Biomedical Engineering Reference
In-Depth Information
the scaffold. The driving force of solute transportation is diffusion since the pores within the gels are
too small for convection to play a significant role. In ionic gels, research has revealed that hydrogel
mesh size and culture conditions such as pH and temperature play an important role in diffusion (
am
Ende et al., 1995
). In biological systems, the hydrophilic polymer and their solutes frequently interact
and ionize with their surroundings, thus becoming an important factor in determining transport behav-
ior. Further investigation has shown that this interaction tends to decrease transport rate of solutes into
the hydrogel (
Collins and Ramirez, 1979
). Another study on the permeability of the hydrogel has also
confirmed the significance of this polymer-solute interaction and shown that it can be controlled by size
exclusion (
Gudeman and Peppas, 1995
).
For nutrient transportation, an important measure for determining the maximum size of solute
that can diffuse into the gel is its porosity. This can be predicted by the mesh size,
∈
, and the aver-
age linear distance between the cross-links. To predict the mesh size, we use an equation contain-
ing the bond length of the polymer backbone,
l
(which is often 1.54 due to the carbon-carbon bone),
the characteristic ratio, C
N
, the average molecular weight between the cross-links,
M
c
, the swollen
polymer volume fraction,
v
2,
s
and the molecular weight of the monomer, M
r
(
Peppas et al., 2006;
Tesoro, 1984
).
1/2
1
3
2
CM
M
Nc
∈=
(
v
)
l
2,
s
r
In tissue-engineered hydrogel, the mesh size of hydrogel has to include the effects of the solution
containing salts, ions, and nutrients. Thus the swollen polymer fraction
v
2,
s
has to be revised to account
for the solution used.
All solute transport models involving hydrogel are based on diffusion. This enables the transport
rate of solutes to be described using Fick's Law (
Crank, 1979; Park and Crank, 1968
). Fickian diffusion
is however only applicable if the gel is amorphous. If the gel is significantly heterogenous, this law is
no longer sufficient.
∂
∂
c
t
i
=∇
.( () )
DC C
∇
ig
i
i
where
c
i
is the concentration of the species
i
and
D
ig
is the concentration-dependent coefficient of spe-
cies
i
in the hydrogel.
Another model based on the free volume theory for water solute and polymer was developed by
Peppas et al
.
to predict the dependency of the solute diffusion coefficient on solute size, mesh size,
degree of swelling, and other structural properties of the hydrogel (
Peppas and Reinhart, 1983
).
(
)
*
kM M
MM
−
−
2
D
D
Kr
Q
1
C
C
SM
2
s
=
exp(
−
1
)
*
−
Sw
N
C
M
where
D
SM
and
D
Sw
are the diffusion coefficients of the solutes in the membrane and solvent. This ratio
is also known as the normalized diffusion coefficient.
k
1
and
k
2
are the structural parameters of the
polymer-water complex.
M
*
is the average critical molecular weight between the cross-links at which
diffusion is excluded.
r
s
is the Stokes hydrodynamic radius of the solute and
Q
m
is the degree of swell-
ing of the hydrogel. This experiment was validated using PVA membrane.
Search WWH ::
Custom Search