Ali Amad
email: ali.amad@chru-lille.fr

Keywords: FKBP5, Borderline personality disorder, SNP, stress axis

Background

Genes associated with the physiological response to stress in the hypothalamic-pituitary-adrenal axis are considered as good candidates for genetic research in borderline personality disorder (BPD).

Methods

In this study, five FKBP5 (a co-chaperone of the glucocorticoid receptor) SNPs (rs3800373, rs9296158, rs737054, rs1360780, rs9470080) were genotyped in a sample of 101 unrelated Caucasian patients with BPD and 111 ethnically matched healthy controls. The interaction between FKBP5 polymorphisms and childhood trauma was also tested.

Results

All FKBP5 polymorphisms genotyped showed significant associations with BPD. A main effect of rs9470080 (p=0.01) and gene x environment (physical abuse) interaction (p=0.01) was found. A gene x environment (emotional abuse) interaction was also found for rs3800373 (p = 0.03). However, these interactions did not remain significant after multiple testing corrections.

Limitations

In this study, only 5 genetic variants were tested and thus tagging of the FKBP5 gene was incomplete.

Moreover, the sample size is moderate.

Conclusion

BPD is associated with FKBP5 polymorphisms and several types of childhood abuse may modulate the effect between FKBP5 SNPs and this disorder.

INTRODUCTION

Borderline personality disorder (BPD) is characterized by a pervasive pattern of emotional lability, disturbed cognition (such as derealization, depersonalization or hallucinations), identity disturbances, impulsivity and interpersonal difficulties (Lieb et al., 2004b). BPD is the most common personality disorder in clinical settings and is estimated to occur in 0.5-5.9% of the general population [START_REF] Skodol | The borderline diagnosis I: psychopathology, comorbidity, and personality structure[END_REF].

The knowledge on the biological factors involved in the pathophysiology of BPD is still scarce. Interestingly, a genetic vulnerability has been identified with a heritability estimated between 40 and 60 % [START_REF] Amad | Genetics of borderline personality disorder: Systematic review and proposal of an integrative model[END_REF]. However, the number of association studies using the candidate gene method is low considering both the heritability and the high frequency of BPD. For now, most candidate genes studied were genes involved in the monoaminergic neurotransmitter systems [START_REF] Leichsenring | Borderline personality disorder[END_REF]Lieb et al., 2004b).

It has recently been proposed that genes associated with the physiological response to stress in the hypothalamic-pituitary-adrenal (HPA) axis could be good candidates for genetic research in BPD [START_REF] Amad | Genetics of borderline personality disorder: Systematic review and proposal of an integrative model[END_REF]. In fact, many arguments support HPA axis dysregulation in BPD [START_REF] Zimmerman | The hypothalamic-pituitary-adrenal axis in borderline personality disorder: a review[END_REF] such as an increased diurnal salivary cortisol in women with BPD (Lieb et al., 2004a) or a non-suppression to the Dexamethasone Suppression Test [START_REF] Wingenfeld | Borderline personality disorder: Hypothalamus pituitary adrenal axis and findings from neuroimaging studies[END_REF]. Moreover, epigenetic modifications have been identified in glucocorticoid receptor genes in patients with BPD [START_REF] Perroud | Increased methylation of glucocorticoid receptor gene (NR3C1) in adults with a history of childhood maltreatment: a link with the severity and type of trauma[END_REF].

Recently, Martin-Blanco et al. have tested the association of genetic variants in the HPA axis by analyzing 47 polymorphisms in 10 HPA axis genes in BPD and controls. They found that two FKBP5 polymorphisms (rs4713902 and rs9470079) showed significant associations with BPD [START_REF] Martín-Blanco | The role of hypothalamus-pituitary-adrenal genes and childhood trauma in borderline personality disorder[END_REF]. Moreover, as the presence of a gene-environment interaction (G × E) is highly likely [START_REF] Amad | Genetics of borderline personality disorder: Systematic review and proposal of an integrative model[END_REF], these authors also explore the effect of childhood trauma in the development of BPD. They found that both FKBP5 polymorphisms were more frequent in patients who reported childhood physical abuse and emotional neglect [START_REF] Martín-Blanco | The role of hypothalamus-pituitary-adrenal genes and childhood trauma in borderline personality disorder[END_REF]. Interestingly, FKBP5 encodes the FK506-binding protein 5, which is involved in the regulation of glucocorticoid receptors and appears as an interesting candidate gene as it has been associated to HPA axis dysregulation in the general population and in patients with psychiatric stress-related disorders, especially in adults with a history of childhood maltreatment [START_REF] Zannas | Gene-environment interactions at the FKBP5 locus: sensitive periods, mechanisms and pleiotropism[END_REF].

The purpose of the present study was to investigate the contribution of different polymorphisms of FKBP5 and to explore the modulating effect of childhood abuse in an independent BPD sample. The Mini International Neuropsychiatric Interview (MINI, French version 5.0.0), a standardized psychiatric interview, was used to screen for major psychiatric disorders and substance abuse. BPD patients were not included if at least one of the following criteria was present: (a) dementia or any syndrome with obvious cognitive impairment, (b) doubts in the ability to give informed consent, (c) a current diagnosis of a psychotic disorder, (d) involvement in a legal procedure at the time of study participation, (e) not of Caucasian descent (to reduce genetic heterogeneity of the sample). Control subjects were also assessed for BPD with the personality disorder questionnaire 4+ (PDQ4) [START_REF] Fossati | Brief communication: criterion validity of the Personality Diagnostic Questionnaire-4+ (PDQ-4+) in a mixed psychiatric sample[END_REF] and were excluded if BPD or major psychiatric disorders or substance abuse were detected currently or in the past. All participants also filled in the Childhood Trauma Questionnaire (CTQ) [START_REF] Bernstein | Development and validation of a brief screening version of the Childhood Trauma Questionnaire[END_REF], a self-administered questionnaire designed to assess traumatic experiences in childhood.

MATERIAL AND METHODS

Participants

The study was approved by the local ethics committee (CPP Nord-Ouest IV, France). Written documentation of informed consent and capacity to provide consent was obtained from each participant before enrollment.

Genotyping

Genetic analyses were carried out on saliva samples (Oragene kit,DNA Genotek, Ottawa, ON, Canada), and DNA was extracted using standard methods. Five FKBP5 SNPs (rs3800373, rs9296158, rs737054, rs1360780, rs9470080) were genotyped using TaqMan SNP genotyping assay (Applied Biosystems, Life Technologies, Thermo Fisher Scientific, Waltham, MA, USA), detected on a real-time PCR DNA Engine OpticonTM 2 system (BIO-RAD, Hercules, CA, USA). Blanks and samples with known FKBP5 genotypes were taken along as quality controls during genotyping.

Statistics

Demographic and clinical characteristics of samples were compared for continuous variables using a univariate analysis of variance and categorical data were analyzed using overall Chisquared (χ2).

Deviations from Hardy-Weinberg equilibrium (HWE) and pairwise linkage disequilibrium (LD) between all the markers were calculated using Haploview (Version 4.1).

Logistic regression models were used to test the effects of each CTQ subscore (i.e., Physical Abuse, Emotional Neglect, Physical Neglect, Sexual Abuse, Emotional Abuse), FKBP5 genotypes, and their interaction in predicting BPD. Logistic regression models were performed in SAS 9.4.

RESULTS

All polymorphisms genotyped were in Hardy-Weinberg equilibrium.

Table 1 summarizes the results of the case-control association analyses. All FKBP5 polymorphisms genotyped showed significant associations with BPD. Haplotype comparisons between BPD and controls showed significant differences in the frequency distribution of FKBP5 (AAACC; p = 0.02) allele combinations (full haplotype data available on request).

In regression models, all childhood trauma exposure showed significant associations with risk of BPD (Supplementary Tables 1 and2). A main effect of rs9470080 (p=0.01) and gene x environment interaction (p=0.01) was found with physical abuse. A gene x environment interaction was also found for rs3800373 (p = 0.03) with emotional abuse. None of these interactions remained significant after multiple testing corrections (Bonferroni correction).

DISCUSSION

The present results support the hypothesis that genetic variation in the HPA axis genes contributes to BPD susceptibility [START_REF] Amad | Genetics of borderline personality disorder: Systematic review and proposal of an integrative model[END_REF][START_REF] Martín-Blanco | The role of hypothalamus-pituitary-adrenal genes and childhood trauma in borderline personality disorder[END_REF]. Indeed, in our sample all FKBP5 polymorphisms genotyped showed significant associations with BPD. Our results confirm the previous study of Marti-Blanco and collaborators who showed that two others FKBP5 polymorphisms were also associated with BPD [START_REF] Martín-Blanco | The role of hypothalamus-pituitary-adrenal genes and childhood trauma in borderline personality disorder[END_REF]. We also found a G x E between two SNPs (rs3800373 and rs9470080) and childhood emotional abuse, even if these results did not remain significant after multiple testing corrections.

FKBP5 is induced following stress exposure via binding of activated GR to several intronic and promoter GR response elements (GREs). The protein itself then binds to the GR complex, reduces the affinity of GR to cortisol and decreases translocation of the GR to the nucleus, providing an ultrashort negative feedback for GR activation on the genomic and protein level [START_REF] Zannas | Gene-environment interactions at the FKBP5 locus: sensitive periods, mechanisms and pleiotropism[END_REF].

FKBP5 has been associated to dysfunctions in HPA axis, both in the general population and in patients with stress-related disorders such as posttraumatic stress disorder (PTSD) [START_REF] Zannas | Gene-Stress-Epigenetic Regulation of FKBP5: Clinical and Translational Implications[END_REF]. Our results might be considered in line with the hypothesis that BPD and PTSD are the two sides of the same coin where one major main key difference could be the age at which trauma occurs [START_REF] Amad | The age-dependent plasticity highlights the conceptual interface between borderline personality disorder and PTSD[END_REF]. Indeed, it has recently been proposed that the conceptual interface between BPD and PTSD could be highlighted by the 'age-dependent neuroplasticity' framework which postulates that a same experience. FKBP5 is thought to be differently regulated according to the different periods of neurodevelopment [START_REF] Zannas | Gene-environment interactions at the FKBP5 locus: sensitive periods, mechanisms and pleiotropism[END_REF] and is also involved in the connectivity of brain regions and circuits related to mood regulation and cognitive function [START_REF] Holz | Role of FKBP5 in emotion processing: results on amygdala activity, connectivity and volume[END_REF]. There is also some evidence of age-dependent neuroplasticity following trauma, as it has been showed that the effects of stressors occurring early in development are stronger and more persistent in comparison with stressors occurring during adulthood [START_REF] Hoffmann | DNA memories of early social life[END_REF].

The present study had several limitations. Firstly, only 5 genetic variants were tested and thus tagging of the FKBP5 gene was incomplete. Secondly, our sample is small compared to others in the field of psychiatric genetics and therefore does not have the power to identify genome-wide associations. However, candidate studies remain of value and may generate interesting findings and hypothesis. Future studies should include internal replication or larger samples to provide sufficient statistical power to detect small effects, as is the case in collaborative studies with large samples.

  101 unrelated Caucasian patients with BPD (male/female = 15.8/84.2; 34.2 ±10.4 years old) and 111 ethnically matched healthy controls (male/female = 9.6/90.4; 24.1 ± 7.5 years old) were recruited from a psychiatric department of a French university hospital in Lille. A current diagnosis of BPD was assigned on the basis of the French version of the Structured Clinical Interview for DSM-IV axis-II. Interviews were conducted by trained and experienced raters. DSM-IV axis I disorders were evaluated with the Mini International Neuropsychiatric Interview.

Acknowledgements

The authors want to thank all participants for their support of the study. The authors also want to thank all the collaborators who helped to collect the data and particularly the IFSI Saint-Venant EPSM Val de Lys Artois.

Conflicts of interest


Sofyane Andjouh

Yves Blache
email: blache@univ-tln.fr

Parallel synthesis of a bis-triazoles library as psammaplin A analogues : a new wave of antibiofilm compounds?

Nowadays, eradication of bacterial biofilms still remains a challenge for chemists and microbiologists in many economical sectors. These include medical health care since they colonize implants such as artificial joints or catheters. 1 While in marine environment, the formation of biofilms on immersed substrata, leads to major economic problems which conducted to the use of toxic biocides to fight against these communities. [2][3][4] In this context, development of original compounds that specifically target the biofilm formation is of great need in view of rational use of antibiotics and/or biocides. Such biofilm inhibitors should have the potential to be used in a preventive treatment of a wide diversity of industrial and/or medical surfaces. Some of the antibiofilm techniques, that are tested today, are based on the observation of sessile marine macroorganisms (sponges, corals) which are constantly exposed to undesirable bacterial colonization (e.g. biofouling). 5 To cope with biofouling and maintain unfouled exterior surfaces, several of them have developed various defense systems. [5][START_REF] Krug | Defense of benthic invertebrates against surface colonization by larvae: A chemical arms race[END_REF][START_REF] Kirschner | [END_REF][8][9] This observation has motivated investment in the research of potential "non-toxic" antibiofilm compounds from their arsenal of secondary metabolites. [10][11][12][13][14] Therefore, use of such secondary metabolites on a large scale appears to be difficult to achieve since they are obtained in small quantities. These factors led to the synthesis of analogues, by maintaining the natural framework in order to retain biological activity. For this purpose, we have developed a new synthetic plan, based on click chemistry, allowing a rapid and efficient synthesis of libraries of bromotyramine/triazole analogues at a suitably large scale. 15,16 Click chemistry is a highly efficient process for the generation of compound libraries. 17 In addition, the 1,2,3-triazole ring has been explored as bioisosteres in medicinal chemistry of several chemical functions. 18 Number of compounds containing this ring have shown a broad spectrum of biological activities. [19][20][21][22] In continuation of our investigations, the present study consists in the preparation of a series of psammaplin A analogues possessing a two triazolic core. Psammaplin A, was extracted from the marine sponge Pseudoceratina sp. and was shown to exhibit interesting biological activities, such as antibacterial or anticancer properties. 23,24 The targeted library (Figure 1)was constructed by considering three points of chemical diversity : 1) a biosoteric replacement of the oxime/amide fonctions by 1,2,3-triazole core, since we have demonstrated that the bioisoteric replacement of an oxime by a 1,2,3-triazole was successful to afford somesinteresting elements of structure-activity relationships (SAR) in the field of antibiofilm compounds derived from the group of bromotyrosine alkaloids. 15,16 . In addition, recent reports described the diversity-oriented synthesis of pyrrolidinyl triazoles as biosisosteres of some pyrrolidinyl oxime (an mPTP blocker as a viable therapeutic target for the treatment of Alzheimer's disease). 25 2) The second point concerns the replacement of the disulfide linker by different chemical classes of linker.3) Finally, substituents on aromatic rings were considered in agreement with those found in the bromotyrosine alkaloids. 26 , 27 Ability of the resulting analogues to inhibit biofilm formation of three bacterial strains was investigated in order to establish SAR.

1 3a (96%) 3c R = -(CH 2 ) 2 -N(CH 3 ) 2 (99%) 3d R = -(CH 2 ) 3 -N(CH 3 ) 2 (98%) 2 (97%) (i) : BBr 3 (1.5eq.)/CH 2 Cl 2 , 0°C, rt, 4h (ii) : NaN 3 /DMF, 5h, 90°C (iii) : K 2 CO 3 ,18-Crown-6, acetone,reflux (i) (ii) (iii) RO N 3 Br RO N 3 Br 3b R = Me (ii)

Scheme 1. Preparation of starting azides 3a-d

The second level of chemical diversity was introduced by three kinds of linkers chosen from commercial sources: alkyl chain containing 3,4 and 6 carbons, two heteroatomoic dialkynes (oxygen and nitrogen), and finally two aromatic systems. The formation of the bis-triazole analogues was then achieved by performing the copper(I)-catalyzed 1,3-dipolar cycloaddition of the organic azides with appropriate dialkynes resulting in the formation of two 1,2,3-triazoles. In general, these reactions usually proceed to completion in 6-36 h at room temperature in water with a variety of organic co-solvents, such as tert-butanol, ethanol, DMF, DMSO, THF or CH 3 CN. 28,[START_REF] Huisgen | 3-Dipolar Cycloaddition Chemistry[END_REF] Ethanol was usually chosen rather than DMF to allow an easier workup and a better purity of products as described in our previous work but in this case DMF was used because of the poor solubility of the resulting bis-triazoles in ethanol. Practically, 1 equivalent of dialkyne was added to a solution of appropriate azide (3a-d, 2.6 equivalents), CuSO 4 /sodium ascorbate in a water/DMF mixture (50/50) and the reaction time was optimized at 24 hours at room temperature. Results reported in table 1 show that all compounds were obtained in excellent yields (>77%), but it is notable that compound 5g bearing an 1,4-linked aromatic ring could not be isolated and purified for further biological tests.

- 93% 4d H -CH 2 -O-CH 2 - 87% 4e H -CH 2 -NH-CH 2 - 63% 4f H 77% 4g H 80% 5a CH 3 -(CH 2 ) 3 - 91% 5b CH 3 -(CH 2 ) 4 - 96% 5c CH 3 -(CH 2 ) 6 - 97% 5d CH 3 -CH 2 -O-CH 2 - 93% 5e CH 3 -CH 2 -NH-CH 2 - 88% 5f CH 3 90% 5g CH 3 Not purified 6a (CH3) 2 N-(CH 2 ) 2 - -(CH 2 ) 3 - 93% 6b (CH3) 2 N-(CH 2 ) 2 - -(CH 2 ) 4 - 94% 6c (CH3) 2 N-(CH 2 ) 2 - -(CH 2 ) 6 - 89% 6d (CH3) 2 N-(CH 2 ) 2 - -CH 2 -O-CH 2 - 98% 6e (CH3) 2 N-(CH 2 ) 2 - -CH 2 -NH-CH 2 - 84% 6f (CH3) 2 N-(CH 2 ) 2 - 84% 6g (CH3) 2 N-(CH 2 ) 2 - 88% 7a (CH3) 2 N-(CH 2 ) 3 - -(CH 2 ) 3 - 89% 7b (CH3) 2 N-(CH 2 ) 3 - -(CH 2 ) 4 - 93% 7c (CH3) 2 N-(CH 2 ) 3 - -(CH 2 ) 6 - 87% 7d (CH3) 2 N-(CH 2 ) 3 - -CH 2 -O-CH 2 - 85% 7e (CH3) 2 N-(CH 2 ) 3 - -CH 2 -NH-CH 2 - 79% 7f (CH3) 2 N-(CH 2 ) 3 - 92% 7g (CH3) 2 N-(CH 2 ) 3 - 88%
In order to assess anti-biofilm activity of these compounds against representative Gramnegative bacterial biofilms, three strains were chosen for their capacity to form biofilms:

Pseudoalteromonas lipolytica (TC8), Pseudoalteromonas ulvae (TC14) and a Paracoccus sp. strain (4M6). [START_REF] Brian-Jaisson | [END_REF] In an initial screening process, all compounds were tested for their ability to modulate biofilm formation at concentration of 200 µM by using our previous method adapted from Leroy et al. using the specific fluorophore Syto ® 61 [31][32] . Partial information about structure-activity relationship (SAR) could be highlighted at this stage: all compounds possessing an alkyl-type linker (series a, b, c) were inactive (less than 50% of inhibition of the adhesion). Replacement of the carbon in the series a by an oxygen (series d) or nitrogen (series e) enhanced the activity. Considering aromatic linkers (series f and g), only the compounds connected in the 1,4-positions were founded to be active (series g). In order to precise structure-activity relationships, effective concentrations to inhibit 50% of the bacterial adhesion (expressed as EC 50 ) were determined for compounds 4d-g, 5d-e, 6d-g, 7d-g which inhibited more than 50% of adhesion at 200 µM. Results of this screen are outlined in Table 2. In this way, first observation was to note that globally the TC14 strain was more sensitive to this class of bis-triazoles than TC8 and 4M6 strains. Among the three classes tested, series g possessing an 1,4-linked aromatic ring as central part (4g, 6g, 7g) were the more potent compounds especially 6g an 7g with EC 50 closed to ampicillin and tributyltin oxide (TBTO). In term of SAR, it is interesting to note that the dimethylaminoethyl chain (6g) as well as the dimethylaminopropyl chain (7g) are common natural framework found in bromotyrosine alkaloïds possessing antifouling properties, and that this class of substituents afforded a beneficial aspect when compared to simple hydroxyl or methyl groups found in alkaloids extracted from sponges such as aplysamines or hemibastadins or simple 2-(3′-Bromo-4′hydroxyphenol)ethanamine. In order to determine if these compounds exhibited a specific anti-biofilm activity or if this observation was simply related to a general toxic effect on the bacteria, a growth inhibition and viability assay was performed. Active compounds 6g and 7g were tested for their capacity to inhibit the growth of the three strains TC14, TC8 and 4M6. Experiments were performed at the high concentration of 100 µM (fig. 2a, 2b, 2c) and using ampicillin at a concentration of 5 µM.

At these concentrations, the two compounds presented bacteriostatic effects on the three bacterial strains. A slight effect was observed for compound 7g while compound 6g exhibited effects much more closed to ampicillin especially on the TC8 and 4M6 strains which seems to be more sensitive than TC14. For viability, the same methodology used for antiadhesion assay with Syto ® 61 was applied using resazurin test at the concentrations of 5, 10, 20, 50, 100, 200 µM. Results at 5 and 100 µM are reported in figure 3 (see supplementary materials for detailed results). At a low concentration of 5 µM, concentration closed to their EC 50 as antibiofilm compounds, compounds 6g and 7g were not lethal to bacteria . This suggested that their anti-biofilm activities were not directly connected to antibacterial effect in contrast to ampicillin which is toxic especially to TC14 and TC8. Furthermore, at the high concentrations (100 µM), compounds6g and 7g presented a slight bactericidal effect on the three strains. In addition, it is important to note that the antibiofilm effect of ampicillin seems to be directly related to its antibacterial effect. In fact, the good antibiofilm activities observed on TC14 and TC8 (EC 50 in the range of 5 µM) were related to high toxicity, while no antibiofilm effect (EC 50 = 146 µM) was associated with a low toxicity on 4M6 strains.

In conclusion, we have used click chemistry to generate a library of psammaplin A analogues based on a bis-triazole framework. In the present paper, we have generated a preliminary screening for analogues that can be designed to be selective against gram negative bacteria. Potent inhibitors of biofilm formation have been identified. Finally, the low toxicity of the more potent anti-biofilm leads allows us to focuse on future interest in the development of these molecules as non-toxic antibiofilm compounds for their potential use as non-toxic co-biocides or co-antibiotic in view of rational eradication of persistent biofilms.

Figure 1 .

 1 Figure 1. Structure of psammaplin A and of targeted library

Figure 2a .Figure 2c .

 2a2c Figure 2a. Effect on TC14 growth of compounds 6g,7g at concentrations of 100 µM

Figure 3 .

 3 Figure 3. effect on TC14, TC8, and 4M6 viability of compounds 6g and 7g at concentrations of 5 and 100 µM.

Table 1 .

 1 Synthesis of psammaplin A analogues

	3a-d	24h, rt DMF/H 2 O(2:1) CuSO 4 /NaAsc linker	RO	Br	N N	N	linker	N	N	N	Br	OR
						28 analogues
							BT1-28
	compound		R							linker	yield
	4a			H							-(CH 2 ) 3 -	92 %
	4b			H							-(CH 2 ) 4 -	87%
	4c			H							-(CH 2 ) 6

  33

Table 2 .

 2 Antibiofilm activity of psammaplin A bioactives analogues

	cpd		TC14 a		TC8 a		4M6 a
		% of adhesion b	EC 50	% of adhesion b	EC 50	% of adhesion b	EC 50
				Series a
	4a 5a 6a 7a	53.1 ± 4.1 > 200 µM 50.4 ± 2.2 > 200 µM 55.8 ± 3.8 > 200 µM 53.8 ± 5.9 > 200 µM	63.5 ± 8.1 50.0 ± 4.9 57.0 ± 2.2 59.9 ± 6.4	> 200 µM > 200 µM > 200 µM > 200 µM	83.4 ± 3.9 49.2 ± 0.8 51.5 ± 3.0 77.2 ± 2.5	> 200 µM > 200 µM > 200 µM > 200 µM
				Series b
	4b 5b 6b 7b	54.4 ± 1.8 > 200 µM 53.3 ± 6.3 > 200 µM 61.5 ± 1.0 > 200 µM 66.5 ± 5.6 > 200 µM	85.6 ± 2.1 56.9 ± 1.7 58.5 ± 4.3 89.2 ± 4.8	> 200 µM > 200 µM > 200 µM > 200 µM	52.4 ± 2.3 50.9 ± 0.3 57.4 ± 1.6 80.7 ± 8.8	> 200 µM > 200 µM > 200 µM > 200 µM
				Series c
	4c 5c 6c 7c	61.7 ± 6.7 > 200 µM 62.7± 3.1 > 200 µM 67.4± 4.0 > 200 µM 71.0 ± 4.1 > 200 µM	75.0 ± 5.2 78.3 ± 0.6 54.4 ± 10.8 72.3 ± 1.4	> 200 µM > 200 µM > 200 µM > 200 µM	78.1 ± 1.2 69.2 ± 0.5 59.5 ± 2.2 84.7 ± 1.4	> 200 µM > 200 µM > 200 µM > 200 µM
				Series d
			127.1 ±		194.9 ± 10.7		198.3 ± 4.1
	4d	40.3 ± 3.3	27.6	50.3 ± 5.8		47.8 ± 0.1
			159.8 ±		180.8 ± 21.3		164.1 ± 6.3
	5d	38.5 ± 7.4	33.5	42.8 ± 6.6		44.9 ± 3.2
	6d	34.8 ± 2.8 91.8 ± 17.9	34.6 ± 5.1	101.6 ± 46.2	40.4 ± 7.8	146.2 ± 81.9
			121.7 ±		>200		>200
	7d	41.7 ± 1.7	59.1	51.6 ± 1.5		53.7 ± 4.0
				Serie e
	4e	29.3 ± 7.5 59.9 ± 27.2	28.9 ± 17.0	80.3±18.9	27.9 ±1 6.0	88.3 ± 46.3
	5e	37.4 ± 0.1 138.4 ± 8.7	48.2 ± 2.2	187.9±3.0	46.3 ± 2.7	194.5 ± 8.0
			126.2 ±		176.5±3		>200
	6e	40.9 ± 5.0	21.6	47.1 ± 1.0		51.8 ± 4.4
	7e	45.0 ± 0.8	>200	55.4 ± 0.4	185.2±16.4	56.3 ± 2.4	>200
	4f 5f 6f 7f	56.8 ± 1.3 > 200 µM 74.1 ± 1.1 > 200 µM 62.2 ± 0.4 > 200 µM 65.3 ± 6.9 > 200 µM	Series f 66.5 ± 11.6 101.1 ± 4.8 65.1 ± 8.8 71.6 ± 2.8	> 200 µM > 200 µM > 200 µM > 200 µM	61.5 ± 4.2 76.2 ± 1.7 66.9 ± 1.8 78.1 ± 2.2	> 200 µM > 200 µM > 200 µM > 200 µM
				Series g
			40.9 ±		>200		59.9 ± 7.7
	4g	31.1 ± 6.2	11.41	58.3 ± 8.7		31.8 ± 3.5
	6g	0 ± 5.3	0.9 ± 0.83	14.6 ± 11.8	5.1±1	10.1 ± 8.1	5.1 ± 1.0
	7g	0.6 ± 0.8	0.4 ± 0.28	5.3 ± 2.5	15.0±3.38	5.1 ± 1.43	3.5 ± 3.0
	TBTO	ND	0.7 ± 0.3	ND	7.0 ± 3.0	ND	4.0 ± 3.0
	ampicillin	ND	9.3 ± 0.2	ND	17.9 ± 0.9	ND	144.1 ± 12.3

a TC14 : Pseudoalteromonas ulvae, TC8 : Pseudoalteromonas lipolytica, 4M6 : Paracoccus sp. b % of adhesion at 200 µM c ND : not determined, EC 50 > 200 µM

Acknowledgments: This work was financially supported by the Université de Toulon (S. A. PhD grant). We are especially grateful to LBCM laboratory (Université de Bretagne Sud, France) for the supply of the 4M6 strain.


M.D Jérémie Bettoni
email: jeremiebettoni@gmail.com

Matthieu Olivetto

Caroline Racz

Stéphanie Dakpé

Non-febrile spontaneous neck pain in a patient with diabetes

Keywords: Dermohypodermatitis, Necrotizing fasciitis, Neck, Management, Negative pressure wound therapy

Text (500 words)

A 71-year-old-man with a medical history of type II diabetes treated by metformin presented to our emergency department for a posterior neck pain that had been worsening for three days. Despite stable hemodynamic values (temperature 36.2°C, blood pressure 134/80 mmHg, heart rate 79 beats/min), the physical examination revealed neck inflammation with multiple purulent pustules (Fig. 1 ) and limited active and passive neck motions due to pain. Laboratory analysis revealed a severe inflammatory syndrome with marked polymorphonuclear hyperleukocytosis (9.9/mm 3 -normal range: 1.5 to 7) and a C-Reactive Protein level of 153 mg/L (normal range, < 5). A CT scan showed diffuse subcutaneous emphysema and musculocutaneous infiltration of the trapezius muscle with no deep accumulation (Fig. 2).

What is your diagnosis?

Clinically, the progressive worsening of a local anaerobic and necrotic skin infection in a patient with diabetes without severe general repercussions must lead to a suspicion of mixed necrotizing bacterial dermohypodermatitis (NBDH) [START_REF] Bouvet | Cellulitis and necrotizing fasciitis: microbiology and pathogenesis[END_REF]. A CT scan allows for visualization of the muscle damage and make the diagnosis of necrotizing fasciitis.

It also helps the surgeon with the debridement procedure [START_REF] Malik | An algorithm for early diagnosis of cervicofacial necrotising fasciitis[END_REF].

Despite the absence of general repercussions at the time of diagnosis, NBDH associated or not with necrotizing fasciitis constitutes a medico-surgical emergency with a life-threatening prognosis [START_REF] Derancourt | Management of necrotizing cellulitis and fasciitis[END_REF] requiring multidisciplinary management based on [START_REF]Conférence de consensus. Erysipèle et fasciite nécrosante : prise en charge[END_REF]:

• treating symptoms of sepsis to correct possible hypovolemia, hydroelectrolytic anomalies, or acidosis and maintaining stable hemodynamic values;

• administering probabilistic broad-spectrum antibiotic therapy, combining penicillin G and clindamycin in the case of head and neck location. Treatment must begin as soon as bacteriological samples are taken (blood culture, tissue, and pustular fluid), targeting both Gram+ and Gram-anaerobic and aerobic bacteria, until bacteriological sample results are received;

• performing surgical exploration under general anesthesia, allowing for excision of the affected tissue. The viability of muscles is assessed macroscopically by their appearance and contraction in response to mechanical stimulation or electrocoagulation. The surgical procedure also allows for collecting deep bacteriological samples and for culture in aerobic and anaerobic conditions, that is essential for the secondary adjustment of antibiotic treatment.

Once surgical debridement has been performed, the surgical site must be left open to limit proliferation and microbial colonization and to allow for abundant washing during nursing care. Once the underlying tissue is deemed of good quality, the use of bud stimulating products or transition to negative pressure wound therapy is possible [START_REF] Frankel | Use of negative pressure wound therapy with instillation in the management of cervicalnecrotizing fasciitis[END_REF]. Depending on the size of the loss of substance and on the quality of the deep layers, reconstruction may be obtained either by controlled wound healing

Figure 2 :

 2 Figure 2 : Axial CT scan with injection of contrast medium showing dermohypodermatitis, myositis

Figure 3 :

 3 Figure 3: Clinical view two months after initial management and one month following split

or by split thickness skin grafting. The use of a pedicled or a free flap is rare and reserved for cases of articular or vascular exposure.

In our case, a split thickness skin graft was performed after 10 days of alginate dressing and 3 weeks of negative pressure wound therapy, with an acceptable esthetic result (Fig. 3).

Conflict of Interest Statement: None


Trung-Kien Hoang

Lionel Vido

Frederic Gillon

Mohamed Gabsi

Structural Optimization to Maximize the Flux Control Range of a Double Excitation Synchronous Machine

Keywords: Double excitation, electric vehicle, permanent magnet, structural optimization, synchronous machine

This paper deals with a structural optimization to maximize the no-load flux control capability of a double excitation synchronous machine (DESM). The air-gap flux in this machine type can be regulated by controlling the field currents. In this paper, this curve in the no-load condition is referred to as the flux control range (FCR). Maximizing the gap between the minimum-flux and maximizing the maximum-flux points of this curve is targeted to improve the controlling effectiveness of the field windings, and reduce field winding's copper losses. This gap is affected by two factors: the magnetic saturation and thermal limits of the machine. Thermal analyses are rarely focused for the DESM type in the literature. The contribution of this paper is to maximize the FCR gap taking into account the thermal limitation. In addition, a general guide for the DESM design will be also discussed.

Introduction

A Double Excitation Synchronous machine (DESM) introduces additional field windings in a conventional permanent magnet synchronous machine (PMSM) [START_REF] Nedjar | A new parallel double excitation synchronous machine[END_REF][START_REF] Vido | Homopolar and bipolar hybrid excitation synchronous machines[END_REF][START_REF] Tapia | Consequent-pole permanent-magnet machine with extended field-weakening capability[END_REF][START_REF] Liang | Permanent magnet electric machine with flux control[END_REF][START_REF] Akemakou | Dual excitation electrical machine, and especially motor vehicle alternator[END_REF][START_REF] Radomski | Alternating current generator[END_REF]. The air-gap flux can be weakened or enhanced by adjusting field currents. It is desirable to improve the effectiveness of the field currents to reduce the copper losses associated with this flux controlling. In this paper, optimizing the air-gap flux characteristic is means to maximize the gap between the minimum-flux and the maximum-flux points, this gap is called the FCR gap. In a research conducted by Nedjar et al., the flux regulations of different DESM structures were compared, and the authors proposed one design, in which the air-gap flux can be completely canceled [START_REF] Nedjar | A new parallel double excitation synchronous machine[END_REF]. Amara et al. showed advantages of a parallel DESM over a series one in terms of the no-load flux control capability [START_REF] Amara | Comparison of open circuit flux control capability of a series double excitation machine and a parallel double excitation machine[END_REF]. In [START_REF] Hoang | Flux control range broadening and torque ripple minimization of a double excitation synchronous motor[END_REF], the FCR was maximized using a parametric design method. All above works, however, did not consider the thermal aspect. Therefore, the obtained results probably overestimated the machine's flux controlling capability. This paper takes into account the thermal limitation so as to more comprehensively evaluate the machine's performances. Due to a numerous model evaluations, an electromagnetic model, which is constructed by using an equivalent magnetic circuit network (EMCN) method, will be adopted instead of the time-consuming finite element method (FEM). The FEM is used to validate the proposed model's accuracy. The thermal analysis is carried out by using a lumped parameter model, where the model's empirical coefficient calibrations are accomplished from measurements. These electromagnetic and thermal models are coupled to each other. The design constraint to be considered in this paper is that the machine must be able to handle the rated and maximum-speed points of a torque envelop curve, which will be introduced later on. The other optimization objective is to minimize the machine's volume since it is necessary for vehicle applications. This paper will be organized as follows: firstly, the DESM topology is presented. Secondly, the machines' modeling by the EMCN and lumped parameter thermal network will be addressed. Thirdly, some design variables and theirs sensitivities are examined. Then, the optimization and result discussion will be introduced, the Multi-objective Particle Swarm Optimization (MOPSO) approach is employed for the bi-objective optimization. Lastly, a conclusion is presented.

DESM prototype

DESM topology

The 3-kW DESM topology is shown in Fig. 1a, which was a prototype presented by Vido et al. [START_REF] Vido | Homopolar and bipolar hybrid excitation synchronous machines[END_REF]. This model belongs to the parallel type, in which the flux sources created by field windings do not pass through the PMs. The parallel type was proved to be advantageous over the series configuration in respect of controlling the no-load flux [START_REF] Amara | Comparison of open circuit flux control capability of a series double excitation machine and a parallel double excitation machine[END_REF]. In this prototype, two toroidal field windings carrying currents in opposite directions are placed in the stator. This arrangement, therefore, helps to avoid sliding contacts. Ferrite PMs are utilized and located in the rotor using the flux concentration principle. The magnetization directions of PMs are displayed in Fig. 1a. Due to the fact that some flux paths are truly three dimensional as detailed later on in Fig. 2 and Fig. 3, solid cores are advised to employ in some regions. With the directions of field currents being assumed in Fig. 1a, the machine is in the flux enhancing mode. Several parameters given in Table . 1 are fixed in the design optimization.

Basic working principle

The parallel double excitation principle of the DESM prototype owns somewhat complex flux paths as shown in Fig. 2 for bipolar flux paths and Fig. 3 for the homopolar flux paths. Simply, homopolar flux paths create only one type of pole (north or south) under the active part. Meanwhile, bipolar flux paths create north and south poles under the active part [START_REF] Vido | Homopolar and bipolar hybrid excitation synchronous machines[END_REF]. Field windings only generate homopolar flux paths, while PMs produce both types. The bipolar flux paths created by PMs in Fig. 2 are similar to those of a conventional PM machine.

FCR of the prototype

The experimental FCR of the prototype is shown in Fig. 1b. The peak-flux quantity in the vertical axis's legend is meant the peak of the no-load phase flux linkage. The maximum-flux and minimum-flux points are also displayed for this particular experiment. These two points depend on the magnetic saturation and thermal limitation of the machine. It is desirable to broaden the FCR gap. As it can be seen, lowering the minimum-flux point to be close to zero represents a highly desired flux weakening capability. Regarding the electromagnetic aspect, the maximum-flux is limited by the magnetic saturation in the stator teeth, while the minimum-flux is limited by the saturation in the end-shield parts. The magnetic flux density maps corresponding to the minimum-flux and maximumflux points in Fig. 1b are displayed in Fig. 4. 3. Electromagnetic and thermal modeling

Electromagnetic modeling by EMCN

The electromagnetic model is accomplished by using the EMCN method. The meshing idea of the machine's network is presented in Fig. 5a. The whole machine is decomposed into three main parts (parts 1, 3 , and 5 shown in Fig. 5a). These main parts are based on the four-reluctance-block network.

It means that at each node, flux paths are allowed to flow in only tangential and radial directions, i.e., a bi-directional block. In order to account for the 3-D flux paths, parts 2 and 4 work as the links between the three main parts. These two parts are based on one-reluctance blocks, where flux only flows in one direction, i.e. an unidirectional block. The nonlinearity is handled by iteratively solve the system equation using the fixed point method. The electromagnetic model provides copper and irons losses calculation as the heat source to the thermal model. The unit core loss [W/m 3 ] is calculated as (1) [START_REF] Lin | A dynamic core loss model for soft ferromagnetic and power ferrite materials in transient finite element analysis[END_REF]. This formula considers harmonic contents.

P Fe = k h f Bα + k e 2π 2 T T 0 dB dt 2 dt (1)
where k h , α and k e are core loss coefficients determined from sample measurements, f is frequency of flux density waveform, and T = 1/f . The copper loss of a winding is computed by [START_REF] Vido | Homopolar and bipolar hybrid excitation synchronous machines[END_REF].

P Cu = I 2 R [1 + β(θ -20)] ( 2
)
where I is the winding's RMS current, R is the winding resistance at 20 , β is the thermal coefficient of the winding at 20 , and θ is the winding temperature.

The accuracy validations against the FEM mothod are shown in Fig. 6a and Fig. 6b for the generated torque and iron loss, respectively.

(a) (b)

Lumped parameter thermal network

A lumped parameter thermal model can benefit from a fast computation while maintaining a good accuracy [START_REF] Nerg | Lumped-parameter-based thermal analysis of a doubly radial forcedair-cooled direct-driven permanent magnet wind generator[END_REF][START_REF] Fodorean | A double excited synchronous machine for direct drive application: Design and prototype tests[END_REF]. The thermal network is shown in Fig. 5b, which is capable of dealing with the transient process by introducing thermal capacitors. As it can be in Fig. 5b, two types of thermal resistance are presented: one uses a simple thermal coefficient, and the others require empirical coefficients. The first type can be easily computed based on the object's geometry. The second one is more challenging, and the coefficients based on experiments or design experiences are usually required.

The cooling, which is the natural air convection for the prototype, is modeled by the thermal resistance R ambient using the surface heat transfer coefficient. For the natural air convection, this coefficient strongly depends on the surface temperature. The heat source consists of copper losses and iron losses derived from the electromagnetic model. The mechanical loss, which consists of windage and bearing friction losses, is neglected. The winding temperature is assumed uniform across the winding. The thermal model validation in the transient mode against the experimental result is displayed in Fig. 7.

In this validation, the rotor does not rotate, phase and field currents are all set to 4 A. The winding's temperature is derived on the basis of the resistance change of that winding. For the design optimization, the machine is assumed to cooled by water, whose the surface heat transfer coefficient is 300 W/ o C/m 2 . The coupling between the electromagnetic and thermal models is accomplished in the way that the thermal model is to calculate windings' temperatures and the electromagnetic model is to recalculated copper losses with the newly updated windings' temperatures. The updated copper losses will update the thermal model with the recalculated copper losses. The process continues until the temperatures converge. Note that, the iron losses are assumed temperature-independent.

Design variables and sensitivity analyses

The design objectives are to maximize the FCR gap and minimize the machine's volume. The design, however, must also satisfy constraints at two operating points of a torque envelop curve: the rated and maximum speed points shown in Fig. 8, which are (27 Nm, 2000 rpm) and (14 Nm, 4000 rpm), respectively. In this section, several design variables will be presented. Their sensitivity analyses will be performed. Aiming at clearly showing influences of variables on the objectives, the constraints are not considered in this step. There are 10 design variables to be considered as shown in Fig. 9. variable x 4 , which is the azimuth PM ratio, is calculated as the occupation of the PM at the radius level (x 2 + l b ), given by (3).

x 4 = W A-PM 2π(x 2 + t b )/12 (3)
where W A-PM is the width of the azimuth PM and t b is the thickness of the rotor yoke, which is given in Fig. 9. For all designs, the ratio between t b and the shaft radius is assumed to be 38%, which is the same as that of the prototype. The variable x 7 , which is the stator tooth surface ratio, is calculated as the portion of the total stator tooth surfaces over the periphery of the inner stator's surface. Among design variables, only two variables x 4 , and x 7 do not influence the machine's volume. However, x 7 affects the armature winding's window and hence the thermal performance of the machine. All other variables will increase the machine's volume as they increase. Therefore, the sensitivity analyses will be presented only for the FCR gap minimization objective. The sensitivity analyses, which are shown in Fig. 10, are based on the dimensions of the prototype with the principle that only one variable changes at a time. Details of FCR curves are displayed in Fig. 11. The results shown in Fig. 11 are obtained by two steps:

1) The maximum field current density J f max is obtained for a given machine based on the thermal analysis with zero armature currents since only the FCR at the no-load condition is concerned.

2) For each machine, the FCR curve is derived from a set of 20 values of the field current density equally spaced from -J f max to J f max , the minimum-flux and maximum-flux points are determined from this set (exhaustive search approach). The influences of design variables as seen in Fig. 10 and Fig. 11 are summarized in the following. Note that, the maximum-flux point is limited due to the magnetic saturation in the stator teeth, and the minimum-flux point is limited due to the magnetic saturation in the end-shields as already shown in Fig. 4.

x 1 -Axial stack length: Increasing this value will increase both the minimum-flux and maximum-flux points as the flux contribution from azimuth PM increases. In addition, the saturation in the stator teeth will be mitigated, the FCR gap will increase as a result.

x 2 -Shaft radius: As the shaft radius increases, the air-gap diameter will increase. In addition, the stator tooth surface will increase as well. So the effectiveness of the field winding will increase in both flux weakening and flux enhancing. In overall, the FCR gap increases as the x 2 increases.

x 3 -Azimuth PM height: Increasing this height will increase the air-gap diameter. Therefore, the minimum-flux and maximum-flux all increase. In addition, the field winding's winding slightly increases leading to early saturations as seen in Fig. 11.

x 4 -Azimuth PM ratio:

Increasing this PM ratio will lower the counter-effective flux created by the field windings, and the FCR gap is improved.

x 5 -Side PM thickness:

The effect of increasing this thickness is similar to that of the azimuth PM ratio. In addition, increasing this value will increase the field winding's window, and the field winding's magnetomotive force (MMF) increases (with the same amount of field current density). Therefore, the saturation occurs earlier as shown in Fig. 11.

x 6 -Rotoric flux collector thickness:

The main effect of increasing this thickness is to increase the field winding's window. As the result, the minimum-flux and maximum-flux values are almost the same for different thicknesses, just the saturation occurs earlier when this thickness increases.

x 7 -Stator tooth surface ratio: Increasing this value has a similar impact as increasing the axial stack length x 1 , the saturation is mitigated and the FCR gap increases.

x 8 -Stator tooth height: Increasing this value will make the machine bigger, the saturation in the stator teeth does not change so that the maximum-flux stays almost constant. However, as the field winding's window slightly gets larger, a high field current density is allowed and a lower minimum-flux can be achieved. Therefore, the FCR gap increases as x 9 increases.

x 9 -Inner stator yoke height: Increasing this value will increase the field winding's window as well as the field winding's MMF (with the same field current density). This explains the "narrow-area" effect of x 9 on the FCR. Moreover, the total field winding's MMF is able to reach a higher value leading to a lower minimum-flux point. The maximum-flux point remains unchanged as the stator teeth's saturation does not vary. Therefore, the FCR gap increases as x 9 increases.

x 10 -End-shield's thickness: Increasing this thickness will lower the air-gap reluctance below the end-shields, this results in a less field current is required to regulate the air-gap flux.

In the following, a bi-objective optimization will be carried out taking into account the torque envelop requirement constraint.

Optimization, results and discussion

Optimization formulation

Since there are constraints for two operating points (rated and maximum-speed points), two subprocedures are required for each machine. These two sub-procedures aim at ensuring if the machine is able to generate the required torques at required speeds without violating the winding's temperature and voltage limits. Because the sub-procedure is not an optimization, a run with 50 randomly-chosen control variable sets (d-, q-axis armature currents and the field current density J f ) is examined to decide if the machine satisfy the constraints. This approach is considered as a compromise between the computation time and the optimization quality. As the machine satisfies two constraints, the FCR gap is obtained based on the approach presented in section 4. The machine's volume is easily computed based on the stator outer diameter and machine's total axial length, i.e., the stack length plus the field windings' width and end-shields' thickness. The optimization is formulated as (4). Note that, the maximizing FCR gap objective is transformed to minimizing "-FCR gap" to have a min-min optimization problem, which is common in optimization demonstrations.

Minimize

X=[x 1 ÷x 10 ] F (X) = -FCR

Optimization result and FEM validation

The MOPSO technique [START_REF] Aubry | Bi-objective sizing optimization of a pm machine drive on an operating profile[END_REF] is used for the optimization. This optimization technique is an evolutionary computation optimization (a search method based on a natural system) developed by Kennedy and Eberhart [START_REF] Kennedy | Particle swarm optimization[END_REF]. A combination of 60 particles and 50 iterations, i.e. 3000 machines are examined, the computation time is 87 hours on a quad-core, 2.93 GHz, 12 Gb of RAM. Note that, this computation time includes two sub-procedures of 50 sets of control variables for each machine. The optimization result, which is presented in a non-dominated pareto-front, is shown in Fig. 12. Note that, due to the stochastic nature of the MOPSO technique, 3 optimization runs were performed to obtained the result. In order to examine in detail the solutions presented in Fig. 12, three machines ("machine 1", "machine 2", and "machine 3" in Fig. 12) are extracted as shown in Fig. 13. The corresponding parameters are shown Table . 2. As seen, the variable x 4 , which is the azimuth PM ratio, prefers the upper boundary of its domain. This is in accordance with the sensitivity analyses of x 4 presented above: increasing this value will lower the counter-effective flux created by the field windings. Therefore, the FCR gap is kept high. The variable x 7 , which is the stator tooth surface ratio, prefers to stay at the lower boundary of its domain. This contradicts the expectation of the variable's trend from its sensitivity analysis, which claimed that increasing this value will lower the magnetic saturation in the stator teeth and the FCR gap increases. However, the small value of x 7 can be explained by the fact that it leaves more room for the armature windings to satisfy the two operating points' torque constraints.

The FEM validations on the FCR curves are shown in Fig. 14. As observed, a good accordance is reported between the EMCN and FEM results. Different ranges for the field current density J f is due to the different field winding's windows as well as other machine's dimensions. However maximum field current densities of these three machines are close to each other. As it will be seen for the "machine 3", the air-gap flux due to PMs can be nearly canceled out, which is highly desirable for the flux weakening control. Another criterion can be considered to evaluate the effectiveness of the field windings. This criterion is defined as the slope M of the FCR curve expressed by [START_REF] Akemakou | Dual excitation electrical machine, and especially motor vehicle alternator[END_REF]. A high value of M means that certain flux can be regulated at the expense of a small amount of field windings' copper losses. Table . 3 summarizes slopes of FCR curves for the three extracted machines, results are obtained by using the EMCN method.

M = FCRgap J f 2 -J f 1 [mH.mm 2 ] (5)
where J f 2 and J f 1 are field current densities corresponding to the the maximum-flux and minimum-flux points, respectively.

General discussion

A DESM is able to regulate the air-gap flux more flexibly compared to conventional PM machines. However, it is accomplished at the expense of a bigger volume and more cost due to the presence of additional field windings. The working principle should be also more complicated especially in case of the parallel configuration as with the DESM topology presented in this paper. An interesting point in choosing machine's dimensions in order to maximize the FCR gap is about the width ratio (or the thickness) of the azimuth PM. As pointed out, this thickness should be designed as high as possible. This might contradict the conventional PM machine designs because the flux weakening of those machines becomes more difficult as the d-axis armature current must pass through this PM. As with the DESM, the flux control can be handled much easier by field windings. Moreover, having a thick azimuth PM helps to reduce the counter-effective flux of the field windings as discussed. This design rule is applicable to the parallel-flux-combination cases with the presence of the counter-effective flux from field windings passing though PMs. Another aspect to be considered when designing the DESM is to better design the thermal contact between the field windings and the iron core. It helps reduce the field windings' copper losses. However, concerning the capability to improve the flux control range, it requires an elaborate analysis since the magnetic saturation might occur ealier than the thermal constraint violation.

Conclusion

An optimization with an objective aiming at improving the no-load flux control range of a DESM has been performed. Some critical operating points of a torque envelop curve were used as constraints. The complexity in both electromagnetic and thermal aspects were well handled by using equivalent circuit networks. One configuration is also found to nearly cancel out the PMs' flux. In the future works, a more comprehensive study to evaluate performances of the DESM in a specific vehicle application will be carried out.

Fig. 1 :

 1 Fig. 1: (a) Reference model of DESM. (b) No-load peak flux according to the field current.

Fig. 2 :Fig. 3 :

 23 Fig. 2: Bipolar flux paths created by PMs

Fig. 4 :

 4 Fig. 4: Magnetic flux density maps of the minimum-flux and maximum-flux points of the prototype. J f is the field current density

Fig. 5 :Fig. 6 :

 56 Fig. 5: Machine's modeling. (a) Meshing idea with the EMCN technique . (b) Thermal network with thermal resistances:R field-yoke -between field winding and the outer stator yoke, R end-field -between the armature's end winding and a field winding, R end-active -between the armature's end winding and armature's active winding, R end-rotor -between the armature's end winding and rotor surface, R phase-teeth -between the armature's active winding and stator teeth, Rair-gap -air gap, R bearing -bearing. Losses: PCuF -field winding's copper losses, PCuP -armature winding's copper loss, PironS1 -the outer stator yoke's core loss, PironS2 -the inner stator yoke's core loss, PironS3 -the stator teeth's core loss, PironR -the rotor's core loss

Fig. 7 :

 7 Fig. 7: Thermal model validation. Phase current 4 A, field current 4 A

Fig. 8 :Fig. 9 :

 89 Fig.8: The torque envelop requirement for the design constraints, the operating points for constraints are marked with circles.

Fig. 10 :

 10 Fig. 10: Sensitivity analyses on the FCR gap. The vertical axis's labels for all sub-figures are "FCR gap [mWb]".

Fig. 11 :

 11 Fig. 11: Sensitivity analyses on the FCR curves. The vertical axis's labels for all sub-figures are "Peak flux/phase/turn [mWb]" and the horizontal axis's labels are "Field current density [A/mm 2 ]. Curves corresponding to the lower and upper variable bounds are marked with dash (-) and plus (+) symbols, respectively.

Fig. 12 :

 12 Fig. 12: Non-dominated solutions optimization result

Fig. 13 :

 13 Fig.13: Three machines extracted from non-dominated solutions in Fig.12

Fig. 14 :

 14 Fig. 14: FEM validation for 3 machines marked in Fig. 12. (a) Machine 1. (b) Machine 2. (c) Machine 3.

Table 2 :

 2 Dimensions of extracted machines in Fig.12

	Variable	Machine 1	Machine 2	Machine 3
	x1 [mm]	34	38.3	36.6
	x2 [mm]	15	16.1	19.8
	x3 [mm]	24	24.9	27.3
	x4	0.8	0.8	0.79
	x5 [mm]	6	8.6	9.5
	x6 [mm]	15	15	17.2
	x7	0.4	0.4	0.4
	x8 [mm]	15	15.1	16.8
	x9 [mm]	9	9	11
	x10 [mm]	5.2	7.2	8.4
	Outer stator diameter [mm]	163.2	173.2	200.6
	Total axial length [mm]	86.4	100.0	106.5

Table 3 :

 3 Summary of the slopes of various FCR curves

		Machine 1	Machine 2	Machine 3
	Maximum flux [mWb]	2.53	3.11	3.51
	Minimum flux [mWb]	0.66	0.44	0.04
	M [mH.mm 2 ]	0.15	0.23	0.38


Marie Valentin

Leslie Radon
email: leslie.radon@imm.fr

Jeanne Duclos

Florence Curt

Nathalie Godart

Troubles bipolaires et anorexie mentale: une étude clinique Bipolar disorders and Anorexia Nervosa: a clinical study

Keywords: Troubles des conduites alimentaires anorexie mentale, troubles bipolaires, antécédents familiaux Eating disorders, anorexia nervosa, bipolar disorders, comorbidity, family history. ABREVIATIONS TCA: Troubles des Conduites Alimentaires AM: Anorexie Mentale BN: Boulimie Nerveuse BP: Trouble Bipolaire BP-

Contexte : L'anorexie Mentale (AM) présente fréquemment des comorbidités avec les troubles de l'humeur, en particulier la dépression, par contre les antécédents individuels et/ou familiaux de troubles bipolaires (BP) a quant à lui été peu étudié. Objectifs : Cette étude a pour objectifs (1) d'évaluer, d'une part, la fréquence des troubles bipolaires auprès de patients souffrant d'anorexie mentale hospitalisés à l'adolescence et leurs parents ;

(2) et d'autre part, de rechercher si les patientes aux antécédents personnels et/ou familiaux de trouble bipolaire présentent des caractéristiques particulières quant à l'expression clinique de leur anorexie mentale, leurs antécédents, les diagnostics secondaires posés, les traitements prescrits. Méthode : 97 patientes, âgées entre 13 et 20 ans, hospitalisées pour anorexie mentale ont été évaluées. Les diagnostics anorexie mentale et trouble bipolaire ont été posés selon les critères du DSM IV-TR. Résultats : Une fréquence élevée de troubles bipolaires de type II et de type V a été observée. Les patientes souffrant d'anorexie mentale et présentant des antécédents personnels ou familiaux de trouble bipolaire ont un début plus précoce de l'anorexie mentale, un nombre d'hospitalisations plus important, un délai plus long entre le début de l'anorexie mentale et l'hospitalisation un nombre plus élevé de tentatives de suicide, et présentent davantage de comorbidités psychiatriques. Conclusion : La présence d'une comorbidité anorexie mentale-trouble bipolaire semble importante et liée à la sévérité de l'anorexie mentale.

INTRODUCTION

L'anorexie mentale (AM) est une pathologie sévère associée à de nombreuses comorbidités [START_REF] Godart | Comorbidity studies of eating disorders and mood disorders. Critical review of the literature[END_REF]. Dès les années 80, certains auteurs ont questionné une comorbidité possible avec les troubles bipolaires (BP) en particulier à l'adolescence [START_REF] Ghadirian | A manic episode in the course of anorexia nervosa with bulimia[END_REF][START_REF] Hsu | Bipolar illness preceded by anorexia nervosa in identical twins[END_REF]. De la même manière, la fréquence des troubles des conduites alimentaires est également élevée chez les patients souffrant de trouble bipolaire [START_REF] Blinder | Psychiatrics comorbidities of female inpatients with eating disorders[END_REF][START_REF] Mcelroy | Comorbidity of bipolar and eating disorders: distinct or related disorders with shared dysregulations?[END_REF][START_REF] Mcelroy | Prevalence and correlates of eating disorders in 875 patients with bipolar disorder[END_REF]. Cependant, l'évaluation de la fréquence d'apparition de trouble bipolaire au sein de population de patients souffrant d'anorexie mentale n'a été que très peu réalisée et le lien entre ces deux troubles ne demeure que trop peu abordé dans la littérature.

Alors que la prévalence sur la vie entière d'au moins un trouble de l'humeur est importante et a été fréquemment étudiée -elle varie entre 64,1 % et 96 % parmi les sujets souffrant d'anorexie mentale [START_REF] Godart | Comorbidity studies of eating disorders and mood disorders. Critical review of the literature[END_REF], soit significativement plus fréquente qu'en population générale féminine où elle est de 17 % [START_REF] Waraich | Prevalence and incidence studies of mood disorders : a systematic review of the literature[END_REF]. La prévalence des troubles bipolaires de type II quant à elle est bien plus faible, et ce, également en population générale féminine (0.4 %) [START_REF] Merikangas | Prevalence and correlates of bipolar spectrum disorder in the world mental health survey initiative[END_REF]. Dans la population générale, Hudson et coll [START_REF] Hudson | The prevalence and correlates of eating disorders in the national Comorbidity Survey Replication[END_REF] ont retrouvé une prévalence d'anorexie mentale de 0,6 % et une prévalence de trouble bipolaire de 3 % chez les anorexies mentales chez 9 282 sujets de plus de 18 ans aux USA.

Les études concernant la comorbidité « trouble bipolaire-anorexie mentale » sont rares : trois chez des anorexies mentales actuelles [START_REF] Piran | Affective disturbance in eating disorders[END_REF][START_REF] Laessle | The significance of subgroups of boulimia and anorexia nervosa : lifetime frequency of psychiatric disorders[END_REF][START_REF] Iwasaki | Comorbidity of axis I disorders among eating-disordered subjects in Japan[END_REF] et trois études de devenir [START_REF] Ivarsson | Depressive disorders in teenage-onset anorexia nervosa: A controlled longitudinal, partly community-based study[END_REF][START_REF] Halmi | Comorbidity of psychiatric diagnoses in anorexia nervosa[END_REF][START_REF] Rastam | Anorexia nervosa in 51 Swedish adolescents: premorbid problems and comorbidity[END_REF]. La fréquence des troubles bipolaires sur la vie varie selon les études entre 0 % auprès de 14, 21 et 62 patientes souffrant d'AM-R [START_REF] Piran | Affective disturbance in eating disorders[END_REF][START_REF] Laessle | The significance of subgroups of boulimia and anorexia nervosa : lifetime frequency of psychiatric disorders[END_REF][START_REF] Iwasaki | Comorbidity of axis I disorders among eating-disordered subjects in Japan[END_REF], chez des AM-R et 6 % chez des 36 patientes souffrant d'anorexie mentale-trouble bipolaire [START_REF] Iwasaki | Comorbidity of axis I disorders among eating-disordered subjects in Japan[END_REF]. Dans les études de devenir, les prévalences actuelles de troubles bipolaires varient entre 0 % chez 51 patientes initialement suivies en ambulatoire après 6,7 ans de suivi [START_REF] Halmi | Comorbidity of psychiatric diagnoses in anorexia nervosa[END_REF] prévalence qui augmente avec le temps puisqu'elle atteint 1,9 % après 10 ans de suivi au sein du même échantillon [START_REF] Rastam | Anorexia nervosa in 51 Swedish adolescents: premorbid problems and comorbidity[END_REF] et 3,2 % parmi 62 patientes souffrant d'anorexie mentale ayant été hospitalisées 10 ans auparavant, significativement plus que le groupe contrôle (0 %) [START_REF] Ivarsson | Depressive disorders in teenage-onset anorexia nervosa: A controlled longitudinal, partly community-based study[END_REF]. En ce qui concerne les prévalences de troubles bipolaires sur la vie dans l'anorexie mentale, celles-ci varient entre 3,2 % parmi 62 femmes hospitalisées 10 ans auparavant pour anorexie mentale, significativement plus que le groupe contrôle (0 %) [START_REF] Ivarsson | Depressive disorders in teenage-onset anorexia nervosa: A controlled longitudinal, partly community-based study[END_REF], et 5,8 % chez 51 femmes suivies 10 ans auparavant en ambulatoire [START_REF] Rastam | Anorexia nervosa in 51 Swedish adolescents: premorbid problems and comorbidity[END_REF]. Par ailleurs, Campos et al. [START_REF] Campos | Occurrence of bipolar spectrum disorder and comorbidities in women with eating disorders[END_REF]. ont quant à eux souligné une prévalence importante (68,1 %) de troubles du spectre bipolaire auprès de 69 patientes adultes souffrant de troubles des conduites alimentaires hospitalisées dans un centre tertiaire. Ces auteurs rapportent également que les sujets présentant à la fois un trouble bipolaire et un trouble des conduites alimentaires souffriraient également plus d'un trouble de consommation de substances (40,4 %) par rapport aux patients souffrant de troubles des conduites alimentaires sans trouble bipolaire (13,6 %) (OR = 4,298; P = 0,03).

Par ailleurs, très peu de travaux se sont intéressés à l'étude conjointe des antécédents familiaux de troubles bipolaires dans l'anorexie mentale chez les patients hospitalisés ou suivis en ambulatoire pour lequel on recherche des troubles bipolaires. Récemment, une étude familiale a rapporté que la présence d'antécédents familiaux de trouble bipolaire augmentait le risque de développer un trouble des conduites alimentaires, en particulier une anorexie mentale chez leurs enfants [START_REF] Bould | Parental mental illness and eating disorders in offspring[END_REF].

Ainsi, il existe des arguments pour penser que le trouble bipolaire est très fréquent chez les patients souffrant de trouble des conduites alimentaires, et ce, en particulier les formes sévères traitées dans les centres tertiaires. Toutefois, peu d'études récentes ont évalué la prévalence des troubles bipolaires chez les patients souffrant d'anorexie mentale sévère à l'adolescence. Or, l'intrication de ces deux troubles est considérée comme un facteur de gravité assombrissant le pronostic du trouble alimentaire et possiblement aussi celui du trouble bipolaire [START_REF] Mury | Comorbidity of bipolar and eating disorders. Epidemiologic and therapeutic aspects[END_REF]. Les troubles anorexiques se déclarant fréquemment avant 18 ans, dépister les troubles bipolaires chez ces patientes permettrait de débuter plus précocement le traitement de ces derniers et permettant ainsi possiblement l'amélioration du pronostic des deux troubles. De même, très peu de travaux se sont intéressés à l'étude des antécédents familiaux de trouble bipolaire dans l'anorexie mentale chez les patients hospitalisés ou suivis en ambulatoire.

Par conséquent, la présente étude en population clinique d'adolescents souffrant d'anorexie mentale a pour objectifs (1) d'une part, d'évaluer la fréquence des troubles bipolaires chez des patients souffrant d'anorexie mentale sévère ayant nécessité une hospitalisation à l'adolescence et dans leur famille ; (2) et d'autre part, de rechercher si les patientes aux antécédents personnels et/ou familiaux de trouble bipolaire présentent des caractéristiques particulières quant à l'expression clinique de leur anorexie mentale, leurs antécédents, les diagnostics secondaires posés, les traitements prescrits. Les données utilisées plus particulièrement pour cette étude sont : les caractéristiques de l'hospitalisation (âge à l'admission, IMC à l'admission et à la sortie du service, IMC de sortie de séparation et de sortie définitive définis par le contrat de poids, durée d'hospitalisation, pose d'une sonde naso-gastrique pour renutrition entérale (si oui, combien de fois et combien de temps), traitement à la sortie, nécessité d'une prise en charge en réanimation) les caractéristiques de l'anorexie mentale (type restrictif ou purgatif, âge de début des troubles, durée d'évolution, IMC minimal et maximal, âge de début du suivi et délai par rapport à l'hospitalisation, nombre d'hospitalisations antérieures) les antécédents psychiatriques des sujets (épisode dépressif, tentative de suicide, consommation de haschisch, fugues, séparation précoce d'avec la mère et troubles de la petite enfance tels que retard psychomoteur, énurésie, encoprésie, anorexie, mérycisme) les antécédents psychiatriques familiaux (père, mère, frères et soeurs)

MÉTHODOLOGIE

Constitution des groupes

Afin de comparer les patientes souffrant d'anorexie mentale présentant une histoire personnelle et/ou familiale de trouble bipolaire avec les autres patientes souffrant d'anorexie mentale, les 96 patientes constituant l'échantillon de cette étude seront réparties en deux groupes (figure 1) :

Le premier groupe a été constitué des patientes présentant à la fois une histoire personnelle d'épisode dépressif et/ou mélancolique et/ou hypomaniaque et des antécédents familiaux de trouble bipolaire avérés ou suspectés. Les patientes ayant présenté un épisode dépressif ou mélancolique et un épisode hypomaniaque peuvent être classées dans le trouble bipolaire de type II. Les patientes ayant présenté un épisode dépressif ou mélancolique et des antécédents familiaux de trouble bipolaire peuvent être classées dans le trouble bipolaire de type V [START_REF] Gorwood | Masques trompeurs et diagnostics différentiels du trouble bipolaire[END_REF].

Le second groupe a été constitué par les autres patientes, sans antécédents personnels ou familiaux identifiés de trouble bipolaire.

Analyses statistiques

Les données ont été collectées et analysées au moyen du logiciel SPSS (Statistical

Package for Social Science) version 20.0. Chaque variable quantitative a été décrite à partir de la moyenne, la médiane, l'écart type, le minimum, le maximum. Les comparaisons statistiques ont été effectuées au moyen du test non paramétrique de Mann-Whitney du fait d'effectifs inférieurs à 30 dans les groupes étudiés. Les variables qualitatives ont été déterminées à partir des fréquences de distribution et de leur comparaison au moyen du test du khi-deux, en utilisant le test exact de Fisher lorsque l'effectif théorique minimum est inférieur à 5. Le seuil de significativité statistique utilisé est α = 0,05. Des analyses multivariées ont été réalisées (régression logistique) pour ajuster les variables concernant des IMC par rapport à l'âge des sujets, mais aussi pour rechercher des liens entre les différentes variables et les antécédents de bipolarité.

RÉSULTATS

Les 96 sujets constituant l'échantillon de cette étude sont issus de catégories socioprofessionnelles plutôt favorisées : dans 47,4 % des cas le père exerce une profession de cadre ou dite intellectuelle supérieure, ainsi que la mère dans 31,6 % des cas. De même, le père exerce une profession intermédiaire dans 20 % des cas, ainsi que la mère dans 22,1 % des cas. Seuls 3,2 % des sujets ont un père sans activité professionnelle (17,9 % d'inactivité pour la mère).

Les données cliniques concernant l'hospitalisation sont rapportées dans le tableau 2. Les patientes de l'échantillon sont en moyenne hospitalisées à l'âge de 16,5 ans ± 1,7, avec un IMC à l'admission de 14,2 ± 1,2 Le début de l'anorexie mentale chez les sujets de notre échantillon a débuté en moyenne à 14,5 ans ± 1,8, soit 2,0 ans ± 1,7 avant leur hospitalisation. Il s'agit d'une AM-R dans 67,7 % des cas. Le nombre moyen d'hospitalisations antérieures pour anorexie mentale est de 0,8 ± 1,5.

La présence ou un antécédent d'épisode dépressif majeur est relevé chez 46,8 % des patientes et le nombre moyen de tentatives de suicide est de 0,22 ± 0,7. Par ailleurs, 4.2 % des sujets consomment du haschisch de manière ponctuelle et 2,1 % de manière régulière. Un antécédent de fugue à l'adolescence est retrouvé chez 8,4 % des patientes. Des troubles de la petite enfance (retard psychomoteur, énurésie, encoprésie, anorexie, mérycisme) sont rapportés pour 16,7 % des patientes et une séparation précoce avec la mère pour 13,7 % des sujets.

Le tableau 1 montre que 6,3 % des sujets (soit 6 sujets) présentent un trouble bipolaire de type II. De plus, 11 patientes (11,5 %) présentent un trouble bipolaire subsyndromique de type V, c'est-à-dire un épisode dépressif ou mélancolique et des antécédents familiaux de trouble bipolaire. Au total, 17,7 % des sujets présentent un trouble appartenant au spectre bipolaire. Le traitement de sortie comprend pour 46,9 % des patientes un antidépresseur, pour 17,7 % un neuroleptique, pour 7,3 % un thymorégulateur, pour 24 % un anxiolytique et pour 6,3 % un hypnotique. Les traitements antidépresseurs sont prescrits dans 6,7 % des cas pour des patientes présentant un trouble obsessionnel compulsif, dans 8,9 % des cas pour des patientes présentant un trouble bipolaire et dans 77,8 % des cas pour des patientes présentant un trouble dépressif.

Sur le plan des antécédents familiaux (voir tableau 3), on retrouve chez les mères des sujets un trouble des conduites alimentaires -c'est-à-dire soit une anorexie mentale soit une boulimie nerveuse-dans 19,8 % des cas, un trouble dépressif majeur dans 53,1 % des cas, un trouble anxieux dans 9,4 % des cas, un trouble de la personnalité dans 8,3 % des cas et un trouble lié à la consommation d'alcool dans 1 % des cas. Par ailleurs, on note chez les pères des sujets aucun trouble des conduites alimentaires, 19,8 % de trouble dépressif majeur, 6,3 % de troubles anxieux, 9,4 % de troubles de personnalité et 14,6 % de troubles liés à la consommation d'alcool. Enfin, dans la fratrie des sujets, on observe 5.2 % de trouble des conduites alimentaires, 19,8 % de trouble dépressif majeur, 6,3 % de troubles anxieux, 9,4 % de troubles de la personnalité et 14,6 % de troubles liés à la consommation d'alcool.

Par ailleurs, nous avons retrouvé un antécédent familial avéré de trouble bipolaire chez 8,3 % des patientes et une forte suspicion auprès de 13,6 % des patientes de notre échantillon.

Par conséquent, les 96 patientes de notre échantillon sont divisées en deux groupes :

Le premier groupe est constitué des 17 patientes présentant à la fois une histoire personnelle d'épisode dépressif et/ou mélancolique et/ou hypomaniaque et des antécédents familiaux de troubles bipolaires avérés ou suspectés Le second groupe est constitué par les 79 autres patientes, sans antécédents personnels ou familiaux identifiés de trouble bipolaire.

Comparaison des deux groupes L'âge moyen est comparable dans les deux groupes observés. Les résultats concernant des variables d'IMC ont été ajustés par rapport à l'âge pour tenir compte de l'évolution de la corpulence au cours de la croissance. Après ajustement par rapport à l'âge, les IMC (à l'entrée, à la sortie, minimal et maximal) observés dans les deux groupes n'étaient pas significativement différents.

Histoire et symptômes des sujets

Le tableau 2 présente les données concernant l'histoire et la symptomatologie des sujets. Dans le groupe de sujets (N = 17) présentant une histoire personnelle ou familiale de trouble bipolaire, nous avons retrouvé: une anorexie mentale ayant débuté à un âge plus précoce (13,4 ans ± 1,7 en moyenne contre 14,8 ans ± 1,8 ; p=0.005), des délais entre le début de l'anorexie mentale et l'hospitalisation (3,4 ans ± 2,3 contre 1,7 an ± 1,4 ; p = 0.004), un nombre d'hospitalisations antérieures pour anorexie mentale plus élevé (1,7 ± 2,4 en moyenne contre 0,6 ± 1,2 ; p = 0,03), des antécédents de dépression nettement plus importants (100 % contre 46,8 % ; p < 0,001), un nombre significativement plus élevé de tentatives de suicide (0,8 ± 1,5 en moyenne contre 0,1 ± 0,4; p = 0,003), une renutrition entérale par sonde naso-gastrique pendant leur hospitalisation (81,3 % des sujets contre 45,5 % ; p = 0,009), un traitement par thymorégulateur à leur sortie (35,3 % des patients contre 1,3 % ; p<0,001).

Antécédents familiaux

En ce qui concerne les antécédents familiaux (voir le tableau 3), aucune différence statistiquement significative n'est observée entre les deux groupes. Toutefois, les troubles liés à la consommation d'alcool ont tendance à être moins souvent retrouvés parmi les pères et la fratrie des sujets du groupe présentant une histoire personnelle ou familiale de trouble bipolaire (N = 17).

DISCUSSION

La prévalence des troubles bipolaires observée dans notre échantillon de patientes présentant une anorexie mentale sévère (c'est-à-dire conduisant à une hospitalisation dans un centre spécialisé dans la prise en charge des troubles des conduites alimentaires) est élevée. En effet, 17,7 % des sujets anorexie mentale présentent un trouble appartenant au spectre bipolaire contre 0.4 % en population générale féminine [START_REF] Merikangas | Prevalence and correlates of bipolar spectrum disorder in the world mental health survey initiative[END_REF]. Les patientes souffrant d'anorexies mentales sévères pour lesquelles il existe une histoire d'antécédents individuels ou familiaux de trouble bipolaire souffrent d'une forme de trouble des conduites alimentaires plus sévère associée à : un début d'anorexie mentale plus précoce (14 ans contre 14,6 ans), un délai plus long entre le début de l'anorexie mentale et l'hospitalisation [START_REF] Hsu | Bipolar illness preceded by anorexia nervosa in identical twins[END_REF][START_REF] Blinder | Psychiatrics comorbidities of female inpatients with eating disorders[END_REF] ans contre 1,7 an), un nombre plus élevé d'hospitalisations antérieures pour anorexie mentale (1,7 contre 0,6), une renutrition entérale par sonde naso-gastrique pendant l'hospitalisation (81,3 % contre 45,5 %) plus fréquente, un nombre plus élevé de tentative de suicide (0,8 contre 0,1), une prévalence d'épisode dépressif majeur plus importante (100 % contre 46,8 %), et un traitement par thymorégulateur plus fréquent (35,3 % contre 1,3 %). Toutefois, nous n'avons retrouvé aucune différence en termes de fréquence d'antécédents familiaux entre les deux groupes de patientes (avec antécédents individuels ou familiaux de trouble bipolaire versus aucun antécédent de trouble bipolaire) mais notre échantillon est relativement restreint.

Nous avons retrouvé une fréquence élevée de trouble bipolaire (17,8 %) auprès de patientes adolescentes souffrant d'anorexie mentale sévère : 6,3 % des sujets présentent un trouble bipolaire de type II et 11,5 % présentent un trouble bipolaire subsyndromique de type V, c'est-à-dire un épisode dépressif ou mélancolique et des antécédents familiaux de trouble bipolaire. Cette prévalence est globalement plus élevée que celle rapportée dans la plupart des études [START_REF] Godart | Comorbidity studies of eating disorders and mood disorders. Critical review of the literature[END_REF][START_REF] Tseng | Prevalence and correlates of bipolar disorders in patients with eating disorders[END_REF]. La différence observée pourrait s'expliquer en partie, d'une part, par l'usage de différentes définitions de trouble bipolaire et, d'autre part, par le fait que nous avons ciblé un échantillon plus homogène que dans les autres études, incluant des sujets présentant une anorexie mentale particulièrement sévère. En effet, il a été observé que l'accès à un niveau de soins plus intensifs sélectionne, notamment dans l'anorexie mentale, les sujets de plus grande gravité avec des comorbidités, en particulier dépressives, plus importantes [START_REF] Godart | Comorbidity studies of eating disorders and mood disorders. Critical review of the literature[END_REF].

Nous avons mis en évidence certains éléments de gravité chez les patientes souffrant d'anorexie mentale sévère pour lesquelles il existe une histoire d'antécédents individuels ou familiaux de trouble bipolaire. Cela pourrait s'expliquer par la plus grande durée d'évolution de l'anorexie mentale et/ou par une anorexie mentale plus sévère. En faveur de cette dernière hypothèse, on observe que ces patientes nécessitent plus souvent au cours de leur hospitalisation une renutrition entérale par sonde nasogastrique, ce qui suggère qu'elles arrivent dans un état somatique plus précaire.

Sur le plan des antécédents familiaux, une étude récente auprès de 158, 679 enfants a montré que le risque de développer un trouble des conduites alimentaires était accru en présence d'antécédents familiaux de trouble bipolaire, de troubles dépressifs ou encore de troubles de la personnalité [START_REF] Bould | Parental mental illness and eating disorders in offspring[END_REF]. À l'inverse, la relation comorbide « anorexie mentale-dépression » chez les femmes augmenterait le risque de présenter une psychopathologie chez leurs enfants [START_REF] Micali | Childhood psychopathology in children of women with eating disorders understanding risk mechanisms[END_REF]. Toutefois le trouble bipolaire demeure mal connu et le retard au diagnostic est fréquent : un délai moyen de 10 ans est rapporté entre le début des troubles et l'instauration d'un traitement approprié [START_REF] Faedda | Precursors of bipolar disorders: a systematic litterature review of prospective studies[END_REF]. Par conséquent, en cas d'antécédents familiaux de trouble bipolaire, un début précoce de l'anorexie mentale peut alerter le clinicien sur la possibilité d'un début masqué d'un tel trouble.

Les tentatives de suicide et les suicides sont très fréquents dans l'anorexie mentale [START_REF] Webb | Suicide, hospital-presenting suicide attempts, and criminality in bipolar disorder: Examination of risk for Multiple Adverse Outcomes[END_REF]. On constate que les patientes souffrant d'anorexie mentale présentent un nombre plus important de tentatives de suicide que les patientes sans antécédents de trouble bipolaire, ce qui est cohérent avec les données actuelles soulignant la fréquence élevée de tentative de suicide chez les sujets souffrant de trouble bipolaire et la nécessité de leur dépistage précoce [START_REF] Campos | Occurrence of bipolar spectrum disorder and comorbidities in women with eating disorders[END_REF][START_REF]Manic-Depressive illness. Bipolar disorders and recurrent depression[END_REF][START_REF] Miller | Excess mortality in bipolar disorders[END_REF].

Sur le plan des comorbidités, les patientes avec une histoire personnelle et/ou familiale de bipolarité ont toutes présenté au moins un épisode dépressif majeur au cours de leur vie, soit significativement plus que celles de l'autre groupe. Les résultats de notre étude mettent en avant la fréquence élevée d'épisode dépressif majeur précoce chez ces adolescentes. La survenue d'un tel épisode dépressif majeur doit alerter le clinicien sur la possibilité d'un développement d'un trouble bipolaire. En effet, comme l'a souligné Akiskal [START_REF] Akiskal | Developmental pathways to bipolarity: are juvenile-onset depressions pre-bipolar[END_REF], la survenue d'un épisode dépressif majeur avant l'âge de 20 ans témoigne d'un risque accru de développer un trouble bipolaire par la suite. Ainsi, 25 % des enfants ou adolescents qui présentent un épisode dépressif majeur développent un trouble bipolaire dans les 2 à 5 ans suivants [START_REF] Akiskal | Developmental pathways to bipolarity: are juvenile-onset depressions pre-bipolar[END_REF]. Par conséquent, la survenue ou la présence d'antécédents d'un trouble dépressif, chez une patiente souffrant d'anorexie mentale peut alerter sur le risque de développement d'un trouble bipolaire.

Ces résultats soulèvent la question du lien entre anorexie mentale et trouble bipolaire. McElroy et al. [START_REF] Mcelroy | Comorbidity of bipolar and eating disorders: distinct or related disorders with shared dysregulations?[END_REF] proposent deux explications de cette comorbidité: (1) les troubles des conduites alimentaires et les troubles bipolaires sont deux entités distinctes ou bien partageant des mécanismes étiologiques mais représentant chacune un risque pour l'autre ; (2) les troubles des conduites alimentaires et trouble bipolaire partagent de nombreuses caractéristiques comme, la pathophysiologie de dérégulation de l'humeur, le comportement alimentaire et le contrôle, ce qui s'appuie sur les résultats des études montrant une association significative entre épisodes dépressifs et antécédents familiaux de trouble bipolaire [START_REF] Mcelroy | Comorbidity of bipolar and eating disorders: distinct or related disorders with shared dysregulations?[END_REF][START_REF] Mcelroy | Prevalence and correlates of eating disorders in 875 patients with bipolar disorder[END_REF][START_REF] Campos | Occurrence of bipolar spectrum disorder and comorbidities in women with eating disorders[END_REF][START_REF] Lunde | The relationship of bulimia and anorexia nervosa with bipolar disorder and its temperamental foundations[END_REF]. Ainsi, cela questionne la place de la prescription des traitements thymorégulateurs chez les patientes souffrant d'anorexie mentale. En effet, si l'épisode anorexique peut être considéré comme un début de trouble bipolaire, alors la survenue, par exemple, d'un épisode hypomaniaque dans ce contexte pourrait justifier de la mise en place d'un traitement thymorégulateur comme s'il s'agissait d'un trouble bipolaire de type II. Cette question nécessite toutefois une grande prudence, en l'absence d'études réalisées sur ce sujet. Actuellement, il n'existe pas de recommandations concernant la prise en charge thérapeutique des patients présentant à la fois une anorexie mentale et un trouble bipolaire. Néanmoins, au vu des résultats de cette présente étude et de la littérature, le clinicien doit se montrer particulièrement vigilant quant au risque de survenue d'un trouble bipolaire chez une patiente souffrant d'anorexie mentale présentant des antécédents familiaux de bipolarité. Comme le soulignent McElroy et al. [START_REF] Mcelroy | Comorbidity of bipolar and eating disorders: distinct or related disorders with shared dysregulations?[END_REF][START_REF] Mcelroy | Prevalence and correlates of eating disorders in 875 patients with bipolar disorder[END_REF], ce dépistage est d'autant plus crucial que les éléments suivants viennent assombrir le pronostic : risque suicidaire est accru, davantage de comorbidités psychiatriques et d'épisodes maniaques, hypomaniaques et dépressifs, un début d'apparition du trouble bipolaire plus précoce, et des cycles rapides. Ces mêmes auteurs soulignent en conclusion de leur revue de la littérature [START_REF] Mcelroy | Comorbidity of bipolar and eating disorders: distinct or related disorders with shared dysregulations?[END_REF], que la présence d'un trouble bipolaire comorbide peut être un facteur de résistance au traitement du trouble alimentaire d'un patient. Selon ces auteurs, les éléments pouvant indiquer la présence d'une bipolarité chez un patient présentant un trouble des conduites alimentaires sont les suivants : épisode dépressif à un âge précoce, autre comorbidité de l'axe I à un âge précoce, récurrences dépressives, activation comportementale ou impulsivité, histoire familiale de bipolarité, mauvaise réponse au traitement habituel des troubles alimentaires. Ces éléments sont cohérents avec les résultats de notre étude.

Limites L'étude présentée ici comporte cependant certaines limites, devant nous rendre prudent pour la généralisation de ces résultats. Tout d'abord, les patients de cette étude ont été hospitalisés dans un centre tertiaire et présentent de fait une anorexie mentale sévère, n'étant ainsi pas représentatifs de l'ensemble des patients souffrant d'anorexie mentale [START_REF] Godart | Comorbidity studies of eating disorders and mood disorders. Critical review of the literature[END_REF]. En effet, les patients souffrant d'un trouble des conduites alimentaires présentent également de nombreuses comorbidités comme le résultat du « biais de Berkson » [START_REF] Berkson | Limitations of the application of fourfold table analysis to hospital data[END_REF]. De plus, elle est réalisée sur un petit échantillon, mais plus important que ceux des études antérieures. Il en résulte l'impossibilité de réaliser certaines comparaisons statistiques en raison d'effectifs trop petits, par exemple entre les différentes catégories de troubles bipolaires, ainsi qu'entre les différents degrés de certitude des antécédents familiaux. Ensuite, la constitution des groupes peut être discutable. Elle repose sur les données de la littérature exposées précédemment, suggérant l'intérêt de l'étude du spectre bipolaire, car les formes les plus sévères sont également les plus rares, mais aussi car les formes subsyndromiques sont les plus fréquentes à l'adolescence. Nous n'avons également pas étudié la différence en termes de comorbidité avec le trouble bipolaire selon le sous-groupe d'anorexie mentale : restrictif versus purgatif. Or, le sous-type d'anorexie mentale le plus fortement associé au trouble bipolaire s'avère être l'anorexie mentale type purgatif [START_REF] Iwasaki | Comorbidity of axis I disorders among eating-disordered subjects in Japan[END_REF][START_REF] Eddy | Longitudinal comparison of anorexia nervosa subtypes[END_REF][START_REF] Godart | Mood disorders in eating disorder patients: Prevalence and chronology of ONSET[END_REF].

Par ailleurs, le recueil des antécédents individuels et familiaux n'a pas été réalisé à partir de questionnaires standardisés des sujets et de leurs apparentés. Les parents ont toutefois été évalués directement, par le biais d'entretiens avec un clinicien et selon les critères du DSM-IV. C'est pourquoi cette étude ne constitue qu'un travail exploratoire préliminaire concernant les liens potentiels entre l'anorexie mentale sévère et les troubles bipolaires. D'autres études plus larges seraient nécessaires pour mieux comprendre ces liens et évaluer notamment le devenir de ces sujets et la meilleure stratégie thérapeutique.

CONCLUSION

En conclusion, il existe chez les patients souffrant d'anorexie mentale sévère à l'adolescence une comorbidité importante et leur intrication semble être un facteur de gravité qui assombrit le pronostic du trouble alimentaire et probablement aussi celui du trouble bipolaire. C'est pourquoi sur le plan clinique, il apparaît indispensable lors de l'évaluation de ces patients de rechercher la co-occurrence de ces deux troubles [START_REF] Mury | Comorbidity of bipolar and eating disorders. Epidemiologic and therapeutic aspects[END_REF][START_REF] Lunde | The relationship of bulimia and anorexia nervosa with bipolar disorder and its temperamental foundations[END_REF] et de développer une nouvelle recherche afin d'explorer le lien entre l'anorexie mentale et les troubles bipolaires.

FIGURE 1 .

 1 FIGURE 1.

FIGURE 1 Tableau 1 .

 11 FIGURE 1. Flow Chart

001 Tableau 2. Comparaison entre les deux groupes en termes de caractéristiques cliniques Variables étudiées

  Tableau 3. Comparaison des antécédents psychiatriques familiaux dans les deux groupes

	Antécédents de troubles de l'humeur Personnel Episode mélancolique ou dépressif + episode hypomaniaque Episode mélancolique ou dépressif Aucun Total Age du début de l'AM (années) Antécédents de troubles bipolaires chez parents ou grand-parents, avec thymoregulateur 2 (2,1 %) 5 (5,2 %) 1 (1 %) 8 (8,3 %) Echantillon total Forte suspicion de Family troubles bipolaires 4 (4,2 %) 6 (6,3 %) 3 (3,1 %) 13 (13,6 %) (N = 96) Avec antécédents de troubles (N = Aucun 0 (0 %) 37 (38,5 %) 38 (39,6 %) 75 (78,1 %) 17) 14,5 ± 1,8 13,4 ± 1,7 Délais entre début de l'AM et hospitalisation (years) 2,0 ± 1,7 3,4 ± 2,3 Age du début du suivi pour AM 14,9 ± 1,7 14,5 ± 1,6 Délais entre début du suivi pour AM et hospitalisation 1,6 ± 1,4 2,2 ± 1,6 Nombre de precedents hospitalisations pour AM 0,8 ± 1,5 1,7 ± 2,4 Nombre de tentatives de suicide 0,22 ± 0,7 0,8 ± 1,5 Antécédents ou presence d'au moins un épisode dépressif 56,3 % 100 % Age à la première consultation psychiatrique 14,4 ± 2,9 14,0 ± 2,0 Nutrition entérale pendant l'hospitalisation 51,6 % 81,3 % Nombre de fois où la nutrition entérale a été utilisée 35,3 ± 21,5 25,9 ± 23,8 Traitement à la sortie incluant un 7,3 % 35,3 % (N = 96) Subjects with a history of bipolar disorder (N = 17) Subjects without a Total 6 (6,3 %) 48 (50 %) 42 (43,7 %) 96 (100 %) Sans antécédents de troubles (N = 79) 14,8 ± 1,8 1,7 ± 1,4 15,1 ± 1,7 1,4 ± 1,3 0,6 ± 1,2 0,1 ± 0,4 46,8 % 14,6 ± 3,1 45,5 % 38,5 ± 20,1 1,3 % history of bipolar disorder (N = 79) p Antécédents maternels Tentative de suicide 4,2 % 11,8 % 2,5 % 0.14 Suicide 1,0 % 5,9 % 0,0 % 0.18 TCA 19,8 % 29,4 % 17,7 % 0.32 Dépression 54,2 % 58,8 % 53,2 % 0.67 Trouble anxieux 9,4 % 5,9 % 10,1 % 1.00 Trouble de la personnalité 8,3 % 11,8 % 7,6 % 0.63 Alcoolisme 1,0 % 5,9 % 0,0 % 0.18 Antécédents paternels Tentative de suicide 1,0 % 0,0 % 1,3 % 1.00 Suicide 0,0 % 0,0 % 0,0 % -TCA 0,0 % 0,0 % 0,0 % -Dépression 19,8 % 23,5 % 19,0 % 0.74 Trouble anxieux 6,3 % 5,9 % 6,3 % 1.00 Trouble de la personnalité 9,4 % 5,9 % 10,1 % 1.00 Alcoolisme 14,6 % 0,0 % 17,7 % 0.07 < 0.Echantillon Total p 0.005 0.004 0.09 0.04 0.03 0,003 < 0.001 0.09 0.009 0.007 thymorégulateur Tentative de suicide 1,0 % 0,0 % 1,3 % 1.00
		Suicide	0,0 %	0,0 %	0,0 %	-
		TCA	5,2 %	0,0 %	6,3 %	0.58
	Antécédents	Dépression	19,8 %	23,5 %	19,0 %	0.74
	chez la fratrie	Troubles anxieux	6,3 %	5,9 %	6,3 %	1.00
		Troubles de la personnalité	9,4 %	5,9 %	10,1 %	1.00
		Alcoolisme	14,6 %	0,0 %	17,7 %	0.07