A photoelastic study of ligament strain

The anterior cruciate ligament (ACL) in the human knee is known to exhibit as large as 10-20% of strain in association with knee flexion, while usual Hookean elastic materials exhibit at most 0.3%. Furthermore the complex ACL in shape deforms in highly variable manners due to the complicated three-dimensional (3-D) movements of the insertions in association with knee flexion. Such large and highly variable deformations of the ACL cannot be adequately quantified by one-dimensional (1-D) and/or localized measurements. In order to measure strains over the entire area of the ACL, the authors employed the photoelastic coating method to analyze stress on the basis of the strains. A specific kind of polyurethane possessing optically high fringe-sensitivity was found to be most suitable for measurement purposes. From the preliminary experiments, it was found that a linear relation with 99% of correlation coefficient between the birefringence order and the strain on the polyurethane film continued up to 45% of strain. This study was done in two steps. In the first step, a study was done using a unique model of a knee joint fabricated in a way which allowed deformation and strain distribution in the model ACL to be directly observed and measured by means of the photoelastic coating method. It was confirmed that the film, having negligible effect on the mechanical properties of some biological soft tissues, closely reflected the strain behavior of the tissue. Thus in the second step, the photoelastic method was employed to measure the strains on an actual ACL during free flexion-extension of the knee. A specially designed apparatus was used to allow a natural motion of the knee. The photoelastic measurements demonstrated the potential utility of the application to measuring strain distributions not only on a model ligament but also on an actual ligament. The measurement of an actual ACL led the following results: the principal strain lines well depicted its fiber directions; a reciprocal function between the anterior and posterior bundles was observed; and there was a zero-strain area on the central and posterior sides near the tibial insertion