A finite element implementation for biphasic contact of hydrated porous media under finite deformation and sliding.

The study of biphasic soft tissue contact is fundamental to understand the biomechanical behavior of human diarthrodial joints. However, to date, only few biphasic finite element contact analyses for three-dimensional physiological geometries under finite deformation have been developed. The objective of this article is to develop a hyperelastic biphasic contact implementation for finite deformation and sliding problem.

Biphasic finite element contact analysis of the knee joint using an augmented Lagrangian method.

Biphasic contact analysis is essential to obtain a more complete understanding of soft tissue biomechanics; however, only a limited number of studies have addressed these types of problems. In this paper, a theoretically consistent biphasic finite element solution of the 2D axisymmetric human knee was developed, and an augmented Lagrangian method was used to enforce the biphasic continuity across the contact interface. The interaction between the fluid and solid matrices of the soft tissues of the knee joint, the stress and strain distributions within the meniscus, and the changes in stress and strain distributions in the articular cartilage of the femur and tibia after complete meniscectomy were investigated.

An augmented Lagrangian finite element formulation for 3D contact of biphasic tissues.

Biphasic contact analysis is essential to obtain a complete understanding of soft tissue biomechanics, and the importance of physiological structure on the joint biomechanics has long been recognised; however, up to date, there are no successful developments of biphasic finite element contact analysis for three-dimensional (3D) geometries of physiological joints. The aim of this study was to develop a finite element formulation for biphasic contact of 3D physiological joints. The augmented Lagrangian method was used to enforce the continuity of contact traction and fluid pressure across the contact interface.

An augmented Lagrangian method for sliding contact of soft tissue.

Despite the importance of sliding contact in diarthrodial joints, only a limited number of studies have addressed this type of problem, with the result that the mechanical behavior of articular cartilage in daily life remains poorly understood. In this paper, a finite element formulation is developed for the sliding contact of biphasic soft tissues. The augmented Lagrangian method is used to enforce the continuity of contact traction and fluid pressure across the contact interface.

Biphasic finite element modeling of hydrated soft tissue contact using an augmented Lagrangian method.

A study of biphasic soft tissues contact is fundamental to understanding the biomechanical behavior of human diarthrodial joints. To date, biphasic-biphasic contact has been developed for idealized geometries and not been accessible for more general geometries. In this paper a finite element formulation is developed for contact of biphasic tissues.

A linear, biphasic model incorporating a brinkman term to describe the mechanics of cell-seeded collagen hydrogels.

Protein-based hydrogels are commonly used as in vitro models of native tissues because they can mimic specific aspects of the three-dimensional extracellular matrix present in vivo. Bulk mechanical stimulation is often applied to these gels to determine the response of embedded cells to biomechanical factors such as stress and strain. This study develops and applies a linear, biphasic formulation of hydrogel mechanics that includes a Brinkman term to account for viscous effects.

A two-dimensional computational model of lymph transport across primary lymphatic valves.

This study utilizes a finite element model to characterize the transendothelial transport through overlapping endothelial cells in primary lymphatics during the uptake of interstitial fluid. The computational model is built upon the analytical model of these junctions created by Mendoza and Schmid-Schonbein (2003, "A Model for Mechanics of Primary Lymphatic Valves," J. Biomed.

The impact of biomechanics in tissue engineering and regenerative medicine.

Biomechanical factors profoundly influence the processes of tissue growth, development, maintenance, degeneration, and repair. Regenerative strategies to restore damaged or diseased tissues in vivo and create living tissue replacements in vitro have recently begun to harness advances in understanding of how cells and tissues sense and adapt to their mechanical environment. It is clear that biomechanical considerations will be fundamental to the successful development of clinical therapies based on principles of tissue engineering and regenerative medicine for a broad range of musculoskeletal, cardiovascular, craniofacial, skin, urinary, and neural tissues.

A study of preconditioned Krylov subspace methods with reordering for linear systems from a biphasic v-p finite element formulation.

A study was conducted on combinations of preconditioned iterative methods with matrix reordering to solve the linear systems arising from a biphasic velocity-pressure (v-p) finite element formulation used to simulate soft hydrated tissues in the human musculoskeletal system. Krylov subspace methods were tested due to the symmetric indefiniteness of our systems, specifically the generalized minimal residual (GMRES), transpose-free quasi-minimal residual (TFQMR), and biconjugate gradient stabilized (BiCGSTAB) methods. Standard graph reordering techniques were used with incomplete LU (ILU) preconditioning.

A Lagrange multiplier mixed finite element formulation for three-dimensional contact of biphasic tissues.

A three-dimensional (3D) contact finite element formulation has been developed for biological soft tissue-to-tissue contact analysis. The linear biphasic theory of Mow, Holmes, and Lai (1984, J. Biomech.

A penetration-based finite element method for hyperelastic 3D biphasic tissues in contact. Part II: finite element simulations.

The penetration method allows for the efficient finite element simulation of contact between soft hydrated biphasic tissues in diarthrodial joints. Efficiency of the method is achieved by separating the intrinsically nonlinear contact problem into a pair of linked biphasic finite element analyses, in which an approximate, spatially and temporally varying contact traction is applied to each of the contacting tissues. In Part I of this study, we extended the penetration method to contact involving nonlinear biphasic tissue layers, and demonstrated how to derive the approximate contact traction boundary conditions.

A penetration-based finite element method for hyperelastic 3D biphasic tissues in contact: Part 1--Derivation of contact boundary conditions.

In this study, we extend the penetration method, previously introduced to simulate contact of linear hydrated tissues in an efficient manner with the finite element method, to problems of nonlinear biphasic tissues in contact. This paper presents the derivation of contact boundary conditions for a biphasic tissue with hyperelastic solid phase using experimental kinematics data. Validation of the method for calculating these boundary conditions is demonstrated using a canonical biphasic contact problem.

Biphasic finite element simulation of the TMJ disc from in vivo kinematic and geometric measurements.

Understanding the biomechanical nature of the degeneration of the temporomandibular joint requires a coupling between experimental measurements and numerical simulation. In this study, geometry measured from MRI, and motion obtained from a specially designed optoelectronic system are fed into a three-dimensional biphasic finite element analysis to generate the spatial and temporal mechanical response of the disc. This study demonstrates how this coupling can effectively predict the biomechanical response of the temporomandibular joint disc to physiological loading.

Mixed and Penalty Finite Element Models for the Nonlinear Behavior of Biphasic Soft Tissues in Finite Deformation: Part II - Nonlinear Examples.

This two-part paper addresses finite element-based computational models for the three-dimensional (3-D) nonlinear analysis of soft hydrated tissues, such as articular cartilage in diarthrodial joints, under physiologically relevant loading conditions. A biphasic continuum description is used to represent the soft tissue as a two-phase mixture of incompressible inviscid fluid and a hyperelastic, transversely isotropic solid. Alternate mixed-penalty and velocity-pressure finite element formulations are used to solve the nonlinear biphasic governing equations, including the effects of strain-dependent permeability and a hyperelastic solid phase under finite deformation.

Mixed and Penalty Finite Element Models for the Nonlinear Behavior of Biphasic Soft Tissues in Finite Deformation: Part I - Alternate Formulations.

This paper addresses finite element-based computational models for the three-dimensional, (3-D) nonlinear analysis of soft hydrated tissues, such as the articular cartilage in diarthrodial joints, under physiologically relevant loading conditions. A biphasic continuum description is used to represent the soft tissue as a two-phase mixture of incompressible, inviscid fluid and a hyperelastic solid. Alternate mixed-penalty and velocity-pressure finite element formulations are used to solve the nonlinear biphasic governing equations, including the effects of a strain-dependent permeability and a hyperelastic solid phase under finite deformation.