Mathematical Modelling of Regeneration of a Tissue-Engineered Trachea - Computational Modeling in Tissue Engineering - page 394

With their ability to self-renew and differentiate into a variety of cell types, the
use of adult stem cells has been proposed as a treatment for a wide range of
different diseases [ 11 ], and their application to organ transplantation represents an
exciting development in the field of regenerative medicine [ 40 ]. Hence there are
valuable opportunities now arising to develop mathematical models for the
emerging field of stem cell-based therapies for tissue engineering. Indeed the main
part of this chapter concerns a description and analysis of a mathematical model
for tracheal regeneration using mesenchymal stem cells (MSCs). But what should
be the goals in developing a mathematical model of tracheal regeneration? Clearly
if a living trachea could be represented faithfully using a mathematical or com-
putational model i.e. an in silico trachea, virtual experiments could be performed
on the model to develop therapies without the expense and ethical concerns of
using live subjects. But is this realistic and if not what are the obstacles to
achieving this? How could a simplified mathematical model that omits much detail
of the biology be of any use for studying regeneration of a tissue-engineered
trachea? Some consideration will be given to such questions in this chapter, which
of course exemplify issues that arise much more generally in systems biology.
The main thrust of this chapter is to (i) present a possible approach to modelling
the regeneration of a tissue-engineered trachea in situ, in the course of which more
general modelling principles will be illustrated, and (ii) to use the model to gain
some insight into the possible causes of success or failure of the transplantation
therapy. Consideration is given to the implantation of a trachea with intra-oper-
ative seeding using different combinations of cells i.e. with or without EPCs
applied to the lumenal surface, and with or without MSCs applied to the outer
surface of the trachea (Fig. 1 c).
In Sect. 2 of this chapter some description of tissue-engineered tracheal
transplantation therapies and the relevant biology is given. This motivates the
formulation of the mathematical model which is described in Sect. 3 . The
numerical methods used to solve the model equations are given in Sect. 4 , and in
Sect. 5 the solutions of the equations are described, representing the cases of
operations involving seeding with different combinations of EPCs and MSCs.
Discussion of the modelling approach used and the results, as well as suggestions
for possible future work, are given in Sect. 6
2 Biological Considerations
The first successful operation involving implantation of a tissue-engineered tra-
chea into a human is reported in [ 47 ], with further reviews and description of the
procedures given in [ 6 , 7 , 37 ]. These works form the basis of the following
description of the therapy and the associated biology given below, which is then
used in the design of the mathematical model in the following section. Due to the
enormous complexity of the tracheal regeneration process the following descrip-
tion represents only a brief and simplified summary.