Analytical and computational estimation of patellofemoral forces in the knee under squatting and isometric motion

Abstract

This study presents an intermediate step in prosthesis design, by introducing a newly developedtwo-dimensional mathematical, and a three-dimensional computational knee model. The analytical model isderived from Newton’s law with respect to the equilibrium equations, thus based on theoreticalassumptions, and experimentally obtained parameter. The numeric model is built from an existingprosthesis, involving three parts as patella, femur and tibia, and currently it is under development. Themodels are capable to predict – with their standard deviation – the patellofemoral (numerically tibiofemoralas well) forces in the knee joint during squatting motion. The reason why the squatting is investigated is dueto its relative simplicity and the fact, that during the movement the forces reach extremity in the knee joint.The obtained forces – as a function of flexion angle – are used firstly as fundaments to the knee designmethod, and secondly to extend the results related to the existing isometric kinetics, where one of the newlyobtained functions appears as an essential – and so far missing – input function. Most results arecompared and validated to the ones found in the relevant literature and put into a dimensionless form inorder to have more general meaning.