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

This study presents an intermediate step in prosthesis design, by introducing a newly developed two-dimensional mathematical, and a three-dimensional computational knee model. The analytical model is derived from Newton’s law with respect to the equilibrium equations, thus based on theoretical assumptions, and experimentally obtained parameter. The numeric model is built from an existing prosthesis, involving three parts as patella, femur and tibia, and currently it is under development. The models are capable to predict – with their standard deviation – the patellofemoral (numerically tibiofemoral as well) forces in the knee joint during squatting motion. The reason why the squatting is investigated is due to 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 design method, and secondly to extend the results related to the existing isometric kinetics, where one of the newly obtained functions appears as an essential – and so far missing – input function. Most results are compared and validated to the ones found in the relevant literature and put into a dimensionless form in order to have more general meaning.