Keywords: Aucoumea klaineana Pierre, steam explosion, acetylated glucomanans, acetylated glucuronoxylans, sapwood, heartwood

Aucoumea klaineana Pierre (okoume) is a tropical hardwood of industrial importance, used for veneers and plywood production. Various conditions of Steam Explosion (SE) treatment (temperature, residence time, pH) have been applied on okoume co-products, sapwood (SW) and heatwood (HW) for the extraction of polymeric hemicelluloses. Conventional extractions with alkali or dimethyl sulfoxide (DMSO) were also performed from delignified SW and HW for comparison. The hemicelluloses extracts have been characterized by HSQC-NMR, FTIR, size exclusion chromatography. The acetyl contents have been determined by HPLC after saponification and from HSQC spectra. Using basic impregnation prior to SE (NaOH-SE), high molecular mass glucuronoxylans (GX, Mw = 65-100 KDa) were recovered in 3-6 % yields. A neutral impregnation (H 2 O-SE) produced O2 and/or O3 acetylated GX and glucomannans (GM), preserving the acetyl moieties in a greater extent compared to the mild DMSO extraction (% Ac ≈ 6.6-8.4% and 1.0-4.1 % w/w respectively). This study provides insights on the composition of SW and HW okoume with a view to further innovative processing and valorization including the preparation of films with advanced properties for food packaging.

Introduction

The economic viability of the biorefineries depends of the optimal valorization of plant resources including the utilization of non-cellulosic constituents. Hemicelluloses are among the main components of wood and constitute a vast, heterogeneous and complex family of polysaccharides, containing diverse sugars and uronic acids [START_REF] Ishii | Chemistry of cell wall polysaccharides[END_REF][START_REF] Chadni | Steam explosion process for the selective extraction of hemicelluloses polymers from spruce sawdust[END_REF]. Hardwood hemicellulosic fraction is mainly composed of glucuronoxylans (≈ 15-30% of wood) which have a backbone of -1,4-linked xylose residues substituted with -linked 4-O-Me--D-glucopyranosyl uronic acid on O-2 of xylosyl residue. Hardwood can also contain a minor amount of glucomannans (≈ 4% of wood) which have a backbone of β-1,4-linked glucopyranosyl / mannopyranosyl units in a linear or slightly branched chain. These polysaccharides are usually diversely acetylated on the sugar backbone [START_REF] Willfor | Polysaccharides in some industrially important hardwood species[END_REF].

Unlike cellulose, which has been used industrially for a very long time, applications involving polymeric hemicelluloses are rare and the potential of hemicelluloses is still very little exploited. However, due to their chemical structure and high molar masses, hemicelluloses can be used to produce promising materials for various applications. One of the most studied applications for polymeric hemicelluloses is the design of films with advanced properties (e.g. biodegradability, edibility, barrier effect) for food packaging [START_REF] Chadni | Elaboration of hemicellulose-based films: Impact of the extraction process from spruce wood on the film properties[END_REF], Zhao et al., 2020).

Various processes have been proposed for the recovery of hemicellulosic polymers from lignocellulosic matrix including alkali extraction of xylans and/or glucuronoxylans from agricultural co-products and liquid hot water extraction [START_REF] Zhao | Hemicellulose-based film potential green films for food packaging[END_REF]). It has also been reported that galactoglucomannans can be recovered from the water stream of thermomechanical pulping of softwood using membrane technologies [START_REF] Kishani | Solubility of Softwood Hemicelluloses[END_REF][START_REF] Willfor | Characterisation of water-soluble galactoglucomannans from Norway spruce wood and thermomechanical pulp[END_REF]. The recovery of acetylated hemicelluloses could be of great interest for biological and material applications since acetylation degree affects the accessibility of polysaccharides to microbes, their solubility in water [START_REF] Michalak | Effects of pH on steam explosion extraction of acetylated galactoglucomannan from Norway spruce[END_REF][START_REF] Voepel | Drug Diffusion in Neutral and Ionic Hydrogels Assembled from Acetylated Galacto-glucomannan[END_REF]) and the physico-chemical properties of hemicelluloses-based materials (e.g. barrier properties of films, [START_REF] Kishani | Solubility of Softwood Hemicelluloses[END_REF].

However, the recovery of acetylated and high molecular mass hemicelluloses from wood with a minimum of degradation is still challenging. In fact, the currently applied methods usually rely on partly modified and deacetylated polysaccharides. For characterization purpose slightly modified and acetylated hemicelluloses can be recovered from holocellulose by DMSO extraction [START_REF] Evtuguin | Characterization of an acetylated heteroxylan from Eucalyptus globulus Labill[END_REF][START_REF] Marques | Acetylated heteroxylan from Agave sisalana and its behavior in alkaline pulping and TCF/ECF bleaching[END_REF].

Steam explosion (SE) is one of the most promising processes for biomass fractionation and pretreatment. SE is a thermo-mechanico-chemical treatment involving a steaming step followed by an explosive decompression provoking a partial breakdown of the lignocellulosic complex [START_REF] Espirito Santo | Physical techniques shed light on the differences in sugarcane bagasse structure subjected to steam explosion pretreatments at equivalent combined severity factors Industrial[END_REF], Marqes el al., 2020[START_REF] Inseemeesak | Fiber extraction and energy recovery from Cocos nucifera Linn mesocarp residues employing steam explosion and anaerobic digestion[END_REF]. This process is commonly used for increasing the accessibility of cellulose to enzymatic hydrolysis and has been developed, even at commercial stage, for cellulosic bioethanol production. More marginally, SE has also been described for high molecular mass hemicelluloses extraction from lignocellulosic biomass. Compared to a hot water extraction, it has been demonstrated by [START_REF] Wojtasz-Mucha | Hydrothermal pretreatment of wood by mild steam explosion and hot water extraction[END_REF] that SE provoked a more effective hemicelluloses extraction due to the advective mass transport during the pressure release step (explosion). [START_REF] Krawczyk | Isolation of hemicelluloses from barley husks[END_REF] reported the isolation of arabinoxylans from barley husks by SE after water impregnation and ultra-filtration. In our group, we studied the extraction of arabinoxylans and galactoglucomannans from spruce by SE [START_REF] Chadni | Steam explosion process for the selective extraction of hemicelluloses polymers from spruce sawdust[END_REF][START_REF] Chadni | Elaboration of hemicellulose-based films: Impact of the extraction process from spruce wood on the film properties[END_REF]. Extraction selectivity as a function of the pH of the SE treatment was demonstrated: for a basic impregnation arabinoglucuronoglynans were recovered in relatively high yields whereas for water impregnation highly acetylated galactoglucomannans were isolated. It was concluded that SE could constitute an effective technique for the recovery of slightly modified and acetylated hemicelluloses from wood of application interest (e.g. food packaging).

Aucoumea klaineana Pierre (okoume) is a fast-growing hardwood species of great industrial importance in Central-Africa. Okoume is primarily used for veneers and plywood production.

In Gabon, the okoume wood industry produces approximatively 1.5 10 6 m 3 of transformed wood and 750 000 m 3 of waste per year currently not properly used. In wood stem, heartwood (HW) is the inner part characterized by its high mechanical properties and sapwood (SP) the outer part with a higher porosity and moisture content. Due to these properties, okoume SW and HW have been considered as low value coproducts, excluded from industrial transformation such as trenching, veneers and plywood production [START_REF] Ngwa Obame | Homolytic and heterolytic cleavage of beta-ether linkages in hardwood lignin by Steam Explosion[END_REF]. There are relatively few publications concerning the comparison between sapwood (SW)/heartwood (HW) composition. Unlike HW, SW is comprised of living cells and allows the water transport and nutrients storage, characterized by a higher porosity and permeability. Willford at al. reported in 2005 the amount and composition of sugars in SW and HW of 11 industrially important hardwood species from temperate areas [START_REF] Willfor | Polysaccharides in some industrially important hardwood species[END_REF]. More recently, extractives content of bark, SW and HW of okoume were described (Engozogho et al., 2015) but to the best of our knowledge, the sugars composition of SW /HW of tropical species has never been investigated. However, in a context of an optimal valorization of bioresources, a better knowledge of the chemical composition of the different parts of industrial wood, including co-products, is needed.

In previous papers, we have described organosolv and SE pretreatment of okoume SW under various conditions for lignin extraction and characterization but also for ethanol production [START_REF] Ngwa Obame | Homolytic and heterolytic cleavage of beta-ether linkages in hardwood lignin by Steam Explosion[END_REF][START_REF] Safou-Tchiama | An investigation of Aucoumea klaineana Pierre heartwood and sapwood wastes potential for cellulosic ethanol production: Ethanol Organosolv Lignin and fermentable sugars recovery[END_REF]. The goal and the novelty of the present work are twofold: (1) to analyze the hemicelluloses composition of HW and SW of a tropical hardwood species and (2) to study the recovery of polymeric hemicelluloses from hardwood during SE pretreatment for further utilizations. A detailed characterization of acetylated hemicelluloses was carried out by NMR and chromatographic methods in order to better understand the parameters impacting the structure of the extracted polysaccharides, to anticipate their future applications and facilitating further processing.

Material and methods

Raw material

The samples used in this study were collected from an Okoume (Aucoumea klaineana Pierre) log in the Nzamaligué natural forest of Gabon by the "Société Equatoriale d'Exploitation Forestière SEEF". The Okoume SW comes from slab waste, while the internal HW from the peeling core co-products.

Conventional hemicelluloses extraction with NaOH and DMSO

Sawdust from Okoume HW and SW (< 0.16 mm) was Soxhlet extracted using toluene / ethanol / methanol (4:1:1 v/v/v) (Safou-Tchiama et al. 2017). The extracted sawdust was dried at 105°C and stored in a plastic bag at room temperature before use. Extract-free sawdust was depectinized with a 1% (w/w) of ammonium oxalate solution (2 h at 80°C) and then dried at 40°C. Delignification was carried out in a water bath under reflux at 70°C by dispersing 1.5 g of depectinized sawdust in 125 mL of deionized water. Subsequently, 1 g of sodium chlorite and 1 mL of glacial acetic acid were added every 2 h until complete bleaching of the biomass. The delignified residue was carefully washed with deionized water Eq. 1 and filtered under vacuum. The white fibrous solid residue (holocellulose) was collected and dried at 40 °C. Alkaline extraction was carried out under magnetic stirring at 70 °C with 1 g of dry holocellulose in 50 mL of 2% (w/w) of NaOH. After 2 hrs, the liquid phase was recovered.

The residue was extracted again with 50 mL of 2% NaOH for 2 hrs. Both liquid phases were acidified with 20% (w/w) of acetic acid to a pH between 5.5 and 6. The hemicelluloses precipitated by the addition of 3 volumes of ethanol were recovered by centrifugation at 4000 rpm for 10 min at room temperature. The recovered hemicelluloses were dried at 40°C and stored in plastic jars before analysis. The hemicelluloses yields were calculated as mass percentage of dry wood. The DMSO extraction of hemicelluloses was performed on holocellulose (1:25 solid/liquid) under magnetic stirring for 15 hrs at 70°C. Three volumes of ethanol were added. The hemicelluloses were recovered by centrifugation at 4000 rpm for 10 min and drying at 40°C. Yields of hemicelluloses were calculated as mass percentage of dry wood.

Extraction of hemicelluloses by steam explosion

Extraction of hemicelluloses by SE has been carried out by adapting the protocol described by [START_REF] Chadni | Steam explosion process for the selective extraction of hemicelluloses polymers from spruce sawdust[END_REF] Sawdust from Okoume HW and SW of about 2 mm size was first dried at 105 °C overnight. Then 50 g of biomass were impregnated for 15 hrs in 1 M aqueous NaOH (solid/liquid ratio 1:7, NaOH-SE) or in water (solid/liquid ratio 1:7, H 2 O-SE) before SE (Fig. 1).

The impregnated sawdust was then filtered and placed directly into a 2 L SE reactor. The sawdust was treated by injection of saturated steam at various temperatures and residence times (see Table 1), then a pneumatic ball valve was opened to abruptly drop the pressure and transport the biomass to the explosion chamber. The steam explosions were set at temperatures between 170 °C and 210°C and a residence time of 5 min to 10 min. The severity factor for each experiment was calculated by correlating temperature and retention time using the following equation [START_REF] Overend | Fractionation of lignocellulosics by steam-aqueous pretreatments[END_REF]: t s is the residence time (min) and T is the temperature (°C).

156

After SE pre-treatment, the hemicelluloses-rich liquid fraction was separated from the treated wood by filtration. For NaOH-SE, the pH was adjusted between 5.5 and 6 with H 2 SO 4 72% (w/v). The liquid fraction was concentrated using a rotary evaporator until a volume of ≈ 100 mL. The hemicelluloses were precipitated with 4 volumes of ethanol, then separated by centrifugation at 40,000 rpm for 10 min. The supernatant was gently removed and the solid (composed of polymeric hemicelluloses) was retained for the dialysis step. The dialysis was performed for 3 days by filling a dialysis tube (cut-off of 2.5 kDa) with the hemicelluloses solubilized in ultrapure water. Finally, the dialysate consisting of hemicelluloses was freezedried.

Measurement of monosaccharides and uronic acids by HPEAC-PAD

The processing and analysis of the chemical composition of the extracts was performed using the National Renewable Energy Laboratory (NREL/TP-510-42618) standard.

Monosaccharide and uronic acid concentrations were quantified by high performance anion exchange chromatography coupled with a pulsed amperometric detector (HPEAC-PAD: Dionex ICS-3000). The separation was carried out on a CarboPac PA20 (Dionex) column at a temperature of 35 °C and with an isocratic eluent flow rate of 0.4 mL.min -1 , with the following composition: 99.2% ultrapure water / 0.8% of 250 mM NaOH (0-20 min) ; 75% ultrapure water / 20% of 250 mM NaOH / 5% 1 M of CH 3 COONa -20 mM NaOH (20-37 min) and 40% of ultrapure water / 20% 250 mM of NaOH / 40% of 1 M CH 3 COONa -20 mM of NaOH (37-45 min) The separation was performed within 45 minutes. Calibration was performed with seven calibration points. This method allowed the simultaneous identification of the following sugars: galactose (Gal), glucose (Glc), mannose (Man), rhamnose (Rha), xylose (Xyl), arabinose (Ara), and glucuronic acid GlcA and galacturonic acid (GalA).

Determination of acetic acid by high performance liquid chromatography (HPLC)

The acetic acid content of hemicelluloses was determined by adapting the protocol of [START_REF] Yuan | Production of feruloyl oligosaccharides from wheat bran insoluble dietary fibre by xylanases from Bacillus subtilis[END_REF]. 1000 µL of the oligosaccharide solution (10 mg in 5 mL of water)) were saponified with NaOH (1250 µL at 0.4 M) for 2 hours in the dark, at room temperature, in a 5 mL volumetric flask. The reaction was stopped by addition of H 3 PO 4 at 0.4 M. This solution was analyzed by high performance liquid chromatography coupled with a UV detector (Shimadzu Prominence) using a Rezex™ RHM-Monosaccharide H + (8%) column with sulfuric acid (H 2 SO 4 -5.10 -3 M) as the mobile phase with an isocratic flow rate of 0.8 mL.min -1 and a temperature of 60°C; the wavelength for detecting acetic acid was 210 nm. An external calibration with 6 calibration points was performed.

Steric Exclusion Chromatography

Prior to the analysis, 5 mg of hemicelluloses were dissolved in 2.25 mL of 0.25 M NaNO 3 .

Molecular weight distributions of hemicelluloses extracts were determined by size exclusion chromatography coupled with a refractive index detector (Shimadzu Prominence). Two columns coupled in series were used (Phenomenex GFC-P2000, 3000) to separate hemicelluloses. The elution temperature was 35°C and the eluent consisted of 0.25 M NaNO 3 with a flow rate of 0.7 mL.min -1 . Pullulan standards of known molar masses were used for calibration.

Fourier transform infrared spectroscopy

The hemicelluloses obtained were subjected to Fourier Transform Infrared Spectroscopy (FTIR) analysis. The infrared spectra were performed using a Thermo Scientific Nicolet 7600 IR-FT spectrometer over a frequency range between 4000 cm -1 and 650 cm -1 .

HSQC 2D NMR and calculation of the Degree of Acetylation (DS Ac )

The 2-dimensional nuclear magnetic resonance (NMR) analyses of heteronuclear singular quantum coherence (HSQC) were performed on a 400 MHz Bruker instrument with a standard Bruker program. The hemicelluloses from the steam explosion and those extracted by NaOH from the bleached wood were dissolved in 99.7% deuterium oxide (D 2 O), while the hemicelluloses extracted by DMSO from the bleached wood were dissolved in 99.9% dimethyl sulfoxide d6 (DMSO-d6). The number of collected complex points was 1024 for the 1H-dimension with a relaxation of 1.5-and 256-time increments were recorded in 13Cdimension. HSQC spectra were taken at room temperature.

The calculation of DS Ac Xylp and DS Ac Manp are given below in Eq. 2 and 3.

Where a) Acetyl content determined by HPLC; b) Sugars content determined by HPEAC-PAD; c) Integration ratio by HSQC-NMR Eq 3. Eq 2.

Results and discussion

Composition

The compositions of okoume sapwood (SW) and heartwood (HW) used in this study and given in the Table 2 are in accordance with previous studies reported by [START_REF] Safou-Tchiama | Survey of the interfacial bonding of some tropical hardwoods towards succinic anhydride and 2-octen-1-yl succinic anhydride molecules: Impact of lignin and carbohydrate polymers structure on the chemical reactivity[END_REF]. In the present study, a comparable amount of Klason lignin and glucose and a substantially lower proportion of xylose and mannose was found.

Table 2

The polymeric hemicelluloses were recovered after SE of okoume SW and HW from the liquid stream of the process by ethanolic precipitation and dialysis. Two different impregnation conditions of wood sawdust prior to SE were examined (neutral and alkali impregnation) and three different experimental conditions (170°C-10 min, 190°C-8 min, 210°C-5 min) in order to examine the influence of the treatment severity on the extract yields and compositions. In this study the severity parameters (S) which combine temperature and duration of the SE treatment have been used (see Material and Methods section and Table 1). The condition sets used in this study were selected considering previously described works [START_REF] Chadni | Steam explosion process for the selective extraction of hemicelluloses polymers from spruce sawdust[END_REF]. For comparison purposes, hemicelluloses were also recovered from okoume SW and HW holocellulose (after bleaching) with two commonly used methods with DMSO and with sodium hydroxide. It was reported that alkali solutions allow the extraction of hemicelluloses from bleached pulps with high yields especially for xylans. Alkaline treatment can cleave ester groups of lignocellulosic complexes in the cell wall and causes the swelling of cellulose facilitating the dissolution of hemicelluloses. On the other hand, DMSO extraction is used for the recovery of slightly modified hemicelluloses, close to their native structures but with lower yields [START_REF] Evtuguin | Characterization of an acetylated heteroxylan from Eucalyptus globulus Labill[END_REF]. Naturally acetylated hemicelluloses have been isolated using this procedure.

Hemicelluloses yields

Fig. 2 gives the hemicelluloses yields recovered from SW and HW after precipitation and dialysis for all the experimental conditions used in this study. As expected, from bleached pulps, higher yields were observed for alkali extractions compared to DMSO method. It is well known that unlike DMSO, alkali treatment can cleave ether and ester linkages between polysaccharides and lignin and effectively releases hemicellulose. The hemicellulose yields recovered by SE from non-bleached SW and HW are closed to those previously reported for spruce and are between 2% and 6% w/w [START_REF] Chadni | Steam explosion process for the selective extraction of hemicelluloses polymers from spruce sawdust[END_REF]. For the reasons mentioned above, a basic impregnation of wood prior to SE has led to higher yields. However, in these latter conditions and in accordance with previous works, an increase of the SE severity led to a decrease of hemicelluloses yields due to degradation reactions such as peeling and alkaline hydrolysis [START_REF] Chadni | Steam explosion process for the selective extraction of hemicelluloses polymers from spruce sawdust[END_REF][START_REF] Chadni | Elaboration of hemicellulose-based films: Impact of the extraction process from spruce wood on the film properties[END_REF].

Sugar compositions and molecular masses

The composition of the hemicelluloses isolated has been established in terms of monomeric sugars by ionic chromatography after a controlled acidic hydrolysis (see experimental section). The quantification of 4-O-MeGlcU being not possible by our chromatographic method, its content was estimated by HSQC NMR (see section 3.5).

The average compositions in sugars corresponding to the 8 extraction conditions applied to SW and HW are given in Table 1. The weight average molecular masses Mw of the polysaccharides, assessed by water-based sized exclusion chromatography, are given in Table 1. Number average (Mn) molecular weights and polydispersities are given in Supplementary Data section S1. Whatever the experimental parameters and starting materiel (SW or HW), for all the extractions involving alkaline conditions (classical alkali extraction or SE after basic impregnation), hemicellulosic extracts were of high molecular weights (Mw ≈ 60 -100 kDa) and mainly composed of xylose with a relatively high proportion of 4-O-MeGlcU suggesting the recovery of polymeric glucuronoxylans (ratio 4-O-MeGlcU / Xyl ≈ 0.35). Xylose was the predominant sugar accounting for 65% to 70% of total amount of hemicellulosic sugars. It has been reported that in hardwood about 60% of noncellulosic sugars was xylose [START_REF] Willfor | Polysaccharides in some industrially important hardwood species[END_REF].

Interestingly, it appears from Table 1 that Relatively high contents in mannose and glucose suggested the co-extraction of glucomannans (GM). A difference in composition was clearly observed between SW and HW, with a higher glucomannan content in SP. For H 2 O-SE extraction, similar trends have been observed with higher GM co-extraction. The relatively high GM content in SW was confirmed from H 2 O-SE extracts. GM have been reported to be the second most abundant hemicellulose in hardwood [START_REF] Sjöström | Wood Chemistry. Fundamentals and Applications[END_REF]. In addition, Willford at al. reported a relatively high GM content in hardwood SW with varying proportions depending on the species.

Mannose accounted for about 10% of the sugars in Populus deltoides SW against only 1 to 2% in Acacia crassicarpa SP [START_REF] Willfor | Polysaccharides in some industrially important hardwood species[END_REF].

As expected the molecular masses of hemicelluloses extracted with DMSO and water-SE were significantly lower. DMSO method solubilizes relatively low molecular mass polysaccharide fragments. [START_REF] Teleman | Isolation and characterization of O-acetylated glucomannans from aspen and birch wood[END_REF] [START_REF] Chadni | Steam explosion process for the selective extraction of hemicelluloses polymers from spruce sawdust[END_REF][START_REF] Chadni | Elaboration of hemicellulose-based films: Impact of the extraction process from spruce wood on the film properties[END_REF]. The relatively low molecular masses obtained using these conditions are justified by the well-known acid-catalyzed hydrolysis of glycosidic linkages in hemicellulose chains.

Table 3

FTIR characterization

FT-IR spectra of SE hemicelluloses from HW (H 2 O-SE and NaOH-SE) are presented in Figure 3.

FT-IR spectra of the other hemicellulosic fractions isolated in this study are given in Supplementary Data section S2. In H 2 O-SE and DMSO extracts, the band at 1730 cm -1 is due to carbonyl groups stretching indicating that the hemicellulosic fractions isolated in neutral conditions are acetylated. This observation was confirmed by the presence of high-intensity band at 1244 cm -1 assigned to C-O deformation bonds of ester functions (Rowley et al., 2013). The bands at 1508 cm -1 (δ C-C ) and 1460 cm -1 (δ C-H of CH 3 -O groups of S and G units) suggest the presence of a high amount of residual lignin in hemicelluloses extracted in basic medium (Sun et al., 2012;Lv et al., 2013). It can also be observed that the band at 895 cm -1 , assigned to C 1 -H bonds of ß-(1-4)-Xylp chain (Sun et al., 2016), is stronger in H 2 O-SE. This is in accordance with the higher xylose contents detected by HPAE-PAD in the H 2 O-SE extracts (section 3.3).

Fig. 3

NMR characterization and acetylation degree

The sugar compositions of the hemicellulosic fractions were confirmed by a 2D NMR study 1 H-13 C HSQC. The spectra were in good accordance with published data of GX and GM. For HW, the main signals were assigned to sugar residues contained in GX (4-O-MeGlcUp and Xylp) [START_REF] Evtuguin | Characterization of an acetylated heteroxylan from Eucalyptus globulus Labill[END_REF][START_REF] Teleman | Isolation and characterization of O-acetylated glucomannans from aspen and birch wood[END_REF][START_REF] Zhao | Characterization of hemicelluloses from Neolamarckia cadamba (Rubiaceae) during xylogenesis[END_REF]. In SW spectra additional cross-linked signals of lower intensities and assigned to Manp and Glcp were detected attesting the presence of GM [START_REF] Campestrini | NMR and rheological study of Aloe barbadensis partially acetylated glucomannan[END_REF][START_REF] Martínez-Abad | Differences in extractability under subcritical water reveal interconnected hemicellulose and lignin recalcitrance in birch hardwoods[END_REF]. HSQC NMR spectra of hemicellulosic fractions are given in Fig. 4 and in Supplementary Materials section S3. The 1 H/ 13 C cross peaks assignments are given in Table 3.

Table 3

In accordance with the FT-IR data, NMR data showed that hemicelluloses recovered with DMSO and H 2 O-SE are all acetylated. This was confirmed by 1 H NMR intense signals at 1 H at ≈ 2.0-2.2 ppm assigned to CH 3 CO group (Supplementary Materials section S4). It has been shown that the presence of acetylated sugar residues in the polysaccharides backbone results in a large number of possible monosaccharide combinations and NMR cross-peaks signals, complicating the spectra considerably [START_REF] Michalak | Effects of pH on steam explosion extraction of acetylated galactoglucomannan from Norway spruce[END_REF]. In alkali conditions, deacetylated polysaccharides were recovered because of a further deacetylation by saponification reactions.

For DMSO and H 2 O-SE hemicelluloses fractions, the acetylation degree was determined by HPLC after saponification (Table 1). The 13 C/ 1 H HSQC NMR correlations also helped to determine distribution patterns of O-acetyl groups in GM and GX backbone. [START_REF] Evtuguin | Characterization of an acetylated heteroxylan from Eucalyptus globulus Labill[END_REF] and O-2,3 acetyl units in xylan and mannan backbones was performed [START_REF] Giummarella | Structural Insights on Recalcitrance during Hydrothermal Hemicellulose Extraction from Wood[END_REF].

The results regarding the acetylation pattern are gathered in Table 4. In DMSO, very different acetylation patterns were observed for SW and HW. Interestingly, SW hemicelluloses are more highly acetylated than HW (4.1% and 1.0% respectively). A comparable trend was observed for the water-SE extracts with significantly higher acetyl contents (6.2% and 8.4% for HW and SW respectively). It has been previously reported that hemicelluloses isolated from hardwood SW exhibited higher degree of branching and lower xylose content [START_REF] Xiao | Unmasking the heterogeneity of carbohydrates in heartwood, sapwood, and bark of Eucalyptus[END_REF] but, to our knowledge, a comparison of the acetyl content of SW and HW hemicelluloses has never been investigated. The higher acetylation degree of SW hemicelluloses reported in the present study could be one of the factors contributing to the higher porosity and water permeability of SW [START_REF] Ramachandriya | Simultaneous saccharification and fermentation of Eastern redcedar heartwood and sapwood using a novel size reduction technique[END_REF]. In okoume SP, comparable results were obtained for DMSO and H 2 O-SE in terms of acetylation pattern.

Both GX and GM are O2 and O3 acetylated, the degree of acetylation being slightly higher for GM compared to GX (DS Ac Manp ≈ 0.25 and DS Ac Xylp = 0.20 respectively). For HW, a significantly higher acetylation degree was also found for H 2 O-SE compared to DMSO, GX being acetylated at position O2 and/or O3 (DS Ac Xylp = 0.26). These results are close to those previously obtained from spruce and the recovery of galactoglucomannans (GGM) by H 2 O-SE with DS Ac ≈ 0.27 -0.35, very similar to the values reported for native Ac-GGM [START_REF] Chadni | Steam explosion process for the selective extraction of hemicelluloses polymers from spruce sawdust[END_REF][START_REF] Chadni | Elaboration of hemicellulose-based films: Impact of the extraction process from spruce wood on the film properties[END_REF]. Thus, these results confirm that SE allowed to extract highly acetylated and slightly modified polymeric hemicelluloses. The acetylation degree of hemicelluloses strongly affecting the physico-chemical properties of the resulting materials (e.g. barrier properties of films, [START_REF] Kishani | Solubility of Softwood Hemicelluloses[END_REF], these experimental results could help to develop an extraction route from okoume waste wood for the design of films and materials with controlled properties.

Table 4 4. Conclusion

Steam explosion (SE) pretreatment was assessed for the extraction of high molecular weight hemicelluloses directly from okoume SW and HW and compared to traditional extraction methods with DMSO and alkali solution performed from bleached wood. The SE parameters which include a short steaming duration and a mechanical defibration limit the polysaccharide hydrolytic breakdown and enhance the efficiency of the subsequent extraction. The recovery of high molecular weight GX was performed using a SE treatment after basic impregnation. On the other hand, after a water pre-soaking, SE allowed the recovery of a mixture of highly O2 and/or O3 acetylated GX and GM. It clearly appeared that H 2 O-SE preserved the acetyl moieties in a greater extent compared to the mild DMSO extraction. The results obtained in our study showed that (1) SE can be employed for the extraction of complex polysaccharides from wood for characterization purposes, (2) okoume wood hemicelluloses are primarily composed of highly acetylated GX with a relatively high amount of acetylated GM in the SW. The impact of this work could involve better recovery of waste from the okoume industry in Gabon with a view to the production of hemicellulosebased materials.

Fig. 1

 1 Fig.1

Fig. 2

 2 Fig.2

  glucuronoxylans of higher molecular masses were recovered with NaOH-SE extraction compared to classical alkali extraction performed from bleached pulp. This observation is in accordance with previous works, the structure of the recovered hemicelluloses from SE being strongly influenced by the rapid pressure release step which open the wood structure and limit the chemical degradations (Wojtasz-Mucha et al. 2017). The compositions of the extracts isolated with DMSO displayed a very different pattern. A lower proportion of 4-O-MeGlcU was observed (ratio 4-O-MeGlcU / Xyl ≈0.05-0.08).

Fig

  Fig. 4.

  determined the 13 C/ 1 H correlations of acylated heteroxylans backbone by homonuclear (TOCSY) and heteronuclear (HSQC) NMR experiments. Camprestrini et al. (2013) characterized acetylated GM by NMR and other techniques. More recently, lignin carbohydrate complexes (LCC) extracted from birch hardwood have been analyzed by 2D NMR (HSQC and TOCSY). Martínez-Abad et al. (2018) described the assignment of the main 13 C/ 1 H HSQC signals of partially acylated GX and GM in the LCC complex by HSQC NMR. In this study, the 1 H and 13 C chemical shifts for the [O-Ac(1→2/3)--D-Xylp] and [O-Ac(1→2/3)--D-Manp] are in good agreement with the values reported earlier. Based on previous studies and using the data from NMR, HPLC and HPEA-PAD, a semi-quantification of O-2, O-3

a

  Impregnation conditions prior to SE; b Severity factor of SE; c Xylose, mannose, glucose, arabinose, galactose, Rhamnose, galacturonic and glucuronic acid %, determined after hydrolysis by HPEAC-PAD; d estimation by HSQC-NMR; e acetic acid quantified by HPLC after saponification; f determined by SEC; g extraction from holocellulose; h extraction from wood by SE

Figure

  Figure 3. FT-IR Spectra of SE-extracted hemicelluloses (H 2 O-SE HW and NaOH-SE HW, S = 3.1)

  extracted GM from birch and aspen wood with DP ≈ 16. Chadni et al. extracted galactoglucomannans from spruce by H 2 O-SE in the same range of severity, producing polysaccharides with comparable molecular masses (≈ 20 kDa)

Table 1 . Composition of sugars, acetic acid (% of dry mass of hemicelluloses molar mass of hemicelluloses) and average (Mw in KDa) of hemicelluloses

 1 Author Contributions: "Conceptualization, N.B., RST; methodology, EMM, IZD.; investigation, EMM; writing-original draft preparation, N.B.; writing-review and editing, N.B., EMM, IZD, RST; supervision, N.B.; funding acquisition, RFT. All authors have read and agreed to the published version of the manuscript."

	Treatment	Impr	a	S°b	Xyl c	GlUOMe	d	Man	c	Glc c	Ara	c	Gal	c	Rha	c	GalA	c	GlcA c	Ac e	Mw f
	NaOH	e	SW				43.1 ± 1.0			n.a		1.7 ± 0.1	2.4 ± 0.1	1.7 ± 0.1	1.1 ± 0.0	2.9 ± 0.1	0.4 ± 0.0	-
				HW				34.1 ± 2.6	11.1		n.a		0.1 ± 0.1	0.3 ± 0.0	1.4 ± 0.1	0.9 ± 0.0	1.6 ± 0.2	0.3 ± 0.0	-
	DMSO	g	SW				16.0 ± 0.8	1.3		17.0 ± 0.6 27.4 ± 1.6 0.7 ± 0.0	1.5 ± 0.0	0.5 ± 0.0	1.1 ± 0.1	0.4 ± 0.0	4.1
				HW				44.3 ± 0.3	2.2		11.5 ± 0.4 11.0 ± 0.2 0.2 ± 0.0	0.9 ± 0.0	0.7 ± 0.1	0.9 ± 0.0	0.3 ± 0.0	1.0
					H 2 O		3.1	47.7 ± 1.7	2.4		11.3 ± 0.8 9.3 ± 0.3	0.5 ± 0.0	5.4 ± 0.2	4.6 ± 0.1	5.4 ± 0.2	9.3 ± 0.2	8.4	9
				SW	H 2 O		3.6	44.5 ± 1.5			5.6 ± 0.2 25.7 ± 1.0 0.4 ± 0.0	4.4 ± 0.2	0.9 ± 0.1	0.9 ± 0.1	0.2 ± 0.0	8.1
					H 2 O		3.9	29.4 ± 0.1			4.9 ± 0.0 34.3 ± 0.2 0.1 ± 0.0	3.4 ± 0.0	0.4 ± 0.0	0.5 ± 0.0	0.1 ± 0.0	8.0
					H 2 O		3.1	54.9 ± 11.7	1.1		2.6 ± 2.6	1.2 ± 0.8	2.2 ± 2.0 10.1 ± 5.5 1.9 ± 1.7	6.8 ± 0.2	0.8 ± 0.0	6.2
				HW	H 2 O		3.6	44.7 ± 2.1			2.3 ± 0.2	1.3 ± 0.1	0.1 ± 0.0	3.2 ± 0.2	0.1 ± 0.1	1.5 ± 0.2	0.2 ± 0.0	7.7
	Steam explosion	h	H 2 O NaOH	3.9 3.1	64.4 ± 1.9 30.7 ± 1.1	10.1		4.2 ± 0.2 n.a	3.1 ± 0.1 0.8 ± 0.0	0.1 ± 0.0 1.4 ± 0.1	5.6 ± 0.2 1.7 ± 0.1	1.5 ±0.0 1.4 ± 0.1	2.0 ± 0.1 0.6 ± 0.0	0.3 ± 0.0 0.4 ± 0.1	6.6 -	6
				SW	NaOH	3.6	24.1 ± 1.

Table 4 . Acetylation degree of hemicelluloses

 4 Ac% a DS Ac Manp b NMR δC/δH ppm DS Ac Xylp c NMR δC/δH ppm Ac: Acetic acid (% of dry mass of hemicelluloses after saponification); b DS AC Manp : Degree of substitution of mannose residue with acetyl groups; c DS ACXylp : Degree of substitution of xylose residue with acetyl groups.

	DMSO	SW HW	4.1 1.0	0,24 0,02	O-2 71.85/5.30 O-3-O-2 -O-3 73.36/4.96	0,18 0,04	O-2 73.85/4.52 O-3 75.45/4.82 O-2 70.25/4.50 O-3 75.45/4.82
		SW	8.4		O-2 73.66/5.28		O-2 71.02/4.50
				0,25	O-3 75.47/5.19	0,20	O-2,3 72.00/4.84
	H 2 O-SE	HW	6.2		O-2 73.13/5.25		O-3 77.13/4.64 O-2 72.55/4.50
				0,08	O-3-	0,26	O-2,3 72.00/4.84
							O-3 77.13/4.64

a Figure 1.

Experimental procedures for hemicelluloses extraction from okoume sawdust

	NaOH SW
	Okoume holocellulose NaOH HW DMSO SW DMSO HW	NaOH extraction Bleachin g DMSO extraction	Okoume sawdust SW or HW	Steam Explosion Cellulosic logR° = 3.06, 3.55 or 3.94 H 2 O or NaOH impregnation pulp NaOH-SE SW NaOH-SE HW H 2 O-SE SW H 2 O-

SE HW Figure 2. Polymeric hemicelluloses yields (% of dry mass of the initial wood)

						SW HW
	(%)
	Yields
	NaOH DMSO 3.06	3.55	3.94	3.06	3.55	3.94
	bleached wood	raw wood: NaOH-SE	raw wood: H2O-SE
		Severities and treatments

Acknowledgments:

The EA 4370 LERMAB is also supported by the French National Research Agency through the Laboratory of Excellence ARBRE (ANR-12-LABXARBRE-01). The National Agency of Fellowships of Gabon (ANBG) and Campus France are thanked for the financial support granted to the PhD student Errol MOUGNALA MOUKAGNI. The authors thank the NMR plateform, Institut Jean Barriol, CRM2, Lorraine University -CNRS.


Adriano N D Lopes
email: adriano@div.cefetmg.br

Valter J S Leite

Luís F P Silva

Álan C Sousa

ESTABILIZA Ç ÃO LOCAL DE SISTEMAS N ÃO LINEARES VIA MODELAGEM FUZZY TAKAGI-SUGENO DISCRETA NO TEMPO

Keywords: Local estabilization, Fuzzy Takagi-Sugeno modeling, Saturating actuators, Discrete-time systems, linear matrix inequalities Estabilização local, Modelagem fuzzy Takagi-Sugeno, Saturação de atuadores, Sistemas discretos no tempo, Desigualdades matriciais lineares

The authors conduct experiments to locally stabilize a nonlinear system subject to actuator saturation. For that they utilize a real system of coupled tanks with a nonlinearity and sensors and actuators with industrial characteristics. Takagi-Sugeno's fuzzy modeling is adopted to obtain a representation of this system in discrete time. The studied controller is composed of a state feedback and a discrete integrator in time with fuzzy-type gains. However the adopted structure is not a PDC (parallel distributed compensation). The synthesis of the fuzzy gains is done via convex optimization procedures that aim to maximize the attraction region in the presence of exogenous signals limited in amplitude. This allows the implementation of the reference tracking, ensuring the convergence of the controlled variable to the desired reference value. A PLC (programmable logic controller) is used for safety interlocking and also as an interface between the controlled system and the computer that implements the fuzzy controller in the Python language. Several experiments are carried out that illustrate the feasibility of the proposal in an industrial environment without the need for greater investments in equipment.

Introdução

A presença de não linearidades em sistemas de controle reais é praticamente inevitável. Essas não linearidades são frequentemente descritas em modelos desenvolvidos a partir das equações físicas de balanço de massa e energia ou mesmo de modelos obtidos em diferentes pontos de operação. Para tratar tais não linearidades, diversas abordagens são encontradas na literatura. Dentre as mais populares está a linearização do modelo em torno de um ponto de operação [START_REF] Hespanha | Linear Systems Theory[END_REF]. Entretanto, a mudança de ponto de operação requer a correspondente mudança nos parâmetros do controlador baseado em um modelo em novo ponto de operação. Nesse contexto, a modelagem fuzzy Takagi-Sugeno (TS) tem se mostrado como uma alternativa bastante interessante ao descrever o sistema (ou modelo) não linear por uma combinação de modelos lineares locais ponderados por funções de pertinência [START_REF] Tanaka | Fuzzy control systems design and analysis: A linear matrix inequality approach[END_REF].

Essa abordagem permite a síntese de controladores fuzzy com uma estrutura distribuída paralela (PDC, do inglês parallel distributed compensation) em que a mesma regra de formação do modelo fuzzy é usada para construir o controlador. Conforme discutido por Gonzalez e Guerra (2014), leis de controle do tipo não-PDC podem levar a melhores resultados, por possuírem um maior grau de liberdade.

No âmbito dos sistemas discretos no tempo o problema de estabilização local de sistemas não lineares foi estudado em vários trabalhos. Veja, por exemplo, [START_REF] Silva | Local stabilization of nonlinear discrete-time system with uncertain time-delay using T-S models[END_REF] que considera sistemas com atrasos nos estados. Klug, Castelan, Leite e [START_REF] Klug | Fuzzy dynamic output feedback control through nonlinear Takagi-Sugeno models. fuzzy sets and systems[END_REF] apresentam uma abordagem convexa para o projeto de compensadores fuzzy dinâmicos via realimentação de saída. Em [START_REF] Klug | Interactive software for modeling and control of nonlinear systems: A T-S fuzzy approach[END_REF] é apresentado um software para realizar a modelagem e controle de sistemas não lineares. [START_REF] Tognetti | H∞ and H 2 nonquadratic stabilisation of discrete-time takagi-sugeno system based on multiinstant fuzzy Lyapunov functions[END_REF] in-XIII Simpósio Brasileiro de Automação Inteligente Porto Alegre -RS, 1 o -4 de Outubro de 2017 vestigam a síntese de controladores via realimentação de estados para sistemas fuzzy TS. Em [START_REF] Du | Fuzzy control for nonlinear uncertain electrohydraulic active suspensions with input constraint[END_REF] é apresentada a aplicação do controle fuzzy em um sistema com restrição na entrada e não linearidades no modelo. Este trabalho traz como contribuição a aplicação de técnicas fuzzy TS discretas no tempo para a síntese de controladores do tipo não-PDC para a estabilização local de sistemas fuzzy TS sob restrição no atuador. Assim a não linearidade da saturação do sinal de controle é tratada separadamente, gerando modelos fuzzy TS locais que possuem saturação do controle. As condições de síntese são propostas como procedimentos convexos. É proposta e aplicada em um sistema real uma realimentação de estados e uma ação integral, ambas do tipo fuzzy TS não-PDC. A amplitude do sinal de referência (sinal exógeno) é considerada no projeto. As condições são aplicadas para o controle de nível em um sistema de tanques com características industriais inspirado em [START_REF] Johansson | The quadruple-tank process: A multivariable laboratory process with an adjustable zero[END_REF]. Em um dos tanques é incluída uma não linearidade e vários testes experimentais são realizados demonstrando os efeitos dos limites da saturação no atuador. Toda a instrumentação do sistema é concentrada em um controlador lógico programável (CLP) que é usado para realizar a) a aquisição de dados, b) o intertravamento de segurança, e c) enviar os comandos para o atuador. O controlador fuzzy é executado em linguagem Python em um computador utilizando um pacote de comunicação (Sousa, 2016). Os resultados demonstram a viabilidade da técnica proposta, inclusive em ambiente industrial. Notação: O conjunto dos reais é denotado por R. 0 e I dotam as matrizes nula e identidade, respectivamente, de dimensões apropriadas. x ∈ R n e M ∈ R n×q são um vetor real com n elementos e uma matriz de dimensões n × q e entradas reais, respectivamente. M T é a transposta de M . M > 0 é uma matriz definida positiva. x (ℓ) ou M (ℓ) denota a ℓ-ésima linha de x ou M . E(P,η) denota o conjunto elipsoidal de pontos no R n tais que x T P x ≤ η -1 .

Formulação do problema

Neste trabalho são tratados sistemas não lineares que podem ser descritos por ẋ

(t) = f (x(t)) + g(x(t))sat(u(t)) y(t) = h(x(t)) (1
i : Se z 1 (k) é M i1 e • • • e z p (k) é M ip , Então x k+1 = A i x k + B i sat(u k ), y k = C i x k ,
(2) em que z j (k), j = 1, . . . , p, são as variáveis escalares de premissa, dependentes apenas dos estados; M ij são os conjuntos fuzzy; p o número de variáveis de premissa. As matrizes A i ∈ R n×n , B i ∈ R n×m e C i ∈ R q×n , i = 1, . . . ,N , são conhecidas. Note que as regras (2) recuperam o sistema (1) por meio da defuzificação e resultando em [START_REF] Tanaka | Fuzzy control systems design and analysis: A linear matrix inequality approach[END_REF]:

x k+1 = A(α k )x k + B(α k )sat(u k ), y k = C(α k )x k , (3)
em que α k(i) = w i (z(k))/ N j=1 w j (z(k)) é a fun- ção de pertinência com w i = p j=1 M ij (z j (k)) e z(k) = z 1 (k) z 2 (k) • • • z p (k) T . Portanto, o
vetor variante no tempo α k ∈ R N depende do estado e precisa ser calculado em tempo real. Esse vetor pertence ao simplex unitário:

Ξ = N i=1 α k(i) = 1, α k(i) ≥ 0, i = 1, . . . , N . (4)
Assim, as matrizes em (3) podem ser reescritas com M ∈ {A,B,C} como

M (α k ) = N i=1 α k(i) Mi, α k ∈ Ξ. (5)
Com a finalidade de incluir o seguimento de referência, neste trabalho é assumida a topologia apresentada na Figura 1, em que a Lei de Controle é definida como

+ + + + - - ū -ū sat(u k ) z -1 Iq K(α k ) K I (α k ) r k y k x k u k u Ik u P k Sistema (1)
Figura 1: Topologia de controle usada.

u k = KI (α k )[(r k +r k-1 )-(y k +y k-1 )]-K(α k )x k (6) com K(α k ) e KI (α k ) os ganhos fuzzy a serem deter- minados.
Conforme a topologia apresentada na Figura 1 é imposta uma saturação ao sinal de controle, portanto é necessário levá-la em consideração, garantindo que as trajetórias dos estados não excursionem fora do conjunto E (P,η) sendo essa uma região de estabilidade assintótica conforme definido em (Tarbouriech et al., 2011, pág. 14). Neste trabalho é tratado o seguinte problema.

XIII Simpósio Brasileiro de Automação Inteligente Porto Alegre -RS, 1 o -4 de Outubro de 2017

Problema 1 Determinar os ganhos KI (α k ) e K(α k ) de tal forma que o sistema não linear (1) em malha fechada a partir da lei de controle ( 6) seja estável, com o rastreamento de uma classe de sinais de referência com o valor de amplitude máximo calculado e com as trajetórias dos estados resultantes sempre excursionando no interior da região E (P,η).

Resultados preliminares

Seguindo o desenvolvimento proposto por Ogata (1995, p. 460-464), uma vez que o sistema (1) discretizado pode ser representado pelo modelo fuzzy TS dado por (3), o diagrama da Figura 1 pode ser reescrito como:

ξ k+1 = A(α k ) B(α k ) 0 0 Âk ξ k + 0 Iq Bk v k + 0 Iq Bw rk (7) v k = sat(ω k ), ω k = -K(α k )ξ k (8) em que ξ k = δx T k δu T k T , com δx k e δu k sendo os
desvios dos vetores de estado e de controle em relação a seus valores de equilíbrio, rk = KI (α k )r k relacionase à variação em torno do valor de referência usado no equilíbrio, e

K(α k ) = -K(α k ) -K(α k ) + KI (α k )C(α k ) A(α k ) Iq -K(α k ) + KI (α k )C(α k ) B(α k )
Portanto, os valores de ū(ℓ) , ℓ = 1, . . , m, referem-se agora ao desvio máximo do sinal de controle em relação ao valor de equilíbrio. Assim, o problema de rastreamento do sistema (1) pode ser resolvido como um problema de estabilização do sistema ( 7)-( 8) sob a perturbação rk . Uma vez determinado o ganho fuzzy K(α k ) podem ser recuperados os ganhos KI (α k ) e K(α k ) usados na topologia apresentada na Figura 1, por meio da relação

K(α k ) KI (α k ) = K(α k ) + 0 Iq × A(α k ) -Iq B(α k ) C(α k )A(α k ) C(α k )B(α k ) -1 (9)
Portanto, ainda que K(α k ) seja obtido como um ganho fuzzy PDC, os valores de K(α k ) e KI (α k ) não podem ser obtidos como uma PDC.

Portanto, busca-se a síntese do ganho

K(α k ) para o sistema ξ k+1 = Â(α k )ξ k + B(α k )sat(ω k ) + Bw rk de forma que para todo sinal r2 k ≤ δ -1
, suas trajetórias iniciadas na origem não deixem o conjunto E (P,η) e para rk = 0, E (P,η) é uma região de estabilidade assintótica. Fica claro, portanto, que a máxima amplitude de r k só pode ser determinada a posteriori, com o conhecimento do maior valor assumido por KI (α k ), ou seja max

α k ∈Ξ |r k | ≤ δ -1/2 max α k ∈Ξ KI (α k ) . ( 10
)
Para lidar com a saturação do sinal de controle, utiliza-se a reescrita dessa não linearidade por meio da zona morta decentralizada, como é proposto por Gomes da [START_REF] Gomes Da | Application of hybrid and polytopic modeling to the stability analysis of linear systems with saturating inputs[END_REF]. Define-se Ψ(ω k ) = sat(ω k ) -ω k , sendo que Ψ(ω k ) corresponde à nãolinearidade de zona morta descentralizada. Assim,

ξ k+1 = ( Â(α k ) -B(α k ) K(α k ))ξ k + B(α k )Ψ(ω k ) + Bw rk . (11)
Na sequência, define-se o seguinte conjunto

S = {ξ k ∈ R n+q : |(-K(α k ) (ℓ) -Ĝ(α k ) (ℓ) )ξ k | ≤ ū(ℓ) }, em que Ĝ(α k ) ∈ R q×n+q dada por (5), com M = G
é uma matriz a ser calculada que introduz um nível de tolerância para a saturação do sinal de controle. Para tratar a não linearidade Ψ(ω k ), utiliza-se a condição de setor generalizada descrita a seguir [START_REF] Tarbouriech | Stability analysis and stabilization of systems presenting nested saturations[END_REF].

Lema 1 Se ξ k ∈ S, então a relação Ψ(ω k ) T T (Ψ(ω k ) + Ĝ(α k )ξ k ) ≤ 0 (12)
é verificada para toda matriz diagonal definida positiva T ∈ R q×q .

Segundo [START_REF] Tarbouriech | Stability analysis and stabilization of systems presenting nested saturations[END_REF], uma condição suficiente para obter a solução para o Problema 1 é alcançada se a seguinte relação é satisfeita ∀ξ k ∈ E (P,η) e ∀r k ∈ W(R,δ), com τ1 > 0 e τ2 > 0, sendo

V (ξ k ) = ξ T k P ξ k e ∆V (ξ k ) = V (ξ k+1 ) -V (ξ k ). ∆V (ξ k ) + (1 -τ1)(ξ T k P ξ k -η -1 ) + τ2(δ -1 -rT k rk ) -2Ψ(ω k ) T T (Ψ(ω k ) -Ĝξ k ) < 0, (13)

Síntese de controlador

O lema seguinte apresenta uma solução para o Problema 1.

Lema 2 Considere o sistema ( 7)-( 8) e um escalar η dado. Se existem uma matriz definida positiva W ∈ R n+q×n+q , uma matriz diagonal positiva S ∈ R q×q e as matrizes U ∈ R n+q×n+q , Yi ∈ R q×n+q e Z ∈ R q×n+q , para i = 1, . . . ,N , que satisfaçam as seguintes LMIs, para m = 1, . . . ,N , n = m, . . . ,N e ℓ = 1, . . . ,q

      -W ( Âm + Ân)U + ( BmYn + BnYm) 2 ⋆ τ1(W -U -U T ) ⋆ ⋆ ⋆ ⋆ ( Bm + Bn)S 2 (Bwm + Bwn) 2 Z T 0 -2S 0 ⋆ -τ2I       < 0, (14) W -U -U T Y T m (ℓ) + Z T (ℓ) Ym (ℓ) + Z (ℓ) -η ū(ℓ) 2 ≤ 0 (15) -(1 -τ1)δ + τ2 < 0 ( 16
)
então as matrizes de ganho

Ki = -YiU -1 , ( 17
)
aplicadas em ( 9) recuperam os ganhos da lei de controle estabilizante ( 6

ξ T k+1 P ξ k+1 -ξ T k P ξ k -2Ψ(ω k ) T T (Ψ(ω k ) -Ĝξ k ) + (1 -τ1)ξ T k P ξ k -τ2 rT k rk < 0, ( 18
)
em que P = W -1 e T = S -1 . Satisfazendo também ( 16), tem-se que (13) é verdadeira e, portanto, garante-se a estabilidade do sistema fuzzy em malha fechada. Com (15) verificada, essa pode ser multiplicada por α k(m) e somada para m = 1, . . . ,N ;o bloco (1,1) pode ser trocado por -U T W -1 U ≤ W -U -U T ; Y e Z substituídos por -KU e -GU ; e o resultado pré e pós multiplicado por diag{U -T ,1} e pelo seu transposto, respectivamente. Aplicando-se o complemento de Schur e pré e pós multiplicado-se por ξ T k e ξ k , tem-se que E (P,η) ⊆ S. Assim, E (P,η) é um conjunto invariante e, sendo que esse conjunto está contido em S, tem-se garantida a estabilidade do sistema não linear em malha fechada mesmo com o sinal de controle sob efeito de saturação [START_REF] Tarbouriech | Stability and Stabilization of Linear Systems with Saturating Actuators[END_REF]. ✷ Uma condição similar a (14), apresentada no Lema 2, pode ser encontrada em [START_REF] Feng | Analysis and Synthesis of Fuzzy Control Systems: A Model-Based Approach[END_REF]) para a estabilização. Neste trabalho, além da estabilização foram incluídas os tratamentos para saturação do sinal de controle e o rastreamento de um sinal de referência a partir da inclusão de um integrador digital na malha de controle, sendo que esse sinal foi tratado como uma perturbação de amplitude limitada, veja [START_REF] Tarbouriech | Stability and Stabilization of Linear Systems with Saturating Actuators[END_REF] para mais detalhes.

4 Estudo de caso: Sistema de tanques O sistema a ser tratado neste trabalho é o de tanques acoplados, que foi inspirado em [START_REF] Johansson | The quadruple-tank process: A multivariable laboratory process with an adjustable zero[END_REF]. Essa planta está disponível no Laboratório de Sinais e Sistemas da Unidade de Divinópolis do CEFET-MG e é composta por quatro tanques com capacidade de 200 litros, dois reservatórios de 400 litros cada e duas motobombas de 1 cv, que são acionadas por meio de inversores trifásicos independentes; os sinais de medição são enviados a um CLP Siemens que é responsável pelo intertravamento da planta e envio dos sinais de controle ao atuador (inversor trifásico). O controle é executado em linguagem Python em um computador que se comunica com o CLP por meio do driver (Sousa, 2016), com T = 4s. A configuração adotada neste trabalho utiliza dois tanques conforme apresentado na Figura 2. Os níveis nos tanques 1 e 2, q i (u(t))

R 12 ( h) D q o (h (t)) 2 h 1 h 2
Figura 2: Sistema de tanques acoplados respectivamente h1(t) e h2(t), são os estados do sistema, sendo h2(t) a variável controlada. A ação de controle é imposta a partir da variação da velocidade da motobomba que manipula a vazão de entrada no Tanque 1, qi(u(t)). As duas válvulas, uma entre os tanques e outra na saída do tanque 2, têm suas aberturas mantidas constantes durante os experimentos.

A área do tanque 2 é constante, A2 = 0,3019m 2 . A não-linearidade inserida no tanque 1 foi proposta por [START_REF] Franco | Síntese convexa de ganhos para compensação robusta de sistemas linearizados por realimentação[END_REF] resultando em uma área útil dada por

A1(h1(t)) = 3r 5 ×(2,7r-cos(2,5π(h 1 (t)-µ)) σ √ 2π e - (h 1 (t)-µ) 2 2σ 2
), com µ = 0,4 , σ = 0,55 e r = 0,31. Para modelar o sistema, foram utilizadas equações de balanço de massa

ḣ1 = R12(h1(t),h2(t))K b u -h1(t) + h2(t) A1(h1(t))R12(h1(t),h2(t) (19) ḣ2
= h1(t) -h2(t) R12(h1(t),h2(t))A2 - 1 A2 qo(h2(t)). (20)
e os parâmetros foram determinados experimentalmente, sendo obtido: K b = 16,55 e R12(∆h) = (0,4321∆h + 12,4676) × 10 -3 , com ∆h = h1(t) -h2(t); a vazão de saída do tanque 2 é dada por qo = (14,2306h2 (t) + 800,2579) × 10 -4 m 3 /s. Utilizando o método de Euler com T = 4s, tem-se

h k+1 = 1 -z 1,k z 3,k z 1,k z 3,k z 1,k A 2 1 - z 1,k +z 2,k A 2 h k + K b T z 3,k 0 u k (21) em que h k = h1(kT ) h2(kT ) T , u k é um sinal sob saturação e as funções não lineares z 1,k = T R 12 , z 2,k = T qo h 2,k
e z 3,k = 1 A 1 podem ser descritas por meio de modelos fuzzy TS conforme metodologia apresentada em [START_REF] Tanaka | Fuzzy control systems design and analysis: A linear matrix inequality approach[END_REF]. Assim, podem ser determinadas as funções de pertinência como Mi(z1(h1,h2)), Ni(z2(h2)) e Oi(z3(h1)) tais que

z 1,k = 2 i=1 Mi(z 1,k )ai, z 2,k = 2 i=1 Nj (z 2,k )bi e z 3,k = 2 i=1 O k (z 3,k ))ci,
XIII Simpósio Brasileiro de Automação Inteligente Porto Alegre -RS, 1 o -4 de Outubro de 2017

em que M1(z 1,k ) = z 1,k -a2 a1 -a2 M2(z 1,k ) = a1 -z 1,k a1 -a2 N1(z 2,k ) = z 2,k -b2 b1 -b2 N2(z 2,k ) = b1 -z 2,k b1 -b2 O1(z 3,k ) = z 3,k -c2 c1 -c2 O2(z 3,k ) = c1 -z 3,k c1 -c2
e, para 0,30m ≤ h1 ≤ 0,80m e 0,17 ≤ h2 ≤ 0,80m, tem-se:

a1 = max h 1 ,h 2 {z1} = 205,46, a2 = min h 1 ,h 2 {z1} = 0,07, b1 = max h 2 {z2} = 245,22, b2 = min h 2 {z2} = 96,94, c1 = max h 1 {z3} = 0,0045, c2 = min h 1 {z3} = 0,0004. Definindo, α ijl,k = 2 i=1 2 j=1 2 l=1 Mi(z 1,k )Nj (z 2,k )O l (z 3,k
), as matrizes da equação discreta no tempo (3) podem ser descritas como

A ijl,k = 2 i=1 2 j=1 2 l=1   1 -aic l aic l ai A2 1 - ai + bj A2   , (22)
B ijl,k = 2 i=1 2 j=1 2 l=1 K b T c l 0 . (23)
De forma equivalente, pode-se escrever que h k+1 = 8 p=1 α p,k k + Bpsat(u k )), em que p = l + 2(j -1) + 4(i -1), Ap = A ijl , e Bp = B ijl . Dessa maneira, foram determinados 8 modos locais que constituem a descrição fuzzy para o sistema ( 19)-(20) em sua versão discreta no tempo. Tendo em vista as características físicas da planta, foi escolhido um δ = 2,17 × 10 -4 gerando assim um max As duas leis de controle calculadas foram implementadas tanto no modelo não linear ( 19)-( 20), quanto na planta física. Os controladores calculados assim como as correspondentes matrizes de Lyapunov W = P -1 obtidas são apresentadas na sequência. Primeiramente, são apresentados os resultados de simulação e experimento obtidos para ū = 15 e em seguida, ū = 30.

W sat(15) =   5,1825
1,3054 -0,0612 1,3054 2,0296 -0,1290 -0,0612 -0,1290 7,2852 tram claramente a viabilidade da ação integral fuzzy proposta neste trabalho, assim como a possibilidade de utilização de equipamentos usuais do meio industrial para a implementação de ações de controle mais avançadas como é o caso da abordagem apresentada neste trabalho.

  ×10 5 Ksat(15) =             0,

Conclusões

Neste trabalho foram estudadas condições convexas para a síntese de compensadores fuzzy Takagi-Sugeno discretos no tempo, sem estrutura paralela distribuída, visando a estabilização local de sistemas não lineares com saturação de atuadores. Os modelos fuzzy TS locais possuem saturação na entrada. As condições propostas, que permitem a síntese de compensadores que maximizam a região de atração, incluem o tratamento de sinais exógenos com amplitude limitada. É proposto um seguimento de referência com um controlador com ganhos fuzzy para a realimentação de estados e para a ação integral. A implementação é feita em linguagem Python, executada em computador que se comunica com um CLP que realiza a implementação dos sinais de controle. A técnica é aplicada em um sistema real não linear para controle de nível. Os resultados experimentais são analisados e demonstram a viabilidade da aplicação da técnica em sistemas in-dustriais.

Agradecimentos

Os autores agradecem ao apoio recebido do CEFET-MG.

  ), isto é, K(α k ) e KI (α k ). Além XIII Simpósio Brasileiro de Automação Inteligente Porto Alegre -RS, 1 o -4 de Outubro de 2017 disso, as seguintes afirmações são garantidas para o sistema não linear (1) em malha fechada, com condições iniciais nulas: i) para r k = 0, o conjunto elipsoidal E (P,1) é uma região de estabilidade assintótica para o sistema fuzzy (3) em malha fechada e, portanto, para o sistema não linear (1); e ii) para algum r k que verifique (10), as trajetórias do sistema em malha fechada não deixarão o conjunto elipsoidal E (P,η).Prova: Se (14) é verificada, então multiplique-a por α k(m) e α k(n) e some o resultado para m = 1, . . . ,N e n = m, . . . ,N .Substitua o bloco (2,2) por-U T W -1 U ≤ W -U -U T ,substitua Y e Z por -KU e -GU . Pré e pós multiplique o resultado por diag{I,U -T ,T,1} e pelo seu transposto, respectivamente. Ao final, aplica-se o complemento de Schur, pré e pós multiplica-se o resultado por ξ T k Ψ(ω k ) T rT k e pelo seu transposto, respectivamente, obtendo-se

  α k ∈Ξ |r k | = 11,35. Ou seja, admitese uma variação de ±11,35cm em torno do valor de referência escolhido para operação do sistema.

Figura 4 :Figura 6 :

 46 Figura 4: Sinal de Controle Saturado, ū = 15.

  Foram considerados os pontos de operação 22, 33 e 27. As figuras 3 e 5 apresentam os estados (h1 no topo e h2 em baixo), enquanto os sinais de controle são apresentados nas figuras 4 e 6, respectivamente. Nessas figuras, o gráfico superior corresponde ao sinal da realimentação de estados, K(α k )x k , o gráfico intermediário ao sinal do integrador e o gráfico inferior contém a subtração dos dois sinais (em azul) e o sinal saturado que foi enviado ao atuador (em vermelho). Nos dois casos pode-se perceber a saturação do sinal de controle. Nas figuras referente aos esta-

														 0,1368 -13,3577 0,5301	
										Ksat(30) =	           1,5079 -14,4927 0,2229 0,1592 -12,4302 0,5195 1,5560 -13,0406 0,2304 0,2955 -12,3159 0,4560 1,4858 -14,4622 0,2193 0,2348 -13,6800 0,4654	          	×10 -3
															1,4794 -12,9324 0,2306
										80
									Nível h 1(cm)	50 60 70							h 1 Simulado h 1 Real
										40
										0		200	400	600	800	1000	1200	1400	1600	1800	2000
										40
									Nível h 2(cm)	20 25 30 35							Referência h 2 Simulado h 2 Real
										0		200	400	600	800	1000	1200	1400	1600	1800	2000
																	Tempo (s)
									Figura 3: Estado com Saturação do Sinal de Con-
									trole, ū = 15.
									dos, 3 e 5, referentes aos estados, são apresentados os
									sinais simulados e os sinais experimentais (mais ruido-
									sos) decorrentes dos experimentos realizados (veja le-
									genda nas figuras para mais detalhes). Observa-se que
									em ambos os casos o sistema controlado (nível h2) e
									condições de operação no sistema real muito próximas
									das obtidas em simulação.	Os resultados demons-
										600
									u P k(%)	0 200 400
										-200
											0	200	400	600	800	1000	1200	1400	1600	1800	2000
			0528 -17,4751 0,2583 0,7337 -17,9945 0,1336 0,1298 -16,2304 0,3103 0,9838 -16,8482 0,1471 0,0979 -17,6512 0,2299 0,7472 -17,9953 0,1329 0,9577 -16,8402 0,1472 0,2020 -16,4294 0,2648	           	×10 -3	600 200 400 0 -200 40 u Ik(%) u 60 80 k(%)	0	200	400	600	800	1000	1200	1400	1600	1800 u k sat(u k ) 2000
	W sat(30) =	 	4,4839 1,1336	1,1336 1,7633	-0,1148 -0,0394	 × 10 5 			0	200	400	600	800	Tempo (s) 1000 1200	1400	1600	1800	2000
			-0,0394 -0,1148	6,2356


J Shen

N Zemiti

A Viquesnel

O Caravaca-Mora

A Courtin

R Garrel

J.-L Dillenseger

P Poignet

Intraoperative Ultrasonography-based Augmented Reality For Application In Image Guided Robotic Surgery

Keywords: Intraoperative ultrasonography, 3D ultrasound calibration, augmented reality, image guidance, transoral robotic surgery

Purpose

Accurate Tumor delineation in the operating room (OR) is a big challenge for surgical oncologist. For instance, the preoperative images used in the transoral robotic surgery (TORS) for tongue base tumor resection cannot reflect the deformation of the soft tissue during the surgery. Furthermore, due to the camera's small field of view and the loss of cross-modality landmarks in the tongue base, it is difficult to register the preoperative imaging modality to the intraoperative stereo camera with deformable registration. We propose an intraoperative ultrasonography (IOUS)-based augmented reality (AR) framework, which is able to accurately delimit the tumor boundaries and provide them to the surgeon's view during the surgery. Instead of some works requiring manual registration [START_REF] Su | Augmented reality during robot-assisted laparoscopic partial nephrectomy: toward real-time 3DCT to stereoscopic video registration[END_REF], additional fiducial markers attached on the organ [START_REF] Liu | Toward intraoperative image-guided transoral robotic surgery[END_REF], or intraoperative imaging modalities which is highly ionizing [START_REF] Liu | Toward intraoperative image-guided transoral robotic surgery[END_REF] [3], our solution uses a safe and cheap US imaging modality and does not use additional fiducial markers disturbing the TORS workflow. Methods Fig. 1 shows the registration pipeline used to achieve AR on stereo camera. A tracking system was defined as the world coordinate system (WCS) w. The transformation between the coordinate system (CS) of the camera c and the WCS was found by calibrating the camera with the WCS based on the mathematical framework given by w T c = w T s s T c , where s represents the CS of an active marker. The tracking system computed the transformation w T s from the CS of the marker s to the WCS, meanwhile, the marker was localized in the 3D camera and its position was used to compute the transformation s T c . After calibrating the stereo camera in the WCS, the preoperative MRI image had to be registered to the WCS, in order to augment the camera view with the information extracted from the MRI. The corresponding mathematical registration framework can be presented as w T m = w T s s T i i T m , where m, i represent the CS of MRI image and US image. The transformation i T m was achieved in our experiment using Elastix toolbox performing a deformable registration between MRI image and US image. B-spline transformation model and Mutual Information similarity measure were used for the registration. The transformation s T i was obtained by US probe calibration. We developed a fast and automatic calibration method based on a custom-made 3D printed phantom and an untracked marker for 3D US probe calibration. Finally, the tracking system measured the position of the marker mounted on the probe and computed the transformation w T s . The performance of the setup was evaluated with 3 soft tissue phantoms made of soft polyvinyl chloride plastic. There was a triangle-shaped object embedded inside of each phantom. The invisible triangle-shaped objects could be distinguished under palpation and US imaging. Fig. 2 shows the experimental setup. The participants were asked to use a calibrated Pointer to localize the boundaries of the invisible targets according to the augmented view projected in a head-mounted display system.

Results

The errors of the US-based AR framework are mainly from MRI/US registration and US probe calibration. The target registration error (TRE) was used to compute the distance, after registration, between corresponding points. MRI and US image registration were performed on the three phantoms. 6 vertexes of the triangle-shaped targets in the MRI and US images were used as landmarks for computing TRE. The root mean square (RMS) of TRE for the three phantoms were 0.313mm, 0.19mm and 0.41mm, respectively. The US probe calibration was evaluated by point reconstruction tests and obtained the RMS of point reconstruction errors of 1.39mm. The presented approach was developed for our clinical application in TORS for tongue base tumor resection. Therefore, we compared our AR framework with conventional procedure where preoperative MRI and manual palpation were used to localize the tumor. With these two approaches, 6 participants estimated the boundaries of the invisible targets inside of the 3 phantoms. The localization accuracy was computed by measuring the overlap between the boundaries estimated by the participants and the ground truth using Dice scores. We found the Dice scores from the experiment based on our AR framework remained clearly higher than those from the experiment based on conventional procedures. We achieved all of the Dice ≥ 0.86 and Hausdorff distance ≤ 3.49mm in the experiment based on AR guidance.

Conclusion

We present a US-based AR framework for accurate tumor delineation in soft tissues. The performance was evaluated in an experiment delineating the boundaries of invisible targets in soft tissue phantoms. With our setup, the participants achieved higher accuracy of boundary delineation than with the conventional procedure. This framework was developed for the clinical application in TORS for tongue base tumor.

Fig. 1 . 2 .

 12 Fig. 1. Registration procedure for augmentation of stereo camera with MRI image Fig. 2. Implementation of IOUS-based AR framework for the experiment with soft tissue phantoms

Acknowledgement

This work was supported in part by the French ANR within the Investissements d'Avenir Program (Labex CAMI, ANR-11-LABX0004, Labex NUMEV, ANR-10-LABX-20, and the Equipex ROBOTEX, ANR-10-EQPX-44-01), the ARC Foundation and by the Région Bretagne.


domain: sdv spi

text:
Charles Pioger

Christophe Jacquet

Alexandre Abitan

Guillau-Anthony Odri

Matthieu Ollivier

Bertrand Sonnery-Cottet

Philippe Boisrenoult

Nicolas Pujol

Litigation in arthroscopic surgery: a 20-year analysis of legal actions in France

Keywords: Litigation, Arthroscopy, Indemnity, France, Surgery

Purpose

The main objective of this study was to identify the epidemiological characteristics of litigation following arthro-scopic procedures, performed in private practice and public hospitals in France. The secondary objective was to establish a risk profile for medical malpractice lawsuits after arthroscopic surgery. Methods All court decisions related to arthroscopic surgery between 1994 and 2020 were collected and reviewed cases from the two main French legal databases (Legifrance and Doctrine). Data were retrospectively collected and included: gender, joint and defendant's specialty involved, reason behind the lawsuit, initial indication and the type of arthroscopic procedure performed. The final verdicts as well as the indemnity awarded to the plaintiff (if any) were recorded. Results One-hundred eighty cases met the inclusion criteria of the study and were analyzed: 58 cases were before administrative courts and 122 were before civil courts. An orthopaedic surgeon was involved alone or in solidum in 45.6% of cases (82/180), followed by anesthesiologists in 5.6% (10/180). The private surgery center or public hospital were implicated in 63.9% (115/180) of cases. The 2 most common joints involved in litigation following arthroscopic surgery were the knee (82.2%, n = 148) and the shoulder (11.1%, n = 20). The main reasons behind the lawsuit were related to postoperative infection in 78/180 cases and to a musculoskeletal complication in 45/180 cases (25%). A failure to inform was also reported in 34/180 cases (18.9%). Of the 180 cases, 122 cases (67.8%) resulted in a verdict for the plaintiff. The average indemnity award for the plaintiff was 77.984 euros [2. 282-1.117.667]. A verdict for the plaintiff was significantly associated with postoperative infection or a wrong-side surgery, while technical error and musculoskeletal complications were more significantly likely to result in a verdict in favor of the defendant (p = 0.003). Conclusion This study evaluated and mapped lawsuits following after arthroscopic surgery in France over a period of more than 20 years. The main joint involved in lawsuits was knee. The main causes of lawsuits following arthroscopic surgery were related to postoperative infection, musculoskeletal complications and failure to inform. Level of Evidence Level IV.

Introduction

Technological advances and increased specialization have led to more ethical and personalized surgery [START_REF] Benson | Ethical standards for orthopaedic surgeons[END_REF]. In parallel, patient information and demands have markedly increased, and questioning the actors of the health care system became more common [START_REF] Ferrara | on Medical Malpractice (2013) Malpractice and medical liability. European Guidelines on Methods of Ascertainment and Criteria of Evaluation[END_REF]. In France and among many surgical specialties, orthopaedics is the most subject to lawsuits. On average, an orthopaedic surgeon faces 17 lawsuits in a career [START_REF] Mouton | Litigation in orthopedic surgery: what can we do to prevent it? Systematic analysis of 126 legal actions involving four university hospitals in France[END_REF][START_REF] Sham | Panorama du risque en établissement de santé sociaux et médico-sociaux, bilan de l'année[END_REF]. Similarly, Jena et al. [START_REF] Jena | Malpractice risk according to physician specialty[END_REF] reported that orthopaedic surgeons were exposed to an annual risk of lawsuits that doubled (14% vs. 7%) compared to other medical and surgical specialties.

The number of arthroscopic procedures performed each year is steadily increasing [START_REF] Garrett | American board of orthopaedic surgery practice of the orthopaedic surgeon: partii, certification examination case mix[END_REF]. This significant increase can be explained in part by the development of reliable techniques for procedures that are now common [START_REF] Colvin | National trends in rotator cuff repair[END_REF][START_REF] Mall | Incidence and trends of anterior cruciate ligament reconstruction in the United States[END_REF] but also by the progress of the industry. New joints such as the hip [START_REF] Colvin | Trends in hip arthroscopy[END_REF], wrist and ankle have become accessible to arthroscopy. Although arthroscopic surgery is considered a safe procedure with easy postoperative recovery period, because it is minimally invasive, it represents a major source of potential malpractice claims against surgeons [START_REF] Shah | Medical malpractice litigation following arthroscopic surgery[END_REF]. Many complications may occur after arthroscopic surgery and be detrimental to the patient's functional prognosis [START_REF] Salzler | Complications after arthroscopic knee surgery[END_REF][START_REF] Shin | Complications after arthroscopic shoulder surgery: a review of the american board of orthopaedic surgery database[END_REF]. While diagnostic or wrong-side surgery should be prevented [START_REF] Miller | editorial commentary: outside the scope of practice-wrong-site surgery should never happen[END_REF], other complications such as infection or the lack of clinical benefit remain inherent to any surgery and lead the patient to file a claim. In France, two recent epidemiological studies have examined the rate of medical malpractice claims in orthopaedic and trauma surgery departments, but neither has specifically focused on arthroscopic surgery [START_REF] Agout | Epidemiology of malpractice claims in the orthopedic and trauma surgery department of a French teaching hospital: a 10-year retrospective study[END_REF][START_REF] Mouton | Litigation in orthopedic surgery: what can we do to prevent it? Systematic analysis of 126 legal actions involving four university hospitals in France[END_REF].

The main objective of this study was to identify the epidemiological characteristics of litigation following arthroscopic procedures, performed in private practice and public hospitals in France. The secondary objective was to establish a risk profile for medical malpractice lawsuits after arthroscopic surgery. It was hypothesized that the knee is the joint most often involved.

Materials and methods

Legal data source

Legal arthroscopic cases from the two main French legal databases (Legifrance and Doctrine) were analyzed. Legifrance is a public service facility used to broadcast law online and focused on administrative procedures since 1539. Doctrine is a legal search engine that centralizes all civil and administrative court decisions in France.

All court decisions related to arthroscopic surgery between 1994 and 2020 were collected and reviewed. The legal cases, anonymized, included decisions of administrative courts and administrative courts of appeal for arthroscopic procedures performed in public hospitals and cases before civil courts and civil courts of appeal concerning private practice.

Data collection

Eligible decisions were identified by applying a search strategy with the following key words: "arthroscopy" or "arthroscopic" and "medical malpractice". This search was performed by four orthopaedic surgeons: two residents and two senior surgeons including one medical expert. In addition, a legal review was carried out by a lawyer to ensure the relevance and correct collection of cases eligible for inclusion.

Data were retrospectively collected in a computerized file and included: gender, date of the triggering event, date before the first instance court and of the appeal (if applicable), the reference of the decision, the joint and the defendant's specialty involved, as well as the city in which the appeal was filed. In addition, the initial indication and the type of arthroscopic procedure performed were recorded. The age of the patient was not available, as part of the anonymization of the databases.

The data collected on the reasons for lawsuits included: wrong-sided surgery, misdiagnosis, failure to inform, inadequate care, infection, thromboembolic events (deep venous thrombosis or pulmonary embolism), cardiovascular, musculoskeletal (stiffness, chronic pain, complex regional pain syndrome), neurological, vascular complications and blockrelated to anesthesia or equipment (broken instrument). The possible death of the patient related to arthroscopic procedure was systematically noted. The final verdicts (in favor of the defendant or the plaintiff) as well as the indemnity awarded to the plaintiff (if any) were recorded.

Eligibility criteria

All court decisions directly related to arthroscopic surgery were considered for study eligibility. Cases of orthopaedic surgery other than arthroscopic procedures and arthroscopic surgery indirectly related to the cause of action were excluded. Similarly, all interim decisions involving only the appointment of an expert were excluded.

Statistical analysis

All data were analyzed using JMP11.0 software (SAS Insti-tute°). As the numerical data did not have a normal distribution, non-parametric analyses were performed (Wilcoxon tests). Comparison of qualitative data was performed using the Fisher test. The alpha threshold of 5% was chosen.

This study was approved by the institutional review board of the hospital and by the scientific committee of our institution. This study was performed in accordance with the ethical standards outlined in the 1964 Declaration of Helsinki. All patient data were all anonymized in the above-mentioned databases.

Results

Cases characteristics

Seventy-one lawsuits from the Legifrance database and 687 from the Doctrine database could be identified. After removal of duplicates, 180 cases met the inclusion criteria of the study and were analyzed: 58 cases were before administrative courts and 122 were before civil courts (Fig. 1). Five cases were identified in the period 1994-1999, 59 in the period 2000-2009 and 116 in the period 2010-2020. Among the included cases, 119 (66.1%) involved male plaintiffs. The median time between the triggering event and verdict of the first instance court was 6.4 years [0.8-36.9]. An appeal was filed, in 60.6% of cases (n = 109) with a median time between the triggering event and the appeal of 8.6 years [2.7-38.7] (Fig. 1).

Regarding the distribution of defendants, an orthopaedic surgeon was involved alone or in solidum in 45.6% of cases (82/180), followed by anesthesiologists in 5.6% (10/180). The private surgery center or public hospital were implicated in 63.9% (115/180). A specific public solidarity fund managed by the National Office for the Indemnification of Medical Accidents (ONIAM) was implicated in 3.3% of cases (6/180). While one case also involved two other specialties (rheumatologist and family medicine), a second involved a company specializing in implantable orthopaedic devices. (Table 1).

Of the 180 cases, 122 cases (67.8%) resulted in a verdict for the plaintiff. Three lawsuits were a result of patient death and only one led to a verdict in favor of the plaintiffs. The average indemnity award for plaintiff verdicts was 77.984 euros [2.282-1.117.667].

The distribution of the cases by joint is summarized in Fig. 2. The 2 most common joints involved in litigation following arthroscopic surgery were the knee (n = 148, 82.2%) and the shoulder (n = 20, 11.1%). Regarding the knee joint, lawsuits were related to either the management of a meniscal tear in 66/148 cases (44.6%) or anterior cruciate ligament (ACL) surgery in 34 cases (23%). The distribution of cases according to the diagnosis is presented in Table 2. The reasons behind the lawsuit were related to postoperative infection in 78/180 cases (43.3%), musculoskeletal complication (stiffness, chronic pain, complex regional pain syndrome) in 45/180 cases (25%). A failure to inform was reported in 34 out of 180 cases (18.9%). The complete distribution of reasons for lawsuit is summarized in Fig. 3.

A comparison between civil and administrative procedure was carried out and reported in Table 3. With respect to the reasons behind the lawsuit, failure to inform and postoperative infection were significantly associated with civil procedures, while litigation for technical error was reported significantly more frequently among administrative procedures.

No significant difference was observed between these two groups concerning the distribution of cases according to the joint involved or the diagnosis. Similarly, no difference was found with respect to the other reasons for lawsuits between administrative and civil procedure.

The rate of verdict in favor of the plaintiff was significantly higher in the civil procedure (76.8%) than in the administrative procedure (48.4%) (p = 0.0006). However, the average indemnity award was comparable between civil and administrative procedure, with, respectively, 79,985 euros

Statistical correlation analysis (a) Correlation between reason for lawsuit and verdict:

In cases where musculoskeletal complication was the reason for the lawsuit, 48.9% of the verdicts were in favor of the plaintiff (p = 0.003). When technical error was invoked, 27.3% of the verdicts were in favor of the plaintiff (p = 0.003). Conversely, for postoperative infection, 87.2% of the verdicts were in favor of the plaintiff and 100% when a wrong-side surgery was the complaint. Consequently, a verdict for the plaintiff was significantly associated with postoperative infection or a wrong-side surgery, while technical error and musculoskeletal complications were more significantly likely to result in a verdict in favor of the defendant. Among the other reasons, no statistically significant correlation was observed. (b) Correlation between reason behind lawsuit and indemnity payment: The average indemnity award for plaintiff verdict was significantly higher when the reason for lawsuit was a neurological complication compared to other reasons (p = 0.045). Similarly, wrong-side surgery was significantly associated with a lower indemnity payment compared to other reasons (p = 0.0004). (c) Correlation between reason behind lawsuit and knee/ shoulder joints: A significantly higher percentage of claims for infection was observed after knee arthroscopies (n = 72/148, 48.6%) compared to shoulder arthroscopies (n = 3/20, 15%) (p = 0.004). No significant difference was found for the other reasons.

Discussion

The most important finding of the present study was that the knee is the most involved joint in malpractice lawsuit following arthroscopic surgery. The current study provided an overall analysis of French litigation after arthroscopic surgery in private and public practice over the period 1994-2020. Of the 180 cases included, the occurrence of an infection (septic arthritis or surgical site) was the most reported reason behind the lawsuit, ahead of musculoskeletal complications (stiffness, chronic pain, unsatisfactory result) and failure to inform. A defense verdict was observed in a significantly higher proportion in private practice. Similarly, the risk of a malpractice claim for failure to inform was four times higher in private practice than in public hospitals. Another finding was that the average award amount for the cases with a verdict for the plaintiff was significantly higher when the reason for the lawsuit was a neurological complication. In our study, the average indemnity amount for cases that had a verdict for the plaintiff (€77.984) have been reported to be well below the average damage award in the United States, which is close to 1 million euros (€932.000) [START_REF] Shah | Medical malpractice litigation following arthroscopic surgery[END_REF]. A recent study on the malpractice claims in orthopaedic traumatology in a public hospital department have reported an average compensation to the plaintiff of 79.497 euros, which is similar to the compensations in our lawsuit [START_REF] Agout | Epidemiology of malpractice claims in the orthopedic and trauma surgery department of a French teaching hospital: a 10-year retrospective study[END_REF]. These values were close to those found by Tarantino et al. in Italy but lower than in England (respectively, 71.524 euros and > 115.615 euros) [START_REF] Atrey | Review of successful litigation against english health trusts in the treatment of adults with orthopaedic pathology: clinical governance lessons learned[END_REF][START_REF] Tarantino | Professional liability in orthopaedics and traumatology in Italy[END_REF]. Moreover, Shah et al. [START_REF] Shah | Medical malpractice litigation following arthroscopic surgery[END_REF] reported that, in the United States, the plaintiffs' claims have been granted in only 26% compared to 67.8% in our study.

There was a high number of infection cases (43.3%, 78/180 cases), similar to the infection cases reported after arthroplasty or trauma surgery in France [START_REF] Agout | Epidemiology of malpractice claims in the orthopedic and trauma surgery department of a French teaching hospital: a 10-year retrospective study[END_REF]. Conversely, Shah et al. [START_REF] Shah | Medical malpractice litigation following arthroscopic surgery[END_REF] showed that about 15% of complaints following arthroscopic procedures were related to postoperative infection in the United States. Musculoskeletal complications were indeed more frequent in their series of 240 cases, but infection remained the leading cause of legal action after knee arthroscopy, which corroborates the results presented in our study. Marmor et al. [21] reported a paradoxically higher proportion of lawsuits for septic arthritis after arthroscopy (42%) than after arthroplasty (27%) after analysis of insurance data. The authors identified several risk factors such as irrelevant indications (especially diagnostic arthroscopy) and also the use of intraoperative corticosteroids, which they advise against [START_REF] Cancienne | Risk Factors for Infection After shoulder arthroscopy in a large medicare population[END_REF][START_REF] Gosal | Intra-articular steroids after arthroscopy for osteoarthritis of the knee[END_REF]. Although 2 cases of septic arthritis after corticosteroid injection during an arthroscopy were observed in our series of cases, there were 13 cases of septic arthritis after diagnostic arthroscopy or arthroscopic lavage.

Another frequently cited reason for filing a lawsuit was the failure to inform. As Mouton et al. [START_REF] Mouton | Litigation in orthopedic surgery: what can we do to prevent it? Systematic analysis of 126 legal actions involving four university hospitals in France[END_REF] pointed out in their analysis of orthopaedic litigation in four university hospitals, the doctor-patient relationship is significantly questioned and remains an avenue of reflection to prevent legal recourse. In our study, the plaintiff invoked a failure to inform, follow-up or care in 1 case out of 5. However, it has been shown that effective communication with a clear explanation of the complications and benefits limits the risk of litigation [START_REF] Adamson | Physician communication skills and malpractice claims. A complex relationship[END_REF][START_REF] Atrey | Review of successful litigation against english health trusts in the treatment of adults with orthopaedic pathology: clinical governance lessons learned[END_REF][START_REF] Levinson | Physician-patient communication. The relationship with malpractice claims among primary care physicians and surgeons[END_REF]. Over the years, case law has only reinforced the surgeon's duty to inform the patient; the surgeon must ensure that the patient fully understands and must be able to prove that he has correctly informed his patient [START_REF] Dugleux | Proof of patient information: analysis of 201 judicial decisions[END_REF][START_REF] Giudici | Oral information in orthopaedics: how should the patient's understanding be assessed?[END_REF][START_REF] Gleyze | Patient information in orthopedic and trauma surgery. Fundamental knowledge, legal aspects and practical recommendations[END_REF]. Similarly to the failure to inform or misdiagnosis claims, lawsuits for wrong-site surgery is avoidable [START_REF] Coudane | Litigation in orthopaedic surgery: new ethical challenges[END_REF][START_REF] Kibler | Value on the front end: making the effective diagnosis for optimal treatment[END_REF][START_REF] Lubowitz | Malpractice Litigation After Arthroscopy[END_REF]. We found this malpractice claim in almost 4% of the cases in our study, and they systematically lead to compensation in favor of the plaintiff. In a recent editorial, Mark D. Miller emphasized that wrong-site surgery should never happen again and called for surgeons' vigilance and mentioning the benefit of the "Sign Your Site" campaign of the American Academy of Orthopedic Surgeons [START_REF] Miller | editorial commentary: outside the scope of practice-wrong-site surgery should never happen[END_REF].

Regarding the knee joint, lawsuits were most frequently related to either the management of a meniscal tear (66/180, 44.6%) or anterior cruciate ligament (ACL) surgery (23%). Bokshan et al. [START_REF] Bokshan | Factors Associated With Physician Loss in Anterior Cruciate Ligament Reconstruction Malpractice Lawsuits[END_REF] evaluated the risk factors for litigation after ACL reconstruction and pointed out that 63% of lawsuits did not involve technical errors (malpositioning of the graft, screws) but occurred mainly after postoperative infection (septic arthritis), persistent pain or limited range of motion. Similarly, we observed a significant incidence of septic arthritis secondary to ACL reconstruction in more than half of the cases. However, the surgeon's responsibility after the infection cases was only called into question if there was a delay in diagnosis or treatment of the infection that did not comply with the recommendations. This result can be explained by the specific system of compensation after care in France, which, except in the event of a lack of prevention, diagnosis or care on the part of the practitioner, charges the establishment with compensation for the damage. (ref Legifrance) Nevertheless, information on the septic risk after arthroscopy must be reinforced.

The limitations of our study included the use of legal databases whose exhaustiveness has not been proven. However, it is likely that the substantial number of cases reported over a period of more than 20 years is a representative sample of legal cases after arthroscopy. On the other hand, these data concerned complaints resulting in a decision by a civil or administrative court and excluded other means of claims in France: insurance settlements, amicable recourse, conciliation and compensation procedures related to the specific public solidarity fund (ONIAM), without secondary legal recourse. It is, therefore, possible that the cases presented do not reflect the true distribution of the various causes of medical malpractice claim after arthroscopy in France. Another weakness of the study was the anonymization of the data provided by the databases, which did not allow us to assess litigation according to the demographic and socio-economic characteristics of patients.

This study highlighted the significant prevalence of litigation in arthroscopic practice. These findings are useful to enable appropriate delivered preoperative information for clinicians when arthroscopic procedure is necessary, to decrease the rate of malpractice claims.

Conclusion

This study evaluated and mapped lawsuits following arthroscopic surgery over a period of more than 20 years. The main source of lawsuits was knee arthroscopy, particularly the management of meniscal tears and anterior cruciate ligament injury. Postoperative infection, musculoskeletal complications and failure to inform were the main causes of litigation after arthroscopy. These results should guide surgeons in providing information to the patient and in the management of a possible complication, to hopefully reduce the number of lawsuits.

Fig. 1

 1 Fig. 1 Flowchart of lawsuits after arthroscopic procedures. n number, AC Administrative court, ACA Administrative court of appeal, CC Civil court, CCA Civil court of appeal

[ 2 .

 2 282-576.882] vs. 77.381 euros [800-1.117.667].

Fig. 2

 2 Fig. 2 Distribution of malpractice cases for each joint after arthroscopic surgery

Fig. 3

 3 Fig.3Reasons for lawsuit following arthroscopic procedures

Table 1

 1 Distribution of defendants involved in the malpractice lawsuit following arthroscopic procedure

	Defendants	Cases (n = 180)
	Private or public surgery center (C), n (%)	86 (47.8)
	Orthopaedic surgeon (O), n (%)	53 (29.4)
	O + C in solidum, n (%)	23 (12.8)
	ONIAM, n (%)	5 (3.3)
	Anesthesiologist (A), n (%)	4 (2.2)
	A + C in solidum, n (%)	3 (1.7)
	O + A + C in solidum, n (%)	3 (1.7)
	O + ONIAM, n (%)	1 (0.6)
	O + Rheumatologist, n (%)	1 (0.6)
	O + Medical device company, n (%)	1 (0.6)

Table 2

 2 Distribution of cases by diagnosis

	Diagnosis	Cases (n = 180)
	Knee, n (%)	/148
	Meniscal tears	66 (44.6)
	CL rupture	34 (23.0)
	Stiffness	5 (3.4)
	Others	17 (11.5)
	No diagnosis	25 (16.9)
	Shoulder, n (%)	/20
	Shoulder rotator cuff injuries	7 (35.0)
	Subacromial impingement	7 (35.0)
	Acromioclavicular Disjunction	2 (10.0)
	Instability	2 (10.0)
	No diagnosis	2 (10.0)
	Wrist, n (%)	/5
	Endoscopic Neurolysis	2 (40.0)
	Traumatology	2 (40.0)
	Tenosynovitis	1 (20.0)
	Ankle, n (%)	/4
	Anterior impingement	4 (100)
	Hip, n (%)	/2
	Femoroacetabular Impingement	1 (50.0)
	No diagnosis	1 (50.0)
	Elbow, n (%)	/1
	Stiffness	1 (100)

Table 3

 3

	Comparison between administrative procedure (public		Administrative procedure (n = 58) Civil procedure (n = 122) P value
	practice) and civil procedure (private practice)	Gender, n Men	40	79	(n.s)*
		Women	18	43
		Time between triggering event	5.6 [0.8-36.9]	6.65 [1.3-23.1]	(n.s)**
		and verdict (in years)
		Appeal (%)	39.7	39.3	(n.s)*
		Reason behind lawsuit (%)
		Technical error	13.8	2.5	0.006*
		Infection	29.3	50	0.01*
		Failure to inform	6.9	24.6	0.004*
		Defendant (%)
		Orthopaedic surgeon	1.7	66.4	< 0.0001*
		Anesthesiologist	0	8.2	0.03*
		Surgery center	96.6	48.4	< 0.001*
		Verdict in favor of plaintiff (%) 48.4	76.2	0.0006*
		Indemnity payment (euros)	79 985 [2282-576 882]	77,381 [800-1 117 667] (n.s)**
		*Fisher test, **Wilcoxon test, n.s non-significant

Acknowledgements

The authors thank the attorneys at law Dana Leib (New York Bar) and Barbara Teissier du Cros (Paris Bar) for their kind help.

Authors' contribution CP has made substantial contributions to conception, study design, acquisition/interpretation of data and in drafting the manuscript. CJ and AA have made substantial contributions to acquisition of data. GO was in charge of the statistical analysis. MO, PB, BSC and NP have been involved in drafting or revising the manuscript critically. Each author has given final approval of the version to be published and agrees to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.

Funding No benefits in any form have been received or will be received related directly or indirectly to the subject of this article.

Compliance with ethical standards

Conflict of interest CP, CJ, AA, PB and GO have nothing to disclose. MO is educational consultant for Stryker and Newclip. BSC is educational consultant and receives royalties from Arthrex. NP is occasional educational consultant for Smith&Nephew, Lima, ZimmerBiomet, Stryker, outside the scope of this work.

Ethical approval

No ethical approval was need for this study.