Mathematical Modelling of Regeneration of a Tissue-Engineered Trachea - Computational Modeling in Tissue Engineering - page 414

(a) (b) EPCs Chondrocytes, GAGs

1 1

0.8 0.8

0.6 0.6

− EPCs, + MSCs
− EPCs, − MSCs
+ EPCs, + MSCs

0.4 0.4

0.2 0.2

+ EPCs, + MSCs
− EPCs, + MSCs
(GAGs)

0 0

0 20 40 60 0 20 40 60

Time (days) Time (days)

Fig. 4 Graphs showing the time courses of a the density of epithelial cells lining the tracheal
lumen, and b the average density of chondrocytes and GAGs within the cartilage ring, calculated
using Eq. ( 52 ). Results are shown for different combinations of cell seeding: in the legend of each
graph a '+' means the indicated cell type is used in seeding, a '-' means that it is not. In b the
curves with circles indicates GAGs, those without circles are chondrocytes

This threshold effect of the EPC seeding density is caused by a bistable
behaviour in the model resulting from the mutual inhibition between EPCs and
macrophages through the action of TGF-b1 and IL-10. Interestingly, Fig. 4 a shows
a short transient downturn in EPC density after about t ¼ 30 days due to the
secretion of TGF-b1 by the proliferating chondrocytes. This demonstrates a dual
role for TGF-b1 in mediating a pro-inflammatory response in the submucosa but
enhancing regeneration of the cartilage through stimulating MSC proliferation and
differentiation into chondrocytes. This accords with results of in vitro studies that
show that the proximity of chondrocytes can suppress proliferation of EPCs [ 30 ].
The model demonstrates that inflammation within the submucosa will also be
detrimental to cartilage regeneration. Figure 4 b shows the time course of the
average density of chondrocytes and GAGs in the cartilage ring for the cases
where MSCs are applied and the trachea is seeded, or not seeded, with EPCs. The
quantities shown were calculated using ( 52 ) with u substituted with N chn or C gag : In
the case where there is no preseeding with EPCs the plateauing of the chondrocyte
density is delayed and more degradation of GAGs occurs because the TNF-a
secreted by the macrophages induces apoptosis of the chondrocytes. If the
parameter values in the model are such that inflammation is too severe, e.g. an
excessive number of macrophages leading to high C tnf levels, or the chondrocytes
are very sensitive to C tnf i.e. d chn 10 in ( 15 ), chondrogenesis will be blocked
and the GAGs completely degraded.
Figure 5 depicts axial cross sections of the trachea showing how the radii of the
tracheal lumen and the inner surface of the cartilage ring vary with time for
the different seeding methods. Given in Table 1 are the corresponding values of
the degree of stenosis of the trachea, defined as the percentage decrease in lumenal
radius, 60 days after implantation i.e. ð R l ; 0 R l ð 60 ÞÞ= R l ; 0 100 % : In the cases
where MSCs are not applied to the trachea, shown in Fig. 5 a and c, stenosis is