The Effect of the Variation in ACL Constitutive Model on Joint Kinematics and Biomechanics Under Different Loads: A Finite Element Study

Abstract

The biomechanics and function of the anterior cruciate ligament (ACL) have been widely studied using both experimental and simulation methods. It is known that a constitutive model of joint tissue is a critical factor in the numerical simulation. Some different ligament constitutive models have been presented to describe the ACL material behavior. However, the effect of the variation in the ligament constitutive model on joint kinematics and biomechanics has still not been studied. In this paper, a three-dimensional finite element model of an intact tibiofemoral joint was reconstructed. Three ACL constitutive models were compared under different joint loads (such as anterior tibial force, varus tibial torque, and valgus tibial torque) to investigate the effect of the change of the ACL constitutive model. The three constitutive models corresponded to an isotropic hyperelasticity model, a transversely isotropic hyperelasticity model with neo-Hookean ground substance description, and a transversely isotropic hyperelastic model with nonlinear ground substance description. Although the material properties of these constitutive equations were fitted on the same uniaxial tension stress-strain curve, the change of the ACL material constitutive model was found to induce altered joint kinematics and biomechanics. The effect of different ACL constitutive equations on joint kinematics depended on both deformation direction and load type. The variation in the ACL constitutive models would influence the joint kinematic results greatly in both the anterior and internal directions under anterior tibial force as well as some other deformations such as the anterior and medial tibial translations under valgus tibial torque, and the medial tibial translation and internal rotation under varus torque. It was revealed that the transversely isotropic hyperelastic model with nonlinear ground substance description (FE model III) was the best representation of the realistic ACL property by a linear regression between the simulated and the experiment deformation results. But the comparison of the predicted and experiment force of ligaments showed that all the three ACL constitutive models represented similar force results. The stress value and distribution of ACL were also altered by the change in the constitutive equation. In brief, although different ACL constitutive models have been fitted using the same uniaxial tension curve and have the similar longitudinal material property, the ACL constitutive equation should still be carefully chosen to investigate joint kinematics and biomechanics due to the different transverse material behavior.

The effect of the material property change of anterior cruciate ligament by ageing on joint kinematics and biomechanics under tibial varus/valgus torques

“…With the ACL changing from younger to older, some significant changes of the joint displacement occurred on the tibial anterior translation and external rotation (about 33%) under tibial valgus torque but only the tibial anterior translation had changed about 14% under the tibial varus torque. It is in accordance with other papers wherein the ACL plays a vital role in resisting the coupled displacements (such as the tibial anterior translation and external rotation in these cases) rather the varus/valgus rotation when the joint is under varus/valgus torque loads [4,30,33].…”

“…The FE models were treated as quasi-static problems using explicit FE techniques in AB-AQUS v6.10 software. The validation of the FE model was achieved in our previous paper [30].…”

Combining Displacement Field and Grip Force Information to Determine Mechanical Properties of Planar Tissue With Complicated Geometry

“…For example, Flynn and Rubin have proposed a three-parameter strain energy density model based on total dilatation, an orthotropic invariant, and a measure of the elas tic distortional deformation [36]. Sun and Sacks have published a planar soft-tissue seven parameter generalized Fung-elastic con stitutive model with two restrictions for numerical stability [37], Other constitutive equations have been published with application to tissue from, e.g., anterior cruciate ligament [38], abdominal aortic aneurysm tissue [39], and healthy renal artery [40].…”

Finite element simulation of articular contact mechanics with quadratic tetrahedral elements

“…Although quadratic tetrahedral elements have been investigated as alternatives to HEX8 elements (e.g., (Cifuentes and Kalbag, 1992; Tadepalli et al, 2011; Weingarten, 1994)), none of these studies investigated their application for simulation of articular contact analyses. The 10-node tetrahedron (TET10) has seen some limited use for contact mechanics (Bunbar et al, 2001; Hao et al, 2011; Tadepalli et al, 2011; Wan et al, 2013; Yang and Spilker, 2006). To our knowledge the 15-node tetrahedron (TET15) has never been used in computational biomechanics and it has seen very limited use in nonlinear computational solid mechanics at all (Danielson, 2014), although it has been used in the fluid mechanics community (Bertrand et al, 1992).…”