA solutions for the classification of the current STD multichannel EGM dataset [START_REF] Ghrissi | Data augmentation for automatic identification of spatiotemporal dispersion electrograms in atrial fibrillation ablation using machine learning[END_REF]. The methods explored included random oversampling (ROS), undersampling, leads shift, time shift and time reversing. Each method has a different value of CIR (Tab. I in [START_REF] Ghrissi | Data augmentation for automatic identification of spatiotemporal dispersion electrograms in atrial fibrillation ablation using machine learning[END_REF]). These methods were designed to preserve the integrity of STD pattern and were approved by partner interventional cardiologists. The classification performance of both a shallow CNN and MLR demonstrated that ROS is the best technique. Indeed, ROS increased the sensitivity value by 30% compared to learning from raw data while maintaining high values of specificity and AUC around 90%. For this reason, we opt for ROS for the remaining data formats considered in the present study.

IV. FEATURE SELECTION FOR EGM CLASSIFICATION

The association between the different data models and classifications algorithms is schematized in Fig. 3. A data model corresponds to the coupling between a data representation and a suitable classifier, as summarized next.

A. Matrix Classification

MLR and a shallow CNN, called LeNet-STD, are used for the classification of EGM matrices. LeNet-STD is chosen as a proof of concept that 2D CNN architectures are adapted to STD detection. We study the effect of the receptive field of the network's first conv layer, denoted f size . We recall that the STD pattern can be detected on a minimum of three bipoles positioned on two adjacent PentaRay branches and the average AFCL value is typically 200 ms. Hence, a natural choice is

f size = 4 × (α 1 • AFCL), with α 1 ∈ Q, α 1 ≥ 1. The value α 1 = 3
2 is proposed in [START_REF] Ghrissi | Data augmentation for automatic identification of spatiotemporal dispersion electrograms in atrial fibrillation ablation using machine learning[END_REF], thus capturing cardiac activations along a minimum of one and a half AFCL, and yielding f size = 4×300. The corresponding model is denoted LeNet-STD (4×300) . We investigate further settings such as f size = 4 × 3 and f size = 4 × 200, whose models are denoted LeNet-STD (4×3) and LeNet-STD (4×200) , respectively. An f size of 4 × 200 is conceived to capture exactly an entire AFCL.

B. 2D Image Classification

A classical window size for image classification is 3×3 [START_REF] Simonyan | Very deep convolutional networks for large-scale image recognition[END_REF]. Indeed, f size = 3 × 3 is the smallest receptive field to capture the patterns of left/right, up/down and center, as explained in [START_REF] Simonyan | Very deep convolutional networks for large-scale image recognition[END_REF]. Hence, MLR and LeNet-STD (3×3) are used for EGM-plot image classification.

C. 3D Image Classification

We perform the classification of 3D images with a deep CNN called VGG16-EGM. VGG16-EGM is the result of transferring the VGG16 architecture. Indeed, we re-use the first trained conv blocks of VGG16 model. The transferred layers serve as feature extractor. Their output is fed to three consecutive FC layers with 1024, 128 and 2 nodes, respectively. Only FC layers have learnable weights. Hence, VGG16-EGM is adapted to 3D image classification and can be trained on the EGM dataset.

D. VAVp Classification

In addition to MLR, SVM is another baseline linear classifier in ML. However, classifying VAVp time series was not possible with SVM because this input has 2500 covariates and SVM is not adapted to such a large amount of variables. We propose to reduce the dimensions of VAVp signals with PCA, as explained in Sec. III-C.2. We use the hard threshold technique at 95% of explained variance to decide the number r of PCs to keep. Then, we feed the reduced version of VAVp to SVM. Linear and Gaussian kernels are benchmarked. The models are denoted respectively PCA-SVM Lin and PCA-SVM Gauss . We also perform classification with a shallow 1D CNN (CNN-1D). Implementation: ML experiments are conducted within the Docker environment, running on Quadro P6000 GPU and Ubuntu 19.10 operating system using Python 3.6.9 programming language, Tensorflow 2.1.0 deep learning library for GPU and Keras API.

V. RESULTS

A. Study Dataset

CARTO data of 15 patients are exported in the present study from the database of the Cardiology Department of Nice University Hospital Center (CHU Pasteur), whose Ethics Committee approved the proposed research. Cartographies of both right and left arias are merged. The study dataset includes a cohort of 35563 10-channel EGM signals of length 2.5 s acquired from both right (RA) and left atria (LA). The recordings include 1804 STD and 33759 non-STD samples. The baseline information of the study patients is given in Tab. I. The population is aged 64 years on average and is composed of 80% male and 20% female patients. The average initial AF cycle in left atrial appendage (LAA) is 156 ms. On average, the ablation intervention lasts 2 h 36 min and requires 155 RF shots for a total of 53 min 57 s. The class imbalance ratio (CIR) of our dataset is given by:

CIR = # STD # non-STD ≈ 5%
where # refers to the number of samples. Based on our finding in the comparative study [START_REF] Ghrissi | Data augmentation for automatic identification of spatiotemporal dispersion electrograms in atrial fibrillation ablation using machine learning[END_REF] and due to the extremely low value of CIR, we opt for ROS to handle the lack of a sufficient amount of STD samples, as justified in Sec. III-F.

B. Classification Results

The identification of STD locations is performed with several ML techniques including TL. For this purpose, we benchmark the different EGM classification models detailed in Sec. IV. Their performance on test sets are given in Tab. II, where values are calculated as the average over 5-fold CV, as explained in Sec. III-D. All standard deviations are inferior to 10 -2 . Hence, all trained models have a low generalization error.

1) Matrix Classification: Both LeNet-STD with its three settings of f size and MLR yield good and comparable performance. However, LeNet-STD slightly overperforms MLR, as the latter obtains values of AUC and F1 equal to 92% and 53% respectively. However, The average values of AUC and F1 are 94% and 58% for LeNet-STD. The choice of f size in LeNet-STD has a small impact on the classification performance but has an important effect on the computational cost. Indeed, F1 scores are 58%, 59% and 60%, respectively, with LeNet-STD (4×3) , LeNet-STD (4×200) and LeNet-STD (4×300) respectively. However, the training times of LeNet-STD (4×300) and LeNet-STD (4×200) are very high compared to LeNet-STD (4×3) as shown in Tab. III.

2) 2D Image Classification: Second, we check if classifying 2D images would give good performance because this is the most intuitive input format. In practice, interventional cardiologist analyze visually EGM subplots to detect STD pattern, so this format seems particularly suitable in this context. However, results in Tab. II show no significant enhancement in performance with 2D images compared to EGM matrices. Here again, we notice that LeNet-STD yields a better performance, with an F1 score of nearly 60%, comparing favorably to the 52% provided by MLR.

3) 3D Image Classification: Applying TL of VGG16 model to 3D images is performed as a proof of concept. VGG16-EGM yields good classification performance with values of Acc, AUC and F1 of 93%, 93% and 55%, respectively. This shows that extracting features from 3D plots with the use of conv blocks, trained on a different application (natural images), does work. However, besides the heavy computational cost of VGG16-EGM, as highlighted in Tab III, synthesizing 3D images reveals heavy too. Several extensions were benchmarked for storing and reading images in an optimal way. 4) VAVp Classification: The overall classification performance of VAVp time series is also good but less effective than the remaining data representations. For instance, the values of F1 score do not exceed 50%. Tab II shows that the performance of CNN-1D is slightly better than that of MLR. MLR beats significantly PCA-SVM, mainly in terms of F1 score. Moreover, the Gaussian kernel outperforms the linear one. The VAVp format does not yield the best value in any of the performance metrics considered in this evaluation and results in the lowest F1 scores, all below 46%.

VI. DISCUSSION

Automatic classification of STD EGMs is possible using suitable ML techniques. Based on the results reported in this work, we can claim that classifying raw EGMs stored in matrices with LeNet-STD (4×3) yields a good balance between performance and computational cost. If we observe the values of precision and F1 across all experiments (Tab. II), we notice poor values (30% with VAVp and inferior to 60% with the remaining features) even though values of TPR are high around 80% and 90% (except with PCA-SVM). However, values of PPV and F1 are high for the training set that is balanced with ROS. This low precision on the test sets can be explained by the fact that both test and validation sets remain highly imbalanced. Hence, even though the trained models can identify better STD samples when the training set is augmented, as highlighted in [START_REF] Ghrissi | Data augmentation for automatic identification of spatiotemporal dispersion electrograms in atrial fibrillation ablation using machine learning[END_REF], information about STD class is still less rich than that of non-STD due the redundancy introduced by ROS. A low precision also indicates that the number of FP is important compared to that of TP. This can be acceptable in biomedical data analysis. On the one hand, TPR rate is high which means that true STDs are well detected. On the other hand, it is always preferable to detect non-STDs as STDs than conversely. This allows the model to tag these FP predictions during the mapping phase and give the cardiologist the opportunity to analyze them later, before ablation. Also, Tab. III shows that our solution can be deployed in real time since the prediction time (inference) of a new data sample can be performed in less than a second (maximal prediction time equal to 0.944 s for VGG16-EGM). If more efficient computational resources are deployed, prediction time can be further decreased. The overall performance achieved with our proposed solutions is good with values of accuracy and AUC around 90%, but better results are expected in a medical decision-aid tool. An accuracy of 95% should be attained for the solution to be considered as sufficiently reliable for clinical use. Also, a higher number of patients would provide a richer EGM database with increased variability across patients.

VII. CONCLUSIONS AND PERSPECTIVES

Automatic detection of atrial areas with STD pattern is a valuable decision-aid tool that would help interventional cardiologists identify potential ablation sites for treating persistent AF in a faster and more reliable manner than the current visual inspection. To identify STD, several features are extracted from EGM recordings either automatically with TL and end-to-end NN training or in a hand-crafted fashion with VAVp time series. These different data representations are classified with the use of adapted ML algorithms giving rise to a variety of EGM classification models. Moreover, we study the effect of some hyperparameters and settings like the choice of receptive fields and kernels in SVM. Based on the analysis of both the classification performance on the test set and the computational cost of the different classification models, the best performance is achieved with LeNet-STD and f size = 4 × 3 for classifying raw EGM matrices. The average performance over 5-fold CV reaches 94% of accuracy and AUC added to an F1-score of 60%. The low precision and F1-score can be explained by the insufficient amount of STD samples even thought the class imbalance issue is alleviated with DA during the training phase. On the other hand, VGG16-EGM demonstrates that extracting features with conv blocks of the VGG16 model, trained on natural images, works as well as shallower architectures like LeNet-STD, but is very expensive computationally. By providing interventional cardiologists with a real-time objective measure of STD, the proposed solution presents the potential to improve the efficiency and effectiveness of this fully patienttailored catheter ablation approach for treating persistent AF. Future work should investigate alternative ML models like long short-term memory (LSTM) neural networks, as they are well adapted to time series classification [START_REF] Hannun | Cardiologistlevel arrhythmia detection and classification in ambulatory electrocardiograms using a deep neural network[END_REF].

Fig. 1 :

 1 Fig. 1: (A) PentaRay multi-spline catheter (BioSense Webster Inc). (B) Dispersion areas defined and delineated via a mapping approach [6]. Channels A 1-2, A 3-4, B 5-6, B 7-8, C 9-10 and C 11-12 display STD contrarily to the remaining ones.

Fig. 3 :

 3 Fig. 3: Classification models adapted to the different EGM data features.

TABLE I :

 I Baseline information about patient's population.

TABLE II :

 II Average classification performance on test set through 5-fold CV.

	Feature	Model	Training cost time nb tr-par	Prediction time (s)
		MLR	00:01:49	400,672	0.139
	Matrix	LeNet-STD (4×3)	00:11:04	1,289,458	0.643
		LeNet-STD (4×200)	00:24:57	1,214,322	0.625
		LeNet-STD (4×300)	00:37:51	1,175,922	0.616
	2D Image	MLR LeNet-STD (3×3)	01:08:57 01:10:15	400,672 1,289,362	0.144 0.618
	3D Image	VGG16-EGM	14:35:28	100,795,778	0.944
	VAVp	PCA-SVM Lin PCA-SVM Gaus	00:10:14 00:55:32	O(m 2 n) O(m 3 r)	0.003 0.002
		MLR	00:12:39	400,672	0.141
		CNN-1D	00:11:25	80,066	0.585

TABLE III :

 III Computational cost of training on balanced dataset and predicting the label of a test data sample. Time is given as hours(hh):minutes(mm):seconds(ss). Symbol nb tr-par stands for the number trainable parameters, which might be inferior to the total number of parameters in case of TL when used as a feature extractor. The number of variables is n = 2500 and r ≈ 300.