Computational Modeling of Mass Transport and Its Relation to Cell Behavior in Tissue Engineering Constructs - Computational Modeling in Tissue Engineering - page 92

where c glc is the glucose concentration (mol m -3 ); and a i are parameters deter-
mined by curve fitting. A similar equation can also be applied to describe the
increase in glycolysis (defined by the glucose uptake rate) for cells exposed to
hypoxic conditions, known as the Pasteur effect [ 81 , 93 , 108 ]. In contrast to these
studies other authors have reported a decrease in glycolysis under hypoxia, which
would be mainly mediated by differences in medium components (e.g., presence of
oxidants) [ 43 , 67 , 68 , 130 ]. These effects should receive special attention in
modeling avascular tissues, and hence also TE substitutes, since nutrient depletion
could readily occur here.
It follows that solute interactions have important consequences in terms of the
model predictive behavior of nutrient and metabolite gradients as well as for the
optimization of experimental configurations. To illustrate this we give an example
of a combined experimental and numerical study of the coupled kinetics for
chondrocytes in an engineered cartilage construct [ 130 ]. In this study the rela-
tionships of oxygen and glucose uptake rates of chondrocytes exposed to different
oxygen tensions, glucose concentrations and pH levels was investigated as well as
the influence of lactate concentration on pH level. It was found that the predicted
cell viability in the construct center was generally enhanced upon implementation
of these relations in the numerical model, an observation that was most significant
at high cell densities [ 130 ]. This interesting cell behavior predicted in silico could
hence be indicative of a cellular rescue mechanism.
5 Signaling Molecules
Growth factors serve important roles as signaling molecules during development
[ 46 , 90 , 119 ] and regeneration [ 17 , 123 ]. Most of these signaling molecules need to
travel through the surrounding extracellular environment either locally (autocrine
signaling) or to more distant locations (paracrine and endocrine signaling) in order
to exert their influence on cell behavior [ 112 ]. In the following paragraphs we will
show how a cell is able to interfere with this transport process and direct this
signaling reaction to provoke its intended effect. More specifically the example of
cellular signaling in the growth plate will be discussed.
Bone elongation occurs through the action of endochondral ossification, which
is driven primarily by the differentiation rate of proliferating chondrocytes into
hypertrophic chondrocytes within the growth plate [ 64 ]. At a molecular level this
process is strongly controlled by two paracrine signaling factors, Indian hedgehog
(Ihh) and parathyroid hormone-related protein (PTHrP) [ 65 , 126 ]. While Ihh
coordinates chondrocyte proliferation, differentiation and osteoblast differentia-
tion, PTHrP mainly keeps the proliferating chondrocytes in a proliferative phase
[ 65 , 124 , 126 ]. Heparan sulphate (HS) complexes associated with proteoglycans in
the ECM of the growth plate serve important roles in morphogenesis by providing
binding sites for specific signaling molecules [ 8 , 48 ]. This specificity depends on