ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

The modeling of soft tissue structures, for many years, has been carried out using well
established approaches; biphasic and poroelastic theories. In these approaches, tissue is
modeled as a two phase immiscible mixture, consisting of incompressible solid matrix
and fluid phases. The extracellular solid matrix of AC is mainly composed of
proteoglycans (PG) and cross-linked collagen (COL) network, which are predominantly
responsible for mechanical functioning of the cartilage. The proteoglycans, negatively
charged molecules, are mainly responsible for compressive loads, while collagen
network is responsible for shear and tensile loads. The mechanical behavior of the
cartilage is incompressible, nonlinear and anisotropic due to the presence of oriented
collagen fibers. Frequently, phenomenological strain- energy functions for solid matrix
combined with the Darcy law for fluid flow are used to model the mechanics of soft
tissues (Baaijens et al., 2010, Klisch et al 2009, Davol et al., 2008). COMSOL
Multiphysics have been gaining attention in recent years to model the complex
biological processes in soft tissues. The long term objective of the present work is to
develop an ACGM similar to the reported model from Ficklin et al. (2009), Klisch et al.,
(2008) by including more realistic knee condyle geometry with the metal implant filling
the assumed defect site in the cartilage and considering dynamic loading situations.
From this model, we want to investigate the effect of mechanical factors and role of
metal implant, which is applied at the defect site to regenerate the articular surface, on
the growth of cartilage around the implant.
3. MATERIALS AND METHODS
In the biphasic theory, articular cartilage is composed of a mixture of extracellular
matrix, composed of proteoglycans and collagens, as the porous solid phase and
interstitial fluid as the fluid phase. Denoting the whole volume of mixture as V, the
volume fraction of each constituent is given by
, ,,,
with subscripts , are for proteoglycans, collagens of solid matrix and is for
fluid phase , respectively. The saturation condition in the cartilage holds as
1, where is solid volume fraction equals to . The porosity of
the model is equal to fluid volume fraction of the mixture ( ).
The total stress acting at a point in the tissue is given by the sum of the solid and fluid
stresses,
where is the effective stress tensor of the solid phase and is the fluid
stress. The extracellular solid phase majorly constitutes proteoglycans and collagens;
therefore the solid phase stress is equal to the sum of individual constituents,
Stress due to other constituents is neglected. The stress equilibrium equation is
0, and the continuity equation (law of conservation of mass) for the mixture is
given by
kp 0
where, is the velocity of the solid phase, is the hydrostatic fluid pressure from the
fluid phase and is the permeability, /. The strain dependent permeability can be
expressed in terms of void ratio, / , as