Biomedical Engineering Reference
In-Depth Information
In the field of tissue engineering, one of the outstanding challenges is to
accurately mimic tissues and to create an environment within the scaffold and its
associated cells and growth factors that promotes the regeneration of functional
tissues. Bone grafts are one of the most successful products on the market. In USA,
the number of bone graft procedures approximates to 500,000 per year. They
represent a worldwide market estimated at around $300 million for bone
replacement and repair and include autologous bone grafts, allogenic and xeno-
genic grafts, as well as synthetic bone materials [
50
]. Skin repair is also an
important field of the tissue engineering, especially in the case of extended third-
degree burns. Every year in the world millions of patients are disabled and require
hospitalization due to the burn injuries, among which more than 300,000 persons
die ultimately [
13
,
120
]. So far three types of skin substitutes, i.e. epidermal
equivalents, dermal equivalents and composite equivalents, have been used in burn
treatment [
96
].
3 In-Silico Approaches
Angiogenesis modelling has gained increased interest over the last decades due to
a greater availability of experimental data as well as further developed compu-
tational capabilities. There are three principal approaches for the mathematical
modelling of vascular ingrowth: continuum models which face the problem from a
macroscopic point of view, at the cell density level; discrete models in which
mathematical rules are formulated at the mesoscopic or cellular scale and hybrid
models which combine both continuum and discrete overviews (see [
4
,
73
,
94
]
for a review).
1
3.1 Continuum Models
Continuum models aim to describe the average behavior of cell populations with
continuum variables. Accordingly, capillary networks are described in terms of
endothelial cell densities. Populations of cells are usually represented in a mac-
roscopic point of view not preserving the identity and properties of individual cells
[
84
]. The main drawbacks of continuum models are that the individual movements
of the cells and capillary tips cannot be tracked, that they require more assump-
tions than discrete models, and that behaviors at the cell level cannot be predicted.
In contrast, these models are less computationally expensive and provide useful
insights into the ways in which different physical mechanisms, such as the strength
1
The authors apologize any related reference with the present work which remained uncited
along the text.
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