Pierrick Coupé
email: pierrick.coupe@u-bordeaux.fr

Gwenaelle Catheline

Enrique Lanuza

José Vicente Manjón

Towards a unified analysis of brain maturation and aging across the entire lifespan: A MRI analysis

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

Introduction

Brain development and aging are key topics in neuroscience. The study of normal brain maturation and age-related brain atrophy is crucial to better understand normal brain development and a large variety of neurological disorders. With the rise of the population age, it is becoming increasingly important to understand the cognitive changes that accompany aging, both normal and pathologic. Moreover, analyzing brain maturation and senescence during the entire lifespan may help to better understand the undergoing process on normal brain development and aging.

Despite the large number of studies dedicated to brain trajectory analysis over the last decades, an important disagreement remains between existing results [START_REF] Walhovd | Consistent neuroanatomical age-related volume differences across multiple samples[END_REF][START_REF] Walhovd | Through Thick and Thin: a Need to Reconcile Contradictory Results on Trajectories in Human Cortical Development[END_REF]. Some studies described early life increase of gray matter (GM) volumes followed by a decrease [START_REF] Giedd | Brain development during childhood and adolescence: a longitudinal MRI study[END_REF][START_REF] Lenroot | Sexual dimorphism of brain developmental trajectories during childhood and adolescence[END_REF][START_REF] Raznahan | How does your cortex grow?[END_REF]) while other works described GM decrease all along the lifespan [START_REF] Ostby | Heterogeneity in subcortical brain development: A structural magnetic resonance imaging study of brain maturation from 8 to 30 years[END_REF][START_REF] Development Cooperative | Total and regional brain volumes in a population-based normative sample from 4 to 18 years: the NIH MRI Study of Normal Brain Development[END_REF][START_REF] Aubert-Broche | A new method for structural volume analysis of longitudinal brain MRI data and its application in studying the growth trajectories of anatomical brain structures in childhood[END_REF][START_REF] Ducharme | Trajectories of cortical thickness maturation in normal brain development--The importance of quality control procedures[END_REF][START_REF] Mills | Structural brain development between childhood and adulthood: Convergence across four longitudinal samples[END_REF]). An extensive review of these inconstancies can be found in [START_REF] Walhovd | Through Thick and Thin: a Need to Reconcile Contradictory Results on Trajectories in Human Cortical Development[END_REF]. For white matter (WM) the picture is inverted, with a consensus for the early life period characterized by an increase. However, less consistent effect of age in adulthood has been reported [START_REF] Jernigan | Postnatal brain development: structural imaging of dynamic neurodevelopmental processes[END_REF][START_REF] Fjell | What is normal in normal aging? Effects of aging, amyloid and Alzheimer's disease on the cerebral cortex and the hippocampus[END_REF]. In addition, time of brain maturation is also different according to the studies [START_REF] Groeschel | Developmental changes in cerebral grey and white matter volume from infancy to adulthood[END_REF][START_REF] Hedman | Human brain changes across the life span: a review of 56 longitudinal magnetic resonance imaging studies[END_REF]. Discrepancies also exist for the shape of trajectories for cortical and subcortical structures, sometimes described as linear, Ushaped (curvilinear) or as more complex polynomial curves. Finally, sometimes sexual dimorphism is described in these studies and sometimes no gender difference is observed [START_REF] Giedd | Brain development during childhood and adolescence: a longitudinal MRI study[END_REF][START_REF] Suzuki | Male-specific volume expansion of the human hippocampus during adolescence[END_REF][START_REF] Lenroot | Sexual dimorphism of brain developmental trajectories during childhood and adolescence[END_REF][START_REF] Lenroot | Sex differences in the adolescent brain[END_REF]. The lack of consensus on brain development and aging prevents us to better understand these highly complex and multi-factor phenomena. The significant divergence between existing results is due to many factors.

First, the use of restricted life periods (e.g., childhood [START_REF] Development Cooperative | Total and regional brain volumes in a population-based normative sample from 4 to 18 years: the NIH MRI Study of Normal Brain Development[END_REF], adolescence (Lenroot andGiedd 2010, Vijayakumar, Allen et al. 2016), adulthood [START_REF] Ziegler | Brain structural trajectories over the adult lifespan[END_REF], etc.) makes difficult the comparison of results, and tends to favor simple models capturing only brain growth or aging. Thus, it prevents global understanding of brain modification across the entire lifespan. Up to now, no study covered the entire lifespan including babies from few months of life to elderly older than 90.

Second, the use of a limited number of scans for certain age range (especially at childhood) may produce unstable results limiting the reproducibility and accuracy of estimations. The large majority of previous studies used less than 100 subjects [START_REF] Walhovd | Consistent neuroanatomical age-related volume differences across multiple samples[END_REF], some studies used several hundreds of subjects [START_REF] Giedd | Structural MRI of pediatric brain development: what have we learned and where are we going?[END_REF][START_REF] Development Cooperative | Total and regional brain volumes in a population-based normative sample from 4 to 18 years: the NIH MRI Study of Normal Brain Development[END_REF][START_REF] Ziegler | Brain structural trajectories over the adult lifespan[END_REF][START_REF] Mills | Structural brain development between childhood and adulthood: Convergence across four longitudinal samples[END_REF] and very few studies used more than 1000 subjects [START_REF] Fjell | Critical ages in the life course of the adult brain: nonlinear subcortical aging[END_REF][START_REF] Potvin | Normative data for subcortical regional volumes over the lifetime of the adult human brain[END_REF].

In addition, the use of non-harmonized acquisition protocols, segmentation tools, labelling protocols [START_REF] Walhovd | Through Thick and Thin: a Need to Reconcile Contradictory Results on Trajectories in Human Cortical Development[END_REF] and volumetric measurements such as absolute volume (Brain Development Cooperative 2012), normalized volumes using intracranial volume [START_REF] Good | A voxel-based morphometric study of ageing in 465 normal adult human brains[END_REF][START_REF] Mills | Structural brain development between childhood and adulthood: Convergence across four longitudinal samples[END_REF], GM volume [START_REF] Ziegler | Brain structural trajectories over the adult lifespan[END_REF] or z-scores [START_REF] Ostby | Heterogeneity in subcortical brain development: A structural magnetic resonance imaging study of brain maturation from 8 to 30 years[END_REF][START_REF] Walhovd | Consistent neuroanatomical age-related volume differences across multiple samples[END_REF], lead to a great discrepancy in reported results [START_REF] Walhovd | Consistent neuroanatomical age-related volume differences across multiple samples[END_REF]. Moreover, some studies are based on crosssectional data while others on longitudinal ones. Consequently, this heterogeneity makes difficult the definition of normative values [START_REF] Potvin | Normative data for subcortical regional volumes over the lifetime of the adult human brain[END_REF] stressing the need of using harmonized protocols over large samples covering the entire lifespan.

Finally, the use of an exigent quality control in the whole measurement process plays a major role in the quality of the final estimated brain models. This step is often not considered enough, while the model estimation greatly depends on a careful quality control [START_REF] Ducharme | Trajectories of cortical thickness maturation in normal brain development--The importance of quality control procedures[END_REF]).

Therefore, one of the most important challenges in neuroscience is to provide a consensual and unified vision of brain maturation and aging. In this study, we have addressed the previously mentioned limiting factors. First, thanks to the new paradigm of BigData sharing in neuroimaging [START_REF] Poldrack | Making big data open: data sharing in neuroimaging[END_REF], we have been able to use a very high number of samples (N=3296) covering the largest lifespan period never studied (from few months to advanced age). Moreover, all the considered MRI scans obtained from several freely available databases were processed using the same advanced MRI processing pipeline [START_REF] Manjon | volBrain: An Online MRI Brain Volumetry System[END_REF]. Thanks to the last advances in image processing, images from different age ranges can be analyzed with the same tool. To get insight on brain maturation and aging at global (i.e., absolute volume) and brain scale (i.e., normalized volume), we have extensively analyzed our results using absolute volumes and relative volumes (normalized by Total Intracranial Volume, TIV). Moreover, to prevent the estimated models to be affected by wrongly processed images [START_REF] Ducharme | Trajectories of cortical thickness maturation in normal brain development--The importance of quality control procedures[END_REF], we have used a demanding three stages quality control process. Finally, to be able to present a unified analysis of brain development and brain aging at the same time we considered hybrid models. Contrary to previous studies based on linear or low order polynomial models, we considered models enable to capture fast growth and complex degenerative processes. This is achieved by combining cumulative exponential function to model rapid growth with saturation resulting from maturation and low order polynomial function to model volume decrease caused by aging.

By putting all these elements together, we are able to show for the first time a global picture of brain trajectory across the entire lifespan. Our results suggest that most of the previous marked disagreements can be explained by the proposed analysis. Previous divergences seem mainly to result from restricted investigations over short periods of the entire life history. Indeed, as shown in the following, the analysis of subjects bellow 8 years of age is important to detect the maturation peak. Similarly, the analysis of subjects older than 80 years is necessary to observe the accelerated atrophy occurring at this age. We hope that the proposed unified analysis will help to reach a consensus on normal brain trajectory.

Material and Methods

Datasets

In this study, we used 3D T1-weight MRI obtained from nine freely available databases covering the entire lifespan. All the considered subjects are normal controls. The summary of used databases is detailed in Table 1 while details are provided latter in this section. The used images have been acquired on 1.5T and 3T over 103 sites. After quality control, 2944 MRI were kept from the 3296 considered subjects. The gender proportion of these selected subjects is 47% of female. The covered age starts from 9 months to 94 years, with an average age of 39.65 year and a standard deviation of 26.62.

Figure 1 shows the age distribution of the used subjects after quality. At least three different datasets are used for all the considered periods except for extreme ages (i.e., [0][1][2][3][4] year and [90-94] year) where only 2 datasets are available. Moreover, more than 50 subjects by 5-years interval are used at the exception of the last [90][91][92][93][94] interval. In the following, more details about the different datasets used in this study are presented.

• C-MIND (N=266, after QC N=236): The images from the C-MIND dataset (https://research.cchmc.org/c-mind/) used in this study consist of 266 control subjects. All the images were acquired at the same site on a 3T scanner. The MRI are 3D T1-weighted MPRAGE high-resolution anatomical scan of the entire brain with spatial resolution of 1 mm 3 acquired using a 32 channel SENSE headcoil.

Image processing

All the images were processed with volBrain online software pipeline (http://volbrain.upv.es). The volBrain system is a fully open access academic platform that we have developed during the last 5 years. This web-based platform offers to freely share our computational resources and our last image processing methods to all researchers over the world. Therefore, we used volBrain in this study since we perfectly know the software, the generated reports facilitate a fast first stage QC and we recently demonstrated its robustness and accuracy [START_REF] Manjon | volBrain: An Online MRI Brain Volumetry System[END_REF]. Recently, volBrain pipeline was compared with two well-known tools used on MR brain analysis (FSL and Freesurfer) showing significant improvements in terms of both accuracy and reproducibility for intra and inter-scanner scan rescan acquisition [START_REF] Manjon | volBrain: An Online MRI Brain Volumetry System[END_REF]. Moreover, we knew that the system was able to process large dataset since volBrain provides automatic brain volumetry in less than 15 minutes (including the generation of a pdf volumetry report summarizing the volumetric results). Since its deployment (2 years ago) volBrain has processed online more than 37.000 brains for more than 1200 users.

The volBrain pipeline consists of a set of steps aimed to improve the quality of the MR images to analyze and to locate them in a common geometric and intensity space prior to perform segmentation at several anatomical levels [START_REF] Manjon | volBrain: An Online MRI Brain Volumetry System[END_REF]. In more details, volBrain pipeline includes the following preprocessing steps: 1) denoising using spatially adaptive non-local means [START_REF] Manjon | Adaptive non-local means denoising of MR images with spatially varying noise levels[END_REF], 2) rough inhomogeneity correction using N4 method [START_REF] Tustison | N4ITK: improved N3 bias correction[END_REF], 3) affine registration to MNI152 space using ANTS software [START_REF] Avants | A reproducible evaluation of ANTs similarity metric performance in brain image registration[END_REF], 4) SPM based fine inhomogeneity correction [START_REF] Ashburner | Unified segmentation[END_REF] and 5) histogram based intensity standardization. After the preprocessing, the intracranial cavity is segmented using NICE method [START_REF] Manjon | Nonlocal intracranial cavity extraction[END_REF], tissue classification is performed using TMS method [START_REF] Manjón | Improved estimates of partial volume coefficients from noisy brain MRI using spatial context[END_REF]) and finally subcortical structures are estimated using an extended version of the non-local label fusion method [START_REF] Coupe | Patch-based segmentation using expert priors: application to hippocampus and ventricle segmentation[END_REF]. All the segmentation methods of volBrain use a library of 50 experts manually labelled cases (covering almost the whole lifespan) needed to perform the labeling process at different levels. More details can be found in [START_REF] Manjon | volBrain: An Online MRI Brain Volumetry System[END_REF].

Statistical Analysis

The statistical analysis was performed with Matlabã software. In order to determine the best general models for each structure, several models were tested from the simplest to the most complex on all the dataset (i.e., female and male at the same time). A model is kept as a potential candidate only when F-statistic based on ANOVA for model vs. constant model is significant (p<0.05) and when all its coefficients are significant using t-statistic (p<0.05). At the end of the selection procedure, we used the Bayesian Information Criterion (BIC) to select the best model among models being significant compared to constant model and having all coefficients significant. BIC provides a measure of the trade-off between bias and variance and thus select the model explaining most the data with minimum parameters. Afterwards, this general model type is applied on female and male separately to estimate gender specific models. At the end, to study trajectory difference in terms of volume and shape between both female and male, 𝛽 " 𝑆𝑒𝑥 + 𝛽 ( 𝑆𝑒𝑥. 𝐴𝑔𝑒 interactions are tested over the selected general model. All the reported parameters (t-statistic, F-statistic, BIC and R 2 ) were internally estimated by Matlabã using default parameters. The following models were considered as potential candidates:

1. Linear model In the literature, structure trajectories have been mainly modeled using low order polynomial function (see [START_REF] Walhovd | Consistent neuroanatomical age-related volume differences across multiple samples[END_REF]) for review). However, to follow structure trajectories across the entire lifespan, we propose to consider hybrid models able to track rapid growth during childhood and to capture complex volume decrease from adulthood to elderly. In the past, fast growth modelling occurring during childhood has been achieved using Poisson curve [START_REF] Lebel | Diffusion tensor imaging of white matter tract evolution over the lifespan[END_REF] or Gompertz-like function [START_REF] Makropoulos | Regional growth and atlasing of the developing human brain[END_REF]. Here, we propose to combine a cumulative exponential function in place of Gompertz-like function, and to combine it with low order polynomial function. At the end, our hybrid models can model fast growth process and complex volume decreases at the same time.

𝑉𝑜𝑙 = 𝛽 0 + 𝛽 1 𝐴𝑔𝑒 + 𝜀 2. Quadratic model 𝑉𝑜𝑙 = 𝛽 0 + 𝛽 1 𝐴𝑔𝑒 + 𝛽 3 𝐴𝑔𝑒 3 + 𝜀 3. Cubic model 𝑉𝑜𝑙 = 𝛽 0 + 𝛽 1 𝐴𝑔𝑒 + 𝛽 3 𝐴𝑔𝑒 3 + 𝛽 4 𝐴𝑔𝑒 4 + 𝜀

Quality Control

As recently shown, the quality control (QC) of image processing pipeline has a critical impact on trajectory results [START_REF] Ducharme | Trajectories of cortical thickness maturation in normal brain development--The importance of quality control procedures[END_REF]. Therefore, in this study we decided to use a demanding multi-stage QC procedure for a careful selection of the involved subjects. First, a visual assessment of input image quality was done for all considered subjects. This assessment was performed by checking screen shots of one sagittal, one coronal and one axial slice in middle of the 3D volume. This step led to remove 219 subjects from the 3296 considered subjects in our study (6.6%). Next, a visual assessment of the image processing quality for all remaining subjects was performed using volBrain reports (see an example of report here: http://volbrain.upv.es/example_report.pdf ). This report provides screenshots of one sagittal, one coronal and one axial slice at middle of the 3D volume for each step of the processing pipeline. All these steps (full head coverage including cerebellum, registration to MNI space, TIV extraction, tissue classification, subcortical structure segmentation, etc.) were carefully checked. This step led to remove 83 subjects from our study (2.5%). Finally, a last control was performed by individually checking all outliers detected using estimated trajectories. A volume was considered as outlier when its value was higher/lower than 2 standard deviations of the estimated model.

For each detected outlier, the segmentation map was opened and displayed over the MRI using a 3D viewer [START_REF] Yushkevich | User-guided 3D active contour segmentation of anatomical structures: significantly improved efficiency and reliability[END_REF]. A careful inspection was performed over the 3D volume. In case of segmentation failure, the subject was removed from the study. This last QC step led to remove 50 subjects (1.5%). Therefore, 2944 of the 3296 considered subjects were kept after our QC procedure.

Results

Maturation and aging of brain tissues

Global gray matter and white matter trajectories

At the global scale (i.e., absolute volumes), we observe an increase of WM volume until 30-40y followed by a volume decrease (see Fig. 2). As it can be noticed, the WM growth at early ages is faster than the senescence at late ages. This is assessed by the selected hybrid model (p<0.001) combining an exponential cumulative distribution model for growth and a cubic model for aging (see Tab. 2). On the other hand, although the same model is selected for GM (p<0.0001), its trajectory is more complex. We can observe a 4-stage trajectory composed of a fast growth until 8-10y followed by a fast decrease until 40ys, then a plateau and finally an accelerated aging-related decrease is visible around 80ys. At the brain scale, when using normalized volumes in % to the TIV (see Supplementary Figure 1), the main difference is found for the GM trajectory. Indeed, at this scale, we observe a decrease of GM all along the lifespan (see Fig. 3) following a cubic model (p<0.0001) (see Tab. 3). The decrease of normalized volumes also follows a complex shape with 3 stages composed of a rapid decrease from 0 to 20y, a plateau from 40 to 80y and a rapid decrease after 80y. It is interesting to note that despite the normalization, the WM growth remains very fast at the brain scale for early age with a hybrid model using an exponential cumulative distribution model for growth. Finally, at global and brain scales, we observe that WM have almost an inverted U-shape model although an asymmetry exists with a faster volume increase related to maturation than volume decrease caused by aging.

Cortical and subcortical gray matter trajectories

To study trajectory differences between cortical and deep gray matter, we performed complementary analyses (see supplementary Tab. 1). First, we estimated the deep GM volume by adding the GM volume of the considered deep structures (i.e., caudate, thalamus, accumbens, globus pallidus, putamen, hippocampus and amygdala). The cortical GM was estimated as the global GM volume (as used in the paper) minus the deep GM volume. Figure 4 shows the estimated trajectories using absolute volume and normalized volume in % of TIV. At the global scale, we can observe that after their maturation peaks, deep and cortical GM volume decreases. However, deep GM volume decreases with almost a constant rate while cortical GM volume follows a more complex trajectory similar to the 4-stage pattern already described for global GM. Similarly, at the brain scale, while the cortical GM follows the 3 stages detailed for global GM, the deep GM follows an almost linear decrease all along the lifespan with an accelerated atrophy after 80y.

Cerebrum and cerebellum trajectories

Finally, we investigated cerebrum and cerebellum trajectories separately. At global scale, selected models for cerebrum and cerebellum are the same and they are similar to the models selected for global GM and WM (see supplementary Tab. 2 and Tab. 3). Moreover, gender differences were found for cerebrum and cerebellum when using absolute volumes. Visually, both structures follow similar trajectories (see Fig. 5 and Fig. 6). However, some differences can be observed. First, the cerebellum has a shorter GM volume decrease after maturation peak. In addition, the magnitude of GM and WM increase during maturation is smaller for the cerebellum than for cerebrum. Finally, the cerebellum has a less pronounced WM decrease after 80y and has a reduced atrophy rate over this period. At the brain scale, selected models are different between cerebrum WM and cerebellum WM. The hybrid model selected for WM cerebrum indicates a faster volume increase for this structure compared to WM cerebellum. The faster maturation during childhood of WM cerebrum is also visible on Figure 5 and Figure 6. The 3-stage trajectory obtained for global GM is observed for cerebellum GM and cerebrum GM. However, the plateau occurring at adulthood appears earlier for cerebellum than for cerebrum. Finally, the atrophy rate of normalized cerebrum volume is faster than cerebellum one.

Deep gray matter structure trajectories

Thalamus, accumbens, caudate, putamen and globus pallidus trajectories

At global scale, we observe that thalamus, accumbens, caudate and putamen follow similar trajectories with fast growth until 10-12y followed by a volume decrease. All selected hybrid models combine an exponential cumulative distribution for growth followed by low polynomial order for volume loss during aging, cubic for caudate (p<0.0001) and putamen (p<0.0001), quadratic for thalamus (p<0.0001) and linear for accumbens (p<0.0001) (see Tab. 2). On the other hand, globus pallidus volume decreases from birth all along lifespan (quadratic model with p<0.0001). Unexpected slight increases of caudate and putamen volumes are visible after 80y. At the brain scale, we can see that thalamus, accumbens, caudate, putamen and globus pallidus show a volume decrease across the entire lifespan. First, thalamus and accumbens exhibit almost monotonous decrease although cubic models have been selected (both with p<0.0001). Second, caudate and putamen present similar slowdown decreases after 50y. The similar trajectories of the caudate and putamen are consistent with their shared nature as dorsal striatal structures [START_REF] Paxinos | The human nervous system[END_REF]). The model selected for these structures is cubic for caudate (p<0.0001) and quadratic for putamen (p<0.0001) (see Tab. 3). Finally, globus pallidus follows a cubic model (p<0.0001) showing a fast decrease between 1y-30y, followed by a plateau between 30y and 80y and then by an accelerated atrophy after 80y.

Amygdala and hippocampus trajectories

At the global scale, amygdala volume shows a slight increase until 18y-20y followed by a long plateau that ends around 70y, followed by an age-related atrophy. The selected hybrid model combines a volume increase following an exponential cumulative distribution and a volume decrease following cubic model (p<0.0001).

The hippocampus trajectory presents a fast volume increase until 8y-10y followed by a slow volume increase until 40y-50y before an atrophic period. Here, the selected hybrid model mixes a volume increase following an exponential cumulative distribution and then an inverted U-shape volume decrease (p<0.0001). At the brain scale, amygdala volume trajectory follows a cubic model (p<0.0001) with a plateau until 70y followed by an atrophy. This result seems to indicate that absolute increase of amygdala volume during childhood is mainly related to brain growth. Moreover, using relative volume, hippocampus exhibit a very specific inverted U-shape trajectory compared to other analyzed subcortical structures. In our study, the hippocampus is the only structure showing volume increase until the middle period of human life. To better investigate this point, we performed a complementary analysis between 18y and 70y. We found that the impact of age on absolute HC volume is significant (p<0.0001) and that the selected model is an inverted U-shape trajectory over this restricted period. According to our results, the hippocampal maturation stops around 50y.

Sexual dimorphism

At the global scale, we observe that males have bigger volumes than females for all considered structures (sex interaction with p<0.0001, see Tab. 2) with the exception of accumbens. Finally, increased atrophy rates for males after 80y is assessed by CSF trajectory, which is the only brain compartment showing significant age*sex (p<0.0001) over the entire lifespan using the considered model. At the brain scale, almost all gender volume differences vanish, except in favor of females for caudate (p=0.05) and thalamus (p=0.05) with marginal significance, and for accumbens (p=0.02) (see Tab. 3). Visually, we can observe bigger relative volume for female hippocampus almost significant (p=0.07) (see Tab. 3 and Fig. 3). Finally, for global GM, caudate, thalamus, globus pallidus and amygdala, trajectories of females seem to indicate a better resistance to the accelerated age-related atrophy occurring after 80y. To investigate this point, we studied sex and sex*age interaction using all subjects with age > 70 years (i.e., 637 subjects composed of 292 males and 345 females). Models estimated using all the subjects (see Tab. 2) are applied over this considered restricted period to evaluate sex and sex*age interactions. We found that using normalized volumes, almost all studied structures show significant sex and sex*age interaction after 70y with the exception of WM and amygdala (see Tab. 4).

Discussion

One of the main questions related to brain tissue properties deals with gray and white matter development/maturation and age-related gray and white matter atrophy.

Knowing when brain tissues stop to mature and when they start to degenerate are key questions in neurology [START_REF] Sowell | Mapping cortical change across the human life span[END_REF]). In the past, both questions have been mainly treated separately in the literature, preventing us to get a global picture of these join phenomena. Moreover, discrepancies between used volumetric measurements (absolute or relative) made difficult to reach a consensus on crucial questions about synaptogenesis and synaptic pruning or myelination and aging.

Towards a consensus?

Marked discrepancies exist in the literature about the best fitting models to describe brain trajectories either in pediatric phase [START_REF] Ducharme | Trajectories of cortical thickness maturation in normal brain development--The importance of quality control procedures[END_REF] or adulthood [START_REF] Fjell | Critical ages in the life course of the adult brain: nonlinear subcortical aging[END_REF]). In our study, hybrid models mixing exponential cumulative distribution growth with low order polynomial senescence were selected for 8/10 of the investigated brain regions when absolute volumes are used. Moreover, the absolute global GM volume follows a complex trajectory with 4 phases: 1) rapid increase from 0 to 8-10y, 2) rapid decrease until 40, 3) a plateau from 40-80y and 4) a rapid decrease after 80y. On the other hand, low order polynomial models better fit when volumes normalized by TIV are used, except for WM (see Tab. 2 and Tab. 3). When global growth effect is corrected, normalized global GM volumes decrease all over lifespan and follow a complex shape with 3 phases: 1) a rapid decrease from 0 to 20y, 2) a plateau from 40 to 80y and 3) a rapid decrease after 80y. This decline of the normalized global GM volume is consistent with the well-known fact that most of the neurogenesis is a prenatal phenomenon [START_REF] Stiles | The basics of brain development[END_REF]. In contrast, WM presents a shape close to the usually described inverted U-shape [START_REF] Walhovd | Consistent neuroanatomical age-related volume differences across multiple samples[END_REF]) that persists after controlling for head size. This result indicates that during the early phase of brain development WM expansion exceeds general growth. The fast simultaneous WM maturation and GM decrease at brain scale from childhood to adolescence are consistent with brain myelination period and cortical thinning process previously observed ex-vivo [START_REF] Huttenlocher | Regional differences in synaptogenesis in human cerebral cortex[END_REF]. When considering cortical GM and deep GM separately, they exhibit a different pattern at both global and brain scales. At brain scale, deep GM shows almost a linear decrease while cortical GM trajectory follows the 3 identified stages for the global GM (see Fig. 4). The steeper decrease of normalized volume for cortical GM in the 0-20y period (compared to the almost linear dynamics of the deep GM) is probably due to the very high pruning rate of the exuberant connectivity generated in the cerebral cortex [START_REF] Stiles | The basics of brain development[END_REF] or is due to myelination of nearby subcortical WM fibers [START_REF] Jernigan | Postnatal brain development: structural imaging of dynamic neurodevelopmental processes[END_REF].

One of the most marked discrepancy in the literature is about the cortical GM trajectory over childhood [START_REF] Walhovd | Through Thick and Thin: a Need to Reconcile Contradictory Results on Trajectories in Human Cortical Development[END_REF]. First studies reported an increase with maturation peak in early school age [START_REF] Giedd | Brain development during childhood and adolescence: a longitudinal MRI study[END_REF][START_REF] Lenroot | Sexual dimorphism of brain developmental trajectories during childhood and adolescence[END_REF][START_REF] Raznahan | How does your cortex grow?[END_REF]). However, mainly monotonic decrease from early childhood have been recently published [START_REF] Ostby | Heterogeneity in subcortical brain development: A structural magnetic resonance imaging study of brain maturation from 8 to 30 years[END_REF][START_REF] Development Cooperative | Total and regional brain volumes in a population-based normative sample from 4 to 18 years: the NIH MRI Study of Normal Brain Development[END_REF][START_REF] Aubert-Broche | A new method for structural volume analysis of longitudinal brain MRI data and its application in studying the growth trajectories of anatomical brain structures in childhood[END_REF][START_REF] Ducharme | Trajectories of cortical thickness maturation in normal brain development--The importance of quality control procedures[END_REF][START_REF] Mills | Structural brain development between childhood and adulthood: Convergence across four longitudinal samples[END_REF]. The first factor that could explain this pronounced divergence is the used volume measurement. In this study, we showed that absolute GM volume follows a 4-stage trajectory with a maturation peak while normalized GM volume follows a 3-stage trajectory exhibiting a decrease all along the lifespan. Therefore, our results are in line with [START_REF] Giedd | Brain development during childhood and adolescence: a longitudinal MRI study[END_REF][START_REF] Shaw | Neurodevelopmental trajectories of the human cerebral cortex[END_REF][START_REF] Groeschel | Developmental changes in cerebral grey and white matter volume from infancy to adulthood[END_REF][START_REF] Raznahan | How does your cortex grow?[END_REF]) using absolute measurement and are consistent with [START_REF] Ostby | Heterogeneity in subcortical brain development: A structural magnetic resonance imaging study of brain maturation from 8 to 30 years[END_REF][START_REF] Mills | Structural brain development between childhood and adulthood: Convergence across four longitudinal samples[END_REF]) using normalized measurement. However, several studies reported monotonic decrease using absolute cortical GM volume over childhood [START_REF] Sowell | Mapping cortical change across the human life span[END_REF][START_REF] Development Cooperative | Total and regional brain volumes in a population-based normative sample from 4 to 18 years: the NIH MRI Study of Normal Brain Development[END_REF][START_REF] Aubert-Broche | A new method for structural volume analysis of longitudinal brain MRI data and its application in studying the growth trajectories of anatomical brain structures in childhood[END_REF][START_REF] Ducharme | Trajectories of cortical thickness maturation in normal brain development--The importance of quality control procedures[END_REF][START_REF] Mills | Structural brain development between childhood and adulthood: Convergence across four longitudinal samples[END_REF][START_REF] Walhovd | Through Thick and Thin: a Need to Reconcile Contradictory Results on Trajectories in Human Cortical Development[END_REF]). This result is in contradiction with studies dedicated to newborn period that report an increase of absolute GM over the first months of life [START_REF] Groeschel | Developmental changes in cerebral grey and white matter volume from infancy to adulthood[END_REF][START_REF] Holland | Structural growth trajectories and rates of change in the first 3 months of infant brain development[END_REF][START_REF] Makropoulos | Regional growth and atlasing of the developing human brain[END_REF]). The fact that several studies did not detect GM maturation peak using absolute measurements seems to be related to two main factors, the lack of subjects younger than 5y and the use of low order polynomial models. Indeed, most of the studies presenting monotonic decrease did not include subjects younger than 4y making difficult the detection of GM volume increase over the first years of life. Moreover, this implies that the model fitting was mainly driven by subjects with already mature brains [START_REF] Sowell | Mapping cortical change across the human life span[END_REF][START_REF] Development Cooperative | Total and regional brain volumes in a population-based normative sample from 4 to 18 years: the NIH MRI Study of Normal Brain Development[END_REF][START_REF] Aubert-Broche | A new method for structural volume analysis of longitudinal brain MRI data and its application in studying the growth trajectories of anatomical brain structures in childhood[END_REF][START_REF] Ducharme | Trajectories of cortical thickness maturation in normal brain development--The importance of quality control procedures[END_REF][START_REF] Mills | Structural brain development between childhood and adulthood: Convergence across four longitudinal samples[END_REF][START_REF] Walhovd | Through Thick and Thin: a Need to Reconcile Contradictory Results on Trajectories in Human Cortical Development[END_REF]. In addition to this potential issue on the used age range, most of these studies were using linear, quadratic or cubic models. Low order polynomial models are not well-designed to capture complex shape such as fast growth with saturation before nonlinear decrease. In our study, we tried to address these two limitations by using subjects younger than 4y old and by considering hybrid models able to handle complex brain change occurring during the first years of life. Finally, it is interesting to note that our results are in line with another study presenting GM trajectory from infancy to young adulthood based on nonlinear piecewise polynomial model [START_REF] Groeschel | Developmental changes in cerebral grey and white matter volume from infancy to adulthood[END_REF].

Deep GM structures are the focus of a great interest due to their important role in various neurodegenerative diseases, and thus have been intensively studied in the past [START_REF] Fjell | Critical ages in the life course of the adult brain: nonlinear subcortical aging[END_REF]. Non-linear trajectories of these structures have been previously described for adulthood [START_REF] Ziegler | Brain structural trajectories over the adult lifespan[END_REF][START_REF] Fjell | Critical ages in the life course of the adult brain: nonlinear subcortical aging[END_REF]. More recently, studies taking advantage of the "BigData sharing" in neuroscience started to analyze subcortical structure volumes from 20y up to advanced ages to define normative values for adult lifespan [START_REF] Potvin | Normative data for subcortical regional volumes over the lifetime of the adult human brain[END_REF]. However, the limited age range of these studies made impossible to estimate full lifespan models. In this study, we have addressed this important problem by considering subjects covering the entire lifespan. Moreover, we extensively analyzed structure trajectories using both absolute and normalized volumes. Therefore, our results present at the same time the structure maturation peaks occurring during childhood based on absolute volumes and the accelerated atrophy related to aging occurring after 80y obtained using normalized volumes. In addition, when deep GM structures are considered at the brain scale, their trajectories present a similar global decrease all along life, except for the medio-temporal regions with a late decrease for amygdala (after 70 years old) and an inverted U-shape for hippocampus. Moreover, an unexpected slight increase of caudate and putamen absolute volumes is visible after 80y. Such observations have been already reported and questioned in several studies [START_REF] Walhovd | Consistent neuroanatomical age-related volume differences across multiple samples[END_REF][START_REF] Fjell | Critical ages in the life course of the adult brain: nonlinear subcortical aging[END_REF][START_REF] Potvin | Normative data for subcortical regional volumes over the lifetime of the adult human brain[END_REF]). Different hypotheses have been proposed such as bias related to survival of subjects with bigger structures, cohort effect, image artifact related to aging or a real phenomenon [START_REF] Potvin | Normative data for subcortical regional volumes over the lifetime of the adult human brain[END_REF]). In our opinion, such volume increases at late ages can be also related to the use of global parametric model with less samples for very old subjects.

The understanding of the amygdalo-hippocampal complex is important in neurology since it is related to crucial tasks such as memory, spatial navigation or emotional behavior. Moreover, hippocampus has been largely studied due to its use as an early biomarker in several neurodegenerative diseases such as Alzheimer's disease [START_REF] Fox | Presymptomatic hippocampal atrophy in Alzheimer's disease[END_REF][START_REF] Jack | Medial temporal atrophy on MRI in normal aging and very mild Alzheimer's disease[END_REF]) but also because it is the main location of adult neurogenesis [START_REF] Eriksson | Neurogenesis in the adult human hippocampus[END_REF][START_REF] Van Praag | Functional neurogenesis in the adult hippocampus[END_REF]. Noteworthy, while amygdala and hippocampus are often associated due to their respective contribution to the limbic system, it appears that they present different trajectories. This fact has been previously reported in recent studies [START_REF] Ziegler | Brain structural trajectories over the adult lifespan[END_REF][START_REF] Fjell | Critical ages in the life course of the adult brain: nonlinear subcortical aging[END_REF][START_REF] Pfefferbaum | Variation in longitudinal trajectories of regional brain volumes of healthy men and women (ages 10 to 85 years) measured with atlas-based parcellation of MRI[END_REF][START_REF] Potvin | Normative data for subcortical regional volumes over the lifetime of the adult human brain[END_REF]. The long maturation period of the hippocampus may be related to the adult neurogenesis. In fact, it has been shown that neurogenesis in the human hippocampus is substantial until at least the fifth decade of life [START_REF] Spalding | Dynamics of hippocampal neurogenesis in adult humans[END_REF], a finding consistent with our analysis. In contrast to the hippocampus, early maturation of the amygdala is consistent with its known function in emotional learning, which allows individuals to avoid aversive events and pursue rewarding experiences [START_REF] Phelps | Contributions of the amygdala to emotion processing: from animal models to human behavior[END_REF]. Accordingly, the amygdala in humans has been shown to be functional early in life [START_REF] Tottenham | A review of adversity, the amygdala and the hippocampus: a consideration of developmental timing[END_REF]. Our results on amygdala are in accordance with most of the previous studies highlighting a minor effect of aging over adulthood [START_REF] Walhovd | Consistent neuroanatomical age-related volume differences across multiple samples[END_REF].

Another important question about brain maturation and aging is related to sexual dimorphism. In the past, this question has been studied mainly over childhood development [START_REF] Giedd | Structural MRI of pediatric brain development: what have we learned and where are we going?[END_REF][START_REF] Development Cooperative | Total and regional brain volumes in a population-based normative sample from 4 to 18 years: the NIH MRI Study of Normal Brain Development[END_REF][START_REF] Aubert-Broche | A new method for structural volume analysis of longitudinal brain MRI data and its application in studying the growth trajectories of anatomical brain structures in childhood[END_REF] or during adolescence [START_REF] Lenroot | Sexual dimorphism of brain developmental trajectories during childhood and adolescence[END_REF][START_REF] Ostby | Heterogeneity in subcortical brain development: A structural magnetic resonance imaging study of brain maturation from 8 to 30 years[END_REF][START_REF] Lenroot | Sex differences in the adolescent brain[END_REF][START_REF] Hu | Volumetric analysis of medial temporal lobe structures in brain development from childhood to adolescence[END_REF]). As previously mentioned, studies on different limited time periods, using nonharmonized tools and different volumetric measurements prevented reaching a consensus. In our study, when using absolute volume, we found that brain structure maturation peaks occur before for female than for male (between 1y-3y earlier). These earlier peaks in females in the maturational phase have been previously described [START_REF] Giedd | Structural MRI of pediatric brain development: what have we learned and where are we going?[END_REF] and were mainly explained by sex differences in growth. We also found a difference around 10-12% of brain size between sexes as previously reported by in-vivo or postmortem studies (Lenroot andGiedd 2010, Brain Development Cooperative 2012). On the other hand, when the impact of brain size is compensated for, both sexes exhibit more similar trajectories. Only the normalized volume of nucleus accumbens presents a marked sexual dimorphism. This region is a key structure in the neural circuitry of addiction, a phenomenon well-known to show sex differences [START_REF] Becker | Sex differences in drug abuse[END_REF]. However, sexual dimorphism of the accumbens volume in humans has not been (to our knowledge) described before. In rats, a higher density of dendritic spines has been shown in females [START_REF] Forlano | Quantitative analysis of pre-and postsynaptic sex differences in the nucleus accumbens[END_REF]. If a similar sex difference would exist in humans, it would be so subtle that only very large experimental samples would reveal it, as it is the case in the present study. Finally, we found that for several structures males are more impacted by aging than females especially after 70y. The fact that women may be less vulnerable to age-related atrophy has been previously reported [START_REF] Gur | Gender differences in age effect on brain atrophy measured by magnetic resonance imaging[END_REF][START_REF] Coffey | Sex differences in brain aging: a quantitative magnetic resonance imaging study[END_REF][START_REF] Carne | Cerebral cortex: an MRI-based study of volume and variance with age and sex[END_REF]. This phenomenon may be related to the protective effect of estrogens and progesterone [START_REF] Green | Neuroprotective effects of estrogens: potential mechanisms of action[END_REF] or related to the fact that women present fewer risk factors (hypertension, tobacco and alcohol consummation…).

Limitations

In our opinion, one of the strengths of our study is to use multiple datasets to be able to cover the entire lifespan. However, this point can be also viewed as a weakness since the use of multiple datasets may introduce bias. Indeed, pooling databases having different age ranges could lead to find artificial differences. It has to be noted that we limited this aspect by using at least 2 different overlapping databases for each 5y intervals. Moreover, the preprocessing pipeline of volBrain has been designed to limit the impact of acquisition protocol by proposing advanced denoising filter and tissue-based intensity normalization. Therefore, after preprocessing, images are better homogenized in terms of signal-to-noise ratio and tissue contrast limiting the impact of using different acquisition protocols and scanners. In addition, during our QC all images with motion and ghosting artifacts were removed as well as the image having high anisotropic voxel resolution. Finally, several studies showed that age-related volume differences are consistent between datasets when using the same analysis tool [START_REF] Fjell | High consistency of regional cortical thinning in aging across multiple samples[END_REF][START_REF] Walhovd | Consistent neuroanatomical age-related volume differences across multiple samples[END_REF][START_REF] Mills | Structural brain development between childhood and adulthood: Convergence across four longitudinal samples[END_REF]. Moreover, recent papers based on a large scale study over adulthood [START_REF] Potvin | Normative data for subcortical regional volumes over the lifetime of the adult human brain[END_REF][START_REF] Potvin | FREESURFER CORTICAL NORMATIVE DATA FOR ADULTS USING DESIKAN-KILLIANY-TOURVILLE AND EX VIVO PROTOCOLS[END_REF] showed that the impact of MRI scanner manufacturer and magnetic strength is negligible compared to impact of age of the structure trajectories.

After our quality control step, no images of subjects younger than 9 months remained. Therefore, the newborn period is not well covered by our samples and thus results obtained before 9 months of life may be inaccurate. Few studies have been published on brain structure trajectory for this since the acquisition is difficult and the image analysis is very challenging due to low contrast before 6 months and fast myelination progression during the first 2 years of life [START_REF] Gilmore | Regional gray matter growth, sexual dimorphism, and cerebral asymmetry in the neonatal brain[END_REF][START_REF] Groeschel | Developmental changes in cerebral grey and white matter volume from infancy to adulthood[END_REF][START_REF] Gilmore | Longitudinal development of cortical and subcortical gray matter from birth to 2 years[END_REF][START_REF] Holland | Structural growth trajectories and rates of change in the first 3 months of infant brain development[END_REF][START_REF] Makropoulos | Regional growth and atlasing of the developing human brain[END_REF]). However, specific tools have been proposed to analyze the newborn life period [START_REF] Makropoulos | Automatic whole brain MRI segmentation of the developing neonatal brain[END_REF][START_REF] Wang | Segmentation of neonatal brain MR images using patch-driven level sets[END_REF]. Nevertheless, up to now, there is no large period lifespan study integrating newborn period with childhood, adolescence, adulthood and elderly.

Here, we described different lifespan trajectories for deep versus cortical structures. Previous studies described heterogeneous trajectories for different parts of the cortex over restricted periods [START_REF] Sowell | Mapping cortical change across the human life span[END_REF], Fjell, Westlye et al. 2009[START_REF] Pfefferbaum | Variation in longitudinal trajectories of regional brain volumes of healthy men and women (ages 10 to 85 years) measured with atlas-based parcellation of MRI[END_REF][START_REF] Walhovd | Through Thick and Thin: a Need to Reconcile Contradictory Results on Trajectories in Human Cortical Development[END_REF][START_REF] Potvin | FREESURFER CORTICAL NORMATIVE DATA FOR ADULTS USING DESIKAN-KILLIANY-TOURVILLE AND EX VIVO PROTOCOLS[END_REF]. Therefore, we plan to investigate trajectory based on cortex parcellation over the entire lifespan in a further study.

Finally, we used cross-sectional analysis to study brain trajectory over the entire lifespan. Using cross-sectional data to analyze a dynamic process can be suboptimal. However, some evidences show that cross-sectional and longitudinal samples produce similar age-related patterns [START_REF] Fjell | Critical ages in the life course of the adult brain: nonlinear subcortical aging[END_REF]. Moreover, the reported lack of consensus is also observed among different longitudinal studies. For instance, the volume of cortical gray matter is highest in childhood according to some longitudinal studies [START_REF] Mills | Structural brain development between childhood and adulthood: Convergence across four longitudinal samples[END_REF], but peaks at puberty according to others [START_REF] Lenroot | Sexual dimorphism of brain developmental trajectories during childhood and adolescence[END_REF]. Therefore, the longitudinal or cross-sectional nature of the data is another factor introducing variability but it is not the unique factor explaining the different results reported in the literature. It is interesting to note that most of the trajectories obtained in our cross-sectional study are in accordance with previous longitudinal studies. First, for childhood, maturation peak between 8-10y for absolute cortical GM volume and earlier peak for females have been reported using longitudinal data [START_REF] Giedd | Brain development during childhood and adolescence: a longitudinal MRI study[END_REF][START_REF] Raznahan | How does your cortex grow?[END_REF]. Moreover, for adolescence, an increase of the absolute WM volume and a decrease of absolute GM volume between 10y and 20y have been observed in previous longitudinal studies [START_REF] Giedd | Brain development during childhood and adolescence: a longitudinal MRI study[END_REF][START_REF] Aubert-Broche | A new method for structural volume analysis of longitudinal brain MRI data and its application in studying the growth trajectories of anatomical brain structures in childhood[END_REF][START_REF] Mills | Structural brain development between childhood and adulthood: Convergence across four longitudinal samples[END_REF]. Finally, for adulthood, our results on normalized subcortical structures volume are highly consistent with results presented in the longitudinal study published by [START_REF] Pfefferbaum | Variation in longitudinal trajectories of regional brain volumes of healthy men and women (ages 10 to 85 years) measured with atlas-based parcellation of MRI[END_REF]. Nevertheless, we think that in a further work, a mixed cross-sectional / longitudinal study [START_REF] Giedd | Brain development during childhood and adolescence: a longitudinal MRI study[END_REF]) could be done since some of the used datasets contain longitudinal data.

Conclusion

We have presented an MRI volumetric brain analysis study covering the entire lifespan based on a very large number of subjects. In this study, we have dealt with main limitations of previous studies to offer a comprehensive analysis of maturation and aging effects at different brain tissues and structures. Absolute and relative measurements have been used to get a complete picture of the brain state at different development stages for both genders. Moreover, optimized models have been used to robustly characterize volume evolution of the different tissues and structures. The results of this study are very helpful to integrate several previous studies covering partial age ranges into a common framework. This enables a better understanding of the observed phenomena. Moreover, the use of the estimated models as normative values can be of inestimable help when analyzing the state of new subjects. Furthermore, disease specific estimated models can be directly compared to the normal models estimated in this study without needing to acquire and analyze a control group. We will include these models in our open access web platform volBrain to provide normality bounds based on the appropriate sex and age for the analysis of new cases. We hope that the online availability of the volBrain online service in combination with the presented models will help our understanding of both normal and pathological human brain.

Figure 1 :

 1 Figure 1: Age distribution of the used MRI after the quality control. Left: Age distribution for all the considered subjects. Right: Age distribution for child younger than 10 years old. Legend indicates the database color and the number of image after quality control.

  4. Linear hybrid model: exponential cumulative distribution for growth with linear model for aging 𝑉𝑜𝑙 = 𝛽 5 . 1 -𝑒 89:; < = + 𝛽 0 + 𝛽 1 𝐴𝑔𝑒 + 𝜀 5. Quadratic hybrid model: exponential cumulative distribution for growth with quadratic model for aging 𝑉𝑜𝑙 = 𝛽 5 . 1 -𝑒 89:; < = + 𝛽 0 + 𝛽 1 𝐴𝑔𝑒 + 𝛽 3 𝐴𝑔𝑒 3 + 𝜀 6. Cubic hybrid model: exponential cumulative distribution for growth with cubic model for aging 𝑉𝑜𝑙 = 𝛽 5 . 1 -𝑒 89:; < = + 𝛽 0 + 𝛽 1 𝐴𝑔𝑒 + 𝛽 3 𝐴𝑔𝑒 3 + 𝛽 4 𝐴𝑔𝑒 4 + 𝜀

Figure 2 :

 2 Figure 2: Volume trajectories based on absolute volume in cm3 for brain tissues and subcortical structures across the entire lifespan. These volume trajectories are estimated according to the age on 2944 subjects from 9 months to 94 years. General model is in black, female model is in magenta and male model is in blue. Dots color represents the different datasets used in this study (see Fig. 1 for dataset color legend).

Figure 3 :

 3 Figure 3: Trajectories based on relative volumes (% total intracranial volume) for brain tissues and subcortical structures across the entire lifespan. These volume trajectories are estimated according to the age on 2944 subjects from 9 months to 94 years. General model is in black, female model is in magenta and male model is in blue. Dots color represents the different datasets used in this study (see Fig. 1 for dataset color legend).

Figure 4 :

 4 Figure 4: Trajectory of the cortical and deep GM volumes in cm3 and % of TIV across the entire lifespan. These volume trajectories are estimated according to the age on 2944 subjects from 9 months to 94 years. General model is in black, female model is in magenta and male model is in blue. Dots color represents the different datasets used in this study (see Fig. 1 for dataset color legend).

Figure 5 :

 5 Figure 5: Trajectory of the cerebrum, cerebrum GM and cerebrum CM volumes in cm3 and % of TIV across the entire lifespan. These volume trajectories are estimated according to the age on 2944 subjects from 9 months to 94 years. General model is in black, female model is in magenta and male model is in blue. Dots color represents the different datasets used in this study (see Fig. 1 for dataset color legend).

Figure 6 :

 6 Figure 6: Trajectory of the cerebellum, cerebellum GM and cerebellum WM volumes in cm3 and % of TIV across the entire lifespan. These volume trajectories are estimated according to the age on 2944 subjects from 9 months to 94 years. General model is in black, female model is in magenta and male model is in blue. Dots color represents the different datasets used in this study (see Fig. 1 for dataset color legend).

Table 1 :

 1 Dataset description. This table provides the name of the dataset, the MR acquisition configuration, the number of considered image before and after QC, the gender proportion after QC and the average mean, standard deviation in parentheses and the interval in brackets.

	DATASET	Acquisition	Before	After	Gender	Age in years
			QC	QC	after QC	after QC
	C-MIND	1 site with 3T MR	266	236	F = 129	8.44 (4.35)
		scanner			M =107	[0.74-18.86]
	NDAR	10 sites with 1.5T	612	382	F = 174	12.39 (5.94)
		and 3T MR scanner			M = 208	[1.08-49.92]
	ABIDE	20 sites with 3T MR	528	492	F = 84	17.53 (7.83)
		scanner			M = 408	[6.50-52.20]
	ICBM	1 sites with 1.5T MR	308	294	F = 142	33.75 (14.32)
		scanner			M = 152	[18-80]
	IXI	3 sites with 1.5T and	588	573	F = 321	49.52 (16.70)
		3T MR scanner			M = 252	[20.0-86.2]
	OASIS	1 sites with 1.5T MR	315	298	F = 187	45.34 (23.82)
		scanner			M = 111	[18 -94]
	AIBL	2 sites with 1.5T and	236	233	F = 121	72.24 (6.73)
		3T MR scanners			M =112	[60 -89]
	ADNI 1	51 sites with 1.5T	228	223	F = 108	75.96 (5.03)
		MR scanner			M = 115	[60 -90]
	ADNI 2	14 sites with 3T MR	215	213	F = 113	74.16 (6.39)
		scanners			M = 100	[56.3 -89]

Total 103 sites with 1.5T and 3T scanners 3296 2944 F =1379 (47%) M = 1565 (53%) 39.65 (26.62) [0.74 -94]

• NDAR (N=612, after QC N=382): The Database for Autism Research

								(NDAR) is
	a national database funded by NIH (https://ndar.nih.gov). This database included
	13 different cohorts acquired on 1.5T MRI and 3T scanners. In our study we used
	415	images	of	control	subjects	from	the	NIHPD
	(http://www.bic.mni.mcgill.ca/nihpd/info/data_access.html) dataset and 197
	images of control subjects from the Lab Study 19 of National Database for Autism
	Research. For the NIHPD, T1-weighted images were acquired at six different
	sites with 1.5 Tesla systems by General Electric (GE) and Siemens Medical
	Systems. The MRI are 3D T1-weighted spoiled gradient recalled (SPGR) echo
	sequence with following parameters: TR = 22-25 ms, TE = 10-11 ms, flip angle
	= 30•, FoV = 256 mm IS × 256 mm AP, matrix size = 256 × 256: 1 × 1 × 1 mm 3
	voxels, 160-180 slices of sagittal orientation. The participants chosen from the
	Lab Study 19 of National Database for Autism Research (NDAR) were scanned
	using a 3T Siemens Tim Trio scanner at each site. The MRI are 3D MPRAGE
	sequence (voxel dimensions : 1.0 × 1.0 × 1.0 mm 3 ; image dimensions: 160 × 224
	× 256, TE = 3.16 ms, TR = 2400 ms).
	• ABIDE

(N=528, after QC N=492): The images

	used in this study consist of 528 control subjects acquired at 20 different sites on
	3T scanner. The MRI are T1-weight MPRAGE image and the details of
	acquisition, informed consent, and site-specific protocols are available on the
	website.
	• ICBM
	from the Autism Brain Imaging
	Data Exchange (ABIDE) dataset (http://fcon_1000.projects.nitrc.org/indi/abide/)

(N=308, after QC N=294): The images

	from the International Consortium
	for Brain Mapping (ICBM) dataset (http://www.loni.usc.edu/ICBM/) used in this
	study consist of 308 normal subjects obtained through the LONI website. The
	MRI are T1-weighted MPRAGE (fast field echo, TR = 17 ms, TE = 10 ms, flip
	angle = 30 °, 256×256 matrix, 1 mm 2 in plane resolution, 1 mm thick slices)
	acquired on a 1.5T Philips GyroScan imaging system (Philips Medical Systems,
	Best, The Netherlands).
	• OASIS (N=315, after QC N=298): The images from the Open Access Series of
	Imaging Studies (OASIS) database (http://www.oasis-brains.org) used in this
	study consist of 315 control subjects. The MRI are T1-weighted MPRAGE image
	(TR = 9.7 ms, TE = 4 ms, TI = 20 ms, flip angle = 10 degrees, slice thickness =
	1.25 mm, matrix size = 256×256, voxel dimensions = 1×1×1.25 mm 3 resliced to 1
	mm 3 , averages = 1) acquired on a 1.5-T Vision scanner (Siemens, Erlangen,
	Germany).
	• IXI

(N=588, after QC N=573): The images

	from the Information eXtraction from
	Images (IXI) database (http://brain-development.org/ixi-dataset/ ) used in this
	study consist of 588 normal subjects. The MRI are T1weighted images collected
	at 3 sites with 1.5 and 3T scanners (FoV = 256 mm × 256 mm, matrix size =
	0.9375 × 0.9375 × 1.2 mm 3 ).
	• ADNI1 (

N=228, after QC N=223): The images

	from the Alzheimer's Disease
	Neuroimaging Initiative (ADNI) database (http://adni.loni.usc.edu ) used in this
	study consist of 228 control subjects from the 1.5T baseline collection. These
	images were acquired on 1.5T MR scanners at 60 different sites across the
	United States and Canada. A standardized MRI protocol to ensure cross-site
	comparability was used. Typical MRI are 3D sagittal MPRAGE (repetition time
	(TR): 2400 ms, minimum full TE, inversion time (TI): 1000 ms, flip angle: 8°, 24
	cm field of view, and a 192×192×166 acquisition matrix in the x-, y-, and z-
	dimensions, yielding a voxel size of 1.25×1.25×1.2 mm 3 , later reconstructed to
	get 1 mm 3 isotropic voxel resolution).
	• ADNI2

(N=213): The images from the ADNI2 database (second phase of

	the
	ADNI project) consist of 215 control subjects. Images were acquired on 3T MR
	scanners with the standardized ADNI-2 protocol, available online
	(www.loni.usc.edu). Typical MRI are T1-weighted 3D MPRAGE sequence
	(repetition time 2300 ms, echo time 2.98 ms, flip angle 9°, field of view 256 mm,
	resolution 1.1 x 1.1 x 1.2 mm 3 ).

• AIBL (N=233): The Australian Imaging, Biomarkers and Lifestyle (AIBL) database (http://www.aibl.csiro.au/) used in this study consists of 236 control subjects. The imaging protocol was defined to follow ADNI's guideline on the 3T scanner (http://adni.loni.ucla.edu/research/protocols/mri-protocols) and a custom MPRAGE sequence was used on the 1.5T scanner.

Table 2 :

 2 Results of model analysis for absolute volumes.

	Absolute volume	Selected	F-Statistic	R 2	Model vs.	Gender	Age*gender
		Model			constant model	interaction	interaction
					p-value of the F-	p-value of the t-	p-value of the t-
					statistic based	statistic on the	statistic on the
					on ANOVA	coefficient	coefficient
	White Matter
	Global	Hybrid 3 rd	472	0.39	p < 0.0001
	Male	order	291	0.43	p < 0.0001	p < 0.0001	p =0.77
	Female		230	0.40	p < 0.0001
	Gray Matter
	Global	Hybrid 3 rd	938	0.56	p < 0.0001
	Male	order	536	0.45	p < 0.0001	p < 0.0001	p =0.19
	Female		529	0.61	p < 0.0001
	CSF
	Global	3 rd order	2770	0.74	p < 0.0001
	Male		813	0.81	p < 0.0001	p = 0.90	p < 0.0001
	Female		1380	0.75	p < 0.0001
	Caudate
	Global	Hybrid 3 rd	590	0.37	p < 0.0001
	Male	order	307	0.37	p < 0.0001	p = 0.006	p = 0.25
	Female		255	0.36	p < 0.0001
	Putamen
	Global	Hybrid 3 rd	593	0.45	p < 0.0001
	Male	order	315	0.45	p < 0.0001	p < 0.0001	p = 0.28
	Female		262	0.43	p < 0.0001
	Thalamus
	Global	Hybrid 2 nd	1730	0.64	p < 0.0001
	Male	order	977	0.65	p < 0.0001	p < 0.0001	p = 0.11
	Female		840	0.65	p < 0.0001
	Globus Pallidus
	Global	2 nd order	494	0.25	p < 0.0001
	Male		203	0.21	p < 0.0001	p < 0.001	p = 0.78
	Female		281	0.29	p < 0.0001
	Hippocampus
	Global	Hybrid 2 nd	177	0.15	p < 0.0001
	Male	order	85.3	0.14	p < 0.0001	p = 0.001	p = 0.99
	Female		90.2	0.16	p < 0.0001
	Amygdala
	Global	Hybrid 3 nd	46.3	0.06	p < 0.0001
	Male	order	23.3	0.06	p < 0.0001	p = 0.045	p = 0.90
	Female		24.0	0.05	p < 0.0001
	Accumbens	Hybrid 1 st
	Global	order	1250	0.46	p < 0.0001
	Male		598	0.43	p < 0.0001	p = 0.37	p = 0.97
	Female		592	0.46	p < 0.0001

Table 3 :

 3 Results of model analysis for relative volumes normalized by TIV.

	Relative volume in	Selected	F-Statistic	R 2	Model vs. constant	Gender interaction	Age*gender
	% of TIV	Model			model	p-value of the t-	interaction
					p-value of the F-	statistic on the	p-value of the t-
					statistic based on	coefficient	statistic on the
					ANOVA		coefficient
	White Matter
	Global	Hybrid 3 rd	837	0.53	p < 0.0001
	Male	order	466	0.54	p < 0.0001	p = 0.32	p =0.41
	Female		369	0.52	p < 0.0001
	Gray Matter
	Global	3 rd order	4030	0.80	p < 0.0001
	Male		2380	0.82	p < 0.0001	p = 0.80	p =0.06
	Female		1920	0.81	p < 0.0001
	CSF
	Global	3 rd order	4450	0.82	p < 0.0001
	Male		2910	0.85	p < 0.0001	p = 0.25	p = 0.003
	Female		1880	0.80	p < 0.0001
	Caudate
	Global	3 rd order	569	0.37	p < 0.0001
	Male		307	0.44	p < 0.0001	p = 0.05	p = 0.31
	Female		282	0.38	p < 0.0001
	Putamen
	Global	2 nd order	1110	0.43	p < 0.0001
	Male		743	0.49	p < 0.0001	p = 0.37	p = 0.37
	Female		471	0.41	p < 0.0001
	Thalamus
	Global	3 rd order	2180	0.69	p < 0.0001
	Male		1540	0.75	p < 0.0001	p = 0.05	p = 0.20
	Female		1050	0.70	p < 0.0001
	Globus Pallidus
	Global	3 rd order	398	0.29	p < 0.0001
	Male		205	0.28	p < 0.0001	p = 0.12	p = 0.83
	Female		215	0.32	p < 0.0001
	Hippocampus
	Global	2 nd order	140	0.09	p < 0.0001
	Male		60	0.07	p < 0.0001	p = 0.07	p = 0.67
	Female		94.9	0.12	p < 0.0001
	Amygdala
	Global	3 rd order	47.2	0.05	p < 0.0001
	Male		29.9	0.05	p < 0.0001	p = 0.56	p = 0.50
	Female		19.5	0.04	p < 0.0001
	Accumbens
	Global	3 rd order	725	0.42	p < 0.0001
	Male		427	0.45	p < 0.0001	p = 0.02	p = 0.65
	Female		368	0.44	p < 0.0001

Table 4 :

 4 Results on normalized volumes for 637 subjects older than 70y. The result for absolute TIV over this restricted period is p=0.50 for gender interaction and p=0.35 for Age*gender interaction.

		Relative volume in % of TIV
		Gender interaction	Age*gender interaction
		p-value of the t-statistic on	p-value of the t-statistic on
		the coefficient	the coefficient
	White Matter	p = 0.14	p =0.14
	Gray Matter	p = 0.0002	p =0.0001
	CSF	p = 0.002	p = 0.0015
	Caudate	p = 0.03	p = 0.01
	Putamen	p = 0.0001	p < 0.0001
	Thalamus	p = 0.001	p = 0.0005
	Globus Pallidus	p = 0.0002	p = 0.0001
	Hippocampus	p = 0.03	p = 0.04
	Amygdala	p = 0.38	p = 0.34
	Accumbens	p = 0.03	p = 0.02

Acknowledgements

We gratefully acknowledge financial support from the French State, managed by the French National Research Ageny in the frame of the Investments for the future Program IdEx Bordeaux (ANR-10-IDEX-03-02, HL-MRI Project), Cluster of excellence CPU and TRAIL (HR-DTI ANR-10-LABX-57). We also want to think the financial support from the CNRS thanks to the multidisciplinary project "Défi imag'In and the dedicated volBrain support. This research was also supported by Spanish TIN2013-43457-R grant from the Ministerio de Economia y competitividad Moreover, this work is based on multiple samples. We wish to thank all investigators of these projects who collected these datasets and made them freely accessible. The C-MIND data used in the preparation of this article were obtained from the C-MIND Data Repository (accessed in Feb 2015) created by the C-MIND study of Normal Brain Development. This is a multisite, longitudinal study of typically developing children from ages newborn through young adulthood conducted by Cincinnati Children's Hospital Medical Center and UCLA and supported by the National Institute of Child Health and Human Development (Contract #s HHSN275200900018C). A listing of the participating sites and a complete listing of the study investigators can be found at https://research.cchmc.org/c-mind. The NDAR data used in the preparation of this manuscript were obtained from the NIH-supported National Database for Autism Research (NDAR). NDAR is a collaborative informatics system created by the National Institutes of Health to provide a national resource to support and accelerate research in autism. The NDAR dataset includes data from the NIH Pediatric MRI Data Repository created by the NIH MRI Study of Normal Brain Development. This is a multisite, longitudinal study of typically developing children from ages newborn through young adulthood conducted by the Brain Development Cooperative Group and supported by the National Institute of Child Health and Human Development, the National Institute on Drug Abuse, the National Institute of Mental Health, and the National Institute of Neurological Disorders and Stroke (Contract #s N01-HD02-3343, N01-MH9-0002, and N01-NS-9-2314, -2315, -2316, -2317, -2319 and -2320). A listing of the participating sites and a complete listing of the study investigators can be found at http://pediatricmri.nih.gov/nihpd/info/participating_centers.html. The ADNI data used in the preparation of this manuscript were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) (National Institutes of Health Grant U01 AG024904). The ADNI is funded by the National Institute on Aging and the National Institute of Biomedical Imaging and Bioengineering and through generous contributions from the following: Abbott, AstraZeneca AB, Bayer Schering Pharma AG, Bristol-Myers Squibb, Eisai Global Clinical Development, Elan Corporation, Genentech, GE Healthcare, GlaxoSmithKline, Innogenetics NV, Johnson & Johnson, Eli Lilly and Co., Medpace, Inc., Merck and Co., Inc., Novartis AG, Pfizer Inc., F. Hoffmann-La Roche, Schering-Plough, Synarc Inc., as well as nonprofit partners, the Alzheimer's Association and Alzheimer's Drug Discovery Foundation, with participation from the U.S. Food and Drug Administration. Private sector contributions to the ADNI are

facilitated by the Foundation for the National Institutes of Health (www.fnih.org). The grantee organization is the Northern California Institute for Research and Education, and the study was coordinated by the Alzheimer's Disease Cooperative Study at the University of California, San Diego. ADNI data are disseminated by the Laboratory for NeuroImaging at the University of California, Los Angeles. This research was also supported by NIH grants P30AG010129, K01 AG030514 and the Dana Foundation. The OASIS data used in the preparation of this manuscript were obtained from the OASIS project funded by grants P50 AG05681, P01 AG03991, R01 AG021910, P50 MH071616, U24 RR021382, R01 MH56584. See http://www.oasis-brains.org/ for more details. The AIBL data used in the preparation of this manuscript were obtained from the AIBL study of ageing funded by the Common-wealth Scientific Industrial Research Organization (CSIRO; a publicly funded government research organization), Science Industry Endowment Fund, National Health and Medical Research Council of Australia (project grant 1011689), Alzheimer's Association, Alzheimer's Drug Discovery Foundation, and an anonymous foundation. See www.aibl.csiro.au for further details. The ICBM data used in the preparation of this manuscript were supported by Human Brain Project grant PO1MHO52176-11 (ICBM, P.I. Dr John Mazziotta) and Canadian Institutes of Health Research grant MOP-34996. The IXI data used in the preparation of this manuscript were supported by the U.K. Engineering and Physical Sciences Research Council (EPSRC) GR/S21533/02 -http://www.brain-development.org/. The ABIDE data used in the preparation of this manuscript were supported by ABIDE funding resources listed at http://fcon_1000.projects.nitrc.org/indi/abide/. ABIDE primary support for the work by Adriana Di Martino was provided by the NIMH (K23MH087770) and the Leon Levy Foundation. Primary support for the work by Michael P. Milham and the INDI team was provided by gifts from Joseph P. Healy and the Stavros Niarchos Foundation to the Child Mind Institute, as well as by an NIMH award to MPM (R03MH096321). http://fcon_1000.projects.nitrc.org/indi/abide/ This manuscript reflects the views of the authors and may not reflect the opinions or views of the database providers.