Patrick Navard
email: patrick.navard@ensmp.fr

Céline Cuissinat

Cellulose swelling and dissolution as a tool to study the fiber structure

Keywords: cellulose, swelling, dissolution, N -methylmorpholine N-oxide, ionic liquids, structure;

The swelling and dissolution mechanisms of cotton or wood fibers cellulose fibers in aqueous (as N -methylmorpholine N-oxide and water mixtures, or soda solutions) or in ionic liquids are studied. Some cellulose samples treated by enzyme mixtures are investigated too. Six dissolution modes are found and detailed. The swelling (homogeneous or by ballooning) is the precursor of the dissolution step, which occurs by bursting of balloons or by unwinding of cellulose structure. These phenomena are due to morphological structure of the native cellulose fibres. The balloons formation reveals the elasticity and semi -permeability of primary and S1 layers, which play the role of a membrane. The intern stresses frozen during biosynthesis are revealed by unwinding. The study allows the influence of the solvent quality on the dissolution mechanism.

Introduction

Cellulose is the major constituent of plant cells and is present in most of them. Cotton and wood cell walls are usually composed of several well known layers or walls that depend on how the plant cells grow [START_REF] Kennedy | Cellulose sources and exploitation, industrial utilization, biotechnology, and physico -chemical properties[END_REF] . Whatever the origin of the native fiber cells, some common morphological architecture can be recognized. In the outer layer, the so -called primary wall (P), fibrils of about 10 nm in diameter are positioned crosswise to a layer of about 50 nm thickness. The secondary wall (S) consists of two layers S1 and S2. The thickness of the S1 layer is, in the case of cotton, about 100 nm and in the case of spruce pulp fibre, about 300 nm. The fibrils are aligned parallel and densely packed into a flat helix, which may be in the opposite direction in subsequent S1 layers. A large part of cellulose chemistry, physics and technology deals with the swelling and the dissolution of native cellulose. Despite cellulose is the more abundant biopolymer produced on Earth and that it may be of greater and greater importance over the next years, a lot of important questions still have to be understood. The first deals with the mode of biosynthesis of the vegetable cell where cellulose is mixed with other polysaccharides and substances. Another is the exact organization of the cellulose structures among natural substances and the origin of its variability. Finally, a question of scientific and technological importance is the way cellulose is dissolved. The swelling of native cellulose in various solvents have been the subject of numerous investigations, most of them being confined to a crude description of the phenomena and a measure of the swelling ratio. The heterogeneous swelling of native cellulose fibres in the form of balloons scattered along the fibre was observed long ago in chemicals like sodium hydroxide/water or a mixture of N -methylmorpholine N-oxide (NMMO) and water. There were several tentative explanations for this phenomenon. For example OTT et al. [START_REF] Ott | Cellulose and cellulose derivatives[END_REF] considers that during swelling in a solvent, the primary wall, considered as poorly soluble, cracks, then slides along the fiber to form protective regions where the cellulose cannot swell. The focus of this work is to describe the swelling and dissolution mechanisms of native cellulose fibers (cotton and wood), in various range of solvents. Owing to the solubility of varying the solvent quality, we are able to propose a systematization of the different dissolution modes, largely influenced and determined by the structure of cellulose fibers. The biosynthesis of cellulose fibers and, thus its morphological architecture, play a main role in the interactions with external agents as swollen or solvent systems.

Experimental part

Samples.

Three native fibers, one bleached cotton and two wood fibers, Buckeye VFC (pine wood pulp obtained after a treatment by vapor hydrolysis, the cooking occurred in a sodium sulfite and soda solution) and Borregaard VHF (fir tree pulp obtained by process with calcium bisulfite) have been used. These samples were treated (in collaboration with Lenzing, Austria, T. Röder) with an enzyme mixture of cellulase and xynalase to obtain cotton and wood cellulosic fibers without outer layers. A peeling rate, the percentage of solubilized sugars analyzed in the supernatant by electrophoresis per fiber weight, characterizes the treated cotton and wood samples. A peeling rate at 10% is giving a cellulose fiber without primary and part of secondary wall. The characteristics of samples are given in figure 1.

Bleached cotton

Buckeye 68.1 57.9 4.7 4.9 63.1 51.9

Figure 1: Properties of (untreated and treated by enzyme mixtures) cotton and wood samples

Solvent systems

The swelling and dissolution treatments are performed in the following solvents:

-aqueous systems: N-methylmorpholine n-oxide (NMMO) and water (with various content of water, from 17 to 45% of water, w/w) or sodium hydroxyde (NaOH) solution at 7.6%.

-non-aqueous systems: mixture of lithium chloride (LiCl) and dimethylacetamide (DMAc) -ionic liquids: Glycolic acid (99%), and -N-butyl-3-methylimidazolium chloride (noted [C 4 mim]Cl), allylmethylimidazolium bromide (noted CP040) and butenylmethylimidazolium bromide (noted CP041). The ionic liquid [C 4 mim]Cl is a cellulose solvent. CP040 and CP041 are known only as swelling agents of cellulose. These swelling and dissolution experiments were performed at the Centre of Excellence for Polysaccharide Research at the University of Jena, Germany, with Prof T; Heinze. The experimental temperature varies as a function of solvent systems used (around 90 °C for NMMO -water mixtures and ionic liquids, -5°C for NaOH solutions).

Observations by optical microscopy

Cellulose and solvent were mixed in a container made of two glass plates. No agitation was applied to the system. About ten fibers were placed between the two glass plates. The fibers can move freely between them. Only one extremity of cellulose fibers is fixed on the plate in order to avoid the fiber to be too much affected by solvent convection, which is causing difficulties for the optical observations. The solvent contained in a pipette was introduced by capillary forces between the two plates. The swelling and dissolution of cellulose fibers were observed by optical microscopy with a Metallux 3 (Leitz) equipped with a Linkam TMS 91 hot stage. The samples are investigated in transmission mode.

Results and discussion

Different dissolution modes.

Five mechanisms can be observed when a cellulose fiber (cotton or wood) is placed in fluid materials:

-mode 1: fast dissolution by disintegration into fragments (e.g. cotton or wood fibers in NMMO -water at 17%) -mode 2: large swelling by ballooning, and dissolution (e.g. cotton or wood fibers in NMMO -water mixtures, from 19 to 23% in water content; and in ionic liquid [C4mim]Cl ) -mode 3: large swelling by ballooning, and no dissolution (e.g. cotton or wood fibers in NaOH 7.6%-water) -mode 4: homogeneous (weak or low) swelling, and no dissolution (e.g. treated and untreated in ionic liquids CP040 and CP041, or cotton and wood fibers in NMMO-water above 45% in water content) -mode 5: no swelling, no dissolution The behaviour varies with the quality of solvent which decreases from mode1 to mode 5. We describe each dissolution mode in the following part. The first explained mode is the mode 2 (swelling by ballooning and dissolution) because it is considered as the reference mode. A complementary study on the mechanism by homogeneous swelling and dissolution by unwinding is presented. This work is based on experiments with treated cotton and wood fiber with a peeling rate at 10% in NMMO -water mixture, from 19 to 23% in water content, or in NaOH 7.6%-water

Mode 1: fast dissolution by disintegration into fragments.

Below 17% of water in NMMO-water mixtures, the cotton and wood fibres are readily dissolved. Figure 5 shows the disintegration of wood fibres into a series of spindle [START_REF] Cuissinat | Swelling and dissolution mechanisms, Part 1: free floating cotton and wood fibres in aqueous NMMO -water systems[END_REF] . No appreciable swelling occurs before the disintegration of fibres structure. The bursting into fragments of cellulose fibres takes place as of the introduction of solvent systems. The cellulose fibres are broken over all their length and burst into fragments The swelling of native cellulose cotton and wood fibers is not homogeneous along a fiber in NMMO-water mixtures or soda solutions or LiCl -DMAc systems. Only some selected places undergo swelling. This localized swelling gives the impression of having balloons growing. This phenomenon (called ballooning) is followed by the dissolution of the fibers. The ballooning effect of cellulose fibers has attracted a lot of attention due to its spectacular appearance and its quite intriguing effect [START_REF] Cuissinat | Swelling and dissolution mechanisms, Part 1: free floating cotton and wood fibres in aqueous NMMO -water systems[END_REF] .

The fibers having a rather regular diameter in a dry state start to swell at given isolated points along the fiber. The zones where the swelling starts increase in size (Figure 2). The fiber has a series of swollen transparent parts, of rounded shape, that we will call balloons. These balloons are growing and reaching a maximum size at which they will burst. We can distinguish different zones within one fiber during the ballooning (seen in Figures 2 and3). These various zones are defined as follows: an unswollen fiber (A), a balloon (B), cellulose swollen then dissolved inside the balloon and membrane (C). Ballooning and dissolution phenomenon are the same for cotton and wood fibers whatever the solvent agent is (NMMOwater from 19 to 23% in water content, ionic liquid [C4mim]Cl or LiCl -DMAc). Thus, ballooning effect and dissolution mode can be only due to the way these cellulose fiber are morphologically structured. All the studied fibers are following the same sequence of events from the start of swelling to the complete dissolution. Swelling and dissolution take place for cotton and wood fibers in four subsequent phases.

-Phase 1 = appearance of balloons along the fibers: after the introduction of the solvent, we observe the appearance of balloons along the fibers. The time needed for their formation depends on the type of native fibers. The balloons do not appear at the same time along the fiber. The balloons give the aspect of a beaded structure, with the beads distributed in more or less regular way depending on the type of native fibers. Balloons do not present a regular circular perimeter. The border shape of the balloon is defined by a kind of ribbon surrounded the balloons (Figure 4). This helical structure can be seen as lines going from one unswollen zone to the next with one turn.

-Phase 2 = bursting of balloons: the balloons continue to swell until they reach a maximal swelling ratio. They remain in this swollen state a certain time (that again depends on the type of native fibers) and then burst. When the membrane (C) burst, the liquid contained inside moves out very quickly. This phenomenon is not simultaneous for all the balloons along a given fiber. Balloon bursting is due to the increase of the osmotic pressure inside the balloon. The scraps of the balloon membrane (C) remain attached to the unswollen sections (A) of the fibers. Another important point is that the inside of the balloon is very fluid at the time of the bursting since it flows out very rapidly. Thus the viscosity should be small which means that cellulose inside the balloon is not a gel but is dissolved.

-Phase 3: dissolution of the unswollen sections (A). This dissolution begins at the section surface (and not at the two extremities) and goes on to the fiber centre.

A B C

-Phase 4: dissolution of the balloon membrane scraps: during this last stage, the scraps of the balloon membrane also dissolve.

Figure 4: Bleached cotton in NMMO -water (20%)

The formation of balloons is an intriguing effect. One obvious question is about the origin of the balloon membrane. It can be explained by studying the structure of the cellulose outer layers and by the experiments carried out with enzymatically treated cotton and wood fibers. Indeed, when performing peeling of a few percent of the outside surface of the cotton or wood fibers, swelling and dissolution occur without ballooning (cf mode 3), homogeneously along the fibers. What we called membrane is thus a fraction of the fiber that can not be dissolved easily and it is semi-permeable and fairly elastic. The experiments performed with treated samples suggest that the membrane resisting dissolution is the primary wall plus all or a fraction of the S1 layer (usually shown with a helical structure).

Mode 3: large swelling by ballooning, and no dissolution

In the case of cotton or wood cellulose in NMMO -water (at water content between 25 and 35%) mixture or in NaOH (at 7.6%) solutions, the swelling occurs by ballooning, but dissolution never occurs [START_REF] Cuissinat | Swelling and dissolution mechanisms, Part 2: free floating cotton and wood fibres in aqueous soda solutions[END_REF] . The phase 1, ever described in dissolution mode 3, takes place but the dissolution steps are never reached by these solvents. In fact, the balloons are growing up to a certain diameter that is controlled by the quality of the solvent and the extension resistance of the membrane. For solvents like the NMMO-water between 25 and 30%, the growth is stopped probably because the resistance of the membrane exceeds the osmotic pressure of the solvent that wishes to dilute the cellulose solution. When the solvent is good enough (NMMO-water at 19, 20 and 23%), its penetration through the membrane is not stopped by the mechanical resistance of the membrane and it continues to enter the balloon to dilute cellulose, thus increasing the expansion of the membrane up to its bursting.

Mode 4: homogeneous (weak to very low) swelling and no dissolution

The cotton and wood fibres swell homogeneously in NMMO-water mixtures with high water content (higher than 35%) or in ionic liquid (CP040 and CP041) (4, 7) . Increasing water content in NMMO-water solvent systems decreases the ability of this mixture to dissolve cellulose. The diameter of native cellulose fibres increases as of the introduction of NMMO-water solutions. The ratio of diameter of swollen fiber by diameter of dried fiber varies between 2.3 and 2.6 for cotton, Borregard and Buckeye fibers. Thus the swelling is low. The fibers stay in this swollen state; they are never dissolving.

Mode 5: no swelling, and no dissolution

It is the case of non solvents.

complementary study: Homogeneous swelling and dissolution by unwinding of structure fibers.

The enzymatically treated cotton and wood fibers [START_REF] Cuissinat | Swelling and dissolution mechanisms, Part 3: enzymatically -treated cotton and wood fibres in aqueous solvents[END_REF] homogeneously swell in aqueous solvents or ionic liquid [C4mim]Cl. No balloon appears during the swelling step. Then they are dissolved. The dissolution occurs by the unwinding of the fibers structure. This step precedes the dissolution phase. The swelling and dissolution mechanisms for the treated fibers can be divided in 3 phases:

-Phase 1: homogeneous swelling of the treated fibers. The treated cotton and wood fibers swell along all its length. The homogeneous swelling is weak. Contrary to the swelling and dissolution mechanism observed in the case of cotton and wood cellulose fibers, the swelling does not occur via ballooning.

-Phase 2: unwinding of the treated cotton and wood fibers. Once the treated cotton and wood fibers are swollen, a unwinding of its structure occurs. The treated cellulose fibers turn on themselves and every fiber is separated in sub-fibers.

-Phase 3: dissolution of the cellulose fibers. The sub-fibers are disintegrated into fragments. Then these fragments are dissolved. Not all the solvent agents reach this last step of dissolution. It depends on its ability to develop interactions with cellulose fibers. The unwinding of structure is a phenomenon particularly interesting to study. The unwinding of treated cotton and wood fibers occurs as describing below. Every treated fiber undergoes a left handed untwisting, which ends up at its separation in sub fibers. Once the fibers are swollen, an intern helical structure is observed and progressively turns on itself. This untwisting can only be due to the release of internal stresses frozen during the biosynthesis of fibers. As the treated cellulose fibers release their internal stresses, the pitch of the helical structure increases (Figure 6). The unwinding of structure is fast. The pitch of the helical structure is at least multiplied by 2 during unwinding. This study seems to support that a unwinding of the helical structure of the fibre is necessary for moderately good solvents to dissolve cellulose.

Conclusion

Using a wide range of solvents, and in particular not very good solvents, we were able to identify several dissolution modes. The main results of this study are the fact that the helical structure that is present in wood and cotton fibres plays a role in dissolution. The balloons are a location where unwinding of the structure occurs in the balloon while the helical arrangement of the fibrils is still present in the unswollen part. Only the region that was able to unwind can be dissolved. The same occurs for peeled samples, where the unwinding precedes the dissolution.

A second important result is the fact that if an unwinding occurs, it means the system is going back into a more thermodynamically stable state. This implies that the helical structure is built under stress, this stress being released when a solvent enters the fibres and allows the fibrils to move.

The last results of this study deals with the ballooning effect. It shows that the outside of the fibre (primary wall plus part of the secondary wall) is not as soluble as the inside of fibre. Whether this is due to its composition or to the fact that it is still in a helical configuration remains to be found

Figure 5 :

 5 Figure 5: wood fibre (Borregaard) swollen in NMMO -water at 17%

Figure 2 :Figure 3 :

 23 Figure 2: Wood fiber (Buckeye VFC) in NMMO -water (20%)

Figure 6 :

 6 Figure 6: Untwisting of treated cellulose fiber (treated cotton wood fiber, peeling rate = 10%) in NMMO -water solution at 20%. Pictures A, B and C are respectively associated to the time 5 min 25s, 5 min 46s and 6 min. The drawing illustrates the increase of the pitch of helical structure


Lucie Moulet
email: lucie.moulet@licef.ca

Olga Marino
email: olga.marino@licef.ca

Richard Hotte
email: richard.hotte@licef.ca

Jean-Marc Labat
email: jean-marc.labat@upmc.fr

Keywords: Online learning, learner model, personalization, competency

Considering learning as a dynamic, evolving, social, and lifelong process which occurs in a wide variety of contexts, we aim to improve online learning by offering learning adaptation possibilities, lifelong learning followup, learning evolution follow-up, openness to the learner's contexts (personal, professional, and academic), and openness to actors involved in the learning process. To achieve this goal, we propose the development of a meta-model for learner models based on competencies, integrating learner production and personal and professional information, IPP, evolving in time and taking into account different viewpoints. This meta-model may be used for creating different kind of learner models which serve different purposes: adaptation of learning to the learner's cognitive state, learning evaluation, self-reflection, team work… From these kinds of models, models representing individuals will be instantiated.

Introduction

Online learning fills the need for lifelong learning and is supported by the development of information technologies. The issues around this theme are multiple. We are especially interested in work done around actors (learner, peers, professor…) and their knowledge and competencies. In this project, we will consider learning as a dynamic, evolving, social, and lifelong process that occurs in a variety of contexts.

Our research issue is how to create a learner model that offers learning adaptation possibilities, lifelong learning and learning evolution follow-up, openness to the learner's contexts (personal, professional, and academic), and openness to the actors involved in the learning process. The learner model needs to be semantically rich, should evolve in time for learning never stops, must take into account the social dimension of learning, and should be formal, and interoperable. In this paper, we will present the conceptual model of a meta-model for learner models. The meta-model allows the design of different kinds of learner model depending on the purposes of these ones (for evaluation, collaboration, self-reflection…). And from those kinds of learner models, we can instantiate learner models modeling individuals. We start by presenting our cognitive learner model. In the following sections, we describe its multi-viewpoint and evolving characteristics as well as the mechanism on which the model interactions are based. We end with the main conclusions and the future work.

A cognitive learner model

We propose a cognitive learner model based on competencies which integrates personal and professional information as well as learner's productions. The model is owned by the learner and connects, as needed and with the learner agreement, to different online learning systems. It is semantically rich (based on competencies), formal, and interoperable. And it may be used for different purposes: adapting learning, facilitating team work, evaluation of learning, self-reflection… Competencies are the heart of our model. We will work with Paquette's definition [START_REF] Paquette | An Ontology-based Referencing of Actors, Operations and Resources in eLearning Systems[END_REF] of a competency: a relation between actor, skill, knowledge and context. We choose this competency approach because it offers a strong semantic referencing to link the learner model with the learning resources. We assume that semantic referencing on competencies is stronger than semantic referencing on knowledge for they consider skills and context. We believe that this semantic referencing is essential for a pertinent personalization according to learner expectations and needs.

The second component of our model is the ePortfolio. It contains the learner's productions. Our learner model will have core competencies as well as domain competencies for each domain the learner is involved in.

The third component is the personal and professional information (PPI), the learner's link to his broad world. Learning is a continuous process which occurs in different contexts, including the personal and professional ones. PPI and learner's productions are linked to the competencies they illustrate.

Multi-viewpoint learner model

We have already stated that learning takes place in the learner's different learning situations and through social interactions [START_REF] Lasnier | Réussir la formation par compétences[END_REF]. Different units of learning as well as actors interact with the learner and should be allowed to register the result of these interactions in the learner model. The learner model is thus seen from different viewpoints. A viewpoint is "A mental position from which things are viewed" [START_REF]WordNet, lexical database for the English language[END_REF].

Our learner model is a multi-viewpoint model composed of the core learner model and the related learner model viewpoints. The core learner model includes objective information such as PPI and productions, as well as the learner information that has the consensus of the different human and machine actors. Linked to this core learner model, there are as many viewpoints as there are differentiated observers allowed to modify the learner model (tutors, professors, peers, learning units, etc.) Those viewpoints are not pre-established but settled by the learning context of the learner (their can be a view point by individual or a viewpoint by roles (learner, professor…)). A viewpoint contains competencies along with links between those competencies and the learner's PPI and productions.

When a modification is proposed by one of the actors in the system, the viewpoint corresponding to this actor is updated with the modification and a modification proposal mechanism is launched. This mechanism is defined outside of the model and takes into account organizational hierarchies and conflict solving strategies. If agreement is obtained, the modification is reflected in the core model.

Evolving learner model

For us, learning is a knowledge building process proceeding from the interaction between a learner and his/her environment [START_REF] De Vries | Apprentissage: référents théoriques pour les EIAH[END_REF]. From this environment the learner pulls off his/her learning conditions. We can then consider learning as a social act which evolves taking into account interaction with the learner's environment, making it a dynamic learning process. A learner model has to reflect this dynamic characteristic and must be evolving too. An evolving learner model updates itself according to the learning progress. Thus, during learning, different versions of the model will be created. Those versions need to be managed.

To deal with this evolutionary dimension, the learner model proposed in the preceding section will be extended to include different learner model versions. For this, we will integrate a version control system into our learner model. The model can then be searched by viewpoint or by version, and the evolution of a competency can be tracked in time.

Learner model interaction

We state that the learner is the owner of his/her model. Thus, any manipulation of the model should have the agreement of the learner. As the model will be in interaction with actors and online learning systems, the learner should agree on those actors and systems interactions. For this, we propose to use contracts. Contracts are used in computer science to specify the relations between different actors (or components or systems or models…) [START_REF] Bachman | Volume II: Technical Concepts of Component-Based Software Engineering[END_REF]. For example, if a learner wishes to take a course at a specific university, this latter may require accessing all information contained in the learner model. This access allowance could be specified in a contract. More precisely in our project, contracts will allow the specification of which kinds of actors can interact with the model and which action each of these actor kinds can take. Contracts can also specify when modifications can take place (evolution characteristic of the model).

Interactions can be of two kinds. The first one consists of extending the model with new information. The second one consists of consulting the information contained in the model (to adapt learning for example).

Conclusion and further work

This research project aims to improve online learning by offering learning adaptation possibilities, lifelong learning follow-up, learning evolution follow-up, openness to the learner's contexts (personal, professional, and academic), and openness to actors involved in the learning process. To achieve this goal, we propose the development of a meta-model for the design of learner models based on competencies that integrate learner production and IPP, that evolve in time as well as learning progress, and that take into account different viewpoints while remaining interoperable. Those models may be of different kinds depending on their purposes: adapting learning to the learner's cognitive state, learning evaluation, self-reflection, teamwork… The strength of this model is its ability to integrate different elements in the same learner model: a learner cognitive model (knowledge and competencies), a learner production model, a multi-viewpoint model, and an evolving model.

The next step of this project is to complete a prototype development. This development has begun and is based on Java, using Castor Project to map Java objects and XML files, and integrating the Subversion version control system to manage the model's evolution in time.


C Peiti

B Vergnes

J M Haudin

Cristallisation du polyéthylène basse densité : mesures rhéologiques et calorimétriques

Keywords: Spectrométrie mécanique, Cristallisation, Branchements longs

Deux polyéthylènes basse densité, obtenus par procédé tubulaire et procédé autoclave, ont été caractérisés par chromatographie d'exclusion stérique. Leur masse molaire moyenne en masse est sensiblement identique, mais le matériau autoclave présente une queue de plus fortes masses. Ceci induit des différences notables sur les conditions de cristallisation. Les mesures de spectrométrie mécanique effectuées en fréquence et température mettent en évidence que le facteur de glissement suit une loi d'Arrhenius dans le domaine fluide et un changement de régime au début de la cristallisation, dû à l'apparition des premiers sphérolites. Les mesures calorimétriques et rhéologiques en condition anisotherme corroborent ces résultats en terme de température de transition.

Introduction

Les polyéthylènes basse densité (PEBD) sont obtenus par polymérisation sous haute pression (supérieure à 50 MPa) et à des températures supérieures à 300°C. On distingue le procédé tubulaire, où la pression est uniforme et le procédé continu, du procédé autoclave, discontinu et où la pression est inhomogène. Ce dernier procédé se traduit par l'obtention de matériaux dont le niveau de branchement est plus élevé. Ces différences de branchement interviennent au niveau des conditions de cristallisation, qui peuvent avoir une incidence sur les propriétés finales des matériaux, utilisés pour la fabrication de films dans des procédés de soufflage de gaine. L'objectif de ce travail est de comparer les températures de cristallisation de deux polyéthylènes, obtenues par deux techniques différentes : la calorimétrie et la rhéométrie. Un rhéomètre ou des systèmes dérivés, comme des platines de cisaillement, ont été utilisés par de nombreux auteurs pour déterminer des cinétiques de cristallisation dans des conditions d'écoulement. L'un des matériaux le plus communément étudié est le polypropylène isotactique [1, 2], mais les polyéthylènes ont été plus récemment investigués. Boutahar et al. [3]

Caractérisations moléculaires et rhéologiques

Nous allons étudier deux PEBD commerciaux, notés A et B, A ayant été obtenu par un procédé tubulaire et B par un procédé autoclave [6]. Les courbes de chromatographie d'exclusion stérique de ces deux produits montrent une queue de plus fortes masses pour le matériau B (Fig. 1). Tableau 2. Représentation de quelques caractéristiques rhéologiques des matériaux à la température de référence de 140°C.

On peut remarquer que le matériau présentant le taux de branchements longs le plus élevé est celui dont la distribution des temps de relaxation est aussi la plus élevée.

Les essais en fréquence à différentes températures ont permis d'établir la courbe de variation du facteur de glissement a T en fonction de l'inverse de la température (Fig. 2). Sur un certain domaine, a T suit une loi d'Arrhenius. Cependant, en dessous d'une certaine température, le facteur de glissement augmente de façon plus importante, ce qui traduit le passage de l'état fluide à l'état solide : le matériau A cristallise à une température supérieure à celle du matériau B. Pour définir le domaine de température de cristallisation des deux matériaux, nous allons comparer les résultats de mesures obtenues en DSC et les mesures rhéologiques obtenues dans les mêmes conditions de refroidissement.

Essais de refroidissement

Mesures calorimétriques

Mesures rhéologiques

Les mesures rhéologiques sont effectuées sur un rhéomètre Arès, en imposant des cycles thermiques entre 180°C et 100°C, comportant une vitesse de chauffage de 10°C/min et des vitesses de refroidissement de 2, 5 et 10°C /min, sur des échantillons stabilisés avec 0,5% d'Irganox 1010.

On mesure les modules à une fréquence de 10 rd/s et une déformation de 1%. L'épaisseur de l'échantillon est de 1,25 mm. Nous avons vérifié, en utilisant d'autres entrefers compris entre 1 et 0,5 mm, que la température de transition n'était pas modifiée pour les différents entrefers. La température obtenue sur les deux modules visqueux et élastiques est identique en fonction des conditions de refroidissement. Nous avons vérifié que l'ajout de stabilisant ne modifiait pas les températures de cristallisation. La température prise en compte pour le début de la cristallisation correspond au changement rapide de la valeur des modules (Fig. 3). La reproductibilité des différents essais permet de connaître cette température avec une incertitude inférieure à 1°C.

Discussion et conclusions

Références

[1] Duplay C., Monasse B., Haudin J.M., Costa J.M. Polymer Int., 48, 320-326 (1999).

[2] Koscher E., Fulchiron R., Influence of shear on polypropylene crystallization: morphology development and kinetics, Polymer, 6931-6942 (2002).

[3] Boutahar K., Carrot C., Guillet J., Macromolecules, 31, 1921Macromolecules, 31, -1929Macromolecules, 31, (1998)).

[4] Bustos F., Cassagnau P., Fulchiron R., Effect of molecular architecture on quiescent and shear induced crystallisation of polyethylene, J. Polym. Sci. Polym. Phys., 1597-1607(2006). [5] Zhang W., Martins J.A., Evaluation of effect of melt memory on shear induced crystallisation of low density polyethylene, Macromol. Rapid Commun., 27 1067Commun., 27 -1072Commun., 27 (2006)).

[6] André J.M., Modélisation thermomécanique et structurale du soufflage de gaine de polyéthylènes, Thèse de Doctorat, Ecole des Mines de Paris (1999)

Fig. 2 .

 2 Fig. 2. Evolution du facteur de glissement a T en fonction de l'inverse de la température, : A, ○ : B.

Fig. 3 .

 3 Fig. 3. Evolution du module élastique en fonction de la température pour différentes vitesses de refroidissement pour le matériau A.

Fig. 4 .

 4 Fig. 4. Evolution des températures de cristallisation avec la vitesse de refroidissement pour les essais de rhéologie te de DSC; (a) matériau A, (b) matériau B.

  une indication assez précise de la température de la matière, avec la température réelle du matériau mesurée dans le calorimètre avec les mêmes conditions de refroidissement.

	en condition isotherme
				temps de début de cristallisation et un nombre de
				Weissenberg, défini par le produit d'un temps de
				relaxation du polymère et du taux de cisaillement de
				l'écoulement. Zhang et Martins [5] ont travaillé sur
				un polyéthylène cisaillé dans un système nommé
				"shear DTA", constitué d'un rhéomètre capillaire et
				d'un analyseur thermique différentiel, sur lequel on
				enregistre une contrainte de cisaillement fonction du
				temps et de la température. Ils montrent que le temps
				de début de la cristallisation isotherme est activé par
				le cisaillement et qu'une saturation de cet effet se
				produit pour une déformation de l'ordre de 3000 (les
				taux de cisaillement appliqués sont compris entre 15
				et 65 s -1 ).
				Dans tous ces systèmes, les auteurs s'intéressent à la
				variation des modules en fonction du temps et en
				déduisent un taux d'avancement représenté par le
				facteur	α	=	max ) ( t G G	--	min min G G	.
				Il existe une bonne corrélation entre les cinétiques
				mesurées par calorimétrie et rhéologie. Par contre,
				ces auteurs ne comparent pas les températures
				respectives obtenues sur les deux dispositifs. Cette
				comparaison est en général assez délicate car, si l'on
				peut facilement étalonner le calorimètre avec un
				corps pur pour évaluer l'influence du gradient
	ont étudié la cinétique de	thermique sur les température de transition, cette
	cristallisation statique d'un polyéthylène haute	méthode est difficilement applicable sur le
	densité (PEHD) dans un rhéomètre. Bustos et al. [4]	rhéomètre: le corps pur, en général de l'indium, a
	ont caractérisé les cinétiques de cristallisation sous	une viscosité très faible et son utilisation sur les
	écoulement de polyéthylènes obtenus par différents	plateaux du rhéomètre n'est pas évidente. Nous
	procédés (radicalaire,	Ziegler,	Phillips et	avons choisi de comparer la température mesurée
	métallocène) et ont établi une corrélation entre le	par la sonde de platine située sous l'outil, qui donne

  Le Tableau 1 reprend les principales caractéristiques moléculaires. Le coefficient g' est le rapport de la viscosité intrinsèque de la molécule branchée à celle de la molécule linéaire de même masse. Il est donc représentatif des branchements longs. Le matériau B a un taux de branchements longs supérieur à celui du matériau A, ce que l'on peut observer sur la courbe de chromatographie.

							Rouse, évalué par des mesures en fréquence dans le
							domaine du plateau caoutchoutique.
							Matériau Temps de	Viscosité	Distribution
							Cole-Cole	limite	des temps de
							(s)	(Pa.s)	relaxation
							A	37 [6]	180 000	240
							B	64 [6]	200 000	425
	Matériau M n		M w	M w /M n g'	M z /M w
			(g/mol)	(g/mol)
		A	12 250 95 000	7,8	0,6	3
		B	13 400 70 000	5,2	0,5	2,55
		Tableau 1. Caractéristiques moléculaires des deux
					matériaux [6].
			70
		Fraction de chaînes de masse donnée (%)	10 20 30 40 50 60
			0
			10 2	10 3	10 4	10 5	10 6	10 7
					Masse molaire (g/mol)
	Fig. 1. Distribution des masses molaires, : A, ○ : B [6].
	Le Tableau 2 reprend les principales caractéristiques
	rhéologiques obtenues par des mesures en fréquence
	à	différentes		températures.	Des	mesures
	complémentaires en fluage ont permis d'obtenir les
	temps longs à la température de référence de 140°C
	et de définir une distribution des temps de relaxation
	comme le rapport des temps longs au temps de


Ghalia Oukaci -Boukellal
email: ghalia.boukellal@ensmp.fr

Audrey Durin

Jean François Agassant

Rudy Valette

DETERMINATION DES PARAMETRES NON LINEAIRES CONSTITUTIFS DE LOIS DE COMPORTEMENT VISCOELASTIQUE PAR MESURES DE CHAMP DANS DES ECOULEMENTS COMPLEXES

Keywords: Polystyrène, viscoélasticité, lois de comportement, rhéologie, biréfringence, vélocimétrie laser Doppler

Les modèles de comportement issus des théories « moléculaires » permettent aujourd'hui de faire le lien entre structure moléculaire et comportement dans des écoulements rhéometriques [1, 2]. Cependant, ces modèles ne donnent plus les mêmes prédictions dès que l'écoulement est complexe ou fortement non-linéaire. Nous montrons à l'aide de mesures de champ de contraintes par biréfringence induite par écoulement et des mesures de champ de vitesses en utilisant la Vélocimétrie Laser Doppler, une méthode d'évaluation et d'identification de différentes lois de comportement viscoélastiques [2-4] en déterminant leurs paramètres constitutifs à partir de ces dernières. Dans ce travail nous confrontons ces modèles viscoélastiques aux résultats expérimentaux obtenus avec un polystyrène industriel.

Introduction

Dans le cadre de la mise en forme de matériaux polymères, on est amené à imposer des écoulements complexes et de grands taux de déformation à des fluides viscoélastiques. Or la prédiction de leurs comportements dans le domaine non linéaire est un problème difficile. En effet, il existe de nombreux modèles, et tous ne sont pas prédictifs pour toutes les formes d'écoulements, en particulier ceux comportant une forte composante elongationnelle. En cherchant l'origine des phénomènes physiques régissant la dynamique des chaînes à l'échelle moléculaire, on devrait pouvoir prévoir le comportement macroscopique des polymères dans le domaine non linéaire. Nous nous sommes donc intéressés aux modèles existants dont les éléments et les paramètres cherchent à traduire de manière statistique à l'échelle macroscopique une réalité physique microscopique. A partir de mesures dans le domaine linéaire, on peut ajuster une partie des paramètres de ces modèles, mais certains nécessitent également des mesures dans le domaine non-lineaire. On cherche des modèles qui nécessitent l'ajustement d'un minimum de ces paramètres (gage de la pertinence du modèle) et donnant un maximum de prédiction, en particulier en élongation. En prend en compte les phénomènes microscopiques pour appréhender le comportement des polymères à l'échelle moléculaire pour pouvoir comparer les prédictions du modèle à différents résultats de mesures rhéologiques pour un polymère réel (polystyrène) et proposons une première méthode d'ajustement de paramètres non-lineaire.

Modèles et prédictions théoriques

On cherche à construire une forme macroscopique des processus de relaxation en se basant sur l'expression du tenseur des conformations . On exprime l'évolution de C en prenant en compte d'une part la déformation des chaînes C due à l'écoulement et d'autre part la relaxation des chaînes par différents processus. Ces phénomènes qui rentrent en jeu pour la construction de ces modèles sont donc:

-La déformation affine du tube.

-La reptation de la chaîne.

-Le convective constrain release (CCR) [START_REF] Ianniruberto | A multi-mode CCR model for entangled polymers with chain stretch[END_REF].

-La rétraction partielle du tube à temps de Rouse de la chaîne. A partir des prédictions sur la conformation, on peut accéder a des quantités mesurables expérimentalement (contraintes, viscosité), et étudier les différences entre les modèles ainsi que l'action des paramètres sur la prédiction de ces grandeurs. Nous allons ici prendre le cas simplifié d'un polymère n'ayant qu'un seul mode de relaxation θ ; et voir quelles sont les prédictions des différents modèles en cisaillement et en élongation uniaxiale transitoire.

G

Modèle de Maxwell surconvecté

On peut généraliser au cas tensoriel l'écriture d'une loi de comportement viscoélastique. L'évolution du tenseur de conformation fait intervenir le tenseur gradient . On cherche à déterminer l'évolution de (ou de C ) avec l'écoulement. Si on se place dans le cas viscoélastique et en considérant que les chaînes se relaxent << en moyenne>>, on peut exprimer l'évolution de par (1):

C F F C ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ - - ∇ + ∇ = I C V C C V C T 3 1 1 θ r r & . ( 1
)
Dans le domaine des petites déformations, à partir du modèle surconvecté (1), on obtient le modèle linéaire :

( ) ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ - - ∇ + ∇ = I C V V C T 3 1 1 3 1 θ r r & (2)
Où le premier terme exprime la déformation des chaînes dû à l'écoulement et le second terme exprime la relaxation avec un temps de caractéristiqueθ , qui dépend du modèle microscopique choisit (Rouse, reptation, CR, …).

La contribution viscoélastique du tenseur des contraintes est alors donnée par :

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ - = I C G 3 1 3 τ . (3)

Modèle de Larson,

Au delà d'une certaine déformation, les phénomènes de relaxations sont activés, dont la rétraction, qui est supposée infiniment rapide. Larson considère que la longueur quadratique moyenne des chaînes reste égale au cours de l'écoulement, afin de rendre compte de la rétraction. En retranchant le terme dynamique dû à l'élongation

( C V C trace dt d : 2 ) ( r ∇ =
) de (1) on obtient le modèle de Larson ( 4) :

( ) ( ) ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ - - ∇ - ∇ + ∇ = I C C C V V C C V C T 3 1 1 : 2 θ r r r & (4)
Avec θ le temps de relaxation par reptation.

Modèle de Marrucci et Ianniruberto [2001]

Ce modèle explique l'effet de la théorie de CCR sur les polymères enchevêtrés, leur idée est de concentrer tous les phénomènes suivant dans une expression complexe d'un temps caractéristique de relaxation : la reptation, CCR (thermique et convectif) et la relaxation de type Rouse. Ce modèle, dit DCR, (double-convection-reptation) prend en considération les phénomènes de CCR et de l'étirement de chaîne (notons qu'il existe dans leur article un raffinement du CCR par une extension dans le cas des polymères polydisperses en incluant la double reptation dans la limite des écoulement lents, ainsi on voit l'apparition d'un nouveau phénomène dit CCR 2). Dans ce modèle, le tenseur des conformations est décomposé en une partie orientation (un tenseur C de trace unitaire) et une variable d'étirement λ (dont le carré représente le carré du vecteur bout-à-bout) qui ont leur dynamique propre. Les paramètres constitutifs de ce modèle sont : le module de cisaillement G, le temps de reptation d θ , le temps de Rouse R θ et une valeur d'extensibilité finie max λ . Les mécanismes sont modélisés de la manière suivante. Le tenseur des contraintes s'exprime par :

) 3 1 ( 1 2 max max I C G - - - = λ λ λ λ τ (5)
Le module plateau est alors conservé mais contient une partie non linéaire exprimée par la variable d'extension finie. On retrouve le tenseur des conformation dans le produit . La dynamique de C est de type « reptation », modélisée par :

C 2 λ ( ) 0 3 1 . 2 : 2 2 2 = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ - + ∇ + ∇ I C C C V C C φ r (6)
tel que le premier terme décrit l'évolution temporelle de l'orientation de tube, le second la rétraction et la reptation.

Ici une équation d'évolution de (au lieu de C) est utilisée, cette équation est justifiée par le fait qu'elle rend aussi bien, voire mieux compte du modèle original intégral de Doi et Edwards.

2

C

φ est ici un temps de reptation équivalent, défini par :

R d C V θ θ φ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∇ + = : 1 2 1 r (7)
qui contient ainsi la dynamique de reptation, puis le CCR, puis tend vers la dynamique de Rouse. Il reste donc à activer la dynamique de l'étirement/rétraction, qui est un phénomène de type Rouse :

λ λ λ θ λ λ λ - - - ∇ = max max 1 : R C V dt d r . ( 8
)

Modèle de Marrucci avec élongation couplée

Maruuci [START_REF] Ianniruberto | Flow-induced orientation and stretching of entangled polymers[END_REF] a cherché à réunir les expressions de l'évolution du tenseur des conformations et de sa trace en une seule équation :

( )I trC ItrC C V C C V C R T 1 3 1 3 1 1 - - ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ - Θ - ∇ ⋅ + ⋅ ∇ = θ r & (9)
Avec :

( ) ( ) k c tr c tr R R θ θ β β θ θ θ = - + - ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - + = Θ 1 ) ( 1 1 ) ( 1 1 1 1 (10)
Le premier terme de l'équation donne le taux de déformation affine de C, les deux termes suivant expriment la relaxation par reptation et par rétraction. On peut vérifier en posant 1 ) ( = C tr , on obtient l'expression de l'évolution de la trace du tenseur de conformation :

( )

( 1 3 1 : 2 ) ( - - ∇ = trC C V C tr R θ ) r (
( ) ( )
1 ) ( 1 1 ) ( 1 1 1 1 1 3 1 3 1 - + - ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - + = Θ - - ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ - Θ - ∇ ⋅ + ⋅ ∇ = c ftr c ftr I ftrC ItrC C f V C C V C R R T β β θ θ θ θ r & )
Ce modèle permet d'allonger les chaînes en élongation uniaxiale transitoire sans pour autant diverger la viscosité.

Matériaux et techniques expérimentales et résultats préliminaires

Le

Rhéometrie dynamique et continue :

Nous avons utilisé un rhéomètre ARES dans la géométrie cône plan pour effectuer les mesures de spectroscopie mécanique.

Rhéometrie élongationnelle

Cette expérience est faite sur le RME, développé par Meissner. Nous considérons les déformations dites HENCKY notées 0 ε

. En traçant la viscosité élongationnelle en fonction du temps en suite, nous avons tracé sur le même graphique la viscosité élongationnelle et la prédiction linéaire. Ce qui présenté sur la (Fig. 2).

On remarque un effet rhédurcissant dans la gamme de taux d'élongation étudiée. La Rhéometrie classique (en dynamique plan-plan, cône plan, capillaire et élongation uniaxiale « RME ») n'est pas suffisante pour déterminer tous les paramètres constitutifs non linéaires de lois de comportements viscoélastiques existants. Nous avons recours à des mesures de champs de contraintes en utilisant la biréfringence induite par écoulement et de champ de vitesses en utilisant la Vélocimétrie Laser Doppler pour valider les prédictions du modèle et éventuellement en ajuster ses paramètres.

Biréfringence induite par écoulement (FIB)

Le champ de contrainte est déterminé à partir des bandes d'isochromes déduites par la FIB (les isochromes ne dépendent que de la différence de contraintes principales). Dans notre cas le polymère fondu devient anisotrope sous l'effet de l'orientation moléculaire dans le champ d'écoulement. λ est la longueur d'onde de la lumière monochromatique et W est la largeur de la filière . La Fig. 3 présente un exemple d'un cliché de biréfringence obtenue pour le PS 648 utilisé. Cette dernière relie la différence de contraintes principales au retardement relatif (ou ce que nous appelons l'ordre de la frange k) et au coefficient rhéo-optique de Brewster C qui est constant pour le même matériau à une température donnée.

Vélocimétrie Laser doppler

Conclusion et discussion

Nous avons vu qu'il n'est pas toujours possible d'ajuster un modèle à des valeurs expérimentales, et que le bon comportement d'un modèle pour un écoulement donné ne garantit pas sa validité pour un autre écoulement. Dans le cas du modèle de Marrucci avec élongation des chaînes couplée, on parvient à un jeu de paramètres non linéaires qui permet d'approcher à la fois les courbes expérimentales en élongation uniaxiale transitoire et en cisaillement. Ce jeu de paramètres, appliqué à la mesure d'un champ de première différence de contraintes principales en élongation plane, donne aussi de bons résultats en comparaison des autres modèles (figure 7). L'extension de la méthode à une optimisation multiécoulements est donc une piste pour améliorer l'identification des paramètres. En outre, afin de rendre plus rapide cette détermination et d'éventuellement faire varier les paramètres linéaires (dans le but de varier si un changement dans le spectre de relaxation peut aider à ajuster les courbes dans le domaine non linéaire), il serait utile d'automatiser le procédé d'identification en utilisant une méthode de régression généralisée à toutes les mesures disponibles. Une fois les paramètres déterminés, on pourra tenter de faire le lien entre ceux-ci et la structure du polymère, en cherchant par exemple à retrouver la distribution de masses moléculaires. Il reste possible d'envisager la construction de nouveaux modèles, on pourra par exemple généraliser au cas non-lineaire les processus de double reptation en couplant deux à deux les relaxations de modes par l'intermédiaire du terme de CCR.

  11)Pour prendre en compte du caractère non gaussien des chaînes, responsable d'une non linéarité dans leurs réponses élastiques, il propose d'ajouter un terme laissant diverger leur raideur aux fortes élongations. Il ajoute alors à ce un nouveau paramètres traduisant l'extensibilité finie des chaînes. On obtient (

Fig. 1 :

 1 Fig.1 : Résultat de mesures de spectroscopie mécanique pour le PS 648 à Tref =180°C avec 10% de déformation Nous avons vérifié la loi empirique de Cox Merz à l'aide de mesures de viscosité en continu. Pour cet effet, nous avons utilisé un rhéomètre capillaire Gottfert à différentes vitesses imposées. Les résultats sont donnés Fig. 1 dans laquelle on observe que les zones terminales sont bien acquises et que le principe empirique de Cox-Merz est vérifié.

Fig. 2 :

 2 Fig.2 : Evolution de la viscosité élongationnelle uniaxiale en fonction dutemps pour le PS 648 à T=180°C.

Fig. 3 :

 3 Fig.3: Clichés de biréfringence d'écoulement pour le Ps 648 dans la géométrie CD à 180°C pour Q=0.25g/s Dans un écoulement plan, en négligeant les effets de bords, le niveau de l'anisotropie peut être mesuré selon les règles optiques en utilisant la loi tensio-optique (13):

Fig. 4 :FréquenceFig. 6 :

 46 Fig.4: La technique de mesure de LDVLe principe de mesure est basé sur l'effet Doppler. Deux faisceaux laser se focalisent dans le canal (Fig.4). Le point d'intersection de ces derniers est matérialisé par une tache dans l'écoulement. Le résultat est un modèle d'interférence spatiale. L'intensité mesurée correspond à la composante

Fig. 7 :

 7 Fig.7 : Comparaison des prédictions de différents modèles en élongation plane pour les paramètres identifié via les expériences en cisaillement et élongation


Bertrand Kerautret
email: kerautre@loria.fr

Jacques-Olivier Lachaud
email: jacques-olivier.lachaud@univ-savoie.fr

Thanh Phuong Nguyen
email: nguyentp@loria.fr

Circular arc reconstruction of digital contours with chosen Hausdorff error

  L'archive ouverte pluridisciplinaire

Introduction

Digital curve representation or approxima- tion by simple primitives is useful for further shape analysis (recognition, matching, etc). Many methods approximate digital curves by a polygonal contour, using corner points or multi-scale analysis [START_REF] Feschet | Multiscale analysis from 1d parametric geometric decomposition of shapes[END_REF]. We propose here to work with higher order primitives like arcs of circle. This representation is more efficient for curved shapes like the one illustrated on the following floating figure and captures better its geometry. In a previous work [START_REF] Kerautret | Curvature based corner detector for discrete, noisy and multi-scale contours[END_REF] we have explored the potential of different curvature estimators for corner detection. Together with a scale parameter, the obtained polygonal reconstructions were able to represent the contour by adapting the number of points according to the local value of curvature (see for example the polygon (a) of the upper floating figure). However as shown in figure (b), the circle arc primitive is much more efficient to represent numerous shapes. The previous example shows how arcs based representation gives a more compact description for the same accuracy (same Hausdorff error δ H , more faithful normals). In this paper we investigate curvature based arc reconstruction by introducing a simple reconstruction algorithm which exploits different recent curvature estimators.

Among previous works about reconstruction of digital contours with higher order primitives, we can mention the work of Rosin et al. [START_REF] Rosin | Segmentation of edges into lines and arcs[END_REF], who constructed firstly a polygonal description and detected fitting arcs by grouping connected lines. Horng et al. [START_REF] Horng | A dynamic programming approach for fitting digital planar curves with line segments and circular arcs[END_REF] and Tortorella [START_REF] Tortorella | A dynamic programming approach for segmenting digital planar curves into line segments and circular arcs[END_REF] introduced curve-fitting methods with an approach based on dynamic programming. Bodansky [START_REF] Bodansky | Approximation of a polyline with a sequence of geometric primitives[END_REF] presented a method for the approximation of a polyline with straight segments, circular arcs and free curves. It contains two steps. The first step is the segmentation of polygonal lines into fragments (short polygonal lines) and the second step is the approximation of the fragments by geometric primitives. If some fragments can not be approximated by geometric primitives with acceptable precision, they are recognized as free curves.

It is obvious that curvature information is meaningful for curve reconstruction by circle arcs and segments. A circle arc corresponds to a constant part in the curvature profile of the studied curve. Some methods have exploited this measure for curve reconstruction. Chen et al. [START_REF] Ventura | Segmentation of planar curves into circular and line segments[END_REF] proposed a method for segmenting a digital curve into lines and arcs from curvature profile in which the number of primitives is given. This procedure contains two stages. The first stage computes a starting set of break points and determines an initial approximation by arcs and lines based on this set. This stage relies on the detection of significant changes along the curvature profile. The second stage is an optimization phase which adjusts the break points until the fitting error is locally minimized. Afterwards, Horng [START_REF] Horng | An adaptive smoothing approach for fitting digital planar curves with line segments and circular arcs[END_REF] proposed an adaptive smoothing approach for decomposition of a digital curve into arcs and lines. The input curve is segmented into arcs and lines according to the smoothed curvature representation. The curvature profile is determined by Gaussian filtering. Then, it is smoothed with an adaptive smoothing technique. Similarly, Salmon et al. [START_REF] Salmon | A new method to detect arcs and segments from curvature profiles[END_REF] presented a method for decomposing a curve into arcs and segments according to the curvature profile too. They used a notion of discrete curvature which is related to the circumscribed circle induced by blurred segments. Their main idea is to extract key points on the curvature profile, which are then used for reconstruction. However the instability of this curvature estimator induces some complex curvature processing which adds new parameters and reduce the applicability of the approach.

We propose here to examine the potentiality of three recent curvature estimators in the context of reconstruction with circle arcs. Their main properties (stability wrt noise especially) are briefly described in Section 2. The reconstruction algorithm is presented in Section 3, and uses indifferently two of these estimators. We finally validate our reconstruction technique with several experimentations in Section 4. The visual curvature reconstruction [START_REF] Liu | A unified curvature definition for regular, polygonal, and digital planar curves[END_REF] and the method of [START_REF] Nguyen | Etude des courbes discrètes: applications en analyse d'images[END_REF] act as reference reconstruction methods.

Recent Curvature Estimators

An overview of different curvature estimators are given in the following and more details can be found in their respective reference (see also the comparative evaluation in [START_REF] Kerautret | Curvature based corner detector for discrete, noisy and multi-scale contours[END_REF]).

Global Minimization Curvature (GMC). Curvature estimation is very problematic since infinitely many shapes have the same digitization. The idea of the GMC estimator [START_REF] Kerautret | Curvature estimation along noisy digital contours by approximate global optimization[END_REF] is to determine, among all possible shapes that have the same digitization as the digital object under study, the shape which minimizes its squared curvature. This shape is the most probable or expected shape if only a digital object is given, since it is the smoothest possible. Then the curvature field estimation is simply the curvature field of the minimal shape.

It is not a trivial task to determine this minimal shape. A phase-field approach is proposed in [START_REF] Bretin | Regularization of discrete contour by willmore energy[END_REF]. In [START_REF] Kerautret | Curvature estimation along noisy digital contours by approximate global optimization[END_REF], the proposed approximate optimization method provides a piecewise constant curvature field, so as the reconstructed shape boundary is made of circular arcs with tangent continuity. Furthermore it takes into account possible noise in the input data, with the use of blurred segments as a preprocess [START_REF] Debled-Rennesson | Optimal blurred segments decomposition of noisy shapes in linear time[END_REF]. This estimator determines a curvature field with the smallest possible number of inflexion points. It is also almost rotation invariant due to processing with maximal digital straight segments. Its stability makes it particularly suitable to our reconstruction algorithm.

Binomial Convolution Curvature (BCC). This estimator was proposed by Malgouyres et al. [START_REF] Esbelin | Convergence of binomial-based derivative estimation for c 2 noisy discretized curves[END_REF][START_REF] Malgouyres | Binomial convolutions and derivatives estimation from noisy discretizations[END_REF] as a discrete alternative to the Gaussian smoothing technique for estimating the curvature of a digital contour. Differential operators of order n are obtained as successive convolutions of m (say) binomial kernels and n difference kernels. The authors have shown that this differential estimator is multigrid convergent for well-chosen m (m depends on the sampling rate and other parameters like maximal curvature), even in the presence of noise. The main problem with this method is how to choose this m for a given input shape, since there is an ad hoc balance to be made between accuracy and smoothness, and some parameters are tricky to estimate. This method is also computationnaly costly for large m. We will nevertheless use it to show that our reconstruction method is relatively independent of the curvature field estimation.

Visual Curvature (VC). The visual curvature has been introduced by Liu, Latecki and Liu [START_REF] Liu | A unified curvature definition for regular, polygonal, and digital planar curves[END_REF]. Its principle is to measure the number of extreme points of the height function along several directions, within a given window around each point. It is thus clear that points on the shape boundary that are also vertex of its convex hull are always extreme points. Furthermore, they introduced a scale parameter which keeps only extreme points surrounded by big enough concave or convex parts. This process filters non-significant features at a given scale. Keeping only the vertices with a non-zero multiscale visual curvature defines a simplified polygon. The sequence of polygons obtained by increasing the scale parameter from 0 to 1 creates a natural filtration of polygons, the simplest one being the convex hull. A drawback of the method is that the visual curvature is only a qualitative estimation of the curvature in the general case. Furthermore, the simplified polygons are not controlled by an error measure. Lastly, this method requires four parameters. The visual curvature technique is recognized as a good feature detector and multiscale contour polygonalizer. Since the estimator is not suitable for our circle arc reconstruction (no distinction between concave/convex area), we will use it only for comparison purpose to assess the quality of our reconstruction method.

Contour Reconstruction with Circle Arcs

We propose a simple strategy to reconstruct a digital contour with the circle arc primitive. The main idea is to decompose the curvature estimation profile so as to find the significant curved areas which can be approximated by a circle arc. For this purpose a split/merge strategy is proposed. Split/merge is governed by a given maximal Hausdorff error E max with respect to the input digital contour. This parameter acts as a scale for the reconstruction. It also induces specific parametrizations of curvature estimators, which will be described in the multiscale reconstruction paragraph.

Algorithm 1 gives an overview of the main reconstruction process. First the curvature profile is decomposed into constant curvature parts. Then the set of local maxima/minima is extracted to define the initial regions as circle arcs. Since the circle arc estimation does not guarantee an error smaller than E max , a split process is first proposed to reduce the error between the circle arc and the curve until it becomes less than the maximal allowed value. The merge phase extends them with their neighborhood regions while the associated circle arc gives an error lower than E max . Before describing the error measure we focus on the problem of arc reconstruction from a contour region. Arc reconstruction. Given a contour region R i

CA 1 CA 2 R R A2 A1 A ′ 2 A ′ 1 A ′ 3 Cb i Cf i Cc i I1 I2
there are several ways to reconstruct a circle arc A i from two endpoints C bi and C fi . A first solution is to use the curvature information to determine the different possible solutions if there exist. Such a reconstruction is illustrated on the following figure by assuming a constant curvature value κ i = 1 R estimated on the contour between C bi and C fi . The two possible centers of the osculating circles of radius R are represented with the intersections I 1 and I 2 of the two dotted circles of center C bi and C fi . From these two points I 1 and I 2 , four circle arcs A 1 , A ′ 1 and A 2 , A ′ 2 are deduced as potential candidates for the reconstruction. Then the sign of the curvature retains only the circle arcs of same convexity. To select the final solution, we compute the distance between each middle arc point with the middle contour point C ci . In the previous illustrating example, the final arc will be A 2 since the euclidean distance between C ci and C A2 is less than the one between C ci and C A1 .

A second method of reconstruction simply assumes that the circle arc should interpolate the middle point C ci of the contour region. In this case the center of the circle arc can be determined if the center point is not collinear with the two other points C bi and C fi . By referring to the previous example the reconstructed circle arc is given by A ′ 3 . The two approaches have been experimented and the latter one gives the best results. Error measure. Through the reconstruction process we need to evaluate the precision of the approximation by computing the error made between the reconstructed circle arcs (A i ) of extremities (C bi , C fi ) and the pieces of digital contour (C i ) defined between the two points. We propose to use the Hausdorff distance δ H (A i , C i ) defined as:

δ H (A i , C i ) = max{max b∈Ci { min a∈Ai d(a, b)}, max a∈Ai {min b∈Ci d(a, b)}}
The first term max b∈Ci {min a∈Ai d(a, b)} is computed in linear time by taking into account for each point C j the angle θ Ai of the circle arc and the angle θ Cj of the contour point C j with the segment O i C fi where O i is center of the circle arc A i . Two cases need to be considered (see Fig. 1(a)). If θ Cj < θ Ai then the minimal distance to the arc can be defined as the distance between C j and the projection C ′ j of C j on the this circle. The minimal distance between C j to any point of A i is thus given by R -||O i C j || where R is the radius of the circle of center O i . If θ Cj is greater than the circle arc angle θ Ai then the projection C ′ j is not located on the circle arc and the error is then defined by the minimal distance between ||C j C fi || and ||C j C bi ||. The second term of the Hausdorff error measure implies a O(N 2 ) complexity since for any point of the arc, the minimum distance with the N points of the contour part C bi C fi is required. We therefore only approximate this measure, by computing the minimal distance only for some sampling points on the circle arc. They are defined so as to obtain at least one sampling point on each quadrant (worst case for a circle arc with angle close to 2π). Thus four points are used to define the error (illustrated on Fig. 1(b)). Merging process. The first merging process is initiated from the constant plot areas which are a local minima/maxima. The advantage of such strategy is to be independent of the choice of the initial contour point. Note that a precision parameter ǫ can be used to consider that two curvature values are equal. Then in order to avoid the presence of inconsistent circle arc, merging is allowed only between two contour regions with the same sign of curvature (definition included in the function isExtendable). It is also necessary to have a strategy for selecting in which order neighboring regions are merged with the considered central region.

θA i θC k θC l Ck C ′ k Cl C ′ l Ai Cb i Cf i Oi Ck P4 P3 P2 P1 Ai Cb i Cf i (
Here, the region whose mean curvature is closest is selected as first candidate to be merged. Such strategy is associated to the functions selectFirstNearest, selectSecondNearest and extendFrontFirst from Algorithm 3.

As described in Algorithm 1 the merging process is applied in a second phase in order to merge the potential arc regions located between two local maxima/minima. Finally, after this process, the function selectMinErrPrimitive is called to optionally verify if the straight segment could improve the reconstruction error. In order to favor circle arc reconstruction the straight segment is chosen only if it implies an error decrease at least equal to E max /2. Extract from S the set Sm containing all the regions which are a local maxima/minima. Stmp = S; while nbElements(Stmp)! = 0 do Stmp = SPLIT REGIONS(Stmp, S, regionIndex, maxArcError); // First extension from mini/maxima regions: while nbElements(Sm)!=0 do Sm = EXTEND PLOT REGIONS(Sm, S, regionIndex, κ, maxArcError); // Second extension from all others regions Su: Su= set of index of valid non maxima/minima regions of the current regions. while nbElements(Su)!=0 do Su = EXTEND PLOT REGIONS(Su, S, regionIndex, κ, maxArcError); // Verify or change primitive for region which are better approximate // by a straight segment: checkBestPrimitive(S, tabRegionIndex, maxArcError); end comes from the stability of the GMC estimator (see [START_REF] Kerautret | Curvature based corner detector for discrete, noisy and multi-scale contours[END_REF] for detailed comparisons).

Algorithm 1: Reconstruction with arcs and segments

Experiments and comparisons

In this section, the experiments and comparisons were performed on a MacBook Pro running Mac OS X 10.6.4, with a processor 2.8 GHz Intel Core 2 Duo and 4GB of memory. Note that most of the experiments presented here are available online [START_REF] Kerautret | Curvature based contour representation demo[END_REF]: the reader may here tests and compares the different methods with its own shapes. First, we reconstruct the kangaroo shape of Fig. 4. Images (a-d) show the reconstructions obtained with the GMC estimator. For all experiments of the figure, resulting arcs are represented alternatively in blue and green color while straight segments are represented in red. The comparison between GMC and BCC (images (e-h)) curvature estimators shows a relative equivalence of the reconstructions: approximately the same accuracy with the same number of primitives (slight advantage of accuracy for GMC). However BCC is much slower, especially at large scale. Note that the initial constant curvature intervals were defined from the same precision parameter ǫ set to 10e -6 for both GMC and BCC estimator.

We also compare our proposed method with the NASR method of Nguyen, who proposed a linear time algorithm for approximate circle arc recognition (chapter 4, page 133) [START_REF] Nguyen | Etude des courbes discrètes: applications en analyse d'images[END_REF]. The method is based on the representation of the contour in the tangent space and shares with the GMC estimator the preprocess with blurred segments (thickness is used as a scale parameter for comparisons). NASR method is faster than GMC and BCC approach (Fig. 4, images (i-l)), but is much less accurate at a comparable scale (i.e. for the same number of primitives). The Fig. 3 displays the number of primitives (segments and arcs) according to the scale. GMC and BCC show comparable evolution while circle arc primitives disappear in NASR at large scales.

As mentioned in Section 2, we also perform comparisons with the classical visual curvature reconstruction ( [START_REF] Liu | A unified curvature definition for regular, polygonal, and digital planar curves[END_REF], see Fig. 5), later called VC. Depending on its parameters, VC is generally faster than GMC, especially at large scale. However, for a given number of primitives, the GMC reconstruction always achieves better accuracy than VC (Hausdorff distance about 6-7 times smaller). Note Fig. 4. Results and comparisons using the Hausdorff distance δH of the same reconstruction process by using GMC and BCC curvature estimators (a-h). Images (i-l) show for comparison, the result with NASR method by using the same scale parameter.

that arcs and segments represent the same cost since each reconstructed arc interpolates the middle region point C Ci (second method of arc reconstruction described in Section 3). To conclude the experimentation, a last comparison was performed on a real photography of a drawing (Fig. 4) with the three different methods GMC, NASR and VC. The resulting representations confirm that GMC is always more precise for a given number of primitives.

Conclusion

This paper has proposed a simple method to reconstruct a digital contour with circular arcs, given a scale parameter that is simply the maximal Hausdorff error. Although the method is not specific to one curvature estimator, the GMC estimator has shown the best adequacy with our algorithm, since it gives precise results while keeping a reasonable execution time. The comparisons with the recent works demonstrate the quality of the proposed reconstruction. In future works, we plane to integrate more information in the reconstruction process, namely the automatic noise detection and the information on flat/curve contour parts [START_REF] Kerautret | Multi-scale analysis of discrete contours for unsupervised noise detection[END_REF], in order to obtain a parameter free contour reconstruction.

Fig. 1 .

 1 Illustration of the evaluation of the Hausdorff distance between the circle arc and the digital contour.

  Data: C = {Ci} n i=0 digital curve, κ = {κi} n i=0 curvature estimation, float maxArcError; Result: curve represented by a set of arcs and segments. begin Decompose κ into a set of constant curvature interval S defined by: {(b0, f0), ..., (bi, fi), ..., (bM , fM )}. For each contour point Ci, store in regionIndex[i] the index k ∈ {0, ..M } of its region S[k].

Fig. 3 .

 3 Fig. 3. Primitive evolution through the change of scale of the shape of Fig. 4.

  GMC: A = 117, S = 12, δH = 1.98797 (f) VC: S = 128, δH = 11.GMC: A = 65, S = 7, δH = 3.95482 (g) VC: S = 72,δH = 26.2247 711 ms. 503 ms. scale=6 scale=0.115 (c) GMC: A = 44, S = 12, δH = 5.9946 (h) VC: S = 55,δH = 35.GMC: A = 34, S = 9, δH = 9.93201 (i) VC: S = 42,δH = 56.328 1479 ms. 507 ms. scale=15 scale=0.19 (e) GMC: A = 23, S = 10, δH = 14.9788 (j) VC: S = 33 , δH = 81.6241 1817 ms. 508 ms.

Fig. 5 .

 5 Fig. 5. Reconstruction results of the proposed method (a-e) at different scales. Comparisons with the Visual Curvature based approach.

(a) GMC scale = 2 ,

 2 E h = 1.99 scale = 5 E h = 4.87 scale = 10 E h = 9.81 scale = 20 E h = 19.85 A = 81, S = 3, 304 ms. A = 40, S = 6, 642 ms. A = 24, S = 2, 975 ms. A = 19, S = 4, 1578 ms (b) NASR scale = 2, E h = 5.10575 scale = 5, E h = 11.77 scale = 10 E h = 11.95 scale = 20 E h = 51.53 A = 25, S = 44, 227 ms. A = 8, S = 31, 294 ms. A = 4, S = 22, 338 ms. A = 1, S = 20, 391 ms (c) VC scale = 1e -4, E h = 3.03 scale = 0.01, E h = 4.24 scale = 0.03 E h = 11.88 scale = 0.399 E h = 58.20 S = 315, 294 ms. S = 161, 296 ms. S = 116, 290 ms. S = 37, 290 ms.

Fig. 6 .

 6 Fig.6. Experiments and comparisons of three methods applied on a photography of a flower drawing. For GMC and NASR, the resulting circle arcs are represented alternatively with blue and green color while straight segments are represented in red.

Algorithm 2: SPLIT REGIONS Data: The set setToCheck of region index to be checked for splitting. The set S of all curve PlotRegions. The rIndex associating each point Ci to its region S [k]. maxArcError: the maximal error allowed for splitting. Result: A set containing all new index of splitted region. for i = 0; i < sizeOf ( Multi-scale reconstruction. The reconstruction process is governed by a maximal error, which naturally induces a multi-scale reconstruction. To speed up the process and enhance the detection of significant points, the curvature estimator should also be tuned to take into account this error. This is easily done for the GMC curvature estimator, whose thickness parameter ν corresponds nicely with the Hausdorff error E max . Fig. 2(a) illustrates the blurred segment of width ν used in the GMC curvature estimator. When using the GMC estimator, the maximal error and the thickness ν are simply set to the chosen scale value. For the reconstruction with the BCC estimator its mask size has a linear dependence with the chosen scale value (although the initial mask size must be somehow determined by the user it was set as the contour size for the following experiment), while the maximal error is set equal to the chosen scale.

Time complexity.

The global reconstruction complexity is first dependant of the curvature estimator. Since the error measure is computed in linear time, the complexity for the split/merging process is in the worst case equal to O(n 2 ) when the contour (composed of n points) is reconstructed with a final arc obtained by adding one point at each step. On average the complexity is equal to O(nlog(n)).

Beside the difference in quality of the reconstructions, which is described in the next section, the choice of GMC or BCC estimator influences the efficiency of the merging process. Fig. 2(b) shows the number of region merges obtained for both estimators. The resulting plot shows that GMC is around 7 times more efficient than BCC for the merging process. The main reason of this difference Algorithm 3: EXTEND REGIONS Data: The set setT oExtend of region index to be checked for merging. The set S of all PlotRegions. The rIndex associating each point Ci to its region S[k]. The curvature estimation κ = {κi} n i=0 , maxArcError: the maximal error allowed after a merge. Result: The set of region indexes which were updated: resultSet for i = 0; i < nbElements (


Merete Osler
email: m.osler@dadlnet.dk

Allan Linneberg

Charlotte Glummer

Torben Jørgensen

Charlotte Glumer

teaching and research institutions in France or abroad, or from public or private research centers.

In 1959 Per From Hansen became the chief of one of the medical departments at the new county Hospital in Glostrup near Copenhagen. Early in his career he had assisted with the collection of data in the Macedonian center of the " Seven Countries Study" and was much inspired by its initator Professor Ancel Keys. Consequently, he showed interest not only for the patients in the department but also in the health status of the population in the community surrounding the hospital, and in 1964, his resident, Leif Hagerup, performed a survey of 50 year olds, born in 1914, concerning coronary risk factors. [START_REF] Hagerup | Coronary heart disease in men and women[END_REF] This was the first population based cohort examined at the Glostrup Hospital and ever since, followups and baseline studies of new cohorts have been going on. [START_REF] Schroll | The Glostrup Population Studies, 1962-1992[END_REF] What does the studies cover and how has it changed?

The main focus of the first and following studies was coronary heart disease (CHD) risk factor epidemiology. In the 1980s Glostrup Hospital became the Danish center of the WHO MONICA study aiming at monitoring trends and determinants of CHD over a 10 year period in different countries. [START_REF]MONICA Monograph and multimedia sourcebook. World's largest study of heart disease, stroke, risk factors, and population trends 1979-2002[END_REF][START_REF] Gerdes | Trends in selected biological risk factors in the Danish MONICA population, 1982-1992[END_REF] However, Per From Hansen was rather visionary and from the very beginning he had close collaboration with psychiatrist Henrik Hoffmeyer, and sociopsychiatric interviews were included in the examination. The studies also had a broader aim: to describe and analyse the health of the population in a more general perspective as well as to go into detail with the specific issues listed in The participants in each cohort have been drawn as random samples from the background population in up to 11 [START_REF] Hagerup | Coronary heart disease in men and women[END_REF][START_REF] Schroll | The Glostrup Population Studies, 1962-1992[END_REF][START_REF]MONICA Monograph and multimedia sourcebook. World's largest study of heart disease, stroke, risk factors, and population trends 1979-2002[END_REF][START_REF] Gerdes | Trends in selected biological risk factors in the Danish MONICA population, 1982-1992[END_REF](5)[START_REF] Hagerup | The Glostrup Population studies. Collection of epidemiologic tables. Reference values for use in cardiovascular population studies[END_REF][START_REF] Drivsholm | Representativeness in population-based studies: a detailed description of non-response in a Danish cohort[END_REF][START_REF] Schroll | A ten year prospective study, 1964-1974, of cardiovascular risk factors in men and women from the Glostrup population born in 1914[END_REF][START_REF] Kuulasmaa | Estimation of contribution of changes in classic risk factors to trends in coronary-event rates across the WHO-MONICA project populations[END_REF][START_REF] Osler | Socioeconomic status and trends in risk factors for cardiovascular diseases in the Danish MONICA population, 1982-1992[END_REF][START_REF] Glumer | Prevalence of diabetes and impaired glucose regulation in a Danish population. The inter99 study[END_REF] municipalities in the Copenhagen region which until the 1980s were considered fairly representative of the general population, [START_REF] Schroll | The Glostrup Population Studies, 1962-1992[END_REF][START_REF] Gerdes | Trends in selected biological risk factors in the Danish MONICA population, 1982-1992[END_REF] but now belongs to a somewhat lower social area of Denmark. Stratified random samples of men and women have been surveyed, characterized by year of birth ( In 1978, a controlled primary intervention on men and women aged 30,40,50 and 60 years was initiated and 4 years later the first of 3 MONICA surveys were started on similar age groups. [START_REF] Gerdes | Trends in selected biological risk factors in the Danish MONICA population, 1982-1992[END_REF] In 1999, the largest study INTER99 was started. It comprises 61 301 inhabitants from which a random sample of 13 016 were invited to a health examination and high-risk intervention. Of them 82 was noneligible. [5] In this way an overall design has been built which covers both cross sectional, longitudinal and timesequential designs as illustrated in Figure 1. Due to the maintained standardized methods since 1964, it has been possible to pool cohorts and to compare disease prevalences and risk factor levels over time.

[Table 1 and Figure 1 Here]

What has been measured?

At all baseline investigations comprehensive clinical and biochemical data as well as data from questionnaires and interviews have been collected ( on the methods used in most examinations has been reported previously. [START_REF] Gerdes | Trends in selected biological risk factors in the Danish MONICA population, 1982-1992[END_REF][5][START_REF] Hagerup | The Glostrup Population studies. Collection of epidemiologic tables. Reference values for use in cardiovascular population studies[END_REF] In brief, an extensive, self administered questionnaire with detailed information on sociodemographic variables, lifestyle (smoking, physical activity, alcohol drinking and food habits) and health was usually completed before a general health examination. At all baseline examinations fasting blood samples were drawn, and analysed for triglycerides, total cholesterol, and fasting glucose. To day a biobank with frozen serum and urine samples and DNA dating back to from early 1980s are stored at the Center. Blood

How often have they been followed up?

Besides the Health 78, MONICA II , MONICA III and the cohorts started in 2006 or later, all the cohorts have been followed up by at least one re-examination ( 1). Further, all cohorts have been followed by register linkages to the Civil Registration System, Cause of Death Registry, the National Patient Registry, the Psychiatric Central Registry, and the Cancer Registry. Social data on education, occupations, and income from 1981 and forth, and drug prescriptions to the cohort in the time period 1995 and forth, have also been linked to the cohorts.

What was attrition like?

An analysis of changes over time in the rate of participation in the baseline examinations shows that it has declined significantly from 1964 to 2006 (Table 2). Due to the existence of the Danish population covering registers it is possible to follow both participants and non-participants with regard to their health and survival. At the latest follow-up for vital status in October 2009, 7 310 of the 38 633 invited cohort members had died. For each cohort we found that baseline non-participants had a higher mortality than participants.

The Hazard ratio did not vary systematically over time. Thus, the lower participation in the latest cohort does not seem to have attenuated the relative difference in mortality between participants and non-participants (Table 2).

[Table 2 Here]

What has been found?

As the "classic epidemiological cohorts" started in the 1950 and 1960s the main focus from the very beginning was CHD. The first study of the 50 years old in 1964, which were the basis of Leif Hagerup's doctoral thesis [START_REF] Hagerup | Coronary heart disease in men and women[END_REF] aimed at carrying out a prevalence The MONICA cohorts have contributed to a number of international and national publications on trends of CHD risk factors. [START_REF]MONICA Monograph and multimedia sourcebook. World's largest study of heart disease, stroke, risk factors, and population trends 1979-2002[END_REF][START_REF] Gerdes | Trends in selected biological risk factors in the Danish MONICA population, 1982-1992[END_REF][START_REF] Kuulasmaa | Estimation of contribution of changes in classic risk factors to trends in coronary-event rates across the WHO-MONICA project populations[END_REF] The cohorts have also been used in an international collaboration on the development of tools for prediction of CHD risk (The PRECARD) ® . Data from the MONICA surveys have also shown social inequalities in biological and behavioural CHD risk factors with the well educated having the most favourable risk profile. A difference that seemed to increase for behavioural risk factors as smoking and a summary index based of 7 risk factors. Thus improved behaviour was mainly seen among the best educated. [START_REF] Osler | Socioeconomic status and trends in risk factors for cardiovascular diseases in the Danish MONICA population, 1982-1992[END_REF] Diabetes has been a focus from the very beginning and oral glucose tolerance tests have been measured in selected cohorts since 1967. These data documented a dramatic increase in the prevalence of type 2 diabetes in the adult population. [START_REF] Glumer | Prevalence of diabetes and impaired glucose regulation in a Danish population. The inter99 study[END_REF] The present focus of the research is on the importance of the metabolic syndrome and genetic factors. This is among others done within the international collaborations deCODE and LuCamp (www.LuCamp.org).

It is well known that Denmark has a major international advantage in epidemiological research through the access to a number of nationwide registers with a range of health further facilitates the construction of population-based studies. However, these registers do not cover health problems that do only to a lesser extent result in a hospital contact and thus are covered by the registers. Thus, during the years the cohorts have provided new knowledge on prevalence, incidence and risk factors of common health conditions such as gallstones,[12] headeache, [START_REF] Lyngberg | Incidence of primary headache: a Danish epidemiologic follow-up study[END_REF] allergy [START_REF] Linneberg | Increasing prevalence of specific IgE to aeroallergens in an adult population: Two cross sectional surveys 8 years apart. The Copenhagen Allergy Study[END_REF] and lower back pain [START_REF] Biering-Sørensen | A one-year prospective study of low back trouble in a general population. The prognostic value of low back history and physical measurements[END_REF] not sufficiently covered by available registers. For example, with the allergy studies in 1990 and 1998 (Table 1) it was possible for the first time in Denmark with the use of standardized objective measures to show a marked increase in the prevalence of allergic diseases such as allergic rhinitis. [START_REF] Linneberg | Increasing prevalence of specific IgE to aeroallergens in an adult population: Two cross sectional surveys 8 years apart. The Copenhagen Allergy Study[END_REF] Recently, by monitoring biomarkers of allergy it was documented that the introduction of the Danish nickel legislation aiming at reducing nickel exposure has successfully reduced the prevalence of nickel allergy supporting that regulation is an efficient measure for prevention of nickel allergy. [START_REF] Thyssen | Nickel allergy in Danish women before and after nickel regulation[END_REF] Now allergy is one of the main research areas at the Centre. The longitudinal design of the oldest cohort studies has created an excellent platform for studies influencing the ageing process, especially the longitudinal data on physical and cognitive function are unique. [START_REF] Avlund | Disability in old age. Longitudinal population-based studies of the disablement process[END_REF][START_REF] Laursen | Computer aided technique for testing cognitive functions validated on a sample of Danes 30 to 60 years of age[END_REF] In the late 1990s selected variables from the studies were pooled with 2 other cohorts in the Copenhagen area in Copenhagen Centre for Prospective Cohort Studies. Data have also been included in a number of international multicenter initiatives (SCORE, One

What are the main strength and weaknesses?

The cohorts consist of repeated random samples living in a well-defined area (covering up to 11 of the Municipalities in the Capital region of Denmark). Thus, the cohorts allow both longitudinal and time-sequential designs. A complete register-based follow-up for mortality and morbidity is also major strengths of our study as well as to provide a very detailed description of non-participation in the health examinations. The many medical and socioeconomic registers in combination with the person identification number provide unique opportunities for follow-up, thus loss-to-follow-up of register-based outcomes is not a serious source of bias in these cohorts. Another strength is the detailed information on health, and lifestyle collected by comparable methods in a period covering more than 40 years. Further, over the years a biobank has been established with samples of urine, serum, and DNA to be used in future and on-going research projects.

The database includes unique data on biomarkers of phenotypes of conditions (e.g. type 2 diabetes, metabolic syndrome and other CHD pre-morbid conditions, asthma, allergies, and osteoporosis) that cannot be assessed properly by questionnaires or registers due to the fact that they are to a great extent underdiagnosed and undertreated. These biomarkers have often been measured repeatedly over time in the same persons and in repeat, crosssectional design allowing for monitoring of trends at individual and population level.

One limitation of these cohorts, is that they only include adults and pertains few information from early life. However, the cohorts especially the 1914 cohort is a

3

 3 Where is the study area and who is in the sample?

  pressure has been measured according to the WHO guidelines, and anthropometric measurements have in all cohorts included at least weight and height. Vital capacity has been measured with spirometry, and cardio-respiratory fitness as aerobic capacity (V0max) with a sub-maximal bicycle ergometer-or step test. Electrocardiography (ECG) and oral glucose tolerance test has been performed in several cohorts. Further, balance tests and meaures of physical function have been performed in the older cohorts. Sociopsychiatric interviews have been performed and participants in the 1936-cohort have also filled out a short version of the Eysenck Personality Inventory. Finally, mental vulnerability has been measured in most cohorts with a Danish questionnaire. During the course of 45 years the unit have maintained a staff educated in standardized epidemiological survey methods, keeping inter-and intra-observer variation to a minimum.

  show the occurrence of CHD, its manifestations and risk factors associated with it. It showed that many risk factors were relatively prevalent in the population with remarkable small gender differences. It was also the intention to repeat the study in order to monitor the incidence of CHD, and this was done 10 years later showing a 1 year rate of myocardial infarction of 7.5 per 1000 men and 4.0 per 1000 females. Important risk factors (Relative Risks>2) were gender, smoking, hypertension, relative weight > 120%, sedentary lifestyle and serum-cholesterol above 8 mmol/l[START_REF] Schroll | A ten year prospective study, 1964-1974, of cardiovascular risk factors in men and women from the Glostrup population born in 1914[END_REF].

  of persons with the use of the personal identification number, which

  Milion, DECODE, MONICA, MORGAM, LuCamp, NORA, The Emerging Risk Factor Collaboration, The Diverse Population Studies, InterSalt and IDACO). In total at the end of 2008, the studies have been included in 30 doctoral thesis, 66 PhDs and 2155 scientific full list of all publications are available at the website (www.regionh.dk/fcfs).

  ageing research. In addition, although the follow-up for some of the cohorts cover a period of more than 40 years, most of the cohorts are small and therefore the number of cases is limited for infrequent outcomes such as specific cancers and psychiatric disorders. However the later cohorts are larger and future follow up will capture more cases.[Textbox 1 Here] Can I get hold of the data and where can I find more?The contact person is Torben Jørgensen, E-mail: tojo@glo.regionh.dk; For more information, please see our webpage at www.regionh.dk/fcfs BL. Ten-year trends in overweight and obesity amog Danish men and women aged 30-60 years. Int J Obes Relat Metab Disord 2000;24:1347-52. 21. Rosenstock S, Jørgensen T, Bonnevie O, Andersen L. Risk factors for peptic ulcer disease: a population based prosepctive cohort study comprising 2416 Danish adults. Gut 2003;52:186-93. 22. Kay L, Jørgensen T. Redefining abdominal syndromes: results of a populationbased study: Scand J Gastroent 1996;31:469-75. 23. Kessel L, Jørgensen T, Glumer C, Larsen M. Early lens ageing is accelerated in subjects with a high risk of ischaemic heart disease: an epidemiological study. BMC Ophtalomolgy 2006;6:16. 24. Husemoen LL, Thomsen TF, Fenger M, Jørgensen T. Changes in lifestyle and total homocysteine in relation to MTHFR (C6//T) genotype: The Inter99 study. Eur J Clin Nutr 2006;60:614-22.

Table

  ). The first investigations in 1964, 1967 and 1976 were on specific birth cohorts aged 50 (born 1914), 70 (born 1897) and 40 (born 1936) years at the time of examination, respectively.

Table

Table 1 &

 1

	Figure
	F o
	r
	R e v i e w
	O n
	l y
	5

Table 1

 1 Cohorts at the Research Center for Prevention and Health Only men examined at the follow-up; (**) excluding the ongoing Health 2008; BP=Blood pressure, ECG= Electrocardiography; OGTT= Oral glucose tolerance test.

	1. Disease specific epidemiology
	Cardiovascular diseases [1,3,4,9,10]
	Endocrinology
	Diabetes [11]
	Thyroid disease [19]
	Obesity [20]
	Cancer
	Gastroenterology
	Gallstone [12]
	Peptic ulcer/H.Pylori [21]
	Abdominal syndromes [22]
	Gynaecology
	Respiratory diseases
	Allergy [14,15]
	Dermatology
	Neurology
	Headache [13]
	Psychiatry and psychology [18]
	Nephrology
	Odontology
	Ophthalmology [23]
	Muscular-skeletal disorders [15]
	Sexology
	2. Social epidemiology [10]
	3. Genetic epidemiology [24]
	4. Aging [17]
	5. Life-style/general health [10]
	6. Sero-epidemiology [4]
	7. Interventional epidemiology [5]

Table 2 .

 2 Participation rates and adjusted hazard ratios for all cause mortality according to status and year of participation. Cohorts at the Research Center for Prevention and Health Age-stratified cohorts in same investigation Cohort comprised of persons in a given age-interval Cohort examined only once Cohort examined more than once

	Year of	Age-adjusted*
	baseline	participation rate (%)
	examinations
	start

Cohorts at the Research Centre for Prevention and Health Lexis- diagram (1964-2007)

		100
		90
		80
		70
		60
	Examination Age	50
		40
		30
		20
		10
		0
		1960	1965	1970	1975	1980 Examination Year 1985 1990	1995	2000	2005	2010
					The 1914 Cohort		The 1897 Cohort
					The 1936 Cohort		The Health78 Study
					The Monica 1 Study		The Monica 2 Study
					The Monica 3 Study		The Inter99 Study
					The Headache Study I	The Headache Study II
					The Copenhagen Allergy Study I	The Copenhagen Allergy Study II
					The Health2006 Study