Florian Szabados
email: florian.szabados@rub.de

Jaroslaw Woloszyn

Martin Kaase

Sören G Gatermann

False-negative test results in the Slidex Staph Plus (bioMérieux) agglutination test are mainly caused by spa-type

Keywords: S. aureus, spa, agglutination, MALDI-TOF MS, t001

    False-negative test results in the Slidex Staph Plus (bioMérieux) agglutination test are mainly caused by -type t001 and t001-related strains

Introduction

A rapid and reliable identification of S. aureus is crucial to decreasing S. aureus associated morbidity. Several commercial agglutination kits are available for identifying S. aureus, but their sensitivity has sometimes been questioned. As a result, test accuracy has been enhanced periodically [START_REF] Croize | Improved identification of Staphylococcus aureus using a new agglutination test. Results of an international study[END_REF][START_REF] Essers | Rapid and reliable identification of Staphylococcus aureus by a latex agglutination test[END_REF][START_REF] Weist | Evaluation of six agglutination tests for Staphylococcus aureus identification depending upon local prevalence of meticillin-resistant S. aureus (MRSA)[END_REF][START_REF] Wichelhaus | Evaluation of modern agglutination tests for identification of methicillin-susceptible and methicillin-resistant Staphylococcus aureus[END_REF][START_REF] Kuusela | Rapid detection of methicillin-resistant Staphylococcus aureus strains not identified by slide agglutination tests[END_REF] by incorporation of more reagents into the kits.

The relative sensitivities of these tests are given by the manufacturers to be between 97.6% and 100%. Recently, Matrix assisted laser desorption/ionisation time of flight mass spectrometry (MALDI-TOF MS) was introduced as a method for bacterial identification [START_REF] Edwards-Jones | Rapid discrimination between methicillin-sensitive and methicillin-resistant Staphylococcus aureus by intact cell mass spectrometry[END_REF][START_REF] Du | Identification of Staphylococcus aureus and determination of its methicillin resistance by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry[END_REF][START_REF] Bernardo | Identification and discrimination of Staphylococcus aureus strains using matrix-assisted laser desorption/ionization-time of flight mass spectrometry[END_REF][START_REF] Walker | Intact cell mass spectrometry (ICMS) used to type methicillin-resistant Staphylococcus aureus: media effects and inter-laboratory reproducibility[END_REF]. Several studies with more than 80 strains of S. aureus have been described. The relative sensitivities of the MALDI-TOF-based S. aureus identification ranged from 93.4% to 100% [START_REF] Carbonnelle | Rapid identification of Staphylococci isolated in clinical microbiology laboratories by matrix-assisted laser desorption ionization-time of flight mass spectrometry[END_REF][START_REF] Rajakaruna | High throughput identification of clinical isolates of Staphylococcus aureus using MALDI-TOF-MS of intact cells[END_REF][START_REF] Seng | Ongoing revolution in bacteriology: routine identification of bacteria by matrix-assisted laser desorption ionization time-of-flight mass spectrometry[END_REF][START_REF] Szabados | Identification of molecularly defined Staphylococcus aureus strains using matrix-assisted laser desorption/ionization time of flight mass spectrometry and the Biotyper 2.0 database[END_REF]. In these studies the sensitivity seems to be dependent on the quality of bacterial characterization, the underlying database and identification system, the investigated proteomic profile range, and on the study design.

To our knowledge, ours is the first study in which MALDI-TOF identification was compared to the agglutination kit Slidex Staph Plus (bioMérieux, Marcy l'Etoile, France). In our study, three molecularly characterized S. aureus strain collections were included. In the first collection, 363 consecutively collected, molecularly defined, single-copy strains of methicillin-susceptible (MSSA) were included. In a second collection, 240 molecularly defined, single-copy strains of methicillin-resistant S. aureus (MRSA) were tested. Further, a molecularly defined MRSA collection (n=104) with a diverse genetic background [START_REF] Kaase | Performance of MicroScan WalkAway and Vitek 2 for detection of oxacillin resistance in a set of methicillin-resistant Staphylococcus aureus isolates with diverse genetic backgrounds[END_REF]

Methods :

Source of isolates

MSSA

In our study 363 clinical, consecutively collected, single-copy strains of methicillinsusceptible S. aureus were included. S. aureus was primarily identified by typical colony morphology and Slidex Staph Plus agglutination test (bioMérieux), or by the GPI-card of the Vitek-2 automated identification system (bioMérieux). The species diagnosis was confirmed using the S. aureus specific primer, SA442, for methicillin susceptible strains (oxacillin MIC from <0.25 to 2 mg/L), as described previously [START_REF] Martineau | Species-specific and ubiquitous-DNA-based assays for rapid identification of Staphylococcus aureus[END_REF]. All strains were SA442 positive and were included in this study (Table 1). A cefoxitin screen incorporated in the Vitek 2 AST-P549 card was negative in all isolates. MRSA S. aureus was primarily identified as described above. Methicillin-resistance determination and cefoxitin screening [START_REF] Swenson | Detection of mecA-mediated resistance using reference and commercial testing methods in a collection of Staphylococcus aureus expressing borderline oxacillin MICs[END_REF] of all strains were done by the Vitek2 automated system (bioMérieux) and the results were interpreted according to the CLSI guidelines. No differences in the interpretation were observed comparing breakpoints suggested by CLSI and EUCAST (http://www.Eucast.org) in our isolates. All isolates identified as MRSA by this method were confirmed by mecA- [START_REF] Shrestha | Rapid identification of Staphylococcus aureus and the mecA gene from BacT/ALERT blood culture bottles by using the LightCycler system[END_REF] and SA442-PCR, as described previously [START_REF] Martineau | Species-specific and ubiquitous-DNA-based assays for rapid identification of Staphylococcus aureus[END_REF], or by a different PCR method. This PCR used primers between the staphylococcal cassette chromosome mec (SCCmec) and the orfX [START_REF] Hagen | Development of a real-time PCR assay for rapid identification of methicillin-resistant Staphylococcus aureus from clinical samples[END_REF]. As the primer binding in orfX is specific for S. aureus A positive PCR war regarded as confirmation of S. aureus. Isolates with a negative cefoxitin screening result, or isolates with an oxacillin MIC of <=2 mg/liter were tested by SA442 and mecA PCR [START_REF] Martineau | Species-specific and ubiquitous-DNA-based assays for rapid identification of Staphylococcus aureus[END_REF]. SA442 and mecA PCR positive strains were defined as MRSA. OrfX positive strains with a positive cefoxitin screening test and an oxacillin MIC > 2 mg/liter were defined as a MRSA. OrfX, SA442, and mecA-PCR positive strains were also defined as a MRSA (irrespective of cefoxitin screening or oxacillin MIC). Overall, 240 consecutively collected single-copy strains of methicillin-resistant S. aureus were included. One MRSA strain in this second collection was oxacillin susceptible (oxacillin MIC of 1 mg/L) using a breakpoint of > 2 mg/L oxacillin (Table1). Moreover, a third MRSA collection of 104 PFGE divergent strains were also included. In this collection, six MRSA strains [START_REF] Kaase | Performance of MicroScan WalkAway and Vitek 2 for detection of oxacillin resistance in a set of methicillin-resistant Staphylococcus aureus isolates with diverse genetic backgrounds[END_REF] were oxacillin susceptible using a breakpoint of > 2 mg/L oxacillin. Both MRSA collections were characterized by pulsedfield gel electrophoresis (PFGE), as described earlier [START_REF] Goering | Epidemiological interpretation of chromosomal macrorestriction fragment patterns analyzed by pulsed-field gel electrophoresis[END_REF]. One isolate of each PFGEgroup was determined by multi-locus sequence typing (MLST), as described previously [START_REF] Enright | Multilocus sequence typing for characterization of methicillin-resistant and methicillin-susceptible clones of Staphylococcus aureus[END_REF]. For spa-typing, the spa gene was amplified by PCR and sequenced. The sequence was compared to the Ridom data base using the BURP (based upon repeat patterns) algorithm [START_REF] Harmsen | Typing of methicillin-resistant Staphylococcus aureus in a university hospital setting by using novel software for spa repeat determination and database management[END_REF][START_REF] Mellmann | Characterization of clonal relatedness among the natural population of Staphylococcus aureus strains by using spa sequence typing and the BURP (based upon repeat patterns) algorithm[END_REF].

Pulsed-field gel electrophoresis

Pulsed-field-gel-electrophoresis was conducted and interpreted, as described before [START_REF] Goering | Epidemiological interpretation of chromosomal macrorestriction fragment patterns analyzed by pulsed-field gel electrophoresis[END_REF].

Electrophoresis of the SmaI-digested DNA was performed with a CHEF-DRIII system (Bio-Rad) using 1.0% agarose gels (Bio-Rad). Subsequently, all PFGE gels were scanned using the Flour-S multiImager system (Bio-Rad) and analyzed using molecular analyst software 1.11 (Bio-Rad).

S. aureus identification by latex agglutination kits

All strains of the MSSA and MRSA collection were tested for agglutination using the commercial staphylococcal agglutination kit Slidex Staph Plus (bioMérieux) in order to compare our local sensitivity data to the data in the literature.

To rule out dominance of certain local prevalent MRSA strains, a MRSA collection of 104 recently described [START_REF] Kaase | Performance of MicroScan WalkAway and Vitek 2 for detection of oxacillin resistance in a set of methicillin-resistant Staphylococcus aureus isolates with diverse genetic backgrounds[END_REF], molecularly characterized, methicillin-resistant S. aureus strains with diverse genetic backgrounds were also tested. The agglutination results of

MALDI-TOF MS

All strains were examined with MALDI-TOF MS using Microflex LT instrument (Bruker Daltonics, Bremen , Germany). Formic acid was used for the sample preparation and the Flexcontrol 3.0 software and Biotyper 2.0 database (Bruker Daltonics) were used to calculate and process the analytical data, as described previously [START_REF] Szabados | Identification of molecularly defined Staphylococcus aureus strains using matrix-assisted laser desorption/ionization time of flight mass spectrometry and the Biotyper 2.0 database[END_REF]. Identification was performed in duplicate and the identification score cut-off was applied on each measurement, according to the manufacturer's instructions.

Statistical analysis

A Fisher's exact probability test was used to calculate the P-value for the experimental data. P-values of <0.05 were considered to be statistically significant.

Results :

In the MSSA collection, the Biotyper 2.0 database gave a correct species diagnosis in all (363 out of 363) strains. The analytical sensitivity of the latex agglutination Slidex Staph Plus kit for the identification of S. aureus was 98.0% (356 out of 363 strains). The seven MSSA isolates, which tested negative using the Slidex Staph Plus (bioMérieux) kit, were characterized using spa-typing. One (MSSA 88) of the seven strains was spa-type t001. The strains MSSA 101 (t015), MSSA 118 (t078), MSSA 166 (t550), MSSA 486 (t495), MSSA 545 (t026) and MSSA 622 (new spa-type with spa-repeat pattern: 04-34-17-32-17) were singletons with regard to the spa-type. The new spa-type was assigned to be spa-type t6091 and deposited in the Ridom database [START_REF] Harmsen | Typing of methicillin-resistant Staphylococcus aureus in a university hospital setting by using novel software for spa repeat determination and database management[END_REF]. The spa-type t001 is often thought to be associated with MRSA; therefore, agglutination negative MSSA strains were tested for the presence of SCCmec using primers between the SCCmec and the orfX region, as described earlier [START_REF] Hagen | Development of a real-time PCR assay for rapid identification of methicillin-resistant Staphylococcus aureus from clinical samples[END_REF][START_REF] Huletsky | New real-time PCR assay for rapid detection of methicillin-resistant Staphylococcus aureus directly from specimens containing a mixture of staphylococci[END_REF]. Six out of seven agglutination-negative MSSA strains (spa types t015, t026, t078, t495, t550, t6091) tested negative in the aforementioned PCRs. This indicates that a SCCmec is not present in these isolates. In one oxacillin-susceptible (oxacillin MIC = 1 mg/L, cefoxitin screen negative) and agglutination-negative strain (spa type t001) the PCRs using primers between the SCCmec element and the orfX region were positive. As expected, the strain was also mecA positive (Table 1). Our isolate was tested for the presence of Pantone Valentine leukocidin (PVL) and was PVL-negative.

The relative sensitivity of the Slidex Staph Plus agglutination test in the MSSA collection was similar to sensitivities reported in the literature [START_REF] Weist | Evaluation of six agglutination tests for Staphylococcus aureus identification depending upon local prevalence of meticillin-resistant S. aureus (MRSA)[END_REF][START_REF] Wichelhaus | Evaluation of modern agglutination tests for identification of methicillin-susceptible and methicillin-resistant Staphylococcus aureus[END_REF].

In the MRSA collection, a correct species diagnosis was achieved using the Biotyper 2.0 database in all (240 out of 240) strains. Interestingly, only 94.5% (227 out of 240 strains, p=0.035) of the molecularly defined and consecutively collected single-copy MRSA strains were identified as S. aureus by the Slidex Staph Plus (bioMérieux) agglutination kit. Thirteen molecularly defined MRSA isolates tested negative and were further characterized by spa-typing. Ten of thirteen agglutination negative strains were spa-type t001: 3236, 3239, 3249, 3250, 3295, 3311, 3327, 3328, 3334, and 3351. The other MRSA strains were singletons: 3216b was t003, 3254 was t587, and 3255 was t480. The sensitivity of the Slidex Staph Plus agglutination results in the MRSA strain collection was lower compared to the MSSA collection and the difference was statistically significant (p=0.035). Forty-nine percent of these strains were of PFGE group 35 (ST 022), 13% were of PFGE group 11 (ST 225), 13% were of PFGE group 13 (ST 008), 2% were of PFGE groups 1 and 7 (ST 228), 4% were of PFGE group 16 (ST 045), and 6% were of other PFGE groups. The distribution of the sequence types was similar to previous reports. To exclude a bias introduced by locally prevalent strains, a molecularly divergent (PFGE) strain collection was also tested. All of the additionally tested 104 MRSA strains were identified as S. aureus using the Biotyper 2.0 database. In this strain collection a sensitivity of only 70.1% (73 out of 104) was observed using agglutination by the Slidex Staph Plus kit (bioMérieux). Four strains tested weakly positive after 30-60 s (4 out of 104). If these isolates were counted as questionable then the sensitivity was 66.3% (69 out of 104). Two different Slidex Staph Plus kit (bioMérieux) Lot IDs were tested by two different blinded investigators to rule out possible differences in test interpretation. The test results were virtually identical and independent of the lot and examiner (data not shown).

To exclude a single manufacturer's antibody composition problem, the Pastorex Staph Plus (Bio-Rad) and Staphytect kits (Oxoid) were additionally tested (Table 2). In the collection of PFGE-divergent strains, a sensitivity of 83.6% (87 out of 104, p=0.035) was observed using agglutination by the Pastorex Staph plus kit (Bio-Rad). Eleven strains tested weakly positive after 30-60 s (11 out of 104). If these isolates were counted as questionable (not positive) then the sensitivities were even lower (68 out of 104, p=1). The sensitivity was 78.8% (82 out of 104, p=0.59) using the Staphytect Plus Kit (Oxoid). Thirteen percent (14 out of 104) tested weakly-positive after 30-60 s (76 out of 104, p=0.66). The sensitivity of all of the tested agglutination kits was thus significantly lower compared to the sensitivity archived by MALDI-TOF MS and the Biotyper 2.0 database. Despite the differences between the agglutination tests, a statistical difference was only observed between the Slidex Staph Plus kit and the Pastorex Staph Plus kit (Bio-Rad) when weak positive results (agglutination after 30 s) were interpreted as true positive results. MRSA strains that had tested negative in the agglutination tests were further characterized using spa-typing [START_REF] Harmsen | Typing of methicillin-resistant Staphylococcus aureus in a university hospital setting by using novel software for spa repeat determination and database management[END_REF] in addition to PFGEtyping. About 71% of these strains were spa-type t001 (22 out of 31), 12.9% of the strains were t480 (4 out of 31), and one strain each was t013, t109 and a new spa-type with a repeat pattern (26-30-17-34-17-20-17-12-16). This new spa-type was assigned to be spa-type t5712 and deposited in the Ridom database [START_REF] Harmsen | Typing of methicillin-resistant Staphylococcus aureus in a university hospital setting by using novel software for spa repeat determination and database management[END_REF]. The spa-types t001, t013, t109, t480, and t5712 were related to each other. Two other spa-types were detected as singletons (t032 and t064). Interestingly, one strain of t008 tested weakly positive or negative (MRSA strain 1565) and one tested positive in the agglutination test (MRSA strain 2748). In the PFGE-divergent MRSA collection the majority (18 of 22) of the spatype t001 characterized strains in the PFGE groups 1 to 10, which corresponds to t001 and t001-relates spa-types, were agglutination negative using the Slidex Staph Plus kit.

Two isolates each were weak positive and positive. Some strains (2 of 10) clustered in PFGE-group 13, which corresponds to t008 and t064. The majority of the latter isolates were agglutination positive.

Discussion:

Most of the fast agglutination tests for the identification of S. aureus lack sensitivity [START_REF] Weist | Evaluation of six agglutination tests for Staphylococcus aureus identification depending upon local prevalence of meticillin-resistant S. aureus (MRSA)[END_REF][START_REF] Kuusela | Rapid detection of methicillin-resistant Staphylococcus aureus strains not identified by slide agglutination tests[END_REF][START_REF] Luijendijk | Comparison of five tests for identification of Staphylococcus aureus from clinical samples[END_REF] compared to highly accurate, molecularly-based identification approaches [START_REF] Martineau | Species-specific and ubiquitous-DNA-based assays for rapid identification of Staphylococcus aureus[END_REF][START_REF] Ghebremedhin | Genetic classification and distinguishing of Staphylococcus species based on different partial gap, 16S rRNA, hsp60, rpoB, sodA, and tuf gene sequences[END_REF]. The agglutination kits differ in antibody composition against targets like protein A, certain capsule types, and fibrinogen(Fg)-or fibronectin(Fn)-binding proteins. A comprehensive description of the antibody composition is not given by the manufacturers. Alternative molecularly based methods, however, are time consuming and a hindrance to a fast identification of S. aureus. Previous studies have shown that the MALDI-TOF MS based identification [START_REF] Du | Identification of Staphylococcus aureus and determination of its methicillin resistance by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry[END_REF][START_REF] Carbonnelle | Rapid identification of Staphylococci isolated in clinical microbiology laboratories by matrix-assisted laser desorption ionization-time of flight mass spectrometry[END_REF][START_REF] Rajakaruna | High throughput identification of clinical isolates of Staphylococcus aureus using MALDI-TOF-MS of intact cells[END_REF][START_REF] Seng | Ongoing revolution in bacteriology: routine identification of bacteria by matrix-assisted laser desorption ionization time-of-flight mass spectrometry[END_REF][START_REF] Szabados | Identification of molecularly defined Staphylococcus aureus strains using matrix-assisted laser desorption/ionization time of flight mass spectrometry and the Biotyper 2.0 database[END_REF] could be an alternative method to molecularly-based methods. The sensitivity of MALDI-TOF identification using the Biotyper 2.0 database in a mass-to-charge ratio of 3000 to 15000 Da was high (707 out of 707) and equal to a molecular method (Table 3). In contrast to this there have been controversial discussions about whether the MALDI-TOF MS technology could serve as a surrogate method for the detection of Pantone Valentine Toxin [START_REF] Bittar | MALDI-TOF-MS for rapid detection of staphylococcal Panton-Valentine leukocidin[END_REF][START_REF] Szabados | The matrix-assisted laser desorption/ionisation time-of-flight mass spectrometry (MALDI-TOF MS)-based protein peaks of 4,448 and 5,302 Da are not associated with the presence of Panton-Valentine leukocidin[END_REF]. Interestingly, the sensitivity of the Slidex Staph Plus kit was lower in MRSA strains than in MSSA (98.0% versus 94.5%, p=0.035). To rule out an overrepresentation of locally predominant strains, a collection of 104 MRSA with different PFGE patterns were tested. In this collection, the sensitivity of the Slidex Staph Plus kit was even lower (Table 3). To rule out a kit-specific problem, two other agglutination tests were also investigated. These kits showed a sensitivity comparable to that of the Slidex Staph Plus kit. If the weakly positive agglutination results were interpreted as a correct identification, our data suggest that the sensitivity of the Pastorex Staph plus kit (Bio-Rad) was slightly higher. The relative sensitivities were given in the manufacturers' data sheet as 99.2% (n=441) for the Slidex Staph Plus kit, 100% (n=439) for the Pastorex Staph Plus kit, and 97.6% for the Staphytect Plus kit. The tube test for free coagulase was used as the reference method in these studies. Moreover, non-S. aureus free coagulase test positive strains and auto-agglutination positive isolates were usually excluded. The relative specificities were given in the manufacturers' data sheet as 98.9% (n=438) for the Slidex Staph Plus kit, 100% (n=138) for the Pastorex Staph-Plus kit and 97.6% for the Staphytect Plus kit. Compared to our study, little information was given with regard to the reference method of S. aureus and non-S. aureus isolates by all three manufacturers. A previous study described a relative sensitivity of 93% and a relative specificity of 72.7% for a MRSA collection [START_REF] Personne | Comparative performances of six agglutination kits assessed by using typical and atypical strains of Staphylococcus aureus[END_REF]. Many agglutination tests were therefore enhanced periodically by incorporation of more reagents into the kits. In recently published studies, high relative sensitivities of about 97.9% [START_REF] Weist | Evaluation of six agglutination tests for Staphylococcus aureus identification depending upon local prevalence of meticillin-resistant S. aureus (MRSA)[END_REF][START_REF] Wichelhaus | Evaluation of modern agglutination tests for identification of methicillin-susceptible and methicillin-resistant Staphylococcus aureus[END_REF][START_REF] Gupta | Comparison of six rapid agglutination tests for the identification of Staphylococcus aureus, including methicillin-resistant strains[END_REF] were published for MSSA and MRSA strain collections. In addition, the relative specificities were given to range from 91.3% (Slidex Staph kit) to 99.1% (Slidex Staph Plus kit) [START_REF] Weist | Evaluation of six agglutination tests for Staphylococcus aureus identification depending upon local prevalence of meticillin-resistant S. aureus (MRSA)[END_REF].

Several factors could be addressed by the phenomenon of a agglutination negative result. In all agglutination reagents, irrespective of the manufacturer, certain surface located targets were detected with specific antibodies. Well characterized surface proteins e.g. immunoglobulin(Ig) G-Fc-binding protein and von Willebrand factorbinding protein A (SpA), fibronectin (Fn)-binding proteins such as FnBP A and FnBP B, the Fg-binding clumping factor (Clf)-A and ClfB [START_REF] Hussain | Expression of Pls (plasmin sensitive) in Staphylococcus aureus negative for pls reduces adherence and cellular invasion and acts by steric hindrance[END_REF] could serve as targets for this approach. In addition, major prevalent capsule types, such as capsule type 5 (CP5) and 8 (CP8) [START_REF] O'riordan | Staphylococcus aureus capsular polysaccharides[END_REF], can mask other surface proteins, such as ClfA [START_REF] Risley | Capsular polysaccharide masks clumping factor A-mediated adherence of Staphylococcus aureus to fibrinogen and platelets[END_REF]. Recently, new nontypeable capsular types were described [START_REF] Cocchiaro | Molecular characterization of the capsule locus from non-typeable Staphylococcus aureus[END_REF][START_REF] Lattar | Capsule expression and genotypic differences among Staphylococcus aureus isolates from patients with chronic or acute osteomyelitis[END_REF][START_REF] Tuchscherr | Antibodies to capsular polysaccharide and clumping factor A prevent mastitis and the emergence of unencapsulated and small-colony variants of Staphylococcus aureus in mice[END_REF]. It is likely that these new capsular types, or a modified composition of the capsular types, could also impair agglutination tests.

Moreover, a 230 kDa surface protein has been recently described [START_REF] Savolainen | Expression of pls, a gene closely associated with the mecA gene of methicillin-resistant Staphylococcus aureus, prevents bacterial adhesion in vitro[END_REF], which was cleaved by plasminogen into to fragments of 175-and 68 kDa respectively, and given the name plasminogen sensitive protein (Pls). It was found that Pls-positive isolates give negative test results in agglutination tests with reagents designed to detect Fn-and Fgbinding proteins and SpA This protein also interferes with adherence and internalization into eukaryotic cells, indicating that the expression of Fn-binding proteins on the surface in these isolates was reduced [START_REF] Hussain | Expression of Pls (plasmin sensitive) in Staphylococcus aureus negative for pls reduces adherence and cellular invasion and acts by steric hindrance[END_REF]. Seven out of 37 isolates were Pls positive [START_REF] Werbick | Staphylococcal chromosomal cassette mec type I, spa type, and expression of Pls are determinants of reduced cellular invasiveness of methicillin-resistant Staphylococcus aureus isolates[END_REF]. Interestingly, two of these isolates were t001, and both were positive for the gene pls. One isolate, however, was not expressing the Pls protein. Nevertheless, the spa-type deduced clonal complex was not able to predict impaired invasiveness, which was argued to be associated with the presence of Pls [START_REF] Werbick | Staphylococcal chromosomal cassette mec type I, spa type, and expression of Pls are determinants of reduced cellular invasiveness of methicillin-resistant Staphylococcus aureus isolates[END_REF]. The difference between our sensitivity data and previously published sensitivities argue for a local emergence of a new MRSA clone, which seems to be associated with spa-type t001. Moreover, it seems to be likely that these isolates were different concerning the expression of surface proteins or capsular types, which were targeted by the agglutination tests. Nevertheless, the underlying mechanism remains to be elucidated.

Although infrequent isolates are relatively overrepresented in this collection, our data also caution against the unreflected use of agglutination tests. Interestingly, about 93.5% of the strains, which were false-negative in our agglutination tests, were also spa-type t001 or a related spa-type (t013, t109, t480 and the new spa-type t5712). In the PFGE-divergent MRSA collection, the majority (18 of 22) of the agglutination false-negative and spa-type t001 strains clustered in PFGE-group 1 to 10, which corresponds to t001 and t001-related strains. The majority of strains (8 of 10), which clustered in PFGEgroup 13 (t008 and t064), were agglutination positive. Two out of four isolates previously characterized as t008 were described to be Pls-positive [START_REF] Werbick | Staphylococcal chromosomal cassette mec type I, spa type, and expression of Pls are determinants of reduced cellular invasiveness of methicillin-resistant Staphylococcus aureus isolates[END_REF]. Single strains, characterized as t001 and t001-related, were agglutination positive and indicate that this phenomenon is not strictly associated with the spa-type. The distribution of the spatypes of agglutination negative strains in the MSSA collection seems to be different from that of the MRSA collections. As a limitation of the MSSA and first MRSA strain collection (consecutively collected) no molecular epidemiology data, such as spa-types were available for all isolates. No data thus could be given with regard to the prevalence of spa-type t001 and agglutination results in these collections. In the PFGE-divergent MRSA collection the majority (82%) of the spa-type t001 characterized strains in the PFGE groups 1 to 10 were agglutination negative using the Slidex Staph Plus kit. One strain, which was primarily included as MSSA using the EUCAST cut-off value for oxacillin of <= 2 and a negative cefoxitin screening, was also characterized as spa-type t001 (Table 1). This strain was positive for the mecA-gene and also the SCCmec/orfXbased PCR to amplify the orfX-region [START_REF] Huletsky | New real-time PCR assay for rapid detection of methicillin-resistant Staphylococcus aureus directly from specimens containing a mixture of staphylococci[END_REF]. In the literature SCCmec/orfX negative and mecA-positive MRSA strains due to for example variation of the SCCmec/orfX-region, were described. SCCmec/orfX positive and mecA-negative MSSA strains, which have lost the mecA-gene, were described also [START_REF] Rupp | Be aware of the possibility of false-positive results in single-locus PCR assays for methicillin-resistant Staphylococcus aureus[END_REF]. Moreover, fewer mutations within the FemXAB protein family were described for phenotypic oxacillin susceptible phenotypes in mecA-positive S. aureus isolates [START_REF] Giannouli | Detection of mutations in the FemXAB protein family in oxacillin-susceptible mecA-positive Staphylococcus aureus clinical isolates[END_REF].

In conclusion, our results argue for an epidemic emergence of a MRSA-strain with an altered surface structure, thus allowing for the agglutination tests to produce falsenegative results. Our results indicate that latex agglutination could miss a significant amount of MRSA depending on the local prevalence of t001 and related strains. Moreover, our data support testing oxacillin-susceptible (oxacillin MIC <=2 mg/L), Slidex Staph Plus kit agglutination negative S. aureus isolates for the presence of mecA to rule out MRSA-isolates with a phenotypic oxacillin MIC below the cut-off value given by EUCAST guidelines. MALDI-TOF MS based identification required more time than agglutination based methods, but the identification was clearly more accurate.

Our results suggest using an alternative identification method in suspected false-negative agglutination tests to increase sensitivity of S. aureus identification.

  was included to rule out dominance of certain local MRSA-strain clusters. The sensitivity of MALDI-TOF MS-based identification was compared to the sensitivity of the agglutination kit Slidex Staph Plus. The sensitivity of the agglutination tests was unexpectedly low in the first MRSA collection. To rule out a problem dependent on a single agglutination test composition, two additional agglutination tests were performed in the pulsed-field gel electrophoresis (PFGE) divergent S. aureus strain collection using the commercial Pastorex Staph plus (Bio-Rad, München,Germany) and Staphytect Plus kits (Oxoid, Basingstoke, UK). Moreover, two lots of Slidex Staph Plus (bioMérieux) were tested by different blinded investigators. MRSA strains that were negative in agglutination tests were characterized by spa-typing to show if this property was associated with certain lineages.

  this collection were compared to two other commercial kits (Pastorex Staph Plus kit Lot ID: 9A2427 [Bio-Rad] and Staphytect Plus kit Lot ID: J61061it). Moreover, two different lots (Lot ID: 0901100771, 0811100478) of Slidex Staph Plus (bioMérieux) were tested by two blinded investigators.

Table 1 : 2 :

 12 Characterization of S. aureus strains used in this study S. aureus strains used in this study were identified by molecular methods and MALDI-TOF MS-based identification. The phenotypic characterization results for oxacillin MIC, the Vitek2 cefoxitin screening test result (AST P459 card) and the PCR results for the detection of mecA-gene and SCCmec (orfX) were given together with the Slidex Staph Plus (bioMérieux) identification test results. Results were given as + for positive and -for negative test results. * isolate was misclassified as MSSA using phenotypic tests. ND = Not determined Table Sensitivity of the S. aureus agglutination kits in a collection of 104 pulsedfield-gel electrophoresis divergent strains. Three agglutination kits were investigated in a MRSA strain collection of 104 pulsedfield-gel electrophoresis divergently tested MRSA strains using the Slidex Staph Plus (bioMérieux), Pastorex Staph Plus (Bio-Rad) and Staphytect Plus kits (Oxoid). Results were given as p (positive), neg (negative) and w (weakly) positive after 30-60 s. The other strains not given in the table were consistent test positive in all agglutination kits. PFGE group "34" represents a group of singletons. Most of the agglutination negatively tested strains were spa-type t001 (22 out of 31 strains) and t001 related (t013, t109, t480 and a new spa-type t5712 ; 7 out of 31 strains).

Table 3 :

 3 Agglutination test and MALDI-TOF MS identification results of three different S. aureus strain collections The sensitivity of the Slidex Staph Plus (bioMérieux) was tested in a strain collection of molecularly defined MSSA (1) and MRSA (2). To rule out a dominance local strains, a third collection of 104 pulsed-field-gel electrophoresis (PFGE) divergent strains were included and tested with the Pastorex Staph Plus (Bio-Rad) and Staphytect Plus kit (Oxoid) and the Slidex Staph Plus (bioMérieux) agglutination test. The relative sensitivity of MALDI-TOF MS based S. aureus identification was superior to all tested agglutination kits.

Acknowledgements

We thank Gurpreet Khaira (Vancouver, Canada) for critically reading the manuscript.

Conflict of interests statement

The authors certify that there is no actual nor potential conflict in relation to this article.


E Coutant

Darai

C Poncelet

R Fauvet

C Yazbeck

C Coutant

E Darai

Professor Emile Daraï
email: emile.darai@tnn.ap-hop-paris.fr

Impact of serum tumor marker determination on the management of women with borderline ovarian tumors: Multivariate analysis of a french multicentre study

Keywords: borderline ovarian tumors, CA125, CEA, CA15-3, CA19-9, tumor markers

Impact of serum tumor marker determination on the management of women with borderline ovarian tumors:

Multivariate analysis of a french multicentre study

INTRODUCTION

Accepted as a distinct histological entity by the International Federation of Gynecology and Obstetrics [START_REF] Federation | Classification and staging of malignant tumors in the female pelvis[END_REF] and the World Health Organization (WHO) [START_REF] Scully | World Health Organization classification and nomenclature of ovarian cancer[END_REF] in the early 1970s, borderline ovarian tumors account for 10% to 20% of ovarian epithelial tumours [START_REF] Bostwick | Ovarian epithelial tumors of borderline malignancy. A clinical and pathologic study of 109 cases[END_REF].

Guidelines for surgical treatment are similar to those for ovarian cancer [START_REF] Federation | Annual report and results of treatment in gynaecologic cancer[END_REF][START_REF] Rota | Clinical relevance of retroperitoneal involvement from epithelial ovarian tumors of borderline malignancy[END_REF]. However, one third of borderline ovarian tumors are diagnosed in women younger than 40 years, and more than 80% of cases are detected early in the disease course, raising issues of fertility-sparing surgery, laparoscopic management, and restaging operations [START_REF] Tazelaar | Conservative treatment of borderline ovarian tumors[END_REF][START_REF] Lim-Tan | Ovarian cystectomy for serous borderline tumors: a follow-up study of 35 cases[END_REF][START_REF] Morice | Clinical outcomes and fertility after conservative treatment of ovarian borderline tumors[END_REF][START_REF] Morice | Results of conservative management of epithelial malignant and borderline ovarian tumours[END_REF][START_REF] Morice | Borderline tumours of the ovary and fertility[END_REF][START_REF] Donnez | Safety of conservative management and fertility outcome in women with borderline tumors of the ovary[END_REF][START_REF] Fauvet | Restaging surgery for women with borderline ovarian tumors: results of a French multicenter study[END_REF][START_REF] Fauvet | Laparoscopic management of borderline ovarian tumors: results of a French multicenter study[END_REF][START_REF] Fauvet | Fertility after conservative treatment for borderline ovarian tumors: a French multicenter study[END_REF][START_REF] Poncelet | Recurrence after cystectomy for borderline ovarian tumors: results of a French multicenter study[END_REF].

Diagnosis of adnexal masses is mainly based on imaging techniques and preoperative serum tumor marker assays [START_REF] Hricak | MRI of the female pelvis: a review[END_REF][START_REF] Molina | A prospective study of tumor markers CA 125 and CA 19.9 in patients with epithelial ovarian carcinomas[END_REF][START_REF] Tamakoshi | Clinical value of CA125, CA19-9, CEA, CA72-4, and TPA in borderline ovarian tumor[END_REF][START_REF] Takemori | Clinical evaluation of MRI in the diagnosis of borderline ovarian tumors[END_REF][START_REF] Bazot | MR imaging compared with intraoperative frozen-section examination for the diagnosis of adnexal tumors; correlation with final histology[END_REF][START_REF] Timmerman | Inclusion of CA-125 does not improve mathematical models developed to distinguish between benign and malignant adnexal tumors[END_REF]. Serum tumor markers have been evaluated in only small series of women with BOT, and their contribution to treatment and follow-up is unclear [START_REF] Darai | Epithelial ovarian carcinoma of low malignant potential[END_REF][START_REF] Gottlieb | CA125 measurement and ultrasonography in borderline tumors of the ovary[END_REF][START_REF] Engelen | Serum CA125, carcinoembryonic antigen, and CA19-9 as tumor markers in borderline ovarian tumors[END_REF].

Elevated serum tumor markers such as CA125, CEA and CA19-9 have been reported in only 25% to 60% of women with BOT [START_REF] Tamakoshi | Clinical value of CA125, CA19-9, CEA, CA72-4, and TPA in borderline ovarian tumor[END_REF][START_REF] Gottlieb | CA125 measurement and ultrasonography in borderline tumors of the ovary[END_REF][START_REF] Engelen | Serum CA125, carcinoembryonic antigen, and CA19-9 as tumor markers in borderline ovarian tumors[END_REF][START_REF] Zanetta | Ultrasound, physical examination, and CA125 measurement for the detection of recurrence after conservative surgery for early borderline ovarian tumors[END_REF].

The aims of this retrospective study were to evaluate the contribution of the serum tumor markers CA125, CA19-9, CEA and CA15.3 to the initial management of women with BOT, and to determine their value for detecting recurrences.

MATERIAL AND METHODS

MATERIAL

From January to December 2001 we conducted a retrospective multicenter study of 360 women treated for BOT between 1990 and 2000 in 13 specialized gynecology units and one cancer center. Women with endometrioid (four cases), Brenner (2 cases) and mixed BOT (32 cases) were excluded from the study. The study population thus comprised 322 patients with serous or mucinous BOT. Data were obtained from hospital records, physicians, and direct contact with the patients. All the charts were thoroughly reviewed on site by one of the authors (RF). Ethical review board approval was obtained for the study.

The histological type was established by reviewing hematoxylin/eosin-stained slides, as recommended by FIGO (4). The following histological criteria were used to identify borderline tumors: (a) stratification of the epithelial lining of the papillae, with microscopic papillary projections or tufts arising from the epithelial lining of the papillae, (b) nuclear atypia, (c) mitotic activity, (d) intracystic clusters of free-floating cells, and (e) absence of stromal invasion. Microinvasion and micropapillary features were also recorded.

METHODS

Surgical treatment was considered conservative when at least one ovary and the uterus were spared. Conservative treatment consisted of unilateral cystectomy (UC) or unilateral salpingo-oophorectomy (USO), as well as bilateral cystectomy (BC) and USO + contralateral UC (USO+UC). Initial surgery was considered to be a complete staging operation when all peritoneal surfaces were carefully inspected and peritoneal washing, multiple random or oriented biopsies, and infra-colonic omentectomy were performed. Appendectomy was also a criterion for complete staging of mucinous borderline tumors. Initial surgery was considered an incomplete staging operation in all other cases, independently of the radical or conservative nature of treatment. The disease was staged as recommended by the International Federation of Gynecology and Obstetrics (4). Five of the 322 women had preoperative serum tumor marker assays that were not mentioned in the charts, and these women were excluded from the statistical analysis.

SERUM TUMOR MARKERS

Serum

STATISTICAL ANALYSIS

Univariate analysis was used to compare epidemiological and surgical data between patients with and without preoperative serum tumor marker assays in the entire study population. Then, in the population of women who had preoperative serum tumor marker assays, univariate analysis was used to compare epidemiological and surgical data in patients with normal and abnormal marker status. The chi-square test and Student's t test were used to compare non continuous and continuous variables in univariate analysis.

Multivariate analysis was used to determine the diagnostic and prognostic relevance of preoperative serum tumor markers, and their contribution to detecting recurrences. The primary endpoint in the multivariate model was recurrence. Preoperative pelvic CT, first-line laparoscopic management, and the use of intra-operative histology were secondary endpoints.

Associations between clinical, sonographic and serum tumor marker parameters (CA-125, CA-19.9, CEA, CA-15.3) and the above endpoints were identified by multivariable logistic regression analysis. When serum markers were assayed, an additional analysis included the marker level as a binary variable (normal or abnormal).

Correlations between parameters were studied to prevent the selection of strongly correlated parameters in the logistic model. As age and menopause were strongly correlated (correlation coefficient 0.77, p<10 -4 ), we decided to consider age alone and to exclude menopause from further multivariate analyses. Odds ratios (OR) and 95% confidence intervals (CI), as well as p-values, were calculated for both dichotomous and continuous variables.

Backwards elimination was used to select prognostic factors for the different endpoints. It started with a model that contained all explanatory variables identified by univariate analysis. This algorithm eliminated non significant variables and refitted the model repeatedly. This analysis used a significance level of 0.2 to retain variables in the model. To minimize erroneous exclusion of serum markers which could be of prognostic relevance, these markers were forced into the models.

To measure the association between predicted probabilities and observed responses, the reliability of the models was studied with Somer's test statistic. The convergence criterion was satisfied in all models. All significance tests were two-tailed and p values < 0.05 were considered significant. SAS software version 8.2 was used for all statistical analyses.

RESULTS

Study population, and distribution of FIGO stage, type of surgery and biomarkers serum levels according to histological subtype

Among the 317 women included in this analysis, respectively 181 and 136 women had serous and mucinous BOT. Among the women with serous and mucinous tumors, respectively 114 and 91 women had preoperative serum tumor marker assays, of whom respectively 55 and 38 had at least one abnormal result. Details are given in Table 1. In the group of serous tumors, 82 had laparoscopy, with laparoconversion in 21 cases, and 99 laparotmy and the distribution according to FIGO stage was Ia, Ib, Ic, II, III, and IV in 114, 28, 18, 8, 12, and 1 patients, respectively. In the group of mucinous tumors, 49 had laparoscopy, with laparoconversion in 9 cases, and 87 laparotomy and the distribution according to FIGO stage was Ia, Ib, Ic, II, III, and IV in 122, 3, 3, 1, 6, and 1 patients, respectively. In the group of serous tumors, the distribution of abnormal biomarkers according to FIGO stage Ia, Ib, Ic, II, III, and IV was 25, 9, 5, 4, 4, and 1 patients, respectively. In the group of mucinous tumors, the distribution of abnormal biomarkers according to FIGO stage Ia, Ib, Ic, II, III, and IV was 30, 1, 2, 0, 3, and 1 patients, respectively.

Epidemiological and surgical characteristics of women with and without preoperative serum tumor marker assays (Table 2).

Two hundred and five of the 317 women had preoperative serum tumor marker assays.

Women with preoperative serum tumor marker assays were older (p=0.001), had higher parity (p=0.03) and were more likely to be menopausal (p=0.02). In addition, these women were more likely to have CT scan (p<0.0001) and/or MRI (p=0.03) before surgery.

Whatever the results of preoperative serum tumor marker assays, women who had these tests were more likely to have radical treatment (p=0.0001) and full staging (p=0.004), including peritoneal washing (p<0.0001) and random peritoneal biopsies (p<0.0001).

Intraoperative histology was more frequent among women who had preoperative serum tumour marker assays (p<0.0001). Recurrences were more frequent in women without preoperative tumour marker assays (p=0.03).

The women who did and did not have preoperative serum tumor marker assays did not differ with respect to their familial history of cancer, number of pregnacy, presenting symptoms, tumor size on sonography, or the use of first-line laparoscopy, exclusively laparoscopic surgery, optimal cytoreductive surgery, or restaging operation. Mean follow-up among women with and without preoperative tumor marker assays was 34.4 ± 2.6 months and 40 ± 5.1 months, respectively (not significant). Mean disease-free survival was similar in the two groups.

Impact of preoperative serum tumor marker assays on BOT management

Ninety-three of the 205 women with preoperative serum tumor marker assays had at least one abnormal result, and were thus considered to have abnormal serum tumor marker status (Table 3). These women were more likely to have large tumors (p=0.001), bilateral tumors (p=0.01) and ascitis (p=0.008). Using multivariate analysis, First line laparoscopy was more frequent in women with abnormal serum tumor markers (OR=9.63; 95%CI=1.40-66.39; p=0.02). Women with abnormal serum tumor markers were more likely to have intraoperative histology (p=0.04) and complete staging (p=0.0008) (Table 4).

Women with normal and abnormal tumor markers did not differ in terms of their mean age, familial history of cancer, parity (including nulliparity), menopausal status, presenting symptoms, or the use of preoperative CT scan, first-line laparoscopy and conservative treatment. Likewise, there was no difference in mean follow-up, disease-free survival or the recurrence rate.

Recurrence was more frequent after conservative treatment (OR= 4.44; 95%CI=1.10-18; p=0.04) and in women with FIGO stage > Ia (OR= 7.84; 95%CI=1.73-35.48; p=0.0008).

Abnormal serum tumor marker status was not associated with the risk of recurrence (Table 5).

Serum tumor markers during follow-up

Eighty-three women had routine serum tumor marker assays during follow-up, four times during the first year and then twice a year. Six women had abnormal results, of whom four had recurrences and two were recurrence-free, as shown by surgery. Seven women with normal serum tumor marker status during follow-up had recurrences diagnosed on clinical and/or sonographic grounds. The sensitivity, specificity and positive and negative predictive values of abnormal serum tumor maker status for recurrences were 66.6%, 90.1%, 36.4% and 97.2%; and their accuracy was 89.2%.

DISCUSSION

In this large retrospective study, serum tumor marker assays modified the surgical management of women with borderline ovarian tumors. Moreover, serum tumor marker abnormalities during follow-up led to the diagnosis of recurrences.

Low incidence of abnormal serum markers in women with borderline ovarian tumors

Our results confirm the low frequency of serum tumor marker abnormalities in both serous and mucinous BOT, as previously shown in small series. Despite sonographic detection of large or complex ovarian tumors in our patients, and despite their management in specialized centers, less than two-thirds of the women were prescribed serum tumor marker assays. Possible explanations include the high frequency (~50%) of normal serum tumor marker status in stage I ovarian cancer [START_REF] Bast | New tumor markers: CA125 and beyond[END_REF], and the fact that several benign disorders (endometriosis, uterine fibroids, pelvic infection, etc.) can be accompanied by elevated serum tumor marker levels. Moreover, using a mathematical model, Timmerman et al underlined the low contribution of CA125 serum tumor marker to distinguish benign from malignant ovarian tumours [START_REF] Timmerman | Inclusion of CA-125 does not improve mathematical models developed to distinguish between benign and malignant adnexal tumors[END_REF]. A previous study has also shown that the sensitivity and specificity of abnormal serum tumor marker status for malignant ovarian lesions are higher in menopausal women [START_REF] Malkasian | Preoperative evaluation of serum CA 125 levels in premenopausal and postmenopausal patients with pelvic masses: discrimination of benign from malignant disease[END_REF]. In the present study, the main determinants of tumor marker assay prescription were older age, menopausal status, and ascitis on sonography.

Impact of preoperative determination of serum tumor markers on management of women with borderline ovarian tumor.

Interestingly, preoperative tumor marker assays modified patient management. Indeed, women who had these assays were more likely to have intra-operative histology and, hence, complete staging. Routine preoperative serum tumor marker assay raises issues of costeffectiveness, and can generate anxiety if the results are abnormal. Several algorithms based on epidemiological characteristics, serum tumor markers and sonography have been proposed

for predicting the histological nature of adnexal masses [START_REF] Timmerman | Inclusion of CA-125 does not improve mathematical models developed to distinguish between benign and malignant adnexal tumors[END_REF]. Despite their reported accuracy, routine use of such algorithms is limited by their complexity. In our study, multivariate analysis showed that abnormal preoperative serum tumor marker status influenced the surgical management of adnexal masses that were subsequently shown to be BOT. Although no report have focused on the prognostic relevance of abnormal serum tumor markers, our data underlined the risk of radical treatment in women with pre-operative abnormal tumor markers, even though there is no proven benefit for patients. Using preoperatively a multiple bioassay utilizing Human epididymal secretory protein E4 (He4) an CA125 in patients with a pelvic mass could be of interest in classifying patients in a high risk group of epithelial ovarian cancer [START_REF] Moore | A novel multiple marker bioassay utilizing He4 and CA 125 for the prediction of ovarian cancer in patients with a pelvic mass[END_REF]. Serum He4 concentration may differentiate malignant ovarian tumors from endometriotic cysts [START_REF] Huhtinen | Serum He4 concentration differentiates malignant ovarian tumours from ovarian endometriotic cyst[END_REF][START_REF] Montagnana | Usefulness of serum He4 in endometriotic cysts[END_REF]. However, data concerning assessment of He4 especially in BOT are scarce and need further studies.

Impact of abnormal serum tumor markers on surgical management of women with borderline ovarian tumor

Abnormal serum tumor marker status was associated with first-line laparoscopy. There are several possible explanations for this apparent paradox. First, by permitting complete evaluation of the abdominal cavity, laparoscopy contributes to the choice of the surgical route.

When macroscopic criteria suggest a benign tumor, an exclusively laparoscopic procedure is considered acceptable. In contrast, a median abdominal incision is often preferable when there are signs of malignity. Second, laparoscopy permits adequate evaluation of the feasibility of optimal surgery or the need for neoadjuvant chemotherapy [START_REF] Fagotti | Role of laparoscopy to assess the chance of optimal cytoreductive surgery in advanced ovarian cancer: a pilot study[END_REF]. Finally, laparoscopic surgery has been shown to be reliable for BOT (12-13, 22, 25, 32).

Relevance of serum tumor marker determination for recurrence detection.

The contribution of serum tumor markers to the follow-up of women with BOT is controversial. This could be due to the relatively low incidence of abnormal serum tumor markers in women with BOT, both preoperatively and during recurrences [START_REF] Morice | Clinical outcomes and fertility after conservative treatment of ovarian borderline tumors[END_REF][START_REF] Fauvet | Laparoscopic management of borderline ovarian tumors: results of a French multicenter study[END_REF][START_REF] Darai | Epithelial ovarian carcinoma of low malignant potential[END_REF][START_REF] Zanetta | Ultrasound, physical examination, and CA125 measurement for the detection of recurrence after conservative surgery for early borderline ovarian tumors[END_REF][START_REF] Maneo | Are borderline tumors of the ovary safely treated by laparoscopy?[END_REF].

In our study, only 83 (26.2%) of 317 women with BOT had routine serum tumor marker assays during follow-up, whereas our findings show that isolated abnormal serum tumor markers can lead to the diagnosis of recurrence.

There is no consensus on the indications of serum tumor marker assays in women treated for BOT. Despite both the low incidence of abnormal serum markers in women with BOT and their low contribution to differentiate benign from malignant ovarian tumors, our results support that the preoperative evaluation of serum tumors markers modified surgical management by increasing the use of first line laparoscopy, intra operative histology and complete staging. Previous studies have shown the high risk of recurrence of serous BOT, probably owing to the higher frequency of bilateral tumors than in women with mucinous BOT. Seidman and Kurman reported that women with serous BOT exhibiting micropapillary features, and women with mucinous BOT with intraepithelial carcinoma, had a higher risk of recurrence (33). Conservative surgery based on cystectomy exposes women to a high risk of persistent and/or recurrent BOT [START_REF] Lim-Tan | Ovarian cystectomy for serous borderline tumors: a follow-up study of 35 cases[END_REF][START_REF] Poncelet | Recurrence after cystectomy for borderline ovarian tumors: results of a French multicenter study[END_REF][START_REF] Maneo | Are borderline tumors of the ovary safely treated by laparoscopy?[END_REF]. As previously reported especially in case of invasive implants, women with FIGO stage > Ia BOT have a high risk of recurrence [START_REF] Maneo | Are borderline tumors of the ovary safely treated by laparoscopy?[END_REF].

Finally, nearly 80% of recurrences are diagnosed during the first two postoperative years [START_REF] Poncelet | Recurrence after cystectomy for borderline ovarian tumors: results of a French multicenter study[END_REF][START_REF] Darai | Epithelial ovarian carcinoma of low malignant potential[END_REF]. It thus seems logical to recommend close follow-up of women treated for BOT, including serum tumor marker determination every 6 months for at least the first two postoperative years. This is particularly the case after conservative treatment, in patients with FIGO stage > Ia, and in patients with serous BOT with micropapillary features or mucinous BOT with intraepithelial carcinoma and in case of microinvasion on tumors or on implants. However, the use of CA125 in the follow up of patients with BOT has been recently discussed to detect recurrence while representing a source of patient's anxiety (34). Further studies are required to evaluate the cost-effectiveness of CA125 determination in the follow-up of women with BOT.

Regarding the limitations of this study, its retrospective nature carries a risk of bias due to confounding factors. Also, our conclusions cannot be extended to patients with other complex but histological benign ovarian tumors. Tumor markers were not assayed in all the women who had recurrences, limiting the impact of our conclusions. Indeed, pre-and postoperative serum tumor markers determinations were not available for all patients experiencing a recurrence in stage I BOT. Moreover, no evaluation of CEA serum level according to smokers or non-smokers had been performed. However, this remains the largest study of the contribution of serum tumor markers to the management of borderline ovarian tumors.

In conclusion, our results suggest that serum tumor markers can improve the preoperative assessment and surgical management of BOT, notably by increasing the use of intra-operative histology. We therefore suggest evaluating serum tumor marker assays for all women with complex adnexal tumors. Moreover, isolated serum tumor marker abnormalities during follow-up can lead to the diagnosis of recurrence.

  levels of CA-125, CA-19.9, CEA and CA-15.3 were measured with radioimmunoassays. Values were considered elevated when CA-125 > 35 IU, CA-19.9 > 40 IU, CEA > 5 IU and CA-15.3 > 30 IU/ml. Serum tumor marker levels in a given patient were considered abnormal if at least one of the markers was elevated.

  benign and malignant types. A clinicopathologic study of 65 advanced stage cases. Am J Surg Pathol 1996;20:1331-45. 34. Oskay-Oezcelik G, du Bois A, Fasching PA, Mahner S, Liebrich C, GlaβA, Schmidt-Wetze S, Sepp L, Münstedt K, Lichtenegger W, Sehouli J. What do patients think about CA-125 monitoring in the follow-up? Results from a multicenter trial in 1 060 patients with ovarian cncer. American Society of Clinical Oncology (ASCO) Meeting 2009. Abstract number 5522, JCO, 2009; 27 (15S) : 282S.

Table 1 : Preoperative CA125, CA19-9, CEA, and CA15-3 assay in women with serous and mucinous borderline ovarian tumors.

 1

		CA125	CA19-9	CEA	CA15-3	All tumor
		N	N	N	N	markers
	Serous BOT
	Patients with tumor	113/181	45/180	59/180 13/181	13/181
	marker assays
	Patients with at least one	51/113	8/45	2/59	2/13
	abnormal marker
	Mucinous BOT
	Patients with tumor	89/136	46/132	52/133 10/133	10/136
	marker assays
	Patients with at least one	31/89	11/46	4/52	2/10
	abnormal marker

Table 2 : Epidemiologic characteristics of women with serous or mucinous borderline ovarian tumours according to tumour marker status.

 2

	Criteria	Patients with	Patients without	P
		marker assays	marker	assays
		(n=205)	(n=112)
	Age (mean±SD)	49.0 ± 1.1	42.8 ± 1.5		0.001
	Parity (mean±SD)	1.5 ± 0.1	1.2 ± 0.1		0.03
	Nulliparous	64/205	52/112		0.01
	Post-menopausal	84/202	30/110		0.017
	Ascitis on sonography	25/86	5/45		0.09
	Preoperative abdominopelvic CT	67/161	17/86		<0.0001
	Preoperative abdominopelvic MRI	22/157	5/96		0.03
	Peritoneal washing	155/204	48/111		<0.0001
	Omentectomy	88/205	35/111		0.06
	Random peritoneal biopsies	92/205	20/110		<0.0001
	Intra-operative histology	108/159	24/67		<0.0001
	Conservative treatment	77/205	68/112		0.0001
	Complete staging during first surgery	49/178	10/90		0.004
	Recurrence	13/205	16/112		0.03
	Patients with missing data were excluded from the analysis.

Table 3 : Impact of abnormal serum tumor markers on surgical management of women with serous or mucinous borderline ovarian tumors who had tumoral marker assays.

 3

	Characteristic	Abnormal	Normal marker	P
		marker status	status
		(93 patients)	(112 patients)
	Exclusive laparoscopic surgery	16/29	40/50	0.007
	Converted laparoscopy	13/29	10/50	0.007
	First-line laparotomic surgery	64/93	62/112	0.007
	Intra-operative histology	53/68	49/80	0.04
	Complete staging during first surgery	33/79	15/88	0.0008
	Patients with missing data were excluded from the analysis.

Table 4 : Logistic regression analysis with first-line laparoscopy as the response variable and including serum marker levels as the explanatory variable (number of observations = 69).

 4 OR= odds ratio; 95% CI = 95% confidence interval; Blank cells indicate that the variable was not included in the final model. The model χ 2 was 46.5, df: 6, p=10 -4 .

	Parameters selected		Univariate analysis	Multivariate analysis
		OR	95%CI	p-value Adjusted OR	95%CI	p-value
	Clinical
	Age (years)	0.97	0.96-0.99	0.0001
	HRT	1.53	0.66-3.54	0.32
	Nulliparity	1.75	1.11-2.79	0.02
	Infertility	3.27	1.55-6.91	0.007
	Family history	0.98	0.51-1.90	0.95
	Imaging
	US visible ascitis	0.22	0.09-0.59	0.001	0.03	0.00 -0.55	0.02
	US tumor size (mm)	0.84	0.79-0.89	<10 -4	0.78	0.66 -0.92	0.003
	US bilateral tumor	0.91	0.50-1.65	0.76	0.05	0.01 -0.55	0.01
	Biological
	Abnormal serum	0.56	0.31-1.02	0.06	9.63	1.40 -66.39	0.02
	markers

Table 5 . Logistic regression analysis with post-operative recurrence as the response variable (number of observations =170).

 5 OR= odds ratio; 95%CI = 95% confidence interval; * This variable was forced into the model; Blank cells indicate that the variable was not included in the final model. The model χ 2 was 14.0, df: 3, p=0.003.

	Parameters selected		Univariate analysis	Multivariate analysis
		OR	95%CI	p-value Adjusted OR	95%CI	p-value
	Clinical
	Age (years)	0.94	0.91-0.96	0.0001
	Nulliparity	4.02	1.81-8.92	0.003
	Infertility	3.68	1.47-9.17	0.0003
	Family history	1.38	0.50-3.86	0.53
	Imaging
	US visible ascitis	2.09	0.60-7.29	0.24
	US tumor size (cm)	0.98	0.91-1.05	0.60
	US bilateral tumor	2.20	0.95-5.10	0.06
	Biological
	Serum markers level	3.30	0.85-12.85	0.07	1.97	0.44-8.83	0.79
	Surgical
	Conservative treatment	4.39	1.83-10.55	0.0004	4.44	1.10-18.00	0.04
	FIGO stage Ia vs others	3.19	1.46-6.97	0.0002	7.84	1.73-35.48 0.0008


Souad Bezzaoucha

Benoît Marx

Didier Maquin

José Ragot

On the Unknown Input Observer Design : a Decoupling Class Approach

This paper deals with state estimation for linear discrete-time systems subject to unknown input. Although many papers have dealt with the problem of Unknown Input Observer design, state decoupling and reconstruction ; the goal is to present a new method allowing to characterize a class of unknown inputs to which the estimation error is decoupled. This contribution considers two problems : exact decoupling and L 2 -attenuation of the unknown input to the state estimation error.

I. INTRODUCTION

The Unknown Input Observer (UIO) design has received considerable interest due to its importance and connection with fault detection problem, since in many cases a part of the system's input is inaccessible (e.g. plant disturbance or actuator failure). Under such circumstances, a conventional observer that requires knowledge of all inputs cannot be used directly, then the UIO was developed to estimate the state of an uncertain system despite the existance of unknown inputs or uncertain disturbances [START_REF] Chang | Design of General Structured Observers for Linear Systems with Unknown Inputs[END_REF], [START_REF] Basile | On the observability of linear, time-invariant systems with unknown inputs[END_REF], [START_REF] Darouach | Full-order observers for linear systems with unknown inputs[END_REF], [START_REF] Guidorzi | On Wonham stabilizability condition in the synthesis of observers for unknown input systems[END_REF], [START_REF] Hostetter | Observing systems with unmeasurable inputs[END_REF], [START_REF] Hou | Design of observers for linear systems with unknown inputs[END_REF].

Several researches were achieved concerning the state estimation in the presence of unknown inputs. They can be gathered into two categories. The first one supposes an a priori knowledge on these nonmeasurable inputs ; in particular, Johnson [START_REF] Johnson | On observers for systems with unknown and inacessible inputs[END_REF] proposes a polynomial approach and Hostetter and Meditch [START_REF] Hostetter | Observing systems with unmeasurable inputs[END_REF] suggest approximating the unknown inputs by the response of a known dynamic system [START_REF] Akhenak | Process input estimation with a multimodel. Application to communication[END_REF]. The second category proceeds either by estimation of the unknown inputs [START_REF] Khedir | State and Sensor Faults Estimation via a Proportional Integral Observer[END_REF] or by their complete elimination from the system equation. However, some of these methods require differentiation of the measured outputs which can amplify the effect of the measurement's noise.

One of the most successful robust observer design methods ressorts to the disturbance decoupling principle [START_REF] Yang | Observers for linear systems with unknown inputs[END_REF] [12] [START_REF] Darouach | Full-order observers for linear systems with unknown inputs[END_REF]. The problem of UIO has been initialised by Basile and Marro [START_REF] Basile | On the observability of linear, time-invariant systems with unknown inputs[END_REF], Guidorzi and Marro [START_REF] Guidorzi | On Wonham stabilizability condition in the synthesis of observers for unknown input systems[END_REF]. Since then, several contributions for UIOs have been proposed [START_REF] Chang | Design of General Structured Observers for Linear Systems with Unknown Inputs[END_REF], [START_REF] Hammouri | Unknown input observer for state affine systems : A necessary and sufficient condition[END_REF]. For these methods, a rank condition relating the output distribution matrix and the input distribution matrices must be satisfied which is sometimes difficult and might be quite restrictive. An approach to simultaneously estimate the unknown input and the system state using the PI observer has been

The authors are with Centre de Recherche en Automatique de Nancy (CRAN), Nancy-University, CNRS, 2 avenue de la Forêt de Haye F-54516 Vandoeuvre-les-Nancy. firstname.name@ensem.inpl-nancy.fr

proposed by [START_REF] Shumsky | Algebraic Approach to the Problem of Fault Accommodation in Nonlinear Systems[END_REF], [START_REF] Ichalal | State and unknown input estimation for nonlinear systems described by Takagi-Sugeno models with unmeasurable premise variables[END_REF] and [START_REF] Ichalal | Simultaneous state and unknown inputs estimation with PI and PMI observers for Takagi Sugeno model with unmeasurable premise variables[END_REF]. However, this observer concerns the case of constant unknown inputs. In [START_REF] Zs | Adaptive observers for TS fuzzy systems with unknown polynomial inputs[END_REF], a model-based oserver design in the presence of polynomial unknown inputs for TS fuzzy systems has been investigated. In [START_REF] Marx | Design of observers for Takagi-Sugeno descriptor systems with unknown inputs and application to fault diagnosis[END_REF], the authors present a method for state-estimation for Takagi-Sugeno descriptor systems affected by UI. Sufficient existence conditions of the unknown inputs decoupling observers are given and strict linear matrix inequalities are solved to determine the gain of the observers so that the estimated state asymptotically tends to the real one.

Summarizing, the UIO design is based either on the decoupling such that the estimation error must not depend on the the UI, or on the synthesis of an Integral Observer for the detection (estimation) of disturbances. But, as much as the authors know, all the proposed strategies impose structural and rank constraints. This work advantage is to propose an exact decoupling instead of an attenuation or a decoupling for a constant UI. Moreover, it is proposed to decompose any UI into two terms. The first one is a sum of exponential functions from which the state estimates can be exactly decoupled. For a given system, the class of the UI satisfying that property is clearly satisfied. The effect of the remaining part of the UI on the state estimates is then attenuated in an L 2 framework. Two cases will be treated, the exact decoupling case and the almost-exact case which consists in decoupling the estimation to a subset of the UI, while attenuing the L 2 gain from the other UI to the estimation. This paper is organised as follows : Section II presents a second order system in order to introduce the decoupling strategy and the Uknown Input Class for exact decoupling notion and how to generate this class. Section III is a generalization of the second section. In section IV, we introduce the notion of partial decoupling and the linear matrix inequalities conditions to ensure the L 2 attenuation of the UI effect on the system. In order to impove the obtained results, a pole placement will also be applied. However, the usual linearization approaches are not suitable to the present problem since BMIs (Bilinear Matrix Inequalities) are to be dealt with. A gain adjustment technique is then applied. This synthesis linearize the inequalities by fixing one of the unknown variable [START_REF] Losser | Ajustement de lois de commande : Application en aéronautique[END_REF]. This kind of procedure can be found in the centrage-XY procedure [START_REF] Iwasaki | The XY-centring algorithm for the dual LMI problem : a new approach to fixed-order control design[END_REF], the D-K iteration mentionned in [START_REF] Rotea | An alternative to the D-K iteration[END_REF] or Yamada's approach [START_REF] Yamada | An LMI approach to local optimization for constantly scaled H ∞ control problems[END_REF]. However, there is no guarantee that the proposed structure assures the algorithm convergence. Finally, in the last section, simulations are presented to show the efficiency of the proposed approach.

II. ILLUSTRATIVE EXAMPLE

To begin with, the procedure is introduced with the help of a simple example being a second order system. The different steps leading to the Uknown Input Class for exact decoupling are detailed. Consider a second order system described by :

x k+1 = Ax k + Bu k + Dη k-1 y k = Cx k + eη k-1 (1)
Vectors x k ∈ R 2 , u k ∈ R, η k ∈ R and y k ∈ R are the system state, input, unknown input and the output vector respectively. The system matrices are real valued, constant and of appropriate dimensions :

x k = x 1k x 2k A = a 11 a 12 a 21 a 22 B = b 1 b 2 C = c 1 c 2 D = d 1 d 2 (2)
The proposed Proportional Integral Observer (PIO) of gain K and the UIO depending on an auxiliary variable z k ∈ R are respectivelly given by the following equations :

   xk+1 = A xk + Bu k + D ηk-1 + K ỹk ŷk = C xk + e ηk-1 ỹk = y k -ŷk (3)
z k+1 = γ 1 ỹk + λ 1 z k ηk+1 = γ 2 z k + λ 2 ηk (4)
with :

K = k 1 k 2
It can be noted that the UIO has a filter structure with as an input the output reconstruction error ỹk . This filter parameters γ 1 , γ 2 , λ 1 and λ 2 allow to modify the gain and time constant of the UIO. In (4), only one integrator is used but this structure can be generalized to multiple integrator observer. However, the choice z k+1 = γ 1 ỹk+1 + λ 1 z k with γ 1 = 1 and λ 1 = 0 leads to z k+1 = ỹk which is equivalent to a first order filter for the UI estimation. The system observer is described by equations ( 3) and ( 4). The gains K, γ 1 , γ 2 , λ 1 and λ 2 are choosen according to the state and UI reconstruction specifications.

In the following, the state and UI estimation errors are expressed as function of the UI. Since the system and its observer are linear, the time operator q, is adequate to express the errors :

xk = x k -xk ηk = η k -ηk
From equations ( 1), ( 3) and ( 4), the state reconstruction error function of the UI is given by :

x1k = N 1 (q) D(q) η k x2k = N 2 (q) D(q) η k (5)      N 1 (q) = (q -λ 1 )(q -λ 2 )( ã12 d2 -ã22 d1 + q d1 ) N 2 (q) = (q -λ 1 )(q -λ 2 )( ã21 d1 -ã11 d2 + q d2 ) D(q) = ((q -λ 1 )(q -λ 2 ) + γe)((q -ã11 )(q -ã22 ) -ã12 ã21 ) +γc 1 ( ã12 d2 -ã22 d1 + q d1 ) + γc 2 ( ã21 d1 -ã11 d2 + q d2 ) with :                ã11 = a 11 -k 1 c 1 ã12 = a 12 -k 1 c 2 ã21 = a 21 -k 2 c 1 ã22 = a 22 -k 2 c 2 d1 = d 1 -k 1 e d2 = d 2 -k 2 e (6)
From ( 5), conditions for the estimation errors to be independent from the UI can easily be derived. Then, the UI familly satisfying an exact decoupling is solution of :

     N 1 (q) D(q) η k = 0 N 2 (q) D(q) η k = 0 (7)
In order to find the solution η k assuring the precedent condition, it is imposed that N 1 (q) and N 2 (q) have the same roots. It should also be checked if some solutions are common to D(q) and N 1 (q) (or N 2 (q)). For the first point, we have the following condition :

ã11 d2 -ã22 d1 ã21 d1 -ã11 d2 = d1 d2 (8)
which imposes a constraint on the observer coefficients k 1 and k 2 . That leads to :

q 0 = ã21 d1 -ã11 d2 d2 (9)
is a common root between N 1 (q),N 2 (q) and D(q). Then ( 7) is written as :

(q -λ 1 )(q -λ 2 )η k = 0 ( 10
)
The solution is given by an UI being the sum of two exponential functions :

η k = A 1 λ k 1 + A 2 λ k 2 ( 11
)
where coefficients A 1 and A 2 are arbitrarily set. Finally, the choice of the observer values λ 1 and λ 2 gives the UI class assuring the exact decoupling of the state error toward the UIO for any values of the coefficients A 1 and A 2 .

III. RECONSTRUCTION ERRORS : DISTURBANCES

DECOUPLING

Let us define the following system equations :

x k+1 = Ax k + Bu k + Dη k-1 y k = Cx k + eη k-1 (12) Vectors x k ∈ R n , u k ∈ R m , η k ∈ R
and y k ∈ R p are the system state, input, unknown input and the output vectors respectively. The system matrices

A ∈ R n×n , B ∈ R n×m , D ∈ R n×1 , C ∈ R p×n et e ∈ R p×1
are real valued and known.

The proposed system observer of gain K and the UIO are respectivelly given by the following equations :

   xk+1 = A xk + Bu k + D ηk-1 + K ỹk ŷk = C xk + e ηk-1 ỹk = y k -ŷk (13)
z k+1 = Γ ỹk + Λz k ηk+1 = γz k + λ ηk ( 14
)
with appropriate dimensions :

z k ∈ R q , K ∈ R n×p , Γ ∈ R q×p , γ ∈ R 1×q , Λ ∈ R q×q and λ ∈ R.
Depending on the value of the UIO parameters, we can have either a proportional observer, an integral or a multiple integral observer. In this particular case, the choice λ 1 = 1 or λ 2 = 1 introduces the two integrators in this filter structure.

By following the same steps as in the previous section, the state and UI reconstruction errors are expressed ; we get from equation ( 14) with the time operator q : ηk = (q -λ ) -1 γz k (15)

(qI q -Λ)z k = Γ ỹk (16)
From ( 15), ( 16), ( 12) and ( 13), we have :

(qI q -Λ)z k = ΓC xk + Γe(η k-1 -ηk-1 )
which leads to :

[(qI q -Λ) + Γe(q -λ ) -1 q -1 γ]z k = ΓC xk + Γeq -1 η k (17)
The state error xk dynamic is obtained from ( 12) and ( 13) :

xk+1 = A xk + D ηk-1 A = A -KC D = D -Ke (18)
From ( 18) and ( 16), we have :

(qI n -A) xk = D ηk-1 = Dq -1 η k -Dq -1 (q -λ ) -1 γz k
That gives the state estimation error :

xk = (qI n -A) -1 Dq -1 η k -(qI n -A) -1 Dq -1 (q -λ ) -1 γz k ( 19
) By replacing this expression in [START_REF] Khedir | State and Sensor Faults Estimation via a Proportional Integral Observer[END_REF], we have :

z k = Z -1 Λη k ( 20
)
with :

Λ = ΓC(qI n -A) -1 D + Γe Z = q(qI q -Λ) + Λ(q -λ ) -1 γ (21)
Finally, replacing [START_REF] Marx | Design of observers for Takagi-Sugeno descriptor systems with unknown inputs and application to fault diagnosis[END_REF] in [START_REF] Iwasaki | The XY-centring algorithm for the dual LMI problem : a new approach to fixed-order control design[END_REF] and [START_REF] Losser | Ajustement de lois de commande : Application en aéronautique[END_REF] to have :

ηk = (q -λ ) -1 γZ -1 Λη k xk = (qI n -A) -1 Dq -1 1 -(q -λ ) -1 γZ -1 Λ η k ( 22
)
the UI estimation error becomes :

ηk = 1 -(q -λ ) -1 γZ -1 Λ η k
From [START_REF] Rotea | An alternative to the D-K iteration[END_REF] we have the state estimation error decoupling condition toward the UI :

(qI n -A) -1 Dq -1 [1 -(q -λ ) -1 γZ -1 Λ]η k = 0 ( 23
)
In order to decouple the state from the UI and assure an exact estimation of it, the following condition has to be verified :

1 -(q -λ ) -1 γZ -1 Λ η k = 0 (24)
Equation ( 24) may be extended as N(q) D(q) η k = 0. From solving this last equation, we have the roots that define the UI class that ensure an exact decoupling of the estimation error toward the UI. This class is written as : ∑ i A i λ i where the λ i correspond to the roots of [START_REF] Yamada | An LMI approach to local optimization for constantly scaled H ∞ control problems[END_REF] and A i are totally free parameters.

IV. PARTIAL DECOUPLING OBSERVER

In the previous section, was detailed how to find the class of UI ensuring an exact decoupling of the UI in respect to the state estimation error. In the following section, a general case with an UI that does not respond to the decoupling condition is considered. In this case, the problem is solved by attenuating the effect (transfer) of the UI to the estimation error and propose linear matrix inequalities to determinate the observer gain so that the estimated state asymptotically tends to the real one. In addition to the two previous cases (exact and partial decoupling), we also have a third one, which is a mixt between the two solutions. In fact, any UI may be decomposed into a sum of two terms η k = η d k +η a k . The first term corresponds to the decoupling term and the second one is the approximaion term onto L 2 attenuation is applied. In subsection A, we only present the attenuation approach ; but, in the simulation section the combined approach will be illustrated.

A. L 2 Attenuation

System and observer equations are given by :

   xk+1 = A xk + D ηk-1 ηk = η k -λ η k-1 -γz k-1 + λ ηk-1 z k+1 = ΓC xk + Γe ηk-1 + Λz k (25)
The corresponding matrix form is given by : e k+1 = A 1 e k + B 1 η a k [START_REF] Zhou | Robust stabilization of linear systems with norm-bounded time-varying uncertainty[END_REF] with :

A 1 =     A D 0 0 0 λ 0 -γ ΓC Γe Λ 0 0 0 1 0     , B 1 =     0 0 1 -λ 0 0 0 0     , e k =     xk ηk-1 z k z k-1     , η a k = η k η k-1 (27)
In particular, [START_REF] Zhou | Robust stabilization of linear systems with norm-bounded time-varying uncertainty[END_REF] gives the UI influence on the estimation errors. To focus on the impact of the UI on the state estimation, a new observer output is considered :

g k = C 1 e k ( 28
)
with : C 1 = I 0 0 0 . Considering the Real Bounded Lemma [START_REF] Boyd | Matrix Inequalities in System and Control Theory[END_REF], the system (26), it is stable and the L 2 gain is bounded by

g k 2 η k 2
< µ if there exists a positive symmetric matrice P and a positive scalar µ such that the following condition holds :

  A T 1 PA 1 -P A T 1 PB 1 C T 1 B T 1 PA 1 B T 1 PB 1 -µ 2 I 0 C 1 0 -µ 2 I   < 0 (29)
According to [START_REF] De Oliveira | A new discrete-time robust stability condition[END_REF] and [START_REF] Peaucelle | A new robust D-stability condition for real convex polytopic uncertainty[END_REF], the previous problem can be reformulated by searching a positive symetric definite matrice P, gains K and G such that :

    -P A T 1 PB 1 C T 1 A T 1 G T B T 1 PA 1 B T 1 PB 1 -µ 2 I 0 0 C 1 0 -µ 2 I 0 GA 1 0 0 -G -G T + P     < 0
(30) where A 1 defined in (28) with the help of (19), depends on K. Let us remark that inequality (31) is not linear. For that reason some transformations are needed to obtain LMIs. Let us write the matrix A 1 such that :

A 1 = A 1 -RKB 1 ( 31
)
with :

A 1 =     A D 0 0 0 λ 0 -γ ΓC Γe Λ 0 0 0 1 0     R =     I 0 0 0     B 1 = C e 0 0
(32) Replacing A 1 by (31) in (30), we have :

    -P A T 1 PB 1 C T 1 A T 1 G T B T 1 PA 1 B T 1 PB 1 -µI 0 0 C 1 0 -µI 0 GA 1 0 0 P -G -G T     +M T N +N T M < 0 (33) with M =     -B T 1 K T 0 0 0     T , N =     0 B T 1 PR 0 GR     T and µ = µ 2
Let us recall the following lemma [START_REF] Zhou | Robust stabilization of linear systems with norm-bounded time-varying uncertainty[END_REF]. Consider two real matrices Π and Λ with appropriate dimensions, for any positive matrix Σ the following inequality holds :

Π T Λ + Λ T Π ≤ Π T ΣΠ + Λ T Σ -1 Λ (34)
Applying this lemma, (33) becomes :

    -P A T 1 PB 1 C T 1 A T 1 G T B T 1 PA 1 B T 1 PB 1 -µI 0 0 C 1 0 -µI 0 GA 1 0 0 P -G -G T     + M T ΣM + N T Σ -1 N < 0 (35)
Applying Schur's complement, we get :

        -P A T 1 PB 1 C T 1 A T 1 G T B T 1 K T 0 B T 1 P B T 1 PB 1 -µI 0 0 0 B T 1 PR C 1 0 -µ 0 0 0 GA 1 0 0 -G -G T + P 0 GR KB 1 0 0 0 -Σ -1 0 0 R T PB 1 0 R T G T 0 -Σ         <0 (36) At last, (36) becomes :         -P A T 1 PB 1 C T 1 A T 1 G T B T 1 F T 0 B T 1 P B T 1 PB 1 -µI 0 0 0 B T 1 PR C 1 0 -µ 0 0 0 GA 1 0 0 -G -G T + P 0 GR FB 1 0 0 0 -Σ T 0 0 R T PB 1 0 R T G T 0 -Σ         <0 (37)
with F = ΣK. The LMI must be solved in P, G, F and the gain K is obtained by K = Σ -1 F.

B. Pole Assignment

The minimization of the attenuation factor µ may result in slow dynamics of the state estimation error. This problem can be solved by pole assignment of the closed loop system in a specified region. The considered region is a disk centred at (q, 0) with radius α. Thus, the condition to answer this constraint is given by the following : find P = P T > 0 and Q = Q T > 0 such that the following LMI [START_REF] Chilali | H in f ty design with pole placement constraints : an LMI approach[END_REF] occurs :

-αQ -qQ + QA -GC (-qQ + QA -GC) T -αP < 0 (38)
with G = QK. We have to solve this LMI regarding to Q and G then we deduce K. Thus, to ensure the stabilty and pole assignment, the conditions (37) and (38) must be fulfilled simultaneously.

C. Gain Ajustement

From matrices F and G definitions, there is a dependence between the two LMIS (37) and (38). Then we have to solve simultaneously these two conditions. It can be noted LMI1(P, K) and LMI2(Q, K). The proposed method is based on an ajustment technique allowing to set some variables and calculate others in an iterative way. More precisely, if the gain K is fixed, we solve LMI1(P, K) regarding to P. Then we solve LMI2(Q, K) regarding to Q and K and we use the obtained result K for another cycle (see table 1). This procedure was choosen in reason of its simplicity, but one should be aware that no optimality or convergence guarantee is given. However, since our study goal is to find a solution to the given conditions, an optimal solution is not a necessity.

Iterative optimisation for gain K :

1) Set i = 0. Chose a stabilisable value K 0 . Put K (i) = K 0 .

2) L 2 attenuation : Find P (i+1) > 0 solution of LMI1(P, K (i) ). 3) Pole assignment : Find Q (i+1) and K (i+1) solution of LMI2(Q, K) . 4) Stopping condition :

-If ||K (i+1) -K (i) || < ε stop the algorithm : At the first step, let us determine the observer gain K with the proposed iterative algorithm. The obtained gain K and attenuation µ for a pole assignment in a disk centred at (0.3,0) with radius 0.2 are :

K f inal = K (i+1) . -Else, set i = i +
K =     0.1467 4.6498 -7.7861 4.4794     µ = 4.78 (39)
The second step consists of finding the UI class for an exact decoupling. Let us recall that the state decoupling condition towards the UI with an exact estimation of the UI is given by [START_REF] Yamada | An LMI approach to local optimization for constantly scaled H ∞ control problems[END_REF]. In this example, it corresponds to an UI composed of a linear combination of six exponential functions : two roots correspond to Λ and λ , the others are two complex conjugate and two real values given by : λ 1 = Λ = 1 ; λ 2 = λ = 0.7 ; λ 3 = 0.36 ; λ 4 = 0.29 λ 5,6 = 0.43 ± 0.02i

Then, the class of UI for an exact decoupling is given by :

η k = A 1 λ k 1 + A 2 λ k 2 + A 3 λ k 3 + A 4 λ k 4 + A 5 a k cos(φ k + ψ) (40) with : a = Re(λ 5 ) 2 + Im(λ 5 ) 2 and cos(φ ) = Re(λ 5 ) 2 2 √ Re(λ 5 ) 2 +Im(λ 5 ) 2
The UI is defined by : In the case where a noise r affects the output measurment, we considere the new output defined as : Our goal is to attenuate the influence of the UI and the measurment noise on the state estimation error. To minimize their effect, we filter the output reconstruction error ỹ with a Low Pass Filter with a constant time of (1 -α) :

η k = 0.1 -0.2(0.7) k + 0.4(0.36) k + 0.2(0.29) k -0.5(0.93) k cos(2.05k) (41)
y k = Cx k + eη k-1 +W r k (42)
ỹ f ,k = α ỹk + (1 -α) ỹ f ,k-1 (43)
By replacing this equation in the observer equations, we get :

xk+1 = A xk + Bu k + D ηk-1 + K ỹ f ,k z k+1 = Γ ỹ f ,k + λ z k (44)
The different output and UI estimate (with and without filter) obtained for a weightning matrix of 10% and a coefficient filter α = 0.25 are presented in the figures 4 and 5 : The simulation results of the UI estimation obtained by the proposed observer are displayed on the previous figures. Solving the LMIs (37) may cause slow dynamics of the observer, so an eigenvalue assignment in a D-region allows to increase the performances of the observer. Also, in case of measurment noise, a filter is added at the output to improve the performances.

VI. CONCLUSION AND PERSPECTIVES

This paper addresses new method to design observers with unknown inputs. The proposed approach is based on a decoupling and estimation procedure such that we decouple the state system towards exponential UI without any rank constraints on the system's matrix. The main result is about the way to find the UI class ensuring an exact decoupling. The proposed work can be extended to the nonlinear case, in particular, systems with Takagi-Sugeno representation.

  1 and go back to step 2. parameters : Λ = 1; λ = 0.7 et Γ = 0.2; γ = -0.4

Finally, the

  considered UI η k can be written as η k = η d k + η a k with η d k corresponds to the UI for exact decoupling and η a k the approximation error. The following figures are obtained for the initial conditions x 0 = 0.5 0.1 0.2 -0.1 T and x0 = -0.5 0.5 -0.4 0.2 T . Fig.1 shows the system inputs. Fig.2 represents the UIs (for the exact η k = η d k and partial decoupling cases η k = η d k + η a k ) and their estimates and Fig 3. represents the state system and their estimate for both situations of exact and partial decoupling. In both situations, the state estimate is satisfactory.

Fig. 2 .Fig. 3 .

 23 Fig. 1. System inputs

Fig. 4 .Fig. 5 .

 45 Fig. 4. UI estimate and system output without filter