Biomedical Engineering Reference
In-Depth Information
Passive processes involving solutes may also contribute significantly to the me-
chanics of biological tissues. Solutes are often charged and their transport through
the tissue's porous solid matrix may be influenced by electrical charges fixed to
this matrix. Depending on their concentration and charge, solutes may significantly
influence the osmotic pressure of the interstitial fluid. In turn, this osmotic pres-
sure can produce significant deformation of the tissue's solid matrix, demonstrating
significant coupling of mechanochemical and mechanoelectrochemical phenomena.
Large solute concentration gradients may induce significant flow of the solvent, a
process known as osmosis. Charged solutes can also induce electrical potentials and
carry electrical currents, or be driven by externally applied potentials or currents.
A broad range of biological processes thus result from a combination of passive
(non-reactive) and active processes involving solvent and solutes, and the ability to
model such processes in a general continuum framework represents an important
tool for biomedical engineers and scientists. Yet, computational tools for modeling
solute transport in neutral and charged deformable media are not widely available.
In recent years, FEBio (Maas et al.,
2012
) has been introduced as an open source
finite element program in the public domain (
www.febio.org
), whose purpose is to
provide such computational tools for the analysis of biological mixtures consisting
of a porous deformable solid matrix and interstitial solvent and solutes. This arti-
cle summarizes the background literature on this topic and describes the governing
equations and some of the features of mixture analyses in FEBio.
17.1.1 Solutes in Porous Media with Non-reactive Processes
In biomechanics, the study of interstitial fluid transport in deformable porous solids
evolved from the mechanics of porous media, such as the consolidation theory de-
rived from the work of Fillunger (
1913
), von Terzaghi (
1933
) and Biot (
1941
), and
the biphasic theory of Mow et al. (
1980
), derived from the mixture theory of Trues-
dell (
1960
) and Bowen (
1976
). The biphasic theory has been applied to the study of
creep and stress-relaxation responses of biological tissues under testing configura-
tions such as confined (Mow et al.,
1980
) and unconfined (Armstrong et al.,
1984
;
Cohen et al.,
1998
) compression, indentation (Mow et al.,
1989
; Athanasiou,
1991
),
and permeation (Lai and Mow,
1980
) for the purpose of extracting material proper-
ties such as equilibrium modulus and hydraulic permeability. Biphasic contact anal-
yses have been used to analyze articular contact mechanics in diarthrodial joints
(Ateshian et al.,
1994
; Ateshian and Wang,
1995
). Mixture and consolidation theo-
ries have also been used in the study of interstitial fluid transport in skin (Oomens
et al.,
1987
), bone (Cowin,
1999
), and cardiovascular tissues (Kenyon,
1976
; Yang
et al.,
1994
).
Electrokinetic phenomena were subsequently coupled with a porous media
framework in the theory of Frank and Grodzinsky (
1987a
), by incorporating an
equation relating the electric current density to gradients in electric potential and
fluid pressure. Their framework was used to analyze phenomena such as streaming
potentials and current-induced stresses in cartilage (Frank and Grodzinsky,
1987b
).
