MD Vito Ag Ricigliano

MD Emanuele Morena

MD Annalisa Colombi

PhD Matteo Tonietto

MSc Mariem Hamzaoui

PhD Emilie Poirion

MD, PhD Michel Bottlaender

PhD Philippe Gervais

MD Celine Louapre

MD, PhD Benedetta Bodini

MD, PhD Bruno Stankoff
email: bruno.stankoff@aphp.fr

Choroid plexus enlargement in inflammatory multiple sclerosis: 3T MRI and translocator protein PET evaluation

Keywords: sclerosis, RRMS = relapsing-remitting multiple sclerosis, PMS = progressive multiple sclerosis, CP = choroid plexus, TSPO = translocator protein

Introduction

In multiple sclerosis (MS), the biological mechanisms underlying central nervous system (CNS) attack are not yet fully understood. [START_REF] Reich | Multiple sclerosis[END_REF] A predominant hypothesis is that an antigen-specific immune activation occurs at first in the periphery and is then transferred into the CNS, mainly through lymphocyte migration across the blood brain barrier. [START_REF] Hemmer | Role of the innate and adaptive immune responses in the course of multiple sclerosis[END_REF][START_REF] Baecher-Allan | Multiple Sclerosis: Mechanisms and Immunotherapy[END_REF] The contribution of an altered blood to cerebrospinal fluid (CSF) barrier and of a CSF clearance deficit remains debated. [START_REF] Vidaurre | Cerebrospinal fluid ceramides from patients with multiple sclerosis impair neuronal bioenergetics[END_REF][START_REF] Wentling | A metabolic perspective on CSF-mediated neurodegeneration in multiple sclerosis[END_REF] The choroid plexuses (CPs) are primarily responsible for the production of the CSF but are also part of the blood-CSF barrier [START_REF] Kaur | The Choroid Plexus in Healthy and Diseased Brain[END_REF] and contribute to the regulation of CNS immunosurveillance. [START_REF] Ghersi-Egea | Molecular anatomy and functions of the choroidal bloodcerebrospinal fluid barrier in health and disease[END_REF][START_REF] Schwartz | The resolution of neuroinflammation in neurodegeneration: Leukocyte recruitment via the choroid plexus[END_REF] In the murine model of experimental autoimmune encephalomyelitis (EAE), inflammation in the CPs and CSF precedes the formation of parenchymal inflammatory infiltrates and the development of demyelinating white matter (WM) lesions, [START_REF] Reboldi | C-C chemokine receptor 6-regulated entry of TH-17 cells into the CNS through the choroid plexus is required for the initiation of EAE[END_REF][START_REF] Schmitt | Brain leukocyte infiltration initiated by peripheral inflammation or experimental autoimmune encephalomyelitis occurs through pathways connected to the CSF-filled compartments of the forebrain and midbrain[END_REF] leading to the hypothesis that CP involvement might be an early phenomenon in human demyelinating diseases.

In post-mortem studies, patients with MS show more antigen-presenting cells in CP stroma, an infiltration of peripheral leukocytes, [START_REF] Rodríguez-Lorenzo | Correction to: Inflammation of the choroid plexus in progressive multiple sclerosis: Accumulation of granulocytes and T cells[END_REF][START_REF] Vercellino | Involvement of the choroid plexus in multiple sclerosis autoimmune inflammation: A neuropathological study[END_REF] a disruption of tight junctions in the CP epithelium, [START_REF] Kooij | Disturbed function of the blood-cerebrospinal fluid barrier aggravates neuro-inflammation[END_REF] and an endothelial overexpression of adhesion molecules involved in lymphocyte migration. [START_REF] Vercellino | Involvement of the choroid plexus in multiple sclerosis autoimmune inflammation: A neuropathological study[END_REF] Despite the body of evidence available from translational and neuropathologic studies, we still lack an in vivo demonstration that CPs could be involved in the inflammatory process characterizing MS.

Non-invasive evaluation of CP morphology with 3D high-field MRI has been recently performed for noninflammatory neurological diseases. [START_REF] Tadayon | Choroid plexus volume is associated with levels of CSF proteins: relevance for Alzheimer's and Parkinson's disease[END_REF][START_REF] Lizano | Association of Choroid Plexus Enlargement With Cognitive, Inflammatory, and Structural Phenotypes Across the Psychosis Spectrum[END_REF] In MS, a higher brightness of CP on T1 post-gadolinium sequences and concurrent MS and CP papilloma have been described. [START_REF] Dixon | Multiple Sclerosis and the Choroid Plexus: Emerging Concepts of Disease Immunopathophysiology[END_REF][START_REF] Kim | Choroid plexus changes on magnetic resonance imaging in multiple sclerosis and neuromyelitis optica spectrum disorder[END_REF] However, to our knowledge, the relationship between inflammation and CP morphology has never been assessed. In the present study, we combined 3D MRI techniques with translocator protein (TSPO) and fluorodeoxyglucose (FDG) PET, [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF][START_REF] Airas | Imaging neuroinflammation in multiple sclerosis using TSPO-PET[END_REF] to explore the alterations of the CPs and their relationship with inflammation on a large sample of patients with MS and age-and sex-matched healthy controls (HC).

Materials and Methods

Study design

For the three prospective studies (EudraCT Number:2008-004174-40;ClinicalTrials.gov:NCT02305264, NCT01651520) on which this secondary analysis was performed, written informed consent was obtained from all participants and the studies were approved by the local ethic committees. The full study protocols can be accessed via https://www.clinicaltrialsregister.eu and https://clinicaltrials.gov. Data generated or analyzed during the study are available from the corresponding author by request.

The study included a convenience series of patients with relapsing-remitting (RRMS) or progressive MS (PMS) (age≥18 years, 1 month after corticosteroid/immunosuppressive therapy), and age-and sex-matched HCs. These were included from three neuroimaging protocols between May 2009 and September 2017 at the Paris Brain Institute, France. Exclusion criteria were: i) impossibility to perform a PET and MRI exam for any reason (e.g. claustrophobia, pace-maker or intra-ocular foreign body); ii) severe or uncontrolled renal, hepatic, hematological, gastrointestinal pulmonary or cardiac disease; iii) other chronic neurological disease;

iii) prior participation in other research protocols or clinical care in the last year such that radiation exposure would exceed the annual guidelines; for women: pregnancy, lactation, lack of efficient contraception.

At study entry, patients with MS were scored on the Expanded Disability Status Scale (EDSS) and divided into three groups: no treatment, on first-line, or second-line treatment. Moreover, the number of relapses and EDSS in the 2 years preceding and following inclusion were collected.

A subgroup underwent a 18 F-DPA-714 PET scan at study entry. After genotyping of the rs6971 polymorphism of the TSPO gene, 20 low-affinity binders were excluded from further analysis, that being an additional exclusion criterion in this neuroimaging protocol. The remaining 37 patients with MS and 19 HCs have been reported in a prior article that dealt with the generation of PET-derived individual maps of innate immune cell activation, [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] whereas the present article focuses on the analysis of the choroid plexuses. From this group, all patients and half of the HC (n=9) were planned to undergo a 18 F-FDG PET scan within the 2 weeks preceding or following the [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-DPA-714 exam (ClinicalTrials.gov:NCT02305264). 3 subjects (1 MS, 2 HC) withdrew after the 18 F-DPA-714 PET scan for personal reasons, leaving a total of 36 patients with MS and 7 HCs for the [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF]

Image acquisition

Patients were scanned on a 3T MRI system with a 32-channel head coil (60 patients with MS/32 HCs on a Siemens TRIO, while 37 patients with MS/12 HCs on a Siemens PRISMA). Acquired sequences included 3D T1-weighted magnetization-prepared rapid gradient echo (MPRAGE, repetition time (TR)/echo time (TE):2300/2.98 ms), T2-weighted (TR/TE:4100/83 ms), and pre-and post-gadolinium (Dotarem, Guerbet Diagnostic Imaging) T1 spin-echo (TR/TE:700/14 ms). [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-DPA-714 and 18 F-FDG PET images were acquired on a Siemens ECAT high-spatial-resolution research tomograph (HRRT; CPS Innovations) with a 90-min or 60-min dynamic acquisition, respectively (Supplemental 1).

Post-processing

In patients with MS, WM lesions were contoured on T2-w scans, and gadolinium-enhancing lesions on postgadolinium T1-SE scans using Jim (v6.0,http://www.xinapse.com/). Binary lesion masks were aligned to 3D-T1 MPRAGE scans with FLIRT (v5.0.9,http://fsl.fmrib.ox.ac.uk/). [START_REF] Jenkinson | A global optimisation method for robust affine registration of brain images[END_REF] After lesion-filling, Freesurfer (v6.0,http://surfer.nmr.mgh.harvard.edu/) was used on 3D-T1 MPRAGE scans to estimate total intracranial volume (TIV) and to segment gray matter, WM and CSF, with manual correction when necessary.

The CPs of the lateral ventricles were manually segmented by three trained neurologists independently (VAGR, EM, AC) (3 year expertise in MRI processing) and systematically corrected by a fourth neurologist (BB, 12 year expertise in MRI processing) on the sagittal, axial and coronal plans of the 3D-T1 MPRAGE scans using ITK-SNAP (v3.8.0,http://www.itksnap.org/), and their volume was calculated (Fig 2a-b).

Readout sessions were performed by each of the three segmenting neurologists with an interval of one week.

The status of the subject (HC or MS) was blinded to the fourth neurologist who corrected the segmentations.

In case of disagreement, images were reviewed by all neurologists at once in a common session, and a final decision on the segmentation was taken by majority. Freesurfer CP segmentation was also performed as a crosscheck. The CPs of the third and fourth ventricles were not included in the analysis, given their inconstant visualization. [START_REF] Horsburgh | Bochdalek's flower basket: applied neuroimaging morphometry and variants of choroid plexus in the cerebellopontine angles[END_REF] The following regions of interest (ROIs) were defined on T1-w scans using Freesurfer: (i) whole brain without ventricles; (ii) cortex; (iii) WM; (iv) thalami, given their role as a crucial barometer of diffuse parenchymal damage in MS; and (v) ventricles. In patients with MS, three additional ROIs were selected: (i) T2-w lesions; (ii) perilesions, corresponding to the 2mm rim surrounding each lesion; (iii) normal-appearing WM (NAWM), defined as the WM without lesions and perilesions on T2-w scans. The volume of CPs and other ROIs was divided by the TIV to obtain the corresponding normalized value.

Voxel-wise [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-DPA-714 distribution volume ratio (DVR) parametric maps were obtained using the Logan graphical analysis based on reference region. [START_REF] García-Lorenzo | Validation of an automatic reference region extraction for the quantification of [18F]DPA-714 in dynamic brain PET studies[END_REF] All ROIs were aligned to the corresponding PET images using FLIRT [START_REF] Horsburgh | Bochdalek's flower basket: applied neuroimaging morphometry and variants of choroid plexus in the cerebellopontine angles[END_REF] to extract the mean DVR values. Mean 18 F-DPA-714 and 18 F-FDG uptake inside the CPs were calculated as the average standardized uptake value (SUV), [START_REF] Hirvonen | Increased in Vivo Expression of an Inflammatory Marker in Temporal Lobe Epilepsy[END_REF][START_REF] Mertens | Distribution Patterns of 18F-labelled Fluoromethylcholine in Normal Structures and Tumors of the Head: A PET/MRI Evaluation[END_REF] after performing partial volume correction of the CPs with the single target correction method in PETPVC (v1.2.0b,https://github.com/UCL/PETPVC; Supplemental 1). [START_REF] Thomas | PETPVC: A Toolbox for Performing Partial Volume Correction Techniques in Positron Emission Tomography[END_REF]

Statistical Analysis

Statistical analyses were performed with STATA (v14.0,https://www.stata.com/), considering two-sided P<.05 as significant. Sample size was calculated to detect a large effect (Cohen's d≥0.8) for the difference in mean CP volume between groups, with power=80%, alpha=0.05.

Wilcoxon-Mann-Whitney and Fisher's exact tests were used as appropriate to assess differences in age, sex, TSPO affinity and MRI scanner between patients with MS and HCs, and in disease duration and treatment between RRMS and PMS. Ordered logistic regressions were used for differences in EDSS between MS subgroups, and for the association of CP volume with 4-year annualized relapse rate (ARR, from 2 years before to 2 years after inclusion), baseline EDSS and 2-year EDSS change.

Multivariable linear regressions were fitted to test: 1) differences between the whole MS group or subgroups and HC, and between MS subgroups, regarding: i) CP volume, adjusting for ventricular and brain volume; ii) CP [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-DPA-714 SUV 60-90 and [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-FDG SUV 45-60 , adjusting for CP volume; iii) CP volume between gadolinium-positive and gadolinium-negative patients with MS;

2) correlations between CP volume and: i) age, sex, disease duration, ROI volumes (adjusting for brain volume in the last case); ii) [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-DPA-714 DVR of parenchymal brain ROIs; ii) CP [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-DPA-714 SUV 60-90 and [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-FDG SUV 45-60 .

Pearson's r was used to assess the strength of correlations, the inter-rater reliability and the manual-Freesurfer correlation of CP segmentation. Regressions were adjusted for: i) age and sex; ii) MRI scanner when MRI variables were tested; iii) brain volume and TSPO affinity in the subgroup receiving DPA; iv) treatment in patients with MS. Results were Bonferroni corrected for multiple comparisons and post-hoc analyses were repeated on RRMS and PMS subgroups.

Results

Patient Characteristics

We evaluated 97 patients with MS (61 with relapsing-remitting RRMS and 36 with progressive PMS) and 44 age-and sex-matched HC. Patients with MS and HC (

Enlarged choroid plexuses are associated with lower brain volume

In patients with MS, larger CPs were associated with lower volume in the whole brain (r:-0.33; 95% CI=-0.49:-0.14; P=.004)(Fig 3a), the thalami (r:-0.37; 95% CI=-0.53:-0.19; P<.001) and the NAWM (r:-0.46; 95% CI=-0.61:-0.29; P=.004) but not in the cortex (r:-0.26; 95% CI=-0.38:0.01; P>.99)(Fig 3b-d). Post-hoc subgroup analysis of RRMS and PMS showed similar results (RRMS: whole brain: r:-0.29; 95% CI=-0.50:-0.03; P=.02; thalami: r:-0.45; 95% CI=-0.63:-0.23; P=.002; NAWM: r:-0.52; 95% CI=-0.68:-0.30; P=.005; PMS: whole brain: r:-0.38; 95% CI=-0.63:-0.06; P=.02; NAWM: r:-0.51; 95% CI=-0.72:-0.22; P=.004).

In HC, CP volume was not associated with any ROI volumes (whole brain: P=.18; thalami: P>.99; WM: P>.99; cortex: P>.99)(Table 2).

Choroid plexus enlargement is associated with brain inflammation and relapses in MS

Choroid plexus volume correlates with T2 lesion load and is higher in patients with active MS.

Enlarged CPs were associated with greater T2-w WM lesion volume in the whole MS group (r:0. In the whole MS group, patients with at least one gadolinium-enhancing lesion had 22% larger CPs (mean volume:18.24.9x10 -4 ) compared with those without active lesions (mean volume:14.94x10 -4 ; coeff:3.7x10 - 4 ; P<.001)(Fig 4b). This result was confirmed on both RRMS (coeff:3.9x10 -4 ; P=.002) and PMS (coeff:4.98x10 -4 ; P=.04).

In the whole MS group, CP volume did not correlate with EDSS, 2-year EDSS change, disease duration or 4year ARR (P=.58, P>.99, P=.20 and P=.19, respectively). In subgroup analysis, a higher 4-year ARR, reflecting a more active disease, was associated with larger CPs in RRMS (r:0.37; 95% CI=0.10:0.55; coeff:1.36x10 3 ; P=.005)(Fig 4c) but not in PMS (P=.66). More in detail, in the RRMS subgroup, patients who experienced ≥1 relapse during the 2-year follow-up (n=18) had larger CPs at baseline (mean volume: 17.54.9x10 -4 ) compared to patients who remained stable over time (n=43, mean volume: 14.73x10 -4 , P=.03).

Enlarged choroid plexuses are associated with greater parenchymal neuroinflammation

In the group receiving DPA, we confirmed that patients with MS had larger CPs compared with HC (29% higher; coeff:2.42x10 -4 ; P=.03). After adjusting for brain volume, in the group of patients with MS, CP enlargement was associated with higher [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] Results of the post-hoc analysis on MS subgroups showed that in RRMS, larger choroid plexuses correlated with higher [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-DPA-714 binding in T2-w lesions (r:0.56; 95% CI=0.08:0.86; P=.04) and the NAWM (r:0.62; 95% CI=0.07:0.88; P=.007). Among patients with PMS, CP enlargement was associated with [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-DPA-714 binding in the thalami (r:0.67; 95% CI=0.37:0.84; P=.001) and the NAWM (r:0.4; 95% CI=0.01:0.69; P=.004)(Table 3). In HC, CP volume was not associated with [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-DPA-714 binding in any ROIs (thalami: P=.10; WM: P=.07; cortex: P=.38)(Table 3).

Choroid plexuses overexpress TSPO in MS

After controlling for CP volume, the CPs of patients with MS exhibited a 18.5% higher [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-DPA-714 SUV curves showed that the group differences were observed in the late frames but not in the initial perfusional frames (P>.99, Supplemental Fig 1). In MS subgroup analysis, the [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-DPA-714 uptake in the CPs differed between MS and HC for RRMS but not for PMS (mean [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] In RRMS, CP size correlated with higher [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-DPA-714 SUV 60-90 (r:0.57; 95% CI=0.37:0.73; P=.009)(Fig 6c), a finding confirmed when removing the two subjects with the lowest and highest value of CP size (P=.04), whereas this correlation was not found in PMS (P=.39). The interaction between CP volume and RRMS/PMS subgroups confirmed this finding (coeff:-209.70; P=.04).

After controlling for CP volume, [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-FDG SUV 45-60 in the CPs was not different between patients with MS and HC, neither in the whole MS group (mean [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-FDG SUV 45-60 in MS:2.560.67, mean [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF]

Discussion

While choroid plexuses (CPs) play an essential role in the homeostasis of the blood-CSF barrier and the recruitment of inflammatory cells into the CNS, [START_REF] Schwartz | The resolution of neuroinflammation in neurodegeneration: Leukocyte recruitment via the choroid plexus[END_REF] few investigations have explored in vivo in humans their contribution to MS pathophysiology. In our study of 97 patients with multiple sclerosis (MS) and 44 healthy controls (HCs) who underwent 3T brain MRI and translocator protein PET, patients with MS had 35% larger choroid plexuses than HCs (mean value in MS:15.94.5x10 -4 , mean value in HC:11.83.8x10 -4 , P=.004).

Moreover, a greater TSPO expression was found in the CPs of patients with MS (mean [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-DPA-714 SUV 60- 90 in MS: 0.7780.23, mean [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-DPA-714 SUV 60-90 in HC: 0.6350.15, P=.01). Interestingly, CP abnormalities were mainly detected at the relapsing-remitting stage, as attested by a significantly greater CP volume (mean value in RRMS:15.54.6x10 -4 , P=.008) and higher CP [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-DPA-714 uptake compared with HC (mean 18 F-DPA-714 SUV 60-90 in RRMS: 0.910.22, P=.007), together with a correlation between CP volume and TSPO expression in this subgroup (r:0.57, P=.009).

In a recent study, an increased brightness was observed on post-gadolinium T1-weighted sequences in the CPs of patients with MS and neuromyelitis optica spectrum disorder. [START_REF] Kim | Choroid plexus changes on magnetic resonance imaging in multiple sclerosis and neuromyelitis optica spectrum disorder[END_REF] Importantly, the approach applied by Kim et al [START_REF] Kim | Choroid plexus changes on magnetic resonance imaging in multiple sclerosis and neuromyelitis optica spectrum disorder[END_REF] was semi-quantitative, as the CPs were enhanced following gadolinium injection in all individuals, with and without disease. In the same study, the CP thickness, evaluated on 2D axial slices, did not significantly differ between patients with MS and controls. [START_REF] Kim | Choroid plexus changes on magnetic resonance imaging in multiple sclerosis and neuromyelitis optica spectrum disorder[END_REF] This result that seems in contrast with our findings is most likely due to the complex morphology of the CPs, which justifies a rigorous manual segmentation on standardized 3D-MRI acquisitions, as performed here, for accurate volume quantification.

In our study, patients with RRMS exhibited enlarged CPs compared with controls, and the difference remained significant when adjusting for ventricular and brain volume. By contrast, in PMS the difference with HC was lost after adjustment, possibly due to a lower statistical power given the smaller sample size, or a more heterogeneous inflammatory component in the CPs.

In post-mortem studies, the CP stroma has shown inflammatory changes, with infiltrating innate cells, [START_REF] Vercellino | Involvement of the choroid plexus in multiple sclerosis autoimmune inflammation: A neuropathological study[END_REF][START_REF] Ling | Origin, Nature, and Some Functional Considerations of Intraventricular Macrophages, With Special Reference to the Epiplexus Cells[END_REF] activated complement deposition and overexpression of adhesion molecules such as VCAM-1. [START_REF] Steffen | ICAM-1, VCAM-1, and MAdCAM-1 are expressed on choroid plexus epithelium but not endothelium and mediate binding of lymphocytes in vitro[END_REF] In PMS, this immune infiltration was moderate and differed with controls only for granulocytes and CD8+ T cells. [START_REF] Rodríguez-Lorenzo | Correction to: Inflammation of the choroid plexus in progressive multiple sclerosis: Accumulation of granulocytes and T cells[END_REF] A deregulation of the HIF-1 pathway, reflecting altered secretory and neuroprotective properties of CPs, has also been described in MS. [START_REF] Rodríguez-Lorenzo | Altered secretory and neuroprotective function of the choroid plexus in progressive multiple sclerosis[END_REF] To what extent inflammatory or secretory changes influence CP volume remains unknown.

Overall, our pathological and imaging findings suggest that the enlarged CP volume in our study may partly be related to an inflammatory component, as reflected by the higher [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-DPA-714 uptake in CPs. CP inflammatory changes could peak in the relapsing-remitting phase, and subsequently become less pronounced or more heterogeneous at later progressive stages. It is unlikely that increased blood flow in the CPs of patients contribute to the higher CP [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-DPA-714 uptake measured by PET, as the detailed analysis of SUV curves along all the PET frames did not show a significant group difference in the initial peak, which corresponds to perfusion (Supplemental Fig 1). Few studies have investigated, in mouse and in normal human brain, TSPO expression in the CPs, showing its localization mainly in epithelial cells and macrophages and to a less extent, in vessels. [START_REF] Betlazar | Cellular Sources and Regional Variations in the Expression of the Neuroinflammatory Marker Translocator Protein (TSPO) in the Normal Brain[END_REF][START_REF] Cosenza-Nashat | Expression of the translocator protein of 18 kDa by microglia, macrophages and astrocytes based on immunohis-tochemical localization in abnormal human brain[END_REF] Based on these findings, the contribution of vascular binding to the 18 F-DPA-714 signal should indeed be minor in this compartment. In addition, post-mortem investigations have shown an ependymal disruption together with scattered microglial infiltration in the CPs of patients with MS, [START_REF] Guo | Pathogenic implications of cerebrospinal fluid barrier pathology in neuromyelitis optica[END_REF] supporting the interpretation that the increase in [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-DPA-714 uptake is related to inflammatory cells rather than to increased expression by epithelial cells. However, given the lack of imaging/pathology correlative analysis, alternative contributors for the CP [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-DPA-714 uptake cannot be fully excluded.

Contrasting with [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-DPA-714 uptake, CP [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-FDG uptake was not correlated with CP size in RRMS, arguing for a [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-DPA-714-specific PET signal in the CPs, most likely related to their inflammation. In this scenario, the lack of difference in [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-FDG uptake between patients and controls may result from the coexistence of a stromal infiltration by macrophages, potentially inducing an increase in FDG uptake, with an epithelial loss in the CPs, that may result in reduced glucose consumption. [START_REF] Guo | Pathogenic implications of cerebrospinal fluid barrier pathology in neuromyelitis optica[END_REF] The presence of innate immune cells with a homeostatic phenotype, characterized by a predominant oxidative metabolism over the glycolytic one, [START_REF] Lauro | Metabolic Reprograming of Microglia in the Regulation of the Innate Inflammatory Response[END_REF] could also explain this result.

Under physiological conditions, CPs act as a unique neuro-immunological interface integrating signals received from the CNS with those coming from circulating immune cells. [START_REF] Schwartz | The resolution of neuroinflammation in neurodegeneration: Leukocyte recruitment via the choroid plexus[END_REF] Following a CNS insult, CPs allow the trafficking of circulating immune cells towards the CSF, where they can adopt an antiinflammatory phenotype. [START_REF] Schwartz | The resolution of neuroinflammation in neurodegeneration: Leukocyte recruitment via the choroid plexus[END_REF] A dysregulation of this immunosurveillance function is considered to play a role in amyotrophic lateral sclerosis, Alzheimer disease, and spinal cord injury. [START_REF] Schwartz | The resolution of neuroinflammation in neurodegeneration: Leukocyte recruitment via the choroid plexus[END_REF][START_REF] Kunis | IFN-γ-dependent activation of the brain's choroid plexus for CNS immune surveillance and repair[END_REF][START_REF] Kunis | Immunization with a Myelin-Derived Antigen Activates the Brain's Choroid Plexus for Recruitment of Immunoregulatory Cells to the CNS and Attenuates Disease Progression in a Mouse Model of ALS[END_REF] In contrast with this protective role, in the EAE model of MS, the CP immune trafficking pathway allows the initial entry of encephalitogenic T-Helper (TH)-17 lymphocytes through a CCR6-CCL20 interaction. [START_REF] Reboldi | C-C chemokine receptor 6-regulated entry of TH-17 cells into the CNS through the choroid plexus is required for the initiation of EAE[END_REF] Converging evidence supports an involvement of the CCR6-CCL20 axis at the CP level in patients with MS, as they showed a much higher expression of CCR6 in cells from the CSF than do the cells from peripheral blood on memory T cells, 9 CD161 high γδ T cells [START_REF] Schirmer | Enriched CD161high CCR6+ γδ T cells in the cerebrospinal fluid of patients with multiple sclerosis[END_REF] and TH-1-like TH17 cells. [START_REF] Van Langelaar | T helper 17.1 cells associate with multiple sclerosis disease activity: perspectives for early intervention[END_REF] These previous basic science findings, taken together with our results showing a correlation between CP volume and WM lesion load and ARR in RRMS, argue for a role of the CP interface in the pathogenesis of the inflammatory events of MS. Whether the CP alterations are an early triggering event, an enhancer of inflammation, or a secondary consequence of lesional activity remains however to be further explored in vivo. By contrast, CP volume did not correlate with disability scores, possibly due to the poor correlation generally found between EDSS and inflammatory disease markers in cross-sectional studies, and to the small changes in EDSS scores in the short follow-up.

The lack of a clear separation between patients with MS and controls regarding CP volumes may limit the use of this metric as a diagnostic biomarker. However, the relationship demonstrated between CP volumes and brain inflammation opens the perspective to use volumetric analysis of CPs as a biomarker of diseaserelated inflammatory activity, an application that should be further assessed in prospective studies. Some limitations must be considered. First, TSPO tracer mainly targets microglia-macrophages (although not selectively [START_REF] Nutma | A quantitative neuropathological assessment of translocator protein expression in multiple sclerosis[END_REF] ), and does not capture the complexity of immune cells involved in MS pathophysiology.

Moreover, this correlative cross-sectional imaging study does not allow to affirm a causal relationship between CP enlargement, parenchymal immune cell activation and neurodegeneration. Longitudinal imaging studies will be needed to define whether CP volume remains stable or rather evolves over the course of the disease, and whether this metric could be used as a predictor of future inflammatory activity. Lastly, on a methodological viewpoint, a more reliable quantitative assessment of CP gadolinium uptake would benefit of dynamic contrast-enhanced scans, as previously applied for acute WM lesions. [START_REF] Absinta | Seven-tesla phase imaging of acute multiple sclerosis lesions: a new window into the inflammatory process[END_REF] Despite these limitations, our findings of in vivo volumetric and inflammatory changes of the choroid plexuses in patients with multiple sclerosis (MS) are compatible with their involvement in the pathophysiology of the disease, as suggested by prior basic science works, particularly in relapsing-remitting patients with an inflammatory profile.

CHOROID

  F-FDG PET part (Fig 1).

  39; 95% CI=0.20:0.55; coeff:8.35; P<.001)(Fig 4a) and in RRMS (r:0.48; 95% CI=0.26:0.65; coeff:11.1; P=.001), but not in PMS (P=.27). Gadolinium-enhancing lesions were present in 26 RRMS and 5 patients with PMS.

  F-DPA-714 binding in the thalami (r:0.44; 95% CI=0.22:0.72; P=.04) and the NAWM (r:0.5; 95% CI=0.20:0.71; P=.005) but not in the cortex (P>.99), in T2-w lesions (P>.99)(Fig 5a) or perilesions (P>.99)(Fig 5b).

  F-DPA-714 SUV 60- 90 , compared with HC (mean 18 F-DPA-714 SUV 60-90 in MS:0.7780.23, mean 18 F-DPA-714 SUV 60-90 in HC:0.6350.15; coeff:0.14; P=.01)(Fig 5c-d, Fig 6a). Both high-and mixed-affinity TSPO binder groups had different results (P=.004 and P=.04, respectively). The results were similar with and without PVC. The analysis of the entire

  F-DPA-714 SUV 60-90 in RRMS:0.910.22; coeff:0.20; P=.007; mean 18 F-DPA-714 SUV 60-90 in PMS:0.7140.21; coeff:0.09; P=.12)(Fig 6b).

FiguresFigure 1 :

 1 Figures

Figure 2 :

 2 Figure 2: Choroid plexus volume is greater in MS compared with HCs.

Figure 3 :

 3 Figure 3: Correlation between choroid plexus volume and brain tissue volumes in MS.

Figure 4 :

 4 Figure 4: Larger choroid plexuses in active MS, correlation with T2 lesion load and annualized relapse

Figure 5 : 18 F

 518 Figure 5: 18 F-DPA-714 DVR and 18 F-DPA-714 SUV 60-90 maps in patients with MS and HC.(a-b)[START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-DPA-714 distribution volume ratio (DVR) maps (axial plane) from a HAB patient with MS,

Figure 6 :

 6 Figure 6: Choroid plexus inflammation is higher in MS compared with HC. (a-b) Box plot showing greater choroid plexus inflammation, measured as 18 F-DPA-714 SUV 60-90 , in patients with MS versus HCs (a), and in RRMS or patients with PMS separately versus HC (b). (c) Added variable

Table 1 )

 1 were not different in terms of age (MS: mean age:42±12 years, HC: mean age:39±14 years, P=.18), sex (MS: 49 women, HC: 23 women, P=.47) and 3T MRI scanner used (MS: TRIO/PRISMA 60/37, HC: TRIO/PRISMA 32/12, P=.14). Median disease duration was 4.8 years and was higher in PMS compared with RRMS (P=.04). Median EDSS was 3, with higher scores in PMS (P<.001). Clinically active disease, defined as 2-year retrospective ARR≠0, was present in 55 out of 97 patients with MS (57%). Treatment type differed between MS types (P<.001), with a greater number of untreated patients with PMS compared with RRMS. The subgroup receiving DPA was composed of 41 patients (13 RRMS and 28 PMS) and 20 HC. After genotyping of the rs6971 polymorphism of the TSPO gene, 5 low-affinity binders (4 MS, 1 HC) were excluded from further analysis, which left 37 patients with MS and 19 HCs. In this subgroup, no difference was present between MS and HC in age (47±14 for MS; 48±11 for HC; P=.92), sex (21 women among patients with MS; 13 women among HC; P=.56), TSPO affinity (proportion high/mixed-affinity binders [HAB/MAB]: 22/15 for MS, 10/9 for HC; P=.42) and scanner (P=.41). Disease duration, EDSS and treatment were different between RRMS and PMS (P=.03, P<.001, and P<.001, respectively). Clinically active disease was present in 16 out of 37 patients with MS (43%).

	Patients

with MS have larger choroid plexuses compared with HC

  :0.55; 95% CI=0.40:0.68; coeff:0.03; P<.001; HC: r:0.50; 95% CI=0.24:0.70; coeff:-0.04; P=.001), but not with age (MS: P=.49; HC: P=.49) or sex (MS: P=.58; HC: P=.29). adjusting for ventricular and brain volume, CP volume remained higher in patients with MS compared with HC (coeff:22.5x10 -5 ; P=.004)(Fig 2c). In the analysis of MS subgroups, only patients with RRMS showed greater CP volume compared with HC (mean value in RRMS:15.54.6x10 -4 ; coeff:21.6x10 -5 ; P=.008; mean value in PMS:16.54.3x10 -4 ; coeff:7x10 -5 ; P=.24), but no difference in CP volume was found when testing MS subgroups against each other (P=.47)(Fig 2d).

	After
	Manually-segmented CP volumes were highly consistent across different operators and correlated with
	Freesurfer segmentation (r=0.89; 95% CI=0.86:0.92; P<.001; r=0.55; 95% CI=0.42:0.65; P<.001,

respectively). Choroid plexus volume, expressed as ratio of TIV, was 35% greater in patients with MS compared with HC (mean value in MS:15.94.5x10 -4 ; mean value in HC:11.83.8x10 -4 ; coeff:4x10 -4 ; P<.001). In both patients with MS and HC, CP volume was strongly correlated with ventricular volume (MS: r

  F-FDG SUV 45-60 in HC:2.480.5; coeff:0.11; P=.62)(Supplemental Fig 1) nor at the subgroup level (mean 18 F-FDG SUV 45-60 in RRMS:2.580.58; coeff:0.14; P=.64; mean 18 F-FDG SUV 45-60 in PMS:2.550.72; coeff:0.25; P=.39). , CP size was not correlated with higher 18 F-FDG SUV 45-60 in any MS forms (RRMS: P=.99;

	Furthermore

PMS: P=.67).

Table 2 : Association between CP volume and volumes of specific brain regions, in all patients with MS, in RRMS and PMS subgroups, and in HCs.

 2 Allvolumes were expressed as ratio of total intracranial volume (TIV). In the multivariable regression model, CP volume was set as independent variable and each one of the other volumes was in turn set as dependent variable, adjusting for age, sex, MRI scanner, whole brain volume (except when this was set as dependent variable) and treatment (only in patients). p-values were Bonferroni corrected for the correlations within whole MS and the HC groups (bold), but not for the correlations within RRMS and PMS subgroups. MS = multiple sclerosis; TIV = total intracranial volume; RRMS = relapsing-remitting MS; PMS = progressive MS; HC = healthy controls; WM = white matter of HC; NAWM = normal-appearing white matter of MS; coeff: multivariable regression coefficient; CI= confidence interval; T2-w = T2-weighted; P = p-value.

						VOLUMES (ratio of TIV)
		GROUP	STATISTICS	WHOLE BRAIN	THALAMIC	WM (NAWM)	CORTEX
				VOLUME		VOLUME		VOLUME	VOLUME
			coeff	-16.84		-0.11		6.27	4.43
		HC	95% CI	-36.47	2.79 -0.82	0.60 -105.77	118.31 -9.73	18.59
			P	.18		>.99		>.99	>.99
			coeff	-26.87		-0.57		-12.49	1.45
	PLEXUS VOLUME	WHOLE MS GROUP	95% CI	-44.85	-8.90 -1.04	-0.10 -21.02	-3.96 -6.74	9.64
	(ratio of TIV)		P	.004		<.001		.004	>.99
			coeff	-23.69		-0.76		-12.73	-1.59
		RRMS	95% CI	-42.73	-4.65 -1.24	-0.28 -21.50	-3.97 -9.92	6.75
			P	.02		.002		.005	.71
			coeff	-30.70		-0.24		-12.12	7.94
		PMS	95% CI	-56.96	-4.45 -0.89	0.42 -23.93	-0.31 -3.51	19.39
			P	.02		.48		.004	.17

Table 3 : Association between CP volume and 18 F-DPA-714 DVR of specific brain regions, in all patients with MS, in RRMS and PMS subgroups, and in HCs

 3 . CP volume was expressed as ratio of total intracranial volume (TIV). In the multivariable regression model, CP volume was set as independent variable and each DVR value in the selected volumes was in turn set as dependent variable, adjusting for age, sex, TSPO affinity, treatment (only in patients) and whole brain volume. p-values were Bonferroni corrected for the correlations within whole MS and the HC groups, (bold), but not for the correlations within RRMS and PMS

Acknowledgments

We warmly thank Mattia Veronese for fruitful discussion and technical help, and François-Xavier Lejeune for the statistical support. We are also thankful to Christine Baron, Christine Manciot, Bertrand Kuhnast, Vincent Lebon (SHFJ, CEA), Geraldine Gourbil (CIC) for their invaluable assistance, the staff of the CENIR (Research neuroimaging unit of the ICM), and the staff of the Unité de Recherche Clinique of Pitié Salpêtrière, in particular Anne Bissery. The clinical studies analyzed in this article were sponsored by APHP (Assistance Publique des Hopitaux de Paris) and have benefited from the following funding: ANR (Agence Nationale de la Recherche), grant MNP2008-007125; ELA (European Leukodystrophy Association, grant 2007-0481); INSERM-DHOS (grant 2008-recherche clinique et translationnelle); Programme Hospitalier de Recherche Clinique (PHRC national, 2010; APHP); Investissements d'avenir ANR-10-IAIHU-06. They benefited additional funding from Foundation ARSEP, ECTRIMS, JNLF (Journées de Neurologie de Langue Française), FRM (Fondation pour la Recherche Médicale), and the Bouvet-Labruyére prize through the Fondation de France. This work was performed on a platform member of the France Life Imaging network (grant ANR-11-INBS-0006).

Author Contributions

Disclosures of Conflicts of Interest

The authors declared no conflict of interest related to this work.

V.A.G.R. reports fees for traveling from Novartis and Roche. E.M., A.C., M.T., M.H., E.P., M.B. and P.G. report no disclosures. C.L. has received consulting or travel fees from Biogen, Novartis, Roche, Sanofi, Teva and Merck Serono, none related to the present work. B.B. reports fees for traveling and speaker's honoraria from Novartis, Genzyme, Roche and Merck Serono, all outside of the submitted work. B.S. reports grants and personal fees for lectures from Roche, Sanofi-Genzyme, and Merck-Serono, personal fees for lectures from Novartis, Biogen and Teva, all outside of the submitted work. 2) T2-weighted (T2-w): TR/TE: 4100/83 ms, resolution: 0.9x0.9x3.0mm 3 );

3) pre-and post-gadolinium T1 spin-echo (TR/TE: 700/14 ms, resolution: 1.0x1.0x3.0mm 3 ).

PET acquisition and quantification

18 F-DPA-714 PET and 18F-FDG PET exams were performed on a 3D high-resolution research tomograph (HRRT; CPS Innovations, Knoxville, TN). The HRRT is a dedicated brain imaging system with a 31.2 cm transaxial and 25.5 cm axial field of view.

18 F-DPA-714 PET acquisition: After a transmission scan using a 137 Cs point source, the 90-minute emission scan was initiated with a 1-minute intravenous bolus injection of [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-DPA-714 (mean 198.4±22.9MBq).

Images were reconstructed using the 3D ordinary Poisson ordered subset expectation maximization algorithm. An additional smoothing filter implementing the point spread function, which has been shown to be effective in reducing the effect of partial volume in PET data, was applied on the reconstructed images, achieving an intra-slice spatial resolution of ~2.5mm full width at half maximum. All the resulting dynamic PET images consisted of 27 time interval images (time frames): six 1min frames for the initial 6 minutes (6x1), followed by 7x2-, and 14x5-minute frames, with a voxel size of 1.22x1.22x1.22mm 3 .

F-FDG PET acquisition:

The 60-min emission scan was initiated with a 1-minute intravenous bolus injection of 18F-FDG (mean = 191±8.5 MBq). All the resulting dynamic PET images consisted of 7 time frames: one 30-minute initial frame (1x30), followed by 6x5-minute frames, with a voxel size of

Reconstructed dynamic PET data of all subjects were realigned for motion correction according to the process of frame-to-reference image registration using SPM, v8. In particular, the first PET frame was excluded as it did not contain enough spatial information to be correctly aligned. Motion correction was then performed with a two-step procedure: all frames were first aligned to the second frame through a rigid transformation, and then all frames were registered to the mean of the frames obtained after the first realignment.

Voxel-wise [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-DPA-714 distribution volume ratio (DVR) parametric maps were calculated using the simplified version of the Logan graphical method based on reference region, which omits the term (k2')

representing the tissue-to-plasma clearance of the reference tissue. The reference region was extracted using a supervised clustering algorithm as detailed in ref 23, while the linear start time of the Logan plot was taken at 20min.

18 F-DPA-714 and 18 F-FDG uptake in the choroid plexuses [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-DPA-714 and [START_REF] Bodini | Individual mapping of innate immune cell activation is a candidate marker of patient-specific trajectories of disability worsening in Multiple Sclerosis[END_REF] F-FDG uptake in the choroid plexuses was defined as the average standardized uptake value (SUV) inside the CPs. The use of SUV instead of DVR relies on the fact that the assumptions for Logan graphical analysis with reference region were not respected in this case (given the different kinetics of tracer exchange between the blood and the tissue in the CPs, and the absence of a blood-brain barrier).

SUV maps of 18 F-DPA-714 were calculated from the frames of the last 30 minutes of acquisition (SUV 60-90 )

as the radioactivity concentration divided by injected dose per body mass.

SUV maps of 18 F-FDG were calculated from the frames of the last 15 minutes of acquisition (SUV 45-60 ) as the radioactivity concentration divided by injected dose per body mass, multiplied by plasma glucose concentration.

Mean 18 F-DPA-714 SUV 60-90 and 18 F-FDG SUV 45-60 in the CPs were extracted for each subject by overlapping the CP masks to the SUV maps, after performing partial volume correction of the CPs with the single target correction method, as implemented in PETPVC.


Philippe Thomas
email: philippe.thomas@cran.uhp-nancy.fr

André Thomas

Philippe Thomas André

How deals with discrete data for the reduction of simulation models using neural network

Keywords: multilayer perceptron, reduced model, simulation, neural network, re-scheduling, supply chain

Simulation is useful for the evaluation of a Master Production/distribution Schedule (MPS). Also, the goal of this paper is the study of the design of a simulation model by reducing its complexity. According to theory of constraints, we want to build reduced models composed exclusively by bottlenecks and a neural network. Particularly a multilayer perceptron, is used. The structure of the network is determined by using a pruning procedure. This work focuses on the impact of discrete data on the results and compares different approaches to deal with these data. This approach is applied to sawmill internal supply chain.

INTRODUCTION

Evaluation of planning or scheduling scenario by simulation is very useful for the decision makers. Indeed, simulation highlights the evolution of the machines states, the WIP (work in process), and the queues. This information is useful in order to perform a "Predictive scheduling" [START_REF] Lopez | Ordonnancement de la production[END_REF] or a rescheduling. The real time systems performing manufacturing checks (production reporting) provide current follow up information very quickly into the management system [START_REF] Khouja | An aggregate production planning framework for the evaluation of volume flexibility[END_REF]). However, it is difficult to use this huge amount of information in order to make decision [START_REF] Pritsker | Simulation for planning and scheduling[END_REF]. At these levels of planning and control and to estimate how the whole physical system works, the "management of critical resources" (bottlenecks) is often pertinent (Vollman et al. 1992). Goldratt and Cox, in "The Goal" (1992) put forward the Theory of Constraints (TOC), which proposes to manage the whole supply chain by bottlenecks control. Dynamic discrete events simulation of material flow permits this management [START_REF] Charpentier | Reducing simulation models for scheduling manufacturing facilities[END_REF]. In fact, simulation models of actual industrial cases are often very complex and the modellers encounter problems of scale [START_REF] Page | An aggregate production planning framework for the evaluation of volume flexibility[END_REF]. Also, many works have highlighted the interest to use simplest (reduced/aggregated) models of simulation [START_REF] Brooks | Simplification in the simulation of manufacturing systems[END_REF][START_REF] Chwif | Discret event simulation model reduction: A causal approach[END_REF][START_REF] Ward | Argument for constructively simple models[END_REF]). In addition, neural networks have proved their abilities to extract performing models from experimental data [START_REF] Thomas | From batch to recursive outlier-robust identification of non-linear dynamic systems with neural networks[END_REF]. So the use of neural networks appears recently as an interesting approach within the framework of the supply chain (Thomas and Thomas 2008a). Neural networks are generally used in order to perform a mapping between continuous spaces. However, in the considered cases, continuous variables (as length, speed …) are mixed with discrete ones (as category, colour …). The main goal of this paper is to investigate how discrete data may be use during learning process in order to assure the quality of neural network used in reduced simulation models. This is studied on one industrial example which is a sawmill flow shop case. In the next part, the used approach of model reduction and the multilayer perceptron are presented. The third part will be devoted to the presentation of the industrial application. The fourth part presents the inputs and output data of the neural network, and the learning. The results are investigated in order to evaluate the comportment of the network in function of the considered data in the last part. [START_REF] Zeigler | Theory of modelling and simulation[END_REF] has been the first to deal with the problem of model reduction. For him, complexity of a model is relative to the number of elements, connections and model calculations. Simplify a discrete simulation model can be performed by using different approaches: in replacing part of the model by a random variable, in degrading the range of values taken by a variable and in grouping parts of a model together. [START_REF] Innis | Simulation model simplification techniques[END_REF] first listed 17 simplification techniques for general modelling. Their approach is comprised of four steps: hypotheses (identify the important parts of the system), formulation (specify the model), coding (build the model) and experiments. [START_REF] Brooks | Simplification in the simulation of manufacturing systems[END_REF] suggest a "simplification of models" approach for cases where the indicators to be followed are the average throughput rates. Other cases have been studied. The reduction algorithm used (Thomas and Thomas 2008a) is an extension of those presented by [START_REF] Charpentier | Reducing simulation models for scheduling manufacturing facilities[END_REF]. Its principal steps are recalled and explained below:

THE MODEL REDUCTION

The algorithm

1. Identify structural bottleneck (work station (WS) which for several years has been mainly constrained in capacity).

2. Identify conjunctural bottleneck for the bundle of Manufacturing Orders (MO) of the considered MPS.

3. Among the WS not listed in 1 and 2, identify those (synchronisation WS) satisfying these conditions:

-present at least in one of the MO using a bottleneck, -widely used considering the whole MO.

4. If all MO have been considered go to 5 else go to 3.

5.

Use neural networks for model the intervals between WS which has been found during preceding steps.

So, WS remaining in the model are either conjunctural or structural bottlenecks or WS which are vital to the synchronization of the MO. All other WS are incorporated in "aggregated blocks" upstream or downstream of bottlenecks.

"Conjunctural bottleneck" is a WS which is saturated for the MPS and predictive scheduling in question. This is to say that it uses all available capacity. By "structural bottleneck" we mean a WS which (in the past) has often been in such a condition. indeed, for one specific portfolio (one MPS) there is only one bottleneck -the most loaded WS -but this WS can be another WS than the traditional bottlenecks.

"Synchronization WS" are resources used jointly with bottlenecks for at least one MO and used for the planning of different MO which do not use bottleneck. To minimize the number of these "synchronization work centers", the WS which have the most in common amongst all this bundle of MO using no bottlenecks and which figure in the routing of at least one MO using bottleneck must be found.

The multilayer perceptron

Works of [START_REF] Cybenko | Approximation by superposition of a sigmoïdal function[END_REF] and [START_REF] Funahashi | On the approximate realisation of continuous mapping by neural networks[END_REF] have proved that a multilayer neural network with only one hidden layer using a sigmoïdal activation function and an output layer using a linear activation function can approximate all non linear functions with the wanted accuracy. This result explains the great interest of this type of neural network which is called multilayer perceptron (MLP). In this research work, our hypothesis lies in the fact that a part of the modelized production system could be approximate by a non linear function obtained thanks to a MLP.

The structure of the MLP is recalled here. Its architecture is shown in figure 1. The i-th neuron in the hidden layer (figure 1) receives n 0 inputs { }

0 n 0 1 0 x , , x L with associated weights { } 0 in 0 1 i 0 w , , w L
. This neuron first computes the weighted sum of the n 0 inputs:

∑ = + = 0 n 1 h 1 i 0 h 1 ih 1 i b x . w z (1)
where 1 i b is a bias or threshold term. The output of the neuron is given by a activation function of the sum in (1):

( )

1 i 1 i z g x = .
(2)

where g(.) is chosen as an hyperbolic tangent:

x 2 x 2 x 2 e 1 e 1 1 e 1 2 ) x ( g - - - + - = - + = . ( 3
)
input layer hidden layer output layer

1 x 1 0 x h 0 x n 0 0 x 1 1 x i 1 x n 1 1 z 1 1 z i 1 z n 1 1 w h 1 1 w ih 1 w n h 1 1 w 1 2 w i 2 w n 1 2 1 b i 1 b 2 z input layer hidden layer output layer 1 1 x 1 0 x 1 0 x h 0 x h 0 x n 0 0 x n 0 0 x 1 1 x 1 1 x i 1 x i 1 x n 1 1 x n 1 1 z 1 1 z 1 1 z i 1 z i 1 z n 1 1 z n 1 1 w h 1 1 w h 1 1 w ih 1 w ih 1 w n h 1 1 w n h 1 1 w 1 2 w 1 2 w i 2 w i 2 w n 1 2 w n 1 2 1 1 b i 1 b i 1 b 2 b 2 z
Fig. 1. Architecture of the multilayer perceptron.

The neuron in the last layer simply performs the following sum, its activation function being chosen linear:

∑ = + = 1 n 1 i 2 1 i 2 i b x . w z (4)
where 2 i w are the weights connecting the output of the hidden neurons with the output neuron and b 2 is the threshold of the output neuron. Now, only the number of hidden neurons is always unknown. In order to determine it, the learning starts from an overparametrized structure. A weight elimination method is used to remove spurious parameters [START_REF] Setiono | Pruned neural networks for regression[END_REF]. The learning of the MLP is performed in three steps:

-Initialisation of the weights of an oversized structure by using the Nguyen Widrow algorithm (1990).

-Learning of the parameters by using Levenberg-Marquard algorithm with robust criterion [START_REF] Thomas | From batch to recursive outlier-robust identification of non-linear dynamic systems with neural networks[END_REF].

-Weights elimination by using the algorithm proposed by [START_REF] Setiono | Pruned neural networks for regression[END_REF].

OVERVIEW OF THE SAWMILL

At the time of the study, the sawmill SIAT had a capacity of 270.000 m3 / year, a 52 million euros turnover and 300 employees. The sawmill objective is to transform logs into main and secondary products respecting a cutting plan. The considered cutting plan is presented into figure 2. The physical industrial production system is composed of sequential WS (kockums saw, trimmer, sorter …) and queues or conveyors (RQM4, RQM5, RQM7 …). The log enters the system in RQM1 then it is steered to RQM4 or 5 according to its characteristics. After that, it passes to the cutting machine (Canter). Then it enters the edger. After this phase, the log is transformed into main and secondary products. The final operation is the cross cutting which consists in cutting up products to length. Two important steps occur during this process. The first one is the choice of the conveyors RQM4 or RQM5 in order to store the arrival log. In function of this choice, the time spending by the log to wait the Canter saw may be very different. The second one is the type of product. When the cutting plan is considered, 2 types of products appear: main and secondary ones. Only the secondary products should use kockums saw when secondary and main products use trimmer. However, when the physical industrial system is considered, 3 types of products should be considered. In fact the Cutting machine Canter works into 3 steps. First, CSMK saw cuts 2 faces of the considered log and produce the 2 secondary products hatched figure 2. These 2 products are driven to kockums saw in order to be finished. Next the log is rotated of 90° and stored into conveyor RQM7. After that, the log is driven once again to the Canter machine. The CSMK saw cuts the 2 other faces of the log, and produce the 2 other secondary products which are driven to kockums saw. At this time, a parallelepiped is obtained which is divided into 3 main products by another saw (MKV). The main products are so driven to the trimmer.

THE SIMULATION MODEL

The reduced model

During preceding works a reduced model has been proposed (Thomas andThomas 2008a, 2008b) based on the fact that the bottleneck of this line is the trimmer [START_REF] Charpentier | Reducing simulation models for scheduling manufacturing facilities[END_REF]. So, only the arrival times of the products in trimmer queue are useful in order to simulate the load of this bottleneck. Also a multilayer perceptron is used to perform this task. Then neural network uses the available shop floor information. The reduced, and so, simplified model is presented on figure 3. The determination of the neural model is the core of the problem.

The data and the learning

Neural network model is a black box obtained with a supervised learning of a non linear relation between input data set and output one. For this, we need to collect the available input data of the process and to determine the desired output (Thomas and Thomas 2008b). First, each log gives information which is collected by a scanner in input of the line. This information is relating to the product dimension, as length (Lg) and 3 values for timber diameter (diaPB ; diaGB ; diaMOY). These variables serve to control the log to RQM4 or RQM5 queues which is additional information (RQM).

Fig. 3. The reduced model

In addition of this dimensional information, the process variables at the time of the log arrival should be characterised. The input stock of the trimmer (Q_trim), the utilisation rate of the trimmer (U_trim) and the number of logs present in the different conveyors RQM4, RQM5 and RQM7 (Q_rqm4; Q_rqm5; Q_rqm7) must be taken. Moreover, the sum of these numbers is also used (Q_rqm = Q_rqm4+Q_rqm5+Q_rqm7). The last type of information is related to the cutting plan of the logs. In fact, each log will be cut into n main or secondary products. In our application, the cutting plan (figure 2) divides the log into 7 products:

-2 secondary products resulting from the first step of cutting process on saw CSMK of the canter line, -2 secondary products resulting from the second step cutting process on saw CSMK of the canter line after staying in the RQM7 queue, -3 main products resulting from the third step of cutting process on saw MKV of the canter line.

These 7 products can be classified into three categories according to the location (CSMK or MKV) and the time during the cutting process (first or second cutting). This information is given by the variable (T_piece). Consequently, neural network inputs are: Lg; diaGB; diaMoy; diaPB; T_piece; Q_trim; U_trim; Q_rqm; Q_rqm4; Q_rqm5; Q_rqm7; RQM. 12775 products are simulated. Among these 12 inputs data, two different categories exist:

-Continuous one (quantitative) [Lg; diaGB; diaMoy; diaPB; Q_trim; U_trim; Q_rqm; Q_rqm4; Q_rqm5; Q_rqm7]. These data are continuous ones and so are well adapted to be used by learning procedure.

-Discrete one (qualitative) [T_piece; RQM]. These data are qualitative. So the study of their impact on the learning process is the core of this paper.

The core of this work is to focus on the use of these discrete variables during the learning. Our objective is to estimate the delay (∆T) corresponding to the duration of the throughput time for the 12775 products. ∆T is measured between the process input time and the trimmer queue input time. In practice ∆T is the output of the neural network:

∑ ∑ = = +         + = ∆ i n 1 i 2 12 1 h 1 i 0 h 1 ih 2 i b b x . w g . w T
(5)

The learning of the network is supervised. So, it is necessary to divide the database into 2 datasets, learning and validation ones. The number of hidden neurons is always unknown and should be determined. In order to determine it, the learning starts from an overparametrized structure and a weight elimination method is used to remove spurious parameters. The initial structure used n i =10 hidden neurons (5).

THE RESULTS

The learning approach corresponds to a local search of a minimum. So, in function of the initial weights, the results may be different. In order to evaluate the dispersion of the results, 30 different sets of initials weights are used. Different structures of the network will be tested in function of one particular discrete input (RQM) which is difficult to learn.

First approach

As seen in the part 4.2, the data RQM indicates which conveyor (RQM4 or RQM5) is used by the considered log. So, the first obvious approach is to give value 4 (resp. 5) to RQM when the conveyor is RQM4 (resp. RQM5). In the table 1, the mean and the standard deviation of the residuals obtained on the learning and the validation data sets are presented. These results show that residuals are always bad. In particular, the mean of residuals obtained may vary, in function of the initial weights, from 17.11s to 213.08s on the learning data set. It can be noticed that the mean of the residual is lower than 30s in only 10% of the cases in learning. In order to determine if some dynamics presents in the data aren't taken into account by the learning, the correlation between the different inputs and the residuals can be performed on the learning data set (table 2). Similar results may be obtained on the validation data set. It can be noticed that Lg, diaGB, diaMoy, T_piece, U_trim presents a correlation coefficient with residuals which is never significant (always smaller than 0.0959). U_trim, Q_rqm, Q_rqm5, Q_rqum7 present a minimal value of correlation to 0 because the pruning algorithm, in some cases, have pruned these inputs. Two inputs have always a significant coefficient correlation with the residual: diaPB and RQM. However RQM is a discrete data. So, the correlation test isn't the most significant. Figure 4 presents an example of the residuals in function of RQM. It can be noticed that two different residuals exist depending of value of RQM. So, in order to estimate the influence of RQM on residuals the best approach is to compare these two samples. For this, two tests can be performed. The first one is the T Student test which tests if the two samples of mean µ 1 and µ 2 have the same mean. The null hypothesis (H0) and its alternative (H1) are:

   ≠ µ - µ = µ - µ 0 : 1 H 0 : 0 H 2 1 2 1 (6)
The second test is the F Fisher test which is the ratio of the two variances 2 max σ and 2 min σ of the samples. The null hypothesis (H0) and its alternative (H1) are:

     > σ σ = σ σ 1 : 1 H 1 : 0 H 2 min 2 max 2 min 2 max (7)
The results of these tests on the 30 tries have always shown that the two samples have means and standard deviations significantly different with a confidence interval of 99%. So, the neural model doesn't succeed to learn the RQM data.

Second approach

The data RQM is the core of the problem. The choice to give value 4 (resp. 5) to RQM when the log uses RQM4 (resp. RQM5) conveyors is not good. So, another approach is to give the value 0 (resp. 1) when RQM4 (resp. RQM5) is used. So, a new neural model is learned. Table 3 presents the mean and the standard deviation of residuals obtained on learning and validation data sets with this new representation of RQM. The line (abs) presents the minimum of the mean in absolute value. These results have to be compared with those presented table 1. The first remark is that the mean of the means residuals is greatly improved with this new approach.

The worst results obtained on the mean are divided by 2 between the first and the second approaches (101.92 in learning instead of 213.08 for the first approach). It can be noticed that the absolute value of the mean of the residual is lower than 30s in 26.67% of the cases in learning instead of 10% of the first approach. As for the preceding approach, the correlation coefficient between the 12 inputs and the residuals are presented in the table 4 for the learning data set. Moreover, in some cases (26.67%), the RQM data presents a correlation coefficient with residuals lower than 0.1 to compare with first approach where this coefficient is always greater than 11.24. However, RQM is always a discrete data. So, the Fisher and the Student tests have to be performed on the two samples corresponding to RQM=1 and RQM=0. For the F test, the standard deviations are always significantly different with a confidence interval of 99%. However, the T test indicates that the means of these two samples are not significantly different in 13.33% of the cases with a confidence interval of 99%. So, the RQM data is better learned with this new approach but the results are unsatisfactory.

Third approach

In order to improve the results, a new input can be added to the network. This input is the complement of RQM:

   4 RQM if : 1 5 RQM if : 0 RQM (8)
So, neural network uses 13 inputs. Table 5 presents mean and standard deviation of residuals obtained on learning and validation data sets with this additional input RQM . The line (abs) presents the minimum of the mean in absolute value. These results have to be compared to the preceding ones. The best results for the mean are greatly improved. We obtain 0.07 on the learning data set (to compare to 8.96 with approach 2). The worst results for the mean of the residuals are improved too, because we obtain 46.75 on the learning data set to compare with 101.92 with the preceding approach (divide by 2). Moreover, standard deviations of the residuals are also improved because its mean value is 460.52 for learning data set when it was of 532.44 for preceding approach. It can be noticed that the absolute value of the mean of residuals is lower than 30s in 90% of the cases instead of 26.67% of the preceding approach. Similar conclusions can be performed on the validation data set. As for the preceding approach, the correlation coefficients between the 13 inputs and residuals are presented in the table 4 for the learning data set. First, it can be noticed that logically, RQM and RQM present the same results. Now, Lg, diaGB, dia_Moy, Q_trim, and U_trim have always a coefficient correlation never significant (always smaller than 0.1). Moreover, in many cases (60%), the RQM data presents a correlation coefficient with the residuals which is lower than 0.1 to compare with the first approach where this configuration represents 26.67% of the cases. However, RQM is always a discrete data. So, the Fisher and the Student tests have to be performed on the two samples corresponding to RQM=1 and RQM=0 ( 0 RQM = and 1 RQM = resp.). For the F test, the standard deviations are always significantly different with a confidence interval of 99%. However, the T test indicates that the means of these two samples are not significantly different in 33.33% of the cases with a confidence interval of 99%. So, this approach greatly improved the results of the learning.

CONCLUSIONS

The use of neural network in order to construct a reduced model of simulation is investigated here. Within this framework, this paper focuses on the use of discrete data during the learning phase of the neural model. The results have shown that some discrete data (RQM) have great impact on the results. This can be explained by the fact that, some discrete data leads to comportments of the system which can be very different. These data imply that some information should be presented under different forms to the network in order to be well taken into account. Our perspectives are to validate this approach on different application cases, and, in particular, on several external supply chains where, at least, one particular enterprise belongs to the different supply chains.

  Fig. 2. The cutting plan

  Fig. 4. Residual function of RQM

Table 1 . Mean and Standard deviation of the residual #1

 1

		learning residual	Validation residual
		Mean	StD	Mean	StD
	Mean	78.61	586.09	74.33	582.06
	StD	43.94	146.50	41.61	145.44
	Min	17.11	408.45	12.35	413.93
	Max	213.08	1168.80	206.75	1170.93

Table 2 . Correlation between inputs and residual #1

 2

		Mean	StD	Min	Max
	Lg	0.0354	0.0245	0.0002	0.0882
	diaGB	0.0118	0.0096	0.0013	0.0342
	dia Moy	0.0393	0.0238	0.0014	0.0843
	diaPB	0.1619	0.0692	0.0640	0.3411
	T_piece	0.0350	0.0261	0.0001	0.0959
	Q_trim	0.0484	0.0324	0.0002	0.1172
	U_trim	0.0298	0.0211	0.0000	0.0813
	Q_rqm	0.0707	0.0467	0.0000	0.1774
	Q_rqm4	0.0628	0.0531	0.0025	0.2280
	Q_rqm5	0.0697	0.0456	0.0000	0.1831
	Q_rqm7	0.0525	0.0355	0.0000	0.1314
	RQM	0.2875	0.1310	0.1124	0.6706

Table 3 . Mean and Standard deviation of the residual #2

 3

		learning residual	Validation residual
		Mean	StD	Mean	StD
	Mean	40.45	532.44	40.31	535.64
	StD	38.83	107.13	39.69	106.20
	Min	-58.28	357.46	-54.49	380.60
	(abs)	8.96		9.65
	Max	101.92	786.74	111.62	816.23

Table 4 . Correlation between inputs and residual #2

 4

		Mean	StD	Min	Max
	Lg	0.0241	0.0199	0.0005	0.0962
	diaGB	0.0216	0.0205	0.0007	0.0982
	Dia Moy	0.0394	0.0260	0.0001	0.1051
	diaPB	0.1145	0.0677	0.0017	0.2526
	T_piece	0.0450	0.0354	0.0000	0.1308
	Q_trim	0.0512	0.0398	0.0063	0.1543
	U_trim	0.0262	0.0213	0.0000	0.0672
	Q_rqm	0.0763	0.0532	0.0242	0.2019
	Q_rqm4	0.0469	0.0322	0.0000	0.1284
	Q_rqm5	0.0754	0.0519	0.0000	0.1837
	Q_rqm7	0.0660	0.0419	0.0000	0.1760
	RQM	0.2048	0.1263	0.0082	0.4461

Table 5 . Mean and Standard deviation of the residual #3

 5

		learning residual	Validation residual
		Mean	StD	Mean	StD
	Mean	11.17	460.52	9.02	465.90
	StD	18.34	83.86	18.69	81.40
	Min	-17.37	333.95	-23.97	341.57
	(abs)	0.07		1.11
	Max	46.75	620.58	39.34	629.02

Table 6 . Correlation between inputs and residual #3

 6

		Mean	StD	Min	Max
	Lg	0.0127	0.0117	0.0000	0.0349
	diaGB	0.0114	0.0120	0.0000	0.0436
	dia Moy	0.0143	0.0159	0.0000	0.0713
	diaPB	0.0446	0.0411	0.0000	0.1554
	T_piece	0.0390	0.0422	0.0000	0.1358
	Q_trim	0.0239	0.0216	0.0000	0.0776
	U_trim	0.0167	0.0120	0.0008	0.0450
	Q_rqm	0.0327	0.0422	0.0004	0.1541
	Q_rqm4	0.0378	0.0443	0.0000	0.1553
	Q_rqm5	0.0375	0.0364	0.0000	0.1333
	Q_rqm7	0.0307	0.0334	0.0000	0.1590
	RQM	0.0821	0.0708	0.0000	0.2738
	RQM	0.0821	0.0708	0.0000	0.2738


Richard Abel

Hilary Sommerlad

Ole Hammerslev

dir Ulrike Schultz

The Global Contention for Law's "Special Character" By Antoine Vauchez

It is a daunting task to review such a rich and prolific volume that brings together no less than 26 chapters and 47 authors. One can only be admiring, particularly as it comes immediately after a first volume which presented portraits of national legal professions in 46 different jurisdictions. Taken together, the two volumes provide an unprecedented amount of data (profession's size, demographics, legal education, governance and ethics regulation, position in the national field of power, etc.) and a unique reference point for all socio-legal scholars. While the first volume reads like an atlas of legal professions, the second one is comparative and theoretical in scope and concretizes the intellectual returns of the former by offering a large array of possible lines of interpretation of the material.

What certainly adds to the great scholarly value of these two volumes is the fact that they come as a sequel, almost 35 years after the first three volumes of 1988-1989 edited by Richard Abel and Philip Lewis entitled Lawyers in Society. The presence of Richard Abel among the four editors of this new edition is testimony to this direct genealogy between both projects which share the same sort of rare encyclopedic ambition. And yet, the editors have profoundly transformed and renewed the contours of the project turning it into a "cross-cultural, inter-disciplinary and international" academic experiment. As explained in the excellent introductory chapter by Ole Hammerslev and Hilary Sommerlad, the editors maintained the Weberian tradition of comparative and historical sociology that featured the first edition, yet now moving it beyond Western-centric approaches. When compared to its predecessor, the present edition does indeed mark a considerable broadening in perspective. While only three chapters had been previously devoted to non-Western countries (Brazil, Japan and Venezuela) at the time, the new edition has a much more international outlook not only in terms of country coverage (46 different country-reports) but also in terms of participation of colleagues from the Global South to this collective undertaking.

INSERT AUTHOR BIO INFORMATION

Antoine

INTELLECTUAL RETURNS

Such widening of the scope brings immediate intellectual returns. While the rather legalistic binary divide between "civil law" and "common law" countries that organized the 1988-1989 edition has remained, it now plays a secondary role as the book does justice to many other regional, transnational and global dynamics that shape law and lawyering.

Global Transformations

It is certainly one of the most striking results of the book that, despite many differences and contingencies, all legal professions of the world are indeed going through common trends, tensions and transformations, many of which only make sense when considered across the globe. The hegemonic power and the reach of Anglo-American law education and law firms are still among the most defining features of the professional practice of law on the global scale. Just as the post-colonial relationship between formal imperial centers and the peripheries of the Global South continues to structure asymmetrical flows of professional credentials, institutional models, and career moves. However, the global picture is much more complex and diversified. Suffice it to look at the first four chapters which present "regional approaches" in Africa, Latin America, the Islamic world and the former Soviet bloc which treat transnational and local idiosyncrasies that do not refer to the traditional Western "core" of legal professionalism.

Beyond Market Control

The new edition also provides with a profoundly renewed research agenda. Famously, the original three volumes were mostly centered around issues of professional market control bringing together an exceptional group of scholars from the field of sociology of profession. The theme has certainly not disappeared as can be seen in Part I on "The Production of Law and Lawyers" and Part VI on the "Sociology of professions": both address the challenges of deregulation and deprofessionalization which undermines the profession's traditional claim for self-regulation and independence. One will actually find excellent updates on some of the most classic research strands on legal professions including issues of access to justice, professional identities, legal education, paralegals, professional ethics, governance, and strategic litigation -all themes which were already well established at the time of the first edition. However, the new edition considerably widens the perspective as it connects socio-legal studies to many new fields of social science research that have emerged over the past 35 years. Part II on "Diversity" has a rich set of chapters on social, gender and ethnic diversification of a profession which has become increasingly attractive world-wide. Similarly, issues of globalization, neo-liberalism, authoritarian turn of regimes, digitalization, post-colonialism, social justice, etc. which were close to absent from the previous volumes, now play a central role. As such, this is much more than a book on the many legal professions of the world. Suffice it to look at the rich bibliographies of the different chapters; to consider the new generations of scholars and research projects brought to the forefront (e.g. the project on Globalization, Lawyers, and Emerging Economies-GLEE); or to read some of the strong theoretical chapters that provide wide-ranging analyses of the intersect among law, lawyering and society (see among others, chapters by Sida Liu, Frank Munger, David Wilkins, David Trubek & Bryon Fong, or Yves Dezalay & Bryant Garth). They are testament to the profound transformations of the research agenda over the past decades and above all a demonstration of the liveliness of socio-legal scholarship.

CONTRADICTIONS, TENSIONS AND EROSION

Overall, the picture of the legal profession that comes out of the volume is one marked by profound tensions and increasing contradictions over the past three decades. With hindsight, it becomes clear that the Western-centered and quasi-aristocratic world of legal professionals, with its gendered, ethnic and elitist structure, was living its very last days at the time of the first edition (1988)(1989). To be sure, some of the trends and tensions had been described and anticipated in the original volumes: the emergence of "BigLaw", the mass entrance of women (and to a lesser extent of minority groups) in the profession, globalization processes, the rise of the BRICS countries, etc. Yet, their size, pace and transformative effects were still imperceptible to the naked eye. The new edition reads as a story into the rapid erosion of the neo-Weberian model of legal professionalism. This erosion can be traced from within the legal profession as do the chapters in the "Diversity" Part of the book. They exemplify the powerful process of diversification of the profession with the acceleration of feminisation (in the US, the overall share of women has moved from the 3% of the 1970s to the 35% of today), a phenomenon which has occurred in virtually all jurisdictions, as well as the democratization of the profession through the entrance of law graduates from ethnic minorities or lower social classes. This may have come with new forms of stratification and segmentation (in terms of status hierarchies, access to leadership positions, etc.) that have allowed for the masculine white culture to perpetuate in some niches of the profession such as in some of its corporate bastions. Yet, overall, the profession has increasingly diversified as it was developing demographically. Similar transformative effects can be identified in terms of legal practice with the growing differentiation and asymmetries of the legal professions between the rise of large law firms serving both corporate interests and the state, on the one hand, and the much more fragmented part of the profession providing services to individual and public interest, on the other. While the dominance of the US Cravath model of big law firms was long in the making, the phenomenon has taken a whole new meaning as it extended globally and moved from a couple of hundreds of lawyers in the 1980s to 12,000 lawyers at Dentons and 7.500 lawyers at the Chinese Yingke, its immediate follower in the ranking which was established less than 20 years ago. Interestingly though, the organizational model of the big law firm itself changed as it spread out beyond the Anglo-American sphere of its origin: while the big law firm traditionally marked how the legal profession had become intertwined with corporate interests, it takes a different meaning in China where it is also deeply connected with forms of State tutelage and sponsorship.

The erosion of legal professionalism is even more marked when considered from the outside as its boundaries are put under strong deregulatory pressure, diluting the distinctiveness of legal expertise. While law and lawyers had long been the yardstick for all professional projects which tried to mimick its State certification and strong internal governance, it is now undermined by the combined effects of neoliberal deregulation, interprofessional competition from the consultancy marketplace, and disruptions from the legal tech pushing to de-professionalize entire segments of legal expertise. As a result, the selfregulated model of legal professionalism which was at the core to the first edition "is not anymore a world-wide model", Frank Munger even noting "the prevalence of non-professional regulation of legal services markets in some parts of the world, together with reduced support for legal professionalism in other jurisdictions".

LAW WITHOUT LAWYERS?

Interestingly though, the demise of lawyers' professional project does not come with that of law as key grammar of power (and of its legitimization). Quite the contrary, if one considers the centrality of law and lawyers in the dispositifs of neoliberalism, global governance [START_REF] Alter | From Colonial to Multilateral International Law: A Global Capitalism and Law Investigation[END_REF]Vauchez 2021) as well as in contemporary forms of autocratic ruling [START_REF] Scheppele | Autocratic Legalism[END_REF]. To grasp such paradox, the traditional toolbox of sociology of profession proves increasingly inadequate as it leaves the issue of power in the background (Sida Liu). In this regard, the choice made by the editors to keep an open-ended construction and adopt no a priori definition of law, lawyers and legal professions proves particularly heuristic. The reader may feel a bit dizzy and bewildered as he/she goes through chapters and moves from one context to another. Yet he/she will get a fuller sense of the extraordinary "functional plasticity" and fluidity of contemporary legal practice.

As lawyers' internal governance units have been profoundly weakened (if existent at all), it is probably more relevant nowadays to analyze legal practice in terms of a weak field (i.e. heteronomous and weakly structured internally) than in terms of a semi-autonomous professional field. A weak or interstitial field [START_REF] Vauchez | Interstitial Power in Fields of Limited Statehood: Introducing a 'Weak Field' Approach to the Study of Transnational Settings[END_REF] taken in-between wellestablished fields (States, markets and, to a lesser extent, the organized civil society) that compete over the definition of law's "special character" (to use Rueschemeyer's words). The structure of the book actually hints in such direction as Part IV (Social justice), Part V (the market) and Part VII (the State) delineate the triadic structure (or gravitational forces) in which legal professions are taken [START_REF] Karpik | French Lawyers: A Study in Collective Action, 1274-1994[END_REF], torn as they are in-between the service of civil society, of corporate actors and of government institutions (the last two been often combined). Hence the variety of national models of lawyering that comparative researchers identify in the book depending on the balance between these three contending forcessome countries been more "state-driven", some more "market-driven" and others featured by the "power of the bar" (see David Wilkins, David Trubek and Bryon Fong's Chapter in the volume). Hence also the variety of "monstruous" cases (or limit-cases) discussed in the volume in which lawyers appear as mere "enablers" enrolled into "grand corruption schemes" of money laundering and tax optimization (Mike Levi); or as the drivers of authoritarian turns deploying law and rule of law as a key tactic of autocratic regimes (Rafael Mrowczynski).

LOOKING FORWARD

As the reader closes the book, he/she certainly feels the scholarly excitement of having expanded the scope of his/her socio-legal imagination. And yet, he/she cannot escape a sense of dismay and disorientation as it seems that his/her very object of research has melted down before his/her eyes. At this stage, it would have been helpful to relieve the unfortunate soul with some forward-looking perspectives and suggestions about where future research efforts should be directed to. While these future fields of inquiry are certainly many, I am tempted to suggest one that would bring this rich patrimony of social science research in closer contact with democratic theory -something sociolegal scholars have often been reluctant to do. As lawyers' independence and self-regulation face the combined pressure of neoliberalism and of the authoritarian turns, the capacity of law to provide a level-playing field where causes and social claims can be recognized and come out ahead is increasingly questioned. While the book shows the continuing power of law and lawyers to shape social reality, it also points at the weakening capacity of law and lawyers to defend the democratic public, thereby forcing us to critically reconsider some of the hopes for social change and democratization that have been placed in law, lawyers and courts over the past decades.

  Vauchez is a CNRS Research Professor in political sociology and law at the Université Paris 1-Sorbonne and a Permanent Visiting professor at iCourts Research centre (Univ. of Copenhagen). His research focuses on the definitional power of law and lawyers in the neoliberal transformation of politics and of States in Europe. His most recent books include: Brokering Europe. Euro-lawyers and the Making of a Transnational Polity (Cambridge University Press, 2015), (with Thomas Piketty et alii : How to Democratize Europe, Harvard Univ. Press, 2019) and The Neoliberal Republic. Corporate Lawyers, Statecraft and the Making of Public-Private France (Cornell Univ. Press, 2021).