A new nonlinear multibody/finite element formulation for knee joint ligaments

Abstract

The focus of this investigation is to study the mechanics of the human knee using a new method that integrates multibody system and large deformation finite element algorithms. The major bones in the knee joint consisting of the femur, tibia, and fibula are modeled as rigid bodies. The ligaments structures are modeled using the large displacement finite element absolute nodal coordinate formulation (ANCF) with an implementation of a Neo-Hookean constitutive model that allows for large change in the configuration as experienced in knee flexion, extension, and rotation. The Neo-Hookean strain energy function used in this study takes into consideration the near incompressibility of the ligaments. The ANCF is used in the formulation of the algebraic equations that define the ligament/bone rigid connection. A unique feature of the ANCF model developed in this investigation is that it captures the deformation of the ligament cross section using structural finite elements such as beams. At the ligament/bone insertion site, the ANCF is used to define a fully constrained joint. This model will reflect the fact that the geometry, placement and attachment of the two collateral ligaments (the LCL and MCL), are significantly different from what has been used in most knee models developed in previous investigations. The approach described in this paper will provide a more realistic model of the knee and thus more applicable to future research studies on ligaments, muscles and soft tissues (LMST). Current finite element models are limited due to simplified assumptions for the spatial and time dependent material properties inherent in the anisotropic and anatomic constraints associated with joint stability, and the static conditions inherent in the analysis. The ANCF analysis is not limited to static conditions and results in a fully dynamic model that accounts for the distributed inertia and elasticity of the ligaments. The results obtained in this investigation show that the ANCF finite elements can be an effective tool for modeling very flexible structures like ligaments subjected to large flexion and extension. In the future, the more realistic ANCF models could assist in examining the mechanics of the knee to study knee injuries and possible prevention means, as well as an improved understanding of the role of each individual ligament in the diagnosis and assessment of disease states, aging and potential therapies.

Functional morphology of the jaw adductor muscles in the Canidae

“…In all the CT scans and dissected specimens, the temporozygomatic suture could be easily perceived as a simple, rather than interdigitated, dark line, which completely separated the zygomatic and temporal bones. The temporozygomatic sutures were modeled as a neo-Hookean material to reflect their hyperplastic properties (Mohamed, Brown, & Shabana, 2010;Weed & Maqueda, 2010). The orbital ligaments were included because work by Herring, Rafferty, Liu, and Lemme (2011) has suggested some involvement with muscle force distribution, in particular, resisting deformation of the zygomatic arches by contraction of the masseter during biting.…”

Control of the extension–flexion cycle of human knees during bicycle riding by a synergy of solitary muscular excitations and contractions

“…Its primary dynamical function is a single dominant degree-of-freedom (DOF): flexion/extension in the sagittal plane, actuated by the two of the largest muscular groups in the human body: m. quadriceps femoris performing knee extension and m. hamstrings performing knee flexion. 1 Modelling and simulation studies of the knee dynamics have usually been based on multi-body models and/or finite element method (see [4,5] and the references therein). In the present paper we extend this approach by including soliton models of excitation and contraction of the extensor-quadriceps and flexor-hamstrings.…”

“…The kink-soliton model(5) for the excitation-contraction coupling (left) with the corresponding inhibition/relaxation coupling (right) of the knee extensors (quadriceps) and flexors (hamstrings), representing the normalized muscular force-length-time relation. Again, time is in seconds, muscle's length-change is in millimeters, giving the contraction amplitude of 2cm for both muscles.…”

“…Biochemically, it is performed by the release of Ca + + ions from the sarcoplasmic triads, their binding by troponin to remove the blocking action of tropomyosin, with the simultaneous rearrangement and exposition of the actin filaments and subsequent activation of myosin cross-bridges, to start the actin-myosin sliding fueled by the ATP hydrolysis (see, e.g [38,39]. and the references therein) 5. Nobel Laureate A.V.…”

Investigating Effects of Losing Fluid on Nonlinear Structural Behavior of Rabbit ACL

“…Regarding the nonlinear behavior of stress-strain curve, some studies focused on hyperelastic properties of ligamentous tissues and strain energy functions. The computational model of the tibiofemoral joint in the human knee was verified in [8] . As 60-70% of the tissue total weight is occupied by water ( [9]), the ligaments are usually considered as a nonlinear incompressible material.…”