Multiphysics Computational Modeling in Cartilage Tissue Engineering - Computational Modeling in Tissue Engineering - page 265

magnitude of this modulation strongly depends on the spatial distribution of the
seeded cells. In our group, a strong effort has been devoted to integrate pore-scale
CFD modeling and mass transport with multicellular simulation, developing
computational models of cell proliferation under interstitial perfusion in a biore-
actor [ 16 , 17 ]. These models accounted for three physical phenomena: (1) cell
proliferation and migration, simulated using established models of cell population
dynamics [ 7 , 28 ], (2) the hydrodynamic flow of culture medium, simulated using
CFD modeling, and (3) oxygen transport from the flowing culture medium to the
cells.
In these models, the increasing oxygen transfer from the culture medium to
the growing cell biomass was included in the mass transport calculation, but the
alteration of the fluid flow due to the growing cell volume was neglected, so that
the simulation results were valid only for very low cell volume fractions, corre-
sponding to initial culture conditions. An alternative perspective is based on
homogeneous continuum approaches [ 29 ] or on porous medium representations,
comprising motile cells and water inside a rigid scaffold material [ 8 , 23 ].
In addition to cell growth kinetics, cell diffusion may be incorporated, to describe
the effects of cell random walks. The values of some parameters used, such as the
rate of cell ingrowth into the porous scaffold, are derived from the literature or by
fit to published experimental data. Results suggest that the rate of tissue growth in
porous scaffolds depends not only on the intrinsic rate of cell proliferation, but also
on the balance of mechanical forces developed inside the tissue. This type of
modeling also shows how the scaffold porosity or surface may be varied to reduce
the tendency of cells to aggregate.
4.2 ECM Accumulation Dynamics
Mathematical models of ECM accumulation have been set up by treating the
cell-scaffold construct either as a homogeneous continuum coupled with the
nutrient field [ 27 ] or at the Microscale level [ 13 ]. In both these approaches, GAG
concentration is assumed as the principal indicator of ECM secretion, distin-
guishing between soluble and bound GAG fractions. In Klein and Sah [ 21 ]an
extension of the previous models is proposed, including in a phenomenological
manner the effect of perfusion velocity on GAG release rate.
5 Homogenized Models of Biomass Growth, Medium Flow
and Mass Transport
The difficulty of handling a domain with an internal time-dependent interface due
to biomass growth with a robust numerical technique has brought many authors to
propose homogenized-averaged approaches formulated at the Macroscale level.