Olivier Fardel

Nessrine Bellamri

Claudie Morzadec

Laurent Vernhet
email: laurent.vernhet@univ-rennes1.fr

Arsenic and the immune system

Keywords: arsenic, immunity, cell stress, DNA damages, epigenetic, immunosuppression

Arsenic and the immune system

Nessrine Bellamri, Claudie Morzadec,

Introduction

Arsenic is a toxic metalloid naturally present at high levels in the earth's crust in many countries worldwide. Arsenic is complexed to a sulphur atom in various mineral ores, such as arsenopyrite, orpiment and realgar. Physical, chemical and/or microbial changes in the soil can promote arsenic mobilization from minerals and its accumulation in groundwater. The consumption of contaminated drinking water is the first source of arsenic exposure for millions of individuals in several Asian and American countries [START_REF] Shakoor | Human health implications, risk assessment and remediation of As-contaminated water: A critical review[END_REF]. Since contaminated groundwater can be used to irrigate and cook cereal crops and other food items, humans can also be exposed to arsenic though the ingestion of vegetables, fruits, grains and rice [START_REF] Carlin | Arsenic and Environmental Health: State of the Science and Future Research Opportunities[END_REF]. In addition, arsenic is used for various industrial activities, including the production of wood preservatives, electronics and pesticides, which can induce occupational exposures [START_REF] Hunt | The mechanistic basis of arsenicosis: pathogenesis of skin cancer[END_REF].

Arsenic speciation includes several inorganic and organic species in different oxidation states. Contaminated drinking water, for example, contains inorganic pentavalent and trivalent forms of arsenic, which are largely absorbed from the human gastrointestinal tract, likely through glucose, phosphate or organic anion transporters and aquaporins. In contrast to mercury or cadmium, arsenic is a metalloid that does not chronically accumulate in specific organs. This compound is rapidly metabolized in the liver through biological methylation, oxidation/reduction and glutathione conjugation. Arsenic biotransformation generates reactive mono-and -dimethylated metabolites that likely contribute to its systemic effects [START_REF] Carlin | Arsenic and Environmental Health: State of the Science and Future Research Opportunities[END_REF]. Arsenic toxicity has been extensively reviewed in several recent articles [START_REF] Shakoor | Human health implications, risk assessment and remediation of As-contaminated water: A critical review[END_REF][START_REF] Carlin | Arsenic and Environmental Health: State of the Science and Future Research Opportunities[END_REF][START_REF] Hunt | The mechanistic basis of arsenicosis: pathogenesis of skin cancer[END_REF]. Chronic ingestion of low concentrations of arsenic initially induces skin lesions but can be toxic to many other organs [START_REF] Naujokas | The broad scope of health effects from chronic arsenic exposure: update on a worldwide public health problem[END_REF]. Long terms effects primarily include cutaneous, respiratory, neurodevelopmental, hepatic, endocrine and cardiovascular disorders [START_REF] Naujokas | The broad scope of health effects from chronic arsenic exposure: update on a worldwide public health problem[END_REF]. This metalloid is classified by the IARC as a carcinogenic compound for humans (group 1), and epidemiological studies have clearly demonstrated that arsenic significantly increases the incidence of skin, bladder and lung cancers [START_REF] Hunt | The mechanistic basis of arsenicosis: pathogenesis of skin cancer[END_REF]. In addition, arsenic modulates the activity of both innate and adaptive immunity by various cellular and molecular mechanisms.

Immunomodulation likely promotes arsenic systemic toxicity, which results from environmental or occupational exposure. However, specific immunosuppressive effects of arsenic may also be beneficial for the treatment of certain immune-related diseases. Thus, the purpose of this review is to summarize our current knowledge on arsenic immunotoxicity.

Effects of arsenic on immune cells

Macrophages and dendritic cells (DCs)

Macrophages and DCs are professional phagocytes that control innate immunity and regulate immune surveillance against infections and cancers. Monocytes constitute major precursors of both macrophages and DCs, especially during inflammatory states. Monocytes migrate in tissues where they differentiate into mature phagocytes. A primary function of macrophages is to engulf and digest microbes, cellular debris and cancer cells by phagocytosis. In response to infection or tissue damage, macrophages secrete a large spectrum of cytokines according to their local environment. Chronic exposure to arsenic significantly impairs the ex-vivo differentiation of peripheral blood monocytes into mature macrophages. Banerjee et al. [START_REF] Banerjee | Chronic arsenic exposure impairs macrophage functions in the exposed individuals[END_REF] reported that monocyte-derived macrophages from arsenicexposed individuals with skin lesions exhibited reduced cell adhesion capacity, F-actin expression, nitric oxide production and phagocytic activity. In vitro, 0.5 to 2 µM arsenic trioxide (ATO) was shown to block the differentiation of human peripheral blood monocytes into functional macrophages by repressing NF-B-related survival pathways [START_REF] Lemarie | Arsenic trioxide induces apoptosis of human monocytes during macrophagic differentiation through nuclear factor-kappaB-related survival pathway down-regulation[END_REF]. Short treatments of human mature macrophages with non-cytotoxic arsenic concentrations (1 to 5 µM, 6 h) was shown to inhibit the transcriptional activity of the liver X receptor, resulting in the decreased expression of its target genes, ABCA1 and SREBP-1c, and impaired cholesterol efflux [START_REF] Padovani | Inhibition of liver x receptor/retinoid X receptormediated transcription contributes to the proatherogenic effects of arsenic in macrophages in vitro[END_REF]. Prolonged treatment (3 to 6 days) with ATO was shown to dedifferentiate macrophages into CD14-expressing monocytic-like cells, notably through the reorganization of the actin cytoskeleton [START_REF] Lemarie | Inorganic arsenic activates reduced NADPH oxidase in human primary macrophages through a Rho kinase/p38 kinase pathway[END_REF]. Metalloid-exposed macrophages display increased secretion of the pro-inflammatory chemokines CXCL2 and CCL18 and a decreased expression of several macrophage markers, including metalloproteinase 7, 9 and 12 [START_REF] Lemarie | Inorganic arsenic activates reduced NADPH oxidase in human primary macrophages through a Rho kinase/p38 kinase pathway[END_REF][START_REF] Bourdonnay | Global effects of inorganic arsenic on gene expression profile in human macrophages[END_REF]. Moreover, these macrophages exhibit an enhanced pro-inflammatory response to the lipopolysaccharide (LPS) endotoxin. Increased exposure to arsenic through contaminated drinking water is also positively correlated with high CD14 expression on monocytes and with elevated plasma levels of pro-inflammatory cytokines, including TNF, and IL-8 [START_REF] Wu | Gene expression of inflammatory molecules in circulating lymphocytes from arsenic-exposed human subjects[END_REF][START_REF] Dutta | Chronic low level arsenic exposure evokes inflammatory responses and DNA damage[END_REF].

Recent studies have shown that arsenic alters the functions of microglia, which are the resident macrophages found in the central nervous system [START_REF] Singh | Isolation and characterization of microglia from adult mouse brain: selected applications for ex vivo evaluation of immunotoxicological alterations following in vivo xenobiotic exposure[END_REF][START_REF] Chen | Arsenic trioxide mediates HAPI microglia inflammatory response and the secretion of inflammatory cytokine IL-6 via Akt/NF-κB signaling pathway[END_REF]. The metalloid notably increased ex-vivo secretion of IL-6 and TNF- from microglia isolated from mice exposed for 7 days to 0.38 mg/kg arsenite [START_REF] Singh | Isolation and characterization of microglia from adult mouse brain: selected applications for ex vivo evaluation of immunotoxicological alterations following in vivo xenobiotic exposure[END_REF]. In vitro, the supernatant of arsenic-exposed-microglial cultures induced murine neuronal cell death [START_REF] Singh | Hijacking microglial glutathione by inorganic arsenic impels bystander death of immature neurons through extracellular cystine/glutamate imbalance[END_REF]. The death process did not result from inflammation but was, rather, caused by a critical cystine/glutamate imbalance induced by arsenic in the microglia. These specific effects may contribute to the increased incidence of developmental neurotoxicity in children chronically exposed to arsenic [START_REF] Tsuji | Low-level arsenic exposure and developmental neurotoxicity in children: A systematic review and risk assessment[END_REF].

DCs are primary antigen-presenting cells that link innate immunity to adaptive immunity.

Once activated by infectious agents or tumor cell antigens, DCs migrate in the peripheral lymph nodes where they activate T cells and promote their polarization. At low concentrations (0.1 to 0.5 µm), arsenite does not block the ability of mature DCs to activate the proliferation of human T cells in vitro, but it significantly inhibits the secretion of IL-12p70 and IL-23, two interleukins that enhance T cell polarization [START_REF] Macoch | Inorganic arsenic impairs differentiation and functions of human dendritic cells[END_REF]. At concentrations higher than 1 µM, arsenic blocks myeloid DC differentiation by inducing monocyte necrosis [START_REF] Macoch | Inorganic arsenic impairs differentiation and functions of human dendritic cells[END_REF], and it decreases the phagocytic activity of immature DCs [START_REF] Bahari | Environmentally relevant dose of arsenic interferes in functions of human monocytes derived dendritic cells[END_REF]. These in vitro experimental results need to be confirmed by investigating DC functions in chronically exposed individuals.

Nevertheless, various reports have shown that quantitative losses and structural lesions of Langherans cells, which are rather similar to dermal DCs, are specifically detected in the skin lesions of exposed individuals [START_REF] Wang | Quantitative and morphological changes of Langerhans cells in Bowen's disease from patients with chronic arsenicism[END_REF][START_REF] Lee | Arsenic mobilizes Langerhans cell migration and induces Th1 response in epicutaneous protein sensitization via CCL21: a plausible cause of decreased Langerhans cells in arsenic-induced intraepithelial carcinoma[END_REF]. Although arsenic can clearly alter DC-induced T cell activation, a specific effect of the metalloid on antigen presentation by DCs remains to be demonstrated.

Lymphocytes

T and B lymphocytes mediate the cellular and humoral responses of adaptive immunity, respectively. The activation of T lymphocytes by DCs stimulates their proliferation and differentiation into various CD4+ T helper cell subtypes and CD8+ T cytotoxic cells.

Numerous studies have demonstrated that arsenic markedly alters both the number and function of human T lymphocytes. Specifically, chronic arsenic exposure is correlated with decreased percentages of peripheral blood CD4+ T cells and CD4/CD8 ratios in children and adults and with reduced ex-vivo proliferation of activated T lymphocytes [START_REF] Soto-Peña | Assessment of lymphocyte subpopulations and cytokine secretion in children exposed to arsenic[END_REF][START_REF] Biswas | Analysis of T-cell proliferation and cytokine secretion in the individuals exposed to arsenic[END_REF][START_REF] Liao | Differential effects of arsenic on cutaneous and systemic immunity: focusing on CD4+ cell apoptosis in patients with arsenic-induced Bowen's disease[END_REF]. Wu et al. [START_REF] Wu | Gene expression of inflammatory molecules in circulating lymphocytes from arsenic-exposed human subjects[END_REF] reported that the expression of various pro-inflammatory cytokines, growth factors and chemokines were upregulated in non-stimulated blood lymphocytes isolated from high arsenic-exposed individuals. The transcript levels of IL-1, IL-6, chemokine C-C motif 2/monocyte chemotactic protein-1 (CCL2/MCP-1), chemokine C-X-C motif ligand 1/growthrelated oncogene alpha (CXCL1/GRO1), CXCL2/GRO2 and matrix metalloproteinase 1 (interstitial collagenase) were significantly increased in lymphocytes from individuals with the highest arsenic blood concentrations (9.6 to 46.5 µg/L). Nevertheless, the ex-vivo secretion of IL-2 from lymphocytes activated with phytohemaglutinin or concanavalin-A was negatively correlated with urinary arsenic levels [START_REF] Soto-Peña | Assessment of lymphocyte subpopulations and cytokine secretion in children exposed to arsenic[END_REF][START_REF] Biswas | Analysis of T-cell proliferation and cytokine secretion in the individuals exposed to arsenic[END_REF]. In vitro experiments have confirmed that low and non-cytotoxic arsenite concentrations significantly repress both the proliferation and IL-2 secretion of human activated T cells [START_REF] Morzadec | Inorganic arsenic impairs proliferation and cytokine expression in human primary T lymphocytes[END_REF][START_REF] Burchiel | Differential susceptibility of human peripheral blood T cells to suppression by[END_REF]. Moreover, studies have revealed that the metalloid selectively inhibits the differentiation of T helper 17 lymphocytes by specifically repressing IL-17 expression, a cytokine that increases anti-infectious defenses but also promotes inflammation in several auto-immune diseases [25]. The In vitro inhibition of T cell proliferation is sex-dependent, i.e., the inhibition is more potent in peripheral blood lymphocytes isolated from females [26]. In utero, arsenic exposure also decreases the percentage of CD4+ T cells in the cord blood [START_REF] Kile | Effect of prenatal arsenic exposure on DNA methylation and leukocyte subpopulations in cord blood[END_REF] and alters the thymic function in newborns [START_REF] Ahmed | In utero arsenic exposure is associated with impaired thymic function in newborns possibly via oxidative stress and apoptosis[END_REF]. In fact, recent studies carried out on murine models showed that chronic arsenic exposure affects the differentiation of T cell precursors in the thymus. Exposure to low doses of arsenite (< 0.1 mL/L) in drinking water for 30 days increases the numbers of CD4+ CD25+ FoxP3-expressing cells, also known as natural regulatory T (nTreg) cells, in the thymus of male Swiss albinos mice [START_REF] Choudhury | Arsenic-induced dose-dependent modulation of the NF-κB/IL-6 axis in thymocytes triggers differential immune responses[END_REF]. Oral arsenite gavage (0.038 to 3.8 ppm) of male Balb/c mice for 30 days specifically promotes the CD4 lineage in the thymus without affecting the tissue ultrastructure [START_REF] Gera | Arsenic exposure impels CD4 commitment in thymus and suppress T cell cytokine secretion by increasing regulatory T cells[END_REF]. However, this treatment also triggers the differentiation of splenic CD4+ T cells into nTreg cells and induces immunosuppression. Further research is thus required to determine the role of nTreg cells in the immunotoxic effects of arsenic in humans.

B lymphocytes, or B cells, mediate humoral immunity by producing and secreting antibodies. In contrast to T cells, the impact of arsenic on human B cells remains to be fully characterized. At low concentrations (0.1 to 2 µM), arsenite has either no effect or modest effects on the in vitro CD40L-dependent Immunoglobulin M antibody-forming cell response of human isolated naïve B lymphocytes, whereas this concentration of arsenite markedly reduces the same response of murine B cells [START_REF] Lu | Establishment of an immunoglobulin m antibody-forming cell response model for characterizing immunotoxicity in primary human B cells[END_REF]. Arsenite and its monomethylated trivalent metabolite, monomethylarsonous acid, have also been demonstrated to reduce in vivo and in vitro murine pre-B cell development from hematopoietic stem cells, likely by interfering with IL-7 signaling, and to repress murine humoral immunity [START_REF] Ezeh | Arsenite selectively inhibits mouse bone marrow lymphoid progenitor cell development in vivo and in vitro and suppresses humoral immunity in vivo[END_REF][START_REF] Ezeh | Monomethylarsonous acid (MMA+3) Inhibits IL-7 Signaling in Mouse Pre-B Cells[END_REF]. It will be interesting to confirm these results with human B cells.

Molecular basis of arsenic immunotoxicity

Oxidative stress and DNA damage

Arsenic is a pro-oxidant metalloid that forms stable complexes with vicinal thiol residues in several proteins and increases the levels of reactive oxygen (ROS) in several cell types, including macrophages and lymphocytes [START_REF] Lemarie | Inorganic arsenic activates reduced NADPH oxidase in human primary macrophages through a Rho kinase/p38 kinase pathway[END_REF][START_REF] Biswas | Curcumin protects DNA damage in a chronically arsenic-exposed population of West Bengal[END_REF]. Previous reports suggest that the effects of arsenic on the viability and functions of macrophages, DCs or lymphocytes can result from oxidative stress and related DNA damage. In this context, at non cytotoxic concentrations (< 1 µM), ATO produces ROS in human monocyte-derived macrophages by directly activating NADPH oxidase at the plasma membrane [START_REF] Lemarie | Inorganic arsenic activates reduced NADPH oxidase in human primary macrophages through a Rho kinase/p38 kinase pathway[END_REF]. To stimulate this superoxide-generating enzymatic complex, the metalloid induces the phosphorylation and subsequent membrane translocation of the p47 phox NADPH oxidase partner through a Rho-kinase/p38-kinase-dependent signaling pathway. Arsenic may also produce ROS and disrupt macrophage functions by inducing the unfolded protein response [START_REF] Srivastava | Unfolded protein response (UPR) signaling regulates arsenic trioxide-mediated macrophage innate immune function disruption[END_REF]. At a higher concentration (5 µM), ATO significantly reduces the mitochondrial transmembrane potential, increases ROS levels and triggers caspase-dependent apoptosis in human CD4+ and CD8+ T cells [START_REF] Gupta | Arsenic trioxide induces apoptosis in peripheral blood T lymphocyte subsets by inducing oxidative stress: a role of Bcl-2[END_REF]. ROS likely contribute to the DNA damage detected in peripheral blood lymphocytes either isolated from arsenic-exposed individuals or treated in vitro with arsenical compounds, by eliciting 8hydroxy-2'-deoxyguanosine adducts and/or repressing DNA repair [START_REF] Biswas | Curcumin protects DNA damage in a chronically arsenic-exposed population of West Bengal[END_REF][START_REF] Kligerman | Methylated trivalent arsenicals as candidate ultimate genotoxic forms of arsenic: induction of chromosomal mutations but not gene mutations[END_REF][START_REF] Andrew | Arsenic exposure is associated with decreased DNA repair in vitro and in individuals exposed to drinking water arsenic[END_REF]. In addition to inducing DNA damage, arsenic impairs gene expression in human immune cells by modulating redox-sensitive signaling pathways. Notably, prevention of oxidative stress by an NADPH oxidase inhibitor or an antioxidant blocks CCL18 and CXCL2 gene expression in arsenic-exposed macrophages [START_REF] Lemarie | Inorganic arsenic activates reduced NADPH oxidase in human primary macrophages through a Rho kinase/p38 kinase pathway[END_REF][START_REF] Bourdonnay | Redox-sensitive regulation of gene expression in human primary macrophages exposed to inorganic arsenic[END_REF]. In addition, in response to cell stress, the transcription factor NRF2 not only regulates the induction of several antioxidant genes but also mediates the arsenic-dependent inhibition of IL12 gene expression in human mature DCs [START_REF] Macoch | Nrf2-dependent repression of interleukin-12 expression in human dendritic cells exposed to inorganic arsenic[END_REF].

Epigenetic effects

Molecular epidemiological studies have suggested that arsenic can regulate gene expression in white blood cells by modifying the epigenome. Increased arsenic exposure through consumption of contaminated drinking water has been positively associated with global DNA methylation in the peripheral blood mononuclear cells of Bangladeshi adults [START_REF] Kile | Prenatal arsenic exposure and DNA methylation in maternal and umbilical cord blood leukocytes[END_REF][START_REF] Niedzwiecki | A dose-response study of arsenic exposure and global methylation of peripheral blood mononuclear cell DNA in Bangladeshi adults[END_REF]. [START_REF] Niedzwiecki | A dose-response study of arsenic exposure and global methylation of peripheral blood mononuclear cell DNA in Bangladeshi adults[END_REF] notably reported that the highest DNA methylation levels are measured in individuals with the highest arsenic exposure [START_REF] Niedzwiecki | A dose-response study of arsenic exposure and global methylation of peripheral blood mononuclear cell DNA in Bangladeshi adults[END_REF]. However, subtle modifications of DNA methylation can also be detected at the gene level. Indeed, in chronically exposed individuals, increased arsenic exposure either reduces or enhances the methylation levels of various genes involved in major cell functions, such as lipid metabolism, intracellular pH regulation or the nuclear factor B signaling pathway [START_REF] Argos | Gene-specific differential DNA methylation and chronic arsenic exposure in an epigenome-wide association study of adults in Bangladesh[END_REF]. Similarly, Engström et al. [START_REF] Engström | enrichment for immune-related gene ontologies associated with the basic functions of T lymphocytes. This finding shows that the metalloid can be immunotoxic by altering epigenetic regulation of gene expression in human T lymphocytes[END_REF] reported that increased arsenic exposure was associated with significant alterations of the CD4+ T cell methylome in Argentinean women. Both hypo-and hypermethylated regions were detected in genes regulating T cell activation and differentiation. Interestingly, among these genes, Engström et al. found that the interferon regulatory factor 1 (IRF1) gene was hyper-methylated and its expression was decreased. In contrast, the ras homolog family member H (RHOH) gene was hypo-methylated and its expression was upregulated. Although these results suggest that arsenic exposure may alter gene expressions by differentially modulating gene methylation levels, additional studies are warranted to assess the causality and clinical significance of this phenomenon. In addition to DNA methylation, other post-translational histone modifications have also been identified in peripheral blood mononuclear cells of adults exposed to arsenic [45,[START_REF] Pournara | Arsenic alters global histone modifications in lymphocytes in vitro and in vivo[END_REF]. Notably, Chervona et al. (2012) reported that in Bangladeshi adults exposed to water containing up to containing 500 µg/L arsenic, total urinary arsenic concentration was positively correlated with the level of histone 3 lysine 9 di-methylation (H3K9me2) and inversely correlated with H3K9 acetylation [45]. Other post-translational histone modifications associated with arsenic exposure differed in a sex-dependent manner. For example, arsenic concentration in water was positively associated with H3K4me3 and H3K27me3 among females but negatively correlated with the same modifications among males. Finally, [START_REF] Pournara | Arsenic alters global histone modifications in lymphocytes in vitro and in vivo[END_REF] reported that the impacts of arsenic on histone residues could also differ between CD4+ and CD8+ T cells [START_REF] Pournara | Arsenic alters global histone modifications in lymphocytes in vitro and in vivo[END_REF]. Increased arsenic exposure in drinking water was negatively correlated with H3K9me3 in CD4+ T cells but not in CD8+ T cells. Metalloid effects on histone residues are thus complex, depending on the cell types and sex, and these effects need to be further explored for a better understanding of their biological significance.

Inhibition of inflammasomes

Inflammasomes are cytoplasmic multiprotein complexes that specifically control the activation of the caspase 1-dependent cleavage of the pro-inflammatory cytokines IL-1 and IL-18 into their active forms. These complexes are primarily generated in macrophages exposed to pathogen-derived stimuli (bacterial toxins), self-derived molecules (uric acid, ATP) and environmental contaminants (silica, asbestos) [START_REF] Howrylak | Inflammasomes: Key Mediators of Lung Immunity[END_REF]. They are composed of nucleotide-binding oligomerization domain-like receptor (NLR) proteins that act as stimuli sensors. In vitro, arsenite and ATO inhibit the NLRP1, NLRP3 and NAIP5/NLRC4 inflammasomes in murine bone marrow-derived macrophages exposed to their respective activating stimuli [START_REF] Maier | The investigators show that trivalent inorganic arsenic inhibits in vitro activation of NLRP1, NLRP3 and NAIP5/NLRC4 inflammasomes in murine bone marrow-derived macrophages by preventing autoproteolytic activation of caspase-1 and subsequent processing and secretion of IL-1. Arsenic also prevents NLRP3-dependent inflammation in a murine peritonis model induced by monosodium urate crystals. These results demonstrate time that inflammasomes constitute molecular targets of the metalloid[END_REF]. Maier et al. [48] demonstrated that, in vivo, arsenite delays the NLRP1-mediated death of mice exposed to anthrax lethal toxin and reduces NLRP3dependent inflammation in mice treated with monosodium urate crystals. Arsenic blocks the maturation of pro-IL-1 by preventing the autoproteolytic and substrate cleavage activities of caspase-1 in murine macrophages [START_REF] Maier | The investigators show that trivalent inorganic arsenic inhibits in vitro activation of NLRP1, NLRP3 and NAIP5/NLRC4 inflammasomes in murine bone marrow-derived macrophages by preventing autoproteolytic activation of caspase-1 and subsequent processing and secretion of IL-1. Arsenic also prevents NLRP3-dependent inflammation in a murine peritonis model induced by monosodium urate crystals. These results demonstrate time that inflammasomes constitute molecular targets of the metalloid[END_REF]. Low concentrations of ATO (0.1 to 1 µM), which fail to repress the upregulation of IL-1 mRNA caused by LPS in human monocyte-derived macrophages (Figure 1A), inhibit the silica-induced secretion of active IL-1 in the macrophage supernatant (Figure 1B). These results suggest that ATO directly impairs the inflammasome activity of human macrophages, i.e., it suppresses the cleavage of pro-IL-1.

Inflammasome complexes may thus constitute important molecular targets of arsenic in humans.

Consequences of arsenic immunotoxicity in humans

Contribution to diseases associated with chronic environmental exposure

As described above, arsenic exerts pleiotropic effects on immune cells, which may initially result in the suppression of major immune functions. Notably, arsenic decreases bacterial phagocytosis by macrophages, reduces T cell proliferation and markedly represses the secretion of pro-inflammatory cytokines by activated DC and T cells. These inhibitions can increase the susceptibility to infection by limiting pathogen eradication. Arsenic-induced immunosuppression likely increases the incidence of lower respiratory tract infections and diarrhea, which frequently develop in young exposed children from low-income countries [START_REF] Rahman | Arsenic exposure in pregnancy increases the risk of lower respiratory tract infection and diarrhea during infancy in Bangladesh[END_REF][START_REF] Smith | Evidence from Chile that arsenic in drinking water may increase mortality from pulmonary tuberculosis[END_REF]. Particularly, increased arsenic exposure was found to promote pulmonary tuberculosis in Chile [START_REF] Smith | Evidence from Chile that arsenic in drinking water may increase mortality from pulmonary tuberculosis[END_REF] and visceral leishmaniosis in India [START_REF] Perry | Arsenic exposure and outcomes of antimonial treatment in visceral leishmaniasis patients in Bihar, India: a retrospective cohort study[END_REF]. In a murine model, chronic exposure to low doses of arsenic also increased morbidity of influenza A infection by repressing DC-mediated immune responses in mice [START_REF] Kozul | Low-dose arsenic compromises the immune response to influenza A infection in vivo[END_REF]. In addition, immunosuppression impairs the surveillance and killing of tumorigenic cells, which may promote lung and skin cancer associated with arsenic exposure [START_REF] Dangleben | Arsenic immunotoxicity: a review[END_REF]. Conversely, arsenic may induce a basal inflammatory state by increasing the secretion of molecules such as TNF- and IL-8 from monocytes/macrophages and lymphocytes. Chronic inflammation and secretion of growth factors, such as IL-8, can also establish microenvironments supportive of tumor development [START_REF] Yuan | The role of interleukin-8 in cancer cells and microenvironment interaction[END_REF]. Epidemiological studies carried out in various countries demonstrate that arsenic significantly increases the risk of atherosclerosis [START_REF] Chen | Arsenic exposure from drinking water, arsenic methylation capacity, and carotid intimamedia thickness in Bangladesh[END_REF][START_REF] Mateen | Chronic arsenic exposure and risk of carotid artery disease: The Strong Heart Study[END_REF]. Several mechanisms may contribute to the development of atherosclerosis, including general pro-inflammatory cytokine secretion [START_REF] Wu | Gene expression of inflammatory molecules in circulating lymphocytes from arsenic-exposed human subjects[END_REF], increased ROS production [START_REF] Lemarie | Inorganic arsenic activates reduced NADPH oxidase in human primary macrophages through a Rho kinase/p38 kinase pathway[END_REF], enhanced monocyte adhesion to vascular endothelium [START_REF] Lemaire | Arsenic Exposure Increases Monocyte Adhesion to the Vascular Endothelium, a Pro-Atherogenic Mechanism[END_REF] and reduced cholesterol efflux from macrophages [START_REF] Padovani | Inhibition of liver x receptor/retinoid X receptormediated transcription contributes to the proatherogenic effects of arsenic in macrophages in vitro[END_REF]. In murine models, at least, methylated metabolites and arsenic-3-methyltransferase play major roles in these proatherogenic effects of arsenic [START_REF] Silva | Effects of Inorganic Arsenic, Methylated Arsenicals, and Arsenobetaine on Atherosclerosis in the Mouse Model and the Role of As3mt-Mediated Methylation[END_REF].

Potential beneficial effects of arsenic-induced immunosuppression

Recently, various experimental studies have suggested that the immunosuppressive properties of arsenic may reduce or treat severe immune-related diseases. Indeed, ATO prevents the development of a lupus-like syndrome in MRL/lpr mice by eliminating activated T cells that cause lymphoproliferation and skin, lung and kidney damage [START_REF] Bobé | Arsenic trioxide: A promising novel therapeutic agent for lymphoproliferative and autoimmune syndromes in MRL/lpr mice[END_REF]. ATO also abrogates chronic sclerodermatous graft-versus-host disease that follows allogenic hematopoietic stem cell transplantation in a murine model [START_REF] Kavian | 4+ T cells and plasmacytoid dendritic cells. These results support the hypothesis that inorganic arsenic may display beneficial effects in the management of chronic graft-versus-host disease in humans[END_REF]. The metalloid inhibits the alloreactive process by selectively killing activated DCs and CD4-positive T cells. In addition, ATO prolongs cardiac and islet allograft survival in acute rejection murine models through the repression of alloreactive CD4+ and CD8+ memory T cells [START_REF] Yan | Inhibition of accelerated rejection mediated by alloreactive CD4 + memory T cells and prolonged allograft survival by arsenic trioxide[END_REF][START_REF] Gao | Arsenic Trioxide Induces T Cell Apoptosis and Prolongs Islet Allograft Survival in Mice[END_REF][START_REF] Li | Arsenic trioxide inhibits accelerated allograft rejection mediated by alloreactive CD8(+) memory T cells and prolongs allograft survival time[END_REF]. Finally, the fact that arsenic blocks inflammasome activity and the subsequent IL-1 production in human macrophages suggests that arsenic may limit chronic inflammation in severe inflammasomemediated disease [START_REF] Howrylak | Inflammasomes: Key Mediators of Lung Immunity[END_REF].

Conclusions

Many human population-based and/or experimental studies strongly suggest that arsenic exerts potent immunotoxic effects towards key human immune cells, such as macrophages, DCs and T lymphocytes (Figure 2). Multiple molecular and cellular mechanisms can mediate arsenic immunotoxicity, including ROS production, alteration of redox-sensitive signaling pathways, DNA damage, epigenetic effects and inflammasome inhibition. Arsenic immunotoxicity likely contributes to the systemic deleterious effects associated with chronic environmental exposure. Notably, arsenic-induced immunosuppression may favor the development of infectious diseases and cancers. On the other hand, data derived from experimental studies using various mouse models support the hypothesis that the immunosuppressive effects of arsenic may be beneficial for limiting the exacerbation of the immune system in severe immune-related diseases. However, further research is still required to determine the role of arsenic immunotoxicity in the systemic effects of arsenic exposure and to investigate the potential use of this metalloid in medical immunosuppressive therapy.

environmental levels of sodium arsenite and monomethylarsonous acid, PloS One. 9 The investigators demonstrate that trivalent inorganic arsenic (As 2 O 3 , 0.25-2 µM) totally inhibits expression and secretion of IL-17A from naive and memory human CD4+ T lymphocytes differentiated into Th17 cells, notably by impairing JNK/C-jun-dependent signalling and RORC-t expression. IL-17A, which plays a key role in anti-infectious defenses but also in the development of various chronic inflammatory diseases, may thus constitute a major target of the arsenic in humans.

Legends

Figure 1. Arsenic trioxide (ATO) inhibits IL-1 secretion from human macrophages without impairing IL-1 mRNA levels. Following the isolation of peripheral blood mononuclear cells by Ficoll gradient centrifugation, human monocytes were selected by an adhesion step and then differentiated into macrophages in RPMI medium containing 50 ng/mL macrophagecolony stimulating factor for 6 days. Macrophages were left untreated (CTR) or pre-treated with ATO for 2 h before stimulation with 20 ng/mL LPS (Escherichia coli 055:B5, Sigma Aldrich, France) for 4 h to increase IL-1 mRNA expression. Next, cells were harvested (A) or cultured with 0 or 100 µg/mL silica (Si) (DQ12 mineral dust silica, DMT GMBH, Germany) for 16 h (B) to activate NLRP3 inflammasome and produce active IL-1 protein. At the end of the treatment, the culture media were collected and the levels of active IL-1 secreted in the supernatant were quantified by ELISA (Duoset ELISA development system kits, R and D system, France) (B). In (A), mRNA levels were determined by RT-qPCR using the fluorescent dye SYBR Green methodology and a CFX384 real-time PCR system (Bio-Rad).

Data are presented relative to mRNA levels found in macrophages treated with LPS and arbitrarily set at the value of 1. Results in (A) and (B) are expressed as the means ± SD of 6 independent experiments. Significant differences were evaluated using ANOVA followed by the multi-range Dunett's t test for multiple comparisons. The criterion for significance of the difference between means was *p < 0.05 or **p<0.01, versus LPS (A) or LPS+Si (B).

(

  2014) e109192. doi:10.1371/journal.pone.0109192.  [25] C. Morzadec, M. Macoch, M. Robineau, L. Sparfel, O. Fardel, L. Vernhet, Inorganic arsenic represses interleukin-17A expression in human activated Th17 lymphocytes, Toxicol. Appl. Pharmacol. 262 (2012) 217-222. doi:10.1016/j.taap.2012.05.004.

Figure 2 .

 2 Figure 2. Effects of arsenic on immune cells and their potential consequences for humans.

atherosclerosis in environmentally exposed individuals. In contrast, experimental studies have demonstrated that the immunosuppressive effects of arsenic may counteract hyperactivity of the immune system in murine models of lupus, chronic sclerodermatous graft-versus-host disease and acute allograft rejection. Moreover, these effects may prevent NLRP3-dependent inflammation from developing in mice exposed to monosodium urate crystals. These results support the idea that arsenic may have beneficial therapeutic immunosuppressive effects for the treatment of certain human diseases.

Acknowledgements

This research was supported by grants from Institut National de la Santé et de la Recherche Médicale (INSERM) and from University of Rennes-1. We thank Dr Valérie Lecureur for her helpful comments and critical reading of the manuscript.


Ankit Chiplunkar
email: ankitchiplunkar@airbus.com

Elisa Bosco
email: elisabosco@airbus.com

Joseph Morlier
email: josephmorlier@isae-supaero.fr

Gaussian Process for Aerodynamic Pressures Prediction in Fast Fluid Structure Interaction Simulations

Keywords: Fluid Structure Interaction, Aerospace, Interpolation, Gaussian Process, Design Of Experiments

The interaction between inertial, elastic and aerodynamic forces for structures subjected to a fluid flow may cause unstable coupled vibrations that can endanger the structure itself. Predicting these interactions is a time consuming but crucial task in an aircraft design process. In order to reduce the computational time surrogate reduced order models can be used in both structural and aerodynamic models. More over it is possible to avoid launching CFD computations at every time step. A database of aerodynamic pressure distribution on the structural component can be created conveniently sampling the space of the structural model DoF. Starting from the knowledge of the precomputed data-set a Gaussian Process can be applied to predict the pressure distribution on an unexplored point of the space of DoF. The knowledge of the standard deviation can be used to give indications on where to launch further CFD computations to enrich the database. This technique will be first applied to a database of pressures obtained using the software Xfoil ® , later it will be applied to CFD simulations of type RANS launched with elsA ® on one Flap track Fairing of an Airbus aircraft.

Introduction

A fluid-structure interaction problem requires the solution of the coupled equations of both the fluid and the structure. This can be computationally highly intensive and extremely time-costly depending on the complexity of the phenomena to be predicted [START_REF] Sandboge | Fluid-structure interaction with OpenFSITM and MD NastranTM structural solver[END_REF]. Such is the case for structures such as the flap track fairing (FTF). Their behavior is geometrically highly nonlinear and depends on the source of excitation. FTFs withhold the mechanisms of deployment of flaps and their shape is conceived not to degrade wing performances. Depending on their position, FTFs can be exposed to high vibrations induced from the engine exhaust for short periods of time during take-off. Failure to predict these vibration problems in the design phase causes the necessity for reinforcement and requires servicing actions with aircraft grounding for repair or replacement of the structure. There is therefore a strong need to develop a method of load prediction that maximizes time efficiency. In the frame of transient fluid structure interaction, at each time step the pressure distribution acting on the structural body has to be recomputed updating the position of the component in the CFD simulation domain.

This can be done either launching a CFD simulation at every time-step or interpolating over a database of precomputed pressure distributions. The second case has the advantage of being a lot faster but is based on the assumptions of the displacement envelope of the component to be analyzed and that the deformations are very small. Interpolating between discrete data points is called as regression in Machine learning literature or Surrogate Modelling in engineering literature. Earlier techniques such as polynomial fitting eg. linear interpolation, quadratic interpolation or splines try to fit a polynomial function on the discrete simulated data-points. [START_REF] Montgomery | Introduction to linear regression analysis[END_REF]. In this paper we will compare two methodologies of performing regression/surrogate modelling. One well tested method is to reduce the dimension of database and rebuild the pressure distribution at a desired point. We would use, Singular Value Decomposition (SVD) to reduce the database and spline to interpolate the reduced database. A second methodology is to build a surrogate model on the whole dataset without performing data reduction, a Gaussian Process or Kriging will be used to interpolate between all data-points. The main advantage of Gaussian Process is that it allows the use of initial information such as smoothness and error distribution into the model in analysis. These kind of assumptions are applicable to physical systems since it is known before hand that the pressure distribution is highly smooth and not necessarily linear or cubic in nature for low Mach numbers.The efficiency of the Gaussian Process will be finally compared to spline interpolation.

The remaining paper is divided as follows; section 2 describes various methods of calculating pressure distributions on a given structure under specified aerodynamic conditions, section 3 explains the basic principles of model reduction through the Singular Value Decomposition technique, section 4 gives the formulation of gaussian process and how to launch it in presence of large number of datapoints. Section 5 compares the results of the Gaussian methodology with respect to earlier techniques. Finally, section 6 concludes the paper with current understanding and future remarks.

Pressure database

The way of building the pressure database depends on the number of degrees of freedom (DoF) activated on the component under analysis. In both the aerodynamic models described in this paper the component will have two degrees of freedom, therefore the database will be three dimensional (third dimension representing pressure).

Xfoil -A simple example

Xfoil ® is a program that can be used for the analysis of subsonic isolated airfoils [START_REF] Drela | XFOIL: An analysis and design system for low Reynolds number airfoils[END_REF]. Various parameters can be changed simultaneously such as properties of the flow or geometric properties of the airfoil itself. Inviscid analysis of the airfoil NACA 3320 is launched for varying angle of attach and Mach number. The space of variables is sampled as in the following vectors shown in figure 1, angle of attack (α) is expressed in [°].

[α] = [-2, -1, 0, 1, 2]; [M] = [0.125, 0.25, 0.375, 0.4];

(1)

The C p distribution for a fixed Mach number and varying angle of attack (α) can be seen in the following figure 1. The assembled database will have the dimensions specified in table 1. The database so obtained has very limited dimensions, allowing fast computations for testing the method, while having the suitable characteristics for this application. The space of variable is regularly sampled and the assembled database will have the dimensions specified in table 2.

Singular Value Decomposition and Interpolation

Singular Value Decomposition is a method for remodeling a set of correlated variables into a set of orthogonal variables [START_REF] Sadek | SVD based image processing applications: state of the art, contributions and research challenges[END_REF]. Basically, SVD transforms the original input space into a new space with independent dimensions. This technique gives us more clearly the idea about which dimensions contribute significantly in the database. Hence it can be used to remove dimensions with low energy content and thereby giving a reduced order model. SVD is regularly used in reducing order of structural FEM's [START_REF] Friswell | Finite element model updating in structural dynamics[END_REF] and aerodynamic meshes [START_REF] Schmid | Dynamic mode decomposition of numerical and experimental data[END_REF] while performing dynamical simulations. In mathematical terms an SVD is the factorisation of a rectangular matrix of real or complex data of dimension m x n, defined as

[A], of the form [U] [Σ] [V ] * . [A] = [U][Σ][V ] T (2)
The matrix [U] is an m x m unitary matrix and its columns are the left singular vectors, [Σ] is an m x n rectangular diagonal matrix containing the singular values and [V ] is a n x n unitary matrix whose transpose has rows that are the right singular vectors. The SVD represents an expansion of the original data in a coordinate system where the covariance matrix is diagonal. In this paper SVD is used to reduce the dimension of the pressure database by neglecting the contribution of the singular values whose energetic content is lower than a certain fixed threshold. After reducing the database, the weights are interpolated to recreate the pressure distribution on the arifoil. Interpolation through data is realized with the built-in Matlab ® function interpn that returns interpolated values of a function of n variables at specific points using, in this specific case, spline interpolation.

Gaussian Process Regression

A gaussian process is an infinite dimensional multi-variate gaussian. Such that any subset of the process is a multivariate gaussian distribution. A gaussian process can be fully parametrized by a mean and covariance function Eq. 3.

y(x) = GP(m(x, θ ), k(x, x , θ )) (3)
A random draw from a Gaussian Process yields a random function around the mean function m(x, θ ) and of the shape as defined by covariance function k(x, x , θ ). Hence, Gaussian Process constitutes a method to define a family of functions whose shape is defined by its covariance function. A popular choice of covariance function is a squared exponential function Eq. 4, because it defines a family of highly smooth (infinitely differentiable) non-linear functions as shown in Fig. 4(a).

k(x, x , θ ) = θ 2 1 exp[- (x -x ) 2 2θ 2 2 ] (4)
A covariance function is fully parametrized by its hyperparameters θ i 's. For the case of Squared exponential kernel the hyperparameters are its amplitude θ 1 and length scale θ 2 .

Given a dataset (x, y) regression deals with finding latent function f between the inputs x and outputs y. While performing polynomial regression it is assumed that the above-mentioned function f comes from a family of polynomial functions. Since Gaussian Processes are such handy tools to define a family of non-linear functions. In a Gaussian Process Regression (GPR) one starts with an initial family of functions defined by a GP called prior Fig. 4(a).

P( f | x, θ ) = GP(y|0, K xx ) (5)
Due to the bayesian setting of GP it is possible to calculate the posterior mean and variance as shown in Eq. 6 and Eq. 7. This means to effectively eliminate all the functions in the prior that do not pass through the specified data points Fig. 4(c).

m(y * ) = k x * x (K xx ) -1 y (6) Cov(y * ) = k x * x * -k x * x (K xx ) -1 k xx * (7)
More over predictions can be improved by choosing a better prior. This involves optimizing the Marginal Likelihood (ML) P(y | x, θ ) calculated as Eq. 8. The probability that the dataset of study (x, y) comes from a family of functions defined by the prior is called the ML [START_REF] Rasmussen | Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)[END_REF]. Hence, when the ML is optimized the optimal θ or family of functions that describe the data are actually found Fig. 4(b).

P(y | x, θ ) = GP(y|0, K xx + σ 2 I) (8)

Distributed Gaussian Process

The above GP approach is intractable for large datasets. For a GP as defined in section 4 the covariance matrix is of size N, where O N 3 time is needed for inference and O N 2 memory for storage. Thus, it is necessary to consider approximate methods in order to deal with large datasets.

Inverting the covariance matrix takes considerable amount of time and memory during the process. Hence, almost all techniques to approximate inference try and approximate the inversion of covariance matrix K xx .

A way to approximate covariance matrix is to learn local experts on subset of data. Traditionally, each subset of data learns a different model from another, this is done to increase the expressiveness in the model [START_REF] Rasmussen | Infinite mixtures of Gaussian process experts[END_REF]. The final predictions are then made by combining the predictions of local experts [START_REF] Chen | Bagging for Gaussian process regression[END_REF].

An alternative way is to tie all the different experts using one single set of hyperparameters [START_REF] Deisenroth | Distributed Gaussian Processes[END_REF]. This is equivalent to assuming one single GP on the whole data-set such that there is no correlation across experts. This tying of experts acts as a regularization and inhibits overfitting. Although ignoring correlation among experts is a strong assumption, it can be justified if the experts are chosen randomly and with enough overlap.

If the dataset is partitioned into M subsets such as D (i) = X (i) , y (i) , i = 1, . . . M.

log p(y|X, θ ) ≈ M ∑ k=1 log p k (y (i) |X (i) , θ ) (9)
The above equation 9 describes the formulation for marginal likelihood. Due to the independence assumption the marginal likelihood can be written as a sum of individual likelihoods and then can be optimized to find the bestfit hyperparameters. After learning the hyperparameters the predictions of local experts can be combined to give mean and variance predictions. The robust Bayesian Committee Machine (rBCM) model combines the various experts using their confidence on the prediction point [START_REF] Deisenroth | Distributed Gaussian Processes[END_REF]. In such manner experts which have high confidence at the prediction points get more weight when compared to experts with low confidence.

m(Y * ) = (Cov(X * )) -2 ∑ β k σ -2 k m k (X * ) (10)
(Cov ( (Y * ))

-2 = ∑ k β k σ -2 k + (1 -∑ k β k )σ -2 * * (11)
In the above equations m k (X * ) and σ k are the mean and covariance predictions from expert k at point X * . σ * * is the auto-covariance of the prior at prediction points X * . β k determines the influence of experts on the final predictions [START_REF] Cao | Generalized Product of Experts for Automatic and Principled Fusion of Gaussian Process Predictions[END_REF] and is given as

β k = 1 2 (log σ -2 * * -log σ -2 k ).

Results

The performance of SVD interpolation, Gaussian Process interpolation performed on individual nodes and distributed Gaussian Process on all the aero nodes together is empirically assessed. The XFoil data-set as described in section 2.1 is the first to be tested. Then the performance on the elsA ® data-set 2.2 is evaluated. Toolbox GPML provided with [START_REF] Rasmussen | Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)[END_REF] is used to perform Gaussian Process regression and distributed GP is inspired from [START_REF] Deisenroth | Distributed Gaussian Processes[END_REF]. The SVD and interpolation analysis is done using built-in matlab functions [START_REF] Mathworks | MATLAB: the language of technical computing. Desktop tools and development environment[END_REF]. All experiments were performed on an Intel quad-core processor with 4Gb RAM. SVD and spline interpolation Transforming the full database with SVD allows to identify the parameters of the system with the highest energetic content. Form figure 6 it can be observed that most of the energetic content of the system is contained in the first two singular values. Therefore the system can be cropped accordingly. Then the prediction in removed doublets is made through spline interpolation.

Xfoil

Gaussian Process -individual nodes Since the Gaussian Process model scales poorly with increasing amount data. Building one single model for all the mesh nodes is not advisable since the number of datapoints will tend to the order of O 4 . Hence in this case individual models were built for all the 182 nodes of the XFoil mesh. This method does not learn the correlations between individual nodes of a mesh and hence some information is lost while building the model.

SVD and GP interpolation

Using the reduced model created earlier, weights are interpolated through Gaussian process regression for individual nodes. This is done to see how the Gaussian process can handle the lack of information after model reduction.

Gaussian Process -large scale To overcome the huge amount of learning and prediction time a distributed Gaussian Process model is built. The dataset was distributed into different experts randomly and each expert had 512 datapoints. Then like earlier cases the performance was verified by calculating the RMSE and MAPE error.

Figures 5(a) and 5(b) denote the two error estimates for different doublets. The SVD and large scale GP perform significantly better than models where individual models are constructed. Large scale GP performs marginally better than SVD. The peaks in the RMSE plots denote cases when the removed doublets are on the edges of database. Hence extrapolation is effectively performed during these experiments. Figure 5(c) shows the time taken to perform prediction for the four different model types. The x axes denotes indexes of removed doublets. The time taken by Large scale GP is highest when compared to SVD and individual interpolation techniques. The SVD interpolation is fastest sometimes performing 30 times faster than large scale GP.

elsA RANS -Application to a Flap Tack Fairing

The data obtained with elsA ® are calculated for a set of αand θ. Refer to 2.2 for a general description of the database. The procedure applied during the analysis is similar to the one described in the previous section. SVD and interpolation After transforming the database through SVD we find that most of the energy content of the database was contained in the first two singular values figure8. When compared to the XFOIL case figure 6 the energy is more concentrated to the first two dimensions in the elsA RANS simulations figure 8. Finally, the prediction from the removed doublets is performed through spline interpolation as described in section 3.

Gaussian Process -individual nodes

The Gaussian Process Regression model as described in section 4 is performed on the elsa RANS data in this section. The elsA RANS simulation has a total of 36802 nodes in the mesh, this combined with the 81 α and θ combinations (9α × 9θ ) will result in a staggering N = 2.9 million data-points. Even if we are willing to wait O N 2 time to perform the prediction our current RAM capacity cannot hold a matrix of size N 2 . Hence we build individual GP models for each node in the mesh. This greatly reduces the memory needed for prediction, while the time for building and prediction of the model increases linearly with number of nodes. But, on the downside we cannot learn the correlation between individual nodes of the mesh.

Gaussian Process -large scale Since the GP model on individual nodes cannot capture inter-node correlations. A distributed GP model as described in section 4.1 is used for prediction. The data-set was distributed into different experts randomly and each expert had 512 data-points. In this case the problem of memory overload is bypassed by distributing the model building to several experts. Then like earlier cases the performance was measured by calculating the RMSE and MAPE error.

Figures 7(a) and 7(b) denote the two error estimates for different doublets. The SVD and large scale GP perform significantly better than GP regression on individual nodes. Large scale GP performs marginally better than SVD. The peaks in the RMSE plots denote cases where the removed doublets are on the edges of database. Hence extrapolation is effectively performed during these experiments. Figure 5(c) shows the time taken to perform prediction for the three different model types. The x axes denotes indexes of removed doublets. The time taken by Large scale GP is highest when compared to SVD and individual interpolation techniques. The SVD interpolation is the fastest sometimes performing 30 times faster than large scale GP.

Conclusion

This paper presents a comparison between three different surrogate model building methods: time-tested surrogate modelling methods such as SVD coupled with spline interpolation and upcoming machine learning methods such as distributed Gaussian Process Regression in simple and large scale mode.

Section 55.0.1 presents a comparison on an XFOIL data-set. Distributed GP performs marginally better when compared to SVD with interpolation, while GP on individual nodes performs the worst. On the contrary SVD with interpolation is significantly faster when compared to the two GP techniques. Section 5.0.2 presents a comparison on elsA RANS simulation comprising of 36802 nodes on the mesh. Again the distributed GP performs marginally better than SVD technique but is a minimum 30 times slower than SVD. Although the GP technique can more efficiently capture non-linearities we see a diminished improvement in performance for the amount of time invested. We leave the weight of deciding between simple and time-tested SVD interpolation vs costly and accurate distributed GP interpolation on the utility function of the final user.

If we keep aside the error induced due to the performing the Gaussian Process interpolation on distributed architecture, the Gaussian Process should give better results when compared to SVD interpolation. This is mostly due to the GP's capability to learn non-linear models. For the current two cases we have shown that the marginal increase in efficiency given by distributed GP is of not the same order of the time spent in learning. In the final manuscript we will also demonstrate the capabilities of interpolation of GP vs SVD in presence of shocks on the CRM in transonic regime [START_REF] Vassberg | Development of a common research model for applied CFD validation studies[END_REF]. Shocks create a mathematical discontinuity in the pressure distribution. In our initial calculations we have found that capability of performing non-linear interpolation and hence distributed GP becomes indispensable for such scenarios.

Figure 1 :

 1 Figure 1: Pressure distribution along the chord of NACA 3320 airfoil. The solid black line at the bottom represents the shape of the airfoil. The colored lines on the top represent various pressure distribution on this airfoil upon varying α and Mach(M) independently.

2. 2

 2 elsA RANS -Application to a Flap Tack Fairing elsA ® [4] is a pluri-function CFD simulation platform that allows representation of internal and external aerodynamics from the low subsonic to the high supersonic flow regime. Several formulations of the 3D Navier-Stokes equations can be chosen for arbitrary moving bodies. In this particular case Reynolds Averaged Navier-Stokes, RANS, equations are used with Spalart-Allmaras turbulence model to simulate the flow around the flap track fairing. (a) elsA -Reynolds Average Navier-Stokes (b) Flap Track Fairing DoF

Figure 2 :

 2 Figure 2: Details of the Flap track Fairing

  value of θthe pressure distribution, in Pa, as a function of the number of the flap track fairing aerodynamic grids and the angle alpha is shown in the following figure 3 whereas the pressure distribution on the flap track fairing at a fixed value of α and θ is shown in figure 3.

Figure 3 :

 3 Figure 3: The following figure shows the evolution of pressure distribution for a constant θ and varying values of α. Y-axes represents the 36802 nodes available on the aero-mesh, whereas the X-axes represents the evolution of α

Figure 4 :

 4 Figure 4: Gaussian Process Regression

  (a) Root Mean Square Error (RMSE) for the four different model types. The x axes denotes indexes of removed doublets. The performance of SVD interpolation is comparable to that of distributed GP interpolation. The peaks in the RMSE plots denote cases when the removed doublets are on the edges of database. Hence extrapolation is effectively performed during these experiments. (b) Mean absolute percentage error (MAPE) for the four different model types. The x axes denotes indexes of removed doublets. The performance of SVD interpolation is comparable to that of distributed GP interpolation. The peaks in the RMSE plots denote cases when the removed doublets are on the edges of database. Hence extrapolation is effectively performed during these experiments. (c) Time taken to perform prediction for the four different model types. The x axes denotes indexes of removed doublets. The time taken by Large scale GP is highest when compared to SVD and individual interpolation techniques. The SVD interpolation is fastest sometimes performing 30 times faster than large scale GP.

Figure 5 :

 5 Figure 5: Results for XFOIL interpolation

Figure 6 :

 6 Figure 6: Singular Values for different Mach numbers

  [α, θ ] doublets are removed one by one from the database to create a new one. Pressure is calculated for the missing [α, θ ] doublets by interpolation, Gaussian procces on the individual nodes and large scale Gaussian process. The methods are finally compared by evaluating the RMSE and MAPE values for each doublet case.

  (a) Root Mean Square Error (RMSE) for the three different model types. The x axes denotes indexes of removed doublets. The performance of SVD interpolation is comparable to that of distributed GP interpolation. The peaks in the RMSE plots denote cases when the removed doublets are on the edges of database. Hence extrapolation is effectively performed during these experiments. (b) Mean absolute percentage error (MAPE) for the three different model types. The x axes denotes indexes of removed doublets. The performance of SVD interpolation is comparable to that of distributed GP interpolation. The peaks in the RMSE plots denote cases when the removed doublets are on the edges of database. Hence extrapolation is effectively performed during these experiments. (c) Time taken to perform prediction for the three different model types. The x axes denotes indexes of removed doublets. The time taken by Large scale GP is highest when compared to SVD and individual interpolation techniques. The SVD interpolation is fastest sometimes performing 30 times faster than large scale GP.

Figure 7 :

 7 Figure 7: Results for elsA interpolation

Figure 8 :

 8 Figure 8: Singular Values for different θvalues for elsA RANS simulations

Table 1 :

 1 Xfoil

	Pressure Database
		N°[-]
	Xfoil Nodes	182
	Sampling in α	5
	Sampling in Mach	4


Ankit Chiplunkar

Joseph Morlier

Operational Modal Analysis in Frequency Domain using Gaussian Mixture Models

Operational Modal Analysis is widely gaining popularity as a means to perform system identification of a structure. Instead of using a detailed experimental setup Operational Modal Analysis relies on measurement of ambient displacements to identify the system. Due to the random nature of ambient excitations and their output responses, various statistical methods have been developed throughout the literature both in the time-domain and the frequency-domain. The most popular of these algorithms rely on the assumption that the structure can be modelled as a multi degree of freedom second order differential system. In this paper we drop the second order differential assumption and treat the identification problem as a curve-fitting problem, by fitting a Gaussian Mixture Model in the frequency domain. We further derive equivalent models for the covariance-driven and the data-driven algorithms. Moreover, we introduce a model comparison criterion to automatically choose the optimum number of Gaussian's. Later the algorithm is used to predict modal frequencies on a simulated problem.

INTRODUCTION

Modal analysis has been widely used as a means of identifying dynamic properties such as modal frequencies, damping ratios and mode shapes of a structural system. Traditionally, the system is subjected to artificial input excitations and output deformations (displacements, velocities or accelerations) are measured. These later help in identifying the modal parameters of the system, this process is called Experimental Modal Analysis (EMA). In the last few decades several algorithms primarily using the assumption of second order differential, Multi Degree Of Freedom (MDOF) system (equation 1) have been developed to find modal parameters in EMA [START_REF] Guillaume | A poly-reference implementation of the least-squares complex frequencydomain estimator[END_REF] [START_REF] Richardson | Parameter estimation from frequency response measurements using rational fraction polynomials[END_REF] .

[M ]{ẍ(t)} + [C]{ ẋ(t)} + [K]{x(t)} = {f (t)}

(1)

Here, [M ], [C] and [K] denote the mass, damping and stiffness matrices respectively. While, {x(t)} and {f (t)} denote the displacement and force vectors at the time t.

Since the last decade Operational Modal Analysis (OMA) has gained considerable interest in the community. OMA identifies the modal parameters only from the output measurements while assuming ambient excitations as random noise. OMA is cheaper because it does not require expensive experimental setup and and can be used in real time operational use cases such as health monitoring [START_REF] Peeters | Industrial relevance of Operational Modal Analysis-civil, aerospace and automotive case histories[END_REF] [4] [START_REF] Rainieri | Automated Operational Modal Analysis as structural health monitoring tool: theoretical and applicative aspects[END_REF] . Several algorithms in OMA can be seen as extensions of EMA algorithms based on the similar assumption of second order MDOF system.

In this paper we approach the problem of finding modal parameters as a problem of curve fitting. We drop the assumption of second order differential MDOF system and use a Gaussian Mixture Model (GMM) [6] [7] to fit the spectral density. Moreover we introduce a criteria called Bayesian Information criteria (BIC) which performs a trade-off on the accuracy of the fit and complexity of the model to estimate the modal order [START_REF] Blumer | Occams razor[END_REF] [9] [START_REF] Roeder | Practical Bayesian density estimation using mixtures of normals[END_REF] .

The remaining paper proceeds as follows, section 2 gives an overview of the traditional operational modal analysis. Sec-

OPERATIONAL MODAL ANALYSIS

As stated earlier the operational modal analysis is an output dependent modal identification technique. The only thing required is the measurement from the accelerometers placed on the structure. Figure 1(a) shows an example of ambient measurements x(t) on a structure. In almost all OMA algorithms the measurement x(t) is assumed to be generated from a random force excitation.

The following subsections describe the various time-domain subsection 2.1 and frequency-domain algorithms subsection 2.2 for performing OMA.

Time-domain OMA

In the time-domain a general auto-regression moving average (ARMA) model can be applied to the measurement x(t) [START_REF] Ljung | System identification, Signal Analysis and Prediction[END_REF] .

Here, the modal parameters can be computed from the coefficients of polynomials in ARMA models [START_REF] Andersen | Identification of civil engineering structures using vector ARMA models[END_REF] .

If we assume that a second order differential (equation 1) completely describes the system dynamics. Then Natural Excitation Technique [START_REF] James | THE NATURAL EXCI-TATION TECHNIQUE (NEXT) FOR MODAL PARANI-ETER EXTRACTION FROM[END_REF] proves that the auto-correlation function k(τ ) in equation 2 can be written as sum of decaying sinusoid's as described by equation 3. The auto-correlation describes the similarity between measurement as a function of time lag τ between them figure 1(b).

k(τ ) = x(t)x(t -τ )dt (2)
Here, k(τ ) denotes the auto-correlation for random vector x(t) as a function of time lag τ .

k(τ ) = Aiexp(-λiτ )sin(Biτ ) (3)
Here, λi and Ai denotes the modal frequency and mode shapes for the i th mode. The above coefficients are found by minimizing the least square error between the measured k(τ ) from equation 2 and the predicted k(τ ) from equation 3. This process is very similar to the Least Square Complex Exponential (LSCE) [START_REF] Spitznogle | Representation and Analysis of Time-Limited Signals Using a Complex Exponential Algorithm[END_REF] [15] [START_REF] Guillaume | A poly-reference implementation of the least-squares complex frequencydomain estimator[END_REF] algorithm developed for time-domain EMA.

Frequency-domain OMA

If we assume the measurement x(t) to be a stationary random process, then according to bochner's theorem [START_REF] Bochner | Lectures on Fourier Integrals[END_REF] the spectral density or power spectrum S(s) can be represented as equation 4.

S(s) = k(τ )exp(-2πis T τ )dτ (4)
Here, S(s) is the power spectrum for the measurement x(t), where s lies in the frequency-damping plane. Figure 1(c) shows the power spectrum calculated for the measurement x(t) shown in figure 1(a).

Initially the Peak Picking technique (PP) [START_REF] Gade | Frequency domain techniques for operational modal analysis[END_REF] was used in the frequency-domain to identify modal frequencies and shapes.

The PP technique is a very easy way to identify modes but Measurement; eg. figure 1

x(t) k(τ ) = x(t)x(t -τ )dt S(s) = k(τ )exp(-2πis T τ )dτ Assumption: Second Order Differential k(τ ) = Aiexp(-λiτ )sin(Biτ ) S(jω) = a k (jω) k b l (jω) l
Assumption: Gaussian Mixture Model

x(t) = GP (0, covSM ) k(τ ) = wicos(2πµiτ )exp{-2π 2 σ 2 i τ 2 } S(s) = wi 1 √ 2πσ 2 i exp{ 1 2σ 2 i (s -µi) 2 } TABLE 1:
Comparison of fitting functions becomes inefficient for complex structures [START_REF] Zhang | An overview of major developments and issues in modal identification[END_REF] . This gave rise to the Frequency Domain Decomposition (FDD) [START_REF] Brincker | Modal identification from ambient responses using frequency domain decomposition[END_REF] where modal frequency are denoted as the eigenvalues of spectral density matrix equation 5.

S(jω) = U ΣU H (5)
Here, modal frequencies and mode shapes can be derived from Σ and U respectively using FDD [START_REF] Brincker | Modal identification from ambient responses using frequency domain decomposition[END_REF] or Enhanced-FDD [START_REF] Brincker | Damping estimation by frequency domain decomposition[END_REF] .

Majority of frequency-domain algorithms in EMA fit a Rational Fractional Polynomial (RFP) [START_REF] Richardson | Parameter estimation from frequency response measurements using rational fraction polynomials[END_REF] in the frequency domain for modal identification [21] [22] . The Rational Fractional Polynomial equation 6 form can be derived if we assume the system to be second order differential equation 1.

S(jω) = a k (jω) k b l (jω) l (6)
Here, the poles of the polynomial denote the modal frequencies, while other modal parameters can be derived from the coefficients a k and b l . The coefficients of the polynomial can be found by minimizing the least squared error. RFP based algorithms face problems since as the number of modes increase the matrix becomes ill-conditioned which gives rise to stability issues in prediction of modal parameters. In the next section we will drop the assumption of second order differential system and treat the modal identification as a purely curve-fitting problem.

GAUSSIAN MIXTURE MODELS (GMM)

Two of the above mentioned OMA algorithms "Natural Excitation Technique" in the time domain and "Rational Fractional Polynomial" in the frequency domain, have a core assumption of second order differential system. This assumption fails for non-linear systems and for cases where modal frequencies are very close. In the following section we propose to use Gaussian Mixture Models to fit the power spectrum curve.

Scale location mixtures of Gaussian's can approximate a curve to arbitrary precision with enough components [START_REF] Plataniotis | Advanced Signal Processing Handbook Theory and Implementation for Radar[END_REF] . Due to the above property GMM's are widely used in machine learning tasks such as speech recognition [START_REF] Stuttle | A Gaussian mixture model spectral representation for speech recognition[END_REF] , financial modelling [START_REF] Xu | On convergence properties of the EM algorithm for Gaussian mixtures[END_REF] , handwriting recognition [START_REF] Bishop | Pattern recognition[END_REF] and many more.

Due to the formulation of GMM, the mean, standard deviation and weight information of the gaussian's can be used to derive the modal frequency, damping and mode shape of the system respectively. For a positive half power spectrum the GMM will be equivalent to equation 7.

S(s)

= Q i wi 1 2πσ 2 i exp{ 1 2σ 2 i (s -µi) 2 } (7)
Here, µi, σi and wi are the mean, standard deviation and weight respectively of the i th gaussian. While, Q denotes the number of gaussians used in the GMM. The mean, standard deviation and weight can be found by minimizing the least square error between measured power spectrum and predicted power spectrum S(s). The method to estimate Q will be explained in more detail in subsection 3.1.

The GMM model in the frequency-domain can be transformed to perform covariance-driven modal identification using the equation 4. If we assume x(t) to be a stationary random process then using to equation 7 and equation 4 we can get equation 8 in the time domain [START_REF] Wilson | Gaussian Process Kernels for Pattern Discovery and Extrapolation Supplementary Material[END_REF] .

k(τ ) = Q i wicos(2πµiτ )exp{-2π 2 σ 2 i τ 2 } (8)
Here, µi, σi and wi are the mean, standard deviation and weight respectively of the i th gaussian. While, Q denotes the number of gaussians used in the GMM, τ is the time lag between two measurement instances. The parameters can be found by minimizing the least squared error.

Moreover, if we assume that x(t) is a zero-mean gaussian process, then we can transform GMM in frequency-domain to time-domain. The equation 7 and equation 8 are equivalent to fitting a zero-mean gaussian process with a spectral mixture covariance function [START_REF] Wilson | Gaussian Process Kernels for Pattern Discovery and Extrapolation[END_REF] .

x(t) = GP (0, covSM (t, t )) (9)
Here, GP denotes a gaussian process [START_REF] Rasmussen | Gaussian processes in machine learning[END_REF] , while covSM represents a spectral mixture covariance function which resembles equation 8 [START_REF] Wilson | Gaussian Process Kernels for Pattern Discovery and Extrapolation[END_REF] .

We would like to emphasize that keeping the computational complexities aside, fitting a spectral mixture gaussian process in time-domain equation 7, fitting equation 8 for covariancedriven modal identification and fitting a GMM equation 7 in the frequency-domain are equivalent. In fact the initial idea of this paper was to fit a Gaussian Process (GP) in the data domain, but GP's are computationally heavy and we achieved a good accuracy by fitting the GMM in frequency domain. Refer to table 1 for a more comprehensive view at various fitting functions.

Bayesian Information Criteria (BIC)

While the modal parameters can be chosen by minimizing the least square error, how to choose the number of modes is a recurring question in several OMA algorithms. This problem is partially resolved by using stabilization diagrams or mode identification functions [START_REF] Allemang | A unified matrix polynomial approach to modal identification[END_REF] [30] [START_REF] Shih | Complex mode indication function and its applications to spatial domain parameter estimation[END_REF] . But in practical situations engineering judgement is required to estimate the optimal modal order.

Here, we use the Bayesian Information Criteria (BIC) [START_REF] Findley | Counterexamples to parsimony and BIC[END_REF] which penalises more complex models to estimate the parameter Q in equation 7. It has been shown earlier that the BIC when applied to GMM's does not underestimate the true number of components [START_REF] Leroux | Consistent estimation of a mixing distribution[END_REF] .

BIC(Q) = n ln(M LE) + k ln(n) (10)
Here, n denotes the number of data-points to fit, M LE denotes the maximum likelihood estimation of the fit and k denote the number of free parameters to fit. The BIC performs a trade-off between the data-fit term n ln(M LE) and the complexity penalty term k ln(n), basically penalizing for over-fitting. Lowest value of BIC is preferred.

RESULTS

In this section we conduct experiments, applying our approach on a simple 3 degree of freedom system with close by modes. As stated earlier in section 3 we fit a Gaussian Mixture Model (GMM) on the spectral density. Later we will compare the Bayesian Information Criteria to find the optimal value of number of gaussians for the measurement.

The toolbox used for this paper is Matlab's Curve Fitting Toolbox [START_REF] Mathworks | Curve fitting toolbox 1: user's guide[END_REF] . All experiments were performed on an Intel quadcore processor with 4Gb RAM. Using the curve fitting toolbox the fitting can be performed by a few lines of code. When compared to other frequency-domain techniques like RFP which suffer from ill-conditioned matrices, the GMM technique is highly stable and finds the coefficient's in seconds.

Figure 2(a) shows the stabilization diagram with increasing number of gaussians Q. We can observe that as the number of Q increases the algorithm starts finding better and better modes. We can also observe that there are three modes which start stabilizing from Q = 5. The, figure 2(b) shows the BIC criterion with increasing number of gaussian's Q. We can see that that the BIC is minimum for Q = 6 and hence if we add anymore gaussian's for our dataset we will be performing over-fitting.

Figure 2(c) shows the 6 constituent gaussians which represent the Q = 6 case. The three principal peaks represent the modal frequencies of the system, these correspond to the stabilized frequencies from figure 2(a). The remaining three peaks are there to compensate for the spectral density not explained by the three principal peaks.

In the current setting of the GMM model we only propose a quick and easy way to identify the most important frequencies of a structural system. Neither the mode shapes nor the damping ratios are estimated in the current format. As can be observed from figure 2(c) the mode shapes are not only dependent on the principal gaussian's but also on the neighbouring gaussian's. Since some part of the spectral density is defined by non-stabilized gaussian's, in future we would like to derive a method to estimate mode-shape and damping ratio such that the contributions of neighbouring gaussian's are also taken into account.

CONCLUSION

In this paper we have proposed to identify model frequencies of a system by curve-fitting a mixture of gaussians in the frequency domain. While the common assumption that the structure can be modelled as a MDOF second order differential system causes stability issues in presence of non-linear systems. The GMM model is mathematically stable, gives results in seconds and can fit a function upto arbitrary accuracy. Moreover we introduce the BIC to identify the optimum num- (b) The BIC criterion with increasing number of gaussian's Q. We can see that that the BIC is minimum for Q = 6 and hence if we add anymore gaussian's for our dataset we will be performing over-fitting (c) Distribution of gaussians for Q = 6.

We can see that the three modal frequencies have majority of the participation in representing the spectral density. Without doubt this is very nascent stage of application of GMM for system identification and there remains problems such as identification of mode-shape and damping ratio in this algorithm. We wish to tackle these problems in the future. We also wish to apply the algorithm on a real world dataset and compare with respect to other time domain and frequency domain techniques.

( a )Figure 1 :

 a1 Figure 1: Different types of measurements for estimation of Modal parameters in OMA

  (a) Auto-correlation; eg. figure 1(b) Power Spectrum; eg. figure 1(c)

( a )

 a Stabilization diagram with increasing number of gaussians Q, the dots denote the stabilized frequencies. We can observe that as the number of Q increases the algorithm starts finding better and better modes.

Figure 2 :

 2 Figure 2: Results of applying GMM on a Spectral density

ACKNOWLEDGMENTS

The author's are really indebted to the encouragement and support provided by, Jonatan Santiago Tonato, Emmanuel Rachelson, Michele Colombo and Sebastien Blanc.