PhD Karine Spiegel
email: karine.spiegel@univ-lyon1.fr

PhD Amandine E Rey

PhD Anne Cheylus

PhD Kieran Ayling

PhD Christian Benedict

MD Tanja Lange

PhD Aric A Prather

PhD Daniel J Taylor

MD Michael R Irwin

PhD Eve Van Cauter

A meta-analysis of the associations between insufficient sleep duration and antibody response to vaccination

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

Results

To date, the SARS-CoV-2 pandemic has involved nearly 650 million officially recorded cases and over 6.5 million deaths. Vaccination was widely expected to be effective in controlling the pandemic. Only 63% of adults worldwide have been fully vaccinated and more contagious variants have emerged. Thus, the vaccination effort needs to continue. In parallel, new threats like monkeypox have emerged and new flu strains are continuously identified, making vaccination a major tool for public health in an increasingly globalized society.

The protection conferred by a given vaccine depends on the magnitude of the individual immune response. Antibody response is a clinically significant biomarker of protection and is an early indicator of immunity. [START_REF] Zuo | Robust SARS-CoV-2-specific T cell immunity is maintained at 6 months following primary infection[END_REF] Recent studies have reported a wide variability in antibody response to the same anti-COVID-19 vaccine in healthy adults not previously infected with SARS-CoV-2. Male sex, older age, excess adiposity, history of smoking, and hypertension have been amongst the demographic and clinical factors identified as predictors of lower antibody titers post-vaccination. [START_REF] Demonbreun | COVID-19 mRNA Vaccination Generates Greater Immunoglobulin G Levels in Women Compared to Men[END_REF][START_REF] Watanabe | Central obesity, smoking habit, and hypertension are associated with lower antibody titres in response to COVID-19 mRNA vaccine[END_REF] None of these risk factors may be targeted by rapid behavioral interventions to optimize the humoral response.

In 2002, an experimental study of sleep restriction in the days surrounding influenza vaccination showed that immunoglobulin (Ig)G antibody titers ten days after inoculation were less than half than those measured in control subjects. [START_REF] Spiegel | Effect of sleep deprivation on response to immunization[END_REF] The role of insufficient sleep duration in individual differences in responses to influenza and hepatitis vaccination has been examined in subsequent studies, with somewhat mixed results, possibly as a consequence of relatively small samples and methodological differences. Recently, several authors have called for a thorough examination of the hypothesis that obtaining healthy amounts of sleep at the time of vaccination might increase and extend the protective effect. [START_REF] Benedict | Could a good night's sleep improve COVID-19 vaccine efficacy?[END_REF][START_REF] Zhu | Advice for COVID-19 vaccination: get some sleep[END_REF][START_REF] Irwin | Sleep and inflammation: partners in sickness and in health[END_REF] In order to summarize the existing evidence and estimate the pooled effect size across studies, we have used a metaanalytical approach. Our objective is to better inform the scientific community and the public about a relatively easily modifiable behavior that may optimize vaccine response in the context of the current COVID-19 pandemic.

Literature search

The PRISMA flow diagram is presented in Figure 1. A total of 165 human studies were retrieved from PubMed that included both sleep* and vaccin* terms, two studies were identified from reference lists, 14, 15 and one 2022 study was obtained from another source. [START_REF] Mason | Metrics from Wearable Devices as Candidate Predictors of Antibody Response Following Vaccination against COVID-19: Data from the Second TemPredict Study[END_REF] 149 articles were excluded after being reviewed by title and abstracts when the design of the study and/or the variables measured would not allow to determine whether nocturnal short sleep duration is linked to antibody response after vaccination in healthy adults. Hence, 19 studies underwent full-text review with discussion during consensus meetings (K.S and E.V.C.).

Twelve studies were excluded for the following reasons: five did not include assessment of sleep duration or antibody response to vaccine; two duplicated the results included in Prather et al. 2020; [START_REF] Prather | Temporal Links Between Self-Reported Sleep and Antibody Responses to the Influenza Vaccine[END_REF][START_REF] Miller | Psychological stress and antibody response to influenza vaccination: when is the critical period for stress, and how does it get inside the body[END_REF][START_REF] Pressman | Loneliness, social network size, and immune response to influenza vaccination in college freshmen[END_REF] three did not evaluate sleep around the time of vaccination; [START_REF] Burns | Perceived stress and psychological well-being are associated with antibody status after meningitis C conjugate vaccination[END_REF][START_REF] Burns | Stress, coping, and hepatitis B antibody status[END_REF][START_REF] Cadavid-Betancur | Seroprevalence of hepatitis B and factors potentially associated in a population-based study in Medellin, Colombia[END_REF] one involved a selection bias where subjects were included only if their sleep duration was greater than 7.5h. [START_REF] Taylor | Is Insomnia a Risk Factor for Decreased Influenza Vaccine Response?[END_REF] ; one measured antibody levels after vaccination against COVID-19 in a time interval ranging from as little as one week to up to 5 months, [START_REF] Mason | Metrics from Wearable Devices as Candidate Predictors of Antibody Response Following Vaccination against COVID-19: Data from the Second TemPredict Study[END_REF] in contrast to all other included studies where the timing of assessment of antibody levels relative to vaccination was fixed.

Further, more than 90% of the participants of this recent study received a mRNA vaccine (Pfizer-BioNTech or Moderna-NIAID). [START_REF] Mason | Metrics from Wearable Devices as Candidate Predictors of Antibody Response Following Vaccination against COVID-19: Data from the Second TemPredict Study[END_REF] For both these vaccines, a more than 6-fold waning of the humoral response over a 6-month period has been reported, preventing the reliable detection of sleep around the time of vaccination on antibody levels measured at highly variable times post-inoculation. 21, 22 Four experimental studies and three prospective cohorts were included in the meta-analysis. [START_REF] Spiegel | Effect of sleep deprivation on response to immunization[END_REF][START_REF] Lange | Sleep enhances the human antibody response to hepatitis A vaccination[END_REF][START_REF] Lange | Sleep after vaccination boosts immunological memory[END_REF][START_REF] Benedict | Acute sleep deprivation has no lasting effects on the human antibody titer response following a novel influenza A H1N1 virus vaccination[END_REF][START_REF] Prather | Sleep and antibody response to hepatitis B vaccination[END_REF][START_REF] Ayling | Positive mood on the day of influenza vaccination predicts vaccine effectiveness: A prospective observational cohort study[END_REF][START_REF] Prather | Temporal Links Between Self-Reported Sleep and Antibody Responses to the Influenza Vaccine[END_REF] Table 1 summarizes the characteristics of the included studies. Because self-reported sleep duration is only modestly correlated with objective sleep duration, [START_REF] Lauderdale | Self-reported and measured sleep duration: how similar are they?[END_REF] we built two separate forest plots according to the assessment method of sleep duration.

Association between insufficient sleep and vaccine response.

The relationship between self-reported short sleep, i.e. < 6 hours (h) / night, and vaccine response did not reach our pre-defined statistical significant criteria (total n=504, ages 18-85, Effect Size and 95% confidence interval (ES[95% CI]) = 0.29 [-0.04, 0.63]; Figure 2A). The overall ES[95% CI] was 0.40 [-0.09, 0.89] for men and 0.21 [-0.29, 0.71] for women. Given that sleep duration and quality are generally reduced in older adults, we conducted an exploratory analysis excluding the study recruiting only adults ≥65 years, an age group not represented in studies that used objective sleep assessment; in the remaining total sample of 299 adults ages 18-60, a significant association emerged (ES[95% CI] = 0.59 [0.12, 1.05]). When analyses were performed for men and women separately, the association between self-reported short sleep and antibody response was significant in men, but not in women (ES [95% CI] = 0.75 [0. 16, 1.34] vs 0.55 [-0.38, 1.47], respectively). ES of 0.50 and above are typically considered as "medium".

For studies that used objective measures of sleep, a robust adverse impact of short sleep on vaccine response was detected (total n=304, ages 18-60, ES=0.79 [0.40, 1.18]; Figure 2B). The pooled ES [95% CI] was 0.86 [0.28, 1.44] for experimental studies (n=133) and 0.67 [0.18, 1.16] for prospective studies (total n=171). ES of 0.80 and above are typically considered as "large". In men, short sleep was associated with a reduced antibody titers with an overall large pooled ES [95% CI] of 0.93 [0.54, 1.33]. In women, this association failed to reach significance with an ES [95% CI] of 0.42 [-0.49, 1.32] (Figure 3).

Discussion

These meta-analyses investigated the association of sleep duration with the response to anti-viral vaccination as assessed by antibody titers and/or seroprotection. The main result is that, when assessed by objective methods, short sleep duration (<6h/night), in adults aged 18-60 was associated with a decrease in response of vaccination with a moderate to large pooled ES. The unequivocal findings from our rigorous meta-analysis are consistent with the conclusion of a recent systematic review. [START_REF] Rayatdoost | Sufficient Sleep, Time of Vaccination, and Vaccine Efficacy: A Systematic Review of the Current Evidence and a Proposal for COVID-19 Vaccination[END_REF] Given that sex impacts the response to vaccine, [START_REF] Demonbreun | COVID-19 mRNA Vaccination Generates Greater Immunoglobulin G Levels in Women Compared to Men[END_REF][START_REF] Flanagan | Sex and Gender Differences in the Outcomes of Vaccination over the Life Course[END_REF] we calculated separate overall ES for men and women. When sleep was assessed objectively, the pooled ES was large and highly significant for men, whereas it was smaller and not significant for women, likely due to the wide variations in sex hormone levels according to phase of the menstrual cycle, use of hormonal contraception, menopausal status and use of hormonal replacement in post-menopausal women. [START_REF] Flanagan | Sex and Gender Differences in the Outcomes of Vaccination over the Life Course[END_REF] None of the studies included in our meta-analysis controlled for these known hormonal modulators of immune function.

While all studies that performed objective sleep assessment were conducted in young and middle-aged subjects, the studies based on self-reported sleep also enrolled 65-85 years old adults. [START_REF] Ayling | Positive mood on the day of influenza vaccination predicts vaccine effectiveness: A prospective observational cohort study[END_REF] Given that sleep duration, sleep quality and vaccination response are generally reduced and more variable in this age range, [START_REF] Poland | A systems biology approach to the effect of aging, immunosenescence and vaccine response[END_REF] we performed an exploratory analysis excluding the older age group. The association between self-reported short sleep and reduced vaccine response was stronger, although it remained smaller than when sleep was objectively assessed, consistent with the observation that self-reported and objective sleep are only moderately correlated and that subjective report tends to overestimate actual sleep duration. [START_REF] Lauderdale | Self-reported and measured sleep duration: how similar are they?[END_REF] The present meta-analyses include data from studies examining associations between sleep duration and antibody responses to the influenza and hepatitis vaccines. At the present time, there are no comparable published data for COVID-19 vaccines. To obtain a comparison relevant to the SARS-COV-2 pandemic ; we estimated the ES of the waning of the humoral immune response to the Pfizer-BioNTech (BNT162b2) COVID-19 vaccine from baseline to an average of two months post-injection using published numerical data. [START_REF] Levin | Waning Immune Humoral Response to BNT162b2 Covid-19 Vaccine over 6 Months[END_REF] The ES for waning over two months was 0.79, essentially identical to the ES estimated for objectively assessed short sleep duration. If, similar to the influenza and hepatitis vaccines, the antibody response to COVID-19 vaccines is adversely affected by insufficient sleep, then insufficient sleep around the time of COVID-19 vaccination may reduce antibody titers in the same range as the waning of the response to the most commonly administered vaccine over two months.

While vaccination remains the most important strategy to control the current pandemic of COVID-19, simple behavioral interventions that might boost vaccine response remain to be identified. As suggested by our meta-analysis, adequate amounts of sleep (at least 6h/night) during the days surrounding the time of vaccination may enhance the humoral response to diverse strains of viruses. Such recommendation of obtaining adequate sleep duration is realistic as at-home behavioral sleep extension has proven to be feasible, acceptable and efficient in a variety of populations. [START_REF] Baron | Behavioral interventions to extend sleep duration: A systematic review and meta-analysis[END_REF] The National Sleep Foundation recommends 7 to 9 h of sleep for healthy adults and 7 to 8 h of sleep for adults > 65 years. [START_REF] Hirshkowitz | National Sleep Foundation's sleep time duration recommendations: methodology and results summary[END_REF]

Inclusion and diversity

We support inclusive, diverse, and equitable conduct of research. Results are expressed as effect sizes and 95% confidence intervals (ES [95% CI]). The area of the block indicates the weight assigned to that study in the meta-analysis while the horizontal line depicts the 95% CI. Positive ES indicate an effect in the hypothesized direction, i.e. short sleep associated with lower level of antibodies or reduced protection status.

Figure legends and table

Experimental sleep deprivation studies

METHOD DETAILS

This meta-analysis followed the PRISMA guidelines [START_REF] Page | The PRISMA 2020 statement: An updated guideline for reporting systematic reviews[END_REF] .

Data sources and search strategy

The PubMed database was searched from the first date available to July 19, 2022 to identify studies that examined the relationship between sleep duration and vaccine response. The combination of the terms "sleep*" and "vaccin*" was searched in the text. Filters were applied to select original articles written in English or French and reporting data on human adults (19+ years).

Two researchers (K.S. and E.V.C.) reviewed titles and abstracts of the retrieved papers to identify potentially relevant articles. Reference lists of included articles were searched to identify articles that may have been missed in the database search. One 2022 paper was identified by another source. When eligibility could not be determined based on the abstract, the full article was reviewed. When multiple published reports from the same study were available, we included only the one with the most detailed information.

Study selection

Studies were selected from the initial search if they met the following criteria: To optimize the quality of the meta-analysis, we obtained from the authors the information needed to calculate the relevant effect size consistently. We did so for experimental papers that used non-parametric testing to compare the means of antibody titers between sleep manipulation groups to obtain log transformed data. For all prospective studies, we requested the raw data to categorize sleep duration as short, intermediate or normal. We calculated effect sizes and 95% confidence intervals (ES [95% CI]) for the impact of short sleep (<6h) versus normal sleep on the response to vaccination. Normal sleep was defined as a sleep duration of >7h to 9h for participants under 65 years and as a sleep duration of >7h to 8h for participants aged ≥ 65 years, consistent with the recommendations proposed by the National Sleep Foundation. 28. Because sex and age influence humoral immune responses to vaccination, [START_REF] Demonbreun | COVID-19 mRNA Vaccination Generates Greater Immunoglobulin G Levels in Women Compared to Men[END_REF][START_REF] Flanagan | Sex and Gender Differences in the Outcomes of Vaccination over the Life Course[END_REF][START_REF] Poland | A systems biology approach to the effect of aging, immunosenescence and vaccine response[END_REF] we calculated a separate effect size for men and women and corrected our analyses for age, except when the sample included only young adults with a narrow age range (<10 years).

Analyses were controlled for all other covariates used in the original papers. Finally, since a recent study has suggested that antibody levels are mostly affected by insufficient sleep on the closest nights around vaccination, [START_REF] Prather | Temporal Links Between Self-Reported Sleep and Antibody Responses to the Influenza Vaccine[END_REF] we asked the authors of the selected papers to provide sleep data collected within no more than 7 days around the date of vaccination. All authors provided the requested information.

Whenever available, both antibody titers and protection status were reported. When results

were reported for individual strains or for different subtypes of antibodies (e.g., IgG1), the most significant result in the expected direction was used.

The quality of the studies included in the meta-analysis was evaluated by the Downs and Black Quality Index score system, 31 a validated checklist, which consists of five subscales (i.e., reporting, external validity, bias, confounding, and power) with a maximum score of 14 for nonrandomized, non-prospective studies. All included studies scored between 14 and 22.

QUANTIFICATION AND STATISTICAL ANALYSIS

In the prospective studies, sleep duration was reported as a continuous variable. The first step of our analysis was to convert sleep duration to a categorical variable with three categories as defined above. We then calculated the impact of short sleep (<6h/night) versus normal sleep on the response to vaccination. Antibody titers were modeled with a linear regression and seroprotection status with a logistic model. All regressions included the sleep category as predictor along with covariates. Regressions and logistic regression models were fitted using the lm() and glm() functions, respectively, in R (version 4.1.1). The sleep contrast (an odds-ratio in the case of logistic models) and the associated 95% CI were calculated using the emmeans package (version 1.7.4.1). For two datasets of seroprotection status (women objective sleep 5

and 3 ]) models showed quasi-separation, which lead to inappropriate estimate (here, infinite upper limit for the odds-ratio) [START_REF] Firth | Bias Reduction of Maximum Likelihood Estimates[END_REF][START_REF] Mansournia | Separation in Logistic Regression: Causes, Consequences, and Control[END_REF] . We addressed this issue with Firth's logistic regression using the logistf package (version 1.24.1). This approach uses a penalty likelihood for the point estimates. Although it is recommended to estimate confidence intervals from profile likelihood, Cochrane Center, Copenhagen, Denmark). Overall ES were calculated assuming random effects model [START_REF] Rosenthal | Writing meta-analytic reviews[END_REF] and were interpreted as small (≥0.20), moderate (≥0.50) or large (≥0.80). [START_REF] Cohen | Statistical Power Analysis for the Behavioral Sciences[END_REF] Due to the small number of studies, heterogeneity among studies was not evaluated using the point estimate I 2 , [START_REF] Higgins | Quantifying heterogeneity in a meta-analysis[END_REF] but by examining confidence intervals, as recently recommended. 39

  However, large-scale studies are needed (i) to define the time window before and after vaccination where optimizing sleep duration is most likely beneficial, (ii) to delineate the impact of sex hormones in the relationship between sleep duration and antibody response to vaccination in women, and (iii) to estimate the amount of sleep debt susceptible of adversely affecting the response. Therefore, collecting information about sleep duration around the time of vaccination and about sex hormone levels in the millions of people who will receive vaccines and boosters against COVID-19 and other viruses, is an unprecedented opportunity to study the role played by sleep duration for vaccine response. E.V.C. identified relevant articles and extracted data; discussion and consensus meetings with A.E.R. & M.R.I resolved differences. K.S. and A.C. performed the statistical analyses. A.E.R. performed the quantitative analysis in Revman v.5.3. The first authors of the papers identified as relevant for this meta-analysis provided data to calculate effect size consistently (K.S., K.A., C.B., T.L., A.A.P., D.J.T.). All the authors participated in the revision of the manuscript and vouch for the accuracy of the data. K.S. and E.V.C. have directly accessed and verified the data included in this meta-analysis. Declaration of interests No author has a conflict of interest directly related to the submitted work. Outside of the submitted work, C.B. report grants from Repha GmBH, A.A.P. is the recipient of an investigatorinitiated research grant from Eisai Co. Ltd, a sponsor-initiated research grant from Big Health, Inc, and serves as a consultant for NeuroGeneces, E.V.C. is a member of the Scientific Advisory Board of the Sleep Number Corporation (Minneapolis, MN), a consultant for Calibrate Health, Inc (Delaware) and the recipient of an investigator-initiated research grant on "Circadian Misalignment in Adrenal Insufficiency" from the Takeda Pharmaceutical Company. K.S., A.E.R., A.C., K.A., T.L., D.T., and M.R.I. have no conflict of interest.

Figure 1 .

 1 Figure 1. Flowchart of study screening and selection.

Figure 2 .

 2 Figure 2. A. Forest plot of subjectively assessed habitual short sleep associated with reduced

Figure 3 .

 3 Figure 3. Forest plots of objectively assessed experimentally shortened sleep duration or

  (1) were performed on healthy human adults who have nocturnal sleep habit or were case-control studies with a group of healthy controls of substantial size (N ≥ 50), (2) assessed antibody titers and/or protection status, (3) performed subjective and/or objective measures of sleep duration, (4) were laboratory-conducted studies of sleep duration manipulation over one or more nights or prospective cohort studies, (5) were peer-reviewed original research papers.Data extraction and quality assessmentTwo investigators (K.S. & E.V.C) extracted data; discussion and consensus meetings with two additional investigators (A.E.R. & M.R.I) resolved differences. Relevant data included the first author's surname, title of the article, year of publication, number of participants, participants age and sex, study design (i.e. prospective vs experimental study), covariates adjusted in the analysis, methods used to evaluate sleep duration (i.e. single survey item, validated questionnaire, sleep diary, actigraphy, or polysomnography), methods used to manipulate experimentally sleep duration (total sleep deprivation or sleep restriction over one or more nights), vaccine response assessed by antibody titers and/or protection status during a specified window of time post-inoculation, and measures of the association.

  we used Wald confidence intervals to ensure symmetry of confidence interval around the point estimate, a required property for quantitative analysis using Revman v.5.3 (Cochrane Collaboration, 2014, Nordic Cochrane Center, Copenhagen, Denmark). For prospective and experimental studies, we then derived the effect sizes and 95% confidence intervals (ES [95% CI]) for short sleep (<6h) versus normal sleep and for sleep restriction or deprivation versus normal sleep, respectively. ES was calculated as standardized mean difference (SMD aka Cohen's d). To calculate ES [95% CI] from the unstandardized coefficient of regression, we used equations (19) and (20) in Wilson 2017 34 (a companion to Lipsey & Wilson 2001 35 ) for the calculation of Cohen's d, equations (2) and (3) for the Hedges' correction for low sample size, and equation (4) for the calculation of the 95% CI. OR and 95%CI of the sleep predictor in logistic regression models were converted to SMD and 95% CI with equation (9) in Wilson 2017 34 . Mean and standard deviation from experimental studies were converted to ES [95% CI]) using Revman v.5.3 (Cochrane Collaboration, 2014, Nordic Cochrane Center, Copenhagen, Denmark). Quantitative analysis was undertaken in Revman v.5.3 (Cochrane Collaboration, 2014, Nordic

Table 1 . Description of studies evaluating response to vaccination as indexed by antibody titers (Ab) and protection status (PS) and sleep duration as experimentally shortened, i.e. total sleep deprivation (TSD) or sleep restriction (partial sleep deprivation, PSD; top), or assessed in prospective studies (bottom).

 1

	Significant findings indicate an association in the hypothesized direction; i.e. sleep deprivation as PSD or TSD or habitual short sleep
	linked with lower Ab or PS. * p<0.05; # p<0.10; NS: no significant; wk: week; PSQI: Pittsburgh Sleep Quality Index Questionnaire.

Acknowledgments

Collectively, the authors acknowledge the support of their respective institutions. The authors are deeply indebted to the statistical expertise and support of Dr. Oussama Abdoun (Lyon Neuroscience Research Center).

Data and code availability

-For each selected study, sample size of each sleep group, mean, beta or odd ratio and respective dispersion parameters used to estimate ES [95% CI] are publicly available at http://dx.doi.org/10.17632/dp45t6f8s6.1 [START_REF] Spiegel | A meta-analysis of the associations between insufficient sleep duration and antibody response to vaccination[END_REF] as of the date of publication.

-This study did not generate original code.

-Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

Summary

Vaccination is a major strategy to control a viral pandemic. Simple behavioral interventions that might boost vaccine responses have yet to be identified. We conducted meta-analyses to summarize the evidence linking the amount of sleep obtained in the days surrounding vaccination to antibody response in healthy adults. Authors of the included studies provided the information needed to estimate the pooled effect size (ES) and 95% confidence intervals (95%CI). [START_REF] Spiegel | Effect of sleep deprivation on response to immunization[END_REF][START_REF] Lange | Sleep enhances the human antibody response to hepatitis A vaccination[END_REF][START_REF] Lange | Sleep after vaccination boosts immunological memory[END_REF][START_REF] Benedict | Acute sleep deprivation has no lasting effects on the human antibody titer response following a novel influenza A H1N1 virus vaccination[END_REF][START_REF] Prather | Sleep and antibody response to hepatitis B vaccination[END_REF][START_REF] Ayling | Positive mood on the day of influenza vaccination predicts vaccine effectiveness: A prospective observational cohort study[END_REF][START_REF] Prather | Temporal Links Between Self-Reported Sleep and Antibody Responses to the Influenza Vaccine[END_REF] The association between self-reported short sleep (<6 hours/night) and reduced vaccine response did not reach our pre-defined statistical significant criteria (total n=504, ages

STAR*METHODS

RESOURCE AVAILABILITY

Lead contact

Further information and requests should be directed to and will be fulfilled by the Lead Contact, Karine Spiegel (karine.spiegel@univ-lyon1.fr).

Materials availability

This study did not generate new unique materials.

KEY RESOURCES


Nicolas Giordani

Lionel Camberlein

Etienne Gaviot

Frédéric Polet

Nicolas Pelletier

Bruno Bêche

Concep

Conception et réalisation d'un micro-psychromètre thermoélectrique basé sur une structure polymère SU-8

Keywords: Microcapteurs thermiques, psychromètres, humidité relative, microfluidique

est destinée au dépôt

Introduction 1.Principes

La mesure de l'humidité constitue un enjeu essentiel dans de nombreux domaines de l'industrie, notamment en matières de traitement et conservation des aliments, analyse de procédés physico-chimiques, contrôle de qualité, et gestion des cultures sous serres. Les méthodes classiques de la psychrométrie, malgré leurs inconvénients (encombrement, temps de réponse), restent considérées comme des références fiables, puisqu'elles reposent sur des principes thermodynamiques parfaitement établis, conduisant à des capteurs peu onéreux. Les réalisations actuelles dérivent du modèle classique de Assmann, où l'humidité relative se déduit de la différence des températures mesurées par un premier capteur au contact de l'air objet de la mesure, et un second, dont la surface active est recouverte d'un mince film d'eau affecté par l'évaporation. Compte tenu de leurs mécanismes thermodynamiques de base [START_REF] Dascalescu | FIG. 5 -Ecarts psychrométriques mesurés en milieu contrôlé (RH%)[END_REF][START_REF] Visscher | Long-term tests of capacitive humidity sensors[END_REF][START_REF] Cretinon | Mesure des paramètres de l'air humide, norme NFX 15-110[END_REF] , les psychromètres ne présentent ni hystérésis ni dérive au long terme, et ne demandent pas de re-étalonnage systématique, à la différence des structures intégrées usuelles (le plus souvent, capteurs à variation de capacité [START_REF] Visscher | Long-term tests of capacitive humidity sensors[END_REF] ). En contrepartie, ce sont des systèmes particulièrement lents, et intrinsèquement invasifs, puisque l'air objet de la mesure est constamment enrichi en vapeur d'eau "consommée" pour la mesure en régime établi. D'autre part, l'information psychrométrique résulte le plus souvent de deux mesures absolues (et localisées) de température dont la précision influence notablement le résultat obtenu. Il apparaît immédiatement que la réduction dimensionnelle apportée par les microtechnologies, conduit à diminuer la quantité d'eau évaporée, et par conséquent, le caractère invasif de la mesure. En outre, le temps de réponse peut être ramené à quelques secondes, lors que les réalisations conventionnelles sont affectées par des valeurs de une à trois minutes, compte tenu des capacités thermiques des éléments de mesure.

Configuration thermoélectrique différentielle distribuée (CDD)

L'effet Seebeck peut être avantageusement utilisé pour caractériser le processus d'évaporation, en distribuant convenablement un réseau de microcanaux sur les jonctions froides d'une thermopile planaire déposée sur un substrat thermiquement isolant ; la tension de sortie résulte alors de la somme des f.e.m p-2/6-locales (en série) de l'ensemble des cellules disposées en une chaîne bimétallique au tracé méandriforme ; les canaux, respectivement secs et humides, permettent de soumettre une jonction sur deux au mécanisme d'évaporation du film d'eau réapprovisionné par capillarité. Nous avons développé plusieurs prototypes, sur la base du polymère photo-imageable SU-8 associé à un substrat de verre, la thermopile (couple Constantan/Or) étant déposée par pulvérisation cathodique avant isolation et montage du réseau de microcanaux adjoint à un réservoir intermédiaire. Le polymère SU-8 (epoxy-photoresist négatif) permet la constitution de micro-structures 3D compatibles avec les process de la microélectronique, à l'aide d'opérations conventionnelles de masquage. Les propriétés thermiques (<0.4W/(m.K)) et mécaniques (rapport dimensionnel hauteur/largeur>15) en font un matériaux d'intérêt notoire pour la réalisation de nombreux systèmes microfluidiques à usage industriel [START_REF] Carlier | Integrated microfluidics based on multilayered SU-8 for mass spectrometry analysis[END_REF][START_REF] Gadre | Fabrication of a fluid encapsulated dermal patch using multilayered SU-8[END_REF] . Des couches de 1 µm à 250 µm d'épaisseur peuvent être déposées en une seule étape de "spin-coating". Après description des prototypes étudiés, nous comparons les résultats des mesures réalisées sur l'un des échantillons avec ceux obtenus à l'aide d'un matériel de référence, compte tenu d'une procédure simplifiée d'étalonnage. Enfin, nous discutons des modifications à apporter aux systèmes en cours de développement, pour une meilleure répétabilité des performances (sensibilité, conformation du film d'eau).

Spécificités et mise en oeuvre

Les dispositifs classiques exploitent la mesure locale et simultanée de deux températures absolues [t, température sèche (°C), et t h température humide (°C)], à l'aide de deux thermorésistances (Pt 100) ou de thermistances de précision. A l'inverse, le concept de CDD conduit à considérer une grande densité de mesures différentielles de faible amplitude (<<T) uniformément distribuées sur la surface sensible de la thermopile, avec une tension de sortie représentative des échanges de chaleur résultant de l'évaporation ; à cet égard, la mesure effectuée constitue une caractérisation thermofluxmétrique [START_REF] Dascalescu | FIG. 5 -Ecarts psychrométriques mesurés en milieu contrôlé (RH%)[END_REF][START_REF] Hladik | Métrologie des propriétés thermophysiques des matériaux[END_REF][START_REF] Camberlein | Capteurs de température à réseau planaire distribué de thermopiles en couches minces[END_REF] ; en effet, en terme de condition fondamentale de fonctionnement en régime établi, la quantité de chaleur apportée par le refroidissement d'une masse d'air donnée (m) doit compenser exactement le flux thermique nécessaire au mécanisme d'évaporation pour en assurer la saturation. Ce processus se répartit sur l'ensemble de la surface active de la thermopile (1 cm²) compte tenu de sa configuration distribuée : si N cellules de thermocouples contribuent à la composition de la tension de sortie V s ,

V s = N.  u .  (V) [1]
avec  u le pouvoir thermoélectrique effectif de l'assemblage bimétallique plaqué, et  la différence de température établie entre deux thermojonctions contiguës. Par ailleurs, la tension de vapeur d'eau caractérisant l'humidité relative de l'air à mesurer peut être exprimée par la relation classique simplifiée :

( )   h t s v t t . P . A . p p h -  - = (Pa) [2]
où p s (th) désigne la pression de vapeur à saturation associée à la température de saturation adiabatique (t h ), P la pression atmosphérique (Pa), t la température de l'air à caractériser, A un paramètre thermodynamique fonction de la nature et des conditions convectives d'écoulement du fluide (A  0.65.10 -3 K -1 ), et  une constante d'étalonnage propre au montage psychrométrique considéré [START_REF] Dascalescu | FIG. 5 -Ecarts psychrométriques mesurés en milieu contrôlé (RH%)[END_REF][START_REF] Cretinon | Mesure des paramètres de l'air humide, norme NFX 15-110[END_REF][START_REF] Reinmuth | Raumlufttchnic[END_REF] . Par définition, l'humidité relative s'exprime,

( ) ( ) ) p / p .( 100 RH t s v % = (%) [3]
Afin d'établir un modèle simple du comportement du système réalisé, la pression de saturation de l'eau, pour une température donnée dans la gamme (0°C<t<100°C), peut être rapportée à la relation phénoménologique simplifiée [START_REF] Giordani | Conception et réalisation de microsystèmes thermoélectriques[END_REF] ,

( )       + + = t . b 1 t . c a exp . p p 0 t s (Pa) [4]
où p 0 =1Pa, et a, b, c présentent respectivement les valeurs a=6,41301547, b=4,277042.10 -3 °C-1 , c=0,10044762 °C-1 . Cette relation, proche de la forme classique de Magnus Teten [START_REF]A guide to the measurement of humidity[END_REF] , est utilisable dans la gamme couverte par la plupart des capteurs psychrométrique, et confère une précision de 0,15% dans la gamme [-1°C<t<100°C] (0,10%, pour 5°C<t<98 °C). D'autre part, la température de point de rosée en découle immédiatement, lors que le recours à la relation métrologique de Sonntag [START_REF] Cretinon | Mesure des paramètres de l'air humide, norme NFX 15-110[END_REF][START_REF] Sonntag | Vapor pressure formulations based on the ITS-90 and the psychrometer formulate -Important new values of the physical constants of 1986[END_REF] n'admet pas de détermination analytique.

La pression atmosphérique et la température "sèche" étant mesurées à part (Pt100 pour les résultats présentés, ou thermorésistance plane de type "Au" dans les réalisations en cours d'étude), l'écart de refroidissement psychrométrique [  T=[t-t h ]=V s /  ] est déduit de la tension Seebeck de sortie, en considérant une constante d'étalonnage  représentative du comportement thermique de la thermopile (sensibilité psychrométrique ; ordre de grandeur 0,4 mV/°C). L'humidité relative est simplement déterminée à partir de l'expression suivante résultant directement des relations 3 et 4 (structure idéale, =1) :

( ) ( )             + + -  -         + + -  - +  - + =  t .

Fabrication

Le prototype étudié exploite une thermopile présentant 80 branches (960 thermoéléments plaqués), recouvertes d'un réseau de microcanaux (largeur 400 µm) réparti en 13 paires sur une surface active de 1cm² . La réalisation, par groupe de quatre capteurs, comprend cinq niveaux de masques (masqueur simple p-4/6-face), et se décompose en six étapes. Un substrat de verre ordinaire de 1mm d'épaisseur [=1W/(m.K))  le champ thermique interne reste quasi-isotherme], est recouvert d'une couche épaisse (250 µm) thermiquement peu conductrice de SU-8 : (Microchem  2100 : masque#1 :  = 0.3W/(m.K)), avant le dépôt des thermoéléments ; à cet effet, une couche de constantan d'épaisseur 600 nm est d'abord déposée par pulvérisation cathodique (RF magnétron) ; une gravure chimique conduit ensuite à l'obtention d'une piste continue de largeur 100 µm, les branches étant séparées de 50µm, dont les contacts d'extrémités permettent de recueillir le signal (masque#2). La technique classique de "lift-off" [START_REF] Camberlein | Capteurs de température à réseau planaire distribué de thermopiles en couches minces[END_REF] permet ensuite de déposer les sections de placage par l'or d'épaisseur 400 nm (longueur de 0,5 mm, largeur nominale 50 µm : masque#3) ; l'or est aussi déposé régulièrement sur un tracé de pistes implémenté près de la thermopile et conduisant à un amplificateur opérationnel CMS (chopper faible bruit). La figure 3 illustre partiellement la configuration alors obtenue [START_REF] Giordani | Conception et réalisation de microsystèmes thermoélectriques[END_REF] (extrémité de la thermopile et circuit imprimé). Une couche protectrice de 10 µm de SU-8 est alors déposée puis gravée pour accéder au C.I. (masque#4). Les microcanaux sont ensuite assemblés après dépôt et gravure (masque#5) d'une couche épaisse de SU-8 (250µm : Microchem  2100). Un traitement plasma est enfin appliqué pour favoriser l'écoulement par capillarité au sein des canaux, et le substrat est localement percé, donnant accès au réservoir d'eau disposé sur la face inférieure. La structure obtenue supporte des opérations de nettoyage où une exposition en température jusqu'à 200°C. La figure 4, (eau colorée avec de la fluorescéine pour l'illustration) présente la répartition du liquide en régime établit.

Résultats et discussion

La validation du concept repose sur l'emploi d'une sonde de référence, et des valeurs connues de la tension de vapeur au dessus de solutions saturées [START_REF] Cretinon | Mesure des paramètres de l'air humide, norme NFX 15-110[END_REF][START_REF]A guide to the measurement of humidity[END_REF] . La dimension des canaux répond aux besoins de manipulation et de nettoyage aisés du système, en maintenant une surface d'échange air-liquide convenable. La thermopile doit satisfaire à une résistance interne minimale (R<40 k  ) pour limiter le bruit de Johnson [START_REF] Gaviot | Planar Differential Radiometers. A quantitative approach to designing enhanced units[END_REF][START_REF] Gaviot | Radiométrie par Absorption Différentielle Distribuée (ADD)[END_REF] , et les matériaux choisis peuvent présenter une auto-compensation de dérive en température [START_REF] Machut | Contribution à l'étude des thermocouples plaqués. Application à l'autocompensation en température de nouveaux capteurs[END_REF][START_REF] Machut | Peltier sensors for measuring the thermal conductivity of fluids[END_REF] . Malgré le faible facteur de mérite de l'association thermoélectrique [Constantan/Orplaqué] (Z Au-Cn = 4.78x10 -5 K -1 ) [START_REF] Gaviot | Planar Differential Radiometers. A quantitative approach to designing enhanced units[END_REF][START_REF] Rowe | CRC Handbook of Thermoelectrics[END_REF] , le niveau de signal, de l'ordre de 5mV (RH%  70%) permet de limiter le gain d'amplification à G=200 pour déterminer l'écart psychrométrique (T=[t-t h ]). La température sèche t étant mesurée par une Pt100 disposée au contact du substrat, le traitement de la relations 5 est effectué avec un PC standard, la pression atmosphérique étant mesurée de façon indépendante, entrée en grandeur externe. Une sonde psychrométrique de référence (Thunder  Sci. Corp. : # 5A-1MP) fait l'objet d'un enregistrement simultané. Cette dernière et le capteur testé sont disposés à 1cm l'un de l'autre, et soumis à un même balayage convectif (flux parallèle aux canaux). Après obtention de l'équilibre thermodynamique au sein du système (volume : 250mm x 120mm x 100mm, t contrôlée à 22°C), la tension de sortie de la thermopile est mesurée. On observe d'autre part,  u = 370.5 µV/°C (avec un comportement linéaire) conduisant à ;  =  .  T, le paramètre  (°C/°C) résultant de la résistance thermique structurale de la thermopile [START_REF] Gaviot | Radiométrie par Absorption Différentielle Distribuée (ADD)[END_REF][START_REF] Gaviot | Thin foil planar radiometers: Application for designing contactless T sensors[END_REF] . Compte tenu des relations 1 à 5, la sensibilité psychrométrique  s'exprime :

FIG. 1 -

 1 FIG. 1 -Configuration du champ thermique exploitable parune thermopile planaire en damier.

 6 ]FIG. 3 -FIG. 4 -

 634 FIG. 3 -Empreintes du circuit imprimé et extrémité de la thermopile.2000µm

  400µm

Conception et fabrication 2.1 ConceptionL'élément sensible est constitué d'une thermopile planaire comprenant typiquement 1000 cellules par cm². Cette CDD, particulièrement adaptée à la miniaturisation, permet la réalisation de nombreux capteurs[START_REF] Hladik | Métrologie des propriétés thermophysiques des matériaux[END_REF][START_REF] Ph | Measurement on the thermoelectric properties of thin bimetallic films[END_REF] dont l'optimisation peut être conduite sous forme numérique et analytique[START_REF] Gaviot | Planar Differential Radiometers. A quantitative approach to designing enhanced units[END_REF][START_REF] Gaviot | Radiométrie par Absorption Différentielle Distribuée (ADD)[END_REF] . La figure1représente une structure générique de thermopile planaire, dont les cellules disposées en damier permettent de quantifier l'effet de gradients de température alternativement disposés en ligne. En pratique, une piste continue de constantan (faible conductivité électrique) est déposée en tracé méandriforme, avant d'être localement plaquée à intervalles réguliers par un ensemble de sections composées d'or (métal à forte conductivité électrique). Les éléments partiellement plaqués au contact des longueurs non recouvertes sont comparables à des thermocouples différentiels classiques disposés en série[START_REF] Ph | Measurement on the thermoelectric properties of thin bimetallic films[END_REF][START_REF] Gaviot | Planar Differential Radiometers. A quantitative approach to designing enhanced units[END_REF][START_REF] Güths | A new sensor to measure fluids velocities: The Peltier anemometer[END_REF] . La disposition agencée en damier permet la détection de champs thermiques répartis de manière linéaire et périodique conduisant à des capteurs de différence de température particulièrement sensibles et linéaires[START_REF] Gaviot | Thin foil planar radiometers: Application for designing contactless T sensors[END_REF] .Concernant la présente application, la différence de température entre jonctions ( en °C) se trouve rapportée directement en proportion avec l'écart en température (  T en °C) observable entre les thermomètres sec et humide d'un psychromètre idéal. La figure 2 illustre la disposition des canaux et le réservoir intermédiaire permettant l'apport par capillarité.

Les valeurs de  et  sont déterminées en considérant la relation 5 en atmosphère sèche renouvelée à flux continu [V s max, mélange azote/oxygène (RH %  0.2 %), t=22°C, T = V s /]. Avec P=1015 hPa, la tension mesurée [V s (22°C, 0%) = 4,77  0,02 mV] entraîne  = 0,315 0,0015 mV/°C et  = 8,865x10 -3 (confirmation par une seconde procédure à t = 30°C). Cette approche équivaut à la détermination du facteur  d'un psychromètre classique. Enfin, compte tenu de la faible capacité thermique de l'assemblage, la mesure présente un temps de réponse réduit ( 90% = 5  0.5 s).

L'écart psychrométrique T résultant directement de Vs, la figure 5 présente les valeurs obtenues en fonction des diverses solutions chimiques utilisées (P=1015 hPa). Considérant les valeurs de T déduites de la sonde de référence et du comportement des solutions saturées, (calcul à partir de la relation de Sonntag [START_REF] Sonntag | Vapor pressure formulations based on the ITS-90 and the psychrometer formulate -Important new values of the physical constants of 1986[END_REF]) , le prototype étudié délivre une information en bon accord avec les valeurs attendues. L'application des relations 5 et 6 conduit ainsi à une mesure correcte de l'humidité relative : en effet, la figure 6 en présente la détermination (tracé en pointillé), les autres tracés (en trait plein) résultant de l'application théorique directe de la relation 5. La pertinence des données expérimentales et théorique valide ainsi le concept présenté. Toutefois, plusieurs problèmes de rupture d'alimentation en eau nous ont conduit à envisager la modification de la conformation du réservoir intermédiaire, en ajoutant un système de cloisonnement favorisant l'apport par capillarité.

Conclusion

Un réseau de microcanaux constitué du polymère photo-imageable SU-8 disposé sur une thermopile planaire, permet de développer une nouvelle famille de psychromètres. Conformément au principe de réduction dimensionnelle applicable aux capteurs de grandeurs intensives, le prototype réalisé permet des mesures rapides et précises conduisant au degré d'humidité relative. Le prototype étudié et présenté supporte les opérations de nettoyage et des températures jusqu'à 200°C. Compte tenu des améliorations en cours d'étude visant à la répétabilité des performances, des applications industrielles en contrôle de qualité ou agroalimentaires (monitoring des cultures sous serre) peuvent être envisagées à court terme.