domain: shs sdv

text:
Yoann Maitre
email: maitreyoann@yahoo.fr

Pierre Micheneau
email: pierre.micheneau@etu.uca.fr

Alexis Delpierre
email: alexis.delpierre@etu.uca.fr

Rachid Mahalli
email: rachid.mahalli@etu.uca.fr

Marie Guerin
email: marie.guerin@etu.uca.fr

Gilles Amador
email: gilles.amadordelvalle@chu-nantes.fr

Frederic Denis
email: frederic.denis@chu-tours.fr

F D ; Methodology

G A ; Resources

G A ; Data

G M A ; Visualization

A D ; Supervision

Did the Brain and Oral Microbiota Talk to Each Other? A Review of the Literature

Keywords: mental health, oral microbiota, oral microbiome, mental disorders Conceptualization, Y

This systematic review aims to investigate the role of the oral microbiome in the pathophysiology of mental health disorders and to appraise the methodological quality of research of the oral-brain axis which is a growing interest area. The PRISMA guideline was adopted, to carry out an electronic search through the MEDLINE database, to identify studies that have explored the role of the oral microbiome in the pathophysiology of mental health disorders published from 2000 up to June 2020. The search resulted in 140 records; after exclusions, a total of 22 papers were included in the present review. In accordance with the role of the oral microbiome in the pathophysiology of mental disorders, four mental disorders were identified: Alzheimer's disease, dementia, and cognitive disorders; autism spectrum disorder; Down's syndrome and mental retardation; and Bipolar disorders. Studies argue for correlations between oral microbiota and Alzheimer's disease, autism spectrum disorders, Down's syndrome, and bipolar disorders. This field is still under-studied, and studies are needed to clarify the biological links and interconnections between the oral microbiota and the pathophysiology of all mental health disorders. Researchers should focus their efforts to develop research on the oral-brain axis in the future.

Introduction

While the microbiota defines the population of microbes in a specific ecosystem, the microbiome refers to microorganisms and their genes. These definitions are important because bacteria that live on different parts of the body (skin, gut, and oral cavity) prefer different nutrients and perform different functions. There is an oral microbiota of the mouth, a microbiota of the skin that has many subcategories (e.g., the armpits, nose, feet), and gut microbiota, among many others. The human microbiota is increasingly recognized as a superorganism that is believed to play a role in health and disease [START_REF] Salvucci | The human-microbiome superorganism and its modulation to restore health[END_REF]. The number of microorganisms inhabiting the human body has been estimated at about 10 14 prokaryotic organisms with an absolute number of species varying according to the microbiome's body location [START_REF] Neish | Microbes in Gastrointestinal Health and Disease[END_REF]. As a rough estimate, the 1000 bacterial species in the gut have 2000 genes per species, which yields 2,000,000 genes, 100 times the approximately 20,000 human genes [START_REF] Turnbaugh | The Human Microbiome Project[END_REF]. This includes bacteria, fungi, viruses, protozoa, and archaea, whose diversity will vary from person to person depending on lifestyle and physiological differences [START_REF] Deo | Oral microbiome: Unveiling the fundamentals[END_REF]. Disruptions to these different microbiomes are increasingly becoming associated with numerous inflammatory, immune, and nervous system-related diseases by a communication pathway called the microbiome-brain axis [START_REF] Young | The role of the microbiome in human health and disease: An introduction for clinicians[END_REF][START_REF] Cani | Human gut microbiome: Hopes, threats and promises[END_REF][START_REF] Lee | -ABS-0321 Relationship between autism and gut microbiome: Current status and update[END_REF][START_REF] Lee | -ABS-0240 Role of human microbiota in skin dermatitis and eczema: A systematic review[END_REF][START_REF] Selvaraj | Role of Low FODMAP Diet and Probiotics on Gut Microbiome in Irritable Bowel Syndrome (IBS)[END_REF][START_REF] Durganaudu | Dietary Glycaemic Index and Type 2 Diabetes Mellitus: Potential Modulation of Gut Microbiota[END_REF].

Research supports microbe-brain interactions, most notably with anxiety and depressive-like behaviors, with accumulating evidence pointing to specific microbial genes that can regulate neurotransmitter activity [START_REF] Rogers | From gut dysbiosis to altered brain function and mental illness: Mechanisms and pathways[END_REF]. The gut microbiome has been shown to play a major role in the development and function of the hypothalamic-pituitary-adrenal axis, [START_REF] Rea | The microbiome: A key regulator of stress and neuroinflammation[END_REF] which mediates the stress response and is of interest in a range of psychiatric disorders, in particular depression and anxiety disorders. Our gut bacteria also heavily influence the immune system [START_REF] Belkaid | Role of the Microbiota in Immunity and Inflammation[END_REF] and may represent the link to the immune dysfunction that is characteristic of mental illnesses such as depression and schizophrenia. In mice, Clostridium produces dopamine. This neurotransmitter enables communication within the nervous system and is a molecule that directly influences behavior [START_REF] Asano | Critical role of gut microbiota in the production of biologically active, free catecholamines in the gut lumen of mice[END_REF]. A strong correlation was shown between functional disorders caused by dysbiosis and the subsequent presence of mood disorders [START_REF] Mangiola | Gut microbiota in autism and mood disorders[END_REF]. The dysregulation of the gut-brain axis has emerged as a possible area of research to better understand the pathophysiology of mental disorders and has provided psychiatry with a new paradigm from which to approach mental illness [START_REF] Liang | Gut-Brain Psychology: Rethinking Psychology From the Microbiota-Gut-Brain Axis[END_REF][START_REF] Stefano | Microbiome, and Brain Regulatory Axis: Relevance to Neurodegenerative and Psychiatric Disorders[END_REF][START_REF] Nguyen | Overview and systematic review of studies of microbiome in schizophrenia and bipolar disorder[END_REF][START_REF] Severance | Autoimmune diseases, gastrointestinal disorders and the microbiome in schizophrenia: More than a gut feeling[END_REF].

In the same way, the human oral microbiota has become a new research focus area aimed at promoting the progress of disease diagnosis, complimenting disease treatment, and developing personalised medicines. Evidence suggests that disturbance to the oral microbiota ecological balance can cause a series of infectious oral diseases including dental caries and periodontal diseases. The oral microbiota is also associated with several systemic diseases, including but not limited to cardiovascular disease, pneumonia, rheumatoid arthritis, pancreatic cancer, colorectal cancer, oesophageal cancer, stroke, and adverse pregnancy outcomes. Accordingly, the oral microbiota is increasingly being recognized as a potential biomarker for human diseases [START_REF] Jia | The oral microbiota-A mechanistic role for systemic diseases[END_REF][START_REF] Sampaio-Maia | The Oral Microbiome in Health and Its Implication in Oral and Systemic Diseases[END_REF][START_REF] Nazir | Prevalence of periodontal disease, its association with systemic diseases and prevention[END_REF][START_REF] Bourgeois | Periodontal Pathogens as Risk Factors of Cardiovascular Diseases, Diabetes, Rheumatoid Arthritis, Cancer, and Chronic Obstructive Pulmonary Disease-Is There Cause for Consideration?[END_REF]. The oral microbiota is composed of a large number of microorganisms housed in a complex environment, that encompasses distinct, small microbial habitats, such as teeth, buccal mucosa, soft and hard palate, and tongue, which form a species-rich heterogeneous ecological system [START_REF] Dewhirst | The Human Oral Microbiome[END_REF]. About 50 to 100 billion bacteria have been identified in the oral cavity and 600 prevalent taxa at the species level, with distinct subsets predominating different habitats [START_REF] Krishnan | A practical guide to the oral microbiome and its relation to health and disease[END_REF]. These species belong to 185 genera and 12 phyla, of which approximately 54% are officially named, 14% are unnamed (but cultivated) and 32% are known only as uncultivated phylotypes [START_REF] Zhao | Variations in oral microbiota associated with oral cancer[END_REF]. The 12 phyla are Firmicutes, Fusobacteria, Proteobacteria, Actinobacteria, Bacteroidetes, Chlamydiae, Chloroflexi, Spirochaetes, Synergistetes, Saccharibacteria and Gracilibacteria [START_REF] Perera | Emerging role of bacteria in oral carcinogenesis: A review with special reference to perio-pathogenic bacteria[END_REF]. Oral-derived bacteria such as Porphyromonas gingivalis and Actinobacillus actinomycetemcomitans can colonize the intestines and persist there, leading to activation of the intestinal immune system and chronic inflammation [START_REF] Espina | Talk to your gut: The oral-gut microbiome axis and its immunomodulatory role in the etiology of rheumatoid arthritis[END_REF].

Oral microbiota such as Streptococcus mutans, Porphyromonas gingivalis, and Gemella haemolysans may play a role in cardiovascular disease [START_REF] Eberhard | Streptococcus mitis and Gemella haemolysans were simultaneously found in atherosclerotic and oral plaques of elderly without periodontitis-A pilot study[END_REF] and oral pathogens, especially Porphyromonas gingivalis and Aggregatibacter actinomycetemcomitans are associated with a high risk of pancreatic cancer [START_REF] Fan | Human oral microbiome and prospective risk for pancreatic cancer: A population-based nested case-control study[END_REF]. In general, the oral microbiota has an impact on the health of the body by digesting food. Salivary DNA sequencing has shown that core species abundance ratios significantly correlate with diet. For example, the abundance of Neisseria and Haemophilus differs between the hunter-gatherers population living in the western part of the island of Luzon, in the east of this island and in the central part of the island of Palawan (Philippines) [START_REF] Lassalle | Oral microbiomes from hunter-gatherers and traditional farmers reveal shifts in commensal balance and pathogen load linked to diet[END_REF]. The oral microbiota can also produce metabolites in the mouth that can affect the development of a range of oral diseases. Microorganisms found on the surfaces of teeth tend to form multispecies biofilm communities that are often embedded in a matrix of extracellular polymeric substances (EPS). The production of EPS and acidic metabolites are closely related to the oral microbiota for dental caries [START_REF] Flemming | Biofilms: An emergent form of bacterial life[END_REF]. In periodontal diseases, polymicrobial communities induce a dysregulated and destructive host response through a mechanism referred to as polymicrobial synergy and dysbiosis induced by a pathogenic triad of Porphyromonas gingivalis, Tannerella forsythia and Treponema denticola named the red complex [START_REF] Holt | Porphyromonas gingivalis, Treponema denticola, and Tannerella forsythia: The 'red complex', a prototype polybacterial pathogenic consortium in periodontitis[END_REF]. The oral microbiota directly influences dental caries and periodontal diseases [START_REF] Lamont | The oral microbiota: Dynamic communities and host interactions[END_REF]. Specific genetic composition and structure of the microbial community can even be identified in the pathogenesis and evolution of periodontal disease. When the microbiota isolated from patients with periodontal disease were compared with health controls, the most striking difference was the relative proportions of the four most abundant phyla, Bacteroidetes, Actinobacteria, Proteobacteria, and Firmicutes [START_REF] Li | Phylogenetic and functional gene structure shifts of the oral microbiomes in periodontitis patients[END_REF][START_REF] Wang | Metagenomic sequencing reveals microbiota and its functional potential associated with periodontal disease[END_REF]. Likewise, we observed change in oral microbiota in systemic diseases like, for example, an elevation of proinflammatory cytokines in saliva patients suffer from oral squamous cell carcinoma [START_REF] Rhodus | NF-kappaB dependent cytokine levels in saliva of patients with oral preneoplastic lesions and oral squamous cell carcinoma[END_REF]. A link between composition and diversity of the oral microbiota and type II diabetes is suspected [START_REF] Tam | Obesity alters composition and diversity of the oral microbiota in patients with type 2 diabetes mellitus independently of glycemic control[END_REF]. There are indications that periodontitis precedes rheumatoid arthritis [START_REF] De Smit | Commentary: Periodontitis and Rheumatoid Arthritis: What Do We Know?[END_REF] and saliva would be able to provide informative clinical markers to obesity [START_REF] Mervish | Associations of the Oral Microbiota with Obesity and Menarche in Inner City Girls[END_REF]. Oral bacteria could, therefore, be linked to or serve as biomarkers for certain systemic diseases. However, it remains to be established whether there is a causal relationship between the oral microbiome and these systemic disorders.

The oral microbiome, therefore, appears crucial for health as it can cause both oral and systemic diseases. Identifying the microbiome in health is the first step of human microbiome research, after which it is necessary to understand the role of the microbiome in the alteration of functional and metabolic pathways associated with the diseased states.

In this perspective, the gut-brain axis is gaining ever more traction in fields investigating the biological and physiological basis of psychiatric, neurodevelopmental, and neurodegenerative and age-related disorders. On the other hand, the impact of the oral microbiota and the physiopathological mechanisms that it generates, to our knowledge, are little emphasized in their relationship with mental disorders.

Therefore, the aim of this systematic review was to investigate the role of the oral microbiome in the pathophysiology of mental health disorders, to appraise the methodological quality of the oral-brain axis research, a young yet fast growing field of interest.

Materials and Methods

The present systematic review was conducted according to the PRISMA guidelines for Systematic Reviews [START_REF] Moher | Preferred reporting items for systematic reviews and meta-analyses: The PRISMA statement[END_REF].

Search Strategy

An electronic search was conducted through the MEDLINE (PubMed) database to identify publications that met the inclusion criteria. High-throughput sequencing techniques for genetic material developed in the 2000s have led to a better understanding of the nature of host-microbiota interactions, the interactions of microorganisms with each other, and their impact on health [START_REF] Sudo | Postnatal microbial colonization programs the hypothalamic-pituitary-adrenal system for stress response in mice[END_REF]. That is why the search was performed from 2000 up to June 2020, in order to identify the studies that explore the role of the oral microbiome in the pathophysiology of mental health disorders, using the following search terms and keywords alone or in combination with the Boolean operator "AND"/ "OR" according to the following equation [Mouth/microbiology [Mesh]) OR "Mouth Diseases/microbiology"[Mesh]) OR "Saliva/microbiology"[Mesh:NoExp]) OR "Mouth Diseases/immunology"[Mesh]) AND "Mental Disorders"[Mesh]].

Study Detection

References of the eligible studies on the topic were manually checked, and two independent operators (F.D. and Y.M.) screened the studies according to the inclusion/exclusion criteria.

Inclusion and Exclusion Criteria

We included experimental or clinical studies (longitudinal, cross-sectional, or randomised studies) that (1) explored the link between the oral microbiome and mental disorders from the inflammatory perspective or (2) explored an association between oral microbiota dysbiosis and mental health symptoms. We excluded conferences, abstracts, reviews, and editorials. Broadly defined, dysbiosis is any change in the composition of resident commensal communities relative to the community found in healthy individuals. As dysbiosis in the microbiome is associated with many diseases [START_REF] Petersen | Defining dysbiosis and its influence on host immunity and disease[END_REF][START_REF] Bäckhed | Defining a Healthy Human Gut Microbiome: Current Concepts, Future Directions, and Clinical Applications[END_REF][START_REF] Trompette | Gut microbiota metabolism of dietary fiber influences allergic airway disease and hematopoiesis[END_REF][START_REF] Hsiao | Microbiota Modulate Behavioral and Physiological Abnormalities Associated with Neurodevelopmental Disorders[END_REF][START_REF] Garrett | Cancer and the microbiota[END_REF], changes observed in the oral microbial composition are hypothesised to contribute to the onset and/or persistence of mental disorders.

Data Collection

Two reviewers (F.D. and Y.M.) independently screened the list of titles and abstracts to identify the potentially relevant papers based on the inclusion criteria. If the abstracts were judged to contain insufficient information, then the full studies were reviewed to decide whether they should be included based on the selection criteria. A scan of the references of the previously selected articles completed the selection. When a discrepancy in the selection decision occurred, the two reviewers engaged in discussion until a consensus was reached. If needed, a third reviewer (G.A.) resolved the possible conflicts concerning eligibility.

Results

Study Selection

The initial studies retrieved from the databases were first selected, and studies that met the eligibility criteria were reviewed and analysed. From 140 studies, 19 were selected. The complementary detection resulted in the selection of three additional articles. Taken together, a total of 22 articles were included in the analysis (Figure 1). Each study that met the inclusion criteria was analysed from several aspects, such as authors, date of publication, the time when the study was conducted, study design, objectives, results, and limitations.

Of the 22 studies included in the analysis (Table 1), four distinct themes in mental health disorders emerged: Alzheimer's disease (AD), dementia, and cognitive disorders [START_REF] Riviere | Molecular and immunological evidence of oral Treponema in the human brain and their association with Alzheimer's disease[END_REF][START_REF] Rai | Possible relationship between periodontitis and dementia in a North Indian old age population: A pilot study[END_REF][START_REF] Sochocka | Association between Periodontal Health Status and Cognitive Abilities. The Role of Cytokine Profile and Systemic Inflammation[END_REF][START_REF] Ilievski | Chronic oral application of a periodontal pathogen results in brain inflammation, neurodegeneration and amyloid beta production in wild type mice[END_REF][START_REF] Poole | Determining the Presence of Periodontopathic Virulence Factors in Short-Term Postmortem Alzheimer's Disease Brain Tissue[END_REF][START_REF] Taguchi | Association between Oral Health and the Risk of Lacunar Infarction in Japanese Adults[END_REF][START_REF] Kamer | TNF-α and antibodies to periodontal bacteria discriminate between Alzheimer's disease patients and normal subjects[END_REF][START_REF] Noble | Serum IgG Antibody Levels to Periodontal Microbiota Are Associated with Incident Alzheimer Disease[END_REF][START_REF] Noble | Periodontitis is associated with cognitive impairment among older adults: Analysis of NHANES-III[END_REF][START_REF] Dominy | Porphyromonas gingivalis in Alzheimer's disease brains: Evidence for disease causation and treatment with small-molecule inhibitors[END_REF][START_REF] Sun | Mixed evidence for the relationship between periodontitis and Alzheimer's disease: A bidirectional Mendelian randomization study[END_REF][START_REF] Watanabe | Oral Cnm-positive Streptococcus Mutans Expressing Collagen Binding Activity is a Risk Factor for Cerebral Microbleeds and Cognitive Impairment[END_REF][START_REF] Bajaj | Specific Gut and Salivary Microbiota Patterns Are Linked with Different Cognitive Testing Strategies in Minimal Hepatic Encephalopathy[END_REF]; autism spectrum disorder (ASD) [START_REF] Qiao | Alterations of oral microbiota distinguish children with autism spectrum disorders from healthy controls[END_REF][START_REF] Hicks | Oral microbiome activity in children with autism spectrum disorder[END_REF][START_REF] Kong | New and Preliminary Evidence on Altered Oral and Gut Microbiota in Individuals with Autism Spectrum Disorder (ASD): Implications for ASD Diagnosis and Subtyping Based on Microbial Biomarkers[END_REF]; Down's syndrome (DS) and mental retardation [START_REF] Amano | Relationship of Periodontopathic Bacteria With Early-Onset Periodontitis in Down's Syndrome[END_REF][START_REF] Reuland-Bosma | Absence of a specific subgingival microflora in adults with Down's syndrome[END_REF][START_REF] Khocht | Association of interleukin-1 polymorphisms with periodontitis in Down syndrome[END_REF][START_REF] Linossier | Differences of the oral colonization by Streptococcus of the mutans group in children and adolescents with Down syndrome, mental retardation and normal controls[END_REF][START_REF] Khocht | Subgingival microbiota in adult Down syndrome periodontitis[END_REF]; and bipolar disorders [START_REF] Cunha | Periodontal condition and levels of bacteria associated with periodontitis in individuals with bipolar affective disorders: A case-control study[END_REF].

Alzheimer's Disease, Dementia, and Cognitive Disorders

Most mental health disorders are related to dementia. Dementia describes a group of symptoms associated with cognitive disorders, such as a decline in memory, reasoning, or other thinking skills. Many different types of dementia exist, and many conditions cause it. AD is the most common cause of dementia [START_REF] Weller | Current understanding of Alzheimer's disease diagnosis and treatment[END_REF]. Although it is a neurodegenerative disease, AD and its symptoms are outlined in the Diagnostic and Statistical Manual of Mental Disorders fifth edition (DMS V) and in the International Classifications of Diseases, 10th Revision (ICD-10) and is recognized as a mental disorder with a neurological origin. In cross-sectional studies, many authors have evoked a correlation between the presence of an inflammatory process whose origin could be periodontal and the presence of dementia or AD [START_REF] Riviere | Molecular and immunological evidence of oral Treponema in the human brain and their association with Alzheimer's disease[END_REF][START_REF] Rai | Possible relationship between periodontitis and dementia in a North Indian old age population: A pilot study[END_REF][START_REF] Sochocka | Association between Periodontal Health Status and Cognitive Abilities. The Role of Cytokine Profile and Systemic Inflammation[END_REF]. The main markers of inflammation to be studied were the cytokine levels produced by unstimulated and LPS-stimulated peripheral blood leukocytes [START_REF] Sochocka | Association between Periodontal Health Status and Cognitive Abilities. The Role of Cytokine Profile and Systemic Inflammation[END_REF] or the plasma CRP [START_REF] Rai | Possible relationship between periodontitis and dementia in a North Indian old age population: A pilot study[END_REF]. Studies using an animal model of periodontitis and human post-mortem brain tissues from subjects with AD strongly suggest that a Gram-negative periodontal pathogen, Porphyromonas gingivalis and/or its product gingipain is/are translocated to the brain [START_REF] Ilievski | Chronic oral application of a periodontal pathogen results in brain inflammation, neurodegeneration and amyloid beta production in wild type mice[END_REF][START_REF] Poole | Determining the Presence of Periodontopathic Virulence Factors in Short-Term Postmortem Alzheimer's Disease Brain Tissue[END_REF]. Taguchi et al. [START_REF] Taguchi | Association between Oral Health and the Risk of Lacunar Infarction in Japanese Adults[END_REF] showed that an increase in periodontal pocket depth tended to be associated with the number of lacunar infarctions in Japanese adults of both sexes. Kamer et al. [START_REF] Kamer | TNF-α and antibodies to periodontal bacteria discriminate between Alzheimer's disease patients and normal subjects[END_REF] showed that both the plasma TNF-α level and the number of positive tests for antibodies against periodontal bacteria were elevated in AD and independently associated with AD, suggesting that antibody levels to periodontal bacteria associate with AD and might help improve the clinical diagnosis of AD. In this perspective, serological marker like gingivalis IgG of periodontitis could be associated with impaired delayed memory and calculation [START_REF] Noble | Serum IgG Antibody Levels to Periodontal Microbiota Are Associated with Incident Alzheimer Disease[END_REF][START_REF] Noble | Periodontitis is associated with cognitive impairment among older adults: Analysis of NHANES-III[END_REF]. Dominy et al. [START_REF] Dominy | Porphyromonas gingivalis in Alzheimer's disease brains: Evidence for disease causation and treatment with small-molecule inhibitors[END_REF] suggested that Porphyromonas gingivalis and gingipains in the brain play a central role in the pathogenesis of AD, providing a new conceptual framework for disease treatment and designed an orally bioavailable, brain-penetrant Kgp inhibitor currently being tested in human clinical studies for AD. Kgp is a component of a protease essential for the pathogenicity of Porphyromonas gingivalis (gingipain) found in the cerebral cortex. However, even with a Mendelian randomization approach that takes into account the genetic variability of periodontal pathogens to investigate the causal relationship between periodontitis and AD bidirectionally in the population of European ancestry, Sun et al. [START_REF] Sun | Mixed evidence for the relationship between periodontitis and Alzheimer's disease: A bidirectional Mendelian randomization study[END_REF] did not find convincing evidence to support periodontitis being a causal factor for the development of AD.

In mice, Watanabe et al. showed that the chronic presence of cnm-positive Streptococcus mutans hematogenously induces cerebral haemorrhage by disrupting the blood-brain barrier. The collagen-binding activity of cnm-positive Streptococcus mutans is closely related to the occurrence of deep cerebral microbleeds and might be a risk factor for cognitive impairment [START_REF] Watanabe | Oral Cnm-positive Streptococcus Mutans Expressing Collagen Binding Activity is a Risk Factor for Cerebral Microbleeds and Cognitive Impairment[END_REF].

Patients with hepatic encephalopathy, which is associated with cognitive dysfunction, have unique microbial signatures in their stool and salivary microbiota [START_REF] Bajaj | Specific Gut and Salivary Microbiota Patterns Are Linked with Different Cognitive Testing Strategies in Minimal Hepatic Encephalopathy[END_REF].

Lastly, using molecular and immunological techniques, Riviere et al. observed Treponema in frozen trigeminal ganglia, brainstem, and cortex samples from human subjects [START_REF] Riviere | Molecular and immunological evidence of oral Treponema in the human brain and their association with Alzheimer's disease[END_REF]

Autism Spectrum Disorder

ASD is a complex neurological and developmental disorder whose aetiology likely involves an interplay between genetic and environmental factors, as well as systemic inflammations [START_REF] Jeste | The neurology of autism spectrum disorders[END_REF].

In a cross-sectional study, a comparative analysis of oral microbiota in ASD children by a sequencing method showed an alteration in the composition and taxonomy of the oral microbiota in ASD patients compared to healthy controls. In this case, dysbiosis in the oral microbial community of ASD patients suggested a potential role for microorganisms in the progression of this disease [START_REF] Qiao | Alterations of oral microbiota distinguish children with autism spectrum disorders from healthy controls[END_REF]. Hicks et al. [START_REF] Hicks | Oral microbiome activity in children with autism spectrum disorder[END_REF] identified distinct oral micro transcriptomic activity in ASD children and suggests oral microbiome profiling as a potential tool to evaluate ASD status. Kong et al. [START_REF] Kong | New and Preliminary Evidence on Altered Oral and Gut Microbiota in Individuals with Autism Spectrum Disorder (ASD): Implications for ASD Diagnosis and Subtyping Based on Microbial Biomarkers[END_REF], in a cross-sectional pilot study, conducted a comparative analysis of the oral and gut microbiomes in patients with ASD. This study identified distinct features of the gut and salivary microbiota that differ between individuals with and without an ASD diagnosis.

Down's Syndrome and Mental Retardation

DS is a genetic disorder caused by the presence of all or part of a third copy of chromosome 21 and is associated with mild to moderate intellectual disability and facial characteristics.

Studies showed [START_REF] Amano | Relationship of Periodontopathic Bacteria With Early-Onset Periodontitis in Down's Syndrome[END_REF][START_REF] Reuland-Bosma | Absence of a specific subgingival microflora in adults with Down's syndrome[END_REF][START_REF] Khocht | Association of interleukin-1 polymorphisms with periodontitis in Down syndrome[END_REF] that the DS population developed an earlier and more extensive periodontal breakdown. However, Reuland-Bosma et al. [START_REF] Reuland-Bosma | Absence of a specific subgingival microflora in adults with Down's syndrome[END_REF] report an absence of specific flora in adults with DS compared to a control group. Despite this finding, several studies have identified certain specificities in DS patient's microbiota. With similar levels of gingival inflammation and plaque accumulation with Porphyromonas gingivalis with specific genotype (type II fimA) may be a determinant for DS early-onset periodontitis as well as non-DS populations [START_REF] Amano | Relationship of Periodontopathic Bacteria With Early-Onset Periodontitis in Down's Syndrome[END_REF]. The score of Streptococcus mutans in saliva close to type k was higher in DS and mental retardation than in control [START_REF] Linossier | Differences of the oral colonization by Streptococcus of the mutans group in children and adolescents with Down syndrome, mental retardation and normal controls[END_REF]. Khocht et al. [START_REF] Khocht | Subgingival microbiota in adult Down syndrome periodontitis[END_REF] have reported that the subgingival microbiological profiles of adults with DS with periodontitis are similar to those found in patients with chronic periodontitis. These authors note, however, significant differences between the groups for some bacterial species (Actinobacillus actinomycetemcomitans, Porphyromonas gingivalis, Tannerella forsythia, Prevotella intermedia, Selenomonas noxia, Propionibacterium acnes gordonii, Streptococcus mitis, and Streptococcus oralis, Streptococcus constellatus Treponema Socranskii). These differences highlight that patients with DS have higher levels of certain bacterial species and specific associations between certain bacterial species and the loss of periodontal attachment. However, the majority of bacteria identified are opportunistic bacteria suggesting the role of a carried by hands contamination (thumb sucking, finger biting). The association between IL-1 (which is a proinflammatory marker of periodontal diseases) polymorphic genotypes and periodontitis differ between the DS and non-DS subjects [START_REF] Khocht | Association of interleukin-1 polymorphisms with periodontitis in Down syndrome[END_REF].

Bipolar Disorders

Bipolar disorder is a mental health condition that causes extreme mood swings that include emotional highs (mania or hypomania) and lows (depression).

Cunha et al. [START_REF] Cunha | Periodontal condition and levels of bacteria associated with periodontitis in individuals with bipolar affective disorders: A case-control study[END_REF] showed that Bipolar disorder was associated with an increased risk for periodontitis and a higher frequency of all evaluated periodontopathogens, as well as a higher total bacterial load like Aggregatibacter actinomycetemcomitans and Porphyromonas gingivalis. The prevalence of periodontitis and the increase of the bacterial load concerning Aggregatibacter actinomycetemcomitans and Porphyromonas gingivalis is especially associated with the depressive phases compared to the manic or euthymic phases [START_REF] Cunha | Periodontal condition and levels of bacteria associated with periodontitis in individuals with bipolar affective disorders: A case-control study[END_REF].

Discussion

While many studies highlight the link between the gut microbiota and mental disorders, studies on the impact of the oral microbiota and the pathophysiological mechanisms are little emphasized in their relationship with mental disorders. We identified 22 studies on the subject only one of which links bipolar disorders to the oral microbiota. No studies have been published on the link between the oral microbiota and schizophrenia or depressive disorders despite these being major psychiatric disorders. The studies carried out in this area mainly concern cognitive disorders associated with AD (13/22 identified studies). The public health problem linked to the growth of AD, dementia, and cognitive disorders in the general population due to its overall aging [START_REF] Prince | World Alzheimer Report[END_REF] is certainly a cause that might explain this preferential research orientation.

The identification of a specific microflora in patients with mental disorders suggests that these disorders could influence the oral microbiome. This hypothesis presumes that the CNS (Central nervous System) is capable of modifying the oral environment to favour the preferential selection of particular microbes, as is the case for the intestinal flora [START_REF] Martin | The Brain-Gut-Microbiome Axis[END_REF]. This hypothesis is tempered by the poor oral condition usually associated with patients with mental disorders. Among persons with severe mental illness, dental caries and periodontal measurement indexes often reach twice the level found in the general population [START_REF] Gurbuz | Oral health and treatment needs of institutionalized chronic psychiatric patients in Istanbul, Turkey[END_REF][START_REF] Ramon | Oral health and treatment needs of institutionalized chronic psychiatric patients in Israel[END_REF]. Many combined factors contribute to the poor oral health of these individuals, including orals infectious diseases interacting with the metabolic disturbances induced by antipsychotic treatments (e.g., diabetes, obesity), and also poor diet and lifestyle choices (e.g., high sugar diet, use of psychoactive substances such as tobacco, and inadequate oral hygiene) [START_REF] Denis | Oral Health Is a Challenging Problem for Patients with Schizophrenia: A Narrative Review[END_REF][START_REF] Vancampfort | Risk of metabolic syndrome and its components in people with schizophrenia and related psychotic disorders, bipolar disorder and major depressive disorder: A systematic review and meta-analysis[END_REF].

Periodontal diseases and dental caries are the two main oral pathologies in humans [START_REF] Petersen | The World Oral Health Report 2003: Continuous improvement of oral health in the 21st century -The approach of the WHO Global Oral Health Programme[END_REF]. The increase in oral bacteria load (Porphyromonas gingivalis, Streptococcus mutans, Treponema denticola, etc.), and the elevated concentrations of the inflammatory markers they induce (TNF α and cytokines), appear to be found in patients suffering from mental illness. Many psychiatric conditions including AD are associated with chronic low-grade inflammation and elevated level of pro-inflammatory cytokines [START_REF] Bauer | Inflammation in psychiatric disorders: What comes first?[END_REF]. Gut microbiota disturbances may represent a possible mechanism linking chronic stress, cytokine production and neuropsychiatric disorders such as depression [START_REF] Kelly | Breaking down the barriers: The gut microbiome, intestinal permeability and stress-related psychiatric disorders[END_REF]. Oral microbiome disturbances may represent another such link achieved through the translocation of microbes from the oral cavity into the bloodstream. The oral microbiome and the gastrointestinal microbiomes share many common microbes, another potential link through which the two sites both contribute to inflammatory diseases. Taken together, it is not surprising that oral and intestinal microbiota show concordant disease associations [START_REF] Said | Dysbiosis of Salivary Microbiota in Inflammatory Bowel Disease and Its Association with Oral Immunological Biomarkers[END_REF]. The oral dysbiosis and the inflammatory phenomena it induces could play a part in the development of mental illnesses, just like intestinal dysbiosis [START_REF] Clapp | Gut microbiota's effect on mental health: The gut-brain axis[END_REF]. Since the oral cavity represents the main entry point to the intestinal tract, it can be assumed that the accumulated evidence regarding the link between the intestinal flora and mental disorder is in favour of future studies related to the oral microbiota [START_REF] Zhao | Variations in oral microbiota associated with oral cancer[END_REF].

Mental illnesses (e.g., schizophrenia, depressive syndromes) involve neurotransmitter dysfunction. Gut bacteria can directly produce neurotransmitters used in the human body including GABA, serotonin, noradrenaline, acetylcholine and dopamine [START_REF] Roshchina | Microbial Endocrinology: Interkingdom Signaling in Infectious Disease and Health[END_REF]. However, the quantities produced by bacteria are relatively small and unlikely to influence human neurotransmission directly to any great extent. The oral microbiota can also produce metabolites. In 2019, Lin et al. explored the association between fluctuations within the oral microbiome and the brain functional network in smokers and suggested the biological pathways underlying for the microbiome-brain link, but were unable to assign causality among the features [START_REF] Lin | Association between the oral microbiome and brain resting state connectivity in smokers[END_REF].

In the interdental biofilm of young and healthy periodontal subjects with no signs of periodontal disease, there are periodontopathogen bacteria such as Porphyromonas gingivalis [START_REF] Ecarrouel | Quantitative Molecular Detection of 19 Major Pathogens in the Interdental Biofilm of Periodontally Healthy Young Adults[END_REF] that also appear to be involved in the development of Alzheimer's disease. Thus, the setting up as the youngest age of individual oral prophylaxis directed towards the interdental spaces, with the use of interdental brushes, would help to combat dysbiosis of the oral microbiota and could potentially prevent the onset of diseases such as Alzheimer's disease [START_REF] Lamont | The oral microbiota: Dynamic communities and host interactions[END_REF][START_REF] Bourgeois | Calibrated interdental brushing for the prevention of periodontal pathogens infection in young adults-A randomized controlled clinical trial[END_REF].

Differences in the gut microbiome profiles of people with ASD have been reported like an increase in the abundance of Clostridium species [START_REF] Parracho | Differences between the gut microflora of children with autistic spectrum disorders and that of healthy children[END_REF] and high levels of Sutterella [START_REF] Williams | Application of Novel PCR-Based Methods for Detection, Quantitation, and Phylogenetic Characterization of Sutterella Species in Intestinal Biopsy Samples from Children with Autism and Gastrointestinal Disturbances[END_REF], although the results vary from study to study. In addition, the oral microbiome of children with ASD differs from that of neurotypical children in several taxa predominantly related to energy metabolism and lysine degradation pathways [START_REF] Hicks | Oral microbiome activity in children with autism spectrum disorder[END_REF]. Although several studies to investigate the effects of various probiotics on ASD symptoms, they are greatly limited by small sample sizes and methodological challenges, and, as such, it is difficult to draw any concrete conclusions [START_REF] Srinivasjois | Probiotic supplementation in children with autism spectrum disorder[END_REF]. Concerning the oral microbiota in people with ASD, multiple studies have identified species specifically associated with this disorder [START_REF] Qiao | Alterations of oral microbiota distinguish children with autism spectrum disorders from healthy controls[END_REF][START_REF] Hicks | Oral microbiome activity in children with autism spectrum disorder[END_REF][START_REF] Kong | New and Preliminary Evidence on Altered Oral and Gut Microbiota in Individuals with Autism Spectrum Disorder (ASD): Implications for ASD Diagnosis and Subtyping Based on Microbial Biomarkers[END_REF].

In accordance with reports of higher level of certain bacterial species in the oral microbiota of patients with, DS, Biagi et al. [START_REF] Biagi | Gut Microbiome in Down Syndrome[END_REF] highlight that the general makeup of their microbiomes were similar to those of healthy individuals, though, some subpopulations of bacteria were more or less abundant in patients with DS. Individuals with DS have elevated levels of Parasporobacterium and Sutterella and reduced levels of Veillonellaceae. Specifically, in this study, Sutterella abundance positively correlated with the Aberrant Behaviour Checklist (ABC) scores individuals with DS. This positive correlation indicates that in the gut at least, this bacterium may contribute to the maladaptive behaviour in patients with various conditions. Several studies examine the composition of the microbiome in patients with bipolar disorder [START_REF] Evans | The gut microbiome composition associates with bipolar disorder and illness severity[END_REF] and report different levels of Faecalibacterium. In 2019, Coello et al. reported that Flavonifractor, a bacterial genus that can induce oxidative stress and inflammation, was associated with bipolar disorder and that probiotics from Lactobacillus and Bifidobacterium appear to have therapeutic potential [START_REF] Coello | Gut microbiota composition in patients with newly diagnosed bipolar disorder and their unaffected first-degree relatives[END_REF]. Cunha et al. [START_REF] Cunha | Periodontal condition and levels of bacteria associated with periodontitis in individuals with bipolar affective disorders: A case-control study[END_REF] who, to the best of our knowledge, are the only authors to have studied the oral microbiota composition in patients with bipolar disorder, found a higher frequency of all periodontopathogens in this populations.

Despite the mounting evidence in support of a link between the oral microbiome and mental health, it must be kept in mind that the relative abundance and diversity of bacteria vary considerably from one individual to another [START_REF]Structure, function and diversity of the healthy human microbiome[END_REF]. As a consequence, studies generally only focus on simple correlations between the abundance of particular taxa and the pathological conditions associated with the host. These association patterns do not allow a discrimination between effect and cause [START_REF] Hooks | Microbiota-gut-brain research: A critical analysis[END_REF].

A consensus has yet to be reached on a precise definition for the characteristics of a bidirectional relationship between the oral microbiome and the brain as it can be advanced in the context of the gut-brain axis [START_REF] Carabotti | The gut-brain axis: Interactions between enteric microbiota, central and enteric nervous systems[END_REF]. The identification of specific oral dysbiosis signatures associated with various mental disorders raises the question of whether the CNS modulate the oral microbiome. This would constitute the complementary element of a bidirectional relationship suggesting the existence of an oral cerebral axis equivalent to the gastrointestinal axis. However, if, within the framework of the intestinal-brain axis, various modulation mechanisms are well established (e.g., alteration of mucus and biofilm production, motility, permeability and immune function [START_REF] Carabotti | The gut-brain axis: Interactions between enteric microbiota, central and enteric nervous systems[END_REF], no mechanism underlying the particular microbial signature in patients with mental disorders has been studied or even envisaged in the many studies included in this review.

Limitations

Although the studies in our review argue for an interrelation between oral and mental pathologies, they should not be over-interpreted due to numerous limitations. The studies are based on relatively small samples and cross-sectional surveys that allow only hypotheses about the existence of an oral-brain axis. The small size of these surveys prevented the subdivision of participants into phenotypic subtypes of their mental disorders. Schizophrenia and mood disorders were not studied. The studies were not designed to take into account the progressive nature of oral dysbiosis and mental disorders over time. Thus, most of the findings still appear to be preliminary, as generally acknowledged by their authors.

The difficulties of diagnosis of psychiatric disorders [START_REF] Kinderman | Drop the language of disorder[END_REF] and the absence of consensus in the definition of the principal oral dysbiosis [START_REF] Leroy | Methodological issues in epidemiological studies of periodontitis-How can it be improved?[END_REF] have led to heterogeneity of the patients' populations between the various studies. In the same way, the methodological variations in the collection of the bacterial samples and the targeted species induce heterogeneity of the results. In this context, it is difficult to have a precise idea of the role of the oral microbiome in the pathophysiology of mental health disorders.

Finally, the evidence for a two-way causal link between the oral microbiota and mental disorders is limited in humans due to a lack of analysis of confounding factors. While age and gender are sometimes considered, important parameters such as lifestyle habits (e.g., smoking, diet, oral hygiene) or functional or immune disorders related to mental disorders or somatic pathologies are rarely taken into account in the analysis.

Perspectives

To clarify the nature of the link between the oral microbiota and the CNS, it appears essential to develop and validate a methodological approach based on a clear definition of oral dysbiosis and the mental disorders studied.

Only follow-up over time will shed light on the link between the oral microbiome and the various psychiatric disorders and will make it possible to take into account their evolution over the life of the patients. To confirm the existence of an oral-brain axis, a prospective study in a cohort of sufficient size should evaluate the role of the different confounding factors reflecting the entanglement between mental disorders and oral dysbiosis (level of oral hygiene, oral monitoring, various medications).

As suggested by the work on the gut-brain axis, it can be assumed that the identification of a particular microbiome associated with a specific mental disorder might eventually constitute an objective complementary diagnostic element of the disease. In the same way, if the bidirectional link between the oral microbiome and the CNS were confirmed, a rebalancing of microbial homeostasis through the use of probiotics could represent a potential therapeutic axis.

Conclusions

Our study argues for correlations between oral microbiota and AD, dementia or cognitive disorders, ASDs, DS, mental retardation, and bipolar disorders. This field remains little explored, and further studies are needed with a larger sample size involving different type of mental disease are required to clarify the biological link or interconnections between the oral microbiota and all mental health disorders and to develop consistent patterns to generate more concrete data.

The concept of the oral brain axis is an area with growing interest that is likely to facilitate the diagnosis of mental disorders by providing novel disease-specific biomarkers. Future research efforts should focus on developing new therapeutic approaches for better patient management, even though there is still a lot to learn about the oral microbiome, and its potential reaction to therapeutic manipulation. While the literature represents a basis for a reciprocal interaction between the oral microbiome and the brain in the context of mental disorders, the exploratory nature of the studies and their many limitations underline the importance of supporting research in this field.

[Figure 1 :Figure 1 .

 11 Figure 1: Flow chart of included studiesFigure 1. Flow chart of included studies.

Table 1 .

 1 Summary of studies that have examined the relationship between oral microbiota and mental disorders.

	Reference(s)	Study Design	Mental Disorder	Objectives	Involved Species	Mains Results and Limitations (*)
						Early-onset periodontitis in DS is
						mainly due to the more susceptible
	Amano et al., 2001 [64] (n = 67)	Cross sectional	Down syndrome	Comparison of bacterial prevalence in samples of subgingival plaque and detection of Pg fimA genotypes in DS patients and non-DS subjects with mental disabilities.	A. actinomycetemcomitans, P. gingivalis, B. forsythus, T. denticola, P. intermedia, P. nigrescens, C. ochracea, C. sputigena, C. rectus, E. corrodens	host for the causative microbial agents including P. gingivalis with type II fimA. * Need to develop genomic analyses to better detect allelic modulations and specific bacterial polymorphisms involved in the
						development of early periodontitis
						in DS patients.
						Presence of oral Treponema in the
						trigeminal ganglia, the brainstem,
						and the cortex of human subjects
						with AD.
	Riviere et al., 2002 [48] (n = 34)	Cross sectional	Alzheimer's disease Cognitive disorders Dementia	Assessment of the oral treponema presence in the human brain, the hippocampus and the trigeminal ganglia in AD patients and controls.	T. amylovorum, T. denticola, T. maltophilum, T. medium T. pectinovorum, T. socranskii, T. vincentii	AD patients were more likely to have Treponema than controls, and they had more different Treponema species in brain
						than controls.
						* Postmortem contamination of
						tissues or assays cannot
						be excluded
						The score of Sm in saliva was
	Linossier et al., 2008 [67] (n = 59/60/60)	Cross sectional	Down syndrome and Mental retardation	Comparison of the concentration and serotype of Sm in the saliva of people with DS, mentally retarded people and healthy controls	S. mutans	higher in DS and mental retarded than in controls. * The deficient hygiene in DS and mental retardation could lead to a wider colonization of the biofilm by
						these bacteria

Reuland-Bosma et al., 2001 [65] (n = 17/17) Cross sectional Down syndrome Investigation of the subgingival microflora in DS subjects and other mentally retarded individuals. Investigation of the subgingival microflora of a "low-risk" and a "high-risk" group formed in DS subjects. A. actinomycetemcomitans, P. gingivalis, P. intermedia, B. forsythus, P. micros, F. nucleatum, C. rectus The higher prevalence of periodontal disease in DS subjects is probably related to the impaired host-response and not to the occurrence of specific periodontal pathogens. * Insufficient consideration of patient age.

Table 1 .

 1 Cont.

	Reference(s)	Study Design	Mental Disorder	Objectives	Involved Species	Mains Results and Limitations (*)
				Test the hypothesis that concentration		AD patients have both elevated
				of TNF α and antibodies raised to		cytokine expression and antibodies
	Kamer et al., 2009 [54] (n = 18/16)	Case-control	Alzheimer's disease Cognitive disorders Dementia	periodontal bacteria would be more elevated in AD compared to normal controls. Investigation of TNF-alpha	A. actinomycetemcomitans, T. forsythia, P. gingivalis	to periodontal bacteria. These measures could contribute to the diagnosis of AD.
				and antibodies as diagnostic		* Small sample size and
				biomarkers for AD.		study design
						Association between a serological
						marker of a common periodontitis
	Noble et al., 2009 [56] (n = 2355)	Cross sectional	Alzheimer's disease Cognitive disorders Dementia	Assessment of the relationship between systemic exposure to periodontal pathogens and cognitive test outcomes.	P gingivalis	pathogen (Pg immunoglobulin G) and poor cognitive test performance. * Difficulty in assessing cognition and the impact of socioeconomic
						status throughout life on the
						prevalence of periodontal disease.
						Association between the carriage of
						the IL-1 rare alleles and
						periodontitis differed between
				Investigation of the distribution of		Down syndrome and
	Khocht et al., 2011 [66] (n = 44/66/83)	Cross sectional	Down syndrome	IL-1 genotypes' in a DS population and examine the association of IL-1 polymorphism with their	Not relevant	healthy patients. DS individuals are more susceptible to periodontal loss of
				periodontal status.		clinical attachment than
						non-Down individuals.
						* Lack of evaluation of the immune
						characteristics of patients.
						Possible role of inflammatory
	Rai et al., 2012 [49] (n = 55/32)	Cross sectional	Alzheimer's disease Cognitive disorders Dementia	Evaluation of the role of inflammatory mediators between periodontitis and dementia.	Not relevant	mediators between periodontitis and dementia. * Hospital patient selection, study
						design, small sample size.

Table 1 .

 1 Cont.

	Reference(s)	Study Design	Mental Disorder	Objectives	Involved Species	Mains Results and Limitations (*)
	Khocht et al., 2012 [68] (n = 212)	Cross sectional	Down syndrome	Determine the subgingival microbial profile in adult-aged individuals with DS. Investigation of the subgingival microbial profile of Down syndrome adults matched with non-DS mentally retarded subjects and mentally normal subjects. Assessment of the association between bacterial species and loss of clinical periodontal attachment in individuals with and without DS.		Similarities between the subgingival microbial composition of individuals with and without DS. Individuals with DS show higher levels of some bacterial species and specific associations between certain bacterial species and loss of periodontal attachment. * Lack of evaluation of the impact of the specific immune status of DS patients.
	Poole et al., 2013 [52] (n = 10)	Cross sectional	Alzheimer's disease Cognitive disorders dementia	Investigation of the link between periodontal disease and AD with a view to identifying the major periodontal disease bacteria and/or bacterial components in brain tissue from 12 h post-mortem delay.	T. denticola, T. forsythia, P. gingivalis	Lipopolysaccharide from Pg can access the AD brain during life suggested an inflammatory role in the existing AD pathology. * Small sample size.
						Periodontal disease progression
						tended to be associated with an
						increased number of
						lacunar infarctions.
	Taguchi et al., 2013 [53] (n = 110)	Cross sectional	Alzheimer's disease Cognitive disorders Dementia	Evaluation of the associations between tooth loss, chronic oral inflammation and asymptomatic lacunar infarction.	Not relevant	* Hospital patient selection, study design, small sample size, uncertain reproducibility of measure of periodontal defects intra-and interexaminer, and lack
						of consideration of other risk
						factors associated with deficient
						infarction (hypertension and high
						total plasma homocysteine).

Table 1 .

 1 Cont.

	Reference(s)	Study Design	Mental Disorder	Objectives	Involved Species	Mains Results and Limitations (*)
					P. gingivalis, T. forsythia,	Serum IgG high concentrations to
	Noble et al., 2014 [55] (n = 110/109)	A case-cohort	Alzheimer's disease Cognitive disorders Dementia	Evaluation of the serum IgG directed against periodontal microbiota as possible predictors of incident AD.	A. actinomycetemcomitans Y4, T. denticola, C. rectus, E. nodatum, A. naeslundii	common periodontal microbiota represents a risk factor for developing incident AD.
					genospecies-2	* Small sample size.
						The collagen binding activity of
						cnm-positive Sm was a risk factor
				Evaluation of the impact of Sm		to the occurrence of deep cerebral
	Watanabe et al., 2016 [59] (n = 279)	Cross sectional	Alzheimer's disease Cognitive disorders Dementia	expression of the Cnm protein on the localization of cerebral microbleeds and its consequences on	S. Mutans	microbleeds and may be a risk factor for cognitive impairment. * Small sample size, study design,
				cognitive decline.		institutional recruitment and
						limited evaluation of
						cognitive deficit.
	Sochocka et al., 2017 [50]	Cross sectional	Alzheimer's disease Cognitive disorders	Evaluation of the correlation between periodontal health	Not relevant	The presence of cognitive decline and the additional source of proinflammatory
						mediators, like periodontal health
						problems, aggravate the systemic
				status and cognitive abilities with relative changes in systemic	inflammation and
	(n = 128)		Dementia	measures of pro-inflammatory and anti-inflammatory cytokines as	neurodegenerative lesions.
				a reflection of systemic inflammation.		* Biases associated with the
						statistical definition of level of
						inflammatory state.
						Identification of distinct oral
						microtranscriptomic activity in
						ASD children relative to both
				Evaluation of oral microbial taxa in		typically developing controls peers
	Hicks et al., 2018 [62] (n = 180/106/60	Cross sectional	Autism spectrum disorder	children with ASD, nonautistic developmental delay and	Oral bacterial taxa	and nonautistic peers with developmental delay.
				typically developing.		* Failure to take into account
						confounding factors
						(gastrointestinal disorders,
						social behaviour).

Table 1 .

 1 Cont.

	Reference(s)	Study Design	Mental Disorder	Objectives	Involved Species	Mains Results and Limitations (*)
	Ilievski et al., 2018 [51] (n = 10/10)	longitudinal with mice.	Alzheimer's disease	Test the hypothesis that repeated exposure of wild type C57BL/6 mice to orally administered Pg results in neuroinflammation, neurodegeneration, microgliosis, astrogliosis and formation of intra-and extracellular amyloid plaque and neurofibrillary tangles.	P. gingivalis	Pg/gingipain was detected in the hippocampi of mice exposed Neuropathological features of AD have been observed in young adult mice after repeated oral application of Pg * No direct or indirect mechanism that could explain these changes could be identified.
						Identification of oral microbial taxa
	Qiao et al., 2018 [61] (n = 32/27)	Cross sectional	Autism spectrum disorder	Exploration of the differences in the salivary and dental microbiota between children with ASD and healthy control.	Oral bacterial taxa	associated with ASD. Identification of characteristic differences in salivary and dental microbiota between people with ASDs and healthy people.
						* Small sample size, study design.
						A specific microbial signature in
						the stool and salivary microbiota is
	Bajaj et al., 2019 [60] (n = 279)	Cross sectional	Alzheimer's disease Cognitive disorders Dementia	Determination of the gut and salivary microbial profiles of patients with and without MHE.	Oral bacterial taxa	associated with individual cognitive impairment in patients with MHE due to cirrhosis. * Study design, small sample size,
						Non-differentiation of initial or
						recurrent cases of MHE.
						Individuals with bipolar affective
						disorder presented higher
				Evaluation of the epidemiological		frequency of Aa and Pg.
	Cunha et al., 2019 [69] (n = 176/176)	Case-control	Bipolar disorders	and microbiological aspects of the potential association between bipolar	A. actinomycetemcomitans, T. denticola, P. gingivalis	* Small sample size, Study design preventing the detection of any
				affective disorder and periodontitis.		temporal influence among bipolar
						disorders, periodontal condition
						and microbiological findings.
						Pg and gingipains in the brain play
				Investigation of the prevalence of Pg		a central role in the pathogenesis of
	Dominy et al., 2019 [57]	Experimental study conducted with mice	Alzheimer's disease Cognitive disorders Dementia	in the AD brain and to elucidate possible Pg dependent mechanisms of action for neurodegeneration and	P. gingivalis	AD. Gingipain inhibitors could be valuable for treating Pg brain colonization and
				AD pathology.		neurodegeneration in
						Alzheimer's disease.

Table 1 .

 1 Cont.

	Reference(s)	Study Design	Mental Disorder	Objectives	Involved Species	Mains Results and Limitations (*)
						Identified distinct features of gut
						and salivary microbiota that differ
				Characterization of oral and		between individuals with and
	Kong et al., 2019 [63] (n = 20/19)	Cross sectional	Autism spectrum disorder	intestinal microbiomes of patients with ASD compared to	Oral bacterial taxa	without an ASD diagnosis. * Large inter-individual variability
				neurotypical patients.		induced by the use of both sibling
						and parental as neurotypical
						controls, small sample size.
						No evidence that periodontitis is a
						causative factor of AD and genetic
						responsibility for AD on the risk of
						periodontitis from the analysis of
						data from the Genome-Wide
				Examination of the potential causal		Association Studies on
	Sun et al., 2020 [58] (n = 4924 /7301)	A bidirectional Mendelian randomization study	Alzheimer's disease Cognitive disorders Dementia	relationship between chronic periodontitis and AD bidirectionally in the population of	Not relevant	periodontitis and AD. * Impossibility in the case of Mendelian randomisation to assess
				European ancestry.		the impact of the duration of the
						periodontal disease on the risk of
						developing AD and risk of no
						detection to the causal link between
						PD and AD induced by the genetic
						tool used to define PD.

AD: Alzheimer's disease; ASD: Autism spectrum disorder; DS: Down syndrome; MHE: Minimal hepatic encephalopathy; PD: Periodontal disease; Pg: Porphyromonas Gingivalis, Sm: Streptococcus mutans; Aa: Aggregatibacter actinomycetemcomitans; TNF: Tumor Necrosis Factor; Il: Interleukin. *: Limitations.

J. Clin. Med. 2020, 9, 3876; doi:10.3390/jcm9123876 www.mdpi.com/journal/jcm

A. gerencseriae, A. israelii, A. naeslundii, A. naeslundii, A. odontolyticus, V. parvula, S. gordonii, S. intermedius, S. mitis, S. oralis, S. sanguinis, A. actinomycetemcomitans, C. gingivalis, C. ochracea, C. sputigena, E. corrodens, C. gracilis, C. rectus, C. showae, E. nodatum, F. nucleatum ss nucleatum F. nucleatum ss polymorphum, F. nucleatum ss vincentii, F. periodonticum, P. micra, P. intermedia, P. nigrescens, S. constellatus, T. forsythia P. gingivalis, T. denticola, E. saburreum, G. morbillorum, L. buccalis, N. mucosa, P. acnes, P. melaninogenica, S. Anginosus, S. noxia, T. socranskii

This research received no external funding.


Michael Döhler
email: michael.doehler@inria.fr

QUANTIFICATION OF STATISTICAL UNCERTAINTIES IN SUBSPACE-BASED OPERATIONAL MODAL ANALYSIS AND THEIR APPLICATIONS

Keywords: Uncertainty quantification, subspace methods, (operational) modal analysis, monitoring

Quantification of statistical uncertainties in subspace-based operational modal analysis and their applications

INTRODUCTION

The identification of dynamic system characteristics from vibration measurements is a fundamental task in engineering. Amongst others, subspace-based system identification methods are well-suited for this purpose. They identify the system matrices of a linear time-invariant state-space model that describes the dynamic system behavior [START_REF] Van Overschee | Subspace Identification for Linear Systems[END_REF], from which the modal parameters are retrieved. The estimates based on data are inherently afflicted with statistical uncertainties due to the unknown ambient excitation, measurement noise and limited data length. The quantification of these uncertainties is tied to the deployed identification method. However, the subspace identification methods only produce point estimates but not their related confidence bounds.

The objective for uncertainty quantification is to obtain the modal parameter estimates and their confidence bounds from the same dataset. While the statistical properties of estimates from subspace methods have been analyzed in great detail in the automatic control literature in the past, e.g. in [START_REF] Bauer | Consistency and asymptotic normality of some subspace algorithms for systems without observed inputs[END_REF][START_REF] Chiuso | The asymptotic variance of subspace estimates[END_REF][START_REF] Bauer | Asymptotic properties of subspace estimators[END_REF], the expressions therein cannot be directly used for an actual covariance estimation in practical applications, since they require in addition e.g. the estimation of the unknown states and their covariances, which are not computed in the modal parameter estimation. A different approach was proposed in [START_REF] Reynders | Uncertainty bounds on modal parameters obtained from stochastic subspace identification[END_REF], where the covariance of estimated parameters is computed easily from the sample covariances of the underlying output data covariances and their related sensitivities.

The sensitivity-based covariance propagation is a simple and powerful tool for uncertainty quantification, and is theoretically justified by the statistical delta method [START_REF] Casella | Statistical Inference (2nd)[END_REF]. It states that a function of an asymptotically Gaussian variable is also asymptotically Gaussian if its sensitivity is non-zero, and gives the respective covariance expression. Since the output covariances that are the basis of any subspace method are asymptotically Gaussian, this strategy can be used for characterizing the statistical distributions and in particular the covariance of the modal parameters and functions thereof.

This paper summarizes some of the developments for uncertainty quantification in the context of subspace methods from the last 15 years. In the first part, theoretical and algorithmic developments are presented regarding the uncertainty quantification of modal parameters for diverse subspace methods, their efficient implementation and the uncertainty quantification of the related modal indicators. In the second part, modal-parameter based methods are presented where the uncertainty information of the underlying modal parameter estimates is integrated, enhancing the originally deterministic methods.

BACKGROUND OF SUBSPACE-BASED SYSTEM IDENTIFICATION AND UNCERTAINTY QUANTIFICATION

In this section, the subspace-based system identification method for modal analysis and the associated uncertainty quantification framework are outlined. The schematics of the framework are presented in Fig. Assume that the vibration behavior of the investigated structure can be modelled by a linear timeinvariant system, and that in the simplest case only outputs are measured while inputs (acting forces) are unknown. Then the system dynamics can be described by the discrete-time state space model

x k+1 = Ax k + w k y k = Cx k + v k , ( 1
)
where A is the state transition matrix, C is the output matrix, and k is the integer time step corresponding to the system at time t = k∆t, where ∆t is the sampling rate. Vector y k ∈ R r contains the measured outputs (such as accelerations, velocities, displacements, strains), and x k ∈ R n is the state vector. The state noise w k ∈ R n is related to the unknown ambient excitation, and vector v k ∈ R r is the output noise.

The modal parameters are related to the eigenvalues and eigenvectors (λ i , φ i ), i = 1, . . . , n, of A and to C by

µ i = log(λ i ) ∆t , f i = |µ i | 2π , ζ i = -Re(µ i ) |µ i | , ϕ i = Cφ i , (2)
where µ i is an eigenvalue of the corresponding continuous-time system, f i is the natural frequency, ζ i is the damping ratio and ϕ i is the mode shape at the output coordinates.

To estimate the matrices A and C from the output data y k of length N , k = 1, . . . , N , and consequently the modal parameters in (2), subspace methods are used. They are based on projecting (or simply multiplying) data Hankel matrices with a future and a past time sample horizon obtaining some matrix Ĥ, such that a consistent estimate of the system's observability matrix can be obtained from the column space of Ĥ. The respective data Hankel matrices can be defined as

Y -= 1 √ N     
    
, where Y -can be built also from a subset of reference sensors or projection channels but not necessarily from all sensors.

There are many subspace methods in the literature [START_REF] Van Overschee | Subspace Identification for Linear Systems[END_REF][START_REF] Benveniste | Nonstationary consistency of subspace methods[END_REF] with different ways to compute Ĥ, but from which the modal parameters are retrieved in the same way. For example, the covariance-driven subspace algorithm [START_REF] Peeters | Reference-based stochastic subspace identification for outputonly modal analysis[END_REF] computes Ĥ = Y + Y -T , which corresponds to a matrix containing the output covariances of the data for different time lags. Their theoretical values satisfy the decomposition

H = OC, where O =      C CA . . . CA p-1      (3)
with the observability and stochastic controllability matrices O and C. With the singular value decomposition (SVD) truncated at the desired model order

Ĥ = U 1 U 0 S 1 0 0 S 0 V T 1 V T 0 , (4)
an estimate Ô = U 1 S 1/2 1
of the observability matrix is obtained. Then, the output matrix C is estimated from the first block row of the observability matrix, and the state transition matrix is estimated from the shift-invariance property in a least-squares sense as  = ( Ô↑ ) † Ô↓ , where Ô↑ and Ô↓ are the observability matrix estimate without the last and first block row, respectively. Ultimately, the modal parameters are obtained from the eigenvalues and eigenvectors of  and from Ĉ as in [START_REF] Bauer | Consistency and asymptotic normality of some subspace algorithms for systems without observed inputs[END_REF].

In engineering practice the modal parameters are obtained at different model orders by successively truncating the SVD in (4) and interpreted in so-called stabilization diagrams with the goal to separate (stable) physical modes from spurious ones. An efficient procedure for the multi-order modal parameter estimation can be achieved by exploiting the structure of the least-squares problem at multiple model orders for estimating Â, as detailed in [START_REF] Döhler | Fast multi-order computation of system matrices in subspacebased system identification[END_REF].

Uncertainty quantification

The delta method is a statistical tool that helps to estimate the covariance of a function of an asymptotically Gaussian variable [START_REF] Casella | Statistical Inference (2nd)[END_REF]. It is used to propagate the sample covariance of the data-related covariances that are computed in the first step of the subspace algorithms through all steps of the algorithm down to the modal parameters or functions thereof. Finally, confidence intervals of the computed parameters can be derived.

The first step of the subspace algorithms involves data projections that involve the computation of output covariances. If inputs (e.g. due to artificial excitation) are available in addition to the measured outputs, then this step also involves input/output covariances of the data. These data-related covariances are asymptotically Gaussian, i.e., √

N ( R -R) → N (0, Σ R )
where R is a vector containing all covariance estimates involved in the chosen subspace method. An estimate ΣR of the covariance can be easily evaluated by the sample covariance based on partitions of the available data. The propagation of this covariance to the modal parameter estimates is then based on the delta method, stating that a function

Ŷ = f ( R) is also asymptotically Gaussian with √ N ( Ŷ -Y ) → N (0, J Y,R Σ R J T Y,R ).
The derivative J Y,R of the function with respect to R is obtained from perturbation theory. For a firstorder perturbation it holds ∆Y ≈ J Y,R ∆R. Hence, perturbing the functional relationship between R and Y analytically and neglecting higher-order terms yields the desired derivative, in particular for cases where the functional relationship is not explicit like for the SVD or eigenvalue decomposition. Subsequently, covariance expressions for the estimates satisfy

ΣY ≈ ĴY,R ΣR Ĵ T Y,R . (5)
With this principle, the uncertainties of the output covariances from the first step of the subspace method can be propagated step by step through the algorithm down to the modal parameters and related quantities. Finally, confidence intervals of the estimates can be established based on the computed covariance and the fact that the distribution of the estimates can be approximated as Gaussian. For example, if Ŷ is the vector containing the modal parameter estimates, then the covariance of each component Ŷi is related to the respective component σ2 Y i on the diagonal of the asymptotic covariance estimate ΣY , and the 95% confidence interval is given by

( Ŷi -2 • 1 √ N σY i , Ŷi + 2 • 1 √ N σY i ),
i.e. this interval contains the true value Y i of the estimate Ŷi with a probability of 95%. To illustrate the Gaussian character of the modal parameter estimates in a practical setting, histograms of the first frequency and damping ratio are shown in Fig. 2 that are obtained from 100 datasets containing experimental data of a wind turbine blade [START_REF] Greś | Uncertainty quantification of modal parameter estimates obtained from subspace identification: An experimental validation on a laboratory test of a large-scale wind turbine blade[END_REF], together with their mean Gaussian approximation provided by the delta method. It can be seen that the Gaussian approximation is appropriate, and that the modal parameter covariance estimated from one dataset (on which the mean fit is based in the figures) describes well the empirical distribution from the histogram.

THEORY AND ALGORITHMIC DEVELOPMENTS

Efficient implementation and uncertainty quantification in stabilization diagrams

The algorithm for uncertainty quantification of modal parameters from covariance-driven subspace identification has been proposed in [START_REF] Reynders | Uncertainty bounds on modal parameters obtained from stochastic subspace identification[END_REF], where the involved analytical sensitivities for the covariance propagation as well as the initial sample covariance are derived. However, in its direct implementation the size of the involved covariance matrices is considerable, which makes it computationally taxing and causing memory problems even for moderately sized problems. To alleviate this problem, a memory efficient and fast computation scheme for this method has been developed in [START_REF] Döhler | Efficient multi-order uncertainty computation for stochastic subspace identification[END_REF] based on a mathematical reformulation of the algorithm, where in particular the structure of the the initial sample covariance estimate is exploited. Moreover, the covariance computation is optimized for multiple model orders in the stabilization diagram in [START_REF] Döhler | Efficient multi-order uncertainty computation for stochastic subspace identification[END_REF], where the fact is exploited that the first columns of the observability matrix estimate at a higher model order are identical to the observability matrix estimate at a lower model order due to the SVD in [START_REF] Bauer | Asymptotic properties of subspace estimators[END_REF]. In this way, redundant operations in the computation of the stabilization diagram uncertainties can be avoided, and the algorithmic speed increased by two orders of magnitude of the maximal model order compared to a direct implementation, resulting in computation times of less than a minute for typical problem sizes.

In Fig. 3 The uncertainty information of the modal alignments in the diagram can then be used to obtain global mode estimates [START_REF] Döhler | Variance computation of modal parameter estimates from UPC subspace identification[END_REF], and to actually obtain the modal alignments by automated statistical clustering approaches [START_REF] Priou | Automated uncertainty-based extraction of modal parameters from stabilization diagrams[END_REF].

Uncertainty quantification for diverse subspace methods

The family of subspace methods is big, including covariance-driven and data-driven methods, methods for output-only (stochastic) system identification, and methods for input/ouput (combined deterministicstochastic) for the case where some of the inputs are known. The uncertainty quantification strategy for the above-mentioned covariance-driven subspace method has been extended to a wide range of different subspace methods in [START_REF] Mellinger | Variance estimation of modal parameters from output-only and input/output subspace-based system identification[END_REF] for the purpose of modal parameter uncertainty quantification.

The main difficulty in the extension to other subspace methods lies in the link between the matrix Ĥ and the data-related covariance matrices, in order to perform the first step of uncertainty propagation. The covariance-driven subspace method is the simplest of the subspace methods for uncertainty quantification, since it only depends on one data-related covariance matrix Y + Y -T . The sample covariance of this matrix is then propagated throughout the method. In other subspace methods, the construction of the initial 'projection matrix' Ĥ, from which the observability matrix is obtained, is more complex. For 'data-driven' methods like UPC [START_REF] Van Overschee | Subspace Identification for Linear Systems[END_REF][START_REF] Peeters | Reference-based stochastic subspace identification for outputonly modal analysis[END_REF], the projection is not immediately linked to output covariances, but is a matrix that grows with the number of data samples. However, it can be shown that the observability matrix can be equivalently related to Ĥ ĤT for the purpose of uncertainty propagation, which is again 'covariance-driven'. For the case of UPC where Ĥ = Y + Y -T (Y -Y -T ) -1 Y -, the algorithm depends on two data-related covariance matrices, namely Y + Y -T and Y -Y -T . In the presence of known inputs, matrix Ĥ depends furthermore on covariance matrices between outputs and inputs, and between inputs.

In [START_REF] Mellinger | Variance estimation of modal parameters from output-only and input/output subspace-based system identification[END_REF], the related uncertainty quantification schemes are developed for different classes of subspace methods, namely

• Output-only orthogonal projection data-driven algorithm (UPC),

• Input/output covariance-driven algorithm,

• Input/output orthogonal projection data-driven (similar to MOESP),

• Input/output oblique projection data-driven (N4SID).

The developed strategies allow an easy extension also to other subspace methods. While the system matrices A and C and the related modal parameters are obtained from the observability matrix in these methods, there is an alternative way to obtain them based on the state sequences in data-driven subspace methods like UPC, for which the uncertainty quantification scheme has been developed recently in [START_REF] Reynders | Uncertainty quantification in data-driven stochastic subspace identification[END_REF].

With the availability of input data, the system matrices B and D of the related input/output state space model can be identified in addition to matrices A and C. With the knowledge of these matrices, the parametric transfer function can be obtained. The associated uncertainties for B and D, and the phase and magnitude of the transfer function have been obtained in [START_REF] Greś | Uncertainty quantification of input matrices and transfer function in input/output subspace system identification[END_REF], showcased in Fig. 4. It can be seen that the computed confidence intervals coincide well with the empirical ones in a Monte Carlo simulation.

Uncertainty quantification of modal indicators

Modal indicators like the Modal Assurance Criterion (MAC) and the Modal Phase Collinearity (MPC) are computed from mode shapes and thus inherit their statistical uncertainties when computed from measurement data. Hence, they will never be exactly one (indicating a perfect mode shape match, or a perfectly real-valued mode shape), but only close to one. Hence, the quantification of the statistical uncertainties is required in order to evaluate if the modal indicators are significantly close to one or not.

The particular difficulty in uncertainty quantification of the modal indicators is their boundedness in the interval [0, 1]. When the theoretical value is one, e.g., when the MAC is evaluated for identical mode shapes or when the MPC is evaluated for a real-valued mode shape, then the distribution of the corresponding estimates accumulates near one and is not Gaussian anymore. Hence the previous first-order framework for uncertainty quantification cannot be used anymore. In [START_REF] Greś | Uncertainty quantification for the Modal Phase Collinearity of complex mode shapes[END_REF][START_REF] Greś | Uncertainty quantification of the Modal Assurance Criterion in operational modal analysis[END_REF] the distribution properties of the MPC and MAC estimates have been derived, as well as the respective confidence intervals. It turns out that the distributions for theoretical values at the border of the interval (i.e., for MAC or MPC equal to one) can be described by means of the second-order delta method, where the distributions can be approximated by a scaled and shifted χ 2 distribution, whereas in the inside of the interval [0, 1] the distributions are asymptotically Gaussian, as illustrated in Fig. 5.

Validation

The presented methods for uncertainty quantification of the modal parameters and the modal indicators have not only been extensively validated in simulation studies, but also on experimental data. A first validation of the uncertainties obtained from the covariance-driven subspace methods was reported in [START_REF] Reynders | Uncertainty quantification in operational modal analysis with stochastic subspace identification: Validation and applications[END_REF] using data of a bridge and of a building from different sensor setups. More recently, an extensive validation study on a laboratory test of a large-scale wind turbine blade was carried out in [START_REF] Greś | Uncertainty quantification of modal parameter estimates obtained from subspace identification: An experimental validation on a laboratory test of a large-scale wind turbine blade[END_REF] based on 100 experimental data sets, covering all of the presented subspace methods and modal indicators. The results confirm that the delta method is, on average, adequate to characterize the distribution of the considered estimates from all the different methods solely based on the quantities obtained from one data set, validating the use of this statistical framework for uncertainty quantification in practice.

Some case studies

Modal parameter uncertainties are particularly useful in the monitoring of structures over time. Some large scale case studies have been reported where the modal parameter uncertainty has been evaluated. One example is the S101 Bridge [START_REF] Greś | Uncertainty quantification of the Modal Assurance Criterion in operational modal analysis[END_REF][START_REF] Döhler | Structural health monitoring with statistical methods during progressive damage test of S101 Bridge[END_REF], where damages were introduced to the bridge while measurement data was collected continuously during four days. The role of the modal parameter uncertainties was evaluated in [START_REF] Pereira | The role of modal parameters uncertainty estimation in automated modal identification, modal tracking and data normalization[END_REF] for the monitoring the Baixo Sabor arch dam during several years, where it was concluded that the uncertainties are particularly useful for removing outliers in the modal parameter tracking. In [START_REF] Nord | Stochastic subspace identification of modal parameters during ice-structure interaction[END_REF], the accuracy of the uncertainty estimates during ice-structure interaction was evaluated, and applied to monitoring data of a lighthouse.

UNCERTAINTIES IN MODAL PARAMETER-BASED METHODS

Modal parameters and modal indicators are used in many engineering applications. Instead of using their point estimates only, the uncertainties of the estimates are an additional valuable information that can enhance methods. In this section two examples are given where the quantified modal parameter uncertainties are integrated into originally deterministic methods, namely for damage localization and for finite element model updating. Furthermore, some application cases are briefly presented.

Flexibility evaluation and DLV-based damage localization

The damage locating vector vector approach [START_REF] Bernal | Load vectors for damage localization[END_REF] computes originally a vector in the null space of the change of flexibility matrix that is computed from input/output measurement data from the reference and from the damaged states, and then applies it as a load (at the sensor coordinates) to a finite element model of the structure to compute the stress field. Damage is located where the resulting stress is zero. The approach has been generalized the output-only case [START_REF] Bernal | Load vectors for damage location in systems identified from operational loads[END_REF], where the required load vector is computed from the null space of the transfer matrix difference, which can be evaluated from the modal parameters solely.

Instead of evaluating the resulting stress deterministically to decide if it is zero or not over a structural component, a statistical evaluation is made in [START_REF] Döhler | Statistical decision making for damage localization with stochastic load vectors[END_REF][START_REF] Marin | Robust statistical damage localization with stochastic load vectors[END_REF][START_REF] Bhuyan | Statistical damage localization with stochastic load vectors using multiple mode sets[END_REF] where the modal parameter uncertainty is propagated to the computed stress field and used for a decision with hypothesis tests. The method has been extended the case of changing temperature in [START_REF] Bhuyan | Vibration-based damage localization with load vectors under temperature changes[END_REF], where the temperature influence is removed from the modal parameters. In these works it has been shown that the performance of the damage localization is largely increased when considering the modal parameter uncertainties, as illustrated in Fig. 6. It can be seen that the rate of successful damage localization is always higher when the considering the uncertainties in the statistical tests compared to the deterministic evaluation of the stress estimates. In a related work [START_REF] Li | Identification and uncertainty quantification of structural flexibility for reliability analysis[END_REF], the uncertainty of the modal parameters as well as assumed uncertainties of finite element model parameters have been propagated to the flexibility matrix estimate and associated computed deflections under static loads with the purpose of reliability analysis.

Finite element model updating

Modal parameters are essential for finite element model updating, and their uncertainties can be valuable for the updating problem. Since the updated model parameters are a function of the modal parameter estimates, the uncertainty of the model parameters due to the uncertainty of the modal parameters can be evaluated by uncertainty propagation. This was carried out in [START_REF] Gautier | Variance analysis for model updating with a finite element based subspace fitting approach[END_REF], where the propagation is performed through each iteration step of the updating minimization problem in a subspace fitting approach. Furthermore, the uncertainties of the modal parameters can be directly considered in the formulation of the objective function as well as in the stopping criterion for the optimization, as developed in [START_REF] Greś | Statistical model-based optimization for damage extent quantification[END_REF]. In this work, model frequencies and mode shapes (via the MAC) are penalized in the objective function when they are outside the confidence bounds of their estimated counterparts, which leads to a steeper objective function. The optimization search can be terminated once the model-based modal parameters are within the confidence bounds of their data-based counterparts, leading to an efficient algorithm for the updating problem.

In Fig. 7, a modal parameter-based objective function is illustrated without and with the consideration of the uncertainties. First of all, it can be seen that the objective function is indeed steeper when considering the uncertainties, which should facilitate the optimization search. Second, it can be seen that the minimum of the objective function (red line) that is computed on the modal parameter estimates is not taken on at the true parameter values (green line) due to the modal parameter uncertainties, but just close to it. This also confirms that convergence of the optimization search to the minimum of the objective function is actually not required, and it is sufficient to stop the search once arrived in the yellow region indicating the values of the objective function where the model-based modal parameters are within the confidence bounds of their estimates.

CONCLUSIONS

The methods for uncertainty quantification in subspace-based operational modal analysis have evolved over the last years, offering computationally efficient tools for a wide range of methods and engineering applications. They also have become part of commercial software [START_REF]ARTeMIS Modal[END_REF]. The methods have shown their adequacy in extensive validation studies as well as in diverse case studies on real structures. Future work on the topic should include, e.g., further integration of the quantified uncertainties in methods for damage diagnosis, including in the data normalization step to remove environmental effects, as well as in data-based reliability analysis.

Figure 1 :

 1 Figure 1: Framework of subspace identification and uncertainty quantification

Figure 2 :

 2 Figure 2: Histograms of modal parameter estimates with the delta method-based Gaussian approximation from [10].

Figure 3 :

 3 Figure 3: Stabilization diagram of Z24 Bridge without (left) and with threshold on standard deviation of frequencies (right).

Figure 4 :

 4 Figure 4: First component of phase and magnitude of H(z) with Monte Carlo and delta method-based confidence intervals from[START_REF] Greś | Uncertainty quantification of input matrices and transfer function in input/output subspace system identification[END_REF].

Figure 5 :

 5 Figure5: Distribution fits of MAC estimates from delta method, together with histograms from Monte Carlo simulation. Left: MAC of estimates of different mode shapes with Gaussian approximation, right: MAC of estimates of equal mode shape with scaled and shifted χ 2 approximation, from[START_REF] Greś | Uncertainty quantification of the Modal Assurance Criterion in operational modal analysis[END_REF].

Figure 6 :

 6 Figure6: Success rates for DLV-based damage localization with and without considering modal parameter uncertainties for different temperature scenarios, from[START_REF] Bhuyan | Vibration-based damage localization with load vectors under temperature changes[END_REF]. Success rates are higher when considering the uncertainties in the evaluation (red vs. black curve, pink vs. blue curve).

Figure 7 :

 7 Figure 7: Modal parameter-based objective function to be minimized in the model updating, for two model parameters in the vicinity of their true values. Without (left) and with consideration of modal parameter uncertainties (right), from [31].

  1.

		Measurements
	Data covariance / projections	Sample covariance of data covariance
	subspace algorithm	analytical sensitivity of subspace algorithm
	Modal parameters	Modal parameter covariance
	Subspace-based modal parameter estimation	Delta method-based uncertainty quantification