Computational Modeling of Mass Transport and Its Relation to Cell Behavior in Tissue Engineering Constructs - Computational Modeling in Tissue Engineering - page 89

Fig. 2 a Schematic representation of cells cultured in a fibrin hydrogel. b Geometry of
axisymmetric model (half of vertical cross-section) which consists of three distinct regions: cells
encapsulated in the hydrogel (black), cells on the hydrogel surface (grey, not shown

proportionally) and culture medium (white). Figure reprinted from [ 25 ]

mathematical model, these authors aimed at providing a methodology for rapid
evaluation of the substitute performance. Experimental input data was obtained
from 19 F nuclear magnetic resonance imaging on a dissolved perfluorocarbon
emulsion inside the carrier. This gave a single averaged read-out of dissolved
oxygen tension which showed a unique relation with the number of viable cells
within the carrier, for a given environmental oxygen tension. Spatiotemporal
evolution of both oxygen and viable cell density were estimated from the math-
ematical model using the average oxygen tension as a fitting parameter. Appli-
cation of this approach therefore allowed for quick measurements on substitute
functioning. Design and optimization of experimental configurations for tissue
substitute cultivation and remodeling is a third important application where
mathematical modeling can be of great value. Starting from this principle com-
parative numerical studies of bioreactor setups for in vitro tissue construct culti-
vation have led to an improvement of cultivation regimes and construct designs
[ 111 , 130 ]. These studies have indicated that reaching a critical cell mass inside
the construct in vitro would require the use of a perfusion culture setup. Enhancing
the transport of small molecules (such as oxygen) in perfusion systems would
however require relatively high perfusion speeds. This regime demands a change
in carrier geometry or biomaterial properties (e.g., stiffer matrix) in order to avoid
permanent damage to the carrier. In this optimization process special attention
should however be attributed to the presence of multiple soluble components,
since changing the transport properties of a given solute might have important
consequences for other solute transport [ 14 , 85 ]. Such altered solute transport