C Duriez

E Coevoet

F Largilliere

T Morales-Bieze

Z Zhang

M Sanz-Lopez

B Carrez

D Marchal

O Goury

J Dequidt

Framework for online simulation of soft robots with optimization-based inverse model

Soft robotics is an emerging field of robotics which requires computer-aided tools to simulate soft robots and provide models for their control. Until now, no unified software framework covering the different aspects exists. In this paper, we present such a framework from its theoretical foundations up to its implementation on top of SOFA, an open-source framework for deformable online simulation. The framework relies on continuum mechanics for modeling the robotic parts and boundary conditions like actuators or contacts using a unified representation based on Lagrange multipliers. It enables the digital robot to be simulated in its environment using a direct model. The model can also be inverted online using an optimization-based method which allows to control the physical robots in the task space. To demonstrate the effectiveness of the approach, we present various soft robots scenarios including ones where the robot is interacting with its environment. The software is freely available from https://project.inria.fr/softrobot/

I. INTRODUCTION

Soft robotics raises interdisciplinary challenges involving material science, mechanical and electrical engineering, control theory, chemistry, physics, biology, computational mechanics and computer science. While the term soft is used, it actually means non rigid and is therefore employed for robots whose mechanical functioning relies on using deformable structures in a way similar to the biological world and organic materials. The use of deformable materials makes them very compliant, which provides natural key positive outcomes. Soft robots exhibit new types of functional capabilities that are complementary to traditional robotics. They can improve the safety of access to fragile parts of an environment by applying minimal pressure to its walls. Moreover, their large number of degrees of freedom combined with a redundant actuation can ease the manoeuvring through soft and confined spaces. This is particularly relevant for medical and surgical robotics [START_REF] Cianchetti | Soft robotics technologies to address shortcomings in today's minimally invasive surgery: The stiff-flop approach[END_REF], manipulation of fragile objects, domestic robotics with safer interactions with humans, arts and entertainment [START_REF] Lipson | Challenges and opportunities for design, simulation, and fabrication of soft robots[END_REF].

However, these outcomes often require a complex design. Building robots capable of complex tasks relies on having modeling and simulation tools [START_REF] Koenig | Design and use paradigms for gazebo, an open-source multi-robot simulator[END_REF], which is now a standard element in toolkits dedicated to rigid robotics. However, no such tool exists in soft robotics. The main reason is related to the motion of soft robots obtained through deformation of the structure rather than by articulations. Therefore, the behavior of soft robots should be modeled using deformable mechanics. Quoting [START_REF]First robosoft working paper[END_REF]: "There exists well established theories as mechanics of continuous media. In robotics, we need to extract minimal models exploitable for analysis, for control, and to help direct goal-oriented design in particular toward control. In this respect, it will require a big effort to build generic modeling tools suited to soft robotics". The presented work is our contribution to this "big effort". The use of continuum mechanics raises several issues. No analytic solution exists in the general case and numerical methods, typically the finite element method (FEM), have to be used. This involves the discretization of the robot geometry which is not trivial (quality of the elements, tradeoff between accuracy and computation time. . . ). In addition, due to their natural compliance, soft robots are often used in contact with their environment, which increases the complexity of the modeling as well as the computational cost as identified in recent surveys about deformable robots [START_REF] Lipson | Challenges and opportunities for design, simulation, and fabrication of soft robots[END_REF], [START_REF] Trivedi | Soft robotics: Biological inspiration, state of the art, and future research[END_REF], [START_REF] Kim | Soft robotics: A bioinspired evolution in robotics[END_REF], [START_REF] Rus | Design, fabrication and control of soft robots[END_REF].

In this paper, we present a new software framework to model and simulate soft robots and their environment. The framework uses continuum mechanical modeling of soft materials combined with the Finite Element Method (FEM) for their numerical resolution. Boundary conditions are defined as constraints for both contacts and robot actuators. This framework unifies several of our previous works among which: the methodology of the inverse optimization to transfer the motion from task space to motion space presented in [START_REF] Coevoet | Introducing interactive inverse FEM simulation and its application for adaptive radiotherapy[END_REF] with direct simulation [START_REF] Duriez | Control of Elastic Soft Robots based on Real-Time Finite Element Method[END_REF], dynamic and quasi-static formulations [START_REF] Bosman | Domain decomposition approach for fem quasistatic modeling and control of continuum robots with rigid vertebras[END_REF]. It also provides contact management as in [START_REF] Courtecuisse | Real-time simulation of contact and cutting of heterogeneous soft-tissues[END_REF] and apparent stiffness control of the structure in case of redundant actuation [START_REF] Largilliere | Stiffness rendering on soft tangible devices controlled through inverse fem simulation[END_REF].

The framework is implemented as a plugin for SOFA, an open-source toolkit geared towards interactive medical simulation. The motivations to use a medical simulation framework for robotic applications are numerous. Medical simulation and soft robotics make use of strongly deformable materials in complex arrangements. SOFA allows the simulation of such a complex arrangement and features many deformable models, several spatio-temporal integration schemes and accurate contacts management. It also interfaces many hardware sensors or haptic devices and finally can be run both offline and online. Using this plugin, we simulate soft robots from the state of the art [START_REF] Hassan | Design and development of a bio-inspired, under-actuated soft gripper[END_REF], [START_REF] Mosadegh | Pneumatic networks for soft robotics that actuate rapidly[END_REF] as well as our own prototypes which include robots for grasping, navigating, handling objects or interacting with humans.

This paper is organized as follows: in Section II, we provide an overview of the modeling and simulation tools for soft robotics. Section III contains the theoretical foundation of our framework. Section IV explains how direct and inverse models are implemented. Section V contains implementation aspects related to the SOFA plugin and Section VI presents examples of soft robots modeled and simulated with our framework.

II. RELATED WORK

Soft robotics is a very recent and active field where researchers are actively exploring robots designs and their usages. One of the difficulty with soft robotics is that softness can be achieved with various approaches from soft materials like silicone [START_REF] Tolley | A resilient, untethered soft robot[END_REF], [START_REF] Martinez | Robotic tentacles with three-dimensional mobility based on flexible elastomers[END_REF] , micro-structured materials [START_REF] Schumacher | Microstructures to control elasticity in 3d printing[END_REF] or specifically designed geometrical arrangement of rigid parts as with Tensegrity structures [START_REF] Caluwaerts | Design and control of compliant tensegrity robots through simulation and hardware validation[END_REF]. In addition to the material itself, actuation systems are very diverse with approaches including cables [START_REF] Hassan | Design and development of a bio-inspired, under-actuated soft gripper[END_REF], pneumatics [START_REF] Shepherd | Multigait soft robot[END_REF], [START_REF] Martinez | Elastomeric origami: Programmable paperelastomer composites as pneumatic actuators[END_REF], shape memory alloys [START_REF] Villanueva | A biomimetic robotic jellyfish (robojelly) actuated by shape memory alloy composite actuators[END_REF] or chemical reaction [START_REF] Mosadegh | Pneumatic networks for soft robotics that actuate rapidly[END_REF].

In the field of rigid robotics, one can use either dedicated products like WorkspaceLt, RoboticSimulation, NI-Robotics RoboNaut or SimRobot or general purpose open-source software like Gazebo [START_REF] Koenig | Design and use paradigms for gazebo, an open-source multi-robot simulator[END_REF]. The cited tools rely on off-theshelves simulation kernels such as Open Dynamics Engine, Bullets, NVidia PhysX or DART. These simulation kernels come from the video-game industry and are often focused on articulated-rigid bodies. They have been successfully used to model and simulate soft robots as in the NASA Tensegrity Robotics Toolkit [START_REF] Caluwaerts | Design and control of compliant tensegrity robots through simulation and hardware validation[END_REF] or in [START_REF] Rieffel | Evolving soft robotic locomotion in physx[END_REF] with the use of PhysX to evaluate the candidate solutions of genetic algorithms. The video-game based simulation frameworks are fast and efficient to compute rigid-body simulations as well as some kind of soft bodies. They are also relatively easy to use as required background knowledge in physical modeling is reduced. The counterpart is that very few of them are capable of modeling physically realistic deformable materials.

When a realistic deformable material simulation is needed, tools from the structural and multi-physics analysis field, as Abaqus or ComSol, are an option. They rely on precise modeling formulations of continuous mechanics and some of them are capable to handle multi-physics. The cost for such capabilities is the slow computation speed and the fact that a good understanding of physical modeling is required. The consequence is that they are only usable for offline simulation of soft robots in combination with CAD software while designing the soft robotic parts [START_REF] Martinez | Elastomeric origami: Programmable paperelastomer composites as pneumatic actuators[END_REF]. Simpler alternatives exist such as Voxelyze. Presented in [START_REF] Hiller | Dynamic Simulation of Soft Multimaterial 3D-Printed Objects[END_REF], it simulates soft materials undergoing large deformations and is associated with VoxCAD a GUI simplifying the editing of the robot. Voxelyze relies on voxels to represent the object. It is used in [START_REF] Cheney | Unshackling evolution: Evolving soft robots with multiple materials and a powerful generative encoding[END_REF] to evaluate through simulation the walking capabilities of soft robots produced by genetic algorithms. In [START_REF] Cheney | Evolving soft robots in tight spaces[END_REF], the same authors added interaction between the robot and its environment. Nevertheless, with a voxel simulation, it is not possible to approximate some geometrical shapes without an exaggerated number of voxels which leads to an increased computation time. In addition, with Voxelyze, the mechanical model is using beam theory on the lattice supporting the voxels. Such an approach may not capture the continuous material deformation in a realistic manner.

Research in the field of surgical and biomedical simulation also developed simulation framework [START_REF] Payan | Soft tissue biomechanical modeling for computer assisted surgery[END_REF]. The interesting point of these frameworks is the focus on deformable objects and complex interactions. A tool like SOFA can simulate a large choice of mechanical models: from rigid-bodies or mass-spring to one implementing realistic hyperelastic material with FEM [START_REF] Faure | Sofa: A multi-model framework for interactive physical simulation[END_REF]. They can operate on a wide range of geometrical descriptions from 1D (curve) and 2D (surface mesh) to 3D (voxels, multi-resolution octrees [START_REF] Nesme | Preserving topology and elasticity for embedded deformable models[END_REF] or hexahedral and tetrahedral mesh). They are capable of handling collisions and contacts precisely as well as to handle multi-physics behaviors [START_REF] Talbot | Towards an interactive electromechanical model of the heart[END_REF], [START_REF] Talbot | Augmented Reality for Cryoablation Procedures[END_REF]. They are also capable of interacting with sensing hardware (Kinect, OptiTrack, LeapMotion) that are commonly used in robotics as well as with haptic devices [START_REF] Peterlik | Constraint-based haptic rendering of multirate compliant mechanisms[END_REF]. A framework like SOFA can be considered as a bridge between video-game and structural analysis approaches and is chosen for this work.

In the following of this paper, we will present the plugin we realized for SOFA that is dedicated to soft robotics.

III. MODELING FOR REAL-TIME SIMULATION

The theoretical foundations of our simulation framework for deformable objects are the ones of continuum mechanics for the material modeling, Lagrangian multipliers for constraints solving, and Signorini's law for contacts.

Let us start with the formulation given by the second law of Newton, that models the dynamic behavior of a body as:

M(q) v = P(t) -F(q, v) + H T λ (1)
where q ∈ R n is the vector of generalized degrees of freedom (for instance, displacement of the nodes of a mesh), M(q) : R n → M n×n is the inertia matrix, v = q ∈ R n is the vector of velocity. F represents internal forces applied to the simulated object depending on the current state and P gathers known external forces. H T is the matrix containing the constraint directions while λ ∈ R n is the vector of Lagrange multipliers containing the constraint force intensities.

In the following, we will present how these different terms can be computed.

A. Mechanical modeling

To compute F, one needs to pick a deformation law. The underlying assumption is that all solids are deformable and the amount of deformation depends only on the external loads. This relationship between the loads and resulting deformations is the constitutive equation. A common equation, the Hooke's law, makes the assumption of linearity of material response to loads. Other laws exists to express nonlinear strain-stress relationship, plastic deformations, brittles or hysteresis behavior. Different laws have different computation costs and one has to carefully choose the law that fits best the needs and computation time constraints. Most of the time, we limit the deformation cases to purely elastic behavior: the robot goes back to its initial shape when the actuation is released and the parameters of the materials are given by the Young modulus and the Poisson's ratio of the Hook's law. Different levels of complexity exist in the elastic deformation law which are: small displacements, large displacements, large deformations but for most of our robots, we rely on large displacements where a non-linear computation is performed to obtain the strain with a linear stress-strain relationship.

Depending on the constitutive equations and the geometrical representation, several possibilities exist in Sofa to model deformable materials. When dealing with 1D structures, one can use beam elements [START_REF] Duriez | New approaches to catheter navigation for interventional radiology simulation[END_REF] or geometrical curves as in [START_REF] Theetten | Quasi-dynamic splines[END_REF]. For 3D structures, there exist mass-spring models, co-rotational FEM [START_REF] Felippa | A systematic approach to the elementindependent corotational dynamics of finite elements[END_REF], embedded deformable solids [START_REF] Nesme | Preserving topology and elasticity for embedded deformable models[END_REF] as well as hyperelastic models to handle large deformations [START_REF] Faure | Sofa: A multi-model framework for interactive physical simulation[END_REF]. More concretely, each of these models can compute the F term in Equation 1.

B. Actuator constraint

In our framework, we handle the actuation by defining specific constraints with Lagrange multipliers on the boundary conditions of the deformable models.

Two types of actuators are considered in this work:

• Cable: when actuation is done by placing cables inside the structure of the robot to pull at certain points and create a deformation. The function δ a (x) measures the length of the cable which is modified by the actuation. λ a is the force applied by the cable on the structure. • Pneumatic: when actuation is done by exerting a variation of pressure on the surface of the deformable material. In such a case, δ a (x) is a measure of the volume of the cavity. λ a is the uniform pressure inside the cavity. It is possible to specify the behavior of the actuator either by assigning the value of λ a or by setting the value of δ a (x) in the resolution process.

C. Contact constraint

When a potential contact on the robot has been detected, δ c (x) measures the shift between the robot and the obstacle at the contact point and λ c is the contact force. In order to add the modeling of the environment, we need to deal with contact mechanics and find the value of λ c . For that, we will rely on a formulation of the complementarity problem using Signorini Conditions [START_REF] Courtecuisse | Real-time simulation of contact and cutting of heterogeneous soft-tissues[END_REF], [START_REF] Faure | Sofa: A multi-model framework for interactive physical simulation[END_REF]:

0 ≤ δ c ⊥ λ c ≥ 0 (2)

D. End effector and task space definition

It is possible to specify a constraint in the task space. It is particularly useful to obtain a direct or inverse model of the robot (see the following section). In this case, δ e (x) measures the shift along x, y and z between controlled point(s), which is (are) considered as effector and desired position(s) or trajectory.

For all constraint types, at each line i of the matrix H, we have

H i = ∂δi(x)
∂x .

IV. NUMERICAL RESOLUTION

In this section, we describe how we integrate in time the equation of the dynamics (Eq. 1) and the numerical approaches used to solve the constraints.

A. Time integration or quasi-static formulation

We integrate equation 1 using a time-stepping implicit scheme (backward Euler) to have unconditional stability. Let us consider the time interval

[t i , t f ] whose length is h = t f -t i : M(v f -v i ) = h (P(t f ) -F(q f , v f )) + hH T λ (3) q f = q i + hv f (4)
The internal forces F are a nonlinear function of the positions and the velocities. We then apply a Taylor series expansion to F and make the following first order approximation:

F(q f , v f )) = F (q i +dq, v i +dv) = f i + δF δq dq+ δF δv dv (5)
Using dq = q f -q i = hv f and dv = v f -v i , we obtain:

M + h δF δv + h 2 δF δq A dv dx = -h 2 δF δq v i -h (f i + p f ) b +hH T λ (6)
where p f is the value of the function P at time t f . The only unknown values are the Lagrange multipliers λ ; their computation is detailed in Section IV-B. In the remainder of this section, we will refer to this system using the matrix A and the vector b.

If the deformable robot is attached to the ground (like a manipulator) and its motion is performed at a low velocity, we can ignore the dynamic part (Eq. 1) and use a static formulation:

P -F (q) + H T λ = 0 (7)
Again, the Taylor series expansion (5) can be used to obtain a unique linearization per simulation step:

δF δq A dq dx = P -f i b +H T λ (8)
We obtain a formulation similar to the dynamic case (Eq. 6) with h = 1.

B. Solving the constraints

From Equation 6 in dynamics or 8 in quasi-statics, the equation has two unknowns: dx which provides the motion of the degrees of freedom and λ i , which is the intensity of the actuators and contact loads. Consequently, the solving process will be executed in two steps.

The first step consists in obtaining a free configuration q free of the robot that is found by solving Equation 8 while considering that there is no actuation and no contact applied to the deformable structure.

Adx free = b (9) q free = q i + h(v i + dx free ) (dynamic) (10)

q free = q i + dx free (quasi -static) (11)
To solve the linear equation (Eq. 9), we use a LDL T factorization of the matrix A. Given this new free position q free for all the nodes of the mesh (i.e. position obtained without load on actuation or contact), we can evaluate the values of δ free i = δ i (q free ), defined in the previous section. The second step is based on an optimization process that provides the value of λ. In the following sections, we will define two cases of use: direct and inverse modeling. In both cases, the approach relies on an optimization process and its output is the value of the Lagrange multipliers. The size of matrix A is often very large so an optimization in the motion space would be computationally very expensive. To perform this optimization in real-time, we propose to project the problem in the constraint space using the Schur complement:

δ i = h 2 H i A -1 H T j Wij λ j + δ free j (12)
The physical meaning of this Schur complement is central in the method. W ij provides a measure of the instantaneous mechanical coupling between the boundary conditions i and j, whether they correspond to an effector, an actuator or a contact. In practice, this projection allows to perform the optimization with the smallest possible number of equations.

It should be emphasized that one of the main difficulties is to compute W ij in a fast manner. No precomputation is possible because the value changes at each iteration. But this type of projection problem is frequent when solving friction contact on deformable objects, thus several strategies are already implemented in SOFA [START_REF] Courtecuisse | Real-time simulation of contact and cutting of heterogeneous soft-tissues[END_REF], [START_REF] Faure | Sofa: A multi-model framework for interactive physical simulation[END_REF].

After solving the optimization process described in the two following subsections (Direct and Inverse modeling), we get the value of λ, and we can compute the final configuration of the soft robot, at the end of each time step using:

dx = dx free + hA -1 H T λ (13)
Which provides the solution to equation 6 or 8. a) Direct modeling of the robot in its environment: the inputs are the actuator values (either δ a or λ a ) and the output is the displacement of the effector. When δ a is the input, the optimization provides the values of λ a as output. In case of contact, an additional output is the contact response λ c (also found by optimization).

As explained above, using the operator W ea , we can get a measure of the mechanical coupling between effector(s) and actuator(s), and with W aa , the coupling between actuators. On a given configuration, W ea provides a linearized relationship between the variation of displacement ∆δ e created on the end-effector and the variation of the effort ∆λ a on the actuators. To get a direct kinematic link between actuators and effector point(s), we need to account for the mechanical coupling that can exist between actuators. This coupling is captured by W aa that can be inverted if actuators are defined on independent degrees of freedoms. Consequently, we can get a kinematic link by rewriting Equation 12:

∆δ e = W ea W -1 aa ∆δ a ( 14
)
This relationship provides (in the most condensed way) the displacement of the effector given the displacements of the actuators. Matrix W ea W -1 aa is equivalent to a jacobian matrix for a standard, rigid robot. This corresponds to a local linearization provided by the FEM model on a given configuration and this relationship is only valid for small variations of ∆δ a , and in contactless cases.

b) Inverse modeling of the robot: the input is the desired position of the effector and the output is the force λ a or the motion δ a that needs to be applied on the actuators in order to minimize the distance with the effector position. λ a is found by optimization and δ a can be obtained using equations 12. We use this method in contactless cases.

The optimization consists in reducing the norm of δ e which actually measures the shift between the end-effector and its desired position. Thus, computing min( 12 δ T e δ e ) can be done by setting a Quadratic Programming (QP) problem:

min 1 2 λ a T W T ea W ea λ a + λ a T W T ea δ free e ( 15
)
subject to (course of actuators) : δ min ≤ δ a = W aa λ a + δ free a ≤ δ max and (case of unilateral effort actuation) :

λ a ≥ 0 (16)
The use of a minimization allows to find a solution even when the desired position is out of the workspace of the robot. In such a case, the algorithm will find the point that minimizes the distance with the desired position while respecting the limits introduced for the stroke of the actuators.

The matrix of the QP, W T ea W ea , is symmetric. If the number of actuators is equal or less than the size of the effector space, the matrix is also positive-definite. In such a case, the solution of the minimization is unique.

In the opposite case, i.e when the number of actuators is greater than the degrees of freedom of the effector points, the matrix of the QP is only semi-positive and the solution could be non-unique. In such a case, some QP algorithms are able to find one solution among all possible solutions [START_REF] Sha | Multiplicative updates for nonnegative quadratic programming in support vector machines[END_REF]. In practice, we add to the cost function of the optimization a minimization of the deformation energy in the actuator space: The QP matrix is regularized by adding W aa (with chosen sufficiently small to keep a good accuracy on the effector motion).

V. IMPLEMENTATION

In the previous section, we have presented the theoretical foundation of our approach. We will now see more concretely how this translates in the SOFA plugin.

A. Concepts of the framework

In a way similar to Gazebo [START_REF] Koenig | Design and use paradigms for gazebo, an open-source multi-robot simulator[END_REF], SOFA has a scene-graph based simulation architecture. A scene contains the robot and its environment and is described in XML or with a Python script. SOFA is also a component based architecture. A robot is then an assembly of elementary components: some components are for rendering, others for contact or topology encoding, others for numerical integration or mechanical modeling. For simulation, the most important components are the Mass (that computes M), the Force Fields (P(t), F and δF δq )), the MechanicalObject (which stores the state vectors q, v, dq).

B. Multi-model and mapping

SOFA also introduced multiple model representation. Multi-model means that in a simulated object a property can be represented in multiple ways. A good example is the shape of a robot. A low resolution tetrahedral mesh can be used for FEM while using a high resolution triangular mesh for the rendering and a low resolution triangle mesh for the contact management.

To connect the representations, SOFA introduces Mappings. Given the position of the degrees of freedom q of a representation, one can define a second representation with p = J(q), where J is a possibly non-linear mapping function.

The strength of Mappings is that constraints on a representation can be transferred to a second representation. Using this tool, we can gather actuators, effectors and contacts from different representations to obtain a full system without having to change the implementation of the components. They are defined regardless of the geometrical dimension of the object (1D, 2D, 3D), geometrical representation (voxel, curve, octree, tetrahedral mesh) or mechanical model.

C. Soft robotic actuators

Using our framework, we have implemented simple actuator designs for cables and pressure.

For cable actuation, the function δ a (q) measures the length of the cable, depending on the position of the degrees of freedom q of the deformable model. To avoid re-coding the model of the cable for each type of degrees of freedom in q, we define the path of the cable on a set of 3D points (x 1 , ..., x n ) that are mapped on the motion of q using a mapping J. In practice, servomotors and pulleys are used to pull the cable. The rotation angle of the motor is either provided as a setpoint or computed using the inverse model. An Arduino R board pilots the motors online. The simulation sends the setpoints to the Arduino with a serial communication protocol.

In the case of pressure actuators, the function δ a (q) measures the volume of the cavity, depending also on the position of the degrees of freedom q of the deformable model. The surface pressure is applied via a Mapping to the underlying volumetric model. We then model and simulate the pneumatic actuator shown in Figure 1. In practice, electronically controlled pneumatic valves are used to apply the computed pressure into the cavities.

VI. RESULTS & VALIDATION

The methodology described in this paper allows for the simulation of soft robots in their environment in real-time. Moreover, the inverse model allows online control in the actuator space. The model and control of various robots with different geometric and mechanical characteristics, as well as different actuation schemes, are presented in this section. Table VI-A provides a quick overview of the results. The computation timing are based on a modern machine (Intel Core i5-4590 CPU). This paper is accompanied by a video that allows to have a better understanding of the results.

A. Graspers

In [START_REF] Hassan | Design and development of a bio-inspired, under-actuated soft gripper[END_REF], the authors present an underactuated grasper design. This grasper is made of silicone and the actuation is done by three cables pulled by a single motor. We successfully modeled this robot and simulated it in real-time. The fingers are simulated using corotational FEM and the cube is a rigid body. Corotational FEM relies on a tetrahedral1 mesh. Contact and friction modeling are added to the object to allow prehension. This design evolved into the grasper of Flexo (Subsect. VI-D) made of 3D printed plastic. A close approach was then used to model and simulate an octopus tentacle and the movement of the simulated tentacle was then compared to the physical one (Fig. 2).

B. Diamond: A platform made of silicone and actuated through cables.

The Diamond platform (Fig. 4) is made of a single piece of silicone. Four cables, pulling the structure, are connected to servomotors for actuation. For simulation, the silicone is modeled using FEM. The robot can then be controlled, either in the simulation or in the real world, from its endpoint thanks to our inverse simulation method. A stereo-vision system is used to track the position of points of interest in the real robots, which are then compared to those given by the simulation. The maximum positioning error obtained by the inverse model in open loop is 2,9mm, the mean error is 1,4mm. More details are given in [START_REF] Duriez | Control of Elastic Soft Robots based on Real-Time Finite Element Method[END_REF] and [START_REF] Largilliere | Real-time control of softrobots using asynchronous finite element modeling[END_REF].

C. Fetch: A pneumatic manipulator made of silicone.

The robotic part presented in Figure 5 is a differential pressure platform. Three cavities with a cylindrical accordion shape are inflated to provide an elongation that will extend or tilt the whole element. Several of these platforms can be stacked to increase the reachable space of the robot. The size of the FEM model of the robot (15456 degrees of freedom) would have prevented from real-time computation. Consequently, we have applied the model reduction method detailed in [START_REF] Bosman | Domain decomposition approach for fem quasistatic modeling and control of continuum robots with rigid vertebras[END_REF] to obtain a strong reduction of the number of degrees of freedom. The model reduction is based on the structure of the robot (continuum robot with rigid vertebrae). We end up with a model based on the degrees of freedom of the rigid vertebrae (here 12 degrees of freedom). The deformations and the pressure actuation model are mapped on these degrees of freedom to accelerate the computation.

D. Flexo: A manipulator made of deformable material actuated with cables

The robot presented in Figure 5 is composed of several sections, each of which are made of 3 fork-rib shapes disposed each 120 degrees around the longitudinal direction. Branches have been modeled with beam elements.

E. Stifface: a soft robot acting as a human computer interface

Deformable robotics allows the creation of novel haptics interfaces with soft materials. We use our framework to simulate and control the Stifface interface. The device, detailed in [START_REF] Largilliere | Stiffness rendering on soft tangible devices controlled through inverse fem simulation[END_REF], is made of silicone and aims to render different apparent stiffness to a user exploring a virtual surface. The silicone is modeled with hyperelastic Neohookean FEM and the cable actuation system is reproduced in the same configuration as in the real device.

F. Sofia: a walking robot

The figure (Fig. 7) presents Sofia, a walking robot. It is made of 6 silicone legs. Its body is an assembly of 3D printed ABS parts with a structural pattern that increases its flexibility. There are 6 servomotors coupled through a crankshaft to the legs, as well as 6 others actuating the structure through cables. The robot was modeled and its walking motion was simulated in a virtual environment before going to the real field.

VII. CONCLUSIONS

This paper presents the mathematical basis as well as a software framework that targets the design, simulation and control of soft robots. This framework relies on a mechanical representation of the robot, its actuators, effector and possible contacts with the environment. Using equations from continuum mechanics, the motion of the robot can be simulated. Moreover, the environment can be taken into account through its mechanical representation in the simulation. An inverse problem optimization automatically computes the actuation to obtain control in the task space. Real-time is obtained in both cases (direct and inverse) using relatively coarse meshes. The capabilities of this framework are illustrated with several examples and we show that a reasonable accuracy between simulated and real soft robots can be obtained.

The modularity of the framework encourages many extensions. For instance, future works may include adding more complex mechanical laws, adding robust control laws or designing complex and dynamic environments. This will increase the computational footprint of the simulation whereas the short computation time needs to be maintained in order to do online control of the robot. Therefore, advanced numerical methods such as reduced-order modeling or dedicated solvers should be considered to achieve sufficient accuracy without increasing the computation cost of the simulation.

Fig. 1 .

 1 Fig. 1. Simulation (left) and real (right) cable actuators (top) and pressure actuators (bottom).

Fig. 2 .Fig. 3 .

 23 Fig. 2. Simulation of the soft grasper described in [36] (top left). Grasper of Flexo (top right). Comparison between simulated (bottom left) and real (bottom right) octopus tentacle based on a similar design.

Fig. 4 .

 4 Fig. 4. Simulated version of the Diamond robot (left) and the physical one (right).

Fig. 5 .

 5 Fig. 5. Top: Control from inverse simulation of two Fetch platforms stacked for the Soft Robotic Toolkit 2015 competition. Bottom: Simulation of Flexo (left) and the real robot (right).

Fig. 6 .

 6 Fig. 6. Simulation of the Stifface interface (left) and real prototype (right).

Fig. 7 .

 7 Fig. 7. The Sofia walking robot simulated in a virtual world (left) and in real during the Robosoft Grand Challenge 2016 (right).

For most of our robots, the volumetric meshes are generated directly in SOFA with the CGAL[START_REF] Fabri | Cgal: The computational geometry algorithms library[END_REF]


Marion Leca

Charléric Bornet

Marc Montana

Christophe Curti

Patrice Patrice

Leca Marion

Bornet Charléric

Montana Marc

Curti Christophe

Patrice Vanelle
email: patrice.vanelle@univ-amu.fr

Les vaccins méningocciques : état des lieux et perspectives Meningococcal vaccines: current state and future outlook

Keywords: Neisseriameningitidis, vaccin, Bexsero®, vaccinologie inverse Neisseria meningitidis, vaccine, Bexsero ®, Trumemba, ® reverse vaccinology

Invasivemeningococcal disease(IMD) is perceived as a serious threat by the public, who are veryinfluencedboth by the media,andbythe medical professions. [START_REF] Turner | The use and misuse of media headlines: lessons from the MeNZBimmunisation campaign[END_REF]These infectionshavedifferentclinical consequences(meningitis,septicemia, arthritis,pneumonia, andpericarditis), which canoccur simultaneously, sometimes inducing misdiagnosis. [START_REF] Strelow | Invasive meningococcal disease[END_REF][START_REF] Stephens | Biology and pathogenesis of the evolutionarily successful, obligate human bacterium Neisseria meningitidis[END_REF] Meningococcal infectionsremaina public healthproblem throughout the world. [START_REF] Strelow | Invasive meningococcal disease[END_REF][START_REF]Meningococcal vaccines: WHO position paper, Novembre2011[END_REF]Indeed, in the context of the developmentand accessibility ofrelatively newvaccines(especiallyagainstHaemophilusinfluenzae typebandStreptococcus pneumoniae), Neisseria meningitidisis considered one ofthemost frequentinfectious causesof deathoutside the neonatal period. [START_REF] Mcintyre | Effect of vaccines on bacterial meningitis worldwide[END_REF][START_REF] Roderick | Advances towards the prevention of meningococcal B disease: a multidimensional story[END_REF][START_REF] Whitney | Decline in invasive pneumococcal disease after the introduction of protein-polysaccharide conjugate vaccine[END_REF]The diversity ofmeningococcal strainsis correlated tothe antigenic variabilityof the bacterialcapsule. [START_REF] Stephens | Epidemic meningitis, meningococcaemia, and Neisseria meningitidis[END_REF][START_REF] Swartley | Capsule switching of Neisseria meningitidis[END_REF] In accordance withserologicalmethods based onthe composition of the polysaccharide capsule, an international nomenclaturewas established toidentify andto monitorprecisely epidemicclones. [START_REF] Yogev | Meningococcal disease: the advances and challenges of meningococcal disease prevention[END_REF]ThisclassifiesNeisseriainto13distinct serogroups, of which6 (A,B, C, W135, X andY) are distinguished by their highvirulencefor humans. [START_REF] Stephens | Biology and pathogenesis of the evolutionarily successful, obligate human bacterium Neisseria meningitidis[END_REF][START_REF] Stephens | Epidemic meningitis, meningococcaemia, and Neisseria meningitidis[END_REF][START_REF] Swartley | Capsule switching of Neisseria meningitidis[END_REF][START_REF] Racloz | The elusive meningococcal meningitis serogroup: a systematic review of serogroup B epidemiology[END_REF] Since theintroductionof polysaccharide conjugate vaccinesagainstserogroupsA, C, W-135 andY, serogroup Bhas emerged asthe basic cause ofIMD, particularly in Europe and NorthAmerica,where itcreates hyperendemic or epidemic situations, especially due to the lack of prophylaxis for this serogroup. [START_REF]Meningococcal vaccines: WHO position paper, Novembre2011[END_REF][START_REF] Racloz | The elusive meningococcal meningitis serogroup: a systematic review of serogroup B epidemiology[END_REF] Thus, the best strategyagainstIMDremainsprimary preventionviameningococcalvaccination, including the development of avaccine targetingserogroup B. [START_REF] Stephens | Biology and pathogenesis of the evolutionarily successful, obligate human bacterium Neisseria meningitidis[END_REF][START_REF] Yogev | Meningococcal disease: the advances and challenges of meningococcal disease prevention[END_REF][START_REF] Kaaijk | Routine vaccination against MenB: Considerations for implementation[END_REF][START_REF] Vipond | History of meningococcal vaccines and their serological correlates of protection[END_REF] 1.Development of a meningococcalgroup B vaccine

The needfor meningococcalgroup B vaccine

The epidemiology ofmeningococcal diseaseis dynamic: allserogroupsvarytemporallyand geographically. [START_REF] Roderick | Advances towards the prevention of meningococcal B disease: a multidimensional story[END_REF][START_REF] Yogev | Meningococcal disease: the advances and challenges of meningococcal disease prevention[END_REF][START_REF] Halperin | The changing and dynamic epidemiology of meningococcal disease[END_REF] Thismarked disparitycan mainly be explainedby differencesin immunity among ethnic groups,andby the influence of environmental factors. [START_REF] Stephens | Biology and pathogenesis of the evolutionarily successful, obligate human bacterium Neisseria meningitidis[END_REF][START_REF] Roderick | Advances towards the prevention of meningococcal B disease: a multidimensional story[END_REF] Each year, IMD estimatesrise by1.2 million casesworldwide, including 135,000deaths. [START_REF] Kaaijk | Routine vaccination against MenB: Considerations for implementation[END_REF]In response to thesealarming statistics, the World Health Organization(WHO)has for example introducedspecificvaccinationcampaignsagainst serogroupAin Africa where it is predominantto limitlargemeningococcalepidemics. [START_REF] Halperin | The changing and dynamic epidemiology of meningococcal disease[END_REF][START_REF] Djingarey | Effectively introducing a new meningococcal A conjugate vaccine in Africa: the Burkina Faso experience[END_REF] However, the threat persists, especially in industrialized countries where serogroup B is involved in most cases of IMD (84% of IMD in Australia, 83% in New Zealand, 76%

in Europe and 35% in the United States).In Europe, the annual incidence of serogroup B is 1 case per 100,000

population. [START_REF] Halperin | The changing and dynamic epidemiology of meningococcal disease[END_REF] According to epidemiology data, some populations are more sensitive to infection. In the United States, nearly 60% of IMD in infants under the age of 59 months is caused by serogroup B. [START_REF] Cohn | Prevention and control of meningococcal disease: recommendations of the Advisory Committee on Immunization Practices (ACIP)[END_REF] In France,the highestincidenceis observedin infantsaged 0-12 months, withthe annual incidencereaching 11.1cases per 100,000 population. This rateis correlated to the immaturity of their immune system.

Ahigh incidence is also observedlater,in young adultsaged 15-24: at 19years, the incidencerisesto 2.89cases per 100,000 population. [START_REF] Christensen | Meningococcal carriage by age: a systematic review and meta-analysis[END_REF][START_REF] Invs | Les infections invasives à méningocoque en France en[END_REF]The social behavior ofyoung adults canfacilitateexposureto strainsagainstwhich theyhave no immunity. [START_REF] Christensen | Meningococcal carriage by age: a systematic review and meta-analysis[END_REF][START_REF] Maclennan | Social behavior and meningococcal carriage in British teenagers[END_REF] IMDs are characterized by theirglobal distribution, theirepidemic potential, their unpredictability(theirpotential toalterthe health ofa healthy individualwithoutany history of illness),theirrapidprogressionand theirminor andnonspecificsymptoms. [START_REF] Stephens | Biology and pathogenesis of the evolutionarily successful, obligate human bacterium Neisseria meningitidis[END_REF][START_REF] Roderick | Advances towards the prevention of meningococcal B disease: a multidimensional story[END_REF][START_REF] Stephens | Epidemic meningitis, meningococcaemia, and Neisseria meningitidis[END_REF][START_REF] Pace | Meningococcal disease: clinical presentation and sequelae[END_REF][START_REF] Maiden | Can we, should we, eradicate the meningococcus?[END_REF]All thesefactorsexplainthe severity of theseinfections, andwhy rapiddiagnosisand immediateinitiation of treatment are vital. [START_REF] Strelow | Invasive meningococcal disease[END_REF] Despite technicalandtherapeutic advances, the overall mortality rate remains between 10%and 15%, and up to 19%

ofsurvivors have disablingsequelaesuch ashearing loss, cognitive dysfunction, motor nerve deficits, seizure disorders, amputation. [START_REF] Cohn | Prevention and control of meningococcal disease: recommendations of the Advisory Committee on Immunization Practices (ACIP)[END_REF][START_REF] Pace | Meningococcal disease: clinical presentation and sequelae[END_REF] Given the severity of meningococcalinfections, developing ameningococcalBvaccinethat can controlthe most of thesedevastating epidemicshas become a realpriority formedical research. [START_REF] Christensen | Meningococcal carriage by age: a systematic review and meta-analysis[END_REF][START_REF] Caron | From tailor-made to ready-to-wear meningococcal B vaccines: longitudinal study of a clonal meningococcal B outbreak[END_REF] 1.2. Special features of serogroup B Meningococcal vaccines targeting serogroups A, C, W-135 and Y have demonstrated their effectiveness. [START_REF] Roderick | Advances towards the prevention of meningococcal B disease: a multidimensional story[END_REF][START_REF] Borrow | Meningococcal surrogates of protection -serum bactericidal antibody activity[END_REF] However, there are a number of reasons why the immunological approach to traditional vaccine development, conjugate or polysaccharide, isout of the question for serogroup B. [START_REF] Roderick | Advances towards the prevention of meningococcal B disease: a multidimensional story[END_REF][START_REF] Vipond | History of meningococcal vaccines and their serological correlates of protection[END_REF][START_REF] Holst | Properties and clinical performance of vaccines containing outer membrane vesicles from Neisseria meningitidis[END_REF][START_REF] Finne | Antigenic similarities between brain components and bacteria causing meningitis. Implications for vaccine development and pathogenesis[END_REF] First, the heterogeneity of intra-serogroup proteins, especially the dominant protein, Porin A (PorA), seriously complicates universal vaccine design. [START_REF] Sacchi | Diversity and prevalence of PorA types in Neisseria meningitidis serogroup B in the United States, 1992-1998[END_REF][START_REF] Feaversim | Meningococcal protein antigens and vaccines[END_REF] Up to now, only specific vaccines prepared from vesicles on the bacterium surface, outer membrane vesicle (OMV),were developed and used as the need arose. They were used fordisease control in epidemic situations in Brazil, Chile, Cuba (VaMencog-BC®), Norway (MenBVac® vaccine), New Zealand (MenZB® vaccine) and recently in France (Norwegian MenBVac® vaccine because of epidemic strain similarity). [START_REF]Meningococcal vaccines: WHO position paper, Novembre2011[END_REF][START_REF] Caron | From tailor-made to ready-to-wear meningococcal B vaccines: longitudinal study of a clonal meningococcal B outbreak[END_REF][START_REF] De Moraes | Protectiveefficacy of a serogroup B meningococcalvaccine in Sao Paulo, Brazil[END_REF][START_REF] Boslego | Efficacy, safety, and immunogenicity of a meningococcal group B (15:P1.3) outer membrane protein vaccine in Iquique, Chile. Chilean National Committee for Meningococcal Disease[END_REF][START_REF] Sierra | Vaccine against group B Neisseria meningitidis: protection trial and mass vaccination results in Cuba[END_REF][START_REF] Bjune | Effect of outer membrane vesicle vaccine against group B meningococcal disease in Norway[END_REF][START_REF] Oster | MeNZB: a safe and highly immunogenic tailormade vaccine against the New Zealand Neisseria meningitidis serogroup B disease epidemic strain[END_REF][START_REF] Oster | Immunogenicity and safety of a strain-specific MenB OMV vaccine delivered to under 5-year olds in New Zealand[END_REF][START_REF] Caron | Evolution of immune response against Neisseria meningitidis B:14:P1.7,16 before and after the outer membrane vesicle vaccine MenBvac[END_REF][START_REF] Holst | The concept of "tailor-made", proteinbased, outer membrane vesicle vaccines against meningococcal disease[END_REF]The composition of these vaccines was determined by a particular bacterial clonal strain, so their effectiveness waslimited to certain epidemic conditions. [START_REF] Holst | Properties and clinical performance of vaccines containing outer membrane vesicles from Neisseria meningitidis[END_REF][START_REF] Feaversim | Meningococcal protein antigens and vaccines[END_REF] For example, the Cuban vaccine, which Secondly, the polysaccharide capsule of serogroup B contains polysialic acid, as do all the capsules of meningococcal virulent serogroups, with the exception of serogroup A which is composed mainly of Nacetylmannosamine-1-phosphate. [START_REF] Stephens | Biology and pathogenesis of the evolutionarily successful, obligate human bacterium Neisseria meningitidis[END_REF] The main difference between serogroups B and C is their linkage patterns: the group B capsule has 2-8 linkagewhile group C has2-9

linkage. [START_REF] Caesar | Neisseria meningitidis serogroup B vaccine development[END_REF] The final structure is sufficiently different to induce specific antibodies for each serogroup. [START_REF] Roderick | Advances towards the prevention of meningococcal B disease: a multidimensional story[END_REF] The derivative of the polysialic acid contained in the serogroup B capsule is found in many human tissues, especially in the central nervous system, and particularlyinadhesion cells (Neural cell Adhesion Molecule N-CAM), highly expressed inthe fetus and the young child in development. [START_REF] Sacchi | Diversity and prevalence of PorA types in Neisseria meningitidis serogroup B in the United States, 1992-1998[END_REF][START_REF] Nedelec | Evidence for autoimmune antibodies directed against embryonic neural cell adhesion molecules (N-CAM) in patients with group B meningitis[END_REF][START_REF] Bansal | Evaluation of synergistic effect of biodegradable polymeric nanoparticles and aluminum based adjuvant forimproving vaccine efficacy[END_REF] The real challenge is therefore to develop a multivalent vaccine to expand vaccine coverage and to avoid the risk of selecting for vaccine escape variants against a pathogen that mimics host molecules. [START_REF] Feaversim | Meningococcal protein antigens and vaccines[END_REF] 1.

Reverse vaccinology, an innovative and promising technique

The conventional approach to vaccine development proceeds via the in vitroculture of the pathogenic organism, allowing potential antigenic components to be individually identified by biochemical, immunological and microbiological methods. [START_REF] Schubert-Unkmeir | Genome-based bacterial vaccines: current state and future outlook[END_REF][START_REF] Serruto | Biotechnology and vaccines: application of functional genomics to Neisseria meningitidis and other bacterial pathogens[END_REF]Finally, each isolated antigen is analyzed to determine its ability to induce protective immunity.

Although this long and tedious technique, termed "classical vaccinology", has led tomany vaccines commonly used today, it still presents some limitations. [START_REF] Serruto | Biotechnology and vaccines: application of functional genomics to Neisseria meningitidis and other bacterial pathogens[END_REF]It cannotbe applied to all micro-organisms,excluding all bacteria difficult to cultivate or non-cultivableand also antigenically variant, especially meningococcal serogroup B. Moreover, antigens expressed only during in vivo infection are not produced under laboratory conditions and therefore not analyzed. [START_REF] Serruto | Biotechnology and vaccines: application of functional genomics to Neisseria meningitidis and other bacterial pathogens[END_REF] Scientists have recently proposed a new concept, called "reverse vaccin7logy". [START_REF] Nedelec | Evidence for autoimmune antibodies directed against embryonic neural cell adhesion molecules (N-CAM) in patients with group B meningitis[END_REF]This new strategy is based on the complete sequencing of the bacterial genome, to identify potential, highly immunogenicantigens, regardless of their expression level. [START_REF] Schubert-Unkmeir | Genome-based bacterial vaccines: current state and future outlook[END_REF][START_REF] Serruto | Biotechnology and vaccines: application of functional genomics to Neisseria meningitidis and other bacterial pathogens[END_REF][START_REF] Danzig | Reverse vaccinology -in search of a genomederived meningococcal vaccine[END_REF][START_REF] Rappuoli | Reverse vaccinology, a genome-based approach to vaccine development[END_REF][START_REF] Serruto | The new multicomponent vaccine against meningococcal serogroup B, 4CMenB: immunological, functional and structural characterization of the antigens[END_REF]This technique presents the advantage of applying to all germs, pathogenic or commensal, cultivable or not. However, it does not detect non-protein antigens such as capsular polysaccharides and glycolipids, whichnevertheless remain promising as components for future vaccines. [START_REF] Rappuoli | Reverse vaccinology, a genome-based approach to vaccine development[END_REF]Reverse vaccinology was applied for the first time in 2000, on a virulent strain of meningococcal group B (MC58). [START_REF] Serruto | The new multicomponent vaccine against meningococcal serogroup B, 4CMenB: immunological, functional and structural characterization of the antigens[END_REF][START_REF] Kelly | Reverse vaccinology and vaccines for serogroup B Neisseria meningitidis[END_REF] The entire sequence of the bacterial genome wasanalyzed:nearly 600 candidate genes encoding for new surface-exposed proteins were identified. [START_REF] Serruto | Biotechnology and vaccines: application of functional genomics to Neisseria meningitidis and other bacterial pathogens[END_REF][START_REF] Rappuoli | Reverse vaccinology, a genome-based approach to vaccine development[END_REF] The predicted proteins were cloned and expressed in Escherichia coli. [START_REF] Schubert-Unkmeir | Genome-based bacterial vaccines: current state and future outlook[END_REF][START_REF] Serruto | Biotechnology and vaccines: application of functional genomics to Neisseria meningitidis and other bacterial pathogens[END_REF][START_REF] Rappuoli | Reverse vaccinology, a genome-based approach to vaccine development[END_REF][START_REF] Kelly | Reverse vaccinology and vaccines for serogroup B Neisseria meningitidis[END_REF] Of these, 350 putative surface proteinswere successfully expressed, purified and then tested on mice. The sera were analyzed, in particular by Western Blot to confirm the expression of these proteins in vivo.Furthermore, enzymelinked immunosorbent assay(ELISA) and fluorescenceactivated cell sorting(FACS) were used to determine the exact location of these proteins and their function. [START_REF] Schubert-Unkmeir | Genome-based bacterial vaccines: current state and future outlook[END_REF][START_REF] Serruto | Biotechnology and vaccines: application of functional genomics to Neisseria meningitidis and other bacterial pathogens[END_REF][START_REF] Rappuoli | Reverse vaccinology, a genome-based approach to vaccine development[END_REF][START_REF] Serruto | The new multicomponent vaccine against meningococcal serogroup B, 4CMenB: immunological, functional and structural characterization of the antigens[END_REF][START_REF] Kelly | Reverse vaccinology and vaccines for serogroup B Neisseria meningitidis[END_REF] Protein antigens selected were classified according to their serum bactericidal activity (SBA) against the target strain.Among the 91 proteins inducing bactericidal antibodies in animals, about 25, not detected by conventional techniques, were selected for their surface location. [START_REF] Serruto | Biotechnology and vaccines: application of functional genomics to Neisseria meningitidis and other bacterial pathogens[END_REF][START_REF] Serruto | The new multicomponent vaccine against meningococcal serogroup B, 4CMenB: immunological, functional and structural characterization of the antigens[END_REF][START_REF] Kelly | Reverse vaccinology and vaccines for serogroup B Neisseria meningitidis[END_REF]Moreover, these antigens were recognized by the serum of patients who haddeveloped meningococcal disease. Finally, only 3 protein antigens were selected for their characteristic properties, allowing thedevelopment of the recombinant protein (rMenB). This was the first example of real success,resulting in a universal vaccine againstmeningococcal group B. [START_REF] Schubert-Unkmeir | Genome-based bacterial vaccines: current state and future outlook[END_REF][START_REF] Rappuoli | Reverse vaccinology, a genome-based approach to vaccine development[END_REF]The new strategywas then applied to the development of vaccines against other pathogens, such as Streptococcus agalactiae, Streptococcus pyogenes, Streptococcus pneumoniae, Chlamydia pneumoniae ... [START_REF] Schubert-Unkmeir | Genome-based bacterial vaccines: current state and future outlook[END_REF][START_REF] Kelly | Reverse vaccinology and vaccines for serogroup B Neisseria meningitidis[END_REF][START_REF] Giuliani | A universal vaccine for serogroup B meningococcus[END_REF] 2. The marketing of the first universal meningococcal serogroup B vaccine

The formulation of the new vaccine

To ensure that protection is the most universal possible and to avoid the emergence of mutants, the ideal solution is to developa multi-antigenic meningococcal vaccine. [START_REF] Feaversim | Meningococcal protein antigens and vaccines[END_REF][START_REF] Serruto | The new multicomponent vaccine against meningococcal serogroup B, 4CMenB: immunological, functional and structural characterization of the antigens[END_REF][START_REF] Vesikari | Immunogenicity and safety of an investigational multicomponent, recombinant, meningococcal serogroup B vaccine (4CMenB) administered concomitantly with routine infant and child vaccinations: results of two randomised trials[END_REF] Reverse vaccinology yielded 3 vaccine antigens, commonly called Neisseria genome-derived antigens (GNA). [START_REF] Rappuoli | Reverse vaccinology, a genome-based approach to vaccine development[END_REF][START_REF] Serruto | The new multicomponent vaccine against meningococcal serogroup B, 4CMenB: immunological, functional and structural characterization of the antigens[END_REF] -Factor H binding protein (fHBP), also named GNA 1870

or rLP 2086 fused to GNA 2091: A surface-exposed lipoprotein expressed by most strains of meningococcal group B, itsexpression is highly variable. [START_REF] Roderick | Advances towards the prevention of meningococcal B disease: a multidimensional story[END_REF][START_REF] Feaversim | Meningococcal protein antigens and vaccines[END_REF][START_REF] Serruto | The new multicomponent vaccine against meningococcal serogroup B, 4CMenB: immunological, functional and structural characterization of the antigens[END_REF][START_REF] Murphy | Sequence diversity of the factor H binding protein vaccine candidate in epidemiologically relevant strains of serogroup B Neisseria meningitidis[END_REF][START_REF] Lucidarme | Characterization of fHbp, nhba (gna2132), nadA, porA, and sequence type in group B meningococcal caseisolates collected in England and Wales during January 2008 and potential coverage of an investigational group B meningococcal vaccine[END_REF] Meningococcal B vaccine includes the sub-variant 1 or the subgroup B, which is the most common. Secreted antibodies are specific and exclusively protect the host against strains presenting this variant.For the development of a universal vaccine, it is therefore advisable to add at least one other antigen, to expand coverage. [START_REF] Murphy | Sequence diversity of the factor H binding protein vaccine candidate in epidemiologically relevant strains of serogroup B Neisseria meningitidis[END_REF] This fHbp protein is implicated in the regulation of the alternative complement pathway essential for bacterial lysis. [START_REF] Roderick | Advances towards the prevention of meningococcal B disease: a multidimensional story[END_REF][START_REF] Serruto | The new multicomponent vaccine against meningococcal serogroup B, 4CMenB: immunological, functional and structural characterization of the antigens[END_REF] Blocking this protein through a vaccine, would help the host's immune system to clear the bacteria from the body.

-Neisseria adhesinA (NadA) or GNA 1994: This protein is present in only 50% of the tested strains, but is found in most clonal hypervirulent serogroup B strains in Europe. [START_REF] Kelly | Reverse vaccinology and vaccines for serogroup B Neisseria meningitidis[END_REF][START_REF] Comanducci | NadA, a novel vaccine candidate of Neisseria meningitidis[END_REF][START_REF] Litt | Putative vaccine antigens from Neisseria meningitidis recognized by serum antibodies of young children convalescing after meningococcal disease[END_REF][START_REF] Capecchi | Neisseria meningitidisNadA is a new invasin which promotes bacterial adhesion to and penetration into human epithelial cells[END_REF] In contrast to the 2 other principal antigens of the vaccine, this trimeric protein is not associated with an accessory protein. [START_REF] Holst | Properties and clinical performance of vaccines containing outer membrane vesicles from Neisseria meningitidis[END_REF][START_REF] Serruto | The new multicomponent vaccine against meningococcal serogroup B, 4CMenB: immunological, functional and structural characterization of the antigens[END_REF][START_REF] Capecchi | Neisseria meningitidisNadA is a new invasin which promotes bacterial adhesion to and penetration into human epithelial cells[END_REF] This protein allows host cell adhesion and invasion, so it would have an indispensable function in asymptomatic carriers. [START_REF] Comanducci | NadA, a novel vaccine candidate of Neisseria meningitidis[END_REF][START_REF] Capecchi | Neisseria meningitidisNadA is a new invasin which promotes bacterial adhesion to and penetration into human epithelial cells[END_REF] The induced antibodies should have the potential to stop bacterial colonization and thus to prevent invasive disease, but this hypothesis was not confirmed by scientific evidence. [START_REF] Feaversim | Meningococcal protein antigens and vaccines[END_REF]In contrast, the secretion of protective antibodies in laboratory animals was proven, and the sera of patients who reported a meningococcal disease recognize the protein: this shows that NadAplays a major role not only in the virulence of meningococci but also in immunogenicity in humans. [START_REF] Feaversim | Meningococcal protein antigens and vaccines[END_REF][START_REF] Comanducci | NadA, a novel vaccine candidate of Neisseria meningitidis[END_REF][START_REF] Litt | Putative vaccine antigens from Neisseria meningitidis recognized by serum antibodies of young children convalescing after meningococcal disease[END_REF] -Neisseria Heparin Binding Antigen (NHBA) or GNA 2132, fused to GNA1030: This is a ubiquitous lipoprotein which is specific for Neisseria species with a variety of proteins. [START_REF] Lucidarme | Characterization of fHbp, nhba (gna2132), nadA, porA, and sequence type in group B meningococcal caseisolates collected in England and Wales during January 2008 and potential coverage of an investigational group B meningococcal vaccine[END_REF] In mice, antibodies developed showed bactericidal activity mediated by the complement, and the sera of patients with a history of meningococcal disease also recognize the protein. [START_REF] Serruto | The new multicomponent vaccine against meningococcal serogroup B, 4CMenB: immunological, functional and structural characterization of the antigens[END_REF][START_REF] Serruto | Neisseria meningitidis GNA2132, a heparin-binding protein that induces protective immunity in humans[END_REF] The 2 accessory proteins, GNA 2091 and GNA 1030, respectively fused tofHbp and NHBA, reinforce the immune responses and enhance the stability of the final recombinant protein. [START_REF] Feaversim | Meningococcal protein antigens and vaccines[END_REF][START_REF] Serruto | The new multicomponent vaccine against meningococcal serogroup B, 4CMenB: immunological, functional and structural characterization of the antigens[END_REF] An outer membrane vesicle (OMV)derived from a serogroup B New Zealand strain (strain NZ98 / 254) is firstly added to these 3principal proteins in order to enhance immunogenicity, followed by an adjuvant, aluminum hydroxide, currently controversial. [START_REF] Toneatto | The first use of an investigational multicomponent meningococcal serogroup B vaccine (4CMenB) in humans[END_REF][START_REF] Giuliani | Measuring antigen-specific bactericidal responses to a multicomponent vaccine against serogroup B meningococcus[END_REF][START_REF] Findlowj | Multicenter, Open-Label, Randomized Phase II Controlled Trial of an Investigational Recombinant Meningococcal Serogroup B Vaccine With and Without Outer Membrane Vesicles, Administered in Infancy[END_REF][START_REF] Gherardi | Macrophagicmyofasciitis: an emerging entity[END_REF] This is the formulationof the new multicomponent vaccine 4CMenB (for 4 components against meningococcus B) recently marketed under the name Bexsero ® .It obtainedmarketing authorization in Europe in January 2013 as the first broad spectrum vaccine for Neisseria meningitidis serogroup B. [START_REF] Roderick | Advances towards the prevention of meningococcal B disease: a multidimensional story[END_REF][START_REF] Kaaijk | Routine vaccination against MenB: Considerations for implementation[END_REF][START_REF] Caesar | Neisseria meningitidis serogroup B vaccine development[END_REF] In August 2013, this vaccine was also approved in Australia, [START_REF] Kaaijk | Routine vaccination against MenB: Considerations for implementation[END_REF] and in January 2015 in United

States. [START_REF]Meningococcal disease[END_REF] In October 2014, another serogroup meningococcal vaccine, Trumemba ® , was licensed in United States. This vaccine consists of two fHBP variants immunologically distincts (A05 and B01). [START_REF]Trumemba highlights of prescribing informations[END_REF]Although clinical trials for this second vaccine were conducted in the United States, Australia but also in Europe, Trumemba ® is not yet licensed in Europe.

The effectiveness of 4CMenB

The relatively low incidence of IMD ruled out performingefficacy studies of the new vaccine prior to marketing authorization. Thus,4CMenB was basically awarded marketing authorization on evidence of immunogenicity and safety data rather than on a formal demonstration of its effectiveness. [START_REF]Meningococcal vaccines: WHO position paper, Novembre2011[END_REF][START_REF] Vipond | History of meningococcal vaccines and their serological correlates of protection[END_REF][START_REF] Van Alphen | Meningococcal B vaccine development and evaluation of efficacy[END_REF] To estimate the effectiveness of a new vaccine, immunogenicity and immunization coverage must be taken into account, and there are standardized analytical methods for a true consensus. [START_REF] Roderick | Advances towards the prevention of meningococcal B disease: a multidimensional story[END_REF][START_REF] Borrow | Meningococcal surrogates of protection -serum bactericidal antibody activity[END_REF]Goldschneiderdemonstrated in 1969 the inverse correlation between the incidence of a disease and the presence of bactericidal antibodies in human sera, meaning that the probability of contracting the disease depends on the amount of circulating antibodies. [START_REF] Borrow | Meningococcal surrogates of protection -serum bactericidal antibody activity[END_REF][START_REF] Goldschneider | Human immunity to the meningococcus. I. The role of humoral antibodies[END_REF] Further to these observations, circulating bactericidal antibodies were accepted as true markers of protection against IMD. [START_REF] Van Alphen | Meningococcal B vaccine development and evaluation of efficacy[END_REF][START_REF] Goldschneider | Human immunity to the meningococcus. I. The role of humoral antibodies[END_REF]The SBA assay is considered the most relevant immunological indicator, the one most closely correlated with clinical efficacy. [START_REF] Van Alphen | Meningococcal B vaccine development and evaluation of efficacy[END_REF][START_REF] Borrow | Neisseria meningitidis group B correlates of protection and assay standardization -international meeting report Emory University[END_REF][START_REF] Holst | Serum bactericidal activity correlates with the vaccine efficacy of outer membrane vesicle vaccines against Neisseria meningitidis serogroup disease[END_REF] This test consists in introducing a viable Neisseria meningitidis suspension in different serum dilutions in the presence of a human complement (hSBA) and then determining the amount of surviving bacteria. [START_REF] Borrow | Neisseria meningitidis group B correlates of protection and assay standardization -international meeting report Emory University[END_REF] The dilution at which more than 50% of bacteria are immediately killed was for the 3 vaccine antigens: fHbp, NadA and PorA [START_REF] Roderick | Advances towards the prevention of meningococcal B disease: a multidimensional story[END_REF][START_REF] Borrow | Meningococcal surrogates of protection -serum bactericidal antibody activity[END_REF][START_REF] Holst | The concept of "tailor-made", proteinbased, outer membrane vesicle vaccines against meningococcal disease[END_REF]. This assay could not be performed for NHBA protein, which was analyzed by ELISA. [START_REF] Santolaya | Immunogenicity and tolerability of a multicomponent meningococcal serogroup B (4CMenB) vaccine in healthy adolescents in Chile: a phase 2b/3 randomised, observer-blind, placebo-controlled study[END_REF] An SBA titer of ≥1:4 is considered a surrogate of protection,although some clinical trials in infants have set the threshold at 5, to be on the safe side. [START_REF] Conseil | de la Santé Publique, vaccination contre les infections invasives à méningocoque B, place du vaccin Bexsero® Availablefrom[END_REF][START_REF] Frasch | Bactericidal antibody is the immunologic surrogate of protection against meningococcal disease[END_REF] However, this technique requires many SBA assays for various endemic strains for each geographic region;in practice, this is impossible, especially with respect to infants, whose serum volumes are very limited. [START_REF] Giuliani | Measuring antigen-specific bactericidal responses to a multicomponent vaccine against serogroup B meningococcus[END_REF][START_REF] Donnelly | Qualitative and quantitative assessment of meningococcal antigens to evaluate the potential strain coverage of protein-based vaccines[END_REF] Because of the diversity of intra-serogroup antigens, a standardized method specific to the 4CMenB vaccine, the Meningococcal Antigenic Typing System(MATS) was developed to estimate vaccination coverage. MATS indicates the probability that the analyzed meningococcal strain will be killed by the serum of an immunized patient.This method allows the characterization and quantification, viaimmuneenzymatic ELISA analysis, of the concentration of each vaccine antigen. [START_REF] Vipond | History of meningococcal vaccines and their serological correlates of protection[END_REF][START_REF] Donnelly | Qualitative and quantitative assessment of meningococcal antigens to evaluate the potential strain coverage of protein-based vaccines[END_REF] Then it compares the expression obtained from theanalyzed strain with standard rates from reference strains. [START_REF] Donnelly | Qualitative and quantitative assessment of meningococcal antigens to evaluate the potential strain coverage of protein-based vaccines[END_REF][START_REF] Vogel | Predicted strain coverage of a meningococcal multicomponent vaccine (4CMenB) in Europe: a qualitative and quantitative assessment[END_REF] This method determines the molecular characterization of meningococcal strains, and identifies clones responsible forepidemics worldwide. [START_REF] Stephens | Biology and pathogenesis of the evolutionarily successful, obligate human bacterium Neisseria meningitidis[END_REF][START_REF] Racloz | The elusive meningococcal meningitis serogroup: a systematic review of serogroup B epidemiology[END_REF]Such vigilance is aimed at rapidlyidentifying emergingstrains not covered by this vaccine, so that immunization policies can be adjusted for maximum effectiveness. [START_REF] Kaaijk | Routine vaccination against MenB: Considerations for implementation[END_REF] The best way to prevent an infectious disease is to eradicate theetiological agent, as done forsmallpox.In the case ofmeningococci, thisaim seems achievable since the number of virulent serogroups is limited, and the only reservoir is human.However, despite the severity of meningococcal disease, eradication of all meningococci is undesirable. [START_REF] Maiden | Can we, should we, eradicate the meningococcus?[END_REF]Indeed, the majority of meningococci, including serogroup B meningococci, form commensal bacterialflora. Thus, their disappearance fromthe human nasopharynx could havesevere consequences for natural immunity. [START_REF] Heyderman | Mucosal immunity and optimizing protection with meningococcal serogroup B vaccines[END_REF]Human microbiome modification could increase the expression of pathogens of unknown virulence previously kept in check by the presence of meningococci. [START_REF] Maiden | Can we, should we, eradicate the meningococcus?[END_REF] The fight against the disease must therefore respect certain limits, primarily targeting encapsulated virulent meningitis.

The development of a universal vaccine against group B has proved a real clinical challenge, requiring decades of research. Finally, however, marketing authorizationis bringing hope ofcontrol of meningococcal epidemics. [START_REF] Yogev | Meningococcal disease: the advances and challenges of meningococcal disease prevention[END_REF][START_REF] Caesar | Neisseria meningitidis serogroup B vaccine development[END_REF] A post-implementation surveillance plan is required to monitor the evolution of bacterial clones and toenhanceimmunization programs. [START_REF] Kaaijk | Routine vaccination against MenB: Considerations for implementation[END_REF][START_REF] Holst | The concept of "tailor-made", proteinbased, outer membrane vesicle vaccines against meningococcal disease[END_REF]

4. 3 . 98 ]

 398 Harmful effects of vaccinationMeningococcus is a recombinant bacteria, inducing wide genetic variability.This pathogen is in fact able to incorporate into its chromosomes DNA captured from its environment, and frequently recombines DNA through the many repetitive sequences encoding components of the cell surface.[START_REF] Racloz | The elusive meningococcal meningitis serogroup: a systematic review of serogroup B epidemiology[END_REF][START_REF] Bucci | Hypermutation in pathogenic bacteria: frequent phase variation in meningococci is a phenotypic trait of aspecializedmutator biotype[END_REF]Similarly, the high frequency of an asymptomatic carriage of meningococcal strains in the commensal flora of the human nasopharynx can facilitate bacterial capsule switching, particularly in cases of simultaneous colonization of different meningococcal serogroups.[START_REF] Swartley | Capsule switching of Neisseria meningitidis[END_REF]For example, in Canada and in Italy, cases of capsule switching between serogroups B and C have been observed.[START_REF] Kertesz | Serogroup B, electrophoretic type 15 Neisseria meningitidis in Canada[END_REF][START_REF] Nair | Protein conjugate polysaccharide vaccines: challenges in development and global implementation[END_REF][START_REF] Stefanelli | First report of capsule replacement among electrophoretic type 37 Neisseria meningitidis strains in Italy[END_REF] The emergence of serogroup W135 connected with the pilgrims'return fromMecca, These examples demonstrate the possibility of genetic exchange between endemic or epidemic strains.This diversity ultimately determines the virulence of the meningococcal strains, the ability of the host to defend itself and thus, indirectly, theimmunizationstrategies to adopt.[START_REF] Stefanelli | First report of capsule replacement among electrophoretic type 37 Neisseria meningitidis strains in Italy[END_REF]Under these circumstances, scientists fear that a mass vaccination program could cause a selection of strains targeted by this vaccine. Indeed, there may beprogressive emergence and the circulation of strains not covered by this vaccine, recalling past experience withpneumococcal vaccines.[START_REF] Swartley | Capsule switching of Neisseria meningitidis[END_REF][START_REF] Snape | The challenge of post-implementation surveillance for novel meningococcal vaccines[END_REF]So far, no capsular substitution has been demonstrated following the introduction of meningococcal vaccines.Nevertheless, post-implementation surveillance must be rigorously applied, in particular using the established typing method for meningococci,termedmultilocussequence typing (MLST).

Neisseria meningitidis serogroup B, but several vaccine candidate vaccines are currently under development. For example, Trumemba ® , a bivalent recombinant lipoprotein 2086 vaccine based on two fHBP,was recently licensed in United States; and a meningococcal pentavalent vaccine (ABCWY) is under study. [100] Other preventive strategiesmay also be worth considering, such as the passive protection given to children by transfer of maternal antibodies during pregnancy. [START_REF] Yogev | Meningococcal disease: the advances and challenges of meningococcal disease prevention[END_REF][START_REF] Kaaijk | Routine vaccination against MenB: Considerations for implementation[END_REF] By helping to reduce the global burden of meningococcal disease, these therapeutics advances should contribute to the progress of modern medicine.

Conflict of interest:The