2-D Inverse Dynamics Knee Model: Aligning Anatomical Knee Model With Squatting Kinematic Data Using Ligament Forces

Abstract

A 2-dimensional anatomical knee model was developed for aligning knee joint related bone structures with experimental kinematic data. The experimental data was collected using motion capture cameras, which recorded the position of reflective markers placed on the human subject. Velocities were calculated by numerically differentiating the marker position with respect to time. Joints, such as the hip, knee, and ankle, were represented by axes of rotation. These axes were determined by calculating the relative instantaneous center of rotation of a body segment with respect to the adjacent body segment. Body-fixed coordinate systems were set for both thigh and shin. Anatomical bone structures were obtained from an x-ray and represented mathematically as polynomials. The femoral bone surface was aligned with the experimental data by superimposing the center of rotation of the shin with respect to thigh with the geometric center of the femoral condyle. The tibial surface was aligned with the experimental data by aligning the bones at minimum flexion and then superimposing the tibia with a shared point between femur and tibia. Ligaments were modeled as non-linear elastic springs. Cruciate ligaments were divided into a posterior and anterior ligament fiber bundle. Cruciate ligament forces were calculated for the squatting exercise for five different femoral geometric centers. Geometric centers were determined using a nonlinear least squares optimization technique. Cruciate ligament forces are discussed in this paper.