Mathematical Modelling of Regeneration of a Tissue-Engineered Trachea - Computational Modeling in Tissue Engineering - page 399

of reepithelization, inflammation, and regeneration of the cartilage. Moreover,
consideration will not be given to revascularisation of the trachea.
In the model a fictitious surgical procedure is considered whereby a decellu-
larised trachea is grafted so as to replace the native trachea of the subject (either a
human or laboratory animal). This is immediately preceded by applying EPCs to
the lining of the tracheal lumen and MSCs being applied to the outer surface (see
Fig. 1 c), but with no application of exogenous growth factors (TGF-b1 and G-CSF
are usually applied locally during the operation). The wound is then sealed and the
subject is allowed to recover without further medical intervention.
The mechanisms that are included in the model are depicted in Fig. 2 which
shows the species that interact within a small cylindrical segment of the trachea
(the dashed rectangles in Fig. 1 c, d), and is divided into radial compartments
representing the epithelium, submucosa and cartilage ring. The arrows represent
migration of cells into the segment: EPCs axially across the surface of the lumen,
macrophages and fibroblasts axially into the submucosa, and MSCs radially by
being applied to the outer surface of the trachea during the operation. The con-
tribution of endogenous MSCs to the regeneration is assumed to be negligible. For
simplicity the migration of macrophages and fibroblasts into the segment is
assumed to be passive i.e. their arrival at the segment boundaries is not in response
to the presence of chemokines within.
Macrophages are assumed to enter the trachea in their (classically) activated
state but undergo apoptosis due to the presence of IL-10 which is produced by
EPCs (the AAM subtype is not included). Consistent with their anti-inflammatory
effect MSCs are also assumed to secrete IL-10. TGF-b1 ; secreted by macrophages,
suppresses the proliferation of EPCs (EMT is not considered in the present model).
The mutually antagonistic effects of TGF-b1 (pro inflammatory) and IL-10 (anti
inflammatory) are central to the mechanism of inflammation and its resolution, as
discussed further in Sect. 5 Fibroblasts migrate into the submucosa to maintain the
ECM, assumed to be composed mainly of collagen; however, the rate at which
fibroblasts secrete the collagen is assumed to be increased by TGF-b1 : Hence if
inflammation persists, so there are high levels of TGF-b1 ; excess collagen will be
deposited, resulting in thickening of the submucosa. The rate of proliferation of
MSCs, and their rate of differentiation into chondrocytes, are assumed to be
increased by TGF-b1 : The pro-inflammatory cytokine TNF-a ; which is produced
by macrophages, is also assumed to stimulate proliferation of MSCs. The MSC-
derived chondrocytes are responsible for maintaining the GAGs in the cartilage but
in the presence of TNF-a they undergo apoptosis. The MSC-derived chondrocytes
are assumed to secrete TGF-b1 ; thereby creating a cycle of self-regeneration
through stimulating MSC proliferation.
The cytokines IL-10, TGF-b1 and TNF-a are allowed to freely diffuse through
the submucosal and cartilage regions. Once inside the trachea the macrophages,
fibroblasts and MSCs migrate randomly but no chemotactic effects on cell
migration by the cytokines is included in the model (see comments at the end of