A fast ligament model with scalable accuracy for multibody simulations

Multibody musculoskeletal models are important tools to perform kinematic, kinetostatic, and dynamic analyses of the whole human body. In these models, bones are regarded as rigid bodies, while different strategies are used to model structures such as muscles and ligaments. In this context, ligaments are often represented using a finite set of spring-like elements to compute the wrench applied to the bones (multibundle model). While this model is fast and easy to be implemented, it can suffer from inaccuracies due to the limited number of fibers and their positioning. In this study, a ligament model is proposed to overcome these limitations, representing the ligament as an infinite distribution of fibers from which the wrench on the bones can be obtained. The model takes advantage of thin-plate spline mapping to model the fiber structure of the ligament by defining a correspondence between the points of the two ligament insertions. The accuracy and the performances of the model are verified on a ligament and compared to the standard multibundle model. Results indicate that the model is faster and more accurate than the multibundle model. Moreover, accuracy can be modified according to the application in order to decrease the computational time.