The Transport of Insulin-Like Growth Factor through Cartilage - Porous Media: Applications in Biological Systems and Biotechnology - page 405

has demonstrated its capability in describing the experimentally observed
mechanical response of cartilage [43] and other biological tissues [41-43].
Like many other biological tissues, articular cartilage exhibits significant
viscoelastic-like behavior (i.e., time-dependent deformation processes under
external loads), and this viscoelastic-like behavior is well described by the
continuum porous media approach [45].
Mow et al. (1980) [46] proposed a so-called biphasic mixture model inde-
pendent of the phenomenological approach to the theory of porous media.
However, the biphasic mixture theory of porous media (based on Bowen's
approach to mixture theory [47]) and the phenomenological theory of
porous media approach lead to the same basic governing equations [42].
The biphasic model has found considerable use to describe cartilage mechan-
ics [42,48-50]. Lai et al. [7] developed a triphasic model by adding ions into the
biphasic model to describe the deformation and stress fields of cartilage under
chemical potentials and mechanical loading. The total stress tensor within the
cartilage can be treated as the sum of the solid matrix elastic stress, intersti-
tial fluid pressure, and chemical-expansion pressure. The triphasic model has
been extended by Gu et al. [51] to include multielectrolytes.
We begin by presenting a basic fully coupled reactive-transport poroelastic
model for cartilage based on the phenomenological theory of porous media.
Later this model is extended to include a wide-range of biological processes
occurring with cartilage involving IGF-I transport, IGF interaction with its
binding proteins (IGFBPs), IGF-I and interstitial fluid flow induced matrix
biosynthesis, and the transport and degradation of matrix molecules.

11.2.2 Basic Solute Transport Model in Cyclically
Loaded Cartilage
In this section, a basic model will be introduced by treating cartilage as a three
phase mixture, a solid phase representing ECM, a fluid phase representing
interstitial fluid, and a solute phase representing a dissolved solute.
The volume fraction of each phase is

φ α = V α
V

(11.1)

where V is the overall volume of cartilage representative volume element
(RVE) and V α is the volume of α phase. The superscripts s , f, and w indicate
the solid, fluid, and solute phase in the RVE, respectively. As the volume of
solute phase is relatively small compared with the solid and fluid phases, it
can be assumed that φ s + φ f

1. With the volume fractions defined above
the concentration of solute relative to the α phase ( c α ) can be expressed as

≈

c α
φ α

c α = (11.2)