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

simulations. Implicit in this setup is the assumption of the equivalence of
macrostructural (tissue) constitutive response and average stress-strain response of the
microstructural (cellular) model. While single cell computational models have provided
invaluable insight into the chondrocyte mechanical environment, human cartilage,
especially at early stages of development and for certain zonal regions, can exhibit
much higher cell concentrations than previously assumed [3]. The predictions of
chondrocyte mechanics as obtained from single cell assumption may not be adequate for
cartilage with high chondrocyte density, due to misrepresentation of macroscopic load
transfer to the cells and the potential to overlook cellular interactions. We have
previously shown, albeit with hyperelastic two- and three-dimensional representations,
the potential mismatches in such variables for increasing strain level and cell density,
specifically for zero, one, and three cell representations [7,8]. Hence, the goal of this
study was to compare the mechanical response of chondrocytes in single and eleven [3]
cell biphasic finite element (FE) models. To guarantee spatial and temporal mechanical
consistency across scales, an embedded model was adopted, where the representative
volume element (RVE) was directly modeled within a homogeneous ECM construct.
Volume averaged effective cellular strains and fluid flux were evaluated as a function of
time and loading.
3. METHODS
A 100x100x100 μm, the commonly assumed representative volume element (RVE),
micro-scale finite element model was embedded in a 1x1x1 mm (tissue-scale)
hexahedral mesh construct (Figure 1). All models were meshed with linear hexahedral
elements using TrueGrid (XYZ Scientific Applications, Inc., Livermore, CA).
For the RVE, two cases were considered: a single (centered) cell and an eleven cell
(randomly distributed, anatomically based for middle zone of cartilage [3])
Figure 1. 1x1x1 mm finite element mesh construct with the embedded 100 um
representative volume element (RVE) micro-scale models. Close-ups of the (b)
single cell and (c) eleven cell model are highlighted. Note the spheres in subplots “b”
and “c” represent the chondron (chondrocyte plus the pericellular matrix).