Clarisse Mallet
email: clarisse.mallet@univ-bpclermont.fr

Hélène Agogué

Frédérique Bonnemoy

Katell Guizien

Francis Orvain

Christine Dupuy

Guizien Katell

Structures of benthic prokaryotic communities and their hydrolytic enzyme activities resuspended from samples of intertidal mudflats: An experimental approach

Keywords: resuspension, mudflat biofilm, Bacteria, Archaea, community structure, hydrolytic activities

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

Introduction

Terrestrial and marine influences converge at tidal flats to produce a complex patchwork of habitats. Research on the productivity of coastal systems has established that intertidal flats influence, both physically and trophically, the adjacent marine and land areas. The intense microbial activity due to microalgae and prokaryotes in these areas results in great biological productivity that is essential for aquaculture. Mudflats are therefore socially and economically extremely important [START_REF] Héral | La Capacité trophique des bassins ostréicoles[END_REF]. Most of the primary production in these areas is due to benthic microalgae, mainly epipelic diatoms [START_REF] Blanchard | Contrôle de la dynamique à court terme du microphytobenthos intertidal par le cycle exondation-submersion[END_REF][START_REF] Leguerrier | Numerical analysis of the food web of an intertidal mudflat ecosystem on the Atlantic coast of France[END_REF] because the turbidity of the waters limits the presence of macrophytes and phytoplankton [START_REF] Mclusky | The estuarine ecosystem[END_REF]. The twice-daily emersion in water and the access to daylight stimulates epipelic microalgae to migrate to the surface of the sediment, where they form a continuous biofilm. This biofilm may contain over 20 mg of chlorophyll (Chl a) per m 2 and its photosynthetic activity can increase the algal biomass, so doubling the size of the biofilm [START_REF] Blanchard | Properties of the dynamics of intertidal microphytobentic biomass[END_REF]. This great productivity can lead to depletion of nitrogen or phosphorus, conditions that stimulate microalgae to secrete exopolymeric substances (EPS).

These EPS are produced mainly by "overflow metabolism" or other processes like locomotion [START_REF] Brouwer | Daily fluctuations of exopolymers in cultures of the benthic diatoms Cylindrotheca closterium and Nitzchia sp. (Bacillariophyceae)[END_REF][START_REF] Orvain | Carbohydrate production in relation to microphytobenthic biofilm development: an integrated approach in a tidal mesocosm[END_REF]. The EPS form a matrix around the microalgae [START_REF] Paterson | Water flow, sediment dynamics and benthic biology[END_REF] that is one of the main resources leading to the rapid development of prokaryotes [START_REF] Goto | Biodegradation of photosynthetically produced extracellular organic carbon from intertidal benthic algae[END_REF][START_REF] Middelburg | The fate of intertidal microphytobenthos carbon: an in situ 13C-labeling study[END_REF][START_REF] Van Duyl | Tidal coupling between carbohydrate concentrations and bacterial activities in diatom-inhabited intertidal mudflats[END_REF]. Bacterial production can be as high as or even higher than the production of the microphytobenthos [START_REF] Hamels | Uncoupling of bacterial production and flagellate grazing in aquatic sediments: a case study from an intertidal flat[END_REF][START_REF] Pascal | Seasonal variation in consumption of benthic bacteria by meio-and macrofauna in an intertidal mudflat[END_REF][START_REF] Van Duyl | Tidal coupling between carbohydrate concentrations and bacterial activities in diatom-inhabited intertidal mudflats[END_REF]. While the production of bacteria fluctuates widely during the year this does not result in fluctuations in their abundance. The poor correlation between biomass and bacterial production has been classically explained by their "top-down" disappearance [START_REF] Thingstad | Control of bacterial growth in idealized food webs[END_REF]. Several experiments designed to study grazing on mudflats (Brouage, France) [START_REF] Pascal | Seasonal variation in consumption of benthic bacteria by meio-and macrofauna in an intertidal mudflat[END_REF] throughout the year have shown that the bacteria consumed by larger animals never exceeded 6% of the bacterial production, so having only a limited impact on bacterial production and stock. However, grazers may stimulate bacterial production by disturbing the biofilm which allows the diffusion of oxygen and nutrients throughout the sediment [START_REF] Alkemade | Experimental evidence for the role of bioturbation by the marine nematode Diplolaimella bruciei in stimulating the mineralization of Spartina anglica detritus[END_REF] or by secreting nutrient-rich compounds such as mucus [START_REF] Riemann | Symbiotic relations of sediment-agglutinating nematodes and bacteria in detrital habitats: the enzyme-sharing concept[END_REF]. The activity of grazers can also increase the resuspension of sediment leading to the export of benthic prokaryotes to the pelagic environment [START_REF] Blanchard | Kinetics of tidal resuspension of microbiota: testing the effects of sediment cohesiveness and bioturbation using flume experiments[END_REF][START_REF] Orvain | The influence of sediment cohesiveness on bioturbation effects due to Hydrobia ulvae on the initial erosion of intertidal sediments: A study combining flume and model approaches[END_REF].

The free-living or particle-associated prokaryotes transferred to the water column may then find their way into coastal waters [START_REF] Teal | Energy flow in the salt-marsh ecosystem of Georgia[END_REF] where they may be consumed by filter-feeding organisms or pelagic grazers [START_REF] Guizien | Microorganism dynamics during a rising tide: Disentangling effects of resuspension and mixing with offshore waters above an intertidal mudflat[END_REF][START_REF] Wainright | Stimulation of heterotrophic microplankton production by resuspended marine sediment[END_REF].

Both tidal currents and wind-induced waves can cause the resuspension of sediment [START_REF] Blanchard | Properties of the dynamics of intertidal microphytobentic biomass[END_REF]. Sediment erosion generally increases with the rate of shear or friction (u* expressed in cm s -1 ). Erosion rates depend on the balance between shear stress and the critical threshold for bed erosion. This threshold depends on properties of the sediment, and physical, geochemical and biological processes [START_REF] Grabowski | Erodibility of cohesive sediment: the importance of sediment properties[END_REF]. The EPS matrix secreted by the benthic microbial communities plays a key role in sediment stabilization/destabilization, and hence in the export and retention of microphytobenthic and prokaryotic biomasses [START_REF] Gerbersdorf | Microbial assemblages as ecosystem engineers of sediment stability[END_REF][START_REF] Underwood | The importance of extracellular carbohydrate production by marine epipelic diatoms[END_REF]. The sequential resuspension of microorganisms in a subtidal setting subjected to increasing hydrodynamics energy has been attributed to differences in sediment erodibility and the behaviour of microorganisms [START_REF] Shimeta | Resuspension of benthic protists at subtidal coastal sites with differing sediment composition[END_REF][START_REF] Grabowski | Erodibility of cohesive sediment: the importance of sediment properties[END_REF]. This sequential resuspension of microorganisms should be enhanced during the erosion of the biofilms that form on the sediment surface in intertidal flats because the vertical structure of the biota is well defined. Chronic erosion (type 0 erosion) generally occurs and can be defined as a fluff layer erosion (i.e. simple detachment of loose aggregates from the sediment matrix, at low bed shear stress). [START_REF] Orvain | The influence of sediment cohesiveness on bioturbation effects due to Hydrobia ulvae on the initial erosion of intertidal sediments: A study combining flume and model approaches[END_REF] demonstrated the relevance of bioturbation by macrofauna in the creation of such a biogenic fluff layer. This chronic erosion can be followed by a catastrophic erosion (namely mass erosion; type I and/or II according to the consolidation status of the bed load), which corresponds to the general bed failure that can be achieved only when wind-induced waves produce high values of bed shear stress that can overpass the critical threshold for mass erosion (i.e. resistance force). This defined vertical distribution is accompanied by a spatial structure due to top-down control by benthic herbivores [START_REF] Weerman | Top-down contral inhibits spatial self-organization of a patterned landscape[END_REF]. The drivers of sequential erosion and the critical erosion thresholds of the microorganisms that make up a biofilm are analyzed in a companion paper (Dupuy et al., this issue). Resuspension of the top few centimeters of sediment can increase the plankton biomass and bacterial growth [START_REF] Wainright | Sediment-to-water fluxes of particulate material and microbes by resuspension and their contribution to the planktonic food web[END_REF]. This affects the coastal planktonic microbial food web due to the direct movement of cells from the sediment into the water column so increasing the seston concentration or the mineralizing capacity [START_REF] Wainright | Stimulation of heterotrophic microplankton production by resuspended marine sediment[END_REF][START_REF] Wainright | Sediment-to-water fluxes of particulate material and microbes by resuspension and their contribution to the planktonic food web[END_REF]. Dissolved nutrients and trophic interactions like bacterivory by nanoflagellates can also have indirect effects [START_REF] Blanchard | Kinetics of tidal resuspension of microbiota: testing the effects of sediment cohesiveness and bioturbation using flume experiments[END_REF][START_REF] Garstecki | Effects of experimental sediment resuspension on a coastal planktonic microbial food web[END_REF]. Resuspension has been shown to increase the abundance and volume of bacteria in both field and experimental studies [START_REF] Ritzrau | Increase of microbial biomass in the benthic turbidity zone of Kiel Bight after resuspension by a storm event[END_REF][START_REF] Wainright | Stimulation of heterotrophic microplankton production by resuspended marine sediment[END_REF], but most of these early studies considered sediment resuspension to be a massive, homogeneous process. The present study resuspension experiments were done to determine whether the sequential resuspension of prokaryotes under varying environmental conditions could alter the direct and indirect effects on planktonic food-web. We monitored the enrichment of resuspended prokaryotic cells and their structure to assess if there was sequential resuspension under all the environmental conditions tested.

We also checked whether prokaryotic cells were alive or dead so as to better identify their indirect effects on the plankton food-web. Lastly, we measured the activities of their hydrolytic enzymes. These enzymes regulate the assimilation of nutrient monomers by microbial cells and therefore play an important part in the cycling of organic matter and remineralization.

Material and Methods

Field sampling

Muddy sediment samples were collected from Marennes-Oléron Bay (Atlantic Coast of France) in July 2008 (Fig. 1) (45°54′50′′N, 01°05′25′′W) during spring tides (17 and 19 July), maximum tides (21 July) and neap tides (22 and 24 July). At each sampling occasion, two 8 cm diameter sediment cores were taken at low tide (middle of the emerged period). Only ridges were sampled since biofilms are not normally found on runnels. The sediment cores were placed in a tank for transport back to the laboratory. The resuspension experiments were done at the time of the immersion period in the field. Three additional 15 cm diameter cores were taken to assess the biotic and abiotic parameters of the top 2 cm of sediment.

Resuspension experiments and instrumentation

The sediment samples were transferred from the cylindrical cores to the bottom of the flume of an erosion device developed by IFREMER. This was modified to form a straight recirculation flume, named "Erodimetre" [START_REF] Guizien | Accounting for rough bed friction factors of mud beds due to biological activity in erosion experiments[END_REF][START_REF] Hir | Instrumentation légère pour la mesure de l"érodabilité des sédiments vaseux ou sablovaseux[END_REF][START_REF] Orvain | Spatio-temporal variations in intertidal mudflat erodability: Marennes-Oléron Bay, western France[END_REF]. The flume was filled with filtered artificial seawater (15L) to obtain a baseline close to 0 for each type of microorganism. The discharge through the erosion device was increased in twenty 5-minute steps to yield bed friction velocities ranging from 0 to 11cm.s -1 .

A total of 6 samples (1.5L each) were taken from the water column of the erodimeter as the flow, and thus shear velocity, was increased. These were used to monitor the resuspension of prokaryotes and the total particle matter (TPM) concentration. The induced bed shear stress was calculated from measurements of the pressure head loss between the upstream and downstream ends of the sample section [START_REF] Guizien | Accounting for rough bed friction factors of mud beds due to biological activity in erosion experiments[END_REF]. Friction velocity was calculated as the square root of the bed shear stress divided by the sea water density. Turbidity and fluorescence were continuously recorded and used to measure chl a and suspended particular matter. Erosion kinetics were analyzed to evaluate the relationship between bed erodibility (erosion rates of suspended particulate matter and chl a biomass) and the sediment properties (abiotic and biotic factors) and their temporal changes over 14 days (Orvain et al., this issue).

From this long set of experiments across a spring-neap tidal cycle, we selected 4 dates for a detailed analysis of the fate of bacterial and archaeal benthic communities after resuspension.

The dates were chosen to evaluate the response of prokaryote resuspension for different biofilm stages of development. The July 17 sample illustrated an increase in tidal range (midtime between neap tides and spring tides, low tide occurs in the morning), those taken on July 20 and 21 (spring tide) corresponded to a maximum tidal range (just before and just after the peak, low tide occurred around noon), while the July 24 sample reflected the response to a decrease in tidal range (midtime between spring tides and neap tides, low tide started after noon).

Abiotic parameters

Salinity and nutrient (NH 4 , NO 3 , NO 2 , PO 4 , silicates) concentrations in the upper layer of the sediment Pore water was separated from 300 mL of fresh sediment by centrifugation (4 °C, 3000 g, 15 min). Several aliquots of interstitial water were obtained by passage through GF/C filters.

Salinity was determined with a refractometer. Ammonia was assayed using the colorimetric Koroleff (1969) technique immediately after filtration. The remainder of the filtered pore water was stored at -20°C. Nitrates, nitrites, silicates and phosphates were assayed using a Skalar automated segmented flow analyzer with classical spectrocolorimetric techniques (adapted from Treguer and Le Corre, 1975).

Carbohydrates and proteins from EPS in the sediment

EPS were extracted from 5 mL sediment as described in [START_REF] Takahashi | Optimising extraction of extracellular polymeric substances (EPS) from benthic diatoms: comparison of the efficiency of six EPS extraction methods[END_REF]. Bound EPS were extracted from pellets by suspending each one with about 1 g of cation exchange resin (Dowex Marathon C, Na+; Sigma-Aldrich) and 5 mL ASW and gently agitating the suspension for 1 h at 4°C. The samples were then centrifuged (15°C, 3000 g, 10 min) and the resulting supernatants were frozen (-20°C). Aliquots (1 mL) of each fraction were used to measure the carbohydrate contents by the Dubois method [START_REF] Dubois | Colorimetric method for determination of sugars and related substances[END_REF] with Dglucose (Sigma-Aldrich) as a standard.

Total particulate matter (TPM): particulate organic (POM) and mineral (PIM) matter

TPM was measured according to [START_REF] Aminot | Manuel des analyses chimiques en milieu marin[END_REF]. Erodimeter seawater samples (100 -500 ml) were filtered through a Whatman GF/C (47 mm in diameter) under reduced pressure <10 mm Hg within 1 h after the end of the experiment. Each filter was heated at 490°C for 2 h to eliminate any organic carbon matter and weighed. Filters that had been used to treat samples were rinsed twice with distilled water to remove salt, dried at 60°C for 12 h and weighed to measure the TPM. The proportions of particulate inorganic matter (PIM) and particulate organic matter (POM) were determined by heating the filters at 490°C for 2h and then weighing them.

Another 40 mL sample of sediment was stored frozen (-20 °C) and freeze-dried for estimation of C and N using a nitrogen and carbon analyser 1500 (CARLO ERBA).

Biotic parameters

The algal biomass in sediment and water was assessed using chlorophyll a as a proxy, which was measured fluorometrically [START_REF] Lorenzen | A method for the continuous measurement of in vivo chlorophyll concentration[END_REF].

Benthic prokaryotes were extracted from the sediment as recommended by [START_REF] Danovaro | Determination of virus abundance in marine sediments[END_REF] and [START_REF] Manini | Synoptic determination of living/dead and active/dormant bacterial fractions in marine sediments[END_REF] and each sample was divided into two aliquots. One was fixed with (1 %) glutaraldehyde and stored at 4°C. The other was stored at 4°C and used to detect "live" and "dead" cells. Prokaryotes were counted in a FACSCalibur flow cytometer (Becton Dickinson) equipped with an air-cooled laser providing 15 mW at 488 nm with the standard filter set-up. Samples were stained with SYBR Green 1 (1:10X, 10,000 fold dilution of commercial stock, Molecular Probes, Oregon, USA) [START_REF] Brussaard | Optimization of procedures for counting viruses by flow cytometry[END_REF][START_REF] Duhamel | Flow cytometric analysis of bacteria-and virus-like particles in lake sediments[END_REF]. Populations of prokaryotes differing in size and fluorescence intensity were identified by plotting side scatter (SSC) against green fluorescence (530 nm wavelength, fluorescence channel 1 of the instrument, FL1). We also identified free and particle-associated prokaryotes (attached cells). The live and dead cells in unfixed samples were measured in samples that had been diluted and stained with SYBR Green 1 (1:10X) and 10µg ml -1 propidium iodide (Sigma Chemical Co.), and incubated for 15 min in the dark at room temperature (Falcioni et al., 2008). A dot plot of red (670 nm fluorescence channel 3, FL3) against green fluorescence (FL1) distinguished live cell clusters (cells with intact membranes and DNA) from dead cells (with compromised membranes). FCM list modes were analysed using CellQuest Pro software (BD Biosciences, version 4.0).

The efficiency with which cells were transferred to the erodimeter water during the erosion was calculated from the enrichment factor (EF):

Where the water cell concentration is in cell.mL -1 , TPM is in mg.mL -1 , and the cell content of the 1 st cm of sediment core is in cell.mg -1 dry sediment.

Potential enzymatic activities

The potential βglucosidase and leucine aminopeptidase activities in sediment were measured essentially as described by Mallet andDebroas (1999, 2001). The saturating concentrations of methylumbelliferone (MUF)-β-D-glucoside used for the sediment and the water samples were the same: 1mM for -glucosidase activity and 100µM of L-leucine-7-amino-4-naphthylamide for leucine aminopeptidase activity. Controls and triplicate sediment samples were incubated at in situ temperature for 45, 75 and 120 min to measure -glucosidase activity and for 10, 30 and 60 min to measure leucine aminopeptidase activity. Water samples were incubated with substrate for 24h to measure -glucosidase activity and for 6h to measure leucine aminopeptidase activity. The fluorescence of the supernatants (14000g at 4°C for 2 min) were also measured (SAFAS FLXXenius spectrofluorimeter) using excitation at 365 nm and emission at 460 nm for -glucosidase activity and excitation at 340 nm and emission at 410 nm for aminopeptidase activity. Solutions of 4-methylumbelliferone (0 -1 μM) for glucosidase activity and 2-naphthylamine (0 -12.5 μM) for aminopeptidase activity were freshly prepared with sediment slurry and used as standards. Specific activities were also calculated by dividing the total fluorescent by the total cell concentration (nmol.cell -1 .h -1 ).

Prokaryotic genetic structure

Genomic DNA was extracted from fresh sediment (equivalent of 650 mg oven-dried sediment) and purified using the Ultra Clean Soil DNA isolation kit (MoBio Laboratories) according to the manufacturer's instructions. Genomic DNA was extracted from water onto 0.2 µm filter (100 mL) and purified by alkaline lysis [START_REF] Batisson | Isolation and characterization of mesotrione-degrading Bacillus sp. from soil[END_REF]. DNA quality was checked by electrophoresis on 1% (w/v) agarose gels and quantified using NanoDrop.

The bacterial (V6-V8 regions) and archaeal 16S rDNA genes were amplified by PCR using the primers GC-968f and 1401r for bacterial DNA and GC-934f and 1386r for archaeal DNA (MWG-Biotech). The PCR mix (50 µL) contained 1X PCR buffer, 2.5 mM MgCl 2 , 200 mM of each dNTP, 20 pmol of each primer, 250 ng mL -1 bovine serum albumin (BSA, Sigma), 1.5 units of HotStart Taq DNA polymerase (Qiagen), and 30 ng sediment DNA extract. The samples were amplified in an iCycler thermocycler (Bio-Rad) using the following programs: for bacteria: 15min at 95°C, 35 cycles of 1min at 97°C, 1min at 58°C and 1min at 72°C, and finally 10min at 72°C; for archaea: 15min at 95°C for, 14 cycles of 45s at 95°C, for 1min at 65°C decreasing to 58.5°C in 0.5°C steps at each cycle, and 30s at 72°C then 20 cycles of 45s at 95°C, 1min at 58°C and 30s at 72°C, and finally 7min at 72°C. PCR products were checked by electrophoresis through 0.8% (w/v) agarose gels and quantified using the DNA quantitation kit fluorescence assay (Sigma). PCR-16S rDNA gene products were analysed by DGGE using a D-Code Universal Mutation Detection System (Bio-Rad). Aliquots of each PCR product (500 ng) were loaded onto 8% polyacrylamide (w/v) denaturating gels with linear gradients of 40-60% (100% denaturant contains 7 M urea and 40% formamide). Gels in 1X TAE buffer (pH 8) were subject to 70 V at 60°C for 16h. The DGGE gels were then stained in 1X TAE buffer containing Gel Star diluted 1/20000 (Lonza, Rockland, ME-USA) and the band patterns digitized using a BioSpectrumAC Imaging System (UVP). The digital data were analysed using Gel ComparII software (Applied Maths, Kortrijk, Belgium). The total band intensity of each lane was normalised among lanes and used to calculate the relative abundance of each major OTUs (%). A DNA band was considered to significant if it accounted for more than 0.5 % of the total lane intensity. The richness (R) was estimated as the number of bands. The richest samples were cloned and sequenced. The genomic DNA in these samples was amplified with 968f/1401r or 934f/1386r primers and cloned into a pGEM-T-Easy vector (Promega) to construct clone libraries. These clones were reamplified and rerun on DGGE gels to compare them with the parent bands. At least two cloned fragments that comigrated with the original bands were sequenced (MWG -Biotech). Sequences were submitted to the National Center for Biotechnology Information (NCBI, BLASTn program [START_REF] Altschul | Gapped BLAST and PSI-BLAST: a new generation of protein database search programs[END_REF] for species assignment and to the CHECK-CHIMERA program of the Ribosomal Database Project (RDP [START_REF] Maidak | A new version of the RDP (ribosomal database project)[END_REF]) to detect potential chimeric artifacts [START_REF] Kopczynski | Recognition of chimeric small-subunit ribosomal DNAs composed of genes from uncultivated microorganisms[END_REF].

Statistical analyses

Statistical analyses were carried out using PAST software (PAlaeontological STatistics, [START_REF] Hammer | PAST: Paleontological Statistics Software Package for Education and Data Analysis[END_REF]. Principal component analysis (PCA) was used to group samples according to environmental variables using the Pearson correlation coefficient. Prior to use one-way analysis of variance (ANOVA), to test difference between sediment cores for a given parameter, normality and homoskedasticity were checked (Shapiro-Wilk test and Levene's test respectively). Differences between individual means were then compared using Tükey's honest significant difference (HSD) post-hoc test. Significance was set at p ≤ 0.05.

Correlations between abiotic parameters and chlorophyll a contents, enzymatic activities and prokaryotic abundances in erodimeter water were checked with the Pearson correlation coefficient (r) and its statistical significance. Pairwise similarity matrices were calculated for the DGGE patterns using the Dice equation for presence/absence and the Bray-Curtis equation for relative peak height data. Dendrograms were generated from the Dice matrix as described by [START_REF] Ward | Hierarchical grouping to optimize an objective function[END_REF]. The consistency of a cluster was described by the cophenetic correlation, which calculates the correlation between the dendrogram-derived similarities and the matrix similarities. Pairwise Analysis of Similarity (ANOSIM, [START_REF] Clarke | Change in Marine Communities: An Approach to Statistical Analysis and Interpretation[END_REF] was used to test if the sediment samples were similar in term of chemical and biological parameters. It tested the hypothesis that parameters within each sediment sample were more similar to each other than to parameters in the other samples. The statistical significance of the separation was given by a Bonferroni-corrected p-value (R, p < 0.05).

Results

Sediment

The biological and chemical parameters of the sediment cores taken at different dates were significantly different (R: 0.55 p: 0.0001, Fig. 2). The July 17 cores were opposite to the other samples (Fig. 2) with significant lowest salinity (Table 1), which implied the highest water content. This date was also characterized by significant lower colloidal carbohydrate concentrations than those of the July 21 and 22 (Table 1). The July 22 samples were also significantly differed to the other sampling dates (Fig. 2) with silica concentrations significantly lower than the other (Table 1). The profiles of the core samples taken on this date seemed to be opposite to those of the July 21 and 24 samples, whose sediments had the highest nitrogen concentrations (Fig. 2; Table 1). The highest prokaryotic abundances were observed in the July 17 and 24 samples (Table 1). For the July 17 and 22 samples, highest leucine aminopeptidase activities were observed with for the July 22 sample highest glucosidase activity too (Table 1).

The structures of the bacterial communities in the four sediment samples differed significantly (R: 0.9, p: 0.008). We found only 3 major phyla: Gamma-Proteobacteria (mainly Pseudomonadales and Chromatiales and unidentified Gamma-Proteobacteria), Actinobacteria and Cyanobacteria (Fig. 3A). The richness (as numbers of DGGE bands) varied from 22 on July 24 to 33 on July 21 (Fig. 3A). Crenarchaeota formed the major group except in the July 17 samples (Fig. 3B). The July 22 cores were the least rich ( 14) and the July 17 cores were the richest (33).

Microorganism resuspensions in the erodimeter water

We gradually increased the shear velocity (u*) in the erosion flume to mimic low to highly turbulent flow. There were two phases of total particulate matter (TPM) erosion. The shear velocity in the first phase was low (u* < 5 cm.s -1 ) and the concentration of particles was very low. Only the biogenic fluff layer was resuspended during this phase. This layer is mostly composed of particles detached from the sediment matrix like the fluff layer or track and/or pseudofecal mounds created by faunal bioturbation). In the second phase mass erosion of the sediment occurred and the number of particles increased (Orvain et al., this issue).

Enrichments of resuspended prokaryotes (total cell fraction) was more effective with velocities below 5 cm.s -1 , before and during the precocious erosion phase, when the biogenic fluff layer was resuspended, as this layer is created by surface fauna activity like tracks (Fig. 4A). The total cell abundance in the erosion flume fluctuated little, from 1.3 10 5 cells.ml -1 on July 17 and 3.6 10 5 cells.ml -1 on July 22 under our controlled conditions. The enrichment in free cells followed the same pattern as that for total prokaryotes (Fig. 4A) and represented 75.1  16.5% of total resuspended cells. Enrichment at the lowest friction was maximal on July 17 and decreased as erosion increased. There was little enrichment in attached cells but it increased during resuspension of the biogenic fluff layer (Fig. 4B). The concentration of attached cells increased when there was mass erosion of the sediment and enrichment reached 25% on July 24 and 44% on July 21. Less than a third of the cells in the erodimeter water were intact (potentially active). Their enrichments followed the same pattern as that of the free cells but there were fewer of them (Fig. 4C). They accounted for only 10% of the total cells on July 17 and 27% on July 21, but their abundance increased to more than 30% of the total cells at the end of the experiment, during sediment mass erosion. The -glucosidase activity fluctuated between 2.4 10 -7 and 1.9 10 -6 nmol.cell -1 h -1 and that of leucineaminopeptidase between 6.5 10 -7 and 4.4 10 -6 nmol.cell -1 h -1 . The activities had lowest values when the shear velocity was less than 5 cm.s -1 , except for the samples collected on July 21 and July 24 (Fig. 5A,B).

The PCA map indicated that the enrichments in total, free and live cells varied inversely as enrichment in total particulate matter, chlorophyll a and the enzyme activities (Fig. 6). The other axis was better characterized by the C:N ratio and the concentration of attached cells.

These two axes clearly separated the samples into two major clusters (Fig. 6). The samples corresponding to mass erosion of sediment, rich in TPM lay on the first axis. Conversely, the samples corresponding to erosion of the biogenic layer lay on the second.

Structure of resuspended prokaryotes

Attached cells accounted for more of the resuspended bacteria than did free cells for all dates (Fig. 7). Bacterial populations were resuspended sequentially, especially for the July 17 and July 24 samples, Gamma-proteobacteria and Pseudomonales appeared first, followed by Actinobacteria and finally the Chromatiales (Fig. 7A) and the Cyanobacteria (Fig. 7E), which were also resuspended at the beginning of the experiment. Nevertheless, enrichment varied with the sampling date both qualitatively (OTUs) and quantitatively (relative abundance of each OTU). Concerning the archaeal community, Archaea were only detected during the mass erosion events. The dominant Archaea were crenarchaeotal populations (mainly unidentified Crenarchaeota, MG I and thermoprotei) (Fig. 8). Archaeal cells were very effectively resuspended, except from the July 17 sample, because the richnesses in the resuspended fractions were greater than those of the sediment. The mass erosion of sediment collected on July 17 produced the greatest richness and diversity and there was a sequential appearance of populations, as for the Bacteria (Fig. 8).

Discussion

It has been claimed that erosion of the sediment bed affects the pelagic trophic network by inhibiting primary production because it increases turbidity. But it may also be affected directly or indirectly by active prokaryotes released from the sediment. We have characterised the sequential release of prokaryotes from bed sediment samples in terms of their structure (free or attached cells and their composition), physiology (alive or dead) and enzyme activity that were resuspended by increasing erosive forces from samples with and without biofilm.

Resuspension of prokaryotic cells

Subtidal sediments remain unconsolidated and are relatively easy to erode. But sediment in intertidal areas exposed to the air tends to become consolidated after recurrent desiccation and biofilm development [START_REF] De Brouwer | Short-term dynamics in microphytobenthos distribution and associated extracellular carbohydrates in surface sediments of an intertidal mudflat[END_REF][START_REF] Orvain | Spatio-temporal variations in intertidal mudflat erodability: Marennes-Oléron Bay, western France[END_REF][START_REF] Porter | Effect of tidal resuspension on benthic-pelagic coupling in an experimental ecosystem study[END_REF][START_REF] Underwood | The importance of extracellular carbohydrate production by marine epipelic diatoms[END_REF]. The sediment samples we studied were very resistant to erosion. Mass erosion was produced only by high shear velocities (u*>5 cm.s -1 ). These shear velocities can only be generated by wind-induced waves in the field. This tendency held for all sediments, despite differences in their chemical characteristics. Very low shear velocities resulted in limited erosion of the TPM in all our experiments. The intensity of this 'fluff layer erosion' varied with the composition of the bed sediment and the critical threshold shear velocity (Dupuy et al., this issue; Orvain et al., this issue).

Prokaryotes were always resuspended during the fluff layer erosion phase when shear velocities were below 5 cm.s -1 and before the great increase in particulate matter erosion at higher shear velocities. Low friction velocities, when the concentrations of TPM were low, produced the greatest enrichment in prokaryotic cells. Enrichment decreased at the end of the fluff layer erosion when mass erosion began. The fluff layer in a mud site can be very important for sediment transport [START_REF] Orvain | Spatio-temporal variations in intertidal mudflat erodability: Marennes-Oléron Bay, western France[END_REF][START_REF] Ziervogel | Do benthic diatoms influence erosion thresholds of coastal subtidal sediments[END_REF], because this material is especially enriched in OM and constitute a chronic erosion compared to the general bed failure, which can be defined as 'catastrophic' [START_REF] Mariotti | Modeling the effect of tides and waves on benthic biofilms[END_REF].

The unconsolidated surface fluff layer, with a water content close to 85-98% of dry weight, was resuspended using low hydrodynamic conditions. The cells were unevenly distributed; they are scattered throughout the top mm of the sediment in the organic matter and this distribution is probably due to the patchy distribution of microphytobenthic biofilms (Dupuy et al., this issue). The surface layers of sediment always contained more bacteria than did the subsurface suboxic sediment layers [START_REF] Parkes | Recent studies on bacterial populations and processes in subseafloor sediments: a review[END_REF]. The decrease in microbial cell counts down through the sediment profile and the shift in community structure probably results from the decreased in organic carbon quality and availability in aged, deeply buried sediments [START_REF] Parkes | Recent studies on bacterial populations and processes in subseafloor sediments: a review[END_REF]. The volume of pore-water may also be a major determinant of prokaryotic abundance in sediments [START_REF] Schmidt | Constancy of bacterial abundance in surficial marine sediments[END_REF]. The force that determines the decrease in prokaryotic abundance and changes in community structure down the vertical profile of a sediment can be a complex mixture of biotic and abiotic factors, such as poor mixing or bioturbation, sediment composition (grain size and distribution, sediment water content), energy stress conditions (low food, electron acceptors, availability of dissolved substrates and metabolites), and/or predatory pressures and competition.

Most of the cells in the water were free. Attached bacteria are less abundant in many pelagic marine ecosystems than are free-living bacteria. They generally account for less than 5% of the total bacteria, but this can rise to 10% [START_REF] Lapoussière | Role of free-living and particle-attached bacteria in the recycling and export of organic material in the Hudson Bay system[END_REF]. However, particleattached bacteria can form a much greater fraction (up to 96%) of the total bacteria in estuarine systems [START_REF] Lapoussière | Role of free-living and particle-attached bacteria in the recycling and export of organic material in the Hudson Bay system[END_REF]. We found that they accounted for less than 20% of the total suspended cells until the shear velocities increased above 5cm.s -1 , except in the samples taken on July 21 (Fig 5A). Previous studies have demonstrated that the abundance (or biomass) of particle-attached bacteria depended on the number and/or size of particles available for attachment [START_REF] Cho | Major role of bacteria in biogeochemical fluxes in the ocean's interior[END_REF][START_REF] Garneau | Importance of particleassociated bacterial heterotrophy in a coastal Arctic ecosystem[END_REF][START_REF] Lapoussière | Role of free-living and particle-attached bacteria in the recycling and export of organic material in the Hudson Bay system[END_REF]. We see a negative relationship between the attached bacteria and the POM in the samples taken on July 21 (r = -0.97, p<0.05) and July 22 (r = -0.88, p<0.05). The high density of motile grazers caused the surface of the bed to be strongly pelletised, which significantly increased the velocity at which eroded sediment settled. These results may also be influenced by the fact that the abundance (or biomass) of particle-attached bacteria is linked to the biogeochemical composition of the suspended material [START_REF] Fandino | Variations in bacterial community structure during a dinoflagellate bloom analyzed by DGGE and 16S rDNA sequencing[END_REF]Wang and Yin, 2009). Particle-attached bacteria can play an important role in the transformation of freshly produced POC despite their small contribution (often less than 30%) to total bacterial biomass [START_REF] Ghiglione | Diversity of total and active free-living vs. particle-attached bacteria in the euphotic zone of the NW Mediterranean Sea[END_REF]. The positive correlation between leucine aminopeptidase activity and attached cells (r=0.45, p<0.05) supports this idea. Extracellular enzymes may be important for the dispersion or release of attached microbial cells.

Few of the resuspended cells were alive, in contrast to the percent of living cells in the sediment (around 50%). Thus dead cells (those with damaged membranes) accounted for the greatest fraction (70 -74%) of resuspended bacterial assemblages in all samples analyzed. These results suggest that the high mechanical stress produced by the shear velocity interferes with the benthic cells, as there were many active cells in the sediment. But whether the cells were attached or free did not seem to be important, as we found significant positive relationships between the attached and active cells (r=0.98, p<0.05) and between free and active cells (r=0.90, p<0.05). Nevertheless, our results corroborate [START_REF] Pusceddu | Sediment resuspension effects on the benthic microbial loop in experimental microcosms[END_REF] who concluded that the metabolically active bacteria can respond differently to resuspensions of sediment produced by low and high energies. They showed that disturbing a sediment with low-energy force produced a slightly positive response from the active bacterial fraction only during the initial resuspension event. But we found high shear velocities also enriched the resuspended active cells (Fig. 4D), unlike [START_REF] Pusceddu | Sediment resuspension effects on the benthic microbial loop in experimental microcosms[END_REF], who observed that the metabolically active bacteria decreased when turbulence was high. We conclude that disturbing the sediment with high-energy forces has little effect on the fraction of metabolically active bacteria resuspended.

Many studies [START_REF] Chróst | Storm-stimulated enzymatic decomposition of organic matter in benthic/pelagic coastal mesocosms[END_REF][START_REF] Cotner | Intense winter heterotrophic production stimulated by benthic resuspension[END_REF][START_REF] Ritzrau | Increase of microbial biomass in the benthic turbidity zone of Kiel Bight after resuspension by a storm event[END_REF][START_REF] Ritzrau | Microbial activity in the benthic boundary layer: Small-scale distribution and its relationship to the hydrodynamic regime[END_REF] have demonstrated that resuspending sediment enhances the microbial dynamics and enzyme activities in the bottom layers of water. The extent to which sediment resuspension affects the enzyme activity in the water column depends on the characteristics of the suspended matter and on the depth of the water column [START_REF] Ziervogel | Enzyme activities in the Delaware Estuary affected by elevated suspended sediment load[END_REF]. We found that the POM was positively correlated with both the -glucosidase (r=0.52, p<0.05) and leucine aminopeptidase (r=0.66, p< 0.05) activities, as was the PIM concentration (r=0.50, p<0.05 for -glucosidase and r=0.63, p< 0.05 for leucine aminopeptidase).

Microphytobenthic algae also channel a major fraction of their total primary production into the synthesis of extracellular polymeric substances and are thus a significant source of oxygen and organic matter for the growth of benthic bacteria (Boer et al., 2009;[START_REF] De Brouwer | Short-term dynamics in microphytobenthos distribution and associated extracellular carbohydrates in surface sediments of an intertidal mudflat[END_REF][START_REF] Underwood | Primary production by phytoplankton and microphytobenthos in estuaries[END_REF]. Both the -glucosidase (r=0.72, p<0.05) and leucine aminopeptidase activities (r=0.77, p< 0.05) were positively correlated with the chlorophyll a concentration. The association of specific enzymes with the EPS matrix may prolong their activities and help them resist fluctuations in the environment. The activities of enzymes and their patterns in the Delaware estuary were probably affected by the sedimentassociated microorganisms resuspended into the bottom water layers, increasing the number of microbial cells and the hydrolytic activities of the extracellular enzymes [START_REF] Ziervogel | Enzyme activities in the Delaware Estuary affected by elevated suspended sediment load[END_REF].

Erosion and enrichment of prokaryotic OTUs

Proteobacteria are the most abundant bacteria in most surface marine sediments. They can account for over 50% of the microbial biomass [START_REF] Bowman | Biodiversity, community structural shifts, and biogeography of prokaryotes within Antarctic continental shelf sediment[END_REF][START_REF] Kim | Rapid phylogenetic dissection of prokaryotic community structure in tidal flat using pyrosequencing[END_REF][START_REF] Pachiadaki | Diversity and spatial distribution of prokaryotic communities along a sediment vertical profile of a deep-sea mud volcano[END_REF]. Gamma-Proteobacteria seems to be the most significant clade in most marine sediments [START_REF] Inagaki | Microbial communities associated with geological horizons in coastal subseafloor sediments from the Sea of Okhotsk[END_REF][START_REF] Feng | Bacterial diversity of water and sediment in the Changjiang estuary and coastal area of the East China Sea[END_REF][START_REF] Polymenakou | Bacterial community composition in different sediments from the Eastern Mediterranean Sea: a comparison of four 16S ribosomal DNA clone libraries[END_REF].

Gamma-Proteobacteria accounted for up to 10% of the total cells in the upper 2-cm layer of sediment and for 20% of the prokaryotic rRNA in the Smeerenburgfjorden sediments [START_REF] Ravenschlag | Quantitative molecular analysis of the microbial community in marine Arctic sediments (Svalbard)[END_REF]. The percentages are lower than those in our samples: Gamma-Proteobacteria accounted for up to 50% of our total cells (Fig. 7). Analysis of the structures of resuspended prokaryotic communities indicated a sequential enrichment in bacterial OTUs with increasing shear velocity. Pseudomonadal OTUs predominated under low stress condition. But the richness of erodimeter water was always lower than that of the sediment.

These increases were partly due to the emergence of Actinobacteria and Chromatiales OTUs.

These Bacteria are often found in sediments like those at Brouage mudflat that are exposed to sunlight due to tides and shallow water [START_REF] Borin | Biodiversity of prokaryotic communities in sediments of different sub-basins of the Venice lagoon[END_REF]. Here, some Cyanobacteria OTUs appeared in the erodimeter water when shear were low, and reappeared when shear velocities were high. The strong hydrodynamic forces encountered at the field site led to constant vertical and horizontal mixing of the upper five centimeters of sediment [START_REF] Hedtkamp | Shallow subtidal sand: Permeability, nutrient dynamics microphytobenthos and organic matter[END_REF]. This can impose strong selective pressure on the microbial community and restrict access to this habitat to a relatively narrow range of Bacteria that can cope with occasional resuspension, the physical abrasion generated by moving sediment particles, grazing, and rapid fluctuations in the concentrations of oxygen and other nutrients (Boer et al., 2009). Some authors have suggested that the bacteria attached to particles are phylogenetically different from free-living bacteria [START_REF] Crump | Phylogenetic analysis of particle-attached and free-living bacterial communities in the Columbia River, its estuary, and the adjacent coastal ocean[END_REF]Gliglione et al., 2009). The present study results do not support this idea: discrepancies may be due to differences in the techniques used, or in the types of particles and trophic conditions. Attached bacteria may be ubiquitous species and probably result from rapid exchanges with the more diverse reservoir of free-living communities. The large number of similar OTUs we found in attached and free-living bacteria leads us to believe that free-living and attached bacteria are not separate entities but interacting assemblages, as suggested by [START_REF] Riemann | Community dynamics of free-living and particle-associated bacterial assemblages during a freshwater phytoplankton bloom[END_REF] The resuspension produced by our technique provided a higher archaeal specific richness ( 30OTUs on average) than Bacteria. However, this applied only to attached cells and samples produced using the highest shear rates (> 7 cm s -1 ). The presence of large amounts of Euryarchaeota and Crenarchaeota generally agrees with the clone library studies of [START_REF] Kim | Archaeal diversity in tidal flat sediment as revealed by 16S rDNA analysis[END_REF][START_REF] Kim | Rapid phylogenetic dissection of prokaryotic community structure in tidal flat using pyrosequencing[END_REF]. But they found that Euryarchaeota seemed to be more abundant and diverse than we do. Most of the archaeal sequences in all our samples were of unidentified classes, but we did find Thermoprotei, a group that includes anaerobes and sulfur reducers.

Methanomicrobia were the most abundant methanogens. Methanomicrobiales may have occurred in the sulfate-free layers because there was less competition from sulfate reducers.

They use substrates released by decaying algae and other organisms, like methylamines and dimethylsulfide. These substrates are not used by most other physiological groups and are mostly found near the surface of the sediment [START_REF] Wilms | Specific bacterial, archaeal, and eukaryotic communities in tidal-flat sediments along a vertical profile of several meters[END_REF].

Conclusions

We have identified two distinct patterns of resuspended prokaryotic cells, produced by applying different shear stresses to the sediment. Friction velocities of less than 5 cm s -1 , corresponding to a normal low choppy tide, lead to the resuspension of cells that are mostly free-living, regardless of the physico-chemical characteristics of the sediment or the development of a biofilm on its surface. These cells are mainly Cyanobacteria and Gamma-Proteobacteria that secreted some extracellular enzymes and can become integrated into, and thus affect, the coastal planktonic microbial food web [START_REF] Garstecki | Effects of experimental sediment resuspension on a coastal planktonic microbial food web[END_REF]. Friction velocities greater than 5 cm s -1 , corresponding to rough tides with waves, favour the resuspension of attached cells. Studies on the effects of fluid shear on microbial activity in the water column have shown that particle-attached bacteria benefit nutritionally more than freeliving forms given that the host particle is large enough [START_REF] Jumars | Constraints on marine osmotrophy in an optimal foraging context[END_REF][START_REF] Lazier | Turbulence and the diffusive layers around small organisms[END_REF]. It is under these circumstances that the greatest proportion of bacterial and archaeal OTUs with different functions are recruited from deep sediment. The shear velocity was strongly correlated with hydrolytic enzyme activities and linked to the increase in resuspended intact cells (potentially active). These attached prokaryotes could provide organic matter to the pelagic zone and enhance the breakdown of benthic organic matter [START_REF] Ståhlberg | Mineralisation of organic matter in coastal sediments at different frequency and duration of resuspension[END_REF]. Resuspended sediments that are rich in organic and inorganic nutrients may stimulate the large scale production of planktonic heterotrophs, even at low temperatures [START_REF] Fiordelmondo | Short-term response of benthic bacteria and nanoflagellates to sediment resuspension: an experimental study[END_REF]). (ungproteobacteria: unidentified Gamma-Proteobacteria).

Figures captions

  . Bacteria often seem to development concomitantly with benthic microalgae and they adapt quickly to microalgal exudates by changing the profile of their enzymatic activities. The composition of our bacterial communities differed markedly, depending on the presence (July 17) or absence (July 21) of a microphytobenthic biofilm, in agreement with Lubarsky et al. (2010) (see also Dupuy et al. this issue).

Figure 1 :

 1 Figure 1: Sampling site.

Figure 2 :

 2 Figure 2: PCA of sediment environmental and biological parameters (showing the variables: samples 1-3 were taken on July 17, 4-6 on July 21, 7-9 on July 22 and 10-12 on July 24).(prot: protein; colloidal: colloidal carbohydrates from EPS; bound: bound carbohydrates from EPS; chloro: chlorophyll a; muf: -glucosidase activity; leu: leucine-aminopeptidase activity; OM: organic matter; cells: prokaryotic abundance).

Figure 3 :

 3 Figure 3: (A) Bacteria and (B) Archaea phyla found in the sediment samples (relative abundance (%), see Materials and Methods for details) (numbers on the graph represent the richness of taxons). (ungproteobacteria: unidentified Gamma-Proteobacteria; uneuryarchaeota: unidentified Euryarchaeota; uncrenarchaeota: unidentified Crenarchaeota; unarchaea: unidentified Archaea).

Figure 4 :

 4 Figure 4: (A) Total and free cells enrichments in the erodimeter water obtained by treating samples collected on July 17, 21, 22 and 24, (B) attached cells enrichment and (C) active cells enrichment, at each threshold friction velocity (u*cm s -1 ).

Figure 5 :

 5 Figure 5: (A) -glucosidase and (B) leucine aminopetidase specific activities in the erodimeter water obtained with each threshold friction velocity (u*cm s -1 ) from samples obtained on July 17, 21, 22 and 24.

Figure 6 :

 6 Figure 6: PCA of erodimeter water environmental and biological parameters (showing the variables; samples 1-6 from July 17, 7-10 from July 21, 11-15 from July 22 and 16-21 from July 24). (attached: enrichment of attached prokaryotic cells; live: enrichment of live prokaryotic cells; tot: enrichment of prokaryotic cells; free: enrichment of free prokaryotic cells; muf: -glucosidase activity; leu: leucine-aminopeptidase activity; MOP: particular organic matter; MP: particulate matter; X: threshold friction velocity (u*); chloro: chlorophyll a).

Figure 7 :

 7 Figure 7: Bacterial phyla in the erodimeter water (relative abundance (%), see Materials and Methods for details) after treating the July 17 sediment at each threshold friction velocity (u*cm s -1 ): attached (A) and free cells (B) DNA ; (C) free cell DNA in the July 21erodimeter water; (D) attached cell DNA in the July 22 erodimeter water; (E) attached and (F) free cell

Figure 8 :

 8 Figure 8: Archaeal phyla recovered (relative abundance (%), see Materials and Methods for details) from the sediment sample at each threshold friction velocity (u*cm s -1 ). Attached cell DNA in the erodimeter water for (A) July 17 of the, (B) July 21, (C) July 22 and (D) July 24.(numbers on the graph represent the richness of taxons). (uneuryarchaeota: unidentified Euryarchaeota; uncrenarchaeota: unidentified Crenarchaeota; unarchaea: unidentified Archaea).

  Fig1

Acknowledgements

This study was supported by the French ANR (National Research Agency) through the VASIREMI project "Trophic significance of microbial biofilms in tidal flats" (contract ANR-420 06-BLAN-0393-01). The English text was edited by Dr Owen Parkes.


Pierre-Henri Tournier

Marcella Bonazzoli

Victorita Dolean

Francesca Rapetti

Frédéric Hecht

Frédéric Nataf

Iannis Aliferis

Ibtissam El Kanfoud

Claire Migliaccio

Maya De Buhan

P.-H Tournier

I El Kanfoud

Ch Pichot

Pierre-Henri Tournier

Marion Darbas

Serguei Semenov

IEEE Christian Pichot Fellow

Numerical Modeling and High Speed Parallel Computing: New Perspectives for Tomographic Microwave Imaging for Brain Stroke Detection and Monitoring

Keywords: High Performance Computing, Parallel computers, Finite element analysis, Microwave antenna arrays, Electromagnetic Diffraction, Microwave Imaging, Biomedical Imaging, Inverse Problems I. INTRODUCTION

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

hemorrhage) [START_REF]Intercollegiate Stroke Working Party. National clinical guideline for stroke[END_REF]. Differentiating between these different types of strokes is an essential part of the initial workup of the patients because the subsequent management and treatment of each patient is vastly different. Rapid and accurate diagnosis is crucial since the only drug currently approved by the FDA for treatment of acute ischemic stroke is intravenous tissue plasminogen activator (tPA) administered within 3 hours of stroke onset. Neuroimaging has to play a vital role in the workup of acute stroke by providing information essential to accurately triage patients, and expedite clinical decisionmaking with regards to treatment. CT and MRI [START_REF] Wegener | Neuroimaging of acute ischaemic stroke: current challenges[END_REF] are actually the "gold" standards but they are bulky diagnostic instruments and cannot be used in continuous brain monitoring. A noninvasive and transportable/portable device would have clear clinical applications at the bedside in a Neurological Intensive Care Unit (NICU).

Microwave tomography is a novel, early development stage imaging modality with a large number of potential attractive medical applications. A difference between the dielectric properties (complex permittivity) of normal and diseased brain tissues is a great potential for this imaging modality. Detecting and identifying strokes is challenging as it corresponds to a small opposite variation of the permittivity values of brain tissues of about +/-10 % of the baseline tissue values for the two types of strokes (ischemic or hemorrhagic) [START_REF] Semenov | Dielectrical spectroscopy of canine myocardium during acute ischemia and hypoxia at frequency spectrum from 100 kHz to 6 GHz[END_REF]. The rapid data acquisition time is another attractive feature of microwave tomography but rapid tomographic reconstructions are mandatory for developing a novel imaging modality with a new paradigm: detecting, identifying and monitoring stroke continuously during treatments by exposing head tissues to low-level microwave incident field and capturing the scattered signal by an array of antennas. Tomographic imaging requires the solution of an inverse problem based on a minimization algorithm. Reconstruction algorithms are computationally intensive with successive solutions of the forward problem needing efficient numerical modeling and high-performance parallel computing. A majority of works in the literature has made use of geometrically simple phantoms or with only a limited amount of tissue-mimicking materials. The modeling must have to accurately take account of the high heterogeneity and complexity of head tissues (skin, fat, skull, bone marrow, brain/white matter, brain/grey matter, cerebrospinal fluid, arteries, etc.) for normal cases and for different possible brain pathology cases (ischemic and hemorrhagic strokes, brain injuries, etc.). Another major point refers to the accurate modeling of the incident field from transmitting and receiving antennas. This interaction is very complex, as it must be seen as a coupling problem between the antennas and the head rather than a simple scattering problem. In addition, the electric field is measured by means of receiving antennas (sensors). Therefore, we do not have access directly to the electric field but only via antenna S parameters. The purpose of this work is to solve the inverse problem associated to a prototype developed by EMTensor GmbH (Vienna, Austria) [START_REF] Semenov | Electromagnetic tomography for brain imaging: from virtual to human brain[END_REF] using state-of-the-art modeling, high-performance and massively parallel computing.

II. TOMOGRAPHIC SYSTEM

The model of microwave imaging is based on BRain IMaging Generation1 (BRIMG1), a tomographic microwave system developed by EMTensor GmbH [START_REF] Semenov | Electromagnetic tomography for brain imaging: from virtual to human brain[END_REF]. The system consists of a cylindrical metallic chamber composed of 5 rings of 32 Transmitting/Receiving antennas (Fig. 1). The antennas are ceramic (ε r = 59) loaded open-ended waveguides. The diameter of the chamber is 285 mm with a height of 280 mm. The rings are 30 mm equally spaced, the first one being located at 40 mm from the top of the chamber. The chamber is filled with a matching liquid medium during measurements. The operating frequency of the system is 0.9 GHz to 1.8 GHz. The data acquisition cycle of the system is fully electronically controlled, allowing for a total data acquisition of about 30 s. The imaging chamber is in horizontal position, allowing easy positioning a human head within an imaging domain (Fig. 2). The head of the patient is introduced in the chamber as shown in Fig. 2. A special thin membrane is used for isolating the human head from the matching liquid and keeping the liquid within the chamber. A carbon loaded silicon rubber (CLSR) is also used for reducing reflection from boundary conditions (Fig. 3). A switching matrix connected to a network analyzer selects the transmitting and receiving antennas. The system is potentially delivering a 160 × 160 matrix of S parameters. The measured S parameters due to the scattered field of an object under investigation are obtained by complex subtraction between two measurements with empty chamber and with the head, respectively. The raw data can be wirelessly transferred to a remote computing center. The HPC machine will compute the tomographic images, which can be quickly transferred from the computing center to the hospital.

III. FORWARD MODELING

We consider the domain Ω ⊂ R 3 for representing the wholechamber (Fig. 1) as an inhomogeneous dissipative nonmagnetic medium of complex permittivity ε(x) . For each transmitting antenna j = 1, . . . N at radial frequency ω, the wave equation for the electric field vector E j (x) with an e iωt time-dependence is

∇ × (∇ × E j ) -k 2 E j = 0 in Ω (1)
with k 2 = k 2 (x) = ω 2 ε r (x)ε 0 µ 0 , where k(x) is the complex wavenumber of the inhomogeneous medium, ε 0 and μ 0 the permittivity and permeability of free space, respectively. The boundary conditions on the perfectly conducting parts Γ c of the walls of the chamber are

F o r R e v i e w O n l y
where n is the unit outward normal to ∂Ω.

The impedance boundary conditions on the aperture of transmitting open-ended waveguide j and receiving waveguide i = 1,..., N, j ≠ i are

(∇ × E j ) × n + iβn × (E j × n) = g j on Γ j (2) (∇ × E j ) × n + iβn × (E j × n) = 0 on Γ i , i ≠ j (3)
where β is the propagation constant of the TE 10 fundamental mode of the waveguide. In equation [START_REF]Intercollegiate Stroke Working Party. National clinical guideline for stroke[END_REF] we impose an incident wave corresponding to the excitation of the fundamental mode E j 0 of the j-th waveguide with

g j = (∇ × E j 0 ) × n + iβn × (E j 0 × n) (4)
On the other hand, equation (3) corresponds to a first order Silver-Müller absorbing boundary condition, approximating a transparent boundary condition on the aperture of the receiving waveguide antenna i = 1,..., N, i ≠ j. On the bottom of the chamber we impose a metallic boundary condition, whereas we impose an impedance boundary condition on the top of the chamber. As a result, the whole boundary value problem for each transmitting antenna t = 1, . . . , N is to find

E j such that ∇ × (∇ × E j ) -k 2 E j = 0 in Ω E j × n = 0 on Γ c (∇ × E j ) × n + iβn × (E j × n) = g j on Γ j (∇ × E j ) × n + iβn × (E j × n) = 0 on Γ i , i ≠ j ⎧ ⎨ ⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ (5) Now, let V = v ∈ H (curl,Ω),v × n = 0 on Γ c { } , where H (curl,Ω) = v ∈ L 2 (Ω) 3 ,∇ × v ∈ L 2 (Ω) 3
{ } is the space of square integrable functions whose curl is also square integrable. For each transmitting antenna j = 1,..., N, the variational form of problem ( 5) is : find

E j ∈ V such that ∇ × E j ( ) . ∇ × v ( ) -k 2 E j .v ⎡ ⎣ ⎤ ⎦ Ω ∫ + iβ E j × n ( ) Γ i 1=1 N ∪ ∫ . v × n ( ) = g j Γ j ∫ .v ∀v ∈ V (6)

IV. HIGH-ORDER EDGE FINITE ELEMENTS

For using a finite element discretization of the variational problem, we introduce a tetrahedral mesh T h of the domain Ω and a finite dimensional subspace V h ⊂ H (curl,Ω) . A simple conformal discretization for space H (curl,Ω) is given by low order Nédélec edge finite elements of polynomial degree r = 1 [START_REF] Nédélec | Mixed finite elements in R 3[END_REF]. In order to have a higher numerical accuracy with the same total number of unknowns, we consider a high order edge element discretization, choosing the high order extension of Nédélec elements presented in [START_REF] Rapetti | High order edge elements on simplicial meshes[END_REF] and [START_REF] Rapetti | Whitney forms of higher degree[END_REF]. We implemented edge elements of degrees 2 and 3 in FreeFem++, an open source domain specific language (DSL) specialized for solving boundary value problems by using variational discretizations (finite elements, discontinuous Galerkin, hybrid methods,...) [START_REF] Hecht | New development in FreeFem++[END_REF]. High order elements can be used by loading the plugin Element Mixte3d and declaring the finite element space fespace using the keywords Edge13d, Edge23d, respectively (standard edge elements of degree 1 are already present in FreeFem++ and called Edge03d).

V. DOMAIN DECOMPOSITION PRECONDITIONING

The discretization of the problem presented in Section III using the high order edge finite elements described in Section IV produces a linear system Au j = b j [START_REF] Nédélec | Mixed finite elements in R 3[END_REF] for each transmitting antenna j. Direct solvers are not suited for such large linear systems arising from complex three dimensional models because of their high memory cost. On the other hand, matrices resulting from high order discretizations are ill conditioned as shown numerically in [START_REF] Rapetti | High order edge elements on simplicial meshes[END_REF] for similar problems, and preconditioning becomes necessary when using iterative solvers. Domain decomposition preconditioners are naturally suited to parallel computing and make it possible to deal with smaller subproblems [START_REF] Dolean | An Introduction to Domain Decomposition Methods: algorithms, theory and parallel implementation[END_REF]. The domain decomposition preconditioner we employ is called Optimized Restricted Additive Schwarz (ORAS)

M ORAS -1 = R s T D s A s -1 R s s=1 N sub ∑ ( 8
)
where N sub is the number of overlapping subdomains Ω s into which the domain Ω is decomposed (Fig. 4). Here, the matrices A s are the local matrices of the subproblems with impedance boundary conditions

(∇ × E) × n + iϖ n × (E × n) as
transmission conditions at the interfaces between subdomains. This preconditioner is an extension of the restricted additive Schwarz method proposed by Cai and Sarkis [START_REF] Cai | A restricted additive Schwarz preconditioner for general sparse linear systems[END_REF], but with more efficient transmission conditions between subdomains than Dirichlet conditions [START_REF] Dolean | Optimized Schwarz methods for Maxwell's equations[END_REF].

In order to describe the matrices R s , D s , let N be an ordered set of the unknowns of the whole domain and let

N = N s s=1 N sub ∪ be its decomposition into the (non disjoint)
ordered subsets corresponding to the different (overlapping) subdomains Ω s . The matrix R s is the restriction matrix from Ω to the subdomain Ω s : it is a #N s × #N Boolean matrix and its (i, j) entry is equal to 1 if the i-th unknown in N s is the j-th one in N. Notice that R s T is then the extension matrix from the subdomain Ω s to Ω. The matrix D s is a #N s × #N s diagonal matrix that gives a discrete partition of unity, i.e.

M ORAS -1 = R s T D s A s -1 R s s=1 N sub ∑ which is called Optimized
Additive Schwarz (OAS), would be symmetric for symmetric problems, but in practice it gives a slower convergence with respect to M ORAS -1 [START_REF] Bonazzoli | Parallel preconditioners for high order discretizations arising from full system modeling for brain microwave imaging[END_REF].These domain decomposition preconditioners are implemented in the HPDDM library [START_REF] Jolivet | Scalable domain decomposition preconditioners for heterogeneous elliptic problems[END_REF], an open source high-performance unified framework for domain decomposition methods. HPDDM can be interfaced with various programming languages and open source finite element libraries such as FreeFem++, which we use in the simulations.

VI. NUMERICAL RESULTS

A. Comparison with Experimental Measurements

The measured physical quantities are the S parameters of the scattering matrix, which are the complex reflection and transmission coefficients measured by the 160 receiving antennas when a signal is transmitted by one of the 160 transmitting antennas. A set of measurements then consists in a complex matrix of size 160 × 160. In order to compute the numerical counterparts of these reflection and transmission coefficients, we use the following formula, which is appropriate in the case of open-ended waveguides

S ij = E j .E i 0 Γ i ∫ E i 0 2 Γ i ∫ , i ≠ j (9)
where E j is the solution of the (5) when the j-th waveguide antenna transmits the signal, and E i 0 is the TE 10 fundamental mode of the i-th receiving waveguide ( E j denotes the complex conjugate of E j ). The S ij with i ≠ j denote the transmission coefficients, and S ii the reflection coefficients.

For a comparison of the computed coefficients S ij with the measured ones, the imaging chamber is filled with a homogenous matching solution in order to reduce the return loss of the ceramic-loaded waveguide antennas and to match with the average brain tissues. The relative complex permittivity of the matching solution chosen for the experiments and numerical solution at frequency f = 1 GHz is ε matching = 44 -i20. The relative permittivity inside the ceramic-loaded waveguides is ε ceramics = 59, assuming a lossless ceramic material. For this test case, the set of experimental data consists in S parameters from the 160 receiving antennas when each antenna from the second ring from the top is transmitting. Figure 4 shows the normalized magnitude (dB) and phase (degree) of the complex coefficients S ij corresponding to a transmitting antenna in the second ring from the top and to the 31 receiving antennas in the middle ring (note that measured coefficients are available only for 17 receiving antennas). The computed coefficients are obtained by solving the direct problem with edge finite elements of polynomial degree r = 2. The normalization is done by dividing every transmission coefficient by the transmission coefficient corresponding to the receiving antenna directly opposite to the transmitting antenna, which is thus set to 1. Since we normalize with respect to the coefficient having the lowest expected magnitude, the magnitude of the transmission coefficients shown in Fig. 5 is larger than 0 dB. We can see that the transmission coefficients computed from the simulation are in very good agreement with the measurements.

B. High-Order Element Efficiency

The goal of the following numerical experiments is to assess the efficiency of the high order finite elements described in Section IV compared to the classical lowest order edge elements in terms of accuracy and computing time, which are of great importance for such an application for brain imaging. For this test case, a non dissipative plastic-filled cylinder of diameter 6 cm and relative permittivity ε cyl = 3 is inserted in the imaging chamber with same background matching medium as defined in Section A. We consider the 32 antennas of the second ring as transmitting antennas at frequency f = 1 GHz, and all the 160 antennas are receiving. Fig. 6. Cross-Section of the chamber showing the magnitude of the real part of the total field E in the chamber with the plastic tube.

We evaluate the error on the reflection and transmission coefficients S ij with respect to the coefficients S ij ref computed from a reference solution. The error is calculated with the following formula

err = S ij -S ij ref 2 j,i ∑ S ij ref 2 j,i ∑ (10)
The reference solution is computed on a fine mesh of approximately 18 million tetrahedra using edge finite elements of degree r = 2, resulting in 114 million unknowns. The section in Fig. 6 shows the computational domain and the magnitude of the real part of the total field E over the cross-section when one antenna of the second ring from the top is transmitting. We compare the computing time and the relative error [START_REF] Bonazzoli | Parallel preconditioners for high order discretizations arising from full system modeling for brain microwave imaging[END_REF] for different numbers of unknowns corresponding to several mesh sizes, for approximation degrees r = 1 (15 pts/λ) and 2 (10 pts/λ) (Table I). We report the results on Fig. 7 As we can see, the higher order approximation (r = 2) allows a given accuracy with much fewer unknowns and much less computation time than the lowest order approximation (r=1).

For example, at a given accuracy err of E ≈ 0.1, the finite element discretization of degree r=1 requires 21 million unknowns and a computing time of 130 seconds, while the high order finite element discretization (r=2) only needs 5 million unknowns, with a corresponding computing time of 62 seconds. It turns out we obtain the same accuracy with 10 points per wavelength with degree r=2 than with 20 points per wavelength with degree r =1.

VII. INVERSE PROBLEM

A. Mathematical Formulation

The inverse problem that we consider consists in finding the unknown complex dielectric permittivity ε(x) in Ω, such that the solutions E j (x) , j = 1,...,N of problem (4) lead to corresponding scattering parameters S ( 14) that coincide with the measured scattering parameters S ij meas , for i, j = 1, . . . , N.

Let κ = k 2 be the unknown complex parameter of the inverse problem, and let us denote by E j (κ ) the solution of the direct problem ( 5) with the complex dielectric permittivity ε.

The corresponding scattering parameters will be denoted by S ij (κ ) for i, j = 1, . . . , N.

The misfit of the parameter κ to the data can be defined with the following cost functional

J (κ ) = 1 2 S ij (κ ) -S ij meas 2 i=1 N ∑ j=1 N ∑ = 1 2 E j (κ ).E i 0 Γ i ∫ E i 0 2 Γ i ∫ -S ij meas 2 i=1 N ∑ j=1 N ∑ (11)
In a classical way, solving the inverse problem consists in minimizing the functional J with respect to the parameter κ .

Computing the differential of J in a given arbitrary direction

δκ yields DJ (κ,δκ ) = Re (S ij (κ ) -S ij meas ) δ E j (κ ).E i 0 Γ i ∫ E i 0 2 Γ i ∫ ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ i=1 N ∑ j=1 N ∑ (12)
for δκ ∈ C and where δ E j (κ ) is the solution of the following linearized problem

∇ × ∇ ×δ E j ( ) -κδ E j = δκ E j in Ω δ E j × n = 0 on Γ c ∇ ×δ E j ( ) × n + iβn × δ E j × n ( ) = 0 on Γ i ,i = 1,..., N ⎧ ⎨ ⎪ ⎪ ⎩ ⎪ ⎪ (13)
We now use the adjoint approach in order to simplify the expression of DJ. This will allow us to compute the gradient efficiently after discretization, with a number of computations independent of the size of the parameter space.

Introducing the solution F j (κ ) of the following adjoint problem

∇ × ∇ × F j ( ) -κ F j = 0 in Ω F j × n = 0 on Γ c ∇ × F j ( ) × n + iβn × F j × n ( ) = S ij (κ ) -S ij meas ( ) E i 0 2 Γ i ∫ E i 0 on Γ i ,i = 1,..., N (14)
we get after some integration by parts (not detailed here)

δκ E j .F j Ω ∫ = (S ij (κ ) -S ij meas ) E i 0 .δ E j Γ i ∫ E i 0 2 Γ i ∫ ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ i=1 N ∑ (15)
Finally, the differential of J can be computed as

DJ (κ,δκ ) = Re δκ E j .F j Ω ∫ ⎡ ⎣ ⎤ ⎦ j=1 N ∑ (16)
We can then compute the gradient to use in a gradient-based local optimization algorithm. The numerical results presented in Section B are obtained using a limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm. Note that every evaluation of J requires the solution of the state problem (5) while the computation of the gradient requires the solution of (5) as well as the solution of the adjoint problem [START_REF] Karypis | A fast and high quality multilevel scheme for partitioning irregular graphs[END_REF]. Moreover, the state and adjoint problems use the same operator. Therefore, the computation of the gradient only needs the assembly of one matrix and its associated domain decomposition preconditioner. Numerical results for the reconstruction of a hemorrhagic stroke from synthetic data are presented in the next section. The cost functional J considered in the numerical results is slightly different from [START_REF] Jolivet | High-performance domain decomposition methods on massively parallel architectures with FreeFem++[END_REF], as we add a normalization term for each pair (i,j) as well as a Tikhonov regularization term

J (κ ) = 1 2 S ij (κ ) -S ij meas 2 S ij empty 2 + α 2 i=1 N ∑ j=1 N ∑ ∇κ 2 Ω ∫ ( 17
)
where the S ij empty refer to the coefficients computed from the simulation with empty chamber, which is the chamber filled only with the homogeneous matching solution as described in the previous section, with no object inside. In this way, the contribution of each (i,j) pair in the cost functional is normalized and does not depend on the amplitude of the coefficient, which can vary greatly between (i,j) pairs as shown in Fig. 5. The Tikhonov regularization term aims at reducing the effects of noise in the data. For now, the regularization parameter α is chosen empirically so as to obtain a visually good compromise between reducing the effects of noise and keeping the reconstructed image pertinent. All calculations carried out in this section can be accommodated in a straightforward manner to the definition (17) of the cost functional.

As is usually the case with most medical imaging techniques, the reconstruction is performed cross-section by cross-section.

For the study, one cross-section corresponds to one of the five rings of 32 antennas. This allows exhibiting another level of parallelism, by solving an inverse problem independently for each of the five rings in parallel. More precisely, each of these inverse problems is solved in a domain truncated around the corresponding ring of antennas, containing at most two other rings (one ring above and one ring below). We impose absorbing boundary conditions on the artificial boundaries of the truncated computational domain.

VIII. NUMERICAL RESULTS

Results in this paper were obtained on Curie supercomputer (http://www-hpc.cea.fr/fr/complexe/tgcc-curie.htm), a system composed of 5,040 nodes composed of two eight-core Intel Sandy Bridge processors clocked at 2.7 GHz. The interconnect is an InfiniBand QDR full fat tree and the MPI implementation used was BullxMPI version 1.2.8.4. Intel compilers and Math Kernel Library in their version 16.0.2.181 were used for all binaries and shared libraries, and as the linear algebra backend for dense computations. One-level preconditioners such as (8) assembled by HPDDM require the use of a sparse direct solver. In the following experiments, we have used either PARDISO [START_REF] Schenk | Solving unsymmetric sparse systems of linear equations with PARDISO[END_REF] from Intel MKL or MUMPS [START_REF] Amestoy | A fully asynchronous multifrontal solver using distributed dynamic scheduling[END_REF]. All linear systems resulting from the edge finite elements discretization are solved by GMRES right-preconditioned with ORAS (8) as implemented in HPDDM. The GMRES algorithm is stopped once the unpreconditioned relative residual is lower than 10 -8 . First, we developed a very accurate virtual model of a human head. Second, we solved the inverse problem with corrupted synthetic data generated using the virtual brain model simulating a hemorrhagic stroke.

1) Virtual Head Model

We want to assess the feasibility of the microwave imaging technique presented in this paper for stroke detection and monitoring through a numerical example in a realistic configuration.

We use synthetic data corresponding to an accurate numerical model of a human head with a simulated hemorrhagic stroke as input for the inverse problem. The numerical model of the virtual head comes from CT and MRI scans and consists of a complex permittivity map of 362 × 434 × 362 data points with a spatial resolution of 500 µm. In the simulation, the head is immersed in the imaging chamber as shown in Fig. 9.

Fig. 9. Imaginary part of the relative complex permittivity of the virtual head model immersed in the imaging chamber with a simulated ellipsoid-shaped hemorrhagic stroke.

2) Reconstructions of a Hemorrhagic Stroke

In order to simulate the evolution of a hemorrhagic stroke, we use a synthetic ellipsoid-shaped stroke whose size (principal axes) increases over time, from 3.9 cm × 2.3 cm × 2.3 cm (small stroke) to 7.7 cm × 4.6 cm × 4.6 cm (large stroke). For this test case, the relative complex permittivity of the ellipsoid is assumed to be inhomogeneous where the relative complex permittivity at each quadrature point of the mesh is taken as the mean value between the original healthy brain permittivity values (baseline values) and the permittivity of blood ( ε r blood = 68 -i44) at f = 1 GHz. The imaging chamber is filled with the matching solution ε r matching = 44 -i20. In a real experiment, a special membrane fitting the shape of the head is used in order to isolate the head from the matching medium (Fig. 3). We do not take this membrane into account in this synthetic test case.

The synthetic data are obtained by solving the direct problem using a mesh composed of 17.6 million tetrahedra (corresponding to approximately 20 points per wavelength) and consist in the computed transmission and reflection coefficients S ij . We subsequently add noise to the real and imaginary parts of the coefficients S ij (10% multiplicative White Gaussian Noise (WGN)), with different values for real and imaginary parts, such as

S ij corrupted = S ij (1+10%AWGN ) (18)
The corrupted data S ij corrupted are then used as input for the inverse problem. Furthermore, we do not assume any priori knowledge on the input data, and we set the initial guess for the inverse problem as the homogeneous matching solution everywhere inside the chamber. We use a piecewise linear approximation of the unknown parameter κ, defined on the same mesh used to solve the state and adjoint problems. For the purpose of parallel computations, the partitioning introduced by the domain decomposition method is also used to compute and store locally in each subdomain every entity involved in the inverse problem, such as the parameter κ and the gradient. The evolution of the stroke can be visually monitored from the real and imaginary parts of the reconstructed complex permittivity. Nevertheless, the threshold to firmly conclude must only be determined from clinical studies on a large number of patients. One important point is to discriminate a hemorrhagic from an ischemic stroke. For this study case, the reconstructed values show an increase of the complex permittivity allowing the assumption of a hemorrhagic stroke versus an ischemic one. The distribution of the relative error on the real and imaginary parts of the reconstructed complex permittivity for the small stroke case is shown in Fig. 12. We compute the relative error using [START_REF] Pellegrini | SCOTCH: A software package for static mapping by dual recursive bipartitioning of process and architecture graphs[END_REF] for each pixel (n,m) of the reconstructed relative complex permittivity. This error can be positive or negative.

err relative (m,n) = ε r reconstructed (m,n) -ε r exact (m,n) ε r exact (m,n) (19)
We note that lowest errors are located outside the brain and in the stroke. This can be expected as the inversion algorithm performs better for homogeneous media such as the matching liquid but also for the stroke, as the complex permittivity value of the stroke is calculated as the mean value between the healthy tissues and the blood. This process tends to average the values, which is more favorable for the inversion algorithm. But, even if the brain is highly heterogeneous, the stroke can be detected and monitored with the proposed algorithm.

We now calculate the L 2 norm of the error of the reconstructed images in such manner as [START_REF] Bonazzoli | Parallel preconditioners for high order discretizations arising from full system modeling for brain microwave imaging[END_REF]. Results are shown in Table III. The L 2 norm is interesting as it gives a global quantitative criterion for estimating the performance of the reconstructed values. The L 2 norm confirms the results shown in Fig. 12 for

F o r R e v i e w O n l y
the small stroke. The error on the real part of the complex relative permittivity is lower than on the imaginary part. It is of the order of 10% for the real part whereas it is about 20% for the imaginary part. III. Average error on the reconstructed values (real and imaginary parts of the complex permittivity).

Although we have shown in section IV B that high order edge elements are efficient when solving the direct problem with very high accuracy, the reconstructed images differ very slightly when using different discretization orders and mesh sizes in the inverse problem. It turns out for our study case that elements of degree r=1 with 10 pts/λ are sufficient for detecting the stroke. Reconstructed images for each test case shown in Figs. 10 and 11 are obtained with a total computing time of less than 2 minutes (94 seconds for the large stroke case) using 4096 cores of Curie. These preliminary results are very encouraging as we are already able to achieve a satisfactory reconstruction time in the perspective of using such an imaging technique for monitoring. This allows clinicians to obtain almost instantaneous images 24/7 or on demand. Although the reconstructed images do not feature the complex heterogeneities of the brain, which is in accordance with what we expect from microwave imaging methods, they allow the characterization of the stroke and its monitoring.

IX. CONCLUSION

The idea behind this work comes from the paradigm to develop a (portable/transportable) microwave imaging system whose raw data are wirelessly transferred to a HPC. The HPC machine will then compute the 3D image of the patient's brain. Once reconstructed, the image is quickly transmitted from the computing center to the hospital for stroke detection (including ischemic/hemorrhagic discrimination) and monitoring during treatment. We have developed a tool that reconstructs a tomographic microwave image of the brain in 94 seconds on 4096 computing cores. This computational time corresponds to clinician acceptance for rapid diagnosis or medical monitoring at the hospital. These images were obtained from corrupted synthetic data from a very accurate model of the complex permittivity of the brain. To our knowledge, this is the first time that such a realistic study (operational acquisition device, highly accurate three-dimensional synthetic data, 10% noise) shows the feasibility of microwave imaging. This study has been possible by the use of massively parallel computers and facilitated by HPDDM and FreeFem++ tools that we developed. The next step will be the validation of these results on clinical data.

Fig. 1 .

 1 Fig. 1. Left: General view of BRIMG1 (courtesy of EMTensor GmbH). Right: Computational domain.

Fig. 2 .

 2 Fig. 2. BRIMG1: Human head measurement (courtesy of EMTensor GmbH)

=

  I ; in particular the matrices D deal with the unknowns that belong to the overlap between subdomains. The preconditioner without the partition of unity matrices D s ,

Fig. 4 .

 4 Fig. 4. Computational domain divided into 128 subdomains.

Fig. 5 .

 5 Fig. 5. Normalized amplitude (top) and phase (bottom) between the computed and measured S-parameters.

Fig. 7 .

 7 Fig. 7. Comparison between degrees r=1 and r=2 on empty, total and scattered fields (amplitude and phase).

Fig. 8 .

 8 Fig.8. Computation time (seconds) and relative error on computed S ij using elements of degree r=1 and r=2 for different mesh sizes and number of unknowns in millions.

Figs. 10

 10 and 11 show the real and imaginary parts of the relative permittivity, respectively, for the three evolution steps of the hemorrhagic stroke, from a healthy brain, a brain with a small and large stroke. Increasing the size of the ellipsoid simulates the evolution of the stroke. Each reconstruction corresponds to the solution of an inverse problem in the truncated domain containing only the first two rings of antennas from the top. The transmitting antennas are on the first ring and receiving antennas on first and second rings. Therefore the scattering matrix contains only 64×32 S ij coefficients. Each reconstruction starts from an initial guess consisting of the homogeneous matching solution. The solution is obtained at about 30 iteration steps when reaching the convergence criterion of 10 -2 for the value of the cost functional using the L-BFGS algorithm.

Fig. 10 .

 10 Fig.10. Transverse cross-section of the virtual brain during the evolution of a simulated hemorrhagic stroke: real part of the relative complex permittivity. Left: virtual brain model. Right: reconstructed permittivity. From top to bottom: healthy brain, brain with small stroke, brain with large stroke.

Fig. 11 .

 11 Fig. 11. Transverse cross-section of the virtual brain during the evolution of a simulated hemorrhagic stroke: imaginary part of the relative permittivity. Left: virtual brain model. Right: reconstructed permittivity. From top to bottom: healthy brain, brain with small stroke, brain with large stroke.

Fig. 12 .

 12 Fig. 12. Small stroke: Distribution of the relative error on the real (left) and imaginary (right) parts of the reconstructed complex permittivity. From top to bottom: healthy brain, brain with small stroke, brain with large stroke.

  and 8. All these simulations are carried out using 512 subdomains with one MPI process and two OpenMP threads per subdomain, for a total of 1024 cores on the Curie supercomputer (http://www-hpc.cea.fr/fr/complexe/tgcccurie.htm).

	Degree 1	Time	Error	Degree 2	Time	Error
		(s)			(s)
	# unknowns			# unknowns
	2,373,214	22	0.384	1,508,916	39	0.242
	8,513,191	53	0.184	5,181,678	62	0.099
	21,146,710	130	0.117	12,693,924	122	0.057
	42,538,268	268	0.083	26,896,130	236	0.036
	73,889,953	519	0.068	45,781,986	396	0.019

Table

I

. Total number of unknowns, computing time (seconds), and relative error on computed S ij.

https://mc.manuscriptcentral.com/apm-ieee

ACKNOWLEDGMENT

This work was granted access to the HPC resources of TGCC@CEA under the allocations 2016-067519 and 2016-067730 made by GENCI. Authors would like to thank the French National Research Agency (ANR) for their support.

This work is supported by ANR grant MEDIMAX (ANR-13-MONU-0012).