Francesca Felisatti

Julie Gonneaud

Cassandre Palix

Antoine Garnier- Crussard

Florence Mézenge

Brigitte Landeau

Anne Chocat

Anne Quillard

Eglantine Ferrand-Devouge

Vincent De

La Sayette

Denis Vivien

Gaël Chételat

Géraldine Poisnel

; Medit

A G -C

Role of Cardiovascular Risk Factors on the Association Between Physical Activity and Brain Integrity Markers in Older Adults

Keywords: EudraCT: 2016-002441-36, IDRCB: 2016-A01767-44, ClinicalTrials NCT02977819

Objective: Physical activity has been associated with a decreased risk for dementia, but the mechanisms underlying this association remain to be determined. Our objective was to assess whether cardiovascular risk factors mediate the association between physical activity and brain integrity markers in older adults.

Methods:

Participants from the Age-Well study underwent, at baseline, a physical activity questionnaire, cardiovascular risk factors collection (systolic blood pressure, body mass index [BMI], current smoker status, HDL-cholesterol, total-cholesterol, insulin) and multimodal neuroimaging (structural-MRI, diffusion-MRI, FDG-PET, Florbetapir-PET). Multiple regressions were conducted to assess the association between physical activity, cardiovascular risk factors, and neuroimaging. Mediation analyses were performed to test whether cardiovascular risk factors mediated the associations between physical activity and neuroimaging.

Results: 134 cognitively unimpaired older adults (≥65 years) were included. Higher physical activity was associated with higher grey matter (GM) volume (ß=0.174, p=0.030) and cerebral glucose metabolism (ß=0.247, p=0.019), but not with amyloid deposition or white matter integrity. Higher physical activity was associated with lower insulin and BMI, but not with the other cardiovascular risk factors. Lower insulin and BMI were related to higher GM volume, but not to cerebral glucose metabolism.

When controlling for insulin and BMI, the association between physical activity and cerebral glucose metabolism remained unchanged, while the association with GM volume was lost. When insulin and BMI were entered in the same model, only BMI remained a significant predictor of GM volume. Mediation analyses confirmed that insulin and BMI mediated the association between physical activity and GM volume.

Analyses were replicated within Alzheimer's disease-sensitive regions, and results remained overall similar.

Conclusions:

The association between physical activity and GM volume is mediated by changes in insulin and BMI. In contrast, the association with cerebral glucose metabolism seems to be independent from cardiovascular risk factors. Older adults practicing physical activity have cardiovascular benefits, through the maintenance of a lower BMI and insulin, resulting in greater structural brain integrity. This study has strong implications as understanding how physical activity affects brain health may help developing strategies to prevent or delay age-related decline.

Introduction

Physical activity is important in preventing pathological aging and dementia, including Alzheimer's Disease (AD). [START_REF] Barnes | The projected effect of risk factor reduction on Alzheimer's disease prevalence[END_REF] Growing evidence indicates that older adults engaging in a higher amount of physical activity have greater brain integrity, [START_REF] Chen | The Effect of Exercise Training on Brain Structure and Function in Older Adults: A Systematic Review Based on Evidence from Randomized Control Trials[END_REF][START_REF] Erickson | Physical Activity and Brain Plasticity in Late Adulthood[END_REF] including increased grey matter (GM) volume, [START_REF] Domingos | Effects of physical activity on brain function and structure in older adults: A systematic review[END_REF] cerebral glucose metabolism, [START_REF] Neth | Relationship Between Risk Factors and Brain Reserve in Late Middle Age: Implications for Cognitive Aging[END_REF][START_REF] Matthews | Physical Activity, Mediterranean Diet and Biomarkers-Assessed Risk of Alzheimer's: A Multi-Modality Brain Imaging Study[END_REF][START_REF] Okonkwo | Physical activity attenuates agerelated biomarker alterations in preclinical AD[END_REF] WM microstructural integrity, 8 along with reduced amyloid burden [START_REF] Okonkwo | Physical activity attenuates agerelated biomarker alterations in preclinical AD[END_REF][START_REF] Matthews | Physical Activity, Mediterranean Diet and Biomarkers-Assessed Risk of Alzheimer's: A Multi-Modality Brain Imaging Study[END_REF][START_REF] Brown | Physical activity and amyloid-β plasma and brain levels: Results from the Australian Imaging, Biomarkers and Lifestyle Study of Ageing[END_REF] and white matter hyperintensities (WMH). 8 However, the relationship between physical activity and brain structure and function is still not fully understood as i) some inconsistencies remained [START_REF] Vemuri | Effect of lifestyle activities on alzheimer disease biomarkers and cognition[END_REF] and ii) the mechanisms by which physical activity exerts its benefits on brain health remain to be determined. Animal studies suggest that physical activity promotes neurogenesis, cell survival, expression of neurotrophic factors, and synaptic plasticity, [START_REF] Erickson | Physical Activity and Brain Plasticity in Late Adulthood[END_REF] while human studies also propose indirect effects of physical activity, via a reduction in cardiovascular risk factors. [START_REF] Barnes | Exercise Improves Vascular Function, but does this Translate to the Brain? Brain Plast[END_REF][START_REF] Walhovd | Blood markers of fatty acids and vitamin D, cardiovascular measures, body mass index, and physical activity relate to longitudinal cortical thinning in normal aging[END_REF] In fact, physical activity has been proven to efficiently reduce cardiovascular risk factors, [START_REF] Cotman | Exercise builds brain health: key roles of growth factor cascades and inflammation[END_REF][START_REF] Strasser | Physical activity in obesity and metabolic syndrome[END_REF] which are known to increase dementia risk and negatively affect brain structure and function. [START_REF] Cox | Associations between vascular risk factors and brain MRI indices in UK Biobank[END_REF] Nevertheless, the role of cardiovascular risk factors on the association between physical activity and brain integrity remains unknown. Most of the studies only controlled for cardiovascular risk factors and found no changes after such correction, [START_REF] Hamer | Association of objectively measured physical activity with brain structure: UK Biobank study[END_REF] but contradictory findings have also been reported. [START_REF] Castro | Fitness, insulin sensitivity, and frontal lobe integrity in adults with overweight and obesity[END_REF] The scarcity of studies combining several neuroimaging modalities in the same sample, and exploring the role of cardiovascular risk factors in the association between physical activity and neuroimaging biomarkers, make it difficult to understand how physical activity contributes to brain health. We investigated whether the association between physical activity and multimodal neuroimaging, including GM volume, cerebral glucose metabolism, amyloid burden, WMH load, and WM microstructure, is mediated by cardiovascular risk factors.

Methods

Participants

Participants from the baseline visit of the Age-Well randomized clinical trial (Medit-Ageing European Project), [START_REF] Poisnel | The Age-Well randomized controlled trial of the Medit-Ageing European project: Effect of meditation or foreign language training on brain and mental health in older adults. Alzheimer's[END_REF] were included (Figure 1). Individuals were recruited from the general population from November 2016 until March 2018. They were all native French speakers, retired for at least 1 year, had at least 7 years of education, and performed within the normal range on standardized cognitive tests. The main exclusion criteria were antecedent of major neurological or psychiatric disorders (including alcohol or drug abuse), presence of a chronic disease or acute unstable illness (including cardiovascular and metabolic affections), and current or recent treatments that may interfere with cognitive functioning. All participants included underwent structural MRI, [START_REF] Poisnel | The Age-Well randomized controlled trial of the Medit-Ageing European project: Effect of meditation or foreign language training on brain and mental health in older adults. Alzheimer's[END_REF] F-florbetapir-PET and [START_REF] Poisnel | The Age-Well randomized controlled trial of the Medit-Ageing European project: Effect of meditation or foreign language training on brain and mental health in older adults. Alzheimer's[END_REF] F-fluorodeoxyglucose (FDG)-PET scans, along with a physical activity questionnaire, blood sampling and a clinical exam including information on cardiovascular risk factors, within a 3-months period.

Baseline data were collected from November 2016 until April 2018.

Standard Protocol Approvals, Registrations, and Patient Consents

The Age-Well randomized clinical trial was approved by local ethics committee (Comité de Protection des Personnes Nord-Ouest III, Caen, France; trial registration number: EudraCT: 2016-002441-36; IDRCB: 2016-A01767-44; ClinicalTrials.gov Identifier: NCT02977819) and all participants gave their written informed consent prior to the examinations.

Image Acquisition

All participants were scanned on the same magnetic resonance imaging (MRI; Philips Florbetapir-and FDG-PET scans were acquired in two separate sessions, with a resolution of 3.76×3.76×4.9 mm 3 (FOV: 157 mm). Forty-seven planes with a voxel size of 1.95×1.95×3.27 mm 3 were obtained. Before the PET acquisition, a transmission scan was performed for attenuation correction. For Florbetapir-PET, each participant (n=133) underwent a 10-min PET scan beginning 50 minutes after the intravenous injection of ~4MBq/Kg of Florbetapir. For the FDG-PET scan, participants (n=92) were fasted for at least 6 hours before scanning. After a 30-min resting period in a quiet and dark environment, ~180 MBq of FDG were intravenously injected as a bolus and a 10-min PET acquisition scan was acquired 50 minutes after injection.

Image processing

T1-weighted MRIs were segmented using FLAIR images and normalized to the Montreal Neurological Institute (MNI) space. GM normalized segments were modulated to correct for nonlinear warping effects using the Statistical Parametric Mapping (SPM12) software's multiple channels segmentation procedure (http://www.fil.ion.ucl.ac.uk/spm/software/spm12).

Raw FLAIR images were coregistered onto their corresponding native space T1weighted MRI, and WMH were segmented by the lesion prediction algorithm LPA [START_REF] Schmidt | Bayesian Inference for Structured Additive Regression Models for Large-Scale Problems with Applications to Medical Imaging[END_REF] implemented in the Lesion Segmentation Toolbox version 2.0.15 (www.statisticalmodelling.de/lst.html) for SPM12. A minimum extend threshold of 0.01 cm³ was set.

Lesion probability maps were binarized by applying a threshold of 0.5 and lesions masks were thus generated. Lesion masks were then visually inspected and corrected for false positives in corticospinal tracts if necessary, using a specific corticospinal tract mask for each participant. [START_REF] Garnier-Crussard | White matter hyperintensities across the adult lifespan: Relation to age, Aβ load, and cognition[END_REF] DKI images were corrected for susceptibility artifacts, eddy current distortions and subject motion using Functional Magnetic Resonance Imaging of the Brain diffusion toolbox (FSL 5.0.9, http://www.fmrib.ox.ac.uk/fsl). DKI data were then processed using Matlab R2012b (MathWorks, Natick, MA) and the Diffusional Kurtosis Estimator software (DKE: Version 2.6; http://nitrc.org/projects/dke) to estimate the diffusional kurtosis tensor. [START_REF] Tabesh | Estimation of tensors and tensor-derived measures in diffusional kurtosis imaging[END_REF] Images were smoothed with a 3.375×3.375×3.375 mm full-width at half-maximum (FWHM) Gaussian filter. Mean kurtosis (MK) and fractional anisotropy (FA) maps, reflecting WM microstructural integrity, [START_REF] Falangola | Age-related non-Gaussian diffusion patterns in the prefrontal brain[END_REF] were then extracted from the diffusional kurtosis estimator. These maps were coregistered to the T1-weighted MRI and normalized to the MNI template by applying the deformation parameters from the corresponding T1-weighted MRI.

PET data were coregistered onto their corresponding MRI, corrected for partial volume effects (PVE) using the Muller-Gartner method, and normalized using the deformation parameters defined from the T1-weighted procedure. Resulting images were quantitatively normalized using the cerebellar GM as the reference region.

Averaged global neuroimaging values were obtained by applying a binary mask of GM for preprocessed T1-weighted and PET images, and a binary mask of WM, for preprocessed DKI images. The cerebellum was excluded from both masks, and only voxels with a probability >60% of being GM and WM were included, to exclude non-GM or WM voxel and reduce the probability of overlap with other tissue classes.

For FLAIR data, the total volume of WMH was extracted, as fully described elsewhere. [START_REF] Garnier-Crussard | White matter hyperintensities across the adult lifespan: Relation to age, Aβ load, and cognition[END_REF] To investigate how the results could apply to AD, neuroimaging values were also extracted in AD-sensitive regions. More specifically, we extracted GM volume in the hippocampus (ROI), glucose metabolism SUVR in the precuneus (from the AAL atlas) and in a posterior cingulate and temporoparietal regions previously determined, [START_REF] Besson | Cognitive and brain profiles associated with current neuroimaging biomarkers of preclinical alzheimer's disease[END_REF] as well as FA in the cingulum (from the JHU WM atlas).

Physical activity

Physical activity over the last 12 months was assessed using a French version of the Modifiable Activity Questionnaire (MAQ), [START_REF] Kriska | Development of Questionnaire to Examine Relationship of Physical Activity and Diabetes in Pima Indians[END_REF] adapted to be self-administered. [START_REF] Vuillemin | Self-Administered Questionnaire Compared with Interview to Assess Past-Year Physical Activity[END_REF] This version of the questionnaire allows assessing the amount of physical activity, including both leisure activities and work activities. Since participants were retired, only the leisure-related physical activity was considered in the present study.

Participants had to report, for each activity they did at least 10 times over the last 12 months (e.g., walking, hiking, biking, gardening, jogging), how much time they spent doing that activity (i.e., how many months per year, time per month and minutes each time). The total physical activity score corresponds to the average hours per week of leisure-time physical activity over the last 12 months. The averaged hours per week was calculated for each activity as follows [(number of months per year) x (number of times per month) x (minutes per time) / 60 (min)] / 52 (week per year), and which were summed to obtain a total score of physical activity.

Cardiovascular risk factors

Cardiovascular risk factors measures included insulin, cholesterol (total and HDL), systolic blood pressure, BMI and smoking habits.

Fasting blood sample were obtained for all participants. The plasma concentration of Insulin (pmol/L) was performed by chemiluminescence assay on automated analyzer COBAS 6000 (Roche diagnostics, Meylan, France), using ready-made commercial reagent kits (Insulin ROCHE). The quantitative determination of total cholesterol (mmol/L) and high-density lipoprotein (HDL; mmol/L) cholesterol concentrations in serum were carried out by an enzymatic staining test in Beckman Coulter Clinical Chemistry AU analyzers (Beckman Coulter, Villepinte, France). Systolic blood pressure (SBP; mm Hg) was averaged over three consecutive assessments at two different times in a seated position at rest. The BMI was objectively obtained during the medical interview and was calculated as weight in kilograms divided by height in meters squared (Kg/m 2 ). Participants were questioned on their smoking habits and were classified as currently smokers (yes) or not (no).

Statistical analysis

We carried out multiple linear regressions, in order to assess whether there was a specific association between (1) physical activity and each neuroimaging value separately, (2) physical activity and each cardiovascular risk factor separately and 3) cardiovascular risk factors and neuroimaging values that were significantly associated with physical activity. Next, to better understand the specific implication of each cardiovascular risk factor to these effects, we replicated the same multiple regression by including cardiovascular risk factors of interest (i.e. found to be associated in the previous analyses) in the same model. All analyses were controlled for age, sex, and education. Analyses with insulin, total and HDL-cholesterol, and SBP were further controlled for hypo-glycaemic, hypo-cholesterol and high-blood pressure treatments, respectively. Models with polynomial terms of different orders for physical activity were considered, to assess which function best described the association between physical activity and neuroimaging global values (Supplemental materials).

Analyses were conducted using the R software (R Core Team, 2019) and considered significant at a p<.05.

Finally, we used causal mediation analyses to examine whether the cardiovascular risk factors mediated these associations.

We tested the mediation effect using "mediation analysis", and we reported the average direct effects and average causal mediation effect estimated using nonparametric bootstrapping based on 5000 bootstrap samples, p<.05.

Data availability

Data is available on request following a formal data sharing agreement and approval by the consortium and executive committee. The data sharing request form can be downloaded at https://silversantestudy.eu/2020/09/25/data-sharing/.

Results

Data of 134 cognitively unimpaired older adults (≥65 years) were analyzed.

Participants' characteristics are detailed in Table 1. Because physical activity, insulin and BMI were not normally distributed, values were log-transformed. One participant had a physical activity score of zero, which cannot be log-transformed. As a result, to be able to include this subject in the analyses, a constant of 1 was added to all physical activity scores before transformation.

Association between physical activity and global neuroimaging measures

Higher physical activity was correlated to higher global GM volume (Figure 2A) and cerebral glucose metabolism (Figure 2B), but not with amyloid burden, WMH volume or WM microstructural integrity (MK; Table 2).

The association between physical activity and GM volume was best described by a linear function. The association between glucose metabolism and physical activity seemed also better described by a linear association, even though some indices suggest that the quadratic model cannot be completely rejected (Supplemental materials, eTable 1).

Association between physical activity and cardiovascular risk factors

Higher physical activity was associated with lower insulin (Figure 2C) and BMI (Figure 2D), but not with total and HDL-cholesterol, SBP or current smoker status (Table 2). Results remained similar when further controlling for treatments (Supplemental materials, eTable 2).

When insulin and BMI were entered in the same model, they were no longer associated with physical activity, suggesting that the link of physical activity with insulin and BMI is not independent one from another. Consistently, insulin and BMI were highly correlated.

Association between cardiovascular risk factors and global neuroimaging measures

We then examined whether the cardiovascular risk factors (insulin, BMI) and the global neuroimaging values (GM volume and cerebral glucose metabolism) found to be associated with physical activity were correlated to each other. Lower insulin (Figure 2E) and BMI (Figure 2F) were both correlated with higher GM volume, but neither of them was associated with cerebral glucose metabolism (Table 3). When BMI and insulin were included in the same model, the correlation of GM volume with insulin was lost, while the association with BMI remained unchanged, suggesting that the association between insulin and GM volume was driven by BMI. Results remained similar when further controlling for treatments (Supplemental materials, eTable 1).

Influence of cardiovascular risk factors on the association between physical activity and neuroimaging

When the association between physical activity and GM volume was controlled for insulin and BMI separately, or simultaneously, the association was lost. On the other hand, the association with cerebral glucose metabolism remained significant when controlling for insulin, BMI or both.

Mediation analyses

To directly assess whether the association between physical activity and global GM volume was mediated by insulin and BMI, we performed mediation analyses. The relationship between physical activity and GM volume was fully mediated by insulin (Figure 3, Model 1) and BMI (Figure 3, Model 2). The indirect effects of insulin and BMI separately were significant (Table 4).

AD-sensitive region of interest

To further investigate whether the effect of physical activity, cardiovascular risk factors and the mediations were present in regions specifically involved in AD, analyses were replicated on GM volume, glucose metabolism and WM microstructural integrity in AD-sensitive ROIs.

As depicted in Table 1, higher physical activity was correlated to higher hippocampal volume and glucose metabolism in the precuneus (Supplemental materials, eFigure 1A,B), but not to global glucose metabolism, suggesting that the link found in the main analyses involves only in part AD-sensitive regions.

We then examined whether the cardiovascular risk factors (insulin, BMI) and the neuroimaging values (hippocampal volume and glucose metabolism of the precuneus) found to be associated with physical activity were correlated to each other. Lower insulin and BMI were correlated with higher hippocampal volume (Table 2; Supplemental materials, eFigure 1C,D). Of note, when adding insulin and BMI into the model, BMI was the best predictor of hippocampal volume. On the other hand, neither insulin, nor BMI were associated with glucose metabolism of the precuneus.

When insulin and BMI were added separately or simultaneously (Table 2) in the regression model between physical activity and hippocampal volume, the association was not significant anymore (although close to the threshold of 0.05).

Mediation analyses confirmed that insulin (Figure 2, Model1) and BMI (Figure2, Model 2) fully mediated the association between physical activity and hippocampal volume. The indirect effects of insulin and BMI separately were significant (Table 3).

Complementary analyses:

Analyses were replicated on FDG-PET data not corrected for PVE, and show similar results (Supplemental materials, eTable 3, eTable 4, eFigure 2).

In addition, to further investigate whether other lifestyle factors drive the association between physical activity and brain integrity, analyses were replicated adjusting for Mediterranean diet adherence and lifetime cognitive activity. Results remained similar (Supplemental materials, eTable 5, eTable 6), suggesting that the associations previously highlighted are not driven by other lifestyle factors.

Discussion

Our multimodal neuroimaging study provides an integrated view of the differential association between physical activity and complementary measures of brain integrity.

In cognitively unimpaired older adults, we found that physical activity was directly associated with cerebral glucose metabolism, while the association with global GM volume was mediated by cardiovascular risk factors, and more specifically insulin and BMI. Similar results were found when focusing on AD-sensitive brain regions.

The finding that physical activity is associated with higher GM volume is in line with previous literature in cognitively unimpaired older adults using self-reported physical activity and related measures such as exercise and fitness. [START_REF] Raichlen | Differential associations of engagement in physical activity and estimated cardiorespiratory fitness with brain volume in middle-aged to older adults[END_REF][START_REF] Arenaza-Urquijo | Distinct effects of late adulthood cognitive and physical activities on gray matter volume[END_REF][START_REF] Boots | Cardiorespiratory fitness is associated with brain structure, cognition, and mood in a middle-aged cohort at risk for Alzheimer's disease[END_REF][START_REF] Matthews | Physical Activity, Mediterranean Diet and Biomarkers-Assessed Risk of Alzheimer's: A Multi-Modality Brain Imaging Study[END_REF] Importantly, this association was mediated by the effect of insulin and BMI. These results tie well with prior studies showing that increased physical activity in older adults was accompanied with lower insulin [START_REF] Brown | Physical activity and amyloid-β plasma and brain levels: Results from the Australian Imaging, Biomarkers and Lifestyle Study of Ageing[END_REF] and BMI [START_REF] Gennuso | Sedentary behavior, physical activity, and markers of health in older adults[END_REF] and other evidence showing that lower insulin and BMI [START_REF] Raji | Brain structure and obesity[END_REF] were linked to greater GM volume in older adults. One conceivable explanation is that physical activity leads to better cardiovascular health, which could in turn lead to a greater preservation of brain structure. [START_REF] Ho | The effects of physical activity, education, and body mass index on the aging brain[END_REF] Obesity and insulin dysfunction may develop with aging, [START_REF] Ryan | Insulin Resistance with Aging[END_REF] and are risk factors for brain atrophy, cognitive impairment and dementia, including AD. [START_REF] Arnold | Brain insulin resistance in type 2 diabetes and Alzheimer disease: Concepts and conundrums[END_REF][START_REF] Raji | Brain structure and obesity[END_REF] Obesity is the most common cause of insulin resistance [START_REF] Sripetchwandee | Links between obesityinduced brain insulin resistance, brain mitochondrial dysfunction, and dementia[END_REF][START_REF] Ryan | Insulin Resistance with Aging[END_REF] and they are both source of inflammation and oxidative stress, [START_REF] Shin | How Does Obesity and Physical Activity Affect Aging?: Focused on Telomere as a Biomarker of Aging[END_REF] that negatively impact brain health and increase AD risk. [START_REF] Corlier | Systemic inflammation as a predictor of brain aging: Contributions of physical activity, metabolic risk, and genetic risk[END_REF] Insulin action in the brain includes neuroprotective, neurotrophic and neuromodulatory functions, and its perturbation may accelerate brain atrophy in AD. [START_REF] Arnold | Brain insulin resistance in type 2 diabetes and Alzheimer disease: Concepts and conundrums[END_REF] Insulin resistance is the main characteristic of Type 2 Diabetes, a disease associated not only with aging, obesity and physical inactivity, [START_REF] De | Alzheimer's Disease Is Type 3 Diabetes-Evidence Reviewed[END_REF] but also with brain atrophy and increased dementia risk. [START_REF] Biessels | Brain changes underlying cognitive dysfunction in diabetes: What can we learn from MRI? In[END_REF] Recently, active lifestyle has been found to protect against the deleterious effects of diabetes on dementia over 12 years, likely through its positive impact on reduced brain volume loss. [START_REF] Marseglia | Can active life mitigate the impact of diabetes on dementia and brain aging? Alzheimer's Dement[END_REF] Interestingly, insulin and BMI were strongly associated in our study, and when insulin and BMI were included in the same model to predict GM volume, BMI remained the only predictor. Therefore, we argue that maintenance of a lower BMI through physical activity could help preventing disturbed insulin metabolism observed in aging, thus promoting brain health.

To date, only one study specifically looked at and found insulin sensitivity to mediate the relation between physical activity and anterior cingulate cortex volume. [START_REF] Castro | Fitness, insulin sensitivity, and frontal lobe integrity in adults with overweight and obesity[END_REF] Thus, our study extends these results to a global measure of GM volume. Only a small number of studies accounted for the effect of BMI on the association between physical activity and GM volume, [START_REF] Matthews | Physical Activity, Mediterranean Diet and Biomarkers-Assessed Risk of Alzheimer's: A Multi-Modality Brain Imaging Study[END_REF][START_REF] Arenaza-Urquijo | Distinct effects of late adulthood cognitive and physical activities on gray matter volume[END_REF][START_REF] Hamer | Association of objectively measured physical activity with brain structure: UK Biobank study[END_REF] but they failed to find a dependent effect of BMI on this association. This contradictory finding might be due, in part, to smaller physical activity assessment periods (e.g., last 7 days) considered in other research, [START_REF] Hamer | Association of objectively measured physical activity with brain structure: UK Biobank study[END_REF] which may have hampered an effect on BMI and, by extension, any possible mediation on the link between physical activity and GM volume. Others included a smaller [START_REF] Arenaza-Urquijo | Distinct effects of late adulthood cognitive and physical activities on gray matter volume[END_REF] or younger sample than the one included here. [START_REF] Matthews | Physical Activity, Mediterranean Diet and Biomarkers-Assessed Risk of Alzheimer's: A Multi-Modality Brain Imaging Study[END_REF] Our findings go beyond previous reports, providing evidence of indirect, cardiovascular risk factorsdependent, association between physical activity and GM volume.

As a second key finding, physical activity was associated with greater cerebral glucose metabolism in a subsample of 92 participants, in agreement with FDG-PET neuroimaging modality; [START_REF] Neth | Relationship Between Risk Factors and Brain Reserve in Late Middle Age: Implications for Cognitive Aging[END_REF][START_REF] Matthews | Physical Activity, Mediterranean Diet and Biomarkers-Assessed Risk of Alzheimer's: A Multi-Modality Brain Imaging Study[END_REF][START_REF] Okonkwo | Physical activity attenuates agerelated biomarker alterations in preclinical AD[END_REF] but see. [START_REF] Vemuri | Effect of lifestyle activities on alzheimer disease biomarkers and cognition[END_REF] Most importantly, the relation between physical activity and cerebral glucose metabolism did not depend on insulin or BMI. The benefits of physical activity on cerebral glucose metabolism may rather act through more direct neuronal effects, such as increased neurogenesis, cell survival, expression of neurotrophic factors, and synaptic plasticity. [START_REF] Erickson | Physical Activity and Brain Plasticity in Late Adulthood[END_REF] The increased nutrient and energy demands of these neural processes are met with increased expression of enzymes implicated in glucose use and metabolism. [START_REF] Cotman | Exercise builds brain health: key roles of growth factor cascades and inflammation[END_REF] Alternatively, benefits of physical activity on cerebral glucose metabolism could be mediated by other factors not measured here. With regards to insulin, the literature is controversial. Some animal studies highlighted the role of insulin in the regulation of brain glucose uptake and metabolism. [START_REF] Lucignani | Journal of Cerebral Blood Floit' and Metabolism Effects of Insulin on Local Cerebral Glucose Utilization in the Rat[END_REF] However, evidence in Humans is contradictory, with studies reporting an association of brain glucose uptake with insulin [START_REF] Byun | Region-specific association between basal blood insulin and cerebral glucose metabolism in older adults[END_REF] and insulin resistance, [START_REF] Willette | Association of insulin resistance with cerebral glucose uptake in late middle-aged adults at risk for Alzheimer disease[END_REF] while others found no correlation with neither of them. [START_REF] Ishibashi | Effects of glucose, insulin, and insulin resistance on cerebral 18F-FDG distribution in cognitively normal older subjects[END_REF] Our results align with prior observations showing that neuron glucose uptake, transport and use can be influenced by, but would not depend on, insulin. [START_REF] Arnold | Brain insulin resistance in type 2 diabetes and Alzheimer disease: Concepts and conundrums[END_REF] Similarly, evidence on the link between BMI and cerebral glucose metabolism in aging individuals is weak and heterogeneous. Higher BMI has been found to be associated with both increased [START_REF] Pegueroles | Obesity impacts brain metabolism and structure independently of amyloid and tau pathology in healthy elderly. Alzheimer's Dement Diagnosis[END_REF] and reduced 5 cerebral glucose metabolism, preventing from drawing clear conclusions. Only a few studies previously examined the association between physical activity and cerebral glucose metabolism in older participants. [START_REF] Neth | Relationship Between Risk Factors and Brain Reserve in Late Middle Age: Implications for Cognitive Aging[END_REF][START_REF] Matthews | Physical Activity, Mediterranean Diet and Biomarkers-Assessed Risk of Alzheimer's: A Multi-Modality Brain Imaging Study[END_REF][START_REF] Okonkwo | Physical activity attenuates agerelated biomarker alterations in preclinical AD[END_REF] Among them, none controlled for insulin, making it difficult to assess whether it might have influenced that relationship. On the other hand, in the ones controlling for BMI, the association between physical activity and cerebral glucose metabolism remained significant. [START_REF] Hamer | Association of objectively measured physical activity with brain structure: UK Biobank study[END_REF] Overall, it remains unclear how much insulin and BMI are involved in the regulation of cerebral glucose metabolism. In the present study however, we did not find these cardiovascular risk factors to be related to cerebral glucose metabolism and neither to mediate the link between physical activity and cerebral glucose metabolism.

Taken together, these two first findings are important to help our understanding of the mechanisms by which physical activity benefits brain health. As a plausible interpretation, some authors proposed that direct and indirect mechanisms are likely interconnected via the modulation of growth factor signaling. [START_REF] Cotman | Exercise builds brain health: key roles of growth factor cascades and inflammation[END_REF] Accordingly, physical activity directly induces the release of neurotrophic factors, which are supposed to activate a cascade of brain responses (i.e. neurogenesis, synaptic plasticity) that independently protect the brain. Physical activity also helps reducing proinflammatory conditions (induced by risk factors such as obesity and related insulin disturbances), which in turn indirectly improves growth factor signaling [START_REF] Cotman | Exercise builds brain health: key roles of growth factor cascades and inflammation[END_REF] and mitigates their deleterious effects on brain health. [START_REF] Corlier | Systemic inflammation as a predictor of brain aging: Contributions of physical activity, metabolic risk, and genetic risk[END_REF] Nevertheless, while results discussed were all statistically significant, it should be mentioned that they were of relatively modest magnitude (small effect sizes).

Of note, our multimodal study suggests that self-reported physical activity is associated with GM volume and cerebral glucose metabolism, but does not correlate with amyloid or markers of WM integrity (WMH and WM microstructure). Even if the effect size (β coefficient) of the link between physical activity and WMH was close to that of the link with GM volume, they did not reach the statistical threshold selected in this study. Previous literature has produced mixed results. [START_REF] Vemuri | Effect of lifestyle activities on alzheimer disease biomarkers and cognition[END_REF]8 Methodological differences with our study, [START_REF] Okonkwo | Physical activity attenuates agerelated biomarker alterations in preclinical AD[END_REF][START_REF] Brown | Physical activity and amyloid-β plasma and brain levels: Results from the Australian Imaging, Biomarkers and Lifestyle Study of Ageing[END_REF][START_REF] Matthews | Physical Activity, Mediterranean Diet and Biomarkers-Assessed Risk of Alzheimer's: A Multi-Modality Brain Imaging Study[END_REF]8 including instruments (fitness test, accelerometry, exercise interventions), time intervals (physical activity on the last 7 days), and mean age of participants (younger than our sample) could possibly explain the divergent findings. Moreover, while higher physical activity was associated with reduced insulin and BMI, we found no associations with SBP, total and HDL-cholesterol or smoking status. Despite prior studies suggesting benefits of physical activity on SBP, total and HDL-cholesterol, [START_REF] Strasser | Physical activity in obesity and metabolic syndrome[END_REF] and smoking habits, [START_REF] Swan | Smoking Predicting Physical Activity in an Aging America[END_REF] evidence in older individuals is scarce [START_REF] Herrod | Exercise and other nonpharmacological strategies to reduce blood pressure in older adults: a systematic review and meta-analysis[END_REF] and conflicting data have been also reported. [START_REF] Strasser | Physical activity in obesity and metabolic syndrome[END_REF] Furthermore, only a minority of studies examined these cardiovascular risk factors as primary outcomes. Further research is warranted to disentangle the influence of physical activity on amyloid burden, WM integrity and cardiovascular risk factors.

Results were also present when focusing on AD-sensitive brain regions. More specifically, physical activity was associated with higher hippocampal volume. This is in agreement with previous literature in cognitively unimpaired older adults, using both self-reported and objective measures of physical activity. [START_REF] Okonkwo | Physical activity attenuates agerelated biomarker alterations in preclinical AD[END_REF][START_REF] Hamer | Association of objectively measured physical activity with brain structure: UK Biobank study[END_REF] Physical activity was also associated with cerebral glucose metabolism in the precuneus, which is in line with previous studies. [START_REF] Dougherty | Moderate Physical Activity is Associated with Cerebral Glucose Metabolism in Adults at Risk for Alzheimer's Disease[END_REF] Our study further indicates that the association between physical activity and hippocampal volume is mediated by a reduction in insulin and BMI, while it was not the case for glucose metabolism in the precuneus. This suggests that results previously discussed for global neuroimaging measures could be extended to AD-sensitive regions. However, physical activity was neither associated with temporo-parietal cerebral glucose metabolism, nor with WM integrity of the cingulum (FA), suggesting that the results could not be generalized to all ADrelated regions.

Our study has some limitations. First, we used a subjective (self-reported questionnaire) instead of an objective measure of physical activity. However, selfreported physical activity has been extensively used in the literature and questionnaires have an acknowledged clinical validity. The one that we used in this study evaluates physical activity over the past year, whereas objective measures often assess physical activity over a short time interval, which could be not enough to detect any changes in the variables examined. Even though imprecision in the measure is likely to occur, validity and reliability of the questionnaire have been previously established. [START_REF] Kriska | Development of Questionnaire to Examine Relationship of Physical Activity and Diabetes in Pima Indians[END_REF] In addition, as participants are cognitively unimpaired, it seems unlikely that major recollection issue affected the questionnaire. Second, we used BMI as indicator of obesity in line with most of the studies. However, controversy exists in the literature as BMI might not be a sensitive index at older ages as it would be instead protective. [START_REF] Fitzpatrick | Midlife and late-life obesity and the risk of dementia: Cardiovascular health study[END_REF] BMI is nonetheless considered a valuable measure that is widely used, allowing for a better comparison with previous studies. Third, the cross-sectional nature of the design prevents us from inferring causal relationship regarding the association of physical activity with GM volume and cerebral glucose metabolism. Thus, we cannot exclude that older adults with a better brain health stay more physically active. Of note, while mediation analyses provide statistical support to theoretically driven hypothesis, they do not explain the biological mechanism underlying these associations. Further studies, including longitudinal and interventional designs should allow answering these questions, and further understanding the factors explaining the effects of physical activity on brain health.

Accumulating evidences highlight the impact of midlife cardiovascular risk factors on brain health. However, we did not address this issue since only current cardiovascular risk factors were available here. [START_REF] Debette | Education, y , mean ± SD (range) 13.14 ± 3.09 (7-22) Physical activity, mean ± SD (range) 6.31 ± 4.91 (0-23.08Insulin, pmol/L, mean ± SD (range) 65.08 ± 32.35 (14-201) BMI, kg/m2, mean[END_REF] The population of our study is relatively healthy, with no severe cardiovascular risk factors. This could prevent generalizability of the results, and explain discrepancy with previous studies including individuals with more severe cardiovascular diseases. Finally, no correction was made for multiple comparisons.

Overall, our results suggest that the associations between physical activity and global GM, including hippocampal volume, are mediated by changes in insulin and BMI. Thus, older adults practicing physical activity have cardiovascular benefits, through the maintenance of lower insulin and BMI, which could in turn promote greater structural brain integrity. In contrast, the association with global and precuneus cerebral glucose metabolism seems to be independent from cardiovascular risk factors. This study has strong implications as understanding how physical activity affects brain health may help developing strategies to prevent, or delay, age-related brain decline.

Achievia 3 .

 3 0T scanner) and positron emission tomography (PET; Discovery RX VCT 64 PET-CT scanner, General Electric Healthcare) cameras at the Cyceron Center (Caen, France). A high-resolution T1-weighted structural image using a 3D fast-field echo sequence (sagittal; repetition time (TR): 7.1 ms, echo time (TE): 3.3ms, field of view (FOV): 256×256 mm 2 , 180 slices, voxel size: 1×1×1 mm 3 ) and a 3D fluid-attenuated inversion recovery (FLAIR; sagittal; TR: 4800 ms, TE: 272 ms, inversion time: 1650 ms; FOV: 250×250 mm 2 , 180 slices, voxel size: 0.98×0.98×1 mm 3 ) were acquired for 133 participants. An echo-planar imaging/spin echo diffusion weighted sequence (DKI) was then performed at multiple shells for 133 participants: 3b-values (0, 1000, 2000 s/mm 2 ) (axial; 30 directions, TR: 6100 ms, TE: 101 ms, flip angle, 90˚, FOV: 216×216 mm2, 48 slices, voxel size: 2.7×2.7×2.7 mm 3 ) and additional blips images with b=0 s/mm 2 (number of signal averages, 9) were acquired in reverse phase encoding direction for susceptibility distortion.

Figure 1 Flow

 1 Figure 1 Flow Diagram of the Inclusion Process. Abbreviations: DKI = diffusion kurtosis imaging; FLAIR = Fluid Attenuated Inversion Recovery; FDG = 18 Ffluorodeoxyglucose; PET = positron emission tomography; WMH = white matter hyperintensities.

Figure 2

 2 Figure 2 Associations between physical activity, neuroimaging values, and cardiovascular risk factors. Physical activity is associated with global neuroimaging values of gray matter volume (A) and glucose metabolism (B), as well as insulin (C) and body mass index (D). Global neuroimaging values of gray matter volume are associated with insulin (G) and body mass index (H). Raw data (i.e., unadjusted) is plotted. Solid lines represent estimated regression lines and shaded areas represent 95% confidence intervals. Statistical values were obtained using multiple linear regressions controlling for age, sex, and education. Physical activity, insulin and body mass index values are log-transformed.Abbreviations: GM = gray matter.

Figure 3

 3 Figure 3 Causal mediation analyses of the association between physical activity and global and hippocampal gray matter volume. Direct effects in filled arrows (simple regressions between variables) are expressed as standardized regression coefficients, and indirect effects in dotted arrows (multiple regressions in which the predictor and the mediator are both added in the model) as partial correlation coefficients. All regressions are adjusted for age, sex and education. Physical activity, insulin and body mass index values are log-transformed. *P > 0.05, **P > 0.01, ***P < 0.001. Abbreviations: GM = gray matter; BMI = body mass index.

  Dr Chetelat reported grants, personal fees and non-financial support from INSERM, grants from European Union's Horizon 2020 research and innovation programme (grant 667696), and Fondation d'entreprise MMA des Entrepreneurs du Future, during conduction of the study; personal fees from Fondation Entrepreneurs MMA, grants and personal fees from Fondation Alzheimer, grants from Région Normandie (Label d'Excellence), Fondation Recherche Alzheimer, and Association France Alzheimer, outside the submitted work. No other disclosures were reported.

	Eric Frison, MD	EUCLID/F-CRIN Clinical Trials Belgium	Methodologist	Study design; interpretation of data interpretation of data
	Platform, Bordeaux, France Eric Salmon, MD, PhD University of Liege, Liege,	Group leader	Obtained funding; study design
	Francis Gheysen, MD	Caen, France Belgium	Independent	Meditation teacher
	Raquel Sanchez, MD,	Institut d'Investigacions	meditation teacher Neurologist	Study design
	Marc Heidmann, MSc PhD	Institut National de la Santé Biomèdiques August Pi i	PhD student	Acquisition, analysis, or
		et de la Recherche Médicale, Sunyer, Barcelona,		interpretation of data
		Lyon, France Spain
	Thien (Titi) Huong Corinne Schimmer,	Lyon, France Université de Caen, Caen,	Meditation teacher Meditation teacher English teacher English teacher
	Name Tran (Dolma) MSc	Location France	Role	Contribution
	Eider M. Arenaza-Frank Jessen, MD, PhD Uniklinik Köln, Cologne, Institut National de la Santé Siya Sherif, PhD Institut National de la Santé	Postdoctoral Cooperation Unit Research engineer Acquisition, analysis, or Study design; acquisition, analysis, or
	Urquijo, PhD	et de la Recherche Médicale, Germany et de la Recherche Médicale,	researcher Leader	interpretation of data interpretation of data;
	Olga Klimecki, PhD	Caen, France University of Geneva, Caen, France	Neurologist	Obtained funding; study design administrative, technical, or material
	Florence Allais, BA	EUCLID/F-CRIN Clinical Trials Geneva, Switzerland	Data manager	Data management support
	Pierre Krolak-Salmon, Edelweiss Touron,	Platform, Bordeaux, France Hospices Civils de Lyon, Institut National de la Santé	Neurologist PhD student	Obtained funding; study design Acquisition, analysis, or
	Claire André, MSc MD, PhD MSc	Institut National de la Santé Lyon, France et de la Recherche Médicale,	PhD student	Acquisition, analysis, or interpretation of data
	Elizabeth Kuhn, MSc	et de la Recherche Médicale, Institut National de la Santé Caen, France	PhD student	interpretation of data Acquisition, analysis, or
	Matthieu Vanhoutte,	Caen, France et de la Recherche Médicale, Institut National de la Santé	Postdoctoral	interpretation of data Acquisition, analysis, or
	Julien Asselineau, PhD EUCLID/F-CRIN Clinical Trials Caen, France PhD et de la Recherche Médicale,	Statistician researcher	Analysis of data interpretation of data;
	Gwendoline Le Du,	Platform, Bordeaux, France Institut National de la Santé Caen, France	Clinical research	Acquisition, analysis, or administrative, technical, or material
	Sebastian Baez Lugo, MSc	University of Geneva, et de la Recherche Médicale,	PhD student assistant	Acquisition, analysis, or interpretation of data; support
	MSc Denis Vivien, PhD	Geneva, Switzerland Caen, France Institut National de la Santé	Group leader	interpretation of data administrative, technical, or material Obtained funding; Administrative,
	Martine Batchelor	Bordeaux, France et de la Recherche Médicale,	Independent	Meditation teacher support technical, or material support
	Valérie LefranC, BA	Institut National de la Santé Caen, France	meditation teacher Clinical research	Acquisition, analysis, or
	Axel Beaugonin Patrik Vuilleumier, MD University of Geneva, Caen, France et de la Recherche Médicale,	Independent assistant Group leader	Meditation teacher interpretation of data; Obtained funding; study design
		Caen, France Geneva, Switzerland	meditation teacher	Administrative, technical, or material
	Alexandre Bejanin, Caitlin Ware, MSc	Institut National de la Santé Institut National de la Santé	Postdoctoral English teacher	Acquisition, analysis, or support English teacher
	PhD Antoine Lutz, PhD	et de la Recherche Médicale, Institut National de la Santé et de la Recherche Médicale,	researcher Group leader assistant	interpretation of data Obtained funding; study design
		Caen, France et de la Recherche Médicale, Caen, France
	Pierre Champetier, Miranka Wirth, PhD	Institut National de la Santé Lyon, France Deutsches Zentrum für	PhD student Group leader	Acquisition, analysis, or Study design
	MSc Natalie MarchanT,	et de la Recherche Médicale, University College London, Neurodegenerative	Group leader	interpretation of data Obtained funding; study design
	PhD	Caen, France United Kingdom Erkrankungen, Dresden,
	Fabienne Collette, PhD University of Liege, Liege, Jose-Luis Molinuevo, Institut d'Investigacions Germany	Group leader Group leader	Obtained funding, study design Obtained funding; study design
	MD, PhD 701	Belgium Biomèdiques August Pi i
	Sophie Dautricourt,	Institut National de la Santé Sunyer, Barcelona,	PhD student	Acquisition, analysis, or
	MD, MSc 702	et de la Recherche Médicale, Spain		interpretation of data
	Inès Moulinet, MSc Robin De Flores PhD 703	Institut National de la Santé Caen, France Institut National de la Santé et de la Recherche Médicale,	PhD student Postdoctoral	Acquisition, analysis, or Acquisition, analysis, or interpretation of data
	Valentin Ourry, MSc 704	et de la Recherche Médicale, Caen, France Caen, France Institut National de la Santé	Researcher PhD student	interpretation of data; administrative, technical, or material Acquisition, analysis, or
	Pascal Delamillieure, 705	Centre Hospitalier et de la Recherche Médicale, Caen, France	Psychiatrist	support Meditation teacher interpretation of data
	MD, PhD Léo Paly, MSc 706	Universitaire de Caen, Caen, Institut National de la Santé	Neuropsychologist Acquisition, analysis, or
	Marion Delarue, MSc 707	et de la Recherche Médicale, France Institut National de la Santé Caen, France	interpretation of data Neuropsychologist Acquisition, analysis, or
	et de la Recherche Médicale, Caen, France Géraldine Rauchs, PhD Institut National de la Santé et de la Recherche Médicale, 708	Researcher	interpretation of data Study design
	Yacila I. Deza-Araujo, PhD Stéphane Rehel, MSc 709	University of Geneva, Geneva, Switzerland Caen, France Institut National de la Santé	Postdoctoral researcher PhD student	Acquisition, analysis, or interpretation of data Acquisition, analysis, or
	Hélène Esperou, MD 710	Institut National de la Santé et de la Recherche Médicale,	Group leader	Sponsor interpretation of data
	Caen, France et de la Recherche Médicale, Paris, France Florence Requier, MSc University of Liege, Liege, 711	PhD student	Acquisition, analysis, or

Table 1 Demographics

 1

	Tables

Table 2 Multiple linear regressions between physical activity and neuroimaging values or cardiovascular risk factors

 2

*P > 0.05, **P > 0.01, ***P < 0.001. Abbreviations: GM = gray matter; WMH = white matter hyperintensities; MK = mean kurtosis; FA = fractional anisotropy; AD = Alzheimer's disease; BMI = body mass index; HDL Cholesterol = high density lipoprotein cholesterol; SBP = systolic blood pressure.

Acknowledgment

The authors thank, Marine Faure, Jeanne Lepetit, Marie Saville and the Cyceron MRI-PET staff members for their help with recruitment and neuroimaging data acquisition, the Inserm administrative, financial and legal departments, Inserm Transfert (Delphine Smagghe) and Aurélia Cognet for the administrative support. We also acknowledge our sponsor (Pole de recherche Clinique at Inserm, Dr Hélène Espérou), the Euclid Team (Dr Eric Frison) for the data management work and all the participants of the study and their family for their contribution.

Study funding

The Age-Well randomized clinical trial is part of the Medit-Ageing project and is supported by the European Union's Horizon 2020 Research and Innovation Program (grant 667696), Region Normandie (Label d'Excellence), and Fondation d'Entreprise MMA des Entrepreneurs du Futur. Institut National de la Santé et de la Recherche Médicale (INSERM) is the sponsor. MSc Felisatti was funded by the European Union's Horizon 2020 Research and Innovation Program (grant 667696) and the MMA IARD SA.

Disclosure


Marc Deschamps

Mostapha Diss

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.

Brexit et transfert des agences européennes :

Pourquoi l'Agence européenne des médicaments ira-t-elle à Amsterdam et l'Autorité bancaire européenne à Paris ?

Marc Deschamps A notre connaissance les éléments qui ont conduit le Conseil européen à ce choix social d'une procédure de vote parmi les procédures que nous venons de rappeler n'ont pas été rendus public.

Le choix d'une procédure de vote concernant la relocalisation des agences européennes

Arrivé à l'idée que la relocalisation des agences européennes devait se faire grâce à un vote, le problème était posé mais non résolu. En effet, la théorie du choix social a démontré que le choix d'un système de vote n'était pas nécessairement neutre quant au résultat du vote. Autrement dit, la théorie du choix social a démontré qu'en prenant les mêmes classements (i.e., les mêmes préférences dans le jargon des économistes), le choix d'une procédure de vote peut influer sur l'identité du gagnant du vote. Se pose donc à nouveau un problème de choix social, lequel concerne cette fois-ci le choix entre les différents systèmes de vote existants. Là encore, à notre connaissance, il n'est pas possible de savoir comment fut choisi le système de vote appliqué que nous allons maintenant présenter.

La procédure de vote concernant la relocalisation des agences européennes et les résultats

La procédure retenue par le Conseil européen a les huit caractéristiques suivantes :

1/ il y a 27 votants (l'ensemble des Etats membres de l'UE à l'exception du Royaume-Uni), 2/ il n'y a pas de procuration possible, 3/ il n'y a pas de quorum, 4/ le vote blanc et le vote nul sont possibles, 5/ chaque votant dispose de 6 points à répartir sur ceux qu'il estime être les 3 meilleurs candidats (3 points pour le premier, 2 points pour le deuxième, et 1 point pour le troisième) (tous les autres candidats recevant 0 points), 6/ il y a au minimum 1 tour et au maximum 3 tours pour choisir le gagnant, 7/ un vote est effectué pour chaque agence, 8/ les candidats pour recevoir une agence correspondent aux villes qui en ont fait la demande (il y a eu 19 villes candidates pour recevoir l'Agence européenne des médicaments et 8 villes candidates pour recevoir l'Autorité bancaire européenne).

Les tours de vote furent organisés de la manière suivante :

Premier tour : Il y a un gagnant si et seulement si une ville obtient 14 fois la première place (cela correspond à la majorité absolue sur 27 votants). En l'absence de gagnant on passe à un deuxième tour.

La théorie du choix social

  1,2 & Mostapha Diss 2A la suite d'un référendum le 23 juin 2016, les Britanniques ont choisi à une majorité de 51,89% (avec un taux de participation de 72,21%) de quitter l'Union européenne. Cela a mécaniquement conduit le gouvernement du Royaume-Uni à mettre en oeuvre l'article 50 du Traité sur l'Union européenne et à notifier au Conseil européen le 29 mars 2017 la décision du Royaume-Uni de quitter l'Union européenne : ce que l'on appelle depuis le « Brexit ». Il s'agit là d'un évènement historique sans précédent, aux conséquences incertaines, tant pour le Royaume-Uni que pour les vingt-sept autres pays de l'Union européenne. Autrement dit, comme le soulignent M. Martin et V.Merlin [2004, p. 54] : « Son objet principal est de répondre à la question suivante : comment peut-on, à partir des préférences exprimées par des individus sur différentes options possibles, déterminer une préférence collective qui rende compte le plus fidèlement de la diversité de ces mêmes préférences ».Ainsi chaque fois qu'un groupe d'au moins deux individus, juges, entreprises, associations, partis politiques, ou Etats, doit choisir parmi plusieurs alternatives un classement et/ou une alternative, il s'agit d'un problème de choix social. A ce titre, la théorie du choix social s'applique par exemple dans un concours tel que celui de Miss France, lors d'une décision d'un tribunal comprenant plusieurs magistrats, lors de l'élection du Président de la République, ou sur Internet dans le classement des recherches par un moteur de recherche.Naturellement ces questions ont depuis longtemps été analysées dans le monde mais c'est en France, au XVIIIème siècle, qu'elles commencèrent à faire l'objet d'une attention soutenue avec les travaux de Condorcet et de Borda. Malheureusement ce sujet tomba par la suite peu à peu en désuétude et ce Etat(s) membre(s) ait (aient) suffisamment de pouvoir au sein du Conseil européen pour imposer aux autres Etats membres deux localisations, puisqu'il avait été convenu que les deux agences ne pourraient être relocalisées dans un même pays. A l'évidence une telle option était à la fois juridiquement et démocratiquement impossible. La deuxième solution envisageable, la coutume, était elle aussi impossible, pour les mêmes raisons, mais également car il n'y a jamais eu auparavant de sortie d'un Etat de l'Union européenne. Il ne restait donc que la troisième solution : le consensus. Depuis les travaux de K. Arrow, les économistes conviennent que la solution du consensus comprend elle-même deux possibilités : le marché et le vote. La solution du marché aurait par exemple consisté une analyse fine de ces questions. Mais le Conseil européen a choisi de ne pas retenir cette option et de procéder à un vote.

	Après
	avoir brièvement rappelé ce qu'est la théorie du choix social, nous présenterons la procédure qui a
	conduit les pays membres de l'Union européenne à choisir d'implanter l'EMA aux Pays-Bas et l'EBA en
	France.
	Dans le cadre de sa conférence lors de la réception du prix en la mémoire d'Alfred Nobel en Economie
	en 1998, A. Sen [1999, p.8] écrit : « […] les choix ''du peuple, par le peuple, pour le peuple''. Ceci est,
	dans une acception générale, le sujet de la théorie du ''choix social'', et il inclut, à l'intérieur de son
	vaste champ, des problèmes divers ayant la caractéristique commune de mettre en relation des
	jugements sociaux et des décisions collectives avec les opinions et les intérêts des individus qui
	composent la société ou le groupe. S'il est une question centrale qui peut être envisagée comme la
	problématique principale motivant la théorie du choix social, c'est la suivante : comment est-il possible
	de parvenir à des jugements agrégés et incontestables au niveau de la société (par exemple au sujet

Les problèmes à résoudre sont gigantesques et d'autant plus délicats que les positions défendues par les différentes parties prenantes au sein du Royaume-Uni sont très hétérogènes. Le rapport d'information du Sénat du 10 octobre 2019 réalisé par les sénateurs J. Bizet et Ch. Cambon au nom du « Groupe de suivi sur le retrait du Royaume-Uni et sur la refondation de l'Union Européenne » offre une belle analyse de la situation, de ses risques, ainsi que des évolutions possibles.

Parmi les très nombreuses questions liées au changement de statut du Royaume-Uni, qui passera du statut d'Etat membre de l'Union européenne à celui d'Etat tiers, figure celle du devenir des agences européennes implantées sur le territoire du Royaume-Uni. Il n'est en effet pas possible de laisser des agences européennes sur le territoire d'un Etat tiers. Concrètement, en l'espèce, il s'agissait de savoir où allaient être réimplantées sur le territoire européen l'Agence européenne des médicaments (EMA) et l'Autorité bancaire européenne (EBA).

L'objet de cette note est d'expliquer la manière dont ce problème a été résolu en mettant en évidence le fait qu'il s'agissait de résoudre ce que les économistes appellent un problème de choix social. du ''bien-être social'' ou de ''l'intérêt public'' ou ''du taux de pauvreté''), étant donné la diversité des préférences, des préoccupations et des difficultés des différents individus qui composent la société ? Comment est-il possible de trouver une base rationnelle pour émettre des jugements agrégés du type ''la société préfère ceci à cela'', ''la société devrait choisir ceci plutôt que cela'' ou ''ceci est socialement juste''». n'est qu'en 1950, avec le travail de K. Arrow et la mise en évidence de ce que l'on appelle depuis le paradoxe d'Arrow, qu'il reprit de la vigueur et devint un champ d'étude reconnu. La méthode adoptée par Arrow consiste à choisir un certain nombre de propriétés qu'il parait raisonnable d'imposer aux procédures d'agrégation, puis à démontrer si la réunion de ces propriétés est possible ou conduit à une incohérence dans le sens où il n'existe aucune procédure d'agrégation vérifiant l'ensemble de ces conditions souhaitables. Aujourd'hui de nombreux chercheurs dans le monde travaillent dans ce domaine et la France reste une terre d'expertise, notamment grâce aux chercheurs du CREM (Centre de Recherches en Economie et Management) à Caen, où se situe le siège social de la "Société pour le choix social et le bien-être". Cette association a pour objectif de promouvoir le progrès de la connaissance en théorie du choix social et en économie du bien-être et de faciliter la communication des chercheurs de nombreuses disciplines travaillant dans ce domaine par l'organisation de conférences, séminaires, ateliers, rencontres biannuelles et par la publication d'une revue. En effet, grâce à Maurice Salles, Caen a été à l'origine de la création de la revue Social Choice and Welfare, la revue internationale de référence du domaine depuis 1984.

Le choix d'une procédure concernant la relocalisation des agences européennes

Face au retrait du Royaume-Uni de l'Union européenne, les vingt-sept autres Etats membres ont dû choisir une méthode pour relocaliser les deux agences européennes actuellement sises au Royaume-Uni. Reprenant la tripartition proposée en 1944 par F. Knight en matière de choix sociaux, ils devaient donc choisir entre : l'autorité, la coutume et le consensus. La première solution envisageable, l'autorité, aurait consisté à ce qu'un (ou plusieurs) à mettre aux enchères entre les pays membres la nouvelle localisation de ces agences. Ainsi chaque pays intéressé (voir même chaque ville intéressée) par recevoir une agence aurait proposé une somme d'argent et les gagnants auraient payé cette somme pour, par exemple, alimenter le budget européen. Il existe là encore de très nombreuses manières d'organiser concrètement des enchères et la théorie économique propose

  Deuxième tour : Ne sont qualifiées au deuxième tour que les 3 villes qui ont obtenu au premier tour le plus de points (ce qui correspond à ce que les économistes considèrent être une version particulière des règles d'élimination à scores). En cas d'ex aequo il peut y avoir plus de 3 villes qualifiées pour le deuxième tour. Pour ce deuxième tour, chacun des 27 votants choisi un gagnant et si une ville est placée 14 fois gagnante alors la procédure s'arrête et elle est déclarée gagnante. Sinon, on passe au troisième et dernier tour. Comme on peut le voir chacun des éléments précédents mérite réflexion et n'est ni naturel, ni incontestable. Parmi les caractéristiques qu'il est possible de relever, on peut noter que pour le premier tour il n'est pas tenu compte des écarts relatif des différentes villes. En effet on peut imaginer un cas où les 27 votants ont les préférences suivantes : 14 pays classent la ville A en premier et la ville B en seconde position et 13 pays classent la ville B en première position et la ville A en dernière position. Dans la procédure retenue, c'est la ville A qui est gagnante malgré le fait que tous les votants classent la ville B soit en première position, soit en deuxième position, alors que 13 votants classent la ville A en dernière position. Au final, c'est Paris qui gagna le vote pour accueillir l'Autorité bancaire européenne et Amsterdam qui gagna le vote pour accueillir l'Agence européenne des médicaments. Un bel exemple supplémentaire de choix social dont il sera intéressant d'analyser la sensibilité des résultats à la procédure de vote choisie.

Troisième tour : Ne sont qualifiées au troisième tour que les 2 villes ayant obtenu au deuxième tour le plus de points). En cas d'ex aequo il peut y avoir trois villes. Pour ce dernier tour, chacun des 27 votants donne 1 point à son favori et la ville gagnante est celle qui obtient le plus de points. En cas d'égalité entre des villes, le Président effectue un tirage au sort.

BETA CNRS et Université de Lorraine.

CRESE EA3190, Univ. Bourgogne Franche-Comté, F-25000 Besançon.