Rojas Castro
email: rojas-castro@u-bordeaux.fr

Madelyn Yiseth

Health conditions and the risk of home injury in French adults: Results from a prospective study of the MAVIE cohort

Keywords: Wounds and Injuries, Home Accident, Falls, Prospective Studies, Prevention

Background Home injury (HI) is a significant cause of mortality and morbidity in adults of all ages. Health conditions significantly impact HI among old adults, but little is known for other adults.

Study design Prospective cohort study

Objective: We assessed the associations between health-related factors and HI's risk in a French study, the MAVIE cohort.

Methods Poisson mixed models were fitted using health-related data information (diseases, treatments, and disabilities) at baseline and the number of injuries prospectively recorded during the follow-up, adjusting for significant socio-demographics and exposure to a range of home activities. Attributable fractions (AFs) were estimated based on RR estimations measured in the fully adjusted models.

Results A total of 6,146 dwelling adults aged 15 or more were followed up for 5.1 years on average. Vertigo or dizziness (RR=2.36, 95% CI 1.06 to 5.01) and sciatica or back pain (RR=1.49, 95% CI 1.08 to 2.05) were independently associated with an increased risk of HI.

These two groups of conditions showed the most significant associations among people aged 15 to 49, whereas musculoskeletal diseases other than rachialgias and arthropathies were the most significant health-related risk factor in people aged 50 and more. Sciatica or back pain represented the highest-burden of HIs in overall adults (8%) and among people aged 15 to 49 (12%).

Conclusion

Our results suggest that adults with musculoskeletal disorders and vertigo or dizziness symptoms have a higher risk of HI, regardless of age.

INTRODUCTION

Home injuries (HIs) represent approximately one-third of the global burden of injuries 1 2 3 . In the EU-28, HIs caused an annual average of 85 thousand fatalities, 1.5 million hospital admissions, and 9 million emergencies between 2012 and 2014 [START_REF] Eurosafe | Injuries in the European Union. Summary of injury statistics for the years 2012-2014[END_REF] . Home has been identified as the most prevalent location for injuries resulting in hospitalization and is second to roads as the location for fatal injuries [START_REF] Keall | Association between the number of home injury hazards and home injury[END_REF] .

HIs affect people of all ages. However, among adults, HIs are more frequent in people aged 65 years or over. Falls are the principal mechanism of fatal and non-fatal HIs [START_REF] Eurosafe | Injuries in the European Union. Summary of injury statistics for the years 2012-2014[END_REF] .

Multiple studies have identified health-related factors associated with falls in the elderly, including: lack of strength gait and balance, mobility impairment [START_REF] Laurence | The Fall in Older Adults: Physical and Cognitive Problems[END_REF][START_REF] Ambrose | Risk factors for falls among older adults: A review of the literature[END_REF][START_REF] Deandrea | Risk factors for falls in community-dwelling older people: A systematic review and meta-analysis[END_REF] , back pain 9 10 , arthropathies 8 11 , dizziness and vertigo 8 12 13 , obesity [START_REF] Cho | BMI and Central Obesity With Falls Among Community-Dwelling Older Adults[END_REF] , diabetes 7 8 11 , cardiovascular conditions 7 8 11 , chronic obstructive pulmonary disease [START_REF] Dionyssiotis | Analyzing the problem of falls among older people[END_REF] , urinary incontinence [START_REF] Deandrea | Risk factors for falls in community-dwelling older people: A systematic review and meta-analysis[END_REF] , visual and hearing impairments [START_REF] Ambrose | Risk factors for falls among older adults: A review of the literature[END_REF] , cognition impairments caused by neurological conditions such as Parkinson's disease, Alzheimer's disease or other types of dementia [START_REF] Laurence | The Fall in Older Adults: Physical and Cognitive Problems[END_REF][START_REF] Ambrose | Risk factors for falls among older adults: A review of the literature[END_REF][START_REF] Deandrea | Risk factors for falls in community-dwelling older people: A systematic review and meta-analysis[END_REF] , and sleeping problems, anxiety or depression 6-8 11 . The presence of two or more concurrent conditions [START_REF] Deandrea | Risk factors for falls in community-dwelling older people: A systematic review and meta-analysis[END_REF] and certain medications, such as psychotropics, antidepressants, anxiolytics, sedatives or hypnotics [START_REF] Seppala | Fall-Risk-Increasing Drugs: A Systematic Review and Meta-Analysis: II. Psychotropics[END_REF] , opioids [START_REF] Yoshikawa | Opioid Use and the Risk of Falls, Fall Injuries and Fractures among Older Adults: A Systematic Review and Meta-Analysis[END_REF] , cardiac medication, diuretics, anti-diabetic medication [START_REF] Ambrose | Risk factors for falls among older adults: A review of the literature[END_REF] , and polypharmacy [START_REF] Zia | Polypharmacy and falls in older people: Balancing evidence-based medicine against falls risk[END_REF] are also associated with falls in the elderly.

Among young and middle-aged adults, understanding the impact of health risk factors on HI is poor 18 19 . Regarding the risk of occupational injuries, there is some evidence of the role of hearing impairments, neurotic illness, diabetes [START_REF] Ritchie | Causes of Death. Our World in Data Published Online First[END_REF] , epilepsy, and sedating medication [START_REF] Palmer | Chronic health problems and risk of accidental injury in the workplace: A systematic literature review[END_REF] .

Conditions such as back pain, sleeping problems, anxiety, depression, cardiovascular diseases, and diabetes [START_REF] Ritchie | Causes of Death. Our World in Data Published Online First[END_REF] can also be frequent in young and middle-aged adults, which justifies evaluating their impact on adults of all ages.

The purpose of this study was to assess associations of health-related factors on the risk of nonfatal HI in adults of all ages in a prospective cohort, the MAVIE cohort.

METHODS

Study design and recruitment

The MAVIE cohort is a web-based prospective cohort study conducted in France, with a longitudinal follow-up of Home, Leisure, and Sports Injuries (HLIs). All households in France and French overseas territories were eligible to participate. The recruitment process began in November 2014. The present study analyzed the data collected up to December 31, 2019.

Cohort management was entirely online, including invitations, registration, and data collection. Participants were recruited through an email invitation sent to their insurees by three mutual insurance companies, press releases, social media, posters, and flyers.

We asked potential participants to choose a household reference member in charge of completing a web-based questionnaire for the household. Consenting members of each household were asked to provide individual information. In an attempt to address the foreseeable underrepresentation of the elderly who may have difficulties using computers, caregivers were invited to represent and participate on behalf of one older person.

Follow-up

Every three months, household reference members received an email reminder to report any injury event to any consenting household members during the follow-up. If no event occurred, respondents were requested to report this. An invitation to report events was also included in the monthly cohort newsletter. Still, events could be reported at any time.

Participant data and selection

The inclusion criteria for participation in the MAVIE cohort were: i) residing in France; ii)

being able to answer the questionnaires in French; iii) having access to and being able to use the Internet (at least the reference member). The baseline sample was defined as the participants aged 15 or over who answered at least one question of the individual inclusion questionnaire. We excluded those who lived in hospitals and retirement or long-term care institutions. We considered only participants who reported at least one feedback during follow-up and respondents to the daily schedule.

Home Injuries

This study focused on unintentional home injuries or its premises. We excluded all events involving illnesses or medical symptoms. We excluded events that occurred before or on the same date as the date of consent and those for which information about the type of medical care or the circumstances of occurrence was not reported. Finally, we excluded injuries that occurred during sleeping time, considered unlikely [START_REF] Kopjar | Population-based Study of Unintentional Injuries in the Home[END_REF] .

Data included activity and location, mechanisms and type of medical care of the injury event.

We defined HIs as severe when emergency care or hospital inpatient care was required.

Individual characteristics

Relative time distribution

Participants were asked to report their typical daily schedule in hours for each home location.

The average duration was also reported for domestic work, gardening, and do-it-yourself (DIY) activities. Time spent on each activity was categorized as frequent (over the 75th percentile), occasional or null.

Socioeconomic, demographic characteristics, and alcohol consumption

Gender, age, occupational status, education level, living situation, household incomes, and alcohol consumption were studied at baseline. Occupational status groups were unemployed, homemakers, and retirees and students and employees. Responses to education status were assigned to educational attainment levels by age groups. We considered a low level of education high school or vocational studies, or lower for participants aged 20 to 54, and primary studies or lower for other ages. Annual household incomes were assigned to classes according to the French population's percentiles reported in 2015 (Low: ≤ 30th percentile, Middle: 30th-80th percentile, High: ≥ 80th percentile). The categories of the frequency of alcohol consumption were less than two times a week, and two or more times a week.

Health conditions and medications

At inclusion, participants were invited to report their history of diseases and treatments over the previous 12 months. Medical conditions were grouped into the following clinically homogeneous categories: cardiovascular diseases, respiratory diseases, digestive diseases, genitourinary diseases, endocrine diseases, sciatica or back pain, arthropathies, other conditions of the musculoskeletal system, eye diseases, depression, anxiety, sleeping disorders (including treatment with antidepressants, anxiolytics or hypnotics), migraine or headache, vertigo or dizziness, chronic mental diseases (Parkinson's disease, Alzheimer's disease or other senile dementia, epilepsy, and antiepileptic medicines), and cancer. Participants were also asked to report whether they were suffering from impairments or disabilities related to vision, hearing, mental, intellectual, or psychological, and mobility.

We defined polypharmacy as a reported number of medications of 4 or more [START_REF] Zia | Polypharmacy and falls in older people: Balancing evidence-based medicine against falls risk[END_REF] , and comorbidity as the report of two or more diseases 22 at any time in the previous 12 months. The history of injuries (excluding sports injuries) over the past 12 months was also reported.

Statistical analyses

Data were analyzed using R version 3.6.1 (The R Foundation for Statistical Computing, Vienna, Austria)

We defined the follow-up period (FP) from the consent date to the latest date among the following: the latest news statement date, the questionnaires update date, the cohort exit date, the death date. We calculated the proportion of time spent awake at home (PTAH) as the proportion of hours on a weekday or weekend day when the person was neither away from home nor sleeping. We considered the time-at-risk as:

Time-at-risk = (PTAH w × No. FPw) + (PTAH wn × No. FPwn) ,
where PTAH w was the time spent awake at home regular weekday, PTAH wn on a regular weekend day, No. FP w the number of weekdays in the follow-up period and No. FP wn the number of weekend days. We calculated the proportion of time-at-risk as:

% Time-at risk = (Time-at-risk/Follow-up duration) ×100%.

Risk factor analysis

Poisson mixed models were used to fit the number of HIs during the estimated time at risk. Random effects were included to take into account the cluster structure of data in households.

All models were fitted using the Template Model Builder R package [START_REF] Brooks | glmmTMB Balances Speed and Flexibility Among Packages for Zero-inflated Generalized Linear Mixed Modeling[END_REF] . Relative risks (RRs) were calculated conditionally upon the random effects, and the 95% confidence intervals were calculated using the profile method [START_REF] Venzon | A Method for Computing Profile-Likelihood-Based Confidence Intervals[END_REF] . We adopted a complete case approach.

We fitted individual crude regression models to each health condition. Then, we conducted a two-step variable selection procedure. First, we adjusted each model by age, gender, and history of injuries in all models, and we selected the most important associations (p adj < 0.10).

Second, we fitted the models to each health-related factor, adjusting for significant adjustment variables selected in the previous step. Finally, we selected the most important associations for the fully adjusted model (excluding comorbidity). Benjamini-Hochberg corrected p-values were computed [START_REF] Benjamini | Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing[END_REF] . The same methodology was used to construct models stratified by two distinct age groups (15 to 49 years old and 50 years old or more).

The attributable fraction (AF) was estimated using the adjusted RR of the fully adjusted models, as suggested by Flegal and colleagues, 2006 [START_REF] Flegal | Using adjusted relative risks to calculate attributable fractions[END_REF] .

RESULTS

Between November 2014 and December 2019, 11,420 adults registered in the MAVIE cohort and responded to baseline questionnaires. Among them, 9,429 were household reference members representing themselves and/or another household member. Sixty-six participants reported that living in a retirement institution, and 3,524 participants did not provide followup data. Another 1,684 participants did not provide their daily schedule (Figure 1). The sample size was 6,146 participants from 5,122 households.

The median follow-up was 4.0 years (Q1=3.6, Q3=4.5). The overall follow-up duration was 4,800 persons-time. The loss to follow-up was 13%.

Among the 6,146 individuals of the study, 244 left the cohort during the follow-up. Nineteen of them were reported by the reference member to have died, 16 from illness, and three of unknown causes. Thirty-one participants left the study due to changes in household composition. The remaining 191 participants did not report any reasons for leaving the study. Socioeconomic, demographic characteristics, and alcohol consumption levels were similar to those of the study sample and baseline sample (Table 1). However, dropout was more frequent among young adults, students, and employees, and among members of low-income households.

Baseline characteristics

Socioeconomic, demographic characteristics, and alcohol consumption

Table 1 shows the socioeconomic, demographic characteristics, and alcohol consumption of the sample at baseline. Sample characteristics differed from those of the overall French population (INSEE Census, 2015). Participants aged 50 to 74 were overrepresented (62% vs. 35% in the French population, 2015). Students and employees were underrepresented (49% vs. 57%). People with low education attainment level were underrepresented (8% vs. 44%). Finally, only 12% of household reference members reported an annual income lower than the 30th percentile of French households.

The median proportion of time spent at home awake was 48% (Q1=36%, Q3=58%). Adults older than 50, unemployed, retirees, homemakers, and those who reported gardening, DIY, and domestic activities were those who spent the most time at home (Supplementary material 1).

Health conditions, diseases, and medications

Among the 6,146 participants, 67% reported at least one health condition (Figure 2). They were older, with a median age of 60 compared to 35 for those who did not report any health condition. Figure 2 shows the most frequently reported health conditions by age group.

Almost half of the participants (48%) reported more than one health condition. The most frequently reported conditions among adults aged 15 to 49 years were depression, anxiety, or sleeping disorders, and among adults aged 50 and more, cardiovascular diseases. Eight percent of participants reported at least one type of injury in the last 12 months.

Home Injuries

During follow-up, 12% of the participants reported at least one HI, of which 946 occurred while awake. Most of HIs were minor injuries, and only 28% required either hospitalization or emergency care. Falling was the main mechanism of HI (39 %), domestic and gardening activities (42%), the most frequents activities, and the garden (25%) the most frequent location (Supplementary Material 2).

Health risk factor analysis

Adjusting for the selected variables of block 1 (Table 2), vertigo or dizziness, sciatica or back pain, arthropathies, other musculoskeletal system diseases, depression, anxiety or sleeping disorders, and comorbidity were associated with an increased risk of HI in adults of all ages with a small or moderate effect (Block 2, Table 2). In the fully adjusted model (Table 3), vertigo or dizziness and sciatica or back pain remained associated with an increased risk of HI and with an AF of 1.9% and 8.1%, respectively. The contribution of depression, anxiety, and sleeping disorders was also important (AF=5.5), but the association was weaker than the conditions named above (RR = 1.28, 95% CI 0.96 to 1.70).

Results of the fully adjusted models were similar for participants aged 15 to 49, but the effects of sciatica or back pain and vertigo or dizziness effects were higher than among adults of all ages (Table 4). The category of other musculoskeletal system diseases covered the only conditions significantly associated with the risk of HI among participants aged 50 or more (Table 4). All models converged, and their residuals were validated, discounting problems, such as over/underdispersion and zero inflation.

DISCUSSION

To our knowledge, we present here the first study to evaluate the association of health conditions with the risk of non-fatal HIs in adults of all ages. We followed up 6,146 cohort participants residing in French households, of whom 12% suffered at least one HI over an average of 5.1 years. The same proportion was 14% among those who reported at least one health condition. Among the 21 health conditions reported at inclusion, we identified sciatica or back pain problems and vertigo or dizziness as the main risk factors, with an estimated AF of 8.1% and 1.9%, respectively. This unprecedented finding of substantially increased risk of HI among adults under 50 years old with sciatica or back pain (RR=2.26) and vertigo or dizziness (RR=4.59) is striking because of these high association measures, but also because of a substantial estimated AF (11.9% and 3.2%, respectively). For people over 50 years old, musculoskeletal diseases (other than rachialgia and arthropathies) are the only condition that remained significant in the fully adjusted model. These same factors associated with mobility emerged when we analyzed falls and shocks only, whereas this was not the case for other HIs. That suggests that most health conditions affecting the risk of HI are increasing the risk of falling. Other factors usually associated with injuries and falls, such as gender, age, vision and hearing impairments, polypharmacy, and alcohol consumption, did not appear to be associated with an increased risk of HI in this study.

Musculoskeletal conditions (including back pain) and sciatica are well-known risk factors for occupational injury, likely due to overexertion. Overexertion was reported only in the 18% of injuries of people suffering from musculoskeletal conditions. Consistent with previous findings, the effects of arthropathies (RR=1.37) and other musculoskeletal conditions (RR=1.57) were more relevant among adults over 50 years old 8 11 . In contrast to previous studies, back pain did not appear to be associated with an increased risk of HI in adults over 50 [START_REF] Marshall | A Prospective Study of Back Pain and Risk of Falls Among Older Community-dwelling Men[END_REF][START_REF] Marshall | A Prospective Study of Back Pain and Risk of Falls Among Older Community-dwelling Women[END_REF] . One possible explanation is that older people may favor chronic conditions over problems such as back pain when self-reporting. We hypothesize that poor posture might affect housework performance, increasing general injury susceptibility. Decreased cognitive function due to chronic pain [START_REF] Moriarty | The effect of pain on cognitive function: A review of clinical and preclinical research[END_REF] or opioid use [START_REF] Yoshikawa | Opioid Use and the Risk of Falls, Fall Injuries and Fractures among Older Adults: A Systematic Review and Meta-Analysis[END_REF] might also raise HI risk.

Vertigo or dizziness increased the risk of HI among young adults, but not among those aged 50 or more. This group of symptoms may be related to vestibular migraine, benign paroxysmal positional vertigo, and Meniere's disease [START_REF] Bisdorff | Migraine and dizziness[END_REF] , rather than age-related conditions such as Parkinson's disease, or cerebellum and oculomotor brain stem syndrome [START_REF] Zarcone | Shared mechanisms of epilepsy, migraine and affective disorders[END_REF] . Other possible causes of vertigo, such as hypoglycemic episodes or postural hypotension, have been partially controlled for by adjusting for other conditions such as endocrine diseases and cardiovascular diseases.

We found a slightly increased risk of HI among those reporting depression, anxiety, or sleeping disorders. Consistently, Palmer and colleagues (2018) highlighted an increased risk of occupational injury among people with emotional conditions, and a moderate effect among sedatives consumers [START_REF] Palmer | Chronic health problems and risk of accidental injury in the workplace: A systematic literature review[END_REF] . Another explanation might be the difficulties in assessing risks and a reduced motivation to correct them in people who have affective psychological disorders. Such an effect was observed for patients with Parkinson's disease [START_REF] Clemson | Case-control study of hazards in the home and risk of falls and hip fractures[END_REF] .

Unlike other studies 20 31 , we found no association regarding age and disability. Because we could account for the time spent at home, our results confirm that exposure time is the main explanation 1 32-34 . A relevant self-perception of disability allows compensation for an increased risk of injury, enabling enhanced care in daily activities and avoiding risky tasks and domestic hazards. People with moderate conditions, more active in domestic work, and less aware of risks might be more exposed to hazards together they might insufficiently regulate their behavior. On the other hand, these effects may be mitigated by the beneficial impacts of domestic activities [START_REF] Jiang | The association between mild cognitive impairment and doing housework[END_REF] , for example, by improving executive functions [START_REF] Tsuchiya | An acute bout of housework activities has beneficial effects on executive function[END_REF] .

Lessons for prevention from our results include better awareness of risks at home for people with diseases related to the musculoskeletal system. Our results also highlight the preventive role of physicians when dealing with vulnerable people. However, HI risk related to the level of activities should not discourage leisure activities and help raise awareness and adaptation of the living environment to the risks by mapping foreseeable hazards.

Limitations and Strengths

Common limitations observed in volunteer-based cohorts and e-cohorts are low response rates, volunteer bias, loss of follow-up, and self-administered questionnaires, leading to selection biases and missing and selective answers. We made continuous efforts to address representativeness, loss to follow-up, and quality of information issues. However, young adults and people from low socioeconomic groups and levels of educational attainment were underrepresented. An overestimation of the prevalence and impact of some diseases is probable. The difficulty of diagnosing the conditions, the ability to recall, the willingness to report (mostly when communicated by reference members), physical and mental quality of life may also affect the report [START_REF] Van Den Akker | Disease or no disease? Disagreement on diagnoses between self-reports and medical records of adult patients[END_REF] . Besides, this study design does not allow us to disentangle the effects of health conditions and treatments. Moreover, information about disease severity, risk behaviors, and risk awareness was not available. Finally, we measured health conditions at a single time point; health changes were not assessed over time.

Conclusion

Despite these limitations, the MAVIE cohort is the injury observatory with the most detailed sociodemographic, contextual, and exposure information to study risk factors of HLIs in France. This information enabled us to control for potential confounders and account for exposure time, the latter being a rare opportunity. Transparency: EL (corresponding author) affirm that the manuscript is an honest, accurate and transparent account of the study being reported; that no important aspects of the study have been omitted; and that any discrepancies from the study as originally planned (and, if relevant, registered) have been explained.

FOOTNOTES

What is already known on the subject?

• There is evidence that a large number of health conditions increase home injury risk in older adults.

• Musculoskeletal system diseases increase the risk of falls at home in older adults through weakness, loss of posture and balance.

• There is a lack of evidence on how health conditions affect the risk of home injury in younger adults.

What this study adds?

• Our results suggest a moderate to high effect of musculoskeletal system diseases and vertigo or dizziness symptoms over home injury risk regardless of age.

• Back pain or sciatica is the group of conditions with the highest attributable fraction of home injury risk among all adults and adults under 50 years old.

FIGURES AND TABLES

Employment Status

Students, Employees

Unemployed, retirees and homemakers 4,395

missing 103

Frequency of alcohol consumption

Less of 2 times a week 4,850 Poisson model was adjusted by the offset term time spent at home during the follow-up, random effect in the variable household, age, gender, history of previous injuries, household income level, living alone, and DIY and gardening . Abbreviations: n = number of responders, HI = number of home injuries, RR = relative risk, CI = confidence interval, p = Pvalues, AF = attributable fraction.

Data Sharing:

  Reasonable requests for patient level data should be made to the corresponding author and will be considered by. INSERM and Calyxis, Pôle d'expertise du risque responsible for any decision regarding the possible reuse of the data.Patient and Public Involvement: Since inclusion, participants to the MAVIE cohort have received summaries of the main conclusions obtained and have at their disposal an application the MAVIE Lab that allows them to experiment with the results.

Figure 1 -Figure 2 -

 12 Figure 1 -Flowchart of study participants Figure 2 -Self-reported health conditions at inclusion: Diseases reported during the 12 months prior to baseline, disabilities, and obesity at the time of inclusion by the analyzed dwelling-adults of the MAVIE cohort, stratified by age groups (at inclusion). Sample size N = 6,146

Table 1 -

 1 Description of the demographic, socioeconomic and other characteristics at inclusion time of MAVIE dwelling-adults: baseline and analyzed sample

	Baseline Sample	Analyzed Sample
	n	(%)	n	(%)

Table 2 -

 2 Individual factors associated with the incidence of HI, relative to the time at risk at home, in adults of the MAVIE cohort per variable including offset term time spent at home during the follow-up and random effect in the variable household. Block 1: Crude models adjustment variables and model including all adjustment variables. Block 2: Crude models of each health conditions and models adjusted for the variables of the block 1. Abbreviations: n = number of responders, HI = number of home injuries, RR = relative risk, CI = confidence interval, p c = P-values ANOVA type II corrected usingBenjamini & Hochberg (1995) method.

	2 times a week or more often	3,247	(40)	2,496	(42)
	missing	3,257		228
	DIY/gardening
	Never	3,124	(39)	2,080	(36)
	Occasional	3,339	(42)	2,519	(43)
	Frequent	1,573	(20)	1,228	(21)
	missing	3,318		319

Table 3 -

 3 Factors associated with the incidence of HI, relative to the time at risk at home, in adults of the MAVIE cohort (fully adjusted model)

		Fully adjusted model*
		(n = 3,842, HI = 529)
	(%)	RR (95% CI)	p	AF (%)

Table 4 -

 4 Factors associated with the incidence of HI, relative to the time at risk at home, in adults of the MAVIE cohort by age group Poisson mixed models including offset term time spent at home during the follow-up and random effect in the variable household. Adjustment variables: Age 15-49 (gender, history of injuries), Age 50+ (gender, history of injuries, living alone, household income level, DIY/gardening, frequency of alcohol consumption). Abbreviations: n = number of responders, HI = number of home injuries, RR = relative risk, CI = confidence interval, AF = attributable fraction, p c = P-values ANOVA type II corrected usingBenjamini & Hochberg (1995) method, p = P-values

			Adjusted models			Fully adjusted models
		(%)	RR (95% CI)	pc	(%)	RR (95% CI)	p AF (%)
	Age 15-49		(n = 1,887, HI = 208)			(n = 1,804, HI = 205)
	Sciatica or back pain
	Yes (vs. No)	(14)	2.40 (1.49 -3.91) <0.001	(14)	2.26 (1.40 -3.65)	0.001	11.9
	Vertigo or dizziness
	Yes (vs. No)	(2)	4.95 (1.76 -13.75)	0.002	(1)	4.59 (1.48 -14.13)	0.007	3.2
	Comorbidity
	≥2 diseases (vs. 1 disease or	(41)	2.15 (1.45 -3.22) <0.001	-	-	-
	not disease)
	Age 50+		(n = 2,915, HI = 472)			(n = 2,59, HI = 468)
	Others musculoskeletal
	system diseases
	Yes (vs. No)	(21)	1.57 (1.19 -2.07)	0.005	(22)	1.45 (1.05 -1.98)	0.023	9.3
	Sciatica or back pain
	Yes (vs. No)	(21)	1.36 (1.03 -1.80)	0.031	(21)	1.09 (0.78 -1.52)	0.602	2.2
	Arthropathies
	Yes (vs. No)	(17)	1.37 (1.02 -1.84)	0.036	(18)	1.14 (0.81 -1.59)	0.458	2.7
	Comorbidity
	≥ 2 diseases (vs. 1 disease or	(53)	1.35 (1.05 -1.75)	0.036	-	-	-
	no disease)

Acknowledgements:

The authors express their thanks to all IETO team members for their help, especially Juan Naredo Turrado, Jeanne Duchesne, Li Lu and Marie-Odile Coste.

Funding: This study was financed jointly by the Institut de recherche en santé publique (IReSP) [CONV 067-00187II], the Agence nationale de sécurité du medicament et des produits de santé [conv 2014S029], the Université de Bordeaux and the Région Nouvelle Aquitaine as part of the Cassiopée project [conv 2014-1R30504 -00003101]. MR is the recipient of an INSERM/Région Nouvelle Aquitaine doctoral grant and is affiliated to the Digital Health program funded by France's Strategic Investment Programme. The MAVIE observatory is coordinated by the INSERM U1219-IETO team and Calyxis, pôle d'expertise du risque, with the support of the mutual insurance companies MAIF, MAAF, MACIF and Decathlon.

Ethical approval:

The French Data Protection Authority approved the protocol of this study.

The study is declared to the CNIL under file number 912292. Identifying data were stored on servers located in a different location from those hosting the main database. Electronic informed consent was collected from all adult participants. participation of children was done under the responsibility and with the consent of a legal guardian.


Lyassine Allou

Lahcen El Maimouni

Stéphane Le Calvé
email: slecalve@unistra.fr

Henry's Law Constant measurements for formaldehyde and benzaldehyde as a function of temperature and water composition

Keywords: Henry's law constant, formaldehyde, benzaldehyde, temperature, salinity, acidity, salt effect, nitric acid

Henry's Law Constants H of formaldehyde and benzaldehyde were determined using a dynamic system based on the water/air equilibrium at the interface within the length of a microporous tube. The measurements were conducted over the range 273 -293 K in (i) deionized water, (ii) 35 g L -1 solution of NaCl simulating seawater and (iii) two nitric acid solutions, i.e. 0.63 and 6.3 wt %. In 6.3 wt % nitric acid solution, H values of benzaldehyde were approximately 30 % higher than those found in pure water although no significant influence was observed for formaldehyde.

Finally, our experimental data were then used to estimate the fractions of formaldehyde and benzaldehyde in atmospheric aqueous phase and their derived atmospheric lifetimes.

In pure water, the obtained data were used to derive the following Arrhenius expressions: ln H = (6423 ± 542)/T -(13.4 ± 2.0) and ln H = (6258 ± 280)/T -(17.5 ± 1.0) for formaldehyde and benzaldehyde, respectively. The H values, calculed at 293 K from Arhenius expressions cited bellow, were the following (in units of M atm -1 ) : H = 5020  1170 (formaldehyde), H = 47  5 (benzaldehyde). The temperature dependence of H permits then to derive the solvation enthalpies for both compounds : Hsolv = -(53.4 ± 4.5) kJ mol -1 and Hsolv = -(52.0 ± 2.3) kJ mol -1 for formaldehyde and benzaldehyde, respectively.

In 35 g L -1 salt solution, the H values were 27 to 66% and 12 to 21% lower than their respective determinations in deionised water, for formaldehyde and benzaldehyde respectively.

The observed salt effect was used to estimate the following Setschenow coefficients at 293 K for 0.6 M NaCl: formaldehyde (0.21) and benzaldehyde (0.09).

Introduction

Aliphatic and aromatic aldehydes constitute an abundant class of volatile organic compounds (VOCs) encountered in air and precipitations (rain, fog). Aldehydes are emitted into the atmosphere as primary pollutants from motor vehicles and industrial emissions, or produced in situ as environmentally intermediates in the photooxidation of other hydrocarbons [START_REF] Atkinson | Gas-phase tropospheric chemistry of organic compounds. Journal of physical and chemical reference data[END_REF][START_REF] Müller | Determination of aldehydes and ketones in the atmosphere : A comparative long time study at an urban and a rural site in Eastern germany[END_REF]. They play a key role in the tropospheric chemistry, since they lead photochemically to many products such as radical species that contribute to ozone (O3) and nitrate acetic peroxy (PAN) productions [START_REF] Atkinson | Atmospheric chemistry of VOCs and NOx[END_REF]. Formaldehyde (FA) and benzaldehyde (BA) represent the dominant species of aliphatic and aromatic carbonyl compounds, respectively.

Formaldehyde is an atmospherically relevant carbonyl compound with an active and important role in the tropospheric photochemistry [START_REF] Smith | Absorption Cross sections of formaldehyde at wavelenths from 300 to 340 nm at 294 and 245K[END_REF]. It is formed in the oxidation pathways of many biogenic and anthropogenic VOCs [START_REF] Sprengnether | Product analysis of the OH oxidation of isoprene and 1,3-butadiene in the presence of NO[END_REF] and emitted directly from biomass fires. It is an efficient precursor of HOX radicals (OH and HO2) which are the major tropospheric oxidant. Formaldehyde is also the main contributor to catalytic ozone loss in the lower stratosphere [START_REF] Mcelroy | The changing stratosphere[END_REF]. In addition, formaldehyde affects strongly the capacity of atmosphere waters (fog, clouds) because it inhibits the oxidation of S(IV) to sulfuric acid and because it is a precursor of formic acid [START_REF] Khare | HCHO, HCOOH and CH3COOH in air and rain water ata rural tripical site in north central India[END_REF][START_REF] Kieber | Rainwater formaldehyde : concentration, deposition and photochemical formation[END_REF][START_REF] Munger | Identification of hydroxymethansulfonate in fog water[END_REF].

Consequently, gaseous formaldehyde concentrations have been measured at different locations. Field measurements have shown concentration of 0.05 ppbv in clean Antarctic tropospheric air in winter [START_REF] Riedel | Variability of formaldehyde in the Antarctic troposphere[END_REF], a value varying between 15 and 20 ppbv in London [START_REF] Williams | A comparison of carbonyl concentrations at urban roadsite and indoor sites[END_REF] and up to 70 ppbv in Los Angeles [START_REF] Williams | A comparison of carbonyl concentrations at urban roadsite and indoor sites[END_REF].

Benzaldehyde can be considered as a model of simple aromatic aldehydes. It can be found in fruit, and is used as a soil fumigant and in the manufacturing of deodorants/air fresheners and loose mineral wool fiber [START_REF] Atkinson | Gas-phase tropospheric chemistry of organic compounds. Journal of physical and chemical reference data[END_REF].

Both FA and BA are polar molecules having high solubilities in water and are expected to be efficiently scavenged from the gas phase by rain and fog [START_REF] Gunz | Atmospheric chemistry of proxides: A review[END_REF][START_REF] Jayne | Uptake of Gas-Phase Formaldehyde by Aqueous Acid Surfaces[END_REF]. Significant levels of formaldehyde ranging between 0.01 and 13 µM were found in rain and fog [START_REF] Gunz | Atmospheric chemistry of proxides: A review[END_REF][START_REF] Jayne | Uptake of Gas-Phase Formaldehyde by Aqueous Acid Surfaces[END_REF] confirming its efficient scavenging from gas phase. Atmospheric deposition represents a significant sink since its concentrations in rain water are approximately three orders of magnitude higher than those in surface waters [START_REF] Nuccio | Biological production of formaldehyde in the marine environment[END_REF].

The partitioning of a given species between the gas and aqueous phases is given by its Henry's law constant H. This latter is a key physical characteristic to describe the behavior of a component in the environment [START_REF] Rice | Henry's Law Constants for pesticides measured as a function of temperature and salinity[END_REF] particularly in order to better understand its fate, its transport, and its removal in the lower troposphere. A detailed inspection of literature data shows a substantial variation in the previous quoted values for formaldehyde [START_REF] Betterton | Henry's Law constants of some environmentally important aldehydes[END_REF][START_REF] Chameides | The photochemistry of a remote marine stratoform cloud[END_REF][START_REF] Gaffney | Gas-Liquid Chemistry of Natural Waters[END_REF][START_REF] Seinfeld | Atmospheric Chemistry and Physic of Air Pollution[END_REF][START_REF] Seyfioglu | Determination of of Henry's law constant of formaldehyde as a function of temperature: Application to air-water exchange in Tahtali Lake in Izmir, Turkey[END_REF][START_REF] Staudinger | A critical review of Henry's law constants for environmental applications[END_REF][START_REF] Warneck | Chemistry of the natural atmosphere[END_REF][START_REF] Zhou | Apparent partition coefficients of 15 carbonyl compounds between air and seawater and between air and freshwater; Implications for air-sea exchange[END_REF] whereas only few determinations have been reported in the cas of benzaldehyde [START_REF] Allen | Determination of Henry's law constant by equilibrium partitioning in a closed system using a new in situ optical absorbance method[END_REF][START_REF] Betterton | Henry's Law constants of some environmentally important aldehydes[END_REF][START_REF] Gaffney | Gas-Liquid Chemistry of Natural Waters[END_REF][START_REF] Hine | The intrinsic hydrophilic character of organics compounds[END_REF][START_REF] Staudinger | A critical review of Henry's law constants for environmental applications[END_REF][START_REF] Zhou | Apparent partition coefficients of 15 carbonyl compounds between air and seawater and between air and freshwater; Implications for air-sea exchange[END_REF]. In addition, only few determinations have been obtained as a function of the water composition for both compounds.

In this study, direct experimental determinations of H for both formaldehyde and benzaldehyde in pure water have been therefore performed via a dynamic equilibrium system between 273 and 293 K. The effects on Henry's law constant of a 35 g L -1 solution of NaCl simulating seawater or 0.63 and 6.3 wt% nitric acid solutions chosen as maximal concentrations of HNO3 reported in tropospheric cloud droplets [START_REF] Gao | Evidence That Nitric Acid Increases Relative Humidity in Low-Temperature Cirrus Clouds[END_REF], have been investigated over the same temperature range. Our experimental determinations have been then compared with literature data and used to discuss the atmospheric lifetimes of both aldehydes.

Experimental Section

Reagents

Aqueous solutions of formaldehyde and benzaldehyde were prepared using Milli-Q Water (18 m cm). Pure benzladehyde (GC grade,  99%) and aqueous formaldehyde solution (30%) were obtained from Fluka Chemical Company and used without further purification. Sodium chloride ( 99.8%) was obtained from Riedel-de Haën Chemical Company. The aqueous concentrations used for the experiments were in the range 13.7 -97.6 mg L -1 for formaldehyde and 8.7-50.5 mg L -1 for benzaldehyde, given that their water solubilities are 55×10 4 mg L -1 (at 293 K) and 0.46×10 4 mg L -1 (at 298 K), respectively. To investigate the effects of acidity and salinity on H values, aqueous solutions of containing either 0.63 -6.3 wt% of HNO3 or 35 g L -1 of NaCl were used.

Dynamic equilibrium system

The measurements of H were conducted using a dynamic equilibrium system shown in Figure 1 and already used in previous work (Feigenbrugel et al., 2004a;Feigenbrugel et al., 2004b;[START_REF] Gautier | Henry's law constants measurements of alachlor and dichlorvos between 283 and 298 K[END_REF][START_REF] Katrib | Uptake measurements of dibasic esters by water droplets and determination of their Henry's law constants[END_REF]. Compressed air was passed through a microporous PTFE membrane tube (180 cm  0.8 cm i.d., Sumitomo Corporation) at a highly controlled flow rate of 0.2 -0.5 L min -1 . The tube was immersed in about 1.0 L of the diluted aqueous solution containing either formaldehyde or benzaldehyde. Phase equilibrium was achieved, for the dissolved compound, at the gas/water interface along the inner surface of the tube. The contact time between the two phases varied between 7 and 36 s depending on the flow rate. At the exit of the reactor, the gas phase containing the studied compound at equilibrium concentration was then diluted using clean dry air (0.5 L min -1 ). The compound present in the gas phase was trapped using two cartridges connected in series and filled with a 2,4-dinitrophenylhydrazine (2,4-DNPH) coated silica gel as derivatises. Benzaldehyde was collected for 20 -60 min whereas intervals of 4 to 6 hours were required to concentrate enough formaldehyde in cartridges.

After sampling, aldehyde was eluted three times by passing 20 mL, 10 mL and 10 mL of acetonirile through the cartridge. The mass of acetonitrile which stayed in the cartridge was measured after each extraction in order to know the dead volume in the cartridge. The experiments revealed that for benzaldehyde more than 97% of the compound was trapped in the first cartridge while for formaldehyde the percentage was about 92%. It should be noted that the mass of aldehyde trapped in the cartridges was always negligible compared to their total mass in the aqueous solution and consequentely, their aqueous concentration were effectively constant during the course of the experiment.

Analysis

The extracted solutions containing the hydrazones were weighed and analysed by HPLC/UV. For this, 20 µL of the extracted solution containing the hydrazones were injected into a reversed-phase column C-18 and were detected at a 360 nm wavelength [START_REF] Marchand | Aldehyde Measurements in indoor environment in Strasbourg (France)[END_REF][START_REF] Marchand | Indoor aldehydes concentrations and determinants in 162 homes in Strasbourg (France)[END_REF]. The hydrazones were separeted with a mobil phase of acetonitrile-water (60/40) isocratically pumped at a flow-rate of 1.5 mL min -1 and quantified from external calibration curves [START_REF] Marchand | Indoor aldehydes concentrations and determinants in 162 homes in Strasbourg (France)[END_REF]. For this, both aldehyde derivatives were prepared according to the method previously described [START_REF] Levart | Determination of aldehydes and ketones in air samples using cryotrapping sampling[END_REF]. Known concentrations of hydrazone were then prepared in acetonitrile and 20 µL of the obtained solution were then injected into the HPLC in order to plot concentration curves versus HPLC peak areas. The calibration curves were linear for the concentration ranges used in this study i.e. between 0.1 and 25 mg L -1 for hydrazone solutions and the correlation coefficients were larger than 0.99. Note that for each series of measurements, two blank cartridges of 2,4-DNPH were used to determine the background aldehydes concentrations.

Results and discussion

Effect of temperature

The Arrhenius plots of the Henry's Law Constants measured for benzaldehyde and formaldehyde in deionized water for a temperature range 273-293 K are presented in Figures 2 and3. The H values (in M atm -1 ) are also listed in Table 1 where the quoted uncertainties vary between 8 and 20 %. These values represent the sum of the uncertainties on the calibration curves (ranging from 1% to 9% for formaldehyde and 1% to 7% for benzladehyde), on the extraction process estimated to be around of 5% by a series of reproductibility tests, on the flow rates (less than 2.5 % under our experimental conditions) and on the aqueous concentration of the formaldehyde and benzaldehyde (up to 3%). Within these experimental errors, H values of both aldehydes are shown to be not sensitive to their aqueous concentration over the ranges stated in the experimental section and to the changes in air flow rate (0.2 -0.5 L min -1 ) as shown in Figure 4. Since H does not not vary with contact time, the equilibrium between solution and vapour is really achieved at the exit of reactor.

In Tables 2 and3, our experimental H values obtained at 293 K and those calculated at 298 K for formaldehyde and benzaldehyde respectively, are compared with previous determinations and estimated values reported in the literature.

For formaldehyde (see Table 2) and in spite of the different techniques used, our value of H agrees raisonably well, within experimental errors, with those reported by [START_REF] Betterton | Henry's Law constants of some environmentally important aldehydes[END_REF], [START_REF] Zhou | Apparent partition coefficients of 15 carbonyl compounds between air and seawater and between air and freshwater; Implications for air-sea exchange[END_REF] and [START_REF] Staudinger | A critical review of Henry's law constants for environmental applications[END_REF]. However, our H value of 3500  900 M atm -1 (calculated at 298 K) is 4 times lower than that reported by Warneck (1998) and approximately 2 times lower than those determined by [START_REF] Seinfeld | Atmospheric Chemistry and Physic of Air Pollution[END_REF] or [START_REF] Gaffney | Gas-Liquid Chemistry of Natural Waters[END_REF]. Figure 2 shows our obtained data compared with previous experimental ones.

For benzaldehyde, our average H value of 47 M atm -1 calculated at 298K is in very good agreement with the previous ones reported by several studies [START_REF] Allen | Determination of Henry's law constant by equilibrium partitioning in a closed system using a new in situ optical absorbance method[END_REF][START_REF] Betterton | Henry's Law constants of some environmentally important aldehydes[END_REF][START_REF] Gaffney | Gas-Liquid Chemistry of Natural Waters[END_REF][START_REF] Hine | The intrinsic hydrophilic character of organics compounds[END_REF][START_REF] Staudinger | A critical review of Henry's law constants for environmental applications[END_REF][START_REF] Zhou | Apparent partition coefficients of 15 carbonyl compounds between air and seawater and between air and freshwater; Implications for air-sea exchange[END_REF]) as illustrated in Table 3. However, as shown in Figure 3, the values of H at low temperatures and particularly that obtained at 273 K are significantly higher than those reported by [START_REF] Betterton | Henry's Law constants of some environmentally important aldehydes[END_REF], [START_REF] Zhou | Apparent partition coefficients of 15 carbonyl compounds between air and seawater and between air and freshwater; Implications for air-sea exchange[END_REF] or [START_REF] Staudinger | A critical review of Henry's law constants for environmental applications[END_REF], but are similar, within experimental errors, to those recently obtained by [START_REF] Allen | Determination of Henry's law constant by equilibrium partitioning in a closed system using a new in situ optical absorbance method[END_REF].

The following Arrhenius expressions can be derived from our data using a weighted analysis fit: ln H (FA) = (6423 ± 542)/T -(13.4 ± 2.0) ; ln H (BA) = (6258 ± 280)/T -(17.5 ± 1.0). The quoted errors are given at the 2 level from the least-squares analysis. Our recommended H values at 293 K, derived from the Arrhenius expressions using a weighted analysis fit, are the following (in units of M atm -1 ) : HFA = 5020  1170 and HBA = 47  5.

The quoted errors correspond to 2 level and are determined from the standard deviations on both slope and intercept of Arrhenius expression. In addition, the temperature dependence are very similar for the two studied compounds meaning that their enthalpies of solvation are approximately the same.

The behaviour of henry's law constants as a function of temperature can be conveniently expressed with a Van't Hoff equation:

H (T) = H293  exp(-H°solv/R (1/T -1/293)) (1)
where H°solv is the solvation enthalpy (J mol -1 ), T is the temperature (K) and R is the ideal gas constant. Assuming that H°solv is not temperature dependent between 273 and 293 K, the values of H°solv for both constituents have been calculed from a plot of ln H versus 1/T, where the slope is -H°solv/R. The linearity of these plots, within experimental uncertainties confirms the validity of equation ( 1). The derived enthalpies of solvation are the following (in units of kJ mol -1 ) : H°solv (FA) = -(52.0  4.5) and H°solv (BA) = -(52  2.3) where the quoted errors correspond to 2σ obtained from the least-squares analysis.

Effect of nitric acid

The measured H values of formaldehyde and benzaldehyde in 0.63 -6.3 wt% nitric acid solutions (maximal acid concentrations of tropospheric cloud droplets) in the range 273 -293 K for HNO3 0.63 wt% (0.1 N) and 268 -293 K for HNO3 6.3 wt% (1N), are reported in Figures 5 and6.

As shown in Figure 6, the experimental Henry's law constants of benzaldehyde are approximately the same for pure water and the lower nitric acid concentration of 0.63 wt%.

Nevertheless, all H values of benzaldehyde in 6.3 wt% nitric acid solution were 30 % higher than their respective values in deionised water. In opposite to benzaldehyde, Henry's law constants of formaldehyde in both nitric acid solutions are approximately the same than those measured in pure water, as displayed in Figure 5.

The question, of course, arises as to why a such difference is observed between the formaldehyde and benzaldehyde uptake behavior in acid medium. First, let us remind that in liquid solution, aldehydes (RCHO) react with water to form gem diol (RCH(OH)2 aq) which is greatly more water-soluble than its precursor. This hydratation pathway increases effective aldehyde solubility in water since its hydratation coefficient khyd is very higher (in case of FA, khyd  2000 at 298 K) [START_REF] Betterton | Henry's Law constants of some environmentally important aldehydes[END_REF] but smaller for larger molecules (khyd = 7.7 at 298 K for phtalaladehyde [START_REF] Mcdonald | The kinetics and equilibrium of the hydration of phthalaldehyde[END_REF]. The partitioning between gas and aqueous phases is then governed by the equilibrium constants as illustrated as follows:

aq hyd g OH RCH k aq RCHO H RCHO 2 ) ( ) ( ) ( ⎯ ⎯ →  ⎯ ⎯→  (2)
Therefore, hydratation subsequently increases the effective Henry's Law Constant of aldehydes. For formaldehyde, this effect can be expressed by the following equation:

) 1 ( ] [ ] ) ( [ ] [ 2 2 hyd g aq aq eff k H HCHO OH CH HCHO H +  = + = (3)
If the medium is strongly acid, an additional way affects the set of equilibriums mentioned above (see Eq. 2) since a protonated form of aldehydes RCH2O + is formed as shown below:

+ + ⎯→  + O RCH H RCHO 2 aq (4)
In this latter equation, the stability of RCH2O + cation strongly depends on the nature of alkyl group R.

As expected, our measured H value of benzaldehyde is quite low in pure water, confirming that its value of khyd is relatively limited, similarly to phtalaladehyde [START_REF] Mcdonald | The kinetics and equilibrium of the hydration of phthalaldehyde[END_REF]. This is in agreement with the observations made by [START_REF] Mcdonald | The kinetics and equilibrium of the hydration of phthalaldehyde[END_REF] who concluded that no hydratation was detected for benzaldehyde.

At low acidity, the protonated form RCH2O + is still negligible as it was observed by Jayne et al. (1992) for both formaldehyde and acetaldehyde. In very low pH, our results suggest that the protonated form seems to be important and partially governs the partitioning of benzaldehyde between the gas and liquid phases.

The equilibrium (4) leads to the soluble cation RCH2O + which is thermodynamically more stable when R is an efficient electron donor group such as a phenyl group (benzaldehyde). In opposite to benzaldehyde, HCH2O + is unstable and break up quickly to regenerate HCHOaq so that the Henry's law constant of formaldehyde is not sensitive to the pH effect. However, at very low pH, the decreasing of H2O activity reduces gem diol formation but supports inevitably the protonated form. Broadly, a compensation of the two effects takes place and finally, the observed Henry law constant does not undergo significant modification.

Effect of salinity

The Arrhenius plots of the Henry's Law Constants, measured for fomaldehyde and benzaldehyde in aqueous solutions of NaCl (35 g L -1 ) simulating seawater for a temperature range 273 -298 K, are presented in Figures 7 and8. The following Arrhenius expressions can be derived from our data using a linear fit: ln HS (FA) = (5548 ± 1320)/T -(10.7± 4.8) and ln HS (BA) = (6015 ± 424) /T -(16.7± 1.4). The quoted errors are given at the 2 level from the least-squares analysis.

As shown in both Figures 7 and8, our H values of benzaldehyde and formaldehyde in salt solutions were respectively 12 to 21% and 27% to 66% lower than their respective values in deionized water. For instance, the determined H values at 293 K in salt solution obtained from Arrhenius expression given above, can be compared with those measured in pure water (in parentheses): formaldehyde , HS = 3770 ± 2590 (H = 5020 ± 1170) ; benzaldehyde, HS = 46 ± 7 (H = 47 ± 5) (in units of M atm -1 ) where the quoted errors correspond to 2σ obtained from the least-squares analysis. This phenomenon is related to the salting-out effect which impacts on the water solubility (reduction in solubility).

The salt effect on the solubility of gases in seawater has been studied theoretically for a variety of small gas molecules [START_REF] Danckwerts | Gas-liquid reactions[END_REF]. The presence of a salt in an aqueous solution changes the water structure in the vicinity of the solute. An empirical relation for the effect of ionic strength on a Henry's law constant H for a given compound in an aqueous solution was given by [START_REF] Setschenow | Über die Konstitution der Salzlösungen auf Grund ihres Verhaltens zu Kohlensäure[END_REF]: log (H / HS) = h (NaCl) (5) where H and HS are the Henry's law coefficients of the compound in pure water and in the salt solution, respectively, (NaCl) is the molarity of the NaCl solution and h is the Setschenow's salting-out coefficient (L mol -1 ). Our results of H and HS at 293 K were used to estimate the following Setschenow coefficients for [NaCl] = 0.6M: h (FA) = 0.21 and h (BA) = 0.09. The solubility at 293 K is then reduced by a factor of 0.34 and 0.13 for formaldhyde and benzaldehyde, respectively.

In the study performed in pure water and natural seawater by [START_REF] Zhou | Apparent partition coefficients of 15 carbonyl compounds between air and seawater and between air and freshwater; Implications for air-sea exchange[END_REF], the values of Setschenow's coefficients h for benzaldehyde were found to be 0.20 and 0.15 at 298 and 283K, respectively. These values are relatively higher than that of 0.09 derived in this work at 293 K. Besides, our h value of formaldehyde disagrees with some observations made in previous studies [START_REF] Dong | [END_REF][START_REF] Zhou | Apparent partition coefficients of 15 carbonyl compounds between air and seawater and between air and freshwater; Implications for air-sea exchange[END_REF] since both studies report H/Hs ratios close to 1. No salt effect on formaldehyde solubility have been detected by [START_REF] Dong | [END_REF] in their experiments conducted with aqueous solution containing either 2M of NaCl or 1M of Na2SO4 or 1M of (NH4)2SO4. However, [START_REF] Swartz | Horizontal bubble train apparatus for heterogeneous chemistry studies : Uptake of gas-phase formaldehyde[END_REF] have observed a low Setschenow's coefficient, equal to 0.07 at 293 K with NaCl concentration ranging from 0 to 4 M [START_REF] Swartz | Horizontal bubble train apparatus for heterogeneous chemistry studies : Uptake of gas-phase formaldehyde[END_REF].

Atmospheric implications

The distribution of soluble gases between the gaseous and droplet phases in the atmosphere is strongly dependent on their Henry's law constant.

Once released in the atmosphere, VOCs can react in the gas phase or can be taken up by liquid water in clouds where they can also be oxidized. For most of them, OH radical is the most efficient oxidizing species in both gas phase [START_REF] Atkinson | Atmospheric chemistry of VOCs and NOx[END_REF] and aqueous phase [START_REF] Ervens | Temperature-dependent rate constants for hydroxyl radical reactions with organic compounds in aqueous solutions[END_REF]. To evaluate the impact of a cloud on the atmospheric chemistry of formaldehyde and benzaldehyde, we compare in this section their atmospheric lifetimes under clear sky (τgas) and cloudy conditions (τmultiphase).

The lifetime of A in the gas phase (τA,gas) taking into account the photolysis and the reaction of A with OH and NO3 radicals, is defined as follows:

g 3 g NO3, g g g OH, g g gas A, ] [NO k ] [OH k J 1 /dt d[A] [A] τ + + = - = (6)
where Jg, kOH,g and kNO3,g are respectively the gas-phase photolysis coefficient, the rate constant of the gas phase reaction of OH and NO3 radicals with A, [OH]g is the mean concentration of OH radicals and [A]g is the concentration of A in the troposphere.

[NO3]g is the night concentration of nitrate radicals.

If we consider now the cloudy atmosphere as a multiphase reactor where both gas and aqueous phases coexist, then the multiphase lifetime of A can be defined as [START_REF] Monod | Kinetics of OHinitiated oxydation of oxigenated organic compounds in the aqueous phase: new rate constants, structureactivity relationships and atmospheric implications[END_REF]:

) OH] [ k (J T HRL ] NO [ k OH] [ k J T HRL 1 aq aq OH, aq WC 3 g NO3, g g OH, g WC multiphase A, +  + + + + = g  (7)
where R the ideal gas constant (in L atm mol -1 K -1 ), Lwc the dimensionless liquid water content of the cloud (typically 4.210 -7 ) [START_REF] Kolb | Laboratory studies of atmospheric heterogeneous chemistry[END_REF], Jaq and kOH,aq are respectively the photolysis coefficient of A and the rate constant of OH reaction with A in aqueous phase, [OH]aq is the mean concentration of OH radicals in the tropospheric aqueous phase.

The rate constants of OH reaction with formaldehyde or benzaldehyde in both aqueous and gas phases have already been reported [START_REF] Chin | Aquatic and surface photochemistry[END_REF]IUPAC, 2009;NIST, 2009;[START_REF] Semadeni | The temperature dependance of the OH radical reactions with some aromatic compounds under simulated tropospheric conditions[END_REF], and are shown in Table 4 together with the Henry's law constants determined in this work. These data have then been used to estimate the partitioning and then the atmospheric lifetimes of both aldehydes under clear sky (τgas), and cloudy conditions (τmultiphase), by using typical concentrations of OH radicals in gas and aqueous phases: [OH]g=110 6 cm -3 and [OH]aq=110 -13 M [START_REF] Monod | Kinetics of OHinitiated oxydation of oxigenated organic compounds in the aqueous phase: new rate constants, structureactivity relationships and atmospheric implications[END_REF]. We assume here that the OH concentration in the gas phase is the same under clear sky and cloudy conditions although it is reduced as soon as clouds are formed, and the magnitude of the decrease strongly depends on the pH value of the droplet [START_REF] Monod | Impact of clouds on the tropospheric ozone budget: Direct effect of multiphase photochemistry of soluble organic compounds[END_REF].

At 293 K, the calculated aqueous fraction are the following: formaldehyde, 3.410 -2 ; benzaldehyde, 3.810 -4 . At 293 K which is the temperature where most of experimental rate constants were measured, the atmospheric lifetimes of formaldehyde and benzaldehyde are slightly reduced in clouds as shown in Table 4. However, the average temperature of tropospheric clouds is 283 K and therefore, the calculated aqueous fraction of formaldehyde rises from 3.410 -2 to 9.610 -2 when the temperature decreases from 293 to 283 K, temperature range where the H value of formaldehyde increases from 5020 to 10900 M atm -1 .

Assuming that the rate constants of OH reactions with formaldehyde or benzaldehyde in the gas and aqueous phases do not vary a lot between 283 and 298 K as it was already observed for many oxygenated VOCs (except when data are available at 283 K), we can then estimate the multiphase lifetimes of both aldehydes at 283 K. These calculated multiphase lifetimes at 283 K (in units of hours) can be compared to those under clear sky in July (in parentheses): formaldehyde, 7.0 (6.7) ; benzaldehyde, 1.2 (18.2). Considering all the uncertainties associated with the above calculations, one can conclude that the oxidation of formaldehyde might be negligible in aqueous phase although that of benzaldehyde could represent its main sink. min -1 ; b 0.3 L min -1 ; c 0.5 L min -1 . Experiments performed with an aqueous concentration of: d  85 mg L -1 ( 2.8×10 -3 M) for formaldehyde; e  25 mg L -1 ( 2.4×10 -4 M) for benzaldehyde. [START_REF] Semadeni | The temperature dependance of the OH radical reactions with some aromatic compounds under simulated tropospheric conditions[END_REF] ; e [START_REF] Atkinson | Kinetics of the gasphase reactions of NO3 radicals with a series of aromatics at 296 ± 2 K Int[END_REF] ; f [START_REF] Zhu | Photodissociation of benzaldehyde in the 280-308 nm region[END_REF] ; g (Chin and Wine, 1994) ; h This work; i (NIST, 2009). [START_REF] Allen | Determination of Henry's law constant by equilibrium partitioning in a closed system using a new in situ optical absorbance method[END_REF][START_REF] Staudinger | A critical review of Henry's law constants for environmental applications[END_REF][START_REF] Zhou | Apparent partition coefficients of 15 carbonyl compounds between air and seawater and between air and freshwater; Implications for air-sea exchange[END_REF][START_REF] Betterton | Henry's Law constants of some environmentally important aldehydes[END_REF] This work

Figure Captions Figure 1 :

 Captions1 Figure Captions

Figure 2 :

 2 Figure 2 : Plot of ln H versus 1000/T for formaldehyde in the temperature range 273 -293 K in deionized water. Our determinations are compared to the experimental data of the literature. Our uncertainties on H values varied typically between 8 and 20 % and are determined as mentioned in the text. Straigth lines represent Arrhenius plots derived by Staudinger and Roberts (blue dash-dot line), by Zhou and Mopper (red long dash line), by Betterton and Hoffmann (green dash-dot line), by Chameides (black dotted line) or in this work (pink solid line).

Figure 3 :

 3 Figure 3 : Plot of ln H versus 1000/T for benzaldehyde in the temperature range 273 -293 K in deionized water. Our determinations are compared to the experimental data of the literature. Our uncertainties on H values varied typically between 8 and 20 % and are determined as mentioned in the text. Straigth lines represent Arrhenius plots derived by Allen et al. (black long dash line), by Staudinger and Roberts (blue dash-dot line), by Zhou and Mopper (red long dash line), by Betterton and Hoffmann (green dash-dot line) or in this work (pink solid line).

Figure 4 :

 4 Figure4: Plot of H versus the flow rate ranging between 0.2 and 0.5 L min -1 for both formaldehyde and benzaldehyde at 293 K. Our errors on H varied typically between 8 and 20 % and are determined as mentioned in the text.

Figure 5 :

 5 Figure 5 : Plot of ln H versus 1000/T for formaldehyde in 0.1N (dotted line) and 1N (dash line) nitric acid solutions in the temperature range 273 -293 K and comparison with values obtained in in deionized water (solid line).

Figure 6 :

 6 Figure 6 : Plot of ln H versus 1000/T for benzaldehyde in 0.1N and 1N nitric acid (dash line for 1N HNO3) solutions in the temperature range 273 -293 K and comparison with values obtained in in deionized water (solid line).

Figure 7 :

 7 Figure 7 : Plot of ln H versus 1000/T in deionized water (solid line) and salt water (dash line) for formaldehyde in the temperature range 273 -293 K.

Figure 8 :

 8 Figure 8 : Plot of ln H versus 1000/T in deionized water (solid line) and salt water (dash line) for benzaldehyde in the temperature range 273 -293 K.

  Figure 1

Figure 3 Q

 3 Figure 3

Table 2 :

 2 Comparison of experimental Henry's law constants for formaldehyde with previous

	507
	508	work.
	509
		T (K)	H (M atm -1 )	d ln H/d(1/T) (K)	T range (K)	Technique	Référence
		298	6.0 × 10 3	-	-	-a	(Gaffney and Senum, 1984)
		293	1.0 × 10 4	6400		TC b	(Chameides, 1984)
		298	7.0 × 10 3
		298	6.3 × 10 3	-		-a	(Seinfeld, 1986)
		293	4.5 × 10 3	7200	278 -318	SCT c	(Betterton and Hoffmann, 1988)
		298	3.0 × 10 3
		298	1.4 × 10 4	-		-a	(Warneck, 1988)
		293 298	4.5 × 10 3 3.1 × 10 3	6500	283 -318	SCT c	(Zhou and Mopper, 1990)
		293	4.7 × 10 3	6800	-	SEST d	(Staudinger and Roberts, 1996)
		298	3.2 × 10 3
		293	5.9 × 10 3	1642	278 -323	SCT c	(Seyfioglu and Odabasi, 2007)
		298	5.4 × 10 3
		293	(5.0 ± 1.2)×10 3 f 6423 ± 542 f 273 -293	DES e	This work
		298	(3.5 ± 0.8) ×10 3 f
	510	a not reported; b Thermodynamic calculation; c SCT: Stripping Column Technique; d SEST:
	511	Single Equilibrium Static Technique; e DES: Dynamic Equilibrium System; f The quoted
	512	errors correspond to 2σ obtained from the least-squares analysis.
	513

Table 3 :

 3 Comparison of experimental Henry's law constants for benzaldehyde with previous work. DES: Dynamic Equilibrium System. g The quoted errors correspond to 2σ obtained from the least-squares analysis.

	T (K)	H (M.atm -1 )	d ln H/d (1/T) (K)	T range (K)	Technique	Reference
	298	36	-	-	SAR a	(Hine and Mookerjee, 1975)
	298	36	-	-	-b	(Gaffney and Senum, 1984)
	293 298	50 37	5100	278 -318	SCT c	(Betterton and Hoffmann, 1988)
	293 298	55 42	4600	283 -318	SCT c	(Zhou and Mopper, 1990)
	293	51	4800	-	SEST d	(Staudinger and Roberts,
	298	39				1996)
	293 298	52 35	7000	-	EPICS e	(Allen et al., 1998)
	293 298	47 ± 5 g 33 ± 3 g	6260 ± 280 g	273 -293	DES f	This work
	a determined from Structure Activity Relationship; b not reported; c SCT: Stripping Column
	Technique; d SEST: Single Equilibrium Static Technique; e Equilibrium Partitioning In
	Closed Systems (EPICS);

f

Table 4 :

 4 Rate constants of OH reaction with formaldehyde and benzaldehyde in both gas and aqueous phases and their corresponding Henry's law constants. The atmospheric lifetimes were calculated at two temperatures, i.e. 298 and 283 K.

	Compound	10 12  k OH, g (cm 3 s -1 )	10 -8  k OH, aq (M -1 s -1 )	10 5  J g (s -1 )	H (M atm -1 )	τ multyiphase January (hours)	τ multiphase July (hours)
		298 K	283K	298 K	283 K	January July	298K	283 K	298K 283 K 298 K 283 K
	Formaldehyde	8.5 a	8.7 a	7.6 g	6.3 g	3.2 c	7.3 c	3480 h 10900 h	13.2	13.0	6.7	7.0
	Benzaldehyde	12 d	13 d	4.4×10 4 i 4.4 × 10 4 i	0.15 f	1.5 f	37 h	111 h	3.1	1.2	2.9	1.2

a (IUPAC, 2009) ; b (Mora-Diez and Boyd, 2002) ; c (Masclet, 2005) ; d

Acknowledgement

This work was supported by the French Ministry of Research through the LEFE/CHAT program. This work was also sponsored in part by the region of Alsace and the REseau Alsace de Laboratoires en Ingénierie et Sciences pour l'Environnement (REALISE).

By default, the experiments were carried out in deionized water with a flow rate of 0.4 L min -1 501 and with an aqueous concentration of  15 mg L -1 ( 5×10 -4 M) for formaldehyde and  10 mg 502 L -1 ( 9.4×10 -5 M) for benzaldehyde. Experiments carried out with an air flow rate of: a 0.2 L 503