Enrique Reyes Rodriguez

Xavier Tardif

Jean-Luc Bailleul

Nadine Allanic

Vincent Sobotka
email: vincent.sobotka@univ-nantes.fr

Thermal design methodology to hybrid manufacturing process of High Performance Thermoplastics Composites

Keywords: Heat transfer, inverse method, high performance thermoplastic composite, sensitivity

. Once a computational model is set up, the optimization problem is treated as an inverse problem subjected to constraints that depend on the process response in terms of temperature cycles. Thus, it requires the calculation of the direct problem, the adjoint-state solution, and the development of the sensitivity equations to implement a first-order gradient-based algorithm. As an application example, a thermo-stamping of HP-TPC with a metal insert followed by an over-molding process has been chosen because of the different stages and materials involved. The first results show a reduction of temperature gradients on the part surface at each stage while arriving at the established temperature level. Further analysis will include a constraint problem taking into account adhesion and/or energy criteria

Introduction

Stamping associated with over-molding process combines several manufacturing techniques to create parts with integrated functions. This approach is advantageous in aeronautics and automotive applications not only to reduce production time, by avoiding secondary operations, but also to fabricate hybrid lightweight structures combining metals, composites, and polymers according to their final purpose. This process could be divided in 5 main stages (Fig 1). First, high-performance thermoplastic composites blankets and metal inserts are preheated with radiation panels. They are then transferred into the mold cavity to be stamped. This press-forming stage is then followed by the over-molding with a thermoplastic resin. The part is cooled down and removed from the mold. Finally, the mold temperature is raised to attain press-forming conditions and to let another cycle start.

The processing of High-performance thermoplastic such as PEEK or PEKK associated with carbon fibers is still subject of research. These materials have high processing temperatures compared with other standard polymers [START_REF]Vitrex.Materials properties guide[END_REF], creating non-negligible temperature differences throughout the entire manufacturing process. Temperature variations could generate thermal expansion and contraction at different locations within the part, leading to thermal residual stresses and, as a consequence, several defects, such as shrinkage, fiber waviness, transverse cracking, delamination, and warpage [START_REF] Parlevliet | Residual stresses in thermoplastic composites-A study of the literature-Part III: Formation of residual stresses[END_REF]. Different studies have shown that the magnitude of residual stresses depends on the processing conditions, as for instance, thermal gradients during the cooling stage [START_REF] Parlevliet | Residual stresses in thermoplastic composites-A study of the literature-Part I: Formation of residual stresses[END_REF]. That is the case of an early investigation made by Manson et al. [START_REF] Manson | Press-forming of continuous-fiber-reinforced thermoplastic composites[END_REF] about the process-induced effects during the preforming of Continuous Fiber thermoplastics composites. They showed that higher cooling rates cause higher voids contents and fiber buckling, damaging the composite material. They also observed that high cooling rates reduce the crystallinity rate of the polymer, reducing their mechanical properties.

Certainly, process conditions affect quality, but it has been proved that they can also have a direct impact on productivity. In the forming stage, high mold temperatures increase cooling time [START_REF] Pandelidis | Optimization of injection molding design. Part II: Molding conditions optimization[END_REF] and hence time cycle [START_REF] Mehnen | Evolutionary optimization of mould temperature control strategies: Encoding and solving the multiobjective problem with standard evolution strategy and kit for evolution algorithms[END_REF]. Longer production times generate higher costs [START_REF] Dimla | Design and optimisation of conformal cooling channels in injection moulding tools[END_REF] and energy consumption. Looking at a different manufacturing stage, such as the pre-heating of materials, optimum processing conditions are important as well, since they can also help to reduce cycle time and material damage [START_REF] Sweeney | Reduction of infra-red heating cycle time in processing of thermoplastic composites using computer modelling[END_REF]. Based on this, it becomes evident, that control of thermal related parameters is an essential element at each manufacturing stage of the process to guarantee quality and productivity. Therefore, to avoid the aforementioned problems, it becomes mandatory to have a thermal design methodology that takes into account the main stages of a manufacturing process, but also other challenging aspects like geometry complexity or interaction between different assembly materials at each manufacturing stage.

In this field, several works have been oriented on the optimization of the thermal profile of the part during the manufacturing process. These studies propose a series of optimization algorithms based on deterministic or stochastic methods or a combination of both, as well as different methodologies based on the conventional or conformal approach. This last approach proposed by Xu [START_REF] Xiaorong | Conformal Cooling and Rapid Thermal Cycling in Injection Molding With 3D Printed Tools[END_REF], has been proved to be very efficient when compared with the conventional approach, to optimize temperature distribution within the part [START_REF] Agazzi | Optimisation thermique des outillages d ' injection thermoplastique[END_REF][START_REF] Dimla | Design and optimisation of conformal cooling channels in injection moulding tools[END_REF][START_REF] Zheng | Design and Simulation-Based Optimization of Cooling Channels for Plastic Injection Mold[END_REF]. Inspired by this method Agazzi [START_REF] Agazzi | Optimisation thermique des outillages d ' injection thermoplastique[END_REF] proposes the creation of a contour (dilated zone) reproducing the shape of the part, as close as possible to the mold's surface [START_REF] Xiaorong | Conformal Cooling and Rapid Thermal Cycling in Injection Molding With 3D Printed Tools[END_REF] reducing computational time since a more reduced geometry is analyzed. The methodology is based on a first-order optimization algorithm throughout an inverse problem. The strategy is applied only to the cooling stage and it was proven to be very efficient in reducing the temperature gradient on the surface while arriving to an established temperature. Hoppmann [START_REF] Ch | Inverse thermalmold design for injection molds[END_REF] extended the methodology proposed by Agazzi [START_REF] Agazzi | Optimisation thermique des outillages d ' injection thermoplastique[END_REF], taking into account a holding time and a different objective function, proving the versatility of the application. On the consulted researches only one kind of manufacturing technique is considered and mostly applied to mono-materials.

This study proposes a design methodology that takes into account all the stages of a thermo-stamping of high-performance thermoplastic composites with a metal insert followed by an overmolding. To do this, an inverse optimization algorithm is proposed, with the aim of obtaining the time and space heat flux distribution that minimizes a target condition, based on quality and productivity criteria.

Thermal design methodology

Model geometry

The selected manufacturing process includes 2 impregnated High-Performance thermoplastic sheets made from carbon or glass fibers, also known as Organosheets [16], one metal insert in the center of the part and an over-molding resin at the top surface. The geometry is going to be studied as a 2D axisymmetric problem as shown in figure 2. The analyzed geometry is built in Comsol Multiphysics ® and has 4 domains corresponding to a metal insert (Ω 1 ), 2 HP-TPC organosheets (Ω 2 ), a dilated zone (Ω 3 ) , and the over-molded region (Ω 4 ). The distance of the dilated zone can be variable. Nevertheless, care must be taken to avoid thermal stresses in the mold part. For this reason, a minimal distance should be established. Here the dilated zone, as a replacement for the mold part, is created with a distance of 15mm as proposed by Agazzi [START_REF] Agazzi | Optimisation thermique des outillages d ' injection thermoplastique[END_REF] and Hopmaan [START_REF] Ch | Inverse thermalmold design for injection molds[END_REF].

This configuration is enough to study all stages of the process. The domains are going to be activated according to the corresponding stage. In the case of preheating, we are going to be focused on the boundary conditions around the part without taking into account the mold dilated zone. Table 1 resume the properties used in the study.

Process conditions

Process design values were estimated according to process requirements and hypotheses made for each stage:  Preheating stage: convection and radiation exchanges between the composite and surroundings are going to be taken into account in a global heat transfer coefficient in order to linearize the problem.

 Transfer stage: all the parameters are considered known, as a result, the global heat transfer coefficient is obtained for a fixed transfer time. This coefficient depends on the speed and trajectory of the part.

 Stamping stage: the initial mold temperature is considered homogenous for the first optimization cycle as per [START_REF] Agazzi | Optimisation thermique des outillages d ' injection thermoplastique[END_REF][START_REF] Ch | Inverse thermalmold design for injection molds[END_REF].

Its value is calculated according to the temperature required within the part and the supposed Thermal Contact Resistance (TCR).

 Over-molding: An injection temperature for the melted polymer is fixed to 360°C. No phase change is assumed. Over-molding time comprises packing phase and cooling.

It is calculated based on the time constant at the overmolded region and thermal diffusion time on the dilated zone.

Computational formulation

The heat transfer problem is solved using the Finite Element Method, considering a transient analysis in each domain at different stages. Assuming constants properties for all materials and no power generation, the heat transfer equation is defined by:

𝜌 𝑖 𝐶𝑝 𝑖 𝜕𝐓 𝑖 (𝑟, 𝑧, 𝑡) 𝜕𝑡 = 𝜆 𝑖 ∆𝐓 𝑖 (𝑟, 𝑧, 𝑡) ∀𝑖 = 1 … 4 (1)
Where 𝑖, correspond to each domain and 𝐓 𝑖 (𝑟, 𝑧, 𝑡) the corresponding temperature field. Boundary conditions of the third kind are imposed on all the internal and external boundaries. Thermal contact resistances are assumed to be constant for all the contact domains. Nevertheless, this value should be properly adapted.

Optimization strategy

The process is divided into three optimization blocks: the first one includes, the preheating and transfer stages, where no dilated zone is included. The aim is to find the heat flux that must be imposed during the preheating stage, on the external surface of the part, to reach a target condition in the part, defined by an objective function at the end of the transfer stage. This means that both stages are considered coupled, and that the searched parameters at the preheating stage are going to depend on the heat transfer evolution at the transfer stage. A second optimization block is for the over-molded stage. The purpose is to find the heat flux distribution as a time and space function to be imposed at the external boundary of the dilated zone during this step of the process. The third block includes the mold rising temperature stage and stamping stage. The aim is to obtain the required heat flux distribution in this stage. Once the first optimization cycle is obtained, subsequent cycles are performed until a stationary condition is reached. The objective function is the same for all the optimization blocks.

Design variable

Looking for a proper heat flux distribution as a function of time and space, to avoid thermal related defects at each manufacturing stage, temperature distribution 𝐓 ∞𝑛 (𝑟, 𝑧, 𝑡) at the external boundaries, is selected as design variables in each optimization block. This temperature is used later to obtain the heat flux distribution.

Objective function

The objective function is the mathematical expression of the searched condition at a specific time in the process. Its formulation depends on the design variables and the problem requirements. To obtain proper quality and productivity different authors have proposed some criteria based on time process and temperature gradient minimization [START_REF] Agazzi | Optimisation thermique des outillages d ' injection thermoplastique[END_REF][START_REF] Ch | Inverse thermalmold design for injection molds[END_REF][START_REF] Park | Optimal cooling system design for the injection molding process[END_REF]15]. In this study, the objective function is composed of two terms. They correspond to a temperature homogeneity and a target value, as proposed by Agazzi [START_REF] Agazzi | Optimisation thermique des outillages d ' injection thermoplastique[END_REF]. These terms are used at each optimized stage and expressed as follow:

𝐽 1 (𝑞 𝑛 ) = ∫ ∫ ‖𝑻 𝑡𝑎𝑟𝑔𝑒𝑡 𝑛 -𝑻 2, 𝑛 (𝑞 𝑛 )‖ 2 𝑑𝑡𝑑𝛤 𝑡 𝑓,𝑛 𝑡 𝑓,𝑛 -𝜏 𝛤 (2) 𝐽 2 (𝑞 𝑛 ) = ∫ ∫ ‖𝑻 ̅ 2,𝑛 (𝑞 𝑛 ) -𝑻 2, 𝑛 (𝑞 𝑛 )‖ 2 𝑑𝑡 𝑡 𝑓,𝑛 𝑡 𝑓,𝑛 -𝜏 𝑑𝛤 * 𝛤 * (3)
Where 𝑛 corresponds to the optimization blocks going from 1 to 3; 𝑞 𝑛 the searched heat flux distribution per block; 𝛤 is an internal boundary (erode segment) located to 1mm from de external surface of the studied part; 𝛤 * is the external boundary of the part; 𝑡 𝑓,𝑛 is the final time of the optimization block. The total function is then the summation of the equations 2 and 3.

Target temperatures per optimization block are defined according to the material process requirements. For the first block, the target temperature depends on the processing temperature window of the material, placed between 320°C and 360°C [START_REF] Lu | The optimization of process parameters and characterization of highperformance CF/PEEK composites prepared by flexible CF/PEEK plain weave fabrics[END_REF] which means that is higher than the melting point in order to be stamped but paying attention to avoid burning the material. Thus, a target temperature of 347°C has been fixed. For the over-molded stage which includes cooling, the target temperature depends on the solidification temperature of the material. For this reason, it has been set to 230°C. For the third block, the target temperature is intended to facilitate adhesion between the composite and the injected polymer. Since higher temperatures help to the healing phenomenon between materials a target temperature at the end of the stamping stage has been set at 340°C.

Constraints

The optimization problem is subjected to upper and lower temperature limits at each optimization block an expressed as follow:

𝑚𝑖𝑛 𝑙𝑖𝑚𝑖𝑡 ≤ 𝐓 ∞ (𝑟, 𝑧, 𝑡) ≤ max 𝑙𝑖𝑚𝑖𝑡 ( 4
)
Lower level is set to 20°C and upper level to 1700°C

Sensitivity analysis

Since sensitivity problem allows to obtain the response of the observed variable 𝑻 2, 𝑛 (𝑞 𝑛 ) in the objective function, with respect to the design variable 𝐓 ∞𝑛 (𝑟, 𝑧, 𝑡), it allows the validation of the dilated thickness, as well as, the location of the eroded segments with respect to the design variables. For each optimization block, a perturbation 𝛿T of a unit is imposed on the design variable. The sensitivity is then obtained at the corresponding eroded zone. The problem is solved using Eq.5 throughout the finite element method, using the same discretization as the direct problem.

𝜌 𝑖 𝐶𝑝 𝑖

𝜕𝛅𝐓 𝑖 (𝑟, 𝑧, 𝑡) 𝜕𝑡 = 𝜆 𝑖 ∆𝛿𝐓 𝑖 ∀𝑖 = 1 … 4 (5)

Optimization Algorithm

The optimization is performed via an inverse technique that employs a conjugate gradient algorithm (fig. 3) . This is a firstorder optimization algorithm that uses the gradient as a search direction to converge towards a local minimum. The gradient expression is obtained throughout the adjoint state, this is very useful when it doesn't exist an explicit relationship between the design variable, 𝐓 ∞𝑛 (𝑟, 𝑧, 𝑡) and the control variable, 𝑻 2, 𝑛 (𝑞 𝑛 ), in the objective function. To obtain the adjoint state equations a Lagrangian is expressed as follow:

ℒ(𝐓 𝑖 , 𝚿 𝑖 ) = ∑ 𝐽(𝐓(𝑞 𝑛 (r, z, t))) ) [START_REF] Manson | Press-forming of continuous-fiber-reinforced thermoplastic composites[END_REF] Where Ψ is the adjoint variable; 𝑡 0,𝑖 and 𝑡 𝑓,𝑖 are the initial and final times in which each domain is activated. The set of the adjoint equations, as well as the gradient expression, are then obtained considering a stationary condition of the Lagrangian. The final expression of the gradient is as follow:

𝐽 𝑇 ∞,𝑖 = ∫ ∫ -ℎ 𝑒𝑥𝑡 Γ 𝑒𝑥𝑡,𝑛 𝑡 Ψ 𝑖 𝑑Γ 𝑒𝑥𝑡,𝑛 𝑑𝑡 (7)
Where Γ 𝑒𝑥𝑡,𝑛 is the external boundary, at the corresponding optimization block, where the heat flux is searched; ℎ 𝑒𝑥𝑡 is the heat transfer coefficient on Γ 𝑒𝑥𝑡,𝑛 and; 𝑡 is the time of the process in which the heat flux is going to be found. The adjoint variables at each domain are obtained solving backwards in time the set of equations, while the deepest descent is calculated using equation 8 for each iteration k.

𝜌 𝑘 = 𝛻𝐽 𝑻 ∞ 𝑘 * 𝑤 𝑘 ∫ ∫ (𝛿𝑇 2 ) 𝑘 𝑑Γ𝑑𝑡 Γ 𝑡 𝑓,𝑛 𝑡 𝑓,𝑛 -𝜏 + ∫ ∫ (𝛿𝑇 2 ̅̅̅̅̅ -𝛿𝑇 2 ) 2 𝑘 𝑑𝛤 * 𝑑𝑡 𝛤 *
𝑡 𝑓,𝑛 𝑡 𝑓,𝑛 -𝜏 [START_REF] Mehnen | Evolutionary optimization of mould temperature control strategies: Encoding and solving the multiobjective problem with standard evolution strategy and kit for evolution algorithms[END_REF] Where 𝛿𝑇 2 is the solution of the sensitivity problem on the composite part (Ω 2 ).

Sensitivity analysis

The sensitivity analysis helps in the determination of the deepest descent. It is also useful to verify that the length of the dilated zone is selected correctly. A greater thickness of the dilated area would give lower sensitivity values making impossible to use the current methodology.

Furthermore, process time also plays an important role. Usually, the higher the time, the more the sensitivity increases. However in the 1 st optimization block, including preheating and transfer stage, the design variable 𝐓 ∞𝑛 (𝑟, 𝑧, 𝑡) is on a different time window of that of the observed temperature 𝑻 2, 𝑛 (𝑞 𝑛 ) at the eroded segment. That means that for higher transfer's times, the observed temperature at the end time is going to be farther in time from the design variable, decreasing the sensitivity with respect the design variable.

With reduced sensitivity values, the inverse method cannot be carried out. That is the case of the stamping stage where the sensitivity has low values due to the short time process fig [START_REF] Parlevliet | Residual stresses in thermoplastic composites-A study of the literature-Part III: Formation of residual stresses[END_REF]. In this stage, even when sensitivity increases with time, there is not enough time to properly use the methodology. This also means, that the temperature profile within the part at the end of the stamping stage depends more on the initial mold temperature profile than the heat flux imposed on the dilated zone over this time.

Knowing the sensitivity, linked to the time process, helps to establish a good time discretization step for the gradient calculation. In this application, the last discretization step must be larger than the time required to attain a sensibility value greater than 0.05. The smaller the time discretization is, in the gradient equation, the less sensitivity we have. Therefore, the results are either more dependent on the initial guess during optimization, or impossible to obtain.

Optimization block 1: Preheating and transfer

On the first optimization block, the aim is to find the heat flux distribution over the external boundaries that minimizes the objective function, defined by a combination of target temperature at the eroded zone and homogeneity on the external surface. The design variable is considered constant in time as done by Hopmann [START_REF] Ch | Inverse thermalmold design for injection molds[END_REF] and Agazzi [START_REF] Agazzi | Optimisation thermique des outillages d ' injection thermoplastique[END_REF]. However, in this case the design variable is in a different time window of that of the objective function. The results are compared with a nonoptimized case, resulting of imposing a constant design variable over time and space. In Fig. 5 it can be seen an improvement of the profile distributions within the part.

In this case, the metal insert and the composite organosheets were heated at the same time. The optimal condition at the end of the transfer stage is used as initial condition for the stamping stage.

Optimization block 2: Over-molding

The optimized temperature distribution at the end of the transfer stage, and a homogenous mold temperature, are taken as initials conditions for the stamping stage. At this moment any optimization is made on this part of the process. Nevertheless, we used the non-optimized final temperature profile of the stamping stage as initial condition for the 2 nd optimization block (Over-molding) . In here, we look for a temperature distribution as a time space function that minimizes the objective function.

After optimization, there is a good agreement between the target temperature and the optimized profile. Average temperature being 223.2 °C before optimization and 229.4°C after optimization, on the bottom erode line of the part, resulting in temperature difference of less than 1°C, with respect the target temperature at the end time.

To obtain this improvement, it can be seen in Fig. 6, that temperature distribution 𝐓 ∞2 (𝑟, 𝑧, 𝑡), on the external boundary Γ 𝑒𝑥𝑡 of the dilated zone, increases with time, which can be contradictory. This behavior is due to a small time step discretization in the gradient calculation, and the initial guess value in the optimization loop. Because, with this conditions, the problem is constraint to have a final profile near of the initial guess (210°C) at the external boundary of the mold. In this way, it cools down in the first steps and then increase the temperature slowly. The optimized heat flux distribution is displayed in Fig 7.

Optimization block 3: Stamping

Since, it is not possible to perform the optimization only in the stamping stage due of a lack of sensitivity. In this optimization block, we take into account the mold rise temperature stage and the stamping stage.

The objective is to find the heat flux distribution, over the temperature rise and stamping combined, that minimizes the objective function. After optimization, noticeable improvement of the temperature profile is obtained. As shown in fig 8, a maximum of 5°C deviation with respect the target is obtained in the optimized case. Fig 9 shows the profile distribution as space function of the heat flux after optimization.

2.5

.

Cycle evolution

We run the optimization block 2 and 3 until a stationary condition is reached. The average temperature is about 340.6°C, This is because the initial temperature profile in the dilated area is higher than the homogenous profile from the first cycle.

Conclusions

An optimization algorithm that combines different stages of a manufacturing process is presented. The methodology includes 3 optimization blocks. The 2nd and 3th blocks use the conformal approach, due to the proven efficiency [START_REF] Agazzi | Optimisation thermique des outillages d ' injection thermoplastique[END_REF][START_REF] Lu | The optimization of process parameters and characterization of highperformance CF/PEEK composites prepared by flexible CF/PEEK plain weave fabrics[END_REF]. This methodology is based on an inverse method to solve the problem subjected to constraints. The numerical problem is solved using the finite element method. A heat flux distribution varying space and time is found. Temperature profile profiles present a good improvement after optimization, with temperature variation smaller than 5°C. Initial guess and time discretization of the gradient plays a key role during the optimization. Due to de dependence of the results on the initial guess of the design variable in the optimization loop, a PSO algorithm is ongoing to find the best initial value, but also another term in the optimization function is going to be suggested to minimize the total energy consumption in the entire process. Experimental validation for a part of the process is going to be considered as well.

Fig. 1 .

 1 Fig. 1. Hybrid manufacturing process example. (a) Preheating (b) Transfer (c) Stamping (d) Over-molding (e) Mold temperature rise

Fig. 3 .

 3 Fig. 3. Conjugate gradient algorithm applied to each optimization block. Adapted from [2]

  ρ 𝑘 = 𝐴𝑟𝑔𝑚𝑖𝑛(𝜙(𝑟)) 𝑘 𝜙(𝑟) = 𝐽(𝑇 ∞ (𝑟, 𝑧, 𝑡) 𝑘 + 𝑟𝑊) Cost Function evaluation 𝐽(𝑞 𝑖 (𝑇 ∞ )) 𝑇 ∞ (𝑟, 𝑧, 𝑡) 𝑘+1 = 𝑇 ∞ (𝑟, 𝑧, 𝑡) 𝑘 + ρ

Fig. 4 .Fig. 5 .

 45 Fig. 4. Sensitivity results for the stamping stage, on the erode line (AB segment) from𝑡 𝑖 : initial time to 𝑡 𝑓 : final time.

Fig. 6 .

 6 Fig. 6. Design variable distribution in time and space .

Fig. 7 2 Fig. 8 .Fig. 9 .

 7289 Fig. 7 Optimized heat flux distribution in time and space for the 2 nd Optimization block (over-molding stage). Heat flux W/m 2

Fig. 10

 10 Fig. 10 Results block2-2nd Cycle: Design variable distribution in time and space. Temperature (°C) Vs. Arc length(m)

Table 1 .

 1 Material Properties

	Part	Material	Conductivity	Density	Heat Cap.	vari
			(𝜆) 𝑊 (𝑚. 𝐾) ⁄	(𝜌) 𝑘𝑔 𝑚 3 ⁄	(Cp)	able
					𝐽 (𝑘𝑔. 𝐾) ⁄
	Metal	Aluminum	238	2700	900	T 1
	insert
	Organo	PEEK-	Long 3	1464	1148	T 2
	-sheet	CF	Trans:0.7
	Mold	Steel	44,5	7850	475	T 3

Fig. 2. Study case. Multi-material approach: geometry composed by for domains. Metal insert (𝜴 𝟏 ) (Aluminium) Dilated zone (Ω 3 ) (Steel) Over-moulded Region (Ω 4 ) (PEEK) Organosheets (Ω 2 ) (PEEK +Carbon fiber)

Table 2 .

 2 Process conditions

	Stage	Processing	Initial temperature
		time (s)
	Preheating	90	20°C
	Transfer	6	Final preheating
	Stamping	6	Final Transfer
	Over-molding	25	Final Stamping

  Three dimensional transietn mold cooling analysis based on galerking finite element formulation with a matrix free conjugate gradient tehcnique. International Journal for Numerical Methods in Engineering,

		39(18), 3049-3064.
	[16]	Organosheet	composite	material.	Available	on:
		https://www.ensingerplastics.com/en/composites/composite-
		materials/organosheet

Acknowledgements

The authors would like to acknowledge the funders of the PERFORM project managed by the IRT Jules Verne (French Institute for Research and Technologies for composite, Metallic and Hybrid Structures) as well as their associated partners of the PERFORM project: Airbus, Daher, Europe Technologies, Faurecia, Loiretech, Naval Group, SAFRAN and Stelia Aerospace.

5

.References


Julie Deninotti

Émilie Anne Denis

come

 The World Health Organization recommends a caesarean section rate of 10 to 15% in each country. France: 21%  C-section may generate dissatisfaction with childbirth (Chalmers et al., 2010): 76% of women consider it as a traumatic event (Ryding, Wijma, & Wijma, 1997).  Moreover, as the baby's health is considered a priority in this situation, mothers have fewer opportunities to express their needs and emotions (Lipson, 1982).  Recruited on social networking groups about Csection and completed selfreport measures online, up to two years after childbirth.  All of them had an unplanned C-section under local anaesthesia.  They were at least 18 and gave birth to a living child.



2-Objectives

Main objective:  Investigate the relationship between a mother's emotion regulation strategy (antecedent-focused vs. responsefocused), her satisfaction with childbirth, and posttraumatic and/or depressive symptoms after unplanned C-section.

b-Measures

Anne Denis Cognitive reappraisal , an antecedent-focused strategy ⇨ Selecting a way of seeing a situation, in order to experience more or less emotions (Gross, 1998).

MCF

Expressive suppression, a response-focused strategy ⇨ Inhibiting the expression of emotions in order not to communicate informations about one's emotional state (Gross, 1998).

3-Results

a-Emotion regulation and satisfaction:

4-Discussion / Conclusion a-Discussion

 Mothers who used expressive suppression, a response-focused strategy, were less satisfied with childbirth. It was shown in previous literature that this strategy tends to decrease positive experience (Gross & John, 2003).  Emotion regulation strategy and maternal (dis)satisfaction were predictors for posttraumatic stress and depression symptoms.  Maternal satisfaction was the best predictor for both posttraumatic stress and depression symptoms.  It can be hypothesized that expressive suppression affects maternal satisfaction, which leads to posttraumatic stress and depression symptoms.  From theoretical elements, we can suppose that the "suppressive" mother expresses less expectations towards social support, therefore she receives less (Butler et al., 2003) b-Conclusion and perspectives  These results imply that the expression of emotions should be encouraged during labour and delivery, especially by providing as much social support as possible, and promoting more personal control in maternal care.



  Perhaps emotion regulation strategies influence satisfaction with childbirth:



  Cognitive reappraisal was not correlated to childbirth satisfaction (r=0.101, =0.487).  Expressive suppression was moderately correlated with childbirth satisfaction (r= -0.314, p<0.05). b -Emotion regulation and satisfaction on postpartum depression symptoms  76% of the participants scored over 12.5 in the EPDS, and therefore suffered from postpartum depression.  Emotion regulation combined with maternal satisfaction could predict the posttraumatic stress score: R²=0.201, p=0.01.

  Author for correspondance: USMB, Laboratoire InterUniversitaire de Psychologie (LIP/PC2S), Chambéry, France Contact: anne.denis@univ-smb.fr / +33 (0)4 79 75 84 63

	Tool	Measure type	Item example	Precisions
	General Information	Description of childbirth, age,	« How many pregnancies have	-
	Questionnaire	educational level	you had ? » « How old are you
			? »
	Emotion Regulation	Measures emotion regulation	« I keep my emotions to	Two emotion regulation
	Questionnaire		myself »	strategies (cognitive
				reappraisal, expressive
				suppression)
	Questionnaire Measuring	Measures satisfaction with	« Did you feel confident during	-
	Attitudes About Labour and	childbirth	labour ? »
	Delivery
	Edinburgh Postnatal Depression	Measures postnatal depression	« In the past 7 days, I have	Score > 12.5 = Depressed
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*


E Elyasi¹

A Perrier

M Bailet

Y Payan

TECHNIQUES TO REDUCE THE COMPUTATIONAL COST OF FINITE ELEMENT MODELS OF THE LOWER LIMB MUSCLES

Keywords:

Modeling the lower limb muscles using the Finite Element (FE) method is required for various applications including injury mechanisms or when stress/strain distribution in the muscle is of interest. When the muscles are represented with 3D FE models, the interaction between the muscles can be taken into account that has an effect on their force production. However, the computational cost of such a method is considerably high. Besides, in many cases, a major part of this computational cost is committed to gain unnecessary information. For instance, when having two FE muscles in contact, both muscles need to get finely meshed to conserve their surface details even if having the stress/strain distribution inside one of the two muscles is not required. As a result, the current study aims to explore a model reduction technique based on mesh embedding to decrease the computational cost of such models. A combination of Computerized Tomography and Magnetic Resonance Imaging (MRI) data obtained from a volunteer subject was used to generate a musculoskeletal model of the quadriceps muscle group. The modeling process was performed in ArtiSynth which is an opensource 3D modeling platform supporting combined simulation of multibody and finite element models. This platform allows the attachment of a passive embedded mesh to a FE body so that it deforms in accordance with the motion of the FE body. Considering that the external forces applied to the passive mesh can be propagated back to the FE body attached to it, contact can be defined between the embedded mesh and any other structure. A full and a reduced model are generated and are used to simulate a passive deep knee flexion to test the reliability of the method. The kinematic outcomes are compared against data points obtained from MRI at different flexion angles. The results show that the proposed methodology can be considered as a substitute to fully FE models without a substantial sacrifice on the outcomes despite having lower computational cost.

INTRODUCTION

Using the Finite Element (FE) method for modeling the muscles of the lower limb can be E. Elyasi, A. Perrier, M. Bailet and Y. Payan 2 beneficial in applications such as injury mechanisms or when stress/strain distribution in the muscle is of interest [START_REF] Mo | A Lower Limb-Pelvis Finite Element Model with 3D Active Muscles[END_REF][START_REF] Stelletta | Modeling of the Thigh: A 3D Deformable Approach Considering Muscle Interactions[END_REF][START_REF] Blemker | A 3D model of muscle reveals the causes of nonuniform strains in the biceps brachii[END_REF][START_REF] Blemker | Rectus femoris and vastus intermedius fiber excursions predicted by three-dimensional muscle models[END_REF]. Having a 3D FE representation of the muscles provides the opportunity to model them in interaction with an environment of other muscles, connective tissue, and bones and not as isolated units that only transmit axial forces to bones via tendons. The surrounding tissues in the muscle's environment can transfer transversal forces to the muscle tissue. These transversal forces have been shown to result in decreasing muscle force production [START_REF] Siebert | Muscle force depends on the amount of transversal muscle loading[END_REF]. Given that the lower limb consists of some of the largest skeletal muscles of the body, the aforementioned effect could be important in its muscular architecture.

However, musculoskeletal (MS) models with 3D FE muscles suffer from having a high preparation time as well as a high computational cost due to the number of elements and complex contact between different muscles. This limitation acts as a major barrier to use them for further applications and especially for dynamic simulations. Furthermore, these models are rarely used for muscle recruitment problems due to the excessive computational burden.

As a result, reducing this time seems to be a big improvement. In this sense, the objective of the current study is to explore the use of a model reduction technique on the MS model of the lower limb that includes the 3D FE representation of the quadriceps muscle group. This method can provide a simplified version of the model and we control the loss of accuracy that it can cause in comparison with the full model (that includes nonlinear hyperelastic material models with complex contacts between muscles).

The proposed technique relies on mesh embedding that is a well-known approach in the computer graphics community but has more recently been applied to biomechanics [START_REF] Nesme | Preserving topology and elasticity for embedded deformable models[END_REF][START_REF] Lloyd | New techniques for combined FEM-Multibody anatomical simulation[END_REF]. The concept behind this technique is that a passive mesh (for instance a surface mesh) can be attached to an underlying FE grid. This passive mesh will be able to deform in accordance with the global deformation of the FE grid. This can be used as a model reduction technique because the number of dynamic DOFs for the resulting system is determined by the number of nodes in the embedding FE grid. By using a coarser FE grid this number can be significantly reduced. It is important to be mentioned that this technique can handle contact between the passive surface mesh and any other component that comes into contact with it using the conventional FE to FE contact detection methods. When the passive mesh comes into contact with another component, the contact force will be simply propagated back to the FE grid and deform the FE grid accordingly.

In the following, the MS model of the lower limb with 3D FE representation of the quadriceps muscles is first described and used to simulate passive deep knee flexion. Subsequently, the mesh embedding technique is explained and gets evaluated on this FE model to see if this technique can be used to reduce the computational cost by replacing the surrounding muscles to the Rectus Femoris (RF) muscle with embedded surfaces without a big compromise on the quality of the results. The kinematic outcomes of the models during passive deep knee flexion get compared against Magnetic Resonance Imaging (MRI) data obtained at different flexion angles for validation purposes.

METHODS

As the first step of the study, an MS model of the lower limb in presence of the quadriceps muscle group represented as 3D FE components is generated to simulate passive deep knee flexion. The motion of the tibiofemoral joint is controlled using the MRI data of a subject collected at various knee flexion angles and the simulation gets validated by comparison of the kinematic outcomes of the patellofemoral joint with the MRI-based kinematic data points. A mesh embedding technique is used on the 3D FE muscle components to get evaluated as a method to reduce the computational cost of the model. The modeling is conducted in Artisynth that is an open-source Java-based modeling platform that allows the combination of the FE method with multibody modeling techniques while supporting contact and constraints [START_REF] Lloyd | ArtiSynth: A Fast Interactive Biomechanical Modeling Toolkit Combining Multibody and Finite Element Simulation[END_REF] as well as embedded meshes [START_REF] Lloyd | New techniques for combined FEM-Multibody anatomical simulation[END_REF] (www.artisynth.org).

Geometry reconstruction

A healthy subject (male, 40 years old, 94 kg, 1.73 m) was volunteered and gave his informed consent for participating in the experimental data collection that was part of a pilot study approved by an ethical committee (MammoBio MAP-VS pilot study, IRMaGe platform, Univ. Grenoble Alpes). The subject underwent a total of 5 sessions of non-weight-bearing MRI using a clinical MRI system (Achieva 3.0T dStream Philips Healthcare) and one session of computed tomography (CT) scan.

The CT scan was taken to capture the surfaces of the bones precisely to be used as a reference for registering the bones segmented from different MRI sets. The first MRI session was performed to obtain the full geometry of the lower limb muscles while the subject was lying still in the supine position (6.99×0.97×0.97 mm 3 intervals respectively in the axial, sagittal, and coronal views). The second MRI was obtained from the subject's right knee to capture the articulation, the connective tissues, muscle insertions, and tendons more precisely (0.31×0.7×0.31 mm 3 intervals in the axial, sagittal and coronal views). The subject was lying in the supine position with an approximate 25° knee flexion.

The third to fifth MRI sessions were conducted to obtain the required data for simulating passive deep knee flexion as well as model validation. For this purpose, the subject was lying in the left lateral recumbent position and positioned his knee at three different flexion angles for each acquisition. The MRI of the right knee was captured having 0.5 mm intervals in all planes. The three different knee positions during the third to fifth MRIs are depicted from the sagittal view in Figure 1. The knee was flexed at 55.6°, 99.6° and 137.5° respectively during the first to the third MRI. Manual segmentation was performed on all the images of the subject in Amira 6.5.0 in order to prepare the model geometry.

Mesh generation

The FE model of the quadriceps muscle group including Rectus Femoris (RF), Vastus Medialis (VM), Vastus Lateralis (VL), Vastus Intermedius (VI), and the quadriceps tendon (QT) was generated using the muscle geometries reconstructed from the MRI segmentation (Figure 2). In order to control the number of finite elements and in particular to avoid very small elements, the segmented muscle surfaces were smoothed to remove the unnecessary surface details and spikes. The end regions where the muscles insert into the bone were also simplified to avoid very small elements and to facilitate the meshing process with methods such as solid map meshing.

The process of mesh generation was conducted in HyperMesh 2019 (Altair Engineering, Inc., USA) to generate hexahedral dominant meshes (with control of element qualities and a limited number of wedge elements) for the four muscle parts as well as for the QT. The maximum element size was approximately 6mm to mesh the muscle parts and resulted in 2100 elements for RF, 1325 for VI, 9290 for VL, and 2308 for VM. For the Quadriceps Tendon (QT), the approximate maximum element size was 3mm which resulted in a mesh with 5200 elements.

Using embedded surface mesh for the quadriceps muscle group

In order to explore the application of the mesh embedding technique on the generated model, we assume that the RF muscle and QT to be the most important components that we want to monitor in terms of stress distribution. The other muscles (VI, VL, and VM) are the surrounding muscles of our main muscle and their stress distribution is assumed not to be a priority. Thus we will be replacing these muscles with embedded surfaces in a coarse FE grid to reduce the overall computational cost.

To describe the further steps of this reduced model, it is first required to explain the mechanism of "attachment" in the Artisynth platform [START_REF] Lloyd | New techniques for combined FEM-Multibody anatomical simulation[END_REF], which enables us to connect surface mesh voxels to a deformable FE body.

The attachment mechanism works by defining the coordinates of the attached component (𝑥 𝑎 ) to be a function of the coordinates of one or more master components to which it is attached (𝑥 𝑚 ) as follows:

𝑥 𝑎 = 𝑓(𝑥 𝑚 ) (1)
This implies that the velocities of these components have a linear relationship similar to:

ẋa = G am (ẋm), G am ≡ ∇f(x m ) (2)
Based on the principle of virtual work, the force ( 𝑓 𝑎 ) of the attached point will be able to propagate back to the master components (𝑓 𝑚 ) as follows:

f m = G am T f a (3)
Now with this background, for a point attached to a FEM (for instance each vertex of the embedded surface mesh that is attached to a FEM grid), its position and velocity is a weighted sum of nearby nodal positions 𝒙 𝒋 as follows:

x a = ∑ w j x j j , ẋa = ∑ j ẋj j (4)
Forces applied to each vertex (𝑓 𝑎 ) then propagate back to each node according to:

𝑓 𝑗 = 𝑤 𝑗 𝑓 𝑎 (5)
Given this information, to apply the technique to the VI, VM, and VL muscles, a coarse FEM grid was generated for these muscles to embed their surface meshes. An example of the embedded mesh in comparison to the normal FE mesh is depicted for the VI muscle in Figure 3. It is important to mention that the embedded surface mesh does not require a high level of treatment and simplification of the insertion sites. This significantly reduced the preparation time of the model. Figure 4 illustrates the model having the RF and QT as finely meshed components and the other muscles represented as surfaces embedded in a coarse FE grid.

Material Properties

The muscle normally experiences large displacements and strains and has a nonlinear stress/strain curve. As a result, when the muscle is in the passive state and has no activation, its behavior can be best represented by using a hyperelastic material model [START_REF] Johansson | A finite-element model for the mechanical analysis of skeletal muscles[END_REF]. In the passive deep flexion simulation of the current study, the focus is mainly put on the overall behavior of the muscles and the patellofemoral kinematics. Therefore, we have assumed that the passive muscle behavior can be modeled with a nearly incompressible isotropic neo-Hookean hyperelastic material model. The parameters used for the quadriceps muscles were defined based on the findings of Affagard et al. who presented an in vivo method to identify the behavior of the thigh muscles based on a displacement field obtained from ultrasound and digital image correlation techniques [START_REF] Affagard | Identification of hyperelastic properties of passive thigh muscle under compression with an inverse method from a displacement field measurement[END_REF]. For the QT, a linear elastic material was assumed; with values of 30 MPa for Young's modulus and 0.46 for the Poisson ratio. The cartilages and bones are modelled as rigid bodies for simplicity reasons and as their impact was assumed to be minimal on the outcomes.

Regarding the embedded parts, to account for the FEM voxels that are either empty or partially filled with the embedded surface mesh, the mass and the stiffness values of the embedding FEM are weighted based on the methods proposed by Nesme et al. to improve the resulting behavior of the model [START_REF] Nesme | Preserving topology and elasticity for embedded deformable models[END_REF]. This technique is fully implemented in Artisynth.

For the patellar ligament and the medial and lateral retinaculum, each of their bundles was represented by a discrete number of strands. Tensile forces were computed assuming each strand behaved as a non-linear stiffening spring at low strains (e<0.06) and having a linear stiffness at higher strains [START_REF] Blankevoort | Ligament-bone interaction in a three-dimensional model of the knee[END_REF]. The patellar ligament was represented with a total of seven bundles consisting of three bundles for the central region and two bundles for each of the medial and lateral regions based on the results of the cadaveric study of Yanke et al. [START_REF] Yanke | Regional mechanical properties of human patellar tendon allografts[END_REF]. The bundle stiffness values were adapted from the literature [START_REF] Yanke | Regional mechanical properties of human patellar tendon allografts[END_REF]. The total stiffness of the central region of the patellar ligament was set to 278 𝑁/𝑚𝑚 2 . The total stiffness of medial and lateral regions were set to 201 𝑁/𝑚𝑚 2 and 173 𝑁/𝑚𝑚 2 respectively. The nominal reference strain was assumed to be 0.02 for all the bundles of the patellar ligament at full extension. Five bundles were defined to represent the medial and lateral patellar retinaculum with the respective total stiffness of 31 𝑁/𝑚𝑚 2 and 97 𝑁/𝑚𝑚 2 adopted from the literature [START_REF] Merican | The structural properties of the lateral retinaculum and capsular complex of the knee[END_REF][START_REF] Laprade | Biomechanical Evaluation of the Medial Stabilizers of the Patella[END_REF] while a 0.01 reference strain was assumed for them.

Load and boundary conditions

The passive deep knee flexion is simulated by imposing the motion of the tibiofemoral joint. As the quadriceps muscles are all connected to QT and the QT is attached to the patellar bone, changing the modeling technique of the quadriceps muscles will affect the kinematics of the patellofemoral joint that is free to react to the forces transmitted to it through the soft tissues and contact forces.

The idea is to impose the motion of the tibiofemoral joint based on the MRI segmented bones at the highest level of flexion and then to take the patellofemoral joint kinematics as the output of the simulation. This output can be directly compared to the bone positions obtained from MRI at various flexion angles and enables us to validate the simulation outcomes by comparing the patellofemoral kinematics. A schematic view of the setup used for the simulation of passive deep knee flexion is depicted in Figure 5.

As demonstrated in Figure 5, the bone positions at 25° knee flexion (the first MRI position) are used to define the initial position of the model. The pelvic bones and femur are fixed in their initial positions. The foot bone and the fibula are constrained to the tibia and considered as a single segment. The patella is free to move in all its six Degrees of Freedom (DOFs) and its motion will be in response to the forces transmitted to it through the muscles and tendons, as well as contact forces. Sliding is modeled between all surfaces (bone, FE muscle, embedded muscle surfaces) that may come into contact. The gravity is neglected and inertial parameters of the segments are not considered as they will not have any impact on the simulation of passive flexion. The reason for this assumption is that the femur and pelvic segments are considered non-dynamic and the motion of the combined shank and foot segments is imposed through a pre-calculated transformation matrix at each time increment.

The nodes located in the proximal insertion of all the four muscles are attached to the femur head (that is supposed to be fixed in this simulation). The nodes of the VI that are closer than one millimeter to the femur surface are attached to the femur. To represent the distal insertion of the four muscles to the QT, a distance limit with the QT is defined for each muscle, and all the nodes that are closer to the QT than the distance limit are attached to the proximal part of the QT. The nodes located in the distal part of the QT are attached to the patella.

Model validation through comparison with MRI based kinematics

Defining the local coordinate frames for the shank, patella, and thigh segments were required to impose the motion of the shank and to extract the kinematics of the patella. The bony landmarks and knee Joint Coordinate System (JCS) are defined based on the ISB standards [START_REF] Wu | ISB recommendation on definitions of joint coordinate system of various joints for the reporting of human joint motion -Part I: Ankle, hip, and spine[END_REF][START_REF] Grood | A joint coordinate system for the clinical description of threedimensional motions: Application to the knee[END_REF]. For the calculation of the translations, the origins of the femur and shank local frames were both defined to be placed midpoint between the medial and lateral femoral epicondyles at neutral position (considered to be the bone positions while taking the CT scan). For the patellar segment, the origin was defined to be located on the most distal point of the patella bone. As the patellofemoral kinematics was observed in response to the passive flexion of the tibia, the tibiofemoral flexion angle was defined as the independent variable and all the 6 DOFs of the patella were considered to be dependent on it.

To compare the kinematic predictions of our knee models with the MRI-based data points, the Normalized Root-Mean-Square Deviation (NRMSD) from the MRI data was computed. Normalization was performed for each DOF because the scale and units are different. The sum of the normalized RSMD is computed over all 6 DOFs (Equation 6) and reported as the total NRMSD for each perturbation.

𝑁𝑅𝑀𝑆𝐷 = ∑ 𝑅𝑀𝑆𝐷 𝑖 𝑋 ̅ 𝑖 𝑖=𝐷𝑂𝐹 (6)
𝑅𝑀𝑆𝐷 𝑖 is the root-mean-square deviation of the patellar motion in its ith DOF from the MRI data points in that DOF. 𝑋 ̅ 𝑖 is the mean of the three MRI data points in the 𝑖th DOF. Lower values of NRMSD mean less deviation from the MRI data points that are directly extracted from images at different flexion angles.

RESULTS AND DISCUSSION

The model of the embedded surface mesh for VI, VL, and VM muscles were successful to simulate the whole deep knee flexion. The deformed state of the full and reduced models at various steps of the simulation is depicted in Figure 6. Regarding the simulation time, the finelymeshed FE model took more than 8 hours to complete while the embedded model took about two hours and a half, despite that the Rectus Femoris and quadriceps tendon are still finely meshed. As previously mentioned, since all our modeled muscles are indirectly connected to the patella, the first comparison of the results between our two simulations was the comparison of the patellofemoral kinematics. The predicted patellofemoral kinematics are demonstrated in Figure 7 and compared with the outputs of the finely meshed FE model. The predicted kinematics by the two models are compared against MRI data points through computing the NRMSD values as presented in Table-1. As the results of this table are suggesting, the patellofemoral kinematic outcomes did not substantially change and were not compromised by using the reduced model.

To perform a preliminary investigation on the impact of changing the modeling technique of the VI, VL, and VM muscles on the predicted stress distribution of the RF muscle, we have also monitored the maximum principal stress in the RF muscle throughout the simulation time. The result is presented in Figure 8. The RF maximum principal stress was not noticeably impacted by changing the modeling technique despite the reduced computational time.

CONCLUSION

The current study evaluated mesh embedding to be used as a model reduction technique in the MS models of the lower limb that represent the muscles with FE components. The full and reduced lower limb models were used to simulate passive deep knee flexion and the kinematic outcomes were compared against the MRI images of the same subject at different flexion angles. The use of the mesh embedding technique was successful to substantially reduce the computational cost of the simulation as well as model preparation time. The outcomes of the reduced model did not show a substantial difference from the full model.

Figure 1 :

 1 Figure 1: The sagittal view of the right knee MRI at three different flexion angles.

Figure 2 :

 2 Figure 2: Generated model of the lower limb for simulation of passive deep knee flexion while modeling the quadriceps muscle group as FE components.

Figure 3 :

 3 Figure 3: The image on the left is the hexahedral dominant mesh with 1325 elements, generated for the VI muscle and used in the finely-meshed FE model. The image on the right is the polygonal surface mesh embedded in a coarse FE mesh composed of 324 voxel elements of a maximum of 2 cm edges.

Figure 4 :

 4 Figure 4: Generated lower limb model while considering the RF and QT as main FE components that are finely meshed (highlighted in yellow). The other muscles are modeled as surface meshes embedded in FE grids.

Figure 5 :

 5 Figure 5: Schematic view of the passive deep knee simulation setup. The position of the combined shank and foot segment is controlled through the transformation matrix obtained from MRI at different knee flexion angles. The thigh and pelvic segments are non-dynamic. The patella is free to move in response to forces transmitted to it through the soft tissues and to contact with the femur.

Figure 6 :

 6 Figure 6: left: The deformed state of the finely-meshed FE model at various steps of passive knee flexion. Right: The deformed state of the model with embedded surrounding muscles at various flexion degrees.

Figure 7 :

 7 Figure 7: The effect of replacing the FE model of the VI, VL, and VM muscles with embedded surface meshes in a FEM grid on the patellofemoral kinematics.

Figure 8 :

 8 Figure 8: Maximum principal stress of the RF muscle that was considered as the main muscle throughout the passive deep knee flexion simulation with finely meshed FE models of the quadriceps muscle group and QT (blue line), and finely meshed RF and QT, but replacing the VI, VL, and VM muscles with surface meshes embedded in coarse FE grids with voxel elements (orange line).

Table 1 :

 1 NRMSD computed for each DOF of the patella from the MRI data points for different models. The sum of the deviation of all DOFs is presented in the last column.

	Patella DOF
	Muscle Model	Lateral Anterior Proximal Flexion Rotation Tilt Sum
	FE model of all muscles	0.21	0.06	0.35	0.08	1.08	1.63 3.40
	Embeded mesh for VI, VM and VL	0.22	0.06	0.37	0.08	1.10	1.69 3.52

ACKNOWLEDGMENT

This work was funded by Fondation pour la Recherche Médicale under the project FRM DIC20161236448. The authors acknowledge the technical support received from John Lloyd during the process of this study.


Olivier Lortholary

Marc Lecuit

Christine Rouzioux

Patrick Berche

Keywords:

Éditorial

> L'enjeu majeur du contrôle de l'épizootie grippale aviaire actuelle due au virus H5N1 est la prévention d'une nouvelle pandémie grippale humaine. Celle-ci pourrait être liée à : [START_REF] Gamblin | The structure and binding properties of the 1918 influenza haemagglutinin[END_REF] un réassortiment du génome de ce virus aviaire avec une souche épidémique humaine entraînant la circulation d'un virus hybride exprimant des antigènes viraux aviaires mais capable d'infecter une population humaine n'ayant pas d'immunité préexistante à ce nouveau virus ; ou (2) à la transmission interhumaine d'un virus aviaire ayant acquis directement un tropisme humain. Le propos de cet Editorial est de préciser sous forme de quelques questions/réponses les implications possibles sur la santé humaine des virus grippaux aviaires et notamment du virus responsable de l'épizootie aviaire actuelle, le virus H5N1 [START_REF] Gamblin | The structure and binding properties of the 1918 influenza haemagglutinin[END_REF][START_REF] Li | Genesis of a highly pathogenic and potentially pandemic H5N1 influenza virus in eastern Asia[END_REF][START_REF] Koopmans | Transmission of H7N7 avian influenza A virus to human beings during a large outbreak in commercial poultry farms in the Netherlands[END_REF][START_REF] Kaye | Avian influenza viruses and their implication for human health[END_REF][START_REF] Beigel | Avian influenza A (H5N1) infection in humans[END_REF][START_REF] Le | Avian flu : isolation of drug-resistant H5N1 virus[END_REF][START_REF] Taubenberger | Characterization of the 1918 influenza virus polymerase genes[END_REF][START_REF] Tumpey | Characterization of the reconstructed 1918 Spanish influenza pandemic virus[END_REF][START_REF] Tiensin | Highly pathogenic avian influenza H5N1, Thailand, 2004[END_REF].

Que sont les virus aviaires ?

Les virus grippaux sont des virus à ARN de la famille des Orthomyxoviridae dont le génome est composé de huit segments. Trois espèces de virus influenzae existent : influenza A, B et C. Les virus A comportent plusieurs sous-types définis par des antigènes de surface que sont l'hémagglutinine (H) et la neuraminidase (N) dont il existe respectivement 15 et 9 types. Ils sont responsables des infections humaines et de celles de plusieurs espèces aviaires ou de mammifères, notamment le porc. Les virus aviaires domestiques sont principalement de sous-types H5 et H7. Ils ne sont pas tous hautement pathogènes, c'est-à-dire capables d'induire une létalité voisine de 100 % chez les espèces aviaires qu'ils infectent, mais la présence d'un virus H5 ou H7 chez les volailles est toujours préoccupante, compte tenu de la létalité potentielle que ces virus peuvent induire dans les élevages. Leur pathogénicité est en partie liée à la présence d'acides aminés basiques (arginine et lysine) au site de clivage de l'hémagglutinine (H), qui est la protéine majeure contrôlant l'adhésion et l'entrée du virus dans les cellules. Le clivage de l'hémagglutinine est une étape clé pour l'internalisation virale et la susceptibilité de cette protéine aux protéases cellulaires est donc déterminante pour le tropisme et la virulence du virus. Le nombre de sous-types antigéniques associés à des épizooties domestiques est limité par comparaison à la diversité des virus grippaux A isolés chez les oiseaux sauvages (malades ou porteurs sains). Le réservoir de virus grippaux chez les porcs joue un rôle important dans le risque de transmission des virus aviaires à l'homme. En effet, les cellules épithéliales du tractus respiratoire du porc co-expriment les récepteurs glucidiques (acides sialiques) des virus grippaux humains mais aussi aviaires. Lors de la pandémie grippale majeure de 1918 (virus H1N1 responsable de la grippe « espagnole » à l'origine de 20 à 40 millions de morts), il semble que le virus ait été transmis directement des espèces aviaires à l'homme. En effet, il s'agit d'un virus dont la séquence semble d'origine uniquement aviaire, sans trace de réassortiment avec une autre souche virale. Il semble également qu'il soit particulièrement virulent, comme le souligne un travail récent démontrant une forte létalité après inoculation chez l'oeuf embryonné de poulet et la souris, même s'il n'existe pas de corrélation parfaite entre pathogénicités murine et humaine. Il a également été montré que ce virus avait acquis la capacité de se lier aux acides sialiques humains. Dans les pandémies de 1957 (H2N2, grippe asiatique responsable de 4 millions de morts) et de 1968 (H3N2, grippe de Hong Kong responsable de 2 millions de morts), le virus transmis à l'homme a été le résultat d'un réassortiment génétique entre des segments génomiques de virus aviaires et humains chez le porc, lequel a conduit à un virus associé à une moindre mortalité chez l'homme. La réapparition du sous-type H1N1 responsable d'une pandémie humaine en 1977 reste inexpliquée. Notamment, le virus n'est pas particulièrement proche de celui isolé à plusieurs reprises chez le porc et responsable, depuis 1918, de nombreux cas d'infections respiratoires dans cette espèce ainsi que de rares cas humains de gravité modérée. Le phénomène nouveau et important est l'apparition, depuis 1997, de cas isolés d'infections humaines liées à un virus H5N1 aviaire dans la région de Hong Kong et depuis dans d'autres pays d'Asie chez des personnes ayant une exposition répétée à des volailles domestiques infectées. Le risque actuel de pandémie peut être lié à la capacité de ce virus aviaire H5N1 de présenter des mutations progressives d'adaptation permettant une sélection d'un virus à plus grande capacité de transmission inter-humaine, sans étape de réassortiment avec un virus humain tel que cela a été observé pendant la pandémie de 1918. Les mutations d'adaptation peuvent se faire au niveau du site récepteur (RBS, receptor-binding site) de l'hémagglutinine, différent entre les virus aviaires et humains et en partie responsable de la barrière d'espèce. Aucune démonstration d'une telle adaptation n'a pour l'instant été mise en évidence, c'est-à-dire que les virus H5N1 actuellement isolés chez l'homme restent porteurs d'un site de fixation au récepteur cellulaire de type aviaire. Le risque de pandémie peut également être lié à un réassortiment entre un virus aviaire et un virus humain tel que cela a été observé lors des deux dernières pandémies à partir du réservoir porcin. Ce réassortiment peut aussi se produire chez l'homme

Quelle est l'épidémiologie de l'infection humaine par le virus H5N1 aujourd'hui ?

De manière générale, les épizooties aviaires récentes se sont accompagnées d'un faible risque de transmission à l'homme avec un risque encore plus faible de transmission inter-humaine. Les cas humains rapportés avec les autres virus que le H5N1 ont été le plus souvent sans gravité particulière, ce qui contraste avec la sévérité des cas asiatiques liés au H5N1. En 1997, le virus H5N1 hautement pathogène dans les espèces aviaires a été isolé chez des volailles d'élevage à Hong Kong avec apparition de 18 cas humains dont 6 sont décédés. Entre 1997 et 2002, le virus a été isolé à Hong Kong, en Corée du Sud et en Chine. En février 2003, ce même virus a été isolé chez 3 membres de la même famille séjournant dans le sud de la Chine en provenance de Hong Kong avec deux décès. En date du 9 novembre 2005, selon l'OMS, un total de 125 cas humains confirmés d'infection à H5N1 dont 64 mortels sont survenus principalement au Vietnam, mais aussi en Thaïlande, au Cambodge et, plus récemment, en Indonésie. Les seuls cas de grippe aviaire survenus depuis l'été 2005 proviennent d'Indonésie, le premier patient atteint étant décédé le 12 juillet. Il importe cependant d'insister sur l'importante barrière d'espèce pour le virus H5N1 expliquant le faible nombre de cas humains rapporté en comparaison à l'importance de l'extension de l'épizootie en Asie. La transmission inter-humaine de l'infection reste aujourd'hui tout à fait exceptionnelle et probablement la conséquence d'un inoculum particulièrement élevé qui permet alors de forcer la barrière d'espèce, les cas groupés familiaux correspondant à une exposition aviaire commune. La contamination se fait principalement au contact de fientes de volailles domestiques infectées, notamment lors du plumage des animaux. D'autres situations sont considérées comme à risque, telles que les visites de poulaillers et la manipulation de carcasses aviaires infectées. La consommation de volailles bien cuites ne pose aucun problème, car le virus ne survit pas à une température de 70 °C. Il ne semble pas exister aujourd'hui de formes asymptomatiques de l'infection chez des sujets contacts de patients infectés par le virus H5N1. Le risque d'infection humaine dans les conditions actuelles semble donc faible, mais la létalité est extrêmement élevée, voisine de 50 %. Par comparaison, la mortalité humaine de la souche de 1918 avoisinait les 2-4 %, et une souche épidémique humaine classique est associée à une mortalité de moins de 1 pour mille.

Quelles sont les manifestations cliniques de la grippe humaine liée au virus H5N1 ?

Une mise au point récemment parue permet de retenir les caractéristiques suivantes : l'incubation chez l'homme de la pathologie associée au virus aviaire H5N1est éventuellement plus prolongée que la grippe humaine commune, allant de 2 à 4 jours avec un maximum de 8 à 17 jours. Les sujets frappés ont été pour la plupart des enfants et des jeunes adultes en bonne santé. Un tableau diarrhéique peut précéder les manifestations respiratoires avec la présence de virus dans les selles. Les signes d'atteinte respiratoire basse liées au virus (toux et dyspnée) sont plus précoces que dans la grippe commune et ne sont pas liés à 1013 une surinfection bactérienne. Des signes d'atteinte du système nerveux central ont été rarement signalés. La présence de lésions inflammatoires dans les poumons des patients décédés suggère que l'importance de la réponse immunitaire de l'hôte pourrait être potentiellement délétère. Une lymphopénie sanguine est souvent rencontrée.

Quels sont les moyens thérapeutiques actuels contre la grippe aviaire ?

Il faut insister sur la nécessité de détecter et d'isoler de manière appropriée les cas importés, mais aussi de prendre en charge de manière appropriée les sujets contacts. Une quantité importante de médicaments antiviraux de la classe des inhibiteurs de la neuraminidase a d'ores et déjà été acquis par les autorités de santé en France pour combattre une situation pandémique. Pour des raisons stratégiques évidentes et compte tenu de l'absence d'indication actuelle de ces traitements, ceux-ci sont stockés par le service de santé des armées et ne sont donc pas disponibles à l'heure actuelle pour le grand public. Quatre millions de traitements en gélules et 10 millions en poudre conditionnée d'oseltamivir (Tamiflu ® ) seront prochainement disponibles ainsi que 200 000 traitements par le zanamivir (Relenza ® ). En cas de nécessité, ces traitements seraient administrés gratuitement aux patients. Il importe de comprendre que l'efficacité de ces médicaments est d'autant plus grande que ceux-ci sont administrés précocement après exposition. Ils ne semblent pas efficaces au-delà de 48 heures post-exposition. Les souches de virus H5N1 restent sensibles aux médicaments antiviraux actuels, mais une altération de sensibilité sous traitement a été récemment rapportée. L'intérêt de ces traitements antiviraux dont l'utilisation massive serait à l'évidence associée à la sélection de mutants résistants avec un risque d'inefficacité thérapeutique ultérieure serait d'attendre la mise à disposition d'un vaccin efficace sur la souche pandémique. Il importe aussi de prendre en compte le risque de surinfection bactérienne, notamment par le pneumocoque chez les sujets fragiles et d'insister sur l'importance de la vaccination anti-pneumococcique préventive dans les populations cibles et le recours à une antibiothérapie en cas de grippe sévère déclarée. Dans les prochains mois, plusieurs millions de masques adaptés seront également disponibles en premier lieu pour le personnel de santé : 50 millions de masques chirurgicaux et 200 millions de masques à haute protection ont déjà été acquis par les autorités de santé en France. Plusieurs vaccins contre le virus H5N1 sont développés par les firmes Sanofi-Pasteur et Chiron, mais ne sont pas encore au stade de la production commerciale. Deux millions de doses ont cependant été commandées en France et 40 millions de doses ont été réservées en cas de pandémie. Il faut rappeler que le vaccin antigrippal habituel n'a aucune efficacité préventive contre la grippe aviaire et que le vaccin pandémique ne pourrait être disponible que plusieurs mois après la mise en évidence du virus responsable de celle-ci.

En conclusion

Afin de minimiser le risque de pandémie, il importe de contrôler de manière urgente l'épizootie aviaire, notamment dans les régions où la densité de population humaine est particulièrement importante et de tenter de renforcer la vaccination antigrippale dans la population mondiale afin de limiter le risque de réassortiment génétique entre virus aviaires et virus humains directement chez l'homme. Le suivi de l'infection chez les oiseaux sauvages et dans les élevages porcins est également fondamental. Pour les voyageurs se rendant actuellement dans les zones d'endémie de grippe aviaire, il faut proscrire les contacts étroits avec les oiseaux malades ou décédés, mais aucune limitation de la consommation de volaille cuite n'est recommandée. Différents plans de lutte contre une pandémie de grippe ont été élaborés dans une quarantaine de pays pour tenter de diminuer au maximum l'impact d'une nouvelle pandémie, mais seul un petit nombre s'est parfaitement bien préparé à ce risque international qui, de toutes les façons, dépassera toutes les capacités de réactivité des systèmes de santé, même ceux des plus performants. olivier.lortholary@nck.ap-hop-paris.fr

‡

  Avian flu : possible implications for human health O. Lortholary, M. Lecuit, C. Rouzioux, P. Berche Université René Descartes-Paris V, Service des Maladies Infectieuses et Tropicales et Service de Microbiologie, Hôpital Necker-Enfants Malades, 149, rue de Sèvres, 75743 Paris Cedex 15 France.

'épidémiologie mondiale de l'épizootie aviaire aujourd'hui ?

  par les virus grippaux classiques H1N1 et H3N2 et co-infecté par un virus aviaire, d'où la proposition de renforcer la vaccination antigrippale contre la souche grippale épidémique humaine annuelle pour limiter ce risque (et qui contient cette année pour l'hémisphère nord des antigènes viraux de souches A H1N1 et H3N2 ainsi que d'une souche B). Les épidémies d'infections liées à des virus aviaires hautement pathogènes étaient relativement rares jusqu'en 1990. En 1997, un virus H5N1 hautement pathogène dans les espèces aviaires a été isolé chez des volailles d'élevage à Hong Kong. Entre 1997 et 2002, ce virus a été isolé à Hong Kong, en Corée du Sud et en Chine. En 2003, une épidémie d'infection aviaire est également survenue aux Pays-Bas liée à un virus H7N7 avec plusieurs dizaines de cas humains, principalement sous forme de conjonctivites. Un décès humain est survenu. Une plus petite épidémie liée à un virus H7 est survenue en Colombie britannique en 2004 avec un faible retentissement chez l'homme. Fin 2003 et en 2004, le virus H5N1 a disséminé dans plusieurs pays d'Asie créant une épizootie aviaire majeure (Corée du Sud, Vietnam, Japon, Thaïlande, Cambodge, Hong Kong, Laos, Chine, Malaisie, Indonésie). En Thaïlande, 56 % des volailles infectées sont des poulets et 27 % des canards, principalement dans le centre nord et l'est du pays ; les canards domestiques peuvent jouer le rôle de réservoirs silencieux du virus hautement pathogène. Le virus H5N1 a été également isolé dans d'autres espèces animales comme les chats domestiques, les tigres et léopards, probablement suite à l'ingestion de carcasses fraîches de volailles. La Fédération de Russie a signalé l'infection de volailles en juillet 2005 et la maladie a ensuite été signalée au Kazakhstan en août 2005.Des oiseaux sauvages infectés ont été retrouvés morts dans ces deux pays. La Mongolie a également détecté du virus H5N1 chez des oiseaux migrateurs retrouvés morts. En octobre 2005, la présence du virus H5N1 a été détectée et confirmée chez des volailles en Turquie et en Roumanie, à proximité de sites connus comme halte d'oiseaux migrateurs venant du nord-est de ces pays. Une surveillance des oiseaux migrateurs est donc désormais réalisée ainsi que des analyses virologiques en cas de morts suspectes d'oiseaux. Lorsqu'un foyer de grippe aviaire domestique est identifié, une mise en quarantaine est effectuée ainsi que l'abattage des animaux infectés et exposés. Ainsi, plus de 150 millions de volailles ont été sacrifiés depuis le début de l'épizootie à H5N1 en Asie avec un retentissement économique important dans les pays concernés. Il est également demandé aux éleveurs d'éviter les contacts entre volailles et porcs afin de diminuer le risque de réassortiment génétique.

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