Naouress Fatfouta
email: naouress.fatfouta@centralesupelec.fr

Julie Stal Le-Cardinal

An ontology-based knowledge management approach supporting simulation-aided design for car crash simulation in the development phase

Keywords: knowledge management, ontology, knowledge model, knowledge retrieval, collaboration, engineering design, crash simulation

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

Introduction

Design involves people with the appropriate expertise undertaking a process to develop a product. This activity takes place within a specific organisation that provides the necessary infrastructure and resources [START_REF] Wallace | Engineering knowledge management[END_REF]. Moreover, design tasks in all industries, including the automotive industry, are now more complex, with increasing timescales and geographically distributed teams [START_REF] Mcmahon | Knowledge management in engineering design: personalization and codification[END_REF]. This research focuses on the development phase of the vehicle design process. At the end of the development phase, the vehicle model is guaranteed to be at the right level of performance and the right manufacturing cost. Development is based both on modelling and simulation, and decision-making is mainly based on simulation. We are, therefore, in the context of simulation-aided design. This research focuses on improving the vehicle design process by mainly reducing time while producing more robust vehicles. The objective is, therefore, to support simulation-aided design. We focus on car crash simulation as it is an essential step in vehicle development [START_REF] Yadav | Investigations into Dynamic Response of Automobile Components during Crash Simulation[END_REF]. Car safety is a crucial factor for car manufacturers since road accidents were the ninth leading cause of disease in the world in 2016 [START_REF] Ritchie | Causes of Death[END_REF] and are expected to be the third by 2020 [START_REF] Patane | Evaluation of Tools & Techniques used for Frontal Crash Analysis[END_REF]. The car crash simulation is expensive, time-consuming and requires considerable effort.

Engineering design process is a knowledge-intensive and collaborative task [START_REF] Wallace | Engineering knowledge management[END_REF], [START_REF] Zha | Knowledge-intensive collaborative design modeling and support: Part I: Review, distributed models and framework[END_REF], [START_REF] Chen | Enabling collaborative product design through distributed engineering knowledge management[END_REF]. It requires multiple designers and experts to conduct multiple tasks involving different areas of knowledge and expertise [START_REF] Sun | Knowledge-intensive support for product design with an ontology-based approach[END_REF]. Cooperative communication among teams is complicated [START_REF] Chen | Enabling collaborative product design through distributed engineering knowledge management[END_REF]. Collaborative engineering design is evolving towards a problemsolving task [START_REF] Chen | Enabling collaborative product design through distributed engineering knowledge management[END_REF] that embodies a significant level of complexity; more than that which is required for a single engineer to work on such problems [START_REF] Zha | Knowledge-intensive collaborative design modeling and support: Part I: Review, distributed models and framework[END_REF]. Engineering design is heavily informational [START_REF] Peng | A collaborative system for capturing and reusing in-context design knowledge with an integrated representation model[END_REF], given that engineering designers spend considerable time locating information in human and nonhuman sources [START_REF] Wallace | Engineering knowledge management[END_REF], [START_REF] Sun | Knowledge-intensive support for product design with an ontology-based approach[END_REF], [START_REF] Peng | A collaborative system for capturing and reusing in-context design knowledge with an integrated representation model[END_REF]; they engage 55.75% of their time in informational behaviour, such as processing, communicating and disseminating information [START_REF] Robinson | An empirical analysis of engineers' information behaviors[END_REF]. They spend less time locating the source when it is a human source than when it is a non-human source, and so it is more efficient to use people as sources of information [START_REF] Robinson | An empirical analysis of engineers' information behaviors[END_REF]. However, due to the current transient nature of modern industrial organisations, experienced designers and experts are not going to be available to consult in the future [START_REF] Wallace | Engineering knowledge management[END_REF]; companies suffer significant setbacks from staff loss, such as the deterioration of their relationships with customers or suppliers and the loss of revenue [START_REF] Alavi | Review: Knowledge Management and Knowledge Management Systems: Conceptual Foundations and Research Issues[END_REF].

The multidisciplinary, highly collaborative and contextual nature of engineering design has raised the need to support integrated and collaborative product development [START_REF] Peng | A collaborative system for capturing and reusing in-context design knowledge with an integrated representation model[END_REF]. Successful collaborative engineering design depends on the ability to manage and share engineering knowledge [START_REF] Chen | Enabling collaborative product design through distributed engineering knowledge management[END_REF]. Therefore, nowadays, knowledge management plays a crucial role in the global economy and it is important for the competitiveness of companies [START_REF] Barão | A knowledge management approach to capture organizational learning networks[END_REF]; knowledge management is recognised in both academic and industrial studies [START_REF] Mcmahon | Knowledge management in engineering design: personalization and codification[END_REF].

In this paper, we propose an ontology-based approach for integrated and collaborative knowledge management. Specifically, we develop a knowledge management system to support simulation-aided design with an application to car crash simulation. Current research focuses on either codification or personalisation of knowledge [START_REF] Peng | A collaborative system for capturing and reusing in-context design knowledge with an integrated representation model[END_REF]. However, an integrated approach combines both the codification of knowledge objects and the transfer of contextual and tacit knowledge via communication. Collaboration also facilitates the sharing of knowledge between different actors. In this paper, the KM support system is based on an integrated knowledge model, an ontology, which captures formal, contextual and problem-solving knowledge. Knowledge retrieval models mimic the reasoning of simulation analysts and experts. This paper is organised as follows. Section 2 presents a literature review on knowledge management in engineering design. Section 3 presents the industrial context describing car crash simulation in vehicle development. Section 4 explains the ontology-based approach to knowledge management and details the knowledge management support system by explaining its activities, blocks and sub-blocks. We propose an evaluation of the knowledge management support system using three use case scenarios that will be detailed in Section 5. A brief discussion is presented in Section 6 and conclusions are outlined in Section 7.

Literature review: knowledge management in engineering design

There are multiple definitions of knowledge management (KM) in literature [START_REF] Kanapeckiene | Integrated knowledge management model and system for construction projects[END_REF], [START_REF] Girard | Defining knowledge management : Toward an applied compendium[END_REF]. However, it is usually defined by its relationship with knowledge. Therefore, we start by defining knowledge.

Many ways of defining knowledge exist in literature. Knowledge is usually defined using a value chain or hierarchical relationship with data and information [START_REF] Mcmahon | Knowledge management in engineering design: personalization and codification[END_REF], [START_REF] Sun | Knowledge-intensive support for product design with an ontology-based approach[END_REF], [START_REF] Peng | A collaborative system for capturing and reusing in-context design knowledge with an integrated representation model[END_REF], [START_REF] Shin | From knowledge theory to management practice: Towards an integrated approach[END_REF]- [START_REF] Heisig | Harmonisation of knowledge management-comparing 160 KM frameworks around the globe[END_REF]: where (1) data is in the form of symbols and words, (2) information is structured data that forms a pattern, finally (3) knowledge is processed information, facts and rules of thumb acquired through experience. Knowledge is difficult to assimilate and has a personal aspect that demonstrates the crucial difference between knowledge and information, a "notion of competence" and not a tangible object [START_REF] Peng | A collaborative system for capturing and reusing in-context design knowledge with an integrated representation model[END_REF]. Knowledge can refer, from different perspectives, to an object, a cognitive state or a capability and it may reside in individuals, social groups, documents, processes, or computer applications and databases [START_REF] Alavi | Review: Knowledge Management and Knowledge Management Systems: Conceptual Foundations and Research Issues[END_REF]. Knowledge can also refer to a state of knowing, the "know-about", a capacity for action, the "know-how", and finally to articulated and captured facts, methods and so on, the "body of knowledge" [START_REF] Apurva | Understanding Knowledge Management: a literature review[END_REF]. Another frequent dichotomy of knowledge is based on its stage of accessibility: explicit, implicit and tacit [START_REF] Mcmahon | Knowledge management in engineering design: personalization and codification[END_REF], [START_REF] Sun | Knowledge-intensive support for product design with an ontology-based approach[END_REF], [START_REF] Peng | A collaborative system for capturing and reusing in-context design knowledge with an integrated representation model[END_REF], [START_REF] Shin | From knowledge theory to management practice: Towards an integrated approach[END_REF]- [START_REF] Beesley | Defining knowledge management (KM) activities: towards consensus[END_REF]. Explicit knowledge, also identified as formal knowledge [START_REF] Peng | A collaborative system for capturing and reusing in-context design knowledge with an integrated representation model[END_REF], is knowledge that can be expressed, codified and documented. Implicit knowledge is also knowledge that can be implied by or inferred from observable behaviour or performance. Tacit knowledge is subconscious and cannot be expressed.

In the context of engineering knowledge, formal knowledge can be codified in different sources, such as a 3D geometric model and a simulation model, and tacit knowledge refers to personal knowledge and experience, such as developing a problem-solving strategy and reasoning on possible decision. In [START_REF] Wallace | Engineering knowledge management[END_REF], the authors explain that information is what is stored and transferred outside the human mind and knowledge only exists when information is interpreted. They classify engineering design knowledge into product knowledge and process knowledge. Thus, when it is stored externally, information can either describe the design process or the product itself. When it is sored un human memory, knowledge can be explicit, implicit and tacit. Explicit knowledge is an explanation of both the process and the product and can be articulated in the form of information. Implicit knowledge is the understanding the engineers have of both process and product and cannot be expressed by engineers themselves; it can be articulated through knowledge elicitation methods. Finally, tacit knowledge is more a matter of intuition and cannot be articulated.

Given the different definitions and perspectives of knowledge, knowledge management (KM) has multiples definitions. Knowledge management refers to identifying and leveraging collective knowledge [START_REF] Alavi | Review: Knowledge Management and Knowledge Management Systems: Conceptual Foundations and Research Issues[END_REF], [START_REF] Barão | A knowledge management approach to capture organizational learning networks[END_REF], [START_REF] Liebowitz | Knowledge management and its link to artificial intelligence[END_REF] and it is usually defined as a process involving multiple sub-processes including knowledge capture, storing, retrieval and transfer [START_REF] Alavi | Review: Knowledge Management and Knowledge Management Systems: Conceptual Foundations and Research Issues[END_REF], [START_REF] Girard | Defining knowledge management : Toward an applied compendium[END_REF], [START_REF] Heisig | Harmonisation of knowledge management-comparing 160 KM frameworks around the globe[END_REF], [START_REF] Al-Emran | The impact of knowledge management processes on information systems: A systematic review[END_REF]. KM is defined as the ability of an organisation to manage, store, value and distribute knowledge [START_REF] Girard | Defining knowledge management : Toward an applied compendium[END_REF]; an organisation is defined as a social unit of people structured and managed to meet a need or to achieve collective goals [START_REF] Barão | A knowledge management approach to capture organizational learning networks[END_REF]. KM is an essential asset in modern institutions; it enables learning from corporate memory, growth, success and innovation [START_REF] Al-Emran | The impact of knowledge management processes on information systems: A systematic review[END_REF]. In projects, KM enables communication improvement, best practice gathering while providing informal knowledge sharing, and productive collaboration [START_REF] Kanapeckiene | Integrated knowledge management model and system for construction projects[END_REF]. Information systems plays a key role in the development of KM as it enables the automation, production and sharing of knowledge [START_REF] Al-Emran | The impact of knowledge management processes on information systems: A systematic review[END_REF]. These systems are called knowledge management systems and they support KM processes [START_REF] Alavi | Review: Knowledge Management and Knowledge Management Systems: Conceptual Foundations and Research Issues[END_REF]. The essential function of KMS is the sharing and reuse of knowledge. Therefore, to achieve this function, the acquisition of knowledge is fundamental. Thus, KMS has to fulfil three functions: acquiring knowledge, storing it and reusing it [START_REF] Zhang | Ontology-based knowledge management system and application[END_REF].

In engineering design, knowledge can be whether in form of tangible objects that can be modified, copied and transferred, or experience learnt and accumulated through a community of expertise; this constitute both approaches of KM, the codification and the personalisation view [START_REF] Peng | A collaborative system for capturing and reusing in-context design knowledge with an integrated representation model[END_REF]. Most common approaches are technology-oriented, called codification approach; the explicit nature of knowledge is underlined, and knowledge need to be formalised and stored in knowledge repositories and transferred via Information and Communication Technologies [START_REF] Peng | A collaborative system for capturing and reusing in-context design knowledge with an integrated representation model[END_REF]. On the other hand, people-oriented, also called personalisation approaches underlines the tacit and context-dependent nature of knowledge; it requires informal human communication to transfer knowledge [START_REF] Liebowitz | Knowledge management and its link to artificial intelligence[END_REF], [START_REF] Saito | A strategy-based ontology of knowledge management technologies[END_REF]. It is argued that a trade-off between the two approaches, called integrated approach, is more effective [START_REF] Mcmahon | Knowledge management in engineering design: personalization and codification[END_REF], [START_REF] Peng | A collaborative system for capturing and reusing in-context design knowledge with an integrated representation model[END_REF], [START_REF] Saito | A strategy-based ontology of knowledge management technologies[END_REF], [START_REF] Ng | Integrated Knowledge Management Strategy: A Preliminary Literature Review[END_REF]. An integrated approach to KM can improve the quality and efficiency of design through the capture and reuse of informal and contextual knowledge.

Knowledge representation and retrieval research areas aim to develop enabling technologies for knowledge management systems [START_REF] Peng | A collaborative system for capturing and reusing in-context design knowledge with an integrated representation model[END_REF]. Ontology-based approaches to knowledge management have been developed for different application in design engineering. Sun et al. [START_REF] Sun | Knowledge-intensive support for product design with an ontology-based approach[END_REF] propose a knowledge management approach to support knowledge intensive product design; they develop an ontology-based product knowledge model including different types of knowledge and propose methodologies for retrieving explicit and tacit knowledge. A prototype of the knowledge support system and an implementation at a paper currency binding' company are also carried out. Zhang et al. [START_REF] Zhang | Ontology-based knowledge management system and application[END_REF] construct a framework for an ontology-based knowledge management system. They also propose an implementation using a mechatronics case and develop part of the ontology-based knowledge retrieval modules. Premkumar et al. [START_REF] Premkumar | A semantic knowledge management system for laminated composites[END_REF] develop an ontology-based semantic knowledge management system to support the design, analysis and manufacturing of laminated composite materials. The system includes an ontological framework for laminated composite materials and their design for manufacturing, and an integrated engineering design framework to facilitate collaboration among domain experts. To our knowledge, no ontology-based knowledge management approach has been developed to support simulation-aided design, and specifically car crash simulation process.

Industrial context: Car crash simulation in vehicle development

This research is conducted within a French multinational automotive company. Two empirical studies have been conducted with the aim of having a better understanding of the development phase of a vehicle development project [START_REF] Sissoko | An empirical study of a dcision-making process supported by simulation in the automotive industry[END_REF], [START_REF] Fatfouta | Empirical Study of Car Crash Simulation Analysis within the Development Phase[END_REF]. The results of these studies explain that simulation is expensive and time consuming, and that there is considerable effort required. The development phase is a succession of digital loops, called design analysis loops, terminating in milestones. These loops involve design and simulation activities and are referred to as digital since the vehicle exists only in the form of numerical models, and both design and simulation activities are numerical. At the end of the development phase, the vehicle model must be at the right level of performance and the right manufacturing cost. The development phase consists of iteratively refining the design specifications, evaluating and validating the vehicle's performance and solving any design issues encountered. This phase is supported by modelling and simulation (M&S); the vehicle is represented by a digital model and the engineering activities are digital. Several variations on a vehicle model exist at the same time, as there are several markets with different expectations. The design reference (DR) represents the knowledge gathered about the vehicle under development and its specifications. The design activity aims to define and adjust the DR. Simulation aims to evaluate the vehicle performance. If a design issue is revealed by the simulation, it must be solved. We focus on solving the design issues encountered during the car crash simulation.

Figure 1 shows the different processes in the development phase with a focus on the car crash simulation. The design process consists of creating and updating the DR. The simulation model generation process consists of creating and updating the digital vehicle models required for the simulation. The customer performance specification process provides the specification of the vehicle to be met. The simulation process evaluates the performance of the vehicle and solves the design issues; a design issue occurs when the performance does not meet the specification. Finally, the decision-making process determines which design changes to incorporate. A design change is a solution to the design issue. Different stakeholders are involved in the different processes, as explained in Table 1. Our focus is on the crash simulation process and mainly on the analysts involved within this process. The analysts' missions are to evaluate and validate vehicle performances and to deliver a vehicle model compliant with multiple requirements. They rely on simulation to evaluate vehicle performance. During the development phase, for a design analysis loop, crash simulation analysts receive the specification and the vehicle model to be evaluated. Once they have obtained the simulation results, they proceed with the interpretation of these results. If the model does not meet one or more requirements, a design issue is identified. The analysts assess and diagnose the design issue, then propose a design change to fix the design issue. If the design change is not satisfactory (unresolved design issue), they consider a new path for another design change. If the design change satisfies the requirement, the project decision-makers decide whether to implement it in the vehicle model. This decision depends on project factors including cost and weight. The decision-making process is not considered in this research; only the resulting decision is considered.

Analysts are required to have knowledge of modelling and simulation. They are also expected to make decisions on paths relating to investigation of design issues and on proposals for design changes. At the end of each design analysis loop, all design changes that have been approved by the different disciplines, such as crash, stress and noise and vibration, are incorporated into the vehicle model, ready for the next loop.

Crash simulation analysts are geographically distributed, and there is only one crash simulation expert and one digital simulation expert in the company [START_REF] Fatfouta | An ontology towards a knowledge-based support of the post-processing phase of car crash simulation[END_REF]. Car crash simulation analysts collaborate with different stakeholders. They collaborate with other crash simulation analysts from other work sites and with simulation analysts from different disciplines, such as noise and vibration simulation analysts. There is a strong collaboration between simulation analysts and simulation experts, as the latter have the most significant expertise within the company. Analysts, designers and customer performance specialists exchange information on the status of the resolution of design issues. Finally, decision-makers participate in the decision-making process regarding the design change to be incorporated into vehicle models.

According to the empirical study [START_REF] Fatfouta | Empirical Study of Car Crash Simulation Analysis within the Development Phase[END_REF], analysts encounter several challenges within car crash simulation. They need to quickly locate all relevant data and knowledge, from different sources, in as little time as possible. Design-issue analysis and design-change proposal formulation need to be improved, in order to reduce the time spent on simulation and reduce bias of less experienced analysts when interpreting simulation results. This paper addresses these issues by proposing an ontology-based knowledge management approach to support simulation-aided design. The knowledge management support system is based on a knowledge model that formalises formal knowledge and knowledge related to the resolution of design issues. Knowledge retrieval models will support the analysis of design issues and design change proposals. Section 4 details the architecture of the KM support system with a focus on engineering knowledge capture and retrieval.

An ontology-based approach for an integrated and collaborative knowledge management

To improve the crash simulation analysis process, time should be reduced and decisions concerning investigation paths and design-change proposals should be substantiated. The crash simulation analysis process is knowledge intensive and highly dependent on expertise. Since there is only one crash simulation expert, it is important to capture the knowledge and expertise and share it with analysts. Collaboration between the different people involved is very important for the process to run smoothly. With these characteristics taken into consideration, we propose an integrated and collaborative knowledge management approach to support analysis and to ensure collaboration with the different stakeholders involved in the design issue resolution process.

In previous work [START_REF] Fatfouta | An ontology towards a knowledge-based support of the post-processing phase of car crash simulation[END_REF], we proposed formalising the knowledge related to car crash simulation using an ontology. The interest in developing ontologies is growing in engineering design as it involves knowledge sharing and the development of a common standard language [START_REF] Saeema | A Methodology for Creating Ontologies for Engineering Design[END_REF], usually used for the formalisation of domain knowledge [START_REF] Premkumar | A semantic knowledge management system for laminated composites[END_REF]. The proposed ontology is called Crash Simulation Post-Processing CSPP ontology, and an overview of this ontology will be given in section 4.1. We also presented the first steps towards the development of the knowledge management support system in later work [START_REF] Fatfouta | Towards a framework for integrated and collaborative knowledge management for engineering design-A case study[END_REF], based on an in-depth literature review of knowledge management frameworks and knowledge management systems architecture while taking into account the specificities of our industrial context, in light of the ontology.

Hence, in this paper, as an extension of the research presented in [START_REF] Fatfouta | Towards a framework for integrated and collaborative knowledge management for engineering design-A case study[END_REF], we focus mainly on the development of the virtual KM support system. First, we define its capabilities, then we present the architecture and specify the blocks and sub-blocks.

The Crash Simulation Post-Processing (CSPP) Ontology

In this section, we briefly explain the Crash Simulation Post-Processing Ontology that we have developed in previous work [START_REF] Fatfouta | An ontology towards a knowledge-based support of the post-processing phase of car crash simulation[END_REF]. The purpose of crash simulation is to evaluate the performance of a specific vehicle model. The ontology, therefore, formalises the knowledge related to design issue resolution, mainly the knowledge related to the postprocessing phase of the crash simulation and the interpretation of the simulation results. The ontology is formalised according to three levels to better structure the engineering knowledge. Firstly, the context level contains information on the context in which the digital test takes place, such as the requirements to be met and the impact configuration, including frontal and rear crashes. Second, the project level formalises the engineering knowledge related to a specific vehicle project, including the vehicle model, the assessment of simulation results, and the resolution of design issues. Finally, the reasoning level formalises the reasoning behind the resolution of design issues. For brevity, we explain only the concepts, mainly at the level of reasoning, that are necessary to understand this paper.

A design issue occurs when requirements are not met by the vehicle. A vehicle model consists of vehicle parts, and each vehicle part has a role to play in the vehicle structure during the crash test and adopts an expected behaviour to ensure this role. Thus, we define a design issue as a behaviour gap between the expected behaviour and a defect behaviour of a vehicle part. A design issue has root causes. A root cause is also defined as a behaviour gap of a vehicle part. An elementary root cause is a root cause to which the analyst can propose a design change. A design change is one or more corrective actions applied to a vehicle part. This reasoning is based on the hypothesis that, first of all, crash simulation is based on physical and mechanical phenomena. Therefore, the behaviour of vehicle parts has limited possibilities of deformation and can be predictable. Secondly, vehicle parts sharing the same role and behaviour would be exposed to similar issues and could, therefore, belong to the same category. Then, issues with similar diagnosis and root causes would share similar corrective actions.

Capabilities of the knowledge management support system

Engineering knowledge related to design-issue resolution includes the design issue, its root causes, and associated design changes, as formalised in the CSPP ontology. We now refer to it as engineering knowledge.

The capabilities of the KM support system can be characterised into three overall capabilities:

• Collaboration: The support system must ensure collaboration between the various stakeholders within vehicle projects. Virtual collaboration is considered in this context.

• Capturing engineering knowledge: the support system must be able to capture engineering knowledge based on the CSPP ontology, classify it, and store it in knowledge repositories.

• Retrieval of engineering knowledge: the support system must be able to retrieve knowledge based on user queries and share it with users. This paper aims to develop an integrated and collaborative knowledge management system. It is integrated since the CSPP ontology combines formal knowledge, such as requirements and models, and tacit knowledge, such as design issue resolution. The integrated aspect is also present in the combination of both methodologies for codification and personalisation of KM. The KM support system ensures the codification of knowledge and the capture of in-context and tacit knowledge through communication. The collaborative aspect is undertaken by ensuring stakeholder collaboration within vehicle projects and enabling communication.

A virtual KM support system for simulation-aided design

Based on pre-defined capabilities, we propose a virtual system to support simulation-aided design within vehicle projects. As shown in Figure 1, the support system consists of four main parts: three layers and a multi-user interface.

Figure 2: The description of the Virtual KM support system, with its three layers and multi-user interface. A representation of the activities performed before interacting with the KM support system is also given (on the right), to identify the inputs required.

The three layers constituting the support system are the resources, methodologies, and models layers:

• The resources layer refers to knowledge repositories in various data and knowledge formats. Repositories may include data and information such as simulation models and reports used and transferred as part of the process. Other explicit and implicit knowledge is stored in knowledge repositories. Implicit and tacit knowledge embedded in the human mind could be shared through communication. Therefore, the KM support system includes a human resource base of employees, detailing their roles, skills, and capabilities. • The models layer consists of models developed to support the implementation of the system, including an integrated knowledge model, a classifier, and two knowledge retrieval models. The integrated knowledge model is the CSPP ontology. The classifier and the two retrieval models will be explained later in Section 4.4.1.

• The methodologies layer represents the methodologies used to conduct KM activities. Based on the capabilities detailed in section 4.2, two principal methodologies are required: "capture knowledge," leading from raw information to knowledge stored in repositories, and " retrieve knowledge," leading from knowledge in repositories to specific knowledge required by the user. We then added " share knowledge" to ensure the continuity of the information flow from the knowledge retrieval to the user. More details on "capture knowledge" and "retrieve knowledge" will be presented in section 4.4.

Finally, the multi-user interface (MUI) ensures interaction between users and the virtual system and collaboration between users within the integrated work environment. Users, including engineers, experts, and teams, can have distributed workspaces for individual tasks and project environments for collaboration if required. The support system must ensure collaboration between stakeholders working on the same project via a virtual environment where they can communicate, interact, and update the current project. The MUI provides multiple activities to ensure user interaction with the system, such as "enter support system," "query," and "transfer to the user." These activities ensure, firstly, the input of input data into the system, secondly, the choice of entering new engineering knowledge or retrieving knowledge, and thirdly, the transfer of the retrieved knowledge to the user. All MUI activities are accessible to the various users. For reasons of clarity, the links between users and MUI activities are not presented in the Figure 2.

The KM support system architecture

In this section, we focus on both the methodologies and models layers of the KM support system. As explained in Section 4.3, and based on the capabilities previously described, the KM support system must have two blocks realizing both "capture knowledge" and "retrieve knowledge" activities. Each block consists of sub-blocks and calls for a specific model to perform each function.

The knowledge capture block:

The KM support system must be capable of capturing engineering knowledge from different resources, such as extracting knowledge from formal knowledge records (such as simulation models, reports) and obtaining knowledge from the user. We focus on capturing the user's engineering knowledge.

The knowledge capture block carries out the "knowledge capture" activity presented in Figure 2. It should allow the user to document new design issues and their resolution. Accordingly, engineering knowledge is entered into the system based on the CSPP ontology. Each design issue is classified into its category via a classifier and then stored in knowledge repositories. Thus, three different sub-blocks are identified to perform three different functions.

Firstly, the Entry sub-block, shown in Figure 2, allows formalising the data and information entered into the system using the knowledge model. Information about the design issue and its resolution will be entered in the fields proposed by the CSPP ontology. The output of this sub-block is the formalised engineering knowledge.

Second, the Classify sub-block, shown in Figure 2, allows the system to classify formalised design issues. This subblock relies on the classifier. The classifier can be based on a statistical or deterministic classification that identifies a set of categories to which the design issues belong. The result of this sub-block is a formalised design issue with its corresponding category.

In this paper, to exemplify, we propose a deterministic classifier based on the categories explained at the reasoning level of the CSPP ontology. Vehicle parts sharing similar roles and behaviours would be subject to similar design issues and then to similar design changes. Therefore, vehicle parts sharing similar roles and behaviours would belong to the same category. In this case, the classifier will sort the design issue according to the vehicle part affected. Based on this reasoning, we propose a classifier based on matrix multiplication, as explained in Figure 3. The first matrix P defines the vehicle parts (vp) by their roles (r) and their behaviours (b) using a pair (r, b). The second matrix C defines the categories (cat) according to the pair (r, b). Finally, the matrix PC classifies the vehicle parts into their respective categories by matrix multiplication of P and C, while maximising pci >0 to 1.

In order to classify a new vehicle part, the designer must be involved. The designer must assign the pair (r,b). If (r,b) exists, the classifier will classify the new vehicle part. If not, the designer shall fill in the matrix C. Finally, the Store sub-block (see Figure 2) allows the system to store the formalised and classified design issue in knowledge repositories, ready to be retrieved later. The knowledge repository space would consist of several clusters representing the categories and containing the associated design issues and their resolution. It would facilitate later retrieval as it would limit the search space.

The knowledge retrieval block:

The knowledge retrieval block realises the "retrieve knowledge" activity presented in Figure 2. Based on the user's query, the knowledge retrieval block must call the appropriate retrieval model. Two queries are possible. First, the user may request a list of design issues that are similar to the design issue under study along with their resolution. For this purpose, the support system accesses the sub-block Search for matching, involving the matching algorithm. The user can also request the most probable design diagnosis (causes) and design change for the design issue under study. For this purpose, the support system accesses the Reasoning on causes / design change sub-block (referred to as Reasoning), involving the reasoning algorithm. The knowledge retrieval block automatically calls the knowledge capture block so that the support system captures the studied design issues. If the knowledge retrieval block does not find an answer to the query, it is supposed to search for the most apt stakeholder to answer the query. This option is not detailed in this paper.

To exemplify the two retrieval models, we propose a filter for the matching algorithm and a probabilistic reasoning for the reasoning algorithm.

For the matching algorithm, we propose a two-step filter, shown in Figure 4. As explained above, the knowledge repository space is divided into clusters of categories of design issues and their resolution. Therefore, similarity means that the design issues belong to the same categories. Thus, the first step will select the categories related to the vehicle part affected by the design issue, and thereby obtain all design issues from these categories. The second step is optional. If necessary, the user can define filter criteria in the query, according to which design issues resulting from the first step will be filtered. The filter criteria will address one or more elements of the definition of the design issue, such as the criterion to be respected and the impact configuration.

Figure 4: The two-step filter for the matching algorithm, with an example for explanation. Knowing the vehicle part affected by the design issue under study, the first step of the matching algorithm would identify the corresponding categories (Cat1) to the vehicle part (vp2) and then list all the respective design issues and their resolution. Then, for the second step, based on the filter criteria, it would retain only the design issues that meet those criteria. The hidden lines are the eliminated design issues.

More explicitly, for the first step, the matching algorithm will go into the PC matrix and extract the categories related to the vehicle part. Then, we will obtain a database containing all the design issues related to the selected categories.

Then, for the second step, based on the filter criteria identified by the user, the matching algorithm will filter the new set of design issues, merely keeping the ones that satisfy these criteria.

Figure 5: (I) presents the list of design issues and their resolution that is the result of the matching algorithm for the design issue under study. (II) explains the construction of the network, where some design issues (DIs) are presented with their respective causes and design changes. The % represents the probability of each node, which is calculated based on a statistical calculation of occurrence from part (I).

The reasoning algorithm must propose the most probable cause of the design issue and the most probable design change. As explained in Figure 5, it starts by calling the matching algorithm, which will identify the categories to be addressed, and thereby all design issues, from these categories, and their resolution. Then, based on probabilistic reasoning, it would establish a network of three layers, including design issues, causes, and design changes, while assigning their probability of occurrence. Hence, the reasoning algorithm will present the most probable causes and the most probable design changes for the design issue under study.

Knowledge management support system, application and evaluation

In this section, for the evaluation of our proposal, we present three use case scenarios with a proof of concept implementation for each model. Each use case scenario will take into account a methodology (capture and retrieval) and the models that will be applied. For the three scenarios, we have built a knowledge base of several design issues and their resolution. This base is built based on real information documented by simulation analysts, and we have duplicated some information in order to have more cases and to be able to calculate probabilities. As shown in Figure 6, the columns represent the fields proposed by the CSPP ontology; not all of them are presented, since we chose some of them to have a complete picture without getting into all details. For each use case scenario, we will document the interaction between the user and the system and present the inputs and outputs of each scenario. Figure 7 shows the main part of the algorithm that interacts with the user to obtain the query and then call the appropriate block or sub-block to answer the query. We used Python 3 for programming.

Use case scenario 1: Capture engineering knowledge

The user must enter a new design issue with its resolution to the KM support system. The KM support system will then access the Knowledge Capture block and call the CSPP ontology and classifier as models.

Figure 8 shows the function "capture_design_issue" responsible for capturing engineering knowledge, classifying it and storing it. Figure 9 describes the interaction between the user and the KM support system while capturing a new design issue and its resolution. The user must enter the various fields provided by the KM support system. The user is then requested to validate the new design issue and its resolution before storing it. As it is shown, the category is automatically generated by the classifier.

Figure 9: The knowledge capture block, with its inputs and outputs. Queries are in green. The result of this block is the creation and storage of a new design issue. The system does not ask the user to enter the category. However, it is assigned later when the system requests validation of the information entered.

Use case scenario 2: retrieval of similar design issues

The user will search for design issues similar to the one under study (last line of Figure 6). Therefore, during the query, the user will ask for "search for matching". The user will also use filter criteria to narrow the search result. The KM support system will then access the Search for matching sub-block and the matching algorithm as a model. Figure 10 presents the function "filter similar" in the algorithm, representing the Search for matching sub-block, with the two steps filter. As mentioned above, for use case scenario 2, the user requests design issues similar to the one under study (represented in the last line of the knowledge base). Figure 11 represents the interaction between the user and the support system and the results of the support system. First, the user selects "similar inputs" in the query and then requests a second step filter based on "impact_config=front." The support system then lists seven design issues and their resolution, similar to the one understudy.

Figure 11: The interaction between the user and the support system and the outputs. Queries are in green. The result is an extraction from the knowledge base. The user has requested design issues similar to the one he has documented and has requested a second step filter using the "impact_config: front" criterion. Seven design issues respond to the query.

Use case scenario 3: Retrieval of most probable causes and design changes

The user is looking for the most likely cause and design change for a design issue they are addressing. Therefore, when querying, the user will request "reason for the cause or design change". The KM support system then accesses the sub-block " Reasoning on causes/ design change" and the reasoning algorithm as a model whose representative function "find_solutions" is shown in Figure 12. To have a better understanding of the construction of the network, we present an example in Figure 13. The network layers in this use case scenario are consistent with the concepts used for the CSPP ontology. Starting by the design issue layer, the layers are: "cause scope", "behaviour gap", elementary cause" and "design change".

Figure 12: The sub-block of the Reasoning on causes/design change represented by the "find solutions" function. In the "test_case _senario," the first step of the matching is performed. Starting from the cause scope layer, its nodes, and their probabilities, the construction of the network consists of identifying, for each layer, the children nodes, and their probabilities, up to the layer of elementary causes or design changes.

As shown in Figure 13, focusing on the first two layers, we begin by identifying the child nodes, from the cause scope layer, of each parent node, from the issue layer. Next, the probability of a child node is the probability of the parent node multiplied by the probability of the arrow (the probability of the cause scope knowing the design issue). If several arrows are pointing at a child node, then the probability is the sum of all the probabilities of the parent nodes multiplied by the probability of their arrows.

Figure 13: A detailed explanation of the proposed network, with its layers, and the calculation of probabilities for each node. The probability of each node is the probability of the parent node multiplied by the probability of the arrow.

For this use case, we present two scenarios: first, the user requests the causes, and second, the user requests the design changes. Figure 14 shows the interaction between the user and the support system when requesting causes and Figure 15 when requesting design changes. Both queries are for the same design issue with the same inputs.

Figure 14: The results of the KM support system for reasoning on causes. Queries are in green. In the end, we can read that two scopes of causes are possible, the CB and the Side_member, with their respective elementary causes and probabilities, in decreasing order.

For the design issue under study, the cause scope can be either the "Crash Box" or the "Side member." For the reasoning on causes (Figure 14), the algorithm stops at the elementary cause layer. It gives, as a result, each cause scope with its respective elementary causes and their probabilities, in descending order. Moreover, for the reasoning on design changes (Figure 15), the algorithm stops at the design change layer. It gives as output the same cause scope (since we are studying the same design issue), with their respective design changes and their probabilities, in descending order.

Figure 15: The results of the KM support system for reasoning on design changes. Queries are in green. In the end, it indicates the same cause scopes, with their respective design changes and probabilities, in decreasing order.

Discussion

The integrated and collaborative knowledge management system aims to support simulation-aided design, based on the different models and technologies used. The KM support system captures engineering knowledge using the CSPP ontology, which is characterised as integrated since it combines formal and tacit knowledge. It also ensures the retrieval of engineering knowledge, based on user queries, using different retrieval models. The retrieval models are developed based on the reasoning already developed in the CSPP ontology, which formalises the resolution of design issues and is independent of the specificities of the vehicle project. This reasoning imitates the tacit knowledge of analysts and experts. The collaborative KM support system not only facilitates the resolution of design issues but also provides contextual and tacit knowledge captured during communication between the different stakeholders of vehicle projects.

The different models, which ensure the capture and retrieval of engineering knowledge, are developed and evaluated using use case scenarios of car crash simulation. The models and technologies used are effective in capturing and retrieving knowledge since the outcomes meet the expected results communicated by analysts and experts.

Time is one of the most important constraints in project development. The KM support system would help reduce crash simulation time by reducing the time spent solving design issues and proposing design changes. During the empirical study conducted within the company, we proved that simulation with more certainty about the results would allow us to gain at least one iteration per issue and so we save about nine hours of computation and about one hour of analysis [START_REF] Fatfouta | Empirical Study of Car Crash Simulation Analysis within the Development Phase[END_REF]. Based on interviews with analysts, they encounter two or three significant design issues for about fifteen impact configurations, per project and design loop. Thus, by saving one iteration per design issue, we would save about thirty-five hours or one week of the design loop, out of the five weeks it usually lasts. Hence, we would save 20% of the analyst's time.

The KM support system would also contribute to more accurate proposals for more effective design changes since proposals are made based on in-depth knowledge of the company. It could lead to the development of more robust vehicle models. The KM support system is also considered a learning tool, where novice analysts would have access to the engineering knowledge retained.

The main functionalities of the system have been developed and applied, although it is still considered a prototype which can be further enhanced. First, there is a need to integrate the different simulation disciplines, such as noise and vibration and stress. Second, a web-based prototype must be developed to facilitate communication between users and the system. Third, users, with different roles, need to work in their virtual spaces and create knowledge as the project progresses, which will enrich the knowledge base and improve the models.

In this paper, the KM support system is applied to the car crash simulation. Although, it can be generalised to different simulation disciplines, such as strength and noise and vibration. The same laws of physics apply to the different disciplines. Based on the analysis of documented design issues from different simulation disciplines, the design issues are mainly described in the same way as for crash simulation as well as the design changes. Only the context level of the ontology should integrate the concepts formalising the requirements of the discipline. The project level of the ontology could also integrate some specificities of the discipline if needed. However, the reasoning level of the ontology would remain the same. Hence, the models implemented within the KMS support system would remain unchanged. Future work on the generalisation of the ontology-based knowledge management approach will be undertaken.

Conclusion

In this paper, we present an ontology-based knowledge management system to support simulation-aided design, specifically car crash simulation. The KM support system includes an integrated ontology-based knowledge model that structures and formalises the formal knowledge and tacit knowledge related to design issue resolution. It also includes various knowledge retrieval methods to satisfy user needs. Moreover, a multi-user interface facilitates and enhances collaboration on vehicle projects.

A prototype and parts of knowledge retrieval methods are implemented. However, the next steps in this research need to focus on large-scale implementation of the support system and the generalisation to different simulation disciplines. The KM support system has been demonstrated to save simulation time. Further research could investigate the autonomy of such a system, whether we should continue to support analysts to analyse and solve design issues, or whether only expert validation would be sufficient.

Figure 1 .

 1 Figure 1. Simulation analyst's activities, focussing on the design issue resolution process, with a glance into the collaboration with other stakeholders

Figure 3 :

 3 Figure 3: The classifier is described, which is based on the multiplication of matrices. An example is drawn for a better understanding. The equations representing each matrix are presented in detail. The matrix PC is the result of the product of the matrix and a normalization at 1 for all matrix elements >1.

Figure 6 :

 6 Figure 6: The knowledge base used for the use case scenarios. The last line represents the example that will be used for the use case scenarios 2 & 3.

Figure 7 :

 7 Figure 7: Presentation of the main part of the algorithm with a detailed description. The main part allows the user to enter the query. Then, depending on the query, it calls the appropriate functions.

Figure 8 :

 8 Figure 8: The knowledge capture block, starting with entry, through to classification and finally storing the design issue and its resolution.

Figure 10 :

 10 Figure 10: The search for matching sub-block, with the matching algorithm represented by the function loc [rows [column = value]]. This function filters the rows of the knowledge base, based on a specified column. For the first step filter, the [column=category], and the second step filter, the value of the column will be entered by the user.

Table 1 : Stakeholders of each process within the development phase

 1

	Process Stakeholders
	Simulation Simulation analyst, synthesis engineer CAE
	Design Designer, synthesis architect
	Simulation model generation Model factory engineers
	Costumer Performance specification PPC, costumer performance leader
	Decision making Designer, synthesis architect, project manager

impact_config","performance","criterion","target","scope_crtierion", "appreciation","category","cause_scope"]] behaviour_gap = database[["cause_scope", "expected_behaviour", "behaviour_gap"]] elementary_cause = database[["behaviour_gap", "elementary_cause" ]] corrective_action = database[["elementary_cause", "corrective_action"]] return {"cause_scope": cause_scope, "behaviour_gap": behaviour_gap,"elementary_cause": elementary_cause, "corrective_action":corrective_action} def get_parameters_cols(df, name):

""" quickly filter the input columns based on list order. Can be specified for each


Guillaume Dupic
email: guillaume.dupic@clermont.unicancer.fr

Lucie Brun

Ioana Molna
email: iona.molnar@clermont.unicancer.fr

Brice Leyrat

Vincent Chassin

Juliette Moreau

Véronique Dedieu

Toufic Khalil

Pierre Verrelle

Michel Lapeyre

Julian Biau

Significant correlation between gross tumor volume (GTV) D98% and local control in multifraction stereotactic radiotherapy (MF-SRT) for unresected brain metastases

Background

Stereotactic radiotherapy (SRT) should be applied with a biologically effective dose with an α/β of 12 (BED12) ≥ 40 Gy to reach a 1-year local control (LC) ≥ 70%. The aims of this retrospective study were to report a series of 81 unresected large brain metastases treated with Linac-based multifraction SRT according to the ICRU 91 and to identify predictive factors associated with LC.

Methods

Included in this study were the first 81 brain metastases (BM) consecutively treated with Linac-based volumetric modulated arc therapy (VMAT) multifraction SRT from 2017 to 2019. The prescribed dose was 33 Gy for the GTV and 23.1 Gy (70% isodose line) for the PTV in 3 fractions (3f). Mean BM largest diameter and GTV were 25.1 mm and 7.2 cc respectively. Mean follow-up was 10.2 months.

Results

LC was 79.7% and 69.7% at 1 and 2 years respectively. Significant predictive factors of LC were GTV D98% (HR = 0.84, CI 95% = 0.75-0.95, p = 0.004) and adenocarcinoma as the histological type (HR = 0.29, CI 95% = 0.09-0.96, p = 0.042) in univariate and multivariate analysis. A threshold of 29 Gy for GTV D98% was significantly correlated to LC (1-year LC = 91.9% for GTV D98% ≥ 29 Gy vs 69.6% for GTV D98% < 29 Gy (p = 0.030)), corresponding to a BED12 = 52.4 Gy. No tumor progression was observed for a BED12 ≥ 53.4 Gy, corresponding to a GTV D98% ≥ 20 Gy /1f and GTV D98% ≥ 29.4Gy 3f. Median OS was 15 months. Symptomatic radionecrosis occurred in 4.9% of cases.

Conclusion

The GTV D98% is a strong reproducible significant predictive factor of LC for brain SRT. Dose prescription should lead to a GTV BED12 98% ≥ 52.4-53.4 Gy to significantly improve LC, corresponding to respectively a GTV D98% ≥ 19.7-20Gy/1f and 29-29.4Gy/3f.

have become increasingly common treatment options for suitable patients with brain metastases [START_REF] Lin | Treatment of Brain Metastases[END_REF]. Wiggenraad et al. showed in a systematic review that local control (LC) after single fraction SRS was highly dependent upon dose and was high (> 80%) after 21 Gy or more and low (< 50%) after 15 Gy or less. Using the biologically effective dose of the linearquadratic model with an α/β of 12 Gy (BED12), they concluded that SRT for brain metastases should preferably be applied with a BED12 ≥ 40 Gy corresponding with a single fraction of 20 Gy (20 Gy/1f ) and three fractions of 8.5 Gy (25.5 Gy/3f ) [START_REF] Wiggenraad | Dose-effect relation in stereotactic radiotherapy for brain metastases. A systematic review[END_REF]. So the largest recorded MF-SRT total prescribed dose to the PTV is 27 Gy in three fractions (range: 23.1-33 Gy) [START_REF] Lehrer | Single versus Multifraction Stereotactic Radiosurgery for Large Brain Metastases: An International Meta-analysis of 24 Trials[END_REF]. The clinical tumor volume (CTV) is often a zero-margin expansion of the gross tumor volume (GTV). The planning target volume (PTV) varies in literature and is generally a 1-2-mm geometrical expansion of the CTV [START_REF] Minniti | Single-Fraction Versus Multifraction (3 × 9 Gy) Stereotactic Radiosurgery for Large (>2 cm) Brain Metastases: A Comparative Analysis of Local Control and Risk of Radiation-Induced Brain Necrosis[END_REF]. According to published studies, actual 1-year LC varies widely, generally between 79-93% (range: 59-100%), due to various differences in techniques and devices used for delivery of MF-SRT and various differences in definitions of LC and radionecrosis among institutions [START_REF] Lehrer | Single versus Multifraction Stereotactic Radiosurgery for Large Brain Metastases: An International Meta-analysis of 24 Trials[END_REF][START_REF] Minniti | Single-Fraction Versus Multifraction (3 × 9 Gy) Stereotactic Radiosurgery for Large (>2 cm) Brain Metastases: A Comparative Analysis of Local Control and Risk of Radiation-Induced Brain Necrosis[END_REF][START_REF] Feuvret | Stereotactic radiotherapy for large solitary brain metastases[END_REF][START_REF] Jeong | Efficacy and Safety of Fractionated Stereotactic Radiosurgery for Large Brain Metastases[END_REF][START_REF] Murai | Fractionated Stereotactic Radiotherapy using CyberKnife for the Treatment of Large Brain Metastases: A Dose Escalation Study[END_REF].

Very few studies have reported doses delivered to the GTV, yet GTV doses are the most reproducible data among studies where various techniques, devices and definitions of target volumes are used. The International Commission on Radiation Units and Measurements (ICRU) report 91 titled "Prescribing, recording, and reporting of stereotactic treatments with small photon beams" was published in 2017 [START_REF] Seuntjens | ICRU report 91. Prescribing, recording, and reporting of stereotactic treatments with small photon beams[END_REF]. ICRU 91 gives recommendations for reporting doses for SRS and MF-SRT (2-12 fractions) with conformal radiotherapy as well as intensity-modulated radiotherapy [START_REF] Wilke | ICRU report 91 on prescribing, recording, and reporting of stereotactic treatments with small photon beams : Statement from the DEGRO/DGMP working group stereotactic radiotherapy and radiosurgery[END_REF]. Reporting for SRT should contain the following information: delineated volumes, prescription and planning aims, description of the treatment planning system, dose documentation to target volumes and organs at risk (OAR), PTV and GTV D50%, Dmean, D2%, D98% (for volumes ≥ 2 cc), OAR Dmean, D2% and VxGy, dose homogeneity HI (homogeneity index), dose conformity CI (conformity index) and dose gradient GI (gradient index) [START_REF] Wilke | ICRU report 91 on prescribing, recording, and reporting of stereotactic treatments with small photon beams : Statement from the DEGRO/DGMP working group stereotactic radiotherapy and radiosurgery[END_REF].

The purposes of this retrospective study were to report a series of 81 unresected brain metastases treated with Linac-based multifraction SRT according to the ICRU 91 and to identify predictive factors associated with local control (LC).

Patients and Methods

Patients' selection and characteristics

Included in this study were the first 81 unresected brain metastases consecutively treated in our institution with Linac-based volumetric modulated arc therapy (VMAT) multifraction stereotactic radiotherapy (MF-SRT, 3 fractions) from February 2017 to December 2019. All patients were aged ≥ 18 years with at least a large brain metastasis ≥ 2 cm in diameter derived from a histologically confirmed systemic cancer. They could have received prior SRT or whole brain radiotherapy (WBRT). Exclusion criteria were small field sizes for SRS < 30 mm, brainstem metastases or prior surgery. Study ethics approval was obtained on 25 September 2020 (CECIC Rhône-Alpes-Auvergne, Grenoble, IRB 592.

All pre-treatment characteristics of the 81, including the brain metastases of the 69 patients, are reported in Table 1. Mean age was 62 years (range: 33-87 years). Most patients were male (59%), in good general state of health with a performance status ≤ 1 (85%), treated for a single brain metastasis (85%) and with no prior SRT (93%) or WBRT (88%). Primary cancers were mostly lung (59%), breast (15%), digestive (7%), melanoma (7%), ovarian (4%) and renal (3%). Adenocarcinoma was the most frequent histological type (73%) with a mutation in 18 % of cases. The mean brain metastasis' largest diameter was 25.1 mm (8-41 mm). A systemic treatment was provided in 66% of cases (58/88) at the time of brain SRS.

Most of these systemic treatments were immunotherapy (22/

Treatment specifications

A planning CT of 1.25-mm thickness was acquired and was matched with the dosimetric magnetic resonance imaging (MRI) sequences of interest using Iplan®, version 4.1 (Brainlab). Three MRI sequences were used: a FLAIR 3D MRI sequence with a 1mm*1mm*1mm voxel size, a T1 3D MPRAGE MRI sequence with contrast agent and a voxel size of 0.8mm*0.8mm*1mm and a T1 EG with a 0.6mm*0.6mm*4mm voxel size. The GTV was defined using post-gadolinium contrast-enhanced T1-weighted MRI sequences. The GTV was then extended symmetrically by 2 mm in all dimensions to create the PTV. Mean GTV and PTV were 7.8 cc (0.5-31.3 cc) and 13.5 cc (1.5-46.2 cc) respectively. The following OAR were contoured: brainstem, eyeballs, lenses, optic nerves, chiasm, cochlea, cranial cavity, and healthy brain (entire cranial cavity -GTV). No margins were added around the OAR to create planning OAR volumes.

All VMAT plans were created with arcs for 6-MV photons. The plans were created with one full coplanar arc and three partial non-coplanar arcs spaced by 45°. The maximum arc rotation amplitude was 160°. The rotation of the collimator was 10°, 350°, 350° and 350° for the first, second, third and fourth arcs respectively. The prescribed dose was 33 Gy for the GTV and 23.1 Gy (70%) for the PTV in three fractions [START_REF] Bernier-Chastagner | Évaluation de la radiothérapie fractionnée en conditions stéréotaxiques des métastases cérébrales de l'adulte : résultats cliniques et médicoéconomiques à 2 ans[END_REF]. Doses were prescribed to the 70% isodose line to achieve 99% target coverage of the PTV. Target coverage could be reduced to meet OAR dose constraints [START_REF] Emami | Tolerance of normal tissue to therapeutic irradiation[END_REF]. Final calculations were performed using the AAA algorithm on Eclipse® TPS version 13.5 (Varian Medical Systems). The arc optimization algorithm, the Progressive Resolution Optimizer used in Rapidarc®, optimized leaf position, dose rate, and gantry speed. Optimization parameters with Normal Tissue Objectives (NTO) were used to spare healthy tissues and were defined as the following: 1) distance from the PTV border (Xstart) = 1 mm, 2) start dose (f0) = target coverage isodose (e.g. 70%), 3) end dose (f∞) = 5% and 4) the fall-off coefficient (k) = 0.3 mm -1 . The maximum dose rate was set at 600 MU/min. Couch parameters were also added to the plan to account for attenuation of the mega-voltage beams. VMAT plans followed the recommendations of the ICRU 83 [12]. All treatment characteristics are reported in Table 1.

All patients were treated with NovalisTx® equipped with a high definition MultiLeaf

Collimator (HD MLC 120) (Varian Medical Systems, Palo Alto, CA, USA and Brainlab, Munich, Germany) using a noninvasive thermoplastic mask plus a localizer box (Brainlab).

For the most part, each fraction was delivered every two days (separated by at least 24 hours).

Overall treatment time (OTT) should not exceed 10 days. Positioning of the patients was performed using an ExacTrac® stereoscopic X-ray system (Brainlab) and a robotic couch with six degrees of freedom. Treatments were permitted when the setup error was < 0.7 mm in translation and 0.7° in rotation.

Follow-up

Follow-up included a clinical examination and MRI every three months during the first two years post MF-SRT and every six months afterwards. Toxicity was evaluated using the National Cancer Institute's Common Toxicity Criteria for Adverse Events version 4.0 (NCI-CTCAE). Tumor progression was defined as any tumor increase visible on contrastenhanced T1-weighted images in at least 2 subsequent MRI results associated with either a cerebral blood volume (CBV) ratio > 2.0 at dynamic susceptibility-weighted contrastenhanced perfusion images (calculated for each lesion by dividing the tumor CBV by the mean CBV value of normal white matter) or a maximum lesion to maximum background uptake ratio (SUVLmax/Bkgrmax) > 1.59 at F-DOPA PET-CT. Stable or shrinking lesions over a 6-month period associated with a CBV ratio < 2.0 or a SUVLmax/Bkgrmax < 1.59 were diagnosed as radionecrosis [START_REF] Minniti | Single-Fraction Versus Multifraction (3 × 9 Gy) Stereotactic Radiosurgery for Large (>2 cm) Brain Metastases: A Comparative Analysis of Local Control and Risk of Radiation-Induced Brain Necrosis[END_REF]. Distant failure was defined by the presence of new brain metastases or leptomeningeal enhancement outside the PTV. Overall survival (OS) was defined as the time between the end of MF-SRS and the patient's death. Mean follow-up was 10.2 months (range: 0.5-31.3 months) (Table 1).

Statistical analysis

Local control (LC), progression-free survival (PFS) and overall survival (OS) were calculated using the Kaplan-Meier method. The Cox proportional hazards model was performed to identify predictive factors of LC and prognostic factors of PFS and OS. A twosided p-value < 0.05 was considered significant. The following factors were included in the univariate analysis for LC: histological type, presence or absence of a mutation, presence or absence of a systemic treatment at the time of brain SRS, prior surgery, prior SRT, prior WBRT, GTV, PTV, conformity index (CI = inverse Paddick), gradient index (GI = total volume receiving ≥ 50% Dcoverage / total volume receiving ≥ 100% Dcoverage), overall treatment time, doses delivered to GTV and PTV (Dmin, D98%, Dmoy, D2%, Dmax), V70% PTV (V70% is the volume of the structure receiving a dose ≥ 70% prescribed dose, i.e. prescription isodose).

Concerning OS, the following factors were included in the univariate analysis in addition to the previously studied LC predictive factors: gender, age, performance status, prognostic classifications (SIR, RPA, GPA, DS-GPA), number of brain metastases, presence or absence of a systemic treatment at the time of brain SRS and presence or absence of a mutation. A logistic regression analysis was performed. Concerning radionecrosis, the following factors were included: age, gender, arterial hypertension, type 2 diabetes, hypercholesterolemia, brain metastases location, prior surgery, prior SRT, prior WBRT, presence or absence of a systemic treatment at the time of brain SRS, GTV, PTV, conformity index, gradient index, overall treatment time, and doses delivered to healthy brain parenchyma (brain -GTV): V23.1Gy, V21Gy, V18Gy, V14Gy, V10Gy, V5Gy (VxGy (cc) is the volume of the structure receiving a dose ≥ x Gy).

Factors associated with a p-value < 0.2 in the univariate analysis were included in the multivariate analysis if they were also selected by the LASSO method. The Wald test and the likelihood ratio test were performed to calculate and verify the p-value for each coefficient in multivariate analyses. For each significant linear correlation observed, a ROC (Receiver Operating Characteristics) curve was performed to identify the best threshold-value. Finally, comparison of LC curves with the obtained threshold was conducted using the log-rank test.

To compare the two groups of patients obtained with the best threshold-value, Fisher's exact test and the Wilcoxon-Mann-Whitney test were used in the analysis of contingency of these two groups to compare two categorical variables and a categorical variable with a continuous variable, respectively. Statistical analysis was performed using R-Project, version 3.6.1 (R-Project, GNU GPL, http://cran.r-project.org/).

Results

Local control (LC) at 6 months, 1 year, and 2 years was 87.5%, 79.7% and 69.7% respectively (Figure 1). Significant predictive factors of LC were GTV D98% (HR = 0.87, CI 95% = 0.78-0.96, p = 0.046) and adenocarcinoma as the histological type (HR = 0.25, CI 95% = 0.08-0.83, p = 0.025) in univariate analysis. GTV D98% (HR = 0.84, CI 95% = 0.75-0.95, p = 0.004) and adenocarcinoma as the histological type (HR = 0.29, CI 95% = 0.09-0.96, p = 0.042) remained significant in multivariate analysis (Table 2). Systemic treatment (presence vs absence) and tumor mutation (presence vs absence) were not significant predictive factor of local control in univariate analysis (HR = 0.42, CI 95% = 0.13-0.39, p = 0.17 and HR = 0.24, CI 95% = 0.03-1.83, p = 0.09 respectively).

The best threshold identified for GTV D98% using ROC curve was 29 Gy (AUC = 0.73, 95%CI = 0.61-0.84). This threshold of 29 Gy for GTV D98% was significantly correlated to LC using the log-rank test (Figure 2). The 1-year LC was 91.9% for GTV D98% ≥ 29 Gy vs 69.6% for GTV D98% < 29 Gy (p=0.030). Except for doses received to target volume, the two groups of patients obtained with this threshold-value did not differ significantly concerning tumor volume (7.2 cc vs 7.2 cc for GTV D98% < 29 Gy and ≥ 29 Gy respectively, p = 0.99) or doses received to healthy brain parenchyma (5.4 cc vs 5.5 cc and 7.4 cc vs 7.3 cc respectively for V23.1Gy and V21Gy) (Table 1). They did differ significantly in prior treatment with SBRT or SRT, which was noticeably higher in the group GTV D98% < 29 Gy (18% vs 9%, p = 0.3 and 12% vs 4%, p = 0.2 respectively) and histological type (18% (6/34) vs 15% (7/47) for the histological type of renal cancer or melanoma, respectively).

Using the linear-quadratic model, the biologically effective dose assuming an α/β of 12 (BED12) for brain metastases at doses of 29 Gy in three fractions was 52.4 Gy, corresponding to a GTV D98% ≥ 19.7 Gy in a single fraction. With a mean follow-up of 8.5 months, no tumor progression was observed for the 17 brain metastases treated with GTV D98% ≥ 29.4 Gy in three fractions, i.e. for a BED12 ≥ 53.4 Gy, corresponding to a GTV D98% ≥ 20 Gy in a single fraction. Progression-free survival (PFS) at 6 months, 1 year, and 2 years was 80.8%, 71.1% and 51.4% respectively (Figure 1). Median PFS was not reached.

Overall survival (OS) at 6 months, 1 year, and 2 years was 74.9%, 50.3% and 39.9% respectively (Figure 1). Median OS was 15 months. Significant prognostic factors of OS in univariate analysis were male gender (HR = 2.38, 95%CI = 1.07-5.29, p = 0.02), performance status (HR = 2.08, CI 95% = 1.40-3.07, p = 0.001), SIR (HR = 0.67, CI 95% = 0.53-0.84, p = 0.001), RPA classification (HR = 2.38, CI 95% = 1.08-5.3, p = 0.02), GPA classification (HR = 0.46, CI 95% = 0.30-0.71, p = 0.001), DS-GPA classification (HR = 0.46, CI 95% = 0.31-0.70, p < 0.001) and presence of a mutation (HR = 0.25, CI 95% = 0.08-0.81, p = 0.006). A prognostic factor of OS that remained significant in multivariate analysis was the presence of a mutation (HR = 0.19, CI 95% = 0.05-0.78, p = 0.02).

Brain radionecrosis (RN) was the most significant complication occurring in 12 (14.8%) out of the 81 treated brain metastases. Median time to RN was 6.7 months (range: 2.7-11.1 months). Symptomatic neurological complications occurred in 4 cases (4.9%) (seizure in 2, motor deficit in 1, intracranial hypertension in 3). The 6-month and 1-year actual risk of RN was 9.3% and 27.6% respectively. The 6-month and 1-year actual risk of symptomatic RN was 4.1% and 8.8% respectively.

Mean volumes of normal brain (brain -GTV) that received doses of 23.1 Gy (V23.1Gy), 21 Gy (V21Gy), 18 Gy (V18Gy), 14 Gy (V14Gy), 10 Gy (V10Gy) and 5 Gy (V5Gy) were 5.8cc, 7.9 cc, 11.5 cc, 18.6 cc, 32.8 cc and 88.0 cc respectively. No factors, including age, gender, arterial hypertension, type 2 diabetes, hypercholesterolemia, brain metastases location, prior surgery, prior SRT, prior WBRT, GTV, PTV, conformity index, gradient index, overall treatment time, doses delivered to normal brain (V23.1Gy, V21Gy, V18Gy, V14Gy, V10Gy and V5Gy) were independent predictive factors of RN in univariate or multivariate analysis, whether for all patients or for patients with a follow-up over 8 months. Other complications observed were headache, seizure and haemorrhage in 1, 1 and 1 patients respectively.

Discussion

To date, the present study is the first to demonstrate a significant threshold of dose delivered to brain metastases correlated to local control. Moreover, this threshold should be reproducible because it concerns the GTV which is always defined in the same way, rather than PTV margins which differ according to the various studies. Furthermore, this study reports a series of 81 unresected large brain metastases treated with Linac-based VMAT multifraction SRT according to the ICRU 91.

In this study, we reported LC for unresected large brain metastases of 80% and 70% at 1 year and 2 years respectively, which are consistent with previous published studies. An international meta-analysis of 24 trials concerning MF-SRT for large brain metastases recently reported in 2019 a 1-year LC of 92.9% and 79.2% (range : 59-100%) respectively for metastases about 2-3 cm in diameter and > 3 cm in diameter [START_REF] Lehrer | Single versus Multifraction Stereotactic Radiosurgery for Large Brain Metastases: An International Meta-analysis of 24 Trials[END_REF]. To date, Wiggenraad et al. are the first and only ones to demonstrate a dose-effect relation in SRT for brain metastases and to conclude on a minimum total dose to be prescribed through SRS in a single fraction. They showed that LC was higher (1-year LC ≥ 70%) with a BED12 ≥ 40 Gy corresponding with a single fraction of 20 Gy (20 Gy/1f ) and three fractions of 8.5 Gy (25.5 Gy/3f ) [START_REF] Wiggenraad | Dose-effect relation in stereotactic radiotherapy for brain metastases. A systematic review[END_REF].

Limitation of this review was that GTV-PTV margins vary often from 0 to 2 mm among published studies, which may lead to a higher or lower dose in the GTV. Therefore, they could not draw conclusions because they could not determine whether higher LC rates were linked to higher prescribed doses or to the GTV-PTV margins used.

The main interest of our study is to focus on the minimum or near-minimum BED12 delivered to the GTV (GTV D98%) and not the marginal BED12 prescribed to the PTV, the former of which is more reproducible because it is not influenced by techniques or devices used for SRT. Dose is always prescribed to the envelope of the tumor whatever the modality employed. What can differ among the teams is the use of margins around GTV to create PTV (0-2 mm), which can make differences for doses received to the GTV. That's why we thought it was important to report received dose to the GTV and not only to the PTV in order to translate these findings to other groups, because GTV is always delineate as the same. What is really important is the dose received to the GTV which corresponds to the tumor and not the dose received to the PTV which depends on the technique employed. Thus, we have demonstrated here that GTV D98% had to be higher than 29 Gy in three fractions (corresponding to a GTV BED12 98% ≥ 52.4 Gy) to significantly improve LC (92% vs 70%, p = 0.030) and maybe higher than 29.4 Gy (≥ 53.4 Gy for GTV BED12 98%) to get closer to a 100% 1-year LC. The threshold-value of 29 Gy enabled the division of the population in our study into two groups with more than 30 brain metastases in each of the groups (34 and 47 for GTV D98% < 29 Gy and ≥ 29 Gy respectively) and a mean follow-up of about 10 months for each group, which enabled us to obtain significant and consistent results. The contingency of these two groups was verified, which enhanced the results of our study. Tumor volume (GTV) did not differ as significantly (7.2 cc vs 7.2 cc for GTV D98% < 29 Gy and ≥ 29 Gy respectively, p = 0.99) as prior treatment with SBRT or SRT, which was noticeably higher in the group GTV D98% < 29 Gy (18% vs 9%, p = 0.3 and 12% vs 4%, p = 0.2 respectively) and histological type (18% (6/34) vs 15% (7/47) for the histological type of renal cancer or melanoma, respectively). Interestingly, differences concerning received doses to target volumes were more significant for received doses to GTV rather than to PTV, which represents another reason why we may have to consider doses received to GTV with greater attention. Finally, higher doses received to GTV were not significantly associated with higher received doses to healthy brain parenchyma (5.4 cc vs 5.5 cc and 7.4 cc vs 7.3 cc respectively for V23.1Gy and V21Gy).

Brain metastases can't be approached as one entity and local control or radiation necrosis can also be dependent on the primary tumor and the administration and timing of systemic treatment. The possible impact of systemic treatment on brain metastases local control has to be considered, even if majority of agents do not have an intracranial response and in this study brain SRS was provided most of time in case of inefficiency of systemic treatments. Traditional systemic chemotherapeutic agents are known to have a limited role in the management of brain metastases, owing to the blood-brain barrier (BBB). However, more and more systemic treatments can be effective on brain metastases. Achrol et al. have reported the intracranial response rates of systemic treatments used for patients with lung cancers (22-57% for immunotherapy, 50-80% for EGFR (encoding epidermal growth factor receptor) TKI (tyrosine kinase inhibitors), 29-81% for ALK inhibitor) or with melanoma (20-58% for BRAF inhibitors). For patients with ER-or PR-positive breast cancers, hormonal therapies have shown evidence of clinical efficacy, such as cytotoxic agents like platinum or taxane-based chemotherapy [START_REF] Achrol | Brain metastases[END_REF]. The anti-VEGF antibody bevacizumab has probably a significant clinical benefit in patients with brain metastases but it has not been systematically studied because these patients were generally excluded in the literature to avoid the potential risk of intracranial hemorrhage [START_REF] Tian | Bevacizumab in Combination with Pemetrexed and Platinum Significantly Improved the Clinical Outcome of Patients with Advanced Adenocarcinoma NSCLC and Brain Metastases[END_REF]. In addition, systemic treatments can increase not only local control but also toxicity and brain radionecrosis, and this all the more that patients receive brain SRS concomitanltly. This is in fact the case for the Trastuzumab emtansine (T-DM1) antibody drug with a brain radionecrosis after SRS occurring in 39-50% of cases vs 10-15% usually [START_REF] Geraud | Preliminary experience of the concurrent use of radiosurgery and T-DM1 for brain metastases in HER2-positive metastatic breast cancer[END_REF][START_REF] Stumpf | Combination of Trastuzumab Emtansine and Stereotactic Radiosurgery Results in High Rates of Clinically Significant Radionecrosis and Dysregulation of Aquaporin-4[END_REF] and BRAF inhibitors with increase of radionecrosis and hemorrhage. So BRAF inhibitors have to be stopped at least 1 day before brain SRS [START_REF] Patel | BRAF inhibitor and stereotactic radiosurgery is associated with an increased risk of radiation necrosis[END_REF]. We have respected in our study current recommendations, that are a time-lapse of at least 1 week between chemotherapy and brain SRS, at least 1 day for BRAF inhibitors and at least 2 days for crizotinib. The other targeted therapies or immunotherapy could be provided concomitantly, according to the European Federation of Neurological Societies scientific task forces and latest published studies.

In our study, systemic treatments at the time of brain SRS were provided in 66% of cases. These systemic treatments were immunotherapy (38%), platinum or taxane-based chemotherapy (33%), hormonal therapies (12%) and targeted therapies (19%) : anti-VEGF antibody (3%), EGFR TKI (5%), ALK inhibitor (3%), PARP inhibitor (3%), BRAF inhibitor (3%) and Her2 inhibitor [START_REF] Feuvret | Stereotactic radiotherapy for large solitary brain metastases[END_REF]. So, there were many different treatments and few patients received the same, which makes very difficult to conclude in this study on the role of systemic treatment as predictive factor. In our study, systemic treatment was not a significant predictive factor of local control, overall survival or brain radionecrosis. Anyway, brain SRS was almost provided in case of inefficiency on brain disease control of systemic treatment, which strengthens data in this study concerning impact of brain SRS on local control. Even if the dosimetric analysis probably does not reflect the results on its own, it contributes significantly to them, all the more so when the results can be improved without modifying the prescribed dose or toxicity or systemic treatments.

Distant failure in the brain was observed in our study in 28.9% and 48.6% of cases at 1 year and 2 years respectively, which is in agreement with previous published studies (range: 39-52%) [START_REF] Chougule | Randomized treatment of brain metastasis with gamma knife radiosurgery, whole brain radiotherapy or both[END_REF][START_REF] Kocher | Adjuvant Whole-Brain Radiotherapy Versus Observation After Radiosurgery or Surgical Resection of One to Three Cerebral Metastases: Results of the EORTC 22952-26001 Study[END_REF][START_REF] Shirato | Stereotactic irradiation without whole-brain irradiation for single brain metastasis[END_REF]. Median OS in our study was 15 months, which was slightly higher than described in literature for patients with ≤ 4 brain metastases [START_REF] Brown | Effect of Radiosurgery Alone vs Radiosurgery With Whole Brain Radiation Therapy on Cognitive Function in Patients With 1 to 3 Brain Metastases: A Randomized Clinical Trial[END_REF][START_REF] Sahgal | Phase 3 trials of stereotactic radiosurgery with or without whole-brain radiation therapy for 1 to 4 brain metastases: individual patient data meta-analysis[END_REF] and allowed for a sufficient follow-up. We confirmed that OS is significantly correlated to the general state of health (performance status), SIR [START_REF] Weltman | Radiosurgery for brain metastases: a score index for predicting prognosis[END_REF], RPA classification [START_REF] Gaspar | Recursive partitioning analysis (RPA) of prognostic factors in three Radiation Therapy Oncology Group (RTOG) brain metastases trials[END_REF], GPA classification [START_REF] Sperduto | A New Prognostic Index and Comparison to Three Other Indices for Patients With Brain Metastases: An Analysis of 1,960 Patients in the RTOG Database[END_REF] and DS-GPA classification [START_REF] Sperduto | Summary report on the graded prognostic assessment: an accurate and facile diagnosis-specific tool to estimate survival for patients with brain metastases[END_REF] and directly correlated to systemic treatment, particularly in cases of the presence of a mutation.

Brain radionecrosis (RN) represents the most common late-delayed radiation effect of SRS. Several factors related to RN are reported, such as total radiation dose, fractionation, tumor volume, conformity index, number of isocenters, previous radiotherapy, use of chemotherapy and infratentorial location, but the main factor is the volume of the brain receiving a specific dose [START_REF] Minniti | Single-Fraction Versus Multifraction (3 × 9 Gy) Stereotactic Radiosurgery for Large (>2 cm) Brain Metastases: A Comparative Analysis of Local Control and Risk of Radiation-Induced Brain Necrosis[END_REF][START_REF] Keller | Hypofractionated Stereotactic Radiation Therapy to the Resection Bed for Intracranial Metastases[END_REF][START_REF] Minniti | Stereotactic radiosurgery for brain metastases: analysis of outcome and risk of brain radionecrosis[END_REF][START_REF] Valéry | Predictive factors of radiation necrosis after radiosurgery for cerebral metastases[END_REF][START_REF] Ruben | Cerebral radiation necrosis: incidence, outcomes, and risk factors with emphasis on radiation parameters and chemotherapy[END_REF][START_REF] Flickinger | Radiosurgery and brain tolerance: an analysis of neurodiagnostic imaging changes after gamma knife radiosurgery for arteriovenous malformations[END_REF]. Therefore, irradiation of healthy brain parenchyma should be reduced as far as possible [START_REF] Voges | Risk analysis of linear accelerator radiosurgery[END_REF][START_REF] Blonigen | Irradiated volume as a predictor of brain radionecrosis after linear accelerator stereotactic radiosurgery[END_REF]. We have reported in our study concerning large brain metastases a RN rate of 15% at the end of the follow-up (5% symptomatic RN), corresponding to 1-year actual RN risk rate of 27.6% and symptomatic RN rate of 8.8% respectively. That is in agreement with the literature, in particular with the rate of symptomatic RN of about 7.4% (range: 0-16%) reported in the meta-analysis of 24 trials concerning MF-SRT for large brain metastases [START_REF] Lehrer | Single versus Multifraction Stereotactic Radiosurgery for Large Brain Metastases: An International Meta-analysis of 24 Trials[END_REF].

Fractionation (3 fractions in general) enables a reduction of the incidence of RN for large brain metastases [START_REF] Manning | Hypofractionated stereotactic radiotherapy as an alternative to radiosurgery for the treatment of patients with brain metastases[END_REF][START_REF] Narayana | Hypofractionated stereotactic radiotherapy using intensity-modulated radiotherapy in patients with one or two brain metastases[END_REF][START_REF] Kwon | Hypofractionated stereotactic radiotherapy for the treatment of brain metastases[END_REF], with a 48-68% relative reduction in comparison to singlefraction SRS (SF-SRS) [START_REF] Lehrer | Single versus Multifraction Stereotactic Radiosurgery for Large Brain Metastases: An International Meta-analysis of 24 Trials[END_REF]. In MF-SRS (3 fractions), the most significant prognostic factor reported to date for RN is the brain volume receiving high doses: V23.1Gy (5.7% of symptomatic RN for V23.1Gy ≥ 5 cc vs 1.4%; 8.6% of symptomatic RN requiring an operation for V23.1Gy ≥ 7 cc vs 0%, p = 0.04) [START_REF] Inoue | Three-fraction CyberKnife radiotherapy for brain metastases in critical areas: referring to the risk evaluating radiation necrosis and the surrounding brain volumes circumscribed with a single dose equivalence of 14 Gy (V14)[END_REF], V21Gy (1-year risk of RN was 14% for V23.1Gy ≥ 20.9 cc vs 4%, p = 0.03) [START_REF] Minniti | Fractionated stereotactic radiosurgery for patients with brain metastases[END_REF] and V18Gy (14% vs 5% respectively for V18Gy > 30.2 cc and V18Gy ≤ 30.2 cc, p = 0.04) [START_REF] Minniti | Single-Fraction Versus Multifraction (3 × 9 Gy) Stereotactic Radiosurgery for Large (>2 cm) Brain Metastases: A Comparative Analysis of Local Control and Risk of Radiation-Induced Brain Necrosis[END_REF]. No factors in our study were independent predictive factors of RN in univariate or multivariate analysis, probably because of the limitation of healthy brain parenchyma (mean V23.1Gy, V21Gy and V18Gy of 5.8 cc, 7.9 cc and 11.5 cc respectively, which are above the previous published thresholds). This can be explained by the use of volumetric modulated arc therapy (VMAT) with non-coplanar arcs in this study. Non-coplanar multiple dynamic conformal arcs (DCA) have often been used in literature to achieve high conformity while sparing healthy tissues [START_REF] Wurm | Novalis frameless image-guided noninvasive radiosurgery: initial experience[END_REF]. More recently, VMAT has been widely developed [START_REF] Ma | Hypofractionated stereotactic radiotherapy for brain metastases: a dosimetric and treatment efficiency comparison between volumetric modulated arc therapy and intensity modulated radiotherapy[END_REF][START_REF] Mayo | Initial experience with volumetric IMRT (RapidArc) for intracranial stereotactic radiosurgery[END_REF][START_REF] Andrevska | The feasibility and benefits of using volumetric arc therapy in patients with brain metastases: a systematic review[END_REF].

1

  Abbreviations:

Figure 1 .

 1 Figure 1. Probability of local control (a), probability of progression-free survival (b) and overall survival (c) for the 69 patients receiving SRT for brain metastases.

Figure 2 .

 2 Figure 2. Comparison of local control curves of all 81 treated brain metastases between those receiving a GTV D98% < 29 Gy in three fractions and those ≥ 29 Gy.

Table 1 .

 1 Patients, brain metastases and SRT characteristics.

Table 2 :

 2 Results of univariate and multivariate analyses on local control, overall survival and radionecrosis incidence.

Table 1 .

 1 Patients, brain metastases and SRT characteristics.

Through a dosimetric study, we showed that the use of VMATnc for large brain metastases provided excellent dosimetric results in terms of target coverage, sparing of healthy brain tissue and low-dose delivery (V23.1Gy and V18Gy reduced by 36% and 25% respectively for VMATnc vs DCA).

GTV D98% is a strong reproducible significant predictive factor of local control in stereotactic radiotherapy for brain metastases. Dose prescription should lead to a GTV BED12 98% ≥ 52.4

Gy to significantly improve LC (92% vs 70%, p = 0.030) and maybe ≥ 53.4 Gy to get closer to a 100% 1-year LC, corresponding to respectively a GTV D98% ≥ 19.7-20 Gy in a single fraction and 29-29.4Gy in three fractions. An external validation of theses thresholds is necessary. Results will need to be confirmed with larger studies, other teams and other treatment techniques. Whatever, this proposed D98% is not a real change of the prescribed dose but an optimization of the actual prescribed dose.