Viot Solène

Câmara-Costa Hugo

Watier Laurence

Francillette Leila

Toure Hanna

Brugel Dominique

Laurent-Vannier Anne

Dellatolas Georges

André Gillibert

Meyer Philippe

Dr Mathilde † Chevignard
email: mathilde.chevignard@ght94n.fr

Assessment of memory functioning over two years following severe childhood traumatic brain injury: results of the TGE cohort

Keywords: severe traumatic brain injury, memory, outcome, longitudinal cohort study, child, adolescent, educational outcome

The aims of this study were (1) to prospectively measure memory functioning following severe childhood Traumatic Brain Injury (TBI), and its evolution over 2 years; (2) to assess demographic and medical factors associated with memory function and recovery; (3) to explore relations between memory and other TBI outcomes.

Methods: Children (aged 0-15 years; n=65) consecutively admitted in a single trauma centre over a 3-year period, who survived severe non-inflicted TBI, were included in a prospective longitudinal study. Memory was assessed in 38 children aged 5-15 years at injury, using the Children's Memory Scale at 3, 12, and 24-months post-injury.

Results: Mean general memory score was low at 3 months (M=90.2, SD=20.3) but within the normal range at 12 and 24 months (M=100.6, SD=23.1 and M=108.6, SD=24.1, respectively), with high variability. Improvement was stronger for immediate visual memory than for other memory indices. Lower general memory score was associated with higher injury severity, lower intellectual ability and functional status, higher overall disability, and ongoing education.

Conclusion:

Memory functioning is highly variable following severe childhood TBI, related to injury severity and functional, cognitive and educational outcomes; improvement is significant during the first-year post-injury, but varies according to the type of memory.

Introduction

Traumatic Brain Injury (TBI) is the main cause of mortality and long-standing disability in children [START_REF] Yeates | A prospective study of short-and long-term neuropsychological outcomes after traumatic brain injury in children[END_REF][START_REF] Schneier | Incidence of Pediatric Traumatic Brain Injury and Associated Hospital Resource Utilization in the United States[END_REF][START_REF] Patteau | Traumatisme crânien chez l'enfant[END_REF]. According to a recent review (4), annual incidence of childhood TBI treated in emergency departments is around 691 per 100 000 in developed countries, with 3-7% of severe injuries [START_REF] Dewan | Epidemiology of Global Pediatric Traumatic Brain Injury: Qualitative Review[END_REF].

TBI occurs in a context of brain immaturity and ongoing development of brain functions.

Besides obvious deficits or loss of previously acquired abilities observed shortly post-injury, new deficits can emerge over time, as the child does not make age-expected acquisitions.

Those deficits can remain unnoticed as long as the theoretical age of acquisition of a particular function or skill is not reached [START_REF] Anderson | Functional Plasticity or Vulnerability After Early Brain Injury?[END_REF].

Severe paediatric TBI, defined by a Paediatric Glasgow Coma Scale (Ped-GCS) Score ≤ 8 [START_REF] Teasdale | Assessment of coma and impaired consciousness. A practical scale[END_REF], causes severe and long-standing impairments. Overall, severe TBI often results in impairments in children's sensory-motor functioning, most often hemiparesis and cerebellar dysfunction, at least in the initial phase [START_REF] Massagli | Association between injury indices and outcome after severe traumatic brain injury in children[END_REF], and in a number of cognitive, behavioural, emotional and social functioning deficits, including deficits in language, visual-spatial skills, processing speed, memory, attention, working memory, and executive functioning [START_REF] Babikian | Neurocognitive outcomes and recovery after pediatric TBI: Metaanalytic review of the literature[END_REF][START_REF] Chevignard | Community integration following severe childhood traumatic brain injury[END_REF][START_REF] Babikian | Chronic Aspects of Pediatric Traumatic Brain Injury: Review of the Literature[END_REF][START_REF] Chevignard | Ecological Assessment of Everyday Executive Functioning at Home and at School Following Childhood Traumatic Brain Injury Using the BRIEF Questionnaire[END_REF][START_REF] Volpe | Neuropsychological outcome of children with traumatic brain injury and its association with late magnetic resonance imaging findings: A cohort study[END_REF][START_REF] Lambregts | Cognitive function and participation in children and youth with mild traumatic brain injury two years after injury[END_REF].

According to a meta-analysis, TBI severity is a major factor influencing outcomes in all cognitive domains [START_REF] Babikian | Neurocognitive outcomes and recovery after pediatric TBI: Metaanalytic review of the literature[END_REF]. Those deficits in turn impact educational achievement [START_REF] Kinsella | Predictors and indicators of academic outcome in children 2 years following traumatic brain injury[END_REF][START_REF] Ewing-Cobbs | Late intellectual and academic outcomes following traumatic brain injury sustained during early childhood[END_REF][START_REF] Kingery | Do Children Who Sustain Traumatic Brain Injury in Early Childhood Need and Receive Academic Services 7 Years After Injury?[END_REF] and autonomy and participation [START_REF] Kingery | Do Children Who Sustain Traumatic Brain Injury in Early Childhood Need and Receive Academic Services 7 Years After Injury?[END_REF][START_REF] Rivara | Disability 3, 12, and 24 Months After Traumatic Brain Injury Among Children and Adolescents[END_REF][START_REF] De Kloet | Determinants of participation of youth with acquired brain injury: A systematic review[END_REF].

Research in the domain of outcomes following childhood brain injury tends to support evidence for some degree of plasticity, but also for early brain vulnerability, especially in the cognitive and behavioural domains, with more severe deficits following early compared to later injury. This is even more pronounced in children who sustained severe injuries, supporting the concept of the "double hazard model" which postulates an interaction (potentiation) of age at injury and injury severity [START_REF] Anderson | Functional Plasticity or Vulnerability After Early Brain Injury?[END_REF][START_REF] Babikian | Chronic Aspects of Pediatric Traumatic Brain Injury: Review of the Literature[END_REF][START_REF] Ewing-Cobbs | Late intellectual and academic outcomes following traumatic brain injury sustained during early childhood[END_REF][START_REF] Verger | Age effects on long-term neuropsychological outcome in paediatric traumatic brain injury[END_REF][START_REF] Anderson | Recovery of intellectual ability following traumatic brain injury in childhood: impact of injury severity and age at injury[END_REF][START_REF] Catroppa | Recovery in memory function in the first year following TBI in children[END_REF]. In most studies to date, outcomes have been reported in samples of children with TBI of various degrees of severity (mild to severe), with relatively small numbers of children with severe injuries, as severe TBI has a relatively low incidence compared to mild /moderate TBI [START_REF] Dewan | Epidemiology of Global Pediatric Traumatic Brain Injury: Qualitative Review[END_REF].

It remains necessary to better understand the deficits caused by early brain lesions, and their evolution over time, in order to better anticipate patients' long-term needs and improve the care and interventions implemented for this population. A state of Chronic Brain Injury (CBI) as a lifelong condition after TBI, has been defined in the Gavelston Brain Injury Conference in 2012 [START_REF] Malec | Recommendations from the 2013 Galveston Brain Injury Conference for implementation of a chronic care model in brain injury[END_REF]. The frequency of an "invisible handicap" after TBI seems even higher in the paediatric than in the adult population [START_REF] Ewing-Cobbs | Late intellectual and academic outcomes following traumatic brain injury sustained during early childhood[END_REF][START_REF] Kingery | Do Children Who Sustain Traumatic Brain Injury in Early Childhood Need and Receive Academic Services 7 Years After Injury?[END_REF].

Memory, defined as the persistence of the information learned over time, allowing its appropriate subsequent reuse, is a complex and dynamic process, divided into four stages: encoding, storage, consolidation and recall. Each stage can be involved in visual and verbal, immediate and delayed modalities, and those processes interact with other cognitive functions, such as executive functions, attention, and intellectual ability [START_REF] Mazeau | Neuropsychologie et troubles des apprentissages chez l'enfant: du développement typique aux dys[END_REF]. Memory develops throughout childhood and adolescence and is essential for any learning, with obvious implication, among other domains of everyday life, in the child's education and school functioning. Tulving describes a sequential process for the development of memory, from procedural memory to episodic memory [START_REF] Tulving | Multiple memory systems and consciousness[END_REF][START_REF] Tulving | Memory systems and the brain[END_REF][START_REF] Tulving | Organization of memory: Quo vadis? In: The cognitive neurosciences[END_REF]. Procedural memory abilities tend to mature earlier in the lifespan, while episodic recall ability matures at a later stage in life [START_REF] Tulving | Multiple memory systems and consciousness[END_REF][START_REF] Tulving | Memory systems and the brain[END_REF][START_REF] Tulving | Organization of memory: Quo vadis? In: The cognitive neurosciences[END_REF].

Numerous studies report that memory skills are impaired following childhood TBI of all severity, with a major repercussion on verbal and visual-spatial memory [START_REF] Lambregts | Cognitive function and participation in children and youth with mild traumatic brain injury two years after injury[END_REF], working memory [START_REF] Phillips | Working memory outcomes following traumatic brain injury in children: A systematic review with meta-analysis[END_REF][START_REF] Gorman | The Effects of Pediatric Traumatic Brain Injury on Verbal and Visual-Spatial Working Memory[END_REF][START_REF] Gorman | Recovery of Working Memory Following Pediatric Traumatic Brain Injury: A Longitudinal Analysis[END_REF], and autobiographical memory [START_REF] Lah | Selective, age-related autobiographical memory deficits in children with severe traumatic brain injury[END_REF][START_REF] Lah | Imagining the Future in Children with Severe Traumatic Brain Injury[END_REF]. Recent studies suggest that TBI alters neuronal structures, including those supporting memory functioning and memory strategies, such as hippocampus, temporal lobe and prefrontal cortex [START_REF] Babikian | Chronic Aspects of Pediatric Traumatic Brain Injury: Review of the Literature[END_REF][START_REF] Verger | Study of the long term sequelae of traumatic brain injury: evaluation of declarative and procedural memory, and its neuroanatomic substrate[END_REF][START_REF] Mccauley | Patterns of Cortical Thinning in Relation to Event-Based Prospective Memory Performance Three Months after Moderate to Severe Traumatic Brain Injury in Children[END_REF][START_REF] Demaster | Memory and the hippocampal formation following pediatric traumatic brain injury[END_REF][START_REF] Paterno | Pathophysiology and Treatment of Memory Dysfunction After Traumatic Brain Injury[END_REF]. However, it remains difficult to know which type, or phase of memory is the most impacted by early TBI [START_REF] Paterno | Pathophysiology and Treatment of Memory Dysfunction After Traumatic Brain Injury[END_REF]. Memory deficits after childhood TBI can also be confounded by multiple factors, such as behavioural or language impairments and should be screened systematically.

Memory difficulties are frequent after childhood TBI. In adults, memory complaints after severe TBI are the most frequent complaint in self-reports, and memory is the third most impaired skill in formal assessments [START_REF] Jourdan | A comprehensive picture of 4-year outcome of severe brain injuries. Results from the PariS-TBI study[END_REF].

Overall, memory impairment is reported to be more severe following severe (compared to mild or moderate) TBI, when compared with healthy matched controls [START_REF] Catroppa | Recovery in memory function in the first year following TBI in children[END_REF], or with controls who sustained an orthopaedic injury [START_REF] Max | Cognitive outcome in children and adolescents following severe traumatic brain injury: influence of psychosocial, psychiatric, and injury-related variables[END_REF]. Severe TBI has been found to be responsible for lower performance in immediate and delayed verbal memory [START_REF] Babikian | Neurocognitive outcomes and recovery after pediatric TBI: Metaanalytic review of the literature[END_REF][START_REF] Lah | Implicit and explicit memory outcome in children who have sustained severe traumatic brain injury: Impact of age at injury (preliminary findings)[END_REF], visual memory (9), working memory [START_REF] Volpe | Neuropsychological outcome of children with traumatic brain injury and its association with late magnetic resonance imaging findings: A cohort study[END_REF][START_REF] Phillips | Working memory outcomes following traumatic brain injury in children: A systematic review with meta-analysis[END_REF], episodic autobiographical memory [START_REF] Lah | Selective, age-related autobiographical memory deficits in children with severe traumatic brain injury[END_REF], and prospective memory [START_REF] Krasny-Pacini | Prospective memory 7 years after severe childhood traumatic brain injury -the TGE 2 prospective longitudinal study[END_REF][START_REF] Mccauley | Incentive Effects on Event-Based Prospective Memory Performance in Children and Adolescents with Traumatic Brain Injury[END_REF][START_REF] Mccauley | Event-based prospective memory performance during subacute recovery following moderate to severe traumatic brain injury in children: Effects of monetary incentives[END_REF][START_REF] Mccauley | Monetary Incentive Effects on Event-Based Prospective Memory Three Months after Traumatic Brain Injury in Children[END_REF]. Visual memory seems to be more resistant to severe TBI than verbal memory, especially several years post-injury, but this could depend on the neural subtracts affected [START_REF] Babikian | Neurocognitive outcomes and recovery after pediatric TBI: Metaanalytic review of the literature[END_REF][START_REF] Babikian | Chronic Aspects of Pediatric Traumatic Brain Injury: Review of the Literature[END_REF].

In addition to injury severity, many other factors may negatively influence memory functioning following childhood TBI, such as younger age at injury, (but not in all studies, see [START_REF] Babikian | Chronic Aspects of Pediatric Traumatic Brain Injury: Review of the Literature[END_REF] for a review), older age at assessment [START_REF] Silberg | The effect of age-at-testing on verbal memory among children following severe traumatic brain injury[END_REF], lower pre-injury level of education and presence of pre-injury learning difficulties [START_REF] Lambregts | Cognitive function and participation in children and youth with mild traumatic brain injury two years after injury[END_REF], lower pre-injury level of child's social abilities and lower socio-economic family background [START_REF] Anderson | Thirty month outcome from early childhood head injury: a prospective analysis of neurobehavioural recovery[END_REF][START_REF] Johnson | Correlates of verbal learning and memory after pediatric traumatic brain injury[END_REF]. Other authors found an effect of longer time since injury, lack of exposure to learning opportunities, or lack of medical treatments/procedures (including rehabilitation) [START_REF] Babikian | Neurocognitive outcomes and recovery after pediatric TBI: Metaanalytic review of the literature[END_REF][START_REF] Anderson | Thirty month outcome from early childhood head injury: a prospective analysis of neurobehavioural recovery[END_REF].

Regarding studies who focused exclusively on children with severe TBI, age at injury was not related to autobiographical memory impairment, but it has been suggested that the deficit in recall of episodic details and in visual-spatial memory worsened in time for children and adolescents [START_REF] Lah | Selective, age-related autobiographical memory deficits in children with severe traumatic brain injury[END_REF][START_REF] Tavano | Cognitive recovery after severe traumatic brain injury in children/adolescents and adults: Similar positive outcome but different underlying pathways?[END_REF]. Memory impairment has also been found to be related to lower intellectual ability [START_REF] Lah | Selective, age-related autobiographical memory deficits in children with severe traumatic brain injury[END_REF].

Therefore, the primary aim of the present study was to prospectively assess memory functioning and its evolution over 2 years following severe childhood TBI. Secondary aims were to assess demographic and medical / severity factors associated with memory function, as well as associations between memory performance and other TBI outcomes, including overall level of disability, intellectual ability, functional and educational outcomes.

Methods

The present work is part of a larger prospective longitudinal study [TGE cohort: Traumatisme Grave de l'Enfant, i.e. Severe Childhood Trauma [START_REF] Krasny-Pacini | Executive function after severe childhood traumatic brain injury -Age-atinjury vulnerability periods: The TGE prospective longitudinal study[END_REF]] initiated at the Paris 5 University Hospital Necker Enfants Malades and conducted in the Rehabilitation Department for Children with Acquired Neurological Injury in the Saint Maurice Hospitals, aiming at determining overall and specific outcomes following severe childhood TBI.

Patients

Participants were children aged 0-15 years consecutively admitted to the paediatric neurosurgical intensive care unit (ICU) of the Necker Enfants Malades Hospital over a threeyear period, within the first 6 hours following severe accidental TBI. Eighty-one children were included at the acute stage of TBI, defined as Glasgow Coma Scale (GCS) score ≤8 [START_REF] Teasdale | Assessment of coma and impaired consciousness. A practical scale[END_REF] at admission and/or an Injury Severity Score (ISS) > 16 [START_REF] Baker | The injury severity score: a method for describing patients with multiple injuries and evaluating emergency care[END_REF]. Causes of TBI were motor vehicle accidents and falls. Exclusion criteria were absence of vital signs upon admission, non-accidental head injury and a previous history of diagnosed neurological, psychiatric or learning disorders. Of the 81 children initially enrolled, 16 died during acute care, leaving 65 children available for follow-up. All children received treatment according to international guidelines for the management of severe TBI in the paediatric neurosurgical ICU of a regional paediatric trauma centre [START_REF] Carney | Guidelines for the acute medical management of severe traumatic brain injury in infants, children, and adolescents[END_REF], and most children (83%) required and received multidisciplinary rehabilitation after acute care. Follow-up comprised serial comprehensive medical and neuropsychological assessments at 3, 12 and 24-months post-injury. The study was approved by the local ethics committee and all parents gave their informed written consent for this observational study.

Among the 65 survivors, 24 (37%) were younger than 5 years at 3-months post-injury, and/or were in a minimally responsive state, incompatible with neuropsychological assessment. In addition, three (5%) children had missing data on at least one of the memory assessments.

Thus, the analysis sample was composed of 38 participants, as indicated in Figure 1.

< Insert figure 1 here >

Measures

Demographic, environmental and pre-injury history Information on the child's pre-injury history and functioning was collected, such as family environment, parental education level (classified into two categories: medium/high: at least one parent graduated from high school; low: none of the parents reached high school graduation) and modalities of previous education: we recorded if the child had stayed back one year or had difficulty and/or extra help at school, according to parental reports.

Injury characteristics

We recorded the following markers of initial TBI severity: TBI severity was defined using the Glasgow Coma Scale (GCS) score [START_REF] Teasdale | Assessment of coma and impaired consciousness. A practical scale[END_REF] which is based on motor, verbal and ocular responses. GCS scores range from 3 to 15: a score ≤8 defines presence of a coma (severe TBI) [START_REF] Marcin | Triage scoring systems, severity of illness measures, and mortality prediction models in pediatric trauma[END_REF].

The Paediatric Trauma Score (PTS) [START_REF] Tepas | The pediatric trauma score as a predictor of injury severity in the injured child[END_REF] sums up the ratings (2, 1, or -1) attributed to 6 assessment categories (3 physiological and 3 anatomical conditions, including weight/body mass index, condition of access to airways, fracture, level of consciousness, systolic blood pressure and condition of wounds). Lower scores indicate more severe injuries. Previous studies have reported good intra-observer reproducibility, developmentally appropriateness of use in children, and significant correlations with outcome measures following traumatic injuries [START_REF] Kaufmann | Evaluation of the Pediatric Trauma Score[END_REF].

The Injury Severity Score (ISS) provides an established anatomical scoring system aimed at assessing trauma severity [START_REF] Baker | The injury severity score: an update[END_REF][START_REF] Copes | The Injury Severity Score revisited[END_REF]. Its appropriateness for use in patients with multiple injuries has been demonstrated based on its correlations with indicators of mortality, disability, and hospitalisation [START_REF] Castello | The Pediatric Risk of Mortality (PRISM) Score and Injury Severity Score (ISS) for predicting resource utilization and outcome of intensive care in pediatric trauma[END_REF]. The ISS is derived from the Abbreviated Injury Scale (AIS), which grades injury severity from 1 (minor injury) to 6 (un-survivable injury) across six body regions. The ISS is computed by summing the squared top three AIS severity scores attributed to the three most severely injured body regions [START_REF] Baker | The injury severity score: a method for describing patients with multiple injuries and evaluating emergency care[END_REF]. The ISS yields values from 0 to 75, with higher scores indicating greater injury severity.

The following medical data was also collected during the acute phase in the intensive care unit: age at injury, cause of injury, presence of a penetrating skull fracture; mean arterial blood pressure; hypotension (drop >10% from normal value of mean arterial pressure for age), intracranial pressure, minimal brain perfusion pressure, occurrence of severe hypoxic episodes (Sa02 <92% with additional oxygen), evidence of intracranial hypo-perfusion upon CT-scan examination and multimodal monitoring, length of coma (in days), occurrence of immediate and/or early seizures.

Outcome measures collected during clinical follow-up at 3, 12, and 24-months post-injury:

Motor deficits: Neurological and functional assessment allowed collecting information relative to the presence or absence of (1) hemiplegia or hemiparesis; (2) signs of cerebellar dysfunction (ataxia and / or coordination disorders).

Post-injury type of education (at 12 and 24-months post-injury): Ongoing type of education was classified into two categories: General education without help, adaptation, or grade retention vs. Specialized or General education with help and/or adaptation and/or grade retention.

Overall level of disability: Glasgow Outcome Scale modified for children (GOS-Peds) ( 57 -"Stories": the child has to listen and remember a short story, and to recall it with as many details as possible, immediately and at 25-35 minutes, and then answer questions about it; -"Word pairs": the child has to remember a list of matched words, with a learning phase where s/he is asked to recall the whole list of words on immediate and delayed recall; s/he also has to recognize the words previously learned among other words; -"Dot location": the child has to remember the position of blue chips, and after a learning phase, to replace them in immediate and delayed recall inside a predawn grid; -"Faces": the child has to remember series of faces and to recognize them, presented among distractors, in immediate and delayed recognition; -"Numbers": forward and backwards digit span; -"Sequences": the child has to recite different types of sequences, such as alphabet, numbers count, days of the week, among others.

The CMS has robust psychometric properties, such as good internal consistency (Cronbach alpha=.88 to .93), good interrater reliability (.98 or above) and good discriminant validity. However, retest allows gains of up to 1 SD when assessment is repeated.

No data from the MEM III was used in the analyses, as only one 16-year-old patient performed this battery at the 2-year follow-up, but he was excluded as he had missing data on one of the previous time points.

Statistical analyses

Data analyses were conducted using the SAS ® software version 9 (66) and R software version 3.5.1. [START_REF] Core | R: A language and environment for statistical computing[END_REF]. Descriptive statistics were used to describe the sociodemographic characteristics, severity indices and, at each time-point (3, 12 and 24-months post-injury), the main outcomes (including memory scores).

Mean and standard deviations of the general memory score and the partial memory indices at all time-points were described, as well as the Pearson's correlation coefficients of memory scores between those periods. Univariate statistical analyses focused on the evolution of the main outcomes across the time-periods. In addition, we performed correlation analyses or ttests to examine the association between general memory and the main TBI outcomes, namely motor deficits, FSIQ, PIFOS, GOS and ongoing education, at each time-point.

Linear mixed models were used to examine associations of general memory score with sociodemographic and injury-related characteristics. For the seven partial memory indices, a linear mixed effects model was estimated, explaining the indices scores from the memory score subtype, the time (three categories, M3, M12, M24) and the interaction between memory score subtype and time. The model included a random intercept for the subject but no random slope as the evolution was not assumed to be linear. A nested contrast was used for the time variable, in order to compare M12 to M3 and M24 to M12. A sum contrast matrix was used for the memory score subtype variable so that each memory score subtype was compared to the average of all memory score subtypes (including the one to be compared).

Consequently, no reference category was chosen. The interaction between time and memory subtypes allowed testing differential evolution of memory subtypes compared to the general average evolution of all memory subtypes. Holm's multiple testing adjustment for p-values was performed on all effects of the linear mixed effects model [START_REF] Holm | A Simple Sequentially Rejective Multiple Test Procedure[END_REF].

Results

Description of the study sample

Demographic and severity characteristics of the 38 participants (31 boys) who underwent memory assessments over the 2-year follow-up are summarized in Table 1. Mean age at injury was 10.7 years; for 17 patients (45%), at least one parent had graduated from high school, and 11 (28%) had a history of pre-injury difficulties at school. < Insert Table 1 here > Outcomes All outcomes assessed at each time point are summarized in Table 2. Overall, motor impairments were relatively frequent at 3 months, but tended to resolve by 12 and 24 months for the majority of participants. Overall disability, measured using the GOS-Peds, indicated "severe disability" at 3-months post-injury for 34% of the patients, with only 5% of "good recovery". Most children remained with moderate to severe disability, with only 24% rated "good recovery" at 24 months. Mean overall intellectual ability (FSIQ) fell one standard deviation below expected value at 3-months, with significant improvement over time, mostly during the first year. Functional impairment was severe at 3-months post-injury, with improvement (decrease) of PIFOS scores mainly from 3 to 12-months post-injury. Children attending general education without help nor adaptation nor grade retention represented 41% of the sample at 12 and 24-months post-injury.

< Insert Table 2 here > Memory assessment

The mean scores of all the memory indices at each time point are summarized in Table 3.

Mean initial General Memory Score 3-months post-TBI (M=90.2) was below the expected value (M=100), but with high variability (SD=20.3, higher than expected: SD=15), with some patients performing in the deficit range while others displayed high performance. Figure 2 illustrates the distribution and high variability of the general memory scores at 3, 12 and 24 months.

< Insert Table 3 here > < Insert Figure 2 here > Univariate analysis (paired t-tests) showed that the general memory score improved significantly between 3 and 12 months (p<.001), and marginally between 12 and 24 months (p<.05) (Table 3). All partial memory indices, with the exception of visual delayed memory and attention/concentration, improved significantly between 3 and 12 months. Between 12 and 24 months, improvements were significant only for the partial memory indices of visual immediate memory and learning. The correlations of all memory scores between 3 and 12months post-injury, and between 12 and 24 months, were significant, except for Visual Immediate Memory between 12 and 24 months, and for Visual Delayed Memory between 3 and 12-months post-TBI.

The linear mixed effects model after Holm's correction for multiple testing showed that (i) initial (3 months) visual delayed memory was higher than the other memory indices (p<.01);

(ii) a general tendency for improvement in memory scores between 3 and 12 months (p<.001), which was independent of the memory subtype; (iii) a general tendency for improvement in memory scores between 12 and 24 months (p<.01); which was significantly higher (p=.03) for the immediate visual memory compared to the other memory indices. The interactions of the above factors with period were not significant. When parental education level, PTS, length of coma and ISS were introduced simultaneously in the model, only PTS remained marginally significantly associated with the general memory score [F(1,33)=3.9, p=.06]. Age at injury, gender, pre-injury school difficulties, lowest GCS Score and other medical / severity variables were not associated with the general memory scores.

Associations between general memory scores and other TBI outcomes

Table 4 describes the associations between the General Memory Score and the other outcome measures at each time point. Higher (better) FSIQ and GOS-Peds scores, and lower (better) PIFOS scores at 3, 12 and 24 months, and absence of motor deficits were significantly associated with higher (better) General Memory Scores at 3 months. Type of ongoing education at 12-months, and marginally at 24 months, was associated with the General Memory Score measured at the same time point.

< Insert Table 4 here>

Discussion

This study aimed to assess memory performance after severe childhood TBI and its evolution over two-years post-injury, and to determine demographic, medical and severity factors associated with memory performance and recovery. We report detailed memory outcomes in a large sample of children who sustained severe TBI and who underwent comprehensive medical and neuropsychological follow-up over two years, with very little attrition. Overall, results indicate relatively severe outcomes (although high variability was noted), with decreased intellectual ability, high proportions of children with persistent moderate to severe disability levels and functional impairments, and high proportions of children requiring school adaptations, extra help, or special education. Memory was significantly impaired at 3-months post-injury, with a high variability in test scores however, some patients displaying severe deficits, while others were functioning at superior levels. Significant improvement of memory performance was found over time, mostly during the first year. Visual memory was relatively preserved when compared to the other indices. Among factors influencing outcome, memory function was mostly correlated to markers of injury severity, and marginally associated to parental education level. Memory function was also associated with other post-injury outcomes such as intellectual ability, level of disability and functional outcome. Finally, memory performance was significantly associated with educational outcomes. At 3-months post-injury, mean general memory score and most memory indices were below expected values. Improvement occurred over time, with mean group performance at 24 months in the normal range, despite the persistent and substantial variability observed in the high performances range. Improvement of general memory score at 24-months post-injury was mostly due to the better recovery of visual immediate memory and learning indices, with much less progress on verbal and attention/concentration scores. This could be partly related to the retest effect, possibly more prominent on the visual skills in our results. The CMS manual indicates that retest can account for differences of up to 1 SD (i.e. 15 points), which could have largely contributed to the improvement observed in this study [START_REF] Cohen | CMS: échelle de mémoire pour enfants[END_REF]. One could suspect possible differences in task difficulty according to the memory sub-tests, or an authentic better preservation/recovery of visual memory skills following childhood TBI, when compared to verbal memory, as suggested by a large meta-analysis [START_REF] Babikian | Neurocognitive outcomes and recovery after pediatric TBI: Metaanalytic review of the literature[END_REF]. Indeed, in our study, impairment and recovery differed, with better overall outcome on visual memory skills. Those results are concordant with those reported by Catroppa & Anderson [START_REF] Catroppa | Recovery in memory function in the first year following TBI in children[END_REF], i.e. less memory improvement one-year post-injury following severe TBI (when compared to mild and moderate TBI), and a larger effect of injury on verbal memory compared to visual memory.

Moreover, the impairment of attention/concentration, strongly related to executive functions and working memory, confirms findings describing the impact of paediatric TBI on working memory skills [START_REF] Phillips | Working memory outcomes following traumatic brain injury in children: A systematic review with meta-analysis[END_REF][START_REF] Levin | Working memory after traumatic brain injury in children[END_REF].

Memory recovery was more pronounced in the first than in the second-year post-injury, consistent with the results of Babikian & Asarnow's meta-analysis and review [START_REF] Babikian | Neurocognitive outcomes and recovery after pediatric TBI: Metaanalytic review of the literature[END_REF][START_REF] Babikian | Chronic Aspects of Pediatric Traumatic Brain Injury: Review of the Literature[END_REF]. Indeed, time since injury has been reported as a significant predictor of memory performance, with recovery occurring mostly in the acute phase [START_REF] Gorman | Recovery of Working Memory Following Pediatric Traumatic Brain Injury: A Longitudinal Analysis[END_REF]. One study found slightly different results, although it focused on children recruited in a rehabilitation department where they had been admitted following severe TBI, which probably biased recruitment towards more severe cases. In this study, little improvement in memory function (collected retrospectively) was observed during the first-year post-injury and at discharge from rehabilitation. At the followup assessment performed at least 3 years following discharge, children's memory performance had not improved any further [START_REF] Van Heugten | Long-term neuropsychological performance in a cohort of children and adolescents after severe paediatric traumatic brain injury[END_REF].

Regarding factors related to memory outcomes at various time points, memory was mostly influenced by initial TBI severity, but not by age at injury or presence of pre-injury difficulties at school. Parental education (used in this study as a marker of socio-economic status) was marginally associated with the memory outcomes. The effect of parental education level on cognitive (including memory) outcomes has been repeatedly reported in the literature [START_REF] Lambregts | Cognitive function and participation in children and youth with mild traumatic brain injury two years after injury[END_REF][START_REF] Johnson | Correlates of verbal learning and memory after pediatric traumatic brain injury[END_REF][START_REF] Moran | The UCLA study of Predictors of Cognitive Functioning Following Moderate/Severe Pediatric Traumatic Brain Injury[END_REF]. It relates to the environment the child lives in, with a positive impact of rich environment on cognitive skills development, including memory [START_REF] Paterno | Pathophysiology and Treatment of Memory Dysfunction After Traumatic Brain Injury[END_REF], due to permanent and various stimuli supporting child's neurodevelopment. However, this socioeconomic status effect has not been found to influence prospective memory or autobiographical memory [START_REF] Lah | Imagining the Future in Children with Severe Traumatic Brain Injury[END_REF][START_REF] Krasny-Pacini | Prospective memory 7 years after severe childhood traumatic brain injury -the TGE 2 prospective longitudinal study[END_REF], including one study performed in in the 7-year follow-up of the TGE cohort [START_REF] Krasny-Pacini | Prospective memory 7 years after severe childhood traumatic brain injury -the TGE 2 prospective longitudinal study[END_REF].

We found no correlation of memory function with age at injury. Other studies in the literature have suggested an effect of age at injury on memory outcomes (9) whereas others did not [START_REF] Tavano | Cognitive recovery after severe traumatic brain injury in children/adolescents and adults: Similar positive outcome but different underlying pathways?[END_REF]. A recent review also reported no effect of age at injury on memory recovery over time [START_REF] Babikian | Chronic Aspects of Pediatric Traumatic Brain Injury: Review of the Literature[END_REF]. According to the latter review, the previously reported effect of age at injury could have been masked by a preponderant effect of time since injury and TBI severity. Also, the development of memory is not linear [START_REF] Mazeau | Neuropsychologie et troubles des apprentissages chez l'enfant: du développement typique aux dys[END_REF][START_REF] Streri | What do We Know about Neonatal Cognition?[END_REF] and maybe the use of larger age-at-injury groups could allow better understanding of the effect of age on outcome following brain insult [START_REF] Krasny-Pacini | Executive function after severe childhood traumatic brain injury -Age-atinjury vulnerability periods: The TGE prospective longitudinal study[END_REF][START_REF] Anderson | Do children really recover better? Neurobehavioural plasticity after early brain insult[END_REF].

In our study, memory function was significantly associated with initial TBI severity at each time point, i.e. PTS, length of coma (similar to findings by [START_REF] Volpe | Neuropsychological outcome of children with traumatic brain injury and its association with late magnetic resonance imaging findings: A cohort study[END_REF][START_REF] Gorman | Recovery of Working Memory Following Pediatric Traumatic Brain Injury: A Longitudinal Analysis[END_REF][START_REF] Tavano | Cognitive recovery after severe traumatic brain injury in children/adolescents and adults: Similar positive outcome but different underlying pathways?[END_REF], with a marginal effect of ISS. This severity effect was present despite the inclusion of children who all sustained severe TBI. This effect has repeatedly been reported in the literature, in various samples, composed of children with mild-to-severe TBI [START_REF] Johnson | Correlates of verbal learning and memory after pediatric traumatic brain injury[END_REF] but also in samples of children with severe TBI [START_REF] Krasny-Pacini | Prospective memory 7 years after severe childhood traumatic brain injury -the TGE 2 prospective longitudinal study[END_REF][START_REF] Tavano | Cognitive recovery after severe traumatic brain injury in children/adolescents and adults: Similar positive outcome but different underlying pathways?[END_REF].

The remaining initial medical / severity data, such as presence of a penetrating skull fracture; hypotension; maximal intracranial pressure and minimal brain perfusion pressure were not significantly associated with memory performance at any time-point. To our knowledge, these severity indices have not previously been studied in relation to memory function.

In the present work, memory function was correlated with other TBI outcomes. First, the General Memory Score was strongly correlated to overall intellectual ability at each time point, which confirms that memory and other more general cognitive skills are closely interdependent, as already described in a sample of children with TBI of various severity levels [START_REF] Lah | Selective, age-related autobiographical memory deficits in children with severe traumatic brain injury[END_REF].

A relatively new finding was significant correlations of memory function at the different time-points with other more general and less obviously related outcomes, such as presence of motor deficits, overall level of disability, or functional outcome, which, to our knowledge, has not been reported previously. Although a recent study determined the relation between functional outcome (defined by the PIFOS) and overall intellectual ability after childhood TBI [START_REF] Ewing-Cobbs | Assessing Recovery and Disability After Physical Trauma: The Pediatric Injury Functional Outcome Scale[END_REF], the link with memory skills has not been explored yet. Similar findings have been reported in childhood stroke, where motor function was found to predict educational outcomes [START_REF] Hawks | Educational Placement After Pediatric Intracerebral Hemorrhage[END_REF][START_REF] Yvon | Long-term motor, functional, and academic outcome following childhood ischemic and hemorrhagic stroke: A large rehabilitation center-based retrospective study[END_REF]. These findings can probably be explained by the deleterious effect of TBI severity on a number of outcomes, reflecting the extent of brain lesions.

Finally, in this study, educational outcomes are worrying, with less than half of the sample following mainstream education without help and/or delay at 12 and 24-months post-injury.

The general memory score influenced subsequent education modalities, with a significant effect at 12-months post-injury, that failed to reach significance at 24 months, confirming deleterious effects of severe TBI on subsequent learning skills and academic achievement.

These findings reinforce those of previous studies, reporting high proportions of poor academic outcome following severe TBI [START_REF] Kinsella | Predictors and indicators of academic outcome in children 2 years following traumatic brain injury[END_REF][START_REF] Ewing-Cobbs | Late intellectual and academic outcomes following traumatic brain injury sustained during early childhood[END_REF][START_REF] Kingery | Do Children Who Sustain Traumatic Brain Injury in Early Childhood Need and Receive Academic Services 7 Years After Injury?[END_REF]. It has already been shown that academic achievement and more general educational outcomes are strongly influenced by cognitive functioning (especially memory, executive functioning and working memory, and intellectual ability) [START_REF] Fulton | Cognitive predictors of academic achievement in young children 1 year after traumatic brain injury[END_REF]. Indeed, cognitive impairments, such as slow processing speed, or attention or working memory deficits, can alter the intake of meaningful information in the classroom [START_REF] Phillips | Working memory outcomes following traumatic brain injury in children: A systematic review with meta-analysis[END_REF]. Further, memory impairment certainly reduces the amount of new learning a child can take in, consolidate, and efficiently reuse, especially if executive functions deficits are also present [START_REF] Arnett | Behavioral and Cognitive Predictors of Educational Outcomes in Pediatric Traumatic Brain Injury[END_REF]. Over time, if the deficits persist, the amount of information and skills that should be acquired (but is not) can increase and in turn lead to increasing difficulty in new skills understanding and mastering [START_REF] Lah | Selective, age-related autobiographical memory deficits in children with severe traumatic brain injury[END_REF]. Our results also show that the attention/concentration index was the most impaired, with few improvements over time. This finding suggests a deleterious impact of attention/concentration impairments on subsequent educational outcomes [START_REF] Phillips | Working memory outcomes following traumatic brain injury in children: A systematic review with meta-analysis[END_REF].

This study has a number of limitations: the main limitation is the lack of inclusion of a matched control group, which would have allowed controlling for the retest effect. The large progression in memory scores observed in this study, and the high scores obtained at 24 months, especially for visual immediate and delayed visual memory could be due to actual progress, and/or less vulnerability of this particular skill, but also to some degree of retest effect. Indeed, for some very high functioning individuals, the psychologist who administered the tests qualitatively noted that they mentioned remembering some of the tests, such as the stories, word pairs or visual memory stimuli. Without a control group and a systematic quantification of the patient's subtests recognition, this cannot be confirmed. Subsequent follow-up of this cohort with the use of a control group could help clarify this point. Secondly, brain imaging was performed, but was not systematically analysed and integrated in the database, which did not allow the analysis of the relations between memory performance, and brain lesions characteristics. Such analyses would have been very useful to support current researches about neural circuits of memory [START_REF] Verger | Study of the long term sequelae of traumatic brain injury: evaluation of declarative and procedural memory, and its neuroanatomic substrate[END_REF][START_REF] Mccauley | Patterns of Cortical Thinning in Relation to Event-Based Prospective Memory Performance Three Months after Moderate to Severe Traumatic Brain Injury in Children[END_REF][START_REF] Demaster | Memory and the hippocampal formation following pediatric traumatic brain injury[END_REF][START_REF] Paterno | Pathophysiology and Treatment of Memory Dysfunction After Traumatic Brain Injury[END_REF] and contribute to explain the large variability in the memory outcomes observed in the present study. Finally, we only used parental education as a measure of socio-economic status, which is not sufficient and should be completed by more precise indicators, such as occupation, family functioning, coping and parenting style, among others.

Conclusion and perspectives

Overall, we report significant, albeit highly variable memory impairment following severe childhood TBI. Improvement seems to occur over 2 years, especially during the first-year post-injury, with different patterns across memory functions, although part of the improvement could be due to the retest effect and this should be confirmed in studies including a control group. Few factors were strongly associated with memory performance, mainly TBI severity markers. Finally, memory outcome was related to other post-injury outcomes, such as motor, functional and intellectual outcomes, and overall level of disability, suggesting deleterious effects of TBI severity across domains. As reported previously and as expected, memory function was also related with the type of ongoing education post-TBI.

Those results suggest that all patients with severe TBI should receive at least a comprehensive neuropsychological assessment, including memory assessment, shortly post-injury, in order to assess strengths and weaknesses and to plan adequate and timely rehabilitation interventions and school adaptations. Subsequent assessments should occur according to progress over time, persisting complaints and difficulties at home and at school. Long-term follow-up should be pursued until transition to adult services.

  ), a recognized gold standard for measuring TBI outcome, yielding 5 categories: (I) good outcome; (II) moderate disability, including hemiparesis and/or cognitive impairments and/or child referral for outpatient rehabilitation therapy; (III) severe disability, including severe motor deficit and/or cognitive assessment in the deficient range and/or referral for inpatient rehabilitation; (IV) minimally responsive or vegetative state, and (V) death. Functional outcome: Paediatric Injury Functional Outcome Scale (PIFOS) (58). The PIFOS is a brief injury-specific multidimensional rating scale completed by parents/caregivers for children aged 3 to 15 years, based on a structured interview assessing a broad range of cognitive, physical, and psychological health areas commonly impacted by paediatric injury in children. This assessment was performed by a trained health care provider during structured interviews, with the same parent for all time points. Neuropsychological assessment Comprehensive neuropsychological assessment was performed by trained professionals, during one or several sessions, according to the patient's fatigue, in the Rehabilitation Department of the Saint-Maurice Hospitals. These assessments comprised standardised tests and questionnaires aimed at evaluating intellectual functioning, executive functioning [e.g. Behavior Rating Inventory of Executive Function (59)], behaviour, and memory. Results of detailed assessment of executive functioning have been published elsewhere [(e.g. (48)]. Memory: Memory assessment was conducted in children aged between 5 years and 15 years 11 months, using the French versions of the Children's Memory Scale (CMS) (60,61), and of the Wechsler Memory Scale (MEM-III) (62) for those aged 16 years and above. The CMS provides eight index scores [Mean (M)=100, Standard Deviation (SD)=15]: Verbal Immediate and Delayed Memory, Visual Immediate and Delayed Memory, Attention/Concentration, Learning, Delayed Recognition and a General Memory Score based on the four verbal and visual immediate and delayed partial scores. Scores are drawn from six main subtests:

  Intellectual functioning: Performance-based assessments evaluated intellectual ability through age-appropriate French versions of the Wechsler Intelligence Scale for Children-III (WISC-III) (63,64) and the Wechsler Preschool and Primary Scale of Intelligence-III (WPPSI-III) (65). The Full-Scale Intellectual Quotient (FSIQ), Verbal and Performance IQ (M=100; SD=15) estimated the patients' intellectual level at each time point.

  Children underwent severe injuries, with an initial median GCS score of 7 [range (3-8)], median ISS of 29 [range (4-50)], mean PTS of 4 [range (-1 -+9)], and a median length of coma of 5.5 days [range (1-22)].

Figure 3

 3 depicts these effects. Correlations between General Memory Scores (GMS) at 3 and 12 months was .82 (p<.001), and .68 (p<.001) between 12 and 24 months. < Insert Figure 3 here > Factors associated with general memory scores The results of the linear mixed effects model indicated that lower general memory scores were significantly associated with lower PTS (increased severity) [(F(1,36)=7.4, p=.01], longer length of coma [F(1,36) =5.9, p=.02], and marginally associated with lower parental education level [F(1,36)=3.3, p=.07] and higher ISS (increased severity) [F(1,36)=3.7, p=.06].

FSIQ*

  p<0.05; ** p<0.01; ***p<0.001; † Two-tailed Wilcoxon signed-rank test (Z); † † Pearson correlation coefficient (r); FSIQ: Full Scale Intellectual Quotient; GOS: Glasgow Outcome Scale; PIFOS: Pediatric Injury Functional Outcome Scale; At each time point, the general memory score was associated with ongoing education, GOS, FSIQ and PIFOS. Motor deficits were associated with general memory at 3 months.

Figure Caption:Figure 1 .

 1 Figure Caption:

Figure 2 .Figure 3 .

 23 Figure 2. Distribution of the general memory score over time (percentage of patients in

Figure 1 •

 1 Figure 1.

Figure 2

 2 Figure 2.

Table 1 . Demographic, pre-injury medical history and TBI severity of the 38 children included in the study. Mean (SD) [range]Table 2 . Main outcomes at 3, 12 and 24-months post-injury (n=38)

 12 Paediatric Injury Functional Outcome Scale. All differences between 3 and 12 months were significant: motor deficits (McNemar's test, p<.001), GOS (paired t-test, p=.01), FSIQ (paired ttest, p<.001), VIQ (p=.01), PIQ (p<.001) and PIFOS (paired t-test, p<.001). Differences between 12 and 24 months were significant for motor deficits (p<.001) and PIQ (p<.05).

	3 months	12 months	24 months

SD: Standard Deviation; FSIQ: Full Scale Intellectual Quotient; VIQ: Verbal IQ; PIQ: Performance IQ; GOS: Glasgow Outcome Scale; PIFOS:

Table 4 . Associations between general memory scores and other outcomes at 3, 12, and 24-months post-injury

 4

	General memory

Acknowledgments

The initial data collection for this study was funded by the Département de la Recherche Clinique et du Développement, AP-HP (Paris, No. PHRC 2003; AOM 03018). In depth analyses and manuscript preparation were funded thanks to a co-funding by the French Ministry of Health's general direction of health and direction of research, studies, assessment and statistics, by the national fund for health insurance of salaried workers, the national fund for health insurance of independent workers, by the national fund for solidarity and autonomy and by the national institute for prevention and education for health, in the call for research projects launched by the IReSP in 2011, and by two grant(s) awarded to Hugo Câmara-Costa: one grant from the French Speaking Society of Research in Children with Disabilities (SFERHE, www.sferhe.org) and one joint grant from the French Traumatic Brain Injury Society (France Traumatisme Crânien -FTC) and the French Speaking Society of Physical Medicine and Rehabilitation (SOFMER, www.sofmer.com).

We wish to thank Mrs. Mélanie Araujo for her work on the data in an earlier phase of the analyses and we also thank the patients and their families for their participation in this study.

We would also like to thank Caroline Barry and Christine Hassler for their valuable remarks.

Results of this study were presented at the 12 th ISPRM conference in Paris in July 2018 and at the 3 rd IPBIS conference in Belfast in September 2018.

Declaration of interest

The authors declare that they have no competing interest.

Demographic characteristics

Gender: Males; n (%) 25 (66) Parental education (at least one parent graduated from high school); n (%) 17 [START_REF] Anderson | Thirty month outcome from early childhood head injury: a prospective analysis of neurobehavioural recovery[END_REF] Previous difficulties at school (extra help or stayed back one year); n (%) 11 [START_REF] Phillips | Working memory outcomes following traumatic brain injury in children: A systematic review with meta-analysis[END_REF] Age at injury (years)


G Rubino

Classic artificial neurons

• A "classic artificial neuron" can be identified with its activation function, that is, can be seen as a real function of a real variable.

Random Neurons

• A Random Neuron is a parametric positive real function of two real positive variables or "ports", one called the "positive port", the other one being the "negative port".

+ - + v ≥ 0 u ≥ 0 z = u r + v ≥ 0 rate r > 0
• We see r > 0, the rate of the neuron, as a parameter.

• There are variants of this model. The main one is z = min(u/(r + v ), 1) (the original one). • Inventor: Erol Gelenbe, Imperial College, in the late 80s.

• Observe that there is nothing random here. Output z as a function of u

We illustrate here the obtained behavior in the case of z = min(u/(r + v ), 1). Output z as a function of v when u ≤ r (in this case the neuron is not saturated).

-RNNs

Output z as a function of v when u ≥ r

z 1 u -r v case of u ≥ r
Output z as a function of v when u ≥ r ; see that as far as v ≤ ur , the neuron is saturated.

A Random Neural Network (RNN) is a set of interconnected RNs. The connections are (multiplicatively) weighted by nonnegative reals.

+

-

z 1 0 x neuron 1 + - z 2 neuron 2 for instance, u 2 = z 1 w + 1,2 v 2 = z 1 w - 1,2 + - z 3 neuron 3 G. Rubino (INRIA Rennes, France)
RNNs & applications Nov 2022 9 / 50 1 -RNNs

Jonctions at input ports are additive: Possible restriction

+ - neuron 3 + - neuron 1 + - neuron 2 u 3 = z 1 w + 1,3 + z 2 w + 2,3 v 3 = z 1 w - 1,3 + z 2 w - 2,3
• This model comes from queuing theory.

• Because of the queuing origin of the RNN tool, in order to respect the standard interpretation of the model, we must have for each neuron i,

j w + i,j + w - i,j = r i .
• This is a constraint to be respected in order to keep the queueing interpretation (and thus, to access all the theory and algorithms associated with). • The same reason explains the use of z = min(u/(r + v ), 1)r instead of z = u/(r + v ) (see below).

-RNNs

The general 3-layer Random Neural Network • Assume the negative ports of input neurons aren't used. Assume a single output neuron, so, a scalar network output. Assume stability. • Call x i the signal arriving at the positive port of input neuron i. Then, we can explicitly write the network output as a function of the inputs.

z o = h∈H i∈I x i r i w + i,h r h + i∈I x i r i w - i,h w + h,o r o + h∈H i∈I x i r i w + i,h r h + i∈I x i r i w - i,h w - h,o
.

• This shows that the output is a rational function of the input. This allows many treatments. Also, for learning, costs (errors) are rational functions of weights, leading to many advantages over other forms.

Outline

π n = (1 -ρ)ρ n , n ∈ N,
where the number ρ = λ/µ = 1 -π 0 is the utilization factor, or load, of the system:

• ρ = Pr( in equilibrium, the system is busy ); if λ ≥ µ, then we have that Pr( there exists t < ∞ such that after t, system is always busy ) = 1. • See then that the load of the queue at infinity, ρ, satisfies

ρ = min λ µ , 1 .
A G-queue

λ + λ - (+) (-)
µ

A basic G-queue: positive (standard) customers arrive with rate λ + ; negative ones arrive with rate λ -; both arrival processes are Poisson; the service rate is µ. To understand the semantics, see the graph below, associated with this model.

0 1 2 3 • • • λ + λ + λ + µ + λ - µ + λ - µ + λ -
We have stability ⇐⇒ λ + < µ + λ -, and if it holds, then ρ = λ + µ + λ -.

Proof of the relationship between G-queues and Random Neurons

• Assume stability and equilibrium.

• Let T + i be the mean input flow of positive customers in equilibrium, T - i that of negative ones, and T + o and T - o the corresponding mean output flows.

• We have T + i = λ + and T - i = λ -.
Then, using the mean flow conservation law for positive customers T + i = T + o , we have

λ + = µρ + λ -ρ,
with ρ the server occupation probability (always in equilibrium), also called the system's load, leading to

ρ = λ + µ + λ -.
From G-queues to G-networks

λ 1 2 p 1-p (+) (-) µ 1 µ 2
A tandem: first queue is an M/M/1; when leaving the first node, with probability p customers go to a second queue as positive ones, and with probability 1 -p as negative signals; service rate at queue i is µ i , i = 1, 2.

Here, theory says, for instance, that stability happens ⇐⇒ λ < µ 1 , µ 2 , and in that case, if

X i = 1( queue i is busy at infinity ), i = 1, 2, we have, for j, k = 0, 1, Pr( at infinity, X 1 = j, X 2 = k ) = ρ j 1 ρ k 2 .
A recurrent G-network

λ + 1 λ - 1 1 µ 1 d 1 λ + 2 λ - 2 2 µ 2 d 2 p + 12 p - 12 p + 21 p -

21

A general recurrent G-network with two nodes. We denote by d i the probability of leaving the network after a service at queue i.

On the weights of a RNN • Think queueing; then, when a customers leaves queue i (necessarily a positive customer), it goes to queue j as a positive customer with some fixed probability p + i,j , and as a negative customer with some fixed probability p - i,j

• Then, the mean throughput (the frequency) of the flow of positive customers (of spikes) from i to j is r i p + i,j =: w + i,j , and of negative ones is r i p - i,j =: w - i,j . • So, the weights here (the things that learn are the mean speed at which signals between neurons move. This actually also hold for "hulid" neurons. • Since for any neuron i in the network, we must have j p + i,j + p - i,j = 1 (add a queue/neuron 0 representing the network's environment), we deduce that j w + i,j + w - i,j = r i

Some current projects at INRIA

Currently, we are working on the development of a tool implementing these RNN models, and adding some new possibilities:

• sensitivity analysis: basically, ∂y j /∂x i , where x i is the ith input and y j is the jth output; • inverting the RNN mapping when the output is a scalar: basically, if we denote y = ν( x) where x is the vector input to the network and y is the real output, then we look for the subset ν -1 (y ≥ y 0 ), that is, the set of input leading to the fact that the output is at least y 0 . Perceptual quality

Outline

• Perceptual quality refers to the (subjective) perception (the view, the feeling) the user has on the "value" of this media transmission system, on the quality of what she receives, on the impact of the degradations due to the transmission over the network.

• Two main characteristics:

• It is, by definition, a subjective concept.

• It lacks a formal definition.

• Critical problem (solved): how to measure it? How to measure it automatically?

• Subjective testing is the standard way of measuring perceived quality.

• A panel of appropriately chosen human observers is built, and a set of media sequences is shown to the panel members. • Following specific rules (absolute rating, comparisons...) the observers say how they perceive the quality of the sequences. • In case of interactive applications, observers can work by pairs, or in some cases, interact with a robot.

Subjective testing

• The result is a table M where component M h,σ is the value given by human h to sequence σ. • A statistical procedure is then followed to filter these results in order to remove outliers. • At the end, if the set of surviving observers is S, the quality of sequence σ, its MOS (Mean Opinion Score) value is

MOS(σ) = 1 |S| h∈S M h,σ .
• The procedure is surprisingly robust: with the same set of sequences but a different panel, the same subjective test gives results extremely close to the first one: if µ σ and µ σ are the MOS values of sequence σ in both panels, the number σ µ σ -µ σ 2 is pretty "small". Objective testing

• Objective testing means evaluating the perceived quality automatically, without using any panel of users. • To give an example, consider video sequences. Some objective testing methods (coming from the coding area) are based on the PNSR (Peak Signal To Noise Ratio) of two images A and B:

• for instance, assume the two images are composed of M rows and N columns of 8-bits pixels (monochrome case). • The MSE (Mean Squared Error) between the two images is

MSE(A, B) = 1 MN M i=1 N j=1 A i,j -B i,j 2 ∈ [0..255 2 ].
• The PSNR between the two images is defined only if they are different (MSE = 0) and its value (in dB) is

PSNR dB (A, B) = 10 log 10 255 2 MSE(A, B)
.

PSQA: Pseudo Subjective Quality Assessment

• In the Dionysos team we promote our solution called PSQA to all the initial problems and many more, for all types of media considered, and for both one-way and two-ways communications. • PSQA is a metric with no reference, automatic, (so far, "optimally") accurate, and it works in real time if necessary or useful. • PSQA is network-dependent and application-dependent.

• It is a parametric approach (a "black-box" approach), mapping QoS parameters and source-based parameters into perceptual quality (into a MOS value).

How PSQA works

• First of all, we select (i) measurable QoS metrics characterizing the state of the network (logically speaking, instantaneous measures), and assumed, a priori, to have an impact on the Perceptual Quality, (ii) and metrics related to the channel or to the source, again, expected to have impact on the PQ.

• Example in video: (i) the instantaneous packet loss rate LR, (ii) the Bit Rate BR and the Frame Rate FR. • Example in VoIP: (i) the instantaneous packet loss rate LR, the average size of a burst of loss packets MLBS, (ii) the Bit Rate BR and the Offset of the FEC (Forward Error Correction) OFEC .

• Let x = (x 1 , . . . , x n ) denote the vector whose components are the n chosen metrics. We call it configuration. • Configurations live in some product space S 1 × • • • × S n .

• Our postulate: PQ depends only on x (when "things go well") and not on signal content. • We select a few short signals (following standards) representative of the application or service target, σ 1 , . . . , σ K . • We build a pretty small set of K configurations (K = 100, 200, ...) by a mix of random sampling and quasi-Monte Carlo (or weak discrepancy sequences). Call them γ 1 , . . . , γ K . • Last, we build a platform allowing to send signals σ i through a simulated or deployed network where we can simultaneously control all components of the configurations.

• Then we send different original σ i using the platform, when the configuration is γ j using one configuration at a time, and obtain a possibly degraded sequence σ j . We show it to a panel of humans and we obtain its PQs Q j . • We thus obtain a set of K sequences, with variable but known PQ (MOS values) coming from subjective testing sessions, and for each, we know which configuration was used to obtain it. • Then, we use a RNN (a G-network), of the classical feedforward type with 3 layers, to learn the mapping from configurations to PQ (a mapping from QoS×"channel state" to MOS values). Data: the M pairs γ j , Q j . • In the example of video, we obtain a function ν(LR, BR, FR). In the VoIP example, we obtain a function ν(LR, MLBS, BR, OFEC ).

Echo State Networks (ESNs)

The main representative of the family. It has • a first recurrent part called reservoir, with fixed weights,

• and a second supervised learning part called readout.

Three-layered neural networks:

• Input layer

• Hidden layer

• Output layer a ∈ Na x ∈ Nx ŷ ∈ Ny
The learning process is restricted to the output weights (readout). • The input space in then projected into a new "larger" space.

• We compute a linear regression from the projected space to the output space. • Thus, the network output ŷ (t) = (ŷ 1 (t), . . w out m,i ρ i (t).

• Learning process: the output weights w out * can be computed using any (fast) procedure, for instance, Least Mean Square algorithms.

• Remark: we can replace this simple structure by, for instance, a classical feedforward 3-level RNN. See the references in the paper describing the model by its creator. • Practical aspects of our uses of RNN in learning:

Outline

"Evaluating Users' Satisfaction in Packet Networks Using Random Neural Networks", G. Rubino, P. Tirilly and M. Varela, Springer-Verlag Lecture Notes in Computer Science, no. 4132, 2006.

•

  We consider b as a parameter of the function/neuron.• There are many different activation functions used in practice:z = tanh(u -b), z = 1(u ≥ b), z = (x -b) + (ReLU), ... • Then, we build Neural Network by interconnecting these functions using real weights...

  . , ŷN b (t)) is computed for any m ∈ 1..N b : y m (t) = w out m,0 + Na+Nx i=1+Na

•

  About the RNN model and the PSQA tool: "Quantifying the Quality of Audio and Video Transmissions over the Internet: The PSQA Approach", G. Rubino, in Design and Operations of Communication Networks: A Review of Wired and Wireless Modelling and Management Challenges, edited by J. Barria, Imperial College Press, 2005.

RNNs & applications Nov 2022

Nov 2022

-An application to QoE analysis Problems with PSNR approach...Same amount of noise in the grass

A 3-layer structure

The graph of a 3-layer RNN of the (2,3,1) type (as before, dashed arrows correspond to flows of negative customers/signals). PSQA (cont.)

• The mapping is based on supervised learning.

• We explored different tools for this supervised learning task, including the ToolBox of Matlab. • The winner was the RNN model.

Why using RNNs in PSQA project?

Because of the favorable comparison with standard software (at the time of the beginning, several years ago). An example: with the same data and the same neural network size, on the left, PSQA, and on the right, Matlab (an old version of the ToolBox on learning techniques).

Auditing the network with PSQA Auditing the network with PSQA (cont.)

A "graphical" overview: ρ u (t) = a u (t)/r u , (in general, we take a u (t) < r u ), for u ∈ 1..N a . • For all reservoir units u = N a + 1, . . . , N a + N x ,

.

• An example of application of PSQA: • An example of extension of the initial RNN tool:

"Echo State Queueing Networks: a combination of Reservoir Computing and Random Neural Networks", S. Basterrech and G. Rubino, in Probability in the Engineering and Informational Sciences, Vol. 31, No. 4, pp. 1-16, 2017.


Marie Deguigne

Marion Legeay

Anne-Sylvie Scholastique

Philippe Chauveau

Alexis Descatha

Reply to "Assessing effectiveness of whole bowel irrigation in poisoning: A laudable effort but still insufficient evidence" We need to emphasise that our study was to investigate the effect of whole-bowel irrigation (WBI) on the clinical evolution of patients in real life. We aimed to describe use of WBI on a large number of patients with multiple of drugs, different supposed dose, and multiple treatments. For the same reason, in real life, the decision to treat a patient by WBI does not always follow the guidelines perfectly. The design of our study and the size of our sample did not allow us to study this effect on cases of monointoxication, with perfectly known ingested doses, and without other specific treatment. We have clearly indicated in the limitation section that "our study did not allow the effectiveness of WBI". We have concluded that "WBI appeared to provide clinical benefits in patients treated in comparison of an untreated group and is associated with an acceptably low risk of direct complications".

As regards the 11 cases of body packers, we chose to include them in order to describe the safety data (no adverse effects of WBI were described in this series). Univariate and multivariate analyses showed that this variable (drug pellet ingestion) had no impact on our outcome (clinical worsening). WBI in body packers is finally recommended by the guidelines despite the risk of rupture that you mention but which is only described exceptionally.2

In conclusion, we agree WBI effectiveness and recommendation should be only achieved after clinical trials as we mentioned in the last sentence of the conclusion. Vodovar et al. should also mention that prospective large-cohort studies mostly have an intervention design (with a control group) or equivalent, such as pragmatic trials as mentioned in our conclusion, to be effective appeared to provide clinical benefits in patients treated in comparison of an untreated group.

  Marie Deguigne 1 , Marion Legeay 2 , Anne-Sylvie Scholastique 2 , Philippe Chauveau 3 , Alexis Descatha 4 1 Grand Ouest Poison Control and Toxicovigilance Center, Angers University Hospital, 4 Rue Larrey 49933 Angers, France. Electronic address: marie.deguigne@chu-angers.fr.

	2 Grand Ouest Poison Control and Toxicovigilance Center, Angers University Hospital, 4 Rue
	Larrey 49933 Angers, France.
	3 Grand Ouest Poison Control and Toxicovigilance Center, Angers University Hospital, 4 Rue
	Larrey 49933 Angers, France; Emergency Department, Château-Gontier Hospital, 1 Quai Du Dr
	Lefèvre, 53200 Château-Gontier-sur-Mayenne, France.

4 Grand Ouest Poison Control and Toxicovigilance Center, Angers University Hospital, 4 Rue Larrey 49933 Angers, France; UNIV Angers, CHU Angers, Univ Rennes, Inserm, EHESP, Irset (Institut de Recherche en Santé, Environnement et Travail) UMR_S1085, F-49000 Angers, France. Dear Editor, We would like to thank Dominique Vodovar et al. for their relevant comments regarding our article "Whole-bowel irrigation in cases of poisoning: A retrospective multicentre study of feasibility, tolerability, and effectiveness".1

Conflict of interest

The authors have no conflicts of interest relevant to this article to disclose.


Aurélie Mahalatchimy

Eloïse Gennet

Michael Morrison

Véronique Andrieu

Julie Véran

Florence Sabatier

Specific guidelines requirements for clinical trials with Advanced Therapy Medicinal Products in the EU

CONCLUSION

Very useful ATMPs specific guidelines for clinical trials covering many different aspects and all currently identified challenges Necessary case by case evaluation of the various aspects of ATIMPs clinical trials mainly due to variability of starting materials and specific characteristics of each ATMP. Various levels of justification and documentation

INTRODUCTION

Advanced Therapy Medicinal Products (ATMPs), a European legal classification of medicinal products based on genes, cells and tissues, raise specific issues in the context of clinical trials (CT). Several normative instruments apply at the European level (see table opposite). The 2019 guidelines from the European Commission on Good Clinical Practice (GCP) both adapt the ICH E6 to ATMPs' characteristics and provide necessary additional measures. However, they are not exhaustive as they explain only some specificities of ATMPs and they remain complementary to the general rules. We will highlight the specific requirements for investigational ATMPs (ATIMPs) to reveal the particular challenges they are addressing and why these challenges warrant separate regulation in order to obtain CT' authorisation for ATIMPs and potentially for further marketing authorisation application (MAA).

This work has been supported by ANR-funded I-BioLex project (ANR-20-CE26-0007-01, coord. A. Mahalatchimy). M. Morrison is funded by the Leverhulme Trust through grant no RPG-2017-330. , such as the French National Agency (ANSM) as it is proposed in France

Information in Investigator Brochure and Protocol

Placebo: Procedure's risk Dosing: For complex dosing ATMPs, adequate level of understanding & compliance by investigator and those involved in CT End of trial: how follow-up activities will be performed after end of trial

Product information in IB:

-product risks; -previous/ concomitant (or required further treatments) potential impact; -treatment failure risk; -emerging issues Risk minimization measures: Where appropriate, measures to protect CT subjects from identified risks:

Non-clinical studies

Case by case assessment of non-clinical data

Administration of out of specifications products

Exceptionally to avoid immediate significant hazard; manufacturer/ sponsor to provide risks evaluation; records of request kept in manufacturing site; relevant authority to be notified

Upstream intervention on subjects and administration procedures

ATMPs Guidelines content and potential challenges targeted

Protection of CT subjects

Informed consent: CT participant information all risks, e.g., treatment failure, irreversible ATIMP nature…


Clement Deleau
email: clement.deleaul@laas.fr

Seat Han Cheng

Frederic Surre

Franck Carcenac

Pierre-François Calmon

Olivier D Bernal

Clement Deleau

Clément Deleau

Han Cheng Seat

Pierre-Franc ¸ois Calmon

Gas Sensor Based on Silicon Nitride Integrated Long Period Grating

Keywords: long period grating, gas sensing, silicon nitride, integrated photonics

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

I. INTRODUCTION

Providing a healthier and cleaner environment is one of the greatest challenge of the XXI st century that must be undertaken to improve people's well being as well as to protect Earth's environment and climate. As a result, it is of utmost importance to monitor, detect and quantify low concentration of certain gases either related to greenhouse effects such as carbon dioxide (CO 2 ) or methane (CH 4 ), or related to indoor air quality such as benzene, toluene or other volatile organic compounds.

For approximately a decade, integrated photonics has been intensely investigated for the development of highly sensitive lab-on-chip sensor applications. Integrated optical chemical sensors typically detect and measure the concentration of analytes via the interaction of the optical field with the surrounding environment, for example using the evanescent part of the mode field. For gas sensing applications, two main approaches are regarded as promising: absorption-based (spectroscopy) and refractometry-based mechanisms. While the former approach can achieve very high sensitivity without any functionalization layer, it relies on specific spectral signature for each gas molecule, which is usually located in the midinfrared (MIR) spectral range (above 3 µm). Consequently, this spectroscopic approach requires both MIR light sources and low-loss materials at these wavelengths such as chalcogenide instead of silicon. On the other hand, refractometric sensors are based on the measurement of the refractive index unit (RIU) change of a sensed region (e.g. top surface of a photonic chip via evanescent wave) induced by the presence or variation in concentration of a gas species [START_REF] Ingvaldsen | Sensitivity to pressure and methane of a cryptophane-a doped polymer[END_REF], [START_REF] Urrutia | A comprehensive review of optical fiber refractometers: Toward a standard comparative criterion[END_REF]. Contrary to spectroscopic sensors, these sensors require a chemo-optical transducer that has both gas-permeability and chemical affinity to the targeted gas molecule. Nevertheless, these sensors are not constrained by the use of a particular operating wavelength and can thus benefit from a wider range of fabrication technologies, photo-emitters and detectors [START_REF] Luan | Silicon photonic biosensors using label-free detection[END_REF]. As a result, various designs for integrated refractometric measurements have been proposed over the years, including integrated interferometers [START_REF] Dullo | Sensitive on-chip methane detection with a cryptophane-a cladded mach-zehnder interferometer[END_REF], ring resonators [START_REF] Yebo | Selective and reversible ammonia gas detection with nanoporous film functionalized silicon photonic micro-ring resonator[END_REF], plasmonics [START_REF] Zaki | Integrated optical sensor using hybrid plasmonics for lab on chip applications[END_REF], photonic crystals [START_REF] Danaie | Design of a label-free photonic crystal refractive index sensor for biomedical applications[END_REF] and gratings [START_REF] Jain | Thermally stable optical filtering using silicon-based comb-like asymmetric grating for sensing applications[END_REF].

In this work, we propose to use the planar multimode Long Period Grating (LPG) described in [START_REF] Deleau | Integrated width-modulated sin long period grating designed for refractometric applications[END_REF] as gas sensing refractometer. The integrated LPG operates on wavelengthselective coupling of two or more co-propagative modes between the core and cladding modes whose effective indices (EI) can be analyzed using the resonance spectral features. This LPG structure consists in a sinusoidal longitudinal modulation of the waveguide's width to allow selective optical mode resonance with a mode contained in the cladding region. To enhance the LPG's sensitivity, the cladding layer is replaced by a porous medium functionalized to CO 2 using Polyhexamethylene Biguanide polymer (PHMB). Preliminary experimental results show a constant sensitivity of 6.3 fm/ppm over CO 2 concentration ranging from [0-20%].

This paper is organized in two main parts. First, in Section II, an overview of the LPG is presented. In Section III, the experimental setup and results are shown followed by a conclusion in section IV.

II. LPG DESIGN

A. LPG principles

LPGs have been successfully exploited in fibers due to their intrinsic capability for coupling energy to outer cladding modes, thereby allowing the optical power to substantially interact with the surrounding external environment. As shown in [START_REF] Jin | Coupled local-mode theory for strongly modulated long period gratings[END_REF], [START_REF] Taylor | Guided wave optics[END_REF], a phase-matching condition between two copropagative optical modes must be fulfilled to enable resonance to result in an exchange of energy. This condition can be derived ©2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. from the Coupled Mode Theory (CMT) [START_REF] Snyder | Optical waveguide theory[END_REF] and expressed as follows:

n ef f,j -n ef f,l = λ res Ω , (1)
where n ef f,j and n ef f,l are the EIs of the two coupled modes j and l, respectively, λ res the center resonant wavelength and Ω the grating period.

The rate of energy exchange between the core and cladding modes upon resonance mainly depends on the modulation amplitude and optical field superposition at the modulated guide interfaces, as previously detailed in [START_REF] Deleau | Integrated width-modulated sin long period grating designed for refractometric applications[END_REF]. In refractometric sensing schemes employing LPGs, the presence of the analyte generally modifies the refractive index (RI) of the equivalent sensing layer which, in turn, modifies the propagation constants of the modes propagating in the waveguide. The difference in EI variation between the two coupled modes leads to a spectral shift of the optical resonance. This spectral shift can in turn be measured to determine the RI variations of the cladding layer itself. By considering (1), the sensitivity of the LPG can thus be expressed as:

S = ∂λ res ∂n sens = λ ∂n ef f,j
∂nsens -

∂n ef f,l ∂nsens n g,j -n g,l , (2)
where n g,x is the group index of the x th mode and n sens the RI of the sensing layer of the mode x. Based on (2) and as shown in [START_REF] Deleau | Integrated width-modulated sin long period grating designed for refractometric applications[END_REF], the LPG sensitivity is enhanced by improving the modal overlap of the modes to couple in the sensing region, which can substantially increase

∂n ef f,x
∂nsens . This is achieved by inducing one of the modes to directly propagate in the sensing region, which is particularly applicable to gas sensors using porous cladding layers.

B. LPG structure and CO 2 functionalization

The LPG architecture consists of a Silicon Nitride (Si 3 N 4 ) sinusoidally width-modulated integrated strip waveguide surrounded by a multimode cladding region, as shown in Fig. 1. As previously mentioned, the cladding layer is used as the sensing layer functionalized to CO 2 , thus potentially increasing the coefficient ∂n ef f,cladding ∂nsens to nearly 1. PHMB is considered here as the polymer host as it has been previously successfully demonstrated in photonic CO 2 sensing designs [START_REF] Mi | Silicon microring refractometric sensor for atmospheric co 2 gas monitoring[END_REF]- [START_REF] Ma | Optical fiber fabry-perot interferometric co 2 gas sensor using guanidine derivative polymer functionalized layer[END_REF]. In addition, PHMB, soluble in water, is a lowtoxicity polymer that is typically used as disinfectant and antisceptic. The high affinity of the polymer to CO 2 makes it a candidate for selector-free gas sensing. Additionally, the RI of PHMB at 1550 nm is ≈1.54 [START_REF] Mi | Silicon microring refractometric sensor for atmospheric co 2 gas monitoring[END_REF], which enables mode propagation on a silicon oxide substrate. The PHMB material is procured as a white powder with 95% purity from JHSS China. Methanol is hereby selected as solvent for its higher surface adhesion to silicon oxide and higher chemical volatility compared to water. The PHMB powder is dissolved with a ratio of 50 mg/mL of methanol and mixed using a magnetic stirrer for 3 hours. A 1.4 µm thin film is next deposited by spin coating onto a silanized 2 × 2 cm 2 photonic chip at a spin rate of 800 rpm. The solvent is next evaporated by annealing at 90 • C for 30 minutes.

III. EXPERIMENTAL RESULTS

A. Experimental Setup for Gas Sensing

To introduce the gas, a glass chamber is used as an impermeable container to allow the control of the gaseous environment into which the photonic chip is immersed, as shown in Fig. 2. The chamber has three openings: one gas inlet and outlet, respectively, and the third to allow the alignment of the fiber array with the grating couplers of the photonic chip to facilitate light injection and measurements. The third opening is sealed using a flexible rubber cover and silicone (as airtight seal) to prevent gas leakage and/or contamination of the gas chamber while enabling fiber array displacements. A commercial CO 2 sensor (MH-Z16) is also inserted into the chamber as reference. Finally, the chamber is placed on top of the magnetic stirrer regulator (stirrer placed inside the gas chamber) to ensure a better homogeneity of the gaseous environment within the chamber itself.

B. Preliminary CO 2 Sensing Results

To detect CO 2 , the LPG sensor is positioned at least 2 mm away from the grating couplers on the layout (Fig. 3), thereby allowing the fiber array to be in full contact with the chip without obstructing the interaction of the gas with PHMB ©2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. in the sensing region. The grating pairs, positioned at both ends of the U-bend, are jointed by waveguides in which the fundamental mode propagates up to and through the LPG sensing region. Consequently, for the analysis of the LPG's output signal, the superposed contributions from the grating couplers and waveguides are first de-embedded from the total output. A normalized coupling spectrum is obtained. Lorrentzian curve fitting is applied to the de-embedded response.

Initial gas sensing tests have been performed by using the low-resolution fast scanning mode of the optical spectrum analyzer, with each scan carried out iteratively every 15 seconds. The measured spectra are analyzed in real-time with a dedicated LabVIEW program. Two experimental barriers are then observed during the measurements:

1) During gas-flow opening, the applied gas pressure is found to lead to an instantaneous virtual spectral shift of the resonance. This could be attributed to a minor variation of grating coupling behavior induced by minor vibrations of the grating coupler upon initial gas flow.

2) The reference CO 2 sensor exhibits an inertia during the measurement, in part due to its small dimension compared to the relatively large volume of the gas enclosure. Depending on the concentration injected, the gas mixture or atmosphere is estimated to generally stabilize or homogenize after a few minutes. Upon introduction of CO 2 into the chamber, the resonance shifts before stabilization of the gaseous atmosphere (i.e. after a few minutes) can be observed in Fig. 4 (a) highlighted as gas flow area. The CO 2 concentration measured by the reference sensor after stabilization of the atmosphere in the chamber is displayed a few minutes after gas flow. To compensate the perturbations induced during measurements by gas surge immediately after valve opening and the relatively slow stabilization of the gaseous atmosphere in the chamber, the measurements have been performed over 1h30 at very low gas flow. Here, high-resolution low-speed scans are instead performed and analyzed against reference measurements. A quasilinear spectral shift is observed, as illustrated in Fig. 4(b). Linear interpolation is then applied on the measured data to obtain a sensitivity of 6.8 fm/ppm. Subsequently, based on the estimated LPG bulk sensitivity [9], the RI sensitivity of the PHMB layer is estimated to be ≈ 4.7•10 -9 RIU/ppm, corroborating the accepted value of ≈ 6•10 -9 RIU/ppm reported in the literature [START_REF] Mi | Silicon microring refractometric sensor for atmospheric co 2 gas monitoring[END_REF]. The discrepancy between these two sensitivity values can be attributed to different coating methods or presence of chemical impurities, thus giving rise to slightly different solubility characteristics.

IV. CONCLUSION

We have presented an integrated LPG sensor architecture functionalized to CO 2 with a PHMB layer. This architecture achieves a sensitivity of 6.8 fm/ppm of CO 2 which corroborates with the PHMB RI sensitivity. As a result, in the future, LPG with higher sensitivity such as the one described in [START_REF] Deleau | High-sensitivity integrated sin rib-waveguide long period grating refractometer[END_REF] can be used to achieve even higher sensitivity close to 32 fm/ppm. This type of design thus appears promising and can benefit from improvements or hybridations, potentially involving new sensing mechanisms, like plasmonics or photonic crystals.

Fig. 1 .

 1 Fig. 1. (a) Illustration of the SiN LPG functionalized with PHMB with (b) its cross section material and RI profile.

Fig. 2 .

 2 Fig. 2. Experimental setup of the CO 2 gas sensor.

Fig. 3 .

 3 Fig. 3. a) layout of the SiN LPGs showing the grating couplers, LPG and U-bend. b) inset zoom of the fabricated SiN LPGs.

Fig. 4 .

 4 Fig. 4. Preliminary results from CO 2 sensing experiment in enclosure under (a) low-resolution fast-spectral scanning mode and (b) high resolution slowspectral scanning mode.

ACKNOWLEDGMENT

The authors would like to thank A. Lecestre for her technical support. All fabrication and characterization of the integrated photonic long period waveguide gratings were supported by both TTIL 2019 (Toulouse Tech Interlabs) and LAAS-CNRS micro and nanotechnologies platform member of the French RENATECH network. ©2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.