Determination of the ligamentous and contact forces in the human tibio-femoral joint using a three-dimensional dynamic anatomical model

This paper describes for the first time the three-dimensional dynamic response of the tibio-femoral joint when subjected to sudden external loads utilizing a three-dimensional dynamic anatomical model. This model consists of two body segments in contact (the femur and the tibia) executing a general three-dimensional dynamic motion within the constraints of the ligamentous structures. Each of the articular surfaces at the tibio-femoral joint was represented by a separate mathematical function. The joint ligaments were modeled as nonlinear elastic springs. The six-degrees-of-freedom joint motions were characterized using six kinematic parameters and ligamentous forces were expressed in terms of these six parameters. Model equations consist of nonlinear second order ordinary differential equations coupled with nonlinear algebraic constraints. An algorithm was developed to solve this Differential-Algebraic Equations (DAE) system employing a DAE solver, namely the Differential/Algebraic System Solver (DASSL) developed at Lawrence Livermore National Laboratory. Model calculations show that as the knee was flexed from 15° to 90°, it underwent internal tibial rotation. However, in the first 15 degrees of knee flexion, this trend was reversed: the tibia rotated internally as the knee was extended from 15° to full extension. This finding is important since it is in agreement with the emerging thought of the need to re-evaluate the so called “screw-home mechanism”