domain: info spi

text:
Florence Zara

Benjamin Delbos

Rémi Chalard

Richard Moreau

Fabrice Jaillet

Arnaud Lelevé

Haptic Training Simulators Design Approach

Keywords: Medical Training Simulation, Virtual Reality, Haptics, Soft-body Simulation

Learning medical gestures requires regular hands-on training to acquire the dexterity needed to perform them without injuring patients. For obvious ethical reasons, this training cannot be carried out directly on the patient. In this context, the use of cadavers has long been the preferred method of training, despite the difficulty of obtaining them and the fact that cadavers deteriorate rapidly. For several years, technologies have led to the development of medical training simulators that combine a numerical simulation (reproducing the organs' behavior during the gesture) with haptic devices (reproducing tactile sensations). As designers of several haptic training simulators, we aim to impart our expertise by detailing in this paper an empirical design methodology for the development of such simulators.

Introduction

During their education, medical students have to learn numerous gestures involving the manipulation of surgical tools. The challenge is to acquire the required dexterity, which permits them to reproduce correctly the maneuvers involving the application of a given amount of force to the patient's tissues. However, gesture training performed directly on patients raises medical and ethical issues, as it exposes patients to risks directly related to teaching. For this reason, the use of animals, cadavers and mannequins has become increasingly popular to ensure practical training before application to real patients. Nevertheless, the use of these patient simulation tools cannot cover all possible medical situations, and the physical realism of these simulators diminishes over time. Indeed, tissues remain permanently deformed after initial use, and physical properties change as the body decomposes, altering blood supply or tissue structure.

In this context, the use of training systems offering Computer-Based-Simulation (CBS) [START_REF] Kunkler | The role of medical simulation: an overview[END_REF] can provide an answer to these training issues as their use enables coverage of a wider range of medical situations. Nonetheless, the effectiveness of such training tools thus depends on the pedagogical validity of the situations proposed and on the appropriate realism of the simulation, with the apprentice immersed in an engaging scenario. The first CBS designed for this purpose are categorized as Virtual Reality Training Simulators (VRTS). They have become increasingly prevalent due to their provision of objective feedback and diverse case scenarios [START_REF] Brydges | Linking simulationbased educational assessments and patient-related outcomes: A systematic review and meta-analysis[END_REF]. Nevertheless, they frequently lack realistic haptic feedback, a crucial element in enhancing the medical skills of the trainee [START_REF] Sainsbury | Evaluation of a virtual reality percutaneous nephrolithotomy (pcnl) surgical simulator[END_REF]. In this context, the use of Virtual Reality (VR) with haptic devices has emerged as a growing option in recent years. These Haptic Training Simulators (HTS) [START_REF] Lelevé | Haptic training simulation[END_REF] integrate a numerical simulation replicating the behavior of organs with a haptic device reproducing kinesthetic sensations. This combination allows learners to perceive the consequences of a medical gesture. Furthermore, they facilitate training with force feedback, aiding trainees in immersing themselves in diverse situations, as highlighted by research such as [START_REF] Overtoom | Haptic feedback, force feedback, and force-sensing in simulation training for laparoscopy: A systematic overview[END_REF][START_REF] He | Robotic simulators for tissue examination training with multimodal sensory feedback[END_REF][START_REF] Sénac | Simulating a syringe behavior using a pneumatic cylinder haptic interface[END_REF].

The challenges of these types of medical simulators are: to ensure patientfriendly learning of medical procedures as part of initial and continuing medical training; to accelerate the learning process by multiplying and targeting the situations encountered; to improve knowledge of the procedure and associated reasoning; in the medium term, to develop new medical procedures and associated assessment methods; in the longer term, to offer tools for pre-operative planning and training in high-risk "patient-specific" operations, i.e. medical simulators directly based on a patient's medical data.

In this paper, we focus on training tools based on a numerical simulation combined with a haptic device. We introduce a proposal for a complete process of design of such simulators for hands-on training in medical and surgical procedures. Yet, we do not include the educational dimension which deals with designing training scenarios and objective assessment, for the sake of clarity. In section 2, we present a brief state-of-the-art on medical training simulators. Section 3 introduces the aforementioned design approach, and section 4 is a discussion about the evolution of these simulators toward patient-specific ones.

State of the Art

As far as we know, the latest general review (larger than the medical scope) about training simulation was proposed in 2020 in [START_REF] Lelevé | Haptic training simulation[END_REF]. Since, some more focused reviews are available, such as [START_REF] He | Robotic simulators for tissue examination training with multimodal sensory feedback[END_REF] for tissue examination, [START_REF] Delbos | Review on needle insertion haptic simulation[END_REF] on needle insertion, [START_REF] Huang | State of the art of virtual reality simulation in anesthesia[END_REF] in anesthesia, or more recently [START_REF] Rotin | Simulation-based medical education in transfusion medicine: Current state and future applications[END_REF] in transfusion medicine, for instance. In 2007, Gardner [START_REF] Gardner | Simulation and simulator technology in obstetrics: past, present and future[END_REF] proposed a state-of-the-art report on the use of simulators in obstetrics and gynecology, accompanied by a classification: anatomical simulators, instrumented anatomical simulators, and virtual-realitybased simulators. We propose updating and extending this classification to any contemporary medical training simulators.

Anatomical Simulators. As they are the least expensive at the purchase time, the most widely used simulators in medicine are anatomical ones that reproduce anatomical landmarks. For example, in obstetric gynecology, the simulator proposed in 1951 by Graves [START_REF] Graves | Educational apparatus for teaching obstetrics and midwifery[END_REF] consists of a woman's dummy on a scale of one, with three levels of gestation, a placenta and a fetal dummy that can be positioned in different ways in the abdomen. The most simple ones are sight-only: they cannot be used to practice any gesture (needle insertion, suturing, etc.) which limits the didactic dimension. More evolved ones feature parts that can reproduce passive haptic feedback (when inserting a needle, for instance), based on materials presenting similar mechanical properties to tissues of interest. Yet, these parts progressively wear out, which can be costly in the long term. For instance, Clifton et al. [START_REF] Clifton | The spinebox: A freely available, openaccess, 3d-printed simulator design for lumbar pedicle screw placement[END_REF] introduced a 3D-printed open-access spine simulator and Robberecht et al. [START_REF] Robberecht | A novel anatomical ceramic root canal simulator for endodontic training[END_REF] a ceramic root canal simulator for endodontic training. It has been demonstrated that 3D printed models are realistic enough and cost-effective to help trainees in the first phases of some other specific medical training (Otolaryngology [START_REF] Sparks | 3d printed myringotomy and tube simulation as an introduction to otolaryngology for medical students[END_REF], and Pediatrics [START_REF] London | Simulation of pediatric anterior skull base anatomy using a 3d printed model[END_REF], for instance).

Instrumented Anatomical Simulators. Instrumented anatomical simulators offer active haptic feedback in addition to the features of anatomical simulators. This feedback is obtained through actuators that are controlled (by the trainer, for instance) to render realistic force interactions between the manikin and the tools or the hand of the trainee. We can cite, as examples in gynecology, the following ones [START_REF] Knapp | dynamic childbirth simulator for teaching maternity patient care[END_REF][START_REF] Eggert | Interactive education system for teaching patient care[END_REF][START_REF] Sielhorst | An augmented reality delivery simulator for medical training[END_REF][START_REF] Riener | Birth simulator (geburtensimulator)[END_REF][START_REF] Allen | Simulating birth to investigate clinicianapplied loads on newborns[END_REF]. Among them, the Noelle simulator from the Gaumard company [START_REF]Gaumard Scientific: S575 noelle with newborn hal[END_REF] represents a complete product in the "learning dummy" philosophy, with simulations designed to teach the reflexes required in different typical situations. For needle insertion, let us cite [START_REF] Esterer | A hybrid, low-cost tissue-like epidural needle insertion simulator[END_REF].

Virtual Reality (VR) Simulators. With the advent of new technologies, a more recent class of simulators concerns VR-based simulators. A numerical simulation reproduces interactions between medical tools and organs. The simulation permits taking into account a patient's morphology in comparison to a plastic dummy. In gynecology, these simulators enable the trainer to visualize the descent of the fetus into the pelvic canal [START_REF] Boissonnat | 3D simulation of delivery[END_REF][START_REF] Geiger | Three-dimensional modeling of human organs and its application to diagnosis and surgical planning[END_REF][START_REF] Kheddar | Preliminary design of a childbirth simulator haptic feedback[END_REF][START_REF] Forster | Clinical use of the birth simulation program "anapelvis 2.0" for prediction of feto-maternal disproportion[END_REF][START_REF] Ballit | Fast soft-tissue deformations coupled with mixed reality toward the next-generation childbirth training simulator[END_REF]. The use of VR glasses [START_REF] Ballit | Fast soft-tissue deformations coupled with mixed reality toward the next-generation childbirth training simulator[END_REF] can enhance the learner's immersion in the virtual world. Letterie [START_REF] Letterie | How virtual reality may enhance training in obstetrics and gynecology[END_REF] highlighted in 2002 the benefits of Virtual Reality for training in obstetrics and gynecology. Augmented Reality simulators also enter this category, such as [START_REF] Da Silva | Augmenting the training space of an epidural needle insertion simulator with hololens[END_REF] for epidural need insertion, [START_REF] Otmane | Virtual & augmented reality for medical training and rehabilitation[END_REF] for rehabilitation, or [START_REF] Luchetti | Augmented reality-based demo for immersive training in horticultural therapy[END_REF] for horticultural therapy.

Haptic Training Simulators (HTS). As anatomical simulators, whether instrumented or not, are based on plastic mannequins, they can not simulate complex tissue interactions and therefore do not offer realistic high-fidelity sensory rendering when medical instruments are in mechanical interaction with tissues. Yet, gesture precision depends on the reaction of tissues and anatomical structures that evolve during the gesture. Also, these simulators cannot reproduce a variety of clinical cases without multiplying the samples, and they wear out in time, which requires purchasing new parts that can be costly in the long term.

In comparison, haptic training simulators provide kinesthetic feedback using a (off-the-shelf or specific, see [START_REF] Sénac | Introducing pneumatic actuators in haptic training simulators and medical tools[END_REF]) haptic device. It is, in general, a robotic arm that is controlled to furnish the end-effector position to the simulation software and to generate a force that resists the motions of the user, computed in real-time by the simulation software. Haptic feedback can also be provided by using complementary tactile devices [START_REF] Overtoom | Haptic feedback, force feedback, and force-sensing in simulation training for laparoscopy: A systematic overview[END_REF][START_REF] Fleer | Learning efficient haptic shape exploration with a rigid tactile sensor array[END_REF]. Nonetheless, this paper focuses on kinesthetic feedback. For example, Buttin et al. [START_REF] Buttin | Biomechanical simulation of the fetal descent without imposed theoretical trajectory[END_REF] proposed in 2013 a childbirth simulator to learn extraction gestures using forceps. The descent of the fetus was simulated according to uterine contraction and expulsion forces. The computed head's position was used to pilot a pneumatic device corresponding to the haptic part of the simulator [START_REF] Herzig | A new design for the birthsim simulator to improve realism[END_REF] comprising a maternal abdomen and a plastic fetus. Concerning needle insertion haptic training (a very common gesture), Correa et al. provided a state-of-the-art in 2019 [START_REF] Corrêa | Haptic interaction for needle insertion training in medical applications: The state-of-the-art[END_REF]. Since, Alamilla et al. introduced such a simulator in a rheumatology context [START_REF] Alamilla | A Virtual Reality and haptic simulator for ultrasound-guided needle insertion[END_REF]. It combines a numerical simulation, providing an ultrasound view of tissues during the gesture [START_REF] Barnouin | A real-time ultrasound rendering with modelbased tissue deformation for needle insertion[END_REF], with two haptic devices (one for the probe and one for the needle). Some other recent haptic training applications cover prostate biopsy procedures [START_REF] Fiard | Simulationbased training for prostate biopsies: towards the validation of the Biopsym simulator[END_REF], intraoperative ultrasound [START_REF] Allgaier | Livrsono -virtual reality training with haptics for intraoperative ultrasound[END_REF], or tissue examination [START_REF] He | Robotic simulators for tissue examination training with multimodal sensory feedback[END_REF].

HTS have been demonstrated as efficient, particularly in laparoscopic surgical training [START_REF] Hagelsteen | Faster acquisition of laparoscopic skills in virtual reality with haptic feedback and 3d vision[END_REF][START_REF] Rangarajan | Systematic review of virtual haptics in surgical simulation: A valid educational tool[END_REF]. Moreover, Sue et al. [START_REF] Siu | Expert laparoscopist performance on virtual reality simulation tasks with and without haptic features[END_REF] performed a relative evaluation of HTS vs. VR ones. Correa et al. [START_REF] Corrêa | Haptic interaction for needle insertion training in medical applications: The state-of-the-art[END_REF] also concluded that simulators coupling virtual reality and haptic feedback are the most promising ones. Nonetheless, the design of such realistic simulators remains challenging.

From Medical Need to Simulator Design

Designing a simulator to train on a medical procedure involves several steps, from identifying the medical need to validating the didactic capacity of the simulator. Moreover, it requires a multidisciplinary approach: in didactics, to produce simulators with a significant contribution to learning by identifying what to simulate and setting up relevant learning scenarios [START_REF] Vadcard | Réflexions à propos de la conception d'environnements de formation par la simulation : le cas de la formation médico-chirurgicale[END_REF]; in computer science and mechanics, to create interactive simulations with a degree of precision appropriate for learning; in robotics, to design a haptic interface adapted to the targeted gestures and restoring the sensations usually felt by physicians during these gestures; and finally clinical, to analyze and validate the various parts of the simulator [START_REF] Fiard | Validating the transfer of skills acquired on a prostate biopsy simulator: a prospective, randomized, controlled study[END_REF]. In the following, we focus on the development of the two technical parts that have to be combined to design a haptic training simulator.

Firstly, the designer has to identify the operation to simulate (Section 3.1 and Fig. 2). This requires getting scientific data to reproduce the phenomena as realistically as necessary for training purposes. Then, one has to design the numerical part (Section 3.2) which simulates the behavior of organs interacting with each other and with medical instruments. It can provide a visual rendering of reality or on the contrary, it may show to the trainee (and also sometimes to the trainer) areas that are usually hidden (Trainee HMI in Fig. 1). Moreover, this numerical part computes the force information required by the haptic device. Section 3.3 describes the design of the haptic part of an HTS (Fig. 1) that enables the trainee to manipulate the usual medical instrument(s) and reproduces the kinesthetic sensations felt during the procedure. The coupling of the two parts is detailed in Section 3.4. The design process generally requires a parallel development between the numerical and the haptic parts. As, in general, precise model parameters are not available in the scientific literature, a test-and-trial process is necessary to tune the simulator based on expert user feedback. This design process ends with the description of the validation steps (Section 3.5).

Common Identifications

To reproduce tissue behavior at a sufficient and necessary level of realism previously identified during the didactic study (Identification of Didactic Approach in Fig. 2), the designer of an HTS must identify the relevant models of the different components of the simulator: the specific trajectories and forces provided by the user on the real instruments and the specific interactions (such as tissues cutting, needle insertion, tissues deformation, etc.) which have to be rendered in the haptic and virtual components.

However, it is difficult to get direct real data to feed the numerical simulation models when it concerns medical gestures. One first approach consists of browsing the scientific and medical literature for data (forces, trajectories, (bio)mechanical behaviors). These data are often rare or not usable for the haptic part design or can provide different values for soft tissues as it is still challenging to characterize them. Therefore, it may be necessary to equip an expert during medical procedures with position/orientation sensors to record the trajectories, and force sensors inserted between their hand and the tools or between the tools and the environment. This process can include expert ones that will be used as reference in a first approach, and novice ones that can deviate much from the latter. Also, the level of precision of the simulation must be determined to obtain realistic behaviors as fast as necessary to update the visual and haptic renderings. Therefore, model simplifications must be applied to reduce computing time.

Designing the VR Part

The complexity of medical simulation makes real-time execution a challenge. It depends on the discretization of the objects into a greater or lesser number of elements or nodes on which the simulation is performed, the physical model used to represent the mechanical behavior of the object with a more or less complex constitutive law and the numerical methods employed during the simulation. Therefore, one has to play with these parameters to adjust the compromise between computation time and accuracy.

From Medical Imaging to Meshes. Various tools are now available to transform through segmentation medical images (CT Scan, MRI) into a mesh representing the objects, often first of all in surface mesh, which can then be used to create a volume mesh of the object. Some manual processing is still required to ensure the quality of the elements created. One can then simplify these meshes to reduce their number of elements while preserving their anatomical features to not induce important errors in the simulation.

Real-Time Simulation. In terms of the physical models employed, two approaches predominate in the medical context: a continuous approach aims to solve the equations of mechanics, and a discrete approach, based on a noncontinuous representation of the material, aims to calculate the motion of interacting particles. For instance, in training on the use of forceps for fetal extraction in a childbirth simulator, the difficulty is to simulate, in interactive time, the deformations undergone by the fetal head during delivery. These deformations are the result of intra-uterine pressures exerted on the skull and the potential use of forceps to extract the fetus. From a mechanical point of view, the fetal head can be seen as an incompressible deformable object with a fine structure. For this reason, the approach adopted by [START_REF] Bailet | Shell finite element model for interactive foetal head deformation during childbirth[END_REF] was to use a surface model, as it allows objects to be modeled with a smaller number of degrees of freedom than a volume model. The challenge then lies in ensuring that the surface model reproduces the complex behavior of a volumetric object, while guaranteeing the conservation of its volume despite the deformations undergone during simulation. In this context, Bailet proposed a model based on shell finite elements, which are surface finite elements derived from thin plate theory. This modeling is combined with a volume preservation method that ensures volume conservation during simulation, and an original parallelization approach that reduces numerical simulation computation time. As discrete models, the mass-spring system has been widely used in computer graphics for its ease of implementation and speed of calculation. However, the behavior reproduced by the system is topology-dependent, i.e. it depends greatly on the configuration of the connections established between the masses by the springs. Moreover, one difficulty lies in the formulation of the spring stiffness to incorporate the mechanical properties of the material (notably Young's modulus and Poisson's ratio). Hopefully, many papers manage to improve this aspect [START_REF] Delingette | Triangular springs for modeling nonlinear membranes[END_REF][START_REF] Natsupakpong | Determination of elasticity parameters in lumped element (mass-spring) models of deformable objects[END_REF][START_REF] Kot | Mass spring models with adjustable poisson's ratio[END_REF][START_REF] Golec | Hybrid 3d massspring system for simulation of isotropic materials with any poisson's ratio[END_REF]. Thanks to these advances, Ballit [START_REF] Ballit | Fast soft-tissue deformations coupled with mixed reality toward the next-generation childbirth training simulator[END_REF] et al. proposed a childbirth simulator integrating a simulation based on the Hyperelastic Mass-Spring Model (HyperMSM). Nonetheless, in the medical field, the Finite Element Model is often preferred for its accuracy. To reduce computing time, a wide range of research improved its computation time thanks to parallelization on GPU or simplifications [START_REF] Faure | SOFA: A Multi-Model Framework for Interactive Physical Simulation[END_REF][START_REF] Zeng | Real-Time FE Simulation for Large-Scale Problems Using Precondition-Based Contact Resolution and Isolated DOFs Constraints[END_REF]. Within this framework, the constitutive law plays an important role in the simulation's complexity. As the soft tissues have non-linear behaviors, the hyperelastic models (Neo-Hooke, Mooney-Rivlin, Yeoh, or St Venant Kirchhoff laws) are generally preferred in a medical simulator as they permit obtaining adequate precision while being simple.

Appropriate Visualization. Depending on the simulator developed, the simulated objects' visualization can vary. For example, the training simulator proposed by HelpMeSee [START_REF] Broyles | Cataract blindness and simulation-based training for cataract surgeons: An assessment of the helpmesee approach[END_REF] offers a realistic view of the eyes comparable to that seen during cataract surgery. In rheumathology, practitioners guide their gestures by observing on-screen the restitution of the ultrasound probe placed on the patient. To be consistent to this practice, the needle insertion simulator proposed by Barnouin et al. [START_REF] Barnouin | A real-time ultrasound rendering with modelbased tissue deformation for needle insertion[END_REF][START_REF] Alamilla | A Virtual Reality and haptic simulator for ultrasound-guided needle insertion[END_REF] offers a real-time ultrasound rendering showing tissue deformation during needle insertion depending on the probe's orientation.

Simulation Validation. The validation process is complex. For instance, how to validate a childbirth simulation without a dynamic MRI or the possibility of putting sensors on a fetal head during its extraction thanks to forceps? A first approach is to rely on medical knowledge of behavior. And the ideal would to rely on other simulations established as "gold standards" to be achieved. These simulations are based on the most accurate modeling possible of the target organs, and a robust resolution method. But these standards necessarily include precision errors, as they are themselves simulations based on medical images produced at a certain resolution, and they are also based on measurements taken on soft tissues, with an error due to experimentation, and so on. Therefore, it is necessary to quantify the error produced throughout the processing chain, to provide the final error of the simulation and make compromises accordingly.

Designing the Haptic part

The haptic part has the responsibility to render a kinesthetic feedback of the simulated gesture. In some rare case, it works in admittance mode: the user ex-erts forces on the haptic device that is controls its position. This was notably the case with the BirthSim [START_REF] Herzig | A new design for the birthsim simulator to improve realism[END_REF][START_REF] Herzig | Stiffness control of pneumatic actuators to simulate human tissues behavior on medical haptic simulators[END_REF][START_REF] Herzig | Nonlinear position and stiffness backstepping controller for a two degrees of freedom pneumatic robot[END_REF] forceps simulator. However, most of the commercial haptic devices work in impedance mode: the trainee positions the end-effector of the haptic device and the latter exerts forces on the trainee's hand to render interaction forces computed by the numerical part. The haptic part features sensors to detect the user inputs (position in impedance mode, interaction forces in admittance mode), the actuators to provide haptic feedback (in general, electric motors, but it can also be pneumatic actuators as in [START_REF] Talhan | Pneumatic actuation in haptic-enabled medical simulators: A review[END_REF]) and a controller to perform the force/motion control synchronized with the numerical part (see Fig. 1). In some cases, they also feature passive parts that are static objects that help trainees get immersed into the simulation (a crane for ventricular puncture, a back for epidural anesthesia, ...). These parts are also refereed as tangible simulation objects as in [START_REF] Costello | A review of simulation training and new 3d computer-generated synthetic organs for robotic surgery education[END_REF].

Dimensioning and Haptic Device Selection. Considering the preliminary identified gestures and phenomena to render that require generating force feedback, one needs to determine the required mechanical characteristics of the haptic device: the number of (actuated or free) Degrees of Freedom (DOFF), its workspace, and the maximum available force. The range of stiffness is also an important parameter: from fat to bones, the range is large and is an important variable for the haptic device dimensioning. In a proof-of-concept approach, a general-purpose haptic device is preferred. In general, they are over-sized but their use then helps refine the technical requirements and design a specific optimized haptic device in a second phase. Commercial haptic devices such as Delta.6 (Force Dimension), Virtuose (Haption), Touch (Geomagic), Falcon (Novint Technologies Inc.), etc., may be used according to the requirements. In this case, to provide a better immersion, the trainees should feel like they are handling the real tool. Using general purpose haptic devices, it is sometimes possible to remove the handle and adapt a fake tool, like an epidural needle in [START_REF] Sénac | Designing an accurate and customizable epidural anesthesia haptic simulator[END_REF] (see Fig. 3 that also illustrates some specific designed haptic device with the pneumatic cylinder emulating a syringe).

Yet, in some cases, no existing haptic device fitting all the requirements is available. For instance, Khedar et al. [START_REF] Kheddar | Preliminary design of a childbirth simulator haptic feedback[END_REF] concluded in 2004 that using a commercial haptic device for a childbirth simulator is not adequate, and that it is clearly necessary to develop a dedicated interface. A sample of specifically designed haptic device can be found in [START_REF] Hoshyarmanesh | Structural design of a microsurgery-specific haptic device: neuroarmplushd prototype[END_REF] concerning microsurgery.

Haptic Behavior Rendering. Once the haptic device chosen or designed, one has to determine which algorithm is adequate and its parameters. Concerning the execution of these algorithms, in general, each haptic device is associated with an SDK to program the haptic behavior (for instance, for the Touch and Phantom Premium (Geomagic), OpenHaptics by 3D Systems). These software packages permit to render standard haptic behaviors (hard or soft contact, friction, etc.). One has then to connect these functions to the numerical part to render force feedback, without having to program the low-level automatic con- trol of the actuators of the haptic device. For specific devices, automatic control is necessary to render force, position and/or stiffness control, such as in [START_REF] Sénac | Simulating a syringe behavior using a pneumatic cylinder haptic interface[END_REF].

Transient Haptic Rendering. The force feedback provided by the haptic device is rarely static as human tissues are composed of soft materials, which usually are anisotropic and inhomogeneous, and exhibit highly non-linear viscoelastic behaviors when they are subject to high strains [START_REF] Misra | Modeling of tool-tissue interactions for computer-based surgical simulation: A literature review[END_REF]. In some cases, like in needle insertion, there exists models indicating the behavior of the needletissue interaction which permit to determine the evolution of the force feedback in time and in the space [START_REF] Delbos | Review on needle insertion haptic simulation[END_REF]. Providing a realistic force feedback requires refining the transitions between different haptic behavior areas, more particularly when they chain themselves in time or in the space. For instance, still in the context of epidural needle insertion, the realistic simulation of the crossing of seven layers of tissues required to provide a model of their stacking. Some pseudo-tactile sensations can also be necessary to be reproduced by the haptic device such as vibrations [START_REF] Sénac | Designing an accurate and customizable epidural anesthesia haptic simulator[END_REF].

Coupling the VR+Haptics

The challenge of developing an HTS is to combine the numerical part embedding the simulation that reproduces realistic organ behavior in interactive time, with a haptic device providing kinesthetic perception, while ensuring the whole's stability. A first difficulty is linked to the necessary refresh rate of haptic devices (minimum 1 kHz) to enable feeling hard contacts, while medical simulations struggle to run as fast. An interface between these two-pace software programs is then necessary. A second difficulty is linked to the sampled nature of haptic control in the presence of hard contacts. At the frontier of the material, the virtual position of the tool oscillates between two positions inside and outside, which generates undesired vibrations. The coupling between haptic interfaces and numerical simulations is then usually performed using a virtual elastic coupling, named method of "god object" introduced by Salisbury et al. in [START_REF] Salisbury | Haptic rendering: introductory concepts[END_REF]. This method has been enhanced later in [START_REF] Vlachos | Using force control for fidelity in low-force medical haptic simulators[END_REF] for low-force applications and in [START_REF] Ortega | A six degree-of-freedom god-object method for haptic display of rigid bodies with surface properties[END_REF] for rigid objects.

Validating the Simulator

The scientific barrier inherent in medical simulator concerns the validation phase: firstly, each part of the simulator must be approved for its behavior; secondly, its suitability for medical training must also be confirmed. Thus, scientific validation of the learning is essential for the use of a simulator in the care of healthcare students and for the further training of healthcare professionals. To this end, Donald Kirkpatrick's model [START_REF] Kirkpatrick | Evaluating training programs : the four levels[END_REF] has been for example recommended by the French National Authority for Health. The validation is decomposed in four steps: (1) reactions -to focus on learner satisfaction after a session on the simulator about the objectives, content, and equipment; (2) knowledge/skillsto check the objectives' achievement in terms of knowledge and skills; (3) behaviors -to analyze the behavioral changes in the professional practice due to acquired skills and abilities; (4) results -to look at the simulation impact on patient management. This assessment can be based on questionnaires.

Discussion

The process depicted here is elaborated on the experience of around ten years of designing various medical HTS. This empirical process is a simple testimony of what has worked, to help in the design of new ones and converge more rapidly with tested solutions. As aforementioned, it is difficult to evaluate the quality of the numerical simulation and the forces felt using haptic devices when it concerns the simulation of a medical gesture. Without objective data available in the scientific literature, one has to use subjective validation provided by a group of experts through tests and trial attempts or acquire medical data. Yet, acquiring data on patients is a very complex task as it necessitates conforming to ethical standards and must not disturb the staff during a medical gesture. Moreover, it is mandatory to test the didactic efficiency of the simulator on a sufficiently large panel of trainees, before its real use. Hence, the skills acquired on simulators must be fully transferable to a real patient.

The interest of a formalized design procedure is to progressively enhance haptic simulations. Emphasizing the difficulties and the critical parameters limits the risk of delays and unplanned costs. This proposal has been thought to be as generic as possible. As it is a first (as far as we know) attempt to model the building of such simulators, enhancement ought to be brought in. For instance, the Augmented Reality (AR), tactile, and acoustic feedback dimensions have not been taken into account. Also, the interactions in dual-user simulations [START_REF] Licona | Collaborative hands-on training on haptic simulators[END_REF] have not been evoked in this paper.

Patients are unique. So, training simulators can only train in generic cases. One challenge of developing such HTS for learning medical gestures concerns the creation of patient-specific simulations. Embedding parameters to enlarge the set of available situations, validated by experts, brings much interest to this kind of hands-on training. Furthermore, if the simulator can tune itself starting from new medical images (MRI, ultrasound) in a human-acceptable time (a few minutes ?), it opens the way to patient-specific simulation and the opportunity to train oneself on the simulator before any operation. Such simulators will enable training, for example, in the resection of a hard-to-reach tumor, to check the feasibility of a vaginal delivery, or to measure the damage to the tissues and ligaments of a parturient woman's pelvic floor following a natural delivery.

The scientific hurdles to overcome are then how to achieve interactive simulation time with models generated on the fly from raw medical image data. Today, using patient-specific data (medical images, tissue elasticity parameters, volume of breath measured by a spirometer, etc.), one has to rapidly build a geometric model of the organs involved in the medical procedure, and to develop a physical model integrating the measured mechanical parameters in order to produce an accurate simulation of the targeted medical procedure for the simulator's numerical part. The accuracy of organ behavior thus becomes a major constraint, which could be slightly relaxed for learning simulators. Making it automatic requires to efficiently segment the images, recognize the organs, and apply corresponding biomechanical models. Nonetheless, a fixed image does not bring sufficient information to guess the model parameters that fit the patient tissues. Ideally, some dynamic imaging input would be better. Nonetheless, this requires to evaluate the ability of the simulator to adapt itself to cases that are unknown in advance. It will require a design based on a training set of data and a validation on a test population as for AI validations, knowing that the dimension of each should be at the scale of thousands cases.

Conclusion

The development of medical training simulators based on virtual reality and haptic techniques aims to improve medical hands-on training. The objective is to enable trainees to acquire the dexterity required for medical gestures by following several exercises in line with the learning process without any risk to the patient. As evoked in this paper, their development requires the designing and programming of (sometimes custom) haptic devices to reproduce kinesthetic sensations and enable interaction with a numerical simulation reproducing the behavior of organs during medical procedures. Even if works bring generic approaches such as needle-insertion haptic simulation, it remains difficult to transpose the results obtained with one simulator to another one for different medical procedures. This is why this paper introduced a empirical design process detailing the haptic and numerical parts, and their coupling, based on more than one decade of design of such simulators. Currently, haptic training simulation evolution leads to mixed simulation integrating tangible objects to manipulate or palpate and RV+haptics. Next generation training simulators should enable patient-specific training, based on specific patient medical imaging inputs.

Fig. 2 .

 2 Fig. 2. Haptic Training Simulator Design Process.

Fig. 3 .

 3 Fig. 3. Adapting a fake needle to a general-purpose haptic device (Haption Virtuose 6D). The coupled Loss-of-Resistance syringe is emulated by a pneumatic cylinder.


; GROSSEAU, P. (1, 2) ; AUDUBERT, F. (3) ; GUILHOT, B. (4, 2) ; BEAUVY, M. (3) ; IACCONI, P. (5) ; BENABDESSELAM, M. (5) (

Abstract

The concept of the fuel for the IV th generation reactors should consist of fuel pellets surrounded with a matrix that must contain fission products. Thanks to their interesting thermo-mechanical properties, carbides are sensed to become this matrix. Among the studied carbides, Ti 3 SiC 2 can be distinguished; actually, its nano-laminated structure confers to it some softness as well as a better toughness than classical carbides like SiC or TiC. However, before to use this remarkable carbide, a study of its behaviour under irradiation must be led. Thus, some characterisations were performed on 75 MeV Kr irradiated specimens. They allowed to underline that TiO 2 (formed on the surface of Ti 3 SiC 2 during the surface preparation) seems to be sputtered by irradiation, and that the unit cell of Ti 3 SiC 2 is dilated along c axis. K Ke ey yw wo or rd ds s: : Ti 3 SiC 2 ; irradiation ; heavy ions ; krypton ; Scanning Electron Microscopy ; Atomic Force Microscopy ; Low-Incidence X-Ray Diffraction

I Introduction:

Within the framework of Generation IV International Forum, new nuclear power plants are studied, as well from the reactor point of view as from the fuel cycle one. They are characterised by an increased security level, a better economic competitiveness, and an ability to recycle all the fuel in order to upgrade fissionable material, and to minimize the long-lived wastes production by the transmutation process. Among the six systems considered, the Gas Fast Reactor (GFR) is studied in France; it is designed for an under helium-pressure, and high-temperature nominal working. The concept of the fuel for this kind of reactor consists of fuel pellets surrounded with a matrix that must contain the fission products. Taking into account the working conditions of the GFR, carbides are sensed to become this matrix; actually, they have remarkable thermomechanical properties, and are neutrons transparent (contrary to metals). However, their behaviour under irradiation is little known nowadays. Ternary Ti 3 SiC 2 seems to get away from other studied carbides. Actually, in 1972 Nickl et al. [START_REF] Nickl | Gasphasenabscheidung im Systeme Ti-C-Si[END_REF] noted that this material, which was synthesised for the first time in 1967 [START_REF] Jeitschko | Die Kristallstruktur von Ti 3 SiC 2 -ein neuer Komplexcarbid-Typ[END_REF], is abnormally soft for a carbide. At the beginning of the 90's, Pampuch, Lis and co-workers [START_REF] Pampuch | Solid Combustion Synthesis of Ti 3 SiC 2[END_REF][START_REF] Lis | Reactions during SHS in a Ti-Si-C system[END_REF][START_REF] Pampuch | Ti 3 SiC 2 -based materials produced by self-propagating high temperature synthesis and ceramic processing[END_REF][START_REF] Lis | New ceramics based on Ti 3 SiC 2[END_REF][START_REF] Lis | Tanihata: Ti 3 SiC 2 -Based Materials Prepared by HIP-SHS Techniques[END_REF][START_REF] Morgiel | Microstructure of Ti 3 SiC 2 -based ceramics[END_REF] led works on synthesis of pure bulk Ti 3 SiC 2 . Their best samples were 80-90 % pure, the residue being TiC. During their works, they showed that Ti 3 SiC 2 is elastically quite stiff (Young's modulus of Proceedings of the 10 th International Conference of the European Ceramic Society, Berlin, 17 au 21 juin 2007, ISBN=3-87264-022-4 2 325 GPa) and confirmed its softness (Vickers hardness of 6 GPa). So they labelled Ti 3 SiC 2 as a "ductile ceramic".

At the end of the 90's, Barsoum et al. understood that Ti 3 SiC 2 forms part of a family of ternary layered compounds with the general formula: M n+1 AX n , where n is 1, 2 or 3, M is an early transition metal, A is an A-group element, and X is C and/or N [START_REF] Barsoum | The M N+1 AX N Phases: A New Class of Solids; Thermodynamically Stable Nanolaminates[END_REF][START_REF] Barsoum | The MAX phases: Unique new carbide and nitride materials -Ternary ceramics turn out to be surprisingly soft and machinable, yet also heat-tolerant, strong and lightweight[END_REF]. Compounds of this family are all elastically stiff, thermally and electrically conductive, readily machinable, relatively soft, thermal shock resistant and unusually damage tolerant. More specifically, pure Ti 3 SiC 2 seems to be stable to at least 1,700 °C in inert atmospheres [START_REF] Barsoum | Synthesis and characterization of a remarkable ceramic: Ti 3 SiC 2[END_REF][START_REF] Barsoum | A progress report on Ti 3 SiC 2 , Ti 3 GeC 2 , and the Hphases, M 2 BX[END_REF], and can be quenched from 1,200 °C to room temperature and remained intact [START_REF] Barsoum | The MAX phases: Unique new carbide and nitride materials -Ternary ceramics turn out to be surprisingly soft and machinable, yet also heat-tolerant, strong and lightweight[END_REF]. Some others properties of Ti 3 SiC 2 are gathered in table 1.

T Ta ab bl le

W m -1 K -1 [15] Heat capacity 110 J mol -1 K -1 [15] Thermal expansion 9.2x10 -6 K -1 [15, 16]
Therefore, the aim of this study is to better grasp the behaviour under irradiation of Ti 3 SiC 2 , of which the mechanical properties offer a real alternative to brittle carbides.

II Experimental:

I II I 1 1 S
Sa am mp pl le es s p pr re ep pa ar ra at ti io on n First, samples are polished in order to obtain a smooth surface. Then, they are annealed at 800 °C for 4 hours under argon atmosphere in order to release internal stresses due to polishing. Eventually, specimens are irradiated with heavy ions in order to simulate the impacts of fission products, of recoil atoms of alpha decays, and to a lesser extend of neutrons. In first approximation, we can consider that the stresses observed are only due to irradiation. I II I 2 2 S Sp pe ec ci im me en ns s a an nd d i ir rr ra ad di ia at ti io on ns s Samples were obtained by pressure sintering of Ti 3 SiC 2 powder. This material is rarely pure: indeed synthesis of Ti 3 SiC 2 implies a non-negligible proportion of powder that is not transformed. Thus, our samples are made of about 75 % of Ti 3 SiC 2 , 20 % of TiC and 5 % of TiSi 2 .

Specimens were irradiated with 86 Kr ions at "Grand Accélérateur National d'Ions Lourds" (GANIL) Caen, France.

The energy of ions was of 75 MeV, and the average flux of 9x10 9 cm -2 s -1 . Two parameters varied for irradiations: dose and temperature. Thus, three different irradiations were performed; table 2 SRIM software allows to evaluate some parameters relative to this irradiation. Thus, the projected range is 7.9 µm, the electronic stopping power is 1.6x10 4 keV µm -1 , and the nuclear stopping power is 66 keV µm -1 . I II I 3 3 C Ch ha ar ra ac ct te er ri iz za at ti io on n t te ec ch hn ni iq qu ue es s In order to understand the noticed phenomenon, the characterisations of the samples are compared with the ones performed on a control sample; it is prepared in the same conditions, and no irradiated. The surface of the materials was observed through Scanning Electron Microscopy (SEM) and Atomic Force Microscopy (AFM). SEM is a Jeol JSM 6400 used with an acceleration voltage of 15 kV and with a secondary electrons detector. AFM is a Nanoscope III A used in contact mode with a 0.12 N m -1 stiffness-constant probe made in silicon nitride. The structure in the irradiated area of Ti 3 SiC 2 was analysed by Low-Incidence X-Ray Diffractometry (LI-XRD). The diffractometer is a Siemens D5000 with a copper anticathode.

III RESULTS and DISCUSSION

During the post-polishing annealing, a white layer has formed on the surface of our samples; this layer could be due to oxidation of Ti 3 SiC 2 . Actually, this material is easily oxidable and it is likely that an oxide would be forming despite argon atmosphere. Moreover, according to literature [START_REF] Gao | On physical and thermochemical properties of high-purity Ti 3 SiC 2[END_REF], oxidation of Ti 3 SiC 2 is beginning by a TiO 2 layer formation before the formation of a TiO 2 +SiO 2 layer at the Ti 3 SiC 2 /TiO 2 interface; so, the white colour of the surface can lead to suppose the TiO 2 presence. Therefore, materials were irradiated in the presence of an oxide layer on their surface. Thereof, characterisation of irradiation damages will have to take into account this oxide presence. I II II I 1 1 S Sc ca an nn ni in ng g E El le ec ct tr ro on n M Mi ic cr ro os sc co op py y The images obtained by SEM for the four samples are gathered in figure 1. We can notice the control sample is made of relieves on a smooth surface. EDX analysis allowed to detect oxygen presence on the whole surface of the sample, as well on the smooth area as on relieves; this confirms the oxide presence. Irradiation of the surface of Ti 3 SiC 2 wasn't null and void. Actually, the higher the dose, the lower the relief; oxide seems to be sputtered by a room temperature irradiation. On the other hand, the high temperature irradiation led to a different behaviour: relieves stay intact whereas the smooth area seems to be damaged. So, oxide would stand up more to a high temperature irradiation than to a room temperature one. Secondly, this microscopy allows to evaluate the roughness of the specimens thanks to a calibration of the height (z axis). Thus, roughness is estimated by the R a parameter, defined by the ISO 4287 norm:

( ) 0 1 . a R z x dx = ∫ ( 1
)
where ℓ is the length on which z(x) is measured. The table 3 presents the average roughness of each sample. Lo ow w--I In nc ci id de en nc ce e X X--R Ra ay y D Di if ff fr ra ac ct ti io on n First LI-XRD should allow to resolve the doubt about the nature of the white layer formed after annealing. Second it should allow to characterise the structural changes in the irradiated area. Figure 3 presents the diffractograms performed at 1° and 3° incidence angles. The penetration depth of X-rays in Ti 3 SiC 2 is estimated at 230 nm for α = 1°, and at 720 nm for α = 3°; as the projected range is of 7.9 µm, the analysed zone for both angles is a damaged zone. The first remark is about the oxide: it's TiO 2 , in its rutile form, which was formed on the specimens before irradiation. Then, we can notice the sputtering of the oxide layer at room temperature: this one is wearing off with the dose increase, like observed with microscopies. We can conclude that the formed rutile doesn't stand up at this irradiation, especially for high doses. Behaviour under irradiation of our sample at 500 °C is also interesting. Microscopies showed a no-sputtered oxide layer. LI-XRD on the one hand confirms this observation, on the other hand gives information about this oxide composition: it isn't only composed of rutile. Actually, anatase, the low temperature stable phase of TiO 2 , is also present. Anatase to rutile transformation occurs at about 600-700 °C but the rutile to anatase transformation is not spontaneous. So, temperature doesn't seem to be the reason of anatase formation. There isn't a lot of paper about the behaviour of TiO 2 under irradiation. Furthermore, the anatase to rutile transition is more often observed: after having irradiated then annealed some anatase specimens, Sumita et al. then Nakao et al. [START_REF] Sumita | Ion-beam modification of TiO 2 film to multilayered photocatalyst[END_REF][START_REF] Nakao | High-energy metal ion implantation into titanium dioxide films[END_REF] noticed a rutile formation. This would be due to the formation of Ti 3+ and Ti 2+ in anatase lattice; the unstable state of Ti 3+ and/or Ti 2+ would probably act as "seeds" for rutile in anatase, and so would lower the crystallisation temperature of rutile to anatase. However, a paper mentions a rutile to anatase transformation after an ions irradiation [START_REF] Fukushima | N+ ion implantation effects on microhardness and adhesion in TiO 2 films[END_REF]; this phenomenon would be explained by a partial relaxation of the internal stress and strain caused by collision events with implanted atoms. But these irradiations were performed at room temperature, and our result is only for the high temperature irradiation. Another track comes from Dalmasso works about Al 2 O 3 , MgO and MgAl 2 O 4 oxides [START_REF] Dalmasso | Caractérisation des défauts ponctuels induits par l'irradiation des les céramiques : Exemple des oxydes alph-Al 2 O 3[END_REF][START_REF] Beauvy | Damages in ceramics for nuclear waste transmutation by irradiation with swift heavy ions[END_REF]. Actually, these materials were irradiated almost at the same experimental conditions, and it results that a partial amorphisation was remarked. Moreover, Kim et al. [START_REF] Kim | Influence of Ar ion-beam assistance and annealing temperatures on properties of TiO 2 thin films deposited by reactive DC magnetron sputtering[END_REF] noted an amorphous to anatase phase transition due to an ion beam. Actually, they made TiO 2 amorphous thin films by a reactive DC magnetron sputtering method, with and without Argon ion-beam assistance. Then, after annealing at 400 °C, they noticed that anatase is formed only for films deposited with ion-beam assistance, others staying amorphous. Therefore, our hypothesis is that irradiation may have caused a rutile to amorphous phase transformation. Then, either the high temperature or the internal stress and strain caused by collision events or both have allowed an amorphous to anatase transformation. Anyway, according to microscopies, it seems that either the temperature avoids the TiO 2 sputtering or anatase protects rutile against sputtering. A last remark is about the 2θ = 40.9° line of Ti 3 SiC 2 . Indeed, this one, which characterises the diffraction of the 008-plan, is highly shifted as a function of irradiation parameters. This shift is due to a lattice parameter change. Thus, we can notice that the c parameter is highly changing. This can be explain by the fact that Ti 3 SiC 2 has a hexagonal structure, and so a strong sensibility along the c axis. Thus, we can assume that the insertion of krypton atoms (and perhaps oxygen atoms from TiO 2 ) in this material is preferentially carried out along this axis. Eventually, we can notice that the higher the temperature, the smaller the change in c parameter. A diffusion of inserted atoms or an annealing of the defects can explain this phenomenon. But these hypotheses are to be confirmed.

T Ta ab bl le e 3 3: : A Av ve er ra ag ge e r ro ou ug gh hn ne es ss s m me ea as su ur re ed d b by y A AF FM M

IV Conclusion:

This study about the irradiation damages in Ti 3 SiC 2 is beginning and characterisations are mostly about the TiO 2 oxide that had been formed after an annealing of the samples. However, these first results are interesting. First of all, rutile seems not to stand up to a 75 MeV Kr room temperature irradiation; it is indeed sputtered by the ion beam. On the other hand, a 500 °C irradiation would allow the formation of anatase. This irradiation led to a no-sputtered oxide; this phenomenon is due to either the temperature or anatase that would protect oxide layer. Eventually, about Ti 3 SiC 2 , its unit cell is dilating along the c axis, certainly because of insertion of krypton, verily oxygen, atoms, and of the moving of atoms in the damaged zone.

4 4

 4 Proceedings of the 10 th International Conference of the European Ceramic Society, Berlin, 17 au 21 juin 2007, ISBN=3-87264-022im ma ag ge es s, , x x2 20 00 00 0 m ma ag gn ni if fi ic ca at ti io on n: : ( (a a) ) c co on nt tr ro ol l s sa am mp pl le e, ro oo om m t te em mp pe er ra at tu ur re e i ir rr ra ad di ia at ti io on n, , ro oo om m t te em mp pe er ra at tu ur re e i ir rr ra ad di ia at ti io on n, C i ir rr ra ad di ia at ti io on n I II II I 2 2 A At to om mi ic c F Fo or rc ce e M Mi ic cr ro os sc co op py y Firstly, AFM (cf. figure2) allows to confirm the observations made by SEM regarding the behaviour of the oxide under irradiation.

F

  Fi ig gu ur re e 2 2: : A AF FM M i im ma ag ge es s, , s sc ca an n o of f ) ) c co on nt tr ro ol l s sa am mp pl le e, an nd d r ro oo om m t te em mp pe er ra at tu ur re e i ir rr ra ad di ia at ti io on n, , ( an nd d r ro oo om m t te em mp pe er ra at tu ur re e i ir rr ra ad di ia at ti io on n, , ( C i ir rr ra ad di ia at ti io on n

3 F

 3 Fi ig gu ur re e 3 3: : D Di if ff fr ra ac ct to og gr ra am ms s

  1) Département PMCC, Centre SPIN, Ecole Nationale Supérieure des Mines de Saint-Etienne, 158 Cours Fauriel 42023 Saint-Etienne, France (2) LPMG UMR 5148, 158 Cours Fauriel 42023 Saint-Etienne, France (3) Commissariat à l'Énergie Atomique de Cadarache, St Paul lez Durance, France (4) École Nationale Supérieure des Mines, Centre CIS, Saint-Étienne, France (5) Université de Nice -Sophia Antipolis, Laboratoire LPES-CRESA, Nice, France "Paper presented at the 10 th International International Conference of the European Ceramic Society, Berlin, 17 au 21 juin 2007"

  recapitulates these parameters.

	Proceedings of the 10 th International Conference of the European Ceramic Society, Berlin, 17 au 21
	juin 2007, ISBN=3-87264-022-4
	T Ta ab bl le e 2 2: : I Ir rr ra ad di ia at ti io on n p pa ar ra am me et te er rs s o of f s sp pe ec ci im me en ns s
	Temperature of irradiation /°C Dose /cm -2
	25	10 14
	25	10 15
	500	10 15
		3

  Proceedings of the 10 th International Conference of the European Ceramic Society, Berlin, 17 au 21 juin 2007, ISBN=3-87264-022-4 5 decrease of the roughness even though the surface state is slightly different than the control sample one.

	I II II I 3 3 L
	Temperature of	Dose /cm -2 Roughness: R a /nm
	irradiation /°C
	Control sample		360
	25	10 14	310
	25	10 15	130
	500	10 15	360
	These measures quantitatively confirm the changes noticed by the microscopies. Thus, at

room temperature the higher the dose, the lower the roughness; relieves are sputtered up to obtain an almost smooth surface. On the other hand, an irradiation at 500 °C doesn't lead to a

  Table4presents an assessment of the Ti 3 SiC 2 lattice parameter for each specimen and each incidence angle.

	T Ta ab bl le e 4 4: : L La at tt ti ic ce e p pa ar ra am me et te er rs s o of f T Ti i 3 3S Si iC C 2 2 a as s a a f fu un nc ct ti io on n o of f i ir rr ra ad di ia at ti io on n p pa ar ra am me et te er rs s
	Incidence	Dose /cm -2 Irradiation	Lattice
	angle		temperature /°C	a /Å	c /Å
	1°	Control sample	3.065	17.65
		10 14	25	3.065	17.68
		10 15	25	3.058	17.89
		10 15	500	3.061	17.76
	3°	Control sample	3.065	17.66
		10 14	25	3.065	17.71
		10 15	25	3.061	17.89
		10 15	500	3.064 17.78

Proceedings of the 10 th International Conference of the European Ceramic Society, Berlin, 17 au 21 juin 2007, ISBN=3-87264-022-4

Acknowledgment

The authors would like to gratefully acknowledge Isabelle Monnet for her great help for the irradiation of the specimens.