Yohann Dabi
email: yohann.dabi@aphp.frtel

Amélia Favier

Léo Razakamanantsoa

Léa Delbos

Mathieu Poilblanc

Philippe Descamps

Francois Golfier

Cyril Touboul

Sofiane Bendifallah

Emile Daraï

Insight on non-coding RNAs from biofluids in ovarian tumors

Keywords: Ovarian tumor, non-coding RNA, borderline ovarian tumor, ovarian cancer

Simple summary: Ovarian cancer is the most lethal gynecologic cancer since often diagnosed at advances stages. Current tools for diagnosis are currently insufficient and include physical examination, ultrasound and pelvic magnetic resonance imaging as well as algorithm combining thoraco-abdomino-pelvic scans and blood markers. In this context, there is a need for new tools not only to assess the diagnosis but also to predict response to chemotherapy and detect recurrences. Previous studies have highlighted the potential value of non-coding RNAs (ncRNA) in tissue samples, but rarely in biofluids. In this review, we aimed to summarize the literature existing on ncRNAs and ovarian tumors in biofluids. Most studies focused on serum and blood with no data in other biofluids and with few ncRNAs investigated using qRT-PCR or microarray, not permitting reflecting the heterogeneity of ovarian cancers.

Abstract: Ovarian tumors are the most frequent raising diagnostic and therapeutic issues linked to a large spectrum of tumors with a continuum from benign to malignant tumors. So far, none of the available diagnostic tools have proven efficient to decide strategy and no consensus exists on the best strategy between 'single test', 'dual testing', 'sequential testing', 'multiple testing options' and 'no testing'. In addition, there is a need of prognostic tool such as biological markers of recurrence and theragnostic tools to detect non-responding women to chemotherapy to adapt therapies. Noncoding non-coding RNAs are classified in small or long based on their nucleotides count. Noncoding RNAs have multiple biological functions such as a role in tumorigenesis, gene regulation and genome protection. These ncRNAs emerge as new potential tools to differentiate benign from malignant tumours and to evaluate prognostic and theragnostic factors. In the specific setting of ovarian tumors, the goal of the present work is to offer an insight on the contribution of biofluid non-coding RNAs (ncRNA) expression.

Introduction

Adnexal masses represent a wide spectrum of tumors of various origins (ovary, fallopian tube, and pelvic organs), among them ovarian tumors are the most frequent raising diagnostic and therapeutic issues linked to a large spectrum of tumors with a continuum from benign to malignant tumors. The true incidence of ovarian tumors in the general population is unknown as most of them are asymptomatic hence undiagnosed [START_REF] Jung | Retrospective evaluation of relevance of care in the management of presumed benign ovarian tumors[END_REF]. It is estimated that 10% of women will undergo surgery for an ovarian mass in their lifetime [START_REF] Bullock | Ovarian Tumors; a Survey of All Surgically Treated Ovarian Tumors in a Large General Hospital over a Ten-Year Period[END_REF].

Ovarian tumors are generally detected at physical examination or at pelvic imaging for various reasons in asymptomatic patients. Less frequently, an ovarian tumor can be source of symptoms, acute pain (torsion of the adnexa), or chronic pelvic pain related to compression of neighboring organs [START_REF] Jung | Retrospective evaluation of relevance of care in the management of presumed benign ovarian tumors[END_REF]. Sometimes, the diagnosis can be made in the context of ovarian cancer (OC) often diagnosed at an advanced stage faced to ascites, bloating, weight loss with peritoneal carcinomatosis [3,[START_REF] Sfog | fr -Société Française d'Oncologie Gynécologie -Un site utilisant WordPress[END_REF].

OC is the fifth cancer and the most lethal gynecologic malignancy with 313,959 new cases per year and 207,252 death per year in 2020 [START_REF] Sung | GLOBOCAN Estimates of Incidence and Mortality Worldwide for 36 Cancers in 185 Countries[END_REF]. Epithelial ovarian cancer (EOC) represents more than 95% of all OC [START_REF] Stewart | Ovarian Cancer: An Integrated Review[END_REF]. During their lifetime, approximately one in seventy women will develop the disease. The median age at diagnosis is 68 years with a maximum incidence in women in their 70s. The disease behaves as a chronic condition with relapses and therefore iterative chemotherapies which lengthen survival [START_REF] Lavoué | Management of Epithelial Ovarian Cancer : French joint recommendations of FRANCOGYN, CNGOF, SFOG, GINECO-ARCAGY and endorsed by INCa. Introduction[END_REF]. The disease survival remains poor of 40% at 5 years and 32% at 10 years as more than 75% of patients are diagnosed at advanced stage disease while the 5-year survival rate for women diagnosed at an early stage reaches 90% underlining the potential benefit of biomarkers of early stages as well as to detect the transition of borderline tumor into invasive cancer [START_REF] Sung | GLOBOCAN Estimates of Incidence and Mortality Worldwide for 36 Cancers in 185 Countries[END_REF].

Except from patients with deleterious mutation for whom a risk reducing surgery is recommended, no screening of OC in the general population has proved its relevance [START_REF] Reiser | Defining Models to Classify between Benign and Malignant Adnexal Masses Using Routine Laboratory Parameters[END_REF]. In routine practice, first line transvaginal ultrasound is used to differentiate benign, borderline or malignant ovarian tumors [START_REF] Froyman | Risk of Complications in Patients with Conservatively Managed Ovarian Tumours (IOTA5): A 2-Year Interim Analysis of a Multicentre, Prospective, Cohort Study[END_REF]. Van Calster et al, evaluating the clinical utility of six prediction models for ovarian malignancy [START_REF] Van Calster | Validation of Models to Diagnose Ovarian Cancer in Patients Managed Surgically or Conservatively: Multicentre Cohort Study[END_REF], found that the ADNEX models with and without cancer antigen 125 (CA125) determination and SRRisk were the best calibrated. However, previous studies have underlined that 18% to 31% of ovarian tumors remain indeterminate after ultrasonography using International Ovarian Tumor Analysis (IOTA) Simple Rules or other ultrasonography scoring systems [START_REF] Froyman | Risk of Complications in Patients with Conservatively Managed Ovarian Tumours (IOTA5): A 2-Year Interim Analysis of a Multicentre, Prospective, Cohort Study[END_REF][START_REF] Meys | Subjective Assessment versus Ultrasound Models to Diagnose Ovarian Cancer: A Systematic Review and Meta-Analysis[END_REF][START_REF] Thomassin-Naggara | Ovarian-Adnexal Reporting Data System Magnetic Resonance Imaging (O-RADS MRI) Score for Risk Stratification of Sonographically Indeterminate Adnexal Masses[END_REF]. MRI is the second line imaging technique to characterize ovarian tumors. Ovarian-Adnexal Reporting Data System Magnetic Resonance Imaging (O-RADS MRI) score consists of 5 categories according to the positive likelihood ratio for a malignant neoplasm [START_REF] Thomassin-Naggara | Masses: Development and Preliminary Validation of an MR Imaging Scoring System[END_REF] with a sensitivity of 0.93 and a specificity of 0.91. However, these results were based on an observational study without randomization, and the score was not integrated into clinical decision-making limiting its utility.

CA125 is the most used biomarker to determine the nature of ovarian tumors [START_REF] Maggino | Prospective Multicenter Study on CA 125 in Postmenopausal Pelvic Masses[END_REF][START_REF] Choi | Comparison of CA 125 Alone and Risk of Ovarian Malignancy Algorithm (ROMA) in Patients with Adnexal Mass: A Multicenter Study[END_REF] although normal levels has been reported in as high as 50% of early stages ovarian cancers [START_REF] Sevinc | Benign Causes of Increased Serum CA-125 Concentration[END_REF] [START_REF] Høgdall | CA125 Expression Pattern, Prognosis and Correlation with Serum CA125 in Ovarian Tumor Patients. From The Danish "MALOVA" Ovarian Cancer Study[END_REF][START_REF] Dunton | Salvaging Detection of Early-Stage Ovarian Malignancies When CA125 Is Not Informative[END_REF]. A recent Cochrane review has evaluated several algorithms to assess the risk of malignancy of ovarian tumors, including biological markers and imaging [START_REF] Davenport | Menopausal Status, Ultrasound and Biomarker Tests in Combination for the Diagnosis of Ovarian Cancer in Symptomatic Women[END_REF]. However, none of these scoring systems had a sufficient relevance to characterize ovarian tumors [START_REF] Davenport | Menopausal Status, Ultrasound and Biomarker Tests in Combination for the Diagnosis of Ovarian Cancer in Symptomatic Women[END_REF].

Finally, a recent review of Funston et al analyzing 18 documents from 11 countries showed that transabdominal/transvaginal ultrasound and the CA125 were the most widely advocated as initial tests [START_REF] Funston | Variation in the Initial Assessment and Investigation for Ovarian Cancer in Symptomatic Women: A Systematic Review of International Guidelines[END_REF]. However, no consensus exists on the best strategy to improve diagnostic performance: 'single test', 'dual testing', 'sequential testing', 'multiple testing options' and 'no testing'. This further underlines the need for new biological tools to diagnose ovarian cancer in the general population as early as possible. In addition, there is a need of prognostic tool such as biological markers of recurrence and theragnostic tools to detect non-responding women to chemotherapy to adapt therapies. Among ncRNAs, those with less than 50 nucleotides are defined as small RNAs (sncRNAs) and those with more than 200 nucleotides are defined as long non-coding RNAs (lncRNAs). SncRNAs are further classified into microRNAs (miRNAs), Piwi interacting RNAs (piRNAs), transfer RNAs (tRNAs), small nuclear RNAs (snRNAs), and small interfering RNAs (siRNAs) [START_REF] Shahrouki | The Non-Coding Oncogene: A Case of Missing DNA Evidence? Front[END_REF][START_REF] Green | Transfer RNA-Derived Small RNAs in the Cancer Transcriptome[END_REF]. LncRNAs are classified into intergenic ncRNAs (lincRNAs), some circular RNAs (circRNAs), and ribosomal RNAs (rRNAs) [START_REF] Cech | The Noncoding RNA Revolution-Trashing Old Rules to Forge New Ones[END_REF][START_REF] Gibb | The Functional Role of Long Non-Coding RNA in Human Carcinomas[END_REF].

Numerous studies indicate that ncRNAs, representing 98% of the transcriptome, are essential for tumorigenesis by regulating the expression of tumour-related genes [START_REF] Fu | Circular RNAs in Hepatocellular Carcinoma: Functions and Implications[END_REF][START_REF] Yang | Long Noncoding RNAs: Fresh Perspectives into the RNA World[END_REF][START_REF] Shen | Transfer RNA-Derived Fragments and TRNA Halves: Biogenesis, Biological Functions and Their Roles in Diseases[END_REF][START_REF]The Functions of Animal MicroRNAs[END_REF][START_REF] Huang | MicroRNA-181a Modulates Gene Expression of Zinc Finger Family Members by Directly Targeting Their Coding Regions[END_REF][START_REF] Ørom | MicroRNA-10a Binds the 5'UTR of Ribosomal Protein MRNAs and Enhances Their Translation[END_REF][START_REF] Doyle | Overview of Extracellular Vesicles, Their Origin, Composition, Purpose, and Methods for Exosome Isolation and Analysis[END_REF][START_REF] Yuan | Plasma Extracellular RNA Profiles in Healthy and Cancer Patients[END_REF].

These ncRNAs emerge as new potential tools to differentiate benign from malignant tumours and to evaluate prognostic and theragnostic factors. In the specific setting of ovarian tumors, the goal of the present work was to offer an insight on the contribution of biofluid non-coding RNAs (ncRNA) expression.

miRNAs

miRNAs are small intracellular RNAs, 22 nucleotides long, capable of inducing the silencing of gene expression by post-transcriptional regulatory mechanisms [START_REF] Bartel | MicroRNAs: Target Recognition and Regulatory Functions[END_REF] or alternatively by binding miRNAs to the 5'UTR regions inducing either activation or repression of translation. The miRNAs synthesis is presented in Figure 1. Numerous studies focusing on tissue samples have demonstrated the role of miRNA in OC characterized by a wide-scale deregulation of miRNAs, and aberrant ex-pression of miRNAs correlated with histotype, histological grade, lymphovascular space involvement, lymph node and distant metastasis as well as FIGO stages [START_REF] Iorio | MicroRNA Signatures in Human Ovarian Cancer[END_REF][START_REF] Dwivedi | Therapeutic Evaluation of MicroRNA-15a and MicroRNA-16 in Ovarian Cancer[END_REF][START_REF] Bhattacharya | MiR-15a and MiR-16 Control Bmi-1 Expression in Ovarian Cancer[END_REF][START_REF] Vang | Identification of Ovarian Cancer Metastatic MiRNAs[END_REF]. Dhar Dwivedi et al reported 53 miRNAs upregulated, and 68 miRNAs downregulated in OC.

In the upregulated miRNAs group, a total of 7605 gene target were found. Among them, miRNA-20a-5p and miRNA 106a-5p regulate 14.1% and 9.4% of target genes, respectively. Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway analysis enrichment was performed for these upregulated miRNAs targets genes identifying 67 and 24 pathways as enriched. Similarly for downregulated miRNAs, a total of 9287 gene targets were identified. miR-26b-5p, miR-519d, miR-15a, and miR-15b regulated respectively 20.8%, 11.3%, 8.6%, and 8.9% of the target genes with 41, 95, and 38 enriched pathways [START_REF] Dwivedi | Small Non-Coding-RNA in Gynecological Malignancies[END_REF].

In contrast to miRNAs expression extensively analyzed in tissue samples, relatively little data are available on their expression in biofluids. This point is particularly important as it could allow preoperative tumor assessment, improving therapeutic strategy and share making decisions. There are published evidences that serum miR-221 [START_REF] Shu | LINC00936/MicroRNA-221-3p Regulates Tumor Progression in Ovarian Cancer by Interacting with LAMA3[END_REF], mir-205 [START_REF] Zhu | Detection of Plasma Exosomal MiRNA-205 as a Biomarker for Early Diagnosis and an Adjuvant Indicator of Ovarian Cancer Staging[END_REF], mir-375 [START_REF] Su | Upregulated Expression of Serum Exosomal MiR-375 and MiR-1307 Enhance the Diagnostic Power of CA125 for Ovarian Cancer[END_REF], mir-210 [START_REF] Shah | Combining Serum MicroRNA and CA-125 as Prognostic Indicators of Preoperative Surgical Outcome in Women with High-Grade Serous Ovarian Cancer[END_REF], mir-34a-5p [START_REF] Robelin | Comparative Analysis of Predictive Values of the Kinetics of 11 Circulating MiRNAs and of CA125 in Ovarian Cancer during First Line Treatment (a GINECO Study)[END_REF], mir-92 [START_REF] Guo | Serum MicroRNA-92 Expression in Patients with Ovarian Epithelial Carcinoma[END_REF], mir-93 [START_REF] Robelin | Comparative Analysis of Predictive Values of the Kinetics of 11 Circulating MiRNAs and of CA125 in Ovarian Cancer during First Line Treatment (a GINECO Study)[END_REF], mir-141 [START_REF] Cirillo | Multi-Analytical Test Based on Serum MiRNAs and Proteins Quantification for Ovarian Cancer Early Detection[END_REF] mir-7 [START_REF] Meng | Diagnostic and Prognostic Potential of Serum MiR-7, MiR-16, MiR-25, MiR-93, MiR-182, MiR-376a and MiR-429 in Ovarian Cancer Patients[END_REF] and mir-429 [START_REF] Cui | The Accuracy of Single MicroRNAs in Peripheral Blood to Diagnose Ovarian Cancer: An Updated Meta-Analysis[END_REF] are upregulated in biofluids of patients with different types of ovarian cancers. On the other hand expression of microRNAs let-7f [START_REF] Zheng | Plasma MiRNAs as Diagnostic and Prognostic Biomarkers for Ovarian Cancer[END_REF], mir-93 [START_REF] Cirillo | Multi-Analytical Test Based on Serum MiRNAs and Proteins Quantification for Ovarian Cancer Early Detection[END_REF], mir-199a [START_REF] Jiang | Identification and Functional Validation of Differentially Expressed MicroRNAs in Ascites-Derived Ovarian Cancer Cells Compared with Primary Tumour Tissue[END_REF] and mir-148a [START_REF] Gong | Decreased Expression of MicroRNA-148a Predicts Poor Prognosis in Ovarian Cancer and Associates with Tumor Growth and Metastasis[END_REF] is downregulated in biofluids of patients with ovarian tumours.

From the diagnostic point of view, Oliveira et al [START_REF] Oliveira | Diagnostic Plasma MiRNA-Profiles for Ovarian Cancer in Patients with Pelvic Mass[END_REF] evaluated the profile of plasma miRNAs on a panel of 46 candidates finding 4 upregulated miRNAs (miR-200c-3p, miR-221-3p, miR-21-5p and miR-484) and two downregulated (miRNA-195-5p and miRNA-451a). However, only 2 miRNAs (miRNA-200c-3p and miRNA-221-3p) were confirmed in a validation cohort. Savolainen et al [START_REF] Savolainen | Expression of the MiR-200 Family in Tumor Tissue, Plasma and Urine of Epithelial Ovarian Cancer Patients in Comparison to Benign Counterparts[END_REF], on a short series of 9 patients, found that miRNA-200a, miRNA-200b and miRNA-200c both in tumor tissue and plasma allowed discrimination between malignant and benign samples. In addition, a correlation was found between the expression of miRNA-200 in urine and plasma with the malignant status of tumors. Another study reported a higher level of miR-590-3p in OC plasma compared to a control group [START_REF] Salem | MiR-590-3p Promotes Ovarian Cancer Growth and Metastasis via a Novel FOXA2-Versican Pathway[END_REF], Chang et al [START_REF] Chang | MicroRNA Expression Profiles in Non-epithelial Ovarian Tumors[END_REF] observed for germ cell tumors of the ovary (OGCT) and sex cord (SCST) specific expression profiles of miRNAs in 9 OGCTs (2 malignant and 7 benign) and 3 SCST. Overexpression of miRNA-373-3p, miRNA-372-3p and miRNA-302c-3p and underexpression of miRNA-199a-5p, miRNA-214-5p and miRNA-202-3p were reproducibly observed in malignant OGCT versus benign OGCT or SCST. Yokoi et al reported a plasma signature composed of 6 miRNAs selected after RT-qPCR (miRNA-200a-3p, miRNA-766-3p, miRNA-26a-5p, miRNA-142-3p, let-7d-5p and miRNA-328 -3p) able to successfully distinguish patients with ovarian cancer from healthy controls (AUC: 0.97; sensitivity, 0.92; and specificity, 0.91) paving the way for screening ovarian cancer [START_REF] Yokoi | A Combination of Circulating MiRNAs for the Early Detection of Ovarian Cancer[END_REF]. Among five miRNAs, Zhu et al observed that only serum miRNA-125b could distinguish benign controls and EOC patients [START_REF] Zhu | A Pilot Study of Circulating MicroRNA-125b as a Diagnostic and Prognostic Biomarker for Epithelial Ovarian Cancer[END_REF]. Moreover, among miR-200 family, Meng et al [START_REF] Meng | Diagnostic and Prognostic Relevance of Circulating Exosomal MiR-373, MiR-200a, MiR-200b and MiR-200c in Patients with Epithelial Ovarian Cancer[END_REF] identified that serum levels of miRNA-200a (p=0.0001), miRNA-200b (p=0.0001), and miRNA-200c (p=0.019) could distinguish benign from malignant ovarian tumors. Resnick et al [START_REF] Resnick | The Detection of Differentially Expressed MicroRNAs from the Serum of Ovarian Cancer Patients Using a Novel Real-Time PCR Platform[END_REF], confirmed that miRNAs in serum could be used as a marker for ovarian cancer in a series of 28 patients based on over-expression of miRNA-21, miRNA-92, miRNA -29a, miRNA-93 and miRNA-126, and underexpression of miRNA-99b, miRNA-127 and miRNA-155. In a meta-analysis on the diagnostic value of serum miRNA-21 expression, including 6 studies with limited sample size, Qiu & Weng reported a pooled respective sensitivity, specificity, and AUC of 0.81 (95%CI: 0.73-0.88), 0.82 (95%CI: 0.75-0.87), and 0.89 (95%CI: 0.85-0.91) imposing further validation [START_REF] Qiu | The Diagnostic Value of Serum MiR-21 in Patients with Ovarian Cancer: A Systematic Review and Meta-Analysis[END_REF]. Recently, Wenyu Wang developed a plasma signature for malignant tumors using extracellular vesicle and identified a panel of eight miRNAs (miR-1246, miR-1290, miR-483, miR-429, miR-34b-3p, miR-34c-5p, miR-145-5p, miR-449a).

Their model had a respective AUC of 0.9762 and 0.9375 in the training and the validation set [START_REF] Wang | Integrated Analysis of Ascites and Plasma Extracellular Vesicles Identifies a MiRNA-Based Diagnostic Signature in Ovarian Cancer[END_REF]. In contrast to several studies focusing on serum miRNAs, Kai Berner et al focused on urinary expression of twelve microRNAs. In their experience, miR-15a was upregulated whereas let-7a was down-regulated in ovarian cancer patients [START_REF] Berner | Evaluation of Circulating MicroRNAs as Non-Invasive Biomarkers in the Diagnosis of Ovarian Cancer: A Case-Control Study[END_REF].

From the prognostic point of view, Zhu et al [START_REF] Zhu | A Pilot Study of Circulating MicroRNA-125b as a Diagnostic and Prognostic Biomarker for Epithelial Ovarian Cancer[END_REF] found that elevated serum miRNA-125b levels were higher in patients with early OC stages (FIGO stages I-II), and with no residual tumor after surgery. In addition, elevated serum miR-125b were correlated with progression-free survival (p = 0.035). Meng et al reported high levels of miRNA-200b and miR-200c were associated with poorer overall survival (p=0.007, p=0.017, respectively) [START_REF] Meng | Diagnostic and Prognostic Relevance of Circulating Exosomal MiR-373, MiR-200a, MiR-200b and MiR-200c in Patients with Epithelial Ovarian Cancer[END_REF]. Gao et al. [START_REF] Gao | MicroRNA-200c and MicroRNA-141 as Potential Diagnostic and Prognostic Biomarkers for Ovarian Cancer[END_REF] including 74 serum samples of OC patients, 19 of borderline tumors and 50 of healthy controls, found that elevated serum miRNA-200c were correlated with improved two-year survival while decreased serum miR-145 levels was associated with disease progression [START_REF] Zuberi | The Promising Signatures of Circulating MicroRNA-145 in Epithelial Ovarian Cancer Patients[END_REF]. Finally, Zuberi et al. observed in OC an association between high expression of serum miR-125b and lymph node and distant metastases [START_REF] Zuberi | Utility of Serum MiR-125b as a Diagnostic and Prognostic Indicator and Its Alliance with a Panel of Tumor Suppressor Genes in Epithelial Ovarian Cancer[END_REF].

From the theragnostic point of view, most studies are based on cell cultures [START_REF] Kazmierczak | The Profile of MicroRNA Expression and Potential Role in the Regulation of Drug-Resistant Genes in Cisplatin-and Paclitaxel-Resistant Ovarian Cancer Cell Lines[END_REF][START_REF] Stasiak | The Profile of MicroRNA Expression and Potential Role in the Regulation of Drug-Resistant Genes in Doxorubicin and Topotecan Resistant Ovarian Cancer Cell Lines[END_REF].

Yang et al [START_REF] Yang | MicroRNA Expression Profiling in Human Ovarian Cancer: MiR-214 Induces Cell Survival and Cisplatin Resistance by Targeting PTEN[END_REF] found that protein kinase B (AKT) pathway activation was regulated by miRNA-214 and miRNA-150. Moreover, Echevarria-Vargas et al reported a cisplatin resistance associated with miR-21 expression [START_REF] Echevarría-Vargas | Upregulation of MiR-21 in Cisplatin Resistant Ovarian Cancer via JNK-1/c-Jun Pathway[END_REF]. Lu et al [START_REF] Lu | MicroRNA Let-7a: A Potential Marker for Selection of Paclitaxel in Ovarian Cancer Management[END_REF] observed that let-7a expression was significantly lower in OC patients sensitive to platinum and paclitaxel compared to those resistant to these agents. Langhe et al reported a panel of 4 miRNAs (let-7i-5p, miRNA-122, miRNA-152-5p and miRNA-25-3p) significantly down-regulated in OC with potential contribution to drug resistance [START_REF] Fa | A Novel Serum MicroRNA Panel to Discriminate Benign from Malignant Ovarian Disease[END_REF]. Finally, in a recent review, Saburi et al [START_REF] Saburi | A Comprehensive Survey into the Role of MicroRNAs in Ovarian Cancer Chemoresistance; an Updated Overview[END_REF] noted a relation between miRNA-30a-5p, miRNA-34a, miRNA-34a-5p, miRNA-98-5p, miRNA-142-5p, miRNA-338-3p, miRNA-708 and cisplatin resistance. Similarly, a relation was noted between miRNA -136, miRNA-338-5p, miRNA-503-5p, miRNA-1246, miRNA-1307 and paclitaxel resistance. Finally, a relation was noted between miRNA509-3p and platinum resistance and between miRNA-744-5p and carboplatin resistance. However, it is important to note that none of these miRNAs have been evaluated in biofluids while this could be a major contributor to adapt chemotherapy.

From the analysis of the literature on miRNAs in biofluids, it appears that there are arguments to suggest their role in physiopathology, in the differential diagnosis between benign and malignant tumors and to a lesser degree with borderline tumors as well as to support their diagnostic, prognostic and theragnostic values. However, these analyses were mainly performed by microarray with validation by RT-qPCR with potential biases linked to the methodology as proven in the context of endometriosis [START_REF] Bendifallah | A Bioinformatics Approach to MicroRNA-Sequencing Analysis Based on Human Saliva Samples of Patients with Endometriosis[END_REF]. Moreover, the small number of studies with limited sample size focusing on the specific evaluation of miRNAs expression in biofluids of patients with ovarian tumors limit their potential clinical utility. Indeed, Langhe et al [START_REF] Fa | A Novel Serum MicroRNA Panel to Discriminate Benign from Malignant Ovarian Disease[END_REF] pointed out that miRNAs are abundant in tissues but often rare in plasma and serum. For the quantification of miRNAs in plasma, the authors stressed that it was essential to use a high-sensitivity platform such as Next Generation Sequencing (NGS). However, no study using NGS and bioinformatic tools to analyze miRNA content in large blood, serum, urine or saliva series are available to determine their role in routine practice.

PiRNAs

piRNAs are small ncRNAs of 24 -32 nucleotides [START_REF] Ishizu | Biology of PIWI-Interacting RNAs: New Insights into Biogenesis and Function inside and Outside of Germlines[END_REF]. piRNA biosynthesis is summarized in Figure 2 [START_REF] Ishizu | Biology of PIWI-Interacting RNAs: New Insights into Biogenesis and Function inside and Outside of Germlines[END_REF][START_REF] Siddiqi | Piwis and Piwi-Interacting RNAs in the Epigenetics of Cancer[END_REF]. Dysregulation of piRNAs and proteins (e.g. PIWI family proteins) has been observed in various cancers including OC [START_REF] Siddiqi | Piwis and Piwi-Interacting RNAs in the Epigenetics of Cancer[END_REF][START_REF] Cheng | PiR-823, a Novel Non-Coding Small RNA, Demonstrates in Vitro and in Vivo Tumor Suppressive Activity in Human Gastric Cancer Cells[END_REF]. The main function of piRNAs is to protect the genome from transposons. Giulio Ferrero et al analyzing piRNA expression in urine, plasma exosomes, and stool observed that urine samples exhibited the highest piRNAs expression [START_REF]Small Non-Coding RNA Profiling in Human Biofluids and Surrogate Tissues from Healthy Individuals: Description of the Diverse and Most Represented Species[END_REF]. The piRNAs production and function are presented in Figure 2. Singh et al. [START_REF] Singh | Genome-Wide Profiling of the PIWI-Interacting RNA-MRNA Regulato-ry Networks in Epithelial Ovarian Cancers[END_REF] found that piRNAs distinguish endometrioid from serous OC with 159 and 143 piRNAs differentially expressed, respectively. Among these piRNAs, 74 were upregulated and 77 down-regulated in endometrioid OC, and 56 upregulated and 81 downregulated in serous OC. piR-52,207 was found to be upregulated in endometrioid OC, and both piR-52,207 and piR-33,733 in serous. Interestingly, among 20 biofluids evaluated by Hulstaert et al [START_REF] Hulstaert | Candidate RNA Biomarkers in Biofluids for Early Diagnosis of Ovarian Cancer: A Systematic Review[END_REF], saliva has the highest fraction of piRNAs. So far, in the specific setting of OC, little data are available on piRNA expression in blood sample allowing to evaluate their potential diagnostic and prognostic value and no study has evaluated saliva piRNA expression.

Transfer-RNAs (tRNAs)

Transfer RNAs (tRNAs) are a source of small regulatory RNAs (tsRNAs) acting on protein translation [START_REF] Dwivedi | Small Non-Coding-RNA in Gynecological Malignancies[END_REF][START_REF] Li | TRNA-Derived Small RNA: A Novel Regulatory Small Non-Coding RNA[END_REF]. Based on the cleavage site, tsRNAs are divided into transfer RNA-derived RNA fragments (tRFs) and tiRNAs [START_REF] Balatti | Role of the TRNA-Derived Small RNAs in Cancer: New Potential Biomarkers and Target for Therapy[END_REF] with tumorigenesis functions [82-86] [87,88]. tRFs are also involved in gene expression, oncogene activation and ovarian cancer progression through association with Ago and PIWI proteins [START_REF] Balatti | TsRNA Signatures in Cancer[END_REF].

Dhar Dwivedi et al. [START_REF] Dwivedi | Small Non-Coding-RNA in Gynecological Malignancies[END_REF] observed that tsRNAs can predict abnormal cell proliferation with high accuracy in serum samples from a cohort of patients healthy controls and benign and malignant tumors [START_REF] Peng | Presence and Diagnostic Value of Circulating TsncRNA for Ovarian Tumor[END_REF]. Eric Y. Peng observed that four tsncRNAs differentially expressed in serum samples had a high diagnostic accuracy for malignancy with an AUC of 0.95. Similarly, serum tRF-03357 and tRF-03358 levels are increased in patients with high-grade OC [START_REF] Zhang | TRNA-Derived Fragment TRF-03357 Promotes Cell Proliferation, Migration and Invasion in High-Grade Serous Ovarian Cancer[END_REF][START_REF] Jia | Transfer RNA-Derived Small RNAs: Potential Applications as Novel Biomarkers for Disease Diagnosis and Prognosis[END_REF]. In addition, i-tRF-GlyGCC is linked to advanced FIGO stages, suboptimal debulking and most importantly with early progression and poor overall survival in EOC patients [START_REF] Jia | Transfer RNA-Derived Small RNAs: Potential Applications as Novel Biomarkers for Disease Diagnosis and Prognosis[END_REF].

Despite, a relative abundant literature on tRNA, no study has focused on their diagnostic, prognostic and theragnostic relevance in the specific setting of OC

Circular RNAs (CircRNAs)

CircRNAs are a large class of ncRNA with more than 70,000 specimen identified in human tissues [START_REF] Sanger | Viroids Are Single-Stranded Covalently Closed Circular RNA Molecules Existing as Highly Base-Paired Rod-like Structures[END_REF][START_REF] Hsu | Electron Microscopic Evidence for the Circular Form of RNA in the Cytoplasm of Eukaryotic Cells[END_REF][START_REF] Chen | CircRNADb: A Comprehensive Database for Human Circular RNAs with Protein-Coding Annotations[END_REF][START_REF] Lai | ExoRBase 2.0: An Atlas of MRNA, LncRNA and CircRNA in Extracellular Vesicles from Human Biofluids[END_REF][START_REF] Guo | Expanded Identification and Characterization of Mammalian Circular RNAs[END_REF][START_REF] Ivanov | Analysis of Intron Sequences Reveals Hallmarks of Circular RNA Biogenesis in Animals[END_REF][START_REF] Kelly | Exon Skipping Is Correlated with Exon Circularization[END_REF]

Long non-coding RNAs (lncRNAs)

lncRNAs act via various pathways to regulate gene expression at different levels [136] with a biogenesis similar to mRNAs (Figure 3) . Arbitrarily, lncRNAs are defined as composed of more than 200 nucleotides mainly between 1,000 and 10,000.

Four different archetypes of lncRNA functions have been described (Figure 3 From the prognostic point of view, some studies have evaluated the value of lncRNAs in blood or serum to predict survival. In the meta-analysis using RT-qPCR, Chen et al evaluated plasma levels of MALAT1 in 47 patients with EOC with metastasis (EOC/DM), 47 patients without metastasis (EOC/NDM), and 47 healthy controls (HC) [147]. Plasma MALAT1 allowed to distinguish EOC/DM and HC with an AUC of 0.884 (95% CI, 0.820-0.949; P<0.001) with respective sensitivity and specificity of 89.4% and 72.3%. Jianming Gong et al, analyzing plasma samples from 66 patients with OC and 54 healthy controls, showed that lncRNA MIR4435-2HG was higher in patients with stage I-II FIGO stages OC but a high overlap of the value between the groups [148].

From theragnostic point of view, Weiwei Xie et al have reviewed the contribution of lncRNAs in response to chemotherapy [149]. The main lncRNAs involved in the cisplatin resistance were HOTAIR, H19, MALAT1, MEG3, XIST, DNM3OS and ANRIL.

Other lncRNAs have been proved to be associated to drug resistance such as LSINCT5, NEAT1 for paclitaxel resistance, UCA1 for paclitaxel-cisplatin resistance, GAS5 for platinum resistance. So far, most of these lncRNA have been merely evaluated on very small series of plasma [150,151] not allowing to draw conclusions on their relevance.

Perspectives et conclusions

Despite an abundant literature on ncRNAs in OC mainly based on cell culture and tissue samples, relatively few data are yet available in biofluid while previous studies [START_REF] Hulstaert | Candidate RNA Biomarkers in Biofluids for Early Diagnosis of Ovarian Cancer: A Systematic Review[END_REF]152,153] have demonstrated the possibility to quantify ncRNAs in various biofluids such as plasma, serum, urine and saliva. Moreover, it is important to note some limits of the previous published studies such as the small sample size, the absence of external validation, and the use in most studies of RT-qPCR and microarrays allowing ncRNA quantification of a predefined set of target sequences while NGS and bioinformatics, representing an unbiased biomarker discovery method, is rarely used. To improve the preoperative diagnosis of ovarian cancer, studies evaluating the expression of ncRNAs in easily accessible biofluids should be promoted, imposing the use of new sequencing technologies. So far, to our knowledge, only two studies, the clinical trial NCT03738319 focusing on ncRNA profile in exosomes of OC patients, [154] and the clinical trial NCT

[155] evaluating the saliva expression of ncRNA in ovarian tumors including, benign, borderline and ovarian cancer, are ongoing.

Figure 1 .

 1 Figure 1. : miRNAs synthesis. Biogenesis of miRNAs is a multistep process, beginning with the transcription of primary miRNAs (pri-miRNAs) by RNA polymerase II. The pri-miRNAs are transformed into precursor miRNAs (pre-miRNAs, 70 nucleotides long) by the RNase III Drosha-DGCR8-DDX5 microprocessor complex, and are then exported to the cytoplasm by Exportin (a Ran-GFP-dependent transporter). In the cytoplasm, pre-miRNAs are cleaved by the RNase Dicer-TAR RNA-binding protein (TRBP) complex, producing mature miRNA. Not all miRNAs pass through the canonical miRNA biogenesis pathway. Special miRNAs called mirtrons are produced from spliced introns with structural features like pre-miRNAs and undergo a miRNA processing pathway that bypasses the Drosha-mediated cleavage step.

Figure 2 :

 2 Figure 2 : piRNAs synthesis and function. Mature piRNAs are generated from the processing of single-stranded RNAs transcribed from piRNA clusters in the genome representing the largest class of non-coding RNAs found in most species. piRNAs can be also generated in the cytoplasm by a mechanism called the "ping-pong" cycle involving piRNA-directed antisense primary cleavage of transposon transcripts by Aubergine and PIWI proteins. piRNAs can modulate histone modifications and DNA methylation in a sequence-specific manner, leading to alterations in chromosomal conformation and gene expression regulation.

  and in many cancerous cell types including OC [95,100-102]. circRNAs have a high prevalence, specificity [103,104], stability [105] and conservation[106] conferring a particular value as biomarkers. Moreover, using 20 biofluids, Hulstaert et al demonstrated that circRNAs are enriched in biofluids compared to tissues[START_REF] Hulstaert | Candidate RNA Biomarkers in Biofluids for Early Diagnosis of Ovarian Cancer: A Systematic Review[END_REF].Indeed, the median circRNA read fraction in biofluids was 84.4% vs 17.5% in tissues. circRNAs act as specific miRNA reservoirs or sponges, as protein or peptide translators, as regulators of gene transcription and expression and interact with RNAbinding proteins (RBPs) impacting on transcription and translation of genes.

Figure 3 : 6 .

 36 Figure 3: CircRNAs Biosynthesis. Biosynthesis of circular RNA (circ-RNA) are expressed from mostly protein-coding genes. It is a multistep process, first the transcription of pre messagerRNA (mRNA), second splicing into mature mRNA then back-splicing into circ-RNA. Circ-RNA are then exported to the cytoplasm to A. act as micro RNA (miRNA) reservoir or transport miRNA; B. act as protein or peptide translators; C. Interact with RNA-binding proteins (RBPs) for transcription or translation of genes.

  )[137].Since the discovery of lncRNAs, more than a thousand publications have been listed in PubMed in the specific setting of OC but only about one percent focused on their expression in biofluids. Numerous studies about lncRNAs, mainly based on OC tissue samples, have demonstrated an association between clinicopathological characteristics such as histological type and grade, FIGO stages, lymph node and distant metastasis and some lncRNAs[138]. In a review including 34 studies involving more than 4,000 women with OC, Hosseini and al observed an association between lncRNAs expression and PFS (HR: 1.88, 95% CI: (1.35-2.62)) and DFS (HR: 6.07, 95% CI: 1.28-28.78)). However, among the 34 studies only one evaluating lncRNA in plasma [139] was included.They concluded that their work support the robust prognostic significance of altered lncRNAs in ovarian cancer but more extensive studies are required.

Figure 3 .

 3 Figure 3. : lncRNAs synthesis and functions. Four different archetypes of lncRNAs functions have been described; (i) lncRNAs can act as molecular signals occurring at a specific time and location to integrate developmental signals, interpret the cellular context, or respond to various stimuli, (ii)lncRNAs act as a molecular decoy by binding to their target proteins following transcription with mainly negative regulation, (iii) lncRNAs act as gene expression guides under a cis-form in the immediate vicinity of genes, and under trans-form for distant genes, and (iv) lncRNAs act as scaffolds.


M Schwartz

K Desbrosses

J Theurel

G Mornieux

Using passive or active back-support exoskeletons during a repetitive lifting task: influence on cardiorespiratory parameters

Keywords: Heart rate, Oxygen consumption, Sex, Workload, Wearable assistive devices

The objective of this laboratory study was to assess the cardiorespiratory consequences related to the use of different back-support exoskeletons during a repetitive lifting task. Fourteen women and thirteen men performed a dynamic stoop lifting task involving full flexion/extension of the trunk in the sagittal plane. This task was repeated for 5 min with a 10 kg load to handle. Four conditions were tested: with a passive exoskeleton (P-EXO), with two active exoskeletons (A-EXO1 and A-EXO2), as well as without exoskeleton (FREE). The oxygen consumption rate and cardiac costs were measured continuously. Results showed a significant reduction in the oxygen consumption rate for all exoskeletons as compared to FREE. This reduction was significantly more important for A-EXO1 (~28%) compared to A-EXO2 (~13%) and P-EXO (~7%). Compared to FREE, the cardiac cost was only reduced for A-EXO1 (~24%). Several factors can explain these differences on the cardiorespiratory parameters observed between exoskeletons: the technology used (passive vs active), the torque provided by the assistive device, the weight of the system, but also the level of anthropomorphism (related to the number of joints used by the exoskeleton). Our results also highlighted the lack of interaction between the exoskeleton and sex. Thereby, the three back-support exoskeletons tested appeared to reduce the overall physical workload associated with a repetitive lifting task both for men and women.

Introduction

Manual handling tasks are generally associated with a high physical workload [START_REF] Mehta | Physiological and biomechanical responses to a prolonged repetitive asymmetric lifting activity[END_REF]. For example, lifting tasks are known to induce exaggerated biomechanical strains on the back and cardiovascular demand. Many workers involved in this kind of task thus remain exposed to risks of development of low-back pain (Brandt et al. 2018) and cardiovascular diseases [START_REF] Holtermann | The physical activity paradox in cardiovascular disease and all-cause mortality: the contemporary Copenhagen General Population Study with 104 046 adults[END_REF]. New technologies, such as occupational back support exoskeletons, have been specifically designed to reduce the workload of the task performed by workers (de Looze et al. 2016;[START_REF] Theurel | Occupational exoskeletons: Overview of their benefits and limitations in preventing work-related musculoskeletal disorders[END_REF][START_REF] Kermavnar | Effects of industrial back-support exoskeletons on body loading and user experience: an updated systematic review[END_REF]. Such systems provide an assistance to the movement, by using deformable materials storing energy like springs or elastic textiles (i.e. passive exoskeletons), or by using robotic motors (i.e. active exoskeletons).

Several studies have shown that back-support exoskeletons can reduce stress on the lower-back muscles during handling tasks (de Looze et al. 2016;[START_REF] Theurel | Occupational exoskeletons: Overview of their benefits and limitations in preventing work-related musculoskeletal disorders[END_REF][START_REF] Kermavnar | Effects of industrial back-support exoskeletons on body loading and user experience: an updated systematic review[END_REF]. In a recent review, [START_REF] Kermavnar | Effects of industrial back-support exoskeletons on body loading and user experience: an updated systematic review[END_REF] reported average decreases in lower-back muscle activity during dynamic handling tasks of 18 and 25%, for passive and active exoskeletons, respectively. The relative decreases observed in muscle activity were nevertheless strongly variable (from 6 to 48%), notably depending on the exoskeleton design: for example, the assistive technologies used (passive versus active) [START_REF] Madinei | Biomechanical assessment of two backsupport exoskeletons in symmetric and asymmetric repetitive lifting with moderate postural demands[END_REF][START_REF] Yin | The effect of mobile wearable waist assist robot on lower back pain during lifting and handling tasks[END_REF], the structure of the exoskeletonstextile versus rigid [START_REF] Schwartz | Effectiveness of soft versus rigid back-support exoskeletons during a lifting task[END_REF])or the stiffness of assistance [START_REF] Frost | PLAD (personal lift assistive device) stiffness affects the lumbar flexion/extension moment and the posterior chain EMG during symmetrical lifting tasks[END_REF]. Moreover, the use of a back-support exoskeleton can lead to many undesired modifications during handling tasks [START_REF] Kermavnar | Effects of industrial back-support exoskeletons on body loading and user experience: an updated systematic review[END_REF][START_REF] Theurel | Occupational exoskeletons: Overview of their benefits and limitations in preventing work-related musculoskeletal disorders[END_REF] on the activity of postural muscle [START_REF] Luger | Using a back exoskeleton during industrial and functional tasks-effects on muscle activity, posture, performance, usability, and wearer discomfort in a laboratory trial[END_REF] and on the kinematics (lower-lumbar flexion [START_REF] Kim | Assessing the potential for "undesired" effects of passive back-support exoskeleton use during a simulated manual assembly task: Muscle activity, posture, balance, discomfort, and usability[END_REF]Koopman et al. 2019b;[START_REF] Simon | Kinematic effects of a passive lift assistive exoskeleton[END_REF], or to a greater knee extension [START_REF] Simon | Kinematic effects of a passive lift assistive exoskeleton[END_REF].

In view of the differences in the amplitude of muscular gains, and the undesired effects of back-support exoskeletons, the question of their benefits in terms of reduction of cardiovascular demand must be asked. The limitation of local muscular constraints should not be done at the expense of an increase in cardiovascular demand. Although studies on this subject are rare, it seems that the use of both passive and active exoskeletons has a beneficial effect on the metabolic responses (Del Ferraro et al. 2020). For instance, with regard to energy expenditure, Baltrusch et al. (2019) found a 17% decrease in metabolic cost during a 5-minute handling task performed with a passive back-support exoskeleton (Laevo), compared to without assistance. Moreover, a 4 to 13% energy expenditure reduction was found during symmetric and asymmetric standing and kneeling lifting tasks when using passive exoskeletons (Laevo V2.5 and BackX) (Alemi et al. 2020). [START_REF] Erezuma | Use of a passive lumbar back exoskeleton during a repetitive lifting task: effects on physiologic parameters and intersubject variability[END_REF] also evaluated the Laevo V2.5 passive exoskeleton and observed a decrease of about 5% in metabolic cost during another lifting task. Finally, the use of an active system (prototype MeBot-Exo) yielded an 18% decrease in energy consumption in a recent study [START_REF] Wei | A hip active assisted exoskeleton that assists the semi-squat lifting[END_REF].

However, regarding the cardiovascular responses, the literature appears to be more contrasted. Previous studies reported that the use of exoskeletons could either induce a decrease in cardiac cost [START_REF] Dewi | On-body personal assist suit for commercial farming: Effect on heart rate, EMG, trunk movements, and user acceptance during digging[END_REF][START_REF] Yin | Effects of wearable power assist device on low back fatigue during repetitive lifting tasks[END_REF] or have no effect [START_REF] Erezuma | Use of a passive lumbar back exoskeleton during a repetitive lifting task: effects on physiologic parameters and intersubject variability[END_REF][START_REF] Luger | Using a back exoskeleton during industrial and functional tasks-effects on muscle activity, posture, performance, usability, and wearer discomfort in a laboratory trial[END_REF][START_REF] Von Glinski | Effectiveness of an on-body lifting aid (HAL(R) for care support) to reduce lower back muscle activity during repetitive lifting tasks[END_REF][START_REF] Ziaei | Evaluation of a passive low-back support exoskeleton (Ergo-Vest) for manual waste collection[END_REF]. For example, during a repeated handling task performed with a 10 kg load, [START_REF] Yin | Effects of wearable power assist device on low back fatigue during repetitive lifting tasks[END_REF] reported a decrease in the mean heart rate with the use of an active exoskeleton (wearable power-assist device developed for the study) compared to without assistance. In contrast, von [START_REF] Von Glinski | Effectiveness of an on-body lifting aid (HAL(R) for care support) to reduce lower back muscle activity during repetitive lifting tasks[END_REF], using another active exoskeleton (HAL ® for Care Support Lumbar Type, Cyberdyne), did not observe any change in cardiovascular responses during a repeated handling task performed with a 17 kg load.

Like the variability of the results of studies concerning the effects of exoskeletons on muscular solicitations, these differences in cardiorespiratory consequences between studies could be related to both the task performed and the characteristics of the exoskeletons. It is therefore difficult to generalize these results and to clearly understand the influence of the exoskeleton design on the cardiorespiratory parameters, markers of the overall physical workload. New data are needed to provide knowledge that will serve both companies wishing to acquire an exoskeleton, and designers to improve their systems.

At the same time, occupational exoskeletons are intended to assist all workers, regardless of sex. However, men and women present physiological differences, such as, for instance, lower average maximal strength for women than men (Cote 2012; [START_REF] Plamondon | Difference between male and female workers lifting the same relative load when palletizing boxes[END_REF]. Thus, relative women's physical effort is greater than that of men for the same handled load. In addition, it has been observed that movement strategies during a lifting task could be sex-dependent, with for instance greater hip flexion for women than men [START_REF] Pan | Sex-dependent differences in lumbo-pelvic coordination for different lifting tasks: A study on asymptomatic adults[END_REF]. When using an exoskeleton, Alemi et al. (2020) reported an interaction effect between exoskeleton and sex on lower-back muscle activity. In their study, the use of the BackX exoskeleton resulted in a significant decrease in trunk extensor muscles activity in men and women while the use of the Laevo V2.5 exoskeleton yielded such a muscular activity reduction only for women. This is not entirely in line with [START_REF] Schwartz | Effectiveness of soft versus rigid back-support exoskeletons during a lifting task[END_REF], who found the same influence on lower-back muscle activity for men and women, whatever the back-support exoskeletons used (Laevo V1 and Corfor). It is also worth noting that most of the studies investigating cardiorespiratory consequences in relation to the use of exoskeletons were conducted with male participants (Del Ferraro et al. 2020). To our knowledge, only two studies have evaluated the sex effect on cardiorespiratory parameters with the use of exoskeletons. [START_REF] Madinei | Biomechanical assessment of two backsupport exoskeletons in symmetric and asymmetric repetitive lifting with moderate postural demands[END_REF] found a significant reduction in the metabolic cost with the use of two models of passive exoskeletons (Laevo and BackX) for women, while this was only observed for one model (Laevo) for men. Contrariwise, similar decreases in metabolic cost were observed for both men and women in another study with the Laevo exoskeleton [START_REF] Erezuma | Use of a passive lumbar back exoskeleton during a repetitive lifting task: effects on physiologic parameters and intersubject variability[END_REF]. Therefore, the generalization of the cardiorespiratory consequences of using back-support exoskeletons for women, while mainly reported for men, may be questionable due to possible sex specificities during lifting tasks. Thus, more information appears necessary to provide valid data for a better understanding of the influence of exoskeleton use on the overall physical workload of all workers.

Considering these different elements, the main objective of this study was to evaluate the effects of back-support exoskeleton design on cardiorespiratory parameters. We hypothesized that, for a standardized lifting task, active exoskeletons would be more effective than passive ones and reduce oxygen consumption rate and cardiac costs.

A second objective was to tease out the possible sex effect on the cardiorespiratory parameters, while wearing exoskeletons.

Materials and methods

Participants

Thirteen men (age: 25 ± 5 years, height: 1.80 ± 0.04 m, weight: 75.5 ± 7.9 kg) and fourteen women (age: 24 ± 6 years, height: 1.66 ± 0.06 m, weight: 63.6 ± 13.3 kg) without musculoskeletal nor cardiorespiratory pathologies participated in this study. All participants realized a training protocol before the experimentations.

This training protocol consisted of five sessions of two hours. During each session, the participants performed different handling tasks (including the one proposed in this study) without and with each exoskeleton. This training period helped to minimize the discovery effect associated with the use of a new equipment. Participants gave their written consent after receiving detailed information about the objectives, protocol and possible risks of this study. A national ethics committee approved the study (n° IDRCB 2019-A02901-56).

Experimental task

The study was conducted in an air-conditioned (with the temperature set at 20°C) and quiet room.

Participants performed a standardized manual lifting task in their sagittal plane, consisting of moving a 10 kg box from a platform positioned at ankle height until the thigh height (corresponding to a full extension of the trunk) and vice versa. These successive actions of lifting and lowering the box corresponded to one cycle.

Participants performed this task continuously for 5 minutes at an imposed rhythm, using a rhythmic beep (15 cycles / minute), and with the stoop technique, meaning that the trunk flexion/extension was realized with the knees almost straight, but without locking the joint. In addition, participants were asked to handle the box with outstretched arms. The position of the feet was fixed, parallel and hip-width apart. This position was marked at the start of the experiment with tape and was identical for each exoskeleton condition. The lifting task was successively performed with three exoskeletons (described below) and without assistance (FREE). The order of these conditions was randomized and a rest period of 10 minutes in a sitting position was respected between each. This rest period of 10 minutes allowed the measured variables returning to baseline before the start of a new lifting task, avoiding any potential carry-over effect.

Exoskeletons

One passive (P-EXO) (Figure 1,A) and two active (A-EXO1 (Figure 1, B) and A-EXO2 (Figure 1,C)) back-support exoskeletons were studied.

Insert Figure 1A, 1B and 1C

P-EXO: this passive exoskeleton is the BackX model (S model, 2019) from SuitX (USA). It weighs 4.5 kg and provides a trunk extension torque using springs and a rigid structure, with a joint at the hip level and support points at thigh and chest levels. It allows different morphological adjustments, different operating modes (instant and angle torque engagement mode) and two assistance levels (low and high). For this study, the exoskeleton was adjusted to each participant and was set to the 'instant' mode with the 'high' assistance level, corresponding approximatively to a maximum torque of 41 Nm (at 90° flexion). This assistance level was chosen according to the weight to be handled.

A-EXO1: this active exoskeleton is the Exoback model (V1, 2020) of RB3D (France). This device weighs 8.4 kg. This exoskeleton consists of a dorsal box integrating the battery and the electric motor. The latter is connected to the thigh supports using cables to transfer the assistance. Its rigid structure comprises two joints (at the hip and lower-back levels) and support points at thigh, buttock and shoulder levels. This system allows morphological adjustments and many technical settings: support level of the trunk during its flexion; assistance level during the trunk extension; assistance level at the end of the movement; reactivity and softness of the system; and holding torque for isometric tasks. For the study, the assistance level was set to 66%, corresponding to 48 Nm. We chose this level given the recommendation of the builder with respect to the weight to be handled.

The reactivity as well as the softness were set at 50% (default settings). The support level and the assistance at the end were set at 20% (default settings). The exoskeleton was adjusted to each participant's morphology.

A-EXO2: this active exoskeleton is the Cray X (2019) from German Bionic (Germany). It weighs 11 kg and is made up of a dorsal box, integrating the hardware and the battery, and of two electric motors placed at the hip level. Its rigid structure comprises one joint (the axis of the motor) and support points at thigh and chest levels. This exoskeleton has different morphological adjustments and technical settings: dynamic and static modes; assistance level provided during the trunk extension; sensitivity and reaction of the system; and counter force (corresponding to the support level of the trunk during its flexion). For this study, the dynamic mode with an assistance set to 40% was selected, which corresponded to 48 Nm and was comparable to A-EXO1. The sensitivity, the reaction and the counter force were set to 5 (default settings on a 0 to 10 scale). The exoskeleton was adjusted to each participant's morphology.

Data recording

Oxygen uptake ( 0 2 , expressed in ml/kg/min) and heart rate (HR, expressed in beats per minute (bpm))

were measured breath-by-breath during the experimentation using a portable respiratory gas analyzer (K4b2, Cosmed, Italy). Prior to the experimental lifting task, resting parameters were recorded during a period of 15 minutes with the participant lying in a quiet room and in the dark. The average 0 2 and HR during the last 5 minutes of this period were considered as resting values.

For each experimental condition, 0 2 and HR were averaged during the last 2 minutes of the lifting task and were considered as working values. Given the submaximal intensity of the exercise (estimated to be ≈36% of 0 2 max for FREE, with 0 2 max values being extrapolated from norms based on participants' age, sex and weight [START_REF] Myers | A Reference Equation for Normal Standards for VO2 Max: Analysis from the Fitness Registry and the Importance of Exercise National Database (FRIEND Registry)[END_REF])., the first 3-minute period prior to the recording ensured a stabilization of the cardiorespiratory parameters. Oxygen consumption rate (expressed in ml/kg/min) and cardiac costs (expressed in bpm) associated with the task were then calculated for each experimental condition by subtracting resting values from the working ones.

In order to check that rest values returned to baseline before starting a new effort, 0 2 was measured during the last 2 minutes of each rest period between lifting tasks. The initial rest value (i.e. 15 minutes lying in a quiet room and in the dark) was 2.93 ± 0.64 ml/kg/min and rest values between lifting tasks were 2.79 ± 0.60, 2.75 ± 0.79 and 2.72 ± 0.69 ml/kg/min, respectively before the tasks 2, 3 and 4. These values were not statistically different (p>0.05).

Statistical analysis

The results are presented as means ± standard deviations. A generalized linear mixed model was used to analyse the main effects of exoskeleton (FREE, P-EXO, A-EXO1 and A-EXO2) and sex (men and women) on oxygen consumption rate and cardiac costs, as well as their interaction effect. These independent variables were set as fixed effects and the participant as a random effect. In case of non-significant interaction, it was removed from the model. Significant effects were analysed using post hoc Bonferroni pairwise comparison tests. Residual normality was verified. The significance level was 5% (p < 0.05). Effect size was evaluated by partial eta

Results

Initial statistical model indicated that the interaction effect between exoskeleton and sex was not significant either for the oxygen consumption rate (p = 0.75) or the cardiac cost (p = 0.39). The interaction was therefore removed from the model in order to keep only the main effects. Then, a significant exoskeleton effects (p < 0.05) on oxygen consumption rate and cardiac costs, and sex effect only on the cardiac cost were reported (Table 1).

Oxygen consumption rate

Exoskeleton effect

For all participants (women and men), the oxygen consumption rate was significantly lower with P-EXO (11.8 ± 2.4 ml/kg/min; p = 0.04, d = 0.37), A-EXO1 (9.1 ± 1.8 ml/kg/min; p < 0.001, d = 1.76) and A-EXO2 (11.0 ± 1.8 ml/kg/min; p < 0.001, d = 0.82) compared to without equipment (FREE: 12.6 ± 2.2 ml/kg/min) (Figure 2). In addition, the oxygen consumption rate was significantly lower for A-EXO1 than for P-EXO (p < 0.001, d = 1.26) and A-EXO2 (p < 0.001, d = 1.05). Concerning the cardiac cost, it was significantly lower with A-EXO1 (45.1 ± 11.5 bpm) compared with FREE (59.7 ± 12.9 bpm; p < 0.001, d = 1.19), P-EXO (57.4 ± 12.9 bpm; p < 0.001, d = 1.01) and A-EXO2 (59.1 ± 10.7 bpm; p < 0.001, d = 1.26) (Figure 3). No significant difference was observed between FREE and P-EXO or A-EXO2.

Insert figure 2

Insert figure 3

Sex effect

During the task, the oxygen consumption rate (all exoskeletons combined) did not significantly differ (p = 0.13, d = 0.40) between men (11.6 ± 2.7 ml/kg/min) and women (10.6 ± 2.0 ml/kg/min). Statistical analyses revealed a significant sex effect on the cardiac cost (p < 0.001, d = 1.09), with a higher value for women (61.7 ± 10.6 bpm) than for men (49.0 ± 12.7 bpm).

Discussion

The influence of different back-support exoskeletons on the cardiorespiratory parameters during a repetitive lifting task was analysed in the present study. The possible effect of sex was also tested here. The primary findings showed that using passive and active exoskeletons could significantly reduce cardiorespiratory responses compared to a control condition performed without equipment, and this regardless of the sex.

Exoskeleton effect

To our knowledge, the present study was the first to compare the effects of passive and active back-support exoskeletons on cardiorespiratory parameters during an identical lifting task. Our results firstly showed that oxygen consumption rate was significantly decreased with all three exoskeletons used compared to the control condition. The amount of reduction was dependent on the exoskeleton design.

The use of the passive exoskeleton (P-EXO, BackX model) reduced the oxygen consumption rate by approximatively 7% during our repeated lifting task. Although significant, this reduction was slightly lower in comparison with previous studies using the same exoskeleton, which reported a 13-14% reduction in energy expenditure with lighter loads, respectively 6.8 kg load (Alemi et al. 2020) and 10% of body weight (≈7.2 kg) [START_REF] Madinei | Biomechanical assessment of two backsupport exoskeletons in symmetric and asymmetric repetitive lifting with moderate postural demands[END_REF]. Inversely, [START_REF] Poon | Evaluation of a trunk supporting exoskeleton for reducing muscle fatigue[END_REF] reported a lack of influence on the oxygen consumption rate when wearing the BackX during a lifting task performed with a heavier load (18 kg). Together, these results suggested that beneficial effects of a passive exoskeleton on the metabolic cost seem to be reduced with the increment of the load to be handled. In practice, this highlights the importance of matching the exoskeleton characteristics to those of the working task (such as the weight to be handled) in order to maximize beneficial effects.

The use of active exoskeletons also resulted in a decrease in the oxygen consumption rate of 28% for the A-EXO1 (Exoback) and 13% for the A-EXO2 (Cray X) compared to the condition without equipment. In their study, [START_REF] Wei | A hip active assisted exoskeleton that assists the semi-squat lifting[END_REF] evaluated another active exoskeleton (prototype MeBot-EXO) and reported an 18% reduction in metabolic cost, even if only three participants were evaluated.

The wide range of oxygen uptake reduction observed among passive and active assistive devices could be partly related to the design of the exoskeleton used. First, although the P-EXO proposes a lighter weight than the A-EXO1 (4.5 versus 8.4 kg), this maximal assistive torque was lower (≈41 versus 48 Nm), which could explain its smaller reduction in the oxygen consumption rate. In addition, without having been able to measure it, it is possible that the torque of the passive exoskeleton, depending on the spring deformation and related to the joint angle, might not be evenly distributed over the range of motion, as shown for another passive exoskeleton (Koopman et al. 2019a). This would be in line with discrepancies in trunk extensor activation with respect to the trunk inclination, observed among different passive exoskeletons [START_REF] Schwartz | Effectiveness of soft versus rigid back-support exoskeletons during a lifting task[END_REF]. In contrast, it is assumed that an active exoskeleton provides a more constant torque throughout the whole range of motion because the motor can generate a steady torque. Last, but not least, the need for a passive system to be actively constrained thanks to both muscle contraction and gravity in order to store energy within springs to be released afterwards, probably reduces its efficiency in terms of the metabolic cost.

In the present study, the use of the two active exoskeletons also yielded different reductions in the oxygen consumption rate, despite an identical task and a similar assistive torque (48 Nm). Differences could be explained by the weight discrepancy, the A-EXO2 being heavier than the A-EXO1 (11 versus 8.4 kg, respectively). Accordingly, the real assistance provided to the user could be weaker for the A-EXO2 due to the loss of energy to compensate for the extra weight of the system, therefore influencing the oxygen uptake. A second hypothesis concerns their level of anthropomorphism. Indeed, the A-EXO1 has been designed with two joints, one at the lower-back level and another at the hip level. The A-EXO2 has only one joint at the hip level.

Considering the relative contribution of hip and back joints to the trunk flexion/extension, the A-EXO1 appears to be more anthropomorphic than the A-EXO2. As participants performed the lifting task with the stoop technique in the present study, the mobilization of both joints over large ranges of motion was required. It is thus possible that the two joints design (A-EXO1) was less disruptive to natural movement and therefore a lower energy consumption. Finally, it is possible that other adjustment parameters (reactivity and softness of the system, for example), set at the factory values in the present study, could also partly affect the differences observed between the two active exoskeletons.

Results dealing with the cardiac cost, the use of the P-EXO (BackX) did not show any changes compared to the condition without an exoskeleton. This result is in agreement with most of the previous studies on other passive systems [START_REF] Luger | Using a back exoskeleton during industrial and functional tasks-effects on muscle activity, posture, performance, usability, and wearer discomfort in a laboratory trial[END_REF][START_REF] Erezuma | Use of a passive lumbar back exoskeleton during a repetitive lifting task: effects on physiologic parameters and intersubject variability[END_REF][START_REF] Ziaei | Evaluation of a passive low-back support exoskeleton (Ergo-Vest) for manual waste collection[END_REF]. Surprisingly, the use of the A-EXO2 (Cray X) did not induce significant changes in the cardiac cost compared to the control condition, whereas the use of the A-EXO1 (Exoback) did, with a 15 bpm reduction (45 versus 60 bpm, for A-EXO1 and FREE, respectively).

Previous studies that evaluated the effect of using active exoskeletons on the cardiac cost also found either a positive influence [START_REF] Yin | Effects of wearable power assist device on low back fatigue during repetitive lifting tasks[END_REF] or no change (von Glinski et al. 2019) compared to without equipment.

Therefore, the effects of back-support exoskeletons on the cardiac cost could depend on their characteristics, as mentioned earlier for the oxygen consumption rate. Moreover, it is worth noting that the present results, based on heart rate values, do not seem as sensitive as based on oxygen uptake in order to highlight differences in the cardiorespiratory response between exoskeletons. Heart rate and oxygen uptake generally evolve in a similar way during a prolonged physical effort. However, some factors could specifically modulate the cardiovascular response. This could be due to environmental factors (ambient noise, temperature...) [START_REF] Schnell | The effects of exposure to environmental factors on Heart Rate Variability: an ecological perspective[END_REF][START_REF] Yamamoto | Evaluation of the effect of heat exposure on the autonomic nervous system by heart rate variability and urinary catecholamines[END_REF] or individual factors (age, sex, stress...) [START_REF] Friedman | An autonomic flexibility-neurovisceral integration model of anxiety and cardiac vagal tone[END_REF][START_REF] Melillo | Nonlinear heart rate variability features for real-life stress detection. Case study: Students under stress due to university examination[END_REF]. As environmental factors were similar in all experiments performed in the laboratory, these would likely not explain the difference between heart rate and oxygen uptake results. With regard to individual factors, as all participants were young people, the age factor can be ruled out. Since the effect of sex has been considered in the statistical model, it can also be discarded. An explanation could be related to a possible discomfort perceived with some exoskeletons, causing potential stress. Indeed, it has been observed that some exoskeletons could generate discomfort at the chest level (Alemi et al. 2020;[START_REF] Kim | Assessing the potential for "undesired" effects of passive back-support exoskeleton use during a simulated manual assembly task: Muscle activity, posture, balance, discomfort, and usability[END_REF][START_REF] Madinei | Biomechanical assessment of two backsupport exoskeletons in symmetric and asymmetric repetitive lifting with moderate postural demands[END_REF], due to a point of force application in this area. As both P-EXO (BackX) and A-EXO2 (Cray X) involved a chest support that could possibly create discomfort during our repeated lifting task, this could influence heart rate responses in another manner than oxygen uptake measures. However, as discomfort was not evaluated in the present study, it remains difficult to relate this parameter to differences between heart rate and oxygen uptake. Future studies are needed to answer this hypothesis and to clearly define which parameter should be used to discriminate exoskeletons in terms of overall physical workload.

To conclude, it appears that the use of both passive and active back-support exoskeletons can reduce the physical workload of a handling task. Nevertheless, active exoskeletons are not necessarily more effective than passive ones, contrarily to our hypothesis. It rather seems that the operating mode (passive versus active), the exoskeleton design (number of joints, weight…) and the level of assistance influence the cardiorespiratory responses and should be considered by the companies with respect to the task to be performed. Accordingly, these different parameters, related to the exoskeleton design, would need to be further investigated in future researches to clarify which must be considered in priority for the prevention of work-related accidents and occupational diseases.

Sex effect

In order to assess whether the cardiorespiratory consequences of wearing an exoskeleton are identical between men and women, the effect of sex on the oxygen consumption rate and cardiac costs was studied. No main sex effect was reported for the oxygen consumption rate, suggesting that the lifting task induced the same absolute physical workload for both men and women. [START_REF] Erezuma | Use of a passive lumbar back exoskeleton during a repetitive lifting task: effects on physiologic parameters and intersubject variability[END_REF], while evaluating a passive back-support exoskeleton (Laevo), also showed no significant differences in metabolic cost between men and women. However, this is in contradiction to [START_REF] Madinei | Biomechanical assessment of two backsupport exoskeletons in symmetric and asymmetric repetitive lifting with moderate postural demands[END_REF], who reported a decrease in the energy expenditure for women but not for men with the use of the passive BackX exoskeleton. These differences could be due to the heterogeneity of the protocols, such as, for instance, the weight to be handled during the lifting task. Indeed, [START_REF] Madinei | Biomechanical assessment of two backsupport exoskeletons in symmetric and asymmetric repetitive lifting with moderate postural demands[END_REF] used a smaller load for women (~ 6.3 kg) and for men (~ 8.1kg) compared to the present study (10 kg for both sexes). As discussed earlier, the relative beneficial effect of wearing the BackX exoskeleton on the metabolic cost could be more important when handling lighter loads. Therefore, smaller relative beneficial effects with heavy loads could minimize a potential difference in metabolic cost between men and women.

Regarding the cardiac cost, our results showed that women had higher values than men (61.7 bpm versus 49.0 bpm). An explanation for this difference in absolute cardiac cost, while the oxygen consumption rate was identical, could be the fact that women would work at a higher percentage of their physiological capacity than men, resulting in a higher heart rate (Barnes and Fu 2018). This heart rate increase would compensate for a lower stroke volume in women (mainly attributed to a smaller heart size) to yield adequate cardiac output.

In conclusion, the present study highlights that passive and active back-support exoskeletons have beneficial effects on overall physical workload for both men and women. This is encouraging for the deployment of exoskeletons to all workers to reduce their physical workload. However, future investigations seem necessary to better understand the potential effect of the handled load on the cardiorespiratory consequences of using an exoskeleton.

Limitations

A first limitation of our study was the use of a standardized protocol carried out in the laboratory. For example, the task performed was only in the sagittal plane. This is not representative of all the tasks done by workers in ecological conditions, which may involve various movements in several planes. However, laboratory experimentations allow controlling the environment and limiting as much as possible measurement biases.

Another limitation was our participant sample. In order to reduce individual heterogeneity and to exclude volunteers with medical restrictions, our sample consisted of healthy young adults. This sample did not represent the general worker population. Our results could then not be extrapolatedfor example, to the problem of job retention for elderly or pathological employees through the use of exoskeletons. Nevertheless, unlike most studies assessing occupational exoskeletons, both men and women were evaluated in the present study in order to expand the knowledge about a wider population. Further studies are needed to consider all potential sources of individual variability.

Conclusions

The use of back-support exoskeletons demonstrated beneficial effect on cardiorespiratory consequences during a repeated lifting task. Oxygen consumption rate and cardiac cost reduction depended on the exoskeleton design.

The assistance modality (passive versus active), the exoskeletons weight as well as their anthropomorphism level (single or multiple joints) could modulate the cardiorespiratory responses. The cardiorespiratory benefits associated with the use of back-support exoskeletons have also been shown to be similar for men and women. To conclude, the back-support exoskeletons tested in this study appear to reduce the overall physical workload of the users during a repetitive lifting task and could therefore make it possible to limit work-related accidents and occupational diseases induced by strenuous handling tasks.

Declarations

  squared ( ) for main effects, and by means of Cohen's d values for post hoc pairwise comparison. Effect size was considered small ( ≥ 0.02; d ≥ 0.20), medium ( ≥ 0.15; d ≥ 0.50), or large ( ≥ 0.35; d ≥ 0.80) according to Cohen (Cohen 1992). All analyses were performed with STATA software (Stata 16, StataCorp, USA).

Figure 1 :

 1 Figure 1: The three exoskeletons used; (A) passive exoskeleton (P-EXO) (BackX, Suit X, USA), (B) active exoskeleton (A-EXO1) (Exoback, RB3D, France), and (C) active exoskeleton (A-EXO2) (CrayX, German Bionic, Germany). Joints of the exoskeletons and support points of the assistance are represented by the white circles and the white arrows, respectively.

Figure 2 :

 2 Figure 2: Mean oxygen consumption rate (ml/kg/min) and standard deviation obtained with the use of the passive exoskeleton (P-EXO, light grey), both active exoskeletons (A-EXO1, dark grey; A-EXO2, dark), and without equipment (FREE, white). *: significant differences between exoskeletons (p < 0.05).

Figure 3 :

 3 Figure 3: Mean cardiac cost (bpm) and standard deviation obtained with the use of the passive exoskeleton (P-EXO, light grey), both active exoskeletons (A-EXO1, dark grey; A-EXO2, dark), and without equipment (FREE, white). *: significant differences between exoskeletons (p < 0.05).

Table 1 :

 1 Main effects of exoskeleton and sex on cardiorespiratory parameters from the general linear mixed model. Significant effects (p < 0.05) are presented in bold type. : effect size partial eta squared.

	Cardiac cost

Funding:

No funding was received for conducting this study.

Availability of data and material:

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable.

Code availability:

14 Not applicable.

Conflicts of interest/Competing interests:

The authors have no relevant financial or non-financial interests to disclose.

Ethics approval:

The experimental protocol received approval from the national ethical committee (n° IDRCB 2019-A02901-56).

Consent to participate:

Participants gave their written consent after receiving detailed information about the objectives, protocol, and possible risks involved.

Authors' contributions:

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Kévin Desbrosses and Mathilde Schwartz. The first draft of the manuscript was written by Mathilde Schwartz and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Alemi MM, Madinei S, Kim S, Srinivasan D, Nussbaum MA ( 2020


Keywords: gravitation, velocity of light, photons, escape velocity, black holes

We show how it is possible to define and study black holes of arbitrary shapes in the framework of Newtonian mechanics.

Introduction

According to Wikipedia, objects whose gravitational fields are too strong for light to escape were first considered in the 18th century by the English astronomical pioneer and clergyman John Michell and a few years later by Pierre-Simon de Laplace. The idea was briefly proposed by Michell in a letter published in November 1784 [START_REF] Michell | On the Means of discovering the Distance, Magnitude, etc. of the Fixed Stars, in consequence of the Diminution of the velocity of their Light, in case such a Diminution should be found to take place in any of them, and such Data should be procured from Observations, as would[END_REF]. It was a natural idea within the framework of Newton's gravitational theory, assuming that light was produced by corpuscles of positive mass, as assumed by Newton. Our present physics models discredit Michell's notion of a light ray shooting directly from the surface of a supermassive star, being slowed down by the star's gravity, stopping, and then free-falling back to the star's surface. Actually the general relativity framework assumes a constant velocity for light and more generally all electro-magnetic waves travelling in the empty space.

The concept reappeared in a slightly different form after the creation of general relativity by Albert Einstein. In 1916, Karl Schwarzschild [START_REF] Schwarzschild | On the gravitational field of a sphere of incompressible fluid according to Einstein's theory[END_REF] found the first modern relativistic solution that would characterize a black hole. Then David Finkelstein, in 1958, first published the interpretation of "black hole" as a region of space from which nothing can escape. It was not until the 1960s that theoretical work showed they were a generic prediction of general relativity, but nowadays almost all texts on black holes mention them only in connection with the general relativity model.

In the recent years, the black hole concept has attracted more and more attention since it is conjectured that a giant black hole is sitting in the center of every galaxy, including our milky way. There are polemics about the existence of such objects in the exact form proposed by Karl Schwarzschild, and indeed it is not clear whether the fine structure of atomic particles really allow the formation of a point singularity, and moreover the effect of gravity at very small distances is not known. It might even become repulsive as conjectured in the framework of some alternative gravitational models.

In the present paper we shall not assume anything for small distances and our main point will be to understand the exact kind of lockdown undergone by both matter and light in the vicinity of a very large mass concentration. Since we wish to understand what happens for arbitrary, not necessarily spherical matter concentrations, we adopt the Newtonian formulation of gravity. As a drawback, we need to drop the assumption of photons travelling exactly at the speed of light. We shall justify this point of view in our conclusion.

The paper is organized as follows: Section 2 is devoted to the classical spherically symmetric case. It is rather natural to consider first the spherically symmetric space because the study of black holes started with the idea of "black stars" and stars are usually close to spherical with a spherically symmetric distribution of mass. Section 3 concerns the case of arbitrary distributions which might turn out to be relevant in the future if we consider low density extremely large lack holes for which symmetrization under gravity is not yet achieved. In Section 4, we apply the results of Sections 2 and 3 to the case of black holes. Section 5 is devoted to a few remarks about cosmology. 1 2 The escape velocity in the spherically symmetric case

The context

In this section, we recall the principle on which John Michell based his proposal on existence of "black stars". Let us consider a spherical body of radius r > 0 with local density depending only on the distance to its center, taken as the origin of coordinates. It has been known for a long time, at least since Gauss, that outside the sphere of radius r, the distributed mass produces the same gravitational field as if the total mass was located at the center. Therefore, in the absence of other forces, the equation of motion of a small body, modelized by a point mass located at the spatial position

u ∈ R 3 is u = - GM u ||u|| 2 (2.1)
where M is the total mass of the body and G the gravitational constant. The equation does not depend on the mass of the small body, which could, in the classical framework, be a photon. Associated with (2.1), we have a conserved energy

E(u, u ) = 1 2 ||u || 2 - GM ||u|| (2.2)
From equation (2.1), it follows that starting from any initial state u 0 , v 0 with

||u 0 || > r, there is a unique local solution u ∈ C 2 ([0, T max ), R 3 ) of (2.1) such that u(0) = u 0 , u (0) = v 0 .
In addition, the only way for the solution u to have a finite time of existence is collapsing to the origin. For this solution to be a true solution of the mechanical problem, we need in addition to warrant ||u(t)|| > r, ∀t ∈ [0, T max ), since the equation ceases to be valid when we enter the ball of radius r. By taking the inner product of both sides of equation (2.1), it is immediate to check that the energy E is conserved:

∀t ∈ [0, T max ), E(u(t), u (t)) = E(u(0), u (0)) (2.3)
Due to the structure of (2.2), it is now clear that if the trajectory u(t) passes through arbitrarily distant points, we must have

E = E(u(0), u (0)) ≥ 0.
It turns out that as soon as this condition is violated, the trajectory u(t) remains bounded, and the condition for boundedness is optimal.

Below the escape velocity.

It turns out that as soon as E < 0, the trajectory cannot escape. We now consider, for some R > r, the sphere

S R = {u ∈ R 3 , ||u|| = R} Our main result is Theorem 2.1. Let u 0 ∈ S R and ||v 0 || 2 < 2GM R . Then ∀t ∈ [0, T max ), ||u(t)|| ≤ R 1 -R||v 0 || 2 2GM (2.4)
Proof. By the energy conservation property, we have

∀t ∈ [0, T max ), 1 2 ||u (t)|| 2 - GM ||u(t)|| = 1 2 ||v 0 || 2 - GM R := -η Hence ∀t ∈ [0, T max ), GM ||u(t)|| = 1 2 ||u (t)|| 2 + η ≥ η = GM R - 1 2 ||v 0 || 2
The resulting inequality

∀t ∈ [0, T max ), ||u(t)|| ≤ GM η = GM GM R -1 2 ||v 0 || 2 is equivalent to (2.4)

Two results of optimality.

The result of Theorem 2.1 is optimal in two directions.

Proposition 2.2. If u 0 ∈ S R and ||v 0 || 2 = 2GM R
, in some cases the solution u grows up, which means that T max = ∞ and lim

t→∞ ||u(t)|| = ∞. Proof. The condition ||v 0 || 2 = 2GM R means E = 0, in which case we have ∀t ∈ [0, T max ), 1 2 ||u (t)|| 2 - GM ||u(t)|| = 0.
Let us consider the case where u 0 , v 0 are colinear in which case the solution and its velocity both remain on a straight line passing through 0. By setting u(t) = y(t)w with w some unit vector, the equation reduces to

y = ± γ |y| 1/2
with γ := 2GM . Looking for positive solutions we end up with two curves

y(t) = R 3/2 ± 3 2 √ γt 2/3
The solution

y + (t) = R 3/2 + 3 2 √ γt 2/3
is growing up, while the solution

y -(t) = R 3/2 - 3 2 √ γt 2/3 (2.5)
collapses with the spherical body in finite time

T max = 2 3 R 3/2 -r 3/2 √ γ Proposition 2.3. Under the hypothesis of Theorem 2.1 the value R 1 -R||v 0 || 2 2GM = GM η is
achieved as a maximum of ||u(t)|| for some particular solutions u.

Proof. Setting γ := 2GM and looking for scalar solutions u = zw with ||w|| = 1 as previously, we end up with the ODEs

z = ± γ |z| -2η 1/2
The solution z > 0 of

z = γ z -2η 1/2 ; z(0) = R (2.6)
corresponds to a solution u = zw of (2.1) with

||u (0)|| 2 = γ R -2η = 2GM R -2η < 2GM
R and grows until it reaches the value

z = γ 2η = GM η .

A more general case

In this section, we consider a bounded open domain Ω of R 3 , and a mass M filling the domain

with local density µ ∈ L 1 (Ω). Therefore M = Ω µ(x)dx. Equation (2.1) is replaced by u = - Ω Gµ(x)(u -x) ||u -x|| 2 dx (3.1)
valid for solutions with positions outside the compact set Ω, in a region where there is no other matter and where the influence of other gravitational sources is negligible. Now the energy becomes

E(u, u ) = 1 2 ||u || 2 - Ω Gµ(x) ||u -x|| dx (3.2)
We observe that whenever u ∈ Ω, we have

GM max x∈Ω ||u -x|| ≤ Ω Gµ(x) ||u -x|| dx ≤ GM dist(u, Ω) (3.3)
The construction of local solutions when u 0 ∈ Ω is routine. We now have Theorem 3.1. Let u 0 ∈ Ω and v 0 ∈ R 3 be such that

||v 0 || 2 < 2 Ω Gµ(x) ||u 0 -x|| dx. (3.4)
Then u is bounded on [0, T max ) and more precisely

∀t ∈ [0, T max ), dist(u(t), Ω) ≤ 2GM Ω 2Gµ(x) ||u 0 -x|| dx -||v 0 || 2 .
(3.5)

Proof. By the energy conservation property the same argument as in the symmetric case now gives, introducing η =

Ω Gµ(x) ||u 0 -x|| dx - 1 2 ||v 0 || 2 , the inequality ∀t ∈ [0, T max ), GM dist(u, Ω) ≥ Ω Gµ(x) ||u -x|| dx = 1 2 ||u (t)|| 2 + η ≥ η.
The conclusion follows immediately.

Corollary 3.2. Let u 0 ∈ Ω and v 0 ∈ R 3 be such that

max x∈Ω ||u 0 -x|| × ||v 0 || 2 < 2GM. Then ∀t ∈ [0, T max ), dist(u(t), Ω) ≤ 2GM Ω 2Gµ(x) ||u 0 -x|| dx -||v 0 || 2 ≤ max x∈Ω ||u 0 -x|| 1 - ||v 0 || 2 max x∈Ω ||u 0 -x|| 2GM .
Remark 3.3. Corollary 3.2 gives an estimate from below of the escape velocity V at some point u 0 ∈ Ω, given in the general case by the inequality

V 2 ≥ 2GM max x∈Ω ||u 0 -x|| .
By introducing the average density d := M |Ω| it can be written in the form

V 2 ≥ |Ω| 2Gd max x∈Ω ||u 0 -x|| .

Application to black holes

A black hole is a massive body for which the escape velocity overpasses the velocity of light c.

General results

Corollary 4.1. Assume that there is no gravitational mass except those in Ω. Let B be a closed ball containing Ω, such that

c 2 max u∈B {max Ω ||u -x||} < 2GM.
Then B is a black hole. More precisely, if a photon enters the region B at some time t 0 , the localization u(t) of the photon satisfies

∀t ∈ [t 0 , T max ), dist(u(t), Ω) ≤ max Ω ||u(t 0 ) -x|| 1 - c 2 max Ω ||u(t 0 )-x|| 2GM
.

Remark 4.2. After Tmax, several things may happen: the photon may disappear in Ω for ever, in which case the inequality remains trivially true but no equation can be written, especially since the photon may be "digested" by the matter inside Ω; it may remain some time in Ω and try to get out again, in which case the corollary can again be applied. Summarizing all the possible cases, we can say that as long as the photon does not disappear, the inequality remains true. So the lockdown is not only local, but global, but this cannot be said directly at the level of the equation which may cease to be satisfied on some time intervals.

Remark 4.3. The hypothesis that there is no gravitational mass except those in Ω is of course never satisfied in reality. But the mathematical theorem must be stated under this condition. In practice physicists will consider that if the other masses are far enough, the lock-down property will be satisfied with almost the same inequality. This is a stability assumption which looks reasonable, but is not at all easy either to formulate or to prove mathematically. Without approximations of this type, nothing can be calculated in the real world.

Remark 4.4. Equation (2.1) shows that if a photon is emitted orthogonally from the surface S R = {u ∈ R 3 , ||u|| = R}, its velocity is decreasing at the beginning of a motion, so we see that the Newtonian framework is inconsistant with the motion of the photon at constant velocity c, as already pointed out in the introduction.

The previous corollay implies the following simpler looking statement:

Corollary 4.5. Assume that there is no gravitational mass except those in Ω. Let B be a closed ball containing Ω, such that

c 2 diam(B) < 2GM. (4.1)
Then B is a black hole. More precisely, if a photon enters the region B at some time t 0 , either the photon disappears in finite time, or its localization u(t) satisfies

∀t ≥ t 0 , dist(u(t), Ω) ≤ diam(B) 1 -c 2 diam(B) 2GM . (4.2)
Remark 4.6. In that last corollary, in the hypothesis we only lose a factor 2 with respect to the spherically symmetric situation. The conclusion is of course weaker, depending on the shape.

Characterization in terms of average density.

In the framework of average densities, Corollary 4.5 can be rewritten in the form Proposition 4.7. Assume that there is no gravitational mass except those in Ω. Let B be a closed ball containing Ω, such that

d > c 2 diam(B) 2G|Ω| . (4.3)
Then B is a black hole.

The spherically symmetric case is especially important. The two conditions (4.4) and (4.5) only differ by a factor 2, and we do not know whether the second condition is optimal in general.

Some very large black holes

An immediate observation is that formula (4.5) allows arbitrary low average densities when r tends to infinity. In [START_REF] Stuckey | The observable universe inside a black hole[END_REF], the author suggested that the entire observable universe may lie in the interior of a black hole. His calculations were done in the relativistic framework. We can recover this result in the newtonian framework as follows: first we can check easily that Now the average density of the observable universe is presently estimated around 10 -23 kg/m 3 , some 5 000 times more. So the necessary condition for a black hole is fullfilled. Then of course everything will depend on what is outside the observable universe...

K = 3 4π c 2 G ∼ 3

Concluding remarks

In this paper, we presented a classical approach to black holes which is completely independent of the Schwarzschild singular model (cf. [START_REF] Schwarzschild | On the gravitational field of a sphere of incompressible fluid according to Einstein's theory[END_REF]) and does not make any hypothesis on the distribution of mass inside the black hole. This approach suggests several remarks.

Remark 5.1. It follows from our last calculation that there might exist, inside our universe, gigantic black holes of about one billion light years diameter having an average density comparable to that of the observable universe. Actually, mass concentrations will usually have a much larger average density, so we can very well imagine that some huge concentrations of baryonic matter are invisible for us. They should manifest themselves by gravitational lens phenomena and could have been confused with dark matter. Moreover, if the usual optical aberrations which are found around "classical" black holes are probably absent in low density gigantic black holes, they could contribute in a more discreet manner to the "ghost light" illuminating the cosmos which is not completely explained today (cf. [START_REF] Montes | Intracluster light: a luminous tracer for dark matter in clusters of galaxies[END_REF]). Finally, if a large proportion of stars were hidden inside such gigantic black holes, this could help to solve Olber's paradox (cf. [START_REF] Harrison | Darkness at night, a riddle of the universe[END_REF][START_REF] Wesson | Olbers's paradox and the spectral intensity of the extragalactic background light[END_REF]) without invoking the hypothesis of a spatially limited universe.

Remark 5.2. There is presently, in connection with general relativity, some kind of consensus to admit that photons have no mass. The mass should be in any case very small, cf. [START_REF] Goldhaber | The Mass of the Photon[END_REF]. If this mass is under 10 -69 kg, it could be impossible to detect it, cf. [START_REF] Vasseur | Limites sur la masse du photon[END_REF].

Remark 5.3. As previously mentioned in Remark 4.4, Newton's framework is inconsistent with a constant velocity of photons. But it might happen that the velocity of light be the velocity of electromagnetic waves, while the velocity of photons could be much lower. It is what happens with electricity, the velocity of electrons is infinitesimal compared to that of the electric signal propagation.

Remark 5.4. Light emanating orthogonally from the surface of a black hole could be a unique example of a light ray stopping without any visible obstacle and coming backwards due to gravity, unfortunately it is probable that nobody will ever be able to observe such a phenomenon even in the distant future: approaching a high density black hole is probably difficult and dangerous, and low density black holes may be out of reach for ever.

As a conclusion, we hope that the naive classical approach of the present paper will lead to further developments in more modern settings.

Proposition 4 . 8 .Remark 4 . 9 .

 4849 In the spherically symmetric case, when Ω = B(x 0 , r) and B = Ω , the sufficient condition following from Theorem 2.1 for B to be a black hole is If Ω = B(x 0 , r) and B = Ω, but the mass distribution in ω is not spherically symmetric, our sufficient condition becomes

  .22.10 26 kg/m. The radius of the observable universe is presently estimated to be r ∼ 4.10 26 m It follows that K/r 2 ∼ (3, 22/16)10 -26 kg/m 3 approximately 2.10 -27 kg/m 3 .