Célia Martinie
email: martinie@irit.fr

Philippe Palanque
email: palanque@irit.fr

Martina Ragosta
email: ragosta@irit.fr

Some Issues with Interaction Design and Implementation in the Context of Autonomous Interactive Critical Systems

Keywords: Intelligent and autonomous systems, automation, user interaction, command and control

). Nowadays, they can be integrated to several critical systems, such as Air Traffic Control management systems, as illustrated by the example presented in the case study. This position paper raises some issues related to the design and implementation of safety-critical user interfaces featuring intelligent and (partly) autonomous behaviors.

INTRODUCTION

Currently, automation is one of the main means for handling increasing complexity in systems. Indeed, automation makes it possible for designers to transfer the burden of operators or users to a system. Parasuraman et al. have defined a classification [START_REF] Parasuraman | A model for types and levels of human interaction with automation[END_REF] of the different levels of automation presented in Figure 1.

These levels of automation have been extensively used for assessing the automation level of command and control systems such as Air Traffic Management applications, aircraft cockpits or satellite ground segments (also called human in-the-loop systems). Thus automation is having a strong impact on workload, team size and human error. However, together with this high potential, automation raises complex issues related to design aspects of user interfaces and user interactions. Good designs are very difficult to perform and to assess especially when abstract properties such as predictability [START_REF] Dix | Formal methods for interactive systems[END_REF], transparency, honesty [START_REF] Graham | Design principles for Interactive Software[END_REF], usability or even user experience [START_REF] Law | Understanding, scoping and defining user experience: a survey approach. 27th int. conf[END_REF].

Command and control systems have to handle standard interactive objects as well as autonomous objects evolving in the same system but that are having potentially a complete independent behavior. In addition to that aspect, designers might want to empower the operators of such systems with (partly) automated tools to organize their work targeting at reducing users' workload and improving the overall performance.

Figure 1. Levels of automation of decision and action selection

Automation has already been studied in a number of disciplines and application fields: design, human factors, psychology, (software) engineering, aviation, health care, games [START_REF] Billings | Aviation Automation: the Search for a Human Centered Approach[END_REF] but the horizon for embedding them systematically into operational systems is not more than 10 years ahead. However, earlier adoptions of automation have not always been entirely successful as demonstrated by many studies in various application domains [START_REF] Palmer | Oops, it didn't arm." -A Case Study of Two Automation Surprises[END_REF] or [START_REF] Sarter | How in the World Did I Ever Get Into That Mode? Mode Error and Awareness in Supervisory Control[END_REF]. One distinguishing feature of the area of safetycritical systems is that system properties such as faulttolerance [START_REF] Randell | System structure for software fault tolerance[END_REF], dependability [START_REF] Avizienis | Basic Concepts and Taxonomy of Dependable and Secure Computing[END_REF] or usability all have to be treated on an equal basis. This position paper focuses on three design and engineering issues for the user interface of (partly) intelligent and autonomous systems: Non direct interaction: the engineering of the user interaction with autonomous systems (e.g. how to integrate autonomous behavior within the entire user interface), especially in cases were autonomous objects are represented on the user interface. For example, the representation (on an air Traffic Controller screen) of an unmanned aerial vehicle (UAV) with which no direct interaction is possible, together with aircrafts with which interaction is possible via an interactive screen (and that information is sent to the pilots). User task migratability: design and engineering of user interfaces and interaction techniques for (partly) autonomous systems in charge of performing in an autonomous way tasks which were previously performed manually by operators. For instance, designing the user interface for an auto pilot in a plane or a cruise control must allow operators to set and/or control the auto pilot behavior.

Reconfigurable automation level at runtime: lies with the fact that automation cannot always be seen as static i.e. defined once for all for a given system but would preferably be dynamic i.e. evolving according to internal and external parameters such as operators' training, experience or workload, system state and for instance occurrence of failures or presence of alarms or environment information such as number of aircraft in the sector, types of aircrafts, presence of bad weather conditions, … It is when addressing such types of problem that the designers have to consider automation over the loop i.e. when automation takes place to adapt the system to better support the operators by means of personalization or by learning from users better strategies.

PROBLEM STATEMENT

One of the current challenges and goals for autonomous behavior are related to the analysis, planning, decision and action cycle as described in [START_REF] Parasuraman | A model for types and levels of human interaction with automation[END_REF]. When interacting with a (partly) autonomous system the user interface and its underlying system should provide ways to support the operator in these activities. More precisely the operator should be supported:

In analyzing the current context of the operations, In identifying one or several plans in order to carry on the current tasks or to handle unexpected events, In deciding amongst the various plans which one is the most appropriate, In inputting the plan into the system aspects such as reusing a previous entered plan or mending an existing one could significantly improve performance,

In triggering the supervisory system to execute the plan which might include some degrees of autonomy (i.e. that the supervisory system has some delegated authority),

In following the execution of the plan allowing the operator to know what has already been performed, what is the currently executed and what will be executed in the future steps.

Of course, the operator in charge of and responsible for the operations should always have the possibility to interrupt the current execution of the plan and possibly to resume it later on.

One solution to that problem could be to reduce the operator role to the one of automation overseer and thus only acting at a high (and abstract) strategic level. Such solution would make it very difficult (and nearly impossible) for the operator to come back to a more low (and concrete) tactical level especially in case of automation degradation or system failure. Thus, other solutions have to be indentified and designed requiring scientific means to assess:

How the operator will be able to identify (from the currently available information about the autonomous system) new plans or modification to current potential plans (or potential configurations)?

How the operator will be able to build new plans or configurations?

How the operator will be able to assess beforehand the impact of a potential new plan or configuration?

How the operator will be able to interact (both monitor and possibly interrupt) with the current configuration under "execution"? This interaction aspect can be particularly complex if, in a proactive system, the configurations are executed in an autonomous way by the supervision system. Additionally such interaction should be conformant to the ones used for normal interactions.

A SAFETY-CRITICAL CASE STUDY

This section refines the concepts presented above in the context of an Air Traffic Control (ATC) case study.

Presentation of the Air Traffic Control AMAN software

The case study is based on a command and control system for Air Traffic Control called AMAN (Arrival MANager) as proposed in [6]. Figure 2 is screenshot of such an interface which is composed of two parts, the left-hand side displaying a standard graphical interface for air traffic control (each icon representing the position of each aircraft in the sector and its flight information) and the right-hand side presenting the AMAN interface consisting of a list of advices proposed by the autonomous systems to the Air Traffic Controller. A detailed view of this AMAN interface is represented in Figure 3. The AMAN system provides support to the controllers in establishing the optimal approach routes for partly autonomous systems (aircrafts). AMAN is a decision support tool for the person in charge of sequencing the aircrafts arrivals, which is called a sequence manager. According to [START_REF] Parasuraman | A model for types and levels of human interaction with automation[END_REF] classification presented in Figure 1, the AMAN systems corresponds to levels 2-3 where the system computes alternatives and proposes them to the operator.

The sequence manager is permanently checking the list provided by AMAN but also analyzing if the provided list is accurate w.r.t. information provided by other persons and entities (executive controller, aircraft pilot, aircraft down going measures, planner…). At any time, if the sequence manager analyses that the displayed sequence is not relevant w.r.t. the current context, she/he can decide not to follow AMAN's advice.

Design opportunities for a learning version of the AMAN tool

As promoted by [START_REF] Stumpf | Integrating rich user feedback into intelligent user interfaces[END_REF], we consider increasing the capabilities (analysis and interaction) of the AMAN tool so that it provides more accuracy and trust to the sequence manager.

Learning capability: as a first step, when the sequence manager does not follow AMAN's advice, the AMAN tool should be capable of learning why its advice has not been followed. Explanations: AMAN tool should provide more information on the elements that were computed to determine the current sequence of aircrafts arrival. This feature would increase the transparency of the tool. Disengagement capability: AMAN tool should provide a way for being disengaged by the user when the contextual information becomes wider and more complex than AMAN is capable to handle. In this kind of context, advices that have a high probability of being wrong or at least irrelevant should not be displayed (reconfiguration of the automation level).

As the AMAN tool is safety-critical and all of these opportunities have to be deeply analyzed w.r.t. dependability constraints as detailed in next section.

LESSONS LEARNED AND MAIN ISSUES

We have considered several engineering approaches to examine these issues. First, The ICO user interface design techniques enables to develop usable and reliable interaction techniques [START_REF] Navarre | A model-based user interface description technique dedicated to interactive systems addressing usability, reliability and scalability[END_REF]. Complemented with task modelling, it can be used to analyze user's task w.r.t. system's behavior [START_REF] Martinie | Formal Tasks and Systems Models as a Tool for Specifying and Assessing Automation Designs[END_REF]. At last, task models can also be used to assess whether the user or the system should handle a particular task in a particular context [START_REF] Martinie | Task-Model Based Assessment of Automation Levels: Application to Space Ground Segments[END_REF]. All of these techniques aim at finding the optimal collaboration solution between the user and the system. However these approaches don't deal with the possible dynamic change of behaviour of the system, especially if it has machine learning capabilities. Additionally, considering that the safety-critical user interfaces require additional design and development paths, we identified the following set of issues that must be considered if the system is (partly) autonomous:

What is usability in a critical context and how to evaluate it, How to guarantee the safety and dependability of the possible interactions, How to analyze and prevent operators' errors, How to design and specify interaction techniques where autonomous behavior from the system interfere with operator input (including the question on how to model that formally [START_REF] Bastide | A Model-Based Approach for Real-Time Embedded Multimodal Systems in Military Aircrafts[END_REF]), How to design interaction so that the operators can foresee the systems' future steps and states, How to design interactions when the automation can fail and how to notify the operators, How to enhance and evaluate aspects of user experience, while fulfilling the constraints of a safetycritical system which has to be secure, safe, reliable and usable.

CONCLUSION AND PERSPECTIVES

The research work presented here has been trying to bring together multiple perspectives for the design and evaluation of intelligent and (partly) autonomous interactive systems.

The contributions presented here have been focusing on the current practice in the safety-critical application domains and particularly in the Air Traffic Control management domain. We argue that automation issues in the safety-critical application domain overlap interaction issues for intelligent and autonomous systems. As of today, proposals have been made to assess and design analysis and decision levels for safety-critical intelligent systems (autonomous and non-autonomous), but engineering means of designing safety-critical interactive machine learning systems are rare, although required for certification and validation purpose.

AUTHORS' BACKGROUND AND INTERESTS

We have a long term experience in the area of interactive command and control systems including design and implementation issues of (partly-) autonomous systems. We have been working closely with main actors in the area of safety critical interactive systems including airtraffic management, aircraft cockpits and satellite ground segments. We have little expertise in the area of intelligent adaptive systems as the difficulties in terms of validation and certification prevent them for being used in safety critical contexts. However, in the domain of ATM for instance, traffic increase within the next few years requires looking at radically new solutions including higher automation levels and adaptive systems. We organized a SIG last year at CHI to try to foster interests of CHI community on automation issues [START_REF] Bernhaupt | Engineering automation in interactive critical systems[END_REF]. We could share that perspective and the conclusions of the SIG during the workshop. Participation to the workshop would also be beneficial to our work by exchanging with knowledgeable researchers in the area of intelligent systems.

HIGH 10 . 1 .

 101 The computer decides everything, acts autonomously, ignoring the human 9. Informs the human only if it, the computer, decides to 8. Informs the human only if asked, or 7. Executes automatically, then necessarily informs the human, and 6. Allows the human a restricted time to veto before automatic execution, or 5. Executes that suggestion if the human approves, or 4. Suggests one alternative 3. Narrows the selection down to a few, or 2. The computer offers a complete set of decision/action alternatives, or LOW The computer offers no assistance: human must take all decisions and actions

Figure 2 .

 2 Figure 2. A screenshot of the user interface of ATC [6].

Figure 3 .

 3 Figure 3. Detailed user interface of the AMAN system.

ACKNOWLEDGMENTS

This work is partly funded by CNES (National Space Studies Center) and Eurocontrol/SESAR research network HALA! (Higher Automation Levels in Aviation).


Jessica Billy

Sabine F Bensamoun

Julie Mercier

Sébastien Durand
email: sebastien.durand@chuv.ch

Applications of ultrasound elastography to hand and upper limb disorders. Applications de l'élastographie ultrasonore dans les pathologies de la main et du membre supérieur

Keywords: Elastographie, Ultrason, Main, Chirurgie, tendon, muscle, nerf, peau Elastography, Ultrasound, Hand, Surgery, tendon, muscle, nerve, skin

come

Ultrasound Elastography

Ultrasound (US) elastography method noninvasively measures the stiffness of the tissue by producing and measuring tissue deformation [START_REF] Giambini | Ultrasound Elastography for Hand Soft Tissue Assessment[END_REF]. Indeed, the stiffness represents the tendency of the tissue to resist at a deformation induced by an applied force and is characterized by the modulus of elasticity (Young's modulus; Pa) defined as follows:

E = σ/ε
where σ is the stress (Pa), corresponding to the normalized force, and ε is the strain (unitless) which represents the deformation of the tissue due to an applied force. This US technique was first introduced in the early 1990s with in vitro experiments [START_REF] Ophir | Elastography: a quantitative method for imaging the elasticity of biological tissues[END_REF], then gradually expanded into clinical practice for diagnostic and sometimes prognostic purposes in the fields of senology, hepatology, thyroid diseases, prostatic diseases, and musculoskeletal conditions [START_REF] Drakonaki | Ultrasound elastography for musculoskeletal applications[END_REF][START_REF] Klauser | Sonoelastography: musculoskeletal applications[END_REF].

Since 1990, different ultrasound elastography (UE) techniques have been used:

The strain imaging of the tissue, which revealed the physical tissue displacement, is estimated by its axial deformation parallel to the externally applied force exerted on body surface using the ultrasound probe (Fig. 1a). This method provides a qualitative evaluation of the stiffness [START_REF] Debernard | A possible clinical tool to depict muscle elasticity mapping using magnetic resonance elastography (MRE)[END_REF]. Two approaches for strain imaging using ultrasound techniques were developed: the strain elastography (SE) and the acoustic radiation force impulse (ARFI) strain imaging. For the strain elastography, tissue displacement is generated by manual external compression with ultrasound transducer [START_REF] Ophir | Elastography: a quantitative method for imaging the elasticity of biological tissues[END_REF] or by an internal physiologic motion (cardiovascular) to assess more deeper located organ [START_REF] Gennisson | Ultrasound elastography: principles and techniques[END_REF]. For ARFI technique, the force is produced by acoustic "pushing pulse". Different methods exist to measure displacement, such as radiofrequency echo correlation-based tracking or Doppler processing [START_REF] Sigrist | Ultrasound Elastography: Review of Techniques and Clinical Applications[END_REF]. As the manual or physiological stresses are not quantifiable, the measured strain provides a qualitative assessment of the stiffness, or a pseudo-quantitative measure (strain ratio) represented with a color map called an elastogram.

The Shear wave imaging uses a dynamic stress to generate shear wave inside the tissue and the measurement of shear wave speed allow the determination of the stiffness. Three approaches exist to obtain shear wave imaging. Firstly, 1D transient elastography performed with the FibroScan® machine (Echosens, Paris, France) composed of a vibration-controlled probe [START_REF] Pouletaut | Impact of Hepatic Iron Overload in the Evaluation of Steatosis and Fibrosis in Patients With Nonalcoholic Fatty Liver Disease Using Vibration Controlled Transient Elastography (VCTE) and MR Imaging Techniques: a Clinical Study[END_REF]. Secondly, ARFI (Acuson S2000; Siemens Medical Solutions, Berlin, Germany) can be used and a portion of its longitudinal waves is converted to shear waves perpendicular to the longitudinal waves [START_REF] Nightingale | Acoustic Radiation Force Impulse (ARFI) Imaging: a Review[END_REF]. With the hypothesis of an isotropic, homogeneous, incompressible medium, shear wave velocity (SWV) is measured and converted to Young's modulus (E) using the equation: E = 3  c² where  is the density and c the shear wave velocity. Thirdly, in 2D shear wave elastography, acoustic radiation force is also used (Fig. 1b), with the Aixplorer ultrasound system (Supersonic Imagine, Aix-en-Provence, France) but multiple focal zones are stimulated and this creates a near cylindrical shear wave cone [START_REF] Bamber | EFSUMB guidelines and recommendations on the clinical use of ultrasound elastography. Part 1: Basic principles and technology[END_REF], permitting real-time monitoring of shear waves in 2D and generating quantitative elastograms superimposed on a B-mode image (Fig. 1c).

Elastography and tendon

Tendon rupture and histological modifications (e.g. disintegration of collagen fibers or mucoid degeneration) in degenerative tendinopathy are expected to lead to a localized decrease in tendon stiffness [START_REF] Balaban | Evaluation of Tendon Disorders with Ultrasonography and Elastography[END_REF] and can be detected by UE earlier than conventional ultrasonography (US) [START_REF] Chen | Shear wave elastographic characterization of normal and torn achilles tendons: a pilot study[END_REF]. Decreased mechanical properties (stiffness values) in degenerative tendinopathy and/or tendon injury compared to healthy tendon have been demonstrated in several studies [START_REF] Chen | Shear wave elastographic characterization of normal and torn achilles tendons: a pilot study[END_REF][START_REF] Turkay | Shear wave elastography findings of de Quervain tenosynovitis[END_REF][START_REF] Zhu | Assessment of common extensor tendon elasticity in patients with lateral epicondylitis using shear wave elastography[END_REF][START_REF] Aubry | Viscoelasticity in Achilles tendinopathy: quantitative assessment by using real-time shear-wave elastography[END_REF][START_REF] Klauser | Sonoelastography of the Common Flexor Tendon of the Elbow with Histologic Agreement: A Cadaveric Study[END_REF] but in some cases of tendinopathy (long-head biceps tendon), UE analysis provides conflicting results [START_REF] Sahan | Evaluation of Tendinosis of the Long Head of the Biceps Tendon by Strain and Shear Wave Elastography[END_REF]. Despite the different data, shear wave elastography (SWE) seems to be a reproducible technique to evaluate tendon elasticity with low inter-observer differences [START_REF] Dewall | Visualizing tendon elasticity in an ex vivo partial tear model[END_REF][START_REF] Yeh | Shear Wave Measurements for Evaluation of Tendon Diseases[END_REF].

SWV of human hand tendons in physiologic in vivo conditions (Figs. 2a,2b,2c) has been analyzed in various studies [START_REF] De Zordo | Real-time sonoelastography of lateral epicondylitis: comparison of findings between patients and healthy volunteers[END_REF]. Experimental studies using flexor tendons of porcine demonstrated that the stiffness of a partially teared tendon is lower in the vicinity of the injury and is dependent on the size of the tear [START_REF] Dewall | Visualizing tendon elasticity in an ex vivo partial tear model[END_REF]. Moreover, the stiffness of a damaged tendon induced by collagenase solution is significantly lower than a normal tendon [START_REF] Chen | Evaluation of Hand Tendon Elastic Properties During Rehabilitation Through High-Frequency Ultrasound Shear Elastography[END_REF]. Fluids accumulation and hematoma associated with acute ruptures appear as signal void areas on SWE [START_REF] Turkay | Shear wave elastography findings of de Quervain tenosynovitis[END_REF][START_REF] Aubry | Viscoelasticity in Achilles tendinopathy: quantitative assessment by using real-time shear-wave elastography[END_REF]. After flexor tendon repair, re-rupture can be much more difficult to assess in B-mode. SWE of the flexor tendon proximally to the lesion demonstrated systematically a significant decrease of SWV compared to healthy side (figs. 2g, 2h, 2i). Injured flexor hand tendons after surgical repair showed altered regional mechanical elastic properties and appeared locally stiffer compared to the healthy side using SWE. The clinical significance of these findings was that the tendon would glide less on rigid local zone and authors propose to focus rehabilitation on these stiffer zones, aiming at improving gliding [START_REF] Chen | Evaluation of Hand Tendon Elastic Properties During Rehabilitation Through High-Frequency Ultrasound Shear Elastography[END_REF].

In their study, Turkay et al. [START_REF] Turkay | Shear wave elastography findings of de Quervain tenosynovitis[END_REF] Medial and lateral epicondylitis have also been analyzed in several studies, all suggesting that pathological tendons are softer than healthy tendons [START_REF] Zhu | Assessment of common extensor tendon elasticity in patients with lateral epicondylitis using shear wave elastography[END_REF][START_REF] Klauser | Sonoelastography of the Common Flexor Tendon of the Elbow with Histologic Agreement: A Cadaveric Study[END_REF][START_REF] De Zordo | Real-time sonoelastography of lateral epicondylitis: comparison of findings between patients and healthy volunteers[END_REF][START_REF] Chen | Evaluation of Hand Tendon Elastic Properties During Rehabilitation Through High-Frequency Ultrasound Shear Elastography[END_REF][START_REF] Park | Diagnostic confidence of sonoelastography as adjunct to greyscale ultrasonography in lateral elbow tendinopathy[END_REF]. Park et al. [START_REF] Park | Diagnostic confidence of sonoelastography as adjunct to greyscale ultrasonography in lateral elbow tendinopathy[END_REF] concluded that UE accuracy was better than US by 7.1% for epicondylitis diagnosis, sensibility and specificity being of 96% and 89%, respectively. Moreover, it has been demonstrated that SWV increases after conservative treatment in patients with lateral epicondylitis [START_REF] Zhu | Assessment of common extensor tendon elasticity in patients with lateral epicondylitis using shear wave elastography[END_REF]. The combined modalities of UE and B-mode ultrasonography provided a statistically significant improvement in the agreement between imaging and histologic results compared with each modality alone [START_REF] Klauser | Sonoelastography of the Common Flexor Tendon of the Elbow with Histologic Agreement: A Cadaveric Study[END_REF] in common flexor tendinopathy at the medial side of the elbow.

In a recent systematic review concerning rotator cuff tears [START_REF] Seth | The application of shear wave elastography with ultrasound for rotator cuff tears: a systematic review[END_REF], SWE has been successfully used to identify the localization and degree of supraspinatus tendon tear, improving the value of ultrasound. Indeed, patients with rotator cuff tears had a lower mean SWV of muscle and tendon under active conditions. Intraclass correlation coefficient was excellent (0.96).

Supraspinatus tendon Stiffness increased between 8 days and 24 weeks after repair [START_REF] Seth | The application of shear wave elastography with ultrasound for rotator cuff tears: a systematic review[END_REF].

Elastography and muscle

With a Young's modulus ranging from 5-40 kPa at rest and up to 300 kPa during passive stretching or active contraction, SWE is a validated method to assess muscle stiffness [START_REF] Shinohara | Real-time visualization of muscle stiffness distribution with ultrasound shear wave imaging during muscle contraction[END_REF][START_REF] Koo | Factors that influence muscle shear modulus during passive stretch[END_REF].

The reliability of the SWE for measuring muscle stiffness has been proven for several muscle groups including lower limb, trunk, upper limbs muscles including the intrinsic muscles of the hand [START_REF] Kim | Can Shoulder Muscle Activity Be Evaluated With Ultrasound Shear Wave Elastography[END_REF][START_REF] Watanabe | Assessment of the passive tension of the first dorsal interosseous and first lumbrical muscles using shear wave elastography[END_REF]. Furthermore, studies suggested using SWE to monitor the muscle activity or muscle force and to demonstrate contraction of accessory muscles [START_REF] Kim | Can Shoulder Muscle Activity Be Evaluated With Ultrasound Shear Wave Elastography[END_REF][START_REF] Durand | Morphological and functional assessment of the flexor carpi radialis brevis using conventional ultrasound and elastography[END_REF]. SWE was also found to be a reliable method to evaluate the functional muscle activity compared to the physiological activity recorded with conventional surface electromyography [START_REF] Xie | Quantifying cervical and axioscapular muscle stiffness using shear wave elastography[END_REF]. SWV of muscle seems to be influenced by sex, age, and dominance of the patient [START_REF] Xie | Quantifying cervical and axioscapular muscle stiffness using shear wave elastography[END_REF][START_REF] Chen | Ultrasound shear wave elastography in the assessment of passive biceps brachii muscle stiffness: influences of sex and elbow position[END_REF]. Moreover, studies have highlighted the importance of the probe orientation, as the stiffness may decrease in a perpendicular position compared to the parallel orientation to the muscle fibers [START_REF] Eby | Validation of shear wave elastography in skeletal muscle[END_REF][START_REF] Gennisson | Viscoelastic and anisotropic mechanical properties of in vivo muscle tissue assessed by supersonic shear imaging[END_REF]. This result showed the anisotropic behavior of the skeletal muscle. The parallel orientation of the probe with the main direction of the muscle fiber is more valid and reliable for SWV measurements.

Increased stiffness values, related to muscle spasticity, were shown in patients with neuromuscular diseases, such as cerebral palsy [START_REF] Brandenburg | Quantifying passive muscle stiffness in children with and without cerebral palsy using ultrasound shear wave elastography[END_REF], Duchenne muscular dystrophy [START_REF] Bensamoun | Elastic properties of skeletal muscle and subcutaneous tissues in Duchenne muscular dystrophy by magnetic resonance elastography (MRE): a feasibility study[END_REF] in passive state, Parkinson's disease or neonatal brachial plexus palsy [START_REF] Chatelier | Muscle elasticity in patients with neonatal brachial plexus palsy using shear-wave ultrasound elastography. Preliminary results[END_REF]. SWE provides an additional objective tool for spasticity evaluation in targeting the right skeletal muscle in a spastic upper limb [START_REF] Lehoux | Shear wave elastography potential to characterize spastic muscles in stroke survivors: Literature review[END_REF] and could be helpful to assess results of Botulinum Toxin injection [START_REF] Gao | Ultrasound Elastography to Assess Botulinum Toxin A Treatment for Post-stroke Spasticity: A Feasibility Study[END_REF] or surgery.

In the study of Li et al., SWE of thenar muscle in hemiplegic patients was performed. The plegic side showed decreased stiffness compared to the healthy side. Changes in muscle stiffness in the follow-up could be used as an objective assessment of rehabilitation degree [START_REF] Li | Quantitative assessment of thenar to evaluate hand function after stroke by Bayes discriminant[END_REF].

In 2017, Lamouille et al. reported the assessment of in vivo muscle tension during transfer of the extensor indicis proprius to the extensor pollicis longus (Fig. 3). SWE measurements were obtained at different stages of surgery including at rest before transferring, during active extension, and after tendon transfer at rest. The investigators showed differences in stiffness values at the various stages of the tendon transfer procedure, providing new insights to improve therapeutic treatments of tendon transfers [START_REF] Lamouille | Extensor indicis proprius tendon transfer using shear wave elastography[END_REF].

Due to the frequency of rotator cuff degenerative lesion, shoulder muscles are of interest, and the most analyzed structures in the upper limb. In non-pathologic shoulders, SWE supraspinatus muscle values gradually decreased with increased passive abduction of the shoulder. In case of large to massive tears, the stiffness of supraspinatus muscle did not vary from adduction to abduction conditions [START_REF] Hatta | Quantitative assessment of rotator cuff muscle elasticity: Reliability and feasibility of shear wave elastography[END_REF]. After rotator cuff surgical repair, the contractile behavior of the supraspinatus muscle increased from 6 weeks to 3 months after surgery and the stiffness reached a steady-state after 3 months. Opposite variation was found for deltoid muscle activity which reached the same level as healthy muscle after 6 months [START_REF] Ishikawa | Changes in shoulder muscle activities and glenohumeral motion after rotator cuff repair: an assessment using ultrasound real-time tissue elastography[END_REF]. This phenomenon is explained by a compensatory role of the deltoid during rotator cuff injury. In addition to human muscle, SWE technique is developed to characterize the muscle stiffness of small rodents to follow the effect of treatment [START_REF] Ternifi | Ultrasound image processing to estimate the structural and functional properties of mouse skeletal muscle[END_REF].

Elastography and nerve

For many years, electroneuromyography (ENMG) has been considered as the main diagnostic tool for peripheral neuropathies. Then, B-mode ultrasound image and doppler examination were found to be of interest in Carpal Tunnel Syndrome (CTS) diagnosis showing 1) an increase in nerve cross sectional area (CSA) proximal to the region where the nerve is compressed, 2) a reduced mobility of the nerve, 3) a modification of the structural properties trough a variation in echogenicity, and 4) an increased vascularity of the nerve. SWE in adjunction to B-mode ultrasound seems to be reliable for entrapment neuropathy diagnosis, with the advantages of being a noninvasive test, accessible and fast for the surgeon. Most SWE studies related to the upper limb nerves were performed on the median nerve (MN) for CTS. Authors have demonstrated that long term edema or high carpal tunnel pressure could lead to increase median nerve stiffness [START_REF] Kantarci | Median nerve stiffness measurement by shear wave elastography: a potential sonographic method in the diagnosis of carpal tunnel syndrome[END_REF]. Reliability and feasibility of the stiffness measurements obtained with SWE realized in healthy MN (N = 40) subjects showed excellent interobserver and intra-observer agreement (0.852-0.930), with no difference between bilateral forearm measurements [START_REF] Zhu | Evaluation of the healthy median nerve elasticity: Feasibility and reliability of shear wave elastography[END_REF]. Attention must be paid to limb positioning during SWE measurements, as it directly affects nerve tension and the stiffness values [START_REF] Rugel | Influence of limb position on assessment of nerve mechanical properties by using shear wave ultrasound elastography[END_REF]. A metaanalysis, composed of 17 studies, using sonoelastography to image the MN at wrist level (N = 1401 wrists) confirmed that the nerve is consistently stiffer in patients with CTS than healthy subjects regardless of the ultrasound elastography technique [START_REF] Lin | Utility of Ultrasound Elastography in Evaluation of Carpal Tunnel Syndrome: A Systematic Review and Meta-analysis[END_REF]. Moreover, studies have successively identified the severity of the nerve disease trough different stages [START_REF] Wee | Shear wave Elastography in the Differentiation of Carpal Tunnel Syndrome Severity[END_REF][START_REF] Sernik | Shear wave elastography is a valuable tool for diagnosing and grading carpal tunnel syndrome[END_REF]. Thus, SWE allowed for a classification of CTS similar as the gold-standard electrodiagnostic, with cases stratified as mild, moderate or severe based on the stiffness of the MN. This was not achievable using B-mode US alone. Both median nerve CSA at the wrist and shear wave velocity were reduced one week after surgical carpal tunnel release, reflecting nerve recovery [START_REF] Wu | Ultrasound and elastography role in pre-and post-operative evaluation of median neuropathy in patients with carpal tunnel syndrome[END_REF]. However, cut-off stiffness values proposed for CTS diagnosis are different according to authors, varying from 40.4 kPa to 79 kPa [START_REF] Kantarci | Median nerve stiffness measurement by shear wave elastography: a potential sonographic method in the diagnosis of carpal tunnel syndrome[END_REF][START_REF] Paluch | Wrist to forearm ratio as a median nerve shear wave elastography test in carpal tunnel syndrome diagnosis[END_REF]. Also, Sugiyama et al. [START_REF] Sugiyama | A Survey of the Median Nerve Elasticity after Volar Locking Plate Fixation Using Ultrasound Elastography[END_REF] proposed SWE technique as an objective, quantitative and noninvasive evaluation test for MN follow-up after volar locking plate osteosynthesis of distal radius fracture, helping to decide on material removal and MN neurolysis timing.

For ulnar nerve neuropathy at the elbow and at the Guyon's canal, SWE appears as a new reliable method to support this diagnosis [START_REF] Paluch | Shear-wave elastography: a new potential method to diagnose ulnar neuropathy at the elbow[END_REF][START_REF] Paluch | Shear-wave elastography in the diagnosis of ulnar tunnel syndrome[END_REF]. Ulnar nerve stiffness with a Young's modulus over 61 kPa and the stiffnesses ratios of the cubital tunnel to distal arm and to mid-arm were 1.68 and 1.75, respectively, provided 100% specificity and sensitivity for the detection of ulnar neuropathy at the elbow [START_REF] Paluch | Shear-wave elastography: a new potential method to diagnose ulnar neuropathy at the elbow[END_REF]. Also, SWE can be used to differentiate ulnar neuropathy at the cubital tunnel from asymptomatic ulnar nerve with medial epicondylitis and healthy uncompressed ulnar nerve [START_REF] Kim | Evaluation of the ulnar nerve with shear-wave elastography: a potential sonographic method for the diagnosis of ulnar neuropathy[END_REF]. Patients with unilateral ulnar tunnel syndrome showed higher CSA and stiffness in the affected side for all positions, i.e., extension, 45° flexion, 90° flexion and at the maximum flexion of the elbow where the stiffness increased [START_REF] Wolny | Changes in Ultrasound Measurements of the Ulnar Nerve at Different Elbow Joint Positions in Patients with Cubital Tunnel Syndrome[END_REF]. In patients with ulnar nerve decompression associated with anterior transposition, post-operative ulnar nerve stiffness increased with elbow joint extension (Fig. 4). However, on the non-operative side, ulnar nerve stiffness increased with elbow flexion [START_REF] Durand | Post-Operative Assessment of Ulnar Nerve Tension Using Shear-Wave Elastography[END_REF].

Recently, SWE was used before ultrasound-guided perineural hydrodissection to identify the level of stiffness of the scar surrounding the radial nerve in two cases of radial nerve palsy after humeral shaft fractures [START_REF] Su | Shear Wave Elastography to Guide Perineural Hydrodissection: Two Case Reports[END_REF].

Elastography and skin

The use of high frequency ultrasonographic transducers has made elastographic assessment of the skin possible [START_REF] Xiang | Quantitative Assessment of Healthy Skin Elasticity: Reliability and Feasibility of Shear Wave Elastography[END_REF]. Most of the previous studies using elastography for skin evaluation included patients with cancers, connective tissue diseases, chronic systemic inflammation, lipodermatosclerosis or patients at risk of ulceration [START_REF] Deprez | On the potential of ultrasound elastography for pressure ulcer early detection[END_REF] but it may also find applications in aesthetic medicine. SWE distinguishes normal skin from scars and could be used to evaluate scar severity, which could be important for patient care and treatment. Additionally, excellent intra-observer and inter-observer reliability was noted, even when the test is performed by a novice clinician versus an experienced sonographer. A direct linear relationship was established between scar thickness, scar pliability and SWV measurements [START_REF] Dejong | A Novel, Reliable Protocol to Objectively Assess Scar Stiffness Using Shear Wave Elastography[END_REF]. In a similar way, SWE was also used to quantify keloid response to treatment after intralesional corticosteroid injection [START_REF] Huang | Quantitative assessment of treatment efficacy in keloids using high-frequency ultrasound and shear wave elastography: a preliminary study[END_REF]. The results showed no statistical differences in thickness between normal skin and treated keloids. SWE values of treated keloids significantly decreased but the data were still higher than normal skin.

Conservative treatment of fingertip amputation using occlusive dressings can lead to soft tissue regeneration. Ultrasonography and SWE were performed on the regenerated fingertips [START_REF] Jafari | First Insights into Human Fingertip Regeneration by Echo-Doppler Imaging and Wound Microenvironment Assessment[END_REF]. Compared to collateral uninjured finger, there were no difference in pulp thickness, but vascularization and stiffness were both significantly higher after fingertip regeneration. SWE appears also as an objective tool to assess elasticity of the skin after flap reconstruction.

In our clinic, we used the UE to measure the stiffness the skin of the hand after fascia superficialis flap surgery following a severe hand trauma (Fig. 5). To our knowledge, this is the first case described. To date, a unique study conducted by a team of plastic surgeons focused on elastography applied to this field [START_REF] Sowa | Objective evaluation of fat tissue induration after breast reconstruction using a deep inferior epigastric perforator (DIEP) flap[END_REF]. They used SWE on subcutaneous fat after deep inferior epigastric perforator (DIEP) flap and found a positive correlation between flap weight and fat tissue stiffness. This result is particularly relevant because fat induration and necrosis are common complications after breast reconstruction with DIEP flaps but are currently only evaluated clinically.

Elastography and other indications in hand and upper extremity.

Extrapolating results from the pre-mentioned tissues, it was felt that UE may be a useful way to assess ligament health and integrity. Decreased SWV in the ulnar collateral ligament of the elbow in the dominant side was observed in baseball pitchers at midseason [START_REF] Gupta | Shear wave elastography of the ulnar collateral ligament in division IA pitchers across a competitive collegiate season[END_REF]. This functional decline of the ulnar collateral ligament was probably associated with structural modification. Another study described the use of SWE to quantify the central band stiffness of interosseous membrane located in the forearm placed in different positions of pronosupination [START_REF] Rougereau | Biomechanical assessment of the central band of the interosseous membrane using shear wave elastography: reliability and reproducibility[END_REF]. The results demonstrated that the stiffness measurements were reproducible between examinators. Authors raised that elastography could help guiding diagnostic and therapy in the management of interosseous membrane lesions. B-mode US image for trigger finger diagnosis shows A1 pulley thickening. Additional UE acquisitions showed A1 pulley stiffness. These two parameters tend to alleviate after corticosteroid injection, being a valid asset for treatment follow-up [START_REF] Miyamoto | Stiffness of the first annular pulley in normal and trigger fingers[END_REF].

To date, measurement methods of acute compartment syndrome are invasive and clinical diagnosis may be challenging. According to Zhang et al. [START_REF] Zhang | An exploratory study of two-dimensional shear-wave elastography in the diagnosis of acute compartment syndrome[END_REF], muscle stiffness indirectly reflects intra-compartmental pressure revealing that SWE may be a noninvasive quantitative diagnostic tool for compartment syndrome diagnosis. In a short study [START_REF] Zhang | An exploratory study of two-dimensional shear-wave elastography in the diagnosis of acute compartment syndrome[END_REF], muscle stiffness was found to be significantly higher than the unaffected side in four patients with actual acute compartment syndrome, but more data are needed before a quantitative cut-off can be established. Chronic compartment syndrome can also be explored using SWE (Fig. 6).

In the oncological field, higher stiffness values are noted for malignant lesions (breast, thyroid, prostate, skin, lymph node) compared to benign masses [START_REF] Berg | Shear-wave elastography improves the specificity of breast US: the BE1 multinational study of 939 masses[END_REF][START_REF] Tang | Diagnostic value of ultrasound elastography for differentiation of benign and malignant axillary lymph nodes: a meta-analysis[END_REF][START_REF] Wang | Does Shear Wave Elastography Provide Additional Value in the Evaluation of Thyroid Nodules That Are Suspicious for Malignancy[END_REF][START_REF] Han | Differential diagnosis of basal cell carcinoma by high-resolution ultrasound elastography[END_REF]. SWE shows higher sensitivity and specificity than traditional B-mode US image to identify malignant lesion [START_REF] Tang | Diagnostic value of ultrasound elastography for differentiation of benign and malignant axillary lymph nodes: a meta-analysis[END_REF] and could avoid invasive risky procedures such as biopsies. Musculoskeletal tumors encompass a vast array of distinct tumor types, the majority of which are usually benign.

Malignant musculoskeletal tumors may express a wider range of stiffness values due to its more heterogeneous structure compared to benign lesions [START_REF] Li | Diagnostic performance of conventional ultrasound and quantitative and qualitative real-time shear wave elastography in musculoskeletal soft tissue tumors[END_REF]. With only a few studies on this topic [START_REF] Li | Diagnostic performance of conventional ultrasound and quantitative and qualitative real-time shear wave elastography in musculoskeletal soft tissue tumors[END_REF][START_REF] Pass | Do quantitative and qualitative shear wave elastography have a role in evaluating musculoskeletal soft tissue masses?[END_REF][START_REF] Winn | Characterization of soft tissue tumours with ultrasound, shear wave elastography and MRI[END_REF][START_REF] Tavare | Shear-Wave Elastography of Benign versus Malignant Musculoskeletal Soft-Tissue Masses: Comparison with Conventional US and MRI[END_REF][START_REF] Schivo | Shear Wave Elastography in the Diagnosis of Hand Tumours[END_REF], no evident correlation was found between stiffness and malignancy detection of musculoskeletal tumors [START_REF] Li | Diagnostic performance of conventional ultrasound and quantitative and qualitative real-time shear wave elastography in musculoskeletal soft tissue tumors[END_REF][START_REF] Pass | Do quantitative and qualitative shear wave elastography have a role in evaluating musculoskeletal soft tissue masses?[END_REF][START_REF] Winn | Characterization of soft tissue tumours with ultrasound, shear wave elastography and MRI[END_REF].

In a recent retrospective study [START_REF] Yuan | Diagnostic accuracy of multiparametric ultrasound for peripheral nerve schwannoma[END_REF], the combination of elastography with 2D imaging and color flow imaging achieved an excellent diagnostic accuracy in schwannomas for patients with softtissues masses located in the limb.

Finally, elastography could be also used for vessels stiffness evaluation. For example, SWE can distinguish between acute and chronic clots by characterizing tissue stiffness in deep vein thrombosis. It was also demonstrated that variation of stiffness in brachial arteries was statistically inferior in patients with known cardiovascular disease when compared to the healthy control group. This could be an early sign of atherosclerosis [START_REF] Gülşen | Brachial Artery Wall Stiffness Assessment by Shear Wave Elastography: A Promising New Diagnostic Tool for Endothelial Dysfunction Detection[END_REF].

Conclusion

Ultrasound Elastography is an accessible non-invasive imaging modality that can be used to measure stiffness in a variety of soft biological tissue. With the growing interest in developing new elastography applications in hand and upper extremity, one should keep in mind technical limitations concerning reproducibility and repeatability. This technique has a promising future but a significant amount of work remains to be done. Indeed, protocol must be standardized as positioning of the joint affects SWV measurement of the surrounding soft tissues. In Authors declare no conflicts of interest.

Figures legends

Fig. Hyperintensity in flexor pollicis longus and pronator quadratus muscles (arrow) are revealed using 3T MRI acquisitions (f). Patient with tendon rupture after flexor digitorum profondus of the index repair (third row). Re-rupture is difficult to identify in B-mode (g) proximally to the rupture. The cartographies of stiffness show lower values for the flexor digitorum profondus of the index (66.1 kPa, 4.7 m.s -1 ) (h) compared to the flexor digitorum superficialis of the index (378.5 kPa, 11.2 m.s -1 ) (i).

  addition, the selection of region of interest (ROI) is operator dependent and may introduce variability. Also, several commercial systems exist leading to the use of different probes with different ranges of frequencies which can impact SWV values. SE provides only qualitative values of stiffness and the external force is difficult to reproduce, or is variable through time, and can generate artifacts. SWE takes a simplistic view on the soft tissues mechanical properties (isotropic, homogeneous, linear elastic, incompressible) to facilitate the process of imaging, but tissues are anisotropic, heterogeneous, viscoelastic and skeletal muscle, for example, accounting for the associated vascular and lymphatic components, is compressible. Despite the above cited limitations, UE has demonstrated important correlation to diffuse and focal disease states in multiple soft tissues of the upper limb. UE holds huge clinical applications in MSK tissues. Continued development of systems and increased formation of clinicians to UE will lead to expand our knowledge of Elastography and its clinical applications in the future.

1 :

 1 Fig. 1: Ultrasound elastography represented by strain elastography (a) and shear wave elastography (b). The colored region represents the 2D quantitative elastogram superimposed

Fig. 2 :

 2 Fig. 2: Shear wave elastography of human flexor pollicis longus tendon in physiological conditions at rest (210.1 kPa, 8.4 m.s -1 ) (a), active flexion (490 kPa, 12.7 m.s -1 ) (b) and passive extension (486.6 kPa, 12.7 m.s -1 ) (c). Patient with anterior interosseous nerve palsy

Fig. 3 :

 3 Fig. 3: Intra operative photographs of the transfer of the extensor indicis proprius to the

Fig. 4 :

 4 Fig. 4: Decompression of the ulnar nerve at the elbow with subcutaneous transposition and

Fig. 5 :

 5 Fig. 5: Temporoparietal fascia free flap (a) for coverage of a large defect of dorsal aspect of

Fig. 6 :

 6 Fig. 6: Patient with chronic compartmental syndrome of the right forearm confirmed using intra

Fig. 1

 1 Fig.1

Fig. 2

 2 Fig.2

Fig. 3

 3 Fig.3

Fig. 4

 4 Fig.4

Fig. 5

 5 Fig.5


Arnaud Quintas

Daniel Caurant
email: daniel-caurant@enscp.fr

Odile Majérus

Thibault Charpentier

Jean-Luc Dussossoy

J-L Dussossoy

Effect of the nature of alkali and alkaline-earth oxides on the structure and crystallization of an aluminoborosilicate glass developed to immobilize highly concentrated nuclear waste solutions

Effect of the nature of alkali and alkaline-earth oxides on

the structure and crystallization of an aluminoborosilicate glass developed to immobilize highly concentrated nuclear waste solutions

INTRODUCTION

New confinement glasses, aimed at immobilizing highly concentrated nuclear waste solutions, stemming from the reprocessing of high discharge burn up nuclear fuel (60 GWj.t -1 ), are currently under study. For instance, a complex rare-earth rich aluminoborosilicate glass (16 wt% rare-earth oxides) has already proved from a technological point of view (chemical durability, waste capacity and low crystallization tendency), to be a good candidate for the immobilization of these concentrated high level radioactive wastes [1,2]. High amounts of alkali (R + ) and alkalineearth (R' 2+ ) cations are present in this glass composition coming either from the waste or from the glass frit mixed with the waste and are incorporated in glass structure. For instance, according to the simulation results of high discharge burn up spent fuel composition [3], Rb 2 O, Cs 2 O, SrO and BaO ions will represent about 17 wt% of all the fission products in waste solutions. A high quantity of sodium will also occur in waste solutions and stems from nuclear spent fuel reprocessing. Both sodium and lithium will be also added in glass frit composition to facilitate nuclear glass fabrication and waste incorporation. To increase the chemical durability of borosilicate nuclear glasses, calcium is also introduced in their composition. In the complex rare earth-rich aluminoborosilicate glass considered here, R 2 O and R'O concentrations (in mol.%) are the following [2]: 8.49 (Na 2 O), 5.36 (CaO), 5.03 (Li 2 O), 0.44 (BaO), 0.33 (Cs 2 O), 0.30 (SrO), 0.07 (Rb 2 O). In previous works [1,4,5], we mainly studied the structure and crystallization tendency of a simplified seven-oxide rare-earth rich aluminoborosilicate glass (SiO 2 , B 2 O 3 , Al 2 O 3 , R'O, R 2 O, ZrO 2 , RE 2 O 3 with RE=La or Nd) derived from the complex glass composition by using the most abundant R' 2+ = Ca 2+ and R + = Na + cations to simulate all the alkaline-earth and alkali cations occurring in wastes. Nevertheless several results concerning the crystallization tendency of the complex glass with all alkali and alkaline-earth cations were given in [2,3]. In this paper, we present the impact of totally changing the nature of alkali (R + = Li + , Na + , K + , Rb + , Cs + ) or alkaline-earth (R' 2+ = Mg 2+ , Ca 2+ , Sr 2+ , Ba 2+ ) cations on both the structure and the crystallization tendency of the simplified glass. Even if K + and Mg 2+ cations will be not present in the complex nuclear glass composition, their effect on glass structure was also studied in this work to complete the alkaline-earth and alkali cations series. The effect of the nature of R + and R' 2+ cations and of their relative proportions on the environment of RE 3+ cations was presented in [6] where we showed that both alkali and alkaline earth cations are present around Nd 3+ ions in non-bridging oxygen atoms (NBOs)-rich regions enabling their stabilization in glass structure.

EXPERIMENTAL PROCEDURE

The simplified seven-oxides glass composition studied in this work is: 61.79 SiO 2 -3.05 Al 2 O 3 -8.94 B 2 O 3 -14.41 R 2 O -6.32 R'O -1.89 ZrO 2 -3.60 RE 2 O 3 (mol.%) (glass A) with RE=La or Nd. Two glass series were prepared for this paper. For the first series (R series), the nature of R + cation was varied from Li + to Cs + (R'= Ca). For the second series (R' series), the nature of R' 2+ cation was varied from Mg 2+ to Ba 2+ (R=Na). All glasses were melted between 1300 and 1400°C in Pt crucibles, quenched and annealed near T g . The structure of all glasses with RE = La was studied by 11 B (160.14 MHz), 27 Al (130.06 MHz) and 23 Na (132.03 MHz) MAS NMR. The chemical shifts ( iso ) of the different nuclei are reported in ppm relative to an external sample of 1 M aqueous boric acid at 19.6 ppm, 1 M aqueous NaCl at 0 ppm and 1 M aqueous Al(NO 3 ) 3 at 0 ppm. In order to simulate the natural cooling of nuclear glasses, all samples were slowly cooled (1°C/min) from 1350°C to room temperature and were then studied by Xray diffraction (XRD), scanning electron microscopy (SEM) and electron probe microanalysis (EPMA).

STRUCTURAL STUDY

Concerning the silicate network, Raman results (not presented in this paper, [7]) show that increasing R + or R' 2+ cations field strength induce a displacement to the right of the 2Q 3 ↔ Q 2 + Q 4 equilibrium in the melt (Q n represents SiO 4 units with 4-n NBOs) in accordance with the increasing glass-in-glass phase separation tendency with cation field strength in binary silicate glasses. According to [8], the field strengths of alkali (Li + , Na + , K + , Rb + , Cs + ) and alkaline-earth (Mg 2+ , Ca 2+ , Sr 2+ , Ba 2+ ) cations in silicate glasses are respectively (0.26, 0.18, 0.12, 0.11, 0.10) and (0.46, 0.36, 0.29, 0.26). No other environment than fourfold coordinated aluminum units was detected by MAS and MQMAS 27 Al NMR (data not shown) in all glasses. The absence of significant evolution between 27 Al MAS NMR spectra (the corresponding NMR parameters are given Fig. 1) when the nature of alkaline-earth is varied (and with R=Na) indicates that (AlO 4 ) -units are preferentially charge compensated by Na + cations rather than by R' 2+ cations. Indeed, 27 Al quadrupolar coupling constant C Q is known to increase with the field strength of charge compensator [9]. Comparison of 27 Al MAS NMR results of glasses of the R' series with that of a glass derived from glass A (referred to as R0 in Fig. 1) but containing only Na + ions confirms that for all glasses of the R' series, the great majority of four-coordinated aluminum are charge compensated by Na + ions within the limit of MAS NMR sensitivity. On the other hand, significant evolution of both C Q and  iso are observed between the samples of the R series when R + cation field strength increases (Fig. 1) showing that the nature of the charge compensators of (AlO 4 ) -units strongly changes for this series. Fig. 1. Evolution of the mean C Q and  iso parameters deduced from 27 Al MAS NMR spectra for R and R' series. For comparison, the parameters of a glass (R0) derived from glass A but containing only Na + ions and of an industrial calcium aluminoborosilicate glass (E) for which AlO 4

-units are essentially compensated by Ca 2+ ions are also shown. MAS NMR data were analyzed according to the method described in [5]. As for the samples containing K + , Rb + or Cs + ions both C Q and  iso decrease with R + cation field strength in comparison with sodium, this shows that for these three glasses the great majority of (AlO 4 ) -units remain charge compensated by alkali cations. Indeed, the presence of high field strength Ca 2+ ions as aluminum charge compensator should have induced significant increase of 27 Al NMR parameters (see Fig. 1 the NMR parameters of the industrial calcium aluminoborosilicate glass (Eglass) for which AlO 4

-units are essentially compensated by Ca 2+ ions). Concerning the glass with Li + , the replacement of all Na + by Li + ions induces an important increase of both 27 Al NMR parameters (Fig. 1). The question is: are (AlO 4 ) - units still preferentially charge compensated by alkali ions (here Li + ) in this glass or does Ca 2+ ions participate to charge compensation? The fact that for R=Li, C Q and  iso parameters remain lower than E-glass ones shows that lithium participate to aluminum charge compensation. Moreover, the comparison of the quadrupolar coupling constant C Q of the glass with Li (C Q =5.8 MHz) with that of a lithium aluminoborosilicate glass with Li + ions as unique charge compensators of (AlO 4 ) -units (C Q =6.05 MHz) [START_REF] Charpentier | Proceedings of the 35 th ITEP winter School[END_REF] seems to indicate that the aluminum tetrahedral units are preferentially charge compensated by Li + ions in our glass. Concerning 11 B MAS NMR results, the evolution of spectra and of the proportion N 4 of (BO 4 ) - units for the R' series is shown in Fig. 2. Fig. 2. 11 B MAS NMR spectra of glasses of the R' series. The evolution of the proportion N 4 of (BO 4 ) -units versus cation radius is also shown. All spectra are normalized on the maximum of the BO 4 peak.

It appears that the substitution of an alkaline earth by a one with a lower field strength leads to an increase of N 4 . Thus, the field strength of R' 2+ cations seems to control N 4 evolution for this series. Similar evolution was observed by replacing calcium by sodium in glass A [5]. Moreover, the small  iso variation of (BO 4 ) -units between -0.66 and -0.53 ppm for the R' series remains close to that of (BO 4 ) -units charge compensated only by Na + ions as in glass A with only sodium ( iso =-0.64 ppm) and far from that of (BO 4 ) -units charge compensated only by Ca 2+ ions as in industrial E-glass ( iso =-0.11 ppm). This shows that tetrahedral boron units remain preferentially charge compensated by Na + ions for all glasses of R' series. However, for the R series, the evolution of N 4 is not monotonous when R + cation field strength decreases and the reason for this seems to be complex. Thus, all these structural results show that the environment of (AlO 4 ) -units will be probably not affected by replacing strontium and barium by calcium in the complex nuclear glass. Moreover, due to the small SrO and BaO concentrations in complex glass composition (see above), N 4 will probably increase only very slightly by introducing these oxides in the melt.

In the complex nuclear glass, (AlO 4 ) -units will be mainly compensated by Na + ions because

[Na 2 O]=8.49 > [Al 2 O 3 ]=3.05 >>[Rb 2 O]+[Cs 2 O] =0.40 mol%.
Nevertheless, because of the significant Li 2 O concentration ([Li 2 O]=5.03 mol%) in complex glass, lithium will probably also participate to the charge compensation of tetrahedral aluminum units. According to 11 B NMR results [5,7], the (BO 4 ) -units charge compensation will be probably preferentially insured by Na + and Li + ions. Nevertheless, Ca 2+ ions will also certainly contribute to this charge compensation.

CRYSTALLIZATION STUDY

Our previous studies [4] For R'=Ca all peaks are attributed to apatite whereas for R'=Mg an unidentified crystalline phase (I) is detected. Pictures of samples for R'=Mg and Ca are shown in the upper part.

Consequently, the nature of R' 2+ cation has a very strong effect on the crystallization tendency of the undercooled melt. The introduction of small SrO and BaO amounts in the complex glass composition is thus not expected to induce the crystallization of new phases. This is in agreement with our results reported in [2] concerning the crystallization of the complex nuclear glass (with both CaO, SrO, MgO, Na 2 O, Li 2 O, Cs 2 O) for which only the calcium apatite phase was observed after slow cooling at 1°C/min. For the R series samples (that all contain CaO) with RE=Nd, XRD, SEM and EPMA shows that the calcium apatite Ca 2+x Nd 8-x (SiO 4 ) 6 O 2-0.5x (x ~ 0.14 to 0.41) phase crystallizes in all the samples during slow cooling. Moreover, for R=Li and Cs, other crystalline phases are detected by XRD and SEM, respectively cristobalite (SiO 2 ) and pollucite (CsAlSi 2 O 6 ) (Fig. 4.). The crystallization of pollucite is directly linked to the presence of 14.41 mol% of Cs 2 O in the R=Cs glass. Because of the low Cs 2 O concentration (0.33 mol%), pollucite does not crystallize in the complex glass [2]. The dark droplets observed in Fig. 4a (R=Li) probably contains the cristobalite crystals and would originate from glass-in-glass phase separation due the presence of a high concentration of Li + cations. Glass-in-glass phase separation and cristobalite crystallization were not observed in the complex glass [2] probably because of the lower Li 2 O concentration in this glass. The replacement of Na by K or Rb has only small effect on the tendency of the undercooled melt to crystallize (apatite only) because R + cations are not incorporated into apatite crystals. Ap.

Ap.

  is detected for the sample containing Mg.

Fig. 3 .

 3 Fig.3. XRD patterns of slowly cooled samples of the R' series with RE=Nd ( K1 Co=0.1789 nm).For R'=Ca all peaks are attributed to apatite whereas for R'=Mg an unidentified crystalline phase (I) is detected. Pictures of samples for R'=Mg and Ca are shown in the upper part.

Fig. 4 .

 4 Fig.4. SEM images (backscattered electrons) of slowly cooled samples of the R series: (a) R= Li, (b) R=Cs. Ap: apatite, Pol: pollucite

May 19-22, 2008

Montpellier (France) May 19-22, 2008