Development of a dynamic multibody 2D-model of the human knee joint

Abstract

The purpose of this work is to present a dynamic model for the biological human knee joint. The model is formulated in the framework of multibody systems methodologies, being the system modeled by two bodies, the femur and tibia. For the purpose of describing the formulation, the femur is fixed, while the tibia is considered to move relative to the femur. These two bones are represented as rigid bodies due to their higher stiffness when compared to that of the articular cartilages. The femur and tibia cartilages are considered to be de-formable structures with specific material characteristics. Based on medical imaging tech-niques, the femur and tibia profiles in the sagittal plane were obtained and used to define the interface geometrical conditions for contact. When the contact is detected, a continuous non-linear force law is applied that calculates the contact forces developed in the interface as function of an indentation. The four basic ligaments present in the knee are also taken into account in the proposed knee joint model, which are modeled as nonlinear elastic springs. The forces produced in the ligaments, together with the contact forces, are introduced into the equations of motion as external forces applied to the system. In addition, an external force is applied on the centre of mass of the tibia, in order to actuate the system mimicking the gait motion. Numerical results obtained from computational simulations are used to discuss the assumptions and procedures adopted in this study.