Sami Barrit
email: samibarrit@gmail.com

Mejdeddine Al Barajraji
email: mejdi.albarajraji@gmail.com

Salim El Hadweh

Olivier Dewitte
email: olivier.de.witte@erasme.ulb.ac.be

Nathan Torcida
email: nathan.torcida.sedano@erasme.ulb.ac.be

Joachim Andre
email: joachim.andre@ulb.be

Fabio Silvio Taccone
email: fabio.taccone@ulb.be

Sophie Schuind
email: sophie.schuind@erasme.ulb.ac.be

Elisa Gouvêa Bogossian
email: elisagobog@gmail.com

Brain Tissue Oxygenation-Guided Therapy and Outcome in Traumatic Brain Injury: A Single-Center Matched Cohort Study

Keywords: brain oxygenation, outcome, protocolized care, head injury, trauma

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

Introduction

Traumatic brain injury (TBI) is a major public health burden, causing death and disability worldwide [START_REF] Injury | Global, regional, and national burden of traumatic brain injury and spinal cord injury, 1990-2016: A systematic analysis for the Global Burden of Disease Study 2016[END_REF]. The global incidence of TBI is estimated to be around 27 to 69 millions of events per year [START_REF] Injury | Global, regional, and national burden of traumatic brain injury and spinal cord injury, 1990-2016: A systematic analysis for the Global Burden of Disease Study 2016[END_REF][START_REF] Dewan | Estimating the global incidence of traumatic brain injury[END_REF]; in order to potentially improve long-term outcomes of these patients, prevention and treatment of secondary brain injury is essential since, secondary brain injury is a major determinant of outcome after TBI [START_REF] Chesnut | The role of secondary brain injury in determining outcome from severe head injury[END_REF]. Intracranial pressure (ICP) and cerebral perfusion pressure (CPP) monitoring are widely used to optimize cerebral hemodynamics after severe TBI, since intracranial hypertension is associated with worse outcome in this setting [START_REF] Badri | Mortality and long-term functional outcome associated with intracranial pressure after traumatic brain injury[END_REF]. However, no high-quality evidence suggests that this approach may improve neurological recovery in TBI patients [START_REF] Carney | Guidelines for the Management of Severe Traumatic Brain Injury, Fourth Edition[END_REF]. Moreover, brain hypoxia, that might exist even in the absence of intracranial hypertension, i.e., because of microvascular dysfunction, systemic hypotension, hypoxemia, fever or anemia, is also an important cause of secondary brain injury and independent predictor of poor outcome [START_REF] Cruz | On-line monitoring of global cerebral hypoxia in acute brain injury. Relationship to intracranial hypertension[END_REF][START_REF] Chesnut | Early and late systemic hypotension as a frequent and fundamental source of cerebral ischemia following severe brain injury in the Traumatic Coma Data Bank[END_REF][START_REF] Marmarou | Impact of ICP instability and hypotension on outcome in patients with severe head trauma[END_REF][START_REF] Bouma | Cerebral circulation and metabolism after severe traumatic brain injury: The elusive role of ischemia[END_REF].

As such, brain tissue oxygen (PbtO 2 ) monitoring allows the detection of brain hypoxia in acute brain injured patients [START_REF] Cruz | On-line monitoring of global cerebral hypoxia in acute brain injury. Relationship to intracranial hypertension[END_REF][START_REF] Bouzat | Beyond intracranial pressure: Optimization of cerebral blood flow, oxygen, and substrate delivery after traumatic brain injury[END_REF]. Although three ongoing randomized clinical trials investigating the effect of PbtO 2 -guided therapy on the outcome of TBI patients, the current evidence suggesting that PbtO 2 -guided therapy provides beneficial effects on survival and neurological recovery is based only one phase-II randomized study [START_REF] Okonkwo | Brain Oxygen Optimization in Severe Traumatic Brain Injury Phase-II: A Phase II Randomized Trial[END_REF] and several retrospective or before-after cohort studies, in which the populations were significantly unbalanced at baseline [START_REF] Nangunoori | Brain tissue oxygen-based therapy and outcome after severe traumatic brain injury: A systematic literature review[END_REF][START_REF] Xie | Mortality and Outcome Comparison Between Brain Tissue Oxygen Combined with Intracranial Pressure/Cerebral Perfusion Pressure-Guided Therapy and Intracranial Pressure/Cerebral Perfusion Pressure-Guided Therapy in Traumatic Brain Injury: A Meta-Analysis[END_REF][START_REF] Lin | A Prospective Randomized Study of Brain Tissue Oxygen Pressure-Guided Management in Moderate and Severe Traumatic Brain Injury Patients[END_REF][START_REF] Spiotta | Brain tissue oxygen-directed management and outcome in patients with severe traumatic brain injury[END_REF][START_REF] Narotam | Brain tissue oxygen monitoring in traumatic brain injury and major trauma: Outcome analysis of a brain tissue oxygen-directed therapy[END_REF][START_REF] Stiefel | Reduced mortality rate in patients with severe traumatic brain injury treated with brain tissue oxygen monitoring[END_REF]. Moreover, some cohort studies have failed to show any significant benefit of PbtO 2 -guided therapy on neurological outcome of these patients [START_REF] Adamides | Focal cerebral oxygenation and neurological outcome with or without brain tissue oxygen-guided therapy in patients with traumatic brain injury[END_REF][START_REF] Meixensberger | Brain tissue oxygen guided treatment supplementing ICP/CPP therapy after traumatic brain injury[END_REF][START_REF] Martini | Management guided by brain tissue oxygen monitoring and outcome following severe traumatic brain injury[END_REF][START_REF] Green | Goal directed brain tissue oxygen monitoring versus conventional management in traumatic brain injury: An analysis of in hospital recovery[END_REF][START_REF] Mccarthy | Neurologic outcomes with cerebral oxygen monitoring in traumatic brain injury[END_REF].

Therefore, the aim of this study was to assess the effectiveness of ICP/PbtO 2 -guided therapy compared to ICP-guided therapy on neurological outcome and global management of TBI patients.

Materials and Methods

We conducted a single-center retrospective cohort study of severe TBI patients admitted to the intensive care unit (ICU) of Erasme Hospital (Brussels, Belgium) from January 2012 to December 2019. All adult (>18 years) patients admitted with severe TBI (Glasgow coma scale, GCS < 9) during the study period were eligible for inclusion, if they needed an ICP monitoring in the first 48 h after admission. The decision to further monitor patients with PbtO 2 probes was determined by device availability, which became standard of care since February 2017. The sole exclusion criterion was imminent death, resulting into early limitation of life-sustaining therapies. This study was approved by the Erasme Hospital (Université Libre de Bruxelles, Brussels, Belgium) ethics committee (2021/099), which waived the need for informed consent. This study was performed in accordance with relevant scientific and ethical guidelines and regulations. We obtained data through the electronic chart system used at Erasme Hospital.

Data Collection

We collected demographic data and presence of comorbidities. Clinical severity scores on admission, such as the Sequential Organ Failure Assessment (SOFA) and the Acute Physiology and Chronic Health Evaluation (APACHE) II scores were recorded [START_REF] Knaus | APACHE II: A severity of disease classification system[END_REF]. The Marshall score was used to classify patients' severity according to the initial computerized tomography scan [START_REF] Marshall | A new classification of head injury based on computerized tomography[END_REF]. The basic therapy intensity level (TIL) score was used to assess the intensity of ICP treatment [START_REF] Maset | Pressure-volume index in head injury[END_REF]. The GCS was assessed on admission and at ICU discharge. Patients who died during ICU stay were considered as GCS of 3 at discharge.

We also recorded interventions received by patients during the ICU stay (such as mechanical ventilation, vasopressor and inotropic support and kidney replacement therapy) and the development of complications, including seizures (i.e., convulsive or nonconvulsive), intracranial hypertension and brain tissue hypoxia. We also recorded the therapeutic interventions used to treat intracranial hypertension and/or tissue hypoxia. We recorded ICU and hospital mortality, the Glasgow Outcome Scale (GOS) [START_REF] Jennett | Assessment of outcome after severe brain damage[END_REF] at 3 months according to the report of the ICU-follow program and the occurrence of unfavorable neurological outcome (UO), defined as a 3-month GOS of 1-3, using medical reports from follow-up visits.

ICP and PbtO 2 were continuously measured using intraparenchymal probes (Neurovent-P, Raumedic, Helmbrechts, Germany and IM3.ST_EU; Integra LifeSciences Corporation, Plainsboro, NJ, USA, respectively). Whenever possible, PbtO 2 probes were placed into the hemisphere at greatest risk for secondary brain injury (i.e., close to the injured/contused area, through a frontal burr hole using a triple-lumen bolt). Probe location was confirmed by CT scan after placement. The adequate functioning of the probe was tested with a 100% oxygen fraction (FiO 2 ) test for a maximum of 15 min . Intracranial hypertension was defined as at least one ICP value exceeding 20 mmHg for at least 5 min at any time. Brain tissue hypoxia was defined by a PbtO 2 below 20 mmHg for at least 5 min [START_REF] Chen | Detection of cerebral compromise with multimodality monitoring in patients with subarachnoid hemorrhage[END_REF]. All patients received tier 0 therapies [START_REF] Hawryluk | A management algorithm for patients with intracranial pressure monitoring: The Seattle International Severe Traumatic Brain Injury Consensus Conference (SIBICC)[END_REF], such as proper head positioning, CPP ≥ 60 mmHg, avoidance of neck compression, control of extra-cerebral cerebral injuries, prevention and treatment of fever and metabolic disturbances [START_REF] Taccone | Use a "GHOST-CAP" in acute brain injury[END_REF].

ICP-guided therapy included different therapeutic interventions (i.e., external ventricular drainage, hyperventilation, increased sedation, osmotic therapy, barbiturates or decompressive craniectomy) aiming to reducing ICP below 20 mmHg. PbtO 2 -guided therapy was considered as all specific therapeutic interventions (induced hypertension, red blood cells transfusions, changes in ventilatory settings and PaCO 2 ) aiming to achieve a PbtO 2 > 20 mmHg.

Study Outcomes

Primary outcome was the impact of ICP/PbtO 2 guided therapy on neurological status at ICU discharge assessed by the GCS. Secondary outcomes included: (a) impact of ICP/PbtO 2 -guided therapy on the development of intracranial hypertension; (b) the impact of ICP/PbtO 2 guided therapy on hospital mortality; (c) the impact of ICP/PbtO 2 on neurological outcome at 3 months.

Statistical Analysis

Descriptive statistics were generated for all variables. Numeric variables were described as median and interquartile intervals 25-75% or mean and standard deviation. Categorical variables were described as numbers and proportions. Normally distributed continuous variables were compared using t Student test and asymmetrically distributed variables were analyzed using Mann-Whitney test. Categorical variables were compared using chi square or Fisher's exact test. A genetic matching (a multivariate matching method using an evolutionary search algorithm based on heuristic rules to optimize covariate balance) [START_REF] Diamond | Genetic Matching for Estimating Causal Effects: A General Multivariate Matching Method for Achieving Balance in Observational Studies[END_REF] was performed based on demographics, comorbidities, and severity scores on admission (Figure 1). Statistics and matching were computed on the open-source R software, version 3.6.3 (R statistical and computing software; http://www.r-project.org/ (accessed on 15th October 2021)) using the MatchIt and Matching packages and the software SPSS 27.0 for MacIntosh. A sensitivity analysis of study outcomes was performed using the entire study cohort; adjusted odds ratio and confidence intervals based on variables on admission with a p value < 0.05 at univariate analysis were computed. A p value < 0.05 was considered statistically significant.

Results

Among 389 admitted patients over the study period, we identified 106 severe TBI patients that met the inclusion criteria. Among those, 35 (33%) were monitored with PbtO2 and received ICP/PbtO2-guided therapy, with a mean age of 51 ± 19 years and being pre-

Results

Among 389 admitted patients over the study period, we identified 106 severe TBI patients that met the inclusion criteria. Among those, 35 (33%) were monitored with PbtO 2 and received ICP/PbtO 2 -guided therapy, with a mean age of 51 ± 19 years and being predominantly male (59%). The most frequent comorbidities were alcohol use and arterial hypertension. Traumatic SAH was observed in 90% of patients and the presence of subdural/epidural hematomas were found in 53% of patients. The median GCS on admission was 5 [START_REF] Chesnut | The role of secondary brain injury in determining outcome from severe head injury[END_REF][START_REF] Badri | Mortality and long-term functional outcome associated with intracranial pressure after traumatic brain injury[END_REF][START_REF] Carney | Guidelines for the Management of Severe Traumatic Brain Injury, Fourth Edition[END_REF][START_REF] Cruz | On-line monitoring of global cerebral hypoxia in acute brain injury. Relationship to intracranial hypertension[END_REF][START_REF] Chesnut | Early and late systemic hypotension as a frequent and fundamental source of cerebral ischemia following severe brain injury in the Traumatic Coma Data Bank[END_REF][START_REF] Marmarou | Impact of ICP instability and hypotension on outcome in patients with severe head trauma[END_REF]. Intracranial hypertension was diagnosed in 73/106 (69%) patients and brain hypoxia in 24/35 (69%) patients. The characteristics of the study population are reported in Table 1. The distribution of patients according to monitoring strategy per year is illustrated in Supplementary Figure S1.

Genetic Matched Cohort

Among the 71 patients in the ICP-guided therapy group, 35 patients were matched with the ICP/PbtO 2 -guided therapy cohort (Figure 1). The characteristics of the two groups are shown in Table 2; groups were well-balanced for most of the relevant variables. GCS at ICU discharge was higher, although not statistically significant, in the ICP/PbtO 2 group when compared to the ICP group [10 (3-14) vs. 3 [START_REF] Chesnut | The role of secondary brain injury in determining outcome from severe head injury[END_REF][START_REF] Badri | Mortality and long-term functional outcome associated with intracranial pressure after traumatic brain injury[END_REF][START_REF] Carney | Guidelines for the Management of Severe Traumatic Brain Injury, Fourth Edition[END_REF][START_REF] Cruz | On-line monitoring of global cerebral hypoxia in acute brain injury. Relationship to intracranial hypertension[END_REF][START_REF] Chesnut | Early and late systemic hypotension as a frequent and fundamental source of cerebral ischemia following severe brain injury in the Traumatic Coma Data Bank[END_REF][START_REF] Marmarou | Impact of ICP instability and hypotension on outcome in patients with severe head trauma[END_REF][START_REF] Bouma | Cerebral circulation and metabolism after severe traumatic brain injury: The elusive role of ischemia[END_REF][START_REF] Bouzat | Beyond intracranial pressure: Optimization of cerebral blood flow, oxygen, and substrate delivery after traumatic brain injury[END_REF][START_REF] Okonkwo | Brain Oxygen Optimization in Severe Traumatic Brain Injury Phase-II: A Phase II Randomized Trial[END_REF][START_REF] Nangunoori | Brain tissue oxygen-based therapy and outcome after severe traumatic brain injury: A systematic literature review[END_REF]; p = 0.46]. The occurrence of intracranial hypertension was significantly lower in the ICP/PbtO 2 -guided than the ICPguided therapy group (16/35, 46% vs. 27/35, 77%; p = 0.01); in particular, PbtO 2 -guided therapy was associated with a relative risk reduction of 41% [95% CIs 11-60%] and an absolute risk reduction of 31% [95% CIs 9-50%] in the risk of developing intracranial hypertension. The occurrence of hospital mortality (13/35, 37% vs. 18/35, 51%; p = 0.34) and UO (19/35, 54% vs. 25/35, 71%; p = 0.22) were numerically lower, although this difference was not statistically significant, in the ICP/PbtO 2 -guided therapy group when compared to the other (Figure 2).

Entire Cohort Analysis

Patients monitored with ICP/PbtO2 were younger and had higher APACHE and SOFA score on admission compared to others (Table 1). However, GCS on admission was similar between the two groups [5 (3-7) vs 5 (3-9), p = 0.72]. The intensity of therapy for intracranial hypertension (basic TIL score) was similar in both groups, although the

Entire Cohort Analysis

Patients monitored with ICP/PbtO 2 were younger and had higher APACHE and SOFA score on admission compared to others (Table 1). However, GCS on admission was similar between the two groups [5 (3-7) vs 5 [START_REF] Chesnut | The role of secondary brain injury in determining outcome from severe head injury[END_REF][START_REF] Badri | Mortality and long-term functional outcome associated with intracranial pressure after traumatic brain injury[END_REF][START_REF] Carney | Guidelines for the Management of Severe Traumatic Brain Injury, Fourth Edition[END_REF][START_REF] Cruz | On-line monitoring of global cerebral hypoxia in acute brain injury. Relationship to intracranial hypertension[END_REF][START_REF] Chesnut | Early and late systemic hypotension as a frequent and fundamental source of cerebral ischemia following severe brain injury in the Traumatic Coma Data Bank[END_REF][START_REF] Marmarou | Impact of ICP instability and hypotension on outcome in patients with severe head trauma[END_REF][START_REF] Bouma | Cerebral circulation and metabolism after severe traumatic brain injury: The elusive role of ischemia[END_REF], p = 0.72]. The intensity of therapy for intracranial hypertension (basic TIL score) was similar in both groups, although the ICP/PbtO 2 guided therapy group received more frequently vasopressors. The incidence of intracranial hypertension was lower in the ICP/PbtO 2 group when compared to the other (16/35, 46% vs. 57/71, 80%; p = 0.001). In the multivariable model, ICP/PbtO 2 -guided therapy was associated with a lower chance of developing intracranial hypertension, when adjusted for Marshall score, GCS on admission and the presence of reactive pupils on admission (Table 3). However, ICP/PbtO 2 -guided therapy had no impact on mortality (unadjusted OR 0.51 [95% CI 0.22-1.18]) nor on neurological outcome (unadjusted OR 0.43 [95% CI 0.19-1.01]), even after adjustment for confounders such as intracranial hypertension, GCS on admission and age (adjusted OR 1.33 [95% CI 0.46-3.87] and adjusted OR 0.71 [95% CI 0.25-2.03], respectively-Supplementary Tables S1 andS2). Supplementary Figure S1B,C) illustrates the rate of hospital mortality and neurological outcome at 3 months over the study period, according to monitoring strategy. The Kaplan-Meier curve of survival according to the monitoring strategies (ICP and ICP/ObtO 2 group) was shown in Supplementary Figure S2. As a sensitivity analysis we also performed a comparison between ICP and ICP/PbtO 2 in patients admitted after 2017, to reduce the possible bias of time in the previous analysis. The results are presented in Supplementary Table S3. Patients had similar GCS, APACHE, SOFA and Marshall scores on admission and had no statistical difference in outcomes (i.e., hospital mortality and GOS at 3 months). The incidence of intracranial hypertension remained lower in the ICP/PbtO 2 group when compared to the other.

Discussion

In this matched cohort study, no significant differences in hospital mortality or the occurrence of UO at 3 months was observed between TBI patients undergoing ICP-guided and ICP/PbtO 2 guided therapy. Interestingly, patients monitored with ICP/PbtO 2 developed less intracranial hypertension than those monitored with ICP alone. These results were also confirmed when the entire study cohort was analyzed.

PbtO 2 values derive from a complex balance between oxygen supply, demand, and extracellular diffusion [START_REF] Bouzat | Beyond intracranial pressure: Optimization of cerebral blood flow, oxygen, and substrate delivery after traumatic brain injury[END_REF][START_REF] Menon | Diffusion limited oxygen delivery following head injury[END_REF]. In the management of TBI, PbtO 2 and ICP/CPP are used as surrogate endpoints of potential pathological processes, such as mass effect, cerebral edema, tissue hypoxia or reduced cerebral blood flow. The relationship among all these biomarkers' variables remains not entirely understood. For instance, brain hypoxia may occur despite ICP/CPP being within normal ranges, due to diffusion-limited oxygen delivery caused by endothelial swelling, microvascular collapse, and perivascular edema [START_REF] Menon | Diffusion limited oxygen delivery following head injury[END_REF]. This supports the rationale behind PbtO 2 -guided therapy [START_REF] Bouzat | Beyond intracranial pressure: Optimization of cerebral blood flow, oxygen, and substrate delivery after traumatic brain injury[END_REF]. Moreover, PbtO 2 is thought to provide unique information as an independent predictor of TBI outcome [START_REF] Oddo | Brain hypoxia is associated with short-term outcome after severe traumatic brain injury independently of intracranial hypertension and low cerebral perfusion pressure[END_REF][START_REF] Eriksson | Cerebral perfusion pressure and intracranial pressure are not surrogates for brain tissue oxygenation in traumatic brain injury[END_REF]. PbtO 2 -guided therapy impact may not be limited to counteract brain hypoxia but also offers an earlier and better preventive effect compared to sole-ICP guided therapy on other processes of secondary brain injury, such as cerebral edema, with a subsequent reduction on the occurrence of intracranial hypertension.

Intracranial hypertension occurs frequently after TBI and is an important mechanism of brain injury that, if left untreated, can lead to death and poor outcome [START_REF] Treggiari | Role of intracranial pressure values and patterns in predicting outcome in traumatic brain injury: A systematic review[END_REF]. The Brain trauma foundation recommended starting treatment for intracranial hypertension when ICP exceeds the threshold of 22 mmHg [START_REF] Carney | Guidelines for the Management of Severe Traumatic Brain Injury, Fourth Edition[END_REF]. However, the management of TBI patients should also include strategies for prevention of ICP surges, such as sedation and analgesia, elevation of the head, optimizing of head venous return, regardless of the ICP level [START_REF] Hawryluk | A management algorithm for patients with intracranial pressure monitoring: The Seattle International Severe Traumatic Brain Injury Consensus Conference (SIBICC)[END_REF]. Moreover, a target of 20-22 mmHg may not be adequate for all patients. The use of adjunctive monitoring such as PbtO 2 [START_REF] Chesnut | A management algorithm for adult patients with both brain oxygen and intracranial pressure monitoring: The Seattle International Severe Traumatic Brain Injury Consensus Conference (SIBICC)[END_REF] can help individualized ICP targets, leading to further reduction of ICP in the presence of brain hypoxia or a higher tolerance for slightly higher ICP if PbtO 2 is adequate and the patients is waking up.

The decrease in the incidence of intracranial hypertension is interesting and may suggest an indirect favorable effect of PbtO 2 -guided therapy on ICP management in line with previous studies. In a randomized trial, Lin et al. [START_REF] Lin | A Prospective Randomized Study of Brain Tissue Oxygen Pressure-Guided Management in Moderate and Severe Traumatic Brain Injury Patients[END_REF] reported a significantly lower mean ICP and higher mean CPP when PbtO 2 monitoring was implemented in the therapeutic algorithm of TBI patients. In the BOOST-II trial [START_REF] Okonkwo | Brain Oxygen Optimization in Severe Traumatic Brain Injury Phase-II: A Phase II Randomized Trial[END_REF], consistent but not significant findings of reduced total intracranial hypertension burden were reported. Even in the retrospective studies where no effect of PbtO 2 -guided therapy on outcome was observed, PbtO 2 -guided therapy led to a trend towards lower levels of ICP and less episodes of brain hypoxia [START_REF] Adamides | Focal cerebral oxygenation and neurological outcome with or without brain tissue oxygen-guided therapy in patients with traumatic brain injury[END_REF][START_REF] Martini | Management guided by brain tissue oxygen monitoring and outcome following severe traumatic brain injury[END_REF][START_REF] Mccarthy | Neurologic outcomes with cerebral oxygen monitoring in traumatic brain injury[END_REF]. A meta-analysis by Xie et al. [START_REF] Xie | Mortality and Outcome Comparison Between Brain Tissue Oxygen Combined with Intracranial Pressure/Cerebral Perfusion Pressure-Guided Therapy and Intracranial Pressure/Cerebral Perfusion Pressure-Guided Therapy in Traumatic Brain Injury: A Meta-Analysis[END_REF] also raised this putative effect of PbtO 2 -monitoring, while not being able to draw firm conclusions about it.

In our study, PbtO 2 -guided therapy had no impact on mortality or neurological outcome, as also reported in other studies [START_REF] Adamides | Focal cerebral oxygenation and neurological outcome with or without brain tissue oxygen-guided therapy in patients with traumatic brain injury[END_REF][START_REF] Meixensberger | Brain tissue oxygen guided treatment supplementing ICP/CPP therapy after traumatic brain injury[END_REF][START_REF] Martini | Management guided by brain tissue oxygen monitoring and outcome following severe traumatic brain injury[END_REF][START_REF] Green | Goal directed brain tissue oxygen monitoring versus conventional management in traumatic brain injury: An analysis of in hospital recovery[END_REF][START_REF] Mccarthy | Neurologic outcomes with cerebral oxygen monitoring in traumatic brain injury[END_REF]. However, the magnitude of the effect might be underestimated by the small number of analyzed patients in our study, as in previous cohorts. Ongoing large randomized trials [START_REF] Payen | Comparison of strategies for monitoring and treating patients at the early phase of severe traumatic brain injury: The multicentre randomised controlled OXY-TC trial study protocol[END_REF][START_REF] Shutter | Brain Oxygen Optimization in Severe Tbi (Boost3): A Comparative Effectiveness Study to Test the Efficacy of a Prescribed Treatment Protocol Based on Monitoring the Partial Pressure of Brain Tissue Oxygen[END_REF][START_REF] The | Trial-A Randomised Controlled Trial That Is Testing Whether a Management Strategy Guided by Early Brain Tissue Oxygen Monitoring in Patients in with Severe Traumatic Brain Injury Improves Long Term Neurological and Functional Outcomes[END_REF] on PbtO 2 -guided therapy for TBI are sufficiently powered to detect significant changes in patient-oriented clinical outcomes (i.e., neurological outcome and survival) and might provide high quality data in the next years. Besides their highly anticipated functional and neurological outcomes, findings of ICP/CPP dynamics (i.e., mean or peak values as the total burden of intracranial hypertension) and management (i.e., targeted medical interventions, the use of decompressive craniectomy or other salvage therapies) would also be of great interest. Interestingly, patients monitored with ICP/PbtO 2 presented longer ICU and hospital stays compared to the ICP group. This may be explained because patients in the ICP/PtbO 2 group, despite similar severity on admission than the others, received more life support therapies, which prolonged survival time.

Due to its retrospective design, this study presents inherent limitations partially addressed by the genetic matching. No dynamic analysis of intracranial hypertension and brain tissue hypoxia episodes nor PbtO 2 -or ICP-guided interventions and their interrelations were performed. As a small single-center experience, the statistical power and generalizability of the findings are limited. Finally, potential confounding factors pertaining to neurocritical care evolution during the 8-years study time frame were not mitigated.

Conclusions

This single center matched cohort study was not able to detect any significant favorable effect on clinical outcomes of the implementation of PbtO 2 -guided therapy in severe TBI patients. However, our findings suggest that PbtO 2 -guided therapy may reduce the burden of intracranial hypertension in this setting.

Supplementary Materials:

The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/brainsci12070887/s1, Table S1: Logistic regression for the association of PbtO2 monitoring and hospital mortality. Table S2: Logistic regression for the association of PbtO2 monitoring and unfavorable neurological outcome (GOS 1-3) at 3 months. Table S3: Characteristics of the study population of patiens admitted from February 2017 to December 2019. Data are presented as mean (±SD), count (%) or median (25th-75th percentiles). Figure S1A: Number of patients included in the study per year according to monitoring strategy; S1B: percentage of non survivors per year according to monitoring strategy. S1C: percentage of patients with unfavorable outcome at 3 months per year according to monitoring strategy. Figure S2: Kaplan Meier curve of survival in ICP and ICP/PbtO2 group

12 Figure 1 .

 121 Figure 1. Flowchart of the genetic matching. TBI: traumatic brain injury; ICP: intracranial pressure; PbtO2: brain tissue oxygenation; ICU: intensive care unit.

Figure 1 .

 1 Figure 1. Flowchart of the genetic matching. TBI: traumatic brain injury; ICP: intracranial pressure; PbtO 2 : brain tissue oxygenation; ICU: intensive care unit.

Figure 2 .

 2 Figure 2. Outcomes according to type of monitoring strategy. Panel (A) hospital mortality; Panel (B) Unfavorable neurological outcome (UO) at 3 months (GOS 1-3). GOS: Glasgow outcome scale.

Figure 2 .

 2 Figure 2. Outcomes according to type of monitoring strategy. Panel (A) hospital mortality; Panel (B) Unfavorable neurological outcome (UO) at 3 months (GOS 1-3). GOS: Glasgow outcome scale.

Table 1 .

 1 Characteristics of the study population. Data are presented as mean (±SD), count (%) or median (25th-75th percentiles).

		All Patients (N = 106)	ICP-Group (N = 71)	ICP/PbtO 2 -Group (N = 35)	p-Value
	Age, years	51 (±19)	54 (±19)	45 (±17)	0.02
	Male gender, n (%)	63 (59)	39 (55)	24 (69)	0.21
	Arterial hypertension, n (%)	27 (26)	20 (28)	7 (20)	0.48
	Diabetes mellitus, n (%)	7 (7)	5 (7)	2 (6)	0.99
	Heart disease, n (%)	11 (10)	9 (13)	2 (6)	0.33
	Previous neurological disease, n (%)	4 (4)	4 (6)	2 (6)	0.30
	Alcohol use, n (%)	36 (34)	26 (37)	10 (29)	0.51
	Smoking, n (%)	19 (18)	14 (20)	5 (14)	0.60
	COPD, n (%)	3 (3)	3 (4)	0	0.55
	Liver cirrhosis, n (%)	5 (5)	5 (6)	1 (3)	0.99
	Cancer, n (%)	2 (2)	1 (1)	1 (3)	0.99
	Chronic kidney disease, n (%)	3 (3)	3 (4)	0	0.55
	On admission
	APACHE score	18 (15-21)	18 (15-21)	20 (17-23)	0.03
	SOFA score	8 (4-10)	6 (4-10)	8 (8-10)	0.01
	GCS on admission	5 (3-8)	5 (3-9)	5 (3-7)	0.72
	Marshall score, n (%)
	1	0	0	0
	2	5 (5)	3 (4)	2 (6)
	3	3 (3)	2 (3)	1 (3)	0.02
	4	27 (26)	25 (35)	2 (6)
	5	69 (65)	39 (55)	30 (86)
	6	2 (2)	2 (3)	0
	Reacting pupils, n (%)	79 (75)	53 (75)	26 (74)	0.99
	Traumatic SAH, n (%)	95 (90)	67 (94)	28 (80)	0.04
	Epidural Hematoma, n (%)	56 (53)	26 (37)	30 (86)	0.001
	Hypotension, n (%)	40 (0.29)	24 (34)	16 (46)	0.29
	Hypoxemia, n (%)	54 (51)	33 (47)	21 (60)	0.22
	Sodium, mmol/L	138 (135-141)	138 (136-141)	137 (135-140)	0.19

Table 1 .

 1 Cont.

		All Patients (N = 106)	ICP-Group (N = 71)	ICP/PbtO 2 -Group (N = 35)	p-Value
	Glucose, mg/dL	136 (124-170)	141 (126-176)	131 (122-167)	0.62
	Hemoglobin, g/dL	12.1 (10.5-13.6)	11.9 (10.7-13.2)	12.2 (10.3-14.5)	0.63
	During ICU stay
	Mechanical ventilation, n (%)	106 (100)	71 (100)	35 (100)	-
	Vasopressors, n (%)	78 (74)	45 (63)	33 (94)	0.001
	Inotropes, n (%)	10 (9)	4 (6)	6 (17)	0.08
	RRT, n (%)	1 (1)	0	1 (3)	0.33
	EVD, n (%)	93 (88)	66 (93)	27 (77)	0.55
	Complications
	Intracranial hypertension, n (%)	73 (69)	57 (80)	16 (46)	0.001
	Brain tissue hypoxia, n (%)	NA	NA	24 (69)	-
	Seizures, n (%)	25 (24)	17 (24)	8 (23)	0.99
	Treatments
	TIL score basic
	1	20 (20)	11 (17)	9 (26)
	2	35 (35)	28 (43)	7 (20)	0.13
	3	16 (16)	10 (15)	6 (17)
	4	29 (29)	16 (25)	13 (37)
	Osmotic therapy, n (%)	61 (58)	43 (61)	18 (51)	0.41
	Hypothermia, n (%)	23 (22)	15 (21)	8 (23)	0.99
	Barbiturates, n (%)	19 (18)	15 (21)	4 (11)	0.29
	Decompressive craniectomy, n (%)	25 (24)	14 (20)	11 (31)	0.23
	Outcomes
	ICU LOS, days	9 (4-17)	7 (3-14)	16 (9-25)	0.001
	Hospital LOS, days	17 (5-42)	10 (4-38)	30 (14-66)	0.006
	GCS at ICU discharge	6 (3-13)	3 (3-12)	10 (3-14)	0.19
	ICU death, n (%)	50 (47)	37 (52)	13 (37)	0.16
	Hospital death, n (%)	51 (48)	38 (54)	13 (37)	0.15
	GOS at 3 months	2 (1-4)	1 (1-4)	3 (1-4)	0.15

COPD = chronic obstructive pulmonary disease; APACHE: acute physiology and chronic health examination; SOFA: sequential organ failure assessment; GCS: Glasgow coma scale; GOS: Glasgow outcome scale; ICU: intensive care unit; LOS: length of stay; TIL: therapy intensity level; RRT: renal replacement therapy; EVD: external ventricular drainage; SAH: subarachnoid hemorrhage.

Table 2 .

 2 Comparison of the study matched cohort, according to the use of intracranial pressure (ICP) or ICP and brain oxygen pressure (PbtO 2 ) monitoring. Data are presented as count (%) or median (25th-75th percentiles).

		ICP-Group N = 35	ICP/PbtO 2 Group N = 35	SMD	p-Value
	Demographics
	Male gender, n (%)	22 (63)	24 (69)	0.12	0.80
	Age, years	47 (34-66)	44 (35-59)	0.24	0.32
	Comorbidities
	Arterial Hypertension, n (%)	7 (20)	7 (20)	0.00	1
	Diabetes mellitus, n (%)	0	2 (6)	0.35	0.49
	Heart disease, n (%)	2 (6)	2 (6)	0.00	1.0
	Previous neurological disease, n (%)	0	0	-	-
	Alcohol, n (%)	10 (29)	10 (29)	0.00	1.0
	Smoking, n (%)	0	0	-	-
	COPD, n (%)	0	0	-	-
	Liver Cirrhosis, n (%)	1 (3)	1 (3)	0.00	1.0
	Cancer, n (%)	1 (3)	1 (3)	0.00	1.0
	Chronic kidney disease, n (%)	1 (3)	0	0.24	0.99
	On ICU admission
	APACHE score	18 (17-21)	20 (17-23)	-0.35	0.32
	GCS score	4 (3-7)	10 (3-14)	-0.07	0.51
	Hemoglobin, g/dL	12.1 (10.3-13.4)	12.2 (10.3-14.5)	-0.05	0.67
	Glucose, mg/dL	129 (115-156)	131 (122-167)	-0.34	0.31
	Sodium, mmol/L	138 (137-141)	137 (135-140)	0.38	0.26
	Reacting pupils, n (%)	26 (74)	26 (74)	0	0.99
	Traumatic SAH, n (%)	15 (43)	16 (46)	0.44	0.15
	Epidural hematoma, n (%)	15 (43)	30 (86)	1.00	0.001
	Hypotension, n (%)	15 (43)	16 (46)	0.05	0.99
	Hypoxemia, n (%)	21 (60)	21 (60)	0.34	1.0
	Marshall CT score
	1	0	0
	2	1 (3)	2 (6)
	3	1 (3)	1 (3)	0.53	0.34
	4	7 (20)	2 (6)
	5	25 (71)	30 (86)
	6	1 (3)	0
	During ICU stay
	Mechanical ventilation, n (%)	35 (100)	35 (100)	-	-
	Vasopressors, n (%)	26 (74)	33 (94)	0.57	0.05
	Inotropic agents, n (%)	2 (6)	6 (17)	0.37	0.26
	RRT, n (%)	0	1 (3)	0.24	0.99
	ECMO, n (%)	0	0	-	-
	EVD placement, n (%)	34 (97)	27 (77)	0.63	0.03
	Intracranial Hypertension, n (%)	27 (77)	16 (46)	0.68	0.01

Table 2 .

 2 Cont.

		ICP-Group N = 35	ICP/PbtO 2 Group N = 35	SMD	p-Value
	Seizures, n (%)	10 (29)	8 (23)	0.13	0.79
	TIL score
	1	5 (14)	1 (34)
	2	13 (37)	7 (20)	0.65	0.09
	3	2 (6)	5(14)
	4	15(43)	11(31)
	Brain tissue hypoxia, n (%)	-	24 (69)	-	-
	Osmotic therapy, n (%)	21 (60)	18 (51)	0.17	0.63
	Barbiturates, n (%)	10 (29)	4 (11)	0.43	0.13
	Hypothermia, n (%)	8 (23)	10 (29)	0.13	0.79
	Decompressive craniectomy, n (%)	11 (31)	11 (31)	0	1.0
	Outcomes
	ICU length of stay, days	7 (3-14)	16 (9-25)	-0.77	0.001
	Hospital of stay, days	14 (3-41)	30 (14-66)	-0.39	0.03
	GCS at ICU discharge	3 (3-12)	10 (3-14)	-0.20	0.46
	Deaths at the ICU, n (%)	18 (51)	13 (37)	0.29	0.34
	Deaths at the hospital, (%)	18 (51)	13 (37)	0.29	0.34
	3-month GOS	1 (1-4)	3 (1-4)	-0.37	0.35
	3-month UO, n (%)	25 (71)	19 (54)	0.36	0.22

COPD: chronic obstructive pulmonary disease; APACHE: acute physiology and chronic health examination; SOFA: sequential organ failure assessment; GCS: Glasgow coma scale; GOS: Glasgow outcome scale; ICU: intensive care unit; LOS: length of stay; TIL: therapy intensity level; RRT: renal replacement therapy; EVD: external ventricular drainage; SAH: subarachnoid hemorrhage; UO: unfavorable outcome; ECMO: extracorporeal membrane oxygenation. Brain Sci. 2022, 12, x FOR PEER REVIEW 8 of 12

Table 3 .

 3 Univariable and multivariable analysis of factors associated with the development of intracranial hypertension during ICU stay. Data is expressed as odds ratio (OR) and 95% confidence intervals (CI).

		Univariable Analysis	Multivariable Analysis
		OR (95% CI)	OR (95% CI)
	Marshall score	1.37 (0.83-2.26)	1.54 (0.84-2.82)
	GCS on admission	0.96 (0.86-1.07)	1.00 (0.88-1.14)
	Reactive pupils	0.30 (0.09-0.95)	0.28 (0.08-1.06)
	PbtO 2 monitoring	0.21 (0.09-0.50)	0.16 (0.06-0.42)

Data Availability Statement: Due to ethical reasons, datasets analyzed/generated in this study can be obtain through the corresponding author upon reasonable request. All other data can be found in the manuscript and in its Supplementary Materials.

Conflicts of Interest:

The authors declare no conflict of interest.


M F Robbe
email: mfrobbe@cea.fr

Y Cariou

M Lepareux

E Treille

Description of the MARS small scale replica of a Fast Breeder Reactor and of the numerical models used to simulate a Hypothetical Core Disruptive Accident in the test-facility

In case of a Hypothetical Core Disruptive Accident (HCDA) in a Liquid Metal Reactor, the interaction between fuel and liquid sodium creates a high pressure gas bubble in the core. The violent expansion of this bubble loads the vessel and the internal structures, whose deformation is important. The experimental test MARS simulates a HCDA in a small scale mock-up containing all the signi cant internal components of a Fast Breeder Reactor. The test-facility is lled with water topped by an argon blanket and the explosion is generated by an explosive charge.

This paper describes the MARS test-facility and presents two numerical modelings used to simulate the test with the CASTEM-PLEXUS code. In the rst model, the main internal structures are described with a classical shell model. The second model represents, in addition, the heat exchangers and pumps by means of a porosity model homogenizing the components with the surrounding uid.

Introduction

In case of a Hypothetical Core Disruptive Accident (HCDA) in a Liquid Metal Reactor, the interaction between fuel and liquid sodium creates a high pressure gas bubble in the core. The violent expansion of this bubble loads the vessel and the internal structures, whose deformation is important.

During the 70s and 80s, the LMFBR integrity was studied with codes specially devoted to the analysis of transient loads resulting from a HCDA : PISCES 2 DELK 1], REXCO 2], MICE, ICECO, ICEPEL, STRAW and SADCAT 3], SURBOUM 4], SEURBNUK/EURDYN 5] 6] 7], ASTARTE 8], CASSIOPEE 9], SIRIUS... In order to validate these codes, experimental programmes and benchmarks were undertaken by several countries : COVA 10] 11] 12] 13] 14], APRICOT 15], WINCON 16], STROVA 17], CONT 18], MARA... The french code SIRIUS 19] 20] 21] was validated on the french experimental programme MARA 22] 23]. Based on a 1/30 scale model of the Superphenix reactor, the French programme MARA involved ten tests of gradual complexity due to the addition of internal deformable structures:

MARA 1 and 2 considered a vessel partially lled with water and closed by a rigid roof 21], MARA 4 represented the main core support structures 24], MARA 8 and 9 were closed by a exible roof 25],

MARA 10 included the core support structures (CSS) and a simpli ed representation of the above core structure (ACS) 26]. The MARS test 27] rested on a 1/20 scale mock-up including all the signi cant internal components.

As other codes using a Lagrangian approach, SIRIUS needed rezonings during calculation because the internal structure presence caused high distortion of the uid meshes. Finite di erences were used for the sodium and the roof and nite elements for the thin vessel. As the argon and the bubble were not meshed, a law related volume to pressure.

At the end of the 80s, it was preferred to add a speci c HCDA sodium-bubble-argon tricomponent constitutive law 28] to the general ALE fast dynamics nite element CASTEM-PLEXUS code. The HCDA constitutive law was quali ed 29] on the CONT benchmark.

In order to demonstrate the CASTEM-PLEXUS capability to predict the behaviour of real reactors 30] 31], axisymmetric computations of the MARA series were confronted with the experimental results. The computations performed at the beginning of the 90s showed a rather good agreement between the experimental and computed results for the MARA 8 and MARA 10 tests even if there were some discrepancies 32]. On the contrary, the prediction of the MARS structure displacements and strains was overestimated 33].

This conservatism was supposed to come from the fact that several MARS non axisymmetric structures like core elements, pumps and heat exchangers were not represented in the CASTEM-PLEXUS model. These structures, acting as porous barriers, had a protective e ect on the containment by absorbing energy and slowing down the uid impacting the containment. For these reasons, we developped in CASTEM-PLEXUS a new HCDA constitutive law taking into account the presence of the internal structures (without meshing them) by means of an equivalent porosity method 34] 35].

Moreover, as the process used for dealing with the uid-structure coupling was improved since then and as it was shown in 36] and 37] that this process improved the precision of the results for the tests MARA8 and MARA10, it was undertaken another comparison between the experimental results of the MARS test.

This paper presents a description of the MARS test-facility as well as the two numerical models used to simulate the test with the CASTEM-PLEXUS code. In the rst simulation, the main internal structures are described with a classical shell model and uses the new process for the uid-structure treatment. The second simulation represents, in addition, the heat exchangers and pumps by means of an homogenization model.

Description of the MARS test-facility

The primary circuit of the Superphenix reactor (Fig. 1) is a "pool" design 38]. The whole core, primary pumps and intermediate heat exchangers are enclosed in the main reactor vessel which is made of stainless steel and welded to the roof slab. The main reactor vessel is encased in a safety vessel also made of stainless steel.

The MARS experiment (Fig. 2) was realised at the CEA-Cadarache in order to simulate a HCDA in a 1/20 scale mock-up of the Superphenix reactor block. The main vessel (1 m diameter and 1 m height) includes all the signi cant internal components of the reactor 27].

The main vessel, of variable thickness (0.8 to 1.6 mm), was an assembly of a cylindrical part and of a two part torospherical bottom. The cylindrical part was made of 316L stainless steel whereas the bottom was made of 304L stainless steel. The two inner vessels were modelled, as well as the anti-convecting device and the main vessel cooling system.

The core cover plug was a rather complicated structure, despite simpli cations compared with the reactor geometry: the model included the top plate, the in-pile shell with its pipes, the spacer plates and the heat-insulation. The core catcher was composed of the catcher plate, support structure, vertical anges, chimney and spacing feet.

The lateral neutron shielding was represented by four radially split shells and their supporting structures. The mass of the unmelted part of the core was simulated by a mixing of aluminium cylinders and steel hexagons xed into two AG3 aluminium plates. The strongback and the diagrid support were respectively represented by a non-axisymmetric ring and a cylinder.

The roof slab was constituted by two circular plates of di erent thicknesses to simulate the reactor roof sti ness. Openings were drilled to enable the passage of the large components and the two rotating plugs were concentrically o as in the reactor.

The main components inserted through the roof slab were modelled: four primary pumps, eight intermediate heat exchangers, four emergency cooling exchangers and two integrated puri cation devices. The various supporting rings (roof slab, core support structure, large components) and joining rings (between the roof slab and the rotating plugs) were represented.

The mass de cit of the mock-up cover simulation was compensated by lead plates providing additional weights on the cover. The safety vessel, the dome, the biological shield plates and the handling machine were represented only by their inertia using lead plates. Rubber-ring bands simulated the heat-insulating material between the roof and the main vessel and the gas intervals of the roof slab.

The thin structures (inner vessels, ba es, lateral neutron shielding, main components, emergency heat exchangers, core cover plug, core catcher, core, joining and supporting rings) were mainly made of 304L stainless steel in order to simulate the austenistic steel of the reactor structures. The massive structures and those made of heterogeneous materials (roof slab, rotating plugs, core support structure, diagrid support) were made of A5 aluminium. The top plate of the core cover plug was made of A42 aluminium.

The sodium coolant at operating conditions was simulated by water at 20 o C. The cover gas of the mock-up was the same as in the reactor (argon).

The test was red using a 80 g low density low pressure explosive charge of L54/16 composition 39]. The charge mass was chosen to simulate the 800 MJ full scale mechanical energy release used in the reference HCDA in the Superphenix reactor. The explosive charge was supported by the base of the core cover plug.

The whole test was well instrumented with: 19 pressure transducers tted on the roof slab and the rotating plugs, 5 accelerometers placed on the reactor cover, 24 strain gauges attached on the main vessel, roof slab support ring and cover joining rings, 3 high speed cameras used to obtain displacements of the main vessel, roof slab and large plug, small plug and core cover plug, residual deformations were evaluated by measuring, before and after the ring, mesh sizes of the grid drawn on the di erent structures.

3 Numerical modeling of the test-facility CASTEM-PLEXUS 40] 41] 42] 43] is a general fast dynamics nite element code devoted to the analysis of problems involving fast transients. It can deal with uids and structures with a possibility of coupling. A speci c CDA constitutive law was implemented in the code in order to be able to represent precisely this kind of explosion 36].

Owing to the symmetry of the mock-up, an axisymmetric representation was chosen for the numerical simulation of the MARS test-facility with the CASTEM-PLEXUS computer code. In a rst simulation, the external structures were modeled by shells or massive structures and the main internal structures were described with a classical shell model. The second simulation represents, in addition, the heat exchangers and pumps by means of a porosity model homogenizing the components with the surrounding uid.

The models of both simulations include a representation of the main vessel with three thin shells of di erent thickness and made of di erent materials for the cylindrical part and the torospherical part of the vessel. The top of the test-facility is described by massive elements for the roof, the small rotating plug and the large rotating plug. The massive xings hanging the test-facility to the rigid frame are represented by a cylindrical shell at the extremity of the roof.

The top closure is assimilated to an axisymmetric structure for the needs of the numerical simulation. The openings in the roof for the passage of the components (pumps, heat exchangers) are simply accounted for by the mass they remove to the roof. Local masses on the top of the roof and of the small and large rotating plugs are added to consider the mass of the instrumentation and of the lead plates compensating the mass de cit of the MARS mock-up in relation to the real reactor. The additional local mass at the centre of the roof top also includes the mass of the internal components (pumps, heat exchangers, puri cation devices). Another local mass is placed at the edge of the roof to simulate the lead plates used in the test-facitility to describe the inertia of the safety vessel, the dome, the biological shield plates and the handling machine.

The core cover plug was simpli ed. The upper part is modeled by the top plate and three plates simulate the heat and neutronic insulation. The in-pile shell and the three spacer plates are also meshed. The pipes are assimilated to two cylinders. The external shell surrounding the plug is also represented.

The joining rings between the roof slab and the three plugs are formed, in the experiment, by two concentric and cylindrical plates linked by a bridle at their top extremity. They are represented with thin shells made of aluminium and joining the top of the massive structures. Complementary shell elements made of rubber and joining the base of the massive structures were added to prevent the going up of argon in the free slit.

The heat-insulating material between the roof and the main vessel is represented by an horizontal rubber-ring band joining the roof base to the main vessel and preventing the upwards motion of argon in the empty slit. The main vessel, hung to the roof in the MARS test-facility, is xed rigidly to the roof in the numerical model.

In the centre of the test-facility, the strongback, the neutron shielding support, the support of the ba es and of the internal vessel being tted together, they are described by a single rigid structure, that we will call the Core Support Structures (CSS). This structure is assimilated to an axisymmetric shell of constant thickness, allocating to it an equivalent mass corresponding to the mass of all the structures. The CSS is supposed to be rigid and to transmit the totality of the forces to the structures xed on it. The CSS is attached to the vessel by a cylindrical collar.

The diagrid support is represented by a thin shell. The core is not meshed: it is simply taken into account by an added mass spreaded along the diagrid. The diagrid support is xed to the core support structure by a swivel link. Concerning the four shells schematizing the neutron shielding in the MARS mock-up, only the central one is modeled. This shell governs the uid port between the core cover plug and the neutron shielding. The three other shells are taken into account by a local added mass located at the base of the rst neutron shielding shell.

The ba es surrounding the outer neutron shielding are assimilated to an axisymmetric structure and represented by a vertical shell. The internal vessel is composed of two shells. Only the central one is meshed; the second one is simply described by an additional local mass at the base of the meshed internal vessel. The shielding, the ba e shell, the internal vessel are embedded on the core support structure.

The core catcher is not meshed because its complex geometry would impose a lot of shells of small dimensions and therefore a very ne local meshing, not compatible with the rest of the model. Consequently, the core catcher is represented by an added mass spreaded along the bottom of the main vessel.

The behaviour of the structures previously quoted is generally described with isotropic elastoplastic constitutive laws. However elastic laws are used to describe the rubber elements of weak resistance joining the di erent parts of the roof and the plugs, the internal and medium cylinders schematizing the pipes of the core cover plug whose comportment is approximated by means of an homogenization of the non-axisymmetric structures. The core support structure behaviour is also supposed linear elastic.

The presence of the internal components (pumps and heat exchangers) is taken into account in a global way in both models. In the rst model, the components are represented by a pressure loss applied along a cylinder located at the average radius of the components. This pressure loss coe cient is estimated from 44] and by supposing that a cylindrical obstacle partially blocks up the port. The surface of this obstacle is given by the ratio between the solid section and the total section for a 1 radian angle.

In the second model, the components are represented by a porosity model consisting in homogenizing the structures with the surrounding uid 34] 35] in order to take into account the structure presence simply. The uid elements comprised between the extreme radii of the peripheral components are selected and homogenized with the structures. The structures are described by their volumic lling rate (47 %). Even if the model allows to take into account a pressure loss by friction, this possibility is not used in this simulation.

The gure 3 presents the mesh used for both simulations of the MARS test. The gures 4 and 5 show the structures for the rst simulation with the pressure loss and the second simulation with the porosity model. In particular, one can see on the gure 5 the presence of a trapezoidal area between the internal vessel and the roof corresponding to the porous zone.

In case of a HCDA, the internal uids are sodium, argon and a gas bubble. In the MARS test, the sodium and bubble are respectively replaced by water and an explosive charge. Water and argon are initially at the atmospheric pressure whereas the explosive charge induces an initial pressure of 288 MPa in the bubble area.

The characteristics taken into the numerical model are: Water : = 998:3 kg/m3 sound speed = 1550 m/s p (0) = 10 5 Pa Argon : = 1:658 kg/m3 c p =c v = 1:67 p (0) = 10 5 Pa Explosive charge : = 400 kg/m3 polytropic coef. = 1:322 p (0) = 2:8810 8 Pa c p =c v = 1:24 In CASTEM-PLEXUS, the uids and solid structures can be described with an Eulerian, Lagrangian or A.L.E. (Arbitrary Lagrange Euler) approach. In the models, all the structures are represented with the lagrangian description and the mesh follows the deformation of the structures. The bubble zone is kept xed. Indeed if the bubble grid was ALE, the mesh would deform very much because of the expansion of the bubble gas at a very high initial pressure and this large deformation would entail numerical di culties to carry out the computation. Moreover, the xed bubble grid is used as a reference for the updating of the ALE surrounding mesh. In the rst simulation, the water and the argon are described with an ALE modeling: the uid grid is updated according to the deformation of the neighbouring structures.

In the second simulation, the water and the argon are described with the ALE grid evolution, apart from the homogenized zone. As the porosity model developed in CASTEM-PLEXUS is only available for the eulerian description, the homogenized zone must be eulerian. Consequently two element layers next to the internal vessel are let out of the homogenized zone to operate the uid-structure coupling. As the porosity model is not available in ALE, the structures in the centre of the test-facility (the four lines of neutron shielding, the core assemblies and the core catcher) cannot be represented by this process.

Two kinds of uid-structure coupling are available in the CASTEM-PLEXUS code. Their main di erences lie in the de nition of the local normal vector used to write the coupling relations between the freedom degrees of the uid and the solid. The rst uid-structure coupling (FS2D instruction) requires the de nition of coupling elements by the user and imposes to the uid nodes to have the same displacements as the structure nodes. However, there is no automatic actualisation of the ALE grid for the elements other than the ones on the coupled lines.

The second coupling (FSA instruction) goes without coupling elements; the code considers directly the uid and solid nodes in contact and writes relations allowing a possible tangential movement of the uid in relation to the structure. The FSA coupling is well adapted to complex geometries but it often implies a user intervention to pilot the displacements of the uid ALE grid.

The FSA coupling was adopted for the MARS test because the presence of the internal structures involves large local displacements of the uid grid. In the previous CASTEM-PLEXUS computations 33], the FS2D coupling was used because the FSA coupling was developed later. However, in the current model, a FS2D coupling persists in a local area.

As the diagrid is merely put down on the core support structure and as both structures are not rigidly linked, the diagrid extremity is linked to the CSS by a swivel contact. Consequently, there are two di erent structure nodes at the same location (the one pertaining to the diagrid and the other to the CSS) whereas there is only one uid node facing the two structure ones. This con guration cannot be processed by the FSA coupling. Therefore a FS2D coupling was settled down at the connection between the diagrid, the core support structure and the uid between the radial shield and the CSS.

The boundary conditions are: Complete blocking of the base of the xing shell hanging the mock-up to the rigid frame, No rotation of all the nodes of the top closure at the intersection between the massive structures and the shells: links between the roof slab, the small and large rotating plugs and the joining rings, links between the roof and the main vessel, the heat-insulating material between the roof and the main vessel and the xing shell,

No horizontal displacement and no rotation of the structure nodes located on the symmetry axis (core cover plug, diagrid, vessel) and of the nodes of the plates simulating the heat and neutronic insulation of the core cover plug, No horizontal displacement of the uid nodes on the symmetry axis, No horizontal displacement of the core support structure, Vertical displacement of the core support structure equal to the vertical displacement of the point at the intersection between the collar and the vessel, Same vertical displacement for the four plates simulating the heat and neutronic insulation of the core cover plug.

To link a shell to a massive structure, it is necessary to impose identical displacements for the nodes of the shell extremity and of the massive structure facing each other. Are concerned the diagrid and the CSS, the roof and the xing shell, the roof and the main vessel, the joining rings of the top closure.

The FSA coupling cannot be used for the nodes at the top extremity of the neutron shielding and the ba e because the code cannot de ne the local normal vector in an opened medium. Therefore the FSA coupling is used all along both shells except at the top extremity. Identical displacements are then imposed for the solid node at the top edge of the shell and the facing uid node. In order to help the code to calculate correctly the ALE mesh updating in the areas of high uid speed or high pressure variations, the user has to de ne relations governing the local displacement of the mesh. Three governing lines were set up.

The rst line imposes to the uid nodes between the lower plate of the core cover plug and the neutron shielding top to stay aligned between both structure nodes during the displacement of the structures. This relation prevents a large deformation of the ALE grid due to the huge ow of the uid going out from the central zone. Besides, this line is used as a reference for the updating of the uid in the central zone.

Two lines impose to the uid nodes between the lateral shielding top and the ba e and between the ba e and the internal vessel to stay aligned between the structure nodes. These lines prevent a distortion of the uid mesh due the large local motions of the structures in that area.

Inside the core cover plug, there is no uid-structure coupling de ned between the internal structures of the plug and the uid because the uid can cross the pipes simulated by vertical cylinders. No uid coupling is de ned between the upper part of the external shell surrounding the plug and the uid because this shell was perforated in the test-facility and uid could pass from the plug to the rest of the mock-up. Consequently, in order to preserve a regular meshing inside the core cover plug, the uid nodes on the vertical lines between the lower plate simulating the heat and neutronic insulation and the upper spacer plate has to stay aligned between the structure nodes of both plates.

Conclusion

In that paper, we describe the MARS test-facility representing a small scale replica of a Fast Breeder Reactor. This mock-up contains all the signi cant internal structures of the reactor block of the Superphenix reactor: core, core support structures, diagrid and diagrid support, neutron shielding, ba es, internal vessel, core catcher, core cover plug, pumps, heat exchangers... The external geometry of the reactor was also represented precisely: roof slab including openings for the passing of the components, rotating plugs, main vessel of variable thickness... The MARS mock-up was used to simulate a Hypothetical Core Disruptive Accident in a Liquid Metal Fast Breeder Reactor. In case of HCDA, the interaction between fuel and liquid sodium creates a high pressure gas bubble in the core. The violent expansion of this bubble loads the vessel and the internal structures, whose deformation is important. The uids intervening in the real accident are sodium, argon and a bubble gas composed of the molten core. In the experiment, the sodium is replaced by water and an explosive charge is placed in the centre of the mock-up to simulate the bubble expansion.

This paper presents a description of the MARS test-facility as well as the two numerical models used to simulate the test with the CASTEM-PLEXUS code. In the rst simulation, the main internal structures are described with a classical shell model while the peripheral components are simply taken into account by means of a pressure loss. In the second simulation, the internal structures are also represented with shells apart from the peripheral components (heat exchangers and pumps) which are represented by means of a porosity model homogenizing the structure with the surrounding uid.

Fig. 1 :

 1 Fig. 1: The Superphenix reactor

Fig. 2 :Fig. 3 :Fig. 4 :Fig. 5 :

 2345 Fig. 2: The MARS test-facility