Computational Modeling of Mass Transport and Its Relation to Cell Behavior in Tissue Engineering Constructs - Computational Modeling in Tissue Engineering - page 83

allows for a spatiotemporal control of their degradation properties [ 71 , 100 ].
Models of in vivo regeneration processes (e.g. fracture healing [ 40 ]) will thereby
give crucial information on the timing and location of remodeling and hence also
proteolytic events. This information can be effectively implemented in treatment
strategies aiming to provide continuous mechanical support to the fracture, by
matching scaffold degradation with new tissue generation [ 105 ], and allows the
cells to re-establish a properly working signaling environment.
In this topic chapter we aim to elucidate how the key actors that govern mass
transport in a TE carrier (i.e., biomaterial, cells, culture environment and solutes)
can influence the overall functioning of this carrier. This will be described in terms
of specific cell behavior that is provoked under defined concentrations and gra-
dients of soluble factors. The influence of the carrier components will be captured
in a series of continuum parameters that are used to formulate the mass transport
problem in a mathematical landscape. Finally for each component illustrations are
given on how to exploit this information in the optimization of culture conditions
and the rational design of setups used for TE applications.

2 General Mass Transport in Carriers

Solute transport in biomaterial carriers (e.g., hydrogels and macro- or microporous
scaffolds) used for TE applications is generally governed by passive diffusion.
Diffusive transport as a primary transport mechanism in carriers can however put
major constraints on the remodeling capabilities of cells that reside within this
material [ 42 ] and hence also on new tissue formation. Since in this setting of
dynamic tissue architecture and composition the transport of solutes with large
molecular weight is most strongly affected [ 9 ], important modulations in cell
signaling can be expected [ 120 ]. However also the transport of small molecules,
such as oxygen, can be impeded as cells grow and new tissue is produced which
gives rise to an imbalance between solute uptake and supply [ 25 ].
For this reason bioreactor systems have been developed which try to overcome
fundamental limitations that are associated with diffusive mass transport. A wide
variability in bioreactor configurations exists that enhance mass transport in and to
the carrier, either by direct perfusion/compression or indirect perfusion/mixing
[ 82 ]. Since movement and exercise are important driving forces for the body's
interstitial fluid flow [ 120 ], special attention will be given here to the influence of
mechanical carrier loading on solute transport.
Based on the previous discussion we introduce the general equation for mass
conservation,

oC i x ; y ; z ; t ð Þ

¼r C i x ; y ; z ; t

ð Þ R i x ; y ; z ; t ð Þ

ot