A Multibody/Finite Element Non-Linear Formulation of a Two-Ligament Knee Joint

Abstract

The focus of this investigation is to study the mechanics of the human knee using a new method that integrates multi-body system and large deformation finite element algorithms. The major bones in the knee joint consisting of the femur, tibia, fibula are modeled as rigid bodies. The ligaments structures are modeled using the large deformation finite element Absolute Nodal Coordinate Formulation (ANCF) with an implementation of a Neo-Hookean constitutive model that allows for large deformations as experienced in knee flexation and rotation. The Neo-Hookean strain energy function used in this study takes into consideration the near incompressibility of the ligaments. The ANCF is used in the formulation of the algebraic equations that define the ligament/bone rigid connection. A unique feature of the ANCF is that it allows for the deformation of the ligament cross-section. At the ligament/bone connection, the ANCF is used to define a fully constrained joint. This aspect of the model reflects the actual structural mechanics of the knee. In addition, this model will reflect the fact that the geometry, placement and attachment of the two collateral ligaments (the LCL and MCL), are significantly different from what has been used in most knee models developed in previous investigations. The approach described in this paper will provide a more realistic model of the knee and thus more applicable to future research studies. The obtained preliminary results of other applications show that the ANCF can be an effective tool for modeling very flexible structures like ligaments subjected to large deformations. In the future, the ANCF models could assist in examining the mechanics of the knee to study knee injuries and possible prevention means, as well as an improved understanding of the role of each individual ligament in the diagnosis and assessment of disease states, aging and potential therapies.