scholarly journals Biphasic Finite Element Modeling of Hydrated Soft Tissue Contact Using an Augmented Lagrangian Method

2011 ◽  
Vol 133 (11) ◽  
Author(s):  
Hongqiang Guo ◽  
Robert L. Spilker
Keyword(s):  
Finite Element ◽  
Augmented Lagrangian ◽  
Soft Tissues ◽  
Augmented Lagrangian Method ◽  
Fluid Pressure ◽  
Lagrangian Method ◽  
Element Formulation ◽  
Biomechanical Behavior ◽  
Contact Formulation ◽  
Biphasic Finite Element

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. The augmented Lagrangian method is used to enforce the continuity of contact traction and fluid pressure across the contact interface, and the resulting method is implemented in the commercial software COMSOL Multiphysics. The accuracy of the implementation is verified using 2D axisymmetric problems, including indentation with a flat-ended indenter, indentation with spherical-ended indenter, and contact of glenohumeral cartilage layers. The biphasic finite element contact formulation and its implementation are shown to be robust and able to handle physiologically relevant problems.

scholarly journals An Augmented Lagrangian Method for Sliding Contact of Soft Tissue

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
Hongqiang Guo ◽  
Jeffrey C. Nickel ◽  
Laura R. Iwasaki ◽  
Robert L. Spilker
Keyword(s):  
Augmented Lagrangian ◽  
Soft Tissues ◽  
Augmented Lagrangian Method ◽  
Fluid Pressure ◽  
Complex Loading ◽  
Lagrangian Method ◽  
Sliding Contact ◽  
Element Formulation ◽  
Contact Interface ◽  
Diarthrodial Joints

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. The resulting method is implemented in the commercial software COMSOL Multiphysics. The accuracy of the new implementation is verified using an example problem of sliding contact between a rigid, impermeable indenter and a cartilage layer for which analytical solutions have been obtained. The new implementation’s capability to handle a complex loading regime is verified by modeling plowing tests of the temporomandibular joint (TMJ) disc.

A 3D Biphasic Finite Element Model of the Human Knee Joint for the Study of Tibiofemoral Contact and Fluid Pressurization

2013 ◽  
Author(s):  
Hongqiang Guo ◽  
Suzanne A. Maher ◽  
Robert L. Spilker
Keyword(s):  
Finite Element ◽  
Fluid Flow ◽  
Knee Joint ◽  
Contact Problem ◽  
Finite Element Model ◽  
Soft Tissues ◽  
Fluid Pressure ◽  
Element Model ◽  
Human Knee Joint ◽  
Biphasic Finite Element

Biphasic theory which considers soft tissue, such as articular cartilage and meniscus, as a combination of a solid and a fluid phase has been widely used to model their biomechanical behavior [1]. Though fluid flow plays an important role in the load-carrying ability of soft tissues, most finite element models of the knee joint consider cartilage and the meniscus as solid. This simplification is due to the fact that biphasic contact is complicated to model. Beside the continuity conditions for displacement and traction that a single-phase contact problem consists of, there are two additional continuity conditions in the biphasic contact problem for relative fluid flow and fluid pressure [2]. The problem becomes even more complex when a joint is being modeled. The knee joint, for example, has multiple contact pairs which make the biphasic finite element model of this joint far more complex. Several biphasic models of the knee have been developed [3–9], yet simplifications were included in these models: (1) the 3D geometry of the knee was represented by a 2D axisymmetric geometry [3, 5, 6, 9]; (2) no fluid flow was allowed between contact surfaces of the soft tissues [4, 8] which is inconsistent with the equation of mass conservation across the contact interface [10]; (3) zero fluid pressure boundary conditions were inaccurately applied around the contact area [7].

scholarly journals An augmented Lagrangian method for solving total variation (TV)-based image registration model

2020 ◽  
Vol 14 ◽  
pp. 174830262097353
Author(s):  
Noppadol Chumchob ◽  
Ke Chen
Keyword(s):  
Image Registration ◽  
Augmented Lagrangian ◽  
Numerical Solutions ◽  
Augmented Lagrangian Method ◽  
Closed Form Solution ◽  
Numerical Algorithms ◽  
Lagrangian Method ◽  
Form Solution ◽  
The Other ◽  
Other Hand

Variational methods for image registration basically involve a regularizer to ensure that the resulting well-posed problem admits a solution. Different choices of regularizers lead to different deformations. On one hand, the conventional regularizers, such as the elastic, diffusion and curvature regularizers, are able to generate globally smooth deformations and generally useful for many applications. On the other hand, these regularizers become poor in some applications where discontinuities or steep gradients in the deformations are required. As is well-known, the total (TV) variation regularizer is more appropriate to preserve discontinuities of the deformations. However, it is difficult in developing an efficient numerical method to ensure that numerical solutions satisfy this requirement because of the non-differentiability and non-linearity of the TV regularizer. In this work we focus on computational challenges arising in approximately solving TV-based image registration model. Motivated by many efficient numerical algorithms in image restoration, we propose to use augmented Lagrangian method (ALM). At each iteration, the computation of our ALM requires to solve two subproblems. On one hand for the first subproblem, it is impossible to obtain exact solution. On the other hand for the second subproblem, it has a closed-form solution. To this end, we propose an efficient nonlinear multigrid (NMG) method to obtain an approximate solution to the first subproblem. Numerical results on real medical images not only confirm that our proposed ALM is more computationally efficient than some existing methods, but also that the proposed ALM delivers the accurate registration results with the desired property of the constructed deformations in a reasonable number of iterations.

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