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Research Papers

Robust and General Method for Determining Surface Fluid Flow Boundary Conditions in Articular Cartilage Contact Mechanics Modeling

[+] Author and Article Information
Sainath Shrikant Pawaskar1

Institute of Medical and Biological Engineering, University of Leeds, Leeds LS2 9JT, UKs.s.pawaskar02@leeds.ac.uk

John Fisher, Zhongmin Jin

Institute of Medical and Biological Engineering, University of Leeds, Leeds LS2 9JT, UK

1

Corresponding author.

J Biomech Eng 132(3), 031001 (Feb 03, 2010) (8 pages) doi:10.1115/1.4000869 History: Received November 14, 2008; Revised October 17, 2009; Posted December 21, 2009; Published February 03, 2010

Contact detection in cartilage contact mechanics is an important feature of any analytical or computational modeling investigation when the biphasic nature of cartilage and the corresponding tribology are taken into account. The fluid flow boundary conditions will change based on whether the surface is in contact or not, which will affect the interstitial fluid pressurization. This in turn will increase or decrease the load sustained by the fluid phase, with a direct effect on friction, wear, and lubrication. In laboratory experiments or clinical hemiarthroplasty, when a rigid indenter or metallic prosthesis is used to apply load to the cartilage, there will not be any fluid flow normal to the surface in the contact region due to the impermeable nature of the indenter/prosthesis. In the natural joint, on the other hand, where two cartilage surfaces interact, flow will depend on the pressure difference across the interface. Furthermore, in both these cases, the fluid would flow freely in non-contacting regions. However, it should be pointed out that the contact area is generally unknown in advance in both cases and can only be determined as part of the solution. In the present finite element study, a general and robust algorithm was proposed to decide nodes in contact on the cartilage surface and, accordingly, impose the fluid flow boundary conditions. The algorithm was first tested for a rigid indenter against cartilage model. The algorithm worked well for two-dimensional four-noded and eight-noded axisymmetric element models as well as three-dimensional models. It was then extended to include two cartilages in contact. The results were in excellent agreement with the previous studies reported in the literature.

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Figures

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Figure 1

Flowchart of the proposed algorithm

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Figure 2

Axisymmetric models of (a) articular cartilage with a rigid spherical indenter and (b) joint contact mechanics of identical articular cartilages

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Figure 3

Finite element mesh of axisymmetric models of (a) articular cartilage with a rigid spherical indenter and (b) joint contact mechanics of identical articular cartilages with node N1 0.2 mm below the lower cartilage surface

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Figure 4

Distribution of the contact pressure at the cartilage surface after (a) 2 s and (b) 1000 s for different surface flow conditions

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Figure 5

Distribution of the pore pressure at the cartilage surface after (a) 2 s and (b) 1000 s for different surface flow conditions

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Figure 6

Fluid velocity directions after 1000 s for (a) contact dependent, (b) free flow, and (c) sealed surface flow conditions

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Figure 7

Distribution of the contact pressure at the cartilage surface after (a) 2 s and (b) 1000 s with contact dependent surface flow conditions for different element types

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Figure 8

Distribution of the pore pressure at the cartilage surface after (a) 2 s and (b) 1000 s with contact dependent surface flow conditions for different element types

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Figure 9

Fluid pore pressure and solid compressive axial stress over time at node N1 for steel block over cartilage (plane/cart) and cartilage over cartilage (cart/cart) configuration

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Figure 10

Fluid velocity directions after 300 s (a) in the contact zone and (b) at the end of the contact zone of the lower cartilage

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