Biomedical Engineering Reference
In-Depth Information
In 1991, Lai and co-workers introduced their triphasic theory (Lai et al.,
1991
)to
model mechanoelectrochemical phenomena in biological tissues. This framework,
also based on mixture theory, explicitly modeled the charged solid matrix, neutral
interstitial solvent, and two interstitial monovalent counter-ions, thus representing
one of the earliest explicit models of solute transport in deformable porous media.
The triphasic theory has been applied to the study of a variety of biological tis-
sues, including articular cartilage, intervertebral disc, cornea, aorta, and brain. This
framework has served as the basis for other related theories of swelling and charged
solute transport in biological tissues (Huyghe and Janssen,
1997
;Guetal.,
1998
).
Mechanochemical phenomena associated with neutral solutes in porous de-
formable media may also be examined with mixture theory, as shown in the
biphasic-solute framework of Mauck et al. (
2003
), which explicitly coupled the
frictional interactions of the solute with the tissue's solid matrix and interstitial sol-
vent. When adapted to semi-permeable membrane transport, this theory reproduced
(Ateshian et al.,
2006
) the classical framework of Kedem and Katchalsky (
1958
).
Biphasic-solute theory has been used to model the response of gels (Albro et al.,
2007
) and cells (Albro et al.,
2009a
) subjected to a change in their osmotic envi-
ronment. This framework has also demonstrated that dynamic loading of a porous
tissue may pump solute from a surrounding bath (Albro et al.,
2008
,
2010
,
2011
).
17.1.2 Finite Element Models for Solutes in Porous Media
Finite element implementations of charged porous media have been presented by
several authors, which are applicable to infinitesimal deformations (Simon et al.,
1996
; Frijns et al.,
1997
; Sun et al.,
1999
; Kaasschieter et al.,
2003
; Yao and Gu,
2007
; Magnier et al.,
2009
) and finite deformations (van Loon et al.,
2003
). Other
investigators have used the analogy between thermal diffusion and solute transport
to simulate a triphasic medium under infinitesimal deformation (Wu and Herzog,
2002
), or have constrained their finite element analyses to modeling the equilib-
rium response to Donnan osmotic swelling under finite deformation (Azeloglu et al.,
2008
; Ateshian et al.,
2009
). The neutral transport of solutes in porous deformable
media was addressed by Sengers et al. (
2004
), who formulated a finite element im-
plementation of a biphasic (uncharged) medium, undergoing finite deformation,
with solute transport and biosynthesis. Steck et al. (
2003
) and Zhang and Szeri
(
2005
) used a commercial finite element code to combine mass (solute) transport
with a poroelastic analysis using a two-stage solution procedure.
Recently, we developed a finite element implementation of neutral solute trans-
port in deformable porous media that incorporated a number of important phenom-
ena at the interface of mechanics and physical chemistry (Ateshian et al.,
2011
):
(i) Solvent and neutral solute transport in deformable anisotropic media, includ-
ing strain-induced alterations in permeability and diffusivity, and strain-induced
anisotropy (Ateshian and Weiss,
2010
). (ii) Momentum exchange between solutes
and the solid matrix, which is responsible for increased hindrance to transport
