The human upper limb is a complex musculoskeletal system that can still perform various tasks with impressive efficacy thanks to the ability of the central nervous system to control and modulate the activation of more than 40 muscles.

Stroke is a leading cause of long-term disability, and individuals who have experienced a stroke often show unusual muscle activation patterns in the limb that was affected. A thorough understanding of these changes in muscle activation is crucial for the development of efficient rehabilitation plans.

So far, the study of the recorded electromyographic (EMG) signals has been the primary option for investigating muscle activation during movement.

Unfortunately, given the number of muscles acting on the shoulder and arm and their positions with respect to each other, a complete upper-limb's muscles EMG recording is not feasible in practice. Numerical musculoskeletal model could represent a very useful alternative approach to gather this kind of information.

This thesis aims at extending an existing upper-limb musculoskeletal model, to capture the overall muscle activations of a subject from its scaled recorded kinematics and a limited number of recorded muscle EMG.

The original model was force-based and its aim was to obtain the muscle forces from inverse dynamics (ID). However, these could not always be physiologically feasible, indeed, after modeling the musculotendon dynamics with a Hill-type model we further reduced their boundaries leading to unfeasible activations solutions. The ID was then reformulated to be activation based ensuring feasible activation and force given the muscle state. Moreover studying patients performing reaching tasks with an exoskeleton can lead to non-smooth kinematics, further restricting the ID possible solutions. A flexible formulation allowing for tolerance of torques at the joints was added.

The purpose of this thesis is to present a tool that can be used to study variations in muscle activations from healthy and stroke patients during their rehabilitation. This means that a large dataset with multiple repetitions of the different tasks and subjects has to be simulated which would not be practical with the initial model. However, with a rigid tendon muscle assumption as well as the precomputation of multiple functions of the model, the computation time could be reduced by almost 2 orders of magnitude when studying multiple movements.

In the last part of the thesis I could show how the model could help with a quantified evaluation and functional diagnosis of stroke patients which is in contrast to current assessment methods. It also establishes a study of the muscle co-contractions and synergies given the full set of muscles acting on the shoulder and arm.

I also developed a forward dynamics methods of the model which aims was at first to be solely driven by muscle activations, but without the closed-loop formulation, it is too unstable in its current state because of the accumulation of numerical errors over a simulation. It is however setting the ground for possible further development.

A graphical user interface was also developed for simpler and adaptable use of the model, in the forward and inverse modes, and for the study of multiple subjects and repetitions.

The achievements presented in the thesis can provide a tool to better understand the mechanisms underlying upper limb control as well as its impairments. Moreover, it sets a