Biomedical Engineering Reference
In-Depth Information
ing from upstream to downstream. (ii) At the boundaries with the baths, the electric
potential
ψ
inside the tissue is not the same as the bath potential
ψ
∗
, because of
the fixed charge density in the tissue. The tissue
electric conductivity
maybeeval-
uated from the ratio of
ψ
d
)/h
,
where
h
is the tissue thickness. (iii) The solvent also flows from the upstream to
the downstream bath, due to the net frictional drag exerted on it by the solutes. This
phenomenon is known as electroosmosis.
and the prescribed potential gradient,
(ψ
u
−
|
I
e
|
17.5 Conclusion
Finite element modeling of mechanoelectrochemical phenomena in deformable
porous biological tissues and cells is a useful tool in the toolbox of biomedical engi-
neers. The examples presented in this chapter provide only the most basic features
of biphasic-solute and triphasic materials in FEBio. More elaborate analyses may be
performed which combine any number of driving mechanisms for deformation and
flow. The ability to describe transport of neutral or charged solutes within a porous
deformable solid matrix, using a formulation that couples these mechanisms, makes
it possible to address phenomena commonly observed in biology and physiology.
FEBio provides this tool in the public domain, allowing users to exchange models
and ideas in a common framework. Being open source, FEBio also allows users to
extend its current capabilities, by adding new constitutive relations or extending ex-
isting frameworks to include additional mechanisms. Current efforts are under way
to extend the existing biphasic-solute and triphasic frameworks to a more general
multiphasic module, where any number of neutral or charged solutes may be mod-
eled. Furthermore, the modeling of chemical reactions among any of the solid and
solute constituents will be incorporated in future extensions of the code. These ex-
tensions will make it possible to model chemical kinetics and growth mechanics in
deformable porous media, further extending the modeling capabilities into the realm
of biology and physiology.
Acknowledgements
The development of FEBio is supported by funds from the National Insti-
tute of General Medical Sciences (NIGMS) of the U.S. National Institutes of Health (GM083925).
References
Albro MB, Chahine NO, Caligaris M, Wei VI, Likhitpanichkul M, Ng KW, Hung CT, Ateshian
GA (2007) Osmotic loading of spherical gels: a biomimetic study of hindered transport in the
cell protoplasm. J Biomech Eng 129(4):503-510
Albro MB, Chahine NO, Li R, Yeager K, Hung CT, Ateshian GA (2008) Dynamic loading of
deformable porous media can induce active solute transport. J Biomech 41(15):3152-3157
Albro MB, Petersen LE, Li R, Hung CT, Ateshian GA (2009a) Influence of the partitioning of
osmolytes by the cytoplasm on the passive response of cells to osmotic loading. Biophys J
97(11):2886-2893
