Continuum Modelling of In Vitro Tissue Engineering: A Review - Computational Modeling in Tissue Engineering - page 248

4 Discussion
In vitro tissue engineering is an emerging field of enormous importance, with the
potential to alleviate the current shortage of tissues and organs for transplant,
which are required for successful clinical intervention in problems associated with
tissue damage, degeneration or failure. In addition, engineered tissues have
applications in toxicology testing and drug screening.
Tissue engineering is an intrinsically interdisciplinary field; the complexity of
the biological and biochemical processes involved obfuscates investigation by
experimental biologists alone. Theoretical contributions from applied mathematics
can provide important insight into tissue growth and clarify how the different
processes interact. In this review, we have provided an exposition of the contri-
bution of continuum mathematical modelling to the generation of new tissues from
cells seeded on porous scaffolds. The mathematical models generate insight into
nutrient-limited growth in static culture, and the dual role of fluid flow in
enhancing nutrient transfer to the growing tissue construct, and in providing a
source of mechanical stimulus to the cells e.g. via fluid shear stress.
It is clear that significant advances in tissue engineering have been made in
recent years and that mathematical modelling is starting to play a central role in
the design of bioreactors and the interpretation of the resulting experimental data
(see, e.g. Shipley et al. ( 2011 ), Shipley and Waters ( 2011 ), Shipley et al. ( 2009 ),
Cinar et al. ( 2003 ), Julien and Whitford ( 2007 ) and references therein). In spite of
this progress, many open problems remain to be addressed. We outline below
some of the theoretical, computational and modelling challenges that lie ahead.
• Appropriateness of continuum limit
As stated above, the mathematical models that we have reviewed typically treat
the developing tissue and its constituents as continua and, as a result, do not
distinguish between individual cells. When studying the initial growth phase of
cells seeded within a tissue construct, it is natural to question the validity of
adopting a continuum approach, particularly if the initial cell seeding density is
low. In such cases, it may be more appropriate to use discrete, cell-based models of
the type developed by Chung et al. ( 2010 ) and Cheng et al. ( 2009 ). In Cheng et al.
( 2009 ), the model has three components: a reaction-diffusion equation for the
nutrient concentration, a cellular automata model describing cell migration, pro-
liferation, and collision, and rules relating cell division rates and migration speeds
to nutrient concentration. The hybrid discrete-continuous model was solved to
study how transport limitations affect the tissue regeneration rates under conditions
encountered in typical bioreactors. In Chung et al. ( 2010 ) a similar hybrid cellular
automata approach is used to investigate the effect of nutrient-limitation on cell
construct development for cartilage tissue engineering. The model was used to
identify seeding strategies that result in enhanced cell number and a uniform cell
distribution for the tissue engineered construct.