A three-dimensional finite element model of the human anterior cruciate ligament: a computational analysis with experimental validation

In this study, the force and stress distribution within the anteromedial (AM) and posterolateral (PL) bundles of the anterior cruciate ligament (ACL) in response to an anterior tibial load with the knee at full extension was calculated using a validated three-dimensional finite element model (FEM) of a human ACL. The interaction between the AM and PL bundles, as well as the contact and friction caused by the ACL wrapping around the bone during knee motion, were included in the model. The AM and PL bundles of the ACL were simulated as incompressible homogeneous and isotropic hyperelastic materials. The multiple-degrees-of-freedom (DOF) knee kinematics of a cadaveric knee were first obtained using a robotic/universal force-moment sensor testing system. These data were used as the boundary conditions for the FEM of the ACL to calculate the forces in the ACL. The calculated forces were compared to the in situ force in the ACL, determined experimentally, to validate the model. The validated FEM was then used to calculate the force and stress distribution within the ACL under an anterior tibial load at full extension. The AM and PL bundles shared the force, and the stress distribution was non-uniform within both bundles with the highest stress localized near the femoral insertion site. The contact and friction caused by the ACL wrapping around the bone during knee motion played the role of transferring the force from the ACL to the bone, and had a direct effect on the force and stress distribution of the ACL. This validated model will enable the analysis of force and stress distribution in the ACL in response to more complex loading conditions and has the potential to help design improved surgical procedures following ACL injuries.     

Computational stability of human knee joint at early stance in Gait: Effects of muscle coactivity and anterior cruciate ligament deficiency

As one of the most complex and vulnerable structures of body, the human knee joint should maintain dynamic equilibrium and stability in occupational and recreational activities. The evaluation of its stability and factors affecting it is vital in performance evaluation/enhancement, injury prevention and treatment managements. Knee stability often manifests itself by pain, hypermobility and giving-way sensations and is usually assessed by the passive joint laxity tests. Mechanical stability of both the human knee joint and the lower extremity at early stance periods of gait (0% and 5%) were quantified here for the first time using a hybrid musculoskeletal model of the lower extremity. The roles of muscle coactivity, simulated by setting minimum muscle activation at 0–10% levels and ACL deficiency, simulated by reducing ACL resistance by up to 85%, on the stability margin as well as joint biomechanics (contact/muscle/ligament forces) were investigated. Dynamic stability was analyzed using both linear buckling and perturbation approaches at the final deformed configurations in gait. The knee joint was much more stable at 0% stance than at 5% due to smaller ground reaction and contact forces. Muscle coactivity, when at lower intensities (<3% of its maximum active force), increased dynamic stability margin. Greater minimum activation levels, however, acted as an ineffective strategy to enhance stability. Coactivation also substantially increased muscle forces, joint loads and ACL force and hence the risk of further injury and degeneration. A deficiency in ACL decreases total ACL force (by 31% at 85% reduced stiffness) and the stability margin of the knee joint at the heel strike. It also markedly diminishes forces in lateral hamstrings (by up to 39%) and contact forces on the lateral plateau (by up to 17%). Current work emphasizes the need for quantification of the lower extremity stability margin in gait.     

Development and validation of a computational model of the knee joint for the evaluation of surgical treatments for osteoarthritis

A three-dimensional (3D) knee joint computational model was developed and validated to predict knee joint contact forces and pressures for different degrees of malalignment. A 3D computational knee model was created from high-resolution radiological images to emulate passive sagittal rotation (full-extension to 65°-flexion) and weight acceptance. A cadaveric knee mounted on a six-degree-of-freedom robot was subjected to matching boundary and loading conditions. A ligament-tuning process minimised kinematic differences between the robotically loaded cadaver specimen and the finite element (FE) model. The model was validated by measured intra-articular force and pressure measurements. Percent full scale error between FE-predicted and in vitro-measured values in the medial and lateral compartments were 6.67% and 5.94%, respectively, for normalised peak pressure values, and 7.56% and 4.48%, respectively, for normalised force values. The knee model can accurately predict normalised intra-articular pressure and forces for different loading conditions and could be further developed for subject-specific surgical planning.     

Simulation of planar soft tissues using a structural constitutive model: Finite element implementation and validation

Computational implementation of physical and physiologically realistic constitutive models is critical for numerical simulation of soft biological tissues in a variety of biomedical applications. It is well established that the highly nonlinear and anisotropic mechanical behaviors of soft tissues are an emergent behavior of the underlying tissue microstructure. In the present study, we have implemented a structural constitutive model into a finite element framework specialized for membrane tissues. We noted that starting with a single element subjected to uniaxial tension, the non-fibrous tissue matrix must be present to prevent unrealistic tissue deformations. Flexural simulations were used to set the non-fibrous matrix modulus because fibers have little effects on tissue deformation under three-point bending. Multiple deformation modes were simulated, including strip biaxial, planar biaxial with two attachment methods, and membrane inflation. Detailed comparisons with experimental data were undertaken to insure faithful simulations of both the macro-level stress–strain insights into adaptations of the fiber architecture under stress, such as fiber reorientation and fiber recruitment. Results indicated a high degree of fidelity and demonstrated interesting microstructural adaptions to stress and the important role of the underlying tissue matrix. Moreover, we apparently resolve a discrepancy in our 1997 study (Billiar and Sacks, 1997. J. Biomech. 30 (7), 753–756) where we observed that under strip biaxial stretch the simulated fiber splay responses were not in good agreement with the experimental results, suggesting non-affine deformations may have occurred. However, by correctly accounting for the isotropic phase of the measured fiber splay, good agreement was obtained. While not the final word, these simulations suggest that affine fiber kinematics for planar collagenous tissues is a reasonable assumption at the macro level. Simulation tools such as these are imperative in the design and simulation of native and engineered tissues.     

A hyperelastic biphasic fibre-reinforced model of articular cartilage considering distributed collagen fibre orientations: continuum basis,computational aspects and applications

Cartilage is a multi-phase material composed of fluid and electrolytes (68–85% by wet weight), proteoglycans (5–10% by wet weight), chondrocytes, collagen fibres and other glycoproteins. The solid phase constitutes an isotropic proteoglycan gel and a fibre network of predominantly type II collagen, which provides tensile strength and mechanical stiffness. The same two components control diffusion of the fluid phase, e.g. as visualised by diffusion tensor MRI: (i) the proteoglycan gel (giving a baseline isotropic diffusivity) and (ii) the highly anisotropic collagenous fibre network. We propose a new constitutive model and finite element implementation that focus on the essential load-bearing morphology: an incompressible, poroelastic solid matrix reinforced by an inhomogeneous, dispersed fibre fabric, which is saturated with an incompressible fluid residing in strain-dependent pores of the collagen–proteoglycan solid matrix. The inhomogeneous, dispersed fibre fabric of the solid further influences the fluid permeability, as well as an intrafibrillar portion that cannot be ‘squeezed out’ from the tissue. Using representative numerical examples on the mechanical response of cartilage, we reproduce several features that have been demonstrated experimentally in the cartilage mechanics literature.