Biomedical Engineering Reference
In-Depth Information
Length scale
Cell-biomaterial
distance
Implant pores
Bioreactor
10
-10
10
-9
10
-8
10
-7
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
1
(meter)
Atom and
small molecule
Macromolecule
Cell
Implant
Time scale
Macromolecule adsorption
on the biomaterial surface
Extracellular
matrix syntesis
3.2 10
3
(seconds)
second
minute
hour
day
week
month
year
Cell adhesion Cell proliferation
and differentation
Biomaterial
resorption
FIGURE 3.6
Time and length scales associated with biological phenomena occurring during
the implant development.
osteoarticular tissue-engineered constructs. Examples of our methodological
approaches aimed at enabling an integrated study of the solute transport
and mechanical phenomena taking place in perfusion bioreactors are reviewed
here. In a first part, the study is focused on oxygen transport. In a second
part, this approach is extended to ionic species under electrochemical coupled
effects.
At the pore length scale
a
, the variables and parameters are written in a
nondimensional form (the “prime” notation is used to signal the nondimen-
sional form of the considered quantity). Thus the oxygen concentration
C
O
2
,
the flow direction coordinate
X
and the transverse coordinate
Y
and
Z
, the
perfusion velocity
u
, and the fluid pressure
p
are reduced, respectively, owing
to a reference concentration
c
0
(the inlet oxygen concentration for instance),
the pore size
a
, a reference velocity
u
0
(the inlet velocity for instance), and
the dynamic viscosity of the perfusing fluid
η
:
a
;
u
=
U
×
C
O
2
=
C
×
c
0
;
X
=
X
×
a
;
Y
=
Y
×
a
;
Z
=
Z
×
u
0
p
=
P
×
ηu
0
/a
(3.10)
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