Author(s)

Sara Sadeqi^1,2, Rodney Summers¹, Deniz U. Erbulut^1,3, Vijay K. Goel^1*

¹Engineering Center for Orthopaedics Research Excellence (E-CORE), Departments of Bioengineering and Orthopaedics, The University of Toledo, Toledo, USA.
²Department of Mechanical, Industrial and Manufacturing Engineering (MIME), The University of Toledo, Toledo, USA.
³Herston Biofabrication Institute, Metro North Hospital and Health Service, Brisbane, Australia.

Accurate representation of soft tissue material properties plays a crucial role in computational biomechanics. Several material models have been used for knee ligaments in finite element (FE) studies, including the neo-Hookean model (widely used) and the Holzapfel-Gasser-Ogden (HGO) model (seldom used). While the coefficients of neo-Hookean models for the knee ligaments are available in the literature, limited data exists for the HGO model. Furthermore, no peer-reviewed comparison of these two material models for the knee ligaments while including the 3D representation of the ligaments for both material models is present in the literature. We used mechanical properties from the tensile test experiments in the literature for each ligament to obtain the HGO material coefficients while accounting for the ligaments’ viscoelastic behavior. Resultant coefficients were then used in an Abaqus/explicit knee model to simulate bipedal landing from a jump. The simulations were repeated with neo-Hookean values from the literature. Knee kinematics plus ACL and MCL strains were evaluated and compared for these two material models. The outputs from the simulations with HGO properties were predominantly within 1.5 standard deviations from the mean in-vitro data. When the material properties changed to Neo-Hookean, the outputs for kinematics and strain values were higher than the HGO case, and in most instances, they were outside the experimental range for ACL and MCL strains (by up to 11.35 SD) as well as some ITR angles (by up to 2.86 SD). Reported HGO material model with optimized coefficients produces a more realistic representation of the ligaments’ material properties, and will help improve the outcomes of FE models for more accurate predictions of knee behavior.

Soft Tissue, Material Properties, Holzapfel-Gasser-Ogden Constitutive Model, Dynamic Finite Element Analysis, Knee Ligaments

Sadeqi, S. , Summers, R. , Erbulut, D. and Goel, V. (2021) Optimization of Material Coefficients in the Holzapfel-Gasser-Ogden Material Model for the Main Four Ligaments of the Knee Joint-A Finite Element Study. Applied Mathematics, 12, 1166-1188. doi: 10.4236/am.2021.1212075.