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

Abstract

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 to scientifi cally defi ne the best 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 evidence the relevance of the hyperelastic behavior of cruciate ligaments in the two-dimensional modeling of the knee. To achieve this, a sequential method of modeling is proposed based on the theory of mechanisms and Davies' method. In a fi rst 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 provides 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 verifying two relevant biomechanical hypotheses: 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 to 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.