José V Manjón
email: jmanjon@fis.upv.es

José E Romero

Roberto Vivo-Hernando

Gregorio Rubio

Fernando Aparici

Mariam De La Iglesia-Vaya

Pierrick Coupé

vol2Brain: A new online Pipeline for whole Brain MRI analysis

Keywords: Segmentation, brain volume analysis, MRI

Automatic and reliable quantitative tools for MR brain image analysis are a very valuable resources for both clinical and research environments. In the last years, this field has experienced many advances with successful techniques based on label fusion and more recently deep learning. However, few of them have been specifically designed to provide a dense anatomical labelling at multiscale level and to deal with brain anatomical alterations such as white matter lesions. In this work, we present a fully automatic pipeline (vol2Brain) for whole brain segmentation and analysis which densely labels (N>100) the brain while being robust to the presence of white matter lesions. This new pipeline is an evolution of our previous volBrain pipeline that extends significantly the number of regions that can be analyzed. Our proposed method is based on a fast multiscale multi-atlas label fusion technology with systematic error correction able to provide accurate volumetric information in few minutes. We have deployed our new pipeline within our platform volBrain (www.volbrain.upv.es) which has been already demonstrated to be an efficient and effective manner to share our technology with users worldwide.

Introduction

Quantitative brain image analysis based on MRI has become more and more popular over the last decade due to its high potential to better understand subtle changes in the normal and pathological human brain. The exponential increase of the current neuroimaging data availability and the complexity of the methods to analyze them make necessary the development of novel approaches able to address challenges related to the new "Big Data" paradigm [START_REF] Van Horn | Human neuroimaging as a "Big Data[END_REF]. Thus, automatic, robust and reliable methods for automatic brain analysis will have a major role in near future, most of them powered by cost-effective cloud-based platforms.

Specifically, MRI brain structure volume estimation is being increasingly used to better understand the normal brain evolution (Coupe el al., 2017) or the progression of many neurological pathologies such as multiple sclerosis [START_REF] Commowick | Objective Evaluation of Multiple Sclerosis Lesion Segmentation using a Data Management and Processing Infrastructure[END_REF] or Alzheimer's disease (Coupe et al., 2019) for example.

The quantitative estimation of the different brain structure volumes requires automatic, robust and reliable segmentation of such structures. Since manual delineation of the full brain is unfeasible for routine brain analysis (this task is too tedious, time consuming and prone to reproducibility errors) many segmentation methods have been proposed over the years. Some of them were initially focused at tissue level such as the famous SPM (Asburner and Friston, 2005). However, this level of detail may be insufficient to detect subtle changes in specific brain structures at early stages of the disease.

For example, hippocampus and lateral ventricle volumes can be used as early biomarkers of Alzheimer disease. At this scale, also cortical and subcortical grey matter structures are of special interest for the neuroimaging community. Classic neuroimaging tools such as the well-known FSL package (Jenkinson et al, 2012) or Freesurfer [START_REF] Fischl | Whole brain segmentation: automated labeling of neuroanatomical structures in the human brain[END_REF] have been widely used over the last 2 decades. More recently, multi-atlas label fusion segmentation techniques have been extensively applied thanks to their ability to combine multiple atlas information minimizing mislabeling due to inaccurate registrations (Coupe et al., 2011[START_REF] Wang | Multi-atlas segmentation with joint label fusion and corrective learning-an open source implementation[END_REF][START_REF] Manjón | Nonlocal Intracranial Cavity Extraction[END_REF][START_REF] Romero | Non-local Automatic Brain Hemisphere Segmentation[END_REF].

However, to segment the whole brain in a large number of structures is still a very challenging problem even for modern multi-atlas based methods [START_REF] Wang | Multi-atlas segmentation with joint label fusion and corrective learning-an open source implementation[END_REF][START_REF] Cardoso | Geodesic Information Flows: Spatially-Variant Graphs and Their Application to Segmentation and Fusion[END_REF]Ledig et al., 2016). First, the need of a large set of densely manually labeled brain scans and second the large amount of computational time needed to combine all those labeled scans to produce the final segmentation.

Fortunately, a fast framework based on collaborative patch-matching was recently proposed (Guiraud et al. 2016) to reduce the computational time required by multi-atlas patch-based methods.

More recently, deep leaning methods have been also proposed for brain structure segmentation. Those methods are mainly patch-based [START_REF] Wachinger | Left precentral gyrus medial segment 84 152 Right superior frontal gyrus medial segment 85 153 Left superior frontal gyrus medial segment 86 154 Right middle temporal gyrus 87 155 Left middle temporal gyrus 88 156 Right occipital pole 89 157 Left occipital pole 90 160 Right occipital fusiform gyrus 91 161 Left occipital fusiform gyrus 92 162 Right opercular part of the inferior frontal gyrus 93 163 Left opercular part of the inferior frontal gyrus 94 164 Right orbital part of the inferior frontal gyrus 95 165 Left orbital part of the inferior frontal gyrus 96 166 Right posterior cingulate gyrus 97 167 Left posterior cingulate gyrus 98 168 Right precuneus 99 169 Left precuneus 100 170 Right parahippocampal gyrus 101 171 Left parahippocampal gyrus 102 172 Right posterior insula 103 173 Left posterior insula 104 174 Right parietal operculum 105 175 Left parietal operculum 106 176 Right postcentral gyrus 107 177 Left postcentral gyrus 108 178 Right posterior orbital gyrus 109 179 Left posterior orbital gyrus 110 180 Right planum polare 111 181 Left planum polare 112 182 Right precentral gyrus 113 183 Left precentral gyrus 114 184 Right planum temporale 115 185 Left planum temporale 116 186 Right subcallosal area 117 187 Left subcallosal area 118 190 Right superior frontal gyrus 119 191 Left superior frontal gyrus 120 192 Right supplementary motor cortex 121 193 Left supplementary motor cortex 122 194 Right supramarginal gyrus 123 195 Left supramarginal gyrus 124 196 Right superior occipital gyrus 125 197 Left superior occipital gyrus 126 198 Right superior parietal lobule 127 199 Left superior parietal lobule 128 200 Right superior temporal gyrus 129 201 Left superior temporal gyrus 130 202 Right temporal pole 131 203 Left temporal pole 132 204 Right triangular part of the inferior frontal gyrus 133 205 Left triangular part of the inferior frontal gyrus 134 206 Right transverse temporal gyrus 135 207 transverse temporal gyrus[END_REF] or 2D (slice-based) [START_REF] Roy | QuickNAT: A fully convolutional network for quick and accurate segmentation of neuroanatomy[END_REF] due to current GPU memory limitations. Current state-of -the-art whole brain deep learning based methods are based on ensembles of local neural networks such as the SLANT method [START_REF] Huo | 3D whole brain segmentation using spatially localized atlas network tiles[END_REF] or more recently the Assemblynet method (Coupe et al., 2020).

The aim of this paper is to present a new software pipeline for whole brain analysis that we have called vol2Brain. It is based on an optimized multi-atlas label fusion scheme that has a reduced execution time thanks to the use our fast collaborative patch-matching approach and has been specifically designed to deal with both normal appearing and lesioned brains (a feature that most of preceding methods ignored). This pipeline automatically provides volumetric brain information at different scales in a very simple manner through a web-based service not requiring any installation or technical requirements in a similar manner as previously done by our volBrain platform that since 2015 has processed online more than 360,000 brains worldwide. In the following sections, the new pipeline will be described and some evidences of its quality will be presented.

Material and Methods

Dataset description

In our proposed method, we used an improved version of the full Neuromorphometrics dataset (http://www.neuromorphometrics.com) which consists of 114 manually segmented brain MR volumes corresponding to subjects with ages covering almost the full lifespan (from 5 to 96 years old). Dense neuroanatomical manual labeling of MRI brain scans was performed at Neuromorphometrics, Inc., following the methods described in [START_REF] Caviness | MRI based brain volumetrics: emergence of a developmental brain science[END_REF].

The original MRI scans were obtained from the following sources: 1) the Open Access and 5) the 20Repeats dataset (http://www.oasis-brains.org/) (N=40).

Before manual labeling all the images were preprocessed with an automated bias field inhomogeneity correction [START_REF] Arnold | Qualitative and quantitative evaluation of six algorithms for correcting intensity nonuniformity effects[END_REF]) and geometrically normalized using 3 anatomical landmarks (anterior commissure (AC), posterior commissure (PC), and midsagittal point). The scans were reoriented and resliced so that anatomical labeling could be done in coronal planes that follow the AC-PC axis. The manual outlining was performed using an in-house software called NVM and the exact specification of each region of interest is defined in 1) Neuromorphometrics' General Segmentation Protocol (http://neuromorphometrics.com/Seg/) ,and 2) the BrainCOLOR Cortical Parcellation Protocol (http://Neuromorphometrics.com/ParcellationProtocol_2010-04-05.PDF). It has to be noted that the exact protocols used to label the scans evolved over time. Because of this, not all anatomical regions were labeled in every group (label number range: max=142, min=136).

Dataset correction

Right after downloading the Neuromorphometrics dataset, we performed a rigorous quality control of the dataset. We discovered that this dataset presented several issues that had to be corrected before using it.

Image resolution, orientation and size

After checking each individual file, we found that they had different acquisition orientations (coronal, sagittal and axial). They also have different resolutions (1x1x1, 0.95x0.93x1.2, 1.26x1.24x12, etc.) and different volume sizes (256x256x307, 256x256x299, 256x256x160, etc.). To standardize them we affine registered all image and corresponding label files to the MNI152 space using ANTS software which resulted in a homogeneous dataset with axial orientation, 1x1x1 mm 3 voxel resolution and a volume size of 181x217x181 voxels. We also checked the image quality and we removed 14 cases from the original dataset that presented strong image artifacts and severe blurring effects. This resulted in a final dataset of 100 cases.

Inconsistent and different number of labels

The selected 100 files from the previous step had 129 common labels from a total of 142 labels. After analyzing these 13 inconsistent labels we decided to treat each of them in a specific manner according to the detected issue. Label file description assigns label numbers from 1 to 207. However, we found that labels 228, 229, 230 and 231 were present in some files. After checking them we realized that labels 228 and 229 corresponded to left a right basal foreground (labels 75 and 76) so we renumbered them.

Labels 230 and 231 just represented few pixels in 3 of the cases and therefore were removed. Labels 63 and 64 (right and left vessel) were not present in all the cases (not always visible) and we decided to renumber them as part of the putamen (labels 57 and 58) as they were inside of it. We removed label 69 (optic chiasm) because it was not present in all the cases and its delineation was very inconsistent. Labels 71, 72 and 73

(cerebellar vermal lobules I-V, VI-VII and VIII-X) were present in 74 of the 100 cases and we decided to re-segment the inconsistent cases so all the cases have these labels (details will be given below). Label 78 (corpus callosum) was only present in 25 cases and we decided to relabel it as right and left white matter (labels 44 and 45). Label 15

(5 th ventricle) was very tiny and only present in few cases (13), thus it was relabeled as lateral ventricles (labels 51 and 52). Finally, we decided to add two new labels that we found important. External CSF (labelled as 1) and left and right white matter lesions (labels 53 and 54). Details on how these labels were added are provided bellow. After all the cleanup the final dataset had a consistent number of 135 labels (see appendix).

Labelling errors

Once the dataset had a homogeneous number of labels, we inspected them to check their quality. After inspecting the dataset visually, we found that boundaries of all the structures in sagittal and axial planes were very irregular. This is probably due to the fact that the original manual delineation was performed in coronal plane. However, one of the main problems we found was the fact that cortical grey matter was severely overestimated and correspondently the CSF and white matter underestimated. This fact has been already highlighted by other researchers [START_REF] Huo | Consistent Cortical Reconstruction and Multi-atlas Brain Segmentation[END_REF] that pointed out this problem in the context of cortical thickness estimation. The same problem arises in the cerebellum although is a bit less pronounced. To solve this problem [START_REF] Huo | Consistent Cortical Reconstruction and Multi-atlas Brain Segmentation[END_REF] used an automatic fusion of the original GM/WM maps and partial volume maps generated by the method TOADS [START_REF] Bazin | Homeomorphic brain image segmentation with topological and statistical atlases[END_REF] to correct the cortical labels.

In this work we have followed a different approach based in the original manual segmentation and the intensity information.

First, we combined all the 135 labels into 7 different classes (cerebrospinal fluid (CSF), cortical grey matter (cGM), cerebral white matter (cWM), subcortical grey matter (sGM), cerebellar grey matter (ceGM), cerebellar white matter (ceWM) and brainstem (B)).

External CSF was not labeled in Neuromorphometrics dataset so we added it using volBrain [START_REF] Manjón | volBrain: an online MRI brain volumetry system[END_REF] (we copied CSF label to those pixels that had label 0 in the original label file). Then, the median value of cGM and cWM was estimated and used to generate the partial volume maps using a linear mixing model [START_REF] Manjón | Robust MRI brain tissue parameter estimation by multistage outlier rejection[END_REF].

Voxels in the cGM and cWM interface were relabeled according to their partial volume content (for example a cGM voxel with a cWM partial volume coefficient bigger than its corresponding cGM partial volume coefficient was relabeled as cWM). The same process was repited for the CSF/cGM interface, ceGM/ceWM interface and ceGM/CSF interface. To ensure the regularity of the new label maps each partial volume map was regularized using a non-local means filter (Coupe et al.,2018). Finally, each case was visually revised and small labelling errors were manually corrected using ITK-SNAP software. Most of the corrections were related with cortical grey matter in the upper part of the brain, misclassifications of white matter lesions as cortical grey matter and CSF related corrections. Figure 1 shows an example of the cGM/cWM tissue maps before and after the correction. After the tissue correction the original structure labels were automatically relabeled to match the new tissue maps. Specifically, those voxels that kept the same tissue type before and after the correction kept their original labels and those that changed were automatically labeled according the most likely label considering their position and intensity. Results were visually reviewed to assess its correctness and manually corrected when necessary. Finally, we realized that subcortical grey matter structures showed important segmentation errors and we decided to re-segment them using volBrain automatic segmentation followed by manual correction when needed. Figure 2 shows an example of the final relabeling result.

LesionBrain dataset

One of the main goals of the proposed pipeline was to make it robust to the presence of white matter (WM) lesions that normally are misclassified as GM in pathological brains. To this end, we included in our library not only healthy cases but also subjects with WM lesions. Specifically, 32 of the 100 cases of the previously described Neuromorphometrics dataset had WM visible lesions with a lesion load range from moderate to severe. We are aware that WM lesions can appear anywhere in the brain but it is also known that they have a priori probability to be located in periventricular areas among others (Coupe et al., 2018).

We found though that the number of cases with lesions on the dataset was not enough to capture the diversity of WM lesion distribution so we decided to expand the dataset using a manually labeled multiple sclerosis dataset. We previously used this dataset to develop a multiple sclerosis (MS) segmentation method (Coupe et al., 2018).

This dataset is composed of 43 MS patients who underwent 3T 3D-T1w MPRAGE and 3D-Fluid-Attenuated Inversion Recovery (FLAIR) MRI. We used only the T1 images since this is the input modality of our proposed pipeline. To further increase the dataset size, we included the left-right flipped version of the images and labels resulting in an extended dataset of 86 cases.

vol2Brain pipeline description

The vol2Brain pipeline is a set of image processing tasks dedicated to improve the quality of the input data and to set them into a specific geometric and intensity space, to segment the different structures and to generate useful volumetric information (see figure 3

Preprocessing

We have used the same preprocessing steps than volBrain pipeline (Manjón and Coupe, 2016) since it has been demonstrated to be very robust (based in our experience processing more than 360.000 subjects worldwide). This preprocessing consists of the following steps. To improve the image quality, first the raw image is denoised using the Spatially Adaptive Non-Local Means (SANLM) filter [START_REF] Manjón | Adaptive Non-Local Means Denoising of MR Images with Spatially Varying Noise Levels[END_REF] and inhomogeneity corrected using the N4 method [START_REF] Tustison | N4ITK: improved N3 bias correction[END_REF]. The resulting image is then affinely registered to the Montreal Neurological Institute (MNI) space using the ANTS software [START_REF] Avants | Symmetric diffeomorphic image registration with cross-correlation: Evaluating automated labeling of elderly and neurodegenerative brain[END_REF]. The image in the MNI space have a size of 181x217x181 voxels with 1 mm 3 voxel resolution. Then we used a second inhomogeneity correction based on SPM8 [START_REF] Ashburner | Unified segmentation[END_REF] toolbox since this model-based method has proven to be quite robust once the data is located at the MNI space. Finally, we intensity normalized the images applying a piecewise linear tissue intensity mapping based on the TMS method [START_REF] Manjón | Robust MRI brain tissue parameter estimation by multistage outlier rejection[END_REF] as described in (Manjón and Coupe, 2016). It is worth to note that the library images were also intensity normalized using the described approach so both library and the case to be segmented share a common geometrical and intensity space.

Multiscale labelling and cortical thickness estimation

After the preprocessing, the images are ready to be segmented and measured. This segmentation is performed in several stages.

ICC Extraction

The first step in the segmentation process is the intracranial cavity extraction (ICC). This is obtained using the method NICE [START_REF] Manjón | Nonlocal Intracranial Cavity Extraction[END_REF]. NICE method is based on a multi-scale non-local label fusion scheme. Details of NICE method can be found in [START_REF] Manjón | Nonlocal Intracranial Cavity Extraction[END_REF]. To further improve the quality of the original NICE method we have increased the size of the original volBrain template library from 100 to 300 cases using the 100 cases of the vol2Brain library and their left-right mirrored version.

Full brain structure segmentation

The (1) where V i corresponds to the search volume, N is the number of subjects in the templates library, y s,j is the label of the voxel x s,j at the position j in the library subject s and w(x i , x s,j )

is the patch similarity defined as:

𝑤(𝑥 𝑖 , 𝑥 𝑠,𝑗 ) = 𝑒𝑥𝑝 -𝐷 𝑖,𝑗,𝑠 ℎ 2
(2) 𝐷 𝑖,𝑗,𝑠 = ‖𝑃(𝑥 𝑖 ) -𝑃(𝑥 𝑠,𝑗 )‖ 2 2

(3) where P(x i ) is the patch centered at x i , P(x s,j ) the patch centered at x j in the templates and ||.|| 2 is the normalized L2 norm (normalized by the number of elements) calculated from the distance between each pair of voxels from both patches P(x i ) and P(x s,j ). h is a normalization parameter that is estimated from the minimum of all patch distances within the search volume.

However, exhaustive patch comparison process is very time consuming (even in reduced neighborhoods, i.e., when the search volume V is small). To reduce the computational burden of this process, we have used a multiscale adaptation of the OPAL method [START_REF] Giraud | An Optimized PatchMatch for multi-scale and multi-feature label fusion[END_REF] previously proposed in [START_REF] Romero | CERES: A new cerebellum lobule segmentation method[END_REF] which takes benefit from the concept of Approximate Nearest Neighbor Fields (ANNF). To further speed up at the process we processed only those voxels that were segmented as ICC by the NICE method.

In patch-based segmentation, the patch size is a key parameter that is strongly related to the structure to be segmented and image resolution. It can be seen in the literature that multi-scale approaches improve segmentation results [START_REF] Manjón | Nonlocal Intracranial Cavity Extraction[END_REF]. In OPAL [START_REF] Giraud | An Optimized PatchMatch for multi-scale and multi-feature label fusion[END_REF] independent and simultaneous multi-scale and multi-feature ANN fields were computed. Thus, we have followed a multi-scale approach were several different ANNs are computed for different patch-size resulting in different label probability maps that have to be combined. In this paper, two patch-size are used and an adaptive weighting scheme is proposed to fuse these maps (Eq. 3).

𝑝(𝑙

) = 𝛼 𝑝 1 (𝑙) + (1 -𝛼)𝑝 2 (𝑙) (3)
where p 1 (l) is the probability map of patch-size 3x3x3 volxels for label l, p 2 (l) the probability map of patch-size 5x5x5 voxels for label l, p(l) is the final probability map for label l and α ∈ [0,1] is the probability mixing coefficient.

Systematic error correction

Any segmentation method is subject to both random and systematic errors. The first error type can be typically minimized by using bootstrapped estimations. Fortunately, the nonlocal label fusion technique estimates the voxel label averaging the votes of many patches which naturally reduces the random classification error. Unfortunately, systematic errors cannot be reduced using this strategy since they are not random.

However, due its nature this systematic bias can be learned and later use this knowledge to correct the segmentation output [START_REF] Wang | Multi-atlas segmentation with joint label fusion and corrective learning-an open source implementation[END_REF].

In (Romero et al,2017), we proposed an error corrector method based on a patch-based ensemble of neural networks (PEC for Patch-based Ensemble Corrector) to increase the segmentation accuracy by reducing the systematic errors. Specifically, a shallow neural network ensemble is trained with image patches of sizes 3x3x3 voxels (fully sampled) and 7x7x7 voxels (subsampled by skipping two voxels at each dimension) from the T1w images, the automatic segmentations, a distance map value, and their x, y and z coordinates at MNI152 space. The distance map we used is calculated for the whole structure as the distance in voxels to the structure contour. This results in a feature vector of 112 features that are mapped to a patch of manual segmentations of size 3x3x3 voxels. We used a multilayer perceptron with two hidden layers of size 83 and 55 neurons resulting in a network with a topology of 112x83x55x27 neurons. An ensemble of 10 neural networks was trained using a boosting strategy. Each new network was trained with a different subset of data which was selected by giving a higher probability of selection to those samples that were misclassified in the previous ensemble. More details can be found in the original paper (Romero et al,2017).

Multiscale label generation

Once the full brain segmentation is performed different scale versions were computed combining several labels to generate more generic ones and allow a multiscale brain analysis. The 135 labels were combined to create a tissue type segmentation map including 8 different tissues (cerebrospinal fluid (CSF), cortical grey matter (cGM), cerebral white matter (cWM), subcortical grey matter (sGM), cerebellar grey matter (ceGM), cerebellar white matter (ceWM), brainstem (BS) and white matter lesions (WML)). The cGM and cWM maps will be later used to compute the cortical thickness.

Also, cerebrum lobe maps were created by combining cortical GM structures. These maps will be used later to computed lobe specific volumes and thickness.

Cortical thickness estimation

To estimate the cortical gray matter thickness, we have used the DiReCT method.

DiReCT was introduced in Das et al. ( 2009) and was made available in ANTs under the program named KellyKapowski. This method is based on the use of a dense nonlinear registration to estimate the distance between the inner and the outer parts of the cortical gray matter. Cortical thickness per cortical label and per lobe were estimated from the thickness map and the corresponding segmentation maps [START_REF] Tustison | Large-scale evaluation of ANTs and FreeSurfer cortical thickness measurements[END_REF].

Report generation

The output produced by the vol2Brain pipeline consists in a pdf and csv files. These files summarize the volumes and asymmetry ratios estimated from the images. If the user provides sex and age of the submitted subject population-based normal volumes and asymmetry bounds for all structures are added for reference purposes. This normality bounds were automatically estimated from the IXI dataset (https://braindevelopment.org/ixi-dataset/) which contains almost 600 normal subjects covering most of the adult lifespan.

Furthermore, the user can access to its user area through volBrain website to download the resulting Nifty files containing the segmentations at different scales (both in native or MNI space). An example of the volumetric report produced by vol2Brain is shown in the appendix.

Experiments and results

In this section some experimental results are shown to highlight the accuracy and reproducibility of the proposed pipeline. A leave-two-out procedure was performed for the 100 subjects of the library (i.e. excluding the case to be segmented and its mirrored version). In the dataset there are 19 cases that were scanned and labelled twice for reproducibility estimation purposes. In this case, a leave-four-out procedure was applied to avoid any problem (i.e. excluding the case to be segmented and its mirrored version of the two acquisitions of the same subject). To measure the segmentation quality the dice index (Zijdenbos et al., 1994) was computed by comparing the manual segmentations with the segmentations obtained with our method. A visual example of the automatic segmentation results is shown in Figure 4.

Results

Since presenting dice results of the 135 labels would be impractical, we have decided to

show the average results for cortical and non-cortical labels as done in previous papers [START_REF] Wang | Multi-atlas segmentation with joint label fusion and corrective learning-an open source implementation[END_REF]. In Table 1, the results of the proposed method are shown with and without the corrective learning step (PEC) to show the impact that this postprocessing has in the final results (it improved the results in all the cases). To further explore the results, we separated them by dataset as it is well known that results within the same dataset are normally better than across datasets. This allows to explore the generalization capabilities of the proposed method. Results are summarized in Table 2. As can be seen, results of the OASIS dataset were the best among datasets.

This makes perfect sense since precisely this dataset is the biggest. CANDI dataset showed the worst results. This dataset had the worst image quality which somehow explains these results. One of the objectives of the proposed method was to be able to deal with images with white mater lesions. This is fundamental since if we do not take into account those regions, they are normally misclassified a cortical or subcortical grey matter (and also affects the cortical thickness estimation) [START_REF] Dadar | Beware of white matter hyperintensities causing systematic errors in FreeSurfer gray matter segmentations![END_REF]. In Table 3 the results of white matter lesion segmentation are shown (left and right lesions were considered together). We separated the results by lesion volume as it is well known that small lesions are more difficult to segment than big ones [START_REF] Manjón | MRI white matter lesion segmentation using an ensemble of neural networks and overcomplete patch-based voting[END_REF].

Method reproducibility

A very important feature for a measurement method is its reproducibility. To measure the reproducibility of the proposed method, we used a subset of our library. Specifically, we used 19 cases of the OASIS subset that were scanned and labeled twice. In this case we have two sources of variability which are related to the inter-image changes and manual labelling differences. To measure the reproducibility, we computed the dice coefficient between the two different segmentations (of each case and its repetition). This was done for both, the manual segmentation (that we used as reference) and the automatic one. Results are summarized in Table 5. As can be seen the proposed method showed a slightly superior reproducibility than manual labeling.

Method comparison

It is difficult to compare the proposed method with similar state of the art methods such as Freesurfer since the labelling protocol is slightly different. For this reason, we have used as reference a freely available and well-known method call Joint Label Fusion [START_REF] Wang | Multi-atlas segmentation with joint label fusion and corrective learning-an open source implementation[END_REF]. This method is a state-of-the-art multi-atlas segmentation approach. To make it fully comparable we used as atlas library the corrected cases of our library. In Table 6, we show the results of the comparison. We compared our proposed method with two versions of the JLF approach, one using an affine registered library (linear) and another using a non-linear registered library. It is worth to note the proposed method uses only linearly registered library (i.e. no non-linear registration was used). As can be noticed the proposed method was far superior to both versions.

Computational time

The proposed method takes around 20 minutes in average to complete the whole pipeline (including cortical thickness estimation and report generation). JLF method takes around 2 hours only for structure segmentations without cortical thickness estimation (excluding the preprocessing which includes several hours of non-linear registration depending on the number of atlases used). Freesurfer normally takes around 6 hours to perform the complete analysis (which also includes surface extraction).

Discussion

We have presented a new pipeline for full brain segmentation (vol2Brain) that is able to segment the brain into 135 different regions in a very efficient and accurate manner. The proposed method also integrates these 135 regions to provide measures at different anatomical scales, including brain tissues and lobes. It also provides cortical thickness measurements per cortical structure and lobe displayed into an automatic report summarizing the results (see appendix).

To create vol2Brain pipeline we had to create a template library that integrates all the anatomical information needed to perform the labelling process. This was a long and laborious work since the original library obtained from Neuromorphometrics did not meet the required quality and we had to invest a significant amount of time to make it ready to use. To create this library, we homogenized the image resolution, orientation and size of the images, removed and relabeled inconsistent labels and corrected systematic labelling errors. Besides, we extended the labelling protocol adding external CSF and white matter lesions. As a result, we generated a highly consistent and high-quality library that not only allowed to develop the current proposed pipeline but will be also a valuable resource for future developments.

The proposed method is based on patch-based multi-atlas label fusion technology.

Specifically, we have used an optimized version of non-local label fusion called OPAL that efficiently finds patch matches needed to label each voxel in the brain reducing the required time to label the full brain from hours to minutes. To further improve the results, we have used a patch-based error corrector which has been previously used in other segmentation problems such as hippocampus subfield labelling [START_REF] Romero | CERES: A new cerebellum lobule segmentation method[END_REF] or cerebellum lobules [START_REF] Carass | Comparing fully automated state-of-the-art cerebellum parcellation from Magnetic Resonance Imaging[END_REF].

We measured the results of the proposed pipeline using a LOO methodology and got an average dice value of 0.8262. This result was obtained from 4 different sub datasets ranking from 0.7831 to 0.8353 showing a good generalization of the proposed method.

This result was quite close to the manual intra-observer accuracy that was estimated in 0.8363 using a reduced dataset. We also compared the proposed method with a related currently available state-of-the-art method for full brain labelling. We demonstrated that vol2Brain was not only far superior to the linear (0.8262 vs 0.7369) and non-linear (0.8262 vs 0.7591) versions of JLF method but also more efficient with a temporal cost of minutes compared to hours.

The proposed vol2Brain pipeline is already available though our volBrain platform (https://volbrain.upv.es). As the rest of the volBrain platform pipelines it receives an anonymized and compressed nifty file thought the website and reports the results 20 minutes later by sending an email to the user. The user can also download the segmentation files though the user area of volBrain platform (an example of the pdf report is shown in the appendix).

We hope that the accuracy and efficiency of the proposed method and the ease of use though the volBrain platform will boost the anatomical analysis of the normal and pathological brain (specially on those cases with white matter lesions).

Conclusion

In this paper, we present a novel pipeline to densely segment the brain and to provide measurements of different features at different anatomical scales in an accurate and efficient manner. The proposed pipeline has been compared with a state-of-the-art related method showing competitive results in term of accuracy and computational time.

Finally, we hope that the online accessibility of the proposed pipeline will facilitate the access of any user around the world to the proposed pipeline making their MRI data analysis simpler and more efficient.

Figure 1 .

 1 Figure 1. Example of cGM/cWM tissue correction.

Figure 2 .

 2 Figure 2. Top row shows the original labelling and bottom row the corrected labeling. Note that external CSF label has been added to the labeling protocol.

  Figure 3. vol2Brain pipeline scheme. In the first row, the preprocessing for any new subject is presented. In the second row, the result of the ICC extraction, structure and tissue segmentations jointly with the cortical thickness estimation are presented. Finally, in the third row the volumetric information is extracted and presented.

  dense segmentation of the full brain is based on a multiscale version the non-local patch-based label fusion technique (Coupe et al., 2011) where patches of the subject to be segmented are compared with patches of the training library to look for similar patterns within a predefined search volume to assign the proper label v as can be

Figure 4 .

 4 Figure 4. Example results of vol2Brain. T1 image, ICC mask, brain tissues, lobes and structures.

  Zijdenbos A.P.,Dawant B. M., Margolin R. A., and Palmer A. C. (1994). Morphometric analysis of white matter lesions in MR images: method and validation. IEEE Transactions on Medical Imaging, 13(4): 716-724.

Table 1 :

 1 Proposed method dice results. The mean Dice is evaluated on the all considered labels (135 without background).

	Method	All labels	Cortical labels	Noncortical labels
	Our method	0.8190 ± 0.0300	0.7912 ± 0.0397	0.8929 ± 0.0173
	Our method + PEC	0.8262 ± 0.0257	0.7996 ± 0.0347	0.8969 ± 0.0157

Table 2 :

 2 Proposed method overall dice results for the full dataset and for each of the subsets.

	All (N=100)	OASIS (N=68)	CANDI (N=6)	ADNI (N=25)	COLIN (N=1)
	0.8262 ± 0.0257	0.8353± 0.0233	0.7831± 0.0326	0.8111 ± 0.0142	0.8353

Table 3 :

 3 Proposed method lesion dice results. *Small(<4 ml), Medium(4 ml to 18 ml), Big(>18 ml).Once the method segments the full brain into 135 labels, those labels are grouped together to provide information at different anatomical scales. Specifically, eight different tissue labels are generated. Dice results are shown in Table4.

	Method	Small (N=76)	Medium (N=21)	Big (N=3)	Avg (N=100)
	lesion	0.5767± 0.1486	0.8281± 0.0500	0.8467± 0.0524	0.6440 ± 0.1589

Table 4 :

 4 Proposed method dice results for each brain tissue.

	CSF	cGM	cWM	sGM
	0.9006 ± 0.0307	0.9543 ± 0.0144	0.9669 ± 0.0131	0.9518 ± 0.0114
	ceGM	ceWM	BS	Lesion
	0.9644 ± 0.0172	0.9448 ± 0.0363	0.9693 ± 0.0137	0.6440 ± 0.1589

Table 5 :

 5 Proposed method dice results. The mean Dice is evaluated on the all considered labels (135 without background).

	Method	All labels	Cortical labels	Noncortical labels
	vol2Brain	0.8405 ± 0.0181	0.8234 ± 0.0206	0.8856 ± 0.0158
	Manual	0.8368 ± 0.0171	0.8198 ± 0.0200	0.8818 ± 0.0163

Table 6 :

 6 Proposed method dice results compared to the results of two versions of JLF method.

	Method	All labels	Cortical labels	Noncortical labels
	vol2Brain	0.8262 ± 0.0257	0.7996 ± 0.0347	0.8969 ± 0.0157
	JLF (linear)	0.7369 ± 0.0292	0.7016 ± 0.0337	0.8305 ± 0.0241
	JLF (non-linear)	0.7591 ± 0.0252	0.7327± 0.0288	0.8291 ± 0.0228

Acknowledgments

This research was supported by the Spanish DPI2017-87743-R grant from the Ministerio de Economia, Industria y Competitividad of Spain. This work benefited from the support of the project DeepvolBrain of the French National Research Agency (ANR-18-CE45-0013). This study was achieved within the context of the Laboratory of Excellence TRAIL ANR-10-LABX-57 for the BigDataBrain project. Moreover, we thank the Investments for the future Program IdEx Bordeaux (ANR-10-IDEX-03-02, HL-MRI Project), Cluster of excellence CPU and the CNRS.

Appendix

In table 1 a list of the 135 labels measured in vol2Brain pipeline is shown.

Report example

Example report of the vol2Brain pipeline. The report summarizes volumetric/asymmetry and thickness information at different scales as long as different captures of the results as a visual quality control.


Dr Vincent Planche
email: vincent.planche@u-bordeaux.fr

José V Manjon

Boris Mansencal

Enrique Lanuza

Thomas Tourdias

Gwenaëlle Catheline

Pierrick Coupé

Structural progression of Alzheimer's disease over decades : the MRI staging scheme

Keywords: Alzheimer, MRI, atrophy, staging, lifespan Alzheimer's disease, ADNI: Alzheimer's Disease Neuroimaging Initiative, AIBL: Australian Imaging, Biomarkers and Lifestyle, CA: Cornu Ammonis, TDP-43: TAR DNA-binding protein 43, LATE: Limbic-predominant Age-related TDP-43 Encephalopathy, NFT: Neurofibrillary tangles, PET: Positron Emission Tomography

The chronological progression of brain atrophy over decades, from presymptomatic to dementia stages, has never been formally depicted in Alzheimer's disease (AD). This is mainly due to the lack of cohorts with long enough MRI follow-ups in cognitively unimpaired young participants at baseline. To describe a spatiotemporal atrophy staging of AD at the whole-brain level, we built extrapolated lifetime volumetric models of healthy and AD brain structures by combining multiple large-scale databases (n=3512 quality controlled MRI from 9 cohorts of subjects covering the entire lifespan, including 415 MRI from ADNI1, ADNI2, and AIBL for AD patients). Then, we validated dynamic models based on cross-sectional data using external longitudinal data. Finally, we assessed the sequential divergence between normal aging and AD volumetric trajectories and described the following staging of brain atrophy progression in AD:

(1) hippocampus and amygdala; (2) middle temporal gyrus; (3) entorhinal cortex, parahippocampal cortex, and other temporal areas; (4) striatum and thalamus and (5) middle frontal, cingular, parietal, insular cortices and pallidum. We concluded that this MRI scheme of atrophy progression in AD was close but did not entirely overlap with Braak staging of tauopathy, with a "reverse chronology" between limbic and entorhinal stages. AD structural progression may be associated with local tau accumulation but may also be related to axonal degeneration in remote sites and other limbic-predominant associated proteinopathies.

Introduction

Alzheimer's disease (AD) is a very slow progressing condition, likely to develop over three or four decades, from its preclinical phase to severe dementia and death. [START_REF] Sperling | Toward defining the preclinical stages of Alzheimer's disease: recommendations from the National Institute on Aging-Alzheimer's Association workgroups on diagnostic guidelines for Alzheimer's disease[END_REF][START_REF] Barthélemy | A soluble phosphorylated tau signature links tau, amyloid and the evolution of stages of dominantly inherited Alzheimer's disease[END_REF] Unfortunately, to date, no longitudinal study has been long enough to describe such a slow progressing evolution through all these stages, and the model of AD progression over time remains partially hypothetical. However, providing insights into the spatio-temporal spreading of brain alterations, which will ultimately lead to the full spectrum of AD clinical symptoms, is crucial in the prospect of future therapeutic actions.

The current model of AD progression is mainly based on the Braak staging of AD tauopathy. [START_REF] Braak | Neuropathological stageing of Alzheimer-related changes[END_REF] This scheme was initially built on the concatenation of post-mortem pathological brain examinations from donors at all the stages of disease progression. Ongoing longitudinal tau-PET imaging studies support the Braak staging. However, the currently available follow-up is still relatively short, and only a few studies aimed at investigating the presymptomatic stages of the disease in cognitively unimpaired participants. [START_REF] Jack | Predicting future rates of tau accumulation on PET[END_REF] Furthermore, first-generation tau-PET tracers do not allow the detailed investigation of medial-temporal structures due to off-target binding in the choroid plexus, and PET-histological correlation studies showed that these tracers lack sensitivity and could only identify patients with Braak stages 4. [START_REF] Soleimani-Meigooni | 18F-flortaucipir PET to autopsy comparisons in Alzheimer's disease and other neurodegenerative diseases[END_REF] Although the ≥ accumulation of AD tauopathy usually precedes measurable atrophy, [START_REF] Joie | Prospective longitudinal atrophy in Alzheimer's disease correlates with the intensity and topography of baseline tau-PET[END_REF] the anatomical progression of brain atrophy in AD may not perfectly match with tau topography, and atrophy can experimentally precede overt cell loss. [START_REF] Fung | Atrophy associated with tau pathology precedes overt cell death in a mouse model of progressive tauopathy[END_REF] Indeed, many other factors are likely to explain brain atrophy in AD: the vascular pathology and the neuroinflammation coupled with AD neuropathological changes, [START_REF] Hayley | Depression, dementia and immune dysregulation[END_REF] interactions with other proteinopathies, [START_REF] Spires-Jones | Interactions of pathological proteins in neurodegenerative diseases[END_REF] network disruption due to local pathology combined with axonal degeneration and distant atrophy, [START_REF] Villain | Sequential relationships between grey matter and white matter atrophy and brain metabolic abnormalities in early Alzheimer's disease[END_REF] local replication rate of tau aggregates, [START_REF] Meisl | In vivo rate-determining steps of tau seed accumulation in Alzheimer's disease[END_REF] and regional differential vulnerabilities to tau pathology and hypometabolism. [START_REF] Joie | Region-specific hierarchy between atrophy, hypometabolism, and β-amyloid (Aβ) load in Alzheimer's disease dementia[END_REF] Thus, the chronological progression over decades of neurodegeneration and brain atrophy in AD has never been formally depicted at the whole-brain level, and it is unknown whether it strictly follows the Braak staging of AD tauopathy.

Because no single longitudinal data over decades is available, we proposed to take advantage of BigData sharing in neuroimaging by analyzing MRI databases of both AD patients and healthy subjects at different ages covering the entire lifespan. From these cross-sectional data,

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we processed a massive number of MRI to generate extrapolated lifespan models of several brain structure volumes evolution. Then, we validated such an approach by comparing profiles extrapolated from these cross-sectional data with independent available "truly" longitudinal data. Finally, we described an MRI staging of volume loss in AD by describing the timing (and severity) of significant divergence between healthy subjects and AD patients' volumetric trajectories.

Methods

Datasets

Normal and AD trajectories of brain atrophy were estimated thanks to the aggregation of 9 open access databases. The number of subjects included in the present study is provided after QC:

-C-MIND: 236 images of control subjects from the C-MIND dataset (https://research.cchmc.org/c-mind/) are used in this study. All the 3D T1-weight (T1w) MPRAGE high-resolution MRI were acquired at the same site on a 3T scanner with spatial resolution of 1 mm 3 acquired using a 32 channel SENSE head-coil. study. We used the longitudinal dataset as defined in [1] and provided on the platform Clinica (http://www.clinica.run). These images are T1w acquired on 3T MR scanners with the ADNI protocol (http://adni.loni.ucla.edu/research/protocols/mri-protocols) and with custom MPRAGE sequence on the 1.5T scanners. In AIBL, the diagnosis of AD was made during clinical review panel meetings [START_REF] Ellis | The Australian Imaging, Biomarkers and Lifestyle (AIBL) study of aging: methodology and baseline characteristics of 1112 individuals recruited for a longitudinal study of Alzheimer's disease[END_REF] , according NINCDS/ADRDA criteria for possible or probable AD [START_REF] Mckhann | Clinical diagnosis of Alzheimer's disease: report of the NINCDS-ADRDA Work Group under the auspices of Department of Health and Human Services Task Force on Alzheimer's Disease[END_REF] .

Image processing

All the considered T1-weighted MRI were processed with AssemblyNet. [START_REF] Coupé | AssemblyNet: A large ensemble of CNNs for 3D whole brain MRI segmentation[END_REF] This software produces whole brain segmentation of fine-grained structures using a large ensemble of deep neural networks. On the 132 structures produced by AssemblyNet following the Neuromorphometrics labels, [START_REF] Klein | 101 labeled brain images and a consistent human cortical labeling protocol[END_REF] The AssemblyNet pipeline included the following steps. After denoising, [START_REF] Manjón | Improved estimates of partial volume coefficients from noisy brain MRI using spatial context[END_REF] images were corrected for inhomogeneity, [START_REF] Tustison | N4ITK: improved N3 bias correction[END_REF] affine-registered into the Montreal Neurological Institute (MNI) space using ANTS [START_REF] Avants | A reproducible evaluation of ANTs similarity metric performance in brain image registration[END_REF] and tissue-based intensity normalized. [START_REF] Manjón | Robust MRI brain tissue parameter estimation by multistage outlier rejection[END_REF] Then, the intracranial cavity was segmented using NICE method. [START_REF] Manjón | Nonlocal intracranial cavity extraction[END_REF] Afterwards, structure segmentation was achieved using 250 U-Nets through a multi-scale framework.

A multi-stage quality control procedure was performed by P.C., blinded of the subject's group, as previously described [START_REF] Coupé | Towards a unified analysis of brain maturation and aging across the entire lifespan: A MRI analysis[END_REF][START_REF] Coupé | Lifespan Changes of the Human Brain In Alzheimer's Disease[END_REF] . First, a visual assessment was done for all input images by checking screen shots of one sagittal, coronal, and axial slice in the middle of the 3D volume.

Images were rejected if partial head coverage, motion artefact, high distortion or abnormal noise level was detected. Then, a visual assessment of processing quality was carried out using the segmentation report which provides screenshots for each step of the pipeline. Images were rejected after this step in case of inaccurate registration in the MNI space, inaccurate intracranial cavity extraction, missing brain structures or over/under-segmentation of brain structures. A last control was performed by individually checking of all outliers (values higher/lower than 2 SD of the estimated model). For each outlier, the segmentation map was inspected using a 3D viewer. In case of segmentation failure, the subject was removed from the study.

Statistical Analyses

To compensate for the variability introduced by head size difference, models were estimated on normalized volumes (% of total intracranial volume). Left and right volumes were added to obtain the final volume structure. Statistics were performed with Matlab using default parameters.

Different strategies were considered to model the trajectories of each brain structure over time, as previously described. [START_REF] Coupé | Lifespan Changes of the Human Brain In Alzheimer's Disease[END_REF] Briefly, the candidate models were tested from the simplest to the most complex: (1) a linear model, (2) a quadratic model, and (3) a cubic model. A model was kept as a potential candidate only when simultaneously F-statistic based on ANOVA (i.e., model vs. constant model) was significant (p<0.05) and when all its coefficients were significant using t-statistic (p<0.05). We finally used the Bayesian Information Criterion (BIC)

F o r R e v i e w O n l y 7
to compare the candidate models. This model selection procedure was applied to all the considered structures.

Afterwards, z-score and "distance" between healthy and AD trajectories were computed on the estimated models. The prediction bounds were estimated with a confidence level of 95%. A brain structure was considered to be significantly smaller in AD compared to healthy aging when the two structural trajectories diverged and when their 95% confidence intervals no longer overlapped.

To compare our lifespan cross-sectional models and longitudinal models over restricted periods, we followed a previously published strategy [START_REF] Fjell | Critical ages in the life course of the adult brain: nonlinear subcortical aging[END_REF] where cross-sectional and longitudinal models were compared using Spearman correlation over the age period defined by longitudinal models. We performed two experiments to analyze model similarities and atrophy pattern similarities. First, we estimated correlations between the models' values for each structure.

Second, we estimated the correlation between vectors containing cross-sectional volume shrinkage and longitudinal atrophy for all the structures simultaneously. These volume changes were estimated as the difference between the value at the starting age of longitudinal models and the final one.

Finally, the sequence of significant divergence of the different brain structures was listed in chronological order to obtain the MRI staging scheme.

Data availability

MRI raw data from the different cohorts are available online (see Acknowledgments). Other data are available from the corresponding author upon reasonable request.

Results

Dataset description

To study structures' trajectories of healthy controls and AD across the entire lifespan, we compiled several open-access databases to construct two datasets. Their composition and characteristics are described in Table

Identification of brain structures diverging between healthy subjects and AD patients trajectories

Figure 2 shows the 19 brain structures (out of the 61 grey matter structures we have tested using AssemblyNet) that significantly diverged during lifespan between AD and healthy aging models. The theoretical starting age of statistically significant divergence between healthy and pathological models appears to be between 38 and 68 years old, depending on the structure.

The most affected structures over time were the amygdala and the hippocampus (distance between healthy and aging model at 90 years old = 3.20 and 2.65 respectively), followed by the entorhinal and parahippocampal cortices (distance = 1.18 and 1.13), the insula, and the inferior temporal gyrus (distance = 0.96 and 0.96).

Comparison of cross-sectional and longitudinal lifespan models

For all the 19 structures detected as significantly different between normal aging and Alzheimer's disease, we noticed a significant correlation between cross-sectional and longitudinal models (p<0.05) in the age range of [55. 5-93.4] for AD patients and [60. 5-92.4] for healthy subjects. The average correlation between the models' values over these 19 structures were 0.91 for AD models and 0.82 for healthy aging models. Moreover, we found significant correlations between cross-sectional volume shrinkage and longitudinal atrophy for both AD and healthy aging trajectories (p<0.05). The atrophy pattern correlation for these 19 structures were 0.90 for AD models and 0.85 for healthy aging models. Figure 3 showed the graphical congruence of models based on cross-sectional and longitudinal data on all the 19 affected structures.

The MRI staging scheme

We then mapped the sequential divergence of healthy and AD trajectories in middle frontal, anterior cingular, parietal (angular gyrus), insular cortices and pallidum.

Discussion

In this study, we combined multiple large-scale MRI databases and whole-brain segmentation of fine-grained structures using a large ensemble of deep neural networks to describe the first exhaustive chronological structural progression of AD over decades and the differential severity of volumetric structure alterations. We finally proposed the following brain MRI staging This MRI staging scheme of atrophy progression is close to but does not fully overlap with Braak staging of AD tauopathy. [START_REF] Braak | Neuropathological stageing of Alzheimer-related changes[END_REF] The main difference between these two staging models is the "reverse chronology" between limbic and entorhinal stages (the earliest stages). Indeed, transentorhinal and entorhinal cortices are the first affected by tau neurofibrillary tangles (Braak stage I and II) before hippocampus (CA1 pyramidal cells) and amygdala (Braak stage III and IV). After these entorhinal and limbic stages, the sequential involvement of the thalamus and the striatum before the isocortical associative areas is concordant between MRI and Braak staging. However, Braak staging can be questioned. A recent 3D mapping of human tau pathology suggests, for instance, a more widespread distribution of neurofibrillary tangles at the early stages of AD: similar levels of tau burden were found in entorhinal areas and the amygdala, the hippocampus, and the temporopolar cortex, supporting our MRI findings. [START_REF] Yushkevich | Three-dimensional mapping of neurofibrillary tangle burden in the human medial temporal lobe[END_REF] Although tau distribution is usually correlated with focal atrophy in AD, recent tau-PET studies support our findings and the "early-stage discrepancy hypothesis" between atrophy and tau staging schemes. On the one hand, Mak et al. reported a disproportionate increase in tau accumulation in widespread regions compared to cortical atrophy that was restricted to the temporal areas during the same period. [START_REF] Mak | In vivo coupling of tau pathology and cortical thinning in Alzheimer's disease[END_REF] On the other hand, Harrison and colleagues reported that atrophy might exceed tau accumulation by including brain regions relatively unaffected by tauopathy. [START_REF] Harrison | Longitudinal tau accumulation and atrophy in aging and alzheimer disease[END_REF] Furthermore, MRI-pathological studies failed to correlate the rate of hippocampal atrophy with early hippocampal tau neurofibrillary tangles during aging. [START_REF] Erten-Lyons | Neuropathologic basis of age-associated brain atrophy[END_REF] In turn, the exceptional vulnerability of hippocampal CA1 pyramidal neurons to AD neuropathological changes [START_REF] West | Differences in the pattern of hippocampal neuronal loss in normal ageing and Alzheimer's disease[END_REF] may explain differential atrophy between the hippocampus and the entorhinal cortex over time.

Experimentally, when pathological tau is specifically expressed in the entorhinal cortex of transgenic mice, atrophy is described in the hippocampus, a remote unaffected brain region at the early stage of this model, through axon degeneration of the perforant pathway (major afference from the entorhinal cortex to the hippocampus). [START_REF] Fung | Atrophy associated with tau pathology precedes overt cell death in a mouse model of progressive tauopathy[END_REF] The pathological accumulation of tau oligomers is also known to impair axonal transport before neurofibrillary tangles formation, inducing early axonal degeneration and the loss of synaptic transmission in the target

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structures. [START_REF] Gyparaki | Tau forms oligomeric complexes on microtubules that are distinct from tau aggregates[END_REF][START_REF] Combs | Tau and Axonal Transport Misregulation in Tauopathies[END_REF] In the case of the amygdala, early atrophy may also be due to the presence of pathological tau in the perirhinal, postrhinal, and transentorhinal cortices (Braak stage I), which give rise to important afferent projections to the amygdala in primates. [START_REF] Mcdonald | Cortical pathways to the mammalian amygdala[END_REF] Finally, atrophy has to be considered as the result of complex cellular processes including cell death associated with tau accumulation, but also from axonal degeneration in remote sites. This diaschisis phenomenon may precede tau tangles in the limbic system, explaining the "early-stage discrepancy" between MRI and Braak staging.

In addition, regional atrophy in AD does not rely on a single biological process, but instead reflects the local impact of many different possible mechanisms leading to neurodegeneration.

Mainly, limbic-predominant age-related TDP-43 encephalopathy (LATE) neuropathological changes are frequent during aging and often associated with AD neuropathological changes.

TDP-43 inclusions are known to accelerate brain atrophy and mainly affect the amygdala (stage 1) and the hippocampus (stage 2). The frequent co-occurrence (up to 75% of cases) of these proteinopathies may explain the excess of limbic atrophy compared to entorhinal atrophy at the early stages of AD. [START_REF] Josephs | Protein contributions to brain atrophy acceleration in Alzheimer's disease and primary age-related tauopathy[END_REF] Indeed, pathological-MRI correlation studies showed that the hippocampus and the amygdala were the most frequently affected regions in TDP-43 positive brains and that the magnitude of atrophy mediated by TDP-43 inclusions was similar to taurelated atrophy. [START_REF] Bejanin | Antemortem volume loss mirrors TDP-43 staging in older adults with non-frontotemporal lobar degeneration[END_REF] From the conceptual point of view, it is essential to keep in mind that the present MRI staging scheme (such as the Braak staging scheme) only describes the most frequent "limbicpredominant" and "typical" progressions of AD. [START_REF] Planche | Clinical relevance of brain atrophy subtypes categorization in memory clinics[END_REF][START_REF] Planche | Evolution of brain atrophy subtypes during aging predicts long-term cognitive decline and future Alzheimer's clinical syndrome[END_REF] This model only describes the "average" structural course of AD and does not apply to "atypical" AD, such as logopenic primary progressive aphasia, posterior cortical atrophy or behavioral AD, which are driven by different patterns of atrophy and represent less common "extremes" of the AD anatomical spectrum [START_REF] Vogel | Subtypes of Alzheimer's disease: questions, controversy, and meaning[END_REF] .

Indeed, the methodology used in the present work does not take into account the recent description by Vogel and colleagues of distinct trajectories of tau deposition in AD [START_REF] Vogel | Four distinct trajectories of tau deposition identified in Alzheimer's disease[END_REF] . This work proposes an alternative to Braak's model concerning tau spreading pattern, underlining the heterogeneity of AD development from one subject to another (not using pathological examination, but cross-sectional tau-PET with its limitations in terms of sensitivity). However, the most prevalent spatiotemporal trajectory of tau pathology was limbic in Vogel's work, and spatial convergence was observed between AD trajectories. Furthermore, our MRI scheme of atrophy progression includes structures characterizing three of the four distinct trajectories of tau deposition, namely amygdala, hippocampus and entorhinal cortex (limbic trajectory),

F o r R e v i e w O n l y
middle temporal gyrus, parahippocampal cortex, and other temporal areas (lateral temporal trajectory) and parietal (angular gyrus) cortices (medial temporal lobe-sparing trajectory). Thus, our "average" MRI staging scheme may not apply to all patients with AD, but to the greatest number, especially because cohorts such as ADNI 1&2 and AIBL included patients with "Alzheimer clinical syndrome" [START_REF] Jack | NIA-AA Research Framework: Toward a biological definition of Alzheimer's disease[END_REF] or "probable" AD criteria [START_REF] Mckhann | Clinical diagnosis of Alzheimer's disease: report of the NINCDS-ADRDA Work Group under the auspices of Department of Health and Human Services Task Force on Alzheimer's Disease[END_REF][START_REF] Mckhann | The diagnosis of dementia due to Alzheimer's disease: recommendations from the National Institute on Aging-Alzheimer's Association workgroups on diagnostic guidelines for Alzheimer's disease[END_REF] (i.e. subjects with a single or multi-domain amnestic presentation, likely to have a limbic-predominant pattern of atrophy).

From the methodological point of view, we acknowledge that the estimated point of divergence between healthy and pathological trajectories remains hypothetical because of the lack of AD patients younger than 55 in the analyzed cohorts. Another limitation of this study is that we cannot exclude that the anatomy of a structure of interest (the definition of boundaries on brain atlas, the precision of segmentation using MRI contrast, …) may impact the capability to depict volumetric modifications; this observation being particularly relevant for the entorhinal cortex. [START_REF] Fung | Comparative Utility of Manual versus Automated Segmentation of Hippocampus and Entorhinal Cortex Volumes in a Memory Clinic Sample[END_REF] Thanks to an external validation using AIBL data, we have shown that our models based on cross-sectional ADNI data are reliable approximate of "true" longitudinal trajectories, at least after 55 years old. Furthermore, the early atrophy in the amygdala and the hippocampus are consistent with a previous work from our group using a different method for structure segmentation. [START_REF] Coupé | Lifespan Changes of the Human Brain In Alzheimer's Disease[END_REF] We also found substantial similarities with a previous article from another lab comparing the pattern of change of subcortical structures estimated on lifespan cross-sectional and longitudinal models in healthy aging. [START_REF] Fjell | Critical ages in the life course of the adult brain: nonlinear subcortical aging[END_REF] Our study is however the first to assess the divergence between this healthy aging trajectory and AD structural progression using inferred lifespan AD model, and at the whole-brain level.

To conclude, we have modeled the "average" global structural progression of AD over the entire course of the disease. We found that the time-course and the severity of structural alterations were close but did not completely overlap with Braak staging. We proposed a descriptive MRI staging scheme that will help better define the disease and interpret future studies looking at the differential vulnerabilities of brain structures to AD pathological processes.

Figure 4 .

 4 Schematically, five major stages in AD structural progression seemed to appear :(1) hippocampus and amygdala; (2) middle temporal gyrus; (3) entorhinal cortex, parahippocampal cortex, and other temporal areas (inferior temporal gyrus, superior temporal gyrus, temporal pole and fusiform gyrus); (4) thalamus and striatum (accumbens, caudate, putamen) and(5)

  scheme of structural progression in AD : (1) hippocampus and amygdala; (2) middle temporal gyrus; (3) entorhinal cortex, parahippocampal cortex, and other temporal areas; (4) striatum and thalamus and (5) middle frontal, cingular, parietal and insular cortices. The most severely affected structures during the entire course of AD were the amygdala and the hippocampus, followed by the entorhinal and parahippocampal cortices.

Figure 1 .

 1 Figure legends

Figure 2 .

 2 Figure 2. Lifespan trajectories based on z-scores of normalized brain volumes for health aging subjects (black line) and AD patients (red line). Black dots represent all healthy individuals and red dots AD patients. The prediction bounds of the models are estimated with a confidence level at 95%. The orange curve represents the distance between the healthy and pathological models. The orange area indicates the time period where confidence intervals of both models do not overlap. Only models detected as significantly different between healthy aging and AD are presented in this figure (19 brain structures out of 61 tested using AssemblyNet).

Figure 3 .

 3 Figure 3. Graphical comparison of cross-sectional (whole lines) and longitudinal (dotted lines) trajectories based on z-scores of normalized brain volumes for health aging (black lines and dots) and AD patients (red lines and dots). Only the 19 structures detected as significantly different between healthy and pathological conditions are represented here. The average correlation coefficients for these 19 structures were 0.91 for AD models and 0.82 for healthy aging models.

Figure 4 .

 4 Figure 4. The MRI staging scheme of structural progression of AD. The figure represents the chronological progression of distances between healthy and AD trajectories. The severity of structural divergence is color-coded according to the bar at the bottom right of the figure.

F

Figure 1 .Figure 2 .Figure 3 .

 123 Figure 1. Illustration of the AssemblyNet segmentation in the three axes. It included the bilateral segmentation of 9 subcortical structures, 17 frontal gyri/lobules, 8 temporal gyri/lobules, 6 parietal gyri/lobules, 8 occipital gyri/lobules, 6 gyri in the limbic cortex, 5 sub-regions of the insular cortex, the ventricle and the cerebellum. 150x46mm (300 x 300 DPI)

Figure 4 .( 2 )

 42 Figure 4. The MRI staging scheme of structural progression of AD. The figure represents the chronological progression of distances between healthy and AD trajectories. The severity of structural divergence is colorcoded according to the bar at the bottom right of the figure. 180x124mm (300 x 300 DPI)

  https://mc.manuscriptcentral.com/braincom Manuscripts submitted to Brain Communications

Table 1 :

 1 from AD patients remained for the analyses. MRI from the longitudinal AIBL database (n=113) were used as an external testing dataset to validate our models. Consequently, we used 2665 MRI from healthy controls to estimate our healthy lifespan models. To infer AD models over the entire lifespan, we combined 1874 healthy controls younger than 55 years of age (all the subjects younger than 55 in the 2665 that were used for healthy aging models) and 332 AD patients older than 55 to build our lifespan AD models.

	F o
	r
	R e v
	i e w
	O
	n l
	y

. After QC, 3512 MRI from healthy controls and 415 Dataset description. This table provides the name of the dataset, the number (n) of considered images (after quality control), the gender proportion, and the average ages and intervals in brackets.

https://mc.manuscriptcentral.com/braincom Manuscripts submitted to Brain Communications

Acknowledgements

The C-MIND data used in the preparation of this article were obtained from the C-MIND Data 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. We wish to thank all investigators of these projects who collected these datasets and made them freely accessible. This manuscript reflects the views of the authors and may not reflect the opinions or views of the database providers.

Funding

This study was achieved within the context of the Human Brain Project, the French National Research Agency for the DeepvolBrain project (ANR-18-CE45-0013), the Laboratory of Excellence TRAIL ANR-10-LABX-57 for the BigDataBrain project and the CNRS/INSERM for the DeepMultiBrain project. VP received grants from Foundation Bettencourt Schueller (CCA-Inserm-Bettencourt). JVM research was supported by the Spanish DPI2017-87743-R grant from the Ministerio de Economia, Industria y Competitividad of Spain. The sponsors did not participate in any aspect of the design or performance of the study, including data collection, management, analysis, and the interpretation or preparation, review, and approval of the manuscript.

Repository created by the C-MIND study of Normal Brain Development. 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). This

Author Contributions

Conception and design of the study: VP, TT, GC and PC. Analysis of data: JVM, BM and PC.

Drafting the manuscript: VP and PC. Revision of the manuscript for important intellectual contents: all authors.

Potential Conflicts of Interest

The authors declare no competing financial interests relative to the present study.


Marius Bozga

Jean-Claude Fernandez

Lucian Ghirvu

Susanne Graf

Jean-Pierre Krimm

Laurent Mounier

IF: A Validation Environment for Timed Asynchronous Systems

Introduction

Formal validation of distributed systems relies on several speci cation formalisms (such as the international standards lotos 15] or sdl 16]), and it requires di erent kinds of tools to cover the whole development process. Presently, a wide range of tools are available, either commercial or academic ones, but none of them ful lls in itself all the practical needs. Commercial tools (like Objectgeode 20], sdt 1], statemate 14],etc.) provide several development facilities, like editing, code generation and testing. However, they are usually restricted to basic veri cation techniques (exhaustive simulation, deadlock detection, etc) and are \closed" in the sense that there are only limited possibilities to interface them with others. On the other hand, there exist many academic tools (like smv 19], hytech 12], kronos 22], uppaal 18], spin 13], invest 2], etc.) o ering a broad spectrum of quite e cient veri cation facilities (symbolic veri cation, on-the-y veri cation, abstraction techniques, etc.), but often supporting only low-level input languages. This may restrict their use at an industrial scale. This situation motivated the development of if, an intermediate representation for timed asynchronous systems together with an open validation environment. This environment ful lls several requirements. First of all, it is able to support di erent validation techniques, from interactive simulation to automatic property checking, together with test case and executable code generation. Indeed, all these functionalities cannot be embodied in a single tool and only tool integration facilities can provide all of them. For a sake of e ciency, this environment supports several levels of program representations. For instance it is well-known that model-checking veri cation of real life case studies usually needs to combine di erent optimization techniques to overcome the state explosion problem. In particular, some of these techniques rely on a syntactic level representation (like static analysis and computations of abstractions) whereas others techniques operate on the underlying semantic level. Another important feature is to keep this environment open and evolutive. Therefore, tool connections are performed by sharing either input/output formats, or libraries of components. For this purpose several well-de ned application programming interfaces (apis) are provided.

The if validation environment relies on three levels of program representation: the speci cation level, the if intermediate level, and the lts semantic model level. The speci cation level is the initial program description, expressed for instance using an existing language. To be processed, this description is (automatically) translated into its if representation. Currently the main input speci cation formalism we consider is sdl, but connections with other languages such as lotos or promela could also be possible. The implicit enumerative representation consists in a set of C functions and data structures allowing to compute on demand the successors of a given state (following the open-caesar 11] philosophy). This piece of C code is generated by the if2c compiler, and it can be linked with a \generic" exploration program performing on-the-y analysis.

In the symbolic representation sets of states and transitions of the lts are expressed by their characteristic predicates over a set of nite variables. These predicates are implemented using decision diagrams (bdds). Existing applications based on this api are symbolic model-checking and minimal model generation.

Finally, the explicit enumerative representation simply consists in an lts le with an associated access library. Although such an explicit representation is not suitable for handling large systems globally, it is still useful in practice to minimize some of its abstractions with respect to bisimulation based relations.

Components description

We brie y present here the main components of the environment, together with some external tools for which a strong connection exists.

The speci cation level components. Objectgeode 20] is a commercial toolset developed by TTT supporting sdl, msc and omt. In particular, this toolset provides an api to access the abstract tree generated from an sdl speci cation. We have used this api to implement the sdl2if translator, which generates operationally equivalent if speci cations from sdl ones. Given the static nature of if, this translation does not cover the dynamical features of sdl (e.g., process instances creation).

The intermediate level components. live 5] implements several algorithms based on static analysis to transform an if speci cation. A rst transformation concerns dead variable resetting (a variable is dead at some control point if its value is not used before being rede ned). This optimisation can be also applied to bu er contents (a message parameter is dead if its value is not used when the message is consumed). Although very simple, such optimisation is particularly e cient for state space generation (reductions up to a factor 100 were frequently observed), while preserving the exact behaviour of the original speci cation The semantic model level components. cadp 9] is a toolset for the veri cation of lotos speci cations. It is developed by the vasy team of Inria Rhône-Alpes and verimag. Two of its model-checkers are connected to the if environment: aldebaran (bisimulation based), and evaluator (alternating-free -calculus).

For both tools, diagnostic sequences are computed on the lts level and they can be translated back into msc to be observed at the speci cation level. kronos 22] is a model-checker for symbolic veri cation of tctl formulae on communicating timed automata. The current connection with the if environment is as follows: control states and discrete variables are expressed using the implicit enumerative representation, whereas clocks are expressed using a symbolic representation (particular polyhedra).

tgv 10] is a test sequence generator for conformance testing of distributed systems (joint work between verimag and the pampa project of irisa). Test cases are computed during the exploration of the model and they are selected by means of test purposes.

Results and perspectives

The if environment has already been used to analyze some representative sdl specications, like sscop, an Atm signalisation layer protocol 8], and mascara, an Atm wireless transport protocol. It is currently used in several on going industrial casestudies, including the real-time multicast protocol pgm, and the control part of the Ariane 5 launcher ight sequencer. The bene ts of combining several techniques, working at di erent program level, were clearly demonstrated. In particular, traditional model-checking techniques (as provided by Objectgeode) were not su cient to complete on these large size examples. Several directions can be investigated to improve this environment. First of all, other formalisms than sdl could be connected to if. In particular, the translation from a subset of uml is envisaged. To this purpose new features will be added to handle dynamic process creation and parametrized network speci cations. From the veri cation point of view, the results obtained using the currently implemented static analysis techniques are very encouraging. We now plan to experiment some more sophisticated algorithms implemented in the invest tool 2], such as structural invariant generation and general abstraction computation techniques for in nite space systems. Another promising approach to verify large systems consists in generating their underlying model in a compositional way: each sub-system is generated in isolation, and the resulting ltss are minimized before being composed with each other. The if environment o ers all the required components to experiment it in an asynchronous framework 17]. The if package can be downloaded at http://www-verimag.imag.fr/DIST SYS/IF.

Fig. 1 .

 1 Fig. 1. An open validation environment for if

  Process transitions are guarded commands consisting of synchronous/asynchronous inputs and outputs, variable assignments, and clock settings. Bu ers have various queuing policies ( fo, stack, bag, etc.), can be bounded or unbounded, and reliable or lossy. A well-de ned api allows to consult and modify the abstract tree of the if representation. Since all the variables, clocks, bu ers and the communication structure are still explicit, high-level transformations based on static analysis (such as live variables computation) or program abstraction can be applied. Moreover, this api is also well suited to implement translators from if to other speci cation formalisms.The semantic model level gives access to the lts representing the behaviour of the if program. Depending on the application considered, three kinds of api are proposed:

The intermediate level corresponds to the if

representation 7]

. In if, a system is expressed by a set of parallel processes communicating either asynchronously through a set of bu ers, or synchronously through a set of gates. Processes are based on timed automata with deadlines 3], extended with discrete variables.

  . A second transformation is based on the slicing technique 21]. It allows to automatically abstract a given speci cation by eliminating some irrelevant parts w.r.t. a given property or test purpose 6]. if2pml 4] is a tool developed at Eindhoven TU to translate if speci cations into

promela.

? Work partially supported by R egion Rhône-Alpes, France