Development of a biomechanical multibody knee model

Abstract

The purpose of this work is to develop a mathematical model for the knee joint under the framework of multibody system dynamics. The model is composed by two bodies: the femur, which is stationary, and the tibia, which is considered to move relative to the femur. Due to their higher stiffness compared to that of the articular cartilages, the femur and tibia are modeled as rigid bodies. The articular cartilages are modeled to be deformable structures with specific material characteristics. The main ligaments of the knee joint are included in the model as nonlinear springs. The geometrical profiles of the intervening contact anatomical structures, namely distal femur and proximal tibia, are extracted from a magnetic resonance image (MRI) and then fitted using piecewise cubic splines. Besides the gravitational force, an external force is applied at the center of mass of tibia to provide a dynamic activity to the model. When the bodies contact each other, a continuous non-linear force law is applied to calculate the contact forces as function of an indentation. The forces produced by the ligaments, together with the contact forces, are introduced into the equations of motion as external forces applied to the system. The mechanical behavior of the knee articular cartilages was evaluated using different contact laws. Computational simulations applying an external force with different amplitude values were also performed and the dynamic response of the ligaments was analyzed.