Viscoelastic properties of soft tissues: application to knee ligaments and tendons
Ligaments play a central role in the stability of the knee. Due to the increase in sport activities of the young population, rupture of the anterior cruciate ligament (ACL) has become a frequent clinical problem. A surgical procedure replacing the deficient ligament is performed to restore the knee's initial stability. Although this surgical technique is widespread and well established, long term clinical results are inconsistent and the stability of the knee is not always restored, leading to premature arthrosis of the knee. This inconsistency of ACL replacement motivated the present study. "Optimal" ACL replacement only can be performed if the static and dynamic properties of the ligament are precisely known. In order to investigate these mechanical properties, an experimental set-up was developed to test human cruciate ligaments, as well as patellar tendon, which is commonly used for cruciate ligament replacement. Traction tests at different constant rates of elongation and stress relaxation tests were performed at controlled temperature (37°C) and humidity (100%). Results showed that cruciate ligaments and patellar tendons exhibit a non-linear elastic behavior in addition to a viscous behavior. The viscous behavior encompassed two phenomena: first a behavior where stress depended on strain rate (short term memory effects) and second a behavior where stress relaxed on a longer time scale (long term memory effects). In order to describe the different mechanical behaviors of the specimens in a general mechanical framework, a theoretical model was developed by simultaneously taking into account the non-linear elastic behavior, the short term memory effects and the long term memory effects. This proceeding satisfied the basic mechanical and thermodynamical requirements. The originality of the present model is based on the fact that the different mechanical behaviors are described in one framework allowing a compact description of the biomechanical properties of different soft tissues. The description of the short term memory effects is new in situations involving large deformations. The model is restricted by considering the specimens as isotropic, homogeneous and incompressible. The identification process of the different mechanical behaviors was facilitated with the proposed model. The non-linear elasticity was described with two parameters, the short term memory effects with one parameter and the long term memory effects with six parameters. No statistical differences were found between the parameters used for the anterior cruciate ligaments, the posterior cruciate ligaments and patellar tendons. The non-linear elastic behavior was implemented in a finite element code. The stress field in an ACL was calculated during a knee flexion and a tibial drawer test. The calculated stress field was inhomogeneous, with the highest stress in the anteriormedial part of the ACL. It was found that internal rotation of the knee generally increased the calculated stress in the ACL. These numerical results agree with in vitro studies given in the literature. The numerical results yielded a stress field in the ligament which was complementary to in vitro studies, where only the resultant ligament force can be measured. Several useful clinical conclusions can be drawn from the present biomechanical study. Diagnosis of an ACL rupture is generally performed by a contralateral comparison of antero-postero knee laxity (tibial drawer test) using a quasi-static load. However, diagnosis of an injured knee would be more accurate if the antero-postero load was dynamically applied to the knee: in this case, a knee with a rupture ACL would not show any effect, whereas a knee with an intact ACL would become stiffer with increasing the strain rate. In case of ACL replacement, the graft should be preconditioned in order to diminish the effects of stress relaxation. During the rehabilitation program after an ACL suture or replacement, flexion of the knee in an internal position should be omitted because internal rotation increases the stresses in the ligament.