Computational Modeling of Mass Transport and Its Relation to Cell Behavior in Tissue Engineering Constructs - Computational Modeling in Tissue Engineering - page 93

the sulfation pattern of the heparan sulphate chains and allows for interactions with
several members of the Hedgehog, transforming growth factor-b (TGFb), bone
morphogenetic protein (BMP), Wingless (Wnt/Wg), and fibroblast growth factor
(FGF) families [ 31 , 48 ].
Simple mathematical models have been developed expressing the total width
between the early hypertrophic zone and the perichondrium using coupling
equations of PTHrP and Ihh concentrations [ 125 ]. As concentrations of both
signaling molecules can be modulated by various transport-related factors (e.g.
mechanical compression, solute binding, changes in diffusivity due to matrix
degradation) the relative importance of these factors on rates of proliferation and
hypertrophy can be rapidly assessed using this model.
In a second model bone growth and morphogenesis is described by differences
in spatial distribution and proliferation rates of proliferative and hypertrophied
chondrocytes [ 37 ]. Underlying this growth process were the regulatory capacities
of the Ihh and PTHrP spatial concentration distributions, that were modeled by a
set of reaction-diffusion equations [ 21 , 75 , 78 ]. In order to obtain a physiological
growth pattern the ratio of diffusion coefficients for both signaling molecules was
bound to certain criteria. The influences of these morphogen diffusion rates on
characteristics of the growth plate were acknowledged already earlier in studies of
the skeletal disorder Exostosin (EXT1) [ 54 , 63 ]. There it was shown that in EXT1
mutations, expressing reduced amounts of HS, the range of Ihh signaling within
the growth plate was increased giving rise to an extended proliferative zone.
Calcification of the matrix surrounding the hypertrophic chondrocytes in the
growth plate triggers the invasion of blood vessels from the metaphyseal bone
[ 58 ]. This capillary invasion is mediated by the expression of vascular endothelial
growth factor (VEGF) in hypertrophic chondrocytes [ 39 ]. Binding of VEGF to
ECM components has thereby been implicated as a possible requisite for cellular
autocrine signaling, giving rise to amplified VEGF gradients that are able to direct
capillary morphogenesis [ 50 , 76 ]. The mechanism underpinning this gradient
amplification results from the combined action of a small interstitial fluid flow,
biasing the secreted protease distribution, and the distribution of liberated VEGF
molecules, influenced by both protease distribution and convective flows [ 35 ].
The use of growth factors (such as VEGF) in controlled-release systems has
been widely proposed for TE strategies aiming at the regeneration of damaged or
diseased tissues [ 29 , 101 , 102 ]. Given the short half-life and residence of free
growth factors in solution, controlled-release strategies hold great promise pro-
viding a means to protect these factors from degradation and internalization [ 77 ,
105 ]. Though such systems can deliver signaling molecules in a time- and space-
controlled manner, the lack of detailed knowledge on in vivo growth factor con-
centrations and possible interfering behavior of administered compounds com-
plicates rational decisions on the required growth factor concentrations [ 60 ]. For
such applications we can however greatly take advantage of the use of numerical
models. In this way a modeling-based design approach was proposed for the
controlled delivery of VEGF in a mouse model of hindlimb ischemia [ 16 ]. Using a
reaction diffusion model to predict VEGF distribution in vivo, a layered scaffold