Hyper-elastic model analysis of anterior cruciate ligament

Abstract

The objectives of this study were to theoretically analyze changes in shape and stress distribution which occur over the entire surface of the anterior cruciate ligament (ACL). While many studies on the cruciate ligaments' tensile characteristics have been conducted, the length patterns and the differential function of the ACL are still controversial issues for two reasons. Highly variable deformations of the ligaments (which are not uniaxial structures such as a bundle of separate fibres) cannot be adequately quantified by one-dimensional and/or localized measurements. Furthermore, it is impossible to directly measure in situ, non-uniform distribution of biaxial strain over the entire surface of the intra-articular ligaments. We employed an alternative approach which may have the potential to solve some of these difficulties. Using the finite element method, in which the ligament was treated as an incompressive hyper-elastic membrane, the finite deformation of the ligament was theoretically analyzed. Boundary conditions were applied by prescribing the displacements at the boundary nodes corresponding to the insertions. Special attention was paid to the distribution of longitudinal strain. The following values were obtained as a function of knee flexion: three-dimensional change in shape and strain distribution, length change of each fibre, length changes in positions along a fibre, resultant pull force on the tibial insertion, and change of strain pattern by anterior–posterior displacement of the tibia. The results demonstrated that strain distribution varied, even along the fibre run, and large strain gradients were observed in the regions near the insertions. It was found that distance between insertions introduced noticeable discrepancies from the length along a curved fibre. The net resultant force at the tibial insertion of the ligament was maximum at 0° of flexion, decreased until 50° of flexion, then slightly increased up to 120° of flexion. Predominantly, the anterior and the posterior displacements of the tibia, respectively, increased and decreased strain in the ligament, however, some portions were even more stretched by the posterior displacement.