Université Montpellier I – U.F.R. S.T.A.P.S

THÈSE Présentée par : Olivier MISSENARD Pour obtenir le grade de Docteur de l’Université Montpellier I Spécialité : Sciences du Mouvement Humain

FATIGUE, BRUIT MOTEUR ET PRÉCISION DE LA MOTRICITÉ HUMAINE

Soutenue publiquement le 19 Septembre 2008

Jury : Emmanuel GUIGON (CR / INSERM Paris)

Examinateur

David GUIRAUD (DR / INRIA Montpellier)

Examinateur

Alain MARTIN (MCU-HDR / Université de Bourgogne)

Rapporteur

Denis MOTTET (PU / Université Montpellier I)

Directeur

Vincent NOUGIER (PU / Université Joseph Fourier - Grenoble I)

Rapporteur

Stéphane PERREY (MCU-HDR / Université Montpellier I)

Co-directeur

Université Montpellier I – U.F.R. S.T.A.P.S

THÈSE Présentée par : Olivier MISSENARD Pour obtenir le grade de Docteur de l’Université Montpellier I Spécialité : Sciences du Mouvement Humain

FATIGUE, BRUIT MOTEUR ET PRÉCISION DE LA MOTRICITÉ HUMAINE

Soutenue publiquement le 19 Septembre 2008

Jury : Emmanuel GUIGON (CR / INSERM Paris)

Examinateur

David GUIRAUD (DR / INRIA Montpellier)

Examinateur

Alain MARTIN (MCU-HDR / Université de Bourgogne)

Rapporteur

Denis MOTTET (PU / Université Montpellier I)

Directeur

Vincent NOUGIER (PU / Université Joseph Fourier - Grenoble I)

Rapporteur

Stéphane PERREY (MCU-HDR / Université Montpellier I)

Co-directeur

Je tiens tout d’abord à remercier Alain Martin et Vincent Nougier pour avoir accepté d’être rapporteur de ce travail. Je remercie également Emmanuel Guigon et David Guiraud pour avoir accepté de faire partie du jury de cette thèse. Un remerciement à double titre envers Emmanuel pour les intéressantes discussions que nous avons pu avoir durant ces quelques années, et pour m’avoir ouvert la porte de son laboratoire. Un grand merci à Denis Mottet et à Stephane Perrey, pour m’avoir donné les moyens nécessaires à la réalisation de cette thèse, pour m’avoir laissé libre dans tous mes choix, pour m’avoir toujours fait confiance, et pour les sympathiques moments que nous avons passés ensemble durant ces trois années. Je tiens à remercier vivement l’ensemble des sujets « anonymes » qui m’ont offert une partie de leur temps pour participer à mes expérimentations. Je remercie également toutes les personnes qui m’ont permis d’avancer sur le plan scientifique en répondant à mes nombreuses interrogations et en partageant d’intéressantes discussions, notamment : François Bonnetblanc, Dave Collins, Laure Fernandez, Nicolas Forestier, Emmanuel Guigon, Kelvin Jones, Julien Lagarde, Nicola Maffiuletti, Sofiane Ramdani, Luc Selen et Daniel Wolpert. Dans la même catégorie je remercie tous les membres du laboratoire « Efficience et déficience motrices » qui ont pu m’aider d’une façon ou d’une autre, et plus particulièrement l’ensemble des doctorants pour les multiples services rendus. Les membres du laboratoire EDM, ainsi que l’équipe de l’association « Adadum », méritent aussi de sincères remerciements pour la sympathique atmosphère qui a régné dans le laboratoire durant ces trois ans. Je souhaite enfin adresser beaucoup plus qu’un remerciement à mes géniteurs, qui comptent énormément pour moi. Il va sans dire que, sans eux, cette thèse n’aurait jamais vu le jour ! Que ceux qui n’apparaissent pas ici ne s’inquiètent pas : ils ont une place tellement profonde dans mon cœur qu’ils n’ont pas réussi à en sortir… Olivier

TABLE DES MATIÈRES

I - Introduction générale............................................................................................. 8 LA VARIABILITE DANS LE SYSTEME SENSORI-MOTEUR ..................................................................................... 9 Origine de la variabilité............................................................................................................................................. 10 Bruit moteur................................................................................................................................................................. 12 Origine du bruit moteur ............................................................................................................................................ 12 Facteurs affectant le bruit moteur.......................................................................................................................... 14 BRUIT MOTEUR, OPTIMALITE, ET STEREOTYPIE DES MOUVEMENTS HUMAINS .................................................... 15 Des mouvements variables mais réussis .............................................................................................................. 15 Contrôle moteur optimal.......................................................................................................................................... 16 Optimalité et stéréotypie des mouvements......................................................................................................... 17 Choix de la fonction de coût .................................................................................................................................... 19 Modélisation en boucle ouverte versus boucle fermée..................................................................................... 20 Importance des propriétés statistiques du bruit moteur .................................................................................. 21 FAIRE FACE AU BRUIT MOTEUR DANS LE CONTROLE DES MOUVEMENTS ............................................................ 22 Loi de Fitts, bruit moteur, et optimalité................................................................................................................. 22 Quel modèle de contrôle optimal stochastique pour la loi de Fitts ?............................................................. 26 Le rôle de la cocontraction....................................................................................................................................... 27 FATIGUE ET CARACTERISTIQUES DE LA PRODUCTION DE FORCE ...................................................................... 28 Définition de la fatigue.............................................................................................................................................. 28 Conséquences de la fatigue pour la production de force sous-maximale ................................................... 30 FATIGUE ET CONTROLE DES MOUVEMENTS ................................................................................................. 37 Réorganisations comportementales..................................................................................................................... 37 Fatigue, variabilité de la force et contrôle de la précision................................................................................ 38 CONCLUSION ........................................................................................................................................ 39

II - Étude 1 - Signal-dependent noise during fatigue ............................................... 41 ABSTRACT ............................................................................................................................................ 43 INTRODUCTION ..................................................................................................................................... 44 METHODS ............................................................................................................................................ 45 RESULTS .............................................................................................................................................. 48 DISCUSSION ......................................................................................................................................... 50

III - Étude 2 – Fatigue, central drive and force control............................................. 54 ABSTRACT ............................................................................................................................................ 56 INTRODUCTION ..................................................................................................................................... 57 METHODS ............................................................................................................................................ 59 Experiment 1: matching the same force levels pre- and post-fatigue........................................................... 59 Experiment 2: matching the same muscle activation levels pre- and post-fatigue................................... 63 Experiment 3: electrical muscle stimulation pre- and post-fatigue............................................................... 64 Statistics........................................................................................................................................................................ 67 RESULTS .............................................................................................................................................. 67 Maximal voluntary contraction.............................................................................................................................. 67 Experiment 1: matching the same force levels pre- and post-fatigue........................................................... 67 Experiment 2: matching the same muscle activation levels pre- and post-fatigue................................... 69 Experiment 3: electrical muscle stimulation pre- and post-fatigue............................................................... 71 DISCUSSION ......................................................................................................................................... 74 Methodological considerations.............................................................................................................................. 75 Role of the increase in central drive ....................................................................................................................... 76 Role of muscle contractile properties .................................................................................................................... 78 Other factors involved in the increase in force variability with fatigue ........................................................ 81 Conclusion.................................................................................................................................................................... 82

IV - Étude 3 - Fitts’ law during fatigue ...................................................................... 84 5

ABSTRACT ............................................................................................................................................ 86 INTRODUCTION ..................................................................................................................................... 87 METHODS ............................................................................................................................................ 89 Experiment....................................................................................................................................................................89 Model .............................................................................................................................................................................95 RESULTS ............................................................................................................................................ 100 Experimental data ................................................................................................................................................... 100 Optimal control model ........................................................................................................................................... 106 DISCUSSION ....................................................................................................................................... 110 Evidence of fatigue .................................................................................................................................................. 110 Fitts’ law as the consequence of an optimal behavior in the presence of signal-dependent noise .... 111 Changes in Fitts’ law with fatigue........................................................................................................................ 112 Optimality in the presence of fatigue.................................................................................................................. 115 Open loop modeling and the role of feedback................................................................................................. 116 Conclusion ................................................................................................................................................................. 117

V - Étude 4 - Cocontraction during fatigue............................................................. 118 ABSTRACT .......................................................................................................................................... 120 INTRODUCTION ................................................................................................................................... 121 METHODS .......................................................................................................................................... 122 RESULTS AND DISCUSSION .................................................................................................................... 127

VI - Discussion générale.......................................................................................... 132 RESUME DES RESULTATS EXPERIMENTAUX................................................................................................ 133 DISCUSSION ....................................................................................................................................... 135 Fatigue et contrôle moteur.................................................................................................................................... 135 Mécanismes explicatifs des réorganisations comportementales................................................................ 137 Une interprétation dans le cadre de modèles du contrôle moteur.............................................................. 140 CONSEQUENCES FONCTIONNELLES, APPLICATIONS, ET PERSPECTIVES ........................................................... 146 Conséquences de la fatigue pour les activités de précision........................................................................... 146 Cocontracter pour conserver la précision malgré la fatigue ?...................................................................... 148 Vers une réévaluation du diagnostic de fatigue ?............................................................................................ 149 CONCLUSION ...................................................................................................................................... 150

VII – Références bibliographiques.......................................................................... 152

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Avant-propos Ce travail a été réalisé au sein du laboratoire Efficience et Déficience Motrices de l’université Montpellier 1 (EA 2991) 1 , dirigé par le Professeur Denis Mottet. Ce laboratoire est rattaché à l’école doctorale Sciences du Mouvement Humain (ED 463), dirigée par le Professeur Reinoud Bootsma. Ce travail a été financé par une allocation de recherche du ministère de l’enseignement supérieur et de la recherche. Cette thèse porte sur les effets de la fatigue musculaire sur le contrôle de la précision motrice. Il s’agit donc d’étudier les conséquences de la fatigue musculaire sur la précision motrice, et de déterminer dans quelle mesure la fatigue perturbe les mécanismes impliqués dans le contrôle de la précision motrice. Ce sujet d’étude se justifie principalement parce que la fatigue musculaire et le contrôle de la précision coexistent dans de nombreuses situations quotidiennes, dans les activités sportives notamment, mais aussi pour les opérateurs au travail. Cette thèse sera divisée en six grandes parties. Elle débutera par une introduction qui présentera le contexte théorique dans lequel nos travaux ont été réalisés, et tentera de résumer l’ensemble des points nécessaires à une bonne compréhension des études réalisées. Dans cette introduction, nous verrons d’abord, indépendamment de la fatigue, comment le système moteur gère le contrôle de la précision. Nous y introduirons la notion de bruit moteur. Puis nous verrons dans quelle mesure la fatigue musculaire est susceptible de perturber le contrôle de la précision motrice. En particulier, nous montrerons que la fatigue peut perturber le contrôle moteur parce qu’elle est la source d’une augmentation du niveau de bruit moteur. Puis les quatre études réalisées seront ensuite présentées sous la forme de publications scientifiques. Les deux premières études portent directement sur l’effet de la fatigue sur le bruit moteur. Les deux études suivantes portent sur l’effet de la fatigue sur les stratégies utilisées par le système moteur pour faire face au bruit moteur. Enfin, Une discussion générale tentera de montrer l’intérêt et la cohérence des différents résultats, ainsi que leurs conséquences fondamentales et appliquées.

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EA 2991. 700 Avenue du Pic St Loup. 34090 Montpellier.

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I - Introduction générale

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La variabilité dans le système sensori-moteur Une caractéristique fondamentale de notre système sensori-moteur est que son fonctionnement présente une variabilité irréductible, qui limite la précision avec laquelle nous pouvons réaliser une tâche. En effet, même les sportifs les plus entraînés et talentueux sont incapables de répéter exactement la même production motrice. Récemment, une grande attention a été portée à la question de l’origine de cette variabilité. De nombreuses études tant expérimentales que théoriques, ont montré que cette variabilité pouvait être due au fait que de nombreux processus dans le système sensori-moteur sont corrompus par du bruit (Faisal et al., 2008, pour une revue) ; le bruit étant défini comme une perturbation aléatoire ou imprédictible qui ne fait pas partie d’un signal.

Figure 1.1. Le bruit dans le système moteur. Adapté, d’après Faisal et al. (2008). Le bruit peut être sensoriel (a), cellulaire (b), ou moteur (c). Il affecte chacun des processus présentés ici. L’action d’intercepter une balle met donc en jeu des processus bruités dans la localisation de la balle, la transmission de l’information dans le système nerveux, et la production du mouvement.

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Origine de la variabilité La figure 1.1 décrit les différents sites où le bruit est successible de perturber le fonctionnement du système nerveux central (SNC) : le bruit peut affecter les processus sensoriels, de transmission de l’information, et de génération de force. Le bruit peut donc potentiellement affecter toutes les étapes de la production d’un mouvement, aussi simple soit-il. Produire un mouvement simple, tel qu’un mouvement de pointage avec le bras, peut être vu comme comprenant 3 étapes (van Beers et al., 2004) : une étape de localisation, où la position de l’effecteur (par exemple la main) et la position de la cible sont évaluées avec des informations sensorielles (feedback sensoriels), une étape de planification, où des commandes motrices 2 sont sélectionnées afin d’amener l’effecteur à la cible, et une étape d’exécution, où le mouvement est réalisé, parce que les commandes motrices sont transmises aux muscles. Durant cette dernière étape, les feedbacks peuvent être utilisés pour réguler le mouvement en ligne. La variabilité motrice peut être générée lors de chacune de ces trois étapes. D’abord, la perception humaine est limitée par du bruit dans l’activité neurale des aires sensorielles. Ce bruit fait par exemple varier les jugements de vitesse ou de direction essai après essai (Newsome et al., 1989). Parce que les processus sensoriels sont bruités, une partie de la variabilité observée dans les mouvements peut provenir d’erreur dans l’étape de localisation. Il semble toutefois que les conséquences de cette variabilité peuvent être minimisées lorsque l’environnement est peu variable. Par exemple, cette étape peut jouer un rôle important quand la main n’est pas visible avant le mouvement (Desmurget et al., 1995), mais contribue faiblement à la variabilité lorsque la main et la cible peuvent être vues simultanément avant le mouvement, et donc qu’il existe moins d’incertitude envers l’environnement (Rossetti et al., 1994). Ensuite, la variabilité des mouvements peut provenir de la variabilité dans l’étape de planification. En effet, Churchland et al. (2006) ont récemment montré que, chez le singe, la variabilité dans la vitesse des mouvements des yeux était positivement corrélée avec la variabilité de l’activité des cortex moteur et pré-moteur durant la

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La commande motrice est définie comme le message nerveux excitateur descendant du cortex moteur pour activer les motoneurones.

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phase préparatoire au mouvement (i.e. quelques centaines de millisecondes avant le début du mouvement). Il a donc été conclu que l’incapacité à planifier le même mouvement de manière répétée expliquait une part non négligeable de la variabilité observée dans les mouvements. Même s’il est difficile de juger dans quelle mesure ces résultats sont transférables à l’homme, il est possible que cette étape joue un rôle – au moins mineur – dans la variabilité des mouvements. Enfin, le rôle de l’étape d’exécution a été étudié par van Beers et al. (2004). Ces auteurs ont montré que, lorsque la variabilité due aux étapes de localisation et de planification était minimisée, les patterns de variabilité cinématique lors de mouvements de pointage étaient principalement expliqués par du bruit généré durant le mouvement. Ce bruit est du au fait que les processus de génération de force par le système moteur sont eux-mêmes bruités : en effet, l’intervalle entre 2 impulsions successives d’un motoneurone présente toujours une variabilité (Stein et al., 2005; Faisal et al., 2008), et la force produite fluctue inévitablement autour de la valeur cible (e.g. Jones et al., 2002). Par ailleurs, durant l’étape d’exécution, les feedbacks sensoriels peuvent être utilisés pour réguler le mouvement en ligne. Le fait que les processus perceptifs soient bruités pourrait logiquement expliquer une partie de la variabilité des mouvements. Il a d’ailleurs été montré que le bruit sensoriel était une cause majeure de la variabilité dans une tâche de poursuite visuelle (Osborne et al., 2005). La variabilité des processus de feedback proprioceptif peut aussi expliquer la variabilité des mouvements réalisés sans vision (Guigon et al., 2008a). Cependant, dans le cas de mouvements de pointage d’une cible ou d’atteinte d’un objet avec vision, il a récemment été montré que l’absence de bruit sensoriel était une condition nécessaire à un modèle de contrôle optimal avec feedback pour reproduire les trajectoires observées empiriquement (Guigon et al., 2008a). Cela suggérait que, dans ce type de tâche, le bruit sensoriel n’influerait que peu la variabilité des mouvements. En conséquence, il est largement admis que le bruit moteur, c’est-à-dire le bruit généré lors de l’exécution du mouvement, est le principal facteur responsable de la variabilité observée dans les mouvements visuo-guidés (Schmidt et al., 1979; Meyer et al., 1988; van Galen & de Jong, 1995; Harris & Wolpert, 1998; Todorov & Jordan, 2002; Tanaka et al., 2006; Guigon et al., 2008a).

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Bruit moteur De nombreux travaux ont cherché à caractériser le bruit moteur observé à différents niveaux de force. La méthode classiquement employée a été d’étudier la variabilité d’une force maintenue quelques secondes pour différents niveaux de force. Ainsi, il a été montré que la variabilité de la force (i.e. l’écart type) augmentait linéairement avec le niveau moyen de force produit (Schmidt et al., 1979; Jones et al., 2002; Todorov, 2002), ce qui impliquait un coefficient de variation (CV) constant pour différents niveaux de force. Les termes bruit signal-dépendant (SDN, pour signaldependent noise), ou bruit multiplicatif, sont utilisés pour illustrer le fait que la variabilité de la force est proportionnelle au niveau moyen de force. Cette relation robuste est valable pour de nombreux groupes musculaires et articulations (Hamilton et al., 2004). Quelques exceptions à cette règle sont à noter. Par exemple, une relation exponentielle entre la force et sa variabilité a déjà été rapportée (Slifkin & Newell, 1999). Aussi, il a été montré expérimentalement que le CV de la force pouvait augmenter aux très faibles forces (i.e. < 5 % de la force maximale) comparé au CV observé à des forces plus importantes (Moritz et al., 2005).

Origine du bruit moteur Plusieurs travaux ont cherché à déterminer les bases physiologiques à l’origine du bruit signal-dépendant dans la production de force. Une première explication provient du fait que, comme n’importe quel autre neurone, le fonctionnement du motoneurone est soumis à un bruit cellulaire qui perturbe le timing des potentiels d’action le long de l’axone et qui a des répercussions au niveau de la jonction neuromusculaire (Stein et al., 2005; Faisal et al., 2008). En outre, il a été montré que plus la fréquence de décharge d’un motoneurone augmente, plus la variabilité des intervalles inter-impulsions augmente (Clamann, 1969; Matthews, 1996; Powers & Binder, 2000). Cependant, ces points ne peuvent pas, à eux seuls, expliquer l’origine du bruit moteur signal-dépendant observé dans la production de force. En particulier, la variabilité de la force d’une seule unité motrice est proportionnelle à la racine carrée de cette force, alors que la variabilité de la force produite par un pool d’unités motrices est généralement reliée linéairement à la force (Jones et al., 2002; Stein et al., 2005).

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Ce paradoxe a été expliqué par Jones et al. (2002), qui ont démontré que la linéarité de la relation entre la force et sa variabilité était due à l’organisation physiologique du pool d’unités motrices. Ces auteurs ont d’abord montré expérimentalement que le SDN n’était pas du à la variabilité dans les processus contractiles du muscle, puisque la variabilité de la force obtenue par stimulation musculaire restait constante pour une large gamme de force. En utilisant le modèle de pool d’unités motrices de Fuglevand et al. (1993), ils ont ensuite démontré que la linéarité du SDN émergeait à cause de la contribution de 3 facteurs : la largeur de gamme de force des différentes unités motrices du pool, la contribution relative des stratégies de production de force (recrutement d’unités motrices ou augmentation de la fréquence de décharge des unités motrices), et le principe de recrutement ordonné des unités motrices (les petites unités motrices sont recrutées avant les grosses, Henneman et al., 1965).

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Figure 1.2. Une représentation schématique du principe de recrutement ordonné des unités motrices. Adapté, d’après Stein et al. (2005). Une unité motrice est composée d’un motoneurone, et de toutes les fibres musculaires qu’il innerve (cylindres). Les barres verticales représentent les impulsions. Un pool d’unités motrices est composé d’unités de différentes tailles. Un même signal d’entrée active les quatre motoneurones, mais les propriétés membranaires individuelles font que leurs seuils de dépolarisation diffèrent. La plus petite unité motrice a le plus petit seuil de dépolarisation (sigmoïde décalée vers la gauche), et par conséquent décharge plus fréquemment. Plus l’unité motrice est grosse, et moins le motoneurone risque de décharger. En conséquence, les petites unités motrices sont recrutées avant les grosses, et déchargent avec une fréquence plus élevée.

Ce dernier facteur a le rôle le plus important, pour la raison suivante : à cause du recrutement ordonné des unités motrices, les grosses unités motrices ont une fréquence de décharge plus faible que les petites unités motrices (cf. figure 1.2). De ce fait, les fibres musculaires des grosses unités motrices, recrutées lorsque la force à produire est importante, génèrent plus de secousses incomplètement fusionnées, et par conséquent produisent des forces plus variables (Faisal et al., 2008).

Facteurs affectant le bruit moteur Les facteurs affectant le SDN ont été étudiés à la fois expérimentalement et théoriquement. Les contributions théoriques (i.e. utilisant un modèle de pool d’unités motrices) présentent l’avantage de pouvoir manipuler des variables

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auxquelles l’expérimentateur a difficilement accès, comme le niveau de synchronisation des différentes unités motrices, par exemple. Il a principalement été montré que la variabilité de la force varie : ƒ Positivement avec la variabilité des intervalles inter-impulsions (interspikes intervals) dans la décharge des motoneurones (Laidlaw et al., 2000; Jones et al., 2002; Moritz et al., 2005). ƒ Positivement avec le niveau de synchronisation des unités motrices (Yao et al., 2000 ; Taylor et al., 2003). ƒ Négativement avec la force maximale d’un muscle et le nombre d’unités motrices qu’il contient (Hamilton et al., 2004).

Bruit moteur, optimalité, et stéréotypie des mouvements humains Nous avons vu que le bruit moteur peut expliquer la majeure partie de la variabilité (des forces, des trajectoires) observée lorsqu’un même mouvement est répété. Mais le bruit moteur n’est pas seulement la cause de la variabilité et de l’imprécision de nos mouvements. Il a aussi et surtout un rôle structurant qui est à l’origine de la stéréotypie des mouvements humains.

Des mouvements variables mais réussis Une des caractéristiques les plus remarquables de la motricité humaine, est que, malgré la présence de bruit moteur, nos mouvements sont la plupart du temps réalisés avec succès (Scott, 2002). L’explication de ce paradoxe réside certainement dans le fait que le SNC est capable de structurer nos mouvements en tenant compte des propriétés statistiques du bruit moteur. Cette hypothèse, qui a été récemment vérifiée expérimentalement (Trommershauser et al., 2005), est à la base d’un cadre théorique qui a été appliqué avec un certain succès à l’étude du contrôle moteur : la théorie du contrôle optimal stochastique (voir pour revues Todorov, 2004; Bays & Wolpert, 2007). L’optimalité implique ici que le SNC génèrerait, au moins dans des tâches familières, le meilleur comportement possible en référence à un critère de performance donné. Le terme stochastique fait ici référence au fait que le SNC

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tiendrait compte de la variabilité des processus neuromoteurs dans l’élaboration des trajectoires des mouvements (Guigon et al., 2008b). Ce cadre théorique a permis de trouver une explication commune à de nombreuses observations expérimentales décrites indépendamment les unes des autres, ce qui est le sceau d’une bonne théorie (Stein et al., 2005). La figure 1.3 illustre l’importance de la prise en compte du bruit moteur dans la sélection des commandes motrices.

Figure 1.3. Illustration de l’importance du bruit moteur dans la sélection des commandes motrices. D’après Harris & Wolpert (1998). Lors d’un mouvement, une même position finale peut être obtenue par des commandes motrices différentes, qui génèrent des trajectoires différentes (a). L’addition de bruit signal-dépendant dans les commandes motrices génère de la variabilité dans la position finale (b). L’importance de cette variabilité est fonction de la commande motrice choisie.

Contrôle moteur optimal Pour résoudre un problème de contrôle optimal, 3 points doivent être spécifiés : les contraintes de la tâche (e.g. la précision du mouvement, le temps de mouvement, etc.), un modèle musculo-squelettique compatible, et une définition quantitative de la performance dans la tâche. Le modèle suppose qu’un contrôleur calcule un signal de contrôle (qui correspond aux commandes motrices) approprié pour une tâche et un critère de performance donné. Ce signal de contrôle est transmis au système musculo-squelettique qui va évoluer selon sa propre dynamique. Le critère de performance, qui est la quantité à minimiser, est décrit comme l’intégrale d’une 16

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fonction de coût. Le coût peut dépendre du signal de contrôle (i.e. des commandes motrices), mais aussi de variables décrivant l’état du système musculo-squelettique (e.g. vitesse, position, etc.). Outre le fait qu’ils expliquent avec succès de nombreux résultats expérimentaux, les modèles de contrôle optimal présentent principalement trois avantages comparés à d’autres modèles du contrôle moteur (voir XI – Discussion générale pour une comparaison critique plus détaillée). D’abord, ils sont théoriquement bien justifiés a priori. En effet, l’organisme en général et le système sensori-moteur en particulier sont le produit de l’évolution, du développement, ou de l’apprentissage. Ces processus, bien qu’agissant avec des échelles temporelles différentes, ont l’objectif commun d’aboutir aux performances comportementales les meilleures et d’éliminer les comportements nuisibles pour la survie de l’espèce (Todorov, 2004; Harris & Wolpert, 2006). Le second avantage est d’ordre fonctionnel. Un modèle de contrôle optimal ne requiert pas en entrée la spécification de la trajectoire à effectuer. Au contraire, pour un critère de performance donné, le modèle va trouver le signal de contrôle qui permet de réaliser le mouvement optimal. La trajectoire n’est donc pas prescrite directement. Enfin, ces modèles sont biologiquement plausibles, puisque les trajectoires qu’ils produisent sont le fruit de l’activation d’un modèle musculo-squelettique relativement réaliste par un signal correspondant à un message nerveux.

Optimalité et stéréotypie des mouvements Le cadre théorique du contrôle optimal fournit une explication pertinente au problème de la redondance articulaire, énoncé par Bernstein (1967). Ce problème peut être énoncé de la façon suivante : étant donné le nombre de degré de liberté de nos articulations et la diversité des synergies musculaires, comment le SNC choisit-il une trajectoire parmi l’infinité de solutions possibles ? Il est en effet clair que le SNC ne choisit pas les trajectoires des mouvements par hasard ou par accident : les trajectoires des mouvements humains sont, pour une situation donnée, relativement similaires entre différents individus. On parle alors d’invariants moteurs. Les invariants moteurs les plus connus sont les profils de vitesse en cloche (e.g. Morasso, 1981), la loi de puissance deux-tiers (e.g. Lacquaniti et al., 1983), ou bien la loi de Fitts (Fitts 1954; Fitts & Peterson, 1964). Dans le cadre du contrôle optimal, les invariants

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moteurs émergeraient en raison de l’optimalité du SNC. En effet, la plupart des invariants moteurs sont bien reproduits par des modèles de contrôle optimal. Par exemple, ces modèles prédisent les trajectoires relativement rectiligne et les profils de vitesse en cloche des mouvements points à points (Hogan, 1984b; Flash & Hogan, 1985; Harris & Wolpert, 1998, voir figure 1.4), la loi de puissance deux-tiers (Todorov & Jordan, 1998; Harris & Wolpert, 1998), la loi de Fitts (Harris & Wolpert, 1998; Tanaka et al., 2006; Guigon et al., 2008a), ou encore la structure de la variabilité cinématique dans des tâches de pointage multidirectionnel (Guigon et al., 2008a), ou dans des tâches de type via-points (Todorov & Jordan, 2002). Ces résultats suggèrent que la stéréotypie des mouvements humains est le résultat du fonctionnement optimal du SNC.

Figure 1.4. Comparaison entre des mouvements observés expérimentalement (Uno et al., 1989) et simulés par le minimum-variance model (Harris & Wolpert 1998). Le modèle reproduit bien les trajectoires et les profils de vitesse empiriquement observés lorsque les sujets doivent pointer les cibles dans un ordre prédéfini. Cela suggère que la stéréotypie des mouvements humains émerge de l’optimalité du fonctionnement du système moteur.

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Choix de la fonction de coût Un problème fondamental pour la théorie du contrôle optimal est le choix de la fonction de coût. Il a par exemple été proposé que le coût à minimiser était le jerk 3 (Hogan, 1984b; Flash & Hogan, 1985), l’énergie dépensée (Nelson, 1983), la variance terminale (Harris & Wolpert, 1998), le temps de mouvement (Tanaka et al., 2006), ou bien l’effort, c'est-à-dire la taille du signal de contrôle (Guigon et al., 2007; 2008a). La plupart des modèles sensorimoteurs optimaux offrent une description précise du comportement moteur, mais ces modèles diffèrent dans la justification a priori du critère de performance. Par exemple, le fait que le SNC cherche à minimiser l’imprécision des mouvements ou l’énergie dépensée semble pertinent, du fait de leur utilité pour l’organisme. Par contre, il semble plus difficile de justifier pourquoi le SNC chercherait à minimiser le jerk, par exemple. Il semble aussi important que le coût soit facilement mesurable par le SNC, ce qui n’est pas le cas pour la minimisation du jerk, par exemple. Enfin, il est important de prendre en compte le rôle du contexte dans lequel a lieu le mouvement dans le choix d’une fonction de coût. Par exemple, si l’on demande à un sujet de sauter le plus haut possible, il est clair que le SNC ne va pas chercher à minimiser l’énergie dépensée par les muscles. Dans certaines tâches, la fonction de coût peut donc être complètement contrainte par le plan expérimental (Trommershauser et al., 2005). Liu & Todorov (2007) ont récemment décrit la façon dont le contexte pouvait déterminer la fonction de coût. Ils ont réalisé une expérience où l’importance relative de la précision du mouvement, de l’énergie dépensée, de la stabilité, ou de la vitesse du mouvement était variée. Ils ont montré que le comportement des sujets était bien prédit par un modèle comprenant une fonction de coût composite, contenant tous ces critères, et où l’importance relative de chaque critère pouvait varier en fonction du contexte. Il semble donc qu’une description générale du contrôle moteur par les modèles optimaux requiert l’utilisation de fonctions de coût composites, capables de refléter la flexibilité de la motricité humaine.

3

Le jerk est la dérivée de l’accélération par rapport au temps

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Modélisation en boucle ouverte versus boucle fermée Parmi les modèles de contrôle optimal stochastique, il est possible de distinguer deux grands types de modèles. Les modèles en boucle ouverte (e.g. Harris & Wolpert 1998; Tanaka et al., 2006), et les modèles en boucle fermée (e.g. Todorov & Jordan, 2002; Guigon et al., 2007, 2008a). Le principal point commun entre ces deux types de modèles est qu’ils comprennent un contrôleur stochastique optimal, c’est-à-dire qui prend en compte les statistiques et la nature du bruit (Guigon et al., 2008b). Les modèles en boucle ouverte planifient les séquences de commandes motrices sans prendre en compte les informations sensorielles arrivant au cours du mouvement. Ces modèles décrivent généralement bien le comportement moyen pour de multiples répétitions d’une tâche. Mais ils présentent des limitations sérieuses (Todorov 2004). D’une part, il apparaît extrêmement improbable que le SNC ignore les multiples informations sensorielles disponibles pendant les mouvements. D’autre part, ces modèles ne peuvent prédire les conséquences d’une perturbation au cours du mouvement. Les modèles en boucle fermée sont appelés modèles de contrôle optimal stochastique avec feedback. Avec ce type de modèle, les feedback non sensoriels et sensoriels (voir Desmurget & Grafton, 2000, pour une revue) sont intégrés par le contrôleur, si bien qu’ils permettent une description beaucoup plus générale du comportement moteur. En pratique, ces modèles comprennent un estimateur qui combine de manière optimale les informations provenant des feedbacks sensoriels (feedbacks proprioceptif, visuel, etc., qui sont disponibles avec délai) et les informations provenant de la copie des commandes motrices (grâce à un modèle interne direct qui converti les commandes motrices en variables renseignant sur l’état du système). Le contrôleur corrige ensuite les erreurs uniquement si elles interfèrent avec le but de la tâche (Todorov & Jordan, 2002). La figure 1.5 présente une comparaison des deux types de modèle, et une description plus détaillée sur les différences entre les deux types de modèle peut être trouvée dans la revue de Todorov (2004).

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Figure 1.5. Contrôle optimal en boucle ouverte et en boucle fermée. Adapté, d’après Scott (2004) et Todorov (2004). Dans le cadre d’un modèle en boucle ouverte (a), le contrôleur sélectionne les commandes motrices appropriées pour réaliser la tâche. Ces commandes ne sont pas modifiées en cours de mouvement : le mouvement est donc uniquement le produit de sa planification. Dans le cadre d’un modèle en boucle fermée (b), le contrôleur planifie le mouvement comme dans un modèle en boucle ouverte. Dès que le mouvement est initié, l’estimateur optimal renvoie une information sur l’état du système au contrôleur, afin qu’il modifie les commandes motrices si nécessaire. L’estimateur combine de manière optimale les informations provenant des feedbacks sensoriels et les informations provenant de la copie des commandes motrices. Le bruit affecte à la fois les commandes motrices et les feedbacks sensoriels.

Importance des propriétés statistiques du bruit moteur L’hypothèse sous-jacente aux modèles de contrôle optimal stochastique (e.g. Harris & Wolpert, 1998; Todorov & Jordan, 2002; Tanaka et al., 2006; Guigon et al., 2008a) est que le SNC est capable de structurer les mouvements en tenant compte des statistiques du bruit moteur. Dans les modèles, il est généralement considéré (e.g. Harris & Wolpert, 1998) que le bruit moteur est un bruit blanc (i.e. sa densité spectrale de puissance est la même pour toutes les fréquences) dont la moyenne est zéro, et dont la variance est :

σ2 =ku

p

(Eq. 1.1)

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Où u est le signal de contrôle et les constantes k et p décrivent le profil du SDN. La valeur 2 est généralement attribuée à p. Cela correspond bien à la plupart des observations expérimentales qui ont estimé la valeur de p à partir de la relation entre la force isométrique et sa variabilité (e.g. Jones et al., 2002; Todorov, 2002). Il a été montré récemment que les prédictions des modèles de contrôle optimal stochastique ne correspondent plus aux observations expérimentales lorsque la valeur de p s’éloigne de 2, à la fois dans le cadre d’un modèle en boucle ouverte (Iguchi et al., 2005), et d’un modèle en boucle fermée (Guigon et al., 2008a). Dans la mesure où la valeur de p influence considérablement les prédictions des modèles de contrôle optimal stochastique, il semble important de pouvoir estimer cette valeur si un tel modèle est utilisé pour décrire un comportement dans des conditions particulières (e.g. fatigue, pathologie, etc.).

Faire face au bruit moteur dans le contrôle des mouvements Pour que les buts des mouvements soient atteints malgré les perturbations aléatoires dues au bruit moteur, nous allons voir que le SNC utilise principalement deux stratégies : la modulation de la vitesse des mouvements, et la modulation de l’impédance mécanique des articulations.

Loi de Fitts, bruit moteur, et optimalité La loi de Fitts est la formalisation du conflit entre la vitesse et la difficulté d’un mouvement (i.e. précision requise et/ou distance de la cible). Pour un mouvement de pointage, par exemple, ce conflit décrit le fait qu’une augmentation de la précision requise ou de la distance de la cible induit une diminution de la vitesse moyenne du mouvement (Woodworth, 1899), qui est accompagnée par des changements systématiques dans la cinématique du mouvement (Mottet & Bootsma, 1999). La loi de Fitts (Fitts 1954; Fitts & Peterson, 1964) relie le temps de mouvement (MT, movement time) et un indice de difficulté (ID) défini comme log2(2D/W), où D est la distance du mouvement et W la taille de la cible à pointer :

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⎛ 2D ⎞ MT = a + b ⋅ log 2 ⎜ ⎟ = a + b ⋅ ID ⎝W ⎠

(Eq. 1.2)

Où a et b sont des constantes déterminées expérimentalement. Bien que la loi de Fitts prédise une relation linéaire, il a été montré qu’une relation de type puissance entre MT et ID pouvait dans certains cas mieux décrire les données expérimentales (Schmidt & Lee, 2005). Pour expliquer cette relation, Fitts (1954) a une interprétation informationnelle, inspirée de la théorie de la communication de Shannon et Weaver (1949). Le théorème 17 de cette théorie propose que le débit informatif soit gouverné par une équation du type : ⎛S + N⎞ C = W ⋅ log 2 ⎜ ⎟ ⎝ N ⎠

(Eq. 1.3)

Où C est la capacité de transmission du signal, W est la bande passante, S est la puissance du signal, et N la puissance du bruit dans le canal de communication. D’après ce théorème, le temps de transmission d’un message dans un canal est proportionnel à la quantité d’information et inversement proportionnel au débit du canal. Fitts fait l’analogie entre l’amplitude du mouvement et la puissance du signal, et entre la variabilité terminale du mouvement et le bruit du signal. Par conséquent, l’ID représenterait l’information dans le système moteur, et le temps de mouvement serait proportionnel à cette quantité d’information à traiter. L’interprétation de Fitts est remarquable dans le sens où il envisage dès 1954 le rôle du bruit comme un facteur limitant. Cependant, un manque de cette interprétation est que l’origine du bruit dans le système sensori-moteur n’est pas spécifiée. En particulier, cette interprétation ne permet pas de déterminer si la loi de Fitts serait la conséquence du bruit dans les processus moteurs, dans les processus sensoriels, ou dans les deux processus. Le rôle du bruit moteur dans le conflit entre la vitesse et la difficulté a pour la première fois été envisagé par Schmidt et al. (1979). Ces auteurs se sont appuyés sur le fait que le bruit moteur est signal-dépendant. A partir de ce principe, leur modèle prédit que la variabilité de la position finale d’un mouvement est proportionnelle à son amplitude, et inversement proportionnelle à sa durée. Ils ont confirmé ces

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résultats expérimentalement pour le cas des mouvements très courts (< 200 ms). Bien qu’il soit limité aux mouvements balistiques, l’intérêt de ce modèle a été d’avoir mis en évidence, pour la première fois, le rôle du bruit moteur dans le contrôle de la précision. Meyer et al. (1988) ont été les premiers à intégrer le bruit moteur dans un modèle optimal afin de décrire le conflit entre la vitesse et la difficulté des mouvements. Le modèle postule qu’un mouvement est composé de sous-mouvements. Le premier sous-mouvement est programmé pour atteindre la cible. Si, à cause du bruit moteur, la cible est manquée, un sous-mouvement de correction est réalisé. Le SNC optimiserait le temps de chacun des sous-mouvements afin de minimiser le temps de mouvement total. La contribution de ce modèle n’est pas négligeable. C’est certainement le modèle qui a expliqué le plus d’observations expérimentales relatives au conflit vitesse / difficulté, et en particulier le fait que sa forme puisse être logarithmique (e.g. Fitts, 1954), ou linéaire (e.g. Schmidt et al., 1979). La critique majeure de ce modèle est qu’il est strictement d’ordre cinématique. En effet, le modèle s’intéresse aux trajectoires des mouvements, mais pas aux phénomènes physiologiques qui les sous-tendent (commandes motrices, système musculosqueletique, etc.). Cette dernière critique ne s’applique pas à 3 modèles récents qui ont montré, dans le cadre du contrôle optimal stochastique, que la loi de Fitts pouvait émerger comme la conséquence d’un fonctionnement optimal pour garantir le succès dans la tâche (i.e. l’atteinte de la cible) en présence de SDN (Harris & Wolpert, 1998; Tanaka et al., 2006; Guigon et al., 2008a). Dans ce cadre, le principe général qui conduit à la loi de Fitts est le suivant : puisque le bruit moteur est signal-dépendant, il existe une relation directe entre la variabilité cinématique d’un mouvement et sa vitesse. Lors d’un pointage vers une cible, par exemple, le contrôleur sélectionne le signal de contrôle neural tel que la variabilité terminale soit inférieure ou égale à celle permise par la cible. Quand la taille de la cible est grande, le mouvement peut être produit avec une vitesse importante (avec des commandes motrices importantes et donc un bruit élevé), parce que la tâche tolère une importante variabilité terminale. Quand la cible est petite, par contre, la vitesse du mouvement doit être réduite (au moyen de plus faibles commandes motrices et donc d’un bruit moindre), si bien que la variabilité terminale n’excédera pas la taille de la cible. La précision des mouvements humains pour un MT donné, ou le temps mis pour exécuter un mouvement d’une

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précision donnée, est donc directement déterminée par le niveau de bruit moteur (Harris & Wolpert, 1998). Ainsi, les modèles optimaux qui intègrent le SDN (Harris & Wolpert, 1998; Tanaka et al., 2006; Guigon et al., 2008a) ont pu simuler la loi de Fitts avec une précision remarquable lorsqu’elle est comparée aux données expérimentales (voir figure 1.6). De nombreuses interprétations alternatives de la loi de Fitts ont été proposées (voir pour revue Elliott et al., 2001). Mais, parce que l’interprétation proposée par les modèles de contrôle optimal (1) repose sur des bases biologiquement plausibles, (2) s’intègre dans une description générale de la motricité humaine, et (3) présente de nombreux avantages par rapport à des théories alternatives (voir IV- Discussion générale), elle semble être la plus pertinente.

Figure 1.6. Loi de Fitts et optimalité. D’après Harris & Wolpert (1998). La loi de Fitts caractérise la relation systématique entre le temps d’un mouvement et un indice de difficulté comprenant l’amplitude du mouvement (A) et la taille de la cible (W). Les données expérimentales de Fitts (1954) (a) sont comparées aux données simulées obtenues avec le minimum-variance model (Harris & Wolpert, 1998) (b). Cette figure suggère que la loi de Fitts est la conséquence d’un fonctionnement optimal du système moteur en présence de bruit signal-dépendant dans les commandes motrices.

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Quel modèle de contrôle optimal stochastique pour la loi de Fitts ? A ce jour, trois modèles ont reproduit la loi de Fitts dans le cadre du contrôle optimal : le minimum-variance model (Harris & Wolpert, 1998), le constrained minimum-time model (Tanaka et al., 2006), et le modèle proposé par Guigon et al. (2008a). On peut se poser la question du choix le plus pertinent parmi ces modèles pour décrire la loi de Fitts. Les 2 premiers modèles sont des modèles en boucle ouverte très proches l’un de l’autre (Harris & Wolpert, 1998; Tanaka et al., 2006). Ils diffèrent principalement dans leur fonction de coût. Le minimum-variance model propose que le critère de performance à minimiser soit la variance terminale des mouvements. Ce modèle ne prédit pas directement la durée des mouvements. Pour reproduire la loi de Fitts dans le cadre de ce modèle, un certain nombre de trajectoires sont simulées avec différents MTs, et le MT retenu est le temps le plus faible qui permet de respecter la contrainte de précision. Cela implique soit que le système moteur simule différents MTs avant de réaliser effectivement le mouvement, soit qu’il existe en mémoire une table de correspondance entre les différents temps de mouvement et les différentes contraintes de précision. Les deux possibilités paraissent peu plausibles (Tanaka et al., 2006). Pour contourner ce problème, le constrained minimum-time model (Tanaka et al., 2006) intègre le temps de mouvement dans sa fonction de coût. Le modèle propose que le SNC cherche à minimiser le temps de mouvement en respectant la contrainte de précision imposée par la tâche. Ainsi, ce modèle, s’il donne des résultats strictement identiques à ceux du minimum-variance model, présente principalement 2 avantages. Premièrement, le modèle prédit directement le temps de mouvement. Deuxièmement, sa fonction de coût correspond parfaitement à la contrainte imposée par le plan expérimental dans une tâche de Fitts, où les sujets doivent terminer leurs mouvements dans une cible spécifiée tout en minimisant leur temps de mouvement (Fitts, 1954; Fitts & Peterson, 1964). Enfin, Guigon et al. (2008a) ont été les premiers à reproduire la loi de Fitts dans le cadre d’un modèle de contrôle optimal avec feedback. Ce modèle offre une description générale du comportement moteur en présence de variabilité en intégrant les feedbacks, ce qui constitue un avantage indéniable comparé aux deux autres modèles. Un résultat particulièrement intéressant était que la loi de Fitts ne pouvait être produite par le modèle qu’en (1) présence de bruit moteur signal-

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dépendant, et (2) absence de bruit sensoriel. Cela confirmait donc, dans le cadre du contrôle optimal en boucle fermé, le résultat trouvé dans le cadre du contrôle optimal en boucle ouverte : le SDN est la cause première de la loi de Fitts, et semble donc être un facteur suffisant pour l’expliquer. En conséquence, ce résultat légitime l’usage, pour l’étude de la loi de Fitts, de modèles optimaux en boucle ouverte, certes réductionnistes, mais plus faciles à manipuler techniquement.

Le rôle de la cocontraction Adapter la vitesse des mouvements à la précision requise n’est pas la seule stratégie utilisée par le SNC pour faire face à l’incertitude due au bruit moteur. En effet, il a été montré expérimentalement que les humains ont la capacité de faire face à une augmentation de la précision requise sans modifier la cinématique de leurs mouvements (Gribble et al., 2003; Osu et al., 2004). Dans ce cas, la stratégie utilisée est la modulation de l’impédance mécanique des articulations, l’impédance mécanique étant ici définie comme le ratio de la force appliquée à un membre sur la vitesse résultante. C’est donc une mesure de la façon dont un membre résiste au mouvement lorsqu’il est soumis à une force. L’impédance peut être mesurée expérimentalement en s’intéressant à la nature de la réponse d’un membre à une perturbation connue appliquée par un robot. La stratégie de modulation d’impédance a d’abord été mise en évidence dans des expériences de pointage dans des champs de force inhabituels. Les sujets devaient effectuer des mouvements dirigés dans un environnement dynamique instable créé par une interface robotique. Dans ce cadre, il a été montré que les humains augmentaient l’impédance pour réussir la tâche en présence des perturbations environnementales (e.g. Burdet et al., 2001). De plus, l’impédance peut être ajustée en fonction de la direction et de l’intensité des perturbations, ce qui en fait une stratégie optimale pour assurer la réussite de la tâche tout en minimisant la dépense énergétique (Franklin et al., 2004). Plus récemment, la stratégie de modulation d’impédance a été observée dans des tâches de pointage à temps de mouvement constant (Selen et al., 2006a) ou de poursuite de cible à vitesse constante (Selen et al., 2006b). Dans les deux cas, lorsque la taille de la cible était diminuée, l’impédance augmentait. Il a donc été proposé que la modulation d’impédance soit une stratégie permettant de minimiser les

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conséquences du bruit moteur sur la précision des mouvements (Selen et al., 2006a, 2006b). Pour moduler l’impédance d’un membre, le SNC utilise la cocontraction, qui est définie comme la contraction simultanée de muscles antagonistes autour d’une articulation (Osu & Gomi, 1999). La cocontraction peut être évaluée par des enregistrements électromyographiques (EMG, e.g. Kellis et al., 2003), et permet d’estimer convenablement le niveau d’impédance (Osu & Gomi, 1999). Des résultats d’études s’intéressant à la relation entre cocontraction et précision du mouvement, s’appuyant sur des enregistrements EMG, ont conforté cette idée. Gribble et al. (2003) ont d’abord montré que, dans des mouvements de pointage à temps constant, la cocontraction augmentait avec la précision requise. Dans le même type de tâche, il a été montré que la précision des mouvements pouvait être améliorée lorsqu’il est demandé aux sujets d’augmenter le niveau de cocontraction (Osu et al., 2004). En conclusion, les différents résultats expérimentaux ont clairement montré que la modulation d’impédance est une stratégie efficace pour faire face à la variabilité due au bruit moteur. Cependant, les modulations d’impédance ou de cocontraction n’ont été observées que dans des tâches de pointage à temps contraint. A ce jour, la façon dont cette stratégie co-existe avec la modulation cinématique des mouvements (le conflit vitesse / précision) est inconnue. Il reste donc à déterminer si la modulation d’impédance est une stratégie naturellement utilisée par le SNC, ou si elle apparaît uniquement lorsque les autres stratégies ne peuvent être utilisés (e.g. lors de mouvements à temps contraint).

Fatigue et caractéristiques de la production de force Nous allons voir ici que la fatigue musculaire affecte non seulement le bruit moteur, mais aussi d’autres aspects de la production de force qui ont potentiellement des conséquences importantes pour le contrôle des mouvements.

Définition de la fatigue La question de la définition de la fatigue a été récemment débattue dans 2 revues de la littérature (Barry & Enoka, 2007; Enoka & Duchateau, 2008). Aujourd’hui,

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la fatigue est le plus souvent définie comme une réduction, induite par l’exercice, de la capacité des muscles à produire de la force ou de la puissance, que la tâche puisse être réalisée ou non (Edwards, 1981; Sogaard et al., 2006; Barry & Enoka, 2007; Enoka & Duchateau, 2008). Cette définition implique que la méthode la plus fiable pour évaluer la présence de fatigue est la mesure du niveau de force maximale (Vollestad, 1997). D’après cette définition, la fatigue n’implique pas nécessairement l’arrêt de la tâche du à l’épuisement des muscles. Au contraire, la fatigue s’installe peu après le début d’une tâche motrice soutenue, et augmente progressivement jusqu’à provoquer l’arrêt de la tâche. Cette définition de la fatigue ignore les causes de la fatigue. Toutefois, cette condition est nécessaire pour une définition générale de la fatigue, tant ses causes peuvent être multiples. La fatigue peut en effet être causée par différents mécanismes, de l’accumulation de métabolites au sein du muscle à la génération par le cortex moteur de commandes nerveuses inadéquates (e.g. Enoka & Duchateau, 2008). La figure 1.7 présente les principaux sites susceptibles de causer la fatigue. Pour des revues détaillées des différents mécanismes, voir notamment Gandevia (2001) pour les facteurs spinaux et supra-spinaux, et Allen et al. (1995) pour les aspects musculaires.

Figure 1.7. Différents sites de la fatigue musculaire. Adapté, d’après Bigland-Ritchie (1981).

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Depuis les travaux d’Angelo Mosso au 19ème siècle (voir Giulio et al., 2006, pour une revue historique), de nombreux travaux ont cherché à déterminer si les causes de la fatigue se situaient dans le muscle ou dans le système nerveux. Cette approche a été à l’origine de la distinction entre la fatigue centrale et la fatigue périphérique. Le problème principal créé par cette distinction est que les processus centraux et périphériques s’influencent mutuellement. Par exemple, au cours d’un exercice fatiguant, la fréquence de décharge des motoneurones est diminuée par l’inhibition des afférences III et IV, à cause des changements métaboliques au sein du muscle (e.g. Bigland-Ritchie et al., 1986; Garland et al., 1994; Fischer & Schafer, 2005). Il est clair ici que la fatigue est en partie due à l’influence réciproque de facteurs situés dans le muscle et dans le système nerveux. En conséquence, sans que cela ne remette en cause l’existence de facteurs centraux et périphériques dans le processus de fatigue, il est aujourd’hui souvent considéré que la distinction systématique entre fatigue centrale et périphérique n’est pas nécessairement utile (Nybo & Secher, 2004; Barry & Enoka, 2007).

Conséquences de la fatigue pour la production de force sous-maximale Nous avons vu que la fatigue est définie comme une diminution de la capacité des muscles à produire leur niveau maximal de force (e.g. Enoka & Duchateau, 2008). Cependant, la fatigue n’affecte pas uniquement la force maximale : la production d’une force sous-maximale, bien que toujours possible, est aussi influencée par la fatigue. Ce point est important, car, dans la vie quotidienne, la grande majorité des activités motrices met en jeu des forces sous-maximales. Plus particulièrement, la fatigue affecte 3 aspects de la production d’une force sous-maximale qui ont une influence fonctionnelle majeure : les vitesses de contraction et de relaxation musculaire, la relation entre l’activation musculaire 4 et la force, et la variabilité de la force.

4

L’activation musculaire représente le nombre d’unités motrices activées et leurs fréquences de décharge.

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Ralentissement de la réponse musculaire Tout d’abord, la fatigue provoque un ralentissement de la réponse musculaire. Ce ralentissement comprend une diminution de la vitesse de raccourcissement, et une diminution de la vitesse de relaxation (figure 1.8). Ces observations ont été réalisées aussi bien chez l’animal (e.g. Curtin & Edman, 1994), que chez l’homme (e.g. Jones et al., 2006). La diminution de la vitesse de contraction est principalement due à l’augmentation des concentrations intracellulaires en H+ et en ADP (Allen et al., 1995). Selon les études, la diminution de la vitesse de raccourcissement avec la fatigue est très variable, et peut aller jusqu’à ~70 %. Si cette variabilité peut être expliquée par les différences de protocoles expérimentaux entre les études, Edman & Mattiazzi (1981) ont montré que plus la baisse de force maximale induite par la fatigue est importante, plus la vitesse de contraction diminue. Concernant la baisse de la vitesse de relaxation, elle est généralement plus prononcée. Les résultats publiés sont encore une fois très variables, et semblent aussi dépendants de l’importance de la fatigue. Par exemple, le temps de relaxation peut être doublé lorsque la force maximale d’une fibre de xénope est diminuée de 20 % (Edman & Mattiazzi, 1981). Par contre, il a été montré que, pour une fibre de xénope dont la force maximale est diminuée de 60 %, le temps de relaxation peut être multiplié par 10 (e.g. Allen et al., 1989). Les deux mécanismes principalement impliqués ici sont le détachement du calcium, et celui des ponts actine / myosine (Allen et al., 1995).

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Figure 1.8. Effet de la fatigue sur la vitesse de la réponse musculaire de l’adductor pollicis à une stimulation électrique (80 Hz) non fatigué (ligne continue supérieure), après une série de contractions fatigantes (ligne continue inférieure), et après 360 s de récupération (courbe pointillée, presque superposée à la courbe obtenue pré-fatigue). D’après Jones et al. (2006). Pour une même stimulation électrique, moins de force est obtenue post-fatigue, et celle-ci se développe et se relâche moins vite.

Modification du gain entre activation musculaire et force La fatigue modifie aussi le lien entre le niveau d’activation musculaire et la force produite (figure 1.9). En effet, pour un niveau de force donné, le niveau d’activation (e.g. commandes motrices, EMG) augmente. Pour quantifier ce phénomène, de nombreux travaux se sont intéressés à l’effet de la fatigue sur la relation entre la force isométrique et l’activité EMG (e.g. Edwards & Lippold, 1956; Bigland-Ritchie, 1981; Kirsch & Rymer, 1992). Les résultats de ces travaux montrent que la relation (souvent) linéaire entre ces deux variables est conservée avec la fatigue, mais que sa pente augmente. L’augmentation semble toutefois être dépendante du muscle qui agit et/ou du protocole fatiguant. Par exemple, Edwards & Lippold (1956) rapportent une hausse de la pente de ~63 % pour le soleus (voir figure 1.9), alors que Kirsch & Rymer (1992) ont rapporté une hausse de la pente de ~200 % pour le brachioradialis, et de ~300 % pour le biceps brachii. Il a été montré récemment, par des études utilisant l’imagerie par résonance magnétique, que l’activité de plusieurs aires du cortex moteur est bien corrélée avec l’activité EMG en situation de fatigue (Liu et al., 2003; van Duinen et al., 2007): cela confirme que l’augmentation de l’EMG observée lors de

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la production d’une force donnée en situation de fatigue témoigne d’une augmentation des commandes motrices nécessaires pour produire la force. Il est largement admis que l’augmentation de l’activation musculaire pour produire une force sous-maximale donnée témoigne du recrutement d’un plus grand nombre d’unités motrices et/ou d’une augmentation de leur fréquence de décharge (e.g. Edwards & Lippold, 1956; Fuglevand et al., 1993; Loscher et al., 1996; Carpentier et al., 2001; Hunter et al., 2003; Sogaard et al., 2006). Ces changements sont d’abord nécessaires pour compenser l’insuffisance contractile des fibres musculaires. Cette insuffisance est principalement due à 3 facteurs (Allen et al., 1995). Le premier est l’accumulation d’acide lactique et de phosphates inorganiques à l’intérieur des cellules musculaires (e.g. Edman & Lou, 1990). Le second facteur est la baisse de la sensibilité au calcium des myofibrilles (e.g. Godt & Nosek, 1989). Le troisième facteur est la diminution de la concentration intracellulaire en calcium, due à une diminution du relâchement de calcium par le réticulum sarcoplasmique (Allen et al., 1995). Aussi, l’augmentation d’activation musculaire permet de compenser l’inhibition due aux afférences III et IV (e.g. Bigland-Ritchie et al., 1986; Garland et al., 1994; Fischer & Schafer, 2005). En effet, ces afférences de petits diamètres répondent à l’accumulation de déchets métaboliques relâchés lors de la contraction musculaire en inhibant le pool de motoneurones. Enfin, il se pourrait que l’augmentation de l’activation musculaire permette aussi de compenser la diminution de la décharge des afférences Ia observée lors de contractions fatigantes (Macefield et al., 1991). Ce dernier point reste cependant controversé dans la mesure où certains auteurs ont rapporté une potentialisation du réflexe H (i.e. le recrutement réflexe des motoneurones-α via la stimulation des afférences Ia) au cours d’un exercice fatiguant, ce qui témoignerait d’une augmentation de l’excitabilité du pool de motoneurone avec la fatigue (Loscher et al., 1996).

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Figure 1.9. Effet de la fatigue sur la relation entre l’EMG intégré (ordonnée) et la force pour le soleus pré- (a) et post-fatigue (b). D’après Edwards & Lippold (1956). Avec la fatigue, la relation peut toujours être décrite par un modèle linéaire (r2 = 0.98 dans les deux cas), mais sa pente augmente.

Augmentation de la variabilité de la force Enfin, parallèlement à l’augmentation de l’activation musculaire nécessaire à la production d’une force, la fatigue influence la variabilité de la force produite (figure 1.10). En effet, il a été montré à de nombreuses reprises que la production d’un niveau de force donné par des muscles fatigués est plus variable comparé à des muscles non fatigués. Ce phénomène est observable quand la fatigue s’installe progressivement au cours d’une contraction musculaire prolongée (e.g. Garland et al., 1994; Hunter et al., 2003; Johnson et al., 2004; Mottram et al., 2005), ou lorsque des contractions isométriques plus courtes sont réalisées après un exercice fatiguant (e.g. Furness et al., 1977; Lavender & Nosaka, 2006; Semmler et al., 2007; Dartnall et al., 2008). Par contre, aucune étude ne s’est, à ce jour, intéressée à l’effet de la fatigue sur la variabilité de la force pour différents niveaux de force. Les mécanismes responsables de cette augmentation de la variabilité de la force avec la fatigue ont reçu assez peu d’attention dans la littérature. Plusieurs hypothèses explicatives ont été proposées, impliquant des facteurs principalement centraux, mais peu d’entre elles ont été vérifiées.

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La seule hypothèse explicative de l’augmentation de la variabilité de la force avec la fatigue vérifiée à ce jour concerne le rôle du réflexe d’étirement. Il a été mis en évidence expérimentalement que ce réflexe pouvait expliquer une partie de la variabilité induite par la fatigue. D’abord, il a été montré que la décharge des afférences à gros diamètre (Ia) est à l’origine d’une partie de l’augmentation de la variabilité. En effet, lorsque la décharge des afférences Ia est expérimentalement minimisée (par vibration tendineuse, par exemple), le tremblement physiologique augmente moins avec la fatigue que lors d’une situation contrôle (Cresswell & Loscher, 2000). Aussi, il a été proposé que le réflexe d’étirement soit impliqué dans le tremblement observé avec la fatigue car sa sensibilité augmente dans un milieu acide (Fischer & Schafer, 2005). Cependant, le rôle du réflexe d’étirement ne peut expliquer qu’une partie de l’augmentation de la variabilité de la force avec la fatigue. Une hypothèse alternative a été récemment invalidée concernant le rôle de la synchronisation de la décharge des unités motrices. Parce que la synchronisation des unités motrices, pour un niveau de force donné, augmente la variabilité de la force (e.g Yao et al., 2000), il a été proposé que ce facteur pourrait aussi expliquer l’augmentation de la variabilité de la force observée avec la fatigue (Dartnall et al., 2008; Holtermann et al., 2008). Bien que Dartnall et al. (2008) aient expérimentalement montré une augmentation de la synchronisation des unités motrices du biceps brachii avec la fatigue dans une tâche de maintien de force isométrique, ils n’ont pas trouvé de concomitance entre les changements de synchronisation des unités motrices et les changements dans la variabilité de la force. En conséquence, la synchronisation des unités motrices ne jouerait qu’un rôle mineur dans l’augmentation de la variabilité de la force avec la fatigue. Deux autres hypothèses explicatives ont été proposées, mais n’ont pas été, à ce jour, directement vérifiées. La première hypothèse concerne le rôle de l’augmentation de l’activation musculaire avec la fatigue. A cause de l’évolution parallèle du niveau d’activation musculaire et de la variabilité de la force avec la fatigue, plusieurs travaux ont avancé l’hypothèse que l’augmentation du niveau d’activation influencerait la variabilité de la force (e.g. Cresswell & Loscher, 2000). Cependant, le lien entre ces 2 variables n’a jamais été démontré. Il est pourtant clair que si la commande motrice augmente à cause de la fatigue, la variabilité de la force devrait augmenter. En effet, la variabilité de la fréquence de décharge des motoneurones est proportionnelle au niveau moyen de la fréquence de décharge

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(Clamann, 1969; Matthews, 1996; Powers & Binder, 2000). Enfin, la seconde hypothèse propose que la variabilité de la décharge des motoneurones due à la fatigue proviendrait d’une adaptation des propriétés intrinsèques du motoneurone (Garland et al., 1994; Johnson et al., 2004). Cette hypothèse s’appuie principalement sur le fait que la fréquence de décharge d’un motoneurone devient progressivement plus variable lorsqu’il subit une activation donnée pour une période prolongée (Laouris et al., 1991). Une augmentation de la variabilité des intervalles interimpulsions a d’ailleurs été mise en évidence en concomitance avec l’apparition de la fatigue lors de contractions prolongées (Enoka et al., 1989; Garland et al., 1994; Johnson et al., 2004). Toutefois, ces études n’ont pas permis de déterminer si l’augmentation de la variabilité des intervalles inter-impulsions était due à une adaptation intrinsèque du motoneurone ou à l’augmentation du niveau d’activation musculaire, si bien que les rôles respectifs de ces 2 facteurs restent flous.

Figure 1.10. Effet de la fatigue sur l’activité EMG et sur la variabilité de la force lors d’une flexion isométrique du coude à 20 % des capacités maximales d’un sujet. D’après Semmler et al. (2007). Les données obtenues avant (gauche) et après (droite) un exercice excentrique fatiguant sont présentées. La fatigue induite par l’exercice excentrique augmente l’activation musculaire nécessaire pour produire la force, et augmente la variabilité de la force.

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Fatigue et contrôle des mouvements Nous allons voir ici que, si plusieurs travaux ont montré que la fatigue induisait des réorganisations comportementales dans le contrôle de la motricité, le bruit moteur, malgré son rôle central, n’a que rarement été considéré comme un facteur responsable de ces changements. Nous verrons que, d’une manière générale, l’origine de ces réorganisations est, à ce jour, mal comprise.

Réorganisations comportementales Plusieurs travaux se sont intéressés aux conséquences fonctionnelles de la fatigue, c’est-à-dire à ses répercussions sur la performance motrice. Les différentes études ont par exemple porté sur des tâches de lancer (Forestier & Nougier, 1998), de sciage (Cote et al., 2002), de pointage (Miles et al., 1997; Jaric et al., 1999; Corcos et al., 2002; Bottas et al., 2005; Schmid et al., 2006), d’oscillation du doigt (Heuer et al., 2002), ou encore de saut à pieds joints (Bonnard et al., 1994). Tous ces travaux ont montré que les changements dans les propriétés du système neuromusculaire induits par la fatigue modifiaient généralement les activations musculaires (e.g. patrons EMG), et dans certains cas les trajectoires des mouvements. Les modifications des activations musculaires et de la cinématique ont été qualifiées de stratégies motrices compensatoires (e.g. Bonnard et al., 1994). Elles permettent dans certains cas la conservation du niveau de performance malgré la fatigue (Heuer et al., 2002; Huffenus et al., 2006; Schmid et al., 2006). Heuer et al., (2002) ont par exemple montré que la cinématique de mouvements d’oscillation du doigt pouvait être identique pré- et post-fatigue, grâce à l’ajustement du timing des bouffées EMG. Dans d’autres cas, la performance est altérée, malgré les stratégies motrices compensatoires. Par exemple, la précision du lancer ou du tir peut diminuer à cause de la fatigue (Hoffman et al., 1992; Forestier & Nougier, 1998; Evans et al., 2003), tout comme la vitesse des mouvements (e.g. Corcos et al., 2002). Si des stratégies motrices compensatoires semblent être systématiquement présentes avec la fatigue, peu d’études se sont intéressées spécifiquement à l’origine de ces changements. Plusieurs hypothèses ont été avancées pour expliquer ces changements : la baisse de la force disponible (Corcos et al., 2002), l’inhibition réflexe due à la décharge des afférences III et IV

(Bottas et al., 2005), ou encore la

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perturbation de la capacité à reproduire un effort ou une position articulaire (e.g. Carson et al., 2002; Walsh et al., 2004). Mais aucune de ces hypothèses n’a été testée spécifiquement. Quelles conclusions peut-on tirer de ces différentes études ? D’abord, la fatigue influence clairement le contrôle moteur en induisant des compensations nécessaires pour réaliser la tâche, bien que ces compensations soient parfois insuffisantes pour conserver un niveau de performance donné. Ensuite, les travaux cités précédemment n’ont pu fournir une explication globale des adaptations comportementales à la fatigue. C’est en partie du au fait que les cadres expérimentaux étaient différents entre les études. Mais c’est surtout du au fait que la plupart des études réalisées ne s’inscrivaient pas dans le cadre d’un modèle général du contrôle moteur. Autrement dit, si ces études ont bien décrit les effets de la fatigue sur le comportement moteur, elles ne faisaient pas de prédictions précises basées sur des hypothèses du fonctionnement du système moteur. Tout l’enjeu est donc aujourd’hui de comprendre pourquoi le SNC choisit une stratégie compensatoire donnée, et pourquoi les adaptations mises en place sont parfois insuffisantes pour maintenir une performance donnée, en s’appuyant sur les modèles les plus pertinents du contrôle moteur. Étant donné (1) l’effet de la fatigue sur le bruit moteur, et (2) l’importance du bruit moteur dans la planification et l’exécution des actions motrices, il semble aujourd’hui approprié d’interpréter les effets de la fatigue dans le cadre des modèles issus de la théorie du contrôle optimal.

Fatigue, variabilité de la force et contrôle de la précision Si plusieurs études ont pu mettre en évidence une diminution de la précision des tirs ou des lancers avec la fatigue (Hoffman et al., 1992; Forestier & Nougier, 1998; Evans et al., 2003), aucune étude ne s’est, à notre connaissance, intéressée spécifiquement à l’effet de la fatigue sur le contrôle de la précision, i.e. a manipulé la précision comme une variable indépendante. Par contre, Selen et al. (2007) se sont récemment intéressés à l’effet de la fatigue sur les mécanismes de contrôle de la précision, dans une tâche de poursuite de cible. Etant donné qu’une augmentation d’impédance articulaire améliore la précision motrice (Osu et al., 2004), et que la fatigue augmente la variabilité de la force (e.g. Garland et al., 1994), ils ont testé l’hypothèse selon laquelle l’impédance devrait être augmentée pour maintenir la 38

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performance dans la tâche en présence de fatigue. Contrairement à leur prédiction, Selen et al. (2007) ont observé que l’impédance diminuait avec la fatigue. Par contre, les sujets parvenaient à réaliser la tâche malgré la fatigue en modifiant la cinématique, c’est-à-dire en restant plus proche du centre de la cible comparé à la situation pré-fatigue. Il semble donc que le SNC puisse exploiter toutes les possibilités permises par la tâche pour la réaliser avec succès en présence de fatigue. Etant donné que le maintien d’un niveau d’impédance articulaire élevé est coûteux énergétiquement (Franklin et al., 2004), les résultats de Selen et al. (2007) suggèrent en outre que, en situation de fatigue, le SNC choisi la stratégie de contrôle la plus économique. Toutefois, la diminution d’impédance observée ici pourrait, dans des tâches ne permettant pas de modifications cinématiques, affecter la précision du geste.

Conclusion A travers cette introduction, le rôle primordial du bruit moteur dans le contrôle des mouvements a été souligné ; bruit moteur qui est à la fois structurant puisqu’il est à l’origine de la stéréotypie des mouvements humains, mais aussi source de l’imprécision de nos mouvements. Par conséquent, la compréhension des effets de la fatigue sur le contrôle moteur ne peut se faire qu’en accordant un rôle central à l’étude de l’effet de la fatigue sur le bruit moteur. Nous avons donc réalisé deux études pour mieux comprendre les effets de la fatigue sur le bruit moteur, puisque, nous l’avons vu, ces effets étaient à la fois insuffisamment décrits, et leurs causes étaient encore mal comprises. La première étude avait pour but de caractériser précisément l’effet de la fatigue sur le bruit moteur pour une large gamme de force sous maximales (étude 1). L’objectif de la seconde étude était de comprendre pourquoi le bruit moteur augmente en situation de fatigue (étude 2). Dans un deuxième temps, deux études ont porté directement sur l’effet de la fatigue sur le contrôle des mouvements. Plus particulièrement, nous nous sommes intéressés aux stratégies utilisées par le SNC pour faire face au bruit moteur. Pour l’étude 3, nous avons choisi une tâche où le bruit moteur a une influence centrale sur la formation des trajectoires des mouvements, la tâche de Fitts (Fitts et Peterson 1964). L’objectif était ici double. D’une part, il s’agissait de déterminer dans 39

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quelle mesure l’effet de la fatigue sur le bruit moteur pouvait expliquer l’effet de la fatigue sur la loi de Fitts. D’autre part, il s’agissait d’évaluer dans quelle mesure les effets de la fatigue pouvaient être expliqués par un modèle général de la motricité humaine, et notamment un modèle de contrôle optimal stochastique. Enfin, dans l’étude 4, nous avons conduit une expérimentation où l’effet de la fatigue sur le bruit moteur était contrôlé. L’objectif était ici de déterminer si la fatigue pouvait aussi influencer le contrôle de la précision des mouvements en affectant la cocontraction.

L’objectif de cette thèse était d’identifier et de comprendre les changements induits par la fatigue dans le contrôle de la précision de la motricité humaine.

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Missenard O, Mottet D & Perrey S. (2008). Muscular fatigue increases signaldependent noise during isometric force production. Neurosci Lett 437, 154-157.

L’hypothèse selon laquelle le SNC est capable de structurer nos mouvements en tenant compte des propriétés statistiques du bruit moteur est aujourd’hui considérée comme centrale pour la compréhension du fonctionnement moteur humain. L’étude du contrôle moteur en situation de fatigue passe donc nécessairement par une description détaillée des effets de la fatigue sur le bruit moteur. C’est l’objet de l’étude 1.

Le bruit moteur peut-il être décrit par le même modèle pré- et post-fatigue ? Si oui, quels sont les changements induits par la fatigue dans les paramètres du modèle ?

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Abstract This study was designed to characterize the effect of fatigue on the relationship between muscular force and its variability over a broad range of submaximal forces. Eight participants had to match 4 levels of isometric force from 7 to 53 % of their maximal capabilities. This task was repeated before and after a fatigue protocol that induced a loss of maximal force of ~31 %. We found that, despite an increase in force variability that was proportional to the force level, the linear scaling of force variability with mean force was preserved during fatigue. Because this linear scaling is a prerequisite for optimal sensorimotor control models, our results broaden the explanatory power of these models to the fatigue case, while at the same time offering new routes towards understanding how the central nervous system adapts to fatigue.

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Introduction An inherent feature of human’s motor system is that force production exhibits unavoidable variability. This feature has two critical effects on movement planning and execution. First, variability in the motor system can be considered as noise that limits movement accuracy e.g. (Schmidt et al., 1979; Meyer et al., 1988). Second, variability in the motor system is responsible, at least in part, for the stereotypical structure of human movements. Indeed, recent modelling studies that have applied optimal control theory to sensorimotor control have proposed that the central nervous system (CNS) plans movements in order to minimize the effects of the variability in the force output of muscles (Harris & Wolpert, 1998; Todorov & Jordan, 2002; Todorov, 2004; Tanaka et al., 2006; Bays & Wolpert, 2007; Guigon et al., 2008a). Based on this assumption, these studies were able to reproduce many kinematic invariants observed in motor behaviour, from bell-shaped velocity profiles (e.g. Morasso, 1981) to Fitts’ law (Fitts, 1954). In the aforementioned studies, it is assumed that the noise is proportional to the magnitude of the signal (multiplicative or signal-dependent noise, SDN), that is, the standard deviation (SD) of force linearly scales with the mean force. Hence, SDN can be modelled as follow (Jones et al., 2002):

σ ( F ) = a ⋅ mean( F )b

(Eq. 2.1)

where F is the muscular force, and a and b are constants determining the profile of SDN. The constant a represents the gain of SDN. To represent a perfectly multiplicative noise, a value of 1 is classically assigned for b (Harris & Wolpert, 1998; Todorov & Jordan, 2002; Tanaka et al., 2006; e.g. Guigon et al., 2008a). This implies that the theoretical log-log relationship between the mean and SD of force is linear and has a slope of 1.0. This linear increase of force variability with force has been experimentally verified by Jones et al. (2002), who reported a slope of 1.05 for the force of the extensor pollicis longus muscle obtained in isometric condition. This result is of importance since many predictions of optimal control models do not hold anymore if the noise scaling is not linear, i.e. if the value of the slope of the log-log relationship is not close to 1 (Iguchi et al., 2005; Guigon et al., 2008a).

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Here we raise the question of the effects of muscular fatigue on the relationship between the force and its variability. Addressing this topic is important given (1) the importance of SDN in current models of sensorimotor control and (2) the fact that fatigue is commonly experienced in every day motor behaviour. Fatigue is defined as an exercise induced reduction in the ability of the muscle to produce force or power, whether or not the task can be sustained (Barry & Enoka, 2007). It is well established that fatigue increases the variability of muscular force (e.g. Enoka et al., 1989; Garland et al., 1994; Johnson et al., 2004). However, the precise way fatigue affects the relationship between the mean and SD of force is currently unknown. Of particular interest is the question of whether or not the scaling of SDN is linear during fatigue as well (i.e. the log-log relationship between the mean and SD of force is linear and has a slope of 1.0). If the scaling of SDN is not linear anymore during fatigue, it would suggest that the use of optimality principles to form movement trajectories is inappropriate during fatigue. Moreover, whether or not the gain of SDN is modified during fatigue (i.e. the intercept of the linear log-log relationship between the mean and SD of force is modified) would give information about the quantitative influence of fatigue on movement trajectories, if the statistical properties of SDN are a determinant for movement planning and execution. To our knowledge, no previous studies have investigated the effect of fatigue on force variability for various levels of submaximal force. Therefore, the aim of the present study was to characterize the effect of fatigue on the relationship between the muscular force and its variability over a broad range of submaximal forces. The results would give a general foundation for interpreting experimental kinematics data obtained during fatigue within the framework of optimal sensorimotor control models.

Methods Eight right handed participants (2 females and 6 males) between the ages of 24 and 46 took part in the study. They had to accurately match various force levels (force matching task) before and after a fatigue protocol. Maximal voluntary contraction (MVC) was assessed at the beginning of the experiment, after the fatigue protocol, and at the end of the experiment, in order to evaluate the effect of fatigue on force generation capabilities (see fig. 2.1C). The study procedures complied with 45

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the Helsinki declaration for human experimentation and were approved by the local ethics committee. Fig. 2.1A shows a schematic representation of the experimental setup. Participants sat in a chair during the whole experiment. The chair was positioned in front of a 19 inch screen with the elbow and forearm of their right arm resting on a manipulandum. The elbow was aligned on the vertical axis of rotation of the manipulandum, and the arm was abducted 90°. Participants grasped a vertical handle so that they could exert force in the horizontal plane.

Figure 2.1. A: Experimental setup during the force matching task and the fatigue protocol. B: Example of force data during a force matching trial at 33 % of maximal voluntary contraction. The grey area represents the period retained for force data analysis. C: Experimental protocol. There was no waiting period between the blocks.

Extension and flexion forces were measured with a strain gauge (accuracy ± 0.5 N, FN3030, FGP Sensors, Les Clayes Sous Bois, France) placed in the plane of rotation of the manipulandum. Force signal was sampled at 1000 Hz with an A/D USB DAQ 6009 National Instrument card (National Instruments, Austin, TX, USA), and stored on a computer for later analysis. For the MVC measurement sessions, participants had to alternately perform 3 maximal isometric flexions and 3 maximal isometric extensions. Contraction duration was 5 s, and contractions were separated by 45 s of rest. Maximal torque was computed as the maximal torque value observed during a 500 ms window. We

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retained the MVC value corresponding to the mean of the 3 MVCs performed. A oneway repeated measures ANOVA was used to test for a significant difference in MVC measured at three times during the experiment. The fatigue protocol consisted of the repetition of 20-s isometric contractions. The workload was fixed at 60% of the MVC measured at the beginning of the experiment. Contractions were elbow flexions and extensions performed alternately, separated by periods of 15 s of passive rest. A screen provided participants visual feedback of their elbow force level. Participants had to continue the task until exhaustion, defined as the inability to maintain the workload for 5 s at least. In the force matching task, each participant was asked to exert a flexion force equal to 7, 13, 33 or 53 % MVC. We did not choose higher forces because we wanted to ensure that participants could achieve and maintain these forces in the fatigue condition as well. A visual feedback was given to indicate the force applied by the arm (see fig. 2.1A). The visual feedback scale did not change with the different force levels. Participants had to increase the flexion force to match the target with a cursor indicated on the visual display, and to maintain this force as steadily as possible. Contractions lasted 10 s. After 6 s, visual feedback of the target and cursor was removed, and participants were asked to keep their effort constant. A green LED lighted for the duration of the contraction, indicating when participants had to exert force and relax. Each contraction was repeated 4 times for each force level. The various force levels were presented in a random order, and there was 15 s of rest between each contraction. To avoid any contribution of visuomotor corrections to force variability, we analysed the last 3 s of each contraction only (see the grey area in fig. 2.1B). Even if participants were asked to keep their effort constant, the removal of visual feedback sometimes led to a drift of the force output. Because this drift was susceptible to add a variability that was not the concern of this study, force data were linearly detrended for the 3 s period of analysis. Force data were filtered with a zero-lag second order Butterworth low-pass filter with a 30 Hz cut-off frequency. Force data were expressed as a percentage of MVC. Force variability was measured with the SD of the detrended force data. The mean force of a given trial was calculated from the raw data, regardless of any nonstationary trends. For each variable, we retained the mean of the 4 trials of a given condition.

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In order to investigate the characteristics of the noise (linear scaling and gain), we performed a regression analysis on the relationship between the mean force and its SD for each participant and for the pool of participants. The regression lines were fitted by the least squares method in the two fatigue conditions (pre- and post-) according to the SDN model presented in Eq. 2.1. Prior to the regression analysis, Eq. 2.1 was logarithmically transformed to: ln(σ ( F )) = b ⋅ ln( mean ( F )) + ln( a )

(Eq. 2.2)

Where the slope b is the scaling factor of SDN and the intercept ln(a) is related to the gain of SDN. The data were logarithmically transformed because we wanted to fit the data with a linear model and to obtain a homogeneous variance across the different conditions. Hence the slope and intercept of the relationship were compared with an analysis of covariance (ANCOVA). Finally, we tested for significant differences in the coefficient of determination (r2) of individual regressions before and after fatigue with a one-way repeated measures analysis of variance (ANOVA). Statistical significance was set at α = 0.05.

Results Mean MVC torques recorded pre-fatigue were 65.3 ± 18.1 Nm (flexion) and 40.3 ± 9.5 Nm (extension). The decline in MVC torque after the fatigue protocol was 30.6 ± 4.2 % for the flexor muscles (MVC1 = 68.3 ± 18.1 Nm vs. MVC2 = 46.9 ± 11.8 Nm, F(2,14) = 20.4, P < 0.01) and 30.0 ± 9.3 % for the extensor muscles (MVC1 = 41.4 ± 9.5 Nm vs. MVC2 = 30.6 ± 7.9 Nm, F(2,14) = 19.5, P < 0.01). MVC values recorded during the terminal MVC session were significantly lower than during the pre-fatigue session, in flexors (MVC3 = 44.1 ± 9.7 Nm, F(2,14) = 20.4, P < 0.01) and extensors (MVC3 = 31.9 ± 8.4 Nm, F(2,14) = 19.5, P < 0.01). Furthermore, the last MVC values were not significantly different from the MVC recorded just after the fatigue protocol (in all cases P > 0.05). Fig. 2.2 shows the evolution of the relationship between the mean and SD of force in the two fatigue conditions. The mean and SD of force for the pool of participants were significantly correlated (P < 0.001) both pre- and post-fatigue: when isometric force levels increased, force variability (SD) increased proportionally. 48

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Consequently, SDN was fitted with Eq. 2.2. The one-way repeated measures ANOVA indicated that there was no significant difference of r2 for the individual regressions pre- and post-fatigue (0.96 ± 0.05 vs. 0.94 ± 0.05, F(1,7) = 1.6, P > 0.05).

Figure 2.2. Effects of fatigue on the relationship between mean and standard deviation (SD) of force. Data are plotted on a log-log scale. The mean force and standard deviation of force are presented for each participant at each force level (7, 13, 33, 53 % of maximal voluntary contraction), pre- and post-fatigue. The black and grey lines represent the linear regression lines (Eq. 2.2) for the pool of participants pre- and post-fatigue, respectively. Inset: Same data plotted on a decimal scale. Regression lines represent the power regression model in Eq. 2.1.

The mean slopes of the relationship between the mean and SD of force for the pool of participants were 1.15 (pre-fatigue) and 0.99 (post-fatigue), and the mean values of the intercept were -4.6 and -3.8, respectively. The individual values of the slope ranged from 1.04 to 1.26 (pre-fatigue) and from 0.77 to 1.21 (post-fatigue). The individual values of the intercept ranged from -5.19 to -3.92 (pre-fatigue) and from 4.33 to -2.96 (post-fatigue). The slopes of the regression lines were not significantly different pre- and postfatigue (F(1,60) = 1.9, P > 0.05). This allowed us to statistically compare their intercepts.

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We found that fatigue significantly increased the intercept of the regression lines (F(1,61) = 21.6, P < 0.05).

Discussion Before discussing these results, we have to assess the validity of our experimental protocol. Our fatigue protocol was designed to induce an important loss of maximal available force. MVC decline is a reliable index to determine whether muscular fatigue occurs (Vollestad, 1997). Consequently, the fatigue protocol we chose was successful in producing muscular voluntary fatigue, since we observed a significant decrease in the MVCs for both elbow extensors and flexors. The fatigue we induced was durable because the decrease of maximal available force was still apparent at the end of the experimental protocol, indicating that the recovery processes were negligible during the post-fatigue force matching session. Once verified that our experimental protocol successfully induced fatigue, we can now address the question that was central to the present experiment. Our aim was to characterize the changes in the relationship between the muscular force and its variability during fatigue. We raised this question for two reasons. First, it is has been shown that humans plan and execute movements by taking into account the statistical properties of this relationship (Harris & Wolpert, 1998; Todorov & Jordan, 2002; Guigon et al., 2008a), revealing the importance of this relationship for motor control. Second, this relationship is susceptible to be affected by muscular fatigue, since fatigue has been shown to increase force variability (e.g. Enoka et al., 1989; Garland et al., 1994; Johnson et al., 2004). It has been shown that SDN can be modelled as a linear process, where the SD of force output scales linearly with the average force output (Schmidt et al., 1979; Jones et al., 2002). For instance, Jones et al. (2002) reported a slope of 1.05 (range 0.62 – 1.86) for the log-log relationship between the mean and SD of force of the extensor pollicis longus. This was close to the theoretical value of 1 that corresponds to a perfectly linear scaling. We reported here a slope of 1.15 for the pre-fatigue condition, with individual values ranging from 1.04 to 1.26. This result was coherent with previous experimental observations (Schmidt et al., 1979; Jones et al., 2002), and legitimates the choice of a slope of 1 to describe SDN scaling in modelling studies

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(Harris & Wolpert, 1998; Todorov & Jordan, 2002; Tanaka et al., 2006; Guigon et al., 2008a). We then wondered if SDN could be described by the same model pre- and postfatigue. We found that the coefficient of determination of the individual regressions between mean force and SD of force was unaffected by fatigue. Hence we concluded that the model classically used (Harris & Wolpert, 1998; Todorov & Jordan, 2002; Tanaka et al., 2006; Guigon et al., 2008a) was still appropriate to describe SDN during fatigue. This allowed us to compare the parameters of the model in the two fatigue conditions. There was no statistical difference between the slopes of the regression lines in the two fatigue conditions. Thus we concluded that fatigue did not affect the linear scaling of SDN. During fatigue, we reported a mean slope of 0.99 (range 0.77 – 1.21), indicating that the scaling factor of the noise was also close to the theoretical value of 1 during fatigue. However, fatigue increased the gain of the SDN (pre-fatigue gain: e-4.6 = 0.01; post-fatigue gain: e-3.8 = 0.02), since the intercept of the relationship between the mean and SD of force significantly increased during fatigue (a parallel shift on log-log scale means an increase in the a value in Eq. 2.1): the relationship was the same in the two fatigue conditions but shifted by the amount of noise added by fatigue (see fig. 2.2). This result is consistent with previous report of an increase in force variability with fatigue (e.g. Enoka et al., 1989; Garland et al., 1994; Johnson et al., 2004), and adds the novel finding that the increase in force variability is proportional to the force level. What are the consequences of these results in the framework of optimal control theories? Two points could be made. First, the fact that the slope of the SDN was close to 1 both pre- and post-fatigue indicates that optimal control models’ predictions should also be accurate during fatigue. It has been shown that it would not be the case if the slope was not close to 1 (Iguchi et al., 2005; Guigon et al., 2008a). With a broader view, our result indicates that the use of optimality principles should also be an efficient way for the CNS to form movement trajectories during fatigue. Second, if the CNS takes into account the statistical properties of SDN to plan and execute movements (Harris & Wolpert, 1998; Todorov & Jordan, 2002; Tanaka et al., 2006; Guigon et al., 2008a), then the predictions of optimal control models will necessarily be modified during fatigue. To illustrate this idea, consider a point-topoint movement with a given accuracy requirement. According to the quoted models, the appropriate neural control signal is selected so that movement final

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variability remains within the target tolerance. The selection of the neural control signal is determined by the noise associated with this control signal. We have shown here that, for a given force, the variability of this force was greater during fatigue. Thus, if the same force is produced during fatigue, the probability to miss the target increases: smaller forces have to be produced during fatigue to respect the accuracy constraint of the movement. Consequently, the models should predict slower movements during fatigue. It is also important to note that force variability is not the single factor that is influenced by fatigue. For instance, fatigue reduces muscle shortening velocity and prolongs relaxation (e.g. Allen et al., 1995). To be accurate during fatigue, the predictions of optimal control models should also consider this latter factor. What could be the causes of the increase in force variability during fatigue? Even if the present study was not designed to answer this question, we discuss here three hypotheses that could explain the changes in the mean force vs. force SD relationship during fatigue. First, increased force variability could arise from the variability of the contractile mechanisms of muscle itself, because an important part of the fatigue-induced perturbations is due to metabolites at the muscular fibre level (for a review, see ref. Allen et al., 1995). Second, it is well documented that, during fatigue, a given force level can only be produced with an increased effort (i.e. magnitude of the motor command) compared with a non-fatigued state (BiglandRitchie, 1981; Kirsch & Rymer, 1992). Given the fact that the noise in the motor command is proportional to the mean level of the motor command (e.g. Churchland et al., 2006), if the magnitude of the motor command has to be increased to achieve a given force level during fatigue, then an increase in the variability of this force is expected. Finally, the third hypothesis deals with the variability of motoneurons firing, independently of the magnitude of the motor command. Indeed, it could be that the increase in the motor units inter-spike-interval (ISI) variability observed with fatigue (Enoka et al., 1989; Garland et al., 1994; Johnson et al., 2004) is not due solely to the increase in motor command, but to intrinsic motoneuron adaptation to fatigue. Anyhow, whatever the cause of the increase in ISI variability, these changes will give rise to accentuated motor output fluctuations (Laidlaw et al., 2000; Enoka et al., 2003; Moritz et al., 2005). In particular, it has been shown, with a model of motor unit pool, that an increase in ISI variability leads to an increase in the intercept of the log-log relationship between the force and its variability and does not affect its slope

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(see fig. 6B in ref. Jones et al., 2002). This latter observation is remarkably in line with the experimental findings of the present study. Note however that it remains to be determined how an increased ISI variability interacts with changes in motor unit twitch tension (e.g. a slower muscle relaxation) to produce a change in overall force variability. Our study cannot conclude regarding these mechanisms but these hypotheses could constitute a foundation for future research. To conclude, we provide here novel finding by characterizing the effect of fatigue on the relationship between the muscular force and its variability over a broad range of submaximal forces. This description is fundamental to interpret the evolution of movement trajectories during fatigue within the framework of optimal sensorimotor control models. We found that, despite an increase in force variability that was proportional to the force level, the linear scaling of force variability with force was preserved during fatigue. A nice consequence of this result is that it broadens the explanatory power of optimal sensorimotor control models to the fatigue case, while at the same time offering new routes towards understanding how the CNS adapts to fatigue.

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Missenard O, Mottet D & Perrey S. (2008). Contribution of central drive to force steadiness impairment with fatigue. Submitted.

Nous avons montré dans l’étude 1 que la fatigue musculaire augmente le gain du bruit multiplicatif observé dans la production de force isométrique, mais ne modifie pas la linéarité de la relation entre le niveau de force et la variabilité de la force. L’objectif de l’étude 2 était d’identifier les causes – aujourd’hui mal comprises – de ces changements. Notre étude a été centrée autour de l’hypothèse selon laquelle l’augmentation du niveau d’activation musculaire serait responsable de l’augmentation de la variabilité de la force avec la fatigue.

L’augmentation de l’activation musculaire peut-elle à elle seule expliquer l’augmentation de la variabilité de la force avec la fatigue ? Sinon, où se situent les facteurs alternatifs responsables ?

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Abstract When a given force is produced by a fatigued muscle, an increase in force variability is generally observed besides the increase in central drive needed to achieve the force. We explored the origin of this impairment of force steadiness by manipulating the contribution of the central drive to the force output. Force variability was studied during short isometric contractions (5 – 53 % of maximal capacities) performed before and after a fatigue protocol that reduced maximum force-generating capacity by ~30%. When participants had to achieve the same absolute force level pre- and post-fatigue (experiment 1), force variability increased whatever the force level. In contrast, the central drive to muscles, assessed by electromyographic activity, increased only for moderate forces. When central drive was controlled by asking participants to match the same level of electromyographic activity pre- and post-fatigue (experiment 2), force variability no longer increased with fatigue, except at low force levels. When central drive was suppressed by asking participants to relax while force was evoked by electrical muscle stimulation (experiment 3), force variability was unaffected by fatigue. We concluded that the increase in central drive is the main responsible for the increase in force variability with fatigue at moderate forces. However, other central sources of force fluctuations, independent of the increase in central drive, come to the fore at low forces.

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Introduction Human muscle fatigue can be defined as an exercise-induced reduction in the ability of muscle to produce force (Enoka & Duchateau, 2008). Despite fatigue, the central nervous system (CNS) can maintain a constant force output at the cost of increasing central command intensity by activating a greater number of motoneurons and/or by increasing their discharge rates. This increased drive to motoneurons results in increased electromyographic (EMG) activity (e.g. Edwards & Lippold, 1956; Fuglevand et al., 1993; Loscher et al., 1996; Carpentier et al., 2001; Hunter et al., 2003; Sogaard et al., 2006). Besides changes in descending motor commands to achieve a given force output, it has been reported that the steadiness of isometric force production is altered during fatigue. It has been observed either when fatigue progressively occurs during a prolonged contraction (e.g. Garland et al., 1994; Hunter et al., 2003; Johnson et al., 2004; Mottram et al., 2005), or when shorter duration isometric contractions are performed after a fatiguing exercise (Furness et al., 1977; Lavender & Nosaka, 2006; Semmler et al., 2007; Dartnall et al., 2008; Missenard et al., 2008a). As such, increased force fluctuations during a voluntary contraction will impair the capacity of an individual to achieve a desired force and will cause movement trajectories to deviate from the desired path (Harris & Wolpert, 1998). This issue is important because, more than force, it is often the accuracy of movements that gives rise to successful performance (Woodworth, 1899). Despite often being evoked in the literature, the role of central drive in the increase in force variability with fatigue has never been properly assessed. For a non fatigued muscle, force fluctuations have been widely attributed to central factors (Enoka et al., 2003). Specifically, force fluctuations have been proposed to be due to the interaction of multiple features of motor-units population activity, including discharge rate variability, motor-units synchronization and low-frequency common oscillation (Taylor et al., 2003). In the case of fatigue, by contrast, force variability may increase because of the increase in central drive. Indeed, motoneuronal recording have indicated that the variability of motoneuron firing increases with the mean level, that is, the standard deviation of the interspike intervals (ISI) increases with the mean interval (Clamann, 1969; Matthews, 1996; Powers & Binder, 2000). This variability in ISI is primarily synaptic in origin (Calvin & Stevens, 1968). Such a signal57

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dependent noise in motoneuronal firing implies that the more important a motor command, the more important the magnitude of variability in the motor output (Harris & Wolpert, 1998; Jones et al., 2002). Consequently, any increase in central drive to muscle should imply an increase in force variability. However, the reason why force variability increases with fatigue is still unclear, because specific neural or peripheral mechanisms responsible for the increase in force variability could be confused with the increase in central drive needed to achieve a given force. We conducted a series of experiments in order to determine the contribution of central drive to the increase in force variability observed during fatigue. In three experiments, we studied changes in force variability with fatigue when the central drive was either (1) left free to increase, (2) controlled to stay at similar levels, or (3) suppressed. In the first experiment, to elicit higher excitatory drive after fatigue, we asked participants to match identical levels of force before and after a fatigue protocol. We measured force output and EMG to determine exactly to which extent the increase in force variability during fatigue would parallel the increase in EMG magnitude needed to achieve a given force. In the second experiment, to cancel the effect of fatigue on the intensity of central drive, participants had to match identical levels of EMG activity pre- and post-fatigue. We measured force output and EMG with the prediction that similar EMG level pre- and post-fatigue should result in lower force output, but should cancel the effect of the increase in central drive on force variability during fatigue, hence allowing other physiological effects of fatigue on force variability to become visible. Because it has been shown that the peripheral muscular machinery itself contributes to a fixed amount of the overall force variability (Jones et al., 2002), we conducted a complementary experiment in order to determine if this amount of variability is increased during fatigue. Indeed, an important part of the fatigue-induced perturbations is due to metabolites at the muscular fiber level (for a review, see Allen et al., 1995), and it could be that these biochemical changes also perturb contractile mechanisms in muscle cell and consequently the steadiness of force output (Faisal et al., 2008). In this third experiment, the contribution of central drive to force was suppressed: we studied the variability of the force evoked by electrical muscle stimulation pre- and post-fatigue. In the three experiments, force fluctuations were studied at low to moderate contraction levels, where the precision of force production is likely to be most

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functionally relevant. The general interest of these results is that they will clarify the causes of the increase in force variability with fatigue, and thus offer new routes toward understanding why neuromuscular performance is impaired during fatigue.

Methods The general sketch of the three experiments is presented in figure 3.1E. For the 3 experiments, force fluctuations were studied before and after a fatigue protocol. Maximal voluntary contraction (MVC) was assessed at the beginning of the experiment, immediately after the fatigue protocol, and at the end of the experiment, in order to evaluate the effect of fatigue on force generation capabilities. The study procedures complied with the Helsinki declaration for human experimentation and were approved by the local ethics committee. All participants gave their written informed consent before undertaking the experiments.

Experiment 1: matching the same force levels pre- and post-fatigue This experiment was designed to determine to which extent the increase in force variability during fatigue would parallel the increase in the magnitude of motor command needed to achieve a given force. Eight right-handed participants were included in this experiment (2 females and 6 males, the range of ages was 24 – 46). They had to accurately match the same absolute force levels (force matching task) before and after a fatigue protocol. We estimated the motor command magnitude with surface EMG measurement, in order to compare the expected increase in force variability with the expected increase in motor command magnitude with fatigue.

Experimental setup Figure 3.1A shows a schematic representation of the experimental setup. Participants sat in a chair during the whole experiment. The chair was positioned in front of a 19 inches screen with the elbow and forearm of their right arm resting on a manipulandum. The elbow was aligned on the vertical axis of rotation of the

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manipulandum, and the arm was abducted 90°. Participants grasped a vertical handle so that they could exert force in the horizontal plane.

Figure 3.1. Experimental setup and example of recorded data. A: Experimental setup during experiments 1 and 2, for the force or EMG matching task and the fatigue protocol. B: Experimental setup during experiment 3, for muscle stimulations and the fatigue protocol. C: Example of elbow flexion force and EMG data during a typical force matching trial at 33 % of maximal voluntary contraction (MVC) in experiment 1. The grey area represents the period retained for force data analysis. D: Example of plantar flexion force data evoked by neuromuscular electrical stimulation (NMES), with stimulation intensity set to evoke ~30% MVC (experiment 3). E: General sketch of the 3 experiments.

Extension and flexion forces were measured with a strain gauge linked to the manipulandum. Pairs of Ag/AgCl electrodes (Contrôle Graphique Medical, Brie-

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Comte-Robert, France) were used to record surface EMG of the biceps brachii, the brachioradialis, and the long and lateral heads of triceps all along the experimental protocol. Electrode location was set according to SENIAM recommendations (Hermens et al., 2000). Inter electrode distance was 10 mm. EMG signal was amplified (× 1000) with Biovison amplifiers (Biovison, Wehrheim, Germany). Force and EMG signals was sampled at 1000 Hz with an A/D USB DAQ 6009 National Instrument card (National Instruments, Austin, TX, USA), and stored on a computer for later analysis.

Maximal voluntary contraction and fatigue protocol For the MVC measurement sessions, participants had to perform alternately 3 maximal isometric flexions and 3 maximal isometric extensions. Contraction duration was 5 s, and contractions were separated by 45 s of passive rest. Maximal torque was computed as the maximal torque value observed during a 500 ms window. We retained the MVC value corresponding to the mean of the 3 MVCs performed. The fatigue protocol was designed in order to fatigue both agonist and antagonist muscles around the elbow joint. It consisted of the repetition of 20-s isometric contractions. The workload was fixed at 60% of the MVC measured at the beginning of the experiment. Contractions were elbow flexions and extensions alternately performed, separated by periods of 15 s of passive rest. A screen provided participants visual feedback of their elbow force level. Participants had to continue the task until exhaustion, defined as the inability to maintain the workload for 5 s at least.

Force matching task In the force matching task, each participant was asked to exert a flexion force equal to 7, 13, 33 or 53 % MVC. We did not choose higher forces to ensure that participants could achieve and maintain these forces in the fatigue condition as well. A visual feedback was given to indicate the force applied by the arm (see fig. 3.1A). Participants had to increase the flexion force to match the target with a cursor indicated on the visual display, and to maintain this force as steadily as possible. Contractions lasted 10 s. After 6 s, visual feedback of the target and cursor was removed, and participants were asked to keep their effort constant. A green LED

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lighted for the duration of the contraction, indicating when participants had to exert force and relax. Each contraction was repeated 4 times for each force level. The various force levels were presented in a random order, and there was 15 s of rest between each contraction.

Data analysis To avoid any contribution of visuomotor corrections to force variability, we analysed the last 3 s of each contraction only (see the grey area in fig. 3.1C). Even if participants were asked to keep their effort constant, the removal of visual feedback sometimes led to a drift of the force output. Because this drift was susceptible to add a variability that was not the concern of this study, force data were linearly detrended for the 3 s period of analysis. Force data were filtered with a zero-lag second order Butterworth low-pass filter with a 30 Hz cut-off frequency. Force data were expressed as a percentage of MVC. To compare force variability between participants and conditions, we used the coefficient of variation (CV) of force, defined as the standard deviation (SD) of the detrended force data divided by the mean and multiplied by 100. The mean force of a given trial was computed from the raw data, regardless of any non-stationary trends. For each variable, we retained the mean of the 4 trials of a given condition. Analysis of EMG was restricted to the period of analysis of force variability. EMG signal was full-wave rectified, and filtered with zero lag (second order Butterworth low-pass filter with a cut-off frequency of 6 Hz) to obtain linear envelope. The EMG linear envelope was normalized relatively to the maximal value obtained during MVCs (EMGmax, the mean rectified and filtered EMG recorded during the 500 ms period corresponding to the maximal torque of the highest MVC trial). EMG linear envelope was computed for the two agonist muscles (biceps brachii and brachioradialis). It was also computed for the two antagonists (long and lateral heads of triceps) in order to evaluate coactivation. Since we found no statistical difference between the evolution of biceps brachii and brachioradialis, or between long and lateral heads of triceps, we only present here the mean signal of the two agonists, referred as flexors EMG, and the mean signal of the two antagonists, referred as extensors EMG.

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Experiment 2: matching the same muscle activation levels pre- and postfatigue This experiment was designed to determine to which extent the increase in central drive could account for the increase in force variability with fatigue. Nine right-handed participants were included in this experiment (3 females and 6 males, the range of ages was 20 – 36). They had to accurately match the same levels of muscle activation (EMG matching task) before and after a fatigue protocol. This was done by providing participants a biofeedback on their elbow flexors EMG. With this experimental protocol, we could control the increase in central drive necessary to match a given force during fatigue and thus cancel its effects on force variability. Consequently, forces were expected to be smaller post-fatigue. This was not an obstacle for the study of force variability, since we compared variability across the different experimental conditions with the CV of force, which corresponds to the variability normalized to the force level.

Experimental setup We used the same experimental setup as in experiment 1.

Maximal voluntary contraction and fatigue protocol We used the same MVC measurements procedure and fatigue protocol as in experiment 1. We also use the same procedure for force and EMG recording.

EMG matching task After the first MVC session, participants performed a force matching task that was necessary to determine the EMG corresponding to different force levels. The procedure was identical as the force matching task in experiment 1. Participants performed elbow flexion force equal to 7, 13, 33 or 53 % MVC in a randomized order (4 trials for each force level). The EMG linear envelope was computed for biceps

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brachii and brachioradialis for each trial. The mean values of the 4 trials for each force level were retained as target EMG levels for the subsequent EMG matching task. The EMG matching task was performed after 10 minutes of rest, and repeated a second time after the fatigue protocol. In this task, a biofeedback of the elbow flexor muscles was provided to participants. The biofeedback was the sum of the linear envelope of biceps brachii and brachioradialis EMGs. Real-time linear envelope was obtained by using a point by point Butterworth filter. Providing a feedback that comprised two agonist muscles was intended to suppress any effects of fatigueinduced changes in muscular synergies. Participants were asked to increase the flexion force to match the target level, and to maintain this force as steadily as possible. Participants were not told that the feedback they received corresponded to their muscle activation. They had to match 4 levels of muscle activation corresponding to forces of 7, 13, 33 and 53 % of their pre-fatigue MVC. Each contraction was repeated 4 times for each EMG level. The various EMG levels were presented in a random order, and there was 15 s of rest between each contraction.

Data analysis We studied the variability of the produced force by analyzing the data similarly to experiment 1.

Experiment 3: electrical muscle stimulation pre- and post-fatigue This experiment was designed to determine to which extent the variability in muscle cell contractile mechanisms could account for the increase in force variability with fatigue. Eight participants were included in this experiment (4 females and 4 males, the range of ages was 20 – 29). Here, the variability of the force evoked by the same muscular stimulation was compared pre- and post-fatigue. By using electrical muscle stimulation, we intended to suppress any variability from the central drive to the muscle. Electrical stimulation over human muscle can generate force directly by activation of motor axons beneath the stimulating electrodes and indirectly by ‘reflex’ recruitment of spinal motoneurons (see Collins, 2007 for a review). In the first 64

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case, stimulation is referred to as neuromuscular electrical stimulation (NMES). NMES is typically delivered using narrow stimulus pulses (50 – 400 μs) delivered at relatively low frequencies (less than 40 Hz). The force obtained this way does not exhibit any marked tendency to increase throughout time, and can be attributed to peripheral processes only. In the second case, stimulation is referred to as wide pulse stimulation (WPS) because stimulation pulses are wider (typically 1 ms) and delivered at higher frequencies (typically 100 Hz). In this case, stimulation gives rise to a continuous increase in force that is added to the force of peripheral origin. It has been demonstrated that this extra-force is due to the stimulation of spinal motoneurons via Ia afferent ‘reflex’ circuits (Collins et al., 2001). Our principal aim here was to evaluate how peripheral contractile mechanisms contribute to the increase in force variability with fatigue. Thus we used NMES to study the variability of peripherally generated force before and after a fatigue protocol. We also studied the variability of the force obtained with WPS, in order to determine if the variability of the force evoked by an indirect stimulation of motoneurons (via Ia afferent) could be affected by fatigue. Indeed, it has been suggested that this mechanism could be an integral part of the normal control of human motoneurons output (Collins et al., 2002).

Experimental setup Figure 3.1B shows a schematic representation of the experimental setup. We reproduced an experimental device largely used when studying electrically induced force (e.g. Collins et al., 2001, 2002). Participants sat with the right hip, knee and ankle flexed (~90 deg) and with the right foot strapped to an isometric strain gauge to record force about the ankle joint.

Maximal voluntary contraction and fatigue protocol Plantar flexion MVC was measured following the same procedure as in experiments 1 and 2. The fatigue protocol differed slightly from experiments 1 and 2: it was not necessary here to fatigue antagonist muscles, because participants were asked to completely relax during muscle stimulations. The only difference was that

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the 20-s isometric contractions were only plantar flexions, and thus always involved the same muscular group for producing force. Muscle stimulation NMES and WPS were repeated before and after the fatigue protocol. Electrical stimulation was applied over the triceps surae via two flexible electrodes. The cathode (13-cm-long; 5-cm-wide) was positioned approximately midway across the medial and lateral heads of the gastrocnemius, ~10–15 cm distal to the crease in the popliteal fossa. The anode (10-cm-long; 5-cm-wide) was placed ~10–15 cm below the cathode. Stimulations were delivered from a Grass S88 stimulator connected in series with a Grass SIU5 isolator and a Grass CCU1 constant-current unit (Grass Instruments, AstroMed, West Warwick, RI), that delivered rectangular pulses. For the NMES condition, we used a fixed pulse width of 200 μs and a fixed pulse frequency of 30 Hz. Modulation of force output was achieved by changing stimulation intensity in order to obtain forces of ~5, 10, 20, 30 and 40 % MVC. Contractions lasted 8 s. Each contraction was repeated 3 times for each force level. For the WPS condition, pulse width was 1 ms and pulse frequency was 100 Hz. Although contractions can be produced by stimuli below motor threshold, they are generally more easily evoked by higher stimulus intensities (Collins et al., 2002). Thus stimulation intensity was adjusted so that a brief stimulation evokes ~5 %MVC (Collins et al., 2002). Contractions lasted 30 s, and were repeated 3 times. NMES at each stimulation intensity and WPS were delivered in a random order. There was 25 s of rest between each contraction. Subjects were instructed to remain relaxed during stimulation, and not to interact with it. They received no feedback about their performance during the experiment.

Data analysis For the NMES condition, we studied the variability of the force during the last 3 s of each contraction with the same procedure as in experiments 1 and 2. For the WPS condition, we studied the evolution of the mean force and its force variability throughout the contraction over 3 s periods centered on 8.5, 13.5, 18.5, 23.5 and 28.5 s. The mean force of a given trial was calculated from the raw data, whereas SD of force was calculated from the detrended data.

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Statistics All values are expressed as mean ± inter-participants standard deviation (SD). In the 3 experiments, repeated measures analysis of variance (ANOVA) with LSD post hoc test was used to identify significant differences. When no interactions were found, we considered simple factor effects. Statistical significance was set at α = 0.05.

Results

Maximal voluntary contraction In experiments 1 and 2, pre-fatigue MVCs ranged from 39.6 to 105.6 Nm and 25.4 to 54.9 Nm for elbow flexion and extension, respectively. In experiment 3, pre-fatigue plantar flexion MVCs ranged from 53.1 to 112.0Nm. In the 3 experiments, the fatigue protocols produced a consistent decrease in maximal voluntary force immediately after the protocol (P < 0.001 in each experiment). The mean decreases in MVC were 30.6 ± 4.2 % and 28.0 ± 7.6 % for elbow flexion, 28.0 ± 9.3 % and 21.4 ± 13.7 % for elbow extension in experiments 1 and 2, respectively. In experiment 3, plantar flexion MVC decreased by 29.0 ± 10.4 %. The last MVC values were significantly smaller than the pre-fatigue MVC in the 3 experiments (in all cases P < 0.001). The decrease in MVC in the last session compared to the first were 33.1 ± 5.5 % and 25.4 ± 9.0 % for elbow flexion, 22.1 ± 11.9 % and 20.2 ± 16.1 % for elbow extension in experiments 1 and 2, respectively. In experiment 3, there was a 18.8 ± 9.3 % decrease in plantar flexion MVC for the last MVC compared to the first.

Experiment 1: matching the same force levels pre- and post-fatigue In this experiment, participants were asked to accurately match the same level of absolute force pre- and post-fatigue. An example of data recorded in this experiment is presented in figure 3.1C. Participants were able to achieve and to maintain the

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required force level pre- and post-fatigue since there was no significant fatigue effect (F1, 7 = 2.0, P > 0.05) or fatigue × force level interaction (F3, 21 = 3.0, P > 0.05) for the mean force. The mean and SD of force for the pool of participants were significantly correlated both pre- and post-fatigue (pre-fatigue: r2 = 0.79, P < 0.001; post-fatigue: r2 = 0.77, P < 0.001): when isometric force levels increased, SD of force increased proportionally. The evolution of force variability across the different experimental conditions is presented in figure 3.2. During fatigue, force variability, as assessed by the CV of force, increased significantly whatever the force level. There was a significant fatigue × force level interaction (F3, 21 = 3.1, P < 0.05) which revealed that the increase in force variability was more pronounced at low (7 and 13 % MVC) than at moderate forces (33 and 53 % MVC).

Figure 3.2. Effect of fatigue when participants had to accurately match the same level of absolute force pre- and post-fatigue (experiment 1). Top: Effect of fatigue on force variability, as assessed by the coefficient of variation (CV) of force. Bottom: Effect of fatigue on elbow flexors electromyographic (EMG) activity, which is the mean of biceps brachii and brachioradialis linear envelope. The increase in force variability with fatigue was significant whatever the target force and more pronounced at low force levels. On the contrary, muscle activation needed to achieve the same absolute force increased post-fatigue only for moderate force levels. Data are means ± s.e.m. * denotes significant difference between pre- and post-fatigue for a given force level.

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There was a significant fatigue × force level interaction (F3, 21 = 21.3, P < 0.001) for the evolution of flexors EMG. Post hoc analysis first revealed that higher forces were associated with higher EMG levels. Second, it indicated that the EMG needed to achieve a given force increased post-fatigue, but not for all force levels (figure 3.2): EMG increased at moderate forces (33 and 53 % MVC), but did not at low forces (7 and 13 % MVC). Coactivation, as assessed by extensors EMG, was unaffected by fatigue (F3, 21 = 2.0, P > 0.05).

Experiment 2: matching the same muscle activation levels pre- and postfatigue Here participants were provided a biofeedback on their elbow flexors EMG and had to match the same level of muscular activation pre- and post-fatigue. The evolution of flexors EMG across the experimental conditions is presented in figure 3.3. Flexors EMG increased with force (F3, 24 = 143.8, P < 0.001), but there was no significant fatigue × force level interaction (F3, 24 = 0.6, P > 0.05) and no fatigue effect (F1, 8 = 0.8, P > 0.05). This indicated that the experimental protocol was successful in imposing a similar level of central drive pre- and post-fatigue. Coactivation, as assessed by extensors EMG, was unaffected by fatigue (F3, 24 =0.7, P > 0.05). The absolute force obtained with the same intensity of central drive was lower post-fatigue (significant fatigue × force level interaction, F3, 24 = 50.3, P < 0.001): post hoc analysis indicated that the decrease in force with fatigue was significant at all force levels (figure 3.3). The mean and SD of force for the pool of participants exhibited a similar relation as in experiment 1. The correlation between these two variables was significant, both pre- and post-fatigue (pre-fatigue: r2 = 0.84, P < 0.001; post-fatigue: r2 = 0.73, P < 0.001). There was a significant force level × fatigue interaction for force variability (F3, 24 = 4.8, P < 0.01): CV of force obtained with the same intensity of central drive was higher post-fatigue at low forces (EMG corresponding to 7 and 13 % MVC) but did not increase significantly at moderate forces (EMG corresponding to 33 and 53 % MVC).

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Figure 3.3. Effect of fatigue when participants had to match the same level of muscle activation pre- and post-fatigue (experiment 2). Top: Evidence that participants had similar levels of muscle activation pre- and post-fatigue, as attested by the absence of effect of fatigue on elbow flexors EMG values, at each EMG level. Middle: Effect of fatigue on force output. Bottom: Effect of fatigue on force variability, as assessed by the coefficient of variation (CV) of force. When muscle activation was similar between preand post-fatigue conditions, less force was obtained post-fatigue, and force variability increased with fatigue at low forces only. Data are means ± s.e.m. * denotes significant difference between pre- and post-fatigue for a given force level.

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Experiment 3: electrical muscle stimulation pre- and post-fatigue

NMES Here involuntary contractions were evoked with narrow pulse (200 μs-wide) at relatively low frequency (30Hz) in order to compare force variability pre- and postfatigue when the force is of peripheral origin. Figure 3.4 shows that, with NMES, we were able to evoke forces that were close to the target levels of 5, 10, 20, 30 and 40 % MVC in the pre-fatigue session. However, for the 3 highest force levels, the absolute forces obtained with the same electrical drive were lower post-fatigue (significant fatigue × force level interaction, F4, 28 = 6.0, P < 0.01).

Figure 3.4. The decrease in muscle force production capabilities with fatigue when contraction is evoked by the same electrical drive (experiment 3). Contractions were evoked by neuromuscular electrical stimulation (NMES), and stimulation intensity was varied in order to obtain various force levels. The decrease in force after fatigue attested of the impairment of muscle contractile properties. Data are means ± s.e.m. * denotes significant difference between pre- and post-fatigue for a given force level.

Contrary to our observations in experiments 1 and 2, the scaling of force SD with mean force was not observed. Figure 3.5 shows a comparison of the scaling of force SD with mean force when force is obtained with a voluntary contraction or with NMES. For the NMES-induced contractions, force SD and mean force for the pool of participants were not correlated both pre- and post-fatigue (pre-fatigue: r2 = 0.02, P > 0.05; post-fatigue: r2 = 0.01, P > 0.05). This indicated that force variability stayed at a relatively stable level with the increase in muscle force (mean SD of force was 0.27 ±

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0.09 % MVC): ANOVA attested that force SD was not significantly affected by the mean force level (F4, 28 = 2.2, P > 0.05). Fatigue did not significantly affect the SD of force, whatever the force level (F1, 7 = 1.0, P > 0.05). This indicated that an identical drive in terms of frequency, whatever its intensity, produced a similar force variability whether it was applied on a fatigued muscle or not (figure 3.4C and 3.4D).

Figure 3.5. A comparison of force variability during voluntary contractions and involuntary contractions evoked by neuromuscular electrical stimulation (NMES). A: Typical detrended force data recorded in experiment 2 (the 3 s period retained for analysis is presented), for different levels of muscle activation, pre- (black) and postfatigue (grey). B: Standard deviation (SD) of force plotted as a function of mean force in experiment 2 (mean values are presented). C: Typical detrended force data recorded in experiment 3, for different levels of stimulation intensity, pre- (black) and post-fatigue (grey). D: SD of force plotted as a function of mean force in experiment 3 (mean values are presented). In both cases, force was obtained with the same excitatory drive pre- and post-fatigue. In the voluntary case (panels A and B, experiment 2), force was obtained with the same muscle activation pre- and post-fatigue by providing participants a biofeedback on their elbow flexors EMG. Here force variability scaled significantly with mean force both pre- and post-fatigue. In the involuntary case (panels C and D, experiment 3), force was obtained with the same electrical drive, and stimulation intensity was varied to evoke various force levels. In this case there was no significant correlation between force variability and mean force. Data on B and D panels are means ± s.e.m.

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WPS Here involuntary contractions were evoked with wide pulse (1 ms-wide) at relatively high frequency (100 Hz) in order to compare force variability pre- and postfatigue when the force also comprises a central component besides the peripheral contribution. In 7 out of 8 participants, stimulation produced an additional reflex-like plantar flexion force superimposed on the force arising from stimulation of the motor axons beneath the stimulating electrodes, both pre- and post-fatigue. The only participant that did not exhibit ‘extra’ force was excluded from statistical analysis. Example of force recorded during WPS stimulation is presented in figure 3.6. Typically, force quickly rose to about 5 % MVC, and then progressively increased until the end of the stimulation. In some trials, force persisted a few seconds after the stimulus was turned off, showing sustained involuntary activity. In one participant we evoked force up to ~40 % MVC, but the increase in force throughout the contraction was generally less important. The mean value for the maximal force evoked in the 7 participants was 16.8 ± 11.9 % MVC. There was a significant fatigue × contraction time interaction for the evolution of mean force (F4, 24 = 4.3, P < 0.01), for which post hoc comparisons attested that force increased significantly throughout the contraction, and stabilized from the 3 s period centered on 23.5 s, both pre- and post-fatigue. Moreover, it showed that force was significantly lower at each point in time during fatigue, and that the decrease was more pronounced at the end of the contraction compared with the beginning (figure 3.6). Force SD did not change significantly throughout the contraction: there was no effect of contraction time (F4, 24 = 0.8, P > 0.05). As in the NMES condition, fatigue had no significant effect on force SD (F1, 6 = 1.5, P > 0.05). The force evoked by WPS was less important during fatigue. Force SD stayed relatively constant throughout the contraction and was unaffected by fatigue. Data are means ± s.e.m. * denotes significant difference between pre- and post-fatigue for a given force level.

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Figure 3.6. Wide pulse electrical muscle stimulation (WPS) pre- and post-fatigue. Top: Typical trials for an individual participant. The abrupt force increase a few seconds after the stimulus onset attests the presence of force evoked by ‘reflex’ recruitment of spinal motoneurons besides force evoked directly by activation of motor axons beneath the stimulating electrodes. Middle: Effect of fatigue and contraction time on force evoked by WPS . Bottom: Effect of fatigue and contraction time on the standard deviation (SD) of the force evoked by WPS.

Discussion The main purpose of this study was to explore the origin of the increase in force variability observed during fatigue. In 3 experiments, we manipulated the

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contribution of the central drive to force production. We studied changes in force variability with fatigue when the central drive was either left free to increase (experiment 1), controlled to stay at similar levels (experiment 2), or suppressed (experiment 3). In the first two experiments, we tested the hypothesis that the increase in central drive necessary to achieve a given force during fatigue could be responsible for the increase in force variability. In the third experiment, we considered the possibility that the increase in force variability during fatigue could also arise from the variability in muscle contractile mechanisms.

Methodological considerations

Evidence of muscle fatigue The fatigue protocols were designed to induce an important and durable loss of maximal available force. MVC decline is considered as a reliable index to determine whether muscular fatigue occurs (Vollestad, 1997). Consequently, the fatigue protocols were successful in producing muscular fatigue, since we observed a significant ~30 % decrease in MVCs for either elbow flexors, elbow extensors, or plantar flexors. This similitude in MVC diminution also indicated that fatigue induced in the 3 experiments was comparable, despite changes in the fatigue protocol in experiment 3. In the 3 experiments, the decrease of maximal available force was still important at the end of the experimental protocol. Consequently, the fatigue that we induced was durable, which indicates that the recovery processes were negligible during the post-fatigue experimental sessions.

Use of surface EMG In experiments 1 and 2, we used non-invasive surface EMG in order to asses central drive to muscles, given that the amplitude of surface EMG is related to the net motor unit activity, that is the recruitment and the discharge rates of the active motor units (Farina et al., 2004). Compared to intra-muscular EMG, which is recorded only on a few motor units that are not necessarily representative of the motor unit pool, surface EMG represents the global excitation signal of the whole pool of motor unit. There are recent evidences that brain activity in several motor areas correlates 75

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with surface EMG magnitude, both during simple force modulations and during motor fatigue (Liu et al., 2003; van Duinen et al., 2007). The use of surface EMG is not without limitations. Specifically, cancellation between the opposite phases of motor unit potentials (amplitude cancellation) and motor units synchronization might affect surface EMG amplitude. If motor unit synchrony does not exert significant effects on the force-EMG relation when EMG is normalized relatively to the maximum (Zhou & Rymer, 2004), amplitude cancellation decreases surface EMG amplitude for a given excitatory drive and can be accentuated by a decrease in muscle fiber conduction velocity (MFCV, Keenan et al., 2006). However, the effect of amplitude cancellation on surface EMG amplitude is relatively low when force levels are low to moderate (Farina et al., 2004). Moreover, it has been experimentally verified that MFCV values return to normal after a fatiguing exercise within less than 3 min in young adults (Hara et al., 1998). In our study, this delay was preserved because of the MVC procedures performed immediately after the fatigue protocol, indicating that any variation in EMG post-fatigue could not be attributed to the effect of fatigue-induced changes in MFCV. Thus we are confident that, despite these limitations, surface EMG was, in the conditions of our experiments, a satisfying indicator of the central drive to muscles.

Role of the increase in central drive In experiments 1 and 2, the relationship between the increase in central drive and the increase in force variability during fatigue was investigated. We found consistent results between the two experiments, with a difference between low and moderate forces in both cases. At moderate forces, we observed that EMG increased in order to achieve a given force level during fatigue. When fatigue progressively occurs during a prolonged contraction or when shorter duration isometric contractions are performed after a fatiguing exercise, an increase in central drive has been repeatedly reported for more than half a century (e.g. Edwards & Lippold, 1956; Fuglevand et al., 1993; Loscher et al., 1996; e.g. Carpentier et al., 2001; Hunter et al., 2003; Sogaard et al., 2006). This increase in EMG amplitude indicates that greater numbers of motoneurons are activated and/or that their discharge rates are increased. This increase in central drive aims at compensating the contractile failure of muscle fibers due to changes in 76

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metabolites (e.g. H+ ions), reduced myofibrillar Ca2+ sensitivity and changes in sarcoplasmic reticulum Ca2+ release (for review see Allen et al., 1995), as well as the inhibitory input to motoneuron pool from group III and IV afferents (Duchateau & Hainaut, 1993). The increase in EMG we reported here at moderate forces was concomitant with an increase in force variability (figure 3.2). However, when the increase in central drive was controlled by imposing participants to match the same EMG magnitude pre- and post-fatigue, the relative force variability associated with a given EMG level was similar pre- and post-fatigue (figure 3.3). This result clearly indicated that the increase in central drive was the critical factor responsible for the increase in force variability during fatigue at moderate forces. The responsibility of the central drive in the increase in force variability probably arises from the fact that noise in motor commands is signal-dependent, that is, noise whose standard deviation increases proportionally with signal magnitude. Indeed, it has been empirically observed that the variability of motoneuronal firing increases with the mean level (Clamann, 1969; Matthews, 1996; Powers & Binder, 2000). Moreover, when the central drive to motoneurons is increased as a muscular contraction is prolonged, a parallel increase in ISI variability of motoneurons has been reported (Enoka et al., 1989; Garland et al., 1994; Johnson et al., 2004). Finally, when the central drive to motoneurons is increased, force variability could be further enhanced by an increase in the gain of Ia afferent reflex loop (Cresswell & Loscher, 2000). Consequently, signal-dependent noise appears to be the most likely candidate to explain the responsibility of the increase in central drive in the increase in force variability during fatigue, at least at moderate forces. At low forces, results were different, but still consistent among experiments 1 and 2. First, in experiment 1, EMG did not increase significantly at low forces in the post-fatigue condition (figure 3.2). This result was not surprising. Indeed, fatigue increases the slope of the force-EMG relationship, which means that the increase in EMG becomes more evident as higher forces are produced (e.g. Edwards & Lippold, 1956; Bigland-Ritchie, 1981; Kirsch & Rymer, 1992). The evolution of the relation between EMG and force in experiment 1 (see figure 3.2) is consistent with the aforementioned reports. Although we did not observe any increase in EMG at low forces in experiment 1, force variability was higher post-fatigue, and exhibited a more pronounced increase

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compared to moderate forces. The latter result was consistent with a recent report, which showed that fatigue had the greatest influence on force fluctuations at low forces (Semmler et al., 2007). In experiment 2, force variability was more important post-fatigue despite the lack of increase in central drive, which was experimentally controlled (figure 3.3). Taken together, these results of experiments 1 and 2 indicate that, at low forces, the increase in force variability observed during fatigue can occur independently of any increase in central drive. It demonstrates that other factors, that are either specific to low forces or that show up at low forces only, are implicated in the increase in force variability.

Role of muscle contractile properties For the electrical stimulation experiment, we chose to study plantar flexion rather than elbow flexion for two reasons. First, it was technically more complicated to evoke moderate force levels by peripheral muscle stimulation, mainly because the brachialis muscle was too profound to be stimulated. Second, we chose to reproduce a setup that has been repeatedly shown to be well-adapted to study forces evoked by muscle stimulation (e.g. Collins et al., 2001, 2002). Even if we did not reproduce experiment 1 for plantar flexion, there is no doubt that force variability also increases with fatigue for plantar flexion, as it has been previously shown by others (e.g. Loscher et al., 1996; Cresswell & Loscher, 2000). We also know that force variability is correlated with mean force during voluntary plantar flexion as during elbow flexion (Yoshitake et al., 2004). This feature is a natural by-product of the organization of motoneurons and muscle fibers, and thus is present whatever the muscle acting (Jones et al., 2002).

NMES Muscle stimulation provides an interesting tool for studying force variability, because it allows controlling irregularities in the excitatory drive to muscle (Merletti et al., 1990). When stimulating with NMES parameters, that is, relatively low frequency and pulse width, force output is due to direct stimulation of the alpha motor axons beneath the electrodes (Collins, 2007). Thus the characteristics of the evoked force and its variability reflect peripheral processes only. 78

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It has been shown that the peripheral muscular machinery itself contributes to a fixed amount of the overall force variability. Indeed, when force is obtained via NMES, force variability remains relatively constant over a wide range of mean force. Jones et al. (2002) demonstrated that this constancy of variability over various mean forces was due to the fact that many features of the evoked contraction differ from a voluntary contraction: all active motor units fire synchronously, further increase in force output is achieved by recruitment alone and not by increasing motoneuron discharge rate, and recruitment order is generally random (see Gregory & Bickel, 2005, for review). Furthermore, when voluntary and NMES-induced contractions are combined, a linear scaling of force variability with mean force is observed, but the relationship between the mean and SD shifts by the amount of noise added by NMES (Jones et al., 2002). In experiment 3, we found that, when force was generated by NMES, no scaling between force variability and mean force was observed, neither pre- nor post-fatigue, as assessed by the lack of correlation between these two variables (figure 3.5). This result was consistent with the idea that the peripheral contractile machinery generates a fixed amount of noise whatever the force level. One point to note is that the fixed amount of variability generated by NMES was probably higher than the peripheral noise actually is, because of the high level of motor unit synchronization induced by electrical stimulation (Yao et al., 2000). Because an important part of the fatigue-induced perturbations is due to metabolites at the muscular fiber level (Allen et al., 1995), it could be that the peripheral amount of variability is increased during fatigue. If fatigue increases the variability of muscle contractile mechanisms, we would expect an increase in the fixed amount of noise generated by NMES. It was not observed experimentally: even though the mean force obtained with the same electrical drive was lower during fatigue, force SD stayed within similar levels pre- and post-fatigue (figure 3.5). This finding showed that, in spite of a significant impairment of muscle contractile force, the variability of the muscle fiber twitch was unchanged. This indicated that peripheral factors were unlikely to contribute to the increase in force variability with fatigue.

WPS

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Muscle stimulation also allows evoking force by ‘reflex’ recruitment of spinal motoneurons, when wide pulse and high frequencies are used (Collins, 2007). Since this mechanism could be an integral part of the normal control of human motoneurons output (Collins et al., 2002), we investigated in complement if the variability in the force produced by WPS would be increased by fatigue. Furthermore, WPS was an interesting means to study the characteristics of forces that involve spinal and peripheral components but not the descending cortical command, in order to determine if the increase in force variability during fatigue could be partly due to changes in intrinsic properties of motoneurons and/or Ia afferents. With WPS, force profiles were similar to what has been previously reported (e.g. Collins et al., 2001, 2002; Collins, 2007), that is continuously increasing extra-force beginning after a few seconds of stimulation. Extra-force could achieve up to ~40% MVC and we sometimes observed involuntary force persistence after the stimulus was turned off. As with NMES, the mean force obtained with the same electrical drive was lower during fatigue. This attested of the contractile impairment induced by fatigue. Yet the typical force profiles of WPS were equivalently observed pre- and post-fatigue (figure 3.6). The variability of the force obtained by WPS did not exhibit a linear scaling with mean force, neither pre- nor post-fatigue (figure 3.6). This was revealed by the fact that the increase in force throughout the contractions was not paralleled by any increase in force variability. As with NMES, this result is consistent with the idea that the scaling of force variability with mean force is the consequence of the natural functioning of the motor unit pool (Jones et al., 2002). Fatigue did not increase force variability with WPS either. The principal consequence of this result is that, if the ‘reflex’ recruitment of spinal motoneurons is an integral part of the normal control of human force output, this mechanism is probably not responsible for the increase in force variability with fatigue. This result also allows drawing conclusions concerning the possibility of changes in intrinsic properties of motoneurons and/or Ia afferents during fatigue. For instance the prolonged activation of motoneurons with sustained extracellular current results in a progressive increase in discharge variability (Laouris et al., 1991), which implicates intrinsic motoneuron adaptation. This mechanism has been hypothesized to explain a part of the fatigue-induced increase in discharge variability besides fatigue-related changes in synaptic input to the motoneurons pool (Garland et al., 1994; Johnson et

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al., 2004). With such an adaptation, the motoneuron would have a more variable firing in response to a given input, and, as a consequence, this would have increased the variability of the force evoked with WPS. As this was not the case in the experiment, we concluded that changes in intrinsic motoneuron and/or Ia afferent properties were unlikely to contribute to force variability during fatigue.

Other factors involved in the increase in force variability with fatigue We have shown that other factors than the increase in central drive contribute to increase force variability during fatigue, especially at low forces. Even though a direct comparison between results obtained with different muscular groups (Experiment 3 vs. 1 and 2) presents limitations, we infer that peripheral factors do not play a significant role in this increase in force variability observed at low forces. Therefore, we will discuss here the potential contribution of factors implying motor units or motor unit population. An important physiological factor that regulates the mechanical output of a muscle is the correlated activity of motor units, i.e. motor unit synchronization and/or motor unit coherence. This factor could contribute to increase force variability with fatigue. Indeed, the correlated activity of motor units decreases the steadiness of muscular force in simulated contractions (e.g. Yao et al., 2000), and it has been experimentally shown that this factor increases after a fatiguing exercise (Dartnall et al., 2008). However, Dartnall et al (2008) showed that the increased correlated behavior of biceps brachii motor units after fatigue was not concomitant with changes in force fluctuations. Consequently, correlated motor unit activity may play here only a minor role in the impaired neuromuscular performance during fatigue. Motor unit activity is also influenced by afferent activity coming from various sensory influences. If increased excitatory and/or inhibitory afferent drive to the motoneuron reinforces or counteracts the cortical descending drive, it is likely that motoneuron discharge will be more variable (Stein et al., 2005). It is clear that such a mechanism can occur independently of any increase in central drive. We have discussed earlier that Ia afferent may contribute to increase force variability when the central drive to motoneurons is increased, because in this case the reflex gain is increased (Cresswell & Loscher, 2000). On the other hand, when the central drive to motoneuron is not increased, there is no reason why Ia afferents

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excitatory activity would be increased (see e.g. Macefield et al., 1991), and thus it is likely that Ia afferents do not play any role in this case. An alternative possibility could be that the increase in force variability is mediated by the increase in stretch reflex sensitivity due to acidic environment during fatigue (Fischer & Schafer, 2005). Contrary to Ia afferents, the inhibitory input to motoneuron pool from group III and IV afferents increases during fatigue, because of metabolites accumulation at muscle level (Bigland-Ritchie et al., 1986; Duchateau & Hainaut, 1993; Fischer & Schafer, 2005). This increase in inhibitory input, by acting against the central drive, likely causes an increase in random fluctuations of the motor neuron membrane potential (Stein et al., 2005). We can hypothesize that this factor will have more influence on force fluctuation at low forces. Indeed, it is likely that, during fatigue, the inhibitory input from III and IV afferents increases by a relatively constant amount whatever the muscle force, because these afferent activities are mainly dependent on the metabolic state of the muscle. Consequently, group III and IV afferents should generate a relatively fixed amount of variability in motoneuron firing and in muscle force. The relative influence of this variability on motor output will therefore be maximized when the difference between this amount of variability and the target force is the smallest, i.e. at low forces. Overall, inhibitory influence from group III and IV afferents appears as a plausible mechanism to explain the increase in force variability that is not due to the increase in central drive at low forces.

Conclusion By manipulating central drive to muscles, we have provided evidence that the increase in central drive to muscle is the main responsible for the increase in force variability during fatigue at moderate forces. In addition, our results revealed the existence of alternative mechanisms that showed up at low forces. We also demonstrated that the peripheral contractile machinery is not the cause of the increased force variability. Consequently, while muscle by itself is mainly responsible for the lower force during fatigue, it seems that the causes of the increased fluctuations of force output are only of central origin. Our results suggest that a better understanding of how and why fatigue impairs force control would need experiments focused on neural mechanisms driving motor behavior.

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Missenard O, Mottet D & Perrey S. (2008). Optimal adaptation of motor behavior to preserve task success in the presence of muscle fatigue. Submitted.

Pour l’étude 3, nous nous sommes intéressés aux effets de la fatigue sur le contrôle des mouvements. Étant donné que la fatigue affecte le bruit moteur (études 1 et 2), nous avons choisi une tâche où le bruit moteur a une influence centrale sur la formation des trajectoires des mouvements, la tâche de Fitts (Fitts et Peterson 1964).

La loi de Fitts est-elle conservée en situation de fatigue ? Si oui, comment évolue-telle ? Dans quelle mesure l’effet de la fatigue sur le bruit moteur peut-il expliquer les changements observés dans la loi de Fitts ? La loi de Fitts reflète-t-elle toujours une stratégie optimale pour effectuer les actions motrices avec succès en situation de fatigue ?

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Abstract When humans are asked to aim at a target as fast and as accurately as they can, they systematically choose a compromise between speed and accuracy that has been formalized as Fitts’ law. It has been demonstrated that Fitts’ law is the result of an optimal strategy to achieve task success in the presence of signal-dependant noise in motor commands. We designed a study to determine how this optimal behavior is adapted to preserve task success in the presence of fatigue-induced changes in the neuromuscular system. We first characterized the effect of fatigue on Fitts’ law in an experiment where participants had to perform fast but accurate elbow flexions and extensions aimed at targets of different sizes, before and after a fatiguing exercise that produced a ~30 % drop in maximal voluntary force. Fatigue induced an upward shift of Fitts’ law, and did not change muscular activations. We then used an optimal control model to determine how fatigue-induced changes in variables such as of noise in motor commands, muscle contraction and relaxation speeds, and the gain between neural activation and muscle force may contribute to changes in Fitts’ law and in muscle activations with fatigue. We found that the evolution of Fitts’ law with fatigue could be accounted for by a model that applied optimality principles to a neuromuscular plant which presented typical fatigue signatures. It suggests that humans are capable to plan optimal movements that take into account acute changes in the neuromuscular system to preserve task success.

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Introduction A noteworthy feature of human movements is that they exhibit considerable trial-by-trial variability. This variability has been largely attributed to noise that corrupts motor commands (van Beers et al., 2004). In the presence of noise, achieving action with success is a continuous challenge for the central nervous system (CNS), even for the simplest every day motor behavior. In recent years, optimal control theory has provided a unifying framework to explain how the CNS can produce successful movements (i.e. movements that achieve task goal) in the presence of noise in motor commands (Harris & Wolpert, 1998; Todorov & Jordan, 2002; Tanaka et al., 2006; Liu & Todorov, 2007; Guigon et al., 2008a). This theory states that the nervous system acts as a stochastically optimal controller, which plans movements taking the statistics of noise into account (see Todorov, 2004 for reviews; see Bays & Wolpert, 2007). Optimal control theory unifies many experimental observations that were previously described in isolation without any common theoretical foundation, which is the hallmark of a good theory (Stein et al., 2005). A remarkable illustration of the fact that humans move with optimality in the presence of biological noise is the speed-accuracy trade-off observed in goal directed movements. When humans are asked to aim at a target as fast and as accurately as they can, they systematically choose a compromise between speed and accuracy in order to satisfy task requirements (Woodworth, 1899). Qualitatively, this speed-accuracy trade-off implies that any increase in relative precision requirements leads to a systematic drop in average speed (Woodworth, 1899), accompanied by systematic changes in movement kinematics (Mottet & Bootsma, 1999). Quantitatively, when aiming at a target of width W located at a distance D, movement time (MT) increases as a function of an index of difficulty (ID) defined as log2(2D/W). This relation has been formalized as Fitts’ law (Fitts, 1954). Optimal control modeling studies have demonstrated that Fitts’ law emerges from the presence of signal dependent noise (SDN) in motor commands, that is, noise whose variance increases proportionally with signal magnitude (Harris & Wolpert, 1998; Tanaka et al., 2006; Guigon et al., 2008a). The central idea is that movements are selected to minimize the negative consequences of SDN. When pointing at a target, for instance, the appropriate neural control signal is selected so that movement final variability remains within the target tolerance. When target 87

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width is large, movement can be produced with a high speed (i.e. with large motor commands and large noise), because the task tolerate a large endpoint variability. When target width is small, movement speed has to be reduced (i.e. with smaller motor commands and small noise), so that endpoint variability remains within the target tolerance. In other words, the accuracy of human movements (Harris & Wolpert, 1998), or equivalently the time needed to produce a movement with a given accuracy (Tanaka et al., 2006), is directly determined by the magnitude of noise. Therefore, Fitts’ law emerges as the consequence of an optimal strategy to achieve task success in the presence of SDN. Besides coping with biological noise, a challenging yet fundamental problem for the CNS is to adapt motor planning to short time-scale changes in the properties of the neuromuscular system. Such a situation is commonly experienced as a consequence of muscle fatigue. Indeed, fatigue, which is defined as an exerciseinduced reduction in the ability of muscle to produce force or power (Enoka & Duchateau, 2008), deeply affects three aspects of the production of muscular force. First, fatigue increases force variability for a given force level (Furness et al., 1977; Lavender & Nosaka, 2006; Semmler et al., 2007; Dartnall et al., 2008; Missenard et al., 2008a). Second, fatigue reduces muscle shortening velocity and prolongs relaxation (Edman & Mattiazzi, 1981; Allen et al., 1995; Jones et al., 2006). Third, fatigue changes the relation between muscle activation and force production: during fatigue, the slope of force – EMG relationship increases (e.g. Edwards & Lippold, 1956; e.g. Bigland-Ritchie, 1981; Kirsch & Rymer, 1992), indicating that an increase in motor commands is needed to achieve a given force during fatigue. These three factors affect the execution of a motor command and, consequently should influence the strategy used by the CNS to achieve task goals. We studied here the effect of muscular fatigue on Fitts’ law. By using muscle fatigue as an intervention, our aim was to determine how optimal behavior is adapted to preserve task success in the presence of changes in the neuromuscular system. We first characterized the effect of fatigue on Fitts’ law in an experiment where participants were asked to perform fast but accurate elbow flexions and extensions aimed at targets of different sizes, before and after a fatiguing exercise. Then, since many of the variables of interest were not directly available for manipulation in human experiments, we ran numerical simulations using an optimal control model (the constrained minimum-time model, Tanaka et al., 2006) to

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determine how fatigue-induced changes in variables such as of noise in motor commands, muscle contraction and relaxation speeds, and the gain between neural activation and muscle force may contribute to the observed changes in Fitts’ law and in muscle activations with fatigue. By combining experiment and simulations, we wanted to verify if the evolution of Fitts’ law with fatigue could be accounted for by a model that apply the same optimality principles to a neuromuscular plant which presents typical fatigue signatures.

Methods

Experiment Participants had to perform fast elbow flexions and extensions aimed at a target, before and after a fatigue protocol consisting in intermittent isometric contractions. Maximal voluntary contraction (MVC) was assessed at 3 different times of the experiment to evaluate the effect of fatigue on force generation capabilities.

Participants Twelve participants (4 females and 8 males) between the ages of 20 and 29 participated in the study. All participants were right-handed with normal or corrected to normal vision and reported no history of neurological or musculoskeletal disorder. All were fit physical education students. All participants gave informed written consent prior to participating in the study. The study procedures complied with the Helsinki declaration for human experimentation and were approved by the local ethics committee.

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Figure 4.1. Methods. A: Experimental setup during the fatigue protocol and maximal voluntary contractions (MVC). The manipulandum was fixed so that elbow angle was 90°. The manipulandum was connected to a strain gauge, allowing the projection of visual feedback of the actual force on the screen (expressed as % MVC). During MVCs, no visual feedback of force was provided to participants. B: Experimental setup during the pointing movement sessions. The manipulandum was free to rotate in the horizontal plan. The manipulandum was connected to a potentiometer to record joint angle. Participants saw a laser representing the actual elbow position on the screen. C: Example of data recorded during a pointing movement in extension. Grey area on position graph represents the target width. Elbow position was low-pass filtered at 6 Hz. Velocity and acceleration profiles were obtained by successive differentiations. EMG of two agonists (triceps long head and triceps lateral head) and antagonists (biceps brachii and brachioradialis) was rectified, and filtered at 6 Hz (grey lines superimposed over rectified EMG). D: Experimental protocol.

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Apparatus Figure 4.1 shows a schematic representation of the experimental setup. Participants sat in front of a 2 × 3 m screen during the whole experiment. The elbow and forearm of their right arm rested on a manipulandum that consisted of a light and almost frictionless aluminum bar. This bar was free to rotate in the horizontal plane. The elbow was aligned on the vertical axis of rotation of the manipulandum, and the arm was abducted 90°. Participants grasped a vertical handle so that they could move the manipulandum in the horizontal plane. When flexing or extending their elbow, participants saw a laser dot moving on the screen, indicating the actual position of the joint. Large straps were used to prevent participants from using their shoulder when performing movements or isometric contractions, and to ensure that movements and contractions were strictly performed with one degree of freedom. During the MVC measurements and the fatigue protocol, the manipulandum was locked at 90°. Extension and flexion forces were recorded with a FN3030 strain gauge (accuracy ± 0.5 N, FGP Sensors, Les Clayes Sous Bois, France) placed in the plane of rotation of the manipulandum. During movements, joint angle was measured by a potentiometer fixed on the axis of rotation of the manipulandum, with 180° corresponding to full elbow extension. Pairs of Ag/AgCl electrodes (Contrôle Graphique Medical, Brie-Comte-Robert, France) were used to record surface EMG of the biceps brachii, the brachioradialis, and the long and lateral heads of triceps all along the experimental protocol. Electrode location was set according to SENIAM recommendations (Hermens et al., 2000). Inter electrode distance was 10 mm. EMG signal was amplified (× 1000 for the MVC measurement and × 5000 for the pointing movements) with Biovison amplifiers (Biovison, Wehrheim, Germany). All the recorded analogical signals were digitalized with an A/D USB DAQ 6009 National Instrument card (National Instruments, Austin, TX, USA), and stored on a computer for later analysis. Sample rate was 1000 Hz for all the sensors.

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Experimental task Familiarization session All participants came to the laboratory one day before the experimentation for a familiarization session. First, they were taught how to perform MVCs. Then, they performed 200 pointing movements to targets of varied widths. The goal of this extensive practice was to get stable levels of within-participants kinematic variability and cocontraction, since these variables have been shown to decrease during the early stages of learning (e.g. Moore & Marteniuk, 1986).

Pointing movements For the pointing movements’ sessions, the manipulandum was free to rotate in the horizontal plane. On the screen, participants could see a vertical line which corresponded to the starting position, the target zone they had to point at, and the laser dot representing the elbow position. For each trial, participants were asked to bring the laser dot in the starting position (65° for extension or 115° for flexion). Once the laser dot has been steadily aligned with the starting position for 1 s, a visual signal indicated that participants were free to initiate their movement. They had to bring the laser dot into the target area, as fast as possible, but without overshooting the target. If an overshoot occurred, the trial was excluded and repeated at the end of the current session. One session consisted in 30 elbow extensions and 30 elbow flexions performed alternately. Three target widths were randomly presented: 8°, 4° and 1°, corresponding to IDs of 3.64, 4.64, and 6.64, respectively. Movement amplitude was 50°. This session was repeated before and after the fatigue protocol. See Figure 4.1B for a schematic representation of the experimental setup during pointing movement sessions.

MVC measurement The manipulandum was fixed so that the elbow angle was set at 90°. Participants had to alternately perform 4 maximal isometric flexions and 4 maximal isometric

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extensions. Contraction duration was 5 s, and contractions were separated by 45 s of passive rest. This was repeated 3 times: at the beginning of the experiment (prefatigue), between the fatigue protocol and the second pointing movement’s session (post-fatigue1) and at the end of the experiment (post-fatigue2).

Fatigue protocol The fatigue protocol consisted in the repetition of 20-s isometric contractions. The workload was fixed at 60% of the MVC measured at the beginning of the experiment. Contractions were elbow flexions and extensions alternately performed, separated by periods of 15 s of passive rest. A visual feedback was projected on the screen to allow participants to control their force level. Participants had to continue the task until exhaustion, when they were unable to maintain the workload for 5 s at least. During this protocol and MVCs, participants were verbally encouraged. Figure 4.1A represents the experimental setup during the fatigue protocol and the MVCs sessions.

Data analysis Joint angle signal was filtered with a second order Butterworth low-pass filter with a cut-off frequency of 6 Hz. Joint angle signal was then successively differentiated in order to obtain angular velocity and acceleration. EMG signal was full-wave rectified, and filtered with zero lag (second order Butterworth low-pass filter with a cut-off frequency of 6 Hz) to obtain linear envelope.

MVC analysis For each 5 s trial, the maximal torque was computed as the maximal torque value observed during a 500 ms window. We retained the MVC value corresponding to the median of the 4 MVCs performed. EMG was recorded during the last MVC of the pre-fatigue session. The maximal EMG value (EMGmax) was the mean rectified and filtered EMG recorded during the 500 ms corresponding to the maximal torque of this trial.

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Kinematic analysis Movement onset was defined as the moment when velocity exceeds 5% of peak velocity (Corcos et al., 2002). Movement end was defined as the last moment when the laser dot enters the target. This criterion for movement end was retained because it corresponded to the criterion used in the modeling component of our study. Movement time (MT) was the time interval between movement onset and movement end. Since MT alone is not sufficient to infer the processes underlying accuracy control (the same MT can be achieved with different kinematics), we analyzed movement kinematics using 3 key variables (Meyer et al., 1988): the maximal value of the acceleration profile (peak acceleration), the minimum value of the acceleration profile (peak deceleration), and the maximal value of the velocity profile (peak velocity).

EMG analysis EMG linear envelope was normalized relatively to EMGmax. To ensure that the level of tonic activity did not influence the phasic activity, EMG baseline was subtracted from the signal for each trial. EMG baseline was defined as the 500-ms mean of EMG linear envelope, centered 750 ms before movement onset, when participants elbow was at rest. The onset of the agonist burst was detected by custom-made software. The correct burst detection was visually inspected, and corrected if necessary. Since it was difficult to locate precisely the end of the agonist burst, we defined this burst as agonist activity from the onset of the burst to the time of peak velocity. Antagonist burst was defined as the antagonist activity from the onset of the agonist burst to the end of the movement (Corcos et al., 2002). To avoid possible effects of fatigue-induced changes in elbow muscular synergies, we computed mean EMG of each synergist pairs (biceps brachiibrachioradias vs. triceps lateral head-triceps long head). For each pair, mean muscular activation was statistically undistinguishable from individual muscular behaviors. Thus, we present only the results for the mean activity of synergist muscles.

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We used surface EMG in order to get an insight into the neural processes underlying movements. We chose to compute 4 variables that were related to the magnitude of motor commands sent to agonist or antagonist muscles: −

peak_EMGago and peak_EMGant (%): the peak value of the agonist and

antagonist bursts, respectively. −

iEMGago and iEMGant (%): the integral of the agonist and antagonist

bursts, respectively. Since bursts duration varied across the trials, we divided these values by the respective burst duration.

Statistics A one-way ANOVA with repeated measures was used to test for a significant difference in MVC measured at three times during the experiment. A three-way ANOVA with repeated measures was used to examine the effects of movement direction (flexion vs. extension), fatigue (pre vs. post) and ID (3.64 vs. 4.64 vs. 6.64) on kinematics and EMG variables. Newman-Keuls post-hoc tests were used. All values were expressed as mean ± inter-participants standard deviation (SD). Statistical significance was set at α = 0.05.

Model The modeling component of this study relied on an optimal control model that has been described in detail by Tanaka et al. (2006). This choice was mainly motivated by two reasons. First, this model assumes that the brain forms movement trajectories by attempting to minimize movement duration under the constraint of meeting an accuracy criterion. This corresponds exactly to a Fitts like experiment, where participants must terminate their movements within a specified target region while attempting to minimize their average movement times (Fitts, 1954; Fitts & Peterson, 1964). Second, this model is able to accurately reproduce many invariant features of human motor behavior from the main sequence of saccadic eye movements to Fitts’ law (Tanaka et al., 2006). Because our implementation of the model closely follows the previously published version, we will only briefly describe the main assumptions and parameters used.

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General principle of the model The model comprises a controller, which calculates, for a given goal, the appropriate control to master the dynamic forces and achieve the goal. The control signal is transmitted to a controlled object (the moving apparatus) which evolves according to its dynamics. The model assumes that the CNS plans movement trajectories before movement. This corresponds to an open-loop control scheme, which does not take feedback signals into account (see Discussion). The general optimal control problem is to find the optimal trajectory that minimizes the total cost (the integral of the cost function over time) associated with moving the controlled object. The model assumes that the control signal is selected to minimize movement duration under a given accuracy constraint, in the presence of SDN in the control signal. The final movement duration to be minimized is denoted tf. The accuracy constraint is (1) that the expected endpoint position of the effector over repeated trials is equal to the target position during a post-movement period tp (final position constraint), and (2), that the mean endpoint positional variance over tp is bounded by the required final variance Vf (final variance constraint). The pure control signal is corrupted by multiplicative noise (i.e. SDN) that has a Gaussian distribution with zero mean. The noise is assumed to be white so that the covariance between noise at time t and t’ is given by: E[ξ (t )ξ (t ' )] = ku p (t )δ (t − t ' )

(4.1)

Where u(t) is the control signal, and k and p are constants. The delta function indicates that there is no correlation between noise at times t and t’. k determines the magnitude of SDN. An important point is the value of the exponent p, which is generally assumed to be 2 (e.g. Harris & Wolpert, 1998; Todorov & Jordan, 2002; Tanaka et al., 2006; e.g. Guigon et al., 2008a). This value of p = 2 is based on the experimental observation that force variability linearly scale with mean force (Schmidt et al., 1979; Jones et al., 2002). This point is of importance since many predictions of optimal control models do not hold anymore if the noise scaling is not linear (Iguchi et al., 2005; Guigon et al., 2008a). We have recently shown that the linear scaling of force variability with mean force is preserved in this fatigue case,

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with a value of p that remains close to 2 (Missenard et al., 2008a). Consequently, we used a constant p = 2 to describe noise scaling in all our simulations. Optimal trajectories were found numerically for a linear model of the arm. The dynamics of the linear motor plant was:

θ ( n ) (t ) + α ( n−1)θ ( n−1) (t ) + K + α 0θ (t ) = β [u (t ) + ξ (t )]

(4.2)

where θ(t) is a scalar representing the effector position (i.e. the horizontal position of the elbow angle). θ(k)(t) is the kth derivative of θ(t) and Eq. 4.2 contains derivatives up to nth order. The coefficients αi and β are determined by the dynamical properties of the arm, and by the muscle model (see Simulation of Fitts’ law). u(t) is a scalar representing the neuronal control signal. ξ(t) is the signaldependent noise term, which describes trial-by-trial variability.

Simulation of Fitts’ law Single-joint movements of the forearm were simulated with the following dynamic equation (Hogan, 1984b): Iθ&& + bθ& = τ

(4.3)

where θ and τ represent the elbow angle and the net muscle torque, respectively. I and b are, respectively, the moment of inertia and the intrinsic viscosity. A second-order linear muscle model with two time constants (muscle activation, ta, and muscle excitation, te) was introduced (Winters & Stark, 1985): d ⎞⎛ d⎞ ⎛ ⎜1 + t a ⎟⎜1 + te ⎟τ = u dt ⎠⎝ dt ⎠ ⎝

(4.4)

This resulted in a fourth-order plant for the forearm (Eq. 4.2) with coefficients

α0 = 0 α1 =

b t a te I

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α2 =

1 ⎛ 1 1 ⎞b +⎜ + ⎟ tate ⎜⎝ ta te ⎟⎠ I

α3 =

b ⎛1 1⎞ +⎜ + ⎟ I ⎜⎝ ta te ⎟⎠

β=

1 t a te I

The four-dimensional state vector contains hand position, velocity, acceleration and jerk. To simulate Fitts’ law, it was assumed that participants were required to place any part of the laser dot of width w within the target of width W with a fixed probability (the success rate). The required final variance of the movement was taken as: Vf = (W + w) / r 2 2

(4.5)

where r was taken as 1.96 to achieve a 95% success rate. We reproduced the conditions of the experiment in the simulations. Movement amplitude was set to 50°. We simulated the 3 target sizes of the experiment. We set W and w so that Vf correspond to IDs of 3.64, 4.64, and 6.64. Finally, we inferred agonist and antagonist muscle activation by splitting the control signal into positive (agonist) and negative (antagonist) parts (Harris & Wolpert, 1998). We retained the absolute mean values of these parts as indexes of muscle activations. Note that this procedure did not allow any quantitative comparison between the simulated activation signal and EMG recorded in the experiment. Indeed, part of EMG signal is devoted to muscular cocontraction, whereas cocontraction is not taken into account in the model. It was however relevant to qualitatively compare the variation of simulated activation signal and observed EMG in the different experimental conditions.

Numerical methods Tanaka et al (2006) demonstrated that the present optimal control problem can be solved analytically for a linear motor plant. Briefly, finding tf is equivalent to

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solving an equation (called the duration equation) comprising known variables such as Vf, the initial and final effector position, and the final control signal required to stabilize the plant in the desired final state for the duration of the post-movement period. In this equation, tf is the only unknown variable. All the simulations were performed with Matlab (The MathWorks, Natick, MA).

Fitting of experimental data To reproduce Fitts’ law in the pre-fatigue case, we used values for the dynamic parameters of Eq. 4.4 that are classically reported for an unfatigued neuromuscular system. Muscle activation time constant ta was set at 30 ms, and muscle excitation te was set at 40 ms (Winters and Stark 1985). We adopted the standard values of 0.25 kg.m2 and 0.20 kg.m2/s for the moment of inertia and the intrinsic viscosity, respectively (van der Helm & Rozendaal, 2000). The strength of SDN (k, Eq. 4.1), which is a free parameter of the model, was set to k = 4.10-5 (Tanaka et al., 2006). In order to simulate Fitts’ law in the post-fatigue case, we manipulated the three parameters that have been reported to be modified by fatigue (see Introduction): the strength of SDN (k, Eq. 4.1), muscle time constants (ta and te) and the gain between the neural control signal and force (β, Eq. 4.2). To estimate the values of these parameters in the post-fatigue case, we fitted the model to the experimental data. We searched for the combination of parameters that reproduced the variation of MT with fatigue with the smallest error. Error was defined as the sum of the absolute differences between each participant’s mean MT variation for each target size and MT variation given by the model for the considered target size. Since the variation of β was theoretically predicted to have no effect on movement times (see Results), we first searched for the best combination of SDN magnitude and muscle time constants that would reproduce the effect of fatigue on Fitts’ law. Multiple combinations were investigated in the plausible physiological range of each parameter. k was varied from k = 4.10-5 (pre-fatigue value) to k = 7.10-5 (+75 %) with a step of 1.10-6. Muscle time constants were varied from ta = 30 ms and te = 40 ms (pre-fatigue values) to ta = 60 ms and te = 80 ms (+100 %) with a step of 1 ms.

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Once this best-fit combination was found, we searched for the value of β that best reproduced the experimental variation of muscle activation with fatigue. Since we did not experimentally observe significant changes in agonist or antagonist muscle activation with fatigue (see Results), we searched for the value of β that minimized changes in agonist and antagonist activation between the pre- and postfatigue simulations. β was varied from the pre-fatigue value to a 50 % smaller value with a step of 1%.

Results

Experimental data

Assessment of muscle fatigue The mean duration of the fatigue protocol, including rest periods between contractions, was 1245 ± 456 s. After the fatigue protocol, participants were unable to produce the same maximal force level compared to pre-fatigue. The decline in MVC torque after the fatigue protocol was 33.0 ± 9.5% for the extensor muscles (prefatigue = 44.8 ± 10.1 Nm vs. post-fatigue1 = 29.6 ± 6.2 Nm, F(2,20) = 42.39, P < 0.001) and 28.0 ± 9.4% for the flexor muscles (pre-fatigue = 68.9 ± 16.8 Nm vs. post-fatigue1 = 48.9 ± 11.0 Nm, F(2,20) = 35.01, P < 0.001). A Student t test showed that there was no statistical difference between the loss of MVC observed in flexion and extension (t(10) = 1.61, P > 0.05). Moreover, fatigue was still important at the end of the experiment. MVC values recorded during the third MVC session were significantly lower than during the prefatigue session, in extensors (post-fatigue2 = 35.3 ± 9.3 Nm, F(2,20) = 42.39, P < 0.001) and in flexors (post-fatigue2 = 56.6 ± 14.9 Nm, F(2,20) = 35.01, P < 0.001). This result provided evidence that fatigue significantly lasted during the whole second pointing movement session. EMGmax did not change significantly across the different MVC sessions, for each of the 4 muscles (in all cases P > 0.05). Thus, the MVC/EMGmax ratios were different in the post-fatigue situation compared with the pre-fatigue (in all cases P < 0.05). This

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indicated that for an identical EMG level, participants were producing less force when their elbow was fatigued.

Effects of ID and fatigue on elbow movements We did not find any significant interaction between neither movement direction (flexion vs. extension) and ID, nor between movement direction and fatigue, for all the dependent variables. This indicated that the effects of ID and fatigue were similar for the two movement directions. Consequently, we analyzed the effects of fatigue and ID independently of movement direction.

Movement time and Fitts’ law In the experiment, movement ended when the position reached the target zone. Hence, undershoot was not possible and, thanks to the practice trials, the mean number of overshoot was very low: 2.2 ± 0.9 (pre-fatigue) and 2.0 ± 1.2 (post-fatigue). There was no difference between the number of overshoot pre- and post-fatigue (Student’s t test, t(10) = 0.39, P > 0.05). Since the accuracy constraint was respected by participants, our first interest was in the evolution of MT, as in the original Fitts and Peterson study (Fitts & Peterson, 1964). Figure 4.2 shows the evolution of Fitts’ law with fatigue. Fitts’ law was fitted with a power regression model both pre- and post-fatigue, which fitted the experimental data better than a linear regression model. Regressions were computed with the mean MT of each participant at each ID. The power model accurately fitted the data both in pre- and post-fatigue cases. The value of the coefficients of determination (r2) was 0.90 both pre-fatigue and post-fatigue. MT significantly increased with ID (F(2, 20) = 7.94, P < 0.001), and with fatigue (F(1,

10)

= 7.72, P < 0.05). There was a significant

interaction between fatigue and ID for MT (F(2, 20) = 4.77, P < 0.05). Post hoc analysis indicated that MT significantly increased with fatigue for each ID, and that the effect of fatigue on MT was more pronounced when ID was high.

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Figure 4.2. Effect of fatigue on Fitts’ Law in the experiment. The index of difficulty (ID) is defined as the logarithm of the ratio between movement amplitude (multiplied by two) and target width. Fitts’ law characterizes the typical increase in movement duration as either the amplitude of movement increases or the target width decreases. Data were fitted with a power regression model (grey and black lines) with a comparable accuracy pre- and post-fatigue (r2 = 0.9 in both cases). Regressions were computed relatively to the mean movement times of each participant. MT significantly increased with ID and with fatigue. There was a significant interaction between fatigue and ID for MT. Post hoc analysis indicated that MT significantly increased with fatigue for each ID, and that the effect of fatigue on MT was more pronounced when ID was high. Data are means ± s.e.m.

Kinematics Figure 4.3 shows an example of the evolution of position, velocity and acceleration profiles across the different target size and fatigue conditions for a typical participant. Changes in kinematic profiles with fatigue and/or ID were assessed with 3 dependent variables: peak acceleration, peak deceleration, and peak velocity. The evolution of these variables across the different experimental conditions is presented in figure 4.4. Peak acceleration, absolute peak deceleration and peak velocity significantly decreased with ID (F(2, 20) = 46.71, P < 0.001, F(2, 20) = 34.16, P < 0.001, F(2, 20) = 63.25, P < 0.001, respectively), and with fatigue (F(1, 10) = 9.89, P < 0.05, F(1, 10) = 6.31, P < 0.05, F(1, 10) = 9.43, P < 0.05, respectively). There was significant ID × fatigue interactions for peak acceleration (F(2,

20)

= 5.63, P < 0.05), peak

deceleration (F(2, 20) = 8.98, P < 0.01) and peak velocity (F(2, 20) = 3.87, P < 0.05). Post-hoc analysis first indicated that these variables decreased as ID increased. Second, it indicated that the 3 variables decreased significantly with fatigue for each ID. Finally, it indicated that these variables decreased more for small ID compared to high.

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Figure 4.3. Effect of index of difficulty (ID) and fatigue on kinematic profiles during elbow extensions Data of a typical participant are presented. Grey areas on position graphs represent the target width. Each curve represents the mean profile of the 10 trials of each condition. These 10 trials were first time-normalized using a spline interpolation. This figure illustrates the homogeneous slowing of movements observed after fatigue.

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Figure 4.4. Effect of index of difficulty (ID) and fatigue on kinematic variables during elbow flexions and extensions. * denotes a significant fatigue × ID interaction. For the 3 variables, there was (1) a significant decrease as ID increased, and (2) a significant decrease with fatigue for each ID. Data are means ± s.e.m.

EMG The evolution of the variables computed from EMG signal across the different experimental conditions is presented in figure 4.5. There was no significant interaction between fatigue and accuracy for the EMG variables. For the agonist muscles activities, peak_EMGago (F(2,20) = 20.66, P < 0.001) and iEMGago (F(2,20) = 17.05, P < 0.001) significantly decreased as ID increased. Concerning the antagonist muscles, peak_EMGant (F(2,20) = 5.95, P < 0.01) and iEMGant (F(2,20) = 27.06, P < 0.001) significantly decreased as ID increased.

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Figure 4.5. Effect of index of difficulty (ID) and fatigue on variables computed from surface electromyography during elbow flexions and extensions. # denotes a significant effect of ID. For the 4 variables, there was a significant decrease as ID increased, and fatigue had no significant effect. Data are means ± s.e.m.

Fatigue had no significant effect on the EMG variables. Both the agonist EMG activity (peak_EMGago: F(2,20) = 0.06, P > 0.05; iEMGago: F(2,20) = 0.00, P > 0.05) and antagonist EMG activity (peak_EMGant: F(2,20) = 0.16, P > 0.05; iEMGant: F(2,20) = 0.04, P > 0.05) were similar during fatigue.

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Optimal control model To determine which aspects of force production were responsible for generating the observed evolution of Fitts’ law with fatigue, an optimal control model was used (Tanaka et al 2006). With the model, we tested how the fatigue-induced variation of the magnitude of SDN (k), muscle time constants (ta and te), and the gain between the neural control signal and force (β, referred as activation gain) contributed to the variation of Fitts’ law. Figure 4.6 shows the effect of changes in these parameters on simulated Fitts’ law and muscle activations.

Magnitude of signal-dependent noise The increase in the magnitude of SDN (k) in a physiologically plausible range changed agonist and antagonist muscle activations. As k increased, activation decreased proportionally. The relative decrease in activation was identical for each ID. The consequence was that increasing k increased the slope of the simulated Fitts’ law. In other words, when ID increased, the increase in MT with SDN became more pronounced. It indicated here that, in the presence of accentuated noise, the controller has to minimize the control signal to minimize the consequence of the noise and preserve movement accuracy.

Muscle time constants Increasing muscle time constants in the model produced only small changes in agonist and antagonist activations. Muscle activation slightly increased with the lengthening of muscle shortening and relaxation, and this small increase was visible only for small IDs. This is because increasing muscle time constants had a small lowpass filtering effect that allowed the selection of a higher and noisier control signal. However, this was insufficient to maintain MTs when muscle was slower: the increase in time constants induced a parallel shift of Fitts’ law. That is, for each target size, the increase in time constants increased MT proportionally.

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Activation gain

Figure 4.6. Effect of signal-dependent noise magnitude (k, Eq. 4.1), of muscle time constants (ta and te, Eq. 4.4), and of the gain between the neural control signal and force (β, Eq. 4.2, referred as activation gain) on simulated Fitts’ law and muscle activations. For Fitts’ law, we simulated 3 target sizes to reproduce the conditions of the experiment. Agonist and antagonist muscle activations were inferred by splitting the neural control signal into positive (agonist) and negative (antagonist) parts and retaining the absolute value. The increase in noise constrained the controller to select smaller activation signal. Consequently, the slope of Fitts’ law increased with the increase in noise. Increasing muscle time constants principally produced a parallel shift of Fitts’ law. With the decrease in activation gain, all Fitts’ law curve completely overlapped, because the controller compensated by increasing the activation signal proportionally to the decrease in activation gain.

Varying the activation gain produced systematic changes in agonist and antagonist activations. When the gain decreased, the controller compensated by increasing the neural control signal proportionally. The relative increase in activation was identical for each ID. Consequently, changes in gain did not affect MT whatever

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the ID. Note that the increase in the control signal did not increase the effect of noise here, because changes in gain are applied to the control signal and to the noise.

Fitting of experimental data We assessed how changes in the model parameters could qualitatively and quantitatively explain the experimental variation of Fitts’ law and muscle activations observed with fatigue. By computing the coefficient of determination (r2), we found that the model with the standard parameters of an unfatigued neuromuscular system could account for 88.1 % of the experimental variance of MT, when fitted to the mean values of MT of each participant in the pre-fatigue case. It was clear from the effect of each single parameter that the evolution of Fitts’ law with fatigue could not be explained by a single factor (see figure 4.6). The combination of parameters that reproduced the variation of Fitts’ law with fatigue with the smallest error comprised an increase in the magnitude of SDN and an increase in the muscle time constants. Specifically, to reproduce the experimental changes, the parameter k had to be increased by 12.5 % (from k = 4.0.10-5 to k = 4.5.10-5), and muscles time constants had to be increased by 20 % (from ta = 30 ms; te = 40 ms to ta = 36 ms; te = 48 ms). With this combination of parameters, the model could account for 86.7 % of the experimental variance of MT in the fatigue case. This was similar to the value of r2 reported in the pre-fatigue case. With these parameter values, we compared the variation of MT with fatigue between the experimentally observed and simulated Fitts’ laws. In the experiment, MT increased with fatigue by 9.2 %, 9.4 % and 8.9 %, for ID of 3.64, 4.64 and 6.64, respectively. With the simulated data, MT increased with fatigue by 10.7 %, 10.1 % and 9.2 %. The comparison between simulated and experimentally observed Fitts’ laws pre- and post-fatigue is presented in figure 4.7. We finally found the value of β that reproduced the experimentally observed variation of muscle activation with fatigue, i.e. no significant changes in EMG activation with fatigue. In other words, we found β such that changes in agonist and antagonist activations induced by the increase in SDN magnitude of and in time constants were minimized. To minimize the variation of activation between pre- and post-fatigue simulations, β was to be decreased by 9 %. With this value, the variation

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(averaged across various IDs) between pre- and post-fatigue activation was 0.7 % for agonist activation and 0.9 % for antagonist activation.

Figure 4.7. A comparison between the experimentally observed and simulated Fitts’ law. Left: Fitts’ law obtained pre- and post-fatigue in the experiment (same data as in figure 4.2). Right: Simulated Fitts’ law in the pre- and post-fatigue cases. For the pre-fatigue case, we did not adjust the model parameters to fit experimental data, but we used standard parameters of an unfatigued muscle. For the post-fatigue case, the parameters used were typical of a fatigued neuromuscular system, i.e. a 12.5 % increase in the strength of signal-dependent noise, a 20 % increase in muscle time constants, and a 9 % decrease in the gain between the neural control signal and muscle force output. The model could explain ~88 % and ~87 % of the experimental variance, in the pre- and post-fatigue cases, respectively.

Figure 4.8 shows the force response of the muscle model to an arbitrary activation with the pre-fatigue and post-fatigue parameters. To obtain the postfatigue force profile, we used the values from the simulations: muscle time constants (ta and te) were increased by 20% and the activation gain (β) was decreased by 9 %.

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Figure 4.8. Effect of fatigue on the contractile characteristics of the muscle model. The force response of the muscle model to an arbitrary activation is presented in the preand post-fatigue cases. The grey rectangle represents the period of activation. To obtain the post-fatigue force profile, muscle time constants were increased by 20% and the gain between the neural control signal and muscle force output was decreased by 9 %. This reproduces typical changes observed during fatigue: muscle contraction and relaxation speeds are slower, and a given neural activation produces less force.

Discussion The aim of the present study was to characterize the effect of fatigue on Fitts’ law in order to determine how optimal behavior is adapted to preserve task success in the presence of changes in the neuromuscular system. We experimentally showed that fatigue induced an upward shift of Fitts’ law, but did not significantly change muscular activations. We then showed, with an optimal control model, that these changes could be accounted for by the facts that fatigue affects (1) force variability, (2) muscle contraction and relaxation speeds, and (3) the gain between neural activation and muscle force output.

Evidence of fatigue In the experiment, the fatigue protocol was designed to induce an important and durable loss of maximal available force. MVC decline is considered as a reliable index to determine whether muscular fatigue occurs (Vollestad, 1997). Consequently, the fatigue protocol was successful in producing muscular fatigue, since we observed a significant ~30 % decrease in MVCs for elbow flexors and elbow extensors. The fatigue we induced was durable because the decrease in maximal 110

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available force was still important at the end of the experimental protocol, indicating that the recovery processes were negligible during the post-fatigue experimental session. We finally showed here that fatiguing the extensors and the flexors around the elbow joint with the same duty-cycle resulted in a similar loss of force in flexion and in extension. Overall, these results were in agreement with our previous studies using the same fatigue protocol (Missenard et al., 2008b, 2008a).

Fitts’ law as the consequence of an optimal behavior in the presence of signal-dependent noise In the pre-fatigue condition, we observed, that MT systematically increased with ID, as predicted by Fitts’ law (Fitts, 1954; Fitts & Peterson, 1964). Numerous studies have shown that this law holds for a variety of movements produced under different experimental conditions (see Elliott et al., 2001 for a review). Our experiment is no exception to this rule. Kinematics and EMG variables exhibited changes with ID that are classically observed in such tasks. First, peak acceleration, peak deceleration and peak velocity decreased with ID, indicating that the increase in MT with ID was due to longer acceleration and deceleration phases. This is in line with previous studies on Fitts’ law (see e.g. Schmidt et al., 1979; see e.g. Meyer et al., 1988). Second, EMG activity of agonist and antagonist groups decreased as ID increased. This is in agreement with number of studies which showed that higher phasic EMG activations are associated with higher movement speed and smaller MT (Corcos et al., 1988; Flanders & Herrmann, 1992; Buneo et al., 1994). Studying Fitts’ law provides the opportunity to get an insight into optimality principles that determine movement planning and execution. Indeed, recent optimal control models have proposed a proper explanation of the speed-accuracy trade-off observed in goal-directed movements (Harris & Wolpert, 1998; Tanaka et al., 2006; Guigon et al., 2008a). These models consider that the CNS plans movements in order to minimize the effects of noise in motor commands sent to muscles. Because noise in motor commands is signal-dependent, large motor commands produce rapid but inaccurate movements, and smaller motor commands produce accurate but slow movements. Accordingly, Fitts’ law emerges as the consequence of an optimal strategy to achieve task with success in the presence of SDN.

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Fitts’ law observed in the pre-fatigue condition was accurately reproduced by the constrained minimum-time optimal model (Tanaka et al., 2006). This model is well adapted to study Fitts’ law (see Methods). For the pre-fatigue case, we did not adjust the model parameters to fit experimental data, but we used standard parameters of an unfatigued muscle. With time constants of the muscle model set to 30 and 40 ms (Winters & Stark, 1985), and noise level set to 4.10-5 (Tanaka et al., 2006), the model explained more than 88 % of the experimental variance of MT with ID. This result reinforces the idea that Fitts’ law is the consequence of the use of optimality principles by the CNS (Meyer et al., 1988; Harris & Wolpert, 1998; Tanaka et al., 2006; Guigon et al., 2008a).

Changes in Fitts’ law with fatigue The shape of Fitts’ law was qualitatively conserved during fatigue. Indeed, it was fitted with a power model with a comparable accuracy (r2 = 0.90 both pre- and postfatigue). Kinematic profiles were also qualitatively similar pre- and post-fatigue (see figure 4.3). Quantitatively, on the other hand, fatigue induced an upward shift of Fitts’ law: movement times associated with a given ID were significantly increased, whatever the ID. The kinematic analysis revealed that this increase in MT was due to a global decrease in acceleration and in deceleration (figure 4.4). This was consistent with the idea that fatigue modified movement kinematics quantitatively but not qualitatively. At the same time that changes occurred in movement trajectories, EMG activities of agonist and antagonist muscles showed no significant changes between pre- and post-fatigue conditions. Since it was speculative to explain the observed changes from experimental data alone, we used a modeling approach to get an insight into the factors responsible for the evolution of Fitts’ law with fatigue. To determine how fatigue-induced changes in the neuromuscular system may contribute to changes in Fitts’ law and in muscle activations with fatigue, we used the optimal control model proposed by Tanaka et al (2006). With the model, we investigated the effect of noise in motor commands, of muscle contraction and relaxation speeds, and of the gain between neural activation and muscle force on Fitts’ law and muscle activation. We chose these parameters because they play an important role in the optimization process and/or in the muscle 112

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model, and because many evidences exist in the literature showing that they are the 3 main neuromuscular variables affected by fatigue. We searched for the combination of parameter values that best fitted the experimental variation of Fitts’ law and muscle activation with fatigue. The best-fit combination comprised a 12.5 % increase in motor commands noise, a 20 % increase in muscle time constants, and a 9 % decrease in the gain between neural activation and muscle force. As in the prefatigue case, the model explained ~87 % of the experimental variance of MT (see figure 4.7). Do the changes in the model parameters correspond to physiological changes that occur in the neuromuscular system during fatigue? Concerning the effect of fatigue on the noise, it has been often reported that force variability is increased after a fatiguing exercise (e.g. Furness et al., 1977; Lavender & Nosaka, 2006; Semmler et al., 2007; e.g. Dartnall et al., 2008; Missenard et al., 2008a). Until recently, the effect of fatigue on the relation between the force and its variability over a broad range of force was unclear. We have recently shown that the linear scaling of mean force with force variability was preserved during fatigue, and that the increase in force variability with fatigue was proportional to the force level (Missenard et al., 2008a). This result had two important consequences for the present study. First, it allowed using a noise exponent of 2 in the model (the parameter p in Eq. 4.1), which was a prerequisite for optimal control model to accurately reproduce experimental data (Iguchi et al., 2005; Guigon et al., 2008a). Second, it clearly showed that fatigue increased the strength of SDN, i.e. the parameter k in Eq. 4.1. Consequently, the increase in the strength of SDN we set here was qualitatively consistent with previous studies of force variability with fatigue. Quantitatively, in the present experiment, we reported a 12.5 % increase in the strength of SDN with fatigue. It was less than the ~100 % increase that has been previously reported (Missenard et al., 2008a). This difference may be due to the fact that the latter study reported results from isometric force measurements, where, contrary to anisometric conditions, force has to be sustained. Besides changes in force variability, it has been shown that fatigue reduces muscle shortening velocity and prolongs relaxation, both in animal (e.g. Edman & Mattiazzi, 1981) and human experiments (e.g. Jones et al., 2006). For instance, Edman and Mattiazzi (1981) found an empirical relationship between percentage depression of force and maximum speed of shortening, which indicated that a 25 % decrease in

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MVC (which was the average decrease across the 4 post-fatigue MVCs performed in flexion and extension in our experiment) corresponded to a decrease in contraction speed of ~17 %. This was coherent with the 20 % increase of muscle time constants in the model, indicating that the relative increase we found for muscle contraction speed was in the typical range of a fatigued muscle. Finally, fatigue modifies the relation between muscle activation and force production. Indeed, it has been well reported that, during fatigue, the slope of forceEMG relationship increases (e.g. Edwards & Lippold, 1956; e.g. Bigland-Ritchie, 1981; Kirsch & Rymer, 1992). This indicates that an increase in motor commands is needed to achieve a given force during fatigue. In our data, there was evidence that fatigue affected the relation between EMG and force output during movement in the fact that fatigue had no significant effect on EMG variables. Indeed, slower movements were observed during fatigue whereas the muscular activation magnitude was unchanged. If the relation between EMG and force output were identical pre- and post-fatigue, a decrease in EMG would be expected. Therefore, this result indicated that the same EMG activity produced less force during movements in the postfatigue condition. Concerning the magnitude of this effect, Edwards and Lippold (1956), for instance, reported that a given force could be achieved during fatigue with a ~63 % increase in EMG activation compared to pre-fatigue. The 9 % decrease in the gain between muscle activation and force output found with the model was quantitatively lower compared to this report. The difference in order of magnitude of changes could be due to the fact that force-EMG relationships are usually computed from isometric measurements. It may be that the increase in EMG with fatigue is less pronounced when force-EMG relationship is assessed in anisometric conditions, when force is not sustained. Taken together, these observations indicate that all the parameter values reported here to model Fitts’ law in the fatigue case are typical of a fatigued neuromuscular system. This point is particularly important because extending the validity of the model to the fatigue case depends on the fact that changes in its parameter values are both qualitatively and quantitatively consistent with the neurophysiology of fatigue.

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Optimality in the presence of fatigue Because the sensorimotor system is a product of evolution, development and learning, many theories of motor function consider that optimality is a hallmark of human behavior. This position legitimates the idea that task goals can be quantified as cost functions, and that computational tools of optimal control can be applied to obtain predictions of motor behavior (Todorov, 2004). Optimal control theory has been very successful in terms of explaining the details of experimental data (e.g. Todorov & Jordan, 2002), and has recently been extended to explain how motor behavior is adapted to different task goals (Liu & Todorov, 2007). However, to date, the question of whether humans are able to adapt optimally to short time-scale changes in the neuromuscular system or in the environment has received little attention. Recently, Driedichsen (2007) reported that humans can adapt optimally to external force field perturbation during bimanual pointing. It has also been shown that human movements are optimally adapted when movement variability is experimentally modified (Trommershauser et al., 2005; Gepshtein et al., 2007). Yet, to our knowledge, there is no previous evidence of optimal adaptation in response to acute internal perturbation, such as fatigue. We showed here that the adaptation of movement trajectories and muscular activations to fatigue could be accurately reproduced within the framework of optimal control. One could argue that this provides somewhat indirect evidence that participants adapt optimally to fatigue-induced changes because we did not adjust the parameters for the fatigue case a priori. Yet, sufficiently precise a priori predictions are extremely difficult to construct based on the available literature, mainly because changes in the neuromuscular system are very specific of the task that induces fatigue (Enoka & Duchateau, 2008). Even though it was not possible to use a priori parameter values in the fatigue case, we have seen above that the necessary changes in parameters to fit the data were typical of fatigue. If the adjustment of the parameters in the fatigue case were not coherent with changes usually observed in the neuromuscular system with fatigue, it would have indicated that the optimal model we chose was not representative of the CNS functioning. It was not the case here, where, in the presence of realistic fatigue signature in the neuromuscular system, we showed that the optimal control model could accurately account for the observed motor behavior. Consequently, it is likely that changes in

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Fitts’ law and muscle activation with fatigue reflected an optimal adaptation to fatigue. This adaptation was necessary to preserve task success during fatigue, i.e. to ensure that movements terminated within the target. Indeed, if motor commands were increased in order to avoid movements slowing in the fatigue case, the increase in noise would increase the probability to miss the target, and therefore movement success would not be guaranteed. Our results extend previous findings that have shown that the CNS is optimal in adapting to external changes in task requirements (Trommershauser et al., 2005; Diedrichsen, 2007; Gepshtein et al., 2007), by showing that the CNS adapts optimally to short-time scale internal changes in the neuromuscular system.

Open loop modeling and the role of feedback We used here a purely open-loop model that did not take feedback signals into account. It is clear that including sensory feedback in the model would allow a more general description of motor behavior (Desmurget & Grafton, 2000; Todorov & Jordan, 2002). However, it has been recently shown, with a stochastic optimal feedback control model, that Fitts’ law was not reproduced in the presence of noise in sensory feedback, contrary to the case where sensory feedback was perfect (Guigon et al., 2008a): it was concluded that Fitts’ law principally arose due to signaldependent noise in motor commands, confirming previous findings (Harris & Wolpert, 1998; Tanaka et al., 2006). This indicated that an open-loop model can be considered sufficient in the particular case of the study of Fitts’ law. An implicit consequence of this use of a pure open-loop model is that we assumed here that the observed adaptation to fatigue concerned motor planning or preparation. This implied that the CNS had prior knowledge of the state of the neuromuscular system, and planed movements as a consequence. The latter assumption is in line with the results of our experiment, showing that fatigue affected kinematics variable such as peak acceleration, which occurred early in the movement (typically ~60 ms after movement onset, see figure 4.3). The choice of an open-loop model also implied that feedback processing was not impaired by fatigue. We assumed that visual feedback was the main sensory source in our pointing movement task which required information in azimuth direction (van Beers et al., 2002), and we did not find any

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reasons why the processing of visual feedback would change because of muscular fatigue.

Conclusion To achieve task goals in the various contexts of every day life, the central nervous system has to adapt to short time-scale changes in the properties of the neuromuscular system, such as those induced by fatigue. We have shown that humans are able to perform accurate movements after fatigue, but at the price of an increase in movement duration. This evolution of Fitts’ law with fatigue could be accounted for by a model that applied optimal control principles to a neuromuscular plant which presented typical fatigue characteristics. Because this finding suggests that humans are capable to plan optimal movements that take into account acute changes in the neuromuscular system state, the increase in movement time that could be interpreted as a deficient control by the central nervous system may actually reflect the best possible strategy for achieving task goals with success. This ability of humans to efficiently take into account short time-scale changes in the properties of the neuromuscular system appears fundamental to move skillfully in various contexts.

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V - Étude 4 - Cocontraction during fatigue

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Missenard O, Mottet D & Perrey S. (2008). The role of cocontraction in the impairment of movement accuracy with fatigue. Exp Brain Res 185, 151-156.

Comprendre les effets de la fatigue sur la loi de Fitts (étude 3) est insuffisant pour offrir une interprétation générale de l’effet de la fatigue sur le contrôle de la précision des mouvements. En effet, le contrôle de la précision des mouvements peut aussi se faire en accentuant les contractions musculaires de part et d’autre d’une articulation. En conséquence, l’objectif de l’étude 4 était de déterminer si la fatigue pouvait influencer le contrôle de la précision des mouvements parce qu’elle affecte la cocontraction.

Les effets de la fatigue sur la précision des mouvements peuvent-ils être expliqués par une diminution de la cocontraction ?

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Abstract The present experiment was designed to test the hypothesis that fatigueinduced impairment in movement accuracy is caused by a decrease in muscle cocontraction rather than a reduced ability to produce muscular force. Seven participants performed fast and accurate elbow extensions aimed at a target, before and after a fatigue protocol. The inertia of the manipulandum was decreased after the fatigue protocol so that the ratio of required to available force during movements was identical pre- and post-fatigue. After the fatigue protocol, movement endpoint accuracy decreased and movement endpoint variability increased. These alterations were associated with a decrease in cocontraction. We concluded that the impairment of movement accuracy during fatigue could not be explained by the lack of available force, but was likely to be due to a fatigue-induced decrease in muscular cocontraction. We then speculate that fatigue influences the relative weights of accuracy and energy economy in the optimisation of sensorimotor control.

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Introduction Muscular fatigue is experienced in many situations where movement control is crucial, from the use of man-machine interfaces to taking a final shot in a professional basketball game. Thus, it is of particular interest to understand the functional consequences of muscular fatigue. Fatigue is classically defined as a loss of maximal available force (e.g. Edwards, 1981). It is likely that this loss of available force affects motor control, especially for movements requiring high forces, but fatigue has also been shown to impair movement accuracy for movements requiring relatively small forces (Hoffman et al., 1992; Jaric et al., 1999). This effect on accuracy, when the level of available force does not seem to be a limiting factor for motor control, suggests that other factors besides the lack of available force may play an important role in the impairment of movement accuracy with fatigue. A likely candidate to explain the impairment of movement accuracy with fatigue is muscular cocontraction, defined as the simultaneous activation of agonist and antagonist muscles around a joint. Indeed, cocontraction has been shown to increase movement endpoint accuracy (e.g. Gribble et al., 2003). Moreover, when participants are requested to use cocontraction to point at a target, endpoint accuracy is improved (Osu et al., 2004). This improvement is mainly attributed to the fact that cocontraction increases limb impedance (Osu & Gomi, 1999), and thus limits the variability induced by neuromuscular noise (Selen et al., 2005). Hence, if fatigue decreases cocontraction, we can predict a decrease in movement endpoint accuracy and an increase in endpoint variability. To our knowledge, the effect of fatigue on cocontraction during aimed arm movements has never been studied. However, it makes sense that fatigue could decrease cocontraction levels. The rationale for this hypothesis is, first, that a decrease in limb impedance during movement has been already observed during fatigue (Selen et al., 2007). Second, cocontraction is metabolically costly since it requires additional muscular activation, and thus it could be decreased in order to minimize energy expenditure when energy reserve is decreased. This study was designed to test the hypothesis that fatigue-induced impairment in movement accuracy is caused by a decrease in muscle cocontraction rather than a reduced ability to produce muscular force.

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Methods Seven right handed participants (3 females and 4 males) between the ages of 24 and 34 took part in the study. They had to perform pointing movements before and after a fatigue protocol. Maximal voluntary contraction (MVC) was measured at the beginning of the experiment, after the fatigue protocol, and at the end of the experiment, in order to evaluate the effect of fatigue on force generation capabilities. All study procedures complied with the Helsinki declaration for human experimentation and were approved by the local ethics committee. Figure 5.1 shows a schematic representation of the experimental setup and the experimental protocol. Participants sat in a chair during the whole experiment. The chair was positioned in front of a 2 × 3 m screen with the elbow and forearm of their right arm resting on a manipulandum that consisted of an aluminium bar. The elbow was aligned on the vertical axis of rotation of the manipulandum, and the arm was abducted 90°. Participants grasped a vertical handle so that they could rotate the manipulandum in the horizontal plane. When flexing or extending their elbow, participants moved a laser dot on the screen, indicating the actual position of the joint.

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Figure 5.1. Experimental setup during the fatigue protocol (A) and pointing movements (B), and experimental protocol (C).

During MVC measurements and fatigue protocol, the manipulandum was locked at 90° (180° corresponding to full elbow extension). Extension and flexion forces were measured with a strain gauge (accuracy ± 0.5 N, FN3030, FGP Sensors, Les Clayes Sous Bois, France) placed in the plane of rotation of the manipulandum. During pointing movements, the elbow angle was measured by a potentiometer fixed on the axis of rotation of the manipulandum. Pairs of Ag/AgCl electrodes (Contrôle Graphique Medical, Brie-Comte-Robert, France) were used to record surface electromyography (EMG) of the biceps brachii, the brachioradialis, and the long and lateral heads of triceps all along the experimental protocol. Electrode location was set according to SENIAM recommendations (Hermens et al., 2000). Inter electrode distance was 10 mm. EMG signal was amplified (× 1000, Biovison, Wehrheim, Germany). All signals were sampled at 1000 Hz with an A/D USB DAQ 6009 National Instrument card (National Instruments, Austin, TX, USA), and stored on a computer for subsequent analysis. For the MVC measurement sessions, participants had to perform alternately 2 maximal isometric flexions and 2 maximal isometric extensions. Contraction duration was 5 s, and contractions were separated by 45 s of passive rest. Maximal torque was computed as the maximal torque value observed during a 500 ms window. We retained the MVC value corresponding to the mean of the 2 MVCs performed. The

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maximal EMG value (EMGmax) was the mean rectified and filtered EMG recorded during the 500 ms corresponding to the maximal torque of the highest trial. The fatigue protocol consisted of the repetition of 20-s isometric contractions. The workload was fixed at 60% of the MVC measured at the beginning of the experiment. Contractions were elbow flexions and extensions performed alternately, separated by periods of 15 s of passive rest. A visual feedback was projected on the screen to allow participants to control their force level. Participants had to continue the task until exhaustion, when they were unable to maintain the workload for at least 5 s. During the pointing movement sessions, participants could not see their arms. For each trial, participants were asked to move the laser dot from the starting position (70°) to the target (110°). Participants were asked to point as accurately as possible without correcting their movement online. To avoid eventual online corrections, the laser dot disappeared 100 ms after movement onset. Since movement accuracy is related to movement time and kinematics (Woodworth, 1899), participants were asked to perform 300 ms movements with a tolerance of ± 30 ms. Participants were informed of their movement endpoint position and movement time 1 s after movement end. If movement time was not in the acceptable range, the trial was repeated. The percentage of trials that did not satisfy the movement time constraint was 33 ± 15 %. A Student t test revealed that this percentage was unaffected by fatigue (t = 0.49, P = 0.64). Movement sessions ended once 15 acceptable trials were performed. An inertial load of 1.5 kg was added on the manipulandum in order to impose the peak torque required during movement. To obtain a peak torque corresponding to 40 % of participants’ MVC both pre- and post-fatigue, we adapted the distance between the load and the axis of rotation of the manipulandum. This distance was computed by taking into account the anthropometric properties of participants’ limbs based on Winter’s tables (Winter, 2005), and the fact that the mean value of peak acceleration was about 2800°.s-2. The value of 2800°.s2 was estimated from a pre-test experiment. The distance D (m) was obtained with the following equation:

D=

124

T − Iforearm − Ihand − Im Apeak L

(Eq. 5.1)

V – Étude 4 - Cocontraction during fatigue

Where T was the required peak torque during movement (40 % of MVC), Apeak was the estimated peak acceleration (2800°.s-2), Iforearm was the inertial moment of the forearm (between 0.010 and 0.024 Nm), Ihand was the inertial moment of the hand (between 0.024 and 0.066 Nm), Im was the inertial moment of the manipulandum (between 0.023 and 0.029 Nm, depending on the handle position), and L was the load added on the manipulandum (1.5 kg). In order to keep the ratio of required to available force constant between the pre- and post-fatigue conditions, the distance between the load and the axis of rotation was computed with respect to the current extension MVCs of each participant. Consequently, for each participant, the inertia of the manipulandum was smaller in the post-fatigue movement session, to compensate for the fatigueinduced decrease in MVC. Figure 5.2 shows an example of data recorded during the movement session. For the 15 acceptable trials in each condition that were retained for analyses, joint angle signal was filtered with a second order Butterworth low-pass filter with a 10 Hz cutoff frequency. Filtered signal was differentiated to obtain angular velocity and acceleration. We distinguished two measures of movement time (Selen et al., 2006a). Movement time used to constrain movement duration (MT1) was defined as the time interval between the first moment when velocity exceeds 10°.s-1 and the following time when the velocity falls to 10°.s-1. Since a terminal backward submovement could occur, we defined the movement time used for all the subsequent analysis (MT2) as the time interval between the first moment when velocity exceeds 10°.s-1 and the last time when the velocity falls to 10°.s-1. We measured movement endpoint accuracy with constant error, defined as the mean distance between the position at movement end and the target location. Movement endpoint variability was assessed by variable error, defined as the mean distance between the endpoint of each trial and the overall average endpoint position within the session. EMG signal obtained during movement was full-wave rectified and filtered with zero lag (second order Butterworth low-pass filter with a cut-off frequency of 6 Hz) to determine the linear envelope. The EMG linear envelope was normalized relative to EMGmax. To avoid possible effects of fatigue-induced changes in elbow muscular synergies, we computed mean EMG of each synergist pairs (triceps lateral headtriceps long head vs. biceps brachii-brachioradialis). Agonist and antagonist activations were defined as the integral of the agonist and antagonist bursts,

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respectively. Since burst duration varied across trials, we divided these values by the respective burst duration. Based on EMG signals, we estimated cocontraction with an index of cocontraction (CI) adapted from Kellis and al. (2003). CI was defined as follow:

CI =

∫

tf

t0

∫

tf

t0

EMG min⋅ dt

[ EMGago + EMGant ] ⋅ dt

× 100

(Eq. 5.2)

Where t0 is movement onset, tf is movement end, EMGmin is at each sampling point in time the EMG signal of the synergist pair which has the lower normalized activity, EMGago the EMG of the agonist pair, and EMGant the EMG of the antagonist pair. The effects of fatigue on the variables computed from the MVC procedures and the movement sessions were assessed with one-way repeated-measures ANOVA. All values are expressed as mean ± inter-participants standard deviation (SD). Statistical significance was set at α=0.05.

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Figure 5.2. Example of movement data analysis. A: filtered position profile. The dashed line represents the target, b velocity profile. Dashed lines represent the values of 10 and -10°.s-1 used for the detection of movement onset and end. C: from top to bottom, rectified electromyographic (EMG) traces of triceps long head, triceps lateral head, biceps brachii, brachioradialis. D: EMG linear envelop of agonists (grey line) and antagonists (black line). The grey area represents EMGmin used for the computation of cocontraction (Eq. 5.2).

Results and discussion We first have to assess the validity of our experimental paradigm. Our fatigue protocol was designed to induce a substantial loss of maximal available force. The decline in MVC torque after the fatigue protocol was 33.9 ± 9.8% for the extensor muscles (MVC1 = 46.9 ± 16.6 Nm vs. MVC2 = 30.3 ± 12.2 Nm, F(2, 12) = 20.4, P < 0.01) and 25.7 ± 10.7% for the flexor muscles (MVC1 = 67.4 ± 19.4 Nm vs. MVC2 = 49.0 ± 14.3 Nm, F(2, 12)=19.5, P < 0.01). MVC values recorded during the terminal MVC session were significantly lower than during the pre-fatigue session, in extensors (MVC3= 36.9 ± 14.3 Nm, F(2, 12)=20.4, P < 0.01) and in flexors (MVC3 = 56.5 ± 18.3 Nm, F(2, 12) = 19.5, P < 0.01). Taken together, these results indicate that our protocol was successful in

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inducing a significant fatigue that lasted during the whole second pointing movement session, in a similar fashion in flexor and extensor muscular groups. We also have to asses the validity of our pointing movement protocol. First, we wanted to avoid any effects of movement kinematics on endpoint accuracy. This was done by imposing MT1 with a tolerance of ± 30 ms. Unexpectedly, MT1 values showed a small but significant decrease in the post-fatigue condition (310 ± 4 ms vs. 297 ± 7 ms, F(1, 6) = 14.0, P < 0.01), and peak velocity increased (246.8 ± 9.9 °.s-1, vs. 261.2 ± 10.3 °.s-1, F(1, 6) = 13.6, P < 0.05). This could have been due to fatigue recovery during the second movement session. However, peak acceleration values were not significantly different pre- vs. post-fatigue (2400 ± 371 °.s-2 vs. 2786 ± 459 °.s-2, F(1, 6) = 3.07, P = 0.13), and, more importantly, we found no significant difference between pre- (489 ± 65 ms) and post-fatigue conditions (528 ± 94 ms) for MT2 values (F(1, 6) = 1.0, P = 0.35). Thus we concluded that, despite small differences for some variables, the movement kinematics was globally similar between the two movement sessions, and could not be the main cause of the decrease in endpoint accuracy with fatigue. Second, we wanted that participants’ peak torques during each movement remained close to 40 % of their current MVC. This was done by adapting the inertial load on the manipulandum. The lack of significant difference in agonist EMG activity in the prevs. post-fatigue session (34.2 ± 10.3 % vs. 37.6 ± 8.1 %, F(1, 6) = 0.94, P = 0.37) indicated that movements required a similar percentage of MVC in the two conditions. This indicated that the ratio of required to available force during movement was not different pre- and post-fatigue, and thus that the load was correctly adapted in the post-fatigue movement session. Once verified that our experimental paradigm successfully induced fatigue and successfully normalised the force required during movements to the current participants’ capabilities, we can now address the questions that are central to the present experiment. The first goal was to demonstrate that fatigue can impair movement accuracy even when the ratio of required to available force is unchanged. The lack of available force can reduce the ability to accelerate and decelerate the limb. Especially, if antagonist muscles are unable to break the movement down, the accuracy can be decreased since antagonist muscles play a major role in the control of the final position (Wierzbicka & Wiegner, 1996). However, this would be a critical factor only in the case of movements requiring forces that are similar to or higher than the available force. This was obviously not the case in the present experiment,

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where the maximal force requirement was maintained constant at 40% of the available force. We observed that variable error and constant error increased significantly post-fatigue, as shown in figure 5.3 (1.7± 0.5° vs 2.0 ± 0.5°, F(1, 6) = 12.9, P < 0.05 and 1.8 ± 0.4° vs. 2.6 ± 0.7°, F(1, 6) = 12.2, P < 0.05, respectively). There was no tendency either for undershoot or overshoot of the target after fatigue since mean movement endpoint position was unchanged (pre-fatigue: 110.4 ± 1.0° vs. postfatigue: 111.0 ± 1.5°, F(1, 6) = 0.87, P = 0.39). This is direct evidence that fatigue can affect movement accuracy even if the ratio of required to available force is unchanged. Consequently, the impairment of endpoint accuracy could not be attributed to the lack of available force. This raises the question of the part played by other factors in the control of movement accuracy during fatigue.

Figure 5.3. Mean values of constant error (A), variable error (B), and cocontraction index (C) in the two movement sessions. Each line corresponds to participant’s individual evolution. Vertical bars represent the inter-participants standard deviation. * Significant difference (P