Biomedical Engineering Reference
In-Depth Information
may be employed to infer the dominant regulatory mechanisms at play in a given
cell line.
3.3.2 Tissue Engineering Scaffolds
While the studies of Lemon, O'Dea and coworkers accommodate explicitly the
momentum transfer between phases (unlike that of Shakeel et al.
2011
) the models
are significantly simplified by assuming that the tissue construct's solid compo-
nents (scaffold, ECM) are rigid, spatially-homogeneous and constant in time,
despite experimental evidence to the contrary (Lemon and King (
2007a
) consider
spatial variation in scaffold density only near the scaffold periphery). By including
additional mass conservation equations of the form (
1
) to govern the scaffold and
ECM density distributions and employing experimental data to initialise the
scaffold distribution, O'Dea et al. (
2012
) have shown that, due to cell-scaffold
adhesion, spatial variations in scaffold density may lead to significant heteroge-
neity in cell and ECM distributions, with implications for their mechanical suit-
ability for implant. In addition, it was highlighted that the model simulation results
can be employed to demonstrate how rates of scaffold degradation and ECM
deposition may be matched in order to maintain mechanical integrity of tissue
constructs.
Despite the general nature of the multiphase formulation (
1
), (
2
), (
6
) and (
7
), all
of the foregoing investigations employ significant modelling assumptions, or
exploit suitable asymptotic limits, to simplify the governing equations, leading to
reduced models that are analytically tractable or more straightforward to solve
numerically. Lemon and co-workers study linear stability, travelling waves and
numerical solution in one spatial dimension; Coletti et al. (
2006
) and Causin and
Sacco (
2011
) consider an immobile cell phase; Chung et al. (
2007
) and Shakeel
et al. (
2011
) simplify the momentum transfer between phases; and O'Dea and
co-workers consider the simplifying limit of asymptotically-small tissue construct
aspect ratio to obtain a one-dimensional model and calculate travelling wave and
numerical solutions. To determine the applicability of such geometric simplifi-
cations, Osborne et al. (
2010
) use finite element methods to construct two
dimensional solutions for bioreactors of varying aspect ratios. Comparison with
results obtained by O'Dea et al. (
2010
) in the long-wavelength limit, demonstrated
that the simplified model captures the majority of the qualitative behaviour;
however, to capture accurately mechanotransduction-affected tissue growth, spa-
tial effects in (at least) two dimensions are required.
The aforementioned studies employ the general multiphase model (
1
), (
2
), (
6
)
and (
7
) in various incarnations to investigate in detail cell-cell and cell-substrate
interactions. However, in all cases, the scaffold phase is modelled as a rigid porous
medium. Deformation of the tissue construct forms a key feature of many
mechanical bioreactor systems (in the specific example outlined in
Sect. 1.1
, this is
provided by macroscale compression of the scaffold by a piston). This can be
accommodated within the multiphase framework by appropriate choice of the
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