Abstract
Orthopaedic companies spend years and millions of dollars developing and verifying new total knee arthroplasty (TKA) designs. Recently, computational models have been used in the hopes of increasing the efficiency of the design process. The most popular predictive models simulate a cadaveric rig. Simulations of these rigs, although useful, do not predict in vivo behavior. Therefore, in this current study, the development of a physiological forward solution, or predictive, rigid body model of the knee is described.
The models simulate a non-weight bearing extension activity or a weight-bearing deep knee bend (DKB) activity. They solve for both joint forces and kinematics simultaneously and were developed from the ground up. The models are rigid body and use Kane's dynamical equations. The model began with a simple two dimensional non-weight bearing extension activity model of the tibiofemoral joint. Step by step the model was expanded. Quadriceps and hamstring muscles were added to drive the motion. Ligaments were added represented by multiple non-linear spring elements. The model was expanded to three-dimensions (3D) allowing out of plane motions and calculation of medial and lateral condylar forces. The patella was added as its own body allowing for simulation of the patellofemoral joint. The model was then converted to a weight bearing deep knee bend activity. A pelvis and trunk were added and muscles were given physiological origin and insertion points. A modified proportional-integral-derivative (PID) controller was implemented to control the rate of flexion and also to assist in joint stability by adjusting the force in individual quadriceps muscles. A method for representing articulating geometry was developed. Once the deep knee bend model was fully developed (Figure 1) it was converted back to a non-weight bearing extension model (Figure 2) resulting in simulations of a normal knee performing a weight bearing and non-weight bearing activity. The tibiofemoral kinematic results were compared to in vivo kinematics obtained from a fluoroscopy study of five normal subjects. Parameters from the CT models of one of these subjects (Subject 3) were used in the model.
The model kinematics behave as the normal knee does in vivo. The kinetic results were within reasonable ranges with a maximum total quadriceps force of 0.86 BW and 4.73 BW for extension and DKB simulations, respectively (Figure 3 and Figure 4). The maximum total tibiofemoral forces were 1.26 BW and 3.70 BW for extension and DKB, respectively. The relationship between the quadriceps force, patella ligament force and patellofemoral forces are consistent with how the extensor mechanism behaves (Figure 3 and Figure 4). The patellofemoral forces are low between 0 and 20 degrees flexion and the patella ligament and quadriceps forces are close in magnitude from 0 to around 70 degrees flexion when the patellofemoral forces increase and the quadriceps forces increase relative to the patella ligament force. The model allows for virtual implantation of TKA geometry and after kinematic and kinetic validation from in vivo TKA data can be used to predict the behavior of TKA in vivo.
