Modeling the human knee joint using the Proper Generalized Decomposition

Notre Dame Univresity-Louaize, department of mechanical engineering, Zouk Mosbeh, Lebanon

^* e-mail: cghnatios@ndu.edu.lb
^** e-mail: ilige.hage@ndu.edu.lb
^*** e-mail: nmetni@ndu.edu.lb

Abstract

Nowadays, human joints specifically movable are active research topics. The lack of effective replacements and the inefficient natural healing of these joints hinders any athlete from pursuing his career if injured in his joints. Therefore, researchers are testing innovative soft materials and biphasic materi- als as replacements of human joints. However, the lack of effective mechanical modeling is slowing the development of new replacements. In this work, we tackle the mechanical modeling of the synovial joint in a human knee. The tibiofemoral joint is modelled during impact. This joint is basically made of a cartilage, a meniscus (both a biphasic material) and the synovial fluid. The modeling is performed using Brinkman equation. However, the rich physics in- volved in the thickness direction requires a large number of degrees of freedom in the mesh to represent the physical phenomenon taking place in a knee joint. Thus, the use of model order reduction techniques appears to be an appealing approach in this situation. In fact, the proper generalized decomposition re- duced the number of degrees of freedom by using domain decomposition. The result of this work shows the pressure and fluid flow in the synovial joint under impact. A post treatment of the solution estimates the force held by each of the fluid and solid components of the cartilage joint. This model could be used to the human knee to estimate its components’ velocities and pressure fields while performing an activity.