Mathematical Modelling of Regeneration of a Tissue-Engineered Trachea - Computational Modeling in Tissue Engineering - page 415

more severe ( [ 30 %) because no chondrogenesis occurs hence GAG degradation
proceeds unabated. In these cases the implant is unstable i.e. the lumenal radius
becomes progressively smaller without levelling out. However when MSCs are
applied, as depicted in Fig. 5 b and d, the chondrocytes, which differentiate from
the MSCs, are able to maintain the cartilage and halt the degradation of the GAGs,
resulting in stable implants with smaller amounts of stenosis (\20 %). Where
there is no seeding of the trachea with EPCs, shown in Fig. 5 a and b, inflam-
mation occurs, resulting in thickening of the submucosa. In the case of (a) this
process is unstable i.e. the thickening is continual whereas in (b) once the
inflammation has been resolved with the aid of the MSCs the thickness of the
submucosa approaches a constant value. Similar observations were reported for
experiments of tissue-engineered tracheas implanted into pigs [ 26 ], where the
outcome was superior when the tracheas were preseeded with MSC-derived
chondrocytes (assuming these cells to contain residual MSCs) and the best results
were obtained when the tracheas were also preseeded with EPCs. The model
results also agree qualitatively agree with the results of experiments of decellu-
larised tracheas implanted into dogs [ 54 ] where it was shown that the intraoper-
ative application of MSCs or bone marrow aspirate reduced the amount of stenosis
and, in accordance with Fig. 4 a, increased the rate of reepithelisation.
Stenosis in the model is a result of dilation of tissue elements arising from
excess secretion of collagen and degradation of GAGs. The increasing width of the
tissue domain causes a dilution of the cell and ECM densities (this dilution effect
appears explicitly as the second term on the right-hand side of ( 47 ), where s ð x ; t Þ is
negative when high rates of stenosis occur). In the submucosa this dilution locally
clears space in the tissue for new cells and ECM to be deposited. Depending on the
degree of inflammation this can bring about a positive feedback effect leading to
continual expansion of the domain. Dynamical stability analysis techniques can
reveal conditions on the parameter values for which this positive feedback arises.
In the simulations a key parameter controlling stability in the model was found to
be A vc ; this being the constant of proportionality relating the rate of dilation of the
submucosa to the net rate of production of collagen. It was found that with all other
parameters held constant there was a threshold value of A vc below which the
dilution was too small to stimulate a sufficient rate of tissue growth to sustain the
positive feedback effect. An increase in the value of A vc above the threshold would
relate to aberrant morphological changes in the ECM which are associated with
fibrosis [ 18 ].
In living tissue in the absence of an epithelial lining, inflammation and stenosis
may also be brought about by residual immune cell activity resulting from con-
tamination and infection via the tracheal lumen [ 26 ]. Fibrotic growth may also be
contributed to by EPCs transforming into myofibroblasts as a result of EMT or by
differentiation of MSCs, effects that are not considered in the present model.
Indeed EMT may explain why the poorest outcomes reported in [ 26 ] were for
seeding with EPCs and without MSC-derived chondrocytes; chronic inflammation
may be causing the transformation of epithelial cells to those with a fibroblastic
phenotype that contributes to fibrosis.