Marcelo De

Castro Fernandes

Dietmar Winkler

Giuseppe Laera

Luigi Vanfretti
email: vanfretti@gmail.com

Sergio A Dorado-Rojas

Tin Rabuzin

Biswarup Mukherjee

Manuel Navarro

Marcelo De Castro
email: marcelo.decastrof@gmail.com

0.0] -[iTesla Power Systems Library (iPSL): A Modelica library for phasor time-domain simulations]

Keywords:

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

Introduction

Following the completion of the iTesla project, the original iTesla Power Systems Library (iPSL) [START_REF] Vanfretti | iTesla power systems library (iPSL): A modelica library for phasor time-domain simulations[END_REF] was forked into a new project, the Open-Instance Power System Library (OpenIPSL). Its primary goal is to provide a robust set of models that can be DOI of original article: https://doi.org/10.1016/j.softx.2016.05.001. used for research and teaching activities involving power system phasor-domain stability studies, while providing a transparent library development framework. Since the release of version 1.5.0 [START_REF] Baudette | Openipsl: Open-instance power system library-update 1.5 to ''iTesla power systems library (iPSL): A modelica library for phasor time-domain simulations[END_REF], the OpenIPSL has also focused its efforts towards developing a user community, feature that can be of tremendous advantage for the library. Therefore, many changes that have been made to this new version of OpenIPSL are developed to foster the user and developer communities. Version 2.0.0 also brings a more robust library base, with structural changes that enhance numerical simulation. Furthermore, the library brings new models, while already-present models have been revisited for cleaning and updating implementations, and fixing bugs. These new modifications are discussed in Section 2.

In addition, a tool that creates a bridge between the OpenIPSL and other power system simulation tools has been developed. In this new library version, a Python tool has been created to automate processes needed to provide starting guess values used by Modelica tools in the initialization of power system's dynamic models. This new tool and its valuable usage to the simulation of power system models assembled with OpenIPSL are briefly described in Section 3.

New features added to the library

Licensing, facilitating contributions and documentation

The previous Mozilla Public License 2.0 was replaced by entity and individual versions of the BSD 3-clause license. This modification facilitates features developed in different collaborations to be securely added to the library.

In addition, to facilitate community contributions, the library now has an automated procedure for verification and storage of signatures on contributor agreements, allowing transparency in library development with multiple contributors. This has been implemented using ''Contributor License Agreement assistant'' (github.com/cla-assistant), and is automated through GitHub services.

The GitHub repository now has more succinct documentation that directly informs users about the library itself. A code of conduct together with contribution guidelines have been added to enable better interactions between users and the multiple developers. Moreover, documentation was added to the new and revisited Modelica models. This, together with the recently-added User's Guide, allows users to be informed about functionalities and characteristics while using the library in a Modelicacompliant tool.

Stable base version

The library now uses Standard International (S.I.) and perunit units in quantities, allowing a better compliance with the Modelica language, and facilitating the development of consistent models. It also enables the Types feature to be used throughout the library, allowing the scaling of differential equations [START_REF] Casella | On the importance of scaling in equation-based modelling[END_REF]. Hence, it culminates previous efforts to date in a robust and stable base version that is compatible with multiple Modelica-compliant tools, such as Dymola ® , OpenModelica ® , Modelon Impact ® and SystemModeler ® . Fig. 1 depicts simulation results obtained using different Modelica-compliant tools for the same OpenIPSL model. A software-to-software validation procedure has been applied to many models in the library, allowing bugs and inefficient implementations to be identified and corrected. Models that underwent this process have a been graphically annotated using a green line around their icons, indicating the verified component model to the user. The validation results are now available publicly for use of third parties, see: https://alsetlab.github.io/ NYPAModelTransformation/reports. In addition, new models have been also added to the library. Examples of such models are the ULTC (Under-Load Tap-Changing) transformer, the GGOV1DU a variant of the general purpose turbine-governor models GGOV1 and the SoftPMU which may allow users to develop and test applications that need estimated bus frequency values for control design [START_REF] Mukherjee | A PMU-based control scheme for islanded operation and re-synchronization of DER[END_REF].

Examples and tests

Originally a set of Application Examples that illustrated how the library can be used to model both common test models and real-world grids was located outside the library itself as an independent package, which created confusion for new users.

Hence, this has been updated and it is now available within OpenIPSL's main package under Examples. As a consequence, the set of examples is now maintained together with the main library, resulting in more efficient continuous development. Furthermore, the library's previous version had a sub-package called Examples that was renamed in this new version to be Tests, because it consists of simulation models that are used for unit testing as the one used for software-to-software validation.

Power flow to records

Since its first version, the OpenIPSL has focused on dynamic simulation and its models are initialized with results from power flow computations. The library, however, does not provide the means for power flow calculations to be performed natively within a Modelica-tool. As a matter of fact, this was done in previous versions of OpenIPSL by using tedious procedures involving calculations in third-party proprietary tools and manually inputting data into models for simulation to be carried out from a particular operation point. This, of course, was a great caveat of the library that needed to be addressed.

To overcome this issue, a new tool has been developed in Python [START_REF] Dorado-Rojas | Power flow record structures to initialize openipsl phasor time-domain simulations with python[END_REF]. The tool is able to carry power flow calculations using GridCal (), an open-source Python library. The results are automatically translated to Modelica records which are used to provide starting guess values used by Modelica-tools to initialize the model for numerical simulations to be carried out. The tool also provides useful documentation and tutorials that ease the tool's integration with the OpenIPSL for new and experienced users and is available publicly at https://github.com/ALSETLab/ SMIB_Tutorial.

Conclusion

The OpenIPSL continues to pursue its main goal of developing a robust library for research and teaching of phasor-domain power systems models as it is shown in this new OpenIPSL release. Many changes have been made to allow a more efficient interaction with the user and developer's community. As a result, contributions to the library have been made a more transparent and simple process, establishing an appropriate framework for the continuous development of the library.

In addition, the complete adoption of S.I. and per-unit units and the usage of types have made individual component models in the library more consistent between each other. The different component models that have been revisited, together with models that have been recently added to the library, also contribute to a more robust version of the OpenIPSL. In fact, version 2.0.0 can be seen as a more stable basis from which the OpenIPSL development can be carried on without significant structural changes. Moreover, a complimentary Python tool, that sets up power flow solutions and automatically populates Modelica records to be used in model initialization has been developed. It greatly benefits OpenIPSL models by bridging a gap between Modelica-based tools that are used mainly for dynamic analysis with those that are used for steady-state analysis.

Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Marcelo de Castro Fernandes reports financial support was provided by Dominion Energy Inc. Giuseppe Laera reports financial support was provided by Dominion Energy Inc.

Fig. 1 .

 1 Fig. 1. Simulation results for the machine's rotor angle in an Single Machine Infinite Bus power system model simulated in different software tools using the plot representation of the respective tools.

Acknowledgments

This work was supported in part by Dominion Energy through sponsored research projects at Rensselaer Polytechnic Institute, United States; in part by the New York State Energy Research and Development Authority (NYSERDA), United States through the Electric Power Transmission and Distribution (EPTD) PON 3770 High Performing Grid Program together with the New York Power Authority (NYPA); and in part by the ERC Program of the National Science Foundation, United States and DOE under NSF Award, United States Number EEC-1041877 and by the CURENT Industry Partnership Program, United States.

Code metadata Current code version v2.0.0 Permanent link to code/repository used for this code version https://github.com/ElsevierSoftwareX/SOFTX-D-22-00373 Code Ocean compute capsule none Legal Code License 3-Clause BSD license Code versioning system used git

Data availability

No data was used for the research described in the article.


Sophie Lallemand

M Le Docteur Ismaël

M Le Professeur

Jorge Lopez-Castroman

M Le

Docteur Mocrane

Abbar M Le Docteur

Ismaël Conejero

Éric Thouvenot

Directeur De

M Le Professeur Éric

Bernard Albat

Michel Brunel

Claude Humeau

Maurice Navarro

Yves Allieu

Bernard Canaud

Claude Jaffiol

Henri Navratil

Robert Alric

Paul-André Chaptal

Charles Janbon

Jacques Othoniel

Bernard Arnaud

Albert-Jean Ciurana

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Neurochirurgie

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Perez Cardiologie

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Pédiatrie

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Cancérologie

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Adultes Psychiatrie D'

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Gynécologie-Obstétrique ;

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DOCTEUR EN MEDECINE Présentée et soutenue publiquement Par

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Introduction en français

Les troubles neurologiques fonctionnels (TNF) sont définis dans le DSM-5 (1) par la présence de symptômes neurologiques, tels qu'une altération de la motricité volontaire (faiblesse, paralysie…) ou des fonctions sensorielles (perturbations sensitives, visuelles…), en l'absence de lésion L'expression anormale de GFAP, marqueur d'activation astrocytaire, intervient lors des processus neuroinflammatoire et neurodégénératif [START_REF] Li | Neurochemical regulation of the expression and function of glial fibrillary acidic protein in astrocytes[END_REF]. Chez les patients souffrant de sclérose en plaque, une maladie neuroinflammatoire et neurodégénérative, l'expression de GFAP a été corrélé avec la sévérité du handicap et des lésions de la substance blanche [START_REF] Abdelhak | Serum GFAP as a biomarker for disease severity in multiple sclerosis[END_REF]. Les données sur la GFAP dans les maladies psychiatriques dont controversées, bien qu'il semble y avoir une atteinte de la fonction astrocytaire avec une diminution des taux de GFAP chez les patients souffrant de dépression [START_REF] Enache | Markers of central inflammation in major depressive disorder: A systematic review and meta-analysis of studies examining cerebrospinal fluid, positron emission tomography and post-mortem brain tissue[END_REF].

Un autre médiateur important de la réponse inflammatoire du système nerveux central, la MCP-1/CCL2, qui est également associée aux rechutes dans la sclérose en plaque, a été identifié dans le sérum de patient déprimés [START_REF] Grassi-Oliveira | Peripheral chemokine levels in women with recurrent major depression with suicidal ideation[END_REF].

A notre connaissance, aucune étude s'est intéressée au lien entre la GFAP ou la MCP-1/CCL2 et les TNF.

Les neurofilaments à chaines légères sont un biomarqueur prometteur en tant qu'aide au diagnostic différentiel entre les troubles neurologiques et psychiatriques [START_REF] Shweiki | Neurofilament light chain as a blood biomarker to differentiate psychiatric disorders from behavioural variant frontotemporal dementia[END_REF]. Les neurofilaments sont des protéines de structure retrouvés exclusivement au niveau des axones des neurones et le renouvellement est faible [START_REF] Khalil | Neurofilaments as biomarkers in neurological disorders[END_REF]. Leur dosage est facilement accessible dans le sang [START_REF] Kuhle | Comparison of three analytical platforms for quantification of the neurofilament light chain in blood samples: ELISA, electrochemiluminescence immunoassay and Simoa[END_REF][START_REF] Gisslén | Plasma Concentration of the Neurofilament Light Protein (NFL) is a Biomarker of CNS Injury in HIV Infection: A Cross-Sectional Study[END_REF]. Leur utilité a été démontrée dans la sclérose en plaque en tant que marqueur diagnostic et pronostic ainsi que pour évaluer la réponse aux traitements [START_REF] Disanto | Serum Neurofilament light: A biomarker of neuronal damage in multiple sclerosis: Serum NfL as a Biomarker in MS[END_REF]. patients with FND that could be considered as state markers as they disappeared during the followup. They also demonstrated an association between baseline brain metabolism with the clinical outcomes at 3 months of follow-up in the inferior frontal gyrus, orbitofrontal cortex, subgenual anterior cingulate cortex, primary motor cortex, supplementary motor area, putamen and thalamus [START_REF] Conejero | Association between brain metabolism and clinical course of motor functional neurological disorders[END_REF].

Identifier
Research on immune system dysregulation in psychiatric disorders has shown growing interest in recent years and numerous studies have highlighted a relationship between psychiatric disorders and low-grade inflammation [START_REF] Büyükaslan | Evaluation Of Mean Platelet Volume, Red Cell Distributed Width And Neutrophil To Lymphocyte Ratio In Conversion Disorder[END_REF][START_REF] Paredes-Echeverri | Autonomic, Endocrine, and Inflammation Profiles in Functional Neurological Disorder: A Systematic Review and Meta-Analysis[END_REF][START_REF] Goldsmith | A meta-analysis of blood cytokine network alterations in psychiatric patients: comparisons between schizophrenia, bipolar disorder and depression[END_REF]. In particular the pro-inflammatory cytokines TNF-α, IL-1β, IL-6, IFN-γ and the anti-inflammatory IL-10 have been among the most studied [START_REF] Dowlati | A Meta-Analysis of Cytokines in Major Depression[END_REF][START_REF] Beurel | The Bidirectional Relationship of Depression and Inflammation: Double Trouble[END_REF]. In fact, their secretion profile is related with an imbalance between the M1 (IL-1β, TNF-α, IL-6 and CCL2

producing) and M2 (IL-10 producing) phenotypes of macrophages and microglia , and has been linked with the neuroinflammatory processes across psychiatric disorders [START_REF] Nakagawa | Diversity and plasticity of microglial cells in psychiatric and neurological disorders[END_REF]. In depressive disorder, a recent meta-analysis reported increased levels of IL-1ra, rsIL-2, IL-6, IL-10, IL-18, TNFα, MCP-1/CCL2, and a decrease of IFN-γ [START_REF] Köhler | Peripheral cytokine and chemokine alterations in depression: a meta-analysis of 82 studies[END_REF].

The research concerning inflammatory process during FND symptoms is at its early stage (8), however several evidence may suggest its involvement in the pathophysiology of motor FND: i) "sickness behaviours" involve behavioural changes partly similar to those observed in patients with motor FND [START_REF] Dimsdale | A Biological Substrate for Somatoform Disorders: Importance of Pathophysiology[END_REF] and are experimentally induced by inflammatory cytokines (IL-1, IL-6 and TNF-α) in animal models [START_REF] Slavich | From stress to inflammation and major depressive disorder: A social signal transduction theory of depression[END_REF][START_REF] Harrison | Inflammation Causes Mood Changes Through Alterations in Subgenual Cingulate Activity and Mesolimbic Connectivity[END_REF] ; ii) peripheral inflammation induces changes of brain activity in regions also involved in motor FND [START_REF] Harrison | Inflammation Causes Mood Changes Through Alterations in Subgenual Cingulate Activity and Mesolimbic Connectivity[END_REF][START_REF] Brydon | Peripheral Inflammation is Associated with Altered Substantia Nigra Activity and Psychomotor Slowing in Humans[END_REF][START_REF] Eisenberger | Inflammation-Induced Anhedonia: Endotoxin Reduces Ventral Striatum Responses to Reward[END_REF] ; iii) inflammatory cytokines have been shown to cross the blood-brain barrier and modulate the functioning of the central nervous system [START_REF] Irwin | Reciprocal regulation of the neural and innate immune systems[END_REF][START_REF] Pavlov | Neural regulators of innate immune responses and inflammation[END_REF][START_REF] Sternberg | Neural regulation of innate immunity: a coordinated nonspecific host response to pathogens[END_REF].

In addition, the levels of GFAP (Glial Fibrillary Acidic Protein) and MCP-1/CCL2 (Monocyte Chemoattractant Protein-1/C-C motif chemokine ligand 2), which underlie the inflammatory response within the central nervous system, are supposed to be associated with motor FND for further reasons. For instance, over expression of GFAP (Glial Fibrillary Acidic Protein) occurs in neuroinflammation and neurodegeneration process and may be a marker of astrocytic activation [START_REF] Li | Neurochemical regulation of the expression and function of glial fibrillary acidic protein in astrocytes[END_REF]. Moreover, GFAP expression has been correlated with the severity of disability and white matter lesions in patients diagnosed with multiple sclerosis [START_REF] Abdelhak | Serum GFAP as a biomarker for disease severity in multiple sclerosis[END_REF] and impaired astrocyte function with a lower GFAP level seems to occur in patients with depression [START_REF] Enache | Markers of central inflammation in major depressive disorder: A systematic review and meta-analysis of studies examining cerebrospinal fluid, positron emission tomography and post-mortem brain tissue[END_REF]. Finally, MCP-1/CCL2 has been identified in the serum of depressed patients [START_REF] Grassi-Oliveira | Peripheral chemokine levels in women with recurrent major depression with suicidal ideation[END_REF] and also associated with multiple sclerosis relapses. However, no study has investigated the link between GFAP or MCP1/CCL2

and FND yet.

Neurofilament light chains are structural proteins found exclusively in the axons of neurons with a low turnover [START_REF] Khalil | Neurofilaments as biomarkers in neurological disorders[END_REF]. Their level in serum is suggested to increase under pathological states involving loss of axonal integrity, thus helping to differentiate between neurological and psychiatric diagnoses [START_REF] Shweiki | Neurofilament light chain as a blood biomarker to differentiate psychiatric disorders from behavioural variant frontotemporal dementia[END_REF] . Their dosage is easily accessible in the blood [START_REF] Kuhle | Comparison of three analytical platforms for quantification of the neurofilament light chain in blood samples: ELISA, electrochemiluminescence immunoassay and Simoa[END_REF][START_REF] Gisslén | Plasma Concentration of the Neurofilament Light Protein (NFL) is a Biomarker of CNS Injury in HIV Infection: A Cross-Sectional Study[END_REF] and their usefulness has been demonstrated in multiple sclerosis, as a diagnostic and prognostic marker and to evaluate the treatment response [START_REF] Disanto | Serum Neurofilament light: A biomarker of neuronal damage in multiple sclerosis: Serum NfL as a Biomarker in MS[END_REF]. Nonetheless, neurofilaments have never been investigated in patients with FND despite growing evidence of their association with cerebral structural modifications.

The identification of peripheral biomarkers associated with motor symptoms and abnormalities of brain metabolism at symptom onset during motor FND would allow clinicians to better understand their pathophysiology and the factors associated with their clinical course. This knowledge would aid developing less invasive diagnostic tools, and thus would improve patient clinical management.

Hence, we hypothesize that blood inflammatory markers are increased in patients with first episode of motor FND, and that their level is associated with the course of motor symptoms. We also hypothesize that inflammatory markers are associated with brain metabolism at baseline and during follow-up in this population.

The aim of our study is to evaluate the levels of neurofilaments, GFAP and inflammatory cytokines in serum in patients with first episode of motor FND at symptom onset and to compare these levels with those of affective controls. We also aimed at evaluating their association with the evolution of motor symptoms during follow-up in patients with motor FND assessed by validated neurological scale. Finally, we studied their association with the modifications of brain metabolism assessed by brain H0 18F-fluorodeoxyglucose positron emission computed tomography (FDG-PET) at baseline and during follow-up in this clinical group.

MATERIALS AND METHODS

Study Design

Methods were adapted from Conejero et al., 2022 (6). Each patient with motor FND defined according to the DSM-IV-TR criteria underwent a resting-state brain H0 18F-fluorodeoxyglucose positron emission computed tomography (FDG-PET), in the department of nuclear medicine of the University Hospital Center of Nîmes (France). In the same day, patients were assessed by a neurologist using the Expanded Disability Status Scale (EDSS) and the National Institute of Health Stroke Scale (NIHSS), and by a psychiatrist using the Halmilton Depression Scale (HAMD) and Hospital Anxiety and Depression scale (HADS). Blood samples were drawn immediately after the consultation. Serum samples were then frozen at -80° for preservation. At the 3 months follow-up visit, all these assessments were repeated. All psychotropic treatments during the 24 hours prior to the FDG-PET were recorded.

For the purposes of the present study, part of the samples collected at inclusion and at 3 months were thawed for biological analyses.

Correlations were performed between the measured biomarkers in the serum, and clinical and brain metabolism data.

Study participants

Patients with FND were included if euthymic at the time of evaluation and were recruited in the 18, IL-1ra and IL-2ra. Each assay was performed in triplicate in patients with motor FND and in affective control individuals.

All the assays were performed in the Hospice Civils university hospital in Lyon, France.

Outcomes

The endpoints to evaluate in patients with a first episode of motor FND, were: i) the levels of biological markers (nerofilaments, GFAP and cytokines) in the serum of patients with motor FND at inclusion and 3 months to follow-up compared with those of affective control individuals; ii) the correlation between the levels of biological markers at baseline in patient with motor FND and their clinical symptoms at inclusion iii) the correlation between the changes of biological markers levels and the changes in EDSS and NIHSS status between inclusion and 3 months.; iv) the correlation between the levels of biological markers at baseline in patient with motor FND and their resting-state brain metabolism at inclusion; v) the correlation between the changes of biological markers levels and the modification of the resting state brain metabolism in patient with motor FND between inclusion and 3 months.

Statistical analysis

Statistical analysis was performed using Prism software and SAS (9.4; SAS Inc., Cary NC). Data were expressed using numbers and associated percentages for categorical variables, and mean (SD) or median [25th percentile -75th percentile] depending on the distribution for quantitative variables. Comparison between cytokine levels of patients with motor FND and of affective controls were performed using Mann-Whitney test for nonparametric data. Correlations between cytokines and neurological scale scores, and between cytokines and metabolic values in each brain region of interest in patients with motor FND were assessed using a nonparametric Spearman rank correlation coefficient. The significance level was set at p < 0.05. No sample size assessment was performed because this was a pilot study.

RESULTS

Sample description

In the current study, seventeen patients with motor FND were involved in the baseline analysis.

Among the twenty-three patients screened, six patients were excluded (2 FDG-PET not performed, 1 comorbid Marchiafava-Bignami disease, 1 bioassay outlier, 1 bioassay not performed and 1 refusal to participate). At 3 we analysed the data of the 14 patients with motor FND (two patients were lost to follow-up and one patient withdrew consent). The flow chart is provided in figure 1.

The baseline clinical and biological characteristics of the patients with a motor FND are reported in Table 1. The median age of the patients with motor FND was 45 [35-51] and 1/17 was a male (6%). The median EDSS score was 2.5 [1 -6] and the median NIHSS score was 2 [0 -4] at inclusion.

The patients with motor FND lost to follow-up at 3 months (n=3) were younger, had a higher median EDSS score at 4 [1 -4] but a lower median NIHSS score at 0 [0 -4] than those who completed the follow up (Age 47 [35 -59]; EDSS score 2.25 [1 -6.5] and NIHSS score 2.5 [0 -4] respectively), without reaching statistical significance. The comparison of patients lost to follow-up with those who completed the neuroimaging, the clinical visits and the biological sampling at 3 months is shown in the supplementary table 1.

Affective control individuals were selected using frequency matching on age and sex corresponding to patients with motor FND included in the study.

Biomarker levels in patients with motor FND and in affective control individuals.

Biomarker levels in serum of patients with motor FND at inclusion and 3 months to follow-up, and in serum of affective control individuals are shown in table 2. Patients with motor FND at baseline had greater level of neurofilament, IFN-γ, IL-10, IL-6, TNF-α, CCL2, and IL-1ra than affective controls individuals (Figure 2). These results were confirmed in a sensibility analysis (Supplementary figure 1).

Correlation between biomarker levels and clinical scores in patients with motor FND at inclusion.

No correlation was found with statistical significance. Data are not shown.

Correlation between biomarker changes and symptom modifications between inclusion and 3 months in patients with motor FND.

No correlation was found between the neurofilaments changes, and the evolution of the clinical scores.

Concerning cytokines, changes in TNF-α levels were positively correlated with changes in NIHSS score between inclusion and 3 months to follow-up (r=0.533, p= 0.0495).

Correlation between biomarker levels and resting-state brain metabolism at inclusion in patients with motor FND.

No correlation was found between the neurofilaments level at inclusion, and the initial brain metabolism at rest.

Regarding cytokines, the level of TNF-α at inclusion was positively correlated with the metabolism of the left supplementary motor area (r = 0.4954; p=0.0432). The level of CCL2 and IL-10 at inclusion was negatively correlated with the metabolism of the left inferior frontal gyrus and right putamen (r= -0.5123; p=0.0355; and r= -0.5368; p=0.0263 respectively).

Correlation between biomarker changes and changes in restingstate brain metabolism between baseline and 3 months in patients with motor FND

Changes of the neurofilament levels were negatively correlated with changes in resting-state brain metabolism in the left and right anterior cingulate cortex from baseline to 3 months follow-up (r = -0.5516; p = 0.0408; and r = -0.5912; p = 0.0260 respectively) (Table 3). Changes of the neurofilament levels were also negatively correlated with changes in the resting-state brain metabolism in the left frontopolar cortex and the left orbito-frontal cortex (r = -0.5385; p = 0.0470).

Regarding cytokines, changes of the IFN-γ levels were positively correlated with changes in resting-state brain metabolism in the left and the right ventral anterior cingulate cortex (r = 0.5912; p = 0.0260; and r = 0.5736; p = 0.0320 respectively). Changes of the IFN-γ levels were also positively correlated with changes in the metabolism of the right putamen at rest (r=0.5956; p = 0.0246).

Correlation between biomarker levels at inclusion and changes in resting-state brain metabolism between baseline and 3 months in patients with motor FND

IFN-γ level at inclusion was negatively correlated with change in resting-state brain metabolism of the left and right ventral anterior cingulate cortex (r = -0;7626; p = 0,0015; and r = -0.7582; p = 0.0017 respectively), and changes in both left and right subgenual anterior cingulate cortex (r = -0.8286; p = 0.0003 for both regions).

DISCUSSION

To our knowledge, this study is the first to evaluate blood biological markers in a population of patient with FND and their association with the course of motor symptoms and brain metabolism over time. At baseline, patients with motor FND had greater level of neurofilament, IFN-γ, IL-10, IL-6, TNF-α, CCL2, and IL-1ra than depressed individuals.

Our results outline that changes of the pro-inflammatory cytokine TNF-α is associated with the evolution of motor FND symptoms during follow-up, and a correlation at baseline with the resting metabolism of regions involved in motor control (the left supplementary motor area), whereas other cytokines (CCL2 and IL-10) are negatively linked with inferior frontal gyrus and right putamen at inclusion.

During follow-up, we found that neurofilaments showed a negative relationship with the ventral anterior cingulate cortex, the orbito-frontal and also the fronto-polar cortex over time, whereas the evolution of IFN-γ level was positively associated with metabolic modifications of putamen and the ventral anterior cingulate cortex.

Finally, IFN-γ level at inclusion was negatively linked with the evolution of in resting-state metabolism of the left and right ventral anterior cingulate cortex. The baseline metabolism and its changes in this latter brain region was related with the evolution of motor FND symptom at 3 months to follow-up [START_REF] Conejero | Association between brain metabolism and clinical course of motor functional neurological disorders[END_REF].

IFN-γ, IL-10, IL-6, TNF-α, CCL2 are all pro-inflammatory cytokines [START_REF] Dowlati | A Meta-Analysis of Cytokines in Major Depression[END_REF], [START_REF] Beurel | The Bidirectional Relationship of Depression and Inflammation: Double Trouble[END_REF] and show increased levels in patients with first episode motor FND at symptom onset compared with affective control individuals. These markers are involved in low grade chronic inflammatory process (31) that may play a role during the early stage of FND symptoms. This effect seems to not depend upon comorbid affective state, nor age or sex as affective controls were matched according to these variables.

The level of TNF-α was positively correlated with changes in NIHSS score between inclusion and 3 months. TNF-α is an inflammatory cytokine produced by macrophages/monocytes during acute inflammation. The dysregulation of TNF-α shown in our study is in accordance with observations made in depression which relate higher levels of TNF-α, and higher levels of TNF-α receptor in several brain regions including amygdala, hypothalamus, hippocampus, and frontal cortex [START_REF] Ma | Pathogenetic and Therapeutic Applications of Tumor Necrosis Factor-α (TNF-α) in Major Depressive Disorder: A Systematic Review[END_REF].

These regions are involved in emotion regulation and also suspected to be implicated in the pathophysiology of FND. In our study, patients were free from depression at inclusion. However both FND and depressive phenotype share features of sickness behaviours which also result from TNF-α and IFN-γ increase in serum [START_REF] Dantzer | From inflammation to sickness and depression: when the immune system subjugates the brain[END_REF]. We found that TNF-α level was linked with metabolism of SMA at baseline, which is a core region implicated in FND motor symptoms [START_REF] Voon | Aberrant supplementary motor complex and limbic activity during motor preparation in motor conversion disorder[END_REF], [START_REF] Conejero | Neuroanatomy of conversion disorder: towards a network approach[END_REF].

We also observed a negative correlation between baseline level of CCL-2 which is involved in recruitment of myeloid immune cells and promotes inflammation, IL-10 (a major antiinflammatory cytokines), and right putamen metabolism at inclusion. Hence, inflammation may underlie putamen hypometabolism which has been found to be associated with motor FND symptoms in the study led by Vuilleumier et al., (2001) (4). Increased initial metabolism of putamen was linked with the clinical improvement of FND patients assessed through EDSS in a recent study [START_REF] Conejero | Association between brain metabolism and clinical course of motor functional neurological disorders[END_REF]. The negative association between IL-10 and putamen metabolism may result from anti-inflammatory cytokines secretion as a balancing mechanism to counter the release of inflammatory cytokines.

The implication of the IFN-γ in the pathophysiology of FND seems more contradictory. Whereas we found a strong negative relationship between initial IFN-γ level and the modifications of bilateral ventral anterior ACC during follow-up, the latter being related with the course of FND symptoms in a recent study [START_REF] Conejero | Association between brain metabolism and clinical course of motor functional neurological disorders[END_REF], the association between the evolution of IFN-γ in serum and the metabolic changes of ACC and right putamen was positive. Hence, the role of the IFN-γ at symptom onset in predicting brain metabolism seems distinct from its influence upon central nervous system during follow-up.

Interestingly, the modifications of neurofilament levels were negatively linked with the modifications of the putamen, the ventral ACC and the orbito-frontal cortex during patients' follow-up. This may highlight possible micro-structural axonal impairment in the brain regions involved upon disease progression. The measure of greater levels of neurofilament levels in FND patients than in affective control individuals is of importance as it may potentially relate to specific biochemical features underlying motor

The origin of the observed peripheral low-grade inflammation in patients with motor FND and the related biochemical pathways leading to alteration of brain functioning remains to be precisely determined, however different hypothesis have recently emerged: i) Cross-sensitization between cytokines and hypothalamo-pituitary axis.

Sensitization is a phenomenon whereby exposure to a particular stimulus triggers an enhanced physiological response when exposed to the same stimulus (homotypic) or to a different stimulus (heterotypic or cross-sensitized). Some authors have shown that in animals, exposure to a stressor sensitizes the hypothalamic-pituitary axis response to subsequent stress [START_REF] Johnson | Prior stressor exposure primes the HPA axis[END_REF] and sensitizes the cytokine innate immune response [START_REF] Johnson | Prior Stressor Exposure Sensitizes LPS-Induced Cytokine Production[END_REF].

Interestingly, evidence have been reported for a hyperactivity of the stress axis and the autonomous nervous system in patients with FND despite contradictory results [START_REF] Boulet | Stress response in dissociation and conversion disorders: A systematic review[END_REF].

ii) Reactivation of the immune system by physical/psychological trauma.

Triggers of inflammatory response may be either psychological or physical stressors.

In functional neurological disorder population, adverse physical event are frequently reported in the 3 months before symptoms onset [START_REF] Cretton | What Does Neuroscience Tell Us About the Conversion Model of Functional Neurological Disorders? JNP[END_REF]. These events may be likely to activate the sensitized innate immunity leading to an enhanced inflammatory response.

iii) Bi-directional relationship between peripheral immune system and the brain.

Brain monitors peripheral innate immune responses through several pathways, including direct action of pro-inflammatory cytokines on the central nervous system.

First, locally produced cytokines may activate afferent neurons located in the vagal nerve. Secondly, the production of proinflammatory cytokines by phagocytic cells residing in the circumventricular organs and the choroid plexus may respond to circulating pathogen-associated molecular patterns. Finally, cytokine may reach the brain through transporter proteins expressed in the blood-brain barrier [START_REF] Dantzer | From inflammation to sickness and depression: when the immune system subjugates the brain[END_REF][START_REF] Dantzer | Sickness Behavior, and Depression[END_REF][START_REF] Khairova | A potential role for pro-inflammatory cytokines in regulating synaptic plasticity in major depressive disorder[END_REF].

Conversely, the central nervous system may modulate the innate immune system through activation of the hypothalamo-pituitary axis and the autonomous nervous system.

Our study should be interpreted considering some limitations. Because all patients had access to optimal routine care, the psychotherapeutic, physiotherapeutic and drugs treatments provided might have differentially influenced their clinical, metabolic, and biological evolution. In addition, small sample size prevented us to control results upon potential confounding factors, or correct significance level for multiple comparisons. Finally, the patients included in our study had heterogeneous clinical presentations, however they all showed at least one limb paresis or a gait disorder. Methodological limitations inherent to our cohort study are discussed in Conejero et al.,

2022.

Our study has several strengths, including the use of ultrasensitive and reproducible assay techniques. All the clinical samples were tested using the same technique in reproducible conditions, in one laboratory setting. The control group was sex and age matched.

CONCLUSION

Our study is the first to evaluate the association between biological features, brain metabolism and clinical evolution in patients with first episode motor FND at symptom onset.

The relationship between neuroinflammation, the modifications of clinical symptoms and the modifications of brain metabolism over time in patients with FND remain to be confirmed in future studies. However, our results suggest an implication of innate immune response and chronic inflammatory processes in the pathophysiology of these disorders. Specifically, the metabolism of motor regions and cortical areas involved in emotional regulation seem related with level of peripheral inflammatory markers. These markers may predict brain metabolic changes over disease course. Besides, the elevation of neurofilament may uncover the occurrence of microstructural axonal impairment, which is not highlighted by conventional or research neuroimaging techniques. Finally, low grade inflammation may be a potential new therapeutic target to treat these highly disabling disorders. ii) Réactivation du système immunitaire par un traumatisme physique/psychologique.

Les déclencheurs de la réponse inflammatoire peuvent être des facteurs de stress psychologiques ou physiques. Dans la population souffrant de troubles neurologiques fonctionnels, des événements physiques traumatiques sont fréquemment signalés dans les trois mois précédant l'apparition des symptômes [START_REF] Cretton | What Does Neuroscience Tell Us About the Conversion Model of Functional Neurological Disorders? JNP[END_REF]. Ces événements sont susceptibles d'activer l'immunité innée sensibilisée, entraînant une réponse inflammatoire accrue.

  organique identifiée. Le diagnostic repose sur des données cliniques démontrant l'incompatibilité entre les symptômes et une affection neurologique ou médicale reconnue (signe de Hoover, manoeuvre d'entrainement), ainsi que sur la réalisation d'examens complémentaires permettant d'éliminer une lésion du système nerveux central. Les troubles neurologiques fonctionnels sont fréquents, avec une prévalence de 5 à 10% chez la patients reçus en consultation de neurologie, et associés à des niveaux élevés d'incapacité physique, équivalent à ceux des patients atteints de sclérose en plaque ou d'épilepsie (2). Malgré la normalité supposée de l'imagerie cérébrale structurelle en pratique courante (3), des modifications du métabolisme cérébrale ont été mises en évidence dans certaines régions clés impliquées dans le contrôle de la motricité et des émotions. Ces anomalies du métabolisme ont été retrouvée dans le cortex cingulaire antérieur, le cortex orbitofrontal, le cortex préfrontal dorsolatéral, le cortex frontopolaire, la jonction temporo-pariétale, l'insula, l'amygdale, le thalamus et les régions cérébrales impliquées dans la motricité volontaire (cortex moteur primaire, aire motrice supplémentaire, noyaux caudés et putamen) (4,5). Récemment, Conejero et al. ont trouvé un hypométabolisme frontal de repos (cortex frontopolaire, cortex orbitofrontal, et aire motrice supplémentaire) au TEP-scan 18-FDG, à la phase aigüe d'apparition des symptômes chez des patients souffrant de TNF, et pouvant être considéré comme un marqueur d'état puisqu'il se normalise lors du suivi. Ils ont également montré une association entre le métabolisme cérébral initial et les symptômes cliniques à 3 mois dans le gyrus frontal inférieur, le cortex orbitofrontal, le cortex cingulaire subgénual, le cortex moteur primaire, l'aire motrice supplémentaire, le putamen et le thalamus (6). La recherche sur les dérèglements du système immunitaire dans les troubles psychiatriques a suscité un intérêt croissant ces dernières années et de nombreuses études ont mis en évidence une relation entre les troubles psychiatriques et la présence d'une inflammation de bas grade (7-9).Les marqueurs inflammatoires les plus étudiés en psychoneuroimmunologie sont le TNF-α, l'IL-1β, l'IL-6, l'IFN-γ (pro-inflammatoire) et l'IL-10 (anti-inflammatoire)[START_REF] Dowlati | A Meta-Analysis of Cytokines in Major Depression[END_REF][START_REF] Beurel | The Bidirectional Relationship of Depression and Inflammation: Double Trouble[END_REF]. Leur profil de sécrétion serait lié à un déséquilibre entre les phénotypes M1 (produisant de l'IL-1β, du TNF-α, de l'IL-6 et du CCL2) et M2 (produisant de l'IL-10) des macrophages et de la microglie, et a été associé aux processus neuroinflammatoires dans les troubles psychiatriques[START_REF] Nakagawa | Diversity and plasticity of microglial cells in psychiatric and neurological disorders[END_REF]. Dans le trouble de l'humeur dépressif unipolaire, une augmentation des taux d'IL-1ra, rsIL-2, IL-6, IL-10, IL-18, TNFα, MCP-1/CCL2, et une diminution de l'IFN-γ ont été rapportés dans une méta-analyse récente[START_REF] Köhler | Peripheral cytokine and chemokine alterations in depression: a meta-analysis of 82 studies[END_REF]. La recherche concernant le processus inflammatoire au cours des symptômes du TNF en est à ses débuts[START_REF] Paredes-Echeverri | Autonomic, Endocrine, and Inflammation Profiles in Functional Neurological Disorder: A Systematic Review and Meta-Analysis[END_REF], mais plusieurs preuves peuvent suggérer son implication dans la physiopathologie du TNF moteur: i) Le « sickness behaviour » implique des changements comportementaux similaires à ceux observés chez les patients avec un trouble neurologique fonctionnel moteur[START_REF] Dimsdale | A Biological Substrate for Somatoform Disorders: Importance of Pathophysiology[END_REF] et peut être induit expérimentalement par des cytokines inflammatoires (IL-1, IL-6 et TNF-α) dans les modèles animaux[START_REF] Slavich | From stress to inflammation and major depressive disorder: A social signal transduction theory of depression[END_REF][START_REF] Harrison | Inflammation Causes Mood Changes Through Alterations in Subgenual Cingulate Activity and Mesolimbic Connectivity[END_REF] ; ii) L'inflammation périphérique induit des changements de l'activité cérébrale dans des régions qui contrôlent également la motricité(16- 18) ; iii) Il a été montré que les cytokines traversent la barrière hémato-encéphalique et module le fonctionnement du système nerveux central[START_REF] Irwin | Reciprocal regulation of the neural and innate immune systems[END_REF][START_REF] Pavlov | Neural regulators of innate immune responses and inflammation[END_REF][START_REF] Sternberg | Neural regulation of innate immunity: a coordinated nonspecific host response to pathogens[END_REF].La GFAP (Glial Fibrillary Acidic Protein) et la MCP-1/CCL2 (Monocyte Chemoattractant Protein-1/C-C motif chemokine ligand 2), qui sous-tendent la réponse inflammatoire dans le système nerveux central, pourraient également être impliquées dans le TNF moteur.

Neurology,

  Emergency and Psychiatry Departments in the University Hospitals of Nimes and Montpellier from 2016, 2 nd of January to 2017, 26th of July. Euthymia was defined as Hamilton Depression Rating Scale score < 7. Inclusion and non-inclusion criteria are described in Conejero et al., 2022 (6).

  iii)Relation bidirectionnelle entre le système immunitaire périphérique et le cerveau.Le cerveau est capable de monitorer les réponses immunitaires innées périphériques par plusieurs voies, incluant l'action directe des cytokines pro-inflammatoires sur le système nerveux central. Premièrement, les cytokines produites localement peuvent activer des neurones afférents situés dans le nerf vague. Ensuite, la production de cytokines pro-inflammatoires par les cellules phagocytaires résidant dans les organes circumventriculaires et les plexus choroïdes peut répondre à des motifs moléculaires associés à des pathogènes circulants. Enfin, les cytokines peuvent atteindre le cerveau par l'intermédiaire de protéines transporteuses exprimées dans la barrière hémato-encéphalique[START_REF] Dantzer | From inflammation to sickness and depression: when the immune system subjugates the brain[END_REF][START_REF] Dantzer | Sickness Behavior, and Depression[END_REF][START_REF] Khairova | A potential role for pro-inflammatory cytokines in regulating synaptic plasticity in major depressive disorder[END_REF]. Inversement, le système nerveux central peut moduler le système immunitaire inné par l'activation de l'axe hypothalamo-pituitaire et du système nerveux autonome. Notre étude doit être interprétée en tenant compte de certaines limites. Comme tous les patients ont eu accès à des soins de routine optimaux, les traitements psychothérapeutiques, physiothérapeutiques et médicamenteux fournis ont pu influencer de manière différentielle leur évolution clinique, métabolique et biologique. De plus, la petite taille de l'échantillon nous a de contrôler les résultats en fonction des facteurs de confusion potentiels, ou de corriger le niveau de significativité pour les comparaisons multiples. Enfin, les patients inclus dans notre étude avaient des présentations cliniques hétérogènes, mais ils présentaient tous au moins une parésie d'un membre ou un trouble de la marche. Les limites méthodologiques inhérentes à notre étude de cohorte sont discutées dans Conejero et al. 2022. Notre étude présente plusieurs points forts, notamment l'utilisation de techniques de dosage ultrasensibles et reproductibles. Tous les échantillons cliniques ont été testés à l'aide de la même technique dans des conditions reproductibles, dans un seul laboratoire. Le groupe témoin était apparié en termes de sexe et d'âge. Conclusion en français Notre étude est la première à évaluer l'association entre les caractéristiques biologiques, le métabolisme cérébral et l'évolution clinique chez les patients présentant un premier épisode de TNF moteur au moment de l'apparition des symptômes. La relation entre la neuroinflammation, les modifications des symptômes cliniques et les modifications du métabolisme cérébral dans le temps chez les patients atteints de TNF reste à confirmer dans des études futures. Cependant, nos résultats suggèrent une implication de la réponse immunitaire innée et des processus inflammatoires chroniques dans la pathophysiologie de ces troubles. Plus précisément, le métabolisme des régions motrices et des zones corticales impliquées dans la régulation émotionnelle semble lié au niveau des marqueurs inflammatoires périphériques. Ces marqueurs peuvent prédire les changements métaboliques du cerveau au cours de la maladie. Par ailleurs, l'élévation des neurofilaments pourrait révéler l'existence d'une atteinte axonale micro-structurale, qui n'est pas mise en évidence par les techniques de neuro-imagerie conventionnelles ou de recherche. Enfin, l'inflammation de bas grade pourrait constituer une nouvelle cible thérapeutique potentielle pour traiter ces troubles très invalidants. Ouverture Une des difficultés à laquelle doit faire face le clinicien/la clinicienne, est l'aspect transnosographique de certains symptômes psychiatriques. Le trouble neurologique fonctionnel en est un exemple comme nous l'avons vu, et l'utilisation de marqueurs clinique, biologique et d'imagerie vont dans les années à venir certainement améliorer la fiabilité diagnostic et l'évaluation du pronostic. Par exemple dans la catégorie des « troubles neurodégénératifs à masque psychiatrique », les neurofilaments pourraient être un marqueur de choix. L'association de l'imagerie par TEP-18FDG, marqueur fonctionnel, aux dosages des neurofilaments, marqueur lésionnel, pourrait permettre de mettre en évidence des anomalies caractéristiques du métabolisme cérébral et d'en déterminer l'origine (lésionnelle neurodégénérative ou non).

Jeff, Thibault, Stella, Iris, Agathe, Carla, Charles, Adèle, j

	Une belle thèse ça ne s'oublie pas, en conviens-tu ?
	Ludo, pour tes recettes siciliennes qui nous ont apporté le courage et la force d'étudier,
	clairement dans la team « bon-vivant » toi aussi, certainement le plus cultivé d'entre nous, toujours
	sympa d'écouter tes petites anecdotes historiques.
	'ai toujours passé de très
	bons moments avec vous, j'ai des chouettes souvenirs des stages passés ensemble, ceux des soirées
	sont un peu plus flous mais les émotions qui s'y rattachent sont assurément bonnes !
	A mes co-internes durant l'internat,
	Raphaël GD, pour ton pragmatisme qui m'a appris comment un psychiatre doit gérer son
	temps de travail, pour ton sens musical qui m'a fait redécouvrir Chopin, pour ton sens clinique qui
	m'a permis de comprendre comment désamorcer une agitation, et enfin pour ton éloquence qui
	elle ne m'a rien apporté de particulier mais que je voulais quand même souligner.
	Sandra, pour m'avoir montré qu'une grande gueule dans un petit corps ça existe,
	autrement dit, tu es haute comme 3 pommes mais on ne te prendra pas pour une poire !
	Manon B, pour m'avoir fait réellement comprendre ce que voulait dire le mot
	« logorrhée », pour tes petits démons qui se cachent dans des poupées russes.
	Amandine, alias Dr Baudy, pour ton côté mysterious girl et tes talents de cuisto qui ont
	mis du level pendant nos améliorés.
	A Morgan et Estelle, pour notre super trio en neurologie, il ne peut y avoir un chat blanc
	que lorsqu'il y a un chat noir, merci Morgan d'avoir endossé ce rôle.
	A Manon B et Cassiana, la team gérontopsy, pour nos recherches diagnostiques toujours
	plus poussées, notre journal club qui n'étaient autre qu'une pause-café, mais aussi nos

discussions plus personnelles qui ont créés une vraie intimité.

Table des matières

 des Introduction en français .........................................................................................................................20 INTRODUCTION .................................................................................................................................23 MATERIALS AND METHODS ...........................................................................................................26 Study Design ............................................................................................................................26 Biological analyses ...................................................................................................................27 Outcomes .................................................................................................................................28 Statistical analysis ...................................................................................................................28 RESULTS .............................................................................................................................................29

	Study

participants ...................................................................................................................26 Control Patients for Biological Analysis .................................................................................27 Standard protocol approvals, registrations, and patient consents .........................................27

  Il existe encore peu d'étude translationnelle dans ce domaine, et à notre connaissance, il n'existe pas d'étude évaluant le lien entre les marqueurs biologiques, le métabolisme cérébral et les données cliniques.Motor functional neurological disorders (FND) are defined in the DSM-V (1) by the presence of neurological symptoms such as motor deficits or abnormal movements, without any identified organic lesion and accompanied with clinical features of internal inconsistency.

	Nous faisons ainsi l'hypothèse d'une relation entre les modifications des marqueurs
	inflammatoires sanguins et l'évolution des symptômes moteur chez les patients souffrant d'un
	premier épisode de trouble neurologique fonctionnel, et que ces marqueurs inflammatoires sont
	également associés au métabolisme cérébral à la phase aigüe et pendant le suivi dans cette Despite the supposed normality of structural brain imaging among patients with motor FND in
	population. L'objectif de notre étude est de mesurer les taux de neurofilaments, GFAP, et des cytokines routine practice (3), changes in brain metabolism have been demonstrated in several key regions
	inflammatoires chez les patients souffrant d'un premier épisode de trouble neurologique involved in motor and emotional control (4). Dysregulated brain regions included the anterior
	fonctionnel, à la phase aigüe d'apparition des symptômes, et de les comparer avec ceux de patients cingulate cortex, orbitofrontal cortex, dorsolateral prefrontal cortex, frontopolar cortex,
	temporoparietal junction, insula, amygdala, thalamus, and motor control regions (primary motor
	cortex, supplementary motor area, caudate nucleus and putamen) (4,5).

des biomarqueurs périphériques associés aux symptômes moteurs et aux anomalies du métabolisme cérébral, survenant à la phase aigüe d'un premier épisode de trouble neurologique fonctionnel, permettrait aux cliniciens de mieux comprendre leur physiopathologie et les facteurs associés à l'évolution clinique, de développer de nouvelles méthodes diagnostiques, et ainsi améliorer la prise en charge clinique du patient. souffrant de sclérose en plaque. Nous avons également pour but d'évaluer leur association avec l'évolution des symptômes moteurs, évalués par des échelles neurologiques validées. Enfin, nous souhaitons étudier leurs associations avec les modifications du métabolisme cérébral, évalué par TEP-scan 18-FDG, à la phase initiale et au cours du suivi. INTRODUCTION Recently, Conejero and al. found a resting-state frontal hypometabolism (frontopolar cortex, orbitofrontal cortex and supplementary motor area) in cerebral FDG-PET at symptom onset in

  Ces régions sont impliquées dans la régulation des émotions et sont également soupçonnées d'être impliquées dans la physiopathologie du TNF. Dans notre étude, les patients ne souffraient pas de dépression à l'inclusion. Cependant, les phénotypes dépressif et du TNF partagent des caractéristiques du « sickness behaviour » qui résultent de l'augmentation du TNF-α et de l'IFN-γ dans le sérum[START_REF] Dantzer | From inflammation to sickness and depression: when the immune system subjugates the brain[END_REF]. Nous avons constaté que le niveau de TNF-α était lié au métabolisme de l'AMS à l'inclusion, qui est une région clé impliquée dans les symptômes moteurs du TNF[START_REF] Conejero | Neuroanatomy of conversion disorder: towards a network approach[END_REF][START_REF] Voon | Aberrant supplementary motor complex and limbic activity during motor preparation in motor conversion disorder[END_REF].

	Discussion en français L'origine de l'inflammation périphérique de bas grade, observée chez les patients atteints de TNF
	moteur, et les voies biochimiques connexes conduisant à une altération du fonctionnement du
	A notre connaissance, il s'agit de la première étude évaluant des marqueurs biologiques sanguins cerveau restent à déterminer avec précision, mais différentes hypothèses ont récemment émergé :
	dans une population de patients souffrant de TNF, et étudiant leurs associations avec l'évolution i) Sensibilisation croisée entre les cytokines et l'axe hypothalamo-pituitaire.
	des symptômes moteurs et du métabolisme cérébral au cours du temps. A l'inclusion, les patients La sensibilisation est un phénomène par lequel l'exposition à un stimulus particulier
	ayant un TNF avaient des taux plus élevés de neurofilaments, d'IFN-γ, d'IL-10, d'IL-6, de TNF-déclenche une réponse physiologique accrue lors d'une exposition au même
	α, de CCL2, et d'IL-1ra, que les sujets dépressifs. stimulus (homotypique) ou à un stimulus différent (hétérotypique ou sensibilisation
	Nos résultats mettent en évidence que l'évolution des taux de TNF-α, une cytokine pro-Nous avons également observé une corrélation négative entre le niveau de base de CCL-2, qui est croisée). Certains auteurs ont montré que chez les animaux, l'exposition à un facteur
	inflammatoire, est associée à l'évolution des symptômes de TNF moteurs pendant le suivi, et impliqué dans le recrutement des cellules immunitaires myéloïdes et favorise l'inflammation, l'IL-de stress sensibilise la réponse de l'axe à un stress
	corrélée, à l'inclusion, avec le métabolisme cérébral de repos de régions impliquées dans le 10 (une cytokine anti-inflammatoire majeure), et le métabolisme du putamen droit à l'inclusion. ultérieur (35) et sensibilise la réponse immunitaire innée aux cytokines (36). De
	contrôle moteur (aire motrice supplémentaire). Deux autres cytokines (CCL2 et IL-10) sont L'inflammation pourrait donc être à l'origine de l'hypométabolisme du putamen qui s'est avéré être manière intéressante, des données ont montré une hyperactivité de l'axe du stress et
	corrélées négativement au gyrus frontal inférieur et au putamen droit à l'inclusion. associé aux symptômes moteurs du TNF dans l'étude menée par Vuilleumier et al. (2001) (4). du système nerveux autonome chez les patients atteints de TNF, malgré des
	Pendant le suivi, nous avons trouvé une relation inverse entre les neurofilaments et le cortex résultats contradictoires (37).
	cingulaire antérieur ventral, les cortex orbitofrontal et fronto-polaire, tandis que l'évolution des
	taux d'IFN-γ était associé positivement aux changements du métabolisme dans le putamen et le
	cortex cingulaire antérieur ventral.
	Enfin, à l'inclusion, les niveaux d'IFN-γ étaient corrélés négativement à l'évolution du
	métabolisme cérébral de repos dans le cortex cingulaire antérieur ventral droit et gauche. Dans ce
	dernier, le métabolisme cérébral initial, ainsi que son évolution, étaient liés aux modifications des
	symptômes moteur après 3 mois de suivi (6).
	Les taux d'IFN-γ, d'IL-10, d'IL-6, de TNF-α, et de CCL2, toutes des cytokines pro-inflammatoires
	(10,11), étaient plus élevés, chez les patients souffrant d'un premier épisode de TNF au moment
	du début des symptômes, par rapport aux contrôles affectifs. Ces marqueurs sont impliqués dans
	le processus d'inflammation chronique de bas grade (31) qui pourrait avoir un rôle au cours de la
	phase aigüe du TNF. Ce résultat ne semble pas dépendre de l'état affectif comorbide, ni de l'âge
	ou du sexe, car les témoins affectifs étaient appariés en fonction de ces variables. Le niveau de
	TNF-α était corrélé positivement aux changements du score NIHSS entre l'inclusion et 3 mois. Le De manière intéressante, les modifications des taux de neurofilaments étaient négativement liées
	TNF-α est une cytokine inflammatoire produite par les macrophages/monocytes lors d'une aux modifications du putamen, du CCA ventral et du cortex orbitofrontal au cours du suivi des
	inflammation aiguë. La dysrégulation du TNF-α retrouvée dans notre étude est en accord avec les patients. Cela peut mettre en évidence une éventuelle altération axonale micro-structurale dans les
	observations faites dans la dépression qui relatent des niveaux plus élevés de TNF-α, et des niveaux régions cérébrales concernées lors de la progression de la maladie. La mesure de niveaux plus
	plus élevés de récepteur de TNF-α dans plusieurs régions du cerveau incluant l'amygdale, élevés de neurofilaments chez les patients atteints de TNF que chez les individus contrôles affectif
	est importante car elle peut potentiellement être liée à des caractéristiques biochimiques
	spécifiques qui sous-tendent les symptômes moteurs.

l'hypothalamus, l'hippocampe et le cortex frontal

[START_REF] Ma | Pathogenetic and Therapeutic Applications of Tumor Necrosis Factor-α (TNF-α) in Major Depressive Disorder: A Systematic Review[END_REF]

. L'augmentation du métabolisme initial du putamen a été reliée à l'amélioration clinique des patients atteints de TNF évaluée par l'EDSS dans une étude récente (6). L'association négative entre l'IL-10 et le métabolisme du putamen peut résulter de la sécrétion de cytokines antiinflammatoires comme mécanisme d'équilibration pour contrer la libération de cytokines inflammatoires. L'implication de l'IFN-γ dans la physiopathologie du TNF semble plus contradictoire. Alors que nous avons trouvé une forte relation négative entre le niveau initial d'IFN-γ et les modifications du CCA ventral bilatéral pendant le suivi, ce dernier étant lié à l'évolution des symptômes du TNF dans une étude récente (6), l'association entre l'évolution de l'IFN-γ dans le sérum et les changements métaboliques du CCA et du putamen droit était positive. Par conséquent, le rôle de l'IFN-γ au début des symptômes dans la prédiction du métabolisme cérébral semble distinct de son influence sur le système nerveux central au cours du suivi.

Remerciements

Lou, découverte sur le tard, merci pour ton sens de l'humour et tes punchlines si bien placées, nos « Jalades », même s'il était difficile de te faire boire autre chose que du perrier.

A Chloé N. et Jessie, la team HDJ, entre nonchalance et bienveillance, ramassis de conneries et clairvoyance. Un beau mélange et une belle alchimie !

Control Patients for Biological Analysis

For control reference, serum samples from 60 depressed patients recruited in the spanish study "Genética, ambiente y trastornos mentales" were sex and age matched to the patients with motor FND and assayed.

Standard protocol approvals, registrations, and patient consents

The study was approved by the local Ethics Committee (CPP Sud Méditerranée III, Nîmes, France, RCP :2014-A01159-38) and by the Institutional Review Board (22.02.01) of the university hospital of Nîmes, France. Experimental methods were carried out in accordance with the ethical guidelines determined by the French National Ministry of Health, Labor and Welfare. The spanish study "Genética, ambiente y trastornos mentales" was approved by the Ethics Committee of the Jiménez Díaz foundation, Spain.

All experimental methods were carried out in accordance with the Declaration of Helsinki. All participants provided written informed consent before entering the study, after the experimental procedure was fully explained. The study is registered at clinicaltrials.gov (NCT05305014).

Biological analyses

Serum concentrations of light chain neurofilaments and GFAP were determined using the SiMoA technique with the SiMoA neurology 2-plex B advantage kit (Quanterix). Each assay was performed in triplicate in patients with motor FND and in affective controls individuals. Serum concentrations of the cytokines, IFN-γ, IL-10, IL-6, TNF-α, CCL2, IL-18, IL-1ra, and IL-2ra were determined using the ELLA protein simple multiplex technique. This procedure corresponds to an automated immunoassay in a microfluidic cartridge allowing parallel analyses. Two cartridges were used, one for the assay of IFN-γ, IL-10, IL-6, TNF-α, and another for the assay of CCL2, IL-SERMENT En présence des Maîtres de cette école, de mes chers condisciples et devant l'effigie d'Hippocrate, je promets et je jure, au nom de l'Etre suprême, d'être fidèle aux lois de l'honneur et de la probité dans l'exercice de la médecine.

Je donnerai mes soins gratuits à l'indigent et n'exigerai jamais un salaire au-dessus de mon travail.

Admis (e) dans l'intérieur des maisons, mes yeux ne verront pas ce qui s'y passe, ma langue taira les secrets qui me seront confiés, et mon état ne servira pas à corrompre les moeurs, ni à favoriser le crime.

Respectueux (se) et reconnaissant (e) envers mes Maîtres, je rendrai à leurs enfants l'instruction que j'ai reçue de leurs pères.

Que les hommes et les femmes m'accordent leur estime si je suis fidèle à mes promesses. Que je sois couvert (e) d'opprobre et méprisé (e) de mes confrères si j'y manque.

ABSTRACT

Background: Lately, evidence of modifications in resting brain metabolism have been demonstrated in patients experiencing a first episode of motor functional neurological disorder.

The aim of this study is to investigate the association between the level of peripheral inflammation markers, the markers of axonal integrity measured in blood and the course of both symptoms and brain metabolism in patients with motor functional neurological disorder.

Methods: For this ancillary study, we used blood samples and 18-FDG PET brain metabolism data from the NCT02329626 prospective pilot study conducted from January 2016 to July 2017. We thawed the blood samples to measure neuronal integrity markers (neurofilaments light chain) and a panel of cytokines in the serum of 17 patients with motor functional neurological disorder. We compared the levels of these markers at inclusion with those measured in a population of depressed individuals (affective controls). The biological data were then correlated to the clinical data and to the brain metabolism measured with 18-FDG PET at inclusion and 3 months to follow-up.

Results: At baseline, there were significantly higher concentration of TNF-α (p < 0,0001), CCL2 (p < 0,0001), IL-1ra (p < 0,0001), IL-6 (p <0,01), IL-10 (p < 0,01) and IFN-γ (p <0,05), in patients with functional neurological disorder compared with the affective control. Also, neurofilament concentration was significantly higher (p < 0,01) in patient with functional neurological disorder compared with the affective control.

Conclusion:

Our data suggest existence of low-grade inflammation associated with functional neurological disorder in the acute phase. The increase in the rate of neurofilament and their correlation with brain metabolism in regions considered as state markers could be a witness of microscopic axonal lesions over disease course.

Keywords


Hina Verma

Karine Le Guen

Shruti Gupta

Rajnish Dhawan

Mohammed H Modi

Philippe Jonnard

Interface analysis of Mg/Sc and Sc/Mg bilayers using X-ray reflectivity

Keywords: Grazing incidence x-ray reflectivity, Interfaces, Soft x-ray reflectivity, Time-offlight secondary ion mass spectroscopy

Mg/Sc and Sc/Mg bilayers were studied to investigate their interfaces. Time-of-flight secondary ion mass spectroscopy and grazing incidence x-ray reflectivity are combined to determine the realistic structure of the bilayer stack: thickness, refractive index, and roughness of layers and interlayers respectively. In addition, soft x-ray reflectivity measurements provide sensitive information about the chemical environment of scandium, when the incident photon energy is tuned in the vicinity of the Sc L-absorption edge (~ 400 eV). Both Mg-on-Sc and Scon-Mg interfaces have high roughness (~1 nm) and a MgSc compound interlayer but are shown to be asymmetric.

Introduction

The water window range, located between the absorption edges of carbon (285 eV) and oxygen (530 eV), is particularly suited for imaging biological samples with high optical contrast. Within this range also falls the nitrogen K absorption edge (395 eV) with characteristic Kα emission at 393 eV. This emission band is quite intriguing for the design and application of multilayer mirrors as optical components for spectroscopic purposes [START_REF] Hombourger | Use of layered synthetic microstructures for the quantitative x-ray analysis of light elements[END_REF]. Crystal spectrometers when equipped with suitable periodic multilayers designed with periods ranging from few to some tens of nanometers can diffract nitrogen K emission band, which is otherwise impossible to achieve with a crystal owing to the long wavelength to disperse [START_REF] Schäfers | Cr/Sc multilayers for the soft-x-ray range[END_REF][START_REF] Mcdermott | Structural and Band Gap Investigation of GaN:ZnO Heterojunction Solid Solution Photocatalyst Probed by Soft X-ray Spectroscopy[END_REF][START_REF] Macnaughton | Electronic structure and charge carriers in metallic DNA investigated by soft x-ray spectroscopy[END_REF].

Different Mg/Sc multilayers with and without Co barrier layer have been previously studied for application in this spectral range [START_REF] Jonnard | Characterization of Sc/Mg multilayers with and without Co barriers layers for x-ray spectroscopy in the water window range[END_REF]. Out of those systems, Sc/Co/Mg/Co multilayer displayed promising results with an expected reflectivity of 32% in the nitrogen K edge energy range. However, it was found that strong interdiffusion takes place at the Mg-on-Sc and Sc-on-Co interfaces, leading to limited reflective properties [START_REF] Jonnard | Characterization of Sc/Mg multilayers with and without Co barriers layers for x-ray spectroscopy in the water window range[END_REF]. Given in figure 1(a) and b) is the simulation of a perfect (without roughness or diffusion) [Mg(3nm)/Sc(3nm)]x25 and [Sc(3nm)/Mg(3nm)/ZrC(1nm)]x25 periodic multilayer systems with more than 50% reflectance at the N K absorption edge of 395 eV. It is thus evident from the simulation that such systems can pose as ideal candidates for application in the N K emission range. However, in reality such perfect systems cannot be achieved as the interdiffusion at interfaces, formation of rough surfaces and even in some cases presence of buried layers hinder the quality and overall optical performance of any multilayer system. Thus, it is a prerequisite to describe precisely the interlayers and have information about the interactions at the surface of the stack, in-between each layer and at the bottom layer and the substrate. Consequently, we now aim to study the bilayer systems made of Mg and Sc to investigate the behaviour of Mg-on-Sc and Sc-on-Mg interface separately. Grazing incidence hard x-ray reflectivity (GIXRR), a non-destructive tool, is used to probe the two bilayer structures to deduce structural parameters: thickness, roughness and density of layers and interlayers. In GIXRR, the optical contrast is not sufficient to identify the small compositional gradients at the interface for thin films of low atomic numbers [START_REF] Kiranjot | Interface asymmetry in AlN/Ni and Ni/AlN interfaces: A study using resonant soft X-ray reflectivity[END_REF][START_REF] Majhi | Soft X-ray Reflection Spectroscopy for Nano-Scaled Layered Structure Materials[END_REF].

Whereas, in the soft x-ray region, near absorption edges, with a marginal change in the composition, the atomic scattering factors vary drastically, in turn enhancing the optical index contrast [START_REF] Wang | Soft x-ray resonant reflectivity of low-Z material thin films[END_REF][START_REF] Nayak | Determination of interlayer composition at buried interfaces using soft x-ray resonant reflectivity[END_REF]. In this study, soft x-ray reflectivity (SXR) is employed to record the reflectivity curves at photon energies around the Sc L2,3 absorption edge. Furthermore, time of flight secondary ion mass spectroscopy (ToF-SIMS) analysis was also done to understand the nature of different layers and interlayers formed. It gives the distribution of layers of inside the stack and provides information of the possible compounds formed as a result of intermixing between the layers.

Experimental

Sample Preparation

[Mg(20nm)/Sc(20nm)]/Si substrate and [Sc(20nm)/Mg(20nm)]/ZrC(1.5nm)/Si substrate (labelled as Mg/Sc and Sc/Mg respectively in the following) samples were fabricated using ion beam sputtering. Commercially available sputtering targets of Mg, Sc and ZrC with 99.5% purity were used. Deposition chamber was evacuated to 10 -5 Pa before sputtering. The targets were sputtered by 1 keV Ar ions using Kauffman ion source with 3 sccm flow. Working pressure was maintained in ~ 0.1 Pa range during the deposition. The sputtering targets were pre-sputtered for ~10 min to remove surface contamination. Samples were then deposited at a typical deposition rate of 0.5 -0.7 nm/min for Mg, Sc and ZrC.

Characterization

Grazing incidence reflectivity measurements using hard x-rays were performed using a table top Bruker D-8 reflectometer equipped with a θ-2θ goniometer and a Cu Kα source (8048 eV). The reflectivity in the soft x-ray region was carried out at the soft x-ray reflectivity beamline at Indus-2 synchrotron source. The beamline operates in the energy region of 100-1500 eV with moderate resolving power (E/ΔE ≈ 1000-6000) and high photon flux of 10 9 -10 11 photons/s [START_REF] Modi | A soft x-ray reflectivity beamline for 100-1500 eV energy range at Indus-2 synchrotron radiation source[END_REF]. The beamline operates under ultra-high vacuum (< 3x10 -7 Pa). The reflectometer is kept in a high vacuum experimental chamber equipped with a two-axis goniometer and a linear translation stage for sample movement. The reflected beam is detected using a Si photodiode connected to a Keithley electrometer. SXR measurement was done for the [Sc/Mg]/ZrC bilayer by tuning the energy of the incident beam around the Sc L-absorption edge, at energies varying from 370 to 420 eV. The data obtained was then fitted using IMD, a program for modelling optical properties of thin films and multilayers, based on Parratt recursive formalism to obtain the structural and optical parameters of the stack: thickness, roughness, density and real and imaginary parts of the optical index of the layers and interlayers [START_REF] Windt | IMD-Software for modeling the optical properties of multilayer films[END_REF][START_REF] Parratt | Surface Studies of Solids by Total Reflection of X-Rays[END_REF]. It utilizes nonlinear least squares curve fitting technique based on χ 2 minimization method to fit the reflectivity curves.

To highlight the morphology of interfaces for bilayers time-of-flight secondary ion mass spectroscopy (ToF-SIMS) measurements were performed. The analysis was done using Bi + ion gun operating at 30 keV and ~2.5 -3.0 pA. The depth profiling was made with a O2 + ion gun operating at 500 eV, ~100 nA over an analysis of 100 μm× 100 μm. Only positive ions were recorded. ToF-SIMS profiles are recorded by measuring the intensity of each incident ion of a given mass as a function of the sputtering time. It must be noted that the time scale is not relative thickness of each layer and that the sputtering yields of two elements is not related to the difference of concentration of these elements [START_REF] Benninghoven | Surface analysis by Secondary Ion Mass Spectrometry (SIMS)[END_REF].

GIXRR fit of the reflectivity data can result in various possible fitted structures when we take into account different thickness, composition and density of constituting layers and interlayers. Hence, we first use ToF-SIMS to determine a priori information on possible structure, by measuring the distribution of elements as a function of sputter time inside the bilayer stacks. Then, the possible structure obtained from the ToF-SIMS analysis is used to fit the measured GIXRR curves for both bilayers.

In the x-ray region, complex refractive index for matter is given by 𝑛 = 1 -𝛿 + 𝑖𝛽, where δ (dispersion coefficient) and β (absorption coefficient) are the optical constants. The SXR curves measured around the Sc L2,3-absorption edge (400 eV), with energies ranging from 370 to 420 eV, are fitted and the values of optical constants δ and β are determined. The calculated values of δ and β for Sc are then plotted as a function of incident energy across the absorption edge. Using the fit values of film thickness, real part of refractive index (δ), and roughness, a depth dependent δ-profile is calculated and plotted as a function of the depth. In case of hard x-ray analyses, the δ-profiles are more analogous to mass density profiles.

However, in case of soft x-rays the presence of different edges affects δ value significantly which then does not vary directly with mass density.

Results and discussion

Figure 2 shows the ToF-SIMS profiles of Mg + , Sc + , Si + ions as well as C + ions obtained on the Mg/Sc bilayer. For sake of clarity, the regions corresponding to Mg and Sc layers and Si substrate are delimited by vertical lines. The progression of Mg and Sc profiles suggests that Mg is diffusing towards the Sc layer, resulting in an interlayer formation. The small increase, between the Sc layer and the substrate could be indicative of an interlayer. Even if there exists no direct relation between the sputtering time and the depth, it takes about four more time to sputter the Sc layer than the Mg one. Knowing that the ratio of the sputtering yields of Mg to Sc by oxygen ion of 1 keV is about 0.5 (it should be the same order of magnitude for 0.5 keV ions), we expect the Sc layer to be at least twice thicker than the layer containing Mg atoms.

Carbon is only present at the surface owing to atmospheric contamination. Now that we have an idea of possible structure of the Mg/Sc bilayer, this information is implemented to fit the measured GIXRR curve. Figure 3(a) shows measured as well as fitted GIXRR data of the Mg/Sc bilayer. The best fit was obtained using a four-layer model consisting of a top layer due to surface oxidation (MgO), an MgSc layer, the nominal Sc layer and an interlayer at the scandium and silicon substrate interface. Table 1 collects the structural parameters of the stack deduced from the fit. From these parameters, the δ-profile is plotted in Figure 3(b). The thickness of the layers containing Mg atoms (4.5 nm) is much lower than the aimed thickness (20 nm), whereas the Sc thickness (17 nm) is a little lower than the aimed one (20 nm). This could come from a problem in the calibration of the Mg and Sc deposition rates or of a low sticking coefficient of magnesium atoms on scandium.

The formation of the interface layer on Mg-on-Sc interface can be understood by the value of the mixing enthalpy of Mg and Sc. It is found that the maximum values of enthalpy calculated from semi-empirical Miedena model [START_REF] Dębski | New features of Entall database: Comparison of experimental and model formation enthalpies[END_REF] for Mg-Sc is -5 kJ/mol. This negative value means that the interface Mg-on-Sc is prone to interdiffusion and a mixed region is likely to be formed as a result of diffusion of Mg atoms into the Sc layer during the deposition. The Sc layer is mostly uniform with a density close to that of the bulk. An increase in the δ-profile is seen at the Sc-on-Si interface. The calculated delta value of the interlayer (16.76 × 10 -6 ), Table 1, suggests that the interlayer formed at the Sc-on-Si interface could either be an oxide of scandium, ScxOy (10.50×10 -6 ) or a scandium silicide (ScSi 10.50×10 -6 ; Sc3Si5 10.69×10 -6 ).

But since the fitted δ value of the interlayer is higher than those of ScxOy, ScSi and Sc3Si5, we suggest that the interlayer is rather a mix of ScSi interlayer with the presence of O atoms resulting into a higher density [START_REF] Thomas | The reaction of scandium thin films with silicon: diffusion, nucleation, resistivities[END_REF][START_REF] Uspenskii | High-reflectivity multilayer mirrors for a vacuum-ultraviolet interval of 35-50??nm[END_REF]. The source of oxygen is the native oxide layer naturally formed of top of the silicon substrate. Similarly, here, the ToF-SIMS analysis result is applied to find a structure suitable to fit the Sc/Mg GIXRR curve. The fitted and measured curves are shown in Figure 5(a). The fitted structure is a six-layer model, that is to say in addition to the nominal layers of Sc, Mg and ZrC, a top layer due to surface oxidation (Sc2O3), an interfacial layer (MgSc) at the Sc-on-Mg interface and a native oxide layer (SiO2) on top of the silicon substrate have to be introduced. As for the previous sample, the thickness of layers containing Mg atoms as well as the layers containing Sc atoms are smaller than the aimed designed ones. On the contrary the ZrC layer thickness is close to the aimed one. The large thickness of the Sc layer prevents the underneath Mg layer from oxidation. The thickness of the MgSc interlayer is limited to 0.9 nm in the Sc/Mg bilayer while it is 1.5 nm in the Mg/Sc bilayer. This shows that Mg-on-Sc and Scon-Mg interfaces are asymmetric. A shoulder of native oxide of SiO2 is expected to be observed at the bottom of ZrC profile, but since the fitted thickness of SiO2 is very small (0.24 nm) it is difficult to see SiO2 on the δ-profile.

Near the absorption edge, refractive index is sensitive to the chemical environment, so any change in local environment of the atom will be reciprocated by the change in its optical parameters [START_REF] Majhi | Soft X-ray Reflection Spectroscopy for Nano-Scaled Layered Structure Materials[END_REF][START_REF] Singh | Growth kinetics and compositional analysis of silicon rich a-SiNx:H film: A soft x-ray reflectivity study[END_REF][START_REF] Modi | Depth analysis of Al/ZrC interfaces using SIMS and x-ray reflectivity[END_REF]. Thus, SXR technique can give elemental sensitive information, by tuning the energy of x-rays to the absorption edges of Sc [START_REF] Fernández-Perea | Determination of optical constants of scandium films in the 20-1000 eV range[END_REF][START_REF] Uspenskii | Efficient method for the determination of extreme-ultraviolet optical constants in reactive materials: application to scandium and titanium[END_REF]. The SXR fitted and measured curves for Sc/Mg bilayer, as function of incident angle at different photon energies around the Sc L absorption edge ranging from 370 to 420 eV are shown in Figure 6.

Figure - 1

 1 Figure -1 (a) and (b) show the simulated reflectance calculated for [Mg(3nm)/Sc(3nm)]x25 and [Sc(3nm)/Mg(3nm)/ZrC(1nm)]x25 multilayer at the incident photon energy of N K edge 395 eV.

Figure 2 -

 2 Figure 2 -ToF-SIMS profile for Mg/Sc Bilayer.

Figure 3 -

 3 Figure 3 -For the Mg/Sc bilayer: (a) experimental and fitted GIXRR curves; (b) in-depth δprofile deduced from the structure used to fit the GIXRR curve.

Figure 4 ,

 4 Figure 4, shows the ToF-SIMS profile of Mg + , Sc + , Zr + , Si + ions as well as C + ions of Sc/Mg bilayer where the different layers are separated delimited by vertical dotted lines. As in the Mg/Sc sample the diffuse transition of the profiles between the Sc and Mg layers suggests the existence of an interlayer at the Sc-on-Mg interface. Owing to the very small thickness of the ZrC layer, it is difficult to know if the shoulder observed on the Mg profile around 360 s could evidence the presence of an interlayer between Mg and ZrC layers or is due a transient sputtering regime. Carbon is only present at the surface owing to atmospheric contamination and is not enough intense to be observed from the ZrC layer.

Figure 4 -

 4 Figure 4 -ToF-SIMS profile of Sc/Mg bilayer.

  SiO2 layer is added due to possible oxidation of the Si substrate. Thickness and roughness of different layers along with their δ and β values for each layer as extracted from the GIXRR analysis are given in Table 2. The fitted optical constants for each of the nominal layers are close to their bulk densities. The delta δ-profile deduced from the chosen structure of the parameters of Table 2 is shown in Figure 5(b).

Figure 5 -

 5 Figure 5 -For the Sc/Mg bilayer: (a) experimental and fitted GIXRR curves; (b) in-depth δprofile deduced from the structure used to fit the GIXRR curve.

Figure 6 -

 6 Figure 6 -Measured (color lines) and fitted (black solid lines) angle-dependent SXR curves at energies across the Sc L2,3 absorption edge. The Reflectivity curve measured for the Sc/Mg bilayer at 8048eV is fitted to determine the complete structure of the stack, i.e. the thickness, roughness and density of each layer and interlayer formed. The SXR curves measured around the Sc L-edge ranging from 370 to 420 eV are then fitted using the structure deduced from the former analysis. The curves are fitted only by changing the refractive index i.e; δ (imaginary part) and β (real part). If we introduce other parameters such as the thickness or roughness, the fitted structure will change for each measured energy. Hence, it will no longer be possible to draw a fair comparison on the variation

Figure 7 -

 7 Figure 7 -Dispersion (δ) (a) and absorption (β) (b) coefficients of Sc layer for photon energies in the vicinity of the Sc L2,3 edge extracted from the fit of SXR curves and compared to CXRO tabulated values. 4 Conclusion

Table 1 -

 1 Structural and optical parameters of the Mg/Sc bilayer, where z and σ are the thickness and roughness of each layer respectively; δ and β are the dispersion and absorption coefficients. The thicknesses and roughness's are given  0.1 nm.

	Layer	z (nm) σ (nm) δ (×10 -6 )	β (×10 -7 )
	MgO	2.93	0.80	11.24	1.23
	MgSc	1.54	0.32	9.79	3.95
	Sc	17.15	1.00	10.84	6.76
	Interlayer	0.51	0.20	16.76	5.95
	Si substrate	-	0.35	7.58	1.73

Table 2 -

 2 Structural and optical parameters of the Sc/Mg bilayer, where z is thickness of each layer, σ being the roughness of each layer δ and β are the dispersion and absorption coefficients. The thicknesses and roughness's are given  0.1 nm.

	Layer	z (

nm) σ(nm) δ (×10 -6 ) β (×10 -7 ) δ (×10 -6 ) (Bulk) β (×10 -7 ) (Bulk)

	Sc2O3	1.47	0.46	11.81	5.85	11.99	5.95
	Sc	12.3	0.36	10.05	7.52	9.10	6.85
	MgSc	0.94	0.25	7.67	4.09	7.67	4.09
	Mg	8.59	1.00	5.88	0.87	5.58	0.83
	ZrC	1.6	0.30	19.29	9.64	19.16	9.57
	SiO2	0.24	0.20	8.71	1.13	7.13	0.92
	Si substrate	-	0.25	7.58	1.73	7.58	1.73

Acknowledgements

Authors are thankful to Mr. Aniruddha Bose and Mr. R.K. Gupta of RRCAT Indore for their support in ToF-SIMS and SXR measurements respectively.

List of figure captions:

1. Figure 1 -(

List of table captions:

1. Table 3 -Structural and optical parameters of the Mg/Sc bilayer, where z and σ are the thickness and roughness of each layer respectively; δ and β are the dispersion and absorption coefficients. The thicknesses and roughness's are given  0.1 nm. 4 -Structural and optical parameters of the Sc/Mg bilayer, where z is thickness of each layer, σ being the roughness of each layer δ and β are the dispersion and absorption coefficients. The thicknesses and roughness's are given  0.1 nm.

Table