T Coste1

F. PETIT3#, S. MOUTTON4#, L. DEVISME5 C Aloui1#

C F Wells6

N Leboucq7

P Verpillat8

M Yvert4

F Rivier9

E Tournier- Lasserve1

Dr T Coste

Rare metabolic disease mimicking COL4A1/COL4A2 fetal brain phenotype

Keywords: COL4A1/COL4A2, corpus callosal dysgenesis, exome sequencing, fetal intracerebral hemorrhage, PDHA1, ventriculomegaly

ABSTRACT

Pathogenic variants of collagen type IV alpha 1 and 2 (COL4A1/COL4A2) genes cause various phenotypic anomalies, including intracerebral hemorrhage and a wide spectrum of developmental anomalies.

Only 20% of fetuses referred for COL4A1/COL4A2 molecular screening (fetuses with a suspected intracerebral hemorrhage) carry a pathogenic variant in these genes, raising questions regarding the causative anomaly in the remaining 80% of these fetuses. We examined, following termination of pregnancy or in-utero fetal death, a series of 113 unrelated fetuses referred for COL4A1/COL4A2 molecular screening, in which targeted sequencing was negative. Using exome sequencing data and a gene-based collapsing test, we searched for enrichment of rare qualifying variants in our fetal cohort in comparison to the Genome Aggregation Database (gnomAD) control cohort (n=71 702). Qualifying variants in pyruvate dehydrogenase E1 subunit alpha 1 (PDHA1) were overrepresented in our cohort, reaching genome-wide significance (P=2.11×10-7). Heterozygous PDHA1 loss-of-function variants were identified in three female fetuses. Among these three cases, we observed microcephaly, ventriculomegaly, germinolytic pseudocysts, agenesis/dysgenesis of the corpus callosum and white-matter anomalies that initially suggested cerebral hypoxic-ischemic and hemorrhagic lesions. However, a careful a-posteriori reanalysis of imaging and postmortem data showed that the observed lesions were also consistent with those observed in fetuses carrying PDHA1 pathogenic variants, strongly suggesting that these two phenotypes may overlap. Exome sequencing should therefore be performed in fetuses referred for COL4A1/COL4A2 molecular screening which are screen-negative, with particular attention paid to the PDHA1 gene. .

CASE SERIES

Exome sequencing was performed in 113 fetuses referred initially (with a suspected intracerebral hemorrhage) for collagen type IV alpha 1 and 2 (COL4A1/COL4A2) gene screening, in which no pathogenic variation was identified. A gene-based collapsing burden test comparing qualifying variants in the 113 fetuses vs the Genome Aggregation Database (gnomAD) public control database ranked the pyruvate dehydrogenase E1 subunit alpha 1 (PDHA1) gene first, showing genome-wide significance (P=2.11×10-7). (For further details of methods, see Appendix S1.) Three qualifying variants of PDHA1 were identified, one in each of three heterozygous female fetuses (Table S1, Figure 1). Two were loss-of-function variants and one was a missense variant. None of these variants was present in public control databases of polymorphisms (gnomAD and the 1000Genomes Project Phase 3 database). The p.(Arg304*) and p.(Arg119Trp) variants have been reported previously, in a large series of patients with pyruvate dehydrogenase complex deficiency (PDCD) (MIM# 312170)1. The main ultrasound findings and careful a-posteriori reanalysis of magnetic resonance imaging (MRI) features of the affected fetuses are summarized in Table 1. This study was approved by the INSERM ethics review committee (IRB00003888) and informed consent was obtained from parents and for the fetuses included in the study.

Case 1

Fetus F1 was the first child of unrelated and healthy parents, without familial history. The first trimester of pregnancy was unremarkable. Ultrasound examination suggestive of bilateral ventricular hemorrhage, with hyposignal on T2-and hypersignal on T1-weighted sequences. Given these findings, we concluded that there had been several hypoxic-ischemic and hemorrhagic injuries associated with neurodevelopmental alterations. The fetal blood count and karyotype were normal. The pregnancy was terminated at 27 weeks. Autopsy showed a female fetus with a weight of 908 g, crown-heel length of 36 cm and moderate microcephaly (head circumference, 24 cm). Macroscopic cerebral study revealed global microcephaly with delayed gyration, partial corpus callosal agenesis and parietal and frontal subependymal pseudocysts. Histological analysis showed occipital leukomalacia, fragmentation of olivary and dentate nuclei and agenesis of the pyramidal tracts. Hemosiderin (a sign of previous hemorrhage) was not detected by Perls staining (Figure 3d). These findings were suggestive of clastic events.

Case 2

Fetus F2 was a female fetus from the third pregnancy of a 34-year-old woman. Her two previous children had normal neurological development. Ultrasound examination at 24 gestational weeks found dilatation of the lateral ventricles and a suspected blood clot in the left lateral ventricle without any other abnormality. Fetal brain MRI at 26 weeks confirmed slight asymmetric ventricular dilatation (width of cerebral right lateral ventricle, 14 mm; left lateral ventricle, 12.5 mm) and revealed the presence of three microcysts, which were interpreted as germinolytic cysts, in the left lateral ventricle. A possible left parietal parenchymal ischemic lesion was also suspected. Fetal MRI performed at 30 weeks showed no change in the dilatation of the lateral ventricles. A subependymal hemorrhage was suspected, without any clot in the ventricles. There were germinolytic microcysts in the right lateral ventricle apparently identical to those in the left one, localized in the ganglionic eminence and organized in a 'string-of-beads' formation. Microcysts were also present in the anterior part of the lateral ventricles with a septate appearance. The corpus callosum appeared thin. An abnormal signal was noted in the deep and superficial white matter of the left parietal hemisphere, on both T2 and diffusion sequences (Figure 2g-i). Cerebral maturation delay was also observed. Biometric data were between the 25th and 50th percentiles. According to the imaging findings, we concluded that the ventriculomegaly was probably the consequence of an intraventricular hemorrhage associated with ischemic lesions in the white matter and a delay in cerebral maturation. After termination of pregnancy, fetal postmortem examination at 31 weeks showed a eutrophic female fetus with a brain weight below the 5th percentile. Macroscopic brain analysis revealed delayed gyration and moderate dilatation of the lateral ventricles, with subependymal cysts at the ventricular junction and other confluent cysts in the right frontal pole (Figure 3e). The corpus callosum appeared thin without agenesis. Perls staining was negative, including around the different cysts.

Case 3

Fetus F3 was from the second pregnancy of an unrelated couple who already had a healthy child, without any familial history. Ultrasound examination at 23 gestational weeks found apparently complete corpus callosal agenesis with mild ventricular enlargement. Karyotyping and polymerase chain reaction analysis for cytomegalovirus were negative. A second ultrasound examination at 28weeks confirmed the corpus callosal agenesis and dilatation of the lateral ventricles (Figure 2n). On brain MRI at 28 weeks (Figure 2j-m), the head circumference was below the 3rd percentile. The cerebral parenchyma showed overall rarefaction, with widened pericerebral spaces. The corpus callosum was almost entirely absent, although a small central segment could be observed (8mm in length from the anteroposterior axis and 2mm in width). The septal cavity was absent. The third ventricle was dilated and appeared ascended. Bilateral ventriculomegaly was slightly asymmetrical (left lateral ventricle, 15 mm; right lateral ventricle, 13 mm). The frontal ventricular horns were dilated and the left frontal ventricular horn presented relatively rectangular contours. The ventricular walls were irregular and on the left side they were relatively indented, without the appearance of nodular heterotopia. Several pseudocystic zones suggestive of germinolytic lesions were observed, located particularly within the left basifrontal white matter and to a lesser extent within the right frontal subependymal region, and bilaterally within the germinative zone in the periphery of the temporal horns. Sagittal sequences showed a slit-like appearance of the lateral ventricular walls, suggesting extensive germinolytic lesions, probably corresponding to the echogenic ribbon that surrounds the ventricular wall on ultrasound. Additionally, there was a clear indentation of the left anterior frontal cortex and adjacent white matter, located at the level of the interhemispheric fissure paramedially, with a lacunar appearance, without radiological evidence of schizencephaly. The T1-and T2weighted gradient echo sequences were not suggestive of hemorrhagic stigma. Although it was still relatively early in gestation, a clear and global delay in gyration was noted. At the subtentorial level, the cerebellar growth parameters were below the 3rd percentile. The vermis appeared complete and the morphology of the fourth ventricle was normal. There was significant widening of all pericerebellar fluid spaces. Overall, a very early clastic event was hypothesized. The pregnancy was terminated at 31 weeks and the parents declined postmortem examination.

DISCUSSION

Our findings highlight that PDHA1 pathogenic variants may lead to ultrasound and brain MRI lesions suggestive of those observed in fetuses carrying COL4A1/COL4A2 pathogenic variants. In addition, our data strongly suggest the utility of exome sequencing in fetuses referred for COL4A1/COL4A2 screening for which targeted sequencing is negative.

Fetal brain anomalies of PDHA1 deficiency could lead to suspicion of lesions associated with COL4A1/COL4A2 pathogenic variants

Primary PDCD is a mitochondrial disorder of carbohydrate oxidation. Molecular alterations in the PDHA1 gene are the main cause of PDCD with an X-linked dominant inheritance pattern and a high frequency of de-novo variants (85-95% in female and 60-63% in male cases)2. The clinical phenotype and phenotype on imaging as well as the age at onset of PDCD are variable, the median age at onset being about 20 months3,4. PDCD may also present during fetal life, with prenatal ultrasound or MRI detecting microcephaly, ventriculomegaly, paraventricular pseudocysts, cerebellar hypoplasia, delayed gyration and/or dysgenesis of the corpus callosum. In addition, stroke-like lesions have been reported in some fetuses5. Fetal autopsy features have been described by Pirot et al.6 in two unrelated female fetuses with PDHA1 variants. The first patient had partial agenesis of the corpus callosum and microcephaly on routine ultrasound at 22 gestational weeks. Fetal MRI showed agenesis of the corpus callosum, microcephaly, colpocephaly, delayed gyral formation, cerebellar hypoplasia and microcavitary periventricular white-matter lesions. Macroscopic and histologic examination of the brain showed pachygyria, polymicrogyria, ventricular dilatation, pseudocysts of the subependymal germinal matrix and basal ganglia microcalcifications. The second fetus had agenesis of the corpus callosum, mild ventricular dilatation and delayed gyration at the 22-week ultrasound examination. Postmortem examination showed extensive subcortical cavitary lesions in the brain, corpus callosal hypoplasia, pseudocysts of the subependymal germinal matrix, dilatation of the ventricles, reactive gliosis and ischemic lesions.

Several clinical and imaging manifestations encountered in PDHA1 deficiency are also encountered in COL4A1/COL4A2 collagenopathy. First, microcephaly can be observed in both conditions, although less consistently in COL4A1/COL4A2 collagenopathy7. Second, ventriculomegaly is a common element in both cases6,8, although it is often classified as moderate in metabolic abnormalities compared with those associated with a hemorrhagic event. Hypoplasia of the corpus callosum, cerebellar hypoplasia, schizencephaly, gyration abnormalities and periventricular leukomalacia are also elements that can be observed in both PDHA1 deficiency and COL4A1/COL4A2-related disorders7,9,10. Dysgenesis of the corpus callosum in PDHA1 fetuses is thought to be developmental; this is in contrast to the corpus callosal lesions of COL4A1 fetuses, which are thought to be the consequence of clastic lesions6. For this reason, an early anomaly of the corpus callosum should lead to suspicion of a PDHA1 mutation. Finally, intracranial calcifications may be observed in both COL4A1/COL4A2 collagenopathy and PDHA1 deficiency6. Some elements, however, tend to be specific to only one of the two conditions. To our knowledge, periventricular germinolytic pseudocysts have not been reported in patients with pathogenic variants in COL4A1/COL4A2. Hemorrhages are usually not detected on brain histological examination, even after Perls staining, in fetuses with PDHA1 deficiency, in contrast to observations in most COL4A1/COL4A2 fetuses. Altogether, these data emphasize the overlap of PDHA1 and COL4A1/COL4A2 phenotypic features in fetuses carrying pathogenic variants.

Shared phenotypic features of fetuses in this series

In our three cases, antenatal brain imaging using ultrasound and particularly MRI raised the possibility of hypoxic-ischemic and/or hemorrhagic lesions, without demonstrating them clearly (non-specific white-matter abnormalities; paraventricular microcysts interpreted as germinolysis without certainty; absence of signs of intraventricular or intraparenchymal hemorrhage). In fetuses F1 and F3, the first sign of concern was an abnormal or absent corpus callosum (partial agenesis of the posterior part in F1 and almost complete agenesis in F3). In fetus F2, the corpus callosum appeared normal on ultrasound examination but a thin corpus callosum was then observed on fetal brain MRI. These corpus callosal abnormalities were confirmed by postmortem examination in two cases; postmortem was not carried out in fetus F3. All three fetuses presented the appearance of pseudo-and/or microcysts at the subependymal level, suggesting germinolysis. In F2, they appeared localized in the ganglionic eminence and organized in a 'string-of-beads' formation. In the same fetus, there were also microcysts in the anterior part of the lateral ventricles with a septate appearance, which was not suggestive of germinolysis. In fetuses F1 and F3, cerebellar hypoplasia was also observed. These different findings are rather unusual for lesions of vascular origin, such as those found in COL4A1/COL4A2 collagenopathy. When hypoxic-ischemic/hemorrhagic lesions are suspected, it is crucial to examine carefully the appearance of microcysts that are not truly undergoing germinolysis, and to look for developmental abnormalities of the corpus callosum and cerebellum that may indicate PDHA1 deficiency, particularly in a female fetus.

Exome sequencing: efficient strategy for fetuses with suspected cerebral hypoxicischemic lesions and ventriculomegaly

This study emphasizes the difficulty in some cases in achieving accurate diagnosis based on fetal phenotypic analysis. In these three fetuses, imaging findings initially suggested a diagnosis based on a hypoxic-ischemic or hemorrhagic event, which led us to conduct firstline targeted sequencing of the COL4A1/COL4A2 genes. The final diagnosis was achieved only after an exome-wide analysis performed using a proband-only strategy. Taken together, these data highlight the importance of genome-wide screening after targeted COL4A1/COL4A2 gene screening, coupled with sequential in-silico analysis of candidate genes, based on a multidisciplinary approach.

ACKNOWLEDGMENTS

We thank sincerely Dr Patricia Blanchet, Dr Alain Couture and Dr Anne Paris for their collaboration on this work. We also thank families for their participation in this study, and clinicians, geneticists and pathologists who referred fetuses enrolled in this study. Finally, we are greatly indebted to Dr Florence Marchelli for her excellent editing of figures. This work was supported by the National Institutes of Health (R01NS096173 grant).


Objective.

Giant cell arteritis (GCA) has a relapsing-remitting course and is associated with a high burden of comorbidities, leading to repeated hospitalizations. This study was undertaken to investigate the burden, risk factors, causes, and outcomes of hospitalization and readmission in GCA patients in a US national cohort.

Methods.

Using the 2017 US National Readmission Database, we identified adults ≥50 years of age hospitalized with GCA between January and June 2017, with at least 6 months of follow-up. We estimated the burden of hospitalization including 6-month risk of readmission, total days spent in hospital, and costs, annually. We examined patient-, hospital-, and index hospitalization-related factors for 6-month readmission and total days of hospitalization using binomial logistic regression.

Results.

Our study included 1,206 patients hospitalized with GCA (70% women, median age 77 years), with 13% of patients experiencing GCA-related ophthalmologic complications at index hospital admission. On follow-up, 3% died, and 34% of patients were readmitted within 6 months, primarily for infections (23%) and cardiovascular diseases (CVDs) (15%). Charlson comorbidity index (CCI) of ≥1, smoking, and obesity were associated with readmission. GCA patients spent a median of 5 days/year in hospital (interquartile range [IQR] 3-11), with those in the top quartile spending 19 days/year in hospital (IQR 14-26).

Conclusion.

GCA patients frequently experience unplanned health care utilization, with 1 in 3 patients experiencing readmission within 6 months, and 3% dying within the follow-up period. Infection and CVDs are common causes of readmission and may be related to glucocorticoid exposure. Population health management strategies are required in these vulnerable GCA patients.

INTRODUCTION

Giant cell arteritis (GCA) is a systemic vasculitis targeting large vessels, mainly affecting women and elderly patients [START_REF] Dejaco | The spectrum of giant cell arteritis and polymyalgia rheumatica: revisiting the concept of the disease[END_REF]. Approximately 1 in 1,900 adults over the age of 50 have GCA, with an annual incidence of 10 per 100,000 adults in this population [START_REF] Li | A meta-analysis of the epidemiology of giant cell arteritis across time and space[END_REF]. The disease follows a relapsing-remitting course, with _15% of patients experiencing major relapse annually [START_REF] Aussedat | Epidemiology of major relapse in giant cell arteritis: a study-level meta-analysis[END_REF]. Even though GCA may not be associated with an increased risk of death [START_REF] Garvey | Incidence, survival, and diagnostic trends in GCA across seven decades in a North American population-based cohort[END_REF], it is associated with increased risk of ophthalmologic complications, cerebrovascular accidents, prolonged glucocorticoid exposure, and a high burden of comorbidities [START_REF] Li | A meta-analysis of the epidemiology of giant cell arteritis across time and space[END_REF][START_REF] Mainbourg | Prevalence of giant cell arteritis relapse in patients treated with glucocorticoids: a meta-analysis[END_REF][START_REF] Mahr | Presentation and real-world management of giant cell arteritis (Artemis Study)[END_REF][START_REF] Castan | Impact of glucocorticoid cumulative doses in a real-life cohort of patients affected by giant cell arteritis[END_REF]. These factors result in a high burden of hospitalization, unplanned health care utilization, and costs [START_REF] Mohammad | Trajectory of healthcare resources utilization in giant cell arteritis: a population-based study[END_REF][START_REF] Babigumira | Estimating the cost of illness of giant cell arteritis in the United States[END_REF].

There is limited information regarding outcomes in patients hospitalized with GCA. Identifying characteristics of patients at high risk of frequent hospitalizations and long hospital stays could help tailor risks and reduce health care costs in elderly patients. Hence, we used the 2017 Nationwide Readmissions Database (NRD), an all-payer database of hospital inpatient stays, developed as part of the Healthcare Cost and Utilization Project (HCUP), to describe the characteristics of hospitalized GCA patients, readmission rates, causes and risk factors for hospitalizations, and costs.

PATIENTS AND METHODS

Data source.

The 2017 NRD is a population-wide longitudinal database developed by the HCUP, sponsored by the Agency for Healthcare Research and Quality (AHRQ). The NRD contains a unique patient identifier that allows linkage of individual patients across hospitalizations within all participating states over the course of a year. It contains demographic, clinical, and nonclinical variables from all community hospitals, public hospitals, and academic medical centers, enabling study of readmission. This database accounts for 49.3% of the US population and contains _85% of discharges from the State Inpatient Databases (obtained from 21 US states). Although primarily designed to examine encounterlevel 30-day risk of readmission metrics, we transformed this data set to create a patient-level longitudinal, nationally representative cohort of hospitalized adults in the US [START_REF] Nguyen | Annual burden and costs of hospitalization for high-need, high-cost patients with chronic gastrointestinal and liver diseases[END_REF].

Study population.

From the 2017 NRD, we identified adults ≥50 years old hospitalized between January 1, 2017 and June 30, 2017, with ≥1 code of GCA (with or without associated polymyalgia rheumatica [PMR]) as a primary or secondary discharge diagnosis, based on International Statistical Classification of Diseases and Related Health Problems, Tenth Revision (ICD-10) codes (see Figure 1 and Supplementary Table 1, available on the Arthritis Care Research website at http://onlinelibrary.wiley.com/doi/10.1002/acr.25081) [START_REF] Mahr | Presentation and real-world management of giant cell arteritis (Artemis Study)[END_REF][START_REF] Hunder | The American College of Rheumatology 1990 criteria for the classification of giant cell arteritis[END_REF][START_REF] Caudrelier | Validation of giant cell arteritis diagnosis code in the French hospital electronic database[END_REF]. The positive predictive value of this approach to GCA diagnosis was >90% in a French study [START_REF] Caudrelier | Validation of giant cell arteritis diagnosis code in the French hospital electronic database[END_REF]. First hospitalization was defined as the index hospitalization. To estimate annual burden and readmission risk, the "atrisk" period for readmission was defined as the period from discharge following index hospitalization to the end of the study year, December 31, 2017, or death. We excluded patients whose index hospitalization was between July and December 2017 (to ensure a minimum 6-month follow-up period for all patients); patients hospitalized with other concomitant autoimmune diseases including rheumatoid arthritis, systemic lupus erythematosus, or vasculitis (to avoid misclassification of attribution); patients who were transferred from another hospital; or those with missing data for the lengths of hospital stays.

Baseline characteristics.

We selected data on relevant patient characteristics during index hospitalization, including age, sex, primary expected payment source (Medicare/Medicaid or other payment, combining private insurances and self-pay), income quartile based on the median household income at the patient's zip code, and relevant comorbidities (diabetes, cardiovascular diseases [CVDs], kidney and lung diseases, gastrointestinal [GI] and liver diseases). From these comorbidities and specific medical conditions, along with the ages of the patient, we derived Charlson comorbidity index (CCI) (see Supplementary Table 2, at http://onlinelibrary.wiley.com/doi/10.1002/acr.25081), which was designed to predict 1-year mortality in patients with a range of comorbid conditions. We also calculated the prevalence of frailty using the Hospital Frailty Risk Score, which was developed and validated in 1.04 million hospitalized patients ≥75 years old [START_REF] Gilbert | Development and validation of a Hospital Frailty Risk Score focusing on older people in acute care settings using electronic hospital records: an observational study[END_REF]. The Hospital Frailty Risk Score is used to screen for frailty and identify a group of patients who are at greater risk of adverse outcomes (e.g., mortality, readmission, length of stay). This score is based on ICD-10 codes and can be readily implemented in hospital information systems. Detailed calculation of this score is shown in Supplementary Table 3 (at http://onlinelibrary.wiley.com/doi/10.1002/acr.25081). We classified the patients as normal (score <5) or pre-frail/frail (score ≥5).

We also selected data regarding hospital characteristics including location (urban area = >1 million residents), teaching status, and bed size (small, medium, or large, based on the number of short-term acute care hospital beds, obtained from the American Hospital Association's annual survey of hospitals). NRD does not include data on outpatient/office visits, medication use, or biologic tests and pathologic results. In addition, we recorded GCA-specific variables, including procedure codes for temporal artery biopsy (TAB). Because GCA-related ophthalmologic complications deeply impact prognosis in GCA patients, we described highly suspected GCA-related ophthalmologic conditions, combining blindness, ischemic optic neuropathy, and retinal artery occlusion occurring 31 days before the index date to the end of the follow-up period (see ICD-10-related codes in Supplementary Table 1 at http://onlinelibrary.wiley.com/doi/10.1002/acr.25081). Additional specific comorbidities of interest (CVDs and risk factors, obesity, dementia, smoking status, and cancers) were recorded based on ICD-10 codes before or around index hospitalization (details regarding codes are shown in Supplementary Table 1).

Outcomes.

To examine unplanned health care utilization, we calculated 1) risk of all-cause readmission at 1 month, 3 months, and 6 months after index hospitalization; 2) annual burden and cost of hospitalization, using total days spent in the hospital in a calendar year as the primary metric including index hospitalization (divided into quartiles) (cost of hospitalizations was computed by multiplying charges for each hospitalization with the cost-to-charge ratios for each hospital for a given year, with inflation adjusted to the year 2017); and 3) percentage of inpatient mortality.

Among patients who were readmitted within 6 months, we classified causes of readmission based on the primary discharge diagnosis as 1) CVDs (combining ischemic heart disease, hypertension and its complications, heart failure, arrythmias, arterial diseases); 2) cerebrovascular diseases (combining stroke, stenosis of precerebral arteries, and seizures); 3) all infections (including respiratory infections, bacteremia and other sepsis, urinary tract infection, or intestinal infections); 4) metabolic diseases (diabetes, kidney diseases, electrolyte disorders); 5) venous thromboembolic events, including pulmonary embolisms; 6) noninfectious respiratory diseases (combining chronic obstructive pulmonary disease, acute and chronic respiratory failure, hypoxemia); 7) GI diseases (gastric and duodenal ulcers, gastroesophageal reflux, GI hemorrhages, ileus, constipation, unspecified colitis); 8) musculoskeletal disorders (combining osteoarthritis, gout, chondrocalcinosis, osteoporosis, trauma, and myopathy); 9) and cancers (solid neoplasms and blood malignancies) (see Supplementary Table 1, at http://onlinelibrary.wiley.com/doi/10.1002/acr.25081). Other discharge codes were classified into "miscellaneous diagnoses."

We evaluated risk factors at index hospitalization associated with 6-month readmission and a high burden of health care utilization (days spent in hospital from the date of index hospitalization). We also evaluated factors associated with GCA-related ophthalmologic complications.

Statistical analysis.

Descriptive statistics were used to describe baseline demographic characteristics, hospital characteristics, and index hospitalization characteristics in GCA patients. Categorical variables are expressed as percentages, and continuous variables are expressed as the median (interquartile range [IQR]). Patients were followed up from date of discharge from index hospitalization until outcome of interest (readmission) or end of the year. Patients who died as inpatients during index hospitalization (no possibility of readmission) were excluded from the analysis. To evaluate the independent impact of baseline factors on 6-month readmission, we performed binomial logistic regression accounting for patient factors (age, sex, annual income level, Medicare/Medicaid status, frailty risk score, CCI), disease factors (GCA with or without PMR, GCA-related ophthalmologic complications), and hospital factors (location, bed size, teaching status, and length of hospital stay for index hospitalization).

Similarly, we examined risk factors associated with the annual burden of hospitalization (total days spent in hospitalization, inclusive of index hospitalization) using conditional linear regression models. We performed multivariate binomial logistic regression analysis to study the risk factors associated with GCA-related ophthalmologic complications, including age, sex, income level, insurance status, hospital characteristics, and main comorbidities (CCI, frailty, or ischemic heart disease). When one of the composite scores of comorbidities (CCI or frailty) was significantly associated with the outcome of interest, we conducted a secondary analysis focusing on specific components relevant in elderly patients: smoking, obesity, diabetes, ischemic heart disease, and dementia. All results from the regression models were represented by the odds ratio (OR) with accompanying 95% confidence interval (95% CI). Statistical analysis was conducted using RStudio version 1.4.1717.

Ethics.

This study was exempt from institutional review board approval because the NRD is a publicly available database containing deidentified patient information. The present study was performed in accordance with the AHRQ's data use agreement.

RESULTS

We identified 2,477 inpatients with ≥1 diagnosis code of GCA in the 2017 NRD database. After excluding patients <50 years old, with index hospitalization after June 30, or with concomitant exclusionary autoimmune diseases, our cohort included 1,206 patients hospitalized with GCA (Figure 1).

Patient characteristics.

Characteristics of the 1,206 GCA patients are shown in Table 1. The median (IQR) age was 77 years (68-84 years); 70% were female. Approximately 13% of patients had a concomitant diagnosis of PMR. Approximately 43% were classified as frail, and 35% had CCI ≥1, most commonly hypertension or related complications (61%), ischemic heart disease (27%), and diabetes (27%); 10% were obese and 20% were smokers. TABs were performed in 34% of patients during the year, and these patients were younger and were more likely to have been admitted to a large and/or a teaching hospital.

The median follow-up period after index hospitalization was 8 months (IQR 7-10). Approximately 13% of patients (n = 156) experienced ophthalmologic events (including blindness in 130 patients); 83% of these events occurred during index hospitalization. GCArelated ophthalmologic complications were more likely to occur in GCA patients without PMR compared with patients with concomitant PMR (OR 3.46 [95% CI 1.69-8.36]), whereas the presence of ischemic heart disease was associated with a lower risk of GCA-related ophthalmologic complications (OR 0.58 [95% CI 0.36-0.88]) (independent of age, sex, income level, Medicare/Medicaid, CCI, frailty score).

Risk and risk factors for readmission.

Of 1,202 patients alive after index hospitalization, we identified 484 patients (40%) with at least one readmission, with a median delay of 54 days (IQR 18-120) (Table 2); 243 (20%) were readmitted ≥2 times. Overall, 1-month, 3-month and 6-month risk of readmission was 13%, 26% and 34%, respectively. Among the 412 patients who were readmitted within 6 months, infections (23%) and CVDs (15%) were the two leading causes of readmission. Only 4% of patients were readmitted with GCA ± PMR as the primary discharge diagnosis, and there was no 6-month readmission for GCA-related ophthalmologic complications (Figure 2). Among hospitalizations for infections, bacteremia/ sepsis (10%) was more numerous than respiratory infections (5%) or intestinal infections (3%). Twenty-five patients (6%) were readmitted for GI diseases, and 7% for musculoskeletal disorders (Figure 2).

On binomial logistic regression analysis, independent risk factors for 6-month readmission were CCI ≥1 (OR 2.13 [95% CI 1.65-2.77]) and the presence of GCA-related ophthalmologic complications (OR 1.46 [95% CI 1.02-2.09]) (Table 3). When testing subcomponents of CCI in the model, smoking (OR 1.92 [95% CI 1.41-2.61]), obesity (OR 1.78 [95% CI 1.17-2.70]), diabetes (OR 1.45 [95% CI 1.09-1.93]), ischemic heart disease (OR 1.56 [95% CI 1.18-2.06]), and dementia (OR 2.72 [95% CI 1.81-4.13]) were independently associated with 6month readmission risk.

Annual burden of hospitalization.

GCA patients spent a median of 5 days (IQR 3-11) in the hospital, inclusive of index hospitalization (Table 2). Patients in the highest quartile for length of hospitalization spent a median of 19 days (IQR 14-26) in the hospital versus 2 days (2-3 days) in the lowest quartile. The median overall cost for hospital stays, inclusive of index hospitalization, was $112,000 (IQR $59,000-194,000); median costs were $181,000 (IQR $143,000-271,000) in the highest quartile compared with $15,000 (IQR $11,000-20,000) in the lowest quartile. The total number of days spent in hospitalization, inclusive of index hospitalization, was higher in men, patients with Medicare/Medicaid, pre-frail or frail patients, patients with high CCI, and patients with index hospitalization in a large hospital (Table 3).

Inpatient mortality.

Thirty-six patients (3%) died as inpatients within the year, of whom 4 died during index hospitalization.

DISCUSSION

GCA is associated with a significant burden of morbidity in older patients, who are at high risk of unplanned health care utilization. In this nationally representative cohort study using the NRD, which includes >85% of all hospital discharges in 21 states, we made several key observations regarding burden, risk factors, and outcomes in patients hospitalized with GCA. First, we observed that ~ 1 in 3 patients hospitalized with GCA are readmitted within 6 months, and ~20% are readmitted twice. On average, GCA patients spend 5 days in the hospital annually, with wide variability; patients in the highest quartile of total time spent in hospital spend almost 3 weeks in the hospital annually. Second, we observed that serious infections and CVDs are the leading causes of readmission in GCA patients, with only a small fraction readmitted primarily for GCA or direct complications from GCA. Third, we identified CCI ≥1, in particular obesity, smoking, and dementia, were novel risk factors associated with readmission. Overall, these findings regarding patterns and drivers of unplanned health care utilization in patients hospitalized with GCA may inform population health management strategies in these vulnerable patients.

There have been few population-based studies examining the burden of unplanned health care utilization in GCA patients. In a population-based cohort study in Olmsted County, Michet et al observed that GCA patients were at higher risk of all-cause hospitalization compared with those without GCA [START_REF] Michet | Hospitalization rates and utilization among patients with giant cell arteritis: a populationbased study from 1987 to 2012[END_REF]. In their cohort, hospitalization due to neurologic events including transient ischemic attack and syncope occurred at a higher frequency in GCA patients. In our cohort, cerebrovascular diseases accounted for readmission in ~ 6% of patients, while infections and CVDs were the leading causes of readmission. In another cohort study using the NRD published only in abstract form, 13% of patients primarily admitted for GCA were readmitted within 30 days, similar to the rate in our cohort [START_REF] Cao | Thirty-day readmission rate in patients who were initially admitted for active giant cell arteritis[END_REF]. However, as opposed to encounter-level analysis, we created a longitudinal cohort of patients to estimate annual burden and costs of hospitalization in GCA patients. The first step in population health management is identifying patients with highest health care utilization and sources of variability in outcomes. We observed that CCI ≥1, particularly smoking, diabetes, ischemic heart disease, and dementia were associated with an increased risk of readmission. We also observed that obesity was a novel risk factor for readmission. This may be related to a higher burden of cardiovascular risk, potential risk of serious infections [START_REF] Charoenngam | Body mass index and risk of clostridioides difficile infection: a systematic review and meta-analysis[END_REF], or potentially a reflection of higher glucocorticoid use leading to weight gain. These risk factors for higher rates of unplanned health care utilization may help identify a subgroup of GCA patients at high risk of readmission who may benefit from a proactive postdischarge monitoring strategy.

In our cohort, ~13% of GCA patients experienced ophthalmologic complications, the vast majority of which were present at time of initial hospitalization. This rate is consistent with other cohorts [START_REF] Mahr | Presentation and real-world management of giant cell arteritis (Artemis Study)[END_REF][START_REF] Pugnet | Predictors of cardiovascular hospitalization in giant cell arteritis: effect of statin exposure. A French population-based study[END_REF][START_REF] Chung | Veterans Health Administration national giant cell arteritis (GCA) database cohort: incident ophthalmic complications in biopsy-negative GCA patients[END_REF]. Interestingly, GCA-related ophthalmologic complications negatively correlated with history of ischemic heart disease. This may be related to the use of antiplatelet agents in patients with ischemic heart disease, which may be associated with a lower risk of GCA-related ophthalmologic complications and other ischemic events [START_REF] Nesher | Low-dose aspirin and prevention of cranial ischemic complications in giant cell arteritis[END_REF]. However, related data mainly involve retrospective studies, and data are heterogenous [START_REF] Martínez-Taboada | Effect of antiplatelet/anticoagulant therapy on severe ischemic complications in patients with giant cell arteritis: a cumulative meta-analysis[END_REF][START_REF] Monti | Systematic literature review informing the 2018 update of the EULAR recommendation for the management of large vessel vasculitis: focus on giant cell arteritis[END_REF]. In our cohort, data regarding medication use were not available. Aside from this impact of medication, there is a small competing risk of death, wherein patients with ischemic heart disease may be more likely to die prior to the development of GCA-related ophthalmologic complications.

Infections and CVDs were the leading causes of readmission in GCA patients. A high prevalence of serious infections was observed in GCA patients. In the Medicare database, serious infections were observed in 28% of GCA patients, with an incidence rate of 10.7 per 100 person-years [START_REF] Tedeschi | Giant cell arteritis treatment patterns and rates of serious infections[END_REF]. In this cohort, 85% of patients had received treatment with high-dose prednisone. In another cohort study in the Health Improvement Research Network, Durand et al observed that 48% of GCA patients developed systemic infections, with most infections occurring within 6 months of GCA diagnosis [START_REF] Durand | Incidence of infections in patients with giant cell arteritis: a cohort study[END_REF]; the risk of serious infection was 55% higher in GCA patients compared with age-and sex-matched non-GCA controls. In another multicenter cohort study, Schmidt et al observed that use of glucocorticoids at a dose of >10 mg/day 12 months after diagnosis was associated with serious infections and death [START_REF] Schmidt | Incidence of severe infections an infection-related mortality during the course of giant cell arteritis: a multicenter, prospective, double-cohort study[END_REF]. We also observed that CVDs were an important cause of readmission in GCA patients. While this risk may be high in older patients, several studies have demonstrated that GCA patients may have 1.5-2.5-fold higher risk of myocardial infarction and stroke [START_REF] Tomasson | Risk for cardiovascular disease early and late after a diagnosis of giant-cell arteritis: a cohort study[END_REF][START_REF] Amiri | Increased risk of cardiovascular disease in giant cell arteritis: a general population-based study[END_REF][START_REF] Li | Giant cell arteritis and vascular disease-risk factors and outcomes: a cohort study using UK Clinical Practice Research Datalink[END_REF][START_REF] Mohammad | Rate of comorbidities in giant cell arteritis: a population-based study[END_REF].

Other than old age, long-term, high cumulative use of glucocorticoids may be a major factor contributing to this increased risk of serious infections and cardiovascular events [START_REF] Castan | Impact of glucocorticoid cumulative doses in a real-life cohort of patients affected by giant cell arteritis[END_REF][START_REF] Gale | Risk associated with cumulative oral glucocorticoid use in patients with giant cell arteritis in real-world databases from the USA and UK[END_REF][START_REF] Wu | Incidence of infections associated with oral glucocorticoid dose in people diagnosed with polymyalgia rheumatica or giant cell arteritis: a cohort study in England[END_REF][START_REF] Broder | Corticosteroid-related adverse events in patients with giant cell arteritis: a claims-based analysis[END_REF]. Glucocorticoid-sparing treatment strategies, such as tocilizumab or JAK inhibitors [START_REF] Burmester | Continuing versus tapering glucocorticoids after achievement of low disease activity or remission in rheumatoid arthritis (SEMIRA): a double-blind, multicentre, randomised controlled trial[END_REF][START_REF] Stone | Trial of tocilizumab in giantcell arteritis[END_REF][START_REF] Prigent | JAK inhibitor effectiveness in giantcell arteritis with large-vessel involvement assessed by 18F-FDG PET-CT[END_REF][START_REF] Pugh | Large-vessel vasculitis[END_REF] are attractive and may decrease the risk of glucocorticoid complications and unplanned health care utilization in GCA patients. Further studies examining the comparative safety and impact on hospitalization and readmission with alternative treatment approaches in GCA patients is warranted. In addition to vaccination campaigns and monitoring cardiovascular risk and diseases, the observed proportion of GI and musculoskeletal diseases among the 6-month readmission causes in this fragile population of GCA patients could lead to specific preventive measures.

The strengths of our study include 1) use of a nationally representative database to study rehospitalization burden, 2) a novel, patient-centered metric of burden of hospitalization in "total days spent in hospital," and 3) assessment of causes of readmissions. Our study has several limitations. First, the analyses are based on administrative codes and only focus on inpatient use, without details of outpatient clinic visits, medication use, and laboratory variables. Indeed, patients diagnosed as having GCA as outpatients were not selected in our study: the prevalence rate of hospitalization and characteristics in these patients could be interesting to study in order to report "low-risk" patients for hospitalizations. Second, causes of readmissions were identified using primary discharge diagnoses, which were grouped by disease system to allow for interpretation. Third, since the NRD uses data from state inpatient databases, it does not track patients across state boundaries. However, in validation studies performed by the HCUP, the rate of cross-state hospitalizations was found to be <5% of all admissions, thereby unlikely to substantially affect our estimates. Moreover, the NRD does not capture out-of-hospital mortality, which may bias the "at risk of hospitalization" time period. Finally, the comparison of the outcomes concerning our hospitalized GCA patients to a matched control group could provide details regarding the specific risk factors associated with readmission rates.

In conclusion, in this nationally representative study of patients hospitalized with GCA, we observed high rates of unplanned health care utilization and considerable variability in the burden of hospitalization, with a small fraction of patients disproportionately contributing to total hospitalization burden and costs. Infections and CVDs, potentially related to prolonged glucocorticoid exposure, contribute as leading causes of readmission. Population health management strategies directed toward identifying high-need, high-cost GCA patients and implementing multicomponent chronic care models may improve quality of care and reduce costs of care.

AUTHOR CONTRIBUTIONS

All authors were involved in drafting the article or revising it critically for important intellectual content, and all authors approved the final version to be submitted for publication. Dr. Goulabchand had full access to all of the data in the study and takes responsibility for the integrity of the data and the accuracy of the data analysis.

Study conception and design.

Goulabchand, Qian, Nguyen, N. Singh, S. Singh.

Acquisition of data.

Goulabchand, Qian, S. Singh.

Analysis and interpretation of data.

Goulabchand, Qian, Nguyen, A. Singh, Roubille, Parreau, N. Singh, S. Singh.


C Hoareau

J.-F De

R Ohayon
email: roger.ohayon@cnam.fr

A FINITE ELEMENT APPROACH FOR HYDROELASTIC VIBRATIONS OF PARTIALLY FILLED PRESTRESSED ELASTIC TANKS

Keywords: Hydroelasticity, Follower forces, Geometric non-linearities, Finite element method

.

INTRODUCTION

This study deals with the Finite Element (FE) computation of hydroelastic vibrations of prestressed elastic tanks with free-surface fluid. The prediction of fluid-structure dynamic behavior is a critical step in aerospace engineering for the design of launchers with liquid propellant or tanks of satellites [START_REF] Morand | Fluid-Structure Interaction[END_REF][START_REF] Schotté | Linearized formulation for fluid-structure interaction: Application to the linear dynamic response of a pressurized elastic structure containing a fluid with a free surface[END_REF]. The use of flexible structures, such as hyperelastic membranes or very thin walls, induces the need of numerical models taking into account the prestressed state due to geometrical non-linearities. The main objective of this work is to estimate the influence of the prestressed state on the dynamic behavior of the fluid-structure system. The proposed approach consists (i) in solving the quasi-static non-linear FE problem of the filled tank submitted to hydrostatic follower forces [START_REF] Hoareau | Non-linear finite element analysis of an elastic structure loaded by hydrostatic follower forces[END_REF], and then (ii) to evaluate the hydroelastic vibrations around the prestressed state. For the dynamical problem, eigenmodes are evaluated around the prestressed state taking into account the added mass effect of the incompressible fluid (Figure 1). Some numerical examples are proposed (i) to validate the model by comparison with some experimental results from the literature [START_REF] Chiba | Nonlinear hydroelastic vibration of a cylindrical tank with an elastic bottom, containing liquid. Part I: Experiment[END_REF] and (ii) to show the efficiency of the approach. The competition between the added-mass and prestressed effects of a partially filled tank with elastic bottom, for various fluid heights, is highlighted through parametric studies.

Solid hypotheses

The structure is supposed homogeneous isotropic elastic and prestressed by hydrostatic follower forces. For the geometrical nonlinear model, we consider the Saint-Venant Kirchhoff constitutive law which is valid for large displacement and small strains. The total structural displacement u t is the sum of two terms: a quasi-static non linear solution u s and the displacement fluctuation around the prestressed state u, such that

u t = u s + u (1)
Note that the displacement fluctuation amplitude is supposed very small compared to a characteristic length of the structure (e.g. the thickness of the tank).

Fluid hypotheses

The fluid is supposed heavy, inviscid, irrotational and incompressible. Moreover, fluid surface tension is neglected which implies that the free surface is plane at the equilibrium. The sloshing vibrations due to gravity effects are not considered in the study. Consequently, the pressure fluctuation p on the free surface Γ is given by

p = 0 on Γ (2)
With all the previous hypotheses, the pressure fluctuation around the prestressed state can be either defined as the eulerian or by the lagrangian fluctuation (see [START_REF] Morand | Fluid-Structure Interaction[END_REF] for details)

p = p L = p E (3)
Fluid-structure interface hypotheses The no-penetration condition at the fluidstructure interface implies that the fluid normal velocity v is equal to the structural normal velocity u:

v • n f = -u • n s on Σ ( 4
)
where Σ is the fluid-structure interface (also called the wetted surface) and n f (resp. n s ) is the outer unitary normal to the fluid domain (resp. to the solid domain).

HYDROELASTICITY WITHOUT PRESTRESSING 2.1 Coupled formulation

A standard (u, p) formulation [START_REF] Morand | Fluid-Structure Interaction[END_REF] is chosen where u is the displacement fluctuations around a reference configuration and p the pressure fluctuations in the fluid domain (Figure 2).

Figure 2: Hydroleastic problem description without pre-stress effect under a small amplitude harmonic load f, with no gravity effect such that the pressure fluctuation is fixed as p = 0 on the free surface Γ.

A volumetric discretization is generated for each domain (Figure 3) with a coincident mesh at the fluid-structure interface Σ h . Let's define u h and p h as a linear combination of shape functions on the discretized domains written as

u h = N q q and p h = N p p (5)
where N q and N p are respectively the shape function matrices of the displacement and pressure fields, and q and p the displacement and pressure unknowns nodal vectors.

Harmonic problem

From the (u, p) formulation we obtain the following harmonic system of equations:

K -ω 2 M q + Cp = F (6) Hp + ω 2 C T q = 0 (7)
where K the linear stiffness matrix, M the solid mass matrix, F the nodal external force vector, H the matrix associated with the bilinear pressure gradient and C the coupling matrix between the nodal displacements and nodal pressure vectors. In matrix form, the previous system can be written

    K C O H   -ω 2   M O -ρ f C T O       q p   =   F 0   (8)
The associated eigenvalue problem is not symmetric and could generate numerical difficulties with classical algorithms. Note that the use of a (u, ϕ) formulation, based on a fluid potential displacement ϕ, can be used to symetrized the problem (see [START_REF] Morand | Fluid-Structure Interaction[END_REF] for details). According to the pressure fluctuation condition on the free surface given by Equation ( 2), the matrix H is invertible and the pressure unknowns can thus be condensed on the solid displacements unknowns

K -ω 2 (M + M a ) q = F (9)
where M a is the so called added mass matrix operator given by

M a = ρ f CH -1 C T (10)
The added mass matrix is symmetric positive definite but full. Its evaluation can leads to some numerical issues out of the scope of this paper.

Effect of the fluid height on the natural frequencies

The eigenvalue problem associated with Equation ( 9) is written as

K -ω 2 (M + M a ) X = 0 (11)
where (ω 2 i , X i ) for i = 1 . . . k are the first k eigenvalues and eigenvectors with ω 1 < ω i < ω k . Note that in linear dynamics, when the fluid height increase during a filling process, the natural frequencies decrease due to the added mass effect [START_REF] Morand | Fluid-Structure Interaction[END_REF].

HYDROELASTICITY AROUND A PRESTRESSED STATE

Let's consider the hydroelastic problem around a prestressed state defined in Figure 4. The total nodal displacement is given by q t = q s + q where q s is the solution of a non-linear quasi-static problem and q is a small amplitude displacement fluctuation. In the following, we assume that q s is already known from a quasi-static nonlinear simulation detailed in [START_REF] Hoareau | Non-linear finite element analysis of an elastic structure loaded by hydrostatic follower forces[END_REF].

Discretized equations

Non-linear static equilibrium The discrete equilibrium equation of a partially filled elastic tank, with geometrical non-linearities, is given by

G(q s ) = F int (q s ) -F ext (q s ) = 0 (12)
where F int and F ext are respectively the internal and external nodal forces. The external forces correspond to the hydrostatic follower forces. Note that no volumetric fluid mesh is needed to solve the quasi-static non-linear equation [START_REF] Hoareau | Non-linear finite element analysis of an elastic structure loaded by hydrostatic follower forces[END_REF].

Dynamic equilibrium For the discrete dynamic problem around the prestressed state, we assume that the total external force F t is the sum of the hydrostatic follower force F ext (q s ) and a small external harmonic load F. The discretized dynamic problem is thus defined by G(q s + q)ω 2 M(q s )q + C(q s )p = F (13)

Hp + ω 2 C T (q s )q = 0 (14) M(q s ) and C(q s ), which are the mass and coupling matrices defined on the current configuration of the solid, are noted M and C in the rest of the paper. Note that contrary to the quasi-static problem, meshes are needed for both fluid and solid volumetric domains in order to generate the discretized operators.

Linearization If the amplitude of the displacement fluctuation q is small compared to the quasi-static displacement solution q s , we obtain, by linearization and using Eq. ( 12), the following relation

G(q s + q) ≃ ∂G (q s ) ∂q q = K tan q (15)
where K tan is the tangent stiffness matrix. This tangent stiffness matrix is given by K tan = K mat + K geo -K fol where K mat is the material tangent stiffness, K geo the geometrical tangent stiffness and K fol the follower tangent stiffness.

C. Hoareau, J.-F. Deü and R. Ohayon

Consequently, Eq. ( 13) and ( 14) gives the linearized hydroelastic problem

K tan -ω 2 M q + Cp = F (16) Hp + ω 2 C T q = 0 (17)
which can be written in matrix form

    K tan C O H   -ω 2   M O ρ f C T O       q p   =   F 0   (18)

Effect of fluid height on natural frequencies

Using the approach detailed in the previous section, we obtain the following eigenvalue problem

K tan -ω 2 (M + M a ) X = 0 (19)
Due to the fact that all the matrix operators depend on the non-linear quasi-static solution, we are not able to predict a priori the eigenvalue evolution, i.e. without solving the problem for each fluid height.

NUMERICAL EXAMPLE

In this section, we perform a parametric study to estimate the influence of the nonlinearities on the dynamic response of an hydroelastic problem. The goal is to compare the added-mass and prestress effects on the eigenvalue problem given by the equation (19). Let's consider a cylinder with rigid walls and an elastic bottom, partially filled with liquid (Figure 5). The influence of the fluid height is studied and our numerical results are compared to the experimental ones given in [START_REF] Chiba | Nonlinear hydroelastic vibration of a cylindrical tank with an elastic bottom, containing liquid. Part I: Experiment[END_REF]. To compute the natural frequencies of the coupled system, we proceed in two steps :

• Firstly, we compute the non-linear quasi-static equilibrium state of the rigid cylinder with a flexible bottom loaded by the hydrostatic follower forces for various fluid heights [START_REF] Hoareau | Non-linear finite element analysis of an elastic structure loaded by hydrostatic follower forces[END_REF].

• Then, we remesh the fluid domain in order to obtain a coincident mesh between the fluid and the solid. This allows us to solve the eigenvalue problems (19) for each fluid height.

On Figure 6 we can see the evolution of first eigenfrequencies in terms of the fluid height (between 0 and 250 mm). Except for the first eigenmode, we can observe first a decrease then an increase of the natural frequencies during the filling process. The decreasing is due to the influence of the added-mass effect and the increasing is due to the prestress effect. Indeed, the added mass effect is related to the kinetic energy of the displaced fluid by the elastic bottom leading to a decrease of the frequencies. On the contrary, the prestress effect leads to a stiffening of the structure. The order of magnitude of the computed natural frequencies is very close to the experimental observations from [START_REF] Chiba | Nonlinear hydroelastic vibration of a cylindrical tank with an elastic bottom, containing liquid. Part I: Experiment[END_REF]. This validate our numercial approach.

In this paper, a Finite Element approach has been proposed to compute the dynamic behaviour of an elastic tank partially filled with fluid. Both the added-mass and the prestress effects on the linearized hydroelastic vibrations are included in the model. Numerical results are obtained for a cylinder with rigid walls and an elastic bottom, partially filled with liquid. These results are in very good agreements with the experimental observations from [START_REF] Chiba | Nonlinear hydroelastic vibration of a cylindrical tank with an elastic bottom, containing liquid. Part I: Experiment[END_REF]. Indeed, the added mass effect decreases the natural frequencies contrary to the pre-stress effect which increases them. The extension to more complex geometries will be the object of further investigations.

Figure 1 :

 1 Figure 1: (a) Reference configuration of the internal surface of a tank ; (b) Current configuration of internal surface of a tank loaded by hydrostatic follower forces; (c) Linearized hydroelastic vibration around a pre-stressed state without gravity effects

Figure 3 :

 3 Figure 3: FE discretization with twenty nodes quadratic volumetric element (HEXA 20) for the solid and fluid domains and height nodes quadratic surfacic elements (QUAD 20) for surfacic domains. The fluid and the solid domains have coincident meshes.

Figure 4 :

 4 Figure 4: (a) Reference configuration without fluid; (b) currrent configuration for a given fluid height; (c) linearized vibration around a prestressed state under a small amplitude excitation f.

Figure 5 :

 5 Figure 5: (a) Filling of a cylinder of diameter D = 357 mm with water ρ f = 1000 kg.m -1 , rigid walls and an elastic bottom of thickness t = 0.357 mm made of plexiglas. The material parameters are the Young Modulus E = 5.47e9 Pa and a Poisson Ration of 0.38 and the plexiglas density ρ s = 1.38 kg.m -3 . The fluid height value is such that h ∈ [0, 250] mm; (b) Hydroelastic vibrations around the pre-stressed state for a given fluid height h.

Figure 6 :

 6 Figure 6: Evolution of natural frequencies in function of the fluid height with K tan = K mat +K geo -K fol