Retinal waves

Recordings from the retina Multi-electrode array (MEA) (Maccione et al. 2014) ΜΕΑ recording of the voltage from a P11 mouse retina in the presence of 10 μM bicuculline. Retinal waves require three components: i) Spontaneous bursting activity ii) Refractory mechanism (slow After HyperPolarisation-sAHP) iii) Coupling (through Acetylcholine neurotransmitter)

Coupled neurons synchronize Isolated Neurons burst independently

Coupled neurons synchronize

Experiments for the emergence of retinal waves

Why study retinal waves?

16

Strategy:

To propose a model (i) suf1iciently close from biophysics to explain and propose experiments and (ii) suf1iciently well posed mathematically to analyse its dynamics upon varying biophysical parameters (developmentpharmacology).

• Modelling one cell bursting

• Modeling cells coupling

• Modelling waves generation, propagation and termination.

Strategy:

To propose a model (i) suf1iciently close from biophysics to explain and propose experiments and (ii) suf1iciently well posed mathematically to analyse its dynamics upon varying biophysical parameters (developmentpharmacology).

• Modelling one cell bursting

• Modeling cells coupling

• Modelling waves generation, propagation and termination.

Mul.scale modelling

From ionic channel to neuron to re.na scale Non linear dynamics, dynamical systems theory, sta.s.cal physics.

Main assumption

There are a few physiological parameters controlling re.nal waves dynamics, evolu.on and variability.

Find these parameters from a mathema.cal analysis Bifurca.on theory

Set of equations for sAHP current

SACs Network

SACs realistic connections SACs on a lattice

SACs become points on a lattice Waves speed

Model synaptic interactions

• Waves speed

Propaga8on threshold

Variability within retinal waves

N-neuron model

• There is a compe88on between 2 mechanisms:

-Period variability which tends to desynchronise -Acetylcholine which tends to synchronise

• There is an intermediate regime of coupling, where variability is maximum • Therefore there is a wide repertoire of paQerns

  emergence of retinal waves Experiment for isolated neurons, Zheng et al., 2006, Nature Retinal waves require three components: i) Spontaneous bursting activity 13 13 Experiment for isolated neurons, Zheng et al., 2006, Nature Retinal waves require three components: i) Spontaneous bursting activity ii) Refractory mechanism (slow After HyperPolarisation-sAHP) 14 Experiment for coupled and isolated neurons, Zheng et al., 2006, Nature Retinal waves require three components: i) Spontaneous bursting activity ii) Refractory mechanism (slow After HyperPolarisation-sAHP) iii) Coupling (through Acetylcholine neurotransmitter) emergence of retinal waves Experiment for coupled and isolated neurons, Zheng et al., 2006, Nature

-

  Weak coupling leads to small localised ac8vity -Moderate coupling leads to propaga8ng pa?erns -Strong coupling leads to complete synchrony of neurons stage II re8nal waves relevant at: • The cells scale (burs.ng, experimental match and predic.ons) • The network scale (waves propaga.on) • The developmental level (evolu.on of ionic channels and synapses). Theore8cal descrip8on via bifurca8on theory • Burs.ng • Interburst variability • Waves paQerns Next step: reac8va8ng waves in adults.

Stages of Retinal Waves During Development Stage I Stage II Stage III

	Spontaneous spatio-temporal
	waves during development
	Disappear short after birth
	when vision is
	functional
	• Retinotopic mapping
	• Nicotinic Acetylcholine Receptors
	(nAChR)
	• Disappear when
	vision is functional
	• Glutamate -
	AMPA receptors
	• Formation of
	retina circuitry
	• Chemical
	synapses not
	formed yet
	• Gap juction-
	mediated

Stages of Retinal Waves During Development Stage I Stage II Stage III

			Variability within retinal waves
	i) i)	Across species Across species	ii) Development
				Godfrey et al. 2007 Godfrey et al. 2007
	0! 37,5! 75! 112,5! 150! 187,5! 187,5! 150! 112,5! 75! 37,5! 0!	Rabbit Rabbit Period (s)! Mouse Chick Turtle Mouse Chick Turtle Period (s)!	• Retinotopic mapping • Nicotinic Acetylcholine Receptors (nAChR) 0! 150! 300! 450! 600! Speed (μm/s)! 0! 150! 300! 450! 600! Speed (μm/s)!	vision is functional • Glutamate -• Disappear when Zheng et al. 2004 Zheng et al. 2004
					AMPA receptors
	• Formation of
		retina circuitry
	• Chemical
		synapses not
		formed yet
	• Gap juction-
		mediated

ii) Development Variability within retinal waves i) Across species

	0! 37,5! 75! 112,5! 150! 187,5!	0! 150! 300! 450! 600!
	Period (s)!	Speed (μm/s)!

Rabbit Mouse Chick Turtle Godfrey et al. 2007 Zheng et al. 2004 ii) Development i) Across species

					Godfrey et al. 2007
	187,5! 150! 112,5! 75! 37,5! 0!	Period (s)!	0! 150! 300! 450! 600!	Speed (μm/s)!	Zheng et al. 2004
	Rabbit	Turtle	Mouse	Chick

gated K+ channel Ca 4 Calcium ions bound to each saturated Calmodulin complex S Saturated Calmodulin molecule (CaM) bind to each channel subunit All 4 subunits R of the channel are bound to activate the channel Gating mechanism CaM Ca Ca Ca Ca Ca Ca Ca Ca Ca Ca Ca Ca Ca Ca Ca CaM CaM CaM S C

		Activated
	Ca-
	R	R	R	R

ii) Development iv) Spatial Variability

	A	ii) Development gach=0.126 nS Network of SACs : Simulated Voltage Isolated Neurons Waves size distribution Network of SACs : Simulated Calcium Concentra.on gach=0.126 nS gach=0.102 nS lin-log log-log gach=0.126 nS gach=0.102 nS
	B
			Zheng et al. 2004 Zheng et al. 2004
	C	gach=0.168 nS gach=0.168 nS gach=0.168 nS	gach=0.21 nS gach=0.21 nS gach=0.21 nS
	E
			36

Morris-Lecar & Fast K+ channelsMembrane potential dynamics

Morris-Lecar & Fast K+ channels

A network model for stage II retinal waves

sAHP current Refractory mechanism

A network model for stage II retinal waves

Ach current Network effect

A network model for stage II retinal waves


Thierry Bastogne

Valérie Jouan-Hureaux

Magalie Thomassin

A new approach for a physicochemical characterization of nanoparticles in complex media: a pilot study

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

A new approach for a physicochemical characterization of nanoparticles in complex media: a pilot study.

T. BASTOGNE 1,2,3 , V. JOUAN-HUREAUX 1 , M. THOMASSIN 1 1 CRAN UL-CNRS UMR 7039, 2 INRIA BIGS, 3 CYBERnano Background. Current techniques used to measure the physicochemical characteristics of nanoparticles in simple media are poorly predictive of their behavior observed during in vivo experiments 1 . As a consequence, some pharmacokinetic or toxicokinetic issues are detected too late.

The proposed solution is composed of three main steps:

1. Sample preparation 2. Measurement phase 3. Statistical analysis 1) Sample preparation relies on a set of (n) serum-free media initially designed for cell culture but used herein to mimic heterogeneity of biological context. Each culture medium is composed of a large number (p), around a hundred, of biological compounds (proteins, vitamins, mineral salts, etc.), which may individually and synergistically interact with the nanoparticle surface. The nanoparticle to be characterized is added to each medium of the kit with the same concentration.

2) Physical characterization. The resulting mixtures are then analyzed by an appropriate technology compatible with complex media to measure the size distribution of constitutive nano-objects. In this pilot study, the nanoparticle size distributions were measured by a Dynamic light scattering system (Nanosight, Malvern), as illustrated in Fig. 1.

3) Statistical analysis. In a third step, all the experimental data coming from the (n) series of measurement are used to solve a " large p small n" regression problem. This statistical analysis informs about the most likely medium compounds to affect the size distribution of nanoparticles compared to their initial dimensions. This communication presents the first results of a pilot study in which the proposed approach was tested on gold nanoparticles mixed in n=9 cell free culture media provided by Thermo Fisher Scientific. A partial least squares method was used to solve the " large p small n" regression problem. The tested media was composed of p=82 compounds split up into four families: amino acids (AA), vitamins (V), mineral salts (S), and other compounds (OC) Preliminary results confirms significant changes of the size distribution between the culture media and the feasibility of the statistical method to identify a set of medium compounds that may explain those variations.

Conclusion

This study demonstrates the proof of concept of the proposed approach by identifying at least 5 amino acids that strongly interact with the surface of the tested NP.

Nanomedicine International Conference and Exhibition, Venice-Italy, Oct 23-25 2018

Methods

In this contribution, we are proposing an innovative approach for the physicochemical characterization of nanoparticles in complex media. The main objective is to quickly identify which medium compounds interact with the NP surface. In this pilot study, the goal is to demonstrate the proof of concept.

Objectives

Fig. 1 :Y

 1 Fig.1: Measured average size distributions of particles for nine samples in which the same con-centration of gold nanoparticles are mixed in nine different serum free culture media. Those data are then used in a "large p small n" regression problem to identify biological compounds of the medium that modify the size distribution of the nanoparticle.


Jose Aguado

Domenico Borzacchiello

Chady Ghnatios

François Lebel

Ram Upadhyay

Christophe Binetruy

Francisco Chinesta

José V Aguado

A Simulation App based on reduced order modeling for manufacturing optimization of composite outlet guide vanes

Keywords: Simulation App, Reduced order modeling, Real time simulation, Numerical simulation, Composites forming processes, Curing, Consolidation, Proper Generalized Decomposition, Parametric solutions, Computational Vademecums

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

Introduction

Efficient simulation of composite manufacturing processes remains even nowadays, in many cases, a challenging issue, mainly when they involve rich 3D behavior, multi-physics and the necessity of solving many scenarios very fast for optimization purposes [START_REF] White | Cure cycle optimization for the reduction of processing-induced residual stresses in composite materials[END_REF][START_REF] Pillai | Intelligent curing of thick section composites using a knowledge-based system[END_REF]. Composites manufacturing processes involve many different physics. For instance, impregnation of fibrous reinforcements involves flow models through porous media, combined with the mould compression for ensuring an appropriate degree of consolidation [START_REF] Shojaei | Modeling and simulation approaches in the resin transfer molding process: a review[END_REF][START_REF] Park | Modeling void formation and unsaturated flow in liquid composite molding processes: a survey and review[END_REF]. During consolidation the resin curing kinetics strongly affects its viscosity and therefore the flow conditions [START_REF] Kardos | Void growth and resin transport during processing of thermosettingmatrix composites[END_REF].

The intimate coupling between the resin flow, the reinforcement permeability, that decreases upon compression of the mould, and the viscosity, that depends on the temperature and the curing degree, can be at the origin of different process defects. Large viscosities imply high pressures that can generate irreversible preform deformations and even local reinforcement displacements creating local inhomogeneity defects. Moreover, residual stresses are another manifestation of this intimate multi-physics coupling [START_REF] White | Cure cycle optimization for the reduction of processing-induced residual stresses in composite materials[END_REF][START_REF] Zobeiry | Computationally efficient pseudoviscoelastic models for evaluation of residual stresses in thermoset polymer composites during cure[END_REF].

Another important issue encountered in the simulation of composites manufacturing is the one related to the process control and optimization [START_REF] Mounier | Multipurpose carbon fiber sensor design for analysis and monitoring of the resin transfer molding of polymer composites[END_REF][START_REF] Schmachtenberg | Application of ultrasonics for the process control of resin transfer moulding (RTM)[END_REF][START_REF] Lawrence | An approach to couple mold design and online control to manufacture complex composite parts by resin transfer molding[END_REF]. In general, optimization implies the definition of a cost function and the search of the optimum process parameters defining the minimum of that cost function. The procedure starts by a guessed set of process parameters. Then the process is simulated using suitable numerical methods. The solution of the model is the most expensive step of the optimization procedure. As soon as the solution is available, the cost function can be evaluated and its optimality checked. If the chosen parameters do not define a minimum (at least local) of the cost function, the process parameters should be updated and the solution recomputed. The procedure continues until reaching the minimum of the cost function. The solution of the process model is a tricky task that demands important computational resources and usually implies extremely large computing times. Thus, usual optimization procedures are inapplicable under the real-time constraint. The same issues are encountered when dealing with inverse analysis in which material or process parameters are expected to be identified from numerical simulation, by looking for the unknown parameters so that computed fields match the ones measured experimentally.

Until now, the solution consisted in using the more and more powerful computing platforms and techniques for speeding up standard discretization techniques. Appealing alternatives for circumventing, or at least alleviating, these issues lie in the use of reduced order modeling (ROM) [START_REF] Chinesta | The Proper Generalized Decomposition for advanced numerical simulations[END_REF][START_REF] Antoulas | A survey of model reduction methods for large-scale systems[END_REF][START_REF] Quarteroni | Reduced Basis Methods for Partial Differential Equations: An Introduction[END_REF] strategies. ROM is based on the observation that the family of parametric solutions of a given model usually contains much less information than it was originally assumed when the discrete model was built. Proper Orthogonal Decomposition, Proper Generalized Decomposition and Reduced Basis are nowadays widely considered from a fundamental and applicative viewpoints.

Proper Orthogonal Decomposition (POD) is a general technique for extracting the most significant characteristics of a system's behavior and representing them in a set of "POD basis vectors" [START_REF] Volkwein | Model reduction using proper orthogonal decomposition[END_REF][START_REF] Willcox | Balanced model reduction via the proper orthogonal decomposition[END_REF]. These basis vectors then provide an efficient (typically low-dimensional) representation of the key system behavior, which proves useful in a variety of ways. The most common use is to project the system governing equations onto the reduced-order subspace defined by the POD basis vectors. This yields an explicit POD reduced model that can be solved in place of the original system. The POD basis can also provide a lowdimensional description in which to perform parametric interpolation [START_REF] Chaturantabut | Nonlinear model reduction via discrete empirical interpolation[END_REF][START_REF] Peherstorfer | Localized discrete empirical interpolation method[END_REF], infill missing or "gappy" data [START_REF] Willcox | Unsteady flow sensing and estimation via the gappy Proper Orthogonal Decomposition[END_REF], hyper-reduced approximations [START_REF] Ryckelynck | Multidimensional a priori hyperreduction of mechanical models involving internal variables[END_REF][START_REF] Amsallem | Design optimization using hyper-reduced-order models[END_REF], and perform model adaptation. There is an extensive literature on POD showing it has broad application across fields. Some review of POD and its applications can be found in [START_REF] Benner | A survey of projection-based model reduction methods for parametric dynamical systems[END_REF][START_REF] Ryckelynck | On the a priori model reduction: Overview and recent developments[END_REF] and the references therein.

Another family of ROM techniques is based on the use of a reduced basis constructed by combining a greedy algorithm and "a posteriori" error indicators [START_REF] Patera | Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations[END_REF][START_REF] Drohmann | Reduced basis approximation for nonlinear parametrized evolution equations based on empirical operator interpolation[END_REF][START_REF] Fritzen | Reduced basis hybrid computational homogenization based on a mixed incremental formulation[END_REF]. As for the POD, the Reduced Basis method requires some amount offline work, but then the reduced basis model can be used online for solving different models with control of the solution accuracy, because the availability of error bounds [START_REF] Rozza | Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations[END_REF]. When the error is unacceptably high, the reduced basis can be enriched by invoking a greedy adaption strategy. Useful review works on the subject are [START_REF] Rozza | Fundamentals of reduced basis method for problems governed by parametrized PDEs and applications[END_REF][START_REF] Hesthaven | Certified reduced basis methods for parametrized partial differential equations[END_REF].

Techniques based on the use of separated representations are at the heart of the so-called Proper Generalized Decomposition (PGD) methods [START_REF] Ammar | A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids[END_REF][START_REF] Ammar | A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. Part II: Transient simulation using space-time separated representation[END_REF][START_REF] Falco | A Proper Generalized Decomposition for the solution of elliptic problems in abstract form by using a functional Eckart-Young approach[END_REF]. Such separated representations were considered in computational mechanics for separating space and time in transient solutions [START_REF] Ladevèze | The large time increment method for the analyze of structures with nonlinear constitutive relation described by internal variables[END_REF][START_REF] Boucinha | Spacetime proper generalized decompositions for the resolution of transient elastodynamic models[END_REF]. Separated representations were employed for solving multidimensional models suffering the so-called curse of dimensionality [START_REF] Chinesta | An overview of the Proper Generalized Decomposition with applications in computational rheology[END_REF][START_REF] Hackbusch | Tensor spaces and numerical tensor calculus[END_REF][START_REF] Lavedèze | On the verification of model reduction methods based on the Proper Generalized Decomposition[END_REF] and in the context of stochastic modeling [START_REF] Nouy | A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations[END_REF]. Then, they were extended for separating space coordinates making possible the solution of models defined in degenerated domains, e.g. plate and shells [START_REF] Bognet | Separated representations of 3D elastic solutions in shell geometries[END_REF] as well as for addressing parametric models where model parameters were considered as model extra-coordinates, making possible the offline calculation of the parametric solution that can be viewed as a metamodel or a computational vademecum, to be used online for real time simulation, optimization, inverse analysis and simulation-based control [START_REF] Chinesta | PGD based computational vademecum for efficient design, optimization and control[END_REF]. Some applications in the context of composites manufacturing processes were addressed in [START_REF] Chinesta | First Steps Towards an Advanced Simulation of Composites Manufacturing by Automated Tape Placement[END_REF] while the multi physics coupling was successfully achieved in [START_REF] Borzacchiello | Reduced order modelling for efficient process optimisation of a hot-wall chemical vapour deposition reactor[END_REF].

This work is intended to propose a first approach using reduced order modeling techniques to enhance adaptability of composite manufacturing process to changeable material and process environments through increased parametric modeling capabilities. The process selected is the consolidation and curing of a real part. Consolidation and curing of thermoset pre-impregnated fibers (from now on, simply referred as pre-pregs) involve different physics: heat transfer, compression of fiber beds, resin flow and chemical reaction. Strong couplings exist between these physics and many material parameters come into play. In this paper we combine several different modeling and simulation strategies for the efficient solution of a generic multi-physic and coupled problem. In particular, we propose a ROM-based segregated approach (rather than a monolithic one) for treating each physics separately. This approach allows applying, in each case, the most convenient ROM technique. Then, coupling is made by defining an appropriate parametrization of the coupling variables. A strategy for coupling ROMs of different kind (i.e. reduced solvers and parametric solutions) is also proposed. The integration of all these models constitutes a Simulation App that allows real-time evaluation of any process conditions. The described methodology can be extended and generalized to other processing technologies.

The rest of the paper is organized as follows. Section 2 presents the manufacturing process as well as the equations describing the physics involved in the manufacturing process of composite outlet guide vanes (OGV). Section 3 describes the simulation strategy, including the different simulation modules based on ROM and their coupling. In particular, we recall the main features of the ROM methods that were implemented, emphasizing both the construction of the reduced models in the offline stage and their utilization in the online stage, as a part of the Simulation App. Finally, Section 4 presents how the simulation modules were integrated into a process-specific simulation tool, a Simulation App. We describe the different functionalities of the application, organized by tabs, allowing to the user to perform the usual pre-processing, simulation and visualization operations. The advantages of process-specific simulation tools, such as the Simulation App, over general-purpose simulation software are discussed, especially in process optimization framework.

Process description and physics modeling

The concept of a Simulation App is presented in this paper through a practical application: the manufacturing process of a composite blade, and more specifically, an outlet guide vane. In this section we are first describing the manufacturing process from a technological point of view. Then we shall present the physics modeling and constitutive behavior for each considered physical phenomena.

Process description

Figure 1 shows the geometry and the computational mesh of the composite OGV part, which is manufactured by press forming and curing of 66 thermoset unidirectional continuous fiber pre-preg layers, i.e. fibers already impregnated with resin in a partially cured stage.

During the forming process, the composite lay-up is heated by conduction from the top and bottom metallic mold walls and consolidated under press. See Figure 2 for details. The heat initiates the cure reaction and the applied pressure provides the force needed to drain the excess of resin out of the composite, to consolidate pre-preg layers and to reduce voids by compressing the air inside. The temperature raise determines the onset of the cure reaction. Because of the exothermic effects of the curing process and the variability of the kinetic and thermal properties of the resin with the temperature and curing degree, the process is highly nonlinear. Moreover, the resin undergoes a strong rheological modification because its viscosity also depends on the temperature and the degree of cure. Therefore the flow conditions vary continuously with time.

The nominal heating cycle is designed so as to apply a constant temperature of 438 K (330 F) on both top and bottom mold walls. The press closure is initially based on a constant closure rate of 0.1524 mm/min (6 mils/min). As the cure reaction advances, the viscosity increases and so the closing force to be applied by the press increases. When the maximum closing force of the press is attained, the control switches to a force-based one. The closure rate is therefore adapted so as to keep the closing force constant. A final technological restriction to be taken into account is the so-called hard-stop condition, occurring when the cumulated displacement reaches its maximum value, 3.3 mm (130 mils).

Remark 1 (On the simulation of the press control system). Observe that the manufacturing process simulation will be nonlinear due to the just described press control system. If a force-based control applies, one has to solve a nonlinear problem in order to find out the closure rate that keeps the force constant at its maximum value.

Thermo-kinetic model

The model governing thermo-kinetic is given by the following partial differential equations:

ρC p (T, α) ∂T ∂t = ∇ • λ∇T + ρ∆H α (1a) α = f kin (T, α), (1b)
where T (x, t) and α(x, t) represent the temperature and curing degree fields, respectively. We shall refer to Equation (1a) and to Equation (1b) as the heat and kinetic equations, respectively. The curing function, denoted by f kin , is

given by the phenomenological model by Kamal and Sourour [START_REF] Kamal | Kinetics and thermal characterization of thermoset cure[END_REF], widely used to describe the conversion kinetics of epoxy systems:

f kin (T, α) = k 1 exp E 1 RT + k 2 α m exp E 2 RT (1 -α) n , (2)
Heat convection is neglected because of the creeping flow approximation and it is assumed there is no dispersion effect, i.e. resin and fiber share the same temperature. The coefficients ρ and C p appearing in Equation (1a) denote the density and the specific heat, while λ stands for the thermal conductivity tensor of the composite part. These were obtained from the properties of the resin and fibers using a linear mixing rule. For the specific heat this reads:

C p (T, α) = V f C pf + (1 -V f ) C pr , (3)
where C pf and C pr are the specific heat of the fibers (depending on the temperature) and the resin, respectively. At the initial conditions, i.e. V f = V f 0 = 57%, it can be rewritten as follows:

C p (T, α) = (p 1 T + p 0 ) α + (q 1 T + q 0 ) (1 -α) , (4)
where coefficients p 0 , p 1 , q 0 and q 1 are defined in Table 1. Note that only this quantity is varying with the temperature, whereas ρ and λ can be reasonably approximated as constants in the system considered in this application. The thermal properties, as well as the coefficients of the kinetic model, were obtained from experimental characterization and are summarized in Table 1.

The solution of the thermo-kinetic model requires defining appropriate initial and boundary conditions. The initial conditions are given by T (x, t = 0) = T 0 and α(x, t = 0) = α 0 . It is important to note that the heat equation, Equation (1a), is global in space whereas the kinetic equation, Equation (1b) is local, that is, the solution at a particular location of the part only depends on the thermo-kinetic history at that location. Therefore, boundary conditions are only needed for the heat conduction equation, and in particular they concern the temperature cycle prescribed at the top and bottom surfaces S + and S -, see Figure 3, that read T (x ∈ S + , t) = T t (t) and T (x ∈ S -, t) = T b (t), respectively. The heat losses through the lateral surfaces L (see Figure 3) can be neglected, that results in ∇T (x, t) • n = 0, being n the unit outwards vector defined on L.

Consolidation model

During the consolidation under press, the excess of resin is drained out of the composite. Assuming that only the resin moves between fibers, that is, preform is compressed but remains nearly at rest, the resin flow model can be described from the Darcy's flow model:

∇ • v = 0 v = -η -1 K • ∇P , (5)
where v, P and η are the velocity, pressure and viscosity fields and K is the permeability tensor. The solution of the flow model requires adequate boundary conditions. In particular it is assumed that in the lateral boundaries L, see Figure 3, the pressure vanishes. On the other hand, it is assumed that the velocity at the top surface corresponds to the compression rate U imposed by the press, which is assumed to be directed vertically, while the resin velocity vanishes at the bottom surface. In summary:

   P (x ∈ L) = 0 v(x ∈ S + ) = (0, 0, -U ) T v(x ∈ S -) = 0 . ( 6
)
As the curing reaction advances, the resin viscosity η tends to increase until the flow is no longer possible or will induce fiber washing. This behavior is taken into account in the following chemo-rheological model:

η (T, α) = η 0 exp B T exp Cα d . (7)
The viscosity evolution is therefore the main link between Equation (1) and Equation ( 5): the thermo-kinetic simulation influences the pressure field through the viscosity, which depends on both the temperature and the curing degree. Note also that, strictly speaking, the thermo-kinetic simulation depends on the consolidation simulation, because, as the excess of resin is drained out under the action of the press, the fiber volume fraction changes, and so the specific heat does, see Equation ( 3). However, this link will be neglected in practice thanks to the semi-implicit linearization scheme that was implemented, see Section 3.4 for details.

Finally, the permeability is also assumed to depend on the fiber volume fraction evolution. The principal components obey the following expressions [START_REF] Gebart | Permeability of unidirectional reinforcements for RTM[END_REF]: Coefficients of Equation ( 7) and Equation ( 8) are defined in Table 1. Observe that the permeability depends on the fiber volume fraction, which in turn, depends on the pressure field, making the consolidation problem nonlinear itself. However, the permeability coefficients can be assumed to be uniform all over the domain, i.e. they do not depend on the space coordinates. This fact will allow for a very simple parametrization of the permeability tensor, see Section 3.3 for details.

K 11 = K 22 = c (1 -V f ) 3 V 2 f and K 33 = c ⊥ V f a V f -1 5/2 . ( 8
)
k 1 1.77 • 10 -5 s -1 k 2 9.30 • 10 2 s -1 E 1 /R 9, 200 K E 2 /R 6,

Simulation based on reduced order modeling

In this section, we describe the simulation strategy, including the different simulation modules based on ROM techniques and their coupling. In particular, we recall the main features of the ROM methods that were implemented, emphasizing both the construction of the reduced models in the offline stage and their utilization in the online stage, as a part of the Simulation App.

The coupled model described in Section 2 involves three primary unknown fields, the temperature T (x, t), the pressure P (x, t) and the curing degree α(x, t). The viscosity field, η(x, t), can be obtained as a post-processing of the temperature and curing degree fields. The nonlinearity associated to the coupling can be efficiently addressed by using a semi-implicit incremental time integration, and treating all coupling terms explicitly, therefore allowing for decoupling of the different problems. Thanks to this strategy, we are able to define different simulation modules, described below, one for each physics involved in the manufacturing process. This approach is particularly effective in the context of ROM, because it allows applying the most suitable techniques depending on the nature of the equations.

It is to be noted that domain changes due too the applied compression will be neglected, i.e. the mould thickness reduction remains small enough.

Reduced order modeling methods

The simulation strategy combines three different numerical techniques: (i) the Proper Orthogonal Decomposition (POD), (ii) the Discrete Empirical Interpolation Method (DEIM) and (iii) the Proper Generalized Decomposition (PGD). In this section we summarize the main ingredients of these three techniques.

The Proper Orthogonal Decomposition

POD extracts the most significant components, measured in 2-norm, in the solutions of a parametric problem from the analysis of a set of "snapshots" (previously computed solutions of a given problem at different times and for different values of the model parameters) and uses them to approximate the solution for a new set of parameters up to a certain degree of accuracy.

Thus, POD allows expressing the unknown field involved in a generic problem u(x, t; µ), with µ the vector containing the model parameters, as

u(x, t; µ) ≈ Nu n=1 a n u (t; µ)φ n u (x), (9)
with usually much lower N u that the number of nodes, denoted by I, used for approximating the unknown field within the finite element framework. When considering discrete approximation spaces, the unknown vector at time t j , j = 1, • • • , J, is denoted by u(t j ; µ), that contains the value of the unknown field at each node x i , i = 1, • • • , I, can be expressed in the following reduced form:

u(t j ; µ) = Φ u a u (t j ; µ), (10)
defining the linear combination of vectors φ n u , constituting the columns of matrix Φ u , by the coeffients a u (t j ; µ), where the subscript • u indicates that the reduced basis and the projection coefficients are associated to the (scalar) field u.

The Discrete Empirical Interpolation Method

When considering a generic nonlinear function g(u(x, t; µ)) its evaluation in the reduced state space from the coefficients a u (t j ; µ) can be very expensive and, as discussed in [START_REF] Chaturantabut | Nonlinear model reduction via discrete empirical interpolation[END_REF][START_REF] Barrault | An "empirical interpolation" method: application to efficient reduced-basis discretization of partial differential equations[END_REF], it may compromise the efficiency of reduced model techniques. One possibility consists of using the POD just described to extract a reduced basis able to approximate the nonlinear term as

g(x, t; µ) ≈ Ng n=1 a n g (t; µ)φ n g (x). (11)
In order to compute the approximation coefficients a n g , with n = 1, • • • , N g , the nonlinear function is reconstructed at any time t j at only N g nodes, denoted by x i g , with i = 1, • • • , N g . The subscript • g stands for the fact of that points being related to the approximation of the nonlinear function on the reduced basis, φ n g . It results in the following linear system to be solved each at each time instance and given set of parameters:

   g(x 1 g , t j ; µ) . . . g(x Ng g , t j ; µ)    =     φ 1 g (x 1 g ) • • • φ Ng g (x 1 g ) . . . . . . . . . φ 1 g (x Ng g ) • • • φ Ng g (x Ng g )        a 1 g (t j ; µ) . . . a Ng g (t j ; µ)    .( 12
)
The remaining question concerns the choice of points x i g , i = 1, • • • , N g . These points are a priori arbitrary, the only contraint being that the matrix involved in Equation ( 12) be invertible. However, in [START_REF] Barrault | An "empirical interpolation" method: application to efficient reduced-basis discretization of partial differential equations[END_REF] authors propose to define these points using a greedy strategy in order to locate them to capture as much information as possible. The resulting points were called "magic points" and for the sake of completeness we describe below their calculation. We start by considering

x 1 g = argmax x |φ 1 g (x)|. (13)
Then we compute d 1 from

d 1 φ 1 g (x 1 g ) = φ 2 g (x 1 g ), (14)
that allows defining the residual r 2 (x), i.e. a contribution in φ 2 g (x) that cannot be explained by φ 1 g (x), from which computing point x 2 g :

x 2 g = argmax x |r 2 (x)| with r 2 (x) = φ 2 g (x) -d 1 φ 1 g (x). ( 15
)
As by construction r 2 (x 1 g ) = 0 we can ensure x 2 g = x 1 g . The procedure is generalized for obtaining the other points involved in the interpolation procedure. Thus, for obtaining point x i g we consider

x i g = argmax x |r i (x)| with r i (x) = φ i g (x) - i-1 j=1 d j φ j g (x). (16)
The coefficients d 1 , • • • , d i-1 must be chosen for ensuring that x i g = x j g , ∀j < i. For this purpose we enforce that the residual r i (x) vanishes at each location x j g , with j < i by solving:

r i (x j g ) = 0 = φ i g (x j g ) - i-1 l=1 d l φ l g (x j g ), j = 1, • • • , i -1, (17)
that constitutes a linear system whose solution leads to the sought-after coefficients

d 1 , • • • , d i-1 .

The Proper Generalized Decomposition

Most of the existing model reduction techniques proceed by extracting a suitable reduced basis and then projecting the problem solution on it. Thus, the reduced basis construction precedes its use in the solution procedure, and one must be careful on the suitability of a particular reduced basis when employed for representing the solution of a particular problem. This issue disappears if the approximation basis is constructed at the same time that the problem is solved. Thus, each problem has its associated basis in which its solution is expressed. One could consider few terms in its approximation, leading to a reduced representation, or all the terms needed for approximating the solution up to a certain accuracy level. The Proper Generalized Decomposition (PGD) proceeds in this manner.

When addressing the solution of a parametric problem u(x, t; µ) its PGDbased separated representation, including parameters as extra-coordinates, reads

u(x, t, µ) ≈ Nu n=1 φ n x (x) φ n t (t) φ n µ (µ). ( 18
)
For additional details the interested reader can refer to [START_REF] Chinesta | PGD based computational vademecum for efficient design, optimization and control[END_REF] and the numerous references therein.

The thermo-kinetic simulation module

A POD approach is applied in order to reduce the computational complexity of the thermo-kinetic simulation. Reduced basis are computed for both primary fields, temperature and curing degree. Other reduced basis are also computed in order to approximate nonlinearities using the DEIM. The training stage, i.e. snapshots generation, and the reduced basis extraction are explained in Section 3.2.1. Then, in Section 3.2.2, the ROM for the thermo-kinetic simulation is assembled. The reduced version of the heat equation is formed by standard Galerkin projection onto the temperature reduced basis. The kinetic equation can be treated in a different manner thanks to its local nature. The computational complexity is reduced in this case by integrating Equation (1b) only in a well-chosen subset of mesh nodes; in particular, that subset will be computed using DEIM.

Training stage and reduced basis extraction

In the training stage, a series of simulations were carried out with a full-order solver based on standard numerical techniques, for different choices of the model parameters. In our case, the following model parameters were identified:

• Initial degree of curing, α 0 , that may differ from one OGV part to another depending on the time the pre-pregs stay out of the freezer before manufacturing.

• Initial temperature, T 0 , that may change depending on the ambient conditions.

• Temperature cycle imposed at both top and bottom walls of the mold, denoted by T t (t) and T b (t), respectively. In the actual process, however, a fixed temperature is kept all along the process, i.e. the variability at both the beginning and the end can be neglected. In addition, both top and bottom temperatures are the same in practice so we can simply denote

T c ≡ T t = T b .
• Initial fiber volume fraction, V f 0 , that may change if the ply stack is modified by adding or removing plies.

We denote by µ m = (α 0 , T 0 , T c , V f 0 ) m , with 1 ≤ m ≤ M , the parameter sampling in order to compute the snapshots. Recall that the objective is to train a ROM from these snapshots. The nonlinear thermo-kinetic coupled problem given by Equation ( 1) was therefore solved to obtain the space-time temperature and curing degree space-time fields, i.e. T (x, t; µ m ) and α(x, t; µ m ).

From these collected data, a reduced basis is extracted for both temperature and curing degree, allowing the introduction of the following approximations:

T (x, t; µ) ≈ N T n=1 a n T (t; µ)φ n T (x) and α(x, t; µ) ≈ Nα n=1 a n α (t; µ)φ n α (x), (19)
where φ n T and φ n α denote the temperature and curing degree basis functions, respectively. Coefficients a n T are to be determined by solving a reduced system, which will be formed by Galerkin projection onto the reduced basis φ n T . On the other hand, coefficients a n α are to be determined by integrating the kinetic equation only in a subset of mesh nodes, denoted by {x n α } Nα n=1 . This means that the kinetic equation may be integrated at only N α locations (very few in practice) leading to important computational time savings. With the reduced basis for the curing degree at hand, these nodes are chosen straightforwardly as explained in Section 3.1.2.

The nonlinear terms in the thermo-kinetic model, namely the specific heat and the curing function, also need a special treatment in order to build an efficient reduced solver. According to Section 3.1.2, a reduced basis has to be formed for both specific heat and curing function.

Observe that the reduced basis for the curing degree can also be used to approximate the curing function. This is because the snapshots of the curing rate, α(x, t; µ m ) (equivalently, f kin (x, t; µ m )), are linear combination of the snapshots of the curing degree α(x, t; µ m ). Therefore, it is clear that the space spanned by both basis would be the same, and in consequence the curing function is approximated using the curing degree basis:

f kin (x, t; µ) ≈ N f n=1 a n f (t; µ)φ n f (x) with φ n f (x) ≡ φ n α (x) (N f = N α ). ( 20
)
As a corollary, the DEIM points for approximating the curing function will also be the same than those for the curing degree, i.e. {x n f }

N f n=1 ≡ {x n α } Nα n=1 . Coefficients a n
f are to be determined by solving an interpolation problem, as shown in Section 3.1.2.

Regarding the specific heat approximation, the snapshots C p (x, t; µ m ) are obtained simply by evaluating Equation (4) using the temperature and curing degree snapshots. Therefore, we introduce the following approximation:

C p (x, t; µ) ≈ N C n=1 a n C (t; µ)φ n C (x), (21)
where φ n C denote the specific heat basis functions. With the the reduced basis at hand, the corresponding DEIM points can be computed; we denote them by {x n C } N C n=1 . Coefficients a n C are to be determined by solving an interpolation problem, as explained in Section 3.1.2.

Assembling the Reduced order model

Let us first focus on the heat equation. We first introduce the approximations of the nonlinear terms, i.e. the specific heat and kinetic rate, given by Equation [START_REF] Benner | A survey of projection-based model reduction methods for parametric dynamical systems[END_REF] and Equation ( 21):

ρ N C n=1 a n C (t; µ)φ n C (x) ∂T ∂t = λ∇ 2 T + ρ∆H Nα n=1 a n f (t; µ)φ n α (x) . ( 22
)
Remark 2 (On the approximation of the kinetic rate). As explained in Section 3.2.1, the kinetic rate is approximated using the basis for the curing degree, and so in the right-hand side of Equation [START_REF] Patera | Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations[END_REF] we use φ n α . However, it is worth to remark for the sake of clarity that we keep the coefficients a n f , which are obviously not the same than a n α .

Using a standard finite element discretization on the mesh, it results in the following discrete matrix form:

N C n=1 a n C (t; µ)M n Ṫ + K T = Nα n=1 a n f (t; µ)b n , (23)
where M n are the different mass matrices, each one related to a specific heat basis function, φ n C (x); K is the conductivity matrix (not to be confused with the permeability tensor, although no distinct notation is used); and b n are the different source vectors related to each curing function basis φ n α . By performing the Galerkin projection of Equation ( 23) onto the reduced basis for the temperature, denoted in its discrete form by Φ T , and taking into account that discrete equivalent of Equation ( 19) is T = Φ T a T , we get:

N C n=1 a n C (t; µ) Mn ȧT + K a T = Nα n=1 a n f (t; µ) bn , (24)
with the following definitions for the reduced operators:

Mn = Φ t T M n Φ T ∈ R N T ×N T , K = Φ t T KΦ T ∈ R N T ×N T and bn = Φ t T b n ∈ R N T ×1 . The transpose is denoted by • t .
Recall that coefficients a n C and a n f are computed, at each time, by solving a linear system of size N C and N α , respectively, as explained in Section 3.1.2.

Finally, the reduced version of the kinetic equation is trivial thanks to its locality. In order to compute the coefficients a n α at each time, we are integrating Equation (1b) at the DEIM points related to the curing degree:

α(x n α , t; µ) = f kin (T (x n α , t; µ), α(x n α , t; µ)) with 1 ≤ n ≤ N α , (25)
which of course gives N α uncoupled ODEs. In discrete form:

α(t; µ) = f kin ( T(t; µ), α(t; µ)), (26)
where α, T, α ∈ R Nα×1 . Coefficients a n α (t; µ) in Equation ( 19) are computed by solving the following interpolation problem:

α(x m α , t; µ) = Nα n=1 a n α (t; µ)φ n α (x m α ) with 1 ≤ m ≤ N α . (27)

Implementation details and results

We report hereafter the details for the numerical implementation of the fullorder solver, used for computing the snapshots:

• The Finite Element mesh is composed of 116, 136 HEX8 elements, with 147, 245 nodes.

• A first-order semi-implicit integration scheme was applied. The simulated time is 2 hours of process, with 20, 000 time steps.

• A Preconditioned Conjugate Gradient is used as linear solver.

• The typical running time, for a single parameter execution, is 5 hours on a 64bit machine with the following specifications: 2.9 GHz Intel Core i5 with 16 Gb 1867 MHz DDR3, running under MacOS X 10.10.5.

Concerning the snapshots generation, we considered random perturbations around the nominal parameters: µ nominal = (α 0 = 0, T 0 = 288 K, T c = 438 K, V f 0 = 57%). The amplitude of the perturbations is in the following ranges:

α 0 ∈ [0, 0.05] (+5%), T 0 ∈ [273, 303] K (±5%), T c ∈ [416, 460] K (±5%), V f 0 ∈ [50,
64]% (±7%). Reduced basis of the following dimension (i.e. number of degrees of freedom of the ROM) were found: N T = 10, N α = 7 and N C = 5, which proves the pertinency of using low dimensional approximations for the thermo-kinetic model. We report hereafter the details for the numerical implementation of the ROM solver:

• A variable order (1-5) Numerical Differentiation Formula (MATLAB ode15s) time integrator was used. The simulated time is 2 hours and the number of time steps varies adaptively. • The typical running time is in the range 1 -10 seconds depending on the process conditions, using the same machine described previously. It is important to emphasize that the simulation took few seconds to completion instead of the many hours needed when solving the full order problem.

• The random access memory (RAM) consumption was measured by running 5 simulations, each one of them for a different set of process parameters selected randomly. The simulation time was set to 1 hour. In such conditions, the averaged memory required is 236 Mb. More details about the RAM consumption of the final implementation will be given in Section 4.

• A posteriori validation of the reduced model was carried out by comparing results with full-order FEM simulations for sets of randomly generated process parameters. The observed relative error measured in the maximum norm is typically of the order of 10 -5 .

Figure 4 and Figure 5 depict the first four modes (the most significant ones) of the temperature and the curing degree. Figure 6 shows the time evolution of the weights related to the temperature and degree of curing modes.

Figure 7 represents the temperature solution issued from the reduced simulation, at four different times, after recombining the basis functions with the reduced coordinates.

The consolidation simulation module

The PGD method was applied in order to reduce the computational complexity of the consolidation model. Recall that the consolidation model is nonlinear itself, because the permeability tensor depends on the fiber volume fraction. However, as explained in Section 2.3, the permeability tensor can be assumed uniform, i.e. not varying through the domain. In consequence, observe that the problem could be linearized by simply considering the permeability tensor as an extra-coordinate in the PGD framework. A similar approach was already addressed in the context of nonlinear soil dynamics [START_REF] Germoso | Efficient PGD-based dynamic calculation of non-linear soil behavior[END_REF]. Hence, in this scenario, we would have a parametric pressure field in the form: P (x, K). And more importantly, the computation of such parametric would now involve a linear problem. This can be understood by thinking of the parametric solution as being a linear solver inside a fixed-point nonlinear scheme.

However, there is an additional difficulty concerning the parametrization of the viscosity field. A low-dimensional parametrization of such field is sought by following a similar approach to that one explained in Section 3.2. In fact, we are seeking for an approximation of the inverse of the viscosity field, see Equation ( 5), as follows:

η -1 (x, t; µ) ≈ Nη n=1 a n η (t; µ)φ n η (x), ( 28
)
where φ n η denotes the basis functions for the inverse of the viscosity, computed from snapshots η -1 (x, t; µ m ), 1 ≤ m ≤ M , by simple evaluation of Equation [START_REF] Mounier | Multipurpose carbon fiber sensor design for analysis and monitoring of the resin transfer molding of polymer composites[END_REF].

Observe that coefficients a n η can be seen in fact as the coordinates of the inverse of the viscosity on the reduced basis, at every instant and choice of parameters. We are therefore introducing them as extra-coordinates in the PGD parametric solution, i.e. P (x, K, a η ). Such parametric solution is now able to provide the pressure field, not only for every possible permeability tensor, but also for every viscosity field living in the reduced basis φ n η . Of course, we hope N η to be small enough.

We shall explain in next section how to compute the coefficients a η in order to be able to evaluate the parametric solution.

Remark 3 (On the dependence of the pressure field on the closure rate). Simulating the closure cycle of the press requires obtaining the pressure field, for a given viscosity field, permeability tensor (i.e. fiber volume fraction) and an imposed closure rate. However, it is worth to remark that the closure rate does not need to be considered as an extra-coordinate of the parametric solution, because of the linearity of the problem to be solved. In other words, the pressure field depends linearly on the closure rate.

The parametric solution of the flow problem, Equation ( 29), within the PGD framework to obtain a separated representation of the parametric pressure field:

P (x, K, a η ) = N P n=1 φ n x (x)φ n K (K)φ n a (a η ). (29)
Even if such solution is related to a multidimensional problem, its linearity makes possible to compute it very efficiently by means of the PGD.

Implementation details and results

We report hereafter the details corresponding to the calculation of the PGD parametric pressure solution:

• The same mesh already described in Section 3.2.3 was used.

• The inverse of the viscosity is parametrized using N η = 3 coordinates, corresponding to the first three modes φ 1 η (x), φ 2 η (x) and φ 3 η (x) that can represent the 95% of the solution.

• The FE mesh for the viscosity in the phase-space (a 1 η , a 2 η , a 3 η ) is made of 6, 307 TET4 elements and 1, 387 nodes.

• The FE mesh for the permeability phase-space k 11 , k 22 , k 33 is made of EDGE2 elements 1D × 1D × 1D, 100 nodes each.

• The PGD convergence criterion was set to 10 -3 on the relative norm of the residual.

Typical execution times are not reported for the consolidation ROM because they are completely negligible: evaluating the parametric pressure is straightforward. The time evolution of the three associated coefficients, a 1 η (t), a 2 η (t) and a 3 η (t), describes a closed curve in the 3D espace defined by them, as depicted in Figure 9, since both the initial and final states are characterized by a uniform high viscosity field.

Finally Figure 10 shows for four different rheologies expressed from vector a η in the viscosity phase-space as well as their four associated pressure fields.

Online simulation strategy: simulation modules coupling

We summarize in this section the operation of the reduced models, with the help of Figure 11. Suppose that the reduced coordinates of the temperature and the curing degree are known from the previous time step; we denote a T (t j-1 ) and a α (t j-1 ), respectively. Note that at time t 0 , these reduced coordinates are obtained from the initial conditions for both temperature and curing degree. Then:

1. We evaluate both the specific heat and the curing function at the previous time step, i.e. a semi-implicit scheme is used. The reduced coordinates of both specific heat and curing function, denoted by a C (t j-1 ) and a f (t j-1 ) respectively, are computed using DEIM.

2. With those reduced coordinates at hand, the thermo-kinetic ROM, Equa- tion [START_REF] Fritzen | Reduced basis hybrid computational homogenization based on a mixed incremental formulation[END_REF] and Equation ( 26), can be assembled as explained in Section 3.2.

V f (t j ) = V f (t j 1 ) Semi-implicit Linearization a C (t j 1 ) a f (t j 1 ) a ↵ (t j 1 ) a T (t j 1 ) a ↵ (t j ) a T (t j ) a ⌘ (t j ) U `(t j ) V f (t j ) K `(t j ) V r (t j ) F `(t j ) U V f U `+1 = U `+ U V `+1 f = V f + V f Press Control Algorithm F `(t j ) F lim  0 P `(t j ) ⌘ U `(t j ) P (x, K `(t j ), a ⌘ (t j ))

3

. By performing a time increment, the reduced coordinates of both temperature and curing degree can be obtained at time t j .

4. Then, the reduced coordinates of the viscosity, a η , can be computed by evaluating the chemo-rheology model and using DEIM.

5. With the previous information at hand, the consolidation module can be run. It involves solving a nonlinear problem because of the press control system, see Section 2.1. The nonlinear iterations are indexed by . We start by assuming that the closure rate is the than in the previous time increment, i.e. U =0 (t j ) = U (t j-1 ). Similarly, we consider

V =0 f (t j ) = V f (t j-1 ).
6. Using Equation ( 8), the permeability tensor can be computed.

7. With the permeability tensor and the reduced coordinates of the viscosity, the parametric PGD solution can be particularized. Recall that this solution has been computed for unitary velocity and so it must be scaled by the actual velocity. We denote by P (t j ) the pressure field at time t j and iteration .

8. The velocity field can be then computed using Equation [START_REF] Kardos | Void growth and resin transport during processing of thermosettingmatrix composites[END_REF]. Integrating on the free boundary S, see Figure 3, the volume of resin drained can be computed, ∆V r . Note that knowing the loss of resin it is trivial to compute the current fiber volume fraction. 9. On the other hand, from the pressure field it is possible to obtain the vertical component of the reaction force to be applied by the press so as to maintain the actual closure rate. The press force can be computed by integrating the pressure field on the upper boundary S + , see Figure 3. However, note that this force only represents the fluid part, i.e. the resin, but it does not take into account the fiber contribution. In order to account for this extra contribution, we consider the Kim's model. [START_REF] Chinesta | The Proper Generalized Decomposition for advanced numerical simulations[END_REF]. With the press force, F (t j ) at hand, the press control can be checked. A Newton-Raphson algorithm is used in order to compute both closure rate and fiber volume fraction correction, denoted by ∆ U and ∆V f .

11. From the corrections, both closure rate and fiber volume fraction can be updated. At convergence, we set: U (t j ) ← U * (t j ) and V f (t j ) ← V * f (t j ), assuming the algorithm converges after * iterations.

12. Observe that the semi-implicit linearization allows excluding the thermokinetic module from the nonlinear problem. Otherwise, at each nonlinear iteration, it would be required to come back to the thermo-kinetic module, to recompute the specific heat, to solve the thermo-kinetic ROM, and so on.

A Simulation App for the OGV manufacturing process

The Simulation App for the OGV manufacturing process is a process-specific application that allows the user to simulate almost in real time different process conditions and visualize the simulation results. Here we understand by real time simulation the one able to provide the results with no perceptible delay after the user makes its request, i.e. in the order of half a second. However, since the Simulation App is designed to be used directly in the manufacturing facility, the input and output delays are also relevant. As it will be explained later, both input and output interfaces were designed so as to enhance the user's reactivity by restricting the input data to the bare minimum, while only relevant output information is displayed. Typically, a standard user takes no more than one minute in order to set up a new simulation, while the time consumed in visualizing and interpreting the results depends mostly on the user's knowledge and experience. The user interacts with the Simulation App through a basic Graphics User Interface (GUI). In order to demonstrate the feasibility and potentiality of this kind of applications, we developed a demonstration version in the MATLAB R environment using GUIDE under MacOS X 10.10.5. This allows creating the GUI very easily. The MATLAB Application Compiler TM was used in order to create a standalone executable file that could run outside MATLAB R and be easily transferred to the final user for demonstration purposes. The standalone version of the Simulation App has been tested on Microsoft Windows R 7 OS. Other proper implementations are of course possible although not explored in this paper, as they are outside of its scope.

The concept of a Simulation App offers several potentialities. Since the application is process-specific, rather than implementing a general purpose visualisation environment, it is possible to first identify the set of quantities of interest as output and then implement a simple and specific visualization interface. For example, if we know in advance that the maximum pressure gradient is an important indicator for defects, as it is the case in OGV manufacturing processes, we can include a functionality that displays the maximum pressure gradient and its location, at each time step. Then, the user can access to this information by simply activating a checkbox.

A similar discussion can be addressed regarding the data input. In a general purpose simulation software, a number of simulation parameters must be entered as user input. Although these have a significant impact within the modeling and simulation framework, they have little significance for the process designer. In order to get to these, the user must convert process parameters (physical measures, material properties) into simulation parameters (boundary and initial conditions, model adjustments) before running the simulation. The Simulation App is designed to perform this conversion automatically according to rules provided beforehand. For instance, the initial fiber volume fraction is computed from process parameters, such as the following: area baseline plykit (stack of composite layers), the resin and fiber mass density, the mass of the convex and concave stack and the fiber areal weight (FAW) and the volatile content, see Figure 12. Therefore, the process designer only enters process parameters, which are the real meaningful information to them, without the need of expertise in multi-physics modeling or numerical methods. The difference between process and simulation parameters is kept transparent to the user in the GUI. By consequence, a Simulation App is not only simulation tool but it also integrates the process knowledge via process-specific inputs and outputs.

The Simulation App is composed of three modules:

1. Pre-processing. This module performs two basic operations: data loading and parameters conversion. Data loading simply reads all pre-computed data required to run the reduced model. This operation only needs to be done once after launching the application, and it is performed in the GUI via the Load Data button. Parameters conversion gathers data entered by the user and computes the simulation parameters. This operation is performed in the GUI via two different tabs: the Parameters Tab, in which some default values that normally do not change are proposed (e.g. resin and fiber specific weight), and the Data Tab, in which process parameters are defined (e.g. temperature cycle, closure rate, etc.) (see Figure 12). The conversion operation is launched by the Update button, and the initial degree of curing and the initial fiber volume content, both being simulation parameters, are computed.

2.

Simulation. This module is driven by a principal function that governs the interaction between the two reduced models explained in previous sections: POD reduced model for the thermo-kinetic simulation and PGD reduced model for the consolidation simulation. Basically, this module takes all data defined in the pre-processing module and runs the ROM model in the time interval of interest defined by the user, as explained in Section 3.4. The user can also choose the number of equally spaced time frames at which the solution wants to be accessed. Additionally, the user can also demand to access to the solution at particular time frames of interest, such as minimum viscosity time frame, see Figure 12 for details.

3.

Visualization. This module allows accessing to both field data and quantities of interest, at any desired time frame. This operation is performed by the GUI via two different tabs: the Display Tab and the Quantities of Interest Tab. In the Display Tab, seven scalar fields can be visualized: curing degree, temperature, viscosity, pressure and the three components of the pressure gradient. They are simultaneously displayed on the external boundary of the part as well as in five sections, see Figure 13. The section view is necessary to appreciate, for instance, the temperature evolution inside the part, which may be higher than in the external boundary due to the exothermic kinetics. Additionally, the location and magnitude of the maximum and minimum of each field can be visualized. In the Quantities of Interest Tab, the time evolution of nine process indicators can be visualized: closure rate, press force, fiber volume fraction or part mass, for instance. See Figure 14 for details. These are the real meaningful information upon which a process designer can evaluate if the process setting is operating as desired or not.

The RAM consumption of the MATLAB R implementation of the Simulation App was measured. Opening the application requires 239 Mb, whereas the amount of memory increases up to 504 Mb after loading data. The amount of memory required for running the simulation depends on the simulation timespan as well as on the process parameters. In the conditions already described in Section 3.2.3, 236 Mb are required on average, which brings the total to 740 Mb. However, the most demanding operation in terms of memory consumption is the Visualization module, which requires up to 1160 Mb. In general, the memory consumption could be drastically reduced in a proper (non demonstrator) implementation of the application. Some parts of the code could also be optimized, for instance, by avoiding reconstruction of the entire fields, since only some slices and the external surface are visualized.

ROM-based Simulation Apps can be a powerful tool for complex composite processes to increase the entitlement yield by adapting for the variation that comes from material chemistry and physical properties in addition to thermal and pressure histories applied during the process. Typical entitlement yield is limited because of the inherent variations and multi-physics interactions. Part quality loss is due to either (i) internal defects, (ii) not meeting dimensional requirements or (iii) poor internal fiber matrix structure. A successful manufacturing process must minimize all three quality components. The Simulation App can be implemented in the manufacturing process seamlessly to make real-time decisions regarding process adaptation possible overcoming inherent variation and truly increasing the entitlement yield of the process. As an example, the Simulation App will take real process measurements as inputs which capture the incoming variation in the pre-processing section and provide quantities of interest e.g. maximum pressure gradient that can be relate to quality. If the quality does not meet requirements, pre-computed sensitivity results can be used to identify corrective process change to bring it within requirements. The corrective process change can be as simple as choosing among predefined process cycles. All this can be made possible only because of real-time models capable of reflecting physics of the entire process.

Conclusions

In this paper we have introduced the Simulation App concept, a process-specific simulation tool based on reduced order modeling techniques. Using a combination of them, we were able to reduce from several hours to few seconds the computational time of a coupled multi-physics and strongly nonlinear model describing the manufacturing process of a composite outlet guide vane. Defining a coupling strategy between the different reduced order models was an essential part of this work. In particular, we presented an approach based on an appropriate parametrization of the coupling fields. The use of such fast simulation in a real-time decision making environment being possible, process-specific pre-processing and visualization functionalities were added, leading to the Simulation App concept.

It has also been demonstrated that the Simulation App provides several advantages over general-purpose simulation software, especially if simulation wants to be used directly in the manufacturing facility. In addition to the computational time reduction, the process specificity of the Simulation App makes it possible to conceive simple yet functional graphic interfaces, for both data input and visualization. The process designer is asked to enter only process parameters while the simulation parameters are limited to the bare minimum. Similarly, the visualization module was designed so as to display only the relevant information, mainly the process indicators upon which decisions are made. Note that, by definition, process indicators are specific to a particular process, which is contrary to the spirit of general-purpose software. Therefore, the Simulation App establishes a link between process parameters and process indicators through a comprehensive numerical simulation which includes not only the physics and their couplings but also technological constraints such as the control loop of the process, if any.

Finally, even if the Simulation App has been presented on a case study of industrial interest, it is easy to imagine building similar tools for other manufacturing processes involving different physics, materials and technology.

Figure 1 :

 1 Figure 1: Global view of the OGV part geometry with cross sectional slice (left) and detail of the computational mesh (right).

Figure 2 :

 2 Figure 2: Global view of the press (left) and detail of an OGV part being produced (right). Images courtesy of General Electric Global Research.

Figure 3 :

 3 Figure 3: Boundary conditions description for the thermo-kinetic problem.

Figure 4 :

 4 Figure 4: First four most significant temperature modes: φ 1 T (x) (top-left); φ 2 T (x) (top-right), φ 3 T (x) (bottom-left) and φ 4 T (x) (bottom-right).

Figure 5 :

 5 Figure 5: First four most significant curing degree modes: φ 1 α (x) (top-left); φ 2 α (x) (top-right), φ 3 α (x) (bottom-left) and φ 4 α (x) (bottom-right).

Figure 6 :

 6 Figure 6: Time evolution of the temperature (left) and curing degree (right) reduced coordinates, a n T (t; µ), related to the first five temperature modes (i.e. n ≤ 5) during the first 100 sec of the simulation, corresponding to a randomly chosen parameter set.

Figure 7 :

 7 Figure 7: Temperature fields at four different times from the thermo-kinetic ROM: t = T /4 (top-left); t = T /2 (top-right); t = 3T /3 (bottom-left) and t = T (bottom-right).

Figure 8 :

 8 Figure 8: First four most significant inverse viscosity modes: φ 1 η (x) (top-left); φ 2 η (x) (top-right), φ 3 η (x) (bottom-left) and φ 4 η (x) (bottom-right). vv

Figure 9 :

 9 Figure 9: Trajectory of coefficients a n η (t) (left) and parametric domain ensuring positive viscosities (right).

Figure 10 :

 10 Figure 10: Four examples showing arbitrary viscosities in the phase-space and their corresponding pressure field. For each example: (i) pressure field in the OGV part (left); (ii) reduced coordinates of the viscosity (red point) in the positive viscosities phase space (right).

Figure 11 :

 11 Figure 11: Schematics showing the operation of both thermo-kinetic and consolidation simulation modules based on ROM, as well as their coupling.

Figure 12 :

 12 Figure 12: Simulation App pre-processing tabs: Parameters tab (left), Data Tab (center) and Simulation Tab (right).

Figure 13 :

 13 Figure 13: Simulation App post-processing: Display tab. Curing degree field after 3.05 min (top). Temperature field at after 20.30 min (mid). Pressure field after 60 min (bottom).

Figure 14 :

 14 Figure 14: Simulation App post-processing: Quantities of Interest tab. Closure rate (top), fiber volume rate (mid) and part mass evolution (bottom) during the simulated time, 60 min.

Table 1 :

 1

			p 0	0.1203 J/gK
		450 K	p 1	0.005 J/gK 2
	n	0.91	q 0	0.5905 J/gK
	m	0.37	q 1	0.0019 J/gK 2
	∆H	570 J/g	ρ resin	1.26 g/cm 3
	η 0 B	3.10 • 10 -12 Pa s 10800 K	ρ fiber V f 0	1.80 g/cm 3 57%
	C	27	λ 11	5.80 W/mK
	d	1.77	λ 22	0.57 W/mK
	c c ⊥ V f a	78.5% 2.50 • 10 -12 m 2 9.43 • 10 -13 m 2	λ 33	0.57 W/mK

Material parameters considered in the physical modeling of the OGV part manufacturing process. Courtesy of GE Global Research.

Christophe Binetruy

Institut de Recherche en Génie Civil et Mécanique (GeM UMR CNRS 6183), Ecole Centrale de Nantes. 1 rue de la Noë, BP 92101, F-44321 Nantes cedex 3, France. e-mail: christophe.binetruy@ec-nantes.fr


Romain Vergne

Romain Pacanowski

Xavier Granier

Patrick Reuter

Enhancing Surface Features with the Radiance Scaling Meshlab Plugin

Keywords: Meshlab, 3D shape depiction, 3D surface analysis, feature highlighting

We present the new Radiance Scaling plugin for Meshlab. This rendering technique allows depicting shape through shading via the modification of light intensities around specific features. The major idea is to correlate the shading with surface feature variations in order to enhance shape details like concavities and convexities. The Radiance Scaling rendering technique works in real-time on modern graphics hardware. As a consequence, surface features can be inspected interactively. Recently, the Radiance Scaling technique has received major interest in the French Archaeology research community, in particular for enhancing details in carved stones and thus improving their legibility.

Introduction

The 3D acquisition of cultural heritage artifacts is becoming more and more common. Most often, the surface of the artifacts is either directly acquired by 3D laser scanning, or obtained by 3D photogrammetric reconstruction, followed by a 3D point to mesh conversion. One of the first motivations for 3D acquisition was to digitally preserve cultural heritage. More recently, it has been shown that for broken artifacts, the separate 3D acquisition of each fragment may offer the possibility to virtually reconstitute the past by computer aided reassembly.

During the virtual inspection of the acquired artifacts, the maybe most important element is the 3D visualization. Nowadays, the advances of computer hardware and especially the graphics cards make it possible to render photo-realistically the meshes of 3D models consisting of millions of polygons.

We are convinced that the inspection of 3D models is further improved when they are visualized nonphoto-realistically with modern 3D expressive visualization techniques. With the exaggeration of several surface features according to the geometry of the 3D model, these techniques may better depict shape characteristics. Emphasizing meaningful portions of the surface and hiding the meaningless ones creates a far more legible pictorial representation, and removes possible ambiguities.

In this work, we present a specific expressive visualization technique called Radiance Scaling that we integrated as a plugin for the 3D model processing software Meshlab. This rendering technique allows depicting shape through shading via the modification of light intensities around specific features like concavities and convexities. The Radiance Scaling rendering technique works in real-time on modern graphics hardware, making it feasible for an interactive inspection in Meshlab.

We believe that the choice to integrate Radiance Scaling as a plugin in Meshlab is the perfect means for a widespread use, because we observed a growing interest in Meshlab, especially in the digital cultural heritage community. This paper is organized as follows. In Section 2, After introducing Meshlab, we show some related work concerning expressive visualization with a special interest for cultural heritage applications. Then, we present the Radiance Scaling Plugin with all its options. In Section 4, we discuss a case study on a concrete example of using the Radiance Scaling plugin for deciphering inscriptions on an epitaph found near St. Emilion, France. Finally, we conclude with directions to future work in Section 5.

Related Work

Meshlab

Meshlab is an advanced 3D model processing software system for the processing, editing, cleaning, healing, inspecting, and visualization of 3D models.

It is particularly interesting for the research community for several reasons. From a general point of view, it is distributed freely, and as open source, and it is portable to a number of operating systems, and deals with a large variety of 3D mesh formats (e.g. PLY, STL, OFF, OBJ, 3DS, VRML 2.0, U3D, X3D and COLLADA), and even point clouds (e.g. imported from photogrammetric reconstruction such as Photosynth).

Meshlab is an extensible system, and from a computer scientist point of view, any developer can contribute to its improvement. The open architecture makes it possible to write I/O plugins for new 3D formats, to develop editing plugins for advanced mesh processing, and to propose new rendering styles, even for programmable graphics hardware. We made use of this latter for the integration of our new radiance scaling technique.

Meshlab has been developed since 2005, and the user and developer community is growing steadily, and especially in the digital cultural heritage context, where it has already proven to be beneficial.

Expressive visualization

The depiction of object shape has been a subject of increased interest in the Computer Graphics community since the work of [START_REF] Saito | Comprehensible rendering of 3-D shapes[END_REF]. Inspired by their pioneering approach, many rendering techniques have focused on finding an appropriate set of lines to depict object shape. In contrast to line-based approaches, other techniques depict object shape through shading. Maybe the most widely used of these is Ambient Occlusion [START_REF] Pharr | Ambient Occlusion[END_REF], which measures the occlusion of nearby geometry. Both types of techniques make drastic choices for the type of material, illumination and style used to depict an object: line-based approaches often ignore material and illumination and depict mainly sharp surface features, whereas occlusion-based techniques convey specifically depend on sky-like lighting environment.

Among the recent techniques, the work of Vergne [START_REF] Vergne | Light warping for enhanced surface depiction[END_REF]) is receiving a raising interest thanks to its simple integration into a large range of shading techniques. For Radiance Scaling (Vergne 2010), the key observation is that reflected lighting variations are correlated to surface feature variations. For example, consider a highlight reflected from a glossy object: by increasing reflected light intensity in convex regions and decreasing it in concave ones, the highlight looks as if it were attracted towards convexities and repelled from concavities. Such an adjustment improves the distinction between concave and convex surface features, and does not only take surface features into account, but also material characteristics.

The Meshlab Plugin Radiance Scaling

For Meshlab, we implemented a simplified version of Radiance Scaling, taking into account the feedback of cultural heritage professionals during several projects. This implementation is a simple plugin, accessible in the Meshlab menu "Render > Shaders". 1. "Enable Radiance Scaling": activate or deactivate the shape enhancement. 2. "Invert Effect": the rules of concavities and convexities are inverted. This has proven to be useful in certain cases for providing more legible results. In fact, it mimics the work of archaeologists when making squeezes of ancient imprints. 3. "Display mode": choose the different shading styles. The different styles are described below. 4. "Enhancement": the enhancement factor that can be adjuster between 0 and 1, with 0.5 its default value. A 0-value corresponds to no enhancement, and thus has the similar effect as turning off the shape enhancement.

Among all the shading possibilities with Radiance Scaling, we decided to implement four of them since they are quite intuitive to use:

1. "Lambertian Radiance Scaling": the object is rendered with diffuse shading. The 14-lines long inscription is situated on a calcaire bloc with a length of 2.1m and a height of 0.7m. The Meshlab Radiance Scaling Plugin helped to decipher the most erased parts of the inscription, and to reject the hypothesis about the presence of an inscription of the name "Emilion".

Conclusions & Future Work

In this paper, we presented the Radiance Scaling Plugin for Meshlab. We have shown that this expressive visualization technique enhances the legibility of acquired 3D models through selective shading, and that the techniques can be made easily accessible via the integration into Meshlab.

In current and future work, we strive to integrate other useful expressive visualization techniques in Meshlab. For instance, we are convinced that the surface relief analysis technique [START_REF] Ammann | Surface Relief Analysis for Illustrative Shading[END_REF]) is particularly useful for the digital squeeze, since details at multiple scales can be analyzed.

Figure 1 :

 1 Figure 1: Selection of the Radiance Scaling Plugin

Figure 2 :

 2 Figure 2: Available options of the Radiance Scaling Plugin

  2. "Lit Sphere Radiance Scaling": A lit sphere (Sloan 2001) encodes the lighting environment and reflective properties into an image of a sphere. For further improving the legibility, a different lit sphere can be used for convex and for concave regions. 3. "Colored Descriptor": Convexities and Concavities are displayed with two distinct colors (blue an red) 4. "Gray Descriptor": we simply show the enhancement factor for each position of the object.

Figure 3 :

 3 Figure 3: A working session with the Radiance Scaling Plugin in Meshlab.

4.

  Case Study : The Epitaph of St. EmilionDuring an archeological study of the medieval Saint Emilion, some researchers were facing problems to decipher the inscriptions of the Costaulus epitaph, situated in one of the underground monuments in Saint Emilion. For the preparation of the virtual inspection of the engraved stone, a 3D acquisition of the artifact was done with a Faro ScanArm (Figure4), by Pascal Mora and Robert Vergnieux PFT3D, CNRS UPS 3551.

Figure 4 :

 4 Figure 4: (a) The Saint Emilion Epitaph. (b) The 3D scanning of the epitaph.

Figure 5 :

 5 Figure 5: The reconstructed 3D model of the epitaph.

Figure 6 :

 6 Figure 6: Shape depiction with the Radiance Scaling Plugin.

Figure 7 :

 7 Figure 7: Radiance Scaling of an engraving with lit sphere.


Adriana Gomes

L De Souza

Dominique Vincent-Genod

Carole Vuillerot

Michel Dubois

Guillaume Thomann

Validation of a digital interface for assessment of motor function based on MFM

Keywords: Digital Tablet, Neuromuscular disease, MFM Scale

Patients with neuromuscular diseases undergo frequent motor assessments. The MFM scale (Motor Function Measure) is a validated scale for all neuromuscular diseases. Tasks 18, 19, and 22 have the potential to have a digitized version on a Tablet. This article proposes to digitalize a first version of items 18, 19 and 22 based on MFM. The results show that the scores were similar for the Tablet version and the paper version.

Introduction

Neuromuscular disorders include a diverse group of diseases that cause muscle weakness and atrophy, leading to motor impairment of varying intensity [START_REF] Urtizberea | Maladies neuromusculaires: évolution des concepts médicos cientifiques et des pratiques de soins[END_REF]. Patients with significant motor loss progressively presented atrophy of distal predominance, significant deformity of the feet bilaterally and often weakness of the hand muscles which may limit daily life activities influencing quality of life [START_REF] Mary | Neuromuscular Diseases: Diagnosis and Management[END_REF].

The motor assessment of patients with neuromuscular disorders should be performed frequently, and the MFM -Motor Function Measure is an assessment applicable to all neuromuscular diseases, developed to highlight the clinical course of the patient and the patients therapeutic effects [START_REF] Vuillerot | Monitoring changes and predicting loss of ambulation in Duchenne muscular dystrophy with the Motor Function Measure[END_REF][START_REF] Benaïm | Analyse de validité de la «Mesure de la fonction motrice»(MFM) en pratique de consultation adulte d'un centre de référence pour maladies neuromusculaires[END_REF][START_REF] Montes | Clinical outcome measures in spinal muscular atrophy[END_REF]. Although the motor assessment scales are practical and easy to apply. These measurement instruments present the disadvantage of the lack of accuracy of the score given during the exercise [START_REF] Rodriguez-Blazquez | Rating Scales in Movement Disorders[END_REF]. The kinematic study of human movement is an ongoing research topic that plays a key role in understanding musculoskeletal pathologies, mild traumatic brain injury, ergonomics, and athletic performance [START_REF] Dingenen | The assessment of movement health in clinical practice: A multidimensional perspective[END_REF]. The technology applied to medicine has revolutionized the processes of diagnosis and treatment of diseases, with the aim of improving and prolonging the life of patients, as well as simplifying and accelerating the work of health professionals. With the development of tablet and Smartphone technologies, these devices have become not only very popular but also have a growing potential for hand therapy applications. Applications on the Tablet allow access to fine motor skills and are easily customizable based on user need. In this way, this article proposes to validate the user-centered tablet technology for an MFM based hand motor assessment. This step allows identifying the needs and expectations of the therapist and the patient.

Review

Currently, the most effective tools for capturing hand movement are electromechanical devices or magnetic sensors (data gloves) [START_REF] Fang | 3D human gesture capturing and recognition by the IMMU-based data glove[END_REF][START_REF] Foxlin | Motion tracking requirements and technologies[END_REF][START_REF] Placidi | Overall design and implementation of the virtual glove[END_REF][START_REF] Shukor | A new data glove approach for Malaysian sign language detection[END_REF]. Despite the great accuracy of the data they have the disadvantages in terms of occasional use because they are very expensive, they hinder the natural movement of the hand and require complex calibration and configuration procedures to obtain accurate measurements.

With the recent arrival of 3D infrared sensors, devices like Microsoft Kinect and Leap Motion can recognize body gestures, allowing a new, more natural and intuitive, form of interaction than previous solutions. For applications that require only hand movement recognition, Leap Motion is one of the best options. According to [START_REF] Coton | Etude de faisabilité de l'analyse de mouvement de doigts par le capteur LeapMotion[END_REF], for a measurement and correct hand detection with Leap Motion, the fingers of the hand should be visible and separate. The hands should not be in contact with each other and the "broken wrist" hand posture is not recommended. The hand should always be maintained in wide and fluid movements, which limits the studies with neuromuscular patients.

The tablets arrived in early 2010 with the launch of Apple's famous IPad. They have been widely accepted by the public and became a technological trend for years to come. The tablet is a portable computer with a user interface built around a screen. Its multi-touch display makes the device responsive to various taps and has the potential to develop specific applications for patients with motor disabilities. Another advantage of using this technology is the ability to develop different applications (software) based on user needs, since they have open platforms providing the creation of specific applications and motivating users.

In the medical context, Tablet research has shown a potential applicability in the treatment of the hand of patients with Parkinson's disease and patients with sequelae of stroke [START_REF] Carabeo | Stroke patient rehabilitation: A pilot study of an androidbased game[END_REF][START_REF] Susini | Danse-doigts, jeu de motricité fine[END_REF]. Applications developed for strength and dexterity training were considered effective and motivating for young patients [START_REF] Kizony | Tablet apps and dexterity: Comparison between 3 age groups and proof of concept for stroke rehabilitation[END_REF]. While not making direct measurements, dexterity can be judged by the quality of the line left on the screen. The speed, acceleration and execution time of the drawings / tasks can also be related to the degree of loss of functionality of the hands [START_REF] Lin | A digital assessment system for evaluating kinetic tremor in essential tremor and Parkinson's disease[END_REF].

In the MFM scale, 6 items are defined to evaluate the distal motricity of the upper limbs. Three of these items (item 18, item 19 and item 22) have been selected to be performed on the screen of a Tablet. The purpose of this research is to verify if the realization of these items through the Tablet would cause great changes in the MFM protocol, which has already been validated with the use of simple materials like paper, pencil and a CD [START_REF] Lattre | Motor function measure: validation of a short form for young children with neuromuscular diseases[END_REF][START_REF] Bérard | A motor function measure scale for neuromuscular diseases. Construction and validation study[END_REF].

Material and Method

Choice of technology

The Tablet selected for the development of the application has a Multi touch screen. Its advantages are the use of a lightweight precision pen and physical attributes such as screen area and thickness. Storage, processing capacity and price are also considered.

Software

Software development is based on the tasks that must be performed in the three MFM items, considering the initial phase, the objects needed to perform the task and the rules. In MFM, the patient has the right to make 2 attempts for each item. The therapist's requirement for simple and fast interfaces were also considered.

Measured

Patients with neuromuscular diseases were included in the study by the physician during the follow-up visit to 3 France assessment centers. Patients have the right to object the participation in the study. If the patient is a minor, he will be informed with his parents about the study. During the proposed MFM assessment, patients would perform items 18, 19, and 22 twice: once in the conventional manner and the other on the Tablet. The order of execution between the paper support and the support of the digital tablet was made at random, fixed by the software created. The therapists who were part of the study were informed of the protocol and procedures with the Tablet.

Results

The Tablet

An investigation was conducted to make the choice of the Tablet. For this study, ASUS Zen Pad 3S 10 was chosen. It passed in multi-touch tests made by the Android Multi Touch Benchmark Test application, which shows all touch screen information (size, pressure, location and number of touches). The price is reasonable compared to its technology. This tablet allows you to use the Z Stylus precision pen.

Software development

A first version of the software was developed based on the MFM evaluation process. A protocol of measures was developed by the therapists from Lyon, France, and several modifications were suggested to make the software easy and quick to use.

Many changes have been made to avoid improper use of buttons and remedy the limitations of technology.

In the final version of the interface, the therapist can modify the position of the drawing according to the patient's need. Only in item 19, the patient's drawn dashes on the screen are visible to avoid influencing the note. A clear button allows the therapist to erase the features of the demonstration. When validating the item, anything written on the Tablet screen, visible or not, will be stored in a PDF file, accessible outside the program.

Measurement result with patient

The total of 37 patients (19 females and 18 males) with NMD were part of this study. An overview of this population is given in Table 1. The evaluation given to the exercises performed on the tablet were very similar to the evaluation given by the traditional method (exercise performed on paper). It can be seen from the graphs (Fig. 1) that there was more disagreement at point 19. But the assumption that the distribution of data is equal between groups cannot be rejected by any of the following: (Wilcoxon Test) p-value = 0.157> 0.05 for Item 18, p-value = 0.058> 0.05 for Item 19 and p-value = 0.317> 0.05 for Item 22 (significance level 5%).

Discussion and conclusion

In this study, three of the 32 MFM items were proposed in a digital version in the Tablet, in order to first explore the potential of technology in the motor assessment process. According to [START_REF] Salvo | Ethics of engagement: User centered designand rhetorical methodology[END_REF], User-Centered Design is a process of collecting user data in order to create important feedback for designers. In this way, identifying the patient's needs to support the hand on the tablet screen while performing exercises and writing with a lightweight and precision pen were the most important criteria for choosing the tablet. The pen chosen offers enough precision and its weight is compensated by the flow of writing. However, the tremors are more exacerbated, and this is what has greatly disturbed the patients.

When comparing the scores of the three items in paper and digital -Tablet versions, similarities were observed. In addition, with the line records during the execution of the executions, the potential of the Tablet was verified as a tool for the therapist's assistance in the manual evaluation of MFM, which will be part of the continuation of this study. Overall application was well received and easily handled by patients and therapists after various modifications related to the practicality of the software. The child showed greater interest in performing the task on the Tablet. This first step of choosing the tablet and using the software was very important to understand the limitations of the technology and understand the demands of both users. User feedback helped refine the restrictions and fix some design errors.

Fig. 1 .

 1 Fig. 1. Evaluation by the therapist for the three items -sheet and tablet comparison

Table 1 .

 1 Population under study

	Sex	Female	19
		Male	18
	Diagnostic	ASI	6	24,3 ± 12,6 years
		CMT	4	15,6 ± 23,8 years
		DMD	13	15,2 ± 14,3 years
		Muscular dystrophy	1	16 years
		Steinert disease	4	23± 18,87 years
		Others Myopathy	4	9 ± 26,25 years
		Others Neuropathy	5	33.76 ± 22.6 years
	ASI -Amyotrophie Spinale Infantile; CMT -Charcot-Marie-Tooth disease; DMD -
	Duchenne Muscular Dystrophy.

Institute of Engineering Univ. Grenoble Alpes

Acknowledgments

Eloïse GRONLIER, Eloïse LIOGIER, Ambre MIRC end Alison RODRIGUES LOUZANO