Valentin Bauer
email: valentin.bauer@universite-paris-saclay.fr

Tifanie Bouchara

Patrick Bourdot
email: patrick.bourdot@universite-paris-saclay.fr

Designing an Extended Reality Application to Expand Clinic-Based Sensory Strategies for Autistic Children Requiring Substantial Support: Participation of Practitioners

Keywords: Autism Spectrum Disorder, design, multi-sensorimotor, augmented reality, mediation, well-being Human-centered computing-Human computer interaction (HCI)-Interaction paradigms-Mixed / augmented reality, Human-centered computing-Interaction design-Interaction design process and methods-User centered design, Social

Extended Reality (XR) has already been used to support interventions for autistic children, but mainly focuses on training the socioemotional abilities of children requiring low support. To also consider children requiring substantial support, this paper examines how to design XR applications in order to expand clinic-based sensory strategies that are often used by practitioners to put them in a secure state, and how to maximize the acceptability of such applications among practitioners. To that respect, a "Mixed Reality platform for Engagement and Relaxation of Autistic children" was designed and developed, which allows to add audio, visual and haptic individualized or common stimuli onto reality. A first Augmented Reality freeplay use case called Magic Bubbles was created based on interviews with stakeholders and on a collaboration with three practitioners. A preliminary study with eleven practitioners confirmed its well-being potential and acceptability. XR design guidelines are finally derived.

INTRODUCTION

Autism Spectrum Disorder (ASD) is a pervasive neurodevelopmental condition with a worldwide prevalence of around one percent [START_REF] Lord | Autism spectrum disorder[END_REF]. Autistic people 1 belong to a spectrum, meaning that they display various sensorimotor and cognitive abilities, as well as co-occurring conditions, e.g. attention disorder [START_REF] Lord | Autism spectrum disorder[END_REF]. Autism is characterized by three main features: social and interaction disorders, focused interests, and sensory disorders. In particular, sensory disorders concern 90% of people over the different sensory channels, including hypersensitivities and hyposensitivities [START_REF] Robertson | Sensory perception in autism[END_REF]. While some individuals need little support (e.g. to conduct academic work), others need substantial support for performing daily tasks (e.g. being nonverbal and displaying intellectual disability) [START_REF] Lord | Autism spectrum disorder[END_REF]. This paper uses the terms Autistic requiring Low Support (ALS) and High Support (AHS) to respectively refer to them. Since AHS children often experience distress, this paper focuses on using digital tools to support practitioners' interventions aimed at making them feel secure.

Three complementary clinic-based sensory strategies are often used with autistic children, and in particular AHS children: Sensory Integration Therapy [START_REF] Ayres | Sensory integration and learning disorders[END_REF][START_REF] Case-Smith | A systematic review of sensory processing interventions for children with autism spectrum disorders[END_REF], Snoezelen [START_REF] Lancioni | Snoezelen: an overview of research with people with developmental disabilities and dementia[END_REF] and Music Therapy [START_REF] Marquez-Garcia | Music Therapy in Autism Spectrum Disorder: a Systematic Review[END_REF]. They display positive outcomes to put children in an optimal state then allowing to perform challenging tasks (e.g. communication), by creating a secure context, regarding the physical space and the childpractitioner relationship. In particular, Sensory Integration Therapy posits the role of the user's body to integrate multisensory interactive processes so that to gradually enhance cognitive abilities. It relies on playful sensory activities (e.g. swinging or brushing) [START_REF] Ayres | Sensory integration and learning disorders[END_REF][START_REF] Case-Smith | A systematic review of sensory processing interventions for children with autism spectrum disorders[END_REF]. Snoezelen aims at making the child feel secure and strengthening the dyadic child-practitioner relationship, through multisensory spaces often including bubble columns [START_REF] Lancioni | Snoezelen: an overview of research with people with developmental disabilities and dementia[END_REF]. Music Therapy gathers a broad range of activities. It includes active techniques where the child directly makes music, and passive techniques where the child listens to the music presented by the practitioner [START_REF] Marquez-Garcia | Music Therapy in Autism Spectrum Disorder: a Systematic Review[END_REF]. Yet, challenges appear regarding these three interventions: equipment may not be flexible enough, which may bore the child over the long term; and Snoezelen equipment may be too expensive for practitioners to afford.

Extended Reality2 (XR) is promising to expand common autism interventions, as proved by recent Virtual Reality (VR) [START_REF] Mesa-Gresa | Effectiveness of Virtual Reality for Children and Adolescents with Autism Spectrum Disorder: An Evidence-Based Systematic Review[END_REF] and Augmented Reality (AR) [START_REF] Berenguer | Exploring the Impact of Augmented Reality in Children and Adolescents with Autism Spectrum Disorder: A Systematic Review[END_REF] reviews. Indeed, autistic children are often attracted by digital tools [START_REF] Grynszpan | Innovative technology-based interventions for autism spectrum disorders: A metaanalysis[END_REF], and XR allows to display secure, individualizable, and precisely controllable multisensory environments. Moreover, the Head-Mounted Display (HMD) technology is well-accepted by autistic children [START_REF] Tarantino | Immersive Applications: What If Users Are in the Autism Spectrum?[END_REF], and may be affordable for health structures. Yet, many practitioners remain reluctant to using XR, due to possible risks linked with over-exposition to screens [START_REF] Harlé | Intensive early screen exposure as a causal factor for symptoms of autistic spectrum disorder: The case for «Virtual Autism[END_REF], e.g. risks of addiction [START_REF] Berenguer | Exploring the Impact of Augmented Reality in Children and Adolescents with Autism Spectrum Disorder: A Systematic Review[END_REF]. Hence, including practitioners during the design process is advised to maximize their acceptability [START_REF] Parsons | Whose agenda? Who knows best? Whose voice?' Co-creating a technology research roadmap with autism stakeholders[END_REF]. This paper adopts such a design process to leverage the HMD potential in order to expand common practitioners' interventions.

Previous XR studies mainly focused on training socio-emotional abilities, leaving sensory strategies unexplored [START_REF] Berenguer | Exploring the Impact of Augmented Reality in Children and Adolescents with Autism Spectrum Disorder: A Systematic Review[END_REF][START_REF] Mesa-Gresa | Effectiveness of Virtual Reality for Children and Adolescents with Autism Spectrum Disorder: An Evidence-Based Systematic Review[END_REF]. Thus, they mainly concerned ALS individuals who can work on such skills [START_REF] Bozgeyikli | A Survey on Virtual Reality for Individuals with Autism Spectrum Disorder: Design Considerations[END_REF]. Yet, contrary to other mediums (e.g. desktop computer, tablet), XR displays high multisensory immersive capabilities, leading stakeholders to advocate for creating XR well-being and sensory-based strategies [START_REF] Bauer | eXtended Reality for Autism Interventions: The importance of Mediation and Sensory-Based Approaches[END_REF]. For instance, in Newbutt et al. [START_REF] Newbutt | Using Virtual Reality Head-Mounted Displays in Schools with Autistic Children: Views, Experiences, and Future Directions[END_REF]'s study, 29 autistic children answered "It relaxes me and I feel calm" to the question "What could or would you use VR HMDs for?". To our knowledge, this paper presents the first HMD-based XR design focusing on expanding clinic-based sensory strategies for AHS children.

So far, a few digitally-augmented multisensory environments targeting autistic children have been designed in collaboration with clinical teams, with positive effects over well-being, engagement and the child-practitioner relationship [START_REF] Garzotto | Magic Room: A Smart Space for Children with Neurodevelopmental Disorder[END_REF][START_REF] Pares | Achieving Dialogue with Children with Severe Autism in an Adaptive Multisensory Interaction: The "MEDIATE" Project[END_REF][START_REF] Ringland | Sensorypaint: A Multimodal Sensory Intervention for Children with Neurodevelopmental Disorders[END_REF]. In such spaces, most physical items were augmented to trigger sensory stimuli based on users' body movements and manipulations. Children could see and act with other people around, including practitioners. While Mediate [START_REF] Pares | Achieving Dialogue with Children with Severe Autism in an Adaptive Multisensory Interaction: The "MEDIATE" Project[END_REF] used free-play activities, the Magic Room [START_REF] Garzotto | Magic Room: A Smart Space for Children with Neurodevelopmental Disorder[END_REF] and Sensory Paint were mainly task-oriented. In terms of contexts, Mediate and the Magic Room were conducted in large spaces, and Sensory Paint used a projected screen, a tangible ball and a kinect camera. Yet, since these bespoke projects were designed for specific clinical contexts, they may not be suitable for stakeholders due to their low portability and potentially expensive price [START_REF] Parsons | Whose agenda? Who knows best? Whose voice?' Co-creating a technology research roadmap with autism stakeholders[END_REF]. Thus, this paper leverages the XR multisensory potential to expand them by using the affordable and portable HMD technology.

The main contribution of this paper is to offer insights about the design of XR applications which aim at expanding clinic-based sensory strategies that are commonly used to make AHS children feel secure. To explore this under-studied aspect, it presents the design of the HMD-based XR application called Magic Bubbles which was developed with the Mixed Reality platform for Engagement and Relaxation of AHS children (MiRERA). The iterative design process conducted in collaboration with practitioners is first detailed. Then, a user study carried out with eleven practitioners is presented, which led to design improvements. XR design guidelines are finally derived. This paper addresses two research questions:

• RQ1: According to practitioners, how to design XR applications in order to expand clinic-based sensory strategies which are commonly used with AHS children?

• RQ2: How to maximize practitioners' acceptability of XR applications which aim at complementing clinic-based sensory strategies for AHS children?

DESIGN PROCESS WITH PRACTITIONERS

The initial XR use case is first presented, and then its adaption and development for a clinical context in collaboration with practitioners.

Methodology

A first use case scenario emerged from interviews that were conducted with 34 autism stakeholders, i.e. 29 practitioners, 4 autistic people and/or their families, and 1 researcher [START_REF] Bauer | eXtended Reality for Autism Interventions: The importance of Mediation and Sensory-Based Approaches[END_REF]. It aims at calming and engaging AHS individuals though a free-play multisensory interaction space, drawing from Sensory Integration Therapy, Snoezelen, and music-therapy interventions. Two main technological possibilities were imagined, i.e. VR vs. AR environments. The latter allowed to adjust the proportion of real and virtual elements based on the practitioner's needs. To be adapted to a real-life clinical context, this main use case was then presented to two psychologists and one psychiatrist. All of them are autism experts working in a day hospital and use digital tools in their daily interventions. This approach thus follows presumptive design principles [START_REF] Frishberg | Design provocations: applying agile methods to disruptive innovation[END_REF], i.e. speeding up the design process by presenting advanced ideas to help practitioners to validate them and generate new ones. In addition to discussions, and also to better understand the specific needs of autistic children, the first author attended three solo sessions and two group sessions conducted by the psychologists and using digital tools (tablet, projected screen, robot), which included three AHS children.

Initial use case

Environment

Two types of stimuli are presented, i.e. generic and individualized. Generic visuals are bubble columns, moving audio bubbles, and water ponds. Indeed, interviews with stakeholders [START_REF] Bauer | eXtended Reality for Autism Interventions: The importance of Mediation and Sensory-Based Approaches[END_REF], the project called Magic Room [START_REF] Garzotto | Magic Room: A Smart Space for Children with Neurodevelopmental Disorder[END_REF], and the positive outcomes of the Snoezelen approach [START_REF] Lancioni | Snoezelen: an overview of research with people with developmental disabilities and dementia[END_REF] suggest that autistic children often like bubbles and bubble columns. Bubbles emerge from water ponds, then explode and reappear, since appearing/disappearing patterns are often appealing [START_REF] Bauer | eXtended Reality for Autism Interventions: The importance of Mediation and Sensory-Based Approaches[END_REF]. All visuals are simple geometric shapes for simplification purposes [START_REF] Bozgeyikli | A Survey on Virtual Reality for Individuals with Autism Spectrum Disorder: Design Considerations[END_REF]. Generic audio stimuli are short musical sounds (e.g. marimba, percussions), inspired from previous studies [START_REF] Garzotto | Magic Room: A Smart Space for Children with Neurodevelopmental Disorder[END_REF], interviews with stakeholders [START_REF] Bauer | eXtended Reality for Autism Interventions: The importance of Mediation and Sensory-Based Approaches[END_REF] and music-therapy activities [START_REF] Marquez-Garcia | Music Therapy in Autism Spectrum Disorder: a Systematic Review[END_REF].

Individualized stimuli are used to create a secure space with familiar objects. Hence, a pink "music" bubble can host the child's preferred music tracks, and an "image" panel can host visuals, e.g. drawings.

The practitioner has to add them prior to start the session. Four sensory interactions are available: psychomotor, audio, visual, and tactile with the controllers' vibrations. Children can move in space and touch virtual objects by using the controllers and/or their body [START_REF] Bartoli | Designing and Evaluating Touchless Playful Interaction for ASD Children[END_REF]. To prompt exploration, moving in space changes the environmental lighting color, drawing upon the audio floor in Mediate [START_REF] Pares | Achieving Dialogue with Children with Severe Autism in an Adaptive Multisensory Interaction: The "MEDIATE" Project[END_REF]. Interactions do not require hitting the controllers' buttons, due to possible fine motor skills disorders. Hitting objects can trigger five types of reactions: (1) audio bubbles to trigger their bubble sounds; (2) bubble column to changes the color of all columns and panels, in line with the Impression Wall in Mediate; (3) panels to change the sounds of the bubbles; (4) ponds to trigger a water splash; and (5) music bubble to trigger the individualized music. Simple feedbacks also show that actions are taken into account, by using controllers' vibrations and/or hovering the surface of objects.

Objects are organized according to their roles to create clutterfree scenes with little information [START_REF] Bozgeyikli | A Survey on Virtual Reality for Individuals with Autism Spectrum Disorder: Design Considerations[END_REF]. They are identified by using simple shapes and colors, as displayed on subfigures 1 A, B, C, D, and include the: bubble columns, audio bubbles, water ponds, panels, music bubble, and image panel. The number of bubbles, panels and columns, can respectively be adjusted from zero to eight, three, and three. To give a sense of agency, a yellow dot shows the direction of sight [START_REF] Garzotto | Wearable Immersive Virtual Reality for Children with Disability: A Case Study[END_REF]. A gradual real-virtual transition helps to prevent anxiety by making the virtual space neutral at the start/end of the experience. To prompt collaboration, children can always see the practitioner (i.e. directly or through an avatar), who can remain physically close to them and use physical guidance. At last, foam carpets delimit the interaction space to enhance comfort and structuration.

Activites

Free-play or task-oriented activities were imagined. Free-play activities consist in a free exploration of the interaction space, and were advised in the interviews previously conducted [START_REF] Bauer | eXtended Reality for Autism Interventions: The importance of Mediation and Sensory-Based Approaches[END_REF]. Task-oriented activities have intended outcomes, and draw from common interventions (e.g. sound lotos3 ) and prior studies [START_REF] Garzotto | Magic Room: A Smart Space for Children with Neurodevelopmental Disorder[END_REF].

Practitioner's Interface

Practitioners can monitor and adjust all stimuli at the start or at run-time, or even stop the experience, through a User-Interface (UI) on a large screen (see subfigures 1 E, F). In particular, the UI allows to: add/remove objects (orange), trigger stimuli (green), add/remove simple feedback (blue), and display contextual information (grey). Feedback include controllers' vibrations, since tactile hypersensitivity is a common autistic trait, and a visual timer to support predictability. Contextual information for instance concerns the time spent while using the application. To prompt exploration, the UI can also be used to trigger unexpected events [START_REF] Alcorn | Motivating Children's Initiations with Novelty and Surprise: Initial Design Recommendations for Autism[END_REF].

Use case adaptation for a day hospital context

To adapt the initial use case for a day hospital context, practitioners made design requirements leading to changes summarized in table 1.

Environment

To prevent sensory overloads, the speed of the bubbles in the column was decreased. Their size and speed were made controllable by stooping/standing, or using the practitioner's UI. To enhance sensory stimulation and generate surprise, a rectangular panel was added to trigger sounds from the controllers with two short melodies created on purpose. To clarify the structuration of space, psychomotricity cones were added to delimit the interaction space.

Categories

Needs from the practitioners (Change Adopted (A); Already Planned in the existing design (AP))

Environment

Collaboration: The child can perceive the real environment and act with his/her practitioner. (A) Meaningful environment: The virtual space has to be connected to the real space and to the other child's activities.

Activities -Actor vs. Spectator conditions

Free-play AR activities were chosen to best suit AHS children, make the environment meaningful, support collaboration, and make a smooth transition between real and virtual spaces. In this context, a psychologist specified that it was not a problem for the child to see the practitioner's monitoring screen, and may even be reassuring. Two conditions were added, i.e. spectator or actor, drawing from passive and active practices in Snoezelen and music therapy interventions. When spectator, the child can move in space, but not interact with objects. All stimuli are triggered by the practitioner and/or automatically. When actor, the child can move in space and interact with all virtual objects. The practitioner can only physically guide them, and trigger stimuli when supporting their actions.

Practitioner's Interface

As the UI suited most practitioners' needs, only a small change was added to support visibility. Indeed, the buttons "Controle soignant" and "Infos Seance" were respectively added to show/hide the main pane and only see the child's view, and to show/hide the informational pane (see subfigures 1 E, F).

Equipment

Equipment choices are detailed in section 2.4, and were mostly driven by the possible behaviours of AHS children, e.g. aggressiveness, or covering their ears with their hands. Since autistic children are often used to wear protection headsets, wearing an HMD was considered to be possible for most of them. For the others who may display tactile hypersensitivity, using a gradual sensory habituation to the HMD may be needed to allow them to wear it.

Apparatus & Development

Magic Bubbles uses the AR see-through platform called MiRERA, which means that a stereoscopic camera is plugged onto the HMD, captures a live feed of the real environment, and then makes it visible inside the HMD, supplemented by virtual objects. The HTC Vive Pro headset was chosen with a Zed Mini camera 4 to get a nonperceivable visual latency of 60ms, a correct resolution of 720 p per camera, and an immersive 90°horizontal Field of View (FoV). The front cameras of the HTC Vive Pro were previously tried but abandoned because they achieved lower results in terms of resolution and latency, being possibly detrimental for autistic children. Other HMD see-through devices were excluded because they displayed a narrower horizontal FoV, e.g. 52°for the Hololens 2 5 . While bandwidth technical limitations did not allow to use non-tethered AR, practitioners still preferred using tethered AR rather than non-tethered VR. Indeed, perceiving the real surroundings and practitioner was a major requirement, and alternatives such as including the practi- tioner's face inside a VR environment on a virtual television screen was deemed impossible for some children who would misunderstand the link between the image and practitioner. The total weight of the system of 563g was not considered to be a problem for autistic children aged more than 11 since it was well accepted in Newbutt et al.'s study [START_REF] Newbutt | Using Virtual Reality Head-Mounted Displays in Schools with Autistic Children: Views, Experiences, and Future Directions[END_REF]. Two HTC Vive controllers are used. Four Vive lighthouse outside-in tracking systems cover the interaction space to avoid tracking loss due to the practitioner being close to the child. Hence, trade-offs were made regarding the portability of the system in relation to its other features. The HMD runs on a desktop computer Dell Precision 3630, with i7 CPU, 32Go of RAM, and the Nvidia Geforce RTX2080. A 27-inch screen allows to monitor child's activities while being far from it.

A video presentation of the software, consisting in a screen capture of the practitioner's UI while hiding the main pane when the application is running, can be found online 6 . Development was done using Unity3D software, Google Resonance Audio for the 3D audio rendering, Steam VR SDK for the AR handling, and ZED SDK to work with the ZED Mini camera. A game control script allows actions to be triggered by the child or practitioner, by handling the main features (e.g. visible/hidden aspects) based on state machines which manage the states of objects. It communicates with other managers: audiovisual manager to handle all audiovisual aspects; player manager to handle user movements and interactions; log manager, which writes in external files the actions of the child and practitioner. Every object sends events to the corresponding manager if an interaction occurs. Unity physics engine handles all collisions.

EVALUATION WITH A CLINICAL TEAM

Pre-tests were conducted with a team of practitioners at a day hospital through two sessions (i.e. pre-test 1 and 2), including nine practitioners who did not participate to the initial design process. This pre-study was required to: validate if the application was consistent regarding their interventions with AHS children, gather design insights to refine the application, and get their approval to then be able to work with AHS children. This section first presents the demographics and method used, and then insights which emerged about the user experience and design.

Participants

Participants include eight women and three men: educators (n=5), clinical psychologists (n=2), co-head of the day hospital (n=1), nurse (n=1), secretary (n=1), and psychology intern (n=1). Two had little XR experience with VR games. Four were 20-30 years old, three were 30-40, one was 40-50 and three were 50-60. Seven participants did the pre-test 1, and the four others did the pre-test 2.

Method

Protocol

Only the actor condition was tested, since this pre-study mainly targeted the suitability of the existing design and interactions used 6 Link to the video presentation: valentinbauer.com/research/doctorat/ for AHS children, as well as possible improvements to that respect.

Practitioners freely tested the application during five minutes or more, in the psychomotricity room of the day hospital (see figure 2). To observe their discovery of the space, no detailed explanation about how the environment works was given prior to start. The two psychologists who participated to the initial design observed their colleagues during the testing, to: think about new AR needs with respect to AHS children; imagine how they could guide the children wearing the HMD; and precise the observable parameters that could be used to assess the state of the children. Due to the sanitary Covid situation, a strict cleaning protocol was used: face masks kept during the experiment, equipment cleaned between participants using disposable wipes, windows regularly opened, and two sessions with different participants separated by ten minutes at least.

Data collection and analysis

During the experience, subjective insights were gathered about the practitioners' experience, through note-taking of their behaviors and comments (the three last sessions were filmed), i.e. smiles/laughs, movement quantity, or type of movements. After the experience, seven semi-directed questions addressed demographics (i.e. age, profession, past XR experience), user experience (i.e. feeling of connection with the real space, comfort, feeling of dizziness), and preferences (i.e. object preferred). Three final open questions concerned: general feelings, possible design improvements, or additional elements that practitioners would like to say.

A descriptive qualitative analysis allowed to identify phrasings and observations representing key aspects of the user experience. They were then grouped into concepts drawing from the prior grounded theory analysis of the interviews conducted with autism stakeholders [START_REF] Bauer | eXtended Reality for Autism Interventions: The importance of Mediation and Sensory-Based Approaches[END_REF]. The number X of participants mentioning each concept will be mentioned inside parenthesis using (n=X).

User experience: Subjective results

All participants enjoyed the experience, which was spontaneously compared to Snoezelen (n=4), even if two of them were anxious prior to start. All participants liked hitting the bubbles, which were the preferred elements along with the water ponds. A psychologist said: "you can play squash if you send the bubbles strong enough against the cupboard". Participants were often surprised, and smiled/laughed when realizing that they could interact with elements.

Most participants felt connected to their real surroundings (n=10), even if they were concerned about feeling "enclosed" in the virtual space prior to start. Hence, this experience reassured them about future testing with AHS children, and made a psychologist confirm that AR has more potential to be accepted by practitioners than VR. Some behaviors suggested a possible feeling of presence (n=4): one participant made a bubble bounce on a psychologist and asked "did you see it?"; two participants hit the ponds with their feet; and one participant described being "in another world".

Sensorimotor behaviors vary between participants, from being very stiff to moving a lot (stooping, jumping etc.), with the whole body being engaged. The experience can potentially be hypo or hyper stimulating, depending on its use with children (n=9).

Most participants felt comfortable with the device (n=8), apart from three of them who: found it heavy (n=1), perceived a discomfort on the nose (n=1), or due to their face mask (n=1). A psychologist ensured that "these issues are not a problem with children since they would directly express [non-verbally] their discomfort if they have any". One participant felt a bit dizzy at the end, due to the HMD not being screwed enough, thus making the image a bit blurry.

Design insights from practitioners

The insights about the suitability of the design for AHS children are first detailed. Then, the insights which were integrated to improve the application are mentioned, and are summarized in table 2.

Concept

Participant proposals

Structuration

Connect all sessions with drawings (n=4) Use a gong sound to end the sessions (n=3) Hide the chaperone (n=7)

Sensoriality

Only interact with controllers (n=3) Vary interactions with the bubbles (n=3) Simplify action-reaction principles (n=3) Prevent from entering inside the column (n=1)

Agency

Add recording possibilities (n=3) Add drawing possibilities (n=4)

Equipment

Pay attention to the wire of the HMD (n=11)

Suitability of the design for AHS children

Psychologists who participated to the initial design found consistent the use of a screen to monitor what the child perceives. Indeed, since they remembered the positions of virtual objects in the real space between sessions, they deemed it suitable to guide children. They also stressed to always keep the same number of elements due to the ritualization of children. To that respect, a basic setup with three bubbles, one bubble column and one panel appeared to be a good trade-off in terms of number of elements. All participants noted that attention has to be paid to the wire between the computer and HMD, so that to not hinder the child. Since non-tethered AR could not be used due to technical constraints (see section 2.4), they again stressed that tethered AR was better suited than non-tethered VR.

New design insights

To support structuration, we added the possibility at the end of the session for the child to make a real drawing that would then be included in the image panel for the next session. The psychologists who participated to the initial design said that it could connect sessions by "leaving traces that they will see again", offer a sense of agency, ritualize sessions, and may allow to infer the child's experience. Thus, hitting the image panel was added to navigate through all of the drawings. We also added a gong sound that the practitioner can trigger to announce the end of the sessions. Also, the grid boundaries of the interaction space (i.e. chaperone) were removed after pre-test 1, as they were described as a "prison" (n=7). About sensoriality, only controllers' interaction was kept after pre-test 1, since it was more intuitive than body interaction. Three types of interaction were added to the simple "hit" for the bubbles to make children more aware of their movements' velocity: grabbing, throwing, or exploding them. The panel which was used to change the bubbles' sounds was removed after pre-test 1, because it did not display a clear action-reaction relationship. Though, sounds can still be changed through the UI. Making the bubbles disappear when approaching the column was also added to prevent over-stimulation.

To give a sense of agency, one recording and one playback bubbles were added to the actor condition after pre-test 1. They allowed to hear back one's voice as in some appealing video games for autistic children (n=1), e.g. Talking Tom Cat [START_REF]Talking Tom Cat[END_REF]. As simplifying action/reaction principles was advised during pre-test 2, only one bubble was finally kept for both actions. Drawing on a large panel was also added after pre-test 2, with controllers or through the UI.

DISCUSSION & RECOMMENDATIONS

In the two first subsections, findings are discussed to address: how to design XR applications to expand clinic-based sensory strategies with AHS children, according to practitioners (RQ1), and how to maximize practitioners' acceptability (RQ2). Table 3 summarizes the main findings. Limits and perspectives are then discussed.

XR design guidelines to support sensory strategies

As in the previous XR multisensory designs focusing on well-being [START_REF] Garzotto | Magic Room: A Smart Space for Children with Neurodevelopmental Disorder[END_REF][START_REF] Pares | Achieving Dialogue with Children with Severe Autism in an Adaptive Multisensory Interaction: The "MEDIATE" Project[END_REF][START_REF] Ringland | Sensorypaint: A Multimodal Sensory Intervention for Children with Neurodevelopmental Disorders[END_REF], practitioners recommended to include the possibility for the child to act and collaborate with them, so that to reinforce the child-practitioner relationship. Hence, an HMD-based AR seethrough system was chosen to maximize immersion while perceiving the practitioner and real surroundings. This paper suggests that AR is well-suited to support clinic-based sensory strategies for AHS children, whereas VR could possibly isolate them. Thus, it extends the AR cognitive-behavioral potential previously outlined [START_REF] Berenguer | Exploring the Impact of Augmented Reality in Children and Adolescents with Autism Spectrum Disorder: A Systematic Review[END_REF], "to cope anxiety, fear and phobias in social situations" [START_REF] Tarantino | Immersive Applications: What If Users Are in the Autism Spectrum?[END_REF].

Practitioners insisted on using free-play activities with AHS children, to provide room for playful and creative experiences, as in the project called Mediate [START_REF] Pares | Achieving Dialogue with Children with Severe Autism in an Adaptive Multisensory Interaction: The "MEDIATE" Project[END_REF]. Indeed, contrary to other multisensory projects [START_REF] Garzotto | Magic Room: A Smart Space for Children with Neurodevelopmental Disorder[END_REF][START_REF] Ringland | Sensorypaint: A Multimodal Sensory Intervention for Children with Neurodevelopmental Disorders[END_REF] which focused more on task-oriented games, our design choices came from three causes: users are AHS children; practitioners have a psychoanalytic background, and encourage emergent behaviors to arise to then work on them; free-play connects with other mediation activities used at the day hospital. Hence, Magic Bubble could be considered as a malleable medium, i.e. a concept commonly used by practitioners to describe open-ended sensorimotor mediation activities, which includes the materials, digital devices, and the practitioner [START_REF] Brun | L'acte de création et ses processus dans les médiations thérapeutiques pour enfants autistes et psychotiques[END_REF]. To our knowledge, this is the first HMD-based AR design for mediation purposes with AHS children.

A secure multisensory AR space was designed to handle the variety of autistic sensory profiles. To this end, the design process was informed by the overall clinical context of the children. This led the psychologists who participated to the initial design to consider the Magic Bubbles' environment as potentially holding, i.e. a concept commonly used by practitioners to describe a nurturing space for generating and supporting exchanges with the practitioner [START_REF] Winnicott | Jeu et réalité: l'espace potentiel[END_REF].

Whereas Magic Bubbles supports various interaction types as in previous multisensory projects [START_REF] Garzotto | Magic Room: A Smart Space for Children with Neurodevelopmental Disorder[END_REF][START_REF] Pares | Achieving Dialogue with Children with Severe Autism in an Adaptive Multisensory Interaction: The "MEDIATE" Project[END_REF][START_REF] Ringland | Sensorypaint: A Multimodal Sensory Intervention for Children with Neurodevelopmental Disorders[END_REF], it is the first to our knowledge to be such flexible and adaptable to clinical contexts, in line with stakeholders' needs [START_REF] Parsons | Whose agenda? Who knows best? Whose voice?' Co-creating a technology research roadmap with autism stakeholders[END_REF]. This feature is particularly due to the affordability and portability of HMD technology. Hence, the platform only uses audiovisual interactive elements and no smart objects to be quickly mounted/dismounted in spaces where permanent installation would be impossible. With the current development of HMD technology, these features will become even more prominent in the next few years. The impact of mainly using audiovisual elements on the child's experience will have to be assessed in comparison with previous projects which mainly used tactile inputs.

Maximizing practitioners' acceptability of XR

Whereas most practitioners had no previous XR experience, Magic Bubbles was well-accepted. They were engaged and agreed to future testing with AHS children. While being concerned about feeling "enclosed" prior to start, because non-appropriate for AHS children, they felt connected with their real surroundings during the experiment. To that respect, this is the first paper to our knowledge which suggests that AR is more suited than VR to expand clinic-based sensory strategies with AHS children, according to practitioners. The acceptability of Magic Bubbles is also due to the fact that it complements other sensory-based mediation activities at the day hospital, e.g. painting, theatre, music making, or video games. In particular, the success of such mediation activities is due to the sensory qualities of the medium in relation to the child sensorimotor abilities, and child-practitioner relationship [START_REF] Brun | L'acte de création et ses processus dans les médiations thérapeutiques pour enfants autistes et psychotiques[END_REF]. Hence, AR is well suited to extend them due to its multisensory potential.

The psychologists who participated to the initial design were enthusiastic, as the project would then be used in a real-life clinical context. Indeed, they stressed that most technology-based approaches are currently tested in laboratories, which raises possible concerns about: biases due to the strong ritualization of AHS children, and non-adaptability of such designs within real-life clinical contexts. While XR reviews [START_REF] Berenguer | Exploring the Impact of Augmented Reality in Children and Adolescents with Autism Spectrum Disorder: A Systematic Review[END_REF][START_REF] Mesa-Gresa | Effectiveness of Virtual Reality for Children and Adolescents with Autism Spectrum Disorder: An Evidence-Based Systematic Review[END_REF] do not clearly mention which studies were conducted in clinical contexts, this paper suggests to take more into account the ecological context when designing autism studies.

Contrary to many practitioners who still remain reluctant to using technology-based approaches [START_REF] Harlé | Intensive early screen exposure as a causal factor for symptoms of autistic spectrum disorder: The case for «Virtual Autism[END_REF], practitioners from our study stressed that using XR with AHS children may be positive if used in a controlled way. Hence, they advise using XR within a secure context, i.e. under the control of a practitioner and with a time limit.

Limits and Work in Progress

Only practitioners' feedback were gathered because the Covid-19 pandemic prevented us from conducting tests with AHS children at the time of this design process. Then, only subjective insights were collected to gather information about the user experience and existing design. At last, gradually asking questions to practitioners about ideas that emerged over time could have offered further insights.

Magic Bubbles is currently being evaluated at a day hospital in collaboration with practitioners, with seven AHS children, i.e. six boys and one girl, aged more than 11. Experimental procedures were approved by the Poléthis Ethics Research Committee of Université Paris-Saclay under reference 226. Children do the 20-minute experience once a week over six weeks, four being actor and three being spectator. Indeed, practitioners deemed that the evolution between spectator and actor conditions could otherwise be frustrating.

Figure 1 :

 1 Figure 1: Design of Magic Bubbles Game -Content: 1 Bubble; 2 Bubble Column; 3 Panel; 4 Water Pond; 5 Music Bubble; 6 Image Panel; 7 Drawing panel (added after the user testing); 8 Recording Bubble (added after the user testing) -Practitioner's UI (E,F): 1 Add/Remove objects; 2 Trigger stimuli; 3 Add/Remove simple feedback; 4 Display contextual information; 5 Show/Display the UI.

Figure 2 :

 2 Figure 2: Left: AR setting at the day hospital -Right -a practitioner testing the application.

Table 1 :

 1 Practitioners' needs about using XR at the day hospital

Table 2 :

 2 Design insights from the testing with practitioners

Table 3 :

 3 Main design insights for using XR with AHS children RQ1 • Use AR rather than VR to prompt collaboration • Use free-play activities • Make the general context secure • Use flexible and portable XR designs RQ2 • Use AR rather than VR for clinical contexts • Consider XR as other mediation tools • Design XR applications within clinical contexts • Use XR in controlled environments to prevent any risks

This paper uses autism stakeholders' preferences in terms of terminology, e.g. identity first-language, with terms such as "autistic individual"[START_REF] Bottema-Beutel | Avoiding Ableist Language: Suggestions for Autism Researchers[END_REF].

Within the Milgram and Kishino[START_REF] Milgram | A Taxonomy of Mixed Reality Visual Displays[END_REF]'s Virtuality continuum, Mixed Reality (MR) covers systems from Augmented Reality (AR) to Augmented Virtuality (AV). Related to the same continuum, we use Extended Reality (XR) terminology to target not only MR, but also Virtual Reality (VR).

Sound lotos are listening games used to identify daily noises, e.g. animals or objects.

https://www.stereolabs.com/zed-mini/

https://www.microsoft.com/fr-fr/hololens

ACKNOWLEDGMENTS

We would like to thank all the practitioners who tested the application, and particularly Marie-Noëlle Clément, Olivier Duris, and Charlotte Labossière for their valuable design insights. This work was supported by a MESRI Funding from Université Paris-Saclay.


Wei Dai

Frédéric Moynier

Marine Paquet

Julien Moureau

Baptiste Debret

Julien Siebert

Yvan Gerard

Ye Zhao

Calcium isotope measurements using a collision cell (CC)-MC-ICP-MS

Calcium is a major element in terrestrial planets and has six stable isotopes, including 40 Ca which is a product of radioactive decay of 40 K (T1/2=1.25 Gyrs). Calcium isotope geochemistry has therefore been used to trace biological and geological processes in various environments as well as radiogenic dating. However, it has been technically impossible to analyze stable and radiogenic isotopes simultaneously and high precision measurements usually require tens of micrograms of Ca. Here, we present high-precision Ca isotopic data, including the stable isotopes 42 Ca, 43 Ca and 44 Ca as well as the radiogenic 40 Ca using a Nu Sapphire multi-collector inductively-coupled-plasma mass-spectrometer (MC-ICP-MS), that is equipped with a collision cell to minimize Ar based interferences. The stable isotopic variations are reported using the delta notation ( 40/44 Ca,  42/44 Ca,  43/44 Ca), which is the permil deviation of a given ratio from the NIST SRM 915b standard. The radiogenic excess is reported as  40 Ca, the per ten thousand deviation of the 40 Ca/ 44 Ca ratio from the same standard, after internal normalization to the 42 Ca/ 44 Ca ratio. We tested the influence of various parameters (Ca concentration, Ca and HNO3 concentration mismatch between sample and standard, effect of matrix elements) on the precision and accuracy of the measurements. We show that, using ~100 ng is sufficient to Revised manuscript with no changes marked Click here to view linked References obtain high precision (<100 ppm, 2SD)  40/44 Ca and  40 Ca using a standard bracketing techniquethis represents an improvement by over an order of magnitude in sensitivity compared to any previous methods. It should be noted that a limitation is that the intensities of the standard and sample must be matched very closely (better than 2%). Following this recommendation, the Ca isotopic compositions of 9 geological samples reported here is consistent with previous data. For example, the  40 Ca value of GSP-2 (3.92 ± 0.48 ‱) is within error with literature data (values between 3.69 and 4.32 ‱). Using this method, it is therefore possible, for the first time, to obtain simultaneously high-precision radiogenic and stable Ca isotopes on small samples, which will certainly open up many novel applications of Ca stable isotopes.

Introduction

Calcium is the sixth most abundant element in the bulk Earth [START_REF] Allègre | The chemical composition of the Earth[END_REF] and is involved in many geological and biological processes [START_REF] Depaolo | Calcium isotopic variations produced by biological, kinetic, radiogenic and nucleosynthetic processes[END_REF][START_REF] Frausto Da Silva | The Biological Chemistry of the Elements[END_REF].

It is the most refractory major element of the solar system with a temperature of 50 % condensation of 1517 K [START_REF] Lodders | Solar System abundances and condensation temperatures of the elements[END_REF] and therefore controls the accretion of the first solids [START_REF] Grossman | Condensation in the primitive solar nebula[END_REF]. Through its predominance in the constitution of marine carbonate sediments (e.g., calcite), it also plays a major role in controlling the carbon cycle [START_REF] Amsellem | Calcium isotopic evidence for the mantle sources of carbonatites[END_REF][START_REF] De La Rocha | Isotopic evidence for variations in the marine calcium cycle over the cenozoic[END_REF][START_REF] Fantle | The effects of diagenesis and dolomitization on Ca and Mg isotopes in marine platform carbonates: Implications for the geochemical cycles of Ca and Mg[END_REF][START_REF] Fantle | Calcium isotopes in the global biogeochemical Ca cycle: Implications for development of a Ca isotope proxy[END_REF]. Calcium has 6 stable isotopes, 40 Ca (96.94 w.t.%), 42 Ca (0.647 w.t.%), 43 Ca (0.135 w.t.%), 44 Ca (2.086 w.t.%%), 46 Ca (0.004 w.t.%) and 48 Ca (0.187 w.t.%) with 40 Ca being a major product of the decay of 40 K (T1/2=1.25 Gyrs). Given that one of its isotopes is radiogenic ( 40 Ca), that it has many stable isotopes spanning a large mass difference, and that its isotopes are formed by various nucleosynthetic mechanisms, there has been an early interest in Ca isotopes to study planetary formation and evolution [START_REF] Russell | Calcium isotope fractionation in ion-exchange chromatography[END_REF]. The measurement of Ca isotopes has been traditionally performed using thermal-ionization mass-spectrometers (TIMS), for both the study of the radiogenic and nucleosynthetic anomalies (e.g. [START_REF] Antonelli | Radiogenic Ca isotopes confirm post-formation K depletion of lower crust[END_REF][START_REF] Caro | 40 K-40 Ca isotopic constraints on the oceanic calcium cycle[END_REF][START_REF] He | Mass-independent and mass-dependent Ca isotopic compositions of thirteen geological reference materials measured by thermal ionisation mass spectrometry[END_REF][START_REF] Kreissig | Ca isotope fingerprints of early crust-mantle evolution[END_REF][START_REF] Lee | Calcium isotopic anomalies in the Allende meteorite[END_REF][START_REF] Marshall | Calcium isotopes in igneous rocks and the origin of granite[END_REF][START_REF] Simon | Calcium isotope composition of meteorites, Earth, and Mars[END_REF] and the stable isotopic variations by using double spike addition [START_REF] Amini | Calcium Isotopes (δ 44/40 Ca) in MPI-DING Reference Glasses, USGS Rock Powders and Various Rocks: Evidence for Ca Isotope Fractionation in Terrestrial Silicates[END_REF][START_REF] Feng | Calcium Isotopic Compositions of Sixteen USGS Reference Materials[END_REF][START_REF] Heuser | Measurement of calcium isotopes using a multicollector TIMS technique[END_REF][START_REF] Huang | Calcium isotopic ratios and rare earth elements abundances from refractory inclusions from the Allende CV3 chondrite[END_REF]Kang et al., 2017;[START_REF] Lehn | Optimization of a 48Ca-43Ca double-spike MC-TIMS method for measuring Ca isotope ratios (δ44/40Ca and δ44/42Ca): limitations from filament reservoir mixing[END_REF][START_REF] Russell | Calcium isotope fractionation in ion-exchange chromatography[END_REF][START_REF] Schmitt | Calcium isotope fractionation during plant growth under a limited nutrient supply[END_REF][START_REF] Simon | Stable calcium isotopic composition of meteorites and rocky planets[END_REF][START_REF] Skulan | Calcium isotope fractionation between soft and mineralized tissues as a monitor of calcium use in vertebrates[END_REF][START_REF] Wu | Calcium isotopic composition of the lunar crust, mantle, and bulk silicate Moon: A preliminary study[END_REF]. The stable isotopic data are usually reported using the  notation against a standard that has historically been the NIST SRM 915a. However, SRM 915a is not commercially available anymore and has been replaced by the SRM 915b that is used in this study. It was previously demonstrated that the /40 Ca of the SRM 915b was 0.72 ‰ relatively to SRM 915a [START_REF] Heuser | The calcium isotope composition (delta Ca-44/40) of NIST SRM 915b and NIST SRM 1486[END_REF], therefore, it is easy to convert the data normalized to SRM915b to SRM915a to keep the values consistent with literature.

In the present paper we will present the data as  x/44 Ca as: With ( 40 Ca/ 44 Ca)normalized representing the 40 Ca/ 44 Ca corrected from the mass-dependent isotopic fractionation after being normalized to the 42 Ca/ 44 Ca ratio using the exponential law and a 42 Ca/ 44 Ca ratio of 0.31221 [START_REF] Russell | Calcium isotope fractionation in ion-exchange chromatography[END_REF].

The development of plasma mass spectrometry has allowed the precise isotopic measurement of Ca isotopes, for both stable isotope analyses (e.g. [START_REF] Amsellem | Calcium isotopic evidence for the mantle sources of carbonatites[END_REF][START_REF] Amsellem | Evolution of the Ca isotopic composition of the mantle[END_REF][START_REF] Antonelli | Calcium isotope evidence for early Archaean carbonates and subduction of oceanic crust[END_REF][START_REF] Brazier | Calcium isotope evidence for dramatic increase of continental weathering during the Toarcian oceanic anoxic event (Early Jurassic)[END_REF][START_REF] Dai | Calcium isotope compositions of mantle pyroxenites[END_REF][START_REF] Fantle | The effects of diagenesis and dolomitization on Ca and Mg isotopes in marine platform carbonates: Implications for the geochemical cycles of Ca and Mg[END_REF][START_REF] Fietzke | Direct measurement of 44Ca/40Ca ratios by MC-ICP-MS using the cool plasma technique[END_REF][START_REF] Hirata | Isotopic Analysis of Calcium in Blood Plasma and Bone from Mouse Samples by Multiple Collector-ICP-Mass Spectrometry[END_REF][START_REF] Li | High-precision Ca isotopic measurement using a large geometry high resolution MC-ICP-MS with a dummy bucket[END_REF][START_REF] Li | One-step chromatographic purification of K, Ca, and Sr from geological samples for high precision stable and radiogenic isotope analysis by MC-ICP-MS[END_REF][START_REF] Valdes | The nature of Earth's building blocks as revealed by calcium isotopes[END_REF] and nucleosynthetic anomalies [START_REF] Schiller | Isotopic evolution of the protoplanetary disk and the building blocks of Earth and Moon[END_REF][START_REF] Schiller | Calcium isotope measurement by combined HR-MC-ICPMS and TIMS[END_REF]. The major limitation is that the 40 Ca is not measurable given that ionization is achieved in an Ar plasma (for conventional MC-ICP-MS) generating an unresolvable isobaric interference on 40 Ca, which would require a resolution of 190,000 to resolve while a typical high-resolution that can be achieved on these instruments is less than 15,000. The approach has been to focus on the 42 Ca to 48 Ca isotopes, leaving aside 96.94 % of the Ca. The samples must be analyzed in medium or highresolution mode to resolve some argide isobaric interferences such as 40 ArH + 2 on 42 Ca, hence requiring a large amount (several tens or hundreds of g) of Ca for precise (i.e., 2SD on the 42 Ca/ 44 Ca ratio better than 100 ppm) measurements [START_REF] Li | High-precision Ca isotopic measurement using a large geometry high resolution MC-ICP-MS with a dummy bucket[END_REF][START_REF] Schiller | Calcium isotope measurement by combined HR-MC-ICPMS and TIMS[END_REF][START_REF] Valdes | The nature of Earth's building blocks as revealed by calcium isotopes[END_REF]. The Sapphire, a novel dual-path MC-ICP-MS equipped with a collision-cell (CC), was launched in 2017 by Nu Instruments. This collision-cell MC-ICP-MS allows the reduction of the amount of Ar + and charged argides via collision and reaction with a neutral and a reactive gas.

Using the instrument located at the Institut de Physique du Globe de Paris (IPGP), France, it was recently demonstrated that high precision measurements of K isotopic compositions can be achieved using 10 times less samples than previous methods [START_REF] Moynier | Potassium isotopic composition of various samples using a dual-path collision-cell-capable multiple-collector inductively coupled plasma mass spectrometer[END_REF]. This instrument is therefore very promising for Ca isotope measurements, including the 40 Ca.

Performing the measurements in low resolution mode allows the use of much lower amounts of samples as previously needed on both TIMS and MC-ICP-MS, and with the possibility to combine both radiogenic and stable isotope measurements. No previous work reported Ca isotopic data using a Sapphire MC-ICP-MS, although one paper reported data on Ca isotopes using a protype CC-MC-ICP-MS [START_REF] Klaver | The Ca isotope composition of mare basalts as a probe into the heterogeneous lunar mantle[END_REF]. [START_REF] Klaver | The Ca isotope composition of mare basalts as a probe into the heterogeneous lunar mantle[END_REF] presented very high precision data using several tens of g of Ca (the solutions were analyzed at 5 ppm), which return a precision of ~0.03

‰ on  40/44 Ca and a precision of ~0.05 ‰ on the  40 Ca. However, the technical details of the method and the estimation of the errors are unpublished to date.

Here, we present the first high precision stable and radiogenic Ca isotopic data using the IPGP CC-MC-ICP-MS Nu Sapphire. We report new data obtained on 9 samples comprising international rock standards that were previously analyzed using various methods. We also report analytical tests investigating the limiting factors of the accuracy such as the effect of K (producing the isobaric KH + interference on 40 Ca), Sr (isobaric interference of 84 Sr ++ , 86 Sr ++ and 88 Sr ++ on 42 Ca, 43 Ca, and 44 Ca respectively), and other elements (Ti, La…). The mismatch of concentration between standard and samples as well as the effect of sample concentration on the precision and accuracy of the measurement were also tested.

Samples and Methods

Samples

The samples analyzed here comprise GSP-2 (granodiorite, United States Geological Survey, USGS), AGV-2 (andesite, USGS), BHVO-2 (basalt, USGS), COQ-1 (carbonatite, USGS), PCC-1 (peridotite, USGS), BIR-1 (basalt, USGS), DTS-2 (dunite, USGS), UB-N (serpentinite, Centre de Recherche Pétrographique et Géochimique, CRPG, France) and Ka10 (carbonatite, Kaisersthul, [START_REF] Amsellem | Calcium isotopic evidence for the mantle sources of carbonatites[END_REF]). We also analyzed two internal Ca standards, Alpha Aesar batch 14407 lot 249290 and VWR batch 455172T and lot 219015005-01.

The selected samples cover a range of chemical and Ca isotopic compositions and all of them have been previously analyzed for their Ca isotopic compositions in multiple laboratories.

Therefore, they are well suited for testing the accuracy of the Nu Sapphire measurements, as well as confirming previous results obtained on standard MC-ICPMS or TIMS.

The effect of the intensity mismatch (between 1 and 50% of mismatch) between sample and standard was tested on the SRM 915b standard. The effect of K, Sr, La and Ti has been also tested on SRM 915b by adding various amounts of each individual element. Finally, the effect of Ca concentration on the accuracy and precision of the data has been tested by analyzing Ca from 100 ppb down to 10 ppb (which for 5 replicates would represent ~500 ng to ~50 ng of Ca, respectively).

Dissolution and chemical purification

The chemical purification was conducted at the Institut de Physique du Globe de Paris (IPGP), using the method from [START_REF] Feng | Calcium Isotopic Compositions of Sixteen USGS Reference Materials[END_REF], in addition to which we performed an extra step to further purify Sr using an Eichrom Sr specific resin.

50 mg of whole rock powders were dissolved using concentrated HF and HCl (5:1 volume ratio) acids in 7 mL PTFE Teflon square digestion vessels with wrench top closures in an oven at 160°C for 3 days. Following evaporation of the HF and HCl, the samples were subsequently treated with a 1:1 volume mix of concentrated HCl and HNO3 and refluxed at 140°C for 3 days in an oven. Prior study of [START_REF] Debret | Ore component mobility, transport and mineralization at mid-oceanic ridges: a stable isotopes (Zn, Cu and Fe) study of the Rainbow massif (Mid-Atlantic Ridge 36°14'N)[END_REF], comparing this method to Parr bomb dissolution techniques, has shown that it can digest all refractory phases that are present in ultramafic rocks (e.g., PCC-1 and UB-N), including spinel. Finally, samples were brought into solution in 6N HCl in closed beakers at 120°C, periodically vibrated in an ultrasonic bath, and then opened and dried at 120°C. The dried samples were redissolved in 4 mol/L HNO3 in preparation for the chemical purification on a 250 L of Eichrom DGA resin. After washing the columns, the samples were loaded in 1 mL of 4 mol/L HNO3. It must be noted that the amount of rock standards loaded on the columns was evaluated to correspond to ~25 g of Ca. The matrix elements were washed by further addition of 6.75 mL of 4 mol/L HNO3. The Ca was collected with 3 mL of water. This procedure was performed twice. Then the samples were further purified from Sr by passing through ~100 L of Eichrom Sr spec resin. After washing the resin, the samples were loaded in 0.5 mL of 3 mol/L HNO3, the calcium was then collected with an additional 1.5 mL of 3 mol/L HNO3. This collected Ca fraction was dried down at 120°C, and several drops of concentrated HNO3 were added and evaporated to decompose potential organic matters leached during the column chemistry. The whole procedure yield is over 99%. The samples were finally redissolved in 0.5 mol/L HNO3 for Sapphire analysis.

Calcium isotopic measurements on the Sapphire

Principle of the Sapphire has been described in [START_REF] Moynier | Potassium isotopic composition of various samples using a dual-path collision-cell-capable multiple-collector inductively coupled plasma mass spectrometer[END_REF] and remains the same here. For Ca isotopic measurements, collision cell pathway of the Nu Sapphire was utilized (low energy, 4 kV acceleration). At the plasma source, the ions are accelerated at 4 kV, and then deflected off-axis and decelerated to a few tens eV to enter the radio frequency (RF) hexapole collision/reaction cell. The RF hexapole reduces mass bias effects compared to quadrupole-based cells due to its larger mass transmission window [START_REF] Moynier | Potassium isotopic composition of various samples using a dual-path collision-cell-capable multiple-collector inductively coupled plasma mass spectrometer[END_REF]. After the collision cell, the ions are re-accelerated to 4 kV and focused back onto the mass spectrometer source slit in the same manner as for the high energy path.

The collision cell was filled with hydrogen for the reaction, and helium as a buffer gas and to contribute to the collisional thermalisation of the ions within the cell in order to maximise transmission through the hexapole ion guide. The relative amount of He and H2 introduced in the cell was optimised to minimise the Ar + , ArH + , ArH2 + and CaH2 + , backgrounds (see Table 1 for the parameters used here).

The samples were introduced as solution into the mass spectrometer using an Apex

Omega desolvating system fitted with a 100 μL/min PFA nebulizer (MicroFlow nebuliser, Elemental Scientific, Omaha, NE, USA) and with standard Ni dry cones ("dry plasma"). Zoom optics were used to optimize focusing and peak coincidence.

Data were collected in static mode (no peak jump), with 40 Ca + measured in a Faraday cup (L6) connected to a pre-amplifier fitted with a 10 10 Ω resistor while 42 Ca (L1), 43 Ca (H3) and 44 Ca (H6) were collected using 10 11 Ω resistors. The intensities of the mass 41 and 43.5 ( 87 Sr ++ ) were monitored on the faraday cup L5 and H5 using 10 11 Ω resistors. Each analysis consisted of a 60second zero measurement in 0.5 mol/L HNO3, followed by one block of 30 cycles with 5 second integrations (Table 1). A 100 second wash was performed in 0.5 mol/L HNO3 following each standard and sample analysis and a transfer time of 60 or 90 seconds was applied. Each sample was measured between 4 and 16 times, bracketed by the SRM 915b standard. The operating parameters of the instrument are listed in Table 1.

In these conditions, the background on the mass 40 was ~700 mV. The signal on the mass 41 was approximatively 25 mV. For comparison, the total signal for 100 ppb of Ca was over 155

V. The mass bias was corrected by measuring the samples alternatively with the SRM 915b standard solution (standard-sample bracketing).

Results and discussion

The Ca isotopic data for the samples are reported in Table 2 and Table S1 with literature data used here. Data for the analytical tests are reported in Tables S2-S5. The analytical errors are reported as the 2 standard-deviation (2SD) of the replicated measurements or as 2 times the standard error (2SE) when specified.

Accuracy and precision

We tested the accuracy of the method by measuring 9 samples that were previously analyzed for their stable Ca isotopic compositions. We further tested the effect of the concentration on the precision and accuracy by varying the concentration of Ca analyzed between 10 and 100 ppb (see below). For direct comparison of the data between different methods, we renormalized the stable isotope fractionation to obtain  44/40 CaSRM915a data using a difference of 0.72 ‰ between SRM 915a and SRM 915b (e.g. [START_REF] Heuser | The calcium isotope composition (delta Ca-44/40) of NIST SRM 915b and NIST SRM 1486[END_REF]. The  44/40 CaSRM915a values obtained on the IPGP Sapphire at 100 ppb are consistent with data previously obtained by either TIMS or MC-ICP-MS (standard bracketing and double spike). For the comparison, we took the average literature values (see Table S1 for the dataset and Figure 1). All samples fall on the 1:1 line (Figure 1), indicating the consistency in the absolute values obtained on the Sapphire with both previous MC-ICP-MS and TIMS measurements. The typical 2 standard deviation (2SD) obtained on samples run at 100 ppb is <0.1‰. For example, the  44/40 CaSRM915a value of BHVO-2, 0.72 ± 0.07 ‰ (2SD, n=7), is within error with literature values such as 0.79 ± 0.09 ‰ [START_REF] He | Mass-independent and mass-dependent Ca isotopic compositions of thirteen geological reference materials measured by thermal ionisation mass spectrometry[END_REF], 0.76 ± 0.10 (Li and Han, 2021), or 0.76 ± 0.08 ‰ [START_REF] Wu | Calcium isotopic composition of the lunar crust, mantle, and bulk silicate Moon: A preliminary study[END_REF]. We also analyzed a calcium solution of a carbonatite that has been previously analyzed on the IPGP Neptune Plus (and using a chemical purification described in Amsellem et al. 2020), Ka10 from the Kaiserstuhl volcano, Germany [START_REF] Amsellem | Calcium isotopic evidence for the mantle sources of carbonatites[END_REF]. The  44/40 CaSRM915a calculated on the Neptune Plus was 0.37 ± 0.06 ‰ (2SD, n=4) [START_REF] Amsellem | Calcium isotopic evidence for the mantle sources of carbonatites[END_REF], which is within error with the value of 0.38 ± 0.09 ‰ (2SD, n=6) acquired on the Sapphire. We also measured replicates for some samples over different mass-spectrometry sessions of the same chemical purification, for example a replicate of Ka10 returns a value of 0.38 ± 0.12 ‰ (2SD, n=6), similar to the result of 0.38 ± 0.09 ‰ (2SD, n=6) from the first analysis. We can assess the massdependence of the measurements using the relationship between  40/44 Ca and  42/44 Ca (Figure 2a) and  43/44 Ca and  42/44 Ca (Figure 2b), in which all the samples fall on the expected 2:1 and 1:2 lines, respectively. In Figure 2a, GSP-2 falls off the 2:1 line, due to the expected presence of radiogenic 40 Ca (see below).

To assess the accuracy and precision of the  40 Ca, we focused on the composition of the USGS standard GSP-2 as it exhibits a clear 40 Ca excess (e.g., 3.69 ± 0.16 ‱ n=25, 2SE [START_REF] He | Mass-independent and mass-dependent Ca isotopic compositions of thirteen geological reference materials measured by thermal ionisation mass spectrometry[END_REF] and 4.32 ± 0.43 ‱ [START_REF] Klaver | The Ca isotope composition of mare basalts as a probe into the heterogeneous lunar mantle[END_REF]). As for the stable isotope fractionation, we further assessed the effect of Ca concentration on the precision and accuracy (see below). For sample GSP-2 analyzed at 100 ppb, we obtained  40 Ca=3.92 ± 0.48 ‱, (2SE, n=6), which is consistent with literature data. Given the fairly large radiogenic 40 Ca component for GSP-2, the  44/40 CaSRM915a calculated in the table 2, has been based on  42/44 Ca rather than the  40/44 Ca as it is done for the other samples, to represent the mass-dependent isotopic fractionation and to be more readily compared to data obtained on traditional MC-ICP-MS.

Effect of the mismatch in HNO3 concentration between sample and standard

The influence of the HNO3 concentration mismatch between the samples and the standard on the accuracy of the Ca isotope composition was evaluated by analyzing the NIST SRM915b at various HNO3 concentrations (between 1 and 5 %) against a NIST SRM915b solution in 3% HNO3 (same concentration used throughout this study). The effect of the concentration mismatch has been previously identified for K isotopes on the Sapphire [START_REF] Moynier | Potassium isotopic composition of various samples using a dual-path collision-cell-capable multiple-collector inductively coupled plasma mass spectrometer[END_REF].

The results are reported in Figure 3 and Table S2. It appears that the  40/44 Ca is not affected by the concentration mismatch (Figure 3a) while  42 Ca and  43 Ca are more significantly affected, leading to an elevation of, for example, ~0.4 ‰ in the case of 5% HNO3. This is also reflected in the variation of the  40 Ca that correlates (R 2 =0.994) with the HNO3 concentration (Figure 3b). The origin of the effect is yet to be determined, but the different behaviors among 40 Ca/ 44 Ca and 42 Ca/ 44 Ca and 43 Ca/ 44 Ca are likely controlled by the abundances of the isotopes. Thus, it is paramount to analyze the Ca isotopic composition in the same HNO3 concentration. In this study we dilute the standards and the samples using the same bottle of 3% HNO3.

Effect of Ca concentration mismatch

To test the effect of intensity mismatch on the accuracy of the Ca isotopic data, we ran tests in which the Ca concentration of the NIST SRM 915b bracketing standard was kept at 100 ppb while the concentration of another NIST SRM 915b run as a sample varied from 50% lower to 50% higher (Figure 4 and Table S3). The  40/44 Ca is clearly affected by the concentration mismatch, the correlation (R 2 =0.84) between the two (Figure 4a) returns  40/44 Ca ~ 0.28×Casample/Castandard-0.25. Therefore, a concentration difference of 1% would create a bias of about 0.02 ‰.  40 Ca is also strongly affected by the Ca concentration mismatch, the correlation (R 2 =0.99) between the two (Figure 4b) returns  40 Ca~-12×Casample/Castandard+12 ‱. Therefore, a mismatch of ~1% creates a bias on  40 Ca of ~0.12 ‱.

It is thus essential to analyze the samples with an intensity match within 1% of the bracketing standard in order to obtain accurate Ca isotopic data. When this protocol is applied, we show here that the Ca isotopic data (both  40/44 Ca and  40 Ca) are accurate and precise. As for K isotopes [START_REF] Moynier | Potassium isotopic composition of various samples using a dual-path collision-cell-capable multiple-collector inductively coupled plasma mass spectrometer[END_REF], the effect of the intensity mismatch is most likely due to a combination of the hexapole setup and of the high background on the mass 40, ~0.75V, compared to a signal of > 155V for a 100 ppb solution. The Ca background therefore represents ~0.5 % of the total Ca signal. It is possible that different instrumental parameters, in particular the hexapole setup, may affect this effect.

Effect of Ca concentration on accuracy and precision

To evaluate the precision and accuracy of the measurements, we analyzed BHVO-2 from 10 to 100 ppb of Ca (from 50 ng to 500 ng of Ca for 5 replicates) (Table S4, Figure 5). All the samples down to 100 ppb have similar  40/44 Ca values and fall within error of literature data when converted to SRM 915a (Figure 5, where the data are re-normalized to  44/40 CaSRM915a). The precision is kept in the same range for the samples analyzed down to 25 ppb Ca (2SD between 0.04 and 0.07 ‰ for  40/44 Ca n=7). However, it doubles for the samples analyzed at 10 ppb (2SD of 0.14 ‰). We therefore suggest to analyze the samples at about 100 ppb (i.e., 500 ng of Ca consumption for 5 measurements) when the samples are not limited. The amount of sample can be reduced, when necessary, with a limited loss in precision and accuracy. This represents a major improvement compared to any previous methods where several tens of micrograms were usually required to reach similar precisions.

Effect of matrix elements

We tested the effect of the presence of several elements: K, Sr, Ti, La (La is taken to represent the rare earth elements which have been suggested to affect the accuracy of Ca isotopic measurements; [START_REF] Sun | Ca isotope systematics of carbonatites: insights into carbonatite source and evolution[END_REF]) on the accuracy and precision of Ca isotopic measurements. As we are using H2 in the collision cell, a fraction of K could combine with H2 to produce 39 KH + and 41 KH + and create isobaric interferences on 40 Ca and 42 Ca, respectively. Double charged strontium isotopes 84 Sr ++ , 86 Sr ++ , and 88 Sr ++ would create isobaric interferences on 42 Ca, 43 Ca and 44 Ca, respectively. We monitored and corrected for these by measuring the intensity of 87 Sr ++ on mass 43.5.

Different amounts of K, Sr, and La were added to the SRM 915b standard solutions (100 ppb) and analyzed against an undoped SRM 915b 100 ppb solution (Table S5, Figures 6 and7).

Therefore 1 % of addition corresponds to ~1 ppb of that element in the 100 ppb Ca solution.

Potassium does not seem to have any effect on the  40/44 Ca until it reaches 2 % (Figure 6a), which corresponds in our case to ~0.6 V of 41 K, above the K observed in any of the natural samples reported here. As expected by the formation of 39 KH + , the  40/44 Ca value increases with the increasing K addition from 0 to 2%. However, for 5% of K addition, the  40/44 Ca decreases back to zero. This may reflect the combination of 39 KH + interference on 40 Ca and a matrix effect generated by K in the plasma. Similarly, the  40 Ca is not affected by K up until 2 % (Figure 6b). Unlike  40/44 Ca, it does not exhibit the anomaly at 5%, but instead follows a negative correlation with the amount of K (Figure 6b). In summary, a K/Ca of 1% does not affect the final Ca isotopic composition within our measurement uncertainty, while a K/Ca ratio of 2% creates a bias on  40/44 Ca of 0.10 ± 0.02 ‰, 2SD and a  40 Ca of -0.74 ± 0.63 ‱. Therefore, we recommend to maintain K/Ca < 1% to assure precise and accurate measurements.

In the case of Sr, we report both the uncorrected and corrected values (using the 87 Sr ++ signal measured at mass 43.5, and a fixed 87 Sr/ 86 Sr ratio of 0.71039) (Table S5). The strontium correction works well up to 0.01 % of Sr (Figure 7), corresponding to a 87 Sr ++ signal of about 4 mV, which is 3 orders of magnitude higher than that in any of the samples reported here after chemical purification. Lanthanum and titanium have smaller matrix effects and do not create any isotopic bias up to 0.1%. However, at 1% they produce a 0.18 and 0.17 ‰ bias on  40/44 Ca (Table S5), respectively. Thus, it is paramount to keep the La/Ca and Ti/Ca ratios under 0.1% to obtain accurate data.

Conclusions

We presented the first Ca isotopic data reported using the Nu Sapphire dual-path collision cell-capable MC-ICP-MS connected to an Apex Omega. The Ca isotopic data (for both stable and radiogenic isotopes) are both accurate and precise. We tested the effect of various parameters including acid molarity mismatch between standard and sample, concentration mismatch, the presence of various matrix elements including Sr and K. We also tested the accuracy and precision of the measurements at various Ca concentrations, from 10 to 100 ppb. The precision obtained at 100 ppb is comparable to previous methods but with an improvement by a factor ~10 in sensitivity (in case of 5 replicates, it corresponds to ~500 ng of Ca). We also showed that data acquired down to 10 ppb (i.e., for 5 replicates ~50 ng of Ca) are still accurate but with a loss in precision (by about a factor 2). It may however be advantageous for future works involving small amounts of materials or Ca-poor samples. 1 andS2) plotted against the values obtained on the Nu Sapphire. The dotted line represents a 1:1 line. Data points from most samples fall on the line, which confirms that the data obtained on the Sapphire are consistent with those from the literature. [START_REF] Amini | Calcium Isotopes (δ 44/40 Ca) in MPI-DING Reference Glasses, USGS Rock Powders and Various Rocks: Evidence for Ca Isotope Fractionation in Terrestrial Silicates[END_REF][START_REF] Amsellem | Calcium isotopic evidence for the mantle sources of carbonatites[END_REF][START_REF] Feng | Calcium Isotopic Compositions of Sixteen USGS Reference Materials[END_REF][START_REF] He | Mass-independent and mass-dependent Ca isotopic compositions of thirteen geological reference materials measured by thermal ionisation mass spectrometry[END_REF][START_REF] Klaver | The Ca isotope composition of mare basalts as a probe into the heterogeneous lunar mantle[END_REF][START_REF] Lehn | Optimization of a 48Ca-43Ca double-spike MC-TIMS method for measuring Ca isotope ratios (δ44/40Ca and δ44/42Ca): limitations from filament reservoir mixing[END_REF][START_REF] Li | One-step chromatographic purification of K, Ca, and Sr from geological samples for high precision stable and radiogenic isotope analysis by MC-ICP-MS[END_REF][START_REF] Liu | Calcium Isotopic Fractionation and Compositions of Geochemical Reference Materials[END_REF][START_REF] Schiller | Calcium isotope measurement by combined HR-MC-ICPMS and TIMS[END_REF][START_REF] Valdes | The nature of Earth's building blocks as revealed by calcium isotopes[END_REF][START_REF] Wu | Calcium isotopic composition of the lunar crust, mantle, and bulk silicate Moon: A preliminary study[END_REF]. *For GSP-2, given the radiogenic component on 40 Ca,  44/40 CaSRM915a is calculating using the  42/44 Ca value rather than the  40/44 Ca values has done for the other samples.

Figure and Table Captions:

Figure 1 :

 1 Figure 1:  44/40 CaSRM915a values from the literature (see Tables1 and S2) plotted against the values obtained on the Nu Sapphire. The dotted line represents a 1:1 line. Data points from most samples fall on the line, which confirms that the data obtained on the Sapphire are consistent with those from the literature.

Figure 2 :

 2 Figure 2:  40/44 Ca versus  42/44 Ca (a) and 43/44 Ca versus  42/44 Ca (b) for the samples analyzed in this study. For  43/44 Ca versus  42/44 Ca (b), all samples fall within error on a 1:2 line, agreeing with the expected mass-dependent isotopic fractionation. For  40/44 Ca versus  42/44 Ca (a), most samples fall on the mass-dependent isotopic fractionation 2:1 line, except GSP-2, which plots off the line as it contains a clear 40 Ca radiogenic excess.

Figure 3 :

 3 Figure 3: Susceptibility of the  40/44 Ca (a) and  40 Ca (b) values to the HNO3 concentration mismatch between sample and standard.The "sample" is SRM 915b standard dissolved in acid at various molarity from 1% to 5% HNO3 and the bracketing standard is SRM 915b at 3% HNO3 (molarity used in the rest of the study). Although the precision and accuracy of the  40/44 Ca values are not affected by the acid concentration mismatch, there is a clear effect on the accuracy of the  40 Ca which correlates (R 2 =0.99) with the molarity mismatch.

Figure 4 :

 4 Figure 4: Effect of the intensity mismatch on the accuracy of the  40/44 Ca (a) and  40 Ca (b) values. The standard (SRM 915b) is kept at 100ppb while the intensity of the "sample" (SRM 915b) is analyzed at various concentrations (from +65% to -46%). Both  40/44 Ca (R 2 =0.84) and  40 Ca (R 2 =0.99) correlate with the intensity mismatch.

Figure 5 :

 5 Figure 5:  40/44 Ca (a) and  40 Ca (b) as a function of the Ca concentration (ppb) for BHVO-2. The stable isotopic fractionation is presented as  44/40 CaSRM915a to facilitate comparison with literature data (represented by the shaded area). The accuracy of both  44/40 CaSRM915a and  40 Ca maintained down to 10ppb, while the precision degraded drastically for the sample analyzed at 10 ppb.

Figure 6 :

 6 Figure 6: Effect of the K content (reported as the K/Ca in %) on the accuracy of the  40/44 Ca (a) and  40 Ca (b) values. The x-axis represents the K content of the solution relative to the Ca concentration (100ppb for all samples) in %. The  40 Ca values correlate (R 2 =0.93) with the K content.

Figure 7 :

 7 Figure7: Effect of the Sr content (reported as Sr/Ca in %) on the accuracy of the  40/44 Ca (a and b) and  40 Ca (c) values. The x-axis represents the Sr content of the solution relative to the Ca concentration (100 ppb for all samples) in %. In figure (a), the black circles represent the data after correcting for the Sr interference using the monitored intensity of 87 ++ . Panel (b) represents a zoom in of the Sr contents between 0 and 0.01% to illustrate that the Sr-correction is efficient in this range. Both  40/44 Ca (R 2 =0.99) and  40 Ca (R 2 =0.99) correlate with the Sr content of the solution.

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 2 Figure 2 Click here to access/download;Figure;Figure 2.pdf

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Table 1 .

 1 Operating parameters of the Sapphire instrument and the desolvator Apex Omega introduction system.

Table 2 :

 2 Calcium isotopic data of the various rock samples analyzed in this study. The literature data represent average values from:

Table 1 Nu Sapphire Instrument Setting used in this study

 1

	RF Power	1300 W
	Coolant gas flow	13-13.5 L/min
	Auxiliary gas flow	0.8-0.9 L/min
	Sampler/skimmer cone material	Ni
	He collision gas flow	2 sccm
	H2 reaction gas flow	5 sccm
	Quad 1	29.1
	Quad 2	-66.9
	Apex parameters
	Argon Sweep Gas Flow	3.60-3.80 L/min
	Nebulizer pressure	35-39.0 psi
	Peripump Speed	17.0 (rpm)
	Peripump Flow	600.0 (µL/min)
	Nebulizer uptake rate	50 or 100 µL/min
	Peltier Cooler temperature	3.0 o C
	Desolvator temperature	155.0 o C
	Spray chamber temperature

Acknowledgments:

We deeply thank the two anonymous reviewers for their constructive comments that greatly improved the quality of the work. We also thank editor Balz Kamber for his comments and efficient handling of our manuscript. F. M. thanks the DIM ACAV+ (Domaine d'Interet Majeur, Astrophysique et Condition d'Apparition de la Vie) of the region Ile de France for providing part of the funding for the Nu Sapphire. F.M. acknowledges funding from the European Research Council under the H2020 framework program/ERC Consolidator Grant Agreement (#101001282-METAL) and financial support of the UnivEarthS Labex program at Sorbonne Paris Cité (#ANR-10-LABX-0023 and #ANR-11-IDEX-0005-02). Parts of this work were supported by IPGP multidisciplinary program PARI.