MD Charles Laidi
email: charles.laidi@childmind.org

Dorothea L Floris

Julian Tillmann

Yannis Elandaloussi

Mariam Zabihi

Tony Charman

Thomas Wolfers

Sarah Durston

Caroline Moessnang

Flavio Dell

Flavio Dell'acqua

Christine Ecker

Eva Loth

Declan Murphy

Simon Baron-Cohen

Jan K Buitelaar

Andre F Marquand

Christian F Beckmann

Vincent Frouin

Marion Leboyer

Edouard Duchesnay

Pierrick Coupé

Josselin Houenou

Cerebellar atypicalities in autism?

Keywords: Cerebellum, MRI, Volumetry, Parcellation, Normative Modelling, Autism Cerebellar anatomy in autism

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.

Introduction

The cerebellum contains more than 50% of the neurons of the brain [START_REF] Li | Using a million cell simulation of the cerebellum: network scaling and task generality[END_REF], has almost 80% of the surface area of the neocortex [START_REF] Sereno | The human cerebellum has almost 80% of the surface area of the neocortex[END_REF] and is known to be involved in a broad range of cognitive functions including social cognition (3,[START_REF] Guell | Triple representation of language, working memory, social and emotion processing in the cerebellum: convergent evidence from task and seed-based resting-state fMRI analyses in a single large cohort[END_REF] A large body of literature, including preclinical (5,[START_REF] Kelly | Regulation of autism-relevant behaviors by cerebellar-prefrontal cortical circuits[END_REF], histopathology, genetics and neuroimaging studies (see Fatemi et al. 2012 [START_REF] Fatemi | Cerebellum and autism[END_REF], Wang et al. 2014 (8) for a full review) has established the implication of the cerebellar circuits in social cognition and the physiopathology of autism spectrum disorder (hereafter "autism").

More than 40 prior studies reported anatomical atypicalities in the cerebellum in autism in relatively small samples. In a meta-analysis, Traut et al. [START_REF] Traut | Cerebellar Volume in Autism: Literature Meta-analysis and Analysis of the Autism Brain Imaging Data Exchange Cohort[END_REF] reported a significantly larger global cerebellar volume in individuals with autism compared to controls, though with a small effect size. Further, they did not replicate this finding in a large sample of 681 subjects from the Autism Brain Imaging Data Exchange (ABIDE) database. Because the studies included in the meta-analysis were generally underpowered, the authors found that the number of significant findings was larger than expected. To date, despite many studies (see Traut et al. 2017 (9) for a complete meta-analysis) investigating the cerebellar structure in autism, no consistent atypicalities have been found.

Several reasons may explain such discrepant findings. First, it may be that there really are no group differences in the cerebellum between individuals with autism and controls and that previous positive findings are the consequence of a publication bias from a large number of small underpowered studies [START_REF] Traut | Cerebellar Volume in Autism: Literature Meta-analysis and Analysis of the Autism Brain Imaging Data Exchange Cohort[END_REF]. Second, there might be differences, but cerebellar morphological alterations in autism are subtle and located only in specific parts of the cerebellum, such as the vermis or Crus I (5,10), which was not investigated in large multicentre studies [START_REF] Traut | Cerebellar Volume in Autism: Literature Meta-analysis and Analysis of the Autism Brain Imaging Data Exchange Cohort[END_REF]. Third, because autism is a heterogeneous condition [START_REF] Waterhouse | The ASD diagnosis has blocked the discovery of valid biological variation in neurodevelopmental social impairment[END_REF][START_REF] Zabihi | Dissecting the Heterogeneous Cortical Anatomy of Autism Spectrum Disorder Using Normative Models[END_REF][START_REF] Floris | Atypical Brain Asymmetry in Autism-A Candidate for Clinically Meaningful Stratification[END_REF][START_REF] Wolfers | From pattern classification to stratification: towards conceptualizing the heterogeneity of Autism Spectrum Disorder[END_REF][START_REF] Lombardo | Big data approaches to decomposing heterogeneity across the autism spectrum[END_REF], there might be distinct subgroups of individuals with autism with different pathophysiological mechanisms and different cerebellar morphological patterns that might be correlated with clinical dimensions such as sensory motor atypicalities [START_REF] Marquand | Understanding Heterogeneity in Clinical Cohorts Using Normative Models: Beyond Case-Control Studies[END_REF][START_REF] Tillmann | Dissecting the phenotypic heterogeneity in sensory features in autism spectrum disorder: a factor mixture modelling approach[END_REF]. In that case, absent or discrepant findings might be related to the heterogeneity of subjects included in the studies, diluting consistent neural features across all subjects. Fourth, different segmentation methods could account for the variability in the results across studies -as different parcellations algorithms have been developed for the cerebellum with various outcomes. To the best of our knowledge, no study has investigated lobular cerebellar atypicalities in autism comparing different parcellation techniques. Last, there is a need to employ novel methods that can quantify individual deviations from a normative pattern without relying on group means, such as normative modelling approaches [START_REF] Wolfers | From pattern classification to stratification: towards conceptualizing the heterogeneity of Autism Spectrum Disorder[END_REF][START_REF] Marquand | Understanding Heterogeneity in Clinical Cohorts Using Normative Models: Beyond Case-Control Studies[END_REF].

Our goal, therefore, was to study cerebellar anatomy of individuals with autism taking into account these methodological and clinical considerations, in a large multicentre sample. First we compared the cerebellar anatomy of individuals with autism and controls using three different standard approaches, at both lobular and voxel levels. Next, to move beyond standard case-control paradigms, we used normative modelling to quantify deviations from a normative pattern to best characterize sample heterogeneity. Finally, we studied how, within autism, cerebellar anatomy was associated with variation in clinical features.

Methods and Materials

Participants

We analyzed data from the EU-AIMS Longitudinal European Autism Project (LEAP) (18)the largest European multicentre initiative aimed at identifying biomarkers in autism. This cohort is a large multi-centre, observational study, which aims to identify and validate stratification biomarkers in autism. We included individuals from the LEAP cohort (individuals with autism and controls recruited in six centres), with an IQ > 70.

Parcellation of cerebellar lobules

All participants were scanned with a 3T MRI scanner at 6 different sites, in (i) Cambridge, UK (Siemens Verio), (ii) London, UK (General Electrics Discovery mr750), Mannheim, Germany (Siemens TimTrio), Nijmegen, Netherlands (Siemens Skyra), Rome, Italy (GE, Signa HDxt) and Utrecht (Phillips Medical System, Achieva / Ingenia CX). High-resolution structural T1weighted volumetric images were acquired with full head coverage, at 1.2-mm thickness with 1.2x1.2-mm in-plane resolution. Acquisition protocols are reported in supplementary material 1. A flow chart describing the quality control steps supplementary material 2), a description of the motion-related artifacts (supplementary material 3), the most frequent parcellation errors (supplementary material 4) and an example of parcellation defects related to a cyst of the posterior fossa (supplementary material 5) are reported in the supplementary material section. A comparison of the subjects included and excluded from the analyses is reported in supplementary material 6. There was no difference in the proportion of autism/TD in the excluded/included subjects, however full-scale IQ and age were lower in the participants excluded from the analyses. We used two different methods to perform parcellation at a lobular level (Figure 1a, 1b and supplementary material 7). First, we used the CERES pipeline (25) (Figure 1b and supplementary material 7). This pipeline relies on an atlas that has been compared to manual tracing [START_REF] Diedrichsen | A probabilistic MR atlas of the human cerebellum[END_REF]. Second, we used the SUIT pipeline (26) (supplementary material 8). Although the SUIT pipeline has not been compared to manual tracing, this toolbox provides a segmentation of the cerebellar vermis, a region previously linked to autism [START_REF] Laidi | Cerebellar anatomical alterations and attention to eyes in autism[END_REF][START_REF] Allen | Differential effects of developmental cerebellar abnormality on cognitive and motor functions in the cerebellum: an fMRI study of autism[END_REF][START_REF] Courchesne | Hypoplasia of cerebellar vermal lobules VI and VII in autism[END_REF][START_REF] Pierce | Evidence for a cerebellar role in reduced exploration and stereotyped behavior in autism[END_REF]. We performed a visual quality check (supplementary material 9) and compared the outcome of both parcellation measures. The description of the parcellation features is reported in supplementary material 9.

Voxel based morphometry analysis

We used VBM SUIT procedure [START_REF] Diedrichsen | A probabilistic MR atlas of the human cerebellum[END_REF] to look at finer-grained differences that parcellationbased approaches might not provide. This method relies on a normalization to a probabilistic atlas of the cerebellar lobules in the anatomical space and is further described in supplementary material 8.

Phenotyping and clinical features

IQ was assessed using the Wechsler Abbreviated Scales of Intelligence. The Autism Diagnostic Observation Schedule measured clinical core symptoms of autism [START_REF] Lord | The autism diagnostic observation schedule-generic: a standard measure of social and communication deficits associated with the spectrum of autism[END_REF]. The full clinical assessment of the LEAP cohort is described elsewhere [START_REF] Charman | The EU-AIMS Longitudinal European Autism Project (LEAP): clinical characterisation[END_REF]. To assess if the clinical dimensions of autism were correlated with the cerebellar morphology while limiting the number of multiple comparisons, we selected 3 clinical variables based on the literature. First, we selected the social responsiveness score (SRS) in order to see how the cerebellar structure was correlated to the severity of autism [START_REF] Mihailov | Cortical signatures in behaviorally clustered autistic traits subgroups: a population-based study[END_REF]. Second, we selected the sensory atypicalities, based on the Short Sensory Profile scale in the EU-AIMS sample [START_REF] Tillmann | Dissecting the phenotypic heterogeneity in sensory features in autism spectrum disorder: a factor mixture modelling approach[END_REF]. Last, we selected the ADHD DSM-IV rating scale to measure severity of ADHD symptoms (supplementary material 10), a frequent comorbidity of autism. Atypicalities of the cerebellum (notably in the vermis of the cerebellum) have been reported in ADHD [START_REF] Shaw | A multicohort, longitudinal study of cerebellar development in attention deficit hyperactivity disorder[END_REF][START_REF] Webb | Cerebellar vermal volumes and behavioral correlates in children with autism spectrum disorder[END_REF][START_REF] Stoodley | The cerebellum and neurodevelopmental disorders[END_REF]. These results suggested that cerebellar atypicalities reported in autism might be at least partly related to comorbid ADHD symptoms. We performed secondary analyses to assess the effect of ADOS Calibrated Severity Score (ADOS-CCS, Shumway et al. 2012) and the Restricted Behaviour Scale Revised (RBS-R) on cerebellar structure.

Normative modelling

This novel method has been described in detail elsewhere [START_REF] Marquand | Understanding Heterogeneity in Clinical Cohorts Using Normative Models: Beyond Case-Control Studies[END_REF] and successfully applied to mental disorders and autism in particular [START_REF] Zabihi | Dissecting the Heterogeneous Cortical Anatomy of Autism Spectrum Disorder Using Normative Models[END_REF][START_REF] Wolfers | From pattern classification to stratification: towards conceptualizing the heterogeneity of Autism Spectrum Disorder[END_REF]. Structural T1-weighted images were preprocessed with the SUIT pipeline (see voxel based morphometry section) which is specifically adapted to the cerebellum [START_REF] Diedrichsen | A probabilistic MR atlas of the human cerebellum[END_REF]. A Gaussian process regression model was trained at each voxel in the control cohort using age, sex, site of inclusion, full scale IQ and intracranial volume as covariates to predict cerebellar grey matter volume. We generated normative probability maps, which quantify the deviation of each participant from the normative model for cerebellar gray matter volume at each voxel. These maps were then compared in patients and controls (see a description of our normative model in supplementary material 11).

Meta-analytical approach and homogeneity measure

To study the variability across the different sites, we repeated our analyses in each site of inclusion. We compared the volume of each cerebellar sub-region with linear models, considering age, sex, intracranial volume and full-scale IQ as covariates. The results were not corrected for multiple tests since our goal was to understand the variability across the different sites. Next, we conducted a meta-analysis across the sites of inclusion and estimated the q and the I2 statistics to study the heterogeneity of our results.

Supervised learning

We conducted classification analyses to predict which individuals belonged to the autism / TD groups based on the cerebellar anatomy. Methods are reported in supplementary material 12.

Statistical analyses

For parcellation analyses, we conducted linear models, using site of inclusion as a random effect and sex, age, full-scale IQ and intracranial volume as covariates. To decide how to consider linear covariates (age and iq) in our model, we tested the best model fit in each site of inclusion between a linear a cubic and a quadratic model (Bedford et al. 2020). Details on the statistical analyses are reported in supplementary material 13. Before performing pairwise comparisons (t-tests) between patients and controls, we ensured that the standardized residuals were normally distributed, as assessed by the Shapiro-Wilk test (P > 0.05) and a QQ-plot. We conducted a Pearson correlation test to assess the correlation between volumetric measures of CERES and SUIT pipeline. Statistical analyses of VBM is reported in supplementary material 8. To test if clinical features (SRS score, short sensory profile and diagnosis of ADHD) were associated with the cerebellar structure, we conducted linear models only in the group of individuals with autism and regressed out the effect of age, sex, intracranial volume, full-scale IQ and MRI scanning site. We conducted heterogeneity focused analyses to understand the influence of age, sex and iq in our statistical models. We compared two models: the first one including the variable of interest (age, sex or iq) and its interaction with diagnosis, and the second not including the variable of interest and the interaction term, as described in Bedford et al. 2020 (supplementary material 14). We studied the effect of diagnosis on cerebellar structure in IQ and age-centred intervals (supplementary material 15). We used the pymatch package (https://github.com/benmiroglio/pymatch) to create a sample of individuals with ASD matched to the neurotypical subjects by age, iq and sex. We subsequently repeated our case control analyses to ensure that the results from the main analyses were not driven by difference between individuals with ASD and controls (see supplementary material 16). In the normative modelling analyses, given the non-parametric distribution of positive and negative deviations in each region of interest, we compared autism and TD with non-parametric Mann-Whitney tests.

Dimensional analyses in a transdiagnostic paediatric cohort

We repeated our dimensional analyses in the Healthy Brain Network cohort (Alexander et al. 2017). In a more heterogenous population of individuals with autism-related symptoms without a formal diagnosis of autism, we studied the influence of the dimensions of autism using the SRS-2 scale and two of its subscales, measuring social / communication impairments or repetitive and restrictive behaviors. A complete description of the study population and its clinical features is reported in supplementary material 17. 1. There was no significant difference in age between patients and controls; however, there were more males than females in patients compared with controls and a higher full-scale IQ in controls compared to patients. Thus, full-scale IQ and sex were included as covariates in our statistical analyses.

Results

Population of the study Demographics of the study population are reported in Table

Comparison of CERES and SUIT pipeline.

We performed cerebellar parcellation using SUIT and CERES pipeline and compared parcellation outcomes of both pipelines (supplementary material 8). We found a strong positive relationship in Crus I (r : 0.72 ; pval < 0.001), the anterior lobe of the cerebellum (r : 0.73 ; pval < 0.001), the postero-inferior lobe of the cerebellum (r : 0.75, pval < 0.001) between SUIT and CERES except for Crus II (r : 0.55 ; pval < 0.001) where we found a moderate positive relationship (supplementary material 18).

Case-control analyses.

Effect of age and IQ. We found that modelling age and IQ with a linear effect was more accurate, as opposed to a cubic or quadratic effect (supplementary material 13).

Parcellation and voxel-based morphometry. We did not find any significant effect of autism diagnosis in our regions of interest using the CERES or SUIT pipeline. Effect of the diagnosis of autism (CERES pipeline) on cerebellar sub-volumes are reported in Table 2 and supplementary material 9. There was no effect of autism diagnosis in the cerebellar vermis or lobule VI-VII part of the vermis (supplementary material 20), a region previously involved in autism. When conducting the analyses at the voxel level (voxel-based morphometry -SUIT pipeline, supplementary material 8), we did not find any effect of diagnosis or any significant sex by diagnosis interaction, which was consistent with our findings using a Region-of-Interest approach.

Heterogeneity of cerebellar anatomy in ASD

We found no case control difference in our analyses, which could be explained by a variability of cerebellar anatomy in ASD related either to sex, age, IQ or the clinical features of ASD. We tested in heterogeneity focused analyses the effect of sex, age and IQ on cerebellar anatomy. Results are reported in supplementary material 14. We found no evidence for a strong heterogeneity related to these variables in our linear models. In addition, we found no significant sex by diagnosis interaction for any of the cerebellar regions. We conducted our analyses only among males or females, which did not change our results (supplementary material 14). Regarding age and IQ , there was no significant (i) age by diagnosis interaction (supplementary material 15), (ii) effect of diagnosis on cerebellar structure in age-centred intervals, (iii) age by IQ interaction or (iv) effect of diagnosis on cerebellar structure in IQ-centred intervals (analyses are reported in supplementary material 15). Repeating our analyses in a sample of ASD individuals matched with controls based on sex and age and IQ did not change our results (supplementary material 16). Within the autism sample and contrary to our hypotheses, there was no significant correlation between the SRS2 t-score (supplementary material 21) or the diagnosis of ADHD or sensory alterations and cerebellar structure. Similarly, there was no association between restricted and repetitive behaviors (supplementary material [START_REF] Shaw | A multicohort, longitudinal study of cerebellar development in attention deficit hyperactivity disorder[END_REF] or ADOS CCS score (supplementary material 23). Last, we selected individuals from an independent transdiagnostic mental health pediatric cohort, with symptoms related to autism, as defined by SRS-2 t-score (SRS-2) > 60. Individuals were recruited in 3 sites of inclusion (supplementary material 17). We defined both a relaxed (n = 352, SRS-2 > 60) and a restricted (n = 79, SRS > 76) sample. We found no effect of (i) total SRS-2, (ii) SRS-SCI (social communication questionnaire), (iii) SRS-RRB (restrictive and repetitive behaviors) on cerebellar structure, nor SRS-2 by FSIQ and SRS-2 by age interaction in both samples. Results are described in supplementary material 17.

Multivariate statistics

Normative Modelling. Despite a good fit of our normative model (Figure 2), we found no increased or decreased deviation in the cerebellar lobules (Figure 3 and supplementary material 24), when comparing individuals with autism to neurotypical control. There was no significant difference either at the whole cerebellum level or at a lobular level. Removing FSIQ from our model did not change our results.

Support vector machine to predict diagnosis. Our model did not predict the diagnostic category (individual with autism vs TD) above the level of chance, when considering as predictive features either regions of interest extracted from the cerebellar parcellation or VBM cerebellar maps. Balanced accuracy did not exceed 52% (supplementary material 25).

Meta-analytical approach and site by site analysis

We compared cerebellar anatomy in individuals with autism and TD in each site of inclusion (see supplementary material 27 for a description of clinical features across each site of inclusion and Figure 4 for the results of the meta-analysis). Using the CERES parcellation, two regions of interest were different in two sites: compared to TD there was an increase in the volume of the lobule VI in individuals with autism recruited in Rome (p = 0.035, uncorrected) and an increase in the volume of Crus II (p = 0.048, uncorrected) in individuals with autism recruited in Cambridge. Using the SUIT parcellation, we found only a reduced volume of the vermis in individuals with autism compared to TD in Nijmegen (p = 0.041). It is important to note that the significant results obtained in two sites with the CERES pipeline were not significant using the SUIT pipeline (despite a good correlation between both measures reported in supplementary material 18). For all significant results, the confidence interval (Figure 4) was large compared to the full sample analysis and very close from 0. The metaanalysis metrics (q statistics and I2, see supplementary material 27) suggested that there was no strong heterogeneity in the results across sites.

Discussion

A broad range of atypicalities in different cerebellar regions have been inconsistently reported in autism in the last decades, mostly in small sample size studies. Our goal was to study the cerebellar anatomy in a large harmonized multicentric European cohort to reconcile previous results from the literature. We combined complementary statistical (both 'traditional' group case control paradigms and individual deviations using normative modelling, supervised learning) and neuroimaging (parcellation, voxel-based morphometry adapted to the cerebellum) methods to fully understand the cerebellar anatomy in autism. We found that regardless of the analytical technique we employed, there was no difference in the cerebellar anatomy. In addition, within autism, there was no correlation between cerebellar anatomy and clinical features. We discuss these results in the context of neuroimaging of autism and replicability / reproducibility issues in neuroimaging.

Like many neurodevelopmental and psychiatric disorders, autism is clinically heterogeneous and conceptualized as a spectrum rather than a condition. In cortical regions, there have been recent attempts to identify subgroups of individuals with autism using neuroanatomical features [START_REF] Bethlehem | A normative modelling approach reveals age-atypical cortical thickness in a subgroup of males with autism spectrum disorder[END_REF][START_REF] Hong | Multidimensional Neuroanatomical Subtyping of Autism Spectrum Disorder[END_REF]. However, to date, reports from MRI studies on cerebellar anatomy in autism are based on "traditional" case-control analysis, and mostly from relatively small samples. These studies typically reported cerebellar alterations in the Crus I region (5,[START_REF] Stoodley | The cerebellum and neurodevelopmental disorders[END_REF], in the anterior lobe [START_REF] Laidi | Cerebellar anatomical alterations and attention to eyes in autism[END_REF] or in the vermis [START_REF] Allen | Differential effects of developmental cerebellar abnormality on cognitive and motor functions in the cerebellum: an fMRI study of autism[END_REF][START_REF] Courchesne | Hypoplasia of cerebellar vermal lobules VI and VII in autism[END_REF][START_REF] Levitt | Cerebellar vermis lobules VIII -X in autism[END_REF], which were correlated to clinical dimensions of autism. In 2017, the group of Roberto Toro (9) published a meta-analysis on 30 studies on cerebellar anatomy in autism and reported a weak but significant association between autism diagnosis and increased global (overall) cerebellar volume (p = 0.049, uncorrected). In addition, Traut et al. ( 9) studied the cerebellar volume in a larger sample (ABIDE dataset) but did not conduct a parcellation analysis and studied the global volume of the cerebellum. However, the cerebellar cortex can be divided between an anterior part -connected to the sensory motor cortex -and a posterior / cognitive part -connected to the associative cortex. Because of this functional topography, it is critical to study the anatomy of the cerebellum at a lobular level. We did not find a difference in terms of cerebellar sub-volume in individuals with autism compared to neurotypical controls. These results were consistent across two different parcellations methods and a voxel wise analysis. All parcellations were visually inspected by an expert rater blind of the diagnosis. These results are consistent with the meta-analysis of Traut et al. [START_REF] Traut | Cerebellar Volume in Autism: Literature Meta-analysis and Analysis of the Autism Brain Imaging Data Exchange Cohort[END_REF] that reported inconclusive results at a lobular level. Thus, we believe that there is no consistent difference in cerebellar morphology when using a classic case-control approach.

The discrepancy of previous results in the literature could be explained by different methods of segmentation and parcellation that they employed [START_REF] Laidi | Cerebellar anatomical alterations and attention to eyes in autism[END_REF][START_REF] Mello | Cerebellar gray matter and lobular volumes correlate with core autism symptoms[END_REF][START_REF] Scott | A comprehensive volumetric analysis of the cerebellum in children and adolescents with autism spectrum disorder[END_REF]. For example, cerebellar segmentation can be performed manually, semi-automatically and fully automatically. Because of the heterogeneity of autism, it is critical to investigate its neuroanatomy in large multicentre samples to avoid false positive results [START_REF] Button | Power failure: why small sample size undermines the reliability of neuroscience[END_REF]. Also, manual and semi-automated segmentation methods are difficult to apply to large samples and there is a need to develop fully automated segmentation algorithms. However, fully automated parcellation methods rely on different atlases [START_REF] Diedrichsen | A probabilistic MR atlas of the human cerebellum[END_REF][START_REF] Park | Derivation of high-resolution MRI atlases of the human cerebellum at 3T and segmentation using multiple automatically generated templates[END_REF]. To the best of our knowledge, our study is the first to compare different parcellation algorithms in a clinical population of individuals with autism. We found a moderate to strong positive relationship between CERES (25) and SUIT [START_REF] Diedrichsen | A probabilistic MR atlas of the human cerebellum[END_REF]. It is important to note that the definition of the lobules differs between both techniques, which rely on different atlases. The CERES pipeline relies on the atlas of Park et al. [START_REF] Park | Derivation of high-resolution MRI atlases of the human cerebellum at 3T and segmentation using multiple automatically generated templates[END_REF] where the vermis is merged into the cerebellar hemisphere. Thus, the Crus II region -where we only found a moderate correlation between both methods -encompasses part of the vermis in the CERES pipeline as compared to the SUIT pipeline where the vermis is isolated from the hemisphere. This difference of definition in the cerebellar parcellation might partly explain the discrepant findings from previous studies. In our study, we analyzed the cerebellar volumetry with both techniques in order to ensure the robustness of our results and in both cases, we did not find differences between autism and neurotypical controls. In addition, we also used the SUIT pipeline [START_REF] Diedrichsen | A probabilistic MR atlas of the human cerebellum[END_REF] to perform analyses at a voxel level.

Our study has several strengths. Most of the prior studies investigating the anatomy of individuals with autism focused on the entire brain and did not investigate the cerebellum specifically. Because of the position of the cerebellum (distinct from the neo-cortex, in the posterior fossa) and its specific anatomical structure (high degree of folding), the analysis of the cerebellum requires specific tools and parcellations algorithms. In addition, it is very difficult to perform an effective quality check in the entire brain, including the cerebellum. In this paper, an expert rater, blind to diagnosis, visually inspected all cerebellar parcellations. To ensure the robustness of our results, we used different parcellation methods and statistical analyses to fully understand how the cerebellar structure might differ in individuals with autism and controls. We believe that to date, this is the most exhaustive study investigating the structural anatomy of the cerebellum in autism.

Several reasons could explain our negative results. One possibility might be lack of statistical power. However, all previous results on cerebellar anatomy included smaller samples (Laidi et al. 2017 [START_REF] Laidi | Cerebellar anatomical alterations and attention to eyes in autism[END_REF], see Traut et al. 2017 for a meta-analysis( 9)) suggesting that, if present, atypicalities could have been detected. In addition, cerebellar atypicalities have been repeatedly reported in other brain disorders such as schizophrenia in samples of the same size as this study [START_REF] Moberget | Cerebellar volume and cerebellocerebral structural covariance in schizophrenia: a multisite mega-analysis of 983 patients and 1349 healthy controls[END_REF][START_REF] Laidi | Cerebellar parcellation in schizophrenia and bipolar disorder[END_REF]). An increased heterogeneity in individuals with autism could also explain our negative results in the case control analyses. In that case, only a subgroup of individuals with ASD, such as individuals with a more severe form of autism, sensory atypicalities, a specific range of IQ or age or more severe restrictive / repetitive behavior, would present cerebellar anatomical atypicalities. In that case, those might not be detected when using classic group mean comparison. To fully explore this hypothesis, we conducted a wide range of analysis to investigate the effect of sex, age, IQ, severity of autism, sensory atypicalities, diagnosis of ADHD, repetitive and restrictive behaviors. In an independent cohort of individuals with autism-related symptoms, with higher heterogeneity compared to the EU-AIMS sample, the severity of autism had no influence on cerebellar structure. Last, we also conducted a normative model analysis to investigate differences at the individual level. However, we detected no significant positive or negative deviations from the norm despite a good fit of our model. Although this approach has been successfully applied and found positive results in the cerebral cortex [START_REF] Zabihi | Dissecting the Heterogeneous Cortical Anatomy of Autism Spectrum Disorder Using Normative Models[END_REF], our results were negative in the cerebellum when using a similar sample.

Our meta-analytical approach revealed marginally significant results (Figure 4). These results were not replicated when using a different parcellation method. This suggests that interpreting results in small samples is not relevant and leads to inconsistent results that are sensitive to parcellation methods. This was the case of the studies published to date on cerebellar parcellation (including a study published by our group [START_REF] Laidi | Cerebellar anatomical alterations and attention to eyes in autism[END_REF]). These results explain how false positive results might arise from the literature with real-life data. Several limits should be considered before interpreting our results. Concerns have been raised regarding the validity of psychometric properties of the Short Sensory Profile scale (Williams et al. 2018). While our paper is focused on cerebellar volumetry using 3T MRI, this approach has limitations. The cerebellum is a highly folded structure with almost 80% of the surface area of the neocortex. Partial volume issues are thus more prominent for the cerebellum. Thus, 7T MRI (2) might be more able to detect atypicalities in cerebellar anatomy of individuals with autism.

To the best of our knowledge, this is the largest study to investigate the anatomy of the cerebellum in autism. Our results strongly suggest that there is no significant difference in cerebellar anatomy between individuals with autism and controls. In the context of replicability and reproducibility issues in science, our paper underlines the interest of using different statistical / neuroimaging methods and a large sample to address the same research question and avoid inconsistent results. Beyond structural anatomy, functional MRI studies with large sample size could unravel altered cerebellar connectivity in autism. We tested the best model fit between linear, quadratic and cubic effect of age across cerebellar regions. We calculated the percentage of site (as described above) at which the linear model was to best fit, compared to quadratic and cubic models across cerebellar regions. We included in our model diagnosis, each age term and its interaction with diagnosis and compared the following models across cerebellar regions: with a lower AIC) than cubic or quadratic models on average in 79% of the site of inclusion across cerebellar regions (from 70% to 92%, see Figure B1), suggesting that including age as a linear term was a good choice.

Tables

We repeated the analysis performed on age on full scale IQ. First, we tested the best model fit between linear, quadratic and cubic effect of IQ measures across cerebellar regions. We calculated the percentage of site (as described above) at which the linear model was to best fit, compared to quadratic and cubic models across cerebellar regions. We included in our model diagnosis, each iq term and its interaction with diagnosis and compared the following models across cerebellar regions : For full scale IQ, the model including linear term was a better fit (as defined with a lower AIC) than cubic or quadratic models on average in 88 % of the sites of inclusion across cerebellar regions (see Figure B), suggesting that including age as a linear term was a good choice.

• a model including the variable of interest (either sex, age, FSIQ, PIQ or VIQ) and an interaction term between this variable of interest and the diagnosis of autism • a model not including the variable of interest or interactions in the model.

In order to compare those two models, we used the AIC (Akaike information criterion) to determine the influence of the variable in the cerebellum, separately in each site of inclusion. Following the same methods as in Bedford et al. 2019, we determine for each region of the cerebellum the number of site for which each model was shown to be the best fit and calculated a weighted average (based on site size) to determine the best model, on average, in a region of the cerebellum taking into account all sites of inclusion. We conducted these analyses using the results of the CERES pipeline described in our manuscript. The CERES pipeline has shown to perform well compared to other cerebellar parcellation techniques in both adult and pediatric populations. In order to avoid increasing the risk of false positive findings, we conducted the following analyses using the outcomes of the CERES pipeline.

Heterogeneity focused analysis of sex

As described above and in Bedford et al. 2020, we compared the AIC of the two following models:

Cereb. volumei = β0 + β1Diagnosis + β2Sex + β3(Diagnosis*Sex) + β4Age + β5 Intracranial Volume + εi Cereb. volumei = β0 + β1Diagnosis + β2Age + β3 Intracranial Volume + εi

Results are reported in Figure A

The model including sex term and its interaction with diagnosis was a better fit (as defined with a lower AIC) on average on 29% of sites of inclusion across cerebellar regions (from 15% to 42%, see Figure A1). Contrary to the work of Bedford et al. this result suggest a relatively low influence of sex in this heterogeneity-focused analysis.

Heterogeneity focused analysis of age

As described above and in Bedford et al., we compared the AIC of the two following models:

Cereb. volumei = β0 + β1Diagnosis + β2Sex + β3Age + β4(Diagnosis*Age) + εi Cereb. volumei = β0 + β1Diagnosis + β2Sex + εi

Results are reported in Figure B

The model including age term and its interaction was a better fit (as defined with a lower AIC) on average in 30% of the site of inclusion across cerebellar regions (from 0 to 42%), suggesting a relatively modest influence of age in the heterogeneity focused analysis. Bedford et al. found for instance that the model with age term and its interaction was a better fit in up to 92% of the site of inclusion across the cortex. The model including full scale IQ term and its interaction was a better fit (as defined with a lower AIC) on average in 20% of the site of inclusion across cerebellar regions (from 0 to 50%, see Figure A3) suggesting a relatively modest influence of age in the heterogeneity focused analysis.

Heterogeneity focused analysis of full-scale IQ

Heterogeneity focused analysis of performance IQ

As described above and in Bedford et al., we compared the AIC of the two following models:

Cereb. volumei = β0 + β1Diagnosis + β2Sex + β3Age + β4(Diagnosis*performance IQ) + εi Cereb. volumei = β0 + β1Diagnosis + β2Sex + εi

Results are reported in Figure D

The model including performance IQ term and its interaction was a better fit (as defined with a lower AIC) on average in 18% of the site of inclusion across cerebellar regions (from 0 to 42%, see Figure A4), suggesting a relatively modest influence of performance IQ in the heterogeneity focused analysis. The model including verbal IQ term and its interaction was a better fit (as defined with a lower AIC) on average in 13% of the site of inclusion across cerebellar regions (from 0 to 23%, see Figure A5), suggesting a relatively modest influence of age in the heterogeneity focused analysis.

Heterogeneity focused analysis of verbal IQ

the CERES pipeline [START_REF] Romero | CERES: A new cerebellum lobule segmentation method[END_REF]. All data were processed on a high computing performance cluster in Bordeaux (PC) by the team that developed the CERES pipeline as in the EU-AIMS sample. Next, an expert rater (YE) -blind of the clinical features of each participant -visually assessed the quality of MRI scans in every slice for each spatial plan of the cerebellum. We identified subjects with non-cerebellar voxels labeled as voxels belonging to the cerebellum and vice versa and subjects with parcellation errors within the cerebellar lobules. All images with parcellation defects were excluded from further analyses.

Statistical analyses

In the relaxed and strict sample (see subject selection section), we investigated if there was a significant effect of the SRS scale on cerebellar anatomy. As we did in the EU-AIMS sample, we included in a linear model SRS2 T-score, age, sex, site of inclusion, ICV and full-scale IQ (FSIQ) as covariates. Following the remarks of Reviewer #1, we tested if (i) there was a SRS by FSIQ interaction and if our results changed without including FSIQ as a covariate. In addition, following the remark of Reviewer #2 (comment n°14) we repeated our analyses with 2 subscales of the SRS. The SRS-2 can be divided into two scores corresponding to the DSM-V autism dimensions : a social communication/interaction score (SCI; sum of Awareness, Cognition, Communication, and Motivation subscales) and a restricted/repetitive behavior score (RRB; Mannerisms subscale) (Frazier et al., 2014;Prigge et al., 2018). In order to differentiate the social component related to autism from the restrictive / repetitive behaviors component, we studied separately the two components of the SRS scale.

Study population

Out of 1453 subjects with structural MRI data and complete clinical assessment (SRS total and subscores, IQ measurement and basic demographic characteristics -age, sex, site of inclusion), we excluded 280 subjects with excessive head motion and low quality of the anatomical image and 279 subjects with parcellation errors. Next we selected only subjects with > 60 SRS2 t-score as described above. The study population is reported in Table A.

Results

We find no significant effect on the SRS score on cerebellar anatomy in the relaxed and the strict sample. Results are reported in Tables B-1 to B-6. We found no FSIQ by SRS interaction and excluding FSIQ from our model did not change our results. Likewise, there was no significant influence of the SRS social communication/interaction score and the SRS restricted/repetitive behavioral score.

FiguresFigure 1 :

 1 Figures

Figure 2 :

 2 Figure 2: Goodness of fit of the normative model in controls

Figure 3 :Figure 4 :Supplementary Material 13 :

 3413 Figure 3: No difference of positive / negative deviations in the regions of interest of the cerebellum in autism vs neurotypical populations

  Cerebellar volumesi = β0 + β1Diagnosis + β2 IQ + β3(Diagnosis*IQ) + β4Sex + β5 ICV + β6 Age + ε Cerebellar volumesi = β0 + β1Diagnosis + β2 IQ + β3(Diagnosis*IQ) + β4 IQ 2 + β5(Diagnosis*IQ 2 ) + β6Sex + β7 ICV + β8 Age + εi Cerebellar volumesi = β0 + β1Diagnosis + β2 IQ + β3(Diagnosis* IQ) + β4 IQ 2 + β4(Diagnosis*IQ 2 ) + β5 IQ 3 + β6(Diagnosis* IQ 3 ) + β7Sex + β8 ICV + β9 Age + εi

  CERES was the overall winner of a cerebellar parcellation challenge (MICCAI 2017), published by Carass et al. 2018 (Carass et al. 2018 Neuroimage). More recently, an independent group (Soros et al). reported that CERES was an accurate and reproducible tool for fully automated segmentation and parcellation of the cerebellum Soros et al. 2021 (Soros et al. 2021 Cerebellum).

  As described above and in Bedford et al., we compared the AIC of the two following models: Cereb. volumei = β0 + β1Diagnosis + β2Sex + β3Age + β4(Diagnosis*Full scale IQ) + εi Cereb. volumei = β0 + β1Diagnosis + β2Sex + εi Results are reported in Figure C

  As described above and in Bedford et al., we compared the AIC of the two following models: Cereb. volumei = β0 + β1Diagnosis + β2Sex + β3Age + β4(Diagnosis * verbal IQ) + εi Cereb. volumei = β0 + β1Diagnosis + β2Sex + εi Results are reported in Figure E

Table 1 :

 1 Study population

		ASD n = 274	Controls n = 219	Statistics	P value
	Site of inclusion (C , K, M, N, R, U)	C : 45, K : 78, M : 21,	C : 32, K : 55, M : 18,	chi-2	NS.
		N : 77, R : 20, U : 33	N : 57, R : 18, U : 39
	Mean Age (SD) [min -max]	17 (5) [7.00 -30]	17 (5) [6 -30]	t-test	NS.
	Sex ratio (% of Males)	0.73	0.64	chi-2	< 0.05
	Mean full scale iq (SD) [min -max]	103 (19) [70 -148]	104 (18) [70 -142]	t-test	< 0.05
	Mean verbal iq (SD) [min -max]	102 (20) [70 -160 ]	104 (18) [70 -158]	t-test	< 0.05
	Mean performance iq (SD) [min -max]	104 (19) [70 -150]	105 (20) [70 -147]	t-test	< 0.05
	Mean ADOS 2 (SD) [min -max]	Social-affect: 6 (2) [1 -10]	NA	NA	NA
		Communication: 4 (2) [1 -10]
		CSS total: 4 (3) [1 -10]
	Mean ADOS CSS (SD) [min-max]	5.2 (3) (1-10)	NA	NA	NA
	Mean ADI -R (SD) [min -max]	Social-affect: 16 (6) [1 -28]	NA	NA	NA
		Communication: 12 (5) [0 -25]
		RRB: 4 (2) [0 -12]
	Mean SRS score (SD) [min -max]	70 (12) [43 -90]	NA	NA	NA
	Diagnosis of ADHD (yes / no)	98 / 144	NA	NA	NA
	Mean RBS-R score (SD) [min -max]	15 (13) [0 -73]	NA	NA	NA
	Mean SSP score (SD) [min -max]	130 (36) [4 -189]	NA	NA	NA
	ASD : individuals with autism spectrum disorders

NS : non significant ; SRS : social responsiveness scale ; RBS : restricted and repetitive behaviorsrevised; SSP : Short Sensory Profile scale, ADOS-CSS : ADOS Calibrated Severity Score ; ADI-R: Autism Diagnostic Interview -Revised ; ADOS 2 : Autism Diagnostic Observation Schedule ; Sites of inclusion : C : Cambridge, K : King's College London, M : Mannheim, N : Nijmegen ; R : Rome, U : Utrecht

Table 2 :

 2 Effect of autism on cerebellar anatomy -CERES analysis

	ROI	pval	tval	[ICinf ; ICsup]	dof			Cohen's f 2
						Group	Sex	Age	Site	ICV	FSIQ
	Cerebellum	0.3824	-0.87	[-2.26 ; 0.87]	10	0.002	0.022	0.040	0.117	0.293	0.005
	Ant. lobe	0.8042	0.25	[-0.24 ; 0.31]	10	0.000	0.024	0.015	0.179	0.184	0.005
	Lobule VI	0.3276	-0.98	[-0.59 ; 0.20]	10	0.002	0.010	0.024	0.046	0.137	0.000
	Crus I	0.3076	-1.02	[-0.91 ; 0.29]	10	0.002	0.007	0.005	0.046	0.118	0.004
	Crus II	0.3616	-0.91	[-0.59 ; 0.21]	10	0.002	0.002	0.034	0.107	0.074	0.004
	Lobule VIIb	0.3627	-0.91	[-0.32 ; 0.12]	10	0.002	0.006	0.017	0.062	0.109	0.011
	Post. Inf. lobe	0.8685	0.17	[-0.51 ; 0.61]	10	0.000	0.016	0.015	0.151	0.215	0.000
	Pval, P-value; tval, t-value; IC., confidence interval; dof, degrees of freedom.
	(diagnosis, sex, site, age, site, ICV and IQ as covariates)

Acknowledgement

This project has received funding from the Innovative Medicines Initiative 2 Joint Undertaking under grant agreement no. 115300 for the project EU-AIMS and no. 777394 for the project AIMS-2-TRIALS. This Joint Undertaking receives support from the European Union's Horizon 2020 research and innovation programme, the European Federation of Pharmaceutical Industries and Associates, Autism Speaks, Autistica, and SFARI. CL is supported by the Bettencourt Schueller Foundation (CCA-INSERM-BETTENCOURT-2018) DLF is supported by funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101025785.

Disclosure

Dr. Tillmann has served as a consultant for Hoffmann-La Roche. Dr. Baron-Cohen has served as an author, consultant, or lecturer for Ability Partner, Clarion Healthcare, Expo Medica, Eli Lilly, GLGroup, Kompetento, Medice, Prima Psychiatry, Prophase, Roche, Shire, and System Analytic; he receives royalties for textbooks and diagnostic tools from Huber/Hogrefe, Kohlhammer, and UTB. Dr. Charman has received research grant support from the Medical Research Council (UK), the National Institute for Health Research, Horizon 2020 and the Innovative Medicines Initiative (European Commission), MQ, Autistica, FP7 (European Commission), the Charles Hawkins Fund, and the Waterloo Foundation; he has served as a consultant for F. Hoffmann-La Roche and Servier; and he has received royalties from Guilford Publications and Sage Publications. Dr. Beckmann is co-founder of SBGneuro. Dr. Buitelaar has served as a consultant, advisory board member, and/or speaker for Angelini, Janssen Cilag BV, Novartis, Medice, Roche, Servier, and Takeda/Shire. Dr. Murphy has received honoraria from Roche and Servier, and he has received grant support from the Medical Research Council (UK), the National Institute for Health Research, and Horizon 2020 and the Innovative Medicines Initiative (European Commission). The other authors report no financial relationships with commercial interests.

Supplementary Materials Supplementary Material 1: MR acquisition protocols

CERES parcellation pipeline [START_REF] Romero | CERES: A new cerebellum lobule segmentation method[END_REF]. This pipeline is freely available online: https://volbrain.upv.es/index.php Suit parcellation and VBM pipeline [START_REF] Allen | Differential effects of developmental cerebellar abnormality on cognitive and motor functions in the cerebellum: an fMRI study of autism[END_REF]. The pipeline can be downloaded online: http://www.diedrichsenlab.org/imaging/suit.htm

Supplementary Material 8: Description of the SUIT pipeline

In the SUIT pipeline, cerebellar structures are automatically isolated from the cerebral cortex based on an anatomical image. This toolbox provides an automated cortical segmentation of the cerebellum, using a probabilistic atlas to assign locations to different cerebellar lobules. We noticed defects in the SUIT pipeline at the isolation step, with non-cerebellar tissues labelled as the cerebellum. This defect has been reported in other studies [START_REF] Moberget | Cerebellar volume and cerebellocerebral structural covariance in schizophrenia: a multisite mega-analysis of 983 patients and 1349 healthy controls[END_REF]. Thus, we created a mask based on the CERES segmentation that isolated the cerebellum more accurately and we used it in the SUIT pipeline. Using the SUIT pipeline, we performed a parcellation analysis and a voxel based morphometry analysis (VBM).

The VBM procedure used was part of the SUIT pipeline (which allows both ROI and VBM analyses). It relies on a normalization to a probabilistic atlas of the cerebellar lobules in the anatomical space. This template preserves the anatomical details of the cerebellum. We performed these analyses in the same sample that we previously analysed in the volumetric analyses (see above). We used a stringent nonparametric 10 000 permutations test (FSL toolbox : https://fsl.fmrib.ox.ac.uk/fsl/fslwiki/Randomise) at a voxel level, in a search space including the total cerebellar grey matter, to assess the effect of diagnosis on cerebellar structures and limit possible false positive results. We conducted linear models, using MRI study site, sex, age, full-scale IQ and intracranial volume as covariates. Ten thousand permutations were performed for each contrast. Only voxels surviving a voxel-wize family-wise error-corrected statistical threshold of p < 0.05 (two tailed, permutation based) were considered significant [START_REF] Moberget | Cerebellar volume and cerebellocerebral structural covariance in schizophrenia: a multisite mega-analysis of 983 patients and 1349 healthy controls[END_REF].

Supplementary Material 9: Quality control procedure and parcellation outcomes

We performed cerebellar with two different methods : CERES and SUIT.

In both cases, all segmentation outcomes were visually inspected by an examiner (CL) with previous experience in cerebellar segmentation and parcellation [START_REF] Laidi | Cerebellar anatomical alterations and attention to eyes in autism[END_REF][START_REF] Laidi | Cerebellar volume in schizophrenia and bipolar I disorder with and without psychotic features[END_REF][START_REF] Laidi | Cerebellar parcellation in schizophrenia and bipolar disorder[END_REF] blind of the diagnosis. To ensure the consistency of parcellation measures with both methods, we studied the correlation between both pipelines (see statistical analysis section) for the anterior lobe, the postero-inferior lobe, Crus I and Crus II region. We studied the grey matter volume of the following regions of interest using both the CERES and the SUIT pipeline: anterior lobe, lobule VI, Crus I, Crus II, lobules VIIb, Lobule VIII and lobules IX-X. We chose these regions of interest based on our previous work [START_REF] Laidi | Cerebellar anatomical alterations and attention to eyes in autism[END_REF][START_REF] Laidi | Cerebellar parcellation in schizophrenia and bipolar disorder[END_REF] ; we did not include in our analyses separately lobules I, II, III, IV and V (anterior lobe) since the volumes are too small to effectively assess visually the quality of the parcellation. In addition, we studied the vermal volume (lobule VI-VII of the vermis, total vermal volume) using the SUIT pipeline, which was not available in the CERES pipeline.

Supplementary Material 10: Assessment of ADHD diagnosis in our cohort

ADHD symptoms were assessed with the DSM-4 ADHD rating scale, covering both inattention and hyper-activity/impulsivity symptoms based on either self-or parent-report. Self-report scores were only used when parent-report scores were unavailable. A categorical variable was computed based on the DSM-4 criteria.

Supplementary Material 11: Normative modeling analysis

Normative modelling has been described in detail elsewhere [START_REF] Marquand | Understanding Heterogeneity in Clinical Cohorts Using Normative Models: Beyond Case-Control Studies[END_REF] and successfully applied to mental disorders and autism in particular [START_REF] Zabihi | Dissecting the Heterogeneous Cortical Anatomy of Autism Spectrum Disorder Using Normative Models[END_REF][START_REF] Wolfers | From pattern classification to stratification: towards conceptualizing the heterogeneity of Autism Spectrum Disorder[END_REF]. Structural T1-weighted images were preprocessed with the SUIT pipeline (see voxel based morphometry section) which is specifically adapted to the [START_REF] Diedrichsen | A probabilistic MR atlas of the human cerebellum[END_REF]. A Gaussian process regression model was trained at each voxel in the control cohort using age, sex, site of inclusion, full scale IQ and intracranial volume as covariates to predict cerebellar grey matter volume. This resulted in a developmental model in the controls. To avoid overfitting, assess generalizability, and determine whether neurotypical individuals fall within the normative range, we used 10-fold cross-validation in neurotypical individuals before retraining the model in the entire sample to make predictions in individuals with autism. We generated normative probability maps, which quantify the deviation of each participant from the normative model for cerebellar gray matter volume at each voxel. These subject-specific Z score images provide a statistical estimate of how much each individual's true volume value differs from the predicted value with reference to the neurotypical pattern at each voxel given the participant's age, sex, and site. Normative probability maps were thresholded at an absolute value of |Z| > 2.6 [START_REF] Scott | A comprehensive volumetric analysis of the cerebellum in children and adolescents with autism spectrum disorder[END_REF][START_REF] Button | Power failure: why small sample size undermines the reliability of neuroscience[END_REF]. We extracted positive and negative deviations for each region of interest (defined with the SUIT atlas) and compared them using non-parametric tests (Mann-Whitney tests) given the non-normal distribution of the deviations. We first conducted the analysis in the whole cerebellum and then in every region of interest of the cerebellum, defined with the SUIT atlas. To evaluate the goodness of fit of our normative model in the neurotypical subjects, we computed a Rho map of the cerebellum showing the correlation between the predicted and the actual values in the cerebellum. In addition, we calculated the symmetric mean square error (SMSE) of our model in the neurotypical subjects.

Supplementary Material 12: Support Vector Machine Methods

Machine learning analyses were performed with support vector machine (SVM), implemented in the python library scikit-learn (https://scikit-learn.org). We tested two different types of features in our machine learning model. First, we selected ROI-based features, based on the CERES parcellation conducted in our previous analyses (see parcellation of cerebellar volume section), in order to introduce anatomical priors in our model. Next, we selected grey matter VBM maps from the SUIT analysis (see voxel based morphometry section).

We regressed out the effect of age, sex, site and full-scale IQ that were considered as confounds in our previous analyses. Thus, the prediction was based on residuals after regression of the confounds.

We evaluated the performance with a double cross-validation (CV) scheme (see de Pierrefeu et al. 2018 (53) for more details). This design was chosen to avoid optimization of the hyperparameter that could overfit the dataset and provide an over-optimistic evaluation of the model. In the outer loop, a set of subjects is considered as the training data, while the remaining data are used as the train data, using a ten-fold cross validation. In the inner loop, the training sets are partitioned into sub-training and validation sets, using a nested five-fold cross validation to set the hyperparameter. The classifier performances were assessed by computing the balanced accuracy, sensitivity and specificity in the test sample.

Supplementary Material 14: Heterogeneity focused analyses

We studied the influence of IQ, sex and age in heterogeneity focused analyses. Because IQ scores are well known to be heterogeneous in autism (with a frequent dissociation between verbal IQ and performance IQ), we studied verbal IQ (VIQ) and performance IQ (PIQ) in addition to full scale IQ (FSIQ).

We reproduced the methods of Bedford et al. 2020 to specifically study in "heterogeneous focused analyses" the importance of sex, age, FSIQ, PIQ and VIQ. We fitted two linear models for each of those 5 variables: To ensure that there was no negative effect of sex, we repeated our main analyses in both males and females separately.

Supplementary Material 16: Matched sample analysis

In our sample, there was difference between patients and controls in sex ratio and full-scale IQ.

To ensure that this difference did not prevent us to found significant findings, we matched ASD and TD sample based on sex, iq and site. We use the pymatch package (https://pypi.org/project/pymatch/) to match patients and controls, based, on sex, age, and full-scale IQ. The result of this matching procedure is reported in Table A.

In this sample, we re-ran our analysis in this matched sample, including ICV and site as covariates. We did not include sex, age, and full-scale IQ as covariate since there was no significant difference in both group. However, adding those covariates did not change our results. Results are reported in


Karlien Dejaeger
email: karlien.dejaeger@ugent.be

Cécile Vignal

Justine Criquet

Marjolein Vanoppen

Emile R Cornelissen

Gabriel Billon

Disinfection by-products in drinking water: Where do they come from and are they safe to drink?

Keywords: Membrane fractionation, Disinfection by-products, Modelling

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.

Introduction

Disinfection of drinking water is a widely used technique to inactivate pathogens. However, harmful disinfection by-products (DBPs) are formed due to the reaction with natural organic matter (NOM) [START_REF] Pals | Human Cell Toxicogenomic Analysis Linking Reactive Oxygen Species to the Toxicity of Monohaloacetic Acid Drinking Water Disinfection Byproducts[END_REF]. Unregulated DBPs, such as haloacetamides (HAcAms), are found in lower concentrations compared to the regulated trihalomethanes and haloacetic acids (HAAs), but it is suggested that their toxicity is much higher [START_REF] Richardson | Occurrence, genotoxicity, and carcinogenicity of regulated and emerging disinfection byproducts in drinking water: A review and roadmap for research[END_REF].

Research with Chinese Hamster Ovary (CHO) cells showed that iodoacetamide has 2 times higher cytotoxicity than iodoacetic acid [START_REF] Wagner | CHO cell cytotoxicity and genotoxicity analyses of disinfection by-products: An updated review[END_REF]. However, limited studies conducted on human cell lines (colonic epithelial cells, CCD 841 CoN) showed that iodoacetic acid is 4 times more cytotoxic than iodoacetamide [START_REF] Sayess | Comparative Cytotoxicity of Six Iodinated Disinfection Byproducts on Nontransformed Epithelial Human Colon Cells[END_REF].

To identify the precursors that are responsible for the formation of these by-products from the complex NOM mixture, the latter is split into smaller fractions with similar chemical or physical properties. Dead-end ultrafiltration membrane fractionation is the most commonly used technique to split NOM by size, but is unable to produce sharply separated fractions [START_REF] Assemi | Characterization of natural organic matter fractions separated by ultrafiltration using flow field-flow fractionation[END_REF]. This research will therefore, (i) seek for a new membrane fractionation method to split NOM into biopolymers (BP), humic substances (HS) and low molecular weight compounds (LMW) to identify DBP precursors after chlorination and (ii) couple this information to the toxicity of HAAs and HAcAms on human intestinal epithelial cells (Caco-2).

Material and Methods

During fractionation, a nano-and ultrafiltration membrane in crossflow is used where both a normal filtration step (step 1) and a diafiltration step (step 2) is executed to ensure a good separation between the three fractions. So far, a model has been constructed that predicts the concentration change for a certain compound during these two steps and was validated with a nanofiltration for different ions in a synthetic ion matrix (Dow NF270). containing increasing concentrations of either chloroacetamide (Cl-AcAm), bromoacetamide (Br-AcAm), iodoacetamide (I-AcAm), dichloroacetamide (Cl 2 -AcAm), trichloroacetamide (Cl 3 -AcAm), chloroacetic acid (Cl-AA), bromoacetic acid (Br-AA) or iodoacetic acid (I-AA) for 24h, 48h and 72h. 10 µL of 5 mg/mL MTT (3-[4,5-dimethyl thiazol-2-yl]-2,5-diphenyl tetrazolium bromide) stock solution was added at the end of the stimulation period. The MTT is reduced by metabolic active cells and converted into formazan crystals. These crystals were dissolved with 100 µL DMSO and absorbance was measured at 570 nm. values compared to the HAAs, similar to the conclusions drawn from CHO cells. However, the IC 50 values found in this study were generally higher than the ones reported for CHO [START_REF] Wagner | CHO cell cytotoxicity and genotoxicity analyses of disinfection by-products: An updated review[END_REF]. Furthermore, the toxicity within one family increases when changing the halogen from Cl to Br to I, except for Cl 2 -AcAm and Cl 3 -AcAm (IC 50 = 15 000 -40 000 µM). To conclude, the unregulated HAcAms appear to be more cytotoxic than the regulated HAAs. Therefore, it is important to identify their precursors through the membrane fractions, and remove them if needed, to control the HAcAm concentrations in drinking water.

Results and Conclusions

Figure 1 . 1 .

 11 Figure 1.1. clearly shows that the model predicts the experimental data very well. The model is ready to be validated for the membrane fractionation process of organic matter.

Figure 1 . 1 .:

 11 Figure 1.1.: Concentration change of chloride, magnesium, sodium and sulphate during normal filtration (step 1 (a,b)) and diafiltration (step 2 (c,d)). Full lines represent experimental data, dashed lines represent predicted data.

Figure 1 . 2 .

 12 Figure 1.2.shows the half maximal inhibitory concentration (IC 50 ) deduced from the dose-response curves (r² > 0.75) for HAcAms and HAAs. HAcAms have overall lower IC 50 values compared to the HAAs, similar to the conclusions drawn from CHO cells. However, the IC 50 values found in this study were generally higher than the ones reported for CHO[START_REF] Wagner | CHO cell cytotoxicity and genotoxicity analyses of disinfection by-products: An updated review[END_REF]. Furthermore, the toxicity within one family increases when changing the halogen from Cl to Br to I, except for Cl 2 -AcAm and Cl 3 -AcAm (IC 50 = 15 000 -40 000 µM).

Figure 1 . 2 :

 12 Figure 1.2: IC 50 values (µM) determined after 24h, 48h and 72h for, (a) chloro-(Cl-AcAm), bromo-(Br-AcAm), iodo-(I-AcAm), dichloro-(Cl 2 -AcAm), trichloroacetamide (Cl 3 -AcAm) and, (b) chloro-(Cl-AA), bromo-(Br-AA) and iodoacetic acid (I-AA). Error bars represent the 95% confidence interval.


Karlien Dejaeger

Justine Criquet

Marjolein Vanoppen

Cécile Vignal

Gabriel Billon

Emile R Cornelissen

Disinfection by-products in drinking water -Precursor identification and hazard assessment

Problem statement

Disinfection by-products in drinking water Precursor identification and hazard assessment Karlien Dejaeger, Justine Criquet, Marjolein Vanoppen, Cécile Vignal, Gabriel Billon and Emile R. Cornelissen Corresponding author: karlien.dejaeger@ugent.be / karlien.dejaeger@univ-lille.fr

Disinfection by-products (DBPs)?

• Formed during the reaction of chlorine with natural organic matter

• > 700 different compounds identified