Application of a three-dimensional poroelastic BEM to modeling the biphasic mechanics of cell-matrix interactions in articular cartilage

Mansoor A. Haider; Farshid Guilak

doi:10.1016/j.cma.2006.08.020

Application of a three-dimensional poroelastic BEM to modeling the biphasic mechanics of cell-matrix interactions in articular cartilage

Mansoor A. Haider, Farshid Guilak

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

Abstract

Articular cartilage exhibits viscoelasticity in response to mechanical loading that is well described using biphasic or poroelastic continuum models. To date, boundary element methods (BEMs) have not been employed in modeling biphasic tissue mechanics. A three-dimensional direct poroelastic BEM, formulated in the Laplace transform domain, is applied to modeling stress relaxation in cartilage. Macroscopic stress relaxation of a poroelastic cylinder in uni-axial confined compression is simulated and validated against a theoretical solution. Microscopic cell deformation due to poroelastic stress relaxation is also modeled. An extended Laplace inversion method is employed to accurately represent mechanical responses in the time domain.

Original language	English
Pages (from-to)	2999-3010
Number of pages	12
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	196
Issue number	31-32
DOIs	https://doi.org/10.1016/j.cma.2006.08.020
State	Published - Jun 15 2007

Keywords

Articular cartilage
Biphasic theory
Boundary element method
Cells
Poroelasticity

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10.1016/j.cma.2006.08.020

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title = "Application of a three-dimensional poroelastic BEM to modeling the biphasic mechanics of cell-matrix interactions in articular cartilage",

abstract = "Articular cartilage exhibits viscoelasticity in response to mechanical loading that is well described using biphasic or poroelastic continuum models. To date, boundary element methods (BEMs) have not been employed in modeling biphasic tissue mechanics. A three-dimensional direct poroelastic BEM, formulated in the Laplace transform domain, is applied to modeling stress relaxation in cartilage. Macroscopic stress relaxation of a poroelastic cylinder in uni-axial confined compression is simulated and validated against a theoretical solution. Microscopic cell deformation due to poroelastic stress relaxation is also modeled. An extended Laplace inversion method is employed to accurately represent mechanical responses in the time domain.",

keywords = "Articular cartilage, Biphasic theory, Boundary element method, Cells, Poroelasticity",

author = "Haider, {Mansoor A.} and Farshid Guilak",

note = "Funding Information: This study was supported by the Whitaker Foundation (RG-020933), the NSF (DMS-0211154), and the NIH (AG15768, AR48182, and AR50245). ",

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AU - Haider, Mansoor A.

AU - Guilak, Farshid

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N2 - Articular cartilage exhibits viscoelasticity in response to mechanical loading that is well described using biphasic or poroelastic continuum models. To date, boundary element methods (BEMs) have not been employed in modeling biphasic tissue mechanics. A three-dimensional direct poroelastic BEM, formulated in the Laplace transform domain, is applied to modeling stress relaxation in cartilage. Macroscopic stress relaxation of a poroelastic cylinder in uni-axial confined compression is simulated and validated against a theoretical solution. Microscopic cell deformation due to poroelastic stress relaxation is also modeled. An extended Laplace inversion method is employed to accurately represent mechanical responses in the time domain.

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KW - Boundary element method

KW - Cells

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Application of a three-dimensional poroelastic BEM to modeling the biphasic mechanics of cell-matrix interactions in articular cartilage

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