Comparison between different muscular models

Muscles are crucial to any living creature since the muscular system is responsible for the movement of the body. Muscles allow us to speak, breath, walk or run for example. They are capable to turn energy into motion and are tremendously sophisticated. They thus aroused the interest of scientists to understand how muscles work and how they can be modelled. Muscle models have been developed for different reasons such as trying to better understand how muscles work by isolating the important components or to explain and predict a force response. Understanding how a healthy muscle works can be crucial to comprehend muscle pathologies in order to heal them. Understanding a muscle and being able to predict its force response can also be used to create prostheses that replace a body segment. Another application for muscular models can be humanoid robots where the muscle activity of humans is more or less duplicated. Most muscular models focus on skeletal muscles since these are the ones that allow us to interact with the environment. The purpose of this master thesis is to review some muscular models of the skeletal muscle and compare them according to different criteria in order to see whether there is a model better than the others and whether it takes the whole complexity of the muscle into account. First, an isolated muscle and its force response with the different muscular models will be compared and then, since a skeletal muscle is usually connected to bones, a bi-muscular articulation will be implemented and compared for the different muscular models. Four types of models, found in the literature, were implemented in this master thesis by using the MATLAB software. These models were chosen for the reason that they all focused on a different aspect of the muscle modelization. All the models work according to a common framework: each model takes as input the muscle length and velocity as well as an activation level. The main output is the force response. Mathematical functions, different for each model, predict the force-response from these inputs. The force-response from each model for the same inputs were then compared to each other and to the literature. They were compared in terms of different criteria such as computation time, their biophysical meaning or their activation dynamics to name a few. Their mechanical impedance, how the muscle resists to an oscillating perturbation, was also analysed for each model. The bi-muscular articulation analysed in this master thesis is the human ankle and two antagonist muscles. The tibia was fixed and only the foot could move with respect to the tibia. The muscles were given similar activation levels for the models and the resulting change in angle and torque could be obtained and compared. The mechanical impedance, of the ankle this time, was analysed for each model as well. Although all four models had similar force responses, one dominated in terms of biophysical meaning and accuracy. The price of this is a heavy computation time that made it unsuited for the implementation of an articulation. The other models had better computational times with a loss of accuracy and biophysical meaning. The activation dynamics of the four models were quite dissimilar: some were more complex and physiologically meaningful than others. Two models had as output only the force-response while one gave also the muscle stiffness and one, the slowest one, gave the muscle stiffness as well as the stored elastic energy in the muscle. Finally, some differences in terms of impedance of the modelled isolated muscle could be noted. The simulated ankle articulation moved in a similar way with the three remaining muscular models and their impedance did not differ much. The models presented in this master thesis are only a handful of the diversity of models that exists in the literature. The models discussed here modelled all the skeletal muscle but there exist also models for other types of muscle.