Research Papers

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

[+] Author and Article Information
Hongqiang Guo1

Robert L. Spilker

Department of Biomedical Engineering,  Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180-3590


Corresponding author.

J Biomech Eng 133(11), 111001 (Nov 17, 2011) (7 pages) doi:10.1115/1.4005378 History: Received October 21, 2011; Accepted October 24, 2011; Published November 17, 2011

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.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

A schematic diagram of the biphasic indentation test with a flat-ended cylindrical indenter

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Figure 2

The (a) axial stress σz , (b) axial strain ɛz , (c) shear stress σrz , and (d) fluid pressure p at several depths predicted by the biphasic contact finite element model and the model of Spilker [19]

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Figure 3

(a) and (c) Distribution of fluid pressure p and axial stress σz (in kPa) at 250 s on the deformed geometry, red arrows indicate fluid velocity. (b) and (d) Continuity of fluid pressure and axial stress between the two bodies along the contact boundary at 250 s.

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Figure 4

A schematic diagram of the biphasic indentation test with a spherical-ended cylindrical indenter

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Figure 5

Distribution of (a) axial displacement (in mm) and (b) fluid pressure (in kPa) at 100 s on deformed geometry, red arrows indicate fluid velocity (b)

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Figure 6

Normal traction distributions along the top boundary of cartilage at 100 s in the biphasic indentation test with a spherical-ended indenter. Lines are the results of finite element contact solution using augmented Lagrangian method, and symbols are results of finite element solution based on Lagrange multiplier method [7].

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Figure 7

A schematic diagram of axisymmetric glenohumeral joint in contact. Regions with dots represent cartilage layers, and open regions are bone.

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Figure 8

Axial displacement (in mm) of the shoulder cartilage on deformed geometry at (a) 5 s and (b) 10 s. Boundary lines are initial position.

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Figure 9

(a) Fluid pressure (in kPa) distribution of the shoulder cartilage on deformed geometry at 10 s. (b) Normal traction distribution along top boundary of glenoid cartilage at 10 s.

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Figure 10

Distributions of (a) maximum and (b) minimum principal elastic stress (in kPa) on deformed geometry at 10 s



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