MD, PhD Isabelle Jalenques
email: ijalenques@chu-clermontferrand.fr

Laura Ciortianu

MD Bruno Pereira

Sophie Michel D'incan

Fabien Lauron

Rondepierre

MD, PhD Michel D'incan

MD Sophie Lauron

PhD Fabien Rondepierre

Isabelle Pr

Jalenques

The prevalence and odds of anxiety and depression in children and adults with hidradenitis suppurativa: Systematic review and meta-analysis

Keywords: Hidradenitis suppurativa, Depression, Anxiety, Systematic review, Meta-analysis /kwmh7vb9zh.2

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

Dermatologists should screen for depression/anxiety in hidradenitis suppurativa patients and refer them for psychiatric evaluation and appropriate treatment when necessary.

Introduction

Hidradenitis suppurativa (HS) is a chronic follicular occlusive disease involving the folliculopilosebaceous unit. Clinically, patients have recurrent inflamed follicular lesions, nodules and abscesses leading to draining sinus tract formation and severe scars in the intertriginous areas.

The association between certain chronic inflammatory skin diseases and psychiatric disorders has been widely studied. Systematic reviews or meta-analyses of the prevalence of depression or anxiety in psoriasis, alopecia areata (AA) and atopic dermatitis (AD) have been published [START_REF] Dowlatshahi | The prevalence and odds of depressive symptoms and clinical depression in psoriasis patients: a systematic review and meta-analysis[END_REF][START_REF] Fleming | The prevalence of anxiety in patients with psoriasis: a systematic review of observational studies and clinical trials[END_REF][START_REF] Lee | Comorbidities in alopecia areata: A systematic review and metaanalysis[END_REF][START_REF] Rønnstad | Association of atopic dermatitis with depression, anxiety, and suicidal ideation in children and adults: A systematic review and meta-analysis[END_REF] . A recent meta-analysis showed a positive significant association between HS and the risk of suicide [START_REF] Phan | Hidradenitis suppurativa and risk of suicide -systematic review and meta-analysis[END_REF] . Previous observational and registry studies on the prevalence of depression and anxiety in patients suffering from HS yielded divergent results [START_REF] Matusiak | Profound consequences of hidradenitis suppurativa: a review[END_REF] . A meta-analysis proposed prevalence rates of anxiety and depression respectively based on 4 and 10 observational studies in adult patients with HS [START_REF] Machado | Depression and Anxiety in Adults With Hidradenitis Suppurativa: A Systematic Review and Meta-analysis[END_REF] . First the exact magnitude of the association between HS and anxiety is still unknown, since the 4 studies included failed to establish an odds ratio. Second, the limited number of studies failed to test many factors that could affect prevalence. Third, numerous further studies have been published recently and hence a new meta-analysis would provide more accurate results. We aimed to make, therefore, a pooled estimate of the prevalence and odds of depression/anxiety in HS patients and to study the relationship between variations in prevalence and study characteristics.

Materials and methods

Literature search

The Items for the Reporting of Systematic Reviews and Meta-Analysis (PRISMA) were followed [START_REF] Liberati | The PRISMA statement for reporting systematic reviews and meta-analyses of studies that evaluate healthcare interventions: explanation and elaboration[END_REF] . In France, ethics approval is not required for this type of research.

Only articles with full text access were retained, those with access only to an abstract were excluded. The full-text articles were independently assessed for inclusion by LC and FR. If several papers analyzed data from the same cohort, we included the article with the most complete data.

All disagreements between the reviewers were adjudicated by consensus between three authors (FR, LC, IJ).

Data extraction

Two of the authors extracted and tabulated data and checked for accuracy (LC, FR). The data collected were sociodemographic (proportion of female included, mean age), medical (mean duration of HS, Hurley stage, proportion of smokers, number of patients/controls with depression/anxiety) and methodological (prospective or retrospective study, number of patients included, method of depression/anxiety assessment, presence of controls).

Risk of bias

Three authors (FR, LC, IJ) assessed the risk of bias for all studies with a specific instrument that has high interrater agreement in assessment of risk of bias in studies measuring disease prevalence [START_REF] Hoy | Assessing risk of bias in prevalence studies: modification of an existing tool and evidence of interrater agreement[END_REF] . Disagreements between the reviewers were adjudicated by consensus between three of the authors. We included all studies irrespective of their risk of bias.

Statistical analysis

Statistical analysis was performed with Stata software (version 13, StataCorp, College Station, TX). Study characteristics were summarized and reported as mean and standard-deviation for continuous parameters, and percentage for categorical variables.

The meta-analysis took into account between-and within-study variability. To address the nonindependence of data caused by study effect, random-effects models [START_REF] Dersimonian | Meta-analysis in clinical trials revisited[END_REF] were preferred over the usual statistical tests to evaluate the prevalence of anxiety and depression. For stratified analyses according to the diagnostic tool used and for comparison between cases and controls, the same statistical approach was adapted. Results were expressed as prevalence and 95% confidence intervals. Heterogeneity in the study results was assessed by examining forest plots and using I 2 statistic, which is the most common metric for measuring the magnitude of between-study heterogeneity and is easily interpretable. I 2 values range between 0% and 100% and are typically considered low for 25%, modest for 25% to 50%, and high for 50% [START_REF] Higgins | Measuring inconsistency in meta-analyses[END_REF] . Publication bias was assessed by funnel plots and confidence intervals. When possible (sufficient sample size), metaregressions were proposed to study the relationship between variations of prevalence and study characteristics such as assessment method, risk of bias, number and age of patients included, proportion of smokers and Hurley stage 3 patients included, and study design (prospective or retrospective). Results were expressed as regression coefficients (Estimated Coefficient [EC]) and 95%CI).

Finally, to verify the robustness of the results, sensitivity analyses were made excluding studies that were not evenly distributed around the base of the funnel. A sensitivity analysis was also performed to study the prevalence estimate only for those studies for which a case-control comparison was possible, to ensure representativeness in terms of prevalence of this subsample.

Results

A total of 356 and 120 articles on depression and anxiety, respectively, were identified. After screening of the titles and abstracts and removal of duplicates, 65 and 33 articles, respectively, remained and were submitted to full-text review. Of these articles, 37 on depression and 21 on anxiety were excluded. A total of 28 and 12 articles were included in the meta-analysis for depression and anxiety, respectively (Figure 1).

HS and Depression

The 28 studies selected for the meta-analysis of the prevalence of depression are given in Table 1 12-39 .

The meta-analysis revealed a high prevalence of depression in HS patients (21% [17-25]) with very wide variations (I 2 = 99.7%). Prevalence varied according to the diagnostic tool used, from 10% [5-15] in studies based on medical records and the ICD/DSM classification to 31% [26-36] in those involving self-administered questionnaires (Figure 2). These results were confirmed by a meta-regression analysis, which indicated that prevalence was significantly higher in surveys with self-administered questionnaires (EC 0.21 [0.12;0.30], p<0.001). Variations between the studies can also be explained by study design, with retrospective studies recording a lower prevalence than prospective ones (EC -0.09 [-0.19;-0.01], p=0.035) and by patient numbers, with studies including more than 500 patients recording a lower prevalence of depression (EC -0.15 [-0.25;-0.05], p=0.005). In contrast, patient age, proportion of smokers, proportion of Hurley stage 3 patients and bias risk had no effect on prevalence.

Analysis of the 10 case-control studies, comprising 78 129 patients and 14 086 989 controls, showed an association between depression and HS (OR 2.01 [1.67-2.48]) (Supplementary Figure 1). Even after exclusion of one study (using a self-administered questionnaire) for funnel plot publication bias (Supplementary Figure 2) the association was still present (OR 1.99 [1.63-2.43]) (Figure 3). Sensitivity analysis showed that the prevalence of depression in patients from the casecontrol studies was close to that observed in our meta-analysis (17% [10-24] before exclusion of the biased article and 15% [8-23] after exclusion).

HS and Anxiety

The 12 studies selected for the meta-analysis of the prevalence of anxiety are listed in Table

1 [START_REF] Shavit | Psychiatric comorbidities in 3207 patients with hidradenitis suppurativa[END_REF][START_REF] Humphries | Wide excision and healing by secondary intent for the surgical treatment of hidradenitis suppurativa: A single-center experience[END_REF][START_REF] Garg | Opioid, alcohol, and cannabis misuse among patients with hidradenitis suppurativa: A population-based analysis in the United States[END_REF][START_REF] Huilaja | Patients with Hidradenitis Suppurativa Have a High Psychiatric Disease Burden: A Finnish Nationwide Registry Study[END_REF][START_REF] Kimball | The Comorbidity Burden of Hidradenitis Suppurativa in the United States: A Claims Data Analysis[END_REF][START_REF] Thorlacius | Increased Suicide Risk in Patients with Hidradenitis Suppurativa[END_REF][START_REF] Tiri | Somatic and psychiatric comorbidities of hidradenitis suppurativa in children and adolescents[END_REF][START_REF] Butt | The associations of depression and coping methods on health-related quality of life for those with hidradenitis suppurativa[END_REF][START_REF] Nielsen | Pain perception in patients with hidradenitis suppurativa[END_REF][START_REF] Blanco | To what extent do disease severity and illness perceptions explain depression, anxiety and quality of life in hidradenitis suppurativa?[END_REF][START_REF] Zimman | Hidradenitis Suppurativa: Estimated Prevalence, Clinical Features, Concomitant Conditions, and Diagnostic Delay in a University Teaching Hospital in Buenos Aires, Argentina[END_REF][START_REF] Patel | Association between hidradenitis suppurativa and hospitalization for psychiatric disorders: a cross-sectional analysis of the National Inpatient Sample[END_REF] .

The meta-analysis showed anxiety to have a prevalence of 12% [6-17] in HS patients with very wide variations (I 2 = 99.9%). Prevalence varied according to the diagnostic tool used, from 6% [1-11] in studies based on medical records and the ICD/DSM classification to 25% [13-36] in those using self-administered questionnaires. (Figure 4). These results were confirmed by a metaregression analysis, which indicated that prevalence was significantly higher in surveys with selfadministered questionnaires (EC 0.19 [0.05;0.32], p=0.011). Variations between the studies can also be explained by study design, with retrospective studies recording a lower prevalence than prospective ones (EC -0.16 [-0.28;-0.04], p=0.012). Patient age, sample size, proportion of smokers included and bias risk had no effect on prevalence.

Analysis of the 7 case-control studies (all retrospective), comprising 77 712 patients and 100 994 135 controls, showed an association between anxiety and HS (OR 1.97 [1.65-2.35]) (Figure 5).

The results were similar irrespective of the diagnostic tool used. Sensitivity analysis showed that the prevalence of anxiety in patients from the case-control studies was close to that observed in our meta-analysis (9% [2-16]).

Discussion

Main findings

This study demonstrated a positive and significant association between HS and depression and anxiety. Additionally, it shows that the prevalence of both depression and anxiety varies according to the assessment method used (with prevalence being higher in studies using self-administered questionnaires), and study design (with prevalence being lower in retrospective studies).

Interpretation

Our meta-analysis was based on 28 studies of depression in 93935 patients and 12 studies of anxiety in 78326 patients. A previous paper analyzed depression in 10 studies involving 40307 patients (9 full text articles and 1 abstract) and anxiety in 4 studies involving 15533 patients (3 full text articles and 1 abstract) [START_REF] Machado | Depression and Anxiety in Adults With Hidradenitis Suppurativa: A Systematic Review and Meta-analysis[END_REF] . Of the 19 full text additional articles of depression incorporated in the present meta-analysis, 7 included controls, 11 were retrospective and used medical records, and 8 were prospective and based on self-administered questionnaires. The number of patients per study ranged from 17 to 32625. Of the 9 full text additional articles of anxiety incorporated in the present paper, 6 were retrospective and used medical records and 3 were prospective and based on self-administered questionnaires. The number of patients per study ranged from 17 to 24266.

Among the additional studies analyzed, 7 on depression and 5 on anxiety comprised pediatric patients. The inclusion of these publications provided an accurate and reliable estimate of the prevalence rates of depression /anxiety and their association with HS, and enabled us to assess various factors likely to affect prevalence such as sample size, study design and patient age.

We observed a higher overall prevalence of depression (21%) among patients with HS than in the general population [START_REF] Lim | Prevalence of Depression in the Community from 30 Countries between 1994 and 2014[END_REF][START_REF]American Psychiatrist Association. Diagnostic and Statistical Manual of Mental Disorders (DSM)[END_REF] . This overall prevalence of depression is slightly higher than that obtained in the paper of Machado et al. (17%). We determined a pooled OR for depression (1.99) that is close to that obtained by Machado [START_REF] Machado | Depression and Anxiety in Adults With Hidradenitis Suppurativa: A Systematic Review and Meta-analysis[END_REF] (1.84).

We observed a higher overall prevalence of anxiety (12%) among patients with HS than that obtained in a previous paper (5%) [START_REF] Machado | Depression and Anxiety in Adults With Hidradenitis Suppurativa: A Systematic Review and Meta-analysis[END_REF] . The 4 studies included by Machado et al. did not allow calculation of OR for anxiety. In our study the OR determined was 1.97, showing a positive and significant association between HS and anxiety.

There are several possible explanations of the increased association between HS and depression or anxiety. Pain, malodorous sweeting and decaying scars impair social and professional activity and affective and sexual life. HS significantly reduce quality of life [START_REF] Matusiak | Profound consequences of hidradenitis suppurativa: a review[END_REF][START_REF] Vinkel | Hidradenitis Suppurativa: Causes, Features, and Current Treatments[END_REF] , particularly in terms of mental health [START_REF] Alavi | Quality-of-life impairment in patients with hidradenitis suppurativa: a Canadian study[END_REF] . This is why a specific quality of life scale currently in development, the HS-QoL-v2 45 , includes items on emotional consequences such as depression and anger. In addition, HS has been associated with cigarette smoking and comorbidities such as inflammatory bowel diseases, cardiovascular diseases and obesity, which are themselves associated with depression and anxiety [START_REF] Matusiak | Profound consequences of hidradenitis suppurativa: a review[END_REF][START_REF] Vinkel | Hidradenitis Suppurativa: Causes, Features, and Current Treatments[END_REF] . Last, there is some evidence that inflammation could be a contributor to depression/anxiety comorbidity in inflammatory skin diseases [START_REF] Farzanfar | Inflammation: A Contributor to Depressive Comorbidity in Inflammatory Skin Disease[END_REF] .

We observed a high heterogeneity across studies for which we suggest several explanations. A major reason for the variation in prevalence rates for both depression and anxiety is the manner in which depression/anxiety is evaluated. The highest prevalence rates were seen in studies using self-report instruments, which are likely to overestimate the prevalence of depression or anxiety.

This tendency has been observed in the community [START_REF] Lim | Prevalence of Depression in the Community from 30 Countries between 1994 and 2014[END_REF] , in other chronic medical illnesses [START_REF] Krebber | Prevalence of depression in cancer patients: a meta-analysis of diagnostic interviews and self-report instruments[END_REF][START_REF] Boeschoten | Prevalence of depression and anxiety in Multiple Sclerosis: A systematic review and meta-analysis[END_REF] , in psoriasis and atopic dermatitis [START_REF] Dowlatshahi | The prevalence and odds of depressive symptoms and clinical depression in psoriasis patients: a systematic review and meta-analysis[END_REF][START_REF] Fleming | The prevalence of anxiety in patients with psoriasis: a systematic review of observational studies and clinical trials[END_REF][START_REF] Rønnstad | Association of atopic dermatitis with depression, anxiety, and suicidal ideation in children and adults: A systematic review and meta-analysis[END_REF] and in the paper of Machado et al. [START_REF] Machado | Depression and Anxiety in Adults With Hidradenitis Suppurativa: A Systematic Review and Meta-analysis[END_REF] . The appropriateness and different cut-off scores of the diagnostic tools to assess clinically significant symptoms could also have contributed to the very wide variations. More importantly, screening tools, compared to methods that use a formal diagnosis of depression/anxiety, can only reveal probable depression/anxiety. A structured clinical psychiatric interview represents the gold standard.

Meta-regression analyses showed that variations can also be attributed to study design and the number of patients included in the studies, with lower prevalence being found in retrospective surveys and in studies involving 500 patients or more. These two factors are closely linked to the method of assessment since retrospective studies are based on medical records and allow inclusion of more patients. We know that the prevalence rates in studies based on medical records are lower than in those using self-report instruments. In addition, the risk of false-negatives in these studies should not be underestimated: if there is not sufficient information about depression/anxiety or if the patient has not been assessed, the uncollected data will not be recorded.

Machado et al. showed no effect of risk of bias (with a scale often used for assessing risk of bias despite some limitations [START_REF] Stang | Critical evaluation of the Newcastle-Ottawa scale for the assessment of the quality of nonrandomized studies in meta-analyses[END_REF][START_REF] Hartling | Testing the Newcastle Ottawa Scale showed low reliability between individual reviewers[END_REF][START_REF] Luchini | Assessing the quality of studies in meta-analyses: Advantages and limitations of the Newcastle Ottawa Scale[END_REF] ) nor of patient age on the prevalence of depression (but the studies included had similar age-groups: 34.3 to 45.8 years). However, the use of a specific tool [START_REF] Hoy | Assessing risk of bias in prevalence studies: modification of an existing tool and evidence of interrater agreement[END_REF] and the integration of studies including children had no effect on prevalence in our meta-analysis. Other meta-regression analyses failed to explain prevalence variations, but for some factors the lack of data made it impossible to show any difference or to assess their effect on prevalence.

Prospective studies with large population-based samples based on a structured or semi-structured clinical psychiatric interview with a record of patients' dermatological data would make it possible to assess the specific prevalence of depression and anxiety disorders such as generalized anxiety, social anxiety, panic disorder and agoraphobia stating the prevalence period studied [START_REF] Gündel | High psychiatric comorbidity in spasmodic torticollis: a controlled study[END_REF][START_REF] Consoli | Low levels of emotional awareness predict a better response to dermatological treatment in patients with psoriasis[END_REF][START_REF] Uguz | Quality of life in patients with chronic idiopathic urticaria: the impact of Axis I and Axis II psychiatric disorders[END_REF][START_REF] Jalenques | High prevalence of psychiatric disorders in patients with skin-restricted lupus: a case-control study[END_REF][START_REF] Dhawan | The Prevalence of Psychiatric Comorbidity in Patients with Prurigo Nodularis[END_REF] .

Limitations

Our meta-analysis was conditioned by the limitations of the studies included. Most of the studies did not provide sufficient details about the patients enrolled, such as the respective proportions of children and adults, the severity of HS (only 9 of the 28 studies on depression and 2 of the 12 on anxiety mentioned the Hurley stage), smoking, and somatic comorbidities, which in certain patients had known associations with depression or anxiety. In the retrospective studies, data were collected over widely varying periods. In studies of alopecia areata it was observed in 50% of patients that psychiatric disorders preexisted before skin disease onset [START_REF] Chu | Psychiatric comorbidities in patients with alopecia areata in Taiwan: a case-control study[END_REF] . In contrast, in the HS studies included in the present work the time elapsed between the onset of depression or anxiety and that of HS was not given. Additionally, owing to lack of information in most of the studies included, we were unable to take into account psychological or pharmacological treatments that can modify mood or anxiety. Last, the variables retrieved from declarative data in some studies also represented a limitation.

Conclusion

This study shows that HS patients have a high burden of depression and anxiety. Prospective studies with large population-based samples based on a structured or semi-structured clinical psychiatric interview should now be performed to refine the analysis.

For the immediate future, however, our results show that clinicians need to be vigilant to the presence of depression or anxiety and to assess whether patients suffering from the conditions should be referred for psychiatric evaluation and appropriate treatment. The numbers on the left represent the number of articles on depression and those on the right on anxiety (n = Depression / Anxiety) Figure 2. Hidradenitis suppurativa. Meta-analysis of the prevalence of depression according to diagnostic tool. Figure 3. Hidradenitis suppurativa. Odds ratio meta-analysis of the association between depression and hidradenitis suppurativa. Figure 4. Hidradenitis suppurativa. Meta-analysis of the prevalence of anxiety according to diagnostic tool. Figure 5. Hidradenitis suppurativa. Odds ratio meta-analysis of the association between anxiety and hidradenitis suppurativa.

  article integrate into what was already known? Divergent results on psychiatric prevalence in patients with hidradenitis suppurativa have been published. • How does it change practice? These meta-analyses show a positive significant association between hidradenitis suppurativa and depression/anxiety. • That is, what does the article mean to the practice of dermatology and what should you do as a result of having read this article? What should change in the way you practice?

Figure 1 .

 1 Figure LegendsFigure 1. Hidradenitis suppurativa. Flow diagram of article selection for the meta-analysis (PRISMA 2009)The numbers on the left represent the number of articles on depression and those on the right on anxiety (n = Depression / Anxiety) Figure2. Hidradenitis suppurativa. Meta-analysis of the prevalence of depression according to diagnostic tool. Figure3. Hidradenitis suppurativa. Odds ratio meta-analysis of the association between depression and hidradenitis suppurativa. Figure4. Hidradenitis suppurativa. Meta-analysis of the prevalence of anxiety according to diagnostic tool. Figure5. Hidradenitis suppurativa. Odds ratio meta-analysis of the association between anxiety and hidradenitis suppurativa.

Acknowledgements

The authors thank J. Watts for advice on the English version of the manuscript.

4 High † Hidradenitis suppurativa severity was assessed according to the three Hurley stages. † † Other controls are patients of other dermatological diseases in two studies and patients with inflammatory bowel disease in one study. Only studies with healthy controls were included in the case-control comparison. † † † The total medical records include medical records with ICD/DSM classification and unspecified medical records in the following ratio: 4/5 for anxiety and 9/9 for depression respectively. Mean age of patients and mean duration of hidradenitis suppurativa are reported in years.


thématique : Coeur de femme Mise au point Spécificités féminines de l'électrocardiogramme et des troubles du rythme Specificities of electrocardiogram and rhythm disorders in women

Points clés

-Les spécificités de l'électrocardiogramme de la femme concernent principalement les paramètres de la repolarisation ventriculaire.

-Les torsades de pointes et les tachycardies ventriculaires idiopathiques sont également plus fréquentes chez la femme.

-L'influence des stéroïdes sexuels est avancée.

-La mort subite est moins fréquente à tout âge et survient en moyenne dix ans plus tard que chez les hommes.

-Les différences de prise en charge des arythmies avec les hommes tendent à s'estomper.

Les différences entre les hommes et les femmes ne sont pas uniquement liées au formatage par les stéréotypes de genre. Quelques spécificités électrocardiographiques existent mais sont sousestimées, notamment au niveau des paramètres traduisant la phase de la repolarisation ventriculaire. Elles sont importantes à connaitre car elles peuvent poser des problèmes diagnostiques avec des pathologies cardiaques à risque. On sait également que les femmes et les hommes diffèrent devant la survenue de plusieurs types d'arythmies cardiaques. Ainsi, la prévalence de la fibrillation atriale ou du syndrome de Brugada est plus élevée chez les hommes, tandis que les femmes sont plus susceptibles de développer des torsades de pointe.

Ces différences pourraient n'être que le reflet de l'existence de disparités entre les sexes au niveau de l'activité électrique cardiaque normale.

permis d'émettre l'hypothèse que les androgènes pourraient contribuer à expliquer les spécificités observées au niveau des paramètres de repolarisation ventriculaire de la femme. Toutefois, leur influence sur les autres paramètres électrocardiographiques a, à ce jour, été peu investiguée.

Electrocardiogramme de repos et d'effort

Qui aurait pu croire que l'électrocardiogramme (ECG), inventé par Augustus Waller au 18 ème siècle et transposé en clinique par Willem Einthoven qui reçut le prix Nobel de médecine en 1924 demeurerait un siècle plus tard un instrument incontournable de la médecine ? Que ce soit une douleur thoracique évocatrice d'un angor ou d'un infarctus, une dyspnée ou des palpitations, l'ECG reste bien souvent le premier examen réalisé après l'interrogatoire et l'examen clinique.

Certaines singularités existent au niveau des paramètres de l'ECG de la femme par rapport à celui de l'homme et doivent être prises en compte pour sa bonne interprétation. 2). [START_REF] Rautaharju | Sex differences in the evolution of the electrocardiographic QT interval with age[END_REF][START_REF] Stramba-Badiale | Are gender differences in QTc present at birth? MISNES Investigators. Multicenter Italian Study on Neonatal Electrocardiography and Sudden Infant Death Syndrome[END_REF][START_REF] Rautaharju | New age-and sex-specific criteria for QT prolongation based on rate correction formulas that minimize bias at the upper normal limits[END_REF] Il a donc été avancé que l'influence des stéroïdes sexuels (testostérone, oestrogène et progestérone) pourraient contribuer à expliquer les différences observées au niveau de la repolarisation ventriculaire entre les femmes et les hommes.

Electrocardiogramme de repos

Un QTc > 460 ms chez l'homme, et > 470 ms chez la femme est considéré comme pathologique et doit faire évoquer un syndrome du QT long. [START_REF] Goldenberg | Long QT syndrome[END_REF][START_REF] Nielsen | Risk prediction of cardiovascular death based on the QTc interval: evaluating age and gender differences in a large primary care population[END_REF] Des valeurs comprises entre 440 -460 ms chez l'homme et 450 -470 ms chez la femme doivent être considérées comme « borderline ».

Le syndrome du QT long touche essentiellement le sujet jeune. Sa prévalence selon les études varie entre 1/2000 et 1/5000 individu. Une prédominance féminine est observée dans toutes les études de grandes cohortes, environ 2/3 des patients présentant un QT long sont des femmes. [START_REF] Nielsen | Risk prediction of cardiovascular death based on the QTc interval: evaluating age and gender differences in a large primary care population[END_REF] Les causes de cette inégalité sont peu connues. Les femmes auraient une réserve de repolarisation moins importante que les hommes, elles disposent de moins de potassium dans la cellule retardant ainsi la repolarisation. Une composante hormonale est également avancée puisqu'avant la puberté on ne constate pas de différence entre les intervalles QT des deux sexes. 2,7,10

Figure 2 : Distribution de la fréquence cardiaque, de l'intervalle QT et QT corrigé en fonction de l'âge et du sexe (en rouge les femmes et en bleu les hommes). D'après Rautaharju PM et al. 7

Autres spécificités de la repolarisation féminine (associée à une repolarisation précoce)

Une variante normale de la repolarisation caractérisée par un sus-décalage du segment ST < 1 mm et des ondes T amples (≤ 13 mm) dans les dérivations précordiales (en particulier V2), est décrite chez environ 20 % des femmes de tout âge. Le point J est légèrement ascensionné (< 1 mm) et le segment ST modérément ascendant (figure 3). [START_REF] Wang | ST-segment elevation in conditions other than acute myocardial infarction[END_REF][START_REF] Surawicz | Prevalence of male and female patterns of early ventricular repolarization in the normal ECG of males and females from childhood to old age[END_REF][START_REF] Mcnamara | Associations of Sex Hormones with Surface Electrocardiogram J Point Amplitude in Healthy Volunteers[END_REF] D'autres particularités distinguent la repolarisation féminine de la repolarisation masculine : l'angle entre le segment ST et l'onde T est moins aigu (< 20°), la forme de l'onde T semble différente entre les deux sexes (la première moitié de l'onde T a une pente plus aiguë chez l'homme tandis que la deuxième moitié de l'onde T (terminal T wave interval) est plus courte chez la femme, ce qui témoigne d'une plus faible dispersion transmurale de la repolarisation ventriculaire. [START_REF] Simonson | Sex Differences in the Electrocardiogram[END_REF][START_REF] Nakagawa | Gender differences in the dynamics of terminal T wave intervals[END_REF] En revanche, il existe peu de données en ce qui concerne les différences sexuelles dans les durées de l'onde P, de l'intervalle PR ou du QRS, [START_REF] Liu | Gender differences in the electrophysiological characteristics of atrioventricular conduction system and their clinical implications[END_REF][START_REF] Dhala | Signal-averaged P-wave analysis of normal controls and patients with paroxysmal atrial fibrillation: a study in gender differences, age dependence, and reproducibility[END_REF][START_REF] Hnatkova | Sex and race differences in QRS duration[END_REF] et ces données semblent parfois contradictoires.

Figure 3 : Variante de repolarisation sur l'ECG féminin (source site internet www.ecardiogram.com) Electrocardiogramme d'effort

La maladie coronarienne, première cause de mortalité dans le monde occidental, se manifeste souvent par de l'angine de poitrine (respectivement premier et deuxième mode de présentation clinique chez la femme et chez l'homme) avec une incidence annuelle de 2% dans la population générale. Toutefois, la symptomatologie chez les femmes est trompeuse. Les symptômes de l'infarctus sont plus volontiers atypiques. Nausée, céphalée ou douleurs dans le dos peuvent remplacer la classique «douleur en étau dans la poitrine irradiant vers la mâchoire ou le bras gauche». Devant l'importance de l'angor d'effort comme symptôme d'alerte de la maladie coronarienne, l'épreuve d'effort s'est imposée et demeure un examen de choix. Il s'agit en effet d'un test relativement sûr et accessible, même pour des médecins non cardiologues. Il fournit des informations aussi bien diagnostiques que pronostiques. Les critères de positivité se basent essentiellement sur les modifications de l'ECG et les symptômes à l'effort. Le sous-décalage de type descendant ou horizontal du segment ST est la plus fréquente des modifications ECG (80 -90%), et c'est sur lui que sont basées la plupart des études et recommandations pour évaluer les performances diagnostiques du test. On le considère comme discriminant lorsqu'il est ≥ 1 mm de 0,06 à 0,08 secondes après le point J (figure 4). [START_REF] Marcadet | French Society of Cardiology guidelines on exercise tests (part 2): Indications for exercise tests in cardiac diseases[END_REF] Sa valeur prédictive augmente avec l'importance du sous-décalage du segment ST.

La littérature accorde au test d'effort standard, lorsqu'il est maximal et que les critères de positivité ECG sont remplis, une spécificité de 77 % et une sensibilité de 72 % chez les hommes. Chez les femmes, la sensibilité et la spécificité se révèlent sensiblement inférieures (61 % et 70 %, respectivement). [START_REF] Tavel | Specificity of electrocardiographic stress test in women versus men[END_REF][START_REF] Fitzgerald | Female False Positive Exercise Stress ECG Testing -Fact Versus Fiction[END_REF] Ceci correspond à un rapport de vraisemblance de 3 chez les hommes et 2 chez les femmes. L'influence d'une plus grande dispersion de l'intervalle QT à l'effort, 22 associé à l'impact de l'activité hormonale et du traitement hormonal substitutif sont avancés pour expliquer ces différences. [START_REF] Morise | The specificity of exercise electrocardiography in women grouped by estrogen status[END_REF]

Figure 4 : Modification de repolarisation lors d'un test d'effort en faveur d'une ischémie myocardique

Troubles du rythme

Il existe une abondante littérature et un consensus d'experts récent sur les différences entre femmes et hommes vis-à-vis des arythmies. [START_REF] Rivero | Sex differences in arrhythmias[END_REF][START_REF] Gowd | The Effect of Female Gender on Cardiac Arrhythmias[END_REF][START_REF] Ehdaie | Sex Differences in Cardiac Arrhythmias: Clinical and Research Implications[END_REF][START_REF] Linde | Sex differences in cardiac arrhythmia: a consensus document of the European Heart Rhythm Association, endorsed by the Heart Rhythm Society and Asia Pacific Heart Rhythm Society[END_REF] De telles différences étaient déjà bien connues pour l'incidence et la prise en charge de la cardiopathie ischémique. L'influence significative du sexe sur la présentation clinique, l'épidémiologie, la physiopathologie, la nature même et la fréquence de nombreux troubles du rythme est dorénavant bien admise, mais les données sont cependant parfois contradictoires. Le sexe peut également influer sur leur prise en charge, les résultats et les risques liés au traitement, mais pour ce dernier point les différences s'estompent progressivement avec le temps. [START_REF] Linde | Sex differences in cardiac arrhythmia: a consensus document of the European Heart Rhythm Association, endorsed by the Heart Rhythm Society and Asia Pacific Heart Rhythm Society[END_REF] Les mécanismes à l'origine de ces différences sont très peu comprises mais plusieurs hypothèses ont été avancées. Les différences hormonales (estrogènes, testostérone), sociales, culturelles, génétiques, et morphologiques (taille) pourraient expliquer les différences liées au sexe. [START_REF] Ehdaie | Sex Differences in Cardiac Arrhythmias: Clinical and Research Implications[END_REF][START_REF] Linde | Sex differences in cardiac arrhythmia: a consensus document of the European Heart Rhythm Association, endorsed by the Heart Rhythm Society and Asia Pacific Heart Rhythm Society[END_REF] Les disparités homme-femme observées dans les paramètres ECG 2-4 sont également susceptibles d'affecter l'apparition des diverses arythmies cardiaques et pourraient ainsi contribuer à expliquer ces différences, de même que le rôle du système nerveux autonome, [START_REF] Huikuri | Sex-related differences in autonomic modulation of heart rate in middle-aged subjects[END_REF] ou les deux.

Coeur de femme et arythmie : quelles spécificités ?

Les femmes ont une fréquence cardiaque plus élevée au repos (3 -5 bpm) et un intervalle QT plus long que les hommes (figure 2). [START_REF] Rautaharju | New age-and sex-specific criteria for QT prolongation based on rate correction formulas that minimize bias at the upper normal limits[END_REF] Les tachycardies sinusales inappropriées sont aussi plus fréquentes, sans doute du fait d'un plus faible niveau d'exercice.

Les femmes et les hommes diffèrent également devant la survenue de plusieurs types d'arythmies cardiaques. Ainsi la prévalence de la fibrillation atriale, celle du syndrome de Brugada ou du syndrome de Wolff-Parkinson-White (présence de voie accessoire de conduction auriculoventriculaire) sont plus élevées chez l'homme, tandis que les femmes sont plus susceptibles de développer des torsades de pointe (on rappelle qu'environ 2/3 des patients présentant un QT long sont de sexe féminin), et deux fois plus de tachycardies jonctionnelles (maladie de Bouveret) que les hommes. [START_REF] Rivero | Sex differences in arrhythmias[END_REF][START_REF] Gowd | The Effect of Female Gender on Cardiac Arrhythmias[END_REF][START_REF] Ehdaie | Sex Differences in Cardiac Arrhythmias: Clinical and Research Implications[END_REF][START_REF] Linde | Sex differences in cardiac arrhythmia: a consensus document of the European Heart Rhythm Association, endorsed by the Heart Rhythm Society and Asia Pacific Heart Rhythm Society[END_REF] De même, certains types de tachycardies ventriculaires en salves (repetitive monomorphic ventricular tachycardia des auteurs anglo-saxons), surviennent en majorité chez des femmes de 20 à 40 ans. Elles se présentent sous la forme d'une extrasystolie ventriculaire monomorphe, infundibulaire droite (plus rarement gauche) avec des salves non soutenues (parfois soutenues) incessantes. [START_REF] Nakagawa | Gender differences in various types of idiopathic ventricular tachycardia[END_REF] De prédominance diurne, la dépendance adrénergique est souvent démontrée. Décrite par Gallavardin pour la première fois en 1920, elle est probablement due à un mécanisme d'automaticité déclenchée utilisant l'AMP cyclique comme médiateur, et associée à une hypersensibilité aux catécholamines. A l'ECG, l'arythmie présente dans la majorité des cas un aspect de retard gauche avec axe vertical, traduisant une origine infundibulaire droite (figure 5). [START_REF] Nakagawa | Gender differences in various types of idiopathic ventricular tachycardia[END_REF] Le pronostic est bénin, l'abstention est de mise en l'absence de tout symptôme. Les bêtabloquants s'avèrent souvent efficaces, de même que le vérapamil. Dans les formes très symptomatiques et réfractaires au traitement pharmacologique, une ablation par radiofréquence peut être proposée. [START_REF] Coggins | Radiofrequency catheter ablation as a cure for idiopathic tachycardia of both left and right ventricular origin[END_REF] Bien que la majorité des ESV proviennent du ventricule droit, certaines naissent de l'infundibulum du ventricule gauche ou au niveau des sinus de Valsalva ; l'aspect morphologique de l'arythmie est alors différent, avec un aspect de retard droit ou intermédiaire en V1 et V2.

Les facteurs déclencheurs de ces tachycardies idiopathiques semblent spécifiques au sexe dans le sens où les changements hormonaux jouent un rôle important dans leur survenue chez la femme. [START_REF] Marchlinski | Sex-specific triggers for right ventricular outflow tract tachycardia[END_REF] Il en est de même des tachycardies supraventriculaires dont la périodicité, plus fréquente dans la phase lutéale, varie avec le cycle menstruel et semble inversement corrélée aux niveaux d'oestrogène.

Figure 5 : Extrasystoles et salves de tachycardie ventriculaire non soutenue sur coeur sain, d'origine infundibulaire droite, enregistrées chez une jeune femme de 32 ans qui consulte pour lipothymies et palpitations

La mort subite cardiaque est moins fréquente chez les femmes à tout âge et survient en moyenne dix ans plus tard que chez les hommes, [START_REF] Haukilahti | Sudden Cardiac Death in Women[END_REF] ce qui est également le cas pour tous les autres types d'arythmies (figure 6). Cette différence peut être liée à l'apparition plus tardive de la maladie coronarienne chez la femme, et explique sans doute l'utilisation moins fréquente du défibrillateur automatique implantable et de la resynchronisation cardiaque même si les différences se corrigent avec le temps. [START_REF] Linde | Sex differences in cardiac arrhythmia: a consensus document of the European Heart Rhythm Association, endorsed by the Heart Rhythm Society and Asia Pacific Heart Rhythm Society[END_REF] En effet, les femmes semblent moins souvent bénéficier de ce type de traitement, alors qu'elles peuvent en tirer bénéfice au moins autant, sinon plus que les hommes. L'étude MADIT-CRT avait ainsi démontré qu'en plus de l'étiologie non-ischémique de la cardiopathie, du caractère typiquement gauche du bloc de branche et d'une largeur de QRS de plus de 150 ms, le sexe féminin était un paramètre indépendant prédicteur d'une réponse positive à la resynchronisation biventriculaire. 33

  QT et QT corrigé en fonction de la fréquence cardiaque (QTc) C'est Bazett qui, dès 1920, a été le premier à décrire que la fréquence cardiaque était plus élevée et le QT plus long chez la femme. 1 De nombreuses études sont venues confirmer ces différences par la suite, et ont permis d'en identifier d'autres qui pour la plupart ne concernent que la phase de repolarisation ventriculaire. 2-4 Le QT est fréquence dépendant car, au cours d'une accélération du rythme cardiaque, dépolarisation et repolarisation sont plus rapides afin d'augmenter leur efficacité propre, conséquence de quoi l'intervalle QT diminue pour des fréquences croissantes. Ainsi, pour une fréquence cardiaque ramenée à 60 cycles/minute, sa valeur normale est ≤ à 440 ms chez l'homme et ≤ à 450 ms chez la femme (figure 1). Son allongement peut être congénital, acquis, ou sporadique.

Figure 1 :

 1 Figure 1 : Calcul de l'intervalle QT et de l'intervalle QT et QT corrigé (QTc) selon la formule de Bazett La différence du QTc humain (~10 ms) n'est pas présent à la naissance ou durant l'enfance, et apparait à la puberté, au moment où les taux d'hormones sexuelles augmentent significativement

Figure 6 :

 6 Figure 6 : Nombre de prises en charge pour troubles du rythme ou de la conduction cardiaque pour 1.000 femmes par tranche d'âge par l'Assurance maladie en France en 2017 (source www.ameli.fr)


Erwan Dupuis
email: erwan.dupuis@cea.fr

Hélène Isnard
email: helene.isnard@cea.fr

Charles Evette
email: charles.evette@cea.fr

Frédéric Chartier
email: frederic.chartier@cea.fr

Hyphenation of capillary electrophoresis with MC-ICP-MS -A novel tool for uranium age dating

Keywords: Capillary electrophoresis, Multi-collector ICP-MS, Stacking, Nuclear forensics, Isotope dilution, Uranium Thorium

Capillary electrophoresis (CE) was hyphenated to multi-collector inductively coupled plasma mass spectrometry (MC-ICP-MS) to determine the model age of a highly enriched uranium (HEU) sample using the 234 U/ 230 Th radiochronometer. The use of hydroxymethylbutyric acid (HMBA) as the CE electrolyte was investigated, and a complexation stacking method was developed to increase the thorium signal obtained. The age of the material was determined by measuring the 230 Th content of the HEU sample using isotope dilution in conjunction with the CE-MC-ICP-MS protocol. The CE-MC-ICP-MS protocol and a standard offline protocol using gravitational chromatography both gave results in accordance within uncertainties with the production date of the HEU sample (March 1965). Liquid waste production was only of a few microliters with the use of CE. The hyphenation of CE with MC-ICP-MS render the measurement of the age of the HEU material in less than one day possible. Obtaining results in a timely fashion is of particular importance for nuclear forensics studies.

Introduction

Uranium is found in natural ores and is thus one of the most common nuclear materials. It is used in nuclear powerplants as fuel. As such, it is not surprising that nuclear forensics studies focus on the analysis of uranium samples [START_REF] Capannesi | Characterization of a suspect nuclear fuel rod in a case of illegal international traffic of fissile material[END_REF][START_REF] Pajo | Investigation of the oxygen isotopic composition in oxidic uranium compounds as a new property in nuclear forensic science[END_REF][START_REF] Han | Measurement of the sulphur isotope ratio ( 34 S/ 32 S) in uranium ore concentrates (yellow cakes) for origin assessment[END_REF][START_REF] Kips | Microscale Isotopic Variation in Uranium Fuel Pellets with Implications for Nuclear Forensics[END_REF]. The provenance of the material is established by determining the elemental and isotopic composition for major but also trace or ultra-trace elements of the sample [START_REF] Krajkó | Application of neodymium isotope ratio measurements for the origin assessment of uranium ore concentrates[END_REF][START_REF] Asai | LA-ICP-MS of rare earth elements concentrated in cationexchange resin particles for origin attribution of uranium ore concentrate[END_REF][START_REF] Donard | Determination of relative rare earth element distributions in very small quantities of uranium ore concentrates using femtosecond UV laser ablation -SF-ICP-MS coupling[END_REF][START_REF] Kristo | Nuclear forensic analysis of uranium oxide powders interdicted in Victoria, Australia[END_REF]. Uranium enrichment needs to be measured to determine the intended use of the material, i.e., for military or civilian purposes [START_REF] Smith | Documentation of a model action plan to deter illicit nuclear trafficking[END_REF].

The age of the material is of great importance to identify its origin. With uranium samples, it is possible to date the last chemical purification of the material using the 234 U/ 230 Th radiochronometer [START_REF] Stanley | A beginner's guide to uranium chronometry in nuclear forensics and safeguards[END_REF][START_REF] Varga | Development and validation of a methodology for uranium radiochronometry reference material preparation[END_REF]. 234 U has a half-life of 2.455 ± 0.006×10 5 a (U, k=1) [START_REF] Bé | Bureau International des Poids et Mesures[END_REF]. It decays into 230 Th, which in turn decays into 226 Ra. With the assumption that there is no 230 Th initially present in the sample, and that the material has behaved as a closed system since its last chemical purification, the age of the material is determined by measuring the respective concentrations of 234 U and 230 Th [START_REF] Varga | Development and validation of a methodology for uranium radiochronometry reference material preparation[END_REF]. Trace amounts of 230 Th are generally still present in the material after chemical purification, yielding results ages older than the true one. As such, ages obtained using the 234 U/ 230 Th radiochronometer are called model ages [START_REF] Kristo | The application of radiochronometry during the 4th collaborative materials exercise of the nuclear forensics international technical working group (ITWG)[END_REF].

As one of the most precise and accurate ways to quantify the elemental concentration of a sample, isotope dilution mass spectrometry (IDMS) is particularly suited for measuring 230 Th and 234 U concentrations [START_REF] Heumann | Isotope dilution mass spectrometry (IDMS) of the elements[END_REF]. Thermal ionization mass spectrometry (TIMS) or multicollector inductively coupled plasma mass spectrometry (MC-ICP-MS) instruments are used in IDMS studies, owing to the low level of measurement uncertainty they provide [START_REF] Kristo | The application of radiochronometry during the 4th collaborative materials exercise of the nuclear forensics international technical working group (ITWG)[END_REF]. The determination of the 230 Th concentration is however impaired by matrix effects due to the high uranium content [START_REF] Varga | Production date determination of uranium-oxide materials by inductively coupled plasma mass spectrometry[END_REF].

Prior to mass spectrometry (MS) measurements, off-line chemical separations are usually used to isolate thorium from its uranium matrix. Those separations are generally carried out using extractant or ion-exchange resins. Such off-line protocols are highly effective and, in combination with mass spectrometry, render possible the determination of the thorium concentration with relative uncertainties between 0.5 and 1.5% [START_REF] Gaffney | Round-robin 230 Th-234 U age dating of bulk uranium for nuclear forensics[END_REF][START_REF] Seth | Accurate measurements of Th-U isotope ratios for carbonate geochronology using MC-ICP-MS[END_REF][START_REF] Williams | 230Th-234U model ages of some uranium standard reference materials[END_REF]. These methods lead to the production of solid waste, made up of the resins themselves, and of a few tens of milliliters of liquid waste [START_REF] Varga | Production date determination of uranium-oxide materials by inductively coupled plasma mass spectrometry[END_REF]. These protocols often involve several steps of conditioning, washing, fraction collection and MS analysis [START_REF] Wallenius | Determination of the age of highly enriched uranium[END_REF].

The online hyphenation of the separation technique with the mass spectrometer makes it possible to reduce the analysis time by to performing all these steps in an automated way.

Additionally, the use of automated separation systems limits cross-contamination of the system and lowers system blanks. [START_REF] Metzger | Automated Separation of Uranium and Plutonium from Environmental Swipe Samples for Multiple Collector Inductively Coupled Plasma Mass Spectrometry[END_REF] Although not for uranium age dating, flow-injection analysis and high-performance liquid chromatography (HPLC) have been used in conjunction with inductively coupled plasma mass spectrometry (ICP-MS) for the separation and online analysis of uranium and thorium in nuclear materials [START_REF] Kumar | HPLC Method for Determination of Th, U and Pu in Irradiated (Th,Pu)O2 using Mandelic Acid as an Eluent[END_REF][START_REF] Hann | Separation of spectral and non-spectral interferences by on-line high performance ion chromatography inductively coupled plasma sector field mass spectrometry (HPIC-ICP-SFMS) for accurate determination of 234 U , 235 U, 238 U and 232 Th in industrial ores[END_REF][START_REF] Aldstadt | Determination of uranium by flow injection inductively coupled plasma mass spectrometry[END_REF].

An alternative to the use of chromatography is capillary electrophoresis (CE), which has already been used for uranium-thorium separations, with an UV detection [START_REF] Macka | Separation of uranium(VI) and lanthanides by capillary electrophoresis using on-capillary complexation with arsenazo III[END_REF]. Capillary electrophoresis limits the production of liquid waste to several microliters owing to the capillary dimensions. The analysis time is also limited thanks to the possibility of hyphenation with ICP-MS. Even though CE-ICP-MS hyphenations were already performed for speciation studies with actinides [START_REF] Kuczewski | Separation of Plutonium and Neptunium Species by Capillary Electrophoresis-Inductively Coupled Plasma-Mass Spectrometry and Application to Natural Groundwater Samples[END_REF][START_REF] Willberger | Investigation of the Electrophoretic Mobility of the Actinides Th, U, Np, Pu, and Am in Different Oxidation States[END_REF], this kind of hyphenation has, to the best of our knowledge, never been applied for uranium age dating in nuclear forensics studies. Capillary electrophoresis was chosen over chromatography for this application with the idea of producing easy-to-use, hyphenated microsystems for rapid age dating in future works. Indeed, eletrokinetic separation techniques do not involve a stationary phase. They offer advantages for microsystems development, as the integration of a stationary phase in a microfluidic channel is often tedious.

Capillary electrophoresis is a powerful technique for the separation of metal species thanks to the use of complexing agents as separation electrolytes. In the nuclear field, alphahydroxyisobutyric acid (HIBA) has been used for separating lanthanides by CE-ICP-MS [START_REF] Day | Application of capillary electrophoresis interfaced to double focusing sector field ICP-MS for nuclide abundance determination of lanthanides produced via spallation reactions in an irradiated tantalum target[END_REF].

Hydroxymethylbutyric acid (HMBA), a molecule similar to HIBA displaying better resolution for light lanthanides, has been utilized in isotachophoresis (ITP) for the same application in an ITP-ICP-MS study [START_REF] Vio | Separation and analysis of lanthanides by isotachophoresis coupled with inductively coupled plasma mass spectrometry[END_REF]. HMBA was chosen in the present study as its complexation with uranium allowed it to be separated from lanthanides, as evidenced by Vio et al. [START_REF] Vio | Separation and analysis of lanthanides by isotachophoresis coupled with inductively coupled plasma mass spectrometry[END_REF].

However, as far as we know, the ability of HMBA to separate uranium from thorium by capillary electrophoresis has yet to be proven.

Capillary electrophoresis also allows an enhancement of the analyte signal with the use of stacking. Stacking consists in inducing a difference in analyte mobility in order to narrow its migration peak and increase its signal [START_REF] Malá | Contemporary sample stacking in CE: A sophisticated tool based on simple principles[END_REF]. A particular method of stacking is called complexation stacking, where metals are complexed during the CE separation as to decrease their mobility [START_REF] Malá | Contemporary sample stacking in CE: A sophisticated tool based on simple principles[END_REF][START_REF] Isoo | Analysis of Metal Ions by Sweeping via Dynamic Complexation and Cation-Selective Exhaustive Injection in Capillary Electrophoresis[END_REF].

In this study, a procedure for determining of the age of a highly-enriched uranium (HEU) sample with a known production date [START_REF] Williams | 230Th-234U model ages of some uranium standard reference materials[END_REF] was developed and validated. The procedure consisted in measuring the 230 Th concentration after spiking with 232 Th and separating it from the uranium with an online CE-MC-ICP-MS hyphenation, with HMBA as the electrolyte. A stacking method was also designed to increase the signal obtained for 230 Th, relative to the low 230 Th amount in the sample.

The first part of this study deals with the development of the U/Th separation by CE and with the development of a thorium stacking method. The second part of the study is the elaboration of a protocol to determine thorium isotope ratios on transient signals by MC-ICP-MS. The 230 Th/ 232 Th isotope ratio was determined during the migration peak obtained by CE, with two different types of detectors -a secondary electron multiplier (SEM) for 230 Th and a Faraday cup for 232 Th. The age obtained with the CE-MC-ICP-MS protocol was compared to the age determined with a standard off-line protocol and with the known production date of the material to validate the analytical procedure.

Materials and methods

Development of uranium-thorium separation by CE-Q-ICP-MS

Standard fused silica capillaries (Polymicro Technologies, Phoenix, USA) were employed.

For capillary preconditioning and rinsing, sodium hydroxide (Titripur, Merck), nitric acid (PlasmaPure, SCP Science) and ultrapure water (18.2 MΩ.cm, Merck Millipore) were used.

In the current study, electrolytes were prepared by dissolving solid HMBA (98%, Sigma-Aldrich) in ultrapure water. The pH of all electrolytes was adjusted to the desired value using a 20-22% ammonia solution (PlasmaPure, SCP Science).

The "synthetic" sample used during optimization of the separation conditions was a mixture of uranium and thorium prepared from 990 ± 5 (U, k=2) µg.g -1 SPEX solutions (SPEX Certiprep), evaporated to dryness and diluted in the separation electrolyte to obtain a thorium and uranium concentration of 0.990 µg.g -1 .

To develop the separation, a commercial CE instrument (Agilent Technologies 7100 CE) was hyphenated to a quadrupole ICP-MS (Agilent Technologies 7700 Series) using a MiraMist CE interface. The details of the experimental setup are presented in Table 1. The length of the capillary could not be shorter than 1 meter, due to the geometry of the CE-ICP-MS setup.

Voltage and pressure were chosen as to maximize the time difference between U and Th migration peaks.

An additional HMBA make-up electrolyte was used in the MiraMist CE nebulizer. The composition of the electrolyte was adapted to each CE experiment and had the same pH and HMBA concentration than the electrolyte located at the outlet of the capillary. Ethanol (HPLC grade, Sigma-Aldrich) was added to the HMBA make-up electrolyte with a 10% ratio (w/w).

Ethanol was added to improve the nebulization process, as prescribed by the MiraMist CE manufacturer, and as reported in several CE-ICP-MS studies [START_REF] Topin | Direct determination of plutonium(V) and neptunium(V) complexation by carbonate ligand with CE-ICP-sector field MS[END_REF][START_REF] Willberger | Determination of the Stability Constants of the Acetate Complexes of the Actinides Am(III), Th(IV), Np(V), and U(VI) Using Capillary Electrophoresis-Inductively Coupled Plasma Mass Spectrometry[END_REF].

Before its first use, the capillary was conditioned by successively flushing it with 0.1M NaOH, 2% nitric acid and ultra-pure water for 20 minutes each. Between the analyses, the capillary was successively flushed with NaOH, water and the separation electrolyte for 6 minutes each.

Injections were performed hydrodynamically. The injection volume was 1% of the capillary volume. The injection volume was raised to 5% of the capillary volume during the development of the stacking protocol.

The migration time of neutral species was detected with a contactless conductivity detector (C 4 D). Analyte electrophoretic mobilities (µep) were calculated from the migration times of the analytes and of the neutral species with Equation 1 [START_REF] Kuhn | Capillary Electrophoresis: Principles and Practice[END_REF].

= ² × ( ) - × × ( ) (1)
In Equation 1, is the length of the capillary, is the distance between the capillary inlet and the C 4 D detector and U is the separation voltage. tm(analyte) is the migration time of the analyte measured with the ICP-MS, tm(neutral species) is the migration time of the neutral species measured with the C 4 D. Simulations were performed as part of the development of the stacking protocol using the Simul5 software [START_REF] Hruška | Simul 5 -Free dynamic simulator of electrophoresis[END_REF].

Development of the 230 Th/ 232 Th measurement protocol by CE-MC-ICP-MS

Samples and spikes

The HEU sample, the age of which was determined in this study, was the certified reference material U-970 (New Brunswick Laboratory, USA). The last chemical purification of this material was performed in March 1965 [START_REF] Williams | 230Th-234U model ages of some uranium standard reference materials[END_REF]. The material was an U3O8 powder, that was weighed before dissolution in HNO3 4M (PlasmaPure, SCP Science) to obtain a diluted HEU solution. U-970 is certified in regards to its 235 U/ total U atom ratio, with a certified value of 0.97663 ± 0.00003 (U, k=2), and in regards to its 234 U/ tot U atom ratio, with a certified value of 0.016653 ± 0.000017 (U, k=2). 230 Th is present in trace amounts in the HEU sample, with a theoretical [ tot U]/[ 230 Th] atom ratio of about 4×10 5 . The concentration of 234 U in the diluted HEU solution was previously determined using isotope dilution associated with thermal ionization mass spectrometry with a 233 U spike, and was 22.96 ± 0.07 µg.g -1 (U, k=2).

The concentration of 230 Th in the HEU sample was measured by isotope dilution with CE-MC-ICP-MS analysis. The 232 Th spike was obtained from 988 ± 5 µg.g -1 (U, k=2) SPEX solutions. The absence of 230 Th in the spike solutions was evidenced by Q-ICP-MS, with a limit of detection in the order of pg.g -1 . Four different isotope-diluted samples were prepared, using two different thorium SPEX solutions. The sample-spike mixtures were evaporated to dryness on a hot plate, and dissolved in an appropriate amount of separation electrolyte prior to injection in the CE system. The concentration of uranium in the sample-spike mixtures varied from 400 to 600 µg.g -1 , corresponding to a 230 Th concentration inferior to 2 ng.g -1 , and to injected 230 Th quantities inferior to 400 fg. The concentration of the 232 Th was below 60 ng.g -1 in the sample-spike mixture, yielding injected 232 Th quantities of less than 12 pg.

CE-MC-ICP-MS experimental setup

The Neptune Plus MC-ICP-MS (Thermo Scientific) ion source was located in a glovebox. A laboratory-built CE setup was employed in the glovebox, comprising notably a hermetic vessel for pressure and high-voltage application. The MiraMist CE interface was also utilized to hyphenate CE with MC-ICP-MS. The details of the experimental setup used here are presented in Table 2. They have been adapted from the ones used in previous investigations [START_REF] Martelat | Precise U and Pu Isotope Ratio Measurements in Nuclear Samples by Hyphenating Capillary Electrophoresis and MC-ICPMS[END_REF].

A double inlet spray chamber allows the introduction of an isotope certified reference material with a dedicated MicroMist nebulizer before and after the migration of the analyte peak without disturbing the separation, using the Intra-Injection Sample Standard Bracketing (IISSB) protocol, previously developed in our laboratory [START_REF] Guéguen | Neodymium isotope ratio measurements by LC-MC-ICPMS for nuclear applications: investigation of isotopic fractionation and mass bias correction[END_REF]. The certified isotope reference material employed is IRMM-183 (European Commission, JRC Geel, Belgium), with certified atom ratios of 0.0032157 ± 0.0000016 (U, k=2) for 235 U/ 238 U and 0.000148358 ± 0.000000054 (U, k=2) for 236 U/ 238 U.

Procedure for MC-ICP-MS isotope ratio measurements

After thorium separation from uranium by CE, the 230 Th/ 232 Th ratio in the HEU sample was measured with the MC-ICP-MS. Due to the low amount of 230 Th present in the HEU sample relative to the uranium content, a SEM was used to acquire the 230 Th signal, while a Faraday cup was used to acquire the 232 Th signal.

Several corrections factors were applied using the uranium certified isotope reference material IRMM-183. Mass bias was taken into account by measuring the 235 U/ 238 U ratio of IRMM-183. The use of uranium CRMs to correct thorium mass bias has proven to be valid with several studies [START_REF] Williams | 230Th-234U model ages of some uranium standard reference materials[END_REF][START_REF] Varga | Validation of reference materials for uranium radiochronometry in the frame of nuclear forensic investigations[END_REF][START_REF] Treinen | US-DOE and CIAE international cooperation in age-dating uranium standards[END_REF]. Hydride formation was calculated by measuring the 238 U 1 H/ 238 U ratio of IRMM-183. The interdetector gain was obtained by measuring the 236 U/ 238 U ratio, correcting it for hydride formation and mass bias, and finally correcting to the certified value to obtain the interdetector gain. This method was adapted from the Hoffmann et al. method [START_REF] Hoffmann | Procedures for accurate U and Th isotope measurements by high precision MC-ICPMS[END_REF]. The stability of the interdetector gain was subsequently verified over the day.

The Linear Regression Slope (LRS) method was used to determine the 230 Th/ 232 Th ratio, as well as the 238 UH/ 238 U, the 235 U/ 238 U and the 236 U/ 238 U ratios of IRMM-183 with transient signals, setting the integration time to 0.131 s. This method allows the determination of isotope ratios on transient signals while minimizing the errors caused by different detector time constants [START_REF] Fietzke | An alternative data acquisition and evaluation strategy for improved isotope ratio precision using LA-MC-ICP-MS applied to stable and radiogenic strontium isotopes in carbonates[END_REF][START_REF] Gourgiotis | Method for isotope ratio drift correction by internal amplifier signal synchronization in MC-ICPMS transient signals[END_REF].

A summary of the measurement protocol developed in this study is presented in Figure 1, along with an outline of the detector configurations used for those measurements, presented in Table 3. The SEM was used to measure low-intensity signals of 230 Th + , 236 U + and 238 U 1 H + . On the NeptunePlus MC-ICP-MS, the SEM is located at the central position of the multicollector array (position C). Faraday cups were used for 238 U + and 235 U + on the low mass side (position L1), and for 238 U + and 232 Th + on the high mass side (position H2). The time in-between two separations using the developed protocol was between two and three hours.

Age determination of the HEU sample

The age of the HEU sample was determined by measuring the 230 Th concentration of the HEU sample by isotope dilution and CE-MC-ICP-MS analysis [START_REF] Heumann | Isotope dilution mass spectrometry (IDMS) of the elements[END_REF]. The thorium concentration in the HEU sample was calculated using Equation 2 [START_REF] Heumann | Isotope dilution mass spectrometry (IDMS) of the elements[END_REF].

[ ℎ] ! " = [ ℎ " ] ! × # ! # ! × $ ! $ ! × %& ' % ( × ) ℎ '*+ ℎ '*' , - (2)
In Equation 2 Finally, the age of the material was determined using Equation 3, derived from the Bateman equations of radioactive decay [START_REF] Hruška | Kohlrausch regulating function and other conservation laws in electrophoresis[END_REF], where 6 7 For the HEU sample, the model-age obtained with the CE-MC-ICP-MS protocol was compared to the model age determined with a standard offline protocol, using the same HEU diluted solution and a 232 Th spike. The standard offline protocol consisted in separating thorium from uranium with a UTEVA resin (Triskem International), after which the thorium fraction was collected. The 230 Th/ 232 Th ratio in the thorium fraction was determined by MC-ICP-MS, measuring both thorium isotopes with a SEM in peak-jumping mode.

Results and discussion

Development of uranium-thorium separation using capillary electrophoresis and complexation stacking

The separation between uranium and thorium was developed, first by selecting the background electrolyte. The ability of HMBA to separate uranium and thorium by CE was verified using CE-Q-ICP-MS, injecting the synthetic sample of uranium and thorium at a concentration of 1 µg.g -1 for both actinides. The electrophoretic mobilities of thorium and uranium were studied over a wide HMBA concentration range (5 to 500 mmol.L -1 ) at a pH of 3 to avoid thorium hydrolysis. Two different HMBA concentrations were further selected to observe the change of migration behavior between a low-complexing electrolyte (HMBA 150 mmol.L -1 ) and a high-complexing one (HMBA 500 mmol.L -1 ). The HMBA concentration and pH were constant along the capillary, as illustrated in the inset of Figure 2a. The results obtained for a uranium-thorium separation conducted using a low-complexing electrolyte -HMBA 150 mmol.L -1 adjusted to a pH of 3 -are presented in Figure 2a, whereas the results obtained using a high-complexing electrolyte are presented in Figure 2b.

Uranium and thorium were baseline separated with both the low-complexing and highcomplexing electrolytes, as visible in Figure 2a and Figure 2b. The duration of the CE runs in Figure 2a and Figure 2b were 50 and 70 minutes respectively, which is uncommon for CE separations. The capillary length (1 m) and the pressure applied to the inlet vial (20 mbar) were chosen as to maximize the time separating the migration of Th(IV) and U(VI), thereby increasing the CE run time. By comparison with the migration time of neutral species in Figure 2a, it can be seen that thorium exhibited a cationic behavior in HMBA 150 mmol.L -1 at a pH of 3, while uranium was slightly anionic, with mobilities of respectively µep(Th)= 1.68×10 -5 cm².V -1 .s -1 and µep(U)= -0.38×10 -5 cm².V -1 .s -1 . As visible in Figure 2b, thorium and uranium migrated long after the neutral species in HMBA 500 mmol.L -1 at a pH of 3, signifying that they were negatively charged, with mobilities of respectively µep(Th)= -6.14×10 -5 cm².V -1 .s -1 and µep(U)= -8.31×10 -5 cm².V -1 .s -1 . The reduction of the thorium and uranium mobilities was consistent with the increase in free ligand concentration caused by the rise in HMBA concentration.

In Figure 2, the concentration ratio between U and Th in the synthetic sample was 1/1.

However, in the HEU sample, the tot U/ 230 Th was about 4×10 5 (see Materials and Methods section). To obtain sufficient intensity for 230 Th, the amount of sample introduced in the capillary was raised, by increasing the sample injection volume. To avoid the deterioration of the peak shape caused by the increase in sample volume, it was necessary to apply a stacking protocol [START_REF] Malá | Contemporary sample stacking in CE: A sophisticated tool based on simple principles[END_REF].

A thorium stacking method employing complexation stacking with a stationary concentration boundary was therefore developed. The stationary concentration boundary induced a difference in thorium mobility across the boundary between the complexing and the noncomplexing zones. Figure 3 presents a schematic description of the composition of electrolytes inside the capillary applying such a method. The capillary composition at the beginning of the separation, depicted in Figure 3, was experimentally obtained by successive hydrodynamic injections of the electrolytes. The sample plug was located left of the stationary boundary, and its composition was identical to the one of the non-complexing zone -except for the presence of thorium and uranium.

When the mobility of thorium decreases to the right of the concentration boundary, stacking occurs. Since thorium and uranium have negative mobilities in HMBA 500 mmol.L -1 pH 3, this electrolyte was chosen for the zone to the right of the boundary, called the complexing zone. As a result of the thorium mobility being negative in the complexing zone, thorium is not only stacked but also focused at the concentration boundary.

Thorium must exhibit a positive mobility in the zone to the left of the concentration boundary, called the non-complexing zone, for focusing to occur. Also, uranium must have a negative mobility in the non-complexing zone, otherwise it would focus alongside thorium on the concentration boundary. Thorium exhibits a positive mobility while that for uranium is negative in HMBA 150 mmol.L -1 pH 3. This electrolyte was therefore chosen for the noncomplexing zone.

Because of the low difference in mobility between thorium and uranium (µep(Th)-µep(U)= 2.06×10 -5 cm².V -1 .s -1 ) in HMBA 150 mmol.L -1 at a pH of 3, it would be difficult to perform the separation using the electrolyte setup presented in Figure 3. To improve the uranium-thorium separation, it was decided to raise the pH of the electrolyte in the sample zone as this would increase the proportion of free ligand in the electrolyte, and have the same effect on the electrophoretic mobilities as increasing the total HMBA concentration. Nevertheless, this effect was temporary, as hydrogen ions migrate very rapidly in the capillary, and since their concentration adjusts due to regulation laws [START_REF] Hruška | Kohlrausch regulating function and other conservation laws in electrophoresis[END_REF]. Simulations were performed to predict the behavior of the electrolyte setup presented in the inset of Figure 4, using the Simul 5 software [START_REF] Hruška | Simul 5 -Free dynamic simulator of electrophoresis[END_REF]. A more detailed description of the calculations and of their interpretation can be found in the Electronic Supplemental Information (ESI), along with Figures S1,S2, and S3 depicting the evolution of ion concentrations in the capillary. Figure S1 shows the HMBA concentration and pH as a function of capillary position at the beginning of the separation. When the simulation started, the sample zone became more acidic due to the migration of hydrogen ions from the non-complexing zone. This resulted in the composition presented in Figure S2, where the sample zone is almost completely acidified. Finally, when the sample zone was completely acidified, hydrogen ions continued to migrate and the complexing zone became more acidic (see Figure S3). The concentration boundary is almost stationary, and only tends to broaden due to diffusion processes. At the end of the separation, the pH of the sample zone was close to 3, while the HMBA concentration was close to 150 mmol.L -1 . The thorium mobility in this medium is positive (μep(Th)= 1.68×10-5 cm².V -1 .s -1 ), leading to thorium focusing at the concentration boundary, after separation from uranium during the transient step where the pH is equal to 4 in the sample zone.

The results of the simulations were experimentally verified using the electrolyte setup presented in the inset of Figure 4. The injection volume was raised to 5 % of the capillary volume. The focusing of thorium greatly improved the thorium signal by concentrating the thorium contained in a large sample volume, here 5% of the capillary volume into a narrow peak. The results obtained for the separation of thorium and uranium with complexation stacking are presented in Figure 4.

As observed in Figure 4, thorium and uranium were separated with 90 seconds of baseline between the two peaks. Furthermore, thorium was focused at the concentration boundary as a narrow and symmetrical peak, confirming the simulations results.

The optimized conditions were HMBA 500 mmol.L -1 pH 3, HMBA 150 mmol.L -1 pH 4, and HMBA 150 mmol.L -1 pH 3 as the complexing electrolyte, the sample zone electrolyte, and the non-complexing electrolyte respectively, as described in Figure 5. All the results presented in this section were obtained using a synthetic sample with a 1/1 Th/U ratio to develop and optimize the stacking method. The results presented in the following sections were obtained by injecting a HEU sample with a tot U/ 230 Th ratio of about 4×10 5 .

Thorium isotope ratio measurements with CE-MC-ICP-MS and determination of the age of the HEU sample

The second part of this study was focused on the development of a method allowing the precise and accurate determination of the 230 Th/ 232 Th isotope ratio with CE hyphenated to MC-ICP-MS. IRMM-183 was injected before and after the CE separation to determine the mass bias and interdetector gain throughout the analytical session, following the analytical strategy described in Figure 1 (see Materials and Methods section). The repeatability of the mass bias correction was evaluated by measuring the 235 U/ 238 U ratio of the IRMM-183

standard injected during a one day analytical session and corrected for mass bias with the bracketed values. Seven values were obtained and averaged. The results are presented in Table S1. The relative standard deviation of the mass-bias corrected 235 U/ 238 U ratio for the IRMM-183 obtained during a one-day analytical session was 3.1 ‰.

The interdetector gain was simultaneously determined by measuring the 236 U/ 238 U ratio of the IRMM-183, detecting 236 U with a SEM and 238 U with a Faraday cup. The repeatability of the interdetector gain correction was evaluated by measuring the 236 U/ 238 U ratio of the IRMM-183 standard injected during a one day analytical session, correcting for the interdetector gain using the bracketed values. Seven values were obtained and averaged. The results are presented in Table S2. The relative standard deviation of the interdetector gain and of the gain-corrected 236 U/ 238 U ratio were respectively 1.7 ‰ and 2.7 ‰. Trueness was evaluated with the relative difference between the gain-corrected and certified 236 U/ 238 U ratios, which was 0.2 ‰, validating the correction of the interdetector gain using the 236 U/ 238 U ratio of IRMM-183.

Overall, precisions and accuracies obtained with the isotope certified reference material were in the per-mil range rendering possible an accurate determination of correction factors for mass bias and interdetector gain needed for the correction of the 230 Th/ 232 Th ratio measured in the HEU sample-spike mixture.

For age determination with CE-MC-ICP-MS, isotope dilution was performed with four sample-spike mixtures (Mixtures 1, 2, 3 and 4), prepared from two different 232 Th spike solutions and the same HEU sample diluted solution qualified for its 234 U concentration at 22.96 ± 0.07 (U, k=2) µg.g -1 (see Samples and spikes, Materials and Methods section). At least three injections were performed for each sample-spike mixture.

Due to the difference in experimental setups, the voltage, pressure and injection volume were For each injection, the mass bias and gain-corrected 230 Th/ 232 Th ratio was used to determine the 230 Th concentration in the HEU sample using equation [START_REF] Capannesi | Characterization of a suspect nuclear fuel rod in a case of illegal international traffic of fissile material[END_REF]. Measurement uncertainties were calculated using the Kragten method of uncertainty propagation [START_REF] Kragten | Calculating Standard Deviations and Confidence Intervals with a Universally Applicable Spreadsheet Technique[END_REF], expressing the uncertainties as combined uncertainties at k=2. To perform the calculation, uncertainties on the mass bias and gain-corrected 230 Th/ 232 Th ratio were evaluated using the standard deviation of three consecutive measurements.

A summary of 230 Th concentrations obtained for the four sample-spike mixtures along with their combined uncertainty (expressed at k=2) is presented in Table 4. An agreement, within uncertainties, was obtained for all the values, regardless of the 232 Th spike solution used. The relative uncertainty was in the percent range, and originated mainly from the uncertainty for the 230 Th/ 232 Th ratio and from the uncertainty regarding the spike concentration. The combined uncertainties obtained for mixtures 1 and 3 were two times higher than for mixtures 2 and 4, and this higher uncertainty was caused by a more pronounced variability in the measured 230 Th/ 232 Th ratio for mixtures 1 and 3. This variability is not caused by a variation of mass bias or interdetector gain correction factors, as it observed on the raw, uncorrected 230 Th/ 232 Th ratio. It is therefore hypothesized that this variation is purely statistical.

The 230 Th concentration of the HEU sample-spike mixture and the associated uncertainty (expressed at k=2) was calculated for each injection using respectively the isotope dilution equation and the Kragten method for uncertainty propagation [START_REF] Kragten | Calculating Standard Deviations and Confidence Intervals with a Universally Applicable Spreadsheet Technique[END_REF]. The model age of the HEU sample and the associated uncertainty (expressed at k=2) was subsequently calculated for each injection using the 230 Th concentration, Equation 2 (see Materials and Methods section) and the Kragten method for uncertainty propagation [START_REF] Kragten | Calculating Standard Deviations and Confidence Intervals with a Universally Applicable Spreadsheet Technique[END_REF]. A summary of the model ages obtained for the different sample-spike mixtures is presented in Figure 6.

The values obtained for the model production date of the HEU sample for the 12 different measurements were in agreement, within uncertainties, with model production dates ranging from June 15 th 1964 to February 3 rd 1966. The mean model production date was May 31 st 1965, with an expanded uncertainty (expressed at k=2) of 209 days, yielding a relative uncertainty of 1.1 % (expressed at k=2). An increase in the injected quantities for uranium and thorium is needed to reach a per-mil level of uncertainty. This increase could be obtained by further increasing the sample volume above 10% of the capillary volume, and/or by using a wider capillary with an internal diameter of 75 µm. The use of a thorium spike with a more precisely known concentration could also lead to a reduction of the measurement uncertainty.

Nevertheless, the mean model production date agreed, within uncertainties, with the known production date of March 1965 (dashed line in Figure 6), therefore validating the CE-MC-ICP-MS protocol developed in this study. The mean model production date was also in agreement, within uncertainties, with the date obtained with the offline protocol using extraction chromatography and offline measurement by MC-ICP-MS, which was November 8 th 1964 with an expanded uncertainty (expressed at k=2) of 168 days (open circle in Figure 6).

Conclusion

The

  , [ tot Th]S is the total thorium concentration in the sample, [ tot Th]Sp the total thorium concentration in the spike, mSp and mS the respective amounts of spike and sample, MS the average thorium molar mass in the sample, MSp the average thorium molar mass in the spike, Sp2 the percentage of 232 Th in the spike, S1 the percentage of 230 Th in the sample, and the isotope ratio of the sample-spike mixture measured with CE-MC-ICP-MS.

  adapted for the HEU sample analysis with CE-MC-ICP-MS. The injection volume was raised to 10% of the capillary volume. The optimized electrolyte setup developed previously was used to perform stacking, to increase the signal obtained on both thorium isotopes.The electropherogram of a thorium-uranium separation performed by CE-MC-ICP-MS for a HEU sample-spike mixture is presented in Figure5. The overall separation and focusing observed in Figure4is reproduced in Figure5. Thorium and uranium migration times were however different between Figure4and Figure5due to the change in injection volume, voltage, pressure and CE instrumentation. Thorium and uranium migration peaks were separated by more than 3 minutes and the shape of the thorium peak indicated that thorium was focused at the concentration boundary. The signal obtained for 230 Th was more than 70 000 cps on the SEM, and more than 30 mV for 232 Th on the Faraday cup, allowing isotope ratio determination. The LRS method was used on the transient 230 Th and 232 Th signals to obtain the 230 Th/ 232 Th ratio in the sample-spike mixture.

  234 U/230 Th radiochronometer was used to determine the age of a HEU sample with a novel CE-MC-ICP-MS protocol. Firstly, the CE separation of thorium and uranium in the HEU sample was optimized. The choice of HMBA as an effective electrolyte to carry out the separation was validated. A new complexation stacking protocol using complexation stacking was implemented to obtain a sufficient230 Th signal with the MC-ICP-MS.Secondly, the combination of CE with MC-ICP-MS rendered possible the determination of the 230 Th content of the HEU sample, using IDMS with a 232 Th spike. The CE-MC-ICP-MS protocol gave a model production date of May 31 st 1965 with an expanded uncertainty of 209 days, in accordance with a standard offline protocol and with the known production date of the HEU sample.

Figure list Figure 1 -Figure 2 a)Figure 3 -Figure 4 -Figure 5 -Figure 6 -

 list123456 Figure list

Table 1 -

 1 CE-MC-ICP-MS is an alternative to existing protocols for 234 U/ 230 Th dating, relying on IDMS or LA-ICP-MS[START_REF] Taylor | State of practice and emerging application of analytical techniques of nuclear forensic analysis: highlights from the 5th Collaborative Materials Exercise of the Nuclear Forensics International Technical Working Group (ITWG)[END_REF]. The required time to obtain a model age, a key factor in nuclear forensics, was only a day with the use of CE-MC-ICP-MS and the technique also limited waste production. CE-MC-ICP-MS protocols could be applied to other samples such as plutonium, with the 238 Pu/ 234 U, 239 Pu/ 235 U, 240 Pu/ 236 U and 241 Pu/ 241 Am radiochronometers.The development of CE microsystems that can be directly hyphenated to MC-ICP-MS is also an area of interest, to further simplify the protocols for the age determination of nuclear materials. Experimental setup used for optimizing the uranium-thorium separation with CE-Q-ICP-MS

Table 2 -

 2 Experimental setup used for isotope ratio measurements of the HEU sample with CE-MC-ICP-MS

Table 3 -

 3 Summary of the detector configurations used on the MC-ICP-MS instrument

Table 4 -

 4 230 Th concentrations obtained for the HEU sample Uncertainties expressed at k=2

Table 4 230

 4 Th concentration (ng.g -1 )

		3.4715 ± 0.064
	Mixture	3.5320 ± 0.064
		3.4839 ± 0.064
		3.4622 ± 0.014
	Mixture	3.4499 ± 0.014
		3.4612 ± 0.014
		3.4727 ± 0.061
	Mixture	3.4276 ± 0.061
		3.4998 ± 0.061
		3.4793 ± 0.061
		3.4605 ± 0.022
	Mixture	3.4582 ± 0.022
		3.4527 ± 0.022

,[START_REF] Han | Measurement of the sulphur isotope ratio ( 34 S/ 32 S) in uranium ore concentrates (yellow cakes) for origin assessment[END_REF]

(Faraday cup)

Acknowledgements

The authors would like to thank Sébastien Mialle and Anthony Nonell for discussions on uncertainty calculations and Benoît Martelat and Laurent Vio for discussions on electrophoretic separations. The authors would also like to thank the anonymous reviewers for their comments, remarks and insight.

Produc�on date CE-MC-ICP-MS injec�ons Average of CE-MC-ICP-MS injec�ons Offline protocol

Model date