Biomedical Engineering Reference
In-Depth Information
In the presence of either an activator or an inhibitor, equation
11.1
can be written
as [
1476
]:
+P
n
2
∂
n
n
n
0
2
n
t
=
D
c
∇
−
−
d
n
,
∂
∂
c
2
c
t
=
D
r
∇
+
P
r
(
n
)
−
τ
c
.
(11.7)
∂
This model does not take into account wound contraction in the final healing
stage. A model of the deformation of epithelial sheets was then developed [
1476
].
Wounded epithelium is assumed to be an isotropic, viscoelastic medium. The
mechanical behavior of a cell sheet depends on the state of the actin cytoskeleton,
hence on the intracellular calcium concentration. Two force types are considered:
intra- and extracellular elastic restoring and active traction forces [
1476
]:
C
=
ρ
a
(
κ
1
D
+
κ
2
∇
·
uI
)+
ρ
a
T
I
,
(11.8)
where
C
is the stress tensor,
ρ
a
the density of actin filaments,
D
: deformation rate
tensor,
T
traction,
κ
1
/
2
elastic parameters,
u
displacement, and
I
the unit tensor.
When a larger region of a tissue is considered such as in dermal wound healing,
cell-matrix interactions must be incorporated in the model. Matrix structure and
density as well as its turnover and reaction influence cell proliferation, differentia-
tion, and migration. Conversely, cells determine matrix composition, turnover, and
deformation.
The change rate of matrix density depends on its production and degradation
rates and on its deformation rate. Cell-matrix interaction is introduced by a force
balance in which the body forces are in equilibrium with the divergence of the
traction stress exerted by the cells on the extracellular matrix and the divergence
of the resistive stress of the extracellular matrix that is composed of an elastoplastic
and a viscous component.
11.7
Respiratory Epithelium Repair
In adult lungs, epithelial cell populations include basal, secretory, ciliated, neuroen-
docrine, and alveolar cells. Under normal conditions, cell turnover in the lung is
relatively low. Nevertheless, when the respiratory epithelium is damaged, stem or
progenitor cell populations are activated to replace lost cells.
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