Relevance of the hyperelastic behavior of cruciate ligaments in the modeling of the human knee joint in sagittal plane

The rupture of the anterior cruciate ligament (ACL) is the most common injury of the human knee. When surgery is required, it is helpful for orthopedic surgeons define scientifically the best insertion position for the graft, which approximates the functionality of an intact ACL. To accomplish that, it is crucial to estimate the force acting on the ligament (or graft) in response to an external load applied to the knee. This force is called the in-situ force. The objective of this research is to propose a modeling methodology of the human knee in the sagittal plane based on the theory of mechanisms and Davies' method. In a first approach the cruciate ligaments are treated as rigid bodies, and in a second approach, as hyperelastic bodies. These two approaches are then compared. The model provide information to assist the preoperative planning, by simulation of the ACL positions and in-situ forces. The proposed methodology consists of four steps and an experimental procedure performed by a robotic manipulator to obtain the in-situ forces. Experimental in-situ forces are used to validate the proposed model. Besides helping the preoperative planning, the model allows to verify two relevant biomechanical hypothesis: 1. During the simulation of the ACL in-situ force, the modeling of the cruciate ligaments as rigid links shows similar results to the modeling which considers the hyperelastic behavior (more complex). 2. The ACL in-situ force can be well approximated when the knee is modeled as a two-dimensional four bar mechanism. Based on the results it can be concluded that: The forces obtained by simulations that consider the hyperelastic behavior of the cruciate ligaments are close from the forces obtained by simulations that consider the cruciate ligaments as rigid bodies. It can also be noted that the simulated results are quite similar to the experimental results, which is important considering that the proposed model is simplified.