Violeta Raverdy

Estelle Chatelain

Guillaume Lasailly

Robert Caiazzo

Jimmy Vandel

Hélène Verkindt

Camille Marciniak

Benjamin Legendre

Pierre Bauvin

Naima Oukhouya-Daoud

Helene Verkindt

Gregory Baud

Mikael Chetboun

Marie-Christine Vantyghem

Viviane Gnemmi

Emmanuelle Leteurtre

Bart Staels

Philippe Lefebvre

Philippe Mathurin

Guillemette Marot

| Francois Pattou

Francois Pattou
email: francois.pattou@univ-lille.fr

Combining diabetes, sex, and menopause as meaningful clinical features associated with NASH and liver fibrosis in individuals with class II and III obesity: A retrospective cohort study

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

INTRODUCTION

Steatotic liver disease (SLD) [START_REF] Rinella | A multi-society Delphi consensus statement on new fatty liver disease nomenclature[END_REF] is a chronic disease characterized by excessive accumulation of triglycerides in hepatocytes and subsequent liver steatosis. If inflammation and liver injury are also present, patients may develop nonalcoholic steatohepatitis (NASH) that may progress to liver fibrosis, cirrhosis, and hepatocellular carcinoma (HCC). In parallel with obesity, the number of NASH cases is expected to increase significantly, with an estimated prevalence of SLD of nearly 30% by 2030 [START_REF] Goossens | Nonalcoholic fatty liver disease burden -Switzerland 2018-2030[END_REF][START_REF] Haldar | Outcomes of liver transplantation for non-alcoholic steatohepatitis: a European liver transplant registry study[END_REF]. Patients with a higher risk of NASH may benefit from current and future efforts to prevent, diagnose, and treat the disease. Until clinically validated and useful biomarkers are developed, the diagnosis of NASH requires a liver biopsy. It is therefore key to determine simple features that will help primary care providers identify subgroups at a higher risk of NASH among individuals with obesity. Among the clinical characteristics associated with the risk of SLD, three in particular deserve special attention: type 2 diabetes (T2D), sex, and menopausal status. First, T2D appears to be the most important predictor of NASH and significant liver fibrosis in individuals with obesity [START_REF] Williams | Prevalence of nonalcoholic fatty liver disease and nonalcoholic steatohepatitis among a largely middle-aged population utilizing ultrasound and liver biopsy: a prospective study[END_REF]. A recent metaanalysis estimated that NASH is present in 37.3% (95% confidence interval [CI]: 24.7-50.0) of patients with T2D while fibrosis is in 17% (95% CI: 7.3-34.9) [START_REF] Younossi | The global epidemiology of NAFLD and NASH in patients with type 2 diabetes: a systematic review and meta-analysis[END_REF]. This bidirectional relationship between T2D and NASH suggests common pathogenic mechanisms [START_REF] Lonardo | Hypertension, diabetes, atherosclerosis and NASH: cause or consequence?[END_REF][START_REF] Portillo-Sanchez | High prevalence of nonalcoholic fatty liver disease in patients with type 2 diabetes mellitus and normal plasma aminotransferase levels[END_REF]. Second, evidence also suggests that NASH is a sex-dimorphic disease, being more frequent in males [START_REF] Lonardo | Sex differences in nonalcoholic fatty liver disease: state of the art and identification of research gaps[END_REF]. Moreover, insulin resistance, hepatic lipid influx, and hepatic adaptation to lipids (e.g., regional fat distribution, visceral adiposity, low-grade systemic inflammation, sarcopenia, hepatic beta-oxidation, and triglyceride synthesis in the liver) are all affected by sex and sex hormones [START_REF] Lonardo | Sex differences in nonalcoholic fatty liver disease: state of the art and identification of research gaps[END_REF][START_REF] Lonardo | Sexual dimorphism of NAFLD in adults. Focus on clinical aspects and implications for practice and translational research[END_REF][START_REF] Lin | Sex-specific autosomal genetic effects across 26 human complex traits[END_REF]. In line with this, PNPLA3 genetic variants have been found to have sex-specific effects on disease progression in primary sclerosing cholangitis [START_REF] Lin | Sex-specific autosomal genetic effects across 26 human complex traits[END_REF].

Genome-wide analysis of transcriptomic liver profile further supports the sexually dimorphic nature of NASH and its link with fibrosis [START_REF] Lefebvre | Hepatic sexual dimorphism -implications for non-alcoholic fatty liver disease[END_REF]. Sex appears therefore as a significant determinant of the progression of NASH and should be included in future practice guidelines [START_REF] Lonardo | Sex differences in nonalcoholic fatty liver disease: state of the art and identification of research gaps[END_REF]. Third, epidemiological studies have consistently reported that the risk of SLD increases after menopause in women [START_REF] Lefebvre | Hepatic sexual dimorphism -implications for non-alcoholic fatty liver disease[END_REF][START_REF] Suzuki | Nonalcoholic fatty liver disease in women[END_REF][START_REF] Distefano | NAFLD and NASH in postmenopausal women: implications for diagnosis and treatment[END_REF], thus identifying natural age-related hormone fluctuations as a disease-modifying factor [START_REF] Lonardo | Sex differences in nonalcoholic fatty liver disease: state of the art and identification of research gaps[END_REF]. Postmenopausal women also have a higher risk of NASH and fibrosis than premenopausal women [START_REF] Lonardo | Fatty liver is associated with an increased risk of diabetes and cardiovascular disease -evidence from three different disease models: NAFLD, HCV and HIV[END_REF][START_REF] Yoneda | The influence of menopause on the development of hepatic fibrosis in nonobese women with nonalcoholic fatty liver disease[END_REF] probably due to the loss of the inhibitory effects of estrogen on stellate cell activation and fibrogenesis [START_REF] Lonardo | Sex differences in nonalcoholic fatty liver disease: state of the art and identification of research gaps[END_REF]. Premature menopause and a longer duration of estrogen deficiency further increase the risk of fibrosis [START_REF] Yang | Gender and menopause impact severity of fibrosis among patients with nonalcoholic steatohepatitis[END_REF].

Additionally, it was shown in T2D that stratifying the disease according to clinical phenotype differs in disease mechanism and progression, risk of complications, and response to treatment [START_REF] Ahlqvist | Novel subgroups of adultonset diabetes and their association with outcomes: a data-driven cluster analysis of six variables[END_REF][START_REF] Raverdy | Data-driven subgroups of type 2 diabetes, metabolic response, and renal risk profile after bariatric surgery: a retrospective cohort study[END_REF][START_REF] Dennis | Disease progression and treatment response in data-driven subgroups of type 2 diabetes compared with models based on simple clinical features: an analysis using clinical trial data[END_REF][START_REF] Zaharia | Risk of diabetesassociated diseases in subgroups of patients with recent-onset diabetes: a 5-year follow-up study[END_REF][START_REF] Stefan | A global view of the interplay between nonalcoholic fatty liver disease and diabetes[END_REF].

Here, we hypothesized that patients could be usefully grouped into qualitative clusters based on simple clinical features associated with increased prevalence of NASH, such as T2D, sex, and menopausal status, which could share an underlying biological level dysfunction. We assessed whether combining these three features could improve SLD stratification in an adult population with obesity with histologically proven NASH and/or significant liver fibrosis. We also tested whether this stratification was related to the clinical, biological, and molecular profiles of the defined subgroups.

METHODS

Study design and patients

This retrospective study analyzed data from the ABOS (Atlas Biologique de l'Obésite Sévère) cohort (NCT01129297), a prospective study aiming to identify determinants for the outcome of bariatric surgery. All ABOS participants who underwent bariatric surgery between 2006 and 2020 at Lille University Hospital were enrolled in the present study (Figure S1). Informed consent was obtained from all participants. Demographic characteristics, anthropomorphic measurements, medical history, medication use, including hormone replacement therapy (HRT), and clinical laboratory tests were prospectively collected before surgery, as previously described [START_REF] Raverdy | Incidence and predictive factors of postprandial Hyperinsulinemic hypoglycemia after roux-en-Y gastric bypass: a five year longitudinal study[END_REF]. Diabetes status was defined at baseline, based on American Diabetes Association guidelines (Supplementary Material and Methods). Menopausal status was classified according to selfreported reproductive information and a history of bilateral oophorectomy.

Liver histology

The SLD/NASH diagnosis and the classification of the SLD cases among participants from the ABOS cohort were performed in the Department of Pathology at Lille University Hospital, France. Liver biopsies were systematically planned during the surgical procedure. Needle biopsies were performed during the first part of the surgical procedure after trocar insertion and abdominal exploration, within 10 min after pneumoperitoneum installation. The Hepafix needle biopsy system was used until 2010, and the MONOPTY needle biopsy system (16G, ref: 121620; C. R. Bard, Tempe AZ, USA) was used thereafter. The same slides were evaluated simultaneously by two different expert liver pathologists, unaware of the clinical information, who gave a consensual central diagnosis as previously published [START_REF] Lefebvre | Hepatic sexual dimorphism -implications for non-alcoholic fatty liver disease[END_REF][START_REF] Lassailly | Bariatric surgery provides long-term resolution of nonalcoholic steatohepatitis and regression of fibrosis[END_REF][START_REF] Lassailly | Bariatric surgery reduces features of nonalcoholic steatohepatitis in morbidly obese patients[END_REF][START_REF] Margerie | Hepatic transcriptomic signatures of statin treatment are associated with impaired glucose homeostasis in severely obese patients[END_REF]. As previously described [START_REF] Lassailly | Bariatric surgery provides long-term resolution of nonalcoholic steatohepatitis and regression of fibrosis[END_REF], the diagnosis of NASH was defined by the presence and pattern of specific histological abnormalities on liver biopsy using the Brunt scoring system for NASH [START_REF] Brunt | Nonalcoholic steatohepatitis: a proposal for grading and staging the histological lesions[END_REF]. Accordingly, NASH diagnosis required the association of liver steatosis, hepatocyte ballooning, and inflammation. Brunt criteria included the following parameters: amount of fat: graded 1-3 according to the percentage of fatty droplets (1, 0%-33%; 2, 34%-66%; 3, 67%-100%) and necroinflammation: graded 0 (absent) to 3 (1, occasional ballooned hepatocytes) and no or very mild inflammation; 2, ballooning of hepatocytes and mild to moderate portal inflammation; 3, intra-acinar inflammation and portal inflammation). Liver fibrosis was assessed semiquantitatively using the Kleiner score (defined as follows: F0, normal; F1, stages are divided into three subclasses: 1a, mild pericellular fibrosis in zone 3, 1b, moderate pericellular fibrosis in zone 3, and 1c, portal fibrosis; F2, perivenular and pericellular fibrosis confined to zone 2 and 3, with or without portal or periportal fibrosis; F3, bridging or extensive fibrosis with architectural distortion and no clear-cut cirrhosis; and F4, cirrhosis) [START_REF] Kleiner | Design and validation of a histological scoring system for nonalcoholic fatty liver disease[END_REF]. Patients with excessive daily alcohol consumption (>30 g/day for male patients, >20 g/day for female patients) and/or nonmetabolic acute, chronic liver disease (alcoholic, drug-induced, or viral hepatitis) were excluded. Biopsies were obtained from individuals who were not in a drug treatment trial and were not receiving any specific drug therapy (Figure S1).

Outcomes

The primary outcome was the diagnosis of NASH defined by the joint presence of steatosis, lobular inflammation, and hepatocellular ballooning [START_REF] Brunt | Nonalcoholic steatohepatitis: a proposal for grading and staging the histological lesions[END_REF] independently of total SLD activity score. The secondary outcome was the diagnosis of moderate-to-advanced liver fibrosis (F ≥ 2) defined by a grade ≥2 according to Kleiner scoring (F ≥ 2) [START_REF] Kleiner | Design and validation of a histological scoring system for nonalcoholic fatty liver disease[END_REF].

Additionally, we evaluated clinico-biological traits available in the ABOS cohort associated with NASH as well as the expression of liver genes previously related to NASH progression.

Microarray data

Transcriptomic data were available in a subset of 869 patients enrolled from 2006 to 2016 [START_REF] Margerie | Hepatic transcriptomic signatures of statin treatment are associated with impaired glucose homeostasis in severely obese patients[END_REF]. Microarray data generation, quality control, and preprocessing have been previously described and are detailed in the Supplementary Material and Methods.

Statistical analysis

A hierarchical clustering was first applied to stratify patients according to binary variables of diabetes status, sex, and menopause for women, without any supervision of outcomes. This clustering was computed with the R function hclust with gower distance calculated using the R package cluster [START_REF] Maechler | Finding Groups in Data[END_REF]. We then calculated the rates of patients with NASH and fibrosis in each subgroup. In parallel, to disentangle the

Study Importance

What is already known?

• Although type 2 diabetes (T2D), male sex, and menopause have been previously associated with a higher risk of nonalcoholic steatohepatitis (NASH) in individuals with obesity, they have always been analyzed separately.

• T2D appears to be the most important predictor of NASH and significant liver fibrosis in individuals with obesity.

• Sex appears as a significant determinant of the progression of NASH.

• Postmenopausal women have a higher risk of NASH and fibrosis than premenopausal women.

What does this study add?

• We showed that combining these simple clinical features improves the stratification of individuals with class II and class III obesity, according to the prevalence of NASH.

• We also identified liver-specific clinico-biological and molecular profiles associated with menopause in women with obesity and T2D, in parallel with the higher prevalence of significant liver disease observed in this subgroup.

How might these results change the direction of research or the focus of clinical practice?

• This study from a large histologically characterized steatotic liver disease (SLD) cohort may provide new insight into disease heterogeneity and suggest new hypotheses to advance precision medicine. Our results highlight the importance of considering sex/menopause in investigating risk factors for the progression of SLD in individuals with T2D and obesity. It is likely that various populations will benefit from pharmacotherapies specific to the metabolic and molecular abnormalities responsible for their SLD. effect of menopause from the effect of age, we run logistic regressions to test the interaction between age and sex with respect to the prevalence of NASH. For that purpose, among T2D patients, we compared the two models with and without interaction through a likelihood ratio test. The interaction was also analyzed after adjustment for other potential confounding factors (body mass index [BMI] and arterial hypertension). In all statistical analyses, age was included as a binary input variable using an empirical cutoff value. This cutoff value was defined as the one that best separates premenopausal and postmenopausal women in our cohort, according to a receiver operating characteristic (ROC) curve analysis (Figure S2). Additionally, we performed sex-specific comparisons between pre-and postmenopausal women on one hand and between men younger and older than the cutoff value on the other hand.

Clinico-biological data were reported as the mean with standard deviation (SD) for continuous variables normally distributed, median with interquartile range (IQR) for other continuous variables and frequencies (in percentages) for categorical variables.

These clinic-biological variables were compared among the defined subgroups using ANOVA for continuous variables normally distributed, Kruskall-Wallis tests for other continuous variables, and χ 2 tests for categorical variables. P values were corrected for multiple comparisons using the Bonferroni method to control the familywise error rate. Proportions of NASH or fibrosis (F ≥ 2) in each subgroup were compared with the average proportion of all subgroups using a binomial test. The clinico-biological variables between NASH and non-NASH individuals were compared using Welch t tests for continuous variables normally distributed, Wilcoxon tests for other continuous variables, and χ 2 tests for categorical variables. A cutoff of 0.05 was chosen on raw p values to select clinical characteristics related to NASH. The same strategy was used to compare these selected variables between pre-and postmenopausal women with T2D and between men with T2D younger and older than the cutoff value. In these analyses, the p values were corrected using Bonferroni method. A cutoff of 0.05 was chosen on adjusted p values for statistical significance. Clinico-biological traits were represented by ratios between two subgroups (postvs. premenopausal status for women, old vs. young for men, NASH vs. non-NASH). The 95% CIs of ratios were computed using the R package DescTools. For comparing NASH and fibrosis (F ≥ 2) in pre-and postmenopausal women with T2D, the statistical power of the khi-2 test was determined. For this, we calculated the effect size as the square of the ratio of the Khi-2 statistic to the number of observations N, which corresponds in our case to Cramer's V. The statistical power was then calculated using the pwr.chisq.test function from the pwr R package (version 1.3-0).

For transcriptomic data, differential analysis between NASH and non-NASH was performed using moderated t tests from the R Bioconductor package limma with a Benjamini-Hochberg correction for multiple testing to control the false discovery rate genes were called differentially expressed if their adjusted p values were below 0.05 and their fold changes (FC) were higher than 1.5 (decrease or increase). Therefore, we focused our analysis on the expression of a subgroup of 25 genes that have been previously associated with the progression of NAFL to severe liver disease (NASH and/or fibrosis [F ≥ 2]) [START_REF] Govaere | Transcriptomic profiling across the nonalcoholic fatty liver disease spectrum reveals gene signatures for steatohepatitis and fibrosis[END_REF] including AKR1B10, ANKRD29, CCL20, CFAP221, CLIC6, COL1A1, COL1A2, DRNA, DUSP8, EPB41L4A, FERMT1, GDF15, HECW1, IL32, ITGBL1, LTBP2, PDGFA, PPAPDC1A, RGS4, SCTR, STMN2, THY1, TNFRSF12A, TYMS, and HSD17B14. Then, the expression of these genes was compared between pre-and postmenopause for women with T2D and between men with T2D younger and older than the cutoff value with Welch t tests. No adjustment was performed on raw p values due to the small number of tests.

The differences were considered significant when raw p values were below 0.05. All statistical analyses were performed using R statistical software version 3.6.3.

RESULTS

Patient characteristics

Among 1545 ABOS participants, we enrolled in the present study 1446 patients with available liver histology who had no exclusion criteria including a history of excessive alcohol consumption and/or having a nonmetabolic acute, chronic liver disease (alcoholic, drug-induced, or viral hepatitis) (Figure S1). The mean age and BMI were 42.0 (±11.7) years and 46.5 (±8.7) kg/m 2 , respectively. The prevalence of NASH and liver fibrosis (F ≥ 2) was, respectively, 9.5% (n = 138, 95% CI: 8.0-11.1) and 11.7% (n = 159, 95% CI: 10.0-13.4), in the overall population and 20.3% (n = 107, 95% CI: 16.9-23.8) and 21.1% (n = 106, 95% CI: 17.6-24.7) in T2D patients and 3.4% (n = 31, 95% CI: 2.2-4.5) and 6.1% (n = 53, 95% CI: 4.5-7.7) in non-T2D patients (Figure 1). In nondiabetic participants, the proportion of NASH was similar in pre-and postmenopausal women (n = 20/613, 3.3%, 95% CI: 1.9-4.7

Stratification of patients

and n = 3/109, 2.75%, 95% 0.0-5.8, respectively) and in men (n = 8/198, 4.0%, 95% CI: 1.3-6.8). Thus, all patients without T2D were combined in a single subgroup of individuals who had a statistically significantly lower than average prevalence of NASH (2.8-fold decrease; 95% CI: 1.9-4.1, p < 0.001). For that reason, we suggest a final stratification focusing on four subgroups: patients without T2D, premenopausal women with T2D, postmenopausal women with T2D, and men with T2D. Similar results among subgroups were observed regarding the proportion of fibrosis (F ≥ 2), the second studied outcome. Among the T2D subgroup, the proportion of patients with fibrosis (F ≥ 2) was 15.5% in premenopausal (n = 32/206, 95% CI: 10.6-20.5), 29.5% in postmenopausal women (n = 33/112, 95% CI: 21.0-37.9, 22.3%), and 22.3% in men (n = 41/184, 95% CI: 16.3-28.3). The proportion of F ≥ 2 in postmenopausal women with T2D and in men with T2D was statistically significantly different from the cohort average proportion (2.9-fold increase, 95% CI: 1.8-4.5, p < 0.001 and 2.5-fold increase, 95% CI: 1.7-3.6, p < 0.001). Among the non-T2D patients, the proportion of fibrosis (F ≥ 2) was 3.8% in premenopausal (n = 22/577; 95% CI: 2.3-5.4), 5.9% in postmenopausal women (n = 6/102, 95% CI:

1.3-10.5), and 13.6% in men (n = 25/184, 95% CI: 8.6-18.5). In contrast, F ≥ 2 prevalence was similar in men with T2D below 50 years Age and sex interaction with respect to the prevalence of NASH in T2D patients

To further explore the distinct role of menopause in women with T2D, we then analyzed the interaction between sex and age with respect to NASH prevalence among all patients with T2D. The likelihood ratio test between the two logistic regression models with and without interaction term showed a statistically significant interaction ( p = 0.048), which remained significant after adjusting for other potential confounding factors (BMI and arterial hypertension), ( p = 0.049). The ROC curve analysis (area under the curve 96.3%, 95% CI: 95.0-97.6) showed that the age cutoff that best separates pre-and postmenopausal women was 50 years (Figure S2). In line with the interaction previously identified, we found that the prevalence of NASH in women with T2D was significantly different between younger and older women ( p = 0.002). In contrast, we observed no significant difference in the proportion of NASH between younger (n = 89) and older men (n = 103) with T2D, respectively (1.2-fold-increase, 95% CI: 0.7-2.0, p = 0.75). Likewise, we observed no significant difference in the proportion of fibrosis (F ≥ 2) between younger and older men with T2D (1.4-fold decrease, 95% CI: 0.7-2.7, p = 0.48).

Distinct clinico-biological profiles related to NASH and menopausal status in women with T2D

Clinical, biological, and liver histology of the subgroups are presented in Table 1. We examined 35 clinico-biological features available in the ABOS cohort and identified 26 of them that were significantly associated with NASH in our cohort (Figure S3). Noteworthy, most features related to impaired glucose control were positively associated with NASH. In contrast, exposure to HRT was negatively associated with an increased prevalence of NASH in women ( p = 0.001).

We then focused on identifying among these 26 clinicobiological traits, those that were specifically associated with NASH induced by menopause in women with T2D. For this, we conducted two parallel analyses, comparing pre-and postmenopausal women with T2D and men with T2D younger and older than the age of 50 years (Figure 2).

The first analysis identified six traits associated with menopause in women with T2D: lower platelet count (Adj. p < 0.001), higher level of serum uric acid (Adj. p = 0.008), gamma-glutamyltransferase (Gamma-GT; Adj. p = 0.02), and serum glutamate oxaloacetate transaminase (SGOT; Adj. p = 0.029), and higher frequency of hypolipidemic (Adj. p < 0.001) and hypotensive treatments (Adj. p < 0.001) (Figure 2A). In the second analysis, which was conducted in men with T2D, the variables associated with age under and over 50 years were higher low-density lipoprotein level and macroglobulin levels as well as a higher frequency of hypolipidemic and hypotensive treatments (Adj. p < 0.001, Adj. p = 0.04, Adj. p < 0.001, and Adj. p < 0.001, respectively) (Figure 2B). Hepatic gene expression profiles related to NASH and menopausal status in women with T2D

T A B L E 1 (Continued) N Non-T2D
Our objective was to investigate whether the specific link between severe liver disease and menopause in women with T2D was associated with specific changes in the liver transcriptome profile. To achieve this, in our cohort, we analyzed the liver expression profile of a subgroup of 25 genes (see Methods) that have previously been linked to the progression of nonalcoholic fatty liver (NAFL) to severe liver diseases, such as NASH and advanced fibrosis [START_REF] Govaere | Transcriptomic profiling across the nonalcoholic fatty liver disease spectrum reveals gene signatures for steatohepatitis and fibrosis[END_REF]. Out of these 25 genes, 23 were available for analysis in the ABOS cohort. Among these 23 genes, we identified two that exhibited significant differential expression with clinically relevant FC (≥1.5) in postmenopausal compared with premenopausal women with T2D. AKR1B10 showed an FC of 1.6 with a p value of 0.011, indicating a significant difference in expression between these two groups. CCL20 demonstrated an FC of 1.7 with a p-value of 0.019 (Table S1, Figure S4). Of note, we did not find any differential expression with clinically relevant FCs among these 23 NASH-related genes, when comparing younger and older men with T2D (Table S1). The distinct expression of these two NASHrelated genes observed after menopause in women with T2D further supports the specific impact of menopause on the development of NASH.

DISCUSSION

In this cross-sectional study, we stratified a large cohort of individuals with class II and class III obesity by combining three simple clinical features: diabetes, sex, and menopausal status. We identified four distinct subgroups with various prevalences of NASH: postmenopausal women with T2D, men with T2D, premenopausal women with T2D, and patients without T2D. Although diabetes, male sex, and menopause have been previously associated with a higher prevalence of NASH in individuals with obesity, they have always been analyzed

separately. In the present study, we identified a new stratification based on the combination of these three simple features, which are all readily available in the primary care setting. Our main finding was the distinct association observed between menopause and the prevalence of severe SLD (NASH and/or liver fibrosis [F ≥ 2]) in women with T2D. In contrast, older age had no significant impact on the prevalence of NASH in men with T2D. In addition, we observed that in the absence of T2D, male sex and postmenopausal status in women had no significant influence on the prevalence of NASH, which remained inferior to 5% in all cases.

One major strength of this study is the large number of unselected patients with severe obesity and a detailed phenotype and liver histology available at enrollment. This enabled us to analyze the

F I G U R E 2
Comparison of the mean, ranks, or frequency of nonalcoholic steatohepatitis-related clinico-biological characteristics (A) between pre-and postmenopausal women with T2D and (B) between men with T2D before and after 50 years. For each analysis, the differences between the mean, rank, or frequency ratio of the two groups were compared using χ2 tests for categorical variables and t tests or Wilcoxon tests for continuous variables. P values were corrected with the Bonferroni method. Continuous variables are represented by means or medians ratio between postmenopausal status and premenopausal status for women and means or medians ratio between men with age ≥50 years and <50 years status. Categorical variables were represented as the percentage ratio between postmenopausal status and premenopausal status for women and means ratio between men with age ≥50 years and <50 years status. In red are variables statistically significantly different only in premenopausal versus postmenopausal women, violet represents statistically significant differences in premenopausal versus postmenopausal women and in men with age <50 years and ≥50 years, blue is statistically significantly differences only in men with age <50 years and ≥50 years, and in gray are the variables not statistically significantly different in each of the comparisons. The y-axis corresponds to the Àlog10 (Adj. p value), and the x-axis displays the log2 of average or frequency. T2D, type 2 diabetes. [Color figure can be viewed at wileyonlinelibrary.com] clinical and biological characteristics associated with NASH across the entire cohort and look for a distinct profile of the disease across the various subgroups. We identified four clinico-biological variables including lower platelet count, higher level of serum uric acid, Gamma-GT, and SGOT that paralleled the higher prevalence of NASH observed in postmenopausal women in the presence of T2D. In contrast, these features were not associated with older age in men with T2D. Hyperuricemia is a known risk factor for SLD, and it has been shown to be higher in women [START_REF] Wu | Association between sex-specific serum uric acid and non-alcoholic fatty liver disease in Chinese adults: a large population-based study[END_REF][START_REF] Liu | Dose-response relationship of serum uric acid with metabolic syndrome and non-alcoholic fatty liver disease incidence: a meta-analysis of prospective studies[END_REF][START_REF] Bao | Association between serum uric acid and nonalcoholic fatty liver disease in nonobese postmenopausal women: a cross-sectional study[END_REF]. In postmenopausal-but not premenopausal-women, serum uric acid levels were found to be associated with SLD, even after adjusting for factors associated with metabolic syndrome. Noteworthy, estrogen replacement therapy was negatively related to NASH in our study, and previous research has linked estrogen deficiency with hyperuricemia [START_REF] Wingrove | The effect of menopause on serum uric acid levels in non-obese healthy women[END_REF][START_REF] Hak | Menopause, postmenopausal hormone use and serum uric acid levels in US women-the third National Health and nutrition examination survey[END_REF][START_REF] Freedman | Relation of serum uric acid to mortality and ischemic heart disease. The NHANES I epidemiologic follow-up study[END_REF]. Finally, in postmenopausal women, uric acid has been associated with inflammation and major adverse cardiovascular events [START_REF] Prasad | Uric acid is associated with inflammation, coronary microvascular dysfunction, and adverse outcomes in postmenopausal women[END_REF]. Adding to the available evidence, our findings suggest that higher uric acid levels may play a distinct role in NASH development, especially among women with T2D. The mechanisms underlying this are still unknown. Lower platelet count found in postmenopausal women with T2D is in line with menopause-related differences in blood count, the low estrogen level in postmenopausal women being considered to be responsible for the decreased platelet count [START_REF] Aldrighi | Platelet activation status decreases after menopause[END_REF][START_REF] Cowman | Age-related changes in platelet function are more profound in women than in men[END_REF] and with age-related changes in platelet function being found more profound in women than in men [START_REF] Cowman | Age-related changes in platelet function are more profound in women than in men[END_REF]. Additionally, it was shown in a randomized clinical trial that combined HRT significantly decreased aminotransferase levels in postmenopausal women with T2D and presumed SLD compared with placebo controls [START_REF] Mckenzie | Effects of HRT on liver enzyme levels in women with type 2 diabetes: a randomized placebo-controlled trial[END_REF]. Collectively, current evidence suggests that estrogen may protect against SLD.

Another strength of our study was the analysis of liver transcriptomic data from the vast majority of the study participants, which allowed us to show that among genes previously linked to NASH and/or liver fibrosis, AKR1B10 and CCL20 were differentially expressed depending on the women's menopausal status. The gene AKR1B10 has been associated with lipid metabolism and oxidative stress [START_REF] Endo | The role of AKR1B10 in physiology and pathophysiology[END_REF][START_REF] Distefano | Diagnostic and prognostic potential of AKR1B10 in human hepatocellular carcinoma[END_REF]. Its increased expression in postmenopausal women with T2D compared with premenopausal women with T2D might indicate a higher level of oxidative stress or lipid accumulation in the liver after menopause in women with T2D. Similarly, the CCL20 gene is involved in the recruitment of immune cells to the site of inflammation [START_REF] Thelen | How chemokines invite leukocytes to dance[END_REF], and its upregulation in postmenopausal women with T2D compared with premenopausal women with T2D might indicate an enhanced inflammatory response in the liver of postmenopausal women with T2D. These two genes are linked to liver inflammation and may also be involved in menopause-related mechanisms that lead to NASH. These two genes may also play a role in the reproductive system and may be involved in menopause-related mechanisms that lead to NASH. Estradiol, for example, is an important regulator of CCL20 by uterine epithelial cells [START_REF] Hickey | Estrogen receptor alpha antagonists mediate changes in CCL20 and CXCL1 secretions in the murine female reproductive tract[END_REF]. Additionally, postmenopausal women had significantly higher levels of AKR1B10 than premenopausal women [START_REF] Hlavac | The role of cytochromes p450 and aldo-keto reductases in prognosis of breast carcinoma patients[END_REF]. This merits further exploration and provides new insight into disease heterogeneity and suggests new hypotheses to advance precision medicine.

One of the limitations of the study is that participants from the ABOS cohort do not reflect a general patient cohort, and our results may not be generalizable to individuals with lower levels of obesity,

where the pathophysiology of SLD may be different. In our study, liver biopsy specimens were indeed obtained during bariatric surgery procedures in all participants. Importantly, these needle biopsies were performed in the first 10 min of the intervention, with the same material used for percutaneous biopsies. This systematic approach allowed us to evaluate accurately and consistently the presence of NASH and liver fibrosis (F ≥ 2) in our study population. This rigorous methodological approach strengthens the reliability of our findings regarding the prevalence rates of NASH and liver fibrosis in this specific patient population.

We acknowledge also the lower prevalence rates of histologically proven NASH and liver fibrosis (F ≥ 2) in our cohort of patients with obesity submitted to bariatric surgery compared to previous studies.

However, our study benefits from a prospective design that involves systematic histologic evaluation of the liver at the time of surgery for all participants. This approach allows for a more accurate assessment of NASH prevalence by avoiding the potential bias of overestimation. It is also important to consider the potential bias of other studies introduced by including only SLD patients specifically referred for liver biopsy. This selective referral for biopsy based on clinical indications, such as elevated liver enzymes, can overestimate the prevalence of NASH [START_REF] Younossi | The global epidemiology of nonalcoholic fatty liver disease (NAFLD) and nonalcoholic steatohepatitis (NASH): a systematic review[END_REF]46]. We also acknowledge that the relative homogeneity of this single-center cohort, primarily of Caucasian ethnicity, and the retrospective design of our study may limit the applicability of the findings to other populations. Moreover, the prevalence of NASH and liver fibrosis (F ≥ 2) was rather low in our cohort, yet the number of patients enrolled in the various subgroups was sufficient to show significant differences in NASH prevalence in these subgroups. Like any study using liver biopsy as a standard, sampling errors can result in misdiagnosis of disease activity and fibrosis stage on biopsy. Finally, although exposure to HRT was negatively associated with an increased risk of NASH in the whole cohort, there were not enough postmenopausal women to draw any conclusions on the potential beneficial association between HRT and the risk of NASH in this population. Finally, future studies on more heterogeneous populations will be needed in order to determine whether our findings are generalizable.

CONCLUSION

The main and novel point addressed by our study is the specific contribution of menopause (as opposed to age) in the higher prevalence of NASH observed in postmenopausal women with T2D as compared with men younger and older than 50 years. We also identified liverspecific clinico-biological and molecular profiles associated with menopause in women with obesity and T2D, in parallel with the higher prevalence of significant liver disease observed in this subgroup. We Prospective studies are needed to determine whether it is possible to treat NASH and its progression as a group of distinct qualitative subtypes.O

  Hierarchical clustering indicated the presence of T2D as the first node separating patients, as shown in Figure 1A,B. Proportions of NASH and fibrosis in the six subgroups of the clustering revealed differences in the T2D patients. Across the T2D subgroups, the proportion of NASH was higher in premenopausal women (n = 33/215, 15.4%; 1.6-fold increased change above the average, 95% CI: 1.1-2.3, p = 0.004), postmenopausal women (n = 36/119, 30.3%, 3.2-fold increased change above average; 95% CI: 2.3-4.3, p < 0.001), and men (n = 38/192, 19.8%, 2.1-fold increased change above the average, 95% CI: 1.5-2.9, p < 0.001). Of note, the proportion of NASH in postmenopausal women with T2D was twice as high as in premenopausal women with T2D (2-fold increase, 95% CI: 1.3-3.0, p = 0.002), and 1.5 times higher than in men with T2D (1.5-fold increase, 95% CI: 1.0-2.3, p = 0.049). In contrast, NASH prevalence was similar in men with T2D below 50 years (21.0%, N = 21/100; 95% CI: 13.0-29.0) versus above 50 years (17.9%, N = 17/95, 95% CI: 10.6-26.4) of age ( p = 0.80).

( 18 .

 18 5%, N = 17/92; 95% CI: 10.2-25.6.0) versus above 50 years of age (27.0%, N = 24/89, 95% CI: 17.8-36.2) ( p = 0.19).

F I G U R E 1

 1 Risk stratification of (A) NASH and (B) fibrosis in the ABOS cohort based on T2D status, male sex, and menopausal status. The cohort was stratified by hierarchical clustering based on T2D status, male sex, and menopausal status in four subgroups displaying distinct prevalence of NASH and/or advanced fibrosis. Diabetes status, male sex, and menopausal status are illustrated in the first three bars under the dendrogram and colored in dark gray for modality TRUE, light gray for modality FALSE, and white for missing values. Each individual presenting with NASH and/or advanced fibrosis is figured as a gray line on the fourth bar under the dendrogram. The last-colored bar indicates the group allocation: Group 1 (green) corresponds to non-T2D patients, group 2 (yellow) for premenopausal women with T2D, group 3 (orange) to men with T2D, and group 4 (brown) to postmenopausal women with T2D. Prevalence of (C) NASH and/or (D) advanced fibrosis (Kleiner fibrosis score ≥2) in the different subgroups. The χ2 test was used for group differences in percentages. Adj. p values with Bonferroni ***<0.001; **<0.01; *<0.05). The black line indicates the average prevalence in the entire cohort and the dashed line indicates 95% CI. NASH, nonalcoholic steatohepatitis; T2D, type 2 diabetes. [Color figure can be viewed at wileyonlinelibrary.com] T A B L E 1 Patient characteristics based on group allocation in ABOS cohort N

  showed that combining these simple clinical features improves the stratification of individuals with class II and class III obesity, according to the prevalence of NASH.Moreover, we also identified specific clinico-biological and molecular profiles associated with the high prevalence of NASH after menopause in women with obesity and T2D. This study of transcriptomic data from a large histologically characterized SLD cohort may provide new insight into disease heterogeneity and suggest new hypotheses to advance precision medicine. Overall, the study results suggest that menopausal women with T2D may share dysfunction of an underlying biological profile. Our results also highlight the importance of considering sex/menopause in investigating risk factors for progression in SLD, given the robust evidence to suggest multifaceted sexual dimorphism in NASH.Studying these patients could provide a more direct path into NASH physiopathology, helping us unravel the intricated physiopathology of NASH. Incorporating sex and menopause status may elucidate sex-specific mechanisms that allow further risk stratification of patients with SLD and promote individualized disease management. Indeed, as more is understood about the heterogeneity of SLD and precision medicine becomes a reality, it is likely that various populations will benefit from pharmacotherapies specific to the metabolic and molecular abnormalities responsible for their SLD.

  Groups were compared using the χ2 test for categorical variables, ANOVA F-tests for continuous variables having normal distribution, and Kruskall-Wallis test for continuous having no normal distribution and Bonferroni correction was applied. Values are mean ± SD, median ± IQR, or n (%).

			Adj. p	1	<10 À5	<10 À5		<10 À5	<10 À5
		Men		79.67 (14.85)	143 (74)	0 (0)		38 (20)	41 (23)
		Postmenopausal	women	76.29 (13.94)	102 (86)	5 (4)		36 (30)	33 (30)
	T2D	Premenopausal	women	76.37 (14.91)	101 (47)	78 (37)		33 (15)	32 (15)
				76.84 (14.96)	249 (27)	316 (45)		31 (3)	53 (6)
				1439	1446	1022		1446	159/1365
				Diastolic blood pressure [mmHg]	Hypotensive treatment [%]	Treatment with HRT	Histological features	NASH [Brunt], N (%)	≥2, N (%) Fibrosis [Kleiner] Grade	Note:

Abbreviations: HRT, hormone replacement therapy; NASH, nonalcoholic steatohepatitis; T2D, type 2 diabetes. *Insulin-treated individuals were not included.

1930739x, 2023, 12, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/oby.23904 by Cochrane France, Wiley Online Library on [18/01/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

Funding information

Programme d'Investissement d'Avenir, Grant/Award Numbers: ANR-16-RHUS-0006, PRECINASH; European Genomic Institute for Diabetes, Grant/Award Number: ANR-10-LABX-0046; Lille University, Grant/Award Number: WILL-CHAlRES-23-001; Fondation pour la Recherche Médicale en France, Grant/Award Number: EQU202303016330 PATTOU; EU Horizon 2020 research and innovation program, Grant/Award Numbers: 875534, IMI-SOPHIA in men with T2D.

AUTHOR CONTRIBUTIONS

CONFLICT OF INTEREST STATEMENT

The authors declared no conflict of interest.

DATA AVAILABILITY STATEMENT

The study protocol and methods as well as the ABOS cohort profile have been published (ClinicalTrials.gov identifier NCT01129297) and are unrestrictedly available. Clinical data sets generated during and/or analyzed during the current study are subject to national data protection laws and restrictions imposed by the ethics committee to ensure the data privacy of the study participants. They are not publicly available; however, they can be applied for through an individual project agreement with the principal investigator of the University Hospital of Lille, France. Affymetrix raw files are available at Gene Expression Omnibus (GEO) under the accession number GSE130991.

SUPPORTING INFORMATION

Additional supporting information can be found online in the Supporting Information section at the end of this article.


A Palacios-Laloy

F Mallet

F Nguyen

F Ong

P Bertet

D Vion

D Esteve

Spectral measurement of the thermal excitation of a superconducting qubit

We report the measurement of the fluctuations of a transmon qubit through the noise spectrum of the microwave signal that measures its state. The amplitude of the Lorentzian noise power spectrum allows to determine the average qubit excitation, in agreement with the estimated thermal radiation reaching the sample. Its width yields the qubit energy relaxation rate which decreases with temperature, contrary to the predictions for a two-level system solely coupled to thermal radiation. This indicates the existence of another non-radiative energy relaxation channel for the qubit.

Superconducting qubits [1] are promising candidates for implementing a solidstate quantum processor. Over the last years, substantial improvements have been made in the coherence times [2,3], fidelity of single-qubit gates [4], readout procedures [START_REF] Mallet | Single-shot qubit readout in circuit quantum electrodynamics to[END_REF][START_REF] Mcdermott | [END_REF] and entanglement of several qubits [7]. In a recent experiment a simple quantum algorithm was operated on a two-qubit elementary processor [8]. One of the requirements for the implementation of larger scale quantum algorithms [9] is that the qubit registers should be properly initialized at the beginning of each computation, with all qubits lying in their ground state. In most superconducting qubit experiments, the initialization is simply realized by waiting long enough before each experimental sequence for the system to reach thermal equilibrium. At cryogenic temperatures in the 10 -30 mK range and for typical qubit resonance frequencies of a few GHz, there is indeed at thermal equilibrium a small (typically less than 1%) probability of finding the qubits in the excited state, which is usually considered negligible. However, given the recent improvement of the overall fidelity of single-and two-qubit gates, the effect of even small thermal fluctuations will require to be considered more quantitatively in the near future. Moreover it is well known in mesoscopic physics that the effective temperature of an electrical degree of freedom such as a superconducting qubit can be in some cases much larger than the temperature of the cryostat, because it can be strongly coupled to out-of-equilibrium electromagnetic radiation coming from the measuring leads, while only weakly to the phonon bath. It is thus important to be able to measure precisely the average excited state population of a single qubit.

Here we propose and demonstrate a method to determine this thermal excited state population in a circuit Quantum Electrodynamics (cQED) setup [10], where a Cooper-pair box qubit of the transmon type [11,3] is coupled to a coplanar waveguide resonator (CPW). The two qubit states shift differently the resonator frequency, so that the phase of a microwave signal reflected by the resonator allows a non-destructive readout as demonstrated in numerous experiments [12]. In the present setup as in most cQED experiments, it is not possible to readout the qubit state in one single experimental sequence due to insufficient signal-to-noise ratio. Note however that such a single-shot readout was recently obtained in cQED by using a non-linear CPW resonator [START_REF] Mallet | Single-shot qubit readout in circuit quantum electrodynamics to[END_REF]. The usual method for reading out the qubit state, using ensembleaveraged measurements of the microwave signal, does not directly provide an absolute measurement of the qubit excitation. However, thermal fluctuations of the qubit state are responsible for a measurable phase noise in the microwave signal reflected by the resonator, with a characteristic Lorentzian power spectrum. In this work we report the observation of this thermal noise and we use it to determine the effective qubit temperature. We note that a related measurement was performed on an ensemble of nuclear spins measured by a SQUID amplifier [13].

The complete experimental setup is shown in Fig 1 . The transmon has its two lowest energy eigenstates |g and |e separated by ω ge /2π =5.304 GHz. It is capacitively coupled with strength g/2π = 45±2 MHz to a superconducting resonator with resonance frequency ω c /2π = 5.796 GHz and bandwidth BW = 30.3 MHz, which serves as qubit readout. With these parameters, the qubit is sufficiently detuned from the resonator for their interaction to be well described by the dispersive Hamiltonian H = χnσ z , where χ is the dispersive coupling constant and n is the intra-resonator photon number operator. The resonator frequency is thus shifted by ±χ/2π = 1.75 MHz when the qubit is in |g or |e respectively. A continuous microwave tone of frequency ω c /2π sent to the resonator input from source V m acquires a qubit state-dependent phase shift which allows a continuous and non-destructive monitoring

2.5ms S ON S OFF 2.5ms V m V m 20dB 30dB 20dB I (t) Q (t) 1-20GHz 4-8GHz 8GHz 37dB T N =2.6K 4K 0.6K 20mK Figure 1.
Microwave setup used for measurements. A microwave signal Vm is sent through the input line containing several attenuators and filters at each temperature stage to the input port of the resonator (shown in green). The reflected signal is separated from the input one by a circulator and goes through a filter and two isolators before reaching the cryogenic amplifier (gain 37 dB and noise temperature 2.6 K). The signal is then demodulated at room temperature with a homodyne demodulation scheme to get its in-phase and quadrature components I(t) and Q(t) respectively (for sake of simplicity details of the room temperature demodulation scheme, including several stages of amplification are not shown). Switching the signal ON and OFF with 1ms period allows to substract the noise background coming from the amplifier.

of this state. This continuous measurement does not induce spurious qubit excitation as long as the the intra-resonator photon number (n ≃ 2.5 in our measurements) is much below the critical photon number n crit = (ω geω c ) 2 /4g 2 ≃ 30 above which the dispersive approximation fails. After reflection on the resonator, the signal is routed through a circulator to a cryogenic amplifier and is then measured by homodyne detection at room-temperature, yielding the two field quadratures I(t) and Q(t). The thermal fluctuations of the qubit state induce some phase noise on the reflected microwave signal, and thus some noise on each quadrature X(t) (X = I, Q).

We start by computing the power spectrum of the qubit thermal fluctuations. Assuming that the bath consists of a bosonic Markovian bath at temperature T , as expected for the impedance of the electromagnetic environment, the qubit dynamics at thermal equilibrium is described by a simple rate equation [START_REF] Cohen-Tannoudji | Atom-Photon Interactions: Basic Processes and Applications[END_REF]

ρ ee = -ρ gg = -Γρ ee + Γn th (1 -2ρ ee ) ( 1
)
where Γ is the qubit energy relaxation rate, and n th (T ) = (exp( ω c /kT ) -1) -1 is the mean photon number at temperature T . This yields a steady-state population of the qubit excited state ρ th ee = n th 1+2n th , or z th = -1 1+2n th after conversion into spin units z(t) = 2ρ ee (t)-1. The corresponding noise power spectrum S z (ω) can be computed as the Fourier Transform of the two-time correlation function C z (τ ) = z(τ )z(0) which is

C z (τ ) = 4 exp (-Γ(1 + 2n th )τ ) 1 -ρ th ee ρ th ee . (2)
After Fourier transform, we obtain

S z (ω) = 4 Γ(1 + 2n th ) Γ 2 (1 + 2n th ) 2 + ω 2 1 -ρ th ee ρ th ee . (3)
Note that these expressions are only approximate because the transmon is not a genuine two-level system but an anharmonic resonator with an infinite number of excited states. The previous expressions are thus only valid in the limit where the population of these higher excited states is negligible, which in our case is true up to temperatures around 100 mK.

We model the effect of the qubit state thermal fluctuations on the measuring signal quadratures X(t) by assuming that the field inside the resonator follows instantaneously the qubit state. Here this assumption is justified by the large bandwidth of the resonator, obtained by chosing a large resonator input capacitor. The quadratures are then simply expressed as X(t) = X + (∆X/2)z(t) + ξ(t), where X is the average reflected signal for a qubit fully unpolarized, ∆X is the change in X when the qubit changes state, and ξ(t) is the total output noise of the amplifier. In the experiment we measure the sum of the noises on both quadratures

S V,ON (ω) = S I (ω) + S Q (ω) = S ξ (ω) + (∆V /2) 2 S z (ω), (4)
where S ξ (ω) is the output amplifier noise power spectrum and (∆V /2) 2 = (∆I/2) 2 + (∆Q/2) 2 is the detector sensitivity. This quantity has the advantage of being insensitive to drifts of the phase between the local oscillator used in the demodulation and the measurement signal. It is worth noting that the mere presence of a continuous measurement of the qubit state has no effect on the dynamics of thermal fluctuations because this dynamics is fully incoherent and entirely goverened by Markovian rate equations [START_REF] Bernu | [END_REF]. The situation is very different when the qubit is continuously measured while being coherently driven, in which case the dynamics changes from diffusive Rabi oscillations to quantum jumps when the measurement strength is increased [START_REF] Palacios-Laloy | Experimental violation of the leggett-garg inequality with weak measurement submitted for[END_REF].

We measure the detector output noise spectrum S V (ω) for a series of temperatures T c . Each spectrum is measured after waiting 15 minutes thermalization time once the cryostat reaches T c . We also verify that the sample is well thermalized by acquiring two noise spectra for each T c , one upon warming up and the second upon cooling down, which are found to be nearly identical. Each spectrum is acquired by sampling I(t) and Q(t) with 100MHz sampling frequency. Each 1024-point set of the sampled signals is Fourier transformed and the amplitude of this transform is squared to obtain the noise spectra S I (ω) and S Q (ω), which are then corrected for the variations of setup gains in frequency and between the I and Q channels. The resulting spectra are summed to form S V,ON (ω). Each 2.5 ms the measurement microwave is turned OFF to measure the noise background of the amplifier S V,OF F (ω) = S ξ (ω) and subtract it from the signal. The resulting noise spectrum S V (ω) = S V,ON (ω) -S V,OF F (ω) is averaged typically 10 6 times.

As shown in Fig 2a, the measured noise spectra S V (ω) have a Lorentzian shape, with an amplitude rapidly increasing with temperature. The amplitude A and width Γ 1 of each spectrum are fitted with a Lorentzian model A Γ 1 /(Γ 2 1 + ω 2 ). According to Eqs 3 and 4, the model predicts that Γ 1 = Γ(1 + 2n th ) and A = ∆V 2 1ρ th ee ρ th ee . The detector sensitivity ∆V 2 is experimentally calibrated in the following way : using exactly the same setup, we ensemble-average V 2 (t) = I 2 (t) + Q 2 (t) under saturation of the qubit g → e transition with a second microwave source at frequency ω ge /2π. This yields ∆V /2 = 2.76 ± 0.14 mV. In this way we can directly extract from the fits the thermally excited state population ρ ee and the relaxation rates Γ 1 as a function of the cryostat temperature T c .

The fitted population (dots in Fig. 2b) agrees with the theoretical average population ρ th ee (red dashed curve), calculated assuming two sources of radiation : the thermal field corresponding to the temperature of the cryostat coldest stage T c , with an average of n th (T c ) photons, and the thermal field radiated by the 30 dB attenuator thermalized at the still temperature T S =600±100 mK, and attenuated (22 ± 0.5 dB) at 20 mK, contributing with n th (T S ) /10 2.2 photons. At the lowest T c , we find a thermally excited state population of 1 ± 0.5%, corresponding to an effective temperature of 55 mK.

At T c = 20 mK, the relaxation rate Γ -1 1 deduced from the width of the Lorentzian noise spectrum (see Fig. 2c) is found to be in excellent agreement with the qubit relaxation time T 1,20mK = 226 ± 7 ns, measured in a standard pulsed sequence. However, at higher T c , we observe that the fitted width decreases, which implies that the qubit energy relaxation time increases with temperature. This couterintuitive result disagrees with our model which predicts a relaxation rate Γ(n th ) = Γ(1 + 2n th ) (see Eq. 1) increasing with temperature due to stimulated emission by the thermal field, yielding the red dashed curve in Fig. 2b (calculated with Γ = T -1 1,20mK ). This indicates that the qubit is not only coupled to its electromagnetic environment but also to another type of bath, causing some additional damping with a different temperature dependence. Additional support for this idea is that the measured relaxation time at 20 mK (226 ns) is significantly shorter than the expected damping time due to relaxation into the the external impedance at zero temperature (600 ns), which indicates the existence of a non-radiative energy decay channel. We finally note that a similar increase of the relaxation time with temperature up to 150 mK was directly observed in a superconducting phase qubit, and attributed to non-equilibrium quasiparticles in the superconducting metal electrodes [START_REF] Martinis | [END_REF]; a similar scenario might explain our results.

In conclusion, we have determined the thermal population of a superconducting qubit coupled to a resonator, even without single-shot detection capability, by studying the noise spectrum of its measuring signal. The population measured is in good agreement with the estimated thermal radiation reaching the sample. We observe however an increase in the relaxation time with temperature in contradiction with this model. This points to the existence of unknown non-radiative decay channels as observed in other qubit experiments [START_REF] Martinis | [END_REF].

Figure 2 .

 2 Figure 2. (a) Noise spectra acquired for several temperatures Tc (color solid lines) and lorentzian fits (dashed black lines). (b) Thermal population of the TLS as a function of temperature: comparison of the experimental data (black dots) with the theoretical prediction (red dashed curve). (c) Relaxation times as a function of temperature extracted from the widths of the loretzian spectra (blue dots) compared to the predictions of the model discussed in the text (red dashed curve) taking Γ -1 = T 1,20mK = 226 ± 7 ns, independently measured in a pulsed experiment at 20 mK.

Acknowledgments

We acknowledge financial support from European project EuroSQIP, Agence Nationale de la Recherche (grant ANR-08-BLAN-0074-01), and Region Ile-de-France for the nanofabrication facility at SPEC. We gratefully thank P. Senat, P. Orfila and J.-C. Tack for technical support, and acknowledge useful discussions within the Quantronics group.


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  'archive ouverte pluridisciplinaire HAL, est destinée au dépôt   Distributed under a Creative Commons Attribution -NonCommercial -ShareAlike| 4.0 International LicenseThe tale of a biologist tainted with informatics wandering in the lands of environmental genomicsEric PelletierTo cite this version:Eric Pelletier. The tale of a biologist tainted with informatics wandering in the lands of environmental genomics. Life Sciences [q-bio]. Université paris saclay, 2020. tel-04402773