Enrica Cavedo
email: enrica.cavedo@gmail.com

PhD Bruno Dubois

MD Olivier Colliot

PhD Simone Lista

PhD Bernard Croisile

MD Guy Louis Tisserand

MD Jaques Touchon

MD Alain Bonafe

MD Pierre J Ousset

MD Olivier Rouaud

MD Fréderic Ricolfi

MD Alain Vighetto

MD Florence Pasquier

MD Samantha Galluzzi

MD Christine Delmaire

MD Mathieu Ceccaldi

MD Nadine Girard

MD Stéphane Lehericy

MD Françoise Duveau

MD Marie Chupin

PhD Marie Sarazin

MD Harald Hampel
email: harald.hampel@icm-institute.org

Reduced regional cortical thickness rate of change in donepezil treated subjects with suspected prodromal Alzheimer's disease

Keywords: Cortical Thickness, Alzheimer's Disease, MRI, Donepezil, Cholinergic system, Clinical Trials, prodromal AD, Mild Cognitive Impairment, Progression

OBJECTIVES: Cortical thinning, previously identified during prodromal stages of AD, is a "candidate" biomarker implemented in AD clinical therapy trials. We have investigated the effect of donepezil treatment on cortical thickness in mild cognitively impaired subjects with the amnestic syndrome of the hippocampal type, a prodromal at risk group for progression to AD dementia. innervated by the medial and lateral cholinergic pathways.

METHODS:

Longitudinal analysis of a community-based multi-centric suspected prodromal AD cohort (92 placebo versus 81 donepezil) enrolled in a double-blind, randomized, placebo-controlled parallel group design using donepezil (10mg/day) has been conducted. The study started in November 2006 and was concluded in August 2010. All subjects underwent two brain structural Magnetic Resonance Imaging (MRI) scans, at baseline and at the end of the trial. Structural MRI images have been processed using the automated pipeline for longitudinal segmentation and surface reconstruction implemented in FreeSurfer. The primary outcome measure of this posthoc study was the cortical thickness annualized percentage change (APC).

RESULTS:

The donepezil group exhibited reduced APC cortical thinning compared to placebo in the Rostral Anterior Cingulate (right: p = 0.048; and left: p = 0.032), the Orbitofrontal (right: p = 0.012 and left p < 0.048), and the right Inferior Frontal (p = 0.022) cortices and in the right Insula (p = 0.010). These results were not statistically significant after Bonferroni correction likely due to insufficient power for cortical thickness measurements in the study group powered for the predefined hippocampus outcome.

CONCLUSIONS:

Our findings support the hypothesis that cortical thickness is a reliable candidate surrogate outcome in early pre-dementia AD trials. In addition, donepezil treatment may have an impact on cortical structure/morphology in areas

Introduction

The current approved treatments with cholinesterase inhibitors are generally considered as moderately and only symptomatically beneficial for late-stage AD dementia patients [START_REF] Johannsen | Assessing therapeutic efficacy in a progressive disease: a study of donepezil in Alzheimer's disease[END_REF] . Evidence of potential biological and disease-modifying properties of cholinesterase inhibitors is controversially and critically discussed. No agent tested in randomized clinical trials in Mild Cognitive Impairment (MCI) has met its primary efficacy objectives, measured by clinical rating instruments [START_REF] Crane | Donepezil treatment of patients with MCI: a 48-week randomized, placebo-controlled trial[END_REF][START_REF] Doody | Donepezil treatment of patients with MCI: a 48-week randomized, placebo-controlled trial[END_REF][START_REF] Doody | Safety and tolerability of donepezil in mild cognitive impairment: open-label extension study[END_REF][START_REF] Feldman | A 24-week, randomized, double-blind study of donepezil in moderate to severe Alzheimer's disease[END_REF][START_REF] Feldman | Efficacy of donepezil on maintenance of activities of daily living in patients with moderate to severe Alzheimer's disease and the effect on caregiver burden[END_REF][START_REF] Feldman | Efficacy and safety of donepezil in patients with more severe Alzheimer's disease: a subgroup analysis from a randomized, placebo-controlled trial[END_REF][START_REF] Gauthier | Efficacy of donepezil on behavioral symptoms in patients with moderate to severe Alzheimer's disease[END_REF][START_REF] Petersen | Vitamin E and donepezil for the treatment of mild cognitive impairment[END_REF][START_REF] Salloway | Efficacy of donepezil in mild cognitive impairment: a randomized placebo-controlled trial[END_REF] .

To date, only one study investigating the use of in vivo biomarkers of AD in Donepezil clinical trial has been conducted [START_REF] Teipel | Effects of donepezil on cortical metabolic response to activation during (18)FDG-PET in Alzheimer's disease: a double-blind cross-over trial[END_REF] . On the other hand, further clinical studies on structural imaging markers in MCI subjects have reported conflicting results [START_REF] Jack | Longitudinal MRI findings from the vitamin E and donepezil treatment study for MCI[END_REF][START_REF] Schuff | An MRI substudy of a donepezil clinical trial in mild cognitive impairment[END_REF][START_REF] Dubois | Donepezil decreases annual rate of hippocampal atrophy in suspected prodromal Alzheimer's disease[END_REF] .

Although cortical-thickness represents a promising structural imaging end point in clinical trials, as it offers a direct assessment of effect sizes expressed in a meaningful metric, [START_REF] Teipel | Relevance of magnetic resonance imaging for early detection and diagnosis of Alzheimer disease[END_REF][START_REF] Hampel | Core candidate neurochemical and imaging biomarkers of Alzheimer's disease[END_REF][START_REF] Teipel | Novel MRI techniques in the assessment of dementia[END_REF] no study has investigated the donepezil effect on the cortical mantle yet. This is a post hoc study based on the data collected in the context of the Hippocampus Study Clinical Trial (NCT00403520). The first aim of the trial was to investigate the effect of Donepezil treatment using the hippocampal rate of changes as primary outcome [START_REF] Dubois | Donepezil decreases annual rate of hippocampal atrophy in suspected prodromal Alzheimer's disease[END_REF] . Here, we are going to consider the impact of donepezil treatment on the thickness rate of change in suspected prodromal AD patients diagnosed using the Free and Cued Selective Reminding Test (FCSRT), a test allowing prognostication of prodromal AD within the group of MCI individuals [START_REF] Wagner | Biomarker validation of a cued recall memory deficit in prodromal Alzheimer disease[END_REF][START_REF] Sarazin | The amnestic syndrome of hippocampal type in Alzheimer's disease: an MRI study[END_REF] .

Methods

Study Population

Participants included in the present study were all the patients who performed a baseline and a follow-up MRI scan during the Hippocampus Study Clinical Trial (NCT00403520) [START_REF] Dubois | Donepezil decreases annual rate of hippocampal atrophy in suspected prodromal Alzheimer's disease[END_REF] . The primary efficacy outcome of the Hippocampus Study was the annualized percentage change (APC) of total hippocampal volume measured by an automated segmentation method. In this post hoc analysis, we explored the effect of Donepezil on the cortical thickness. Each patients received at least 1 dose of doubleblind study medication, and had baseline and follow-up clinical and Magnetic Resonance Imaging (MRI) assessment.

The details of the patient characteristics have been previously described [START_REF] Dubois | Donepezil decreases annual rate of hippocampal atrophy in suspected prodromal Alzheimer's disease[END_REF] . Briefly, a total of 332 patients were screened within the national network of Memory Resources and Research Centres (MRRC) consisting of 28 regional university expert centres with neurologists, geriatricians, neuropsychologists, biological and neuroimaging resources in each centre.

Inclusion criteria were: 1) more than 50 years of age; 2) a progressive hippocampal amnestic syndrome defined by Free Recall  17 or Total Recall < 40 on the FCSRT; and 3) no dementia with a CDR stage of 0.5 and preserved cognition and functional performance. Subjects who met the eligibility criteria were enrolled in the randomization phase beginning with Visit 1. From the total population of individuals randomized in the clinical trial (103 Placebo and 113 Donepezil), for the present study we considered exclusively patients who performed MRI at baseline and at the end of the treatment (Placebo=92 and Donepezil= 82).

Study Design

This was a multi-centre double-blind, randomized, placebo-controlled trial with a treatment period of 12 months. The sample power of the study was calculated according to the primary aim of the Hippocampus Study Clinical Trial, and not for the aim of the present study. [START_REF] Dean | CVLT, California Verbal Learning Test:Adult Version : Manual[END_REF] , Trial Making Tests (TMT) A and B [START_REF] Reitan | The Halstead-Reitan Neuropsychological Test Battery: Theory and clinical interpretation[END_REF] , and the Benton Test [START_REF] Benton | The revised visual retention test: The Psychological Corporation[END_REF] . Following baseline evaluation, patients were randomly assigned to one group out of two, corresponding to either active treatment or placebo (1 capsule of 5-mg donepezil daily for Weeks 0 to 6, then 2 capsules of 5-mg donepezil [i.e., 10 mg] daily from Week 6 to Month 12 for doubleblind treatment; or 1 placebo capsule daily for Weeks 0 to 6, then 2 capsules daily from Week 6 to Month 12 for double-blind treatment, respectively). The study protocol was approved by the institutional review board of each site, and informed consent was obtained from all subjects.

Acquisition of MR images

Brain MRI scans were acquired in each centre at baseline and after at the end of treatment period. All the MRI were performed using 1.5 Tesla or 3 Tesla MRI scanners qualified by the central MRI analysis core at the Cogimage team, Centre de Recherche de l'institut du Cerveau et de la Moelle Épinière (CRICM). The sequences used in the present manuscript were 3D T1-weighted images. The 3D T1-weighted scan parameters for scans at 1.5T were: TR = 10 ms, TE = minimum, flip angle: 10, PREP time: 600, bandpass: 12.50 khz, axial orientation; 1.3mm slice thickness, contiguous (124 slices), Imaging matrix size: 256 x 256, Field of view: 240 x 240 ; for scans at 3T were: TR = 3.9 ms, TE = 2100 ms, flip angle: 15, PREP time: 1100 ms, sagittal orientation with 1 mm slice thickness, contiguous (144 slices), Acquisition matrix size: 256 x 192, Field of view: 256 x 192. The expert neuroradiologist in charge of quality control verified artifacts of movements, ringing, wrap around and metal artifacts, moreover they attested that the sequences were acquired according to protocol parameters. After the quality control of images, one 3D T1-weighted scan was identified as corrupted and it was excluded from the all statistical and the neuroimaging analysis.

Cortical Thickness Reconstruction and Surface Analysis

To extract reliable thickness estimates, images were automatically processed with the longitudinal stream [START_REF] Bernal-Rusiel | Statistical analysis of longitudinal neuroimage data with Linear Mixed Effects models[END_REF] in FreeSurfer (http://surfer.nmr.mgh.harvard.edu/) version 5.1. Details on the longitudinal pipeline used to analyzing data are described at the following link (https://surfer.nmr.mgh.harvard.edu/fswiki/LongitudinalProcessing).

Specifically an unbiased within-subject template space and image is created using robust, inverse consistent registration [START_REF] Reuter | Highly accurate inverse consistent registration: a robust approach[END_REF] . Several processing steps, such as skull stripping, Talairach transforms, atlas registration as well as spherical surface maps and parcellations are then initialized with common information from the within-subject template, significantly increasing reliability and statistical power [START_REF] Reuter | Within-subject template estimation for unbiased longitudinal image analysis[END_REF] . Based on gyral and sulcal anatomy, the cortex was segmented using the Desikan-Killiany Atlas [START_REF] Desikan | An automated labeling system for subdividing the human cerebral cortex on MRI scans into gyral based regions of interest[END_REF] .

For each of cortical regions, mean cortical thickness was calculated as the distance (in mm) between the pial and gray/white matter surfaces. A quality control of data was performed, the Pial and the white matter Surfaces were checked in order to remove any non brain tissue and non-white matter tissue respectively. The cortical thickness was smoothed with 10 mm FWHM Gaussian kernel to improve the signal-to-noise ratio and statistical power.

Statistical Analysis

Demographic, clinical and neuropsychological features were compared between subject groups (Placebo vs Donepezil). Chi-square test was performed on categorical variables, while the one-way analysis of variance (ANOVA) was utilized for continuous variables. Since the assumption of normality was violated, baseline cortical thicknesses measures were transformed according to a Two-Step Approach for Transforming Continuous Variables to Normal. The first step involves transforming the original variable toward statistical uniformity (i.e., satisfies the preponderance of diagnostics tests for uniformity) by calculating the fractional rank of each score, then fractional rank obtained from the previous step were transformed to normal using the inverse normal distribution function [START_REF] Templeton | A Two-Step Approach for Transforming Continuous Variables to Normal: Implications and Recommendations for IS Research[END_REF] . Normalized baseline cortical thickness measures have been compared between groups using the ANOVA.

Annualized Percentage Change (APC) of cortical thickness, in all the regions extracted from FreeSurfer pipeline, were computed as follows:

Then, the cortical thickness APC were compared between placebo and donepezil using the Wilcoxon-Mann-Whitney test. Surface analyses were performed using MATLAB (http://fr.mathworks.com) and the QDEC toolbox of FreeSurfer (www.surfer.nmr.mgh.harvard.edu). One-year changes in bilateral cortical structures were investigated using the Linear Mixed Effects Models. The results were projected onto the template. The surface analyses were rethresholded using a two-stage false discovery rate of 0.05 (FDR2 < 0.05).

Power analysis

Since the original Hippocampus Study trial was not designed for examine cortical thickness, an estimation of samples size needed to detect a thickness change of a certain number of millimetres between placebo and treatment patients was estimated.

Sample size requirements were estimated using the following formula:

2 × 𝐾 × ( 𝜎 𝜇1 -𝜇2 ) 2
, where K = constant, which is a function of α (0.05) and β=0.2 (80%) ; σ is the standard deviation of cortical thickness APC in the untreated group, μ are the mean values of cortical thickness APC in the treatment and placebo groups.

The following modification was included: the sample size thus derived was increased by 10% to allow for losses at follow-up.

Results

From the total sample of 316 individuals (103 Placebo and 113 Donepzil) randomized in the trial, 174 individuals (92 Placebo and 82 Donepezil) underwent both baseline and follow-up MRI scans. One subject of them was excluded from analysis due to a corrupted scan. No significant differences were found at baseline sociodemographic as well as in cognitive features between groups (Table 1). The Apolipoprotein E (APOE) genotype was present in 18 (47.3%) patients in the placebo group and 18 (60%) in the donepezil showing no substantial differences (p = 0.215) between the two groups.

The baseline cortical thickness, for all brain regions considered, did not show any significant statistical differences between the two groups (Table 2).

As detailed in the Figure 1, a significant difference in the regional cortical thickness APC was observed between groups. In particular, the Placebo group compared with the Donepezil showed a higher APC in the right and left Rostral Anterior Cingulate Cortex -1.14% vs -0.38% (p = 0.048) and -1.28% vs 0.07% (p = 0.032) respectively, in the left Caudal Anterior Cingulate Cortex -1.07% vs 0.16% (p= 0.033), in the right and left Orbitofrontal Cortex -1.04% vs -0.001% (p = 0.012) and -0.54% vs 0.43% (p < 0.048) respectively, in the right Inferior Frontal Cortex -0.94% vs 0.23% (p = 0.022), and in the right Insula -1.06% vs 0.013% (p = 0.010).

Post-hoc analysis by the mixed effects model (Figure 2) revealed that, during the 12 months of treatment period, cortical thickness was significantly decreased in the Placebo group compared with the Donepezil in the in the right Lateral Orbitofrontal cortex (difference in slope 0.0023; p = 0.026), in the right Middle temporal Cortex (difference in slope 0.0027; p = 0.027) and in the right Insula (difference in slope 0.0027; p = 0.015). Both the cortical thickness APC comparisons and the results on the mixed effect model did not survived after Bonferroni correction. Surface differences were described in Figure 3 revealing a cortical thinning of Placebo group compared to the Donepezil in the Left Superior Temporal, Left Orbitofrontal, Right Supramarginal and Right Insula cortices. This result did not survive after FDR correction.

Power analysis

The mean (SD) cortical thickness APC for Donepezil group was -0.51 (2.18), while in the Placebo group was -0.95 (2.10). Based on these values, to have 80% power to detect a drug effect at 5% significance level (α= 0.05), 187 patients would be needed for each treatment arm. This assumes a 1 year-placebo-controlled trial with a 10% patients drop-out rate

Discussion

To our knowledge, this is the first study investigating the effect of donepezil treatment on regional brain cortical thickness in suspected prodromal AD patients with amnestic syndrome of hippocampal type. Our results highlight the presence of a trend of stability in the cortical thickness APC in the Anterior Cingulate Cortex, in the left Orbitofrontal Cortex, in the Inferior Frontal Cortex, and in the right Insula in suspected prodromal AD patients treated with donepezil. These findings have been furthermore supported by data obtained from the Longitudinal Mixed Model and the cortical surface comparison of cortical thickness APC between groups. Indeed, we have found a trend of reduced cortical surface in the placebo group compared with the donepezil after one year of Donepezil treatment in the following regions: Orbitofrontal, Superior, and Caudal Middle Frontal Cortices, Superior Temporal, Supra Marginal, Precuneus, Inferior Parietal, and Insula. Some of these areas have been recognised to be of key importance since they are supposed to represent the cortical signature of Prodromal AD patients [START_REF] Bakkour | The cortical signature of prodromal AD: regional thinning predicts mild AD dementia[END_REF][START_REF] Dickerson | MRI cortical thickness biomarker predicts AD-like CSF and cognitive decline in normal adults[END_REF] . Although our results did not survive after multiple comparisons, they still remain promising since they have showed a statistical trend toward a significant impact of donepezil treatment in preserving cortical thickness in suspected prodromal AD patients. One possible reason explaining why our results did not survive to multiple comparison corrections might due to the fact that the sample power of the current study was not calculated for the present purpose but for the original aim of the Hippocampus Study Trial. Indeed, the necessary sample size to obtain a statistically significant effect in the cortical thickness APC between Placebo and Donepezil should be substantially higher, 187 patients for each arm, as revealed by the sample power analysis. Notably, in line with a previous study revealing an increased resting state metabolism in the left prefrontal cortex (and in the right hippocampus) of AD patients treated with Donepezil [START_REF] Teipel | Effects of donepezil on cortical metabolic response to activation during (18)FDG-PET in Alzheimer's disease: a double-blind cross-over trial[END_REF] , we also found a significant reduced cortical thinning in left Orbitofrontal Cortex and Anterior Cingulate Cortex in this group.

Previous studies investigating the donepezil effect on different structural imaging markers, such as the hippocampus, the brain lateral ventricles, and the whole brain volumes, showed contrasting results. A randomized double-blind, placebo-controlled mono-center study on 67 patients with mild-to-moderate AD found a small decrease in left hippocampal volume after 24-week of donepezil compared with the placebotreated subjects [START_REF] Krishnan | Randomized, placebocontrolled trial of the effects of donepezil on neuronal markers and hippocampal volumes in Alzheimer's disease[END_REF] . Results from the Alzheimer's Disease Cooperative Study (ADCS) MCI Donepezil/Vitamin E study conducted on 131 MCI patients showed a statistical trend towards a possible slowing of the hippocampal atrophy rate by donepezil [START_REF] Jack | Longitudinal MRI findings from the vitamin E and donepezil treatment study for MCI[END_REF] . A more recent study conducted by Schuff and colleagues [START_REF] Schuff | MRI of hippocampal volume loss in early Alzheimer's disease in relation to ApoE genotype and biomarkers[END_REF] on aMCI subjects reported significant differences in favour of the donepezil group for the total ventricular region and the cortical region (whole brain volumes) but not for the hippocampal volume.

Recently, our group confirmed the data by Schuff and colleagues [START_REF] Schuff | MRI of hippocampal volume loss in early Alzheimer's disease in relation to ApoE genotype and biomarkers[END_REF] for ventricular and whole brain volumes. In addition, we observed a significant reduction in the annual rate of hippocampal atrophy in suspected prodromal AD patients treated with donepezil 33 .

Regional cortical thickness reduction is used as a predictive indicator of AD-related neurodegeneration in MCI subjects [START_REF] Dickerson | MRI cortical thickness biomarker predicts AD-like CSF and cognitive decline in normal adults[END_REF][START_REF] Lerch | Automated cortical thickness measurements from MRI can accurately separate Alzheimer's patients from normal elderly controls[END_REF] . Our results revealed unilateral treatment differences in several brain regions that might be due to normal variation and specialization of function and structure. Brain asymmetry is believed to be evolutionally adaptive, reducing possible interference between hemispheres [START_REF] Toga | Mapping brain asymmetry[END_REF] .

Based on the hypothesis that donepezil may attenuate amyloid-induced neuronal toxicity [START_REF] Svensson | Tacrine and donepezil attenuate the neurotoxic effect of A beta(25-35) in rat PC12 cells[END_REF][START_REF] Wolf | Muscarinic regulation of Alzheimer's disease amyloid precursor protein secretion and amyloid beta-protein production in human neuronal NT2N cells[END_REF] , it is conceivable that 12 months of donepezil treatment might have a neuroprotective effect on the cortex. In vitro studies demonstrated that lesions of the cholinergic nucleus basalis of Meynert promote the ex vivo synthesis of Aβ precursor protein (AβPP) in the cerebral cortex [START_REF] Wallace | Amyloid precursor protein in the cerebral cortex is rapidly and persistently induced by loss of subcortical innervation[END_REF] . Recently, an in vivo neuroimaging study described a correlation between basal forebrain atrophy and elevated cortical amyloid load in preclinical and pre-dementia stages of AD [START_REF] Grothe | Basal forebrain atrophy and cortical amyloid deposition in nondemented elderly subjects[END_REF] , thus reflecting the association found in several human autopsy studies between amyloid pathology and cholinergic atrophy in AD [START_REF] Perry | Correlation of cholinergic abnormalities with senile plaques and mental test scores in senile dementia[END_REF][START_REF] Beach | Senile plaques, amyloid beta-protein, and acetylcholinesterase fibres: laminar distributions in Alzheimer's disease striate cortex[END_REF][START_REF] Arendt | Neuronal loss in different parts of the nucleus basalis is related to neuritic plaque formation in cortical target areas in Alzheimer's disease[END_REF] . Cortical amyloid accumulation might induce cholinergic cell death involving alterations in the levels of intracellular calcium and/or production of toxic and inflammatory mediators such as nitric oxide, cytokines, and reactive oxygen intermediates [START_REF] Kar | Interactions between betaamyloid and central cholinergic neurons: implications for Alzheimer's disease[END_REF] . On the other hand, a cholinergic stimulation alters positively the mechanisms of amyloid processing, thus protecting neurons from neurodegeneration induced by Aβ [START_REF] Svensson | Tacrine and donepezil attenuate the neurotoxic effect of A beta(25-35) in rat PC12 cells[END_REF] .

In this study, we found a trend toward a statistical significance for cortical thinning reduction in the cortical areas innervated by the medial and lateral cholinergic pathways [START_REF] Selden | Trajectories of cholinergic pathways within the cerebral hemispheres of the human brain[END_REF] in suspected prodromal AD patients receiving one year of donepezil treatment.

One of the main strengths of the present study is the refined target population deriving from a large-scale community-based multi-centre cohort of subjects included on the basis of the FCSRT, a memory test reported to be highly correlated with hippocampal volume and CSF levels changes of the Alzheimer type [START_REF] Wagner | Biomarker validation of a cued recall memory deficit in prodromal Alzheimer disease[END_REF][START_REF] Sarazin | The amnestic syndrome of hippocampal type in Alzheimer's disease: an MRI study[END_REF] .

The study presents potential limitations. First of all, the data used in the present research were not specifically powered for the aims of the present study, thus reducing the significance of the results. The protocol of the study did not include information on the settings of the subjects of the population or on race and ethnicity characteristics or data in terms of lifestyle. The latter, in particular, given its practical aspects -nutrition, hydration, and physical activity -has become significant in terms of AD prevention. We did not collect sufficient data on APOE ε4 genotype to exclude the hypothesis that our results were not significantly impacted by the presence of APOE ε4 genotype. Finally, the subjects have not been followed for a long enough period of time in order to determine the incidence of incipient AD in each group.

Overall, our findings support the hypothesis that cortical thickness might be used as surrogate outcome in pre-dementia AD clinical trials. Moreover, our findings suggest that donepezil may have an impact on cortical morphology in prodromal AD patients.

A potentially disease-modifying effect of approved cholinesterase inhibitors represents a result of pivotal clinical interest. Further studies are needed to confirmed this first investigation. Moreover, established measurement of the basal forebrain cholinergic nuclei volume, such as the nucleus basalis of Meynert and its subnuclei, as well as their in vivo white matter connections to subcortical and cortical areas, are of interest to detect the specific donepezil effect on the brain's cholinergic system. Means and standard deviations are reported, P Values denote significant differences at ANOVA.

Left

  The cortical thickness APC comparisons were supplemented post hoc by the linear mixed effects regression model with random intercepts, controlling for scanner platforms, to compare the difference in the cortical thickness change between placebo and donepezil patients in relation to treatment. Bonferroni correction for comparisons was applied to the cortical thickness APC comparisons and to the mixed effect regression model results. The statistical analyses were performed using SPSS v.22.00.

Funding and Disclosure:FiguresFigure 1 .

 1 Figures

Figure 2 .

 2 Figure 2. Individual trajectories of Cortical Thickness change. Graphs display

Figure 3 .

 3 Figure 3. Surface differences between placebo and donepezil groups detected

Table 1 : Baseline Demographic and Clinical Characteristics of patients performing baseline and follow-up MRI.

 1 Means and standard deviations are reported for continuous variables, numbers and percentages for the dichotomous ones. P-values denote significant differences at ANOVA and Chi-square tests.

	Tables
		Placebo	Donepezil	P Value
		(n = 92)	(n = 81)
	Age, years	73.17 (6.63)	73.24 (6.67)	0.966
	Sex, n (%)
	Male	44 (47.8)	39 (48.1)	0.544
	Female	48 (52.1)	42 (51.8)
	APOE ε4 carriers, n (%)	18 (47.3)	18 (60)	0.215
	Missing	54	43
	Education, n (%)
	No education	1 (0.01)	0 (0.0)	0.330
	Primary	7 (7.6)	8 (9.8)
	Certificate of Primary Education	43 (46.7)	30 (37)
	Secondary	14 (15.2)	21 (25.9)
	Higher education	27 (29.3)	22 (27.1)
	Follow-up MRI (months)	9.65 (4.78)	10.07 (4.43)	0.537
	FCSRT (Free recall)	11.32 (5.61)	12.21 (5.40)	0.289
	FCSRT (Total recall)	29.55 (9.93)	31.37 (8.91)	0.210
	Hamilton Rating Scale for	3.22 (2.94)	2.83 (2.49)	0.352
	Depression

Table 2 : Baseline Right and Left Cortical thickness (mm) of 173 patients.

 2

Acknowledgement

We would like to acknowledge Prof Touchon and Dr Aimeur who participated in the study. We would like to acknowledge Dr Line Garnero who deceased during the study, without her support and experience this study would never have been undertaken.


Luc Meunier

Laurent Orgéas

Grégory Chagnon

Denis Favier

A multiscale approach to model the mechanical behaviour of heterogeneous hyperelastic membranes

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

INTRODUCTION

Many structures and materials such as thin heterogeneous and/or fibre-reinforced elastomers structures, thin living tissues, manufactured woven or non-woven 2D textiles, behave as a first and reasonable approximation as elastic and anisotropic membranes undergoing finite strains.

In this work, we propose to estimate, from a theoretical and numerical multiscale approach, the mesoscale effective mechanical properties of such membranes, (i) starting from the description of both the microstructure and the mechanical equilibrium of the membranes at the microscale, and (ii) assuming that the involved materials at the microscale behave as hyperelastic bodies.

Firstly, the above micromechanical problem at the heterogeneity scale is upscaled by using the homogenisation method with multiple scale asymptotic expansions for periodic structures [START_REF] Bensoussan | Asymptotic Analysis for Periodic Structures[END_REF][START_REF] Sanchez-Palencia | Non-Homogeneous Media and Vibration Theory[END_REF][START_REF] Caillerie | Thin elastic and periodic plates[END_REF][START_REF] Auriault | Heterogeneous medium. is an equivalent macroscopic description possible?[END_REF][START_REF] Pruchnicki | Overal properties of thin hyperelastic plate at finite strain with edge effects using asymptotic method[END_REF].

The homogenisation also provides suitable localisation problems to be solved within the Representative Elementary Volumes (REV) in order to compute the effective hyperelastic responses of the membranes.

Secondly, these boundary values problems are implemented into a Finite Elements software and the effective mesoscale properties of heterogeneous membranes are investigated quantitatively. The considered membrane is rather simple: it is made up of hyperelastic materials and it exhibits crenellated cross sections. Hence, its associated REV is subjected to meso-scopic in plane loadings ( uniaxial/biaxial tensions, pure shear) and A multiscale approach to model the mechanical behaviour of heterogeneous hyperelastic membranes L. Meunier, L. Orgéas, G. Chagnon & D. Favier In memory of Luc Meunier CNRS/Université de Grenoble, Laboratoire Sols-Solides-Structures-Risques (3S-R), Grenoble Cedex, France ABSTRACT: Within the framework given by the homogenisation method with multiple scale asymptotic expansions, a theoretical and numerical analysis is proposed in order to study the mesoscale behaviour of hyperelastic thin membranes exhibiting geometrical or material heterogeneities at the microscale. Results deduced from this multiscale approach are then used to analyse the mechanical behaviour of a crenellated thin membrane made up of a compressible Neo-Hookean material. their resulting mesoscopic behaviours (stress levels, evolving anisotropy) are analysed and discussed.

PROBLEM STATEMENT

We consider a thin heterogeneous plate, e.g. that shown in figure 1(a), with an initial average thickness e 0 along the e 3 direction and with a characteristic in-plane initial macroscopic dimension L 0 (in (e 1 , e 2 )). The plate is made up of a periodic assembly of Representative Elementary Volumes (REV) with a characteristic in-plane initial dimension l 0 . It is supposed that the thickness e 0 and the REV in-plane length l 0 are of the same order of magnitude, i.e e 0 /l 0 ≈ O(1), and that they are very small with respect to the in-plane size L 0 of the plate, i.e e 0 /L 0 ≈ l 0 /L 0 ≈ O(ε), the scale separation parameter ε being very small. A typical example of such REV's is shown in figure 1(b).

For a sake of simplicity, we assume here that the plate is only subjected to in quasi-static and in-plane mechanical loadings without volumetric forces. With the example shown in figure 1(b), this means that the upper Γ + and lower Γ -surfaces of the REV are not loaded.

By noting respectively X _ and _ x the initial and current position vectors of materials points and u _(_ X) = _

x -X _ the displacement vector, the first momentum balance equation corresponding to this problem and to be solved in the initial configuration is:

Div X π = 0, (1)
where Div X is the divergence operator with respect to the initial configuration and position vectors _ X.

hyperelastic materials and we have also avoided any a priori assumption on the first order displacement field u ( ) . 0 The reader is referred to his work (P ruchnicki 1998) and to that of Meunier [START_REF] Meunier | Etude Du Comportement Mécanique de Membranes de Silicone Á Anisotropie Contrôlée: Application À la Conception de Muscles Artificiels[END_REF]) for details about the theoretical developments. We briefly summarise hereafter the main results deduced from the approach:

• From the assumptions stated for W, it can be shown that the first order displacement field only depends on the in-plane mesoscopic space variable, i.e. u u Y

( ) ( ) ( ). 0 0 = • The mesoscopic equivalent continuum is a 2D
membrane. In the ( , ) e e 1 2 plane, its first momentum balance equation in the initial configuration is expressed as:

Div X π ( ) 0 = 0 , ( 8
)
where the mesoscopic first order Piola-K irchhoff stress tensor π ( ) 0 is defined as

π π ( ) ( ) , 0 0 0 1 0 = ∫ V V d Ω (9)
such a volume averaging being performed on the initial solid domain Ω 0 of the REV, of initial volume V 0 . The local first order stress tensor π ( ) 0 involved in the last equation is defined from:

π ( ) ( ) ( ) ( ) ( ) ( ) ( ) , 0 0 1 0 1 = + + ∂ ∂ W F H F H (10)
where

F G r a d u ( ) ( ) 0 0 = + δ X (11)
and

H Grad u (1) = X ε ( ) 1 (12)
From (2), it also follows that π ( ) 0 verifies:

π π ( ) ( ) ( ) ( ) . 0 0 0 0 ⋅ = ⋅ F F t t ( 13
: 0 π ( ) ( ) ( ) ( , ) 0 0 0 = ∂ ∂ W F F microstructure , (14)
• The first order stress tensor π ( ) 0 can be obtained by solving in the REV the following boundary value problem:

Div 0 F H F H H Grad u X X W π π π ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( ) 0 0 0 1 0 1 1 = = + + = ∂ ∂ (1) ε ( ) , 0 ⋅ = ⎧ ⎨ ⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ ⎫ ⎬ ⎪ ⎪ ⎪ ⎭ ⎪ ⎪ ⎪ - N 0 on in + 0 Γ Γ Ω ( 15
)
where the first order periodic fluctuation of the displacement field ε u ( ) 1 is the unknown field, N is the unit vector normal to the external surfaces Γ + and Γ -, and where F ( ) 0 is given and constant within the entire REV.

APPLICATION TO A SIMPLE MEMBRANE

By following the previous theoretical framework, it is now possible to compute the effective properties of hyperelastic membranes.

Considered membrane geometry and material

For that purpose, we consider a thin plate made up of upper and lower crenellated profiles. It is shown in figure 1(a). The corresponding REV and its dimensions are given in figure 1(b). As shown from this figure, the upper and lower crenellated profiles are identical but they are not parallel: they respectively make an angle ±α/2 = ±32.5° with respect to the e 1 direction.

For the sake of simplicity, the membrane is assumed to be made up of a unique material, the mechanical behaviour of which is defined from the compressible Neo-Hookean hyperelastic strain energy function (5). The constitutive parameters associated with this function, i.e. μ and k, are assumed to be constant in the whole REV, they were set to 1 and 1000 MPa, respectively. Hence, the considered material can be regarded as quasi-incompressible.

In order to study the mesoscopic mechanical behaviour of such an heterogeneous membrane, i.e.

to analyse the relationship between π ( ) ( ) , 0 0 F and the membrane microstructure (see ( 14)), the that π 22 (0) is higher than π 11 (0) (20% higher when λ 11 = 2). • Stress-elongation curves for β ≥ 0 exhibit a curvature with a constant sign: this is directly due to the Neo-Hookean nature of the membrane material.

• Such an expected behaviour is not observed at all for stress elongation curves obtained with β = -1 and β = -0.5. Indeed, for these two mechanical loadings which involve compression stress components π 22 (0) , the sign of the curvature suddenly change around λ 11 = 1.25 and λ 11 = 1.75 when β = -1 and β = -0.5, respectively (see the circles sketched in the graphs of figure 3). This change results in an anomalous increase of the strain hardening of π 11 (0)

and in an anomalous strain softening of π 22 (0) By closely looking at the deformed shapes of the REV just after these transition zones (see figure 3), one can clearly see that the REV has been subjected to a local buckling along the e 2 direction, such a buckling being induced by the imposed meso-scopic compression elongation along this direction.

CONCLUSIONS

Within the framework proposed by the homogeni-sation method with multiple scale asymptotic expansions, and more precisely by pursuing the work of Pruchnicki [START_REF] Pruchnicki | Overal properties of thin hyperelastic plate at finite strain with edge effects using asymptotic method[END_REF], we have proposed a method to analyse from numerical simulation the mesoscopic mechanical behaviour of heterogeneous hyperelastic membranes.

In particular, it has been shown that a membrane made up of a unique homogeneous material but with geometrical heterogeneities at the REV scale could exhibit significant anisotropy and possible microstructure instabilities such as buckling.

A deeper analysis of these phenomena as functions of both the membrane geometry (e.g. the inclination angle α) and the imposed mesoscopic loading should be required.

The method also permits to analyse the mechanical behaviour under various mechanical loadings, thus allowing to constitute a precious and exhaustive database in order to propose relevant analytical forms of the mesoscopic law ( 14). This work is planned.

Before, its relevance must be proved. For that purpose, its prediction could be compared to what could be observed experimentally on similar heterogeneous membranes with a homogeneous hyperelastic material such as silicone rubber [START_REF] Meunier | Experimental and numerical study of the mechanical behaviour of an unfilled silicone rubber[END_REF]). This work is also planned.

  with respect to the first order 2D transformation gradient F ( )