Biomedical Engineering Reference
In-Depth Information
Acknowledgements
Aurélie Carlier is a PhD fellow of the Research Foundation Flanders
(FWO-Vlaanderen). The work is part of Prometheus, the Leuven Research and Development Di-
vision of Skeletal Tissue Engineering of that Katholieke Universiteit Leuven:
www.kuleuven.be/
Appendix
The equations contain the following model parameters:
Ca(t)
H
Ca
4
+
J(t)
=
J
in
.
Ca(t)
A
m
0
.m(t)
K
m
+
A
m
(t)
=
m(t)
2
.
exp
2
.
Ca(t)
2
a
cm
c
cm
1
−
b
cm
β
cm
(t)
=
−
c
cm
g
b
(t)
6
.F
11
.
exp
F
12
2
Y
11
.g
b
(t)
6
H
11
+
2
.
Ca(t)
1
F
1
(t)
=
−
−
A
b
0
.m(t)
K
b
+
A
b
(t)
=
m(t)
2
.
exp
2
.
Ca(t)
2
a
cb
c
cb
1
−
b
cb
β
cb
(t)
=
−
c
cb
G
gb
.g
b
(t)
H
gb
+
E
gb
(t)
=
g
b
(t)
R(t)
=
c
m
(t)
−
c
m
(t
−
t
3
)
.
G
con
.g
b
(t)
H
con
+
g
b
(t)
The following scaling factors were chosen for the non-dimensionalization of the
model variables:
t
T
,
c
m
c
0
,
c
b
c
0
,
m
m
0
t
=
c
m
=
c
b
=
m
=
b
m
0
g
b
g
0
Ca
Ca
0
b
Ca
=
,
g
b
=
,
=
1 day was considered to be a representative unit time for the pro-
cess under study (similar to fracture healing models e.g. Geris et al. [
50
]). Represen-
tative concentrations for the collagen content (
m
0
=
The time
T
=
0
.
1g
/
ml) and growth factors
(
g
0
=
100 ng
/
ml) are adopted from Geris et al. [
50
]. A typical value for the cell den-
sity (
c
0
=
10
6
cells
/
ml) is derived from Bailón-Plaza and van der Meulen [
48
]. The
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