The most basic property of a muscle is its ability to contract and produce force when stimulated. A muscle is mainly composed of cells consisting of myofibrils with its basic unit called as a sarcomere. A sarcomere is composed of actin and myosin responsible for the muscle contraction. The Hill-type muscle model is the most commonly used model to simulate the behavior of a muscle. A muscle can produce its maximum force at isometric conditions. The level of force produced in the muscle is determined by the the frequency of the signals from the CNS. The force production is also a function of force-muscle current velocity and force-muscle current length relations. A muscle contains two types of sensors / i.e. muscle spindle and golgi tendon organ, which give rise to the feedback control of the muscle length and muscle contraction velocity. In this study a 1-D model of a muscle is formed step by step in Simulink. In the models the muscle mechanics has been investigated and the results are compared with the previous works.

In the classic Hill model for muscle contraction, the split between the muscle and tendon is arbitrary and the problem lacks a unique solution. Instead of reformulating the problem to a differential-algebraic equation and solving for a set of initial conditions, a constant tendon length is commonly assumed in musculoskeletal simulation tools. This assumption has not been thoroughly tested and introduces errors of unknown magnitude to the simulations. In this thesis, the contractile element of the Hill model is modelled as a friction clutch in parallel to a viscous damper. This provides an evolution law for the muscle length by which the muscle speed is numerically calculated taking into account a non-zero tendon speed. A simple biceps curl is simulated with the friction clutch model and compared to corresponding commercial musculoskeletal simulations. Overall, the results are similar, in particular for the muscle lengths which are almost identical in every simulation (0.00-0.42% difference). The difference in tendon speed is 0.00-3.26%, with upwards tendencies. In general, the error percentage of the tendon speed appears to decrease by the same amount that the contraction speed is reduced. Conclusively, it can be said that the introduced friction clutch model delivers comparative outcomes to a commercial musculoskeletal simulation software, while not assuming a constant tendon length. However, while presenting a relatively simple solution, an increased computation time is to be expected due to the need of a differential equation solver. Further investigation regarding implementation and computing times in more complex simulations may provide an alternative approach to conventional musculoskeletal simulations.

L'estimation des forces musculaires nécessite le développement d'un modèle biomécanique. Une des étapes essentielle de ce type d'approche est la modélisation de l'interaction au sein du complexe muscle-tendon entre trois composants, les fibres musculaires, l'aponévrose et le tendon par un modèle de type Hill. L'objectif de ce travail doctoral était d'identifier les paramètres dans le modèle de type Hill qui jouent un rôle important dans l'estimation des forces musculaires et de proposer une méthode pour les définir. L’échographie a été utilisée pour estimer la relation force-déformation in vivo du tendon et de l'aponévrose, et le comportement in vivo des fibres musculaires au cours de la contraction pour chaque sujet et comme un moyen de quantifier la précision des modèles en mesurant le comportement in vivo des fibres musculaires et les comparer aux sorties du modèle. L'utilisation d'une définition de l'Élément Élastique en série spécifique au sujet dans les modèles biomécaniques joue un rôle important pour des activités où les forces musculaires sont importantes. Lors de tâches isométriques maximales, la relation force-déformation du tendon spécifique au sujet combiné à des contraintes sur la géométrie initiale conduit à des estimations de forces musculaires plus faibles et un comportement différent des fibres. En ce qui concerne des activités comme le hopping et la course, l’utilisation d’une relation force-déformation du complexe tendon-aponévrose spécifique au sujet permet d’estimer des forces musculaires plus grandes et entraîne un découplage du comportement des fibres musculaires plus important par rapport au complexe muscle-tendon. Pour des activités de marche, la définition de l’élément en série dans le modèle de type-Hill n'influence pas les forces musculaires. L'échographie apparaît comme un outil intéressant pour personnaliser les modèles et pourrait être appliqué sur des patients ayant un trouble neuromusculosquelettique. / The estimation of forces produced by the muscle-tendon complex around a joint needs the development of a neuromusculoskeletal model. One of essential step of this approach is the modeling by a Hill-type muscle model of the interaction within the muscle-tendon complex between three components: the muscle fiber, the aponeurosis, and the tendon. The objective of this work was to identify the parameters used as input into Hill-type muscle model that play an important role in muscle force estimation and to propose a method to define them. The ultrasonography has been used to estimate in vivo tendon and aponeurosis force-strain relationships, and the in vivo behavior of muscle fiber during the contraction for each subject. In addition, a method was proposed to quantify the model accuracy by estimating the in vivo behavior of muscle fiber and compare it with model outputs. The use of subject-specific definition of Series Elastic Element into the EMG-driven model plays an important role for activity at high level of muscle forces. During maximal isometric contraction, the subject-specific tendon force-strain relationship combined with constraint on initial muscle geometry (i.e., fiber length and muscle thickness) leads to lower estimated muscle forces and to a different behavior for the muscle fiber. Concerning highly dynamic tasks such as running and \textit{hopping}, the use of subject specific force-strain relationship for the tendon-aponeurosis complex allows to estimate higher muscle forces and leads to a heavier decoupling behavior between muscle fiber and muscle-tendon complex.The estimation of forces produced by the muscle-tendon complex needs the development of a neuromusculoskeletal model. One of essential step of this approach is the modeling by a Hill-type muscle model of the interaction within the muscle-tendon complex between three components: the muscle fiber, the aponeurosis, and the tendon. The objective of this work was to identify the parameters used as input into Hill-type muscle model that play an important role in muscle force estimation and to propose a method to define them. The ultrasonography has been used to estimate in vivo tendon and aponeurosis force-strain relationships, and the in vivo behavior of muscle fiber during the contraction for each subject. In addition, a method was proposed to quantify the model accuracy by estimating the in vivo behavior of muscle fiber and compare it with model outputs. The use of subject-specific definition of Series Elastic Element into the EMG-driven model plays an important role for activity at high level of muscle forces. During maximal isometric contraction, the subject-specific tendon force-strain relationship combined with constraint on initial muscle geometry (fiber length and muscle thickness) leads to lower estimated muscle forces and to a different behavior for the muscle fiber. Concerning highly dynamic tasks such as running and hopping, the use of subject specific force-strain relationship for the tendon-aponeurosis complex allows to estimate higher muscle forces and leads to a heavier decoupling behavior between muscle fiber and muscle-tendon complex. Concerning dynamic tasks with low force level such as walking, the estimation of muscle force was not influenced by the Series Elastic Element definition. The ultrasonography appears as a useful tool to personalize neuromusculoskeletal models and could be used for patient with neuromusculoskeletal disorders showing an alteration of tendon mechanical properties allowing to quantify the effect of rehabilitation program.